LMFDB - Embedded newform 8031.2.a.d.1.16

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			1.16
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)

$f(q)$	$=$	$q-2.29731 q^{2} +1.00000 q^{3} +3.27764 q^{4} -1.75176 q^{5} -2.29731 q^{6} -2.80141 q^{7} -2.93514 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q-2.29731 q^{2} +1.00000 q^{3} +3.27764 q^{4} -1.75176 q^{5} -2.29731 q^{6} -2.80141 q^{7} -2.93514 q^{8} +1.00000 q^{9} +4.02433 q^{10} -2.45364 q^{11} +3.27764 q^{12} +2.25402 q^{13} +6.43572 q^{14} -1.75176 q^{15} +0.187652 q^{16} -5.18626 q^{17} -2.29731 q^{18} +8.49658 q^{19} -5.74163 q^{20} -2.80141 q^{21} +5.63679 q^{22} +3.10657 q^{23} -2.93514 q^{24} -1.93135 q^{25} -5.17819 q^{26} +1.00000 q^{27} -9.18203 q^{28} -9.24846 q^{29} +4.02433 q^{30} -0.848665 q^{31} +5.43919 q^{32} -2.45364 q^{33} +11.9145 q^{34} +4.90739 q^{35} +3.27764 q^{36} -3.17523 q^{37} -19.5193 q^{38} +2.25402 q^{39} +5.14165 q^{40} -3.81066 q^{41} +6.43572 q^{42} +9.34709 q^{43} -8.04217 q^{44} -1.75176 q^{45} -7.13676 q^{46} -6.08687 q^{47} +0.187652 q^{48} +0.847910 q^{49} +4.43691 q^{50} -5.18626 q^{51} +7.38788 q^{52} +2.99390 q^{53} -2.29731 q^{54} +4.29819 q^{55} +8.22254 q^{56} +8.49658 q^{57} +21.2466 q^{58} +7.66876 q^{59} -5.74163 q^{60} -10.0057 q^{61} +1.94965 q^{62} -2.80141 q^{63} -12.8708 q^{64} -3.94850 q^{65} +5.63679 q^{66} -1.83840 q^{67} -16.9987 q^{68} +3.10657 q^{69} -11.2738 q^{70} +3.44369 q^{71} -2.93514 q^{72} +4.09433 q^{73} +7.29449 q^{74} -1.93135 q^{75} +27.8488 q^{76} +6.87367 q^{77} -5.17819 q^{78} -4.70200 q^{79} -0.328721 q^{80} +1.00000 q^{81} +8.75429 q^{82} -5.10058 q^{83} -9.18203 q^{84} +9.08506 q^{85} -21.4732 q^{86} -9.24846 q^{87} +7.20179 q^{88} +2.35583 q^{89} +4.02433 q^{90} -6.31445 q^{91} +10.1822 q^{92} -0.848665 q^{93} +13.9834 q^{94} -14.8839 q^{95} +5.43919 q^{96} +3.24977 q^{97} -1.94791 q^{98} -2.45364 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	−2.29731	−1.62444	−0.812222	−	0.583348i	$-0.801742\pi$
$2$	−2.29731	−1.62444	−0.812222	+	0.583348i	$0.801742\pi$
$3$	1.00000	0.577350
$3$	1.00000	0.577350
$4$	3.27764	1.63882
$5$	−1.75176	−0.783409	−0.391705	−	0.920091i	$-0.628114\pi$
$5$	−1.75176	−0.783409	−0.391705	+	0.920091i	$0.628114\pi$
$6$	−2.29731	−0.937874
$7$	−2.80141	−1.05883	−0.529417	−	0.848362i	$-0.677589\pi$
$7$	−2.80141	−1.05883	−0.529417	+	0.848362i	$0.677589\pi$
$8$	−2.93514	−1.03773
$9$	1.00000	0.333333
$10$	4.02433	1.27260
$11$	−2.45364	−0.739802	−0.369901	−	0.929071i	$-0.620608\pi$
$11$	−2.45364	−0.739802	−0.369901	+	0.929071i	$0.620608\pi$
$12$	3.27764	0.946174
$13$	2.25402	0.625153	0.312577	−	0.949893i	$-0.398808\pi$
$13$	2.25402	0.625153	0.312577	+	0.949893i	$0.398808\pi$
$14$	6.43572	1.72002
$15$	−1.75176	−0.452301
$16$	0.187652	0.0469130
$17$	−5.18626	−1.25785	−0.628926	−	0.777465i	$-0.716505\pi$
$17$	−5.18626	−1.25785	−0.628926	+	0.777465i	$0.716505\pi$
$18$	−2.29731	−0.541482
$19$	8.49658	1.94925	0.974625	−	0.223844i	$-0.0718608\pi$
$19$	8.49658	1.94925	0.974625	+	0.223844i	$0.0718608\pi$
$20$	−5.74163	−1.28387
$21$	−2.80141	−0.611318
$22$	5.63679	1.20177
$23$	3.10657	0.647765	0.323882	−	0.946097i	$-0.395012\pi$
$23$	3.10657	0.647765	0.323882	+	0.946097i	$0.395012\pi$
$24$	−2.93514	−0.599133
$25$	−1.93135	−0.386270
$26$	−5.17819	−1.01553
$27$	1.00000	0.192450
$28$	−9.18203	−1.73524
$29$	−9.24846	−1.71740	−0.858698	−	0.512482i	$-0.828726\pi$
$29$	−9.24846	−1.71740	−0.858698	+	0.512482i	$0.828726\pi$
$30$	4.02433	0.734739
$31$	−0.848665	−0.152425	−0.0762124	−	0.997092i	$-0.524283\pi$
$31$	−0.848665	−0.152425	−0.0762124	+	0.997092i	$0.524283\pi$
$32$	5.43919	0.961522
$33$	−2.45364	−0.427125
$34$	11.9145	2.04331
$35$	4.90739	0.829500
$36$	3.27764	0.546274
$37$	−3.17523	−0.522004	−0.261002	−	0.965338i	$-0.584053\pi$
$37$	−3.17523	−0.522004	−0.261002	+	0.965338i	$0.584053\pi$
$38$	−19.5193	−3.16645
$39$	2.25402	0.360932
$40$	5.14165	0.812967
$41$	−3.81066	−0.595126	−0.297563	−	0.954702i	$-0.596174\pi$
$41$	−3.81066	−0.595126	−0.297563	+	0.954702i	$0.596174\pi$
$42$	6.43572	0.993053
$43$	9.34709	1.42542	0.712709	−	0.701460i	$-0.247468\pi$
$43$	9.34709	1.42542	0.712709	+	0.701460i	$0.247468\pi$
$44$	−8.04217	−1.21240
$45$	−1.75176	−0.261136
$46$	−7.13676	−1.05226
$47$	−6.08687	−0.887861	−0.443930	−	0.896061i	$-0.646416\pi$
$47$	−6.08687	−0.887861	−0.443930	+	0.896061i	$0.646416\pi$
$48$	0.187652	0.0270852
$49$	0.847910	0.121130
$50$	4.43691	0.627475
$51$	−5.18626	−0.726221
$52$	7.38788	1.02451
$53$	2.99390	0.411243	0.205622	−	0.978632i	$-0.434078\pi$
$53$	2.99390	0.411243	0.205622	+	0.978632i	$0.434078\pi$
$54$	−2.29731	−0.312625
$55$	4.29819	0.579567
$56$	8.22254	1.09878
$57$	8.49658	1.12540
$58$	21.2466	2.78981
$59$	7.66876	0.998387	0.499194	−	0.866491i	$-0.333630\pi$
$59$	7.66876	0.998387	0.499194	+	0.866491i	$0.333630\pi$
$60$	−5.74163	−0.741241
$61$	−10.0057	−1.28110	−0.640552	−	0.767915i	$-0.721294\pi$
$61$	−10.0057	−1.28110	−0.640552	+	0.767915i	$0.721294\pi$
$62$	1.94965	0.247606
$63$	−2.80141	−0.352945
$64$	−12.8708	−1.60885
$65$	−3.94850	−0.489751
$66$	5.63679	0.693841
$67$	−1.83840	−0.224596	−0.112298	−	0.993675i	$-0.535821\pi$
$67$	−1.83840	−0.224596	−0.112298	+	0.993675i	$0.535821\pi$
$68$	−16.9987	−2.06139
$69$	3.10657	0.373987
$70$	−11.2738	−1.34748
$71$	3.44369	0.408691	0.204346	−	0.978899i	$-0.434493\pi$
$71$	3.44369	0.408691	0.204346	+	0.978899i	$0.434493\pi$
$72$	−2.93514	−0.345910
$73$	4.09433	0.479205	0.239603	−	0.970871i	$-0.422983\pi$
$73$	4.09433	0.479205	0.239603	+	0.970871i	$0.422983\pi$
