LMFDB - Embedded newform 8027.2.a.f.1.12

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [8027,2,Mod(1,8027)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(8027, 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("8027.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 8027 = 23 \cdot 349 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	8027.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:	$64.0959177025$
Analytic rank:	$0$
Dimension:	$176$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.12
Character	$\chi$	$=$	8027.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-2.54982 q^{2} -0.805163 q^{3} +4.50159 q^{4} -2.33665 q^{5} +2.05302 q^{6} +2.59075 q^{7} -6.37861 q^{8} -2.35171 q^{9} +O(q^{10})$	\(q-2.54982 q^{2} -0.805163 q^{3} +4.50159 q^{4} -2.33665 q^{5} +2.05302 q^{6} +2.59075 q^{7} -6.37861 q^{8} -2.35171 q^{9} +5.95805 q^{10} -5.57295 q^{11} -3.62451 q^{12} +4.69859 q^{13} -6.60596 q^{14} +1.88139 q^{15} +7.26113 q^{16} -5.12218 q^{17} +5.99645 q^{18} -1.42827 q^{19} -10.5186 q^{20} -2.08598 q^{21} +14.2100 q^{22} +1.00000 q^{23} +5.13582 q^{24} +0.459944 q^{25} -11.9806 q^{26} +4.30900 q^{27} +11.6625 q^{28} +6.55232 q^{29} -4.79720 q^{30} +3.56282 q^{31} -5.75737 q^{32} +4.48714 q^{33} +13.0607 q^{34} -6.05369 q^{35} -10.5864 q^{36} -5.48592 q^{37} +3.64183 q^{38} -3.78313 q^{39} +14.9046 q^{40} -0.275877 q^{41} +5.31887 q^{42} -3.49173 q^{43} -25.0871 q^{44} +5.49513 q^{45} -2.54982 q^{46} -2.00135 q^{47} -5.84639 q^{48} -0.287997 q^{49} -1.17278 q^{50} +4.12419 q^{51} +21.1511 q^{52} -1.80962 q^{53} -10.9872 q^{54} +13.0221 q^{55} -16.5254 q^{56} +1.14999 q^{57} -16.7072 q^{58} +2.39334 q^{59} +8.46923 q^{60} -4.11937 q^{61} -9.08457 q^{62} -6.09271 q^{63} +0.158006 q^{64} -10.9790 q^{65} -11.4414 q^{66} -2.86809 q^{67} -23.0580 q^{68} -0.805163 q^{69} +15.4358 q^{70} +13.9161 q^{71} +15.0006 q^{72} -12.0871 q^{73} +13.9881 q^{74} -0.370330 q^{75} -6.42947 q^{76} -14.4381 q^{77} +9.64631 q^{78} -4.26933 q^{79} -16.9667 q^{80} +3.58569 q^{81} +0.703437 q^{82} -8.54324 q^{83} -9.39022 q^{84} +11.9688 q^{85} +8.90328 q^{86} -5.27568 q^{87} +35.5477 q^{88} -15.6449 q^{89} -14.0116 q^{90} +12.1729 q^{91} +4.50159 q^{92} -2.86866 q^{93} +5.10310 q^{94} +3.33736 q^{95} +4.63562 q^{96} -12.7431 q^{97} +0.734341 q^{98} +13.1060 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 176 q + 19 q^{2} + 22 q^{3} + 203 q^{4} + 28 q^{5} + 9 q^{6} + 30 q^{7} + 51 q^{8} + 204 q^{9}+O(q^{10}) $ 176 * q + 19 * q^2 + 22 * q^3 + 203 * q^4 + 28 * q^5 + 9 * q^6 + 30 * q^7 + 51 * q^8 + 204 * q^9	\( 176 q + 19 q^{2} + 22 q^{3} + 203 q^{4} + 28 q^{5} + 9 q^{6} + 30 q^{7} + 51 q^{8} + 204 q^{9} + 18 q^{10} + 11 q^{11} + 46 q^{12} + 87 q^{13} - 6 q^{14} + 29 q^{15} + 257 q^{16} + 14 q^{17} + 72 q^{18} + 34 q^{19} + 45 q^{20} + 23 q^{21} + 62 q^{22} + 176 q^{23} + 33 q^{24} + 272 q^{25} + 31 q^{26} + 82 q^{27} + 80 q^{28} + 75 q^{29} - 30 q^{30} + 73 q^{31} + 71 q^{32} + 30 q^{33} + 23 q^{34} + 44 q^{35} + 264 q^{36} + 236 q^{37} - 21 q^{38} + 17 q^{39} + 43 q^{40} + 51 q^{41} + 38 q^{42} + 51 q^{43} + 12 q^{44} + 127 q^{45} + 19 q^{46} + 45 q^{47} + 61 q^{48} + 268 q^{49} + 55 q^{50} - 3 q^{51} + 166 q^{52} + 63 q^{53} - 32 q^{54} + 11 q^{55} - 9 q^{56} + 72 q^{57} + 98 q^{58} + 95 q^{59} - 7 q^{60} + 73 q^{61} + 12 q^{62} + 19 q^{63} + 365 q^{64} + 19 q^{65} - 28 q^{66} + 138 q^{67} + 16 q^{68} + 22 q^{69} + 100 q^{70} + 85 q^{71} + 129 q^{72} + 118 q^{73} - 21 q^{74} - 