LMFDB - Embedded newform 8031.2.a.d.1.17

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			1.17
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)

$f(q)$	$=$	$q-2.23840 q^{2} +1.00000 q^{3} +3.01043 q^{4} +3.52664 q^{5} -2.23840 q^{6} +3.86222 q^{7} -2.26174 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q-2.23840 q^{2} +1.00000 q^{3} +3.01043 q^{4} +3.52664 q^{5} -2.23840 q^{6} +3.86222 q^{7} -2.26174 q^{8} +1.00000 q^{9} -7.89403 q^{10} +0.290198 q^{11} +3.01043 q^{12} +6.93421 q^{13} -8.64518 q^{14} +3.52664 q^{15} -0.958176 q^{16} -2.17483 q^{17} -2.23840 q^{18} +5.98923 q^{19} +10.6167 q^{20} +3.86222 q^{21} -0.649580 q^{22} -3.39102 q^{23} -2.26174 q^{24} +7.43720 q^{25} -15.5215 q^{26} +1.00000 q^{27} +11.6269 q^{28} +3.36852 q^{29} -7.89403 q^{30} +8.45991 q^{31} +6.66827 q^{32} +0.290198 q^{33} +4.86813 q^{34} +13.6207 q^{35} +3.01043 q^{36} +0.432639 q^{37} -13.4063 q^{38} +6.93421 q^{39} -7.97635 q^{40} -2.64243 q^{41} -8.64518 q^{42} -3.53822 q^{43} +0.873622 q^{44} +3.52664 q^{45} +7.59046 q^{46} -8.10488 q^{47} -0.958176 q^{48} +7.91671 q^{49} -16.6474 q^{50} -2.17483 q^{51} +20.8749 q^{52} +4.48957 q^{53} -2.23840 q^{54} +1.02343 q^{55} -8.73534 q^{56} +5.98923 q^{57} -7.54009 q^{58} -4.73435 q^{59} +10.6167 q^{60} +5.64914 q^{61} -18.9366 q^{62} +3.86222 q^{63} -13.0099 q^{64} +24.4545 q^{65} -0.649580 q^{66} -12.3304 q^{67} -6.54717 q^{68} -3.39102 q^{69} -30.4884 q^{70} -4.33581 q^{71} -2.26174 q^{72} -7.46483 q^{73} -0.968419 q^{74} +7.43720 q^{75} +18.0301 q^{76} +1.12081 q^{77} -15.5215 q^{78} -12.8170 q^{79} -3.37914 q^{80} +1.00000 q^{81} +5.91482 q^{82} -7.77358 q^{83} +11.6269 q^{84} -7.66984 q^{85} +7.91995 q^{86} +3.36852 q^{87} -0.656354 q^{88} +16.8607 q^{89} -7.89403 q^{90} +26.7814 q^{91} -10.2084 q^{92} +8.45991 q^{93} +18.1420 q^{94} +21.1219 q^{95} +6.66827 q^{96} +9.09868 q^{97} -17.7208 q^{98} +0.290198 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	−2.23840	−1.58279	−0.791393	−	0.611307i	$-0.790644\pi$
$2$	−2.23840	−1.58279	−0.791393	+	0.611307i	$0.790644\pi$
$3$	1.00000	0.577350
$3$	1.00000	0.577350
$4$	3.01043	1.50521
$5$	3.52664	1.57716	0.788581	−	0.614931i	$-0.210816\pi$
$5$	3.52664	1.57716	0.788581	+	0.614931i	$0.210816\pi$
$6$	−2.23840	−0.913822
$7$	3.86222	1.45978	0.729890	−	0.683564i	$-0.239571\pi$
$7$	3.86222	1.45978	0.729890	+	0.683564i	$0.239571\pi$
$8$	−2.26174	−0.799647
$9$	1.00000	0.333333
$10$	−7.89403	−2.49631
$11$	0.290198	0.0874981	0.0437491	−	0.999043i	$-0.486070\pi$
$11$	0.290198	0.0874981	0.0437491	+	0.999043i	$0.486070\pi$
$12$	3.01043	0.869036
$13$	6.93421	1.92320	0.961602	−	0.274449i	$-0.0884956\pi$
$13$	6.93421	1.92320	0.961602	+	0.274449i	$0.0884956\pi$
$14$	−8.64518	−2.31052
$15$	3.52664	0.910575
$16$	−0.958176	−0.239544
$17$	−2.17483	−0.527473	−0.263737	−	0.964595i	$-0.584955\pi$
$17$	−2.17483	−0.527473	−0.263737	+	0.964595i	$0.584955\pi$
$18$	−2.23840	−0.527596
$19$	5.98923	1.37402	0.687012	−	0.726646i	$-0.258922\pi$
$19$	5.98923	1.37402	0.687012	+	0.726646i	$0.258922\pi$
$20$	10.6167	2.37397
$21$	3.86222	0.842805
$22$	−0.649580	−0.138491
$23$	−3.39102	−0.707077	−0.353538	−	0.935420i	$-0.615022\pi$
$23$	−3.39102	−0.707077	−0.353538	+	0.935420i	$0.615022\pi$
$24$	−2.26174	−0.461676
$25$	7.43720	1.48744
$26$	−15.5215	−3.04402
$27$	1.00000	0.192450
$28$	11.6269	2.19728
$29$	3.36852	0.625518	0.312759	−	0.949833i	$-0.398747\pi$
$29$	3.36852	0.625518	0.312759	+	0.949833i	$0.398747\pi$
$30$	−7.89403	−1.44125
$31$	8.45991	1.51944	0.759722	−	0.650248i	$-0.225335\pi$
$31$	8.45991	1.51944	0.759722	+	0.650248i	$0.225335\pi$
$32$	6.66827	1.17879
$33$	0.290198	0.0505171
$34$	4.86813	0.834878
$35$	13.6207	2.30231
$36$	3.01043	0.501738
$37$	0.432639	0.0711255	0.0355627	−	0.999367i	$-0.488678\pi$
$37$	0.432639	0.0711255	0.0355627	+	0.999367i	$0.488678\pi$
$38$	−13.4063	−2.17479
$39$	6.93421	1.11036
$40$	−7.97635	−1.26117
$41$	−2.64243	−0.412679	−0.206339	−	0.978481i	$-0.566155\pi$
$41$	−2.64243	−0.412679	−0.206339	+	0.978481i	$0.566155\pi$
$42$	−8.64518	−1.33398
$43$	−3.53822	−0.539574	−0.269787	−	0.962920i	$-0.586953\pi$
$43$	−3.53822	−0.539574	−0.269787	+	0.962920i	$0.586953\pi$
$44$	0.873622	0.131703
$45$	3.52664	0.525721
$46$	7.59046	1.11915
$47$	−8.10488	−1.18222	−0.591109	−	0.806591i	$-0.701310\pi$
$47$	−8.10488	−1.18222	−0.591109	+	0.806591i	$0.701310\pi$
$48$	−0.958176	−0.138301
$49$	7.91671	1.13096
$50$	−16.6474	−2.35430
$51$	−2.17483	−0.304537
$52$	20.8749	2.89483
$53$	4.48957	0.616690	0.308345	−	0.951275i	$-0.400225\pi$
$53$	4.48957	0.616690	0.308345	+	0.951275i	$0.400225\pi$
$54$	−2.23840	−0.304607
$55$	1.02343	0.137999
$56$	−8.73534	−1.16731
$57$	5.98923	0.793293
$58$	−7.54009	−0.990062
$59$	−4.73435	−0.616360	−0.308180	−	0.951328i	$-0.599720\pi$
$59$	−4.73435	−0.616360	−0.308180	+	0.951328i	$0.599720\pi$
$60$	10.6167	1.37061
$61$	5.64914	0.723299	0.361649	−	0.932314i	$-0.382214\pi$
$61$	5.64914	0.723299	0.361649	+	0.932314i	$0.382214\pi$
$62$	−18.9366	−2.40496
$63$	3.86222	0.486593
$64$	−13.0099	−1.62624
$65$	24.4545	3.03320
$66$	−0.649580	−0.0799577
$67$	−12.3304	−1.50640	−0.753198	−	0.657794i	$-0.771490\pi$
$67$	−12.3304	−1.50640	−0.753198	+	0.657794i	$0.771490\pi$
$68$	−6.54717	−0.793960
$69$	−3.39102	−0.408231
$70$	−30.4884	−3.64407
$71$	−4.33581	−0.514567	−0.257283	−	0.966336i	$-0.582827\pi$
$71$	−4.33581	−0.514567	−0.257283	+	0.966336i	$0.582827\pi$
$72$	−2.26174	−0.266549
$73$	−7.46483	−0.873693	−0.436846	−	0.899536i	$-0.643905\pi$
$73$	−7.46483	−0.873693	−0.436846	+	0.899536i	$0.643905\pi$