$74$	7.29449	0.847967
$75$	−1.93135	−0.223013
$76$	27.8488	3.19447
$77$	6.87367	0.783327
$78$	−5.17819	−0.586315
$79$	−4.70200	−0.529016	−0.264508	−	0.964383i	$-0.585210\pi$
$79$	−4.70200	−0.529016	−0.264508	+	0.964383i	$0.585210\pi$
$80$	−0.328721	−0.0367521
$81$	1.00000	0.111111
$82$	8.75429	0.966749
$83$	−5.10058	−0.559862	−0.279931	−	0.960020i	$-0.590312\pi$
$83$	−5.10058	−0.559862	−0.279931	+	0.960020i	$0.590312\pi$
$84$	−9.18203	−1.00184
$85$	9.08506	0.985413
$86$	−21.4732	−2.31551
$87$	−9.24846	−0.991539
$88$	7.20179	0.767714
$89$	2.35583	0.249717	0.124859	−	0.992175i	$-0.460152\pi$
$89$	2.35583	0.249717	0.124859	+	0.992175i	$0.460152\pi$
$90$	4.02433	0.424202
$91$	−6.31445	−0.661934
$92$	10.1822	1.06157
$93$	−0.848665	−0.0880025
$94$	13.9834	1.44228
$95$	−14.8839	−1.52706
$96$	5.43919	0.555135
$97$	3.24977	0.329964	0.164982	−	0.986297i	$-0.447243\pi$
$97$	3.24977	0.329964	0.164982	+	0.986297i	$0.447243\pi$
$98$	−1.94791	−0.196769
$99$	−2.45364	−0.246601
$100$	−6.33028	−0.633028
$101$	−7.63959	−0.760167	−0.380084	−	0.924952i	$-0.624105\pi$
$101$	−7.63959	−0.760167	−0.380084	+	0.924952i	$0.624105\pi$
$102$	11.9145	1.17971
$103$	−4.04730	−0.398793	−0.199396	−	0.979919i	$-0.563898\pi$
$103$	−4.04730	−0.398793	−0.199396	+	0.979919i	$0.563898\pi$
$104$	−6.61587	−0.648740
$105$	4.90739	0.478912
$106$	−6.87791	−0.668042
$107$	5.56409	0.537901	0.268950	−	0.963154i	$-0.413323\pi$
$107$	5.56409	0.537901	0.268950	+	0.963154i	$0.413323\pi$
$108$	3.27764	0.315391
$109$	10.3952	0.995679	0.497840	−	0.867269i	$-0.334127\pi$
$109$	10.3952	0.995679	0.497840	+	0.867269i	$0.334127\pi$
$110$	−9.87428	−0.941475
$111$	−3.17523	−0.301379
$112$	−0.525691	−0.0496731
$113$	−7.59173	−0.714170	−0.357085	−	0.934072i	$-0.616229\pi$
$113$	−7.59173	−0.714170	−0.357085	+	0.934072i	$0.616229\pi$
$114$	−19.5193	−1.82815
$115$	−5.44195	−0.507465
$116$	−30.3131	−2.81450
$117$	2.25402	0.208384
$118$	−17.6175	−1.62182
$119$	14.5288	1.33186
$120$	5.14165	0.469366
$121$	−4.97963	−0.452693
$122$	22.9863	2.08108
$123$	−3.81066	−0.343596
$124$	−2.78162	−0.249797
$125$	12.1420	1.08602
$126$	6.43572	0.573339
$127$	−13.0228	−1.15559	−0.577793	−	0.816183i	$-0.696086\pi$
$127$	−13.0228	−1.15559	−0.577793	+	0.816183i	$0.696086\pi$
$128$	18.6899	1.65197
$129$	9.34709	0.822965
$130$	9.07093	0.795573
$131$	5.68784	0.496949	0.248474	−	0.968638i	$-0.420071\pi$
$131$	5.68784	0.496949	0.248474	+	0.968638i	$0.420071\pi$
$132$	−8.04217	−0.699981
$133$	−23.8024	−2.06393
$134$	4.22337	0.364844
$135$	−1.75176	−0.150767
$136$	15.2224	1.30531
$137$	−12.9978	−1.11048	−0.555238	−	0.831691i	$-0.687373\pi$
$137$	−12.9978	−1.11048	−0.555238	+	0.831691i	$0.687373\pi$
$138$	−7.13676	−0.607521
$139$	9.24871	0.784466	0.392233	−	0.919866i	$-0.371703\pi$
$139$	9.24871	0.784466	0.392233	+	0.919866i	$0.371703\pi$
$140$	16.0847	1.35940
$141$	−6.08687	−0.512607
$142$	−7.91124	−0.663897
$143$	−5.53057	−0.462489
$144$	0.187652	0.0156377
$145$	16.2010	1.34542
$146$	−9.40596	−0.778443
$147$	0.847910	0.0699345
$148$	−10.4073	−0.855471
$149$	−12.1723	−0.997191	−0.498596	−	0.866835i	$-0.666151\pi$
$149$	−12.1723	−0.997191	−0.498596	+	0.866835i	$0.666151\pi$
$150$	4.43691	0.362273
$151$	1.82874	0.148820	0.0744102	−	0.997228i	$-0.476293\pi$
$151$	1.82874	0.148820	0.0744102	+	0.997228i	$0.476293\pi$
$152$	−24.9387	−2.02279
$153$	−5.18626	−0.419284
$154$	−15.7910	−1.27247
$155$	1.48665	0.119411
$156$	7.38788	0.591504
$157$	1.45731	0.116306	0.0581528	−	0.998308i	$-0.481479\pi$
$157$	1.45731	0.116306	0.0581528	+	0.998308i	$0.481479\pi$
$158$	10.8020	0.859358
$159$	2.99390	0.237431
$160$	−9.52813	−0.753265
$161$	−8.70278	−0.685875
$162$	−2.29731	−0.180494
$163$	9.16800	0.718093	0.359047	−	0.933320i	$-0.383102\pi$
$163$	9.16800	0.718093	0.359047	+	0.933320i	$0.383102\pi$
$164$	−12.4900	−0.975305
$165$	4.29819	0.334613
$166$	11.7176	0.909464
$167$	−14.1048	−1.09146	−0.545729	−	0.837962i	$-0.683747\pi$
$167$	−14.1048	−1.09146	−0.545729	+	0.837962i	$0.683747\pi$
$168$	8.22254	0.634383
$169$	−7.91938	−0.609183
$170$	−20.8712	−1.60075
$171$	8.49658	0.649750
$172$	30.6364	2.33600
$173$	2.68120	0.203848	0.101924	−	0.994792i	$-0.467500\pi$
$173$	2.68120	0.203848	0.101924	+	0.994792i	$0.467500\pi$
$174$	21.2466	1.61070
$175$	5.41051	0.408996
$176$	−0.460431	−0.0347063
$177$	7.66876	0.576419
$178$	−5.41207	−0.405652
$179$	3.04203	0.227372	0.113686	−	0.993517i	$-0.463734\pi$
$179$	3.04203	0.227372	0.113686	+	0.993517i	$0.463734\pi$
$180$	−5.74163	−0.427956
$181$	−7.76215	−0.576956	−0.288478	−	0.957487i	$-0.593149\pi$
$181$	−7.76215	−0.576956	−0.288478	+	0.957487i	$0.593149\pi$
$182$	14.5062	1.07527
$183$	−10.0057	−0.739646
$184$	−9.11822	−0.672204
$185$	5.56222	0.408943
$186$	1.94965	0.142955
$187$	12.7252	0.930561
$188$	−19.9506	−1.45504
$189$	−2.80141	−0.203773
$190$	34.1931	2.48062
$191$	−10.7338	−0.776668	−0.388334	−	0.921519i	$-0.626949\pi$
$191$	−10.7338	−0.776668	−0.388334	+	0.921519i	$0.626949\pi$
$192$	−12.8708	−0.928871
$193$	−12.3210	−0.886884	−0.443442	−	0.896303i	$-0.646243\pi$
$193$	−12.3210	−0.886884	−0.443442	+	0.896303i	$0.646243\pi$
$194$	−7.46573	−0.536009
$195$	−3.94850	−0.282758
$196$	2.77915	0.198510
$197$	−17.5441	−1.24997	−0.624984	−	0.780638i	$-0.714894\pi$
$197$	−17.5441	−1.24997	−0.624984	+	0.780638i	$0.714894\pi$
$198$	5.63679	0.400589
$199$	23.8096	1.68782	0.843909	−	0.536486i	$-0.180249\pi$
$199$	23.8096	1.68782	0.843909	+	0.536486i	$0.180249\pi$
$200$	5.66879	0.400844
$201$	−1.83840	−0.129671
$202$	17.5505	1.23485
$203$	25.9087	1.81844