12 q^{75} + 52 q^{76} + 75 q^{77} + 97 q^{78} + 74 q^{79} + 8 q^{80} + 280 q^{81} + 67 q^{82} + 10 q^{83} - 51 q^{84} + 169 q^{85} - 39 q^{86} - 6 q^{87} + 159 q^{88} + 38 q^{89} + 22 q^{90} + 90 q^{91} + 203 q^{92} + 230 q^{93} + 63 q^{94} + 30 q^{95} + 107 q^{96} + 161 q^{97} + 58 q^{98} + 7 q^{99}+O(q^{100}) \) 176 * q + 19 * q^2 + 22 * q^3 + 203 * q^4 + 28 * q^5 + 9 * q^6 + 30 * q^7 + 51 * q^8 + 204 * q^9 + 18 * q^10 + 11 * q^11 + 46 * q^12 + 87 * q^13 - 6 * q^14 + 29 * q^15 + 257 * q^16 + 14 * q^17 + 72 * q^18 + 34 * q^19 + 45 * q^20 + 23 * q^21 + 62 * q^22 + 176 * q^23 + 33 * q^24 + 272 * q^25 + 31 * q^26 + 82 * q^27 + 80 * q^28 + 75 * q^29 - 30 * q^30 + 73 * q^31 + 71 * q^32 + 30 * q^33 + 23 * q^34 + 44 * q^35 + 264 * q^36 + 236 * q^37 - 21 * q^38 + 17 * q^39 + 43 * q^40 + 51 * q^41 + 38 * q^42 + 51 * q^43 + 12 * q^44 + 127 * q^45 + 19 * q^46 + 45 * q^47 + 61 * q^48 + 268 * q^49 + 55 * q^50 - 3 * q^51 + 166 * q^52 + 63 * q^53 - 32 * q^54 + 11 * q^55 - 9 * q^56 + 72 * q^57 + 98 * q^58 + 95 * q^59 - 7 * q^60 + 73 * q^61 + 12 * q^62 + 19 * q^63 + 365 * q^64 + 19 * q^65 - 28 * q^66 + 138 * q^67 + 16 * q^68 + 22 * q^69 + 100 * q^70 + 85 * q^71 + 129 * q^72 + 118 * q^73 - 21 * q^74 - 12 * q^75 + 52 * q^76 + 75 * q^77 + 97 * q^78 + 74 * q^79 + 8 * q^80 + 280 * q^81 + 67 * q^82 + 10 * q^83 - 51 * q^84 + 169 * q^85 - 39 * q^86 - 6 * q^87 + 159 * q^88 + 38 * q^89 + 22 * q^90 + 90 * q^91 + 203 * q^92 + 230 * q^93 + 63 * q^94 + 30 * q^95 + 107 * q^96 + 161 * q^97 + 58 * q^98 + 7 * 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 $

$2$	−2.54982	−1.80300	−0.901498	−	0.432783i	$-0.857532\pi$
$2$	−2.54982	−1.80300	−0.901498	+	0.432783i	$0.857532\pi$
$3$	−0.805163	−0.464861	−0.232431	−	0.972613i	$-0.574668\pi$
$3$	−0.805163	−0.464861	−0.232431	+	0.972613i	$0.574668\pi$
$4$	4.50159	2.25079
$5$	−2.33665	−1.04498	−0.522491	−	0.852645i	$-0.674997\pi$
$5$	−2.33665	−1.04498	−0.522491	+	0.852645i	$0.674997\pi$
$6$	2.05302	0.838143
$7$	2.59075	0.979213	0.489606	−	0.871944i	$-0.337140\pi$
$7$	2.59075	0.979213	0.489606	+	0.871944i	$0.337140\pi$
$8$	−6.37861	−2.25518
$9$	−2.35171	−0.783904
$10$	5.95805	1.88410
$11$	−5.57295	−1.68031	−0.840154	−	0.542348i	$-0.817536\pi$
$11$	−5.57295	−1.68031	−0.840154	+	0.542348i	$0.817536\pi$
$12$	−3.62451	−1.04631
$13$	4.69859	1.30315	0.651577	−	0.758582i	$-0.274108\pi$
$13$	4.69859	1.30315	0.651577	+	0.758582i	$0.274108\pi$
$14$	−6.60596	−1.76552
$15$	1.88139	0.485772
$16$	7.26113	1.81528
$17$	−5.12218	−1.24231	−0.621156	−	0.783687i	$-0.713337\pi$
$17$	−5.12218	−1.24231	−0.621156	+	0.783687i	$0.713337\pi$
$18$	5.99645	1.41338
$19$	−1.42827	−0.327667	−0.163834	−	0.986488i	$-0.552386\pi$
$19$	−1.42827	−0.327667	−0.163834	+	0.986488i	$0.552386\pi$
$20$	−10.5186	−2.35204
$21$	−2.08598	−0.455198
$22$	14.2100	3.02959
$23$	1.00000	0.208514
$23$	1.00000	0.208514
$24$	5.13582	1.04834
$25$	0.459944	0.0919889
$26$	−11.9806	−2.34958
$27$	4.30900	0.829268
$28$	11.6625	2.20401
$29$	6.55232	1.21673	0.608367	−	0.793656i	$-0.291825\pi$
$29$	6.55232	1.21673	0.608367	+	0.793656i	$0.291825\pi$
$30$	−4.79720	−0.875845
$31$	3.56282	0.639902	0.319951	−	0.947434i	$-0.396334\pi$
$31$	3.56282	0.639902	0.319951	+	0.947434i	$0.396334\pi$
$32$	−5.75737	−1.01777
$33$	4.48714	0.781110
$34$	13.0607	2.23988
$35$	−6.05369	−1.02326
$36$	−10.5864	−1.76441
$37$	−5.48592	−0.901879	−0.450940	−	0.892554i	$-0.648911\pi$
$37$	−5.48592	−0.901879	−0.450940	+	0.892554i	$0.648911\pi$
$38$	3.64183	0.590782