$74$	−0.968419	−0.112576
$75$	7.43720	0.858774
$76$	18.0301	2.06820
$77$	1.12081	0.127728
$78$	−15.5215	−1.75747
$79$	−12.8170	−1.44202	−0.721011	−	0.692923i	$-0.756322\pi$
$79$	−12.8170	−1.44202	−0.721011	+	0.692923i	$0.756322\pi$
$80$	−3.37914	−0.377800
$81$	1.00000	0.111111
$82$	5.91482	0.653182
$83$	−7.77358	−0.853261	−0.426631	−	0.904426i	$-0.640300\pi$
$83$	−7.77358	−0.853261	−0.426631	+	0.904426i	$0.640300\pi$
$84$	11.6269	1.26860
$85$	−7.66984	−0.831911
$86$	7.91995	0.854031
$87$	3.36852	0.361143
$88$	−0.656354	−0.0699676
$89$	16.8607	1.78723	0.893616	−	0.448833i	$-0.148160\pi$
$89$	16.8607	1.78723	0.893616	+	0.448833i	$0.148160\pi$
$90$	−7.89403	−0.832104
$91$	26.7814	2.80745
$92$	−10.2084	−1.06430
$93$	8.45991	0.877251
$94$	18.1420	1.87120
$95$	21.1219	2.16706
$96$	6.66827	0.680577
$97$	9.09868	0.923831	0.461915	−	0.886924i	$-0.347162\pi$
$97$	9.09868	0.923831	0.461915	+	0.886924i	$0.347162\pi$
$98$	−17.7208	−1.79007
$99$	0.290198	0.0291660
$100$	22.3892	2.23892
$101$	2.45743	0.244523	0.122262	−	0.992498i	$-0.460985\pi$
$101$	2.45743	0.244523	0.122262	+	0.992498i	$0.460985\pi$
$102$	4.86813	0.482017
$103$	0.980438	0.0966054	0.0483027	−	0.998833i	$-0.484619\pi$
$103$	0.980438	0.0966054	0.0483027	+	0.998833i	$0.484619\pi$
$104$	−15.6834	−1.53788
$105$	13.6207	1.32924
$106$	−10.0495	−0.976090
$107$	−9.40205	−0.908930	−0.454465	−	0.890765i	$-0.650170\pi$
$107$	−9.40205	−0.908930	−0.454465	+	0.890765i	$0.650170\pi$
$108$	3.01043	0.289679
$109$	2.30514	0.220792	0.110396	−	0.993888i	$-0.464788\pi$
$109$	2.30514	0.220792	0.110396	+	0.993888i	$0.464788\pi$
$110$	−2.29084	−0.218423
$111$	0.432639	0.0410643
$112$	−3.70068	−0.349682
$113$	8.94876	0.841829	0.420914	−	0.907100i	$-0.361709\pi$
$113$	8.94876	0.841829	0.420914	+	0.907100i	$0.361709\pi$
$114$	−13.4063	−1.25561
$115$	−11.9589	−1.11517
$116$	10.1407	0.941539
$117$	6.93421	0.641068
$118$	10.5974	0.975567
$119$	−8.39966	−0.769995
$120$	−7.97635	−0.728138
$121$	−10.9158	−0.992344
$122$	−12.6450	−1.14483
$123$	−2.64243	−0.238260
$124$	25.4679	2.28709
$125$	8.59513	0.768771
$126$	−8.64518	−0.770174
$127$	−7.23437	−0.641947	−0.320973	−	0.947088i	$-0.604010\pi$
$127$	−7.23437	−0.641947	−0.320973	+	0.947088i	$0.604010\pi$
$128$	15.7848	1.39519
$129$	−3.53822	−0.311523
$130$	−54.7388	−4.80091
$131$	−13.5077	−1.18017	−0.590085	−	0.807341i	$-0.700906\pi$
$131$	−13.5077	−1.18017	−0.590085	+	0.807341i	$0.700906\pi$
$132$	0.873622	0.0760390
$133$	23.1317	2.00577
$134$	27.6003	2.38430
$135$	3.52664	0.303525
$136$	4.91890	0.421792
$137$	2.05042	0.175179	0.0875896	−	0.996157i	$-0.472084\pi$
$137$	2.05042	0.175179	0.0875896	+	0.996157i	$0.472084\pi$
$138$	7.59046	0.646143
$139$	−10.3956	−0.881740	−0.440870	−	0.897571i	$-0.645330\pi$
$139$	−10.3956	−0.881740	−0.440870	+	0.897571i	$0.645330\pi$
$140$	41.0040	3.46547
$141$	−8.10488	−0.682554
$142$	9.70528	0.814449
$143$	2.01230	0.168277
$144$	−0.958176	−0.0798480
$145$	11.8796	0.986543
$146$	16.7093	1.38287
$147$	7.91671	0.652959
$148$	1.30243	0.107059
$149$	−16.6757	−1.36612	−0.683062	−	0.730360i	$-0.739352\pi$
$149$	−16.6757	−1.36612	−0.683062	+	0.730360i	$0.739352\pi$
$150$	−16.6474	−1.35926
$151$	11.5579	0.940565	0.470282	−	0.882516i	$-0.344152\pi$
$151$	11.5579	0.940565	0.470282	+	0.882516i	$0.344152\pi$
$152$	−13.5461	−1.09873
$153$	−2.17483	−0.175824
$154$	−2.50882	−0.202166
$155$	29.8351	2.39641
$156$	20.8749	1.67133
$157$	6.14195	0.490181	0.245090	−	0.969500i	$-0.421182\pi$
$157$	6.14195	0.490181	0.245090	+	0.969500i	$0.421182\pi$
$158$	28.6895	2.28241
$159$	4.48957	0.356046
$160$	23.5166	1.85915
$161$	−13.0969	−1.03218
$162$	−2.23840	−0.175865
$163$	−23.8970	−1.87176	−0.935878	−	0.352325i	$-0.885391\pi$
$163$	−23.8970	−1.87176	−0.935878	+	0.352325i	$0.885391\pi$
$164$	−7.95485	−0.621170
$165$	1.02343	0.0796736
$166$	17.4004	1.35053
$167$	8.34360	0.645647	0.322824	−	0.946459i	$-0.395368\pi$
$167$	8.34360	0.645647	0.322824	+	0.946459i	$0.395368\pi$
$168$	−8.73534	−0.673946
$169$	35.0832	2.69871
$170$	17.1682	1.31674
$171$	5.98923	0.458008
$172$	−10.6516	−0.812174
$173$	−17.5420	−1.33370	−0.666848	−	0.745194i	$-0.732357\pi$
$173$	−17.5420	−1.33370	−0.666848	+	0.745194i	$0.732357\pi$
$174$	−7.54009	−0.571612
$175$	28.7241	2.17134
$176$	−0.278061	−0.0209597
$177$	−4.73435	−0.355856
$178$	−37.7410	−2.82881
$179$	13.2259	0.988546	0.494273	−	0.869307i	$-0.335434\pi$
$179$	13.2259	0.988546	0.494273	+	0.869307i	$0.335434\pi$
$180$	10.6167	0.791322
$181$	−6.18723	−0.459893	−0.229947	−	0.973203i	$-0.573855\pi$
$181$	−6.18723	−0.459893	−0.229947	+	0.973203i	$0.573855\pi$
$182$	−59.9475	−4.44360
$183$	5.64914	0.417597
$184$	7.66962	0.565412
$185$	1.52576	0.112176
$186$	−18.9366	−1.38850
$187$	−0.631132	−0.0461529
$188$	−24.3992	−1.77949
$189$	3.86222	0.280935
$190$	−47.2791	−3.42999
$191$	−13.8259	−1.00040	−0.500202	−	0.865909i	$-0.666741\pi$
$191$	−13.8259	−1.00040	−0.500202	+	0.865909i	$0.666741\pi$
$192$	−13.0099	−0.938907
$193$	−9.62618	−0.692908	−0.346454	−	0.938067i	$-0.612614\pi$
$193$	−9.62618	−0.692908	−0.346454	+	0.938067i	$0.612614\pi$
$194$	−20.3665	−1.46223
$195$	24.4545	1.75122
$196$	23.8327	1.70234
$197$	2.75902	0.196572	0.0982862	−	0.995158i	$-0.468664\pi$
$197$	2.75902	0.196572	0.0982862	+	0.995158i	$0.468664\pi$
$198$	−0.649580	−0.0461636
$199$	2.34645	0.166335	0.0831677	−	0.996536i	$-0.473496\pi$
$199$	2.34645	0.166335	0.0831677	+	0.996536i	$0.473496\pi$
$200$	−16.8210	−1.18943
$201$	−12.3304	−0.869718
$202$	−5.50070	−0.387028
$203$	13.0099	0.913119