$204$	−16.9987	−1.19015
$205$	6.67536	0.466227
$206$	9.29792	0.647817
$207$	3.10657	0.215922
$208$	0.422972	0.0293278
$209$	−20.8476	−1.44206
$210$	−11.2738	−0.777967
$211$	26.9075	1.85239	0.926196	−	0.377043i	$-0.123059\pi$
$211$	26.9075	1.85239	0.926196	+	0.377043i	$0.123059\pi$
$212$	9.81292	0.673954
$213$	3.44369	0.235958
$214$	−12.7824	−0.873790
$215$	−16.3738	−1.11669
$216$	−2.93514	−0.199711
$217$	2.37746	0.161393
$218$	−23.8810	−1.61743
$219$	4.09433	0.276669
$220$	14.0879	0.949807
$221$	−11.6899	−0.786351
$222$	7.29449	0.489574
$223$	−4.01058	−0.268568	−0.134284	−	0.990943i	$-0.542874\pi$
$223$	−4.01058	−0.268568	−0.134284	+	0.990943i	$0.542874\pi$
$224$	−15.2374	−1.01809
$225$	−1.93135	−0.128757
$226$	17.4406	1.16013
$227$	−3.18945	−0.211691	−0.105846	−	0.994383i	$-0.533755\pi$
$227$	−3.18945	−0.211691	−0.105846	+	0.994383i	$0.533755\pi$
$228$	27.8488	1.84433
$229$	7.71437	0.509780	0.254890	−	0.966970i	$-0.417961\pi$
$229$	7.71437	0.509780	0.254890	+	0.966970i	$0.417961\pi$
$230$	12.5019	0.824348
$231$	6.87367	0.452254
$232$	27.1455	1.78219
$233$	22.0441	1.44415	0.722077	−	0.691812i	$-0.243188\pi$
$233$	22.0441	1.44415	0.722077	+	0.691812i	$0.243188\pi$
$234$	−5.17819	−0.338509
$235$	10.6627	0.695558
$236$	25.1354	1.63618
$237$	−4.70200	−0.305428
$238$	−33.3773	−2.16353
$239$	5.82790	0.376976	0.188488	−	0.982076i	$-0.439641\pi$
$239$	5.82790	0.376976	0.188488	+	0.982076i	$0.439641\pi$
$240$	−0.328721	−0.0212188
$241$	−23.9962	−1.54573	−0.772864	−	0.634572i	$-0.781177\pi$
$241$	−23.9962	−1.54573	−0.772864	+	0.634572i	$0.781177\pi$
$242$	11.4398	0.735375
$243$	1.00000	0.0641500
$244$	−32.7952	−2.09950
$245$	−1.48533	−0.0948944
$246$	8.75429	0.558153
$247$	19.1515	1.21858
$248$	2.49095	0.158176
$249$	−5.10058	−0.323236
$250$	−27.8940	−1.76417
$251$	−5.84290	−0.368800	−0.184400	−	0.982851i	$-0.559034\pi$
$251$	−5.84290	−0.368800	−0.184400	+	0.982851i	$0.559034\pi$
$252$	−9.18203	−0.578413
$253$	−7.62242	−0.479217
$254$	29.9174	1.87719
$255$	9.08506	0.568929
$256$	−17.1949	−1.07468
$257$	6.25488	0.390168	0.195084	−	0.980786i	$-0.437502\pi$
$257$	6.25488	0.390168	0.195084	+	0.980786i	$0.437502\pi$
$258$	−21.4732	−1.33686
$259$	8.89512	0.552716
$260$	−12.9418	−0.802614
$261$	−9.24846	−0.572465
$262$	−13.0667	−0.807266
$263$	8.38099	0.516794	0.258397	−	0.966039i	$-0.416806\pi$
$263$	8.38099	0.516794	0.258397	+	0.966039i	$0.416806\pi$
$264$	7.20179	0.443240
$265$	−5.24457	−0.322172
$266$	54.6816	3.35274
$267$	2.35583	0.144174
$268$	−6.02561	−0.368073
$269$	16.3249	0.995349	0.497674	−	0.867364i	$-0.334187\pi$
$269$	16.3249	0.995349	0.497674	+	0.867364i	$0.334187\pi$
$270$	4.02433	0.244913
$271$	12.8104	0.778177	0.389088	−	0.921200i	$-0.372790\pi$
$271$	12.8104	0.778177	0.389088	+	0.921200i	$0.372790\pi$
$272$	−0.973212	−0.0590096
$273$	−6.31445	−0.382168
$274$	29.8600	1.80391
$275$	4.73885	0.285763
$276$	10.1822	0.612898
$277$	6.10825	0.367009	0.183505	−	0.983019i	$-0.441256\pi$
$277$	6.10825	0.367009	0.183505	+	0.983019i	$0.441256\pi$
$278$	−21.2472	−1.27432
$279$	−0.848665	−0.0508082
$280$	−14.4039	−0.860797
$281$	17.3212	1.03330	0.516649	−	0.856197i	$-0.327179\pi$
$281$	17.3212	1.03330	0.516649	+	0.856197i	$0.327179\pi$
$282$	13.9834	0.832701
$283$	27.1869	1.61610	0.808048	−	0.589117i	$-0.200524\pi$
$283$	27.1869	1.61610	0.808048	+	0.589117i	$0.200524\pi$
$284$	11.2872	0.669772
$285$	−14.8839	−0.881649
$286$	12.7054	0.751289
$287$	10.6752	0.630140
$288$	5.43919	0.320507
$289$	9.89728	0.582193
$290$	−37.2188	−2.18557
$291$	3.24977	0.190505
$292$	13.4198	0.785332
$293$	−25.6662	−1.49943	−0.749717	−	0.661758i	$-0.769811\pi$
$293$	−25.6662	−1.49943	−0.749717	+	0.661758i	$0.769811\pi$
$294$	−1.94791	−0.113605
$295$	−13.4338	−0.782146
$296$	9.31974	0.541699
$297$	−2.45364	−0.142375
$298$	27.9635	1.61988
$299$	7.00228	0.404952
$300$	−6.33028	−0.365479
$301$	−26.1851	−1.50928
$302$	−4.20118	−0.241751
$303$	−7.63959	−0.438883
$304$	1.59440	0.0914452
$305$	17.5276	1.00363
$306$	11.9145	0.681104
$307$	29.8759	1.70511	0.852553	−	0.522641i	$-0.175053\pi$
$307$	29.8759	1.70511	0.852553	+	0.522641i	$0.175053\pi$
$308$	22.5294	1.28373
$309$	−4.04730	−0.230243
$310$	−3.41531	−0.193976
$311$	−3.76490	−0.213488	−0.106744	−	0.994287i	$-0.534042\pi$
$311$	−3.76490	−0.213488	−0.106744	+	0.994287i	$0.534042\pi$
$312$	−6.61587	−0.374550
$313$	−1.09930	−0.0621363	−0.0310681	−	0.999517i	$-0.509891\pi$
$313$	−1.09930	−0.0621363	−0.0310681	+	0.999517i	$0.509891\pi$
$314$	−3.34789	−0.188932
$315$	4.90739	0.276500
$316$	−15.4115	−0.866963
$317$	5.14275	0.288845	0.144423	−	0.989516i	$-0.453867\pi$
$317$	5.14275	0.288845	0.144423	+	0.989516i	$0.453867\pi$
$318$	−6.87791	−0.385694
$319$	22.6924	1.27053
$320$	22.5465	1.26039
$321$	5.56409	0.310557
$322$	19.9930	1.11417
$323$	−44.0655	−2.45187
$324$	3.27764	0.182091
$325$	−4.35331	−0.241478
$326$	−21.0618	−1.16650
$327$	10.3952	0.574856
$328$	11.1848	0.617580
$329$	17.0518	0.940098
$330$	−9.87428	−0.543561
$331$	−3.52015	−0.193485	−0.0967424	−	0.995309i	$-0.530842\pi$
$331$	−3.52015	−0.193485	−0.0967424	+	0.995309i	$0.530842\pi$
$332$	−16.7179	−0.917513
$333$	−3.17523	−0.174001
$334$	32.4030	1.77301
$335$	3.22043	0.175951
$336$	−0.525691	−0.0286788
$337$	−19.3979	−1.05667	−0.528334	−	0.849036i	$-0.677183\pi$
$337$	−19.3979	−1.05667	−0.528334	+	0.849036i	$0.677183\pi$
$338$	18.1933	0.989585
$339$	−7.59173	−0.412326
$340$	29.7776	1.61492
$341$	2.08232	0.112764
$342$	−19.5193	−1.05548
$343$	17.2345	0.930578
$344$	−27.4350	−1.47920
$345$	−5.44195	−0.292985