$39$	−3.78313	−0.605786
$40$	14.9046	2.35662
$41$	−0.275877	−0.0430848	−0.0215424	−	0.999768i	$-0.506858\pi$
$41$	−0.275877	−0.0430848	−0.0215424	+	0.999768i	$0.506858\pi$
$42$	5.31887	0.820720
$43$	−3.49173	−0.532483	−0.266242	−	0.963906i	$-0.585782\pi$
$43$	−3.49173	−0.532483	−0.266242	+	0.963906i	$0.585782\pi$
$44$	−25.0871	−3.78203
$45$	5.49513	0.819166
$46$	−2.54982	−0.375951
$47$	−2.00135	−0.291928	−0.145964	−	0.989290i	$-0.546628\pi$
$47$	−2.00135	−0.291928	−0.145964	+	0.989290i	$0.546628\pi$
$48$	−5.84639	−0.843854
$49$	−0.287997	−0.0411424
$50$	−1.17278	−0.165856
$51$	4.12419	0.577502
$52$	21.1511	2.93313
$53$	−1.80962	−0.248571	−0.124285	−	0.992247i	$-0.539664\pi$
$53$	−1.80962	−0.248571	−0.124285	+	0.992247i	$0.539664\pi$
$54$	−10.9872	−1.49517
$55$	13.0221	1.75589
$56$	−16.5254	−2.20830
$57$	1.14999	0.152320
$58$	−16.7072	−2.19377
$59$	2.39334	0.311587	0.155793	−	0.987790i	$-0.450207\pi$
$59$	2.39334	0.311587	0.155793	+	0.987790i	$0.450207\pi$
$60$	8.46923	1.09337
$61$	−4.11937	−0.527431	−0.263715	−	0.964601i	$-0.584948\pi$
$61$	−4.11937	−0.527431	−0.263715	+	0.964601i	$0.584948\pi$
$62$	−9.08457	−1.15374
$63$	−6.09271	−0.767609
$64$	0.158006	0.0197507
$65$	−10.9790	−1.36177
$66$	−11.4414	−1.40834
$67$	−2.86809	−0.350393	−0.175197	−	0.984533i	$-0.556056\pi$
$67$	−2.86809	−0.350393	−0.175197	+	0.984533i	$0.556056\pi$
$68$	−23.0580	−2.79619
$69$	−0.805163	−0.0969303
$70$	15.4358	1.84493
$71$	13.9161	1.65154	0.825771	−	0.564005i	$-0.190740\pi$
$71$	13.9161	1.65154	0.825771	+	0.564005i	$0.190740\pi$
$72$	15.0006	1.76784
$73$	−12.0871	−1.41469	−0.707344	−	0.706870i	$-0.750107\pi$
$73$	−12.0871	−1.41469	−0.707344	+	0.706870i	$0.750107\pi$
$74$	13.9881	1.62608
$75$	−0.370330	−0.0427621
$76$	−6.42947	−0.737511
$77$	−14.4381	−1.64538
$78$	9.64631	1.09223
$79$	−4.26933	−0.480337	−0.240169	−	0.970731i	$-0.577203\pi$
$79$	−4.26933	−0.480337	−0.240169	+	0.970731i	$0.577203\pi$
$80$	−16.9667	−1.89694
$81$	3.58569	0.398410
$82$	0.703437	0.0776817
$83$	−8.54324	−0.937743	−0.468871	−	0.883266i	$-0.655339\pi$
$83$	−8.54324	−0.937743	−0.468871	+	0.883266i	$0.655339\pi$
$84$	−9.39022	−1.02456
$85$	11.9688	1.29819
$86$	8.90328	0.960065
$87$	−5.27568	−0.565613
$88$	35.5477	3.78939
$89$	−15.6449	−1.65836	−0.829180	−	0.558982i	$-0.811192\pi$
$89$	−15.6449	−1.65836	−0.829180	+	0.558982i	$0.811192\pi$
$90$	−14.0116	−1.47695
$91$	12.1729	1.27607
$92$	4.50159	0.469323
$93$	−2.86866	−0.297466
$94$	5.10310	0.526344
$95$	3.33736	0.342406
$96$	4.63562	0.473121
$97$	−12.7431	−1.29387	−0.646935	−	0.762545i	$-0.723949\pi$
$97$	−12.7431	−1.29387	−0.646935	+	0.762545i	$0.723949\pi$
$98$	0.734341	0.0741796
$99$	13.1060	1.31720
$100$	2.07048	0.207048
$101$	−9.85761	−0.980869	−0.490435	−	0.871478i	$-0.663162\pi$
$101$	−9.85761	−0.980869	−0.490435	+	0.871478i	$0.663162\pi$
$102$	−10.5160	−1.04123
$103$	−0.370649	−0.0365212	−0.0182606	−	0.999833i	$-0.505813\pi$
$103$	−0.370649	−0.0365212	−0.0182606	+	0.999833i	$0.505813\pi$
$104$	−29.9705	−2.93885
$105$	4.87421	0.475674
$106$	4.61422	0.448172
$107$	1.95601	0.189094	0.0945472	−	0.995520i	$-0.469860\pi$
$107$	1.95601	0.189094	0.0945472	+	0.995520i	$0.469860\pi$
$108$	19.3974	1.86651
$109$	19.7890	1.89544	0.947720	−	0.319103i	$-0.103382\pi$
$109$	19.7890	1.89544	0.947720	+	0.319103i	$0.103382\pi$
$110$	−33.2039	−3.16587
$111$	4.41706	0.419249
$112$	18.8118	1.77755
$113$	6.81442	0.641046	0.320523	−	0.947241i	$-0.396141\pi$
$113$	6.81442	0.641046	0.320523	+	0.947241i	$0.396141\pi$