$204$	−6.54717	−0.458393
$205$	−9.31891	−0.650861
$206$	−2.19461	−0.152906
$207$	−3.39102	−0.235692
$208$	−6.64419	−0.460692
$209$	1.73806	0.120224
$210$	−30.4884	−2.10390
$211$	−0.143224	−0.00985996	−0.00492998	−	0.999988i	$-0.501569\pi$
$211$	−0.143224	−0.00985996	−0.00492998	+	0.999988i	$0.501569\pi$
$212$	13.5155	0.928251
$213$	−4.33581	−0.297085
$214$	21.0455	1.43864
$215$	−12.4780	−0.850996
$216$	−2.26174	−0.153892
$217$	32.6740	2.21805
$218$	−5.15981	−0.349467
$219$	−7.46483	−0.504427
$220$	3.08095	0.207718
$221$	−15.0807	−1.01444
$222$	−0.968419	−0.0649961
$223$	18.5092	1.23947	0.619733	−	0.784812i	$-0.287241\pi$
$223$	18.5092	1.23947	0.619733	+	0.784812i	$0.287241\pi$
$224$	25.7543	1.72078
$225$	7.43720	0.495813
$226$	−20.0309	−1.33244
$227$	−0.387560	−0.0257232	−0.0128616	−	0.999917i	$-0.504094\pi$
$227$	−0.387560	−0.0257232	−0.0128616	+	0.999917i	$0.504094\pi$
$228$	18.0301	1.19408
$229$	9.46427	0.625417	0.312708	−	0.949849i	$-0.398764\pi$
$229$	9.46427	0.625417	0.312708	+	0.949849i	$0.398764\pi$
$230$	26.7688	1.76508
$231$	1.12081	0.0737438
$232$	−7.61872	−0.500193
$233$	12.9169	0.846216	0.423108	−	0.906079i	$-0.360939\pi$
$233$	12.9169	0.846216	0.423108	+	0.906079i	$0.360939\pi$
$234$	−15.5215	−1.01467
$235$	−28.5830	−1.86455
$236$	−14.2524	−0.927754
$237$	−12.8170	−0.832552
$238$	18.8018	1.21874
$239$	9.40408	0.608299	0.304150	−	0.952624i	$-0.401628\pi$
$239$	9.40408	0.608299	0.304150	+	0.952624i	$0.401628\pi$
$240$	−3.37914	−0.218123
$241$	−8.82818	−0.568673	−0.284336	−	0.958725i	$-0.591773\pi$
$241$	−8.82818	−0.568673	−0.284336	+	0.958725i	$0.591773\pi$
$242$	24.4339	1.57067
$243$	1.00000	0.0641500
$244$	17.0063	1.08872
$245$	27.9194	1.78371
$246$	5.91482	0.377115
$247$	41.5306	2.64253
$248$	−19.1341	−1.21502
$249$	−7.77358	−0.492631
$250$	−19.2393	−1.21680
$251$	8.99702	0.567887	0.283943	−	0.958841i	$-0.408357\pi$
$251$	8.99702	0.567887	0.283943	+	0.958841i	$0.408357\pi$
$252$	11.6269	0.732427
$253$	−0.984069	−0.0618679
$254$	16.1934	1.01606
$255$	−7.66984	−0.480304
$256$	−9.31285	−0.582053
$257$	1.55159	0.0967858	0.0483929	−	0.998828i	$-0.484590\pi$
$257$	1.55159	0.0967858	0.0483929	+	0.998828i	$0.484590\pi$
$258$	7.91995	0.493075
$259$	1.67095	0.103828
$260$	73.6184	4.56562
$261$	3.36852	0.208506
$262$	30.2355	1.86796
$263$	−8.13137	−0.501402	−0.250701	−	0.968065i	$-0.580661\pi$
$263$	−8.13137	−0.501402	−0.250701	+	0.968065i	$0.580661\pi$
$264$	−0.656354	−0.0403958
$265$	15.8331	0.972621
$266$	−51.7780	−3.17471
$267$	16.8607	1.03186
$268$	−37.1197	−2.26745
$269$	−27.7028	−1.68907	−0.844536	−	0.535499i	$-0.820124\pi$
$269$	−27.7028	−1.68907	−0.844536	+	0.535499i	$0.820124\pi$
$270$	−7.89403	−0.480415
$271$	−0.319479	−0.0194070	−0.00970348	−	0.999953i	$-0.503089\pi$
$271$	−0.319479	−0.0194070	−0.00970348	+	0.999953i	$0.503089\pi$
$272$	2.08387	0.126353
$273$	26.7814	1.62088
$274$	−4.58966	−0.277271
$275$	2.15826	0.130148
$276$	−10.2084	−0.614475
$277$	−11.2595	−0.676517	−0.338259	−	0.941053i	$-0.609838\pi$
$277$	−11.2595	−0.676517	−0.338259	+	0.941053i	$0.609838\pi$
$278$	23.2694	1.39561
$279$	8.45991	0.506481
$280$	−30.8064	−1.84103
$281$	−10.5110	−0.627036	−0.313518	−	0.949582i	$-0.601508\pi$
$281$	−10.5110	−0.627036	−0.313518	+	0.949582i	$0.601508\pi$
$282$	18.1420	1.08034
$283$	23.3686	1.38912	0.694559	−	0.719436i	$-0.255600\pi$
$283$	23.3686	1.38912	0.694559	+	0.719436i	$0.255600\pi$
$284$	−13.0527	−0.774533
$285$	21.1219	1.25115
$286$	−4.50432	−0.266346
$287$	−10.2056	−0.602420
$288$	6.66827	0.392931
$289$	−12.2701	−0.721772
$290$	−26.5912	−1.56149
$291$	9.09868	0.533374
$292$	−22.4723	−1.31509
$293$	−13.1096	−0.765872	−0.382936	−	0.923775i	$-0.625087\pi$
$293$	−13.1096	−0.765872	−0.382936	+	0.923775i	$0.625087\pi$
$294$	−17.7208	−1.03350
$295$	−16.6964	−0.972100
$296$	−0.978519	−0.0568752
$297$	0.290198	0.0168390
$298$	37.3268	2.16228
$299$	−23.5140	−1.35985
$300$	22.3892	1.29264
$301$	−13.6654	−0.787659
$302$	−25.8711	−1.48871
$303$	2.45743	0.141176
$304$	−5.73874	−0.329139
$305$	19.9225	1.14076
$306$	4.86813	0.278293
$307$	16.0024	0.913305	0.456652	−	0.889645i	$-0.349048\pi$
$307$	16.0024	0.913305	0.456652	+	0.889645i	$0.349048\pi$
$308$	3.37412	0.192258
$309$	0.980438	0.0557752
$310$	−66.7828	−3.79301
$311$	−27.5517	−1.56231	−0.781156	−	0.624336i	$-0.785370\pi$
$311$	−27.5517	−1.56231	−0.781156	+	0.624336i	$0.785370\pi$
$312$	−15.6834	−0.887897
$313$	−2.65325	−0.149970	−0.0749852	−	0.997185i	$-0.523891\pi$
$313$	−2.65325	−0.149970	−0.0749852	+	0.997185i	$0.523891\pi$
$314$	−13.7481	−0.775852
$315$	13.6207	0.767437
$316$	−38.5846	−2.17055
$317$	6.89330	0.387166	0.193583	−	0.981084i	$-0.437989\pi$
$317$	6.89330	0.387166	0.193583	+	0.981084i	$0.437989\pi$
$318$	−10.0495	−0.563546
$319$	0.977539	0.0547317
$320$	−45.8812	−2.56484
$321$	−9.40205	−0.524771
$322$	29.3160	1.63372
$323$	−13.0255	−0.724761
$324$	3.01043	0.167246
$325$	51.5711	2.86065
$326$	53.4910	2.96259
$327$	2.30514	0.127474
$328$	5.97650	0.329997
$329$	−31.3028	−1.72578
$330$	−2.29084	−0.126106
$331$	−22.5854	−1.24141	−0.620703	−	0.784046i	$-0.713153\pi$
$331$	−22.5854	−1.24141	−0.620703	+	0.784046i	$0.713153\pi$
$332$	−23.4018	−1.28434
$333$	0.432639	0.0237085
$334$	−18.6763	−1.02192
$335$	−43.4848	−2.37583
$336$	−3.70068	−0.201889
$337$	−10.4074	−0.566925	−0.283462	−	0.958983i	$-0.591483\pi$
$337$	−10.4074	−0.566925	−0.283462	+	0.958983i	$0.591483\pi$
$338$	−78.5303	−4.27148
$339$	8.94876	0.486030
$340$	−23.0895	−1.25220
$341$	2.45505	0.132949
$342$	−13.4063	−0.724929
$343$	3.54054	0.191171