$346$	−6.15956	−0.331140
$347$	21.4505	1.15152	0.575760	−	0.817619i	$-0.304706\pi$
$347$	21.4505	1.15152	0.575760	+	0.817619i	$0.304706\pi$
$348$	−30.3131	−1.62495
$349$	25.8336	1.38284	0.691420	−	0.722453i	$-0.256986\pi$
$349$	25.8336	1.38284	0.691420	+	0.722453i	$0.256986\pi$
$350$	−12.4296	−0.664392
$351$	2.25402	0.120311
$352$	−13.3458	−0.711335
$353$	−34.6083	−1.84202	−0.921008	−	0.389544i	$-0.872633\pi$
$353$	−34.6083	−1.84202	−0.921008	+	0.389544i	$0.872633\pi$
$354$	−17.6175	−0.936361
$355$	−6.03251	−0.320173
$356$	7.72155	0.409242
$357$	14.5288	0.768948
$358$	−6.98849	−0.369353
$359$	−6.68072	−0.352595	−0.176298	−	0.984337i	$-0.556412\pi$
$359$	−6.68072	−0.352595	−0.176298	+	0.984337i	$0.556412\pi$
$360$	5.14165	0.270989
$361$	53.1919	2.79957
$362$	17.8321	0.937233
$363$	−4.97963	−0.261363
$364$	−20.6965	−1.08479
$365$	−7.17227	−0.375414
$366$	22.9863	1.20151
$367$	6.47671	0.338082	0.169041	−	0.985609i	$-0.445933\pi$
$367$	6.47671	0.338082	0.169041	+	0.985609i	$0.445933\pi$
$368$	0.582954	0.0303886
$369$	−3.81066	−0.198375
$370$	−12.7782	−0.664305
$371$	−8.38714	−0.435438
$372$	−2.78162	−0.144220
$373$	12.8884	0.667338	0.333669	−	0.942690i	$-0.391713\pi$
$373$	12.8884	0.667338	0.333669	+	0.942690i	$0.391713\pi$
$374$	−29.2338	−1.51165
$375$	12.1420	0.627012
$376$	17.8658	0.921359
$377$	−20.8462	−1.07364
$378$	6.43572	0.331018
$379$	29.2807	1.50405	0.752024	−	0.659136i	$-0.229078\pi$
$379$	29.2807	1.50405	0.752024	+	0.659136i	$0.229078\pi$
$380$	−48.7842	−2.50258
$381$	−13.0228	−0.667178
$382$	24.6588	1.26165
$383$	−5.95805	−0.304442	−0.152221	−	0.988346i	$-0.548643\pi$
$383$	−5.95805	−0.304442	−0.152221	+	0.988346i	$0.548643\pi$
$384$	18.6899	0.953765
$385$	−12.0410	−0.613666
$386$	28.3052	1.44069
$387$	9.34709	0.475139
$388$	10.6516	0.540752
$389$	33.9977	1.72375	0.861875	−	0.507121i	$-0.169290\pi$
$389$	33.9977	1.72375	0.861875	+	0.507121i	$0.169290\pi$
$390$	9.07093	0.459324
$391$	−16.1115	−0.814792
$392$	−2.48874	−0.125700
$393$	5.68784	0.286914
$394$	40.3043	2.03050
$395$	8.23676	0.414436
$396$	−8.04217	−0.404134
$397$	−2.12609	−0.106705	−0.0533527	−	0.998576i	$-0.516991\pi$
$397$	−2.12609	−0.106705	−0.0533527	+	0.998576i	$0.516991\pi$
$398$	−54.6981	−2.74177
$399$	−23.8024	−1.19161
$400$	−0.362422	−0.0181211
$401$	1.57759	0.0787810	0.0393905	−	0.999224i	$-0.487458\pi$
$401$	1.57759	0.0787810	0.0393905	+	0.999224i	$0.487458\pi$
$402$	4.22337	0.210643
$403$	−1.91291	−0.0952888
$404$	−25.0398	−1.24578
$405$	−1.75176	−0.0870455
$406$	−59.5205	−2.95395
$407$	7.79088	0.386180
$408$	15.2224	0.753621
$409$	−5.08983	−0.251676	−0.125838	−	0.992051i	$-0.540162\pi$
$409$	−5.08983	−0.251676	−0.125838	+	0.992051i	$0.540162\pi$
$410$	−15.3354	−0.757360
$411$	−12.9978	−0.641134
$412$	−13.2656	−0.653550
$413$	−21.4833	−1.05713
$414$	−7.13676	−0.350753
$415$	8.93498	0.438601
$416$	12.2600	0.601098
$417$	9.24871	0.452911
$418$	47.8934	2.34254
$419$	1.31365	0.0641760	0.0320880	−	0.999485i	$-0.489784\pi$
$419$	1.31365	0.0641760	0.0320880	+	0.999485i	$0.489784\pi$
$420$	16.0847	0.784851
$421$	−18.3200	−0.892861	−0.446430	−	0.894818i	$-0.647305\pi$
$421$	−18.3200	−0.892861	−0.446430	+	0.894818i	$0.647305\pi$
$422$	−61.8150	−3.00911
$423$	−6.08687	−0.295954
$424$	−8.78751	−0.426759
$425$	10.0165	0.485871
$426$	−7.91124	−0.383301
$427$	28.0302	1.35648
$428$	18.2371	0.881523
$429$	−5.53057	−0.267018
$430$	37.6158	1.81399
$431$	39.1908	1.88776	0.943878	−	0.330293i	$-0.107148\pi$
$431$	39.1908	1.88776	0.943878	+	0.330293i	$0.107148\pi$
$432$	0.187652	0.00902841
$433$	−7.93709	−0.381432	−0.190716	−	0.981645i	$-0.561081\pi$
$433$	−7.93709	−0.381432	−0.190716	+	0.981645i	$0.561081\pi$
$434$	−5.46177	−0.262173
$435$	16.2010	0.776781
$436$	34.0717	1.63174
$437$	26.3952	1.26265
$438$	−9.40596	−0.449434
$439$	35.6507	1.70151	0.850757	−	0.525559i	$-0.176144\pi$
$439$	35.6507	1.70151	0.850757	+	0.525559i	$0.176144\pi$
$440$	−12.6158	−0.601434
$441$	0.847910	0.0403767
$442$	26.8554	1.27738
$443$	−4.61869	−0.219441	−0.109720	−	0.993962i	$-0.534996\pi$
$443$	−4.61869	−0.219441	−0.109720	+	0.993962i	$0.534996\pi$
$444$	−10.4073	−0.493907
$445$	−4.12683	−0.195631
$446$	9.21356	0.436275
$447$	−12.1723	−0.575729
$448$	36.0565	1.70351
$449$	6.14361	0.289935	0.144967	−	0.989436i	$-0.453692\pi$
$449$	6.14361	0.289935	0.144967	+	0.989436i	$0.453692\pi$
$450$	4.43691	0.209158
$451$	9.35002	0.440275
$452$	−24.8830	−1.17040
$453$	1.82874	0.0859215
$454$	7.32716	0.343881
$455$	11.0614	0.518565
$456$	−24.9387	−1.16786
$457$	−11.2368	−0.525634	−0.262817	−	0.964846i	$-0.584651\pi$
$457$	−11.2368	−0.525634	−0.262817	+	0.964846i	$0.584651\pi$
$458$	−17.7223	−0.828109
$459$	−5.18626	−0.242074
$460$	−17.8368	−0.831644
$461$	5.21404	0.242842	0.121421	−	0.992601i	$-0.461255\pi$
$461$	5.21404	0.242842	0.121421	+	0.992601i	$0.461255\pi$
$462$	−15.7910	−0.734662
$463$	−17.6521	−0.820364	−0.410182	−	0.912004i	$-0.634535\pi$
$463$	−17.6521	−0.820364	−0.410182	+	0.912004i	$0.634535\pi$
$464$	−1.73549	−0.0805682
$465$	1.48665	0.0689419
$466$	−50.6421	−2.34595
$467$	−3.83733	−0.177570	−0.0887852	−	0.996051i	$-0.528298\pi$
$467$	−3.83733	−0.177570	−0.0887852	+	0.996051i	$0.528298\pi$
$468$	7.38788	0.341505
$469$	5.15011	0.237810
$470$	−24.4956	−1.12990
$471$	1.45731	0.0671491
$472$	−22.5089	−1.03606
$473$	−22.9344	−1.05453
$474$	10.8020	0.496151
$475$	−16.4099	−0.752937
$476$	47.6204	2.18268
$477$	2.99390	0.137081
$478$	−13.3885	−0.612376
$479$	−32.7601	−1.49685	−0.748423	−	0.663222i	$-0.769188\pi$