$114$	−2.93227	−0.274632
$115$	−2.33665	−0.217894
$116$	29.4958	2.73862
$117$	−11.0497	−1.02155
$118$	−6.10260	−0.561790
$119$	−13.2703	−1.21649
$120$	−12.0006	−1.09550
$121$	20.0578	1.82344
$122$	10.5036	0.950956
$123$	0.222126	0.0200284
$124$	16.0384	1.44029
$125$	10.6085	0.948856
$126$	15.5353	1.38400
$127$	−3.21708	−0.285470	−0.142735	−	0.989761i	$-0.545590\pi$
$127$	−3.21708	−0.285470	−0.142735	+	0.989761i	$0.545590\pi$
$128$	11.1119	0.982158
$129$	2.81141	0.247531
$130$	27.9944	2.45527
$131$	−12.3306	−1.07733	−0.538664	−	0.842521i	$-0.681071\pi$
$131$	−12.3306	−1.07733	−0.538664	+	0.842521i	$0.681071\pi$
$132$	20.1992	1.75812
$133$	−3.70029	−0.320856
$134$	7.31313	0.631758
$135$	−10.0686	−0.866570
$136$	32.6724	2.80163
$137$	1.88343	0.160912	0.0804560	−	0.996758i	$-0.474362\pi$
$137$	1.88343	0.160912	0.0804560	+	0.996758i	$0.474362\pi$
$138$	2.05302	0.174765
$139$	−14.2618	−1.20967	−0.604835	−	0.796351i	$-0.706761\pi$
$139$	−14.2618	−1.20967	−0.604835	+	0.796351i	$0.706761\pi$
$140$	−27.2512	−2.30315
$141$	1.61142	0.135706
$142$	−35.4837	−2.97772
$143$	−26.1850	−2.18970
$144$	−17.0761	−1.42301
$145$	−15.3105	−1.27147
$146$	30.8199	2.55068
$147$	0.231885	0.0191255
$148$	−24.6953	−2.02995
$149$	−4.74266	−0.388534	−0.194267	−	0.980949i	$-0.562233\pi$
$149$	−4.74266	−0.388534	−0.194267	+	0.980949i	$0.562233\pi$
$150$	0.944276	0.0770998
$151$	12.9508	1.05392	0.526959	−	0.849891i	$-0.323332\pi$
$151$	12.9508	1.05392	0.526959	+	0.849891i	$0.323332\pi$
$152$	9.11036	0.738948
$153$	12.0459	0.973853
$154$	36.8147	2.96661
$155$	−8.32508	−0.668687
$156$	−17.0301	−1.36350
$157$	13.1157	1.04674	0.523372	−	0.852104i	$-0.324674\pi$
$157$	13.1157	1.04674	0.523372	+	0.852104i	$0.324674\pi$
$158$	10.8860	0.866046
$159$	1.45704	0.115551
$160$	13.4530	1.06355
$161$	2.59075	0.204180
$162$	−9.14286	−0.718331
$163$	6.99681	0.548032	0.274016	−	0.961725i	$-0.411648\pi$
$163$	6.99681	0.548032	0.274016	+	0.961725i	$0.411648\pi$
$164$	−1.24189	−0.0969750
$165$	−10.4849	−0.816247
$166$	21.7837	1.69075
$167$	−22.2886	−1.72474	−0.862370	−	0.506278i	$-0.831021\pi$
$167$	−22.2886	−1.72474	−0.862370	+	0.506278i	$0.831021\pi$
$168$	13.3056	1.02655
$169$	9.07677	0.698213
$170$	−30.5182	−2.34064
$171$	3.35887	0.256860
$172$	−15.7183	−1.19851
$173$	−19.5038	−1.48284	−0.741421	−	0.671040i	$-0.765848\pi$
$173$	−19.5038	−1.48284	−0.741421	+	0.671040i	$0.765848\pi$
$174$	13.4521	1.01980
$175$	1.19160	0.0900767
$176$	−40.4659	−3.05023
$177$	−1.92703	−0.144845
$178$	39.8918	2.99002
$179$	1.22468	0.0915369	0.0457684	−	0.998952i	$-0.485426\pi$
$179$	1.22468	0.0915369	0.0457684	+	0.998952i	$0.485426\pi$
$180$	24.7368	1.84377
$181$	−8.76576	−0.651553	−0.325777	−	0.945447i	$-0.605626\pi$
$181$	−8.76576	−0.651553	−0.325777	+	0.945447i	$0.605626\pi$
$182$	−31.0387	−2.30074
$183$	3.31676	0.245182
$184$	−6.37861	−0.470237
$185$	12.8187	0.942448
$186$	7.31456	0.536330
$187$	28.5457	2.08747
$188$	−9.00927	−0.657069
$189$	11.1636	0.812030
$190$	−8.50968	−0.617357
$191$	−20.6322	−1.49290	−0.746448	−	0.665443i	$-0.768243\pi$
$191$	−20.6322	−1.49290	−0.746448	+	0.665443i	$0.768243\pi$
$192$	−0.127220	−0.00918135
$193$	−18.2631	−1.31461	−0.657304	−	0.753626i	$-0.728303\pi$
$193$	−18.2631	−1.31461	−0.657304	+	0.753626i	$0.728303\pi$
$194$	32.4927	2.33284
$195$	8.83987	0.633036
$196$	−1.29644	−0.0926032
$197$	11.1773	0.796351	0.398176	−	0.917309i	$-0.369643\pi$
$197$	11.1773	0.796351	0.398176	+	0.917309i	$0.369643\pi$
$198$	−33.4179	−2.37491