$344$	8.00255	0.431469
$345$	−11.9589	−0.643846
$346$	39.2660	2.11096
$347$	−32.0055	−1.71814	−0.859071	−	0.511856i	$-0.828958\pi$
$347$	−32.0055	−1.71814	−0.859071	+	0.511856i	$0.828958\pi$
$348$	10.1407	0.543598
$349$	−14.5280	−0.777665	−0.388833	−	0.921308i	$-0.627122\pi$
$349$	−14.5280	−0.777665	−0.388833	+	0.921308i	$0.627122\pi$
$350$	−64.2959	−3.43676
$351$	6.93421	0.370121
$352$	1.93512	0.103142
$353$	−27.7234	−1.47557	−0.737784	−	0.675036i	$-0.764128\pi$
$353$	−27.7234	−1.47557	−0.737784	+	0.675036i	$0.764128\pi$
$354$	10.5974	0.563244
$355$	−15.2909	−0.811555
$356$	50.7580	2.69017
$357$	−8.39966	−0.444557
$358$	−29.6047	−1.56466
$359$	8.27196	0.436577	0.218289	−	0.975884i	$-0.429953\pi$
$359$	8.27196	0.436577	0.218289	+	0.975884i	$0.429953\pi$
$360$	−7.97635	−0.420391
$361$	16.8709	0.887940
$362$	13.8495	0.727913
$363$	−10.9158	−0.572930
$364$	80.6235	4.22582
$365$	−26.3258	−1.37795
$366$	−12.6450	−0.660967
$367$	6.37771	0.332914	0.166457	−	0.986049i	$-0.446767\pi$
$367$	6.37771	0.332914	0.166457	+	0.986049i	$0.446767\pi$
$368$	3.24920	0.169376
$369$	−2.64243	−0.137560
$370$	−3.41527	−0.177551
$371$	17.3397	0.900233
$372$	25.4679	1.32045
$373$	7.36321	0.381252	0.190626	−	0.981663i	$-0.438948\pi$
$373$	7.36321	0.381252	0.190626	+	0.981663i	$0.438948\pi$
$374$	1.41272	0.0730503
$375$	8.59513	0.443850
$376$	18.3312	0.945357
$377$	23.3580	1.20300
$378$	−8.64518	−0.444660
$379$	11.7167	0.601844	0.300922	−	0.953649i	$-0.402706\pi$
$379$	11.7167	0.601844	0.300922	+	0.953649i	$0.402706\pi$
$380$	63.5859	3.26189
$381$	−7.23437	−0.370628
$382$	30.9478	1.58343
$383$	22.6357	1.15663	0.578315	−	0.815813i	$-0.303710\pi$
$383$	22.6357	1.15663	0.578315	+	0.815813i	$0.303710\pi$
$384$	15.7848	0.805513
$385$	3.95269	0.201448
$386$	21.5472	1.09673
$387$	−3.53822	−0.179858
$388$	27.3909	1.39056
$389$	−25.2611	−1.28079	−0.640393	−	0.768047i	$-0.721229\pi$
$389$	−25.2611	−1.28079	−0.640393	+	0.768047i	$0.721229\pi$
$390$	−54.7388	−2.77181
$391$	7.37489	0.372964
$392$	−17.9056	−0.904367
$393$	−13.5077	−0.681372
$394$	−6.17580	−0.311132
$395$	−45.2009	−2.27430
$396$	0.873622	0.0439011
$397$	7.22366	0.362545	0.181273	−	0.983433i	$-0.441978\pi$
$397$	7.22366	0.362545	0.181273	+	0.983433i	$0.441978\pi$
$398$	−5.25229	−0.263273
$399$	23.1317	1.15803
$400$	−7.12615	−0.356307
$401$	−35.9858	−1.79704	−0.898522	−	0.438929i	$-0.855358\pi$
$401$	−35.9858	−1.79704	−0.898522	+	0.438929i	$0.855358\pi$
$402$	27.6003	1.37658
$403$	58.6627	2.92220
$404$	7.39791	0.368060
$405$	3.52664	0.175240
$406$	−29.1214	−1.44527
$407$	0.125551	0.00622335
$408$	4.91890	0.243522
$409$	−26.5415	−1.31239	−0.656195	−	0.754591i	$-0.727835\pi$
$409$	−26.5415	−1.31239	−0.656195	+	0.754591i	$0.727835\pi$
$410$	20.8594	1.03017
$411$	2.05042	0.101140
$412$	2.95154	0.145412
$413$	−18.2851	−0.899751
$414$	7.59046	0.373051
$415$	−27.4146	−1.34573
$416$	46.2391	2.26706
$417$	−10.3956	−0.509073
$418$	−3.89048	−0.190290
$419$	8.91875	0.435709	0.217855	−	0.975981i	$-0.430094\pi$
$419$	8.91875	0.435709	0.217855	+	0.975981i	$0.430094\pi$
$420$	41.0040	2.00079
$421$	−30.4897	−1.48598	−0.742988	−	0.669304i	$-0.766592\pi$
$421$	−30.4897	−1.48598	−0.742988	+	0.669304i	$0.766592\pi$
$422$	0.320593	0.0156062
$423$	−8.10488	−0.394073
$424$	−10.1543	−0.493134
$425$	−16.1746	−0.784585
$426$	9.70528	0.470222
$427$	21.8182	1.05586
$428$	−28.3042	−1.36813
$429$	2.01230	0.0971546
$430$	27.9308	1.34694
$431$	20.3523	0.980336	0.490168	−	0.871628i	$-0.336935\pi$
$431$	20.3523	0.980336	0.490168	+	0.871628i	$0.336935\pi$
$432$	−0.958176	−0.0461003
$433$	1.57148	0.0755205	0.0377602	−	0.999287i	$-0.487978\pi$
$433$	1.57148	0.0755205	0.0377602	+	0.999287i	$0.487978\pi$
$434$	−73.1374	−3.51071
$435$	11.8796	0.569581
$436$	6.93945	0.332339
$437$	−20.3096	−0.971540
$438$	16.7093	0.798400
$439$	−11.6788	−0.557398	−0.278699	−	0.960379i	$-0.589903\pi$
$439$	−11.6788	−0.557398	−0.278699	+	0.960379i	$0.589903\pi$
$440$	−2.31473	−0.110350
$441$	7.91671	0.376986
$442$	33.7566	1.60564
$443$	−15.8835	−0.754646	−0.377323	−	0.926082i	$-0.623155\pi$
$443$	−15.8835	−0.754646	−0.377323	+	0.926082i	$0.623155\pi$
$444$	1.30243	0.0618106
$445$	59.4617	2.81875
$446$	−41.4309	−1.96181
$447$	−16.6757	−0.788732
$448$	−50.2470	−2.37395
$449$	−10.6541	−0.502798	−0.251399	−	0.967883i	$-0.580891\pi$
$449$	−10.6541	−0.502798	−0.251399	+	0.967883i	$0.580891\pi$
$450$	−16.6474	−0.784767
$451$	−0.766830	−0.0361086
$452$	26.9396	1.26713
$453$	11.5579	0.543035
$454$	0.867513	0.0407144
$455$	94.4484	4.42781
$456$	−13.5461	−0.634354
$457$	−17.2302	−0.805994	−0.402997	−	0.915201i	$-0.632032\pi$
$457$	−17.2302	−0.805994	−0.402997	+	0.915201i	$0.632032\pi$
$458$	−21.1848	−0.989901
$459$	−2.17483	−0.101512
$460$	−36.0015	−1.67858
$461$	11.5652	0.538644	0.269322	−	0.963050i	$-0.413200\pi$
$461$	11.5652	0.538644	0.269322	+	0.963050i	$0.413200\pi$
$462$	−2.50882	−0.116721
$463$	−18.1541	−0.843693	−0.421846	−	0.906667i	$-0.638618\pi$
$463$	−18.1541	−0.843693	−0.421846	+	0.906667i	$0.638618\pi$
$464$	−3.22763	−0.149839
$465$	29.8351	1.38357
$466$	−28.9132	−1.33938
$467$	−4.07265	−0.188460	−0.0942299	−	0.995550i	$-0.530039\pi$
$467$	−4.07265	−0.188460	−0.0942299	+	0.995550i	$0.530039\pi$
$468$	20.8749	0.964944
$469$	−47.6226	−2.19901
$470$	63.9802	2.95119
$471$	6.14195	0.283006
$472$	10.7079	0.492870
$473$	−1.02679	−0.0472117
$474$	28.6895	1.31775
$475$	44.5431	2.04378
$476$	−25.2866	−1.15901
$477$	4.48957	0.205563
$478$	−21.0501	−0.962808
$479$	16.6390	0.760258	0.380129	−	0.924934i	$-0.375880\pi$