$479$	−32.7601	−1.49685	−0.748423	+	0.663222i	$0.769188\pi$
$480$	−9.52813	−0.434898
$481$	−7.15703	−0.326333
$482$	55.1267	2.51095
$483$	−8.70278	−0.395990
$484$	−16.3214	−0.741883
$485$	−5.69280	−0.258497
$486$	−2.29731	−0.104208
$487$	−9.46480	−0.428891	−0.214445	−	0.976736i	$-0.568794\pi$
$487$	−9.46480	−0.428891	−0.214445	+	0.976736i	$0.568794\pi$
$488$	29.3683	1.32944
$489$	9.16800	0.414591
$490$	3.41227	0.154151
$491$	31.6587	1.42874	0.714369	−	0.699769i	$-0.246714\pi$
$491$	31.6587	1.42874	0.714369	+	0.699769i	$0.246714\pi$
$492$	−12.4900	−0.563092
$493$	47.9649	2.16023
$494$	−43.9969	−1.97952
$495$	4.29819	0.193189
$496$	−0.159254	−0.00715070
$497$	−9.64721	−0.432736
$498$	11.7176	0.525080
$499$	1.26867	0.0567936	0.0283968	−	0.999597i	$-0.490960\pi$
$499$	1.26867	0.0567936	0.0283968	+	0.999597i	$0.490960\pi$
$500$	39.7972	1.77979
$501$	−14.1048	−0.630154
$502$	13.4230	0.599096
$503$	−12.6141	−0.562437	−0.281218	−	0.959644i	$-0.590739\pi$
$503$	−12.6141	−0.562437	−0.281218	+	0.959644i	$0.590739\pi$
$504$	8.22254	0.366261
$505$	13.3827	0.595522
$506$	17.5111	0.778462
$507$	−7.91938	−0.351712
$508$	−42.6840	−1.89380
$509$	6.32011	0.280134	0.140067	−	0.990142i	$-0.455268\pi$
$509$	6.32011	0.280134	0.140067	+	0.990142i	$0.455268\pi$
$510$	−20.8712	−0.924193
$511$	−11.4699	−0.507399
$512$	2.12225	0.0937909
$513$	8.49658	0.375133
$514$	−14.3694	−0.633807
$515$	7.08989	0.312418
$516$	30.6364	1.34869
$517$	14.9350	0.656841
$518$	−20.4349	−0.897857
$519$	2.68120	0.117692
$520$	11.5894	0.508229
$521$	17.9487	0.786347	0.393174	−	0.919464i	$-0.371377\pi$
$521$	17.9487	0.786347	0.393174	+	0.919464i	$0.371377\pi$
$522$	21.2466	0.929938
$523$	−41.5723	−1.81783	−0.908915	−	0.416981i	$-0.863088\pi$
$523$	−41.5723	−1.81783	−0.908915	+	0.416981i	$0.863088\pi$
$524$	18.6427	0.814410
$525$	5.41051	0.236134
$526$	−19.2538	−0.839504
$527$	4.40140	0.191728
$528$	−0.460431	−0.0200377
$529$	−13.3492	−0.580401
$530$	12.0484	0.523350
$531$	7.66876	0.332796
$532$	−78.0158	−3.38242
$533$	−8.58932	−0.372045
$534$	−5.41207	−0.234203
$535$	−9.74692	−0.421396
$536$	5.39596	0.233070
$537$	3.04203	0.131273
$538$	−37.5035	−1.61689
$539$	−2.08047	−0.0896122
$540$	−5.74163	−0.247080
$541$	−12.2581	−0.527018	−0.263509	−	0.964657i	$-0.584880\pi$
$541$	−12.2581	−0.527018	−0.263509	+	0.964657i	$0.584880\pi$
$542$	−29.4295	−1.26411
$543$	−7.76215	−0.333106
$544$	−28.2090	−1.20945
$545$	−18.2099	−0.780024
$546$	14.5062	0.620810
$547$	−14.1658	−0.605686	−0.302843	−	0.953040i	$-0.597936\pi$
$547$	−14.1658	−0.605686	−0.302843	+	0.953040i	$0.597936\pi$
$548$	−42.6021	−1.81987
$549$	−10.0057	−0.427035
$550$	−10.8866	−0.464207
$551$	−78.5803	−3.34763
$552$	−9.11822	−0.388097
$553$	13.1722	0.560141
$554$	−14.0326	−0.596186
$555$	5.56222	0.236103
$556$	30.3140	1.28560
$557$	−23.0186	−0.975330	−0.487665	−	0.873031i	$-0.662151\pi$
$557$	−23.0186	−0.975330	−0.487665	+	0.873031i	$0.662151\pi$
$558$	1.94965	0.0825352
$559$	21.0685	0.891105
$560$	0.920882	0.0389144
$561$	12.7252	0.537260
$562$	−39.7923	−1.67854
$563$	−7.41952	−0.312696	−0.156348	−	0.987702i	$-0.549972\pi$
$563$	−7.41952	−0.312696	−0.156348	+	0.987702i	$0.549972\pi$
$564$	−19.9506	−0.840071
$565$	13.2989	0.559487
$566$	−62.4569	−2.62526
$567$	−2.80141	−0.117648
$568$	−10.1077	−0.424111
$569$	11.8135	0.495248	0.247624	−	0.968856i	$-0.420350\pi$
$569$	11.8135	0.495248	0.247624	+	0.968856i	$0.420350\pi$
$570$	34.1931	1.43219
$571$	6.04744	0.253077	0.126539	−	0.991962i	$-0.459613\pi$
$571$	6.04744	0.253077	0.126539	+	0.991962i	$0.459613\pi$
$572$	−18.1272	−0.757937
$573$	−10.7338	−0.448409
$574$	−24.5244	−1.02363
$575$	−5.99988	−0.250212
$576$	−12.8708	−0.536284
$577$	−4.93053	−0.205261	−0.102630	−	0.994720i	$-0.532726\pi$
$577$	−4.93053	−0.205261	−0.102630	+	0.994720i	$0.532726\pi$
$578$	−22.7371	−0.945740
$579$	−12.3210	−0.512043
$580$	53.1012	2.20491
$581$	14.2888	0.592801
$582$	−7.46573	−0.309465
$583$	−7.34596	−0.304238
$584$	−12.0174	−0.497285
$585$	−3.94850	−0.163250
$586$	58.9632	2.43575
$587$	9.32458	0.384867	0.192433	−	0.981310i	$-0.438362\pi$
$587$	9.32458	0.384867	0.192433	+	0.981310i	$0.438362\pi$
$588$	2.77915	0.114610
$589$	−7.21075	−0.297114
$590$	30.8616	1.27055
$591$	−17.5441	−0.721669
$592$	−0.595838	−0.0244888
$593$	−12.9838	−0.533179	−0.266590	−	0.963810i	$-0.585897\pi$
$593$	−12.9838	−0.533179	−0.266590	+	0.963810i	$0.585897\pi$
$594$	5.63679	0.231280
$595$	−25.4510	−1.04339
$596$	−39.8963	−1.63422
$597$	23.8096	0.974462
$598$	−16.0864	−0.657822
$599$	−3.33003	−0.136061	−0.0680307	−	0.997683i	$-0.521672\pi$
$599$	−3.33003	−0.136061	−0.0680307	+	0.997683i	$0.521672\pi$
$600$	5.66879	0.231427
$601$	41.0700	1.67528	0.837640	−	0.546222i	$-0.183935\pi$
$601$	41.0700	1.67528	0.837640	+	0.546222i	$0.183935\pi$
$602$	60.1552	2.45174
$603$	−1.83840	−0.0748654
$604$	5.99394	0.243890
$605$	8.72309	0.354644
$606$	17.5505	0.712941
$607$	−31.4038	−1.27464	−0.637320	−	0.770599i	$-0.719957\pi$
$607$	−31.4038	−1.27464	−0.637320	+	0.770599i	$0.719957\pi$
$608$	46.2145	1.87425
$609$	25.9087	1.04988
$610$	−40.2664	−1.63034
$611$	−13.7199	−0.555049
$612$	−16.9987	−0.687132
$613$	27.4437	1.10844	0.554220	−	0.832370i	$-0.313017\pi$
$613$	27.4437	1.10844	0.554220	+	0.832370i	$0.313017\pi$
$614$	−68.6342	−2.76985
$615$	6.67536	0.269176
$616$	−20.1752	−0.812882
$617$	18.5514	0.746850	0.373425	−	0.927660i	$-0.378183\pi$
$617$	18.5514	0.746850	0.373425	+	0.927660i	$0.378183\pi$
$618$	9.29792	0.374017
$619$	37.9304	1.52455	0.762275	−	0.647253i	$-0.224082\pi$
$619$	37.9304	1.52455	0.762275	+	0.647253i	$0.224082\pi$