$199$	20.1595	1.42907	0.714533	−	0.699602i	$-0.246639\pi$
$199$	20.1595	1.42907	0.714533	+	0.699602i	$0.246639\pi$
$200$	−2.93380	−0.207451
$201$	2.30928	0.162884
$202$	25.1352	1.76850
$203$	16.9754	1.19144
$204$	18.5654	1.29984
$205$	0.644629	0.0450228
$206$	0.945090	0.0658475
$207$	−2.35171	−0.163455
$208$	34.1171	2.36559
$209$	7.95967	0.550582
$210$	−12.4284	−0.857638
$211$	−6.81171	−0.468938	−0.234469	−	0.972124i	$-0.575335\pi$
$211$	−6.81171	−0.468938	−0.234469	+	0.972124i	$0.575335\pi$
$212$	−8.14618	−0.559482
$213$	−11.2048	−0.767738
$214$	−4.98747	−0.340937
$215$	8.15895	0.556436
$216$	−27.4854	−1.87015
$217$	9.23040	0.626600
$218$	−50.4584	−3.41747
$219$	9.73209	0.657633
$220$	58.6199	3.95216
$221$	−24.0670	−1.61892
$222$	−11.2627	−0.755904
$223$	22.3364	1.49576	0.747878	−	0.663836i	$-0.231073\pi$
$223$	22.3364	1.49576	0.747878	+	0.663836i	$0.231073\pi$
$224$	−14.9159	−0.996612
$225$	−1.08166	−0.0721105
$226$	−17.3755	−1.15580
$227$	4.61136	0.306066	0.153033	−	0.988221i	$-0.451096\pi$
$227$	4.61136	0.306066	0.153033	+	0.988221i	$0.451096\pi$
$228$	5.17678	0.342840
$229$	5.94990	0.393180	0.196590	−	0.980486i	$-0.437013\pi$
$229$	5.94990	0.393180	0.196590	+	0.980486i	$0.437013\pi$
$230$	5.95805	0.392862
$231$	11.6251	0.764873
$232$	−41.7947	−2.74395
$233$	9.57400	0.627214	0.313607	−	0.949553i	$-0.398463\pi$
$233$	9.57400	0.627214	0.313607	+	0.949553i	$0.398463\pi$
$234$	28.1749	1.84185
$235$	4.67647	0.305059
$236$	10.7739	0.701318
$237$	3.43751	0.223290
$238$	33.8369	2.19332
$239$	−6.18467	−0.400053	−0.200027	−	0.979790i	$-0.564103\pi$
$239$	−6.18467	−0.400053	−0.200027	+	0.979790i	$0.564103\pi$
$240$	13.6610	0.881813
$241$	−18.4702	−1.18977	−0.594884	−	0.803811i	$-0.702802\pi$
$241$	−18.4702	−1.18977	−0.594884	+	0.803811i	$0.702802\pi$
$242$	−51.1438	−3.28765
$243$	−15.8141	−1.01447
$244$	−18.5437	−1.18714
$245$	0.672949	0.0429931
$246$	−0.566382	−0.0361112
$247$	−6.71085	−0.427001
$248$	−22.7259	−1.44309
$249$	6.87871	0.435920
$250$	−27.0499	−1.71078
$251$	−18.4607	−1.16523	−0.582615	−	0.812748i	$-0.697970\pi$
$251$	−18.4607	−1.16523	−0.582615	+	0.812748i	$0.697970\pi$
$252$	−27.4269	−1.72773
$253$	−5.57295	−0.350369
$254$	8.20299	0.514701
$255$	−9.63680	−0.603480
$256$	−28.6492	−1.79058
$257$	7.90883	0.493339	0.246670	−	0.969100i	$-0.420664\pi$
$257$	7.90883	0.493339	0.246670	+	0.969100i	$0.420664\pi$
$258$	−7.16859	−0.446297
$259$	−14.2127	−0.883132
$260$	−49.4228	−3.06507
$261$	−15.4092	−0.953803
$262$	31.4408	1.94242
$263$	21.0069	1.29534	0.647670	−	0.761921i	$-0.275743\pi$
$263$	21.0069	1.29534	0.647670	+	0.761921i	$0.275743\pi$
$264$	−28.6217	−1.76154
$265$	4.22846	0.259752
$266$	9.43508	0.578502
$267$	12.5967	0.770907
$268$	−12.9110	−0.788663
$269$	−18.6069	−1.13448	−0.567240	−	0.823552i	$-0.691989\pi$
$269$	−18.6069	−1.13448	−0.567240	+	0.823552i	$0.691989\pi$
$270$	25.6732	1.56242
$271$	25.2772	1.53548	0.767741	−	0.640761i	$-0.221381\pi$
$271$	25.2772	1.53548	0.767741	+	0.640761i	$0.221381\pi$
$272$	−37.1928	−2.25515
$273$	−9.80117	−0.593194
$274$	−4.80240	−0.290124
$275$	−2.56325	−0.154570
$276$	−3.62451	−0.218170
$277$	28.5315	1.71429	0.857145	−	0.515074i	$-0.172236\pi$
$277$	28.5315	1.71429	0.857145	+	0.515074i	$0.172236\pi$
$278$	36.3650	2.18103
$279$	−8.37874	−0.501622
$280$	38.6141	2.30763
$281$	−14.3823	−0.857977	−0.428988	−	0.903310i	$-0.641130\pi$
$281$	−14.3823	−0.857977	−0.428988	+	0.903310i	$0.641130\pi$
$282$	−4.10882	−0.244677
$283$	24.3571	1.44788	0.723939	−	0.689864i	$-0.242330\pi$