$479$	16.6390	0.760258	0.380129	+	0.924934i	$0.375880\pi$
$480$	23.5166	1.07338
$481$	3.00001	0.136789
$482$	19.7610	0.900088
$483$	−13.0969	−0.595928
$484$	−32.8612	−1.49369
$485$	32.0878	1.45703
$486$	−2.23840	−0.101536
$487$	24.2639	1.09950	0.549751	−	0.835329i	$-0.314723\pi$
$487$	24.2639	1.09950	0.549751	+	0.835329i	$0.314723\pi$
$488$	−12.7769	−0.578383
$489$	−23.8970	−1.08066
$490$	−62.4948	−2.82323
$491$	21.3897	0.965305	0.482653	−	0.875812i	$-0.339673\pi$
$491$	21.3897	0.965305	0.482653	+	0.875812i	$0.339673\pi$
$492$	−7.95485	−0.358632
$493$	−7.32595	−0.329944
$494$	−92.9619	−4.18256
$495$	1.02343	0.0459996
$496$	−8.10608	−0.363974
$497$	−16.7459	−0.751154
$498$	17.4004	0.779729
$499$	13.0195	0.582833	0.291417	−	0.956596i	$-0.405873\pi$
$499$	13.0195	0.582833	0.291417	+	0.956596i	$0.405873\pi$
$500$	25.8750	1.15717
$501$	8.34360	0.372765
$502$	−20.1389	−0.898844
$503$	−26.0964	−1.16358	−0.581791	−	0.813338i	$-0.697648\pi$
$503$	−26.0964	−1.16358	−0.581791	+	0.813338i	$0.697648\pi$
$504$	−8.73534	−0.389103
$505$	8.66646	0.385653
$506$	2.20274	0.0979237
$507$	35.0832	1.55810
$508$	−21.7786	−0.966267
$509$	−20.4713	−0.907374	−0.453687	−	0.891161i	$-0.649892\pi$
$509$	−20.4713	−0.907374	−0.453687	+	0.891161i	$0.649892\pi$
$510$	17.1682	0.760219
$511$	−28.8308	−1.27540
$512$	−10.7237	−0.473924
$513$	5.98923	0.264431
$514$	−3.47309	−0.153191
$515$	3.45765	0.152362
$516$	−10.6516	−0.468909
$517$	−2.35202	−0.103442
$518$	−3.74024	−0.164337
$519$	−17.5420	−0.770009
$520$	−55.3097	−2.42549
$521$	21.9830	0.963095	0.481547	−	0.876420i	$-0.340075\pi$
$521$	21.9830	0.963095	0.481547	+	0.876420i	$0.340075\pi$
$522$	−7.54009	−0.330021
$523$	−16.6029	−0.725993	−0.362997	−	0.931790i	$-0.618246\pi$
$523$	−16.6029	−0.725993	−0.362997	+	0.931790i	$0.618246\pi$
$524$	−40.6639	−1.77641
$525$	28.7241	1.25362
$526$	18.2012	0.793612
$527$	−18.3988	−0.801466
$528$	−0.278061	−0.0121011
$529$	−11.5010	−0.500042
$530$	−35.4408	−1.53945
$531$	−4.73435	−0.205453
$532$	69.6363	3.01912
$533$	−18.3232	−0.793665
$534$	−37.7410	−1.63321
$535$	−33.1577	−1.43353
$536$	27.8881	1.20458
$537$	13.2259	0.570738
$538$	62.0100	2.67344
$539$	2.29742	0.0989568
$540$	10.6167	0.456870
$541$	27.8847	1.19886	0.599429	−	0.800428i	$-0.295394\pi$
$541$	27.8847	1.19886	0.599429	+	0.800428i	$0.295394\pi$
$542$	0.715121	0.0307171
$543$	−6.18723	−0.265520
$544$	−14.5023	−0.621782
$545$	8.12939	0.348225
$546$	−59.9475	−2.56551
$547$	−25.0886	−1.07271	−0.536356	−	0.843992i	$-0.680199\pi$
$547$	−25.0886	−1.07271	−0.536356	+	0.843992i	$0.680199\pi$
$548$	6.17264	0.263682
$549$	5.64914	0.241100
$550$	−4.83105	−0.205997
$551$	20.1748	0.859476
$552$	7.66962	0.326441
$553$	−49.5019	−2.10504
$554$	25.2032	1.07078
$555$	1.52576	0.0647651
$556$	−31.2951	−1.32721
$557$	46.3561	1.96417	0.982085	−	0.188441i	$-0.0603434\pi$
$557$	46.3561	1.96417	0.982085	+	0.188441i	$0.0603434\pi$
$558$	−18.9366	−0.801652
$559$	−24.5348	−1.03771
$560$	−13.0510	−0.551505
$561$	−0.631132	−0.0266464
$562$	23.5279	0.992464
$563$	28.2134	1.18905	0.594526	−	0.804076i	$-0.297340\pi$
$563$	28.2134	1.18905	0.594526	+	0.804076i	$0.297340\pi$
$564$	−24.3992	−1.02739
$565$	31.5591	1.32770
$566$	−52.3082	−2.19868
$567$	3.86222	0.162198
$568$	9.80650	0.411471
$569$	9.29836	0.389807	0.194904	−	0.980822i	$-0.437561\pi$
$569$	9.29836	0.389807	0.194904	+	0.980822i	$0.437561\pi$
$570$	−47.2791	−1.98031
$571$	−23.9676	−1.00301	−0.501506	−	0.865154i	$-0.667220\pi$
$571$	−23.9676	−1.00301	−0.501506	+	0.865154i	$0.667220\pi$
$572$	6.05787	0.253292
$573$	−13.8259	−0.577584
$574$	22.8443	0.953503
$575$	−25.2197	−1.05173
$576$	−13.0099	−0.542078
$577$	11.0278	0.459094	0.229547	−	0.973298i	$-0.426275\pi$
$577$	11.0278	0.459094	0.229547	+	0.973298i	$0.426275\pi$
$578$	27.4654	1.14241
$579$	−9.62618	−0.400050
$580$	35.7625	1.48496
$581$	−30.0232	−1.24557
$582$	−20.3665	−0.844217
$583$	1.30287	0.0539593
$584$	16.8835	0.698645
$585$	24.4545	1.01107
$586$	29.3446	1.21221
$587$	−37.6933	−1.55577	−0.777885	−	0.628407i	$-0.783707\pi$
$587$	−37.6933	−1.55577	−0.777885	+	0.628407i	$0.783707\pi$
$588$	23.8327	0.982844
$589$	50.6683	2.08775
$590$	37.3731	1.53863
$591$	2.75902	0.113491
$592$	−0.414545	−0.0170377
$593$	9.98553	0.410057	0.205028	−	0.978756i	$-0.434271\pi$
$593$	9.98553	0.410057	0.205028	+	0.978756i	$0.434271\pi$
$594$	−0.649580	−0.0266526
$595$	−29.6226	−1.21441
$596$	−50.2009	−2.05631
$597$	2.34645	0.0960338
$598$	52.6338	2.15236
$599$	20.0191	0.817957	0.408978	−	0.912544i	$-0.365885\pi$
$599$	20.0191	0.817957	0.408978	+	0.912544i	$0.365885\pi$
$600$	−16.8210	−0.686716
$601$	−7.15242	−0.291753	−0.145877	−	0.989303i	$-0.546600\pi$
$601$	−7.15242	−0.291753	−0.145877	+	0.989303i	$0.546600\pi$
$602$	30.5886	1.24670
$603$	−12.3304	−0.502132
$604$	34.7941	1.41575
$605$	−38.4961	−1.56509
$606$	−5.50070	−0.223451
$607$	3.72236	0.151086	0.0755429	−	0.997143i	$-0.475931\pi$
$607$	3.72236	0.151086	0.0755429	+	0.997143i	$0.475931\pi$
$608$	39.9378	1.61969
$609$	13.0099	0.527189
$610$	−44.5945	−1.80558
$611$	−56.2009	−2.27365
$612$	−6.54717	−0.264653
$613$	38.9407	1.57280	0.786399	−	0.617718i	$-0.211943\pi$
$613$	38.9407	1.57280	0.786399	+	0.617718i	$0.211943\pi$
$614$	−35.8197	−1.44557
$615$	−9.31891	−0.375775
$616$	−2.53498	−0.102137
$617$	−35.5392	−1.43075	−0.715376	−	0.698739i	$-0.753745\pi$
$617$	−35.5392	−1.43075	−0.715376	+	0.698739i	$0.753745\pi$
$618$	−2.19461	−0.0882802
$619$	−8.50824	−0.341975	−0.170988	−	0.985273i	$-0.554696\pi$
$619$	−8.50824	−0.341975	−0.170988	+	0.985273i	$0.554696\pi$