$620$	4.87272	0.195693
$621$	3.10657	0.124662
$622$	8.64915	0.346799
$623$	−6.59964	−0.264409
$624$	0.422972	0.0169324
$625$	−11.6131	−0.464525
$626$	2.52544	0.100937
$627$	−20.8476	−0.832573
$628$	4.77653	0.190604
$629$	16.4676	0.656604
$630$	−11.2738	−0.449159
$631$	−10.0404	−0.399702	−0.199851	−	0.979826i	$-0.564046\pi$
$631$	−10.0404	−0.399702	−0.199851	+	0.979826i	$0.564046\pi$
$632$	13.8010	0.548976
$633$	26.9075	1.06948
$634$	−11.8145	−0.469213
$635$	22.8128	0.905296
$636$	9.81292	0.389107
$637$	1.91121	0.0757249
$638$	−52.1316	−2.06391
$639$	3.44369	0.136230
$640$	−32.7401	−1.29417
$641$	4.04719	0.159855	0.0799273	−	0.996801i	$-0.474531\pi$
$641$	4.04719	0.159855	0.0799273	+	0.996801i	$0.474531\pi$
$642$	−12.7824	−0.504483
$643$	33.3862	1.31662	0.658312	−	0.752745i	$-0.271271\pi$
$643$	33.3862	1.31662	0.658312	+	0.752745i	$0.271271\pi$
$644$	−28.5246	−1.12403
$645$	−16.3738	−0.644719
$646$	101.232	3.98293
$647$	24.0657	0.946119	0.473060	−	0.881030i	$-0.343149\pi$
$647$	24.0657	0.946119	0.473060	+	0.881030i	$0.343149\pi$
$648$	−2.93514	−0.115303
$649$	−18.8164	−0.738608
$650$	10.0009	0.392268
$651$	2.37746	0.0931800
$652$	30.0494	1.17683
$653$	38.4136	1.50324	0.751620	−	0.659596i	$-0.229273\pi$
$653$	38.4136	1.50324	0.751620	+	0.659596i	$0.229273\pi$
$654$	−23.8810	−0.933821
$655$	−9.96371	−0.389314
$656$	−0.715079	−0.0279191
$657$	4.09433	0.159735
$658$	−39.1734	−1.52714
$659$	28.4907	1.10984	0.554920	−	0.831904i	$-0.312749\pi$
$659$	28.4907	1.10984	0.554920	+	0.831904i	$0.312749\pi$
$660$	14.0879	0.548371
$661$	−16.2457	−0.631885	−0.315943	−	0.948778i	$-0.602321\pi$
$661$	−16.2457	−0.631885	−0.315943	+	0.948778i	$0.602321\pi$
$662$	8.08688	0.314305
$663$	−11.6899	−0.454000
$664$	14.9709	0.580985
$665$	41.6961	1.61690
$666$	7.29449	0.282656
$667$	−28.7310	−1.11247
$668$	−46.2303	−1.78870
$669$	−4.01058	−0.155058
$670$	−7.39832	−0.285822
$671$	24.5505	0.947763
$672$	−15.2374	−0.587796
$673$	−0.695752	−0.0268193	−0.0134096	−	0.999910i	$-0.504269\pi$
$673$	−0.695752	−0.0268193	−0.0134096	+	0.999910i	$0.504269\pi$
$674$	44.5629	1.71650
$675$	−1.93135	−0.0743377
$676$	−25.9569	−0.998342
$677$	21.8572	0.840040	0.420020	−	0.907515i	$-0.362023\pi$
$677$	21.8572	0.840040	0.420020	+	0.907515i	$0.362023\pi$
$678$	17.4406	0.669801
$679$	−9.10394	−0.349377
$680$	−26.6659	−1.02259
$681$	−3.18945	−0.122220
$682$	−4.78374	−0.183179
$683$	−19.2333	−0.735943	−0.367971	−	0.929837i	$-0.619948\pi$
$683$	−19.2333	−0.735943	−0.367971	+	0.929837i	$0.619948\pi$
$684$	27.8488	1.06482
$685$	22.7690	0.869957
$686$	−39.5931	−1.51167
$687$	7.71437	0.294321
$688$	1.75400	0.0668706
$689$	6.74831	0.257090
$690$	12.5019	0.475938
$691$	−11.7611	−0.447415	−0.223707	−	0.974656i	$-0.571816\pi$
$691$	−11.7611	−0.447415	−0.223707	+	0.974656i	$0.571816\pi$
$692$	8.78802	0.334070
$693$	6.87367	0.261109
$694$	−49.2784	−1.87058
$695$	−16.2015	−0.614557
$696$	27.1455	1.02895
$697$	19.7631	0.748581
$698$	−59.3478	−2.24635
$699$	22.0441	0.833783
$700$	17.7337	0.670271
$701$	24.7024	0.932995	0.466498	−	0.884522i	$-0.345516\pi$
$701$	24.7024	0.932995	0.466498	+	0.884522i	$0.345516\pi$
$702$	−5.17819	−0.195438
$703$	−26.9786	−1.01752
$704$	31.5804	1.19023
$705$	10.6627	0.401581
$706$	79.5062	2.99225
$707$	21.4016	0.804891
$708$	25.1354	0.944648
$709$	−13.8461	−0.520001	−0.260000	−	0.965608i	$-0.583723\pi$
$709$	−13.8461	−0.520001	−0.260000	+	0.965608i	$0.583723\pi$
$710$	13.8586	0.520103
$711$	−4.70200	−0.176339
$712$	−6.91468	−0.259139
$713$	−2.63644	−0.0987354
$714$	−33.3773	−1.24911
$715$	9.68821	0.362318
$716$	9.97068	0.372622
$717$	5.82790	0.217647
$718$	15.3477	0.572771
$719$	9.93971	0.370689	0.185344	−	0.982674i	$-0.440660\pi$
$719$	9.93971	0.370689	0.185344	+	0.982674i	$0.440660\pi$
$720$	−0.328721	−0.0122507
$721$	11.3382	0.422255
$722$	−122.198	−4.54775
$723$	−23.9962	−0.892427
$724$	−25.4415	−0.945527
$725$	17.8620	0.663379
$726$	11.4398	0.424569
$727$	12.8929	0.478170	0.239085	−	0.970999i	$-0.423153\pi$
$727$	12.8929	0.478170	0.239085	+	0.970999i	$0.423153\pi$
$728$	18.5338	0.686908
$729$	1.00000	0.0370370
$730$	16.4769	0.609839
$731$	−48.4764	−1.79297
$732$	−32.7952	−1.21215
$733$	52.1154	1.92493	0.962463	−	0.271411i	$-0.0874904\pi$
$733$	52.1154	1.92493	0.962463	+	0.271411i	$0.0874904\pi$
$734$	−14.8790	−0.549195
$735$	−1.48533	−0.0547873
$736$	16.8972	0.622840
$737$	4.51078	0.166157
$738$	8.75429	0.322250
$739$	6.24155	0.229599	0.114800	−	0.993389i	$-0.463377\pi$
$739$	6.24155	0.229599	0.114800	+	0.993389i	$0.463377\pi$
$740$	18.2310	0.670184
$741$	19.1515	0.703547
$742$	19.2679	0.707346
$743$	45.2922	1.66161	0.830805	−	0.556563i	$-0.187880\pi$
$743$	45.2922	1.66161	0.830805	+	0.556563i	$0.187880\pi$
$744$	2.49095	0.0913227
$745$	21.3228	0.781209
$746$	−29.6088	−1.08405
$747$	−5.10058	−0.186621
$748$	41.7088	1.52502
$749$	−15.5873	−0.569548
$750$	−27.8940	−1.01855
$751$	21.6782	0.791047	0.395524	−	0.918456i	$-0.370563\pi$
$751$	21.6782	0.791047	0.395524	+	0.918456i	$0.370563\pi$
$752$	−1.14221	−0.0416522
$753$	−5.84290	−0.212927
$754$	47.8903	1.74406
$755$	−3.20350	−0.116587
$756$	−9.18203	−0.333947
$757$	6.32002	0.229705	0.114852	−	0.993383i	$-0.463360\pi$
$757$	6.32002	0.229705	0.114852	+	0.993383i	$0.463360\pi$
$758$	−67.2668	−2.44324
$759$	−7.62242	−0.276676
$760$	43.6865	1.58467
$761$	−40.5624	−1.47039	−0.735193	−	0.677858i	$-0.762908\pi$
$761$	−40.5624	−1.47039	−0.735193	+	0.677858i	$0.762908\pi$
$762$	29.9174	1.08379
$763$	−29.1212	−1.05426
$764$	−35.1814	−1.27282