$283$	24.3571	1.44788	0.723939	+	0.689864i	$0.242330\pi$
$284$	62.6448	3.71728
$285$	−2.68712	−0.159171
$286$	66.7672	3.94802
$287$	−0.714729	−0.0421891
$288$	13.5397	0.797833
$289$	9.23675	0.543338
$290$	39.0390	2.29245
$291$	10.2603	0.601470
$292$	−54.4111	−3.18417
$293$	2.42978	0.141949	0.0709746	−	0.997478i	$-0.477389\pi$
$293$	2.42978	0.141949	0.0709746	+	0.997478i	$0.477389\pi$
$294$	−0.591264	−0.0344832
$295$	−5.59241	−0.325603
$296$	34.9925	2.03390
$297$	−24.0139	−1.39343
$298$	12.0929	0.700525
$299$	4.69859	0.271727
$300$	−1.66708	−0.0962486
$301$	−9.04620	−0.521414
$302$	−33.0221	−1.90021
$303$	7.93699	0.455968
$304$	−10.3708	−0.594808
$305$	9.62553	0.551156
$306$	−30.7149	−1.75585
$307$	−7.78825	−0.444499	−0.222250	−	0.974990i	$-0.571340\pi$
$307$	−7.78825	−0.444499	−0.222250	+	0.974990i	$0.571340\pi$
$308$	−64.9946	−3.70341
$309$	0.298433	0.0169773
$310$	21.2275	1.20564
$311$	16.0437	0.909756	0.454878	−	0.890554i	$-0.349683\pi$
$311$	16.0437	0.909756	0.454878	+	0.890554i	$0.349683\pi$
$312$	24.1311	1.36616
$313$	−24.1866	−1.36711	−0.683555	−	0.729899i	$-0.739567\pi$
$313$	−24.1866	−1.36711	−0.683555	+	0.729899i	$0.739567\pi$
$314$	−33.4426	−1.88728
$315$	14.2365	0.802138
$316$	−19.2188	−1.08114
$317$	−19.4406	−1.09189	−0.545946	−	0.837820i	$-0.683830\pi$
$317$	−19.4406	−1.09189	−0.545946	+	0.837820i	$0.683830\pi$
$318$	−3.71520	−0.208338
$319$	−36.5158	−2.04449
$320$	−0.369205	−0.0206392
$321$	−1.57491	−0.0879027
$322$	−6.60596	−0.368136
$323$	7.31585	0.407065
$324$	16.1413	0.896738
$325$	2.16109	0.119876
$326$	−17.8406	−0.988100
$327$	−15.9334	−0.881117
$328$	1.75971	0.0971638
$329$	−5.18501	−0.285859
$330$	26.7346	1.47169
$331$	−26.7069	−1.46794	−0.733972	−	0.679180i	$-0.762335\pi$
$331$	−26.7069	−1.46794	−0.733972	+	0.679180i	$0.762335\pi$
$332$	−38.4582	−2.11067
$333$	12.9013	0.706987
$334$	56.8318	3.10970
$335$	6.70174	0.366155
$336$	−15.1466	−0.826313
$337$	6.41473	0.349433	0.174716	−	0.984619i	$-0.444099\pi$
$337$	6.41473	0.349433	0.174716	+	0.984619i	$0.444099\pi$
$338$	−23.1441	−1.25888
$339$	−5.48672	−0.297998
$340$	53.8784	2.92197
$341$	−19.8555	−1.07523
$342$	−8.56453	−0.463117
$343$	−18.8814	−1.01950
$344$	22.2723	1.20084
$345$	1.88139	0.101290
$346$	49.7311	2.67356
$347$	7.44496	0.399666	0.199833	−	0.979830i	$-0.435960\pi$
$347$	7.44496	0.399666	0.199833	+	0.979830i	$0.435960\pi$
$348$	−23.7490	−1.27308
$349$	−1.00000	−0.0535288
$349$	−1.00000	−0.0535288
$350$	−3.03837	−0.162408
$351$	20.2462	1.08066
$352$	32.0855	1.71017
$353$	−6.46175	−0.343924	−0.171962	−	0.985104i	$-0.555011\pi$
$353$	−6.46175	−0.343924	−0.171962	+	0.985104i	$0.555011\pi$
$354$	4.91359	0.261154
$355$	−32.5172	−1.72583
$356$	−70.4271	−3.73263
$357$	10.6848	0.565498
$358$	−3.12271	−0.165041
$359$	17.5803	0.927851	0.463925	−	0.885874i	$-0.346441\pi$
$359$	17.5803	0.927851	0.463925	+	0.885874i	$0.346441\pi$
$360$	−35.0513	−1.84737
$361$	−16.9601	−0.892634
$362$	22.3511	1.17475
$363$	−16.1498	−0.847645
$364$	54.7974	2.87216
$365$	28.2433	1.47832
$366$	−8.45715	−0.442062
$367$	−27.9795	−1.46052	−0.730258	−	0.683172i	$-0.760600\pi$
$367$	−27.9795	−1.46052	−0.730258	+	0.683172i	$0.760600\pi$
$368$	7.26113	0.378513
$369$	0.648784	0.0337743
$370$	−32.6854	−1.69923
$371$	−4.68829	−0.243404
$372$	−12.9135	−0.669534
$373$	−14.3746	−0.744290	−0.372145	−	0.928175i	$-0.621378\pi$
$373$	−14.3746	−0.744290	−0.372145	+	0.928175i	$0.621378\pi$
$374$	−72.7864	−3.76369
$375$	−8.54160	−0.441086