$620$	89.8163	3.60711
$621$	−3.39102	−0.136077
$622$	61.6716	2.47281
$623$	65.1197	2.60897
$624$	−6.64419	−0.265981
$625$	−6.87407	−0.274963
$626$	5.93902	0.237371
$627$	1.73806	0.0694116
$628$	18.4899	0.737827
$629$	−0.940916	−0.0375168
$630$	−30.4884	−1.21469
$631$	39.2334	1.56186	0.780929	−	0.624620i	$-0.214746\pi$
$631$	39.2334	1.56186	0.780929	+	0.624620i	$0.214746\pi$
$632$	28.9887	1.15311
$633$	−0.143224	−0.00569265
$634$	−15.4300	−0.612802
$635$	−25.5130	−1.01245
$636$	13.5155	0.535926
$637$	54.8961	2.17506
$638$	−2.18812	−0.0866285
$639$	−4.33581	−0.171522
$640$	55.6672	2.20044
$641$	−4.10554	−0.162159	−0.0810795	−	0.996708i	$-0.525837\pi$
$641$	−4.10554	−0.162159	−0.0810795	+	0.996708i	$0.525837\pi$
$642$	21.0455	0.830601
$643$	−46.8839	−1.84892	−0.924460	−	0.381280i	$-0.875483\pi$
$643$	−46.8839	−1.84892	−0.924460	+	0.381280i	$0.875483\pi$
$644$	−39.4272	−1.55365
$645$	−12.4780	−0.491322
$646$	29.1564	1.14714
$647$	−35.4813	−1.39491	−0.697456	−	0.716627i	$-0.745685\pi$
$647$	−35.4813	−1.39491	−0.697456	+	0.716627i	$0.745685\pi$
$648$	−2.26174	−0.0888496
$649$	−1.37390	−0.0539304
$650$	−115.437	−4.52780
$651$	32.6740	1.28059
$652$	−71.9401	−2.81739
$653$	−4.96346	−0.194235	−0.0971177	−	0.995273i	$-0.530962\pi$
$653$	−4.96346	−0.194235	−0.0971177	+	0.995273i	$0.530962\pi$
$654$	−5.15981	−0.201765
$655$	−47.6367	−1.86132
$656$	2.53192	0.0988547
$657$	−7.46483	−0.291231
$658$	70.0682	2.73154
$659$	−26.0942	−1.01649	−0.508244	−	0.861213i	$-0.669705\pi$
$659$	−26.0942	−1.01649	−0.508244	+	0.861213i	$0.669705\pi$
$660$	3.08095	0.119926
$661$	33.4721	1.30191	0.650957	−	0.759114i	$-0.274368\pi$
$661$	33.4721	1.30191	0.650957	+	0.759114i	$0.274368\pi$
$662$	50.5552	1.96488
$663$	−15.0807	−0.585686
$664$	17.5818	0.682308
$665$	81.5772	3.16343
$666$	−0.968419	−0.0375255
$667$	−11.4227	−0.442289
$668$	25.1178	0.971838
$669$	18.5092	0.715606
$670$	97.3364	3.76043
$671$	1.63937	0.0632873
$672$	25.7543	0.993493
$673$	−46.4364	−1.78999	−0.894996	−	0.446073i	$-0.852822\pi$
$673$	−46.4364	−1.78999	−0.894996	+	0.446073i	$0.852822\pi$
$674$	23.2958	0.897321
$675$	7.43720	0.286258
$676$	105.616	4.06214
$677$	3.19771	0.122898	0.0614490	−	0.998110i	$-0.480428\pi$
$677$	3.19771	0.122898	0.0614490	+	0.998110i	$0.480428\pi$
$678$	−20.0309	−0.769282
$679$	35.1411	1.34859
$680$	17.3472	0.665235
$681$	−0.387560	−0.0148513
$682$	−5.49538	−0.210429
$683$	6.00072	0.229611	0.114806	−	0.993388i	$-0.463375\pi$
$683$	6.00072	0.229611	0.114806	+	0.993388i	$0.463375\pi$
$684$	18.0301	0.689400
$685$	7.23110	0.276286
$686$	−7.92514	−0.302583
$687$	9.46427	0.361085
$688$	3.39024	0.129252
$689$	31.1316	1.18602
$690$	26.7688	1.01907
$691$	14.4853	0.551048	0.275524	−	0.961294i	$-0.411149\pi$
$691$	14.4853	0.551048	0.275524	+	0.961294i	$0.411149\pi$
$692$	−52.8090	−2.00750
$693$	1.12081	0.0425760
$694$	71.6410	2.71945
$695$	−36.6614	−1.39065
$696$	−7.61872	−0.288787
$697$	5.74684	0.217677
$698$	32.5194	1.23088
$699$	12.9169	0.488563
$700$	86.4718	3.26833
$701$	7.34635	0.277468	0.138734	−	0.990330i	$-0.455697\pi$
$701$	7.34635	0.277468	0.138734	+	0.990330i	$0.455697\pi$
$702$	−15.5215	−0.585822
$703$	2.59118	0.0977281
$704$	−3.77545	−0.142293
$705$	−28.5830	−1.07650
$706$	62.0561	2.33551
$707$	9.49111	0.356950
$708$	−14.2524	−0.535639
$709$	15.0951	0.566907	0.283454	−	0.958986i	$-0.408520\pi$
$709$	15.0951	0.566907	0.283454	+	0.958986i	$0.408520\pi$
$710$	34.2270	1.28452
$711$	−12.8170	−0.480674
$712$	−38.1346	−1.42915
$713$	−28.6877	−1.07436
$714$	18.8018	0.703639
$715$	7.09665	0.265400
$716$	39.8155	1.48797
$717$	9.40408	0.351202
$718$	−18.5160	−0.691009
$719$	25.7561	0.960540	0.480270	−	0.877121i	$-0.340539\pi$
$719$	25.7561	0.960540	0.480270	+	0.877121i	$0.340539\pi$
$720$	−3.37914	−0.125933
$721$	3.78666	0.141023
$722$	−37.7637	−1.40542
$723$	−8.82818	−0.328323
$724$	−18.6262	−0.692238
$725$	25.0523	0.930420
$726$	24.4339	0.906826
$727$	−27.2861	−1.01199	−0.505993	−	0.862538i	$-0.668874\pi$
$727$	−27.2861	−1.01199	−0.505993	+	0.862538i	$0.668874\pi$
$728$	−60.5726	−2.24497
$729$	1.00000	0.0370370
$730$	58.9276	2.18101
$731$	7.69503	0.284611
$732$	17.0063	0.628573
$733$	51.4956	1.90203	0.951016	−	0.309142i	$-0.100042\pi$
$733$	51.4956	1.90203	0.951016	+	0.309142i	$0.100042\pi$
$734$	−14.2758	−0.526931
$735$	27.9194	1.02982
$736$	−22.6122	−0.833498
$737$	−3.57826	−0.131807
$738$	5.91482	0.217727
$739$	44.3579	1.63173	0.815866	−	0.578241i	$-0.196261\pi$
$739$	44.3579	1.63173	0.815866	+	0.578241i	$0.196261\pi$
$740$	4.59320	0.168850
$741$	41.5306	1.52566
$742$	−38.8132	−1.42488
$743$	−48.1439	−1.76623	−0.883115	−	0.469157i	$-0.844558\pi$
$743$	−48.1439	−1.76623	−0.883115	+	0.469157i	$0.844558\pi$
$744$	−19.1341	−0.701491
$745$	−58.8091	−2.15460
$746$	−16.4818	−0.603441
$747$	−7.77358	−0.284420
$748$	−1.89998	−0.0694701
$749$	−36.3127	−1.32684
$750$	−19.2393	−0.702521
$751$	30.5777	1.11580	0.557898	−	0.829909i	$-0.311608\pi$
$751$	30.5777	1.11580	0.557898	+	0.829909i	$0.311608\pi$
$752$	7.76591	0.283194
$753$	8.99702	0.327870
$754$	−52.2845	−1.90409
$755$	40.7604	1.48342
$756$	11.6269	0.422867
$757$	27.4481	0.997618	0.498809	−	0.866712i	$-0.333771\pi$
$757$	27.4481	0.997618	0.498809	+	0.866712i	$0.333771\pi$
$758$	−26.2265	−0.952591
$759$	−0.984069	−0.0357194
$760$	−47.7722	−1.73288
$761$	37.1786	1.34772	0.673862	−	0.738857i	$-0.264634\pi$
$761$	37.1786	1.34772	0.673862	+	0.738857i	$0.264634\pi$
$762$	16.1934	0.586625
$763$	8.90294	0.322308
$764$	−41.6218	−1.50582
$765$	−7.66984	−0.277304