$765$	9.08506	0.328471
$766$	13.6875	0.494549
$767$	17.2855	0.624145
$768$	−17.1949	−0.620467
$769$	−0.793233	−0.0286047	−0.0143024	−	0.999898i	$-0.504553\pi$
$769$	−0.793233	−0.0286047	−0.0143024	+	0.999898i	$0.504553\pi$
$770$	27.6619	0.996866
$771$	6.25488	0.225264
$772$	−40.3838	−1.45344
$773$	−17.3523	−0.624119	−0.312059	−	0.950063i	$-0.601019\pi$
$773$	−17.3523	−0.624119	−0.312059	+	0.950063i	$0.601019\pi$
$774$	−21.4732	−0.771838
$775$	1.63907	0.0588771
$776$	−9.53853	−0.342413
$777$	8.89512	0.319111
$778$	−78.1033	−2.80014
$779$	−32.3776	−1.16005
$780$	−12.9418	−0.463389
$781$	−8.44960	−0.302351
$782$	37.0131	1.32359
$783$	−9.24846	−0.330513
$784$	0.159112	0.00568258
$785$	−2.55284	−0.0911149
$786$	−13.0667	−0.466075
$787$	−29.1672	−1.03970	−0.519849	−	0.854258i	$-0.674012\pi$
$787$	−29.1672	−1.03970	−0.519849	+	0.854258i	$0.674012\pi$
$788$	−57.5034	−2.04847
$789$	8.38099	0.298371
$790$	−18.9224	−0.673229
$791$	21.2676	0.756187
$792$	7.20179	0.255905
$793$	−22.5532	−0.800886
$794$	4.88429	0.173337
$795$	−5.24457	−0.186006
$796$	78.0394	2.76603
$797$	−8.51145	−0.301491	−0.150746	−	0.988573i	$-0.548167\pi$
$797$	−8.51145	−0.301491	−0.150746	+	0.988573i	$0.548167\pi$
$798$	54.6816	1.93571
$799$	31.5681	1.11680
$800$	−10.5050	−0.371407
$801$	2.35583	0.0832390
$802$	−3.62421	−0.127975
$803$	−10.0460	−0.354517
$804$	−6.02561	−0.212507
$805$	15.2452	0.537321
$806$	4.39455	0.154791
$807$	16.3249	0.574665
$808$	22.4233	0.788848
$809$	32.1869	1.13163	0.565816	−	0.824531i	$-0.308561\pi$
$809$	32.1869	1.13163	0.565816	+	0.824531i	$0.308561\pi$
$810$	4.02433	0.141401
$811$	48.9581	1.71915	0.859575	−	0.511009i	$-0.170728\pi$
$811$	48.9581	1.71915	0.859575	+	0.511009i	$0.170728\pi$
$812$	84.9196	2.98009
$813$	12.8104	0.449281
$814$	−17.8981	−0.627327
$815$	−16.0601	−0.562561
$816$	−0.973212	−0.0340692
$817$	79.4183	2.77850
$818$	11.6929	0.408834
$819$	−6.31445	−0.220645
$820$	21.8794	0.764063
$821$	33.8094	1.17996	0.589979	−	0.807419i	$-0.299136\pi$
$821$	33.8094	1.17996	0.589979	+	0.807419i	$0.299136\pi$
$822$	29.8600	1.04149
$823$	−32.2973	−1.12581	−0.562907	−	0.826520i	$-0.690317\pi$
$823$	−32.2973	−1.12581	−0.562907	+	0.826520i	$0.690317\pi$
$824$	11.8794	0.413839
$825$	4.73885	0.164986
$826$	49.3539	1.71724
$827$	−12.0691	−0.419683	−0.209841	−	0.977735i	$-0.567295\pi$
$827$	−12.0691	−0.419683	−0.209841	+	0.977735i	$0.567295\pi$
$828$	10.1822	0.353857
$829$	1.15294	0.0400431	0.0200216	−	0.999800i	$-0.493627\pi$
$829$	1.15294	0.0400431	0.0200216	+	0.999800i	$0.493627\pi$
$830$	−20.5264	−0.712483
$831$	6.10825	0.211893
$832$	−29.0111	−1.00578
$833$	−4.39748	−0.152364
$834$	−21.2472	−0.735730
$835$	24.7081	0.855058
$836$	−68.3309	−2.36328
$837$	−0.848665	−0.0293342
$838$	−3.01786	−0.104250
$839$	21.9698	0.758483	0.379241	−	0.925298i	$-0.376185\pi$
$839$	21.9698	0.758483	0.379241	+	0.925298i	$0.376185\pi$
$840$	−14.4039	−0.496981
$841$	56.5340	1.94945
$842$	42.0867	1.45040
$843$	17.3212	0.596575
$844$	88.1933	3.03574
$845$	13.8728	0.477240
$846$	13.9834	0.480760
$847$	13.9500	0.479327
$848$	0.561811	0.0192927
$849$	27.1869	0.933054
$850$	−23.0110	−0.789270
$851$	−9.86407	−0.338136
$852$	11.2872	0.386693
$853$	−7.38042	−0.252701	−0.126350	−	0.991986i	$-0.540326\pi$
$853$	−7.38042	−0.252701	−0.126350	+	0.991986i	$0.540326\pi$
$854$	−64.3941	−2.20352
$855$	−14.8839	−0.509020
$856$	−16.3314	−0.558195
$857$	28.0421	0.957899	0.478949	−	0.877843i	$-0.341018\pi$
$857$	28.0421	0.957899	0.478949	+	0.877843i	$0.341018\pi$
$858$	12.7054	0.433757
$859$	−15.4740	−0.527966	−0.263983	−	0.964527i	$-0.585036\pi$
$859$	−15.4740	−0.527966	−0.263983	+	0.964527i	$0.585036\pi$
$860$	−53.6675	−1.83005
$861$	10.6752	0.363811
$862$	−90.0336	−3.06656
$863$	−28.3734	−0.965842	−0.482921	−	0.875664i	$-0.660424\pi$
$863$	−28.3734	−0.965842	−0.482921	+	0.875664i	$0.660424\pi$
$864$	5.43919	0.185045
$865$	−4.69681	−0.159696
$866$	18.2340	0.619616
$867$	9.89728	0.336129
$868$	7.79246	0.264493
$869$	11.5370	0.391367
$870$	−37.2188	−1.26184
$871$	−4.14379	−0.140407
$872$	−30.5114	−1.03325
$873$	3.24977	0.109988
$874$	−60.6381	−2.05111
$875$	−34.0148	−1.14991
$876$	13.4198	0.453412
$877$	−24.1493	−0.815464	−0.407732	−	0.913102i	$-0.633680\pi$
$877$	−24.1493	−0.815464	−0.407732	+	0.913102i	$0.633680\pi$
$878$	−81.9007	−2.76402
$879$	−25.6662	−0.865699
$880$	0.806563	0.0271892
$881$	3.52544	0.118775	0.0593875	−	0.998235i	$-0.481085\pi$
$881$	3.52544	0.118775	0.0593875	+	0.998235i	$0.481085\pi$
$882$	−1.94791	−0.0655897
$883$	22.7848	0.766771	0.383385	−	0.923589i	$-0.374758\pi$
$883$	22.7848	0.766771	0.383385	+	0.923589i	$0.374758\pi$
$884$	−38.3154	−1.28869
$885$	−13.4338	−0.451572
$886$	10.6106	0.356469
$887$	18.3306	0.615481	0.307740	−	0.951470i	$-0.400427\pi$
$887$	18.3306	0.615481	0.307740	+	0.951470i	$0.400427\pi$
$888$	9.31974	0.312750
$889$	36.4822	1.22357
$890$	9.48062	0.317791
$891$	−2.45364	−0.0822002
$892$	−13.1453	−0.440136
$893$	−51.7176	−1.73066
$894$	27.9635	0.935239
$895$	−5.32889	−0.178125
$896$	−52.3581	−1.74916
$897$	7.00228	0.233799
$898$	−14.1138	−0.470983
$899$	7.84884	0.261774
$900$	−6.33028	−0.211009
$901$	−15.5271	−0.517283
$902$	−21.4799	−0.715203
$903$	−26.1851	−0.871384
$904$	22.2828	0.741115
$905$	13.5974	0.451992
$906$	−4.20118	−0.139575
$907$	1.39389	0.0462835	0.0231417	−	0.999732i	$-0.492633\pi$
$907$	1.39389	0.0462835	0.0231417	+	0.999732i	$0.492633\pi$
$908$	−10.4539	−0.346924
$909$	−7.63959	−0.253389
$910$	−25.4114	−0.842380
$911$	49.5615	1.64205	0.821023	−	0.570896i	$-0.193404\pi$