$376$	12.7659	0.658348
$377$	30.7867	1.58559
$378$	−28.4651	−1.46409
$379$	−30.0028	−1.54114	−0.770569	−	0.637356i	$-0.780028\pi$
$379$	−30.0028	−1.54114	−0.770569	+	0.637356i	$0.780028\pi$
$380$	15.0234	0.770687
$381$	2.59028	0.132704
$382$	52.6085	2.69169
$383$	−8.55415	−0.437097	−0.218548	−	0.975826i	$-0.570132\pi$
$383$	−8.55415	−0.437097	−0.218548	+	0.975826i	$0.570132\pi$
$384$	−8.94685	−0.456567
$385$	33.7369	1.71939
$386$	46.5677	2.37023
$387$	8.21153	0.417416
$388$	−57.3644	−2.91223
$389$	14.8713	0.754007	0.377003	−	0.926212i	$-0.376954\pi$
$389$	14.8713	0.754007	0.377003	+	0.926212i	$0.376954\pi$
$390$	−22.5401	−1.14136
$391$	−5.12218	−0.259040
$392$	1.83702	0.0927835
$393$	9.92813	0.500808
$394$	−28.5002	−1.43582
$395$	9.97595	0.501944
$396$	58.9977	2.96475
$397$	7.50289	0.376559	0.188280	−	0.982115i	$-0.439709\pi$
$397$	7.50289	0.376559	0.188280	+	0.982115i	$0.439709\pi$
$398$	−51.4030	−2.57660
$399$	2.97934	0.149153
$400$	3.33972	0.166986
$401$	38.8624	1.94070	0.970349	−	0.241710i	$-0.0777081\pi$
$401$	38.8624	1.94070	0.970349	+	0.241710i	$0.0777081\pi$
$402$	−5.88826	−0.293680
$403$	16.7403	0.833892
$404$	−44.3749	−2.20774
$405$	−8.37850	−0.416331
$406$	−43.2843	−2.14817
$407$	30.5728	1.51544
$408$	−26.3066	−1.30237
$409$	20.0350	0.990666	0.495333	−	0.868703i	$-0.335046\pi$
$409$	20.0350	0.990666	0.495333	+	0.868703i	$0.335046\pi$
$410$	−1.64369	−0.0811760
$411$	−1.51647	−0.0748017
$412$	−1.66851	−0.0822016
$413$	6.20056	0.305110
$414$	5.99645	0.294709
$415$	19.9626	0.979925
$416$	−27.0515	−1.32631
$417$	11.4831	0.562329
$418$	−20.2957	−0.992697
$419$	12.9460	0.632453	0.316226	−	0.948684i	$-0.397584\pi$
$419$	12.9460	0.632453	0.316226	+	0.948684i	$0.397584\pi$
$420$	21.9417	1.07064
$421$	−29.2626	−1.42617	−0.713087	−	0.701076i	$-0.752704\pi$
$421$	−29.2626	−1.42617	−0.713087	+	0.701076i	$0.752704\pi$
$422$	17.3686	0.845492
$423$	4.70661	0.228843
$424$	11.5429	0.560572
$425$	−2.35592	−0.114279
$426$	28.5702	1.38423
$427$	−10.6723	−0.516467
$428$	8.80515	0.425613
$429$	21.0832	1.01791
$430$	−20.8039	−1.00325
$431$	−3.80195	−0.183133	−0.0915667	−	0.995799i	$-0.529187\pi$
$431$	−3.80195	−0.183133	−0.0915667	+	0.995799i	$0.529187\pi$
$432$	31.2882	1.50536
$433$	36.3491	1.74683	0.873414	−	0.486978i	$-0.161901\pi$
$433$	36.3491	1.74683	0.873414	+	0.486978i	$0.161901\pi$
$434$	−23.5359	−1.12976
$435$	12.3274	0.591056
$436$	89.0819	4.26625
$437$	−1.42827	−0.0683233
$438$	−24.8151	−1.18571
$439$	−32.7284	−1.56204	−0.781022	−	0.624504i	$-0.785301\pi$
$439$	−32.7284	−1.56204	−0.781022	+	0.624504i	$0.785301\pi$
$440$	−83.0626	−3.95985
$441$	0.677286	0.0322517
$442$	61.3667	2.91891
$443$	−22.5145	−1.06970	−0.534849	−	0.844947i	$-0.679632\pi$
$443$	−22.5145	−1.06970	−0.534849	+	0.844947i	$0.679632\pi$
$444$	19.8838	0.943643
$445$	36.5568	1.73296
$446$	−56.9538	−2.69684
$447$	3.81862	0.180614
$448$	0.409354	0.0193402
$449$	4.32248	0.203991	0.101995	−	0.994785i	$-0.467477\pi$
$449$	4.32248	0.203991	0.101995	+	0.994785i	$0.467477\pi$
$450$	2.75803	0.130015
$451$	1.53745	0.0723957
$452$	30.6757	1.44286
$453$	−10.4275	−0.489925
$454$	−11.7581	−0.551837
$455$	−28.4438	−1.33347
$456$	−7.33532	−0.343508
$457$	−8.44306	−0.394950	−0.197475	−	0.980308i	$-0.563274\pi$
$457$	−8.44306	−0.394950	−0.197475	+	0.980308i	$0.563274\pi$
$458$	−15.1712	−0.708903
$459$	−22.0715	−1.03021
$460$	−10.5186	−0.490435
$461$	−24.3164	−1.13253	−0.566264	−	0.824224i	$-0.691612\pi$
$461$	−24.3164	−1.13253	−0.566264	+	0.824224i	$0.691612\pi$