$766$	−50.6678	−1.83070
$767$	−32.8290	−1.18539
$768$	−9.31285	−0.336049
$769$	53.1637	1.91713	0.958565	−	0.284873i	$-0.0919514\pi$
$769$	53.1637	1.91713	0.958565	+	0.284873i	$0.0919514\pi$
$770$	−8.84770	−0.318849
$771$	1.55159	0.0558793
$772$	−28.9789	−1.04297
$773$	−18.6715	−0.671568	−0.335784	−	0.941939i	$-0.609001\pi$
$773$	−18.6715	−0.671568	−0.335784	+	0.941939i	$0.609001\pi$
$774$	7.91995	0.284677
$775$	62.9180	2.26008
$776$	−20.5789	−0.738738
$777$	1.67095	0.0599449
$778$	56.5443	2.02721
$779$	−15.8261	−0.567030
$780$	73.6184	2.63596
$781$	−1.25825	−0.0450236
$782$	−16.5079	−0.590323
$783$	3.36852	0.120381
$784$	−7.58561	−0.270915
$785$	21.6604	0.773094
$786$	30.2355	1.07847
$787$	−23.8414	−0.849853	−0.424927	−	0.905228i	$-0.639700\pi$
$787$	−23.8414	−0.849853	−0.424927	+	0.905228i	$0.639700\pi$
$788$	8.30585	0.295884
$789$	−8.13137	−0.289484
$790$	101.178	3.59974
$791$	34.5621	1.22889
$792$	−0.656354	−0.0233225
$793$	39.1723	1.39105
$794$	−16.1694	−0.573832
$795$	15.8331	0.561543
$796$	7.06382	0.250370
$797$	−10.7766	−0.381727	−0.190864	−	0.981617i	$-0.561129\pi$
$797$	−10.7766	−0.381727	−0.190864	+	0.981617i	$0.561129\pi$
$798$	−51.7780	−1.83292
$799$	17.6267	0.623589
$800$	49.5932	1.75338
$801$	16.8607	0.595744
$802$	80.5505	2.84434
$803$	−2.16628	−0.0764465
$804$	−37.1197	−1.30911
$805$	−46.1879	−1.62791
$806$	−131.311	−4.62522
$807$	−27.7028	−0.975186
$808$	−5.55807	−0.195532
$809$	17.5616	0.617433	0.308717	−	0.951154i	$-0.400101\pi$
$809$	17.5616	0.617433	0.308717	+	0.951154i	$0.400101\pi$
$810$	−7.89403	−0.277368
$811$	23.5377	0.826519	0.413260	−	0.910613i	$-0.364390\pi$
$811$	23.5377	0.826519	0.413260	+	0.910613i	$0.364390\pi$
$812$	39.1655	1.37444
$813$	−0.319479	−0.0112046
$814$	−0.281034	−0.00985023
$815$	−84.2761	−2.95206
$816$	2.08387	0.0729500
$817$	−21.1912	−0.741387
$818$	59.4104	2.07723
$819$	26.7814	0.935818
$820$	−28.0539	−0.979685
$821$	−21.6498	−0.755583	−0.377792	−	0.925891i	$-0.623316\pi$
$821$	−21.6498	−0.755583	−0.377792	+	0.925891i	$0.623316\pi$
$822$	−4.58966	−0.160083
$823$	−55.9162	−1.94912	−0.974558	−	0.224137i	$-0.928044\pi$
$823$	−55.9162	−1.94912	−0.974558	+	0.224137i	$0.928044\pi$
$824$	−2.21750	−0.0772502
$825$	2.15826	0.0751411
$826$	40.9293	1.42411
$827$	46.4686	1.61587	0.807936	−	0.589270i	$-0.200584\pi$
$827$	46.4686	1.61587	0.807936	+	0.589270i	$0.200584\pi$
$828$	−10.2084	−0.354767
$829$	−10.1661	−0.353084	−0.176542	−	0.984293i	$-0.556491\pi$
$829$	−10.1661	−0.353084	−0.176542	+	0.984293i	$0.556491\pi$
$830$	61.3649	2.13001
$831$	−11.2595	−0.390588
$832$	−90.2132	−3.12758
$833$	−17.2175	−0.596551
$834$	23.2694	0.805754
$835$	29.4249	1.01829
$836$	5.23232	0.180964
$837$	8.45991	0.292417
$838$	−19.9637	−0.689635
$839$	53.6151	1.85100	0.925499	−	0.378749i	$-0.123646\pi$
$839$	53.6151	1.85100	0.925499	+	0.378749i	$0.123646\pi$
$840$	−30.8064	−1.06292
$841$	−17.6531	−0.608727
$842$	68.2481	2.35198
$843$	−10.5110	−0.362019
$844$	−0.431166	−0.0148413
$845$	123.726	4.25630
$846$	18.1420	0.623733
$847$	−42.1591	−1.44860
$848$	−4.30180	−0.147725
$849$	23.3686	0.802007
$850$	36.2053	1.24183
$851$	−1.46709	−0.0502912
$852$	−13.0527	−0.447177
$853$	30.6359	1.04895	0.524477	−	0.851425i	$-0.324261\pi$
$853$	30.6359	1.04895	0.524477	+	0.851425i	$0.324261\pi$
$854$	−48.8379	−1.67120
$855$	21.1219	0.722352
$856$	21.2650	0.726823
$857$	55.3382	1.89032	0.945158	−	0.326614i	$-0.105908\pi$
$857$	55.3382	1.89032	0.945158	+	0.326614i	$0.105908\pi$
$858$	−4.50432	−0.153775
$859$	23.7130	0.809076	0.404538	−	0.914521i	$-0.367432\pi$
$859$	23.7130	0.809076	0.404538	+	0.914521i	$0.367432\pi$
$860$	−37.5643	−1.28093
$861$	−10.2056	−0.347807
$862$	−45.5566	−1.55166
$863$	28.3533	0.965156	0.482578	−	0.875853i	$-0.339700\pi$
$863$	28.3533	0.965156	0.482578	+	0.875853i	$0.339700\pi$
$864$	6.66827	0.226859
$865$	−61.8644	−2.10345
$866$	−3.51760	−0.119533
$867$	−12.2701	−0.416715
$868$	98.3627	3.33865
$869$	−3.71947	−0.126174
$870$	−26.5912	−0.901525
$871$	−85.5014	−2.89710
$872$	−5.21362	−0.176556
$873$	9.09868	0.307944
$874$	45.4610	1.53774
$875$	33.1962	1.12224
$876$	−22.4723	−0.759270
$877$	45.1513	1.52465	0.762326	−	0.647193i	$-0.224057\pi$
$877$	45.1513	1.52465	0.762326	+	0.647193i	$0.224057\pi$
$878$	26.1418	0.882242
$879$	−13.1096	−0.442176
$880$	−0.980623	−0.0330568
$881$	19.9183	0.671065	0.335533	−	0.942029i	$-0.391084\pi$
$881$	19.9183	0.671065	0.335533	+	0.942029i	$0.391084\pi$
$882$	−17.7208	−0.596689
$883$	24.7484	0.832850	0.416425	−	0.909170i	$-0.363283\pi$
$883$	24.7484	0.832850	0.416425	+	0.909170i	$0.363283\pi$
$884$	−45.3994	−1.52695
$885$	−16.6964	−0.561242
$886$	35.5535	1.19444
$887$	53.5694	1.79868	0.899341	−	0.437247i	$-0.144046\pi$
$887$	53.5694	1.79868	0.899341	+	0.437247i	$0.144046\pi$
$888$	−0.978519	−0.0328369
$889$	−27.9407	−0.937101
$890$	−133.099	−4.46149
$891$	0.290198	0.00972201
$892$	55.7206	1.86566
$893$	−48.5420	−1.62440
$894$	37.3268	1.24840
$895$	46.6428	1.55910
$896$	60.9642	2.03667
$897$	−23.5140	−0.785111
$898$	23.8481	0.795823
$899$	28.4973	0.950440
$900$	22.3892	0.746305
$901$	−9.76405	−0.325288
$902$	1.71647	0.0571522
$903$	−13.6654	−0.454755
$904$	−20.2398	−0.673166
$905$	−21.8201	−0.725326
$906$	−25.8711	−0.859509
$907$	32.1970	1.06908	0.534542	−	0.845142i	$-0.320484\pi$
$907$	32.1970	1.06908	0.534542	+	0.845142i	$0.320484\pi$
$908$	−1.16672	−0.0387190
$909$	2.45743	0.0815077
$910$	−211.413	−7.00828
$911$	−41.9211	−1.38891	−0.694454	−	0.719537i	$-0.744354\pi$
$911$	−41.9211	−1.38891	−0.694454	+	0.719537i	$0.744354\pi$