$911$	49.5615	1.64205	0.821023	+	0.570896i	$0.193404\pi$
$912$	1.59440	0.0527959
$913$	12.5150	0.414187
$914$	25.8143	0.853863
$915$	17.5276	0.579445
$916$	25.2849	0.835438
$917$	−15.9340	−0.526187
$918$	11.9145	0.393236
$919$	−53.0950	−1.75144	−0.875721	−	0.482818i	$-0.839613\pi$
$919$	−53.0950	−1.75144	−0.875721	+	0.482818i	$0.839613\pi$
$920$	15.9729	0.526611
$921$	29.8759	0.984443
$922$	−11.9783	−0.394483
$923$	7.76216	0.255495
$924$	22.5294	0.741164
$925$	6.13248	0.201635
$926$	40.5525	1.33264
$927$	−4.04730	−0.132931
$928$	−50.3041	−1.65131
$929$	−42.5297	−1.39535	−0.697677	−	0.716412i	$-0.745783\pi$
$929$	−42.5297	−1.39535	−0.697677	+	0.716412i	$0.745783\pi$
$930$	−3.41531	−0.111992
$931$	7.20434	0.236113
$932$	72.2525	2.36671
$933$	−3.76490	−0.123257
$934$	8.81554	0.288453
$935$	−22.2915	−0.729010
$936$	−6.61587	−0.216247
$937$	25.6060	0.836513	0.418256	−	0.908329i	$-0.362641\pi$
$937$	25.6060	0.836513	0.418256	+	0.908329i	$0.362641\pi$
$938$	−11.8314	−0.386309
$939$	−1.09930	−0.0358744
$940$	34.9485	1.13990
$941$	−30.8492	−1.00566	−0.502828	−	0.864387i	$-0.667707\pi$
$941$	−30.8492	−1.00566	−0.502828	+	0.864387i	$0.667707\pi$
$942$	−3.34789	−0.109080
$943$	−11.8381	−0.385501
$944$	1.43906	0.0468373
$945$	4.90739	0.159637
$946$	52.6876	1.71302
$947$	23.3301	0.758125	0.379062	−	0.925371i	$-0.376247\pi$
$947$	23.3301	0.758125	0.379062	+	0.925371i	$0.376247\pi$
$948$	−15.4115	−0.500541
$949$	9.22872	0.299577
$950$	37.6986	1.22310
$951$	5.14275	0.166765
$952$	−42.6442	−1.38211
$953$	−29.1852	−0.945402	−0.472701	−	0.881223i	$-0.656721\pi$
$953$	−29.1852	−0.945402	−0.472701	+	0.881223i	$0.656721\pi$
$954$	−6.87791	−0.222681
$955$	18.8029	0.608449
$956$	19.1018	0.617796
$957$	22.6924	0.733542
$958$	75.2601	2.43154
$959$	36.4122	1.17581
$960$	22.5465	0.727686
$961$	−30.2798	−0.976767
$962$	16.4419	0.530109
$963$	5.56409	0.179300
$964$	−78.6508	−2.53317
$965$	21.5834	0.694793
$966$	19.9930	0.643264
$967$	−24.1871	−0.777805	−0.388903	−	0.921279i	$-0.627146\pi$
$967$	−24.1871	−0.777805	−0.388903	+	0.921279i	$0.627146\pi$
$968$	14.6159	0.469773
$969$	−44.0655	−1.41559
$970$	13.0781	0.419914
$971$	33.4399	1.07314	0.536568	−	0.843857i	$-0.319720\pi$
$971$	33.4399	1.07314	0.536568	+	0.843857i	$0.319720\pi$
$972$	3.27764	0.105130
$973$	−25.9095	−0.830619
$974$	21.7436	0.696710
$975$	−4.35331	−0.139417
$976$	−1.87760	−0.0601004
$977$	59.6187	1.90737	0.953686	−	0.300805i	$-0.0972552\pi$
$977$	59.6187	1.90737	0.953686	+	0.300805i	$0.0972552\pi$
$978$	−21.0618	−0.673481
$979$	−5.78036	−0.184741
$980$	−4.86839	−0.155515
$981$	10.3952	0.331893
$982$	−72.7300	−2.32091
$983$	20.3765	0.649908	0.324954	−	0.945730i	$-0.394651\pi$
$983$	20.3765	0.649908	0.324954	+	0.945730i	$0.394651\pi$
$984$	11.1848	0.356560
$985$	30.7330	0.979236
$986$	−110.190	−3.50917
$987$	17.0518	0.542766
$988$	62.7717	1.99703
$989$	29.0374	0.923335
$990$	−9.87428	−0.313825
$991$	44.9842	1.42897	0.714486	−	0.699650i	$-0.246661\pi$
$991$	44.9842	1.42897	0.714486	+	0.699650i	$0.246661\pi$
$992$	−4.61605	−0.146560
$993$	−3.52015	−0.111708
$994$	22.1626	0.702956
$995$	−41.7086	−1.32225
$996$	−16.7179	−0.529726
$997$	25.5869	0.810345	0.405172	−	0.914240i	$-0.367211\pi$
$997$	25.5869	0.810345	0.405172	+	0.914240i	$0.367211\pi$
$998$	−2.91454	−0.0922580
$999$	−3.17523	−0.100460

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	8031.2.a.d.1.16	✓	132

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
8031.2.a.d.1.16	✓	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)

\(f(q)\)	\(=\)	\(q-2.29731 q^{2} +1.00000 q^{3} +3.27764 q^{4} -1.75176 q^{5} -2.29731 q^{6} -2.80141 q^{7} -2.93514 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q-2.29731 q^{2} +1.00000 q^{3} +3.27764 q^{4} -1.75176 q^{5} -2.29731 q^{6} -2.80141 q^{7} -2.93514 q^{8} +1.00000 q^{9} +4.02433 q^{10} -2.45364 q^{11} +3.27764 q^{12} +2.25402 q^{13} +6.43572 q^{14} -1.75176 q^{15} +0.187652 q^{16} -5.18626 q^{17} -2.29731 q^{18} +8.49658 q^{19} -5.74163 q^{20} -2.80141 q^{21} +5.63679 q^{22} +3.10657 q^{23} -2.93514 q^{24} -1.93135 q^{25} -5.17819 q^{26} +1.00000 q^{27} -9.18203 q^{28} -9.24846 q^{29} +4.02433 q^{30} -0.848665 q^{31} +5.43919 q^{32} -2.45364 q^{33} +11.9145 q^{34} +4.90739 q^{35} +3.27764 q^{36} -3.17523 q^{37} -19.5193 q^{38} +2.25402 q^{39} +5.14165 q^{40} -3.81066 q^{41} +6.43572 q^{42} +9.34709 q^{43} -8.04217 q^{44} -1.75176 q^{45} -7.13676 q^{46} -6.08687 q^{47} +0.187652 q^{48} +0.847910 q^{49} +4.43691 q^{50} -5.18626 q^{51} +7.38788 q^{52} +2.99390 q^{53} -2.29731 q^{54} +4.29819 q^{55} +8.22254 q^{56} +8.49658 q^{57} +21.2466 q^{58} +7.66876 q^{59} -5.74163 q^{60} -10.0057 q^{61} +1.94965 q^{62} -2.80141 q^{63} -12.8708 q^{64} -3.94850 q^{65} +5.63679 q^{66} -1.83840 q^{67} -16.9987 q^{68} +3.10657 q^{69} -11.2738 q^{70} +3.44369 q^{71} -2.93514 q^{72} +4.09433 q^{73} +7.29449 q^{74} -1.93135 q^{75} +27.8488 q^{76} +6.87367 q^{77} -5.17819 q^{78} -4.70200 q^{79} -0.328721 q^{80} +1.00000 q^{81} +8.75429 q^{82} -5.10058 q^{83} -9.18203 q^{84} +9.08506 q^{85} -21.4732 q^{86} -9.24846 q^{87} +7.20179 q^{88} +2.35583 q^{89} +4.02433 q^{90} -6.31445 q^{91} +10.1822 q^{92} -0.848665 q^{93} +13.9834 q^{94} -14.8839 q^{95} +5.43919 q^{96} +3.24977 q^{97} -1.94791 q^{98} -2.45364 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 132 q + 4 q^{2} + 132 q^{3} + 156 q^{4} + 20 q^{5} + 4 q^{6} + 44 q^{7} + 9 q^{8} + 132 q^{9}+O(q^{10}) \) 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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