$912$	−5.73874	−0.190029
$913$	−2.25588	−0.0746588
$914$	38.5680	1.27572
$915$	19.9225	0.658618
$916$	28.4915	0.941386
$917$	−52.1695	−1.72279
$918$	4.86813	0.160672
$919$	−40.9233	−1.34993	−0.674967	−	0.737848i	$-0.735842\pi$
$919$	−40.9233	−1.34993	−0.674967	+	0.737848i	$0.735842\pi$
$920$	27.0480	0.891746
$921$	16.0024	0.527297
$922$	−25.8875	−0.852559
$923$	−30.0654	−0.989616
$924$	3.37412	0.111000
$925$	3.21763	0.105795
$926$	40.6361	1.33539
$927$	0.980438	0.0322018
$928$	22.4622	0.737357
$929$	−1.04611	−0.0343217	−0.0171609	−	0.999853i	$-0.505463\pi$
$929$	−1.04611	−0.0343217	−0.0171609	+	0.999853i	$0.505463\pi$
$930$	−66.7828	−2.18989
$931$	47.4150	1.55396
$932$	38.8855	1.27374
$933$	−27.5517	−0.902001
$934$	9.11621	0.298292
$935$	−2.22578	−0.0727906
$936$	−15.6834	−0.512628
$937$	−15.5843	−0.509116	−0.254558	−	0.967058i	$-0.581930\pi$
$937$	−15.5843	−0.509116	−0.254558	+	0.967058i	$0.581930\pi$
$938$	106.598	3.48056
$939$	−2.65325	−0.0865854
$940$	−86.0471	−2.80655
$941$	26.0718	0.849915	0.424957	−	0.905213i	$-0.360289\pi$
$941$	26.0718	0.849915	0.424957	+	0.905213i	$0.360289\pi$
$942$	−13.7481	−0.447938
$943$	8.96054	0.291795
$944$	4.53635	0.147645
$945$	13.6207	0.443080
$946$	2.29836	0.0747261
$947$	55.1334	1.79159	0.895797	−	0.444463i	$-0.146606\pi$
$947$	55.1334	1.79159	0.895797	+	0.444463i	$0.146606\pi$
$948$	−38.5846	−1.25317
$949$	−51.7627	−1.68029
$950$	−99.7052	−3.23486
$951$	6.89330	0.223531
$952$	18.9979	0.615724
$953$	33.3356	1.07985	0.539923	−	0.841715i	$-0.318453\pi$
$953$	33.3356	1.07985	0.539923	+	0.841715i	$0.318453\pi$
$954$	−10.0495	−0.325363
$955$	−48.7589	−1.57780
$956$	28.3103	0.915621
$957$	0.977539	0.0315993
$958$	−37.2448	−1.20333
$959$	7.91917	0.255723
$960$	−45.8812	−1.48081
$961$	40.5700	1.30871
$962$	−6.71522	−0.216507
$963$	−9.40205	−0.302977
$964$	−26.5766	−0.855975
$965$	−33.9481	−1.09283
$966$	29.3160	0.943226
$967$	−19.7823	−0.636157	−0.318079	−	0.948064i	$-0.603038\pi$
$967$	−19.7823	−0.636157	−0.318079	+	0.948064i	$0.603038\pi$
$968$	24.6887	0.793525
$969$	−13.0255	−0.418441
$970$	−71.8252	−2.30617
$971$	−24.0082	−0.770461	−0.385230	−	0.922820i	$-0.625878\pi$
$971$	−24.0082	−0.770461	−0.385230	+	0.922820i	$0.625878\pi$
$972$	3.01043	0.0965595
$973$	−40.1499	−1.28715
$974$	−54.3123	−1.74028
$975$	51.5711	1.65160
$976$	−5.41288	−0.173262
$977$	−0.946724	−0.0302884	−0.0151442	−	0.999885i	$-0.504821\pi$
$977$	−0.946724	−0.0302884	−0.0151442	+	0.999885i	$0.504821\pi$
$978$	53.4910	1.71045
$979$	4.89295	0.156379
$980$	84.0494	2.68486
$981$	2.30514	0.0735973
$982$	−47.8788	−1.52787
$983$	38.5079	1.22821	0.614105	−	0.789224i	$-0.289517\pi$
$983$	38.5079	1.22821	0.614105	+	0.789224i	$0.289517\pi$
$984$	5.97650	0.190524
$985$	9.73009	0.310026
$986$	16.3984	0.522231
$987$	−31.3028	−0.996379
$988$	125.025	3.97757
$989$	11.9982	0.381520
$990$	−2.29084	−0.0728075
$991$	−1.04516	−0.0332006	−0.0166003	−	0.999862i	$-0.505284\pi$
$991$	−1.04516	−0.0332006	−0.0166003	+	0.999862i	$0.505284\pi$
$992$	56.4129	1.79111
$993$	−22.5854	−0.716726
$994$	37.4839	1.18892
$995$	8.27509	0.262338
$996$	−23.4018	−0.741515
$997$	50.3801	1.59555	0.797777	−	0.602952i	$-0.206009\pi$
$997$	50.3801	1.59555	0.797777	+	0.602952i	$0.206009\pi$
$998$	−29.1429	−0.922501
$999$	0.432639	0.0136881

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	8031.2.a.d.1.17	✓	132

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
8031.2.a.d.1.17	✓	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)

\(f(q)\)	\(=\)	\(q-2.23840 q^{2} +1.00000 q^{3} +3.01043 q^{4} +3.52664 q^{5} -2.23840 q^{6} +3.86222 q^{7} -2.26174 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q-2.23840 q^{2} +1.00000 q^{3} +3.01043 q^{4} +3.52664 q^{5} -2.23840 q^{6} +3.86222 q^{7} -2.26174 q^{8} +1.00000 q^{9} -7.89403 q^{10} +0.290198 q^{11} +3.01043 q^{12} +6.93421 q^{13} -8.64518 q^{14} +3.52664 q^{15} -0.958176 q^{16} -2.17483 q^{17} -2.23840 q^{18} +5.98923 q^{19} +10.6167 q^{20} +3.86222 q^{21} -0.649580 q^{22} -3.39102 q^{23} -2.26174 q^{24} +7.43720 q^{25} -15.5215 q^{26} +1.00000 q^{27} +11.6269 q^{28} +3.36852 q^{29} -7.89403 q^{30} +8.45991 q^{31} +6.66827 q^{32} +0.290198 q^{33} +4.86813 q^{34} +13.6207 q^{35} +3.01043 q^{36} +0.432639 q^{37} -13.4063 q^{38} +6.93421 q^{39} -7.97635 q^{40} -2.64243 q^{41} -8.64518 q^{42} -3.53822 q^{43} +0.873622 q^{44} +3.52664 q^{45} +7.59046 q^{46} -8.10488 q^{47} -0.958176 q^{48} +7.91671 q^{49} -16.6474 q^{50} -2.17483 q^{51} +20.8749 q^{52} +4.48957 q^{53} -2.23840 q^{54} +1.02343 q^{55} -8.73534 q^{56} +5.98923 q^{57} -7.54009 q^{58} -4.73435 q^{59} +10.6167 q^{60} +5.64914 q^{61} -18.9366 q^{62} +3.86222 q^{63} -13.0099 q^{64} +24.4545 q^{65} -0.649580 q^{66} -12.3304 q^{67} -6.54717 q^{68} -3.39102 q^{69} -30.4884 q^{70} -4.33581 q^{71} -2.26174 q^{72} -7.46483 q^{73} -0.968419 q^{74} +7.43720 q^{75} +18.0301 q^{76} +1.12081 q^{77} -15.5215 q^{78} -12.8170 q^{79} -3.37914 q^{80} +1.00000 q^{81} +5.91482 q^{82} -7.77358 q^{83} +11.6269 q^{84} -7.66984 q^{85} +7.91995 q^{86} +3.36852 q^{87} -0.656354 q^{88} +16.8607 q^{89} -7.89403 q^{90} +26.7814 q^{91} -10.2084 q^{92} +8.45991 q^{93} +18.1420 q^{94} +21.1219 q^{95} +6.66827 q^{96} +9.09868 q^{97} -17.7208 q^{98} +0.290198 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 132 q + 4 q^{2} + 132 q^{3} + 156 q^{4} + 20 q^{5} + 4 q^{6} + 44 q^{7} + 9 q^{8} + 132 q^{9}+O(q^{10}) \) 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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