$462$	−29.6418	−1.37906
$463$	−8.54814	−0.397266	−0.198633	−	0.980074i	$-0.563650\pi$
$463$	−8.54814	−0.397266	−0.198633	+	0.980074i	$0.563650\pi$
$464$	47.5772	2.20872
$465$	6.70305	0.310847
$466$	−24.4120	−1.13086
$467$	11.1149	0.514337	0.257169	−	0.966367i	$-0.417210\pi$
$467$	11.1149	0.514337	0.257169	+	0.966367i	$0.417210\pi$
$468$	−49.7414	−2.29930
$469$	−7.43052	−0.343110
$470$	−11.9242	−0.550021
$471$	−10.5603	−0.486591
$472$	−15.2662	−0.702684
$473$	19.4592	0.894736
$474$	−8.76503	−0.402591
$475$	−0.656924	−0.0301417
$476$	−59.7375	−2.73806
$477$	4.25571	0.194856
$478$	15.7698	0.721295
$479$	−4.38695	−0.200445	−0.100222	−	0.994965i	$-0.531955\pi$
$479$	−4.38695	−0.200445	−0.100222	+	0.994965i	$0.531955\pi$
$480$	−10.8318	−0.494403
$481$	−25.7761	−1.17529
$482$	47.0957	2.14515
$483$	−2.08598	−0.0949153
$484$	90.2920	4.10418
$485$	29.7763	1.35207
$486$	40.3231	1.82909
$487$	−2.45905	−0.111430	−0.0557152	−	0.998447i	$-0.517744\pi$
$487$	−2.45905	−0.111430	−0.0557152	+	0.998447i	$0.517744\pi$
$488$	26.2758	1.18945
$489$	−5.63357	−0.254759
$490$	−1.71590	−0.0775164
$491$	16.4487	0.742318	0.371159	−	0.928569i	$-0.378960\pi$
$491$	16.4487	0.742318	0.371159	+	0.928569i	$0.378960\pi$
$492$	0.999920	0.0450799
$493$	−33.5622	−1.51156
$494$	17.1115	0.769881
$495$	−30.6241	−1.37645
$496$	25.8701	1.16160
$497$	36.0533	1.61721
$498$	−17.5395	−0.785963
$499$	30.6398	1.37163	0.685814	−	0.727777i	$-0.259446\pi$
$499$	30.6398	1.37163	0.685814	+	0.727777i	$0.259446\pi$
$500$	47.7553	2.13568
$501$	17.9459	0.801765
$502$	47.0715	2.10090
$503$	−34.1722	−1.52366	−0.761832	−	0.647774i	$-0.775700\pi$
$503$	−34.1722	−1.52366	−0.761832	+	0.647774i	$0.775700\pi$
$504$	38.8630	1.73109
$505$	23.0338	1.02499
$506$	14.2100	0.631713
$507$	−7.30828	−0.324572
$508$	−14.4820	−0.642535
$509$	30.4163	1.34818	0.674088	−	0.738651i	$-0.264537\pi$
$509$	30.4163	1.34818	0.674088	+	0.738651i	$0.264537\pi$
$510$	24.5721	1.08807
$511$	−31.3147	−1.38528
$512$	50.8268	2.24625
$513$	−6.15441	−0.271724
$514$	−20.1661	−0.889489
$515$	0.866079	0.0381640
$516$	12.6558	0.557141
$517$	11.1535	0.490528
$518$	36.2397	1.59228
$519$	15.7037	0.689316
$520$	70.0306	3.07104
$521$	8.14948	0.357035	0.178518	−	0.983937i	$-0.442870\pi$
$521$	8.14948	0.357035	0.178518	+	0.983937i	$0.442870\pi$
$522$	39.2906	1.71970
$523$	19.8083	0.866157	0.433079	−	0.901356i	$-0.357427\pi$
$523$	19.8083	0.866157	0.433079	+	0.901356i	$0.357427\pi$
$524$	−55.5072	−2.42484
$525$	−0.959435	−0.0418732
$526$	−53.5638	−2.33549
$527$	−18.2494	−0.794958
$528$	32.5817	1.41794
$529$	1.00000	0.0434783
$530$	−10.7818	−0.468332
$531$	−5.62846	−0.244254
$532$	−16.6572	−0.722180
$533$	−1.29623	−0.0561461
$534$	−32.1194	−1.38994
$535$	−4.57051	−0.197600
$536$	18.2944	0.790199
$537$	−0.986067	−0.0425519
$538$	47.4442	2.04546
$539$	1.60499	0.0691320
$540$	−45.3249	−1.95047
$541$	1.94251	0.0835150	0.0417575	−	0.999128i	$-0.486704\pi$
$541$	1.94251	0.0835150	0.0417575	+	0.999128i	$0.486704\pi$
$542$	−64.4524	−2.76847
$543$	7.05786	0.302882
$544$	29.4903	1.26439
$545$	−46.2400	−1.98070
$546$	24.9912	1.06953
$547$	18.3804	0.785891	0.392945	−	0.919562i	$-0.371456\pi$
$547$	18.3804	0.785891	0.392945	+	0.919562i	$0.371456\pi$
$548$	8.47841	0.362180
$549$	9.68756	0.413455
$550$	6.53583	0.278689
$551$	−9.35846	−0.398684
$552$	5.13582	0.218595
$553$	−11.0608	−0.470352
$554$	−72.7502	−3.09086
$555$	−10.3211	−0.438108
$556$	−64.2008	−2.72272
$557$	37.5538	1.59121	0.795604	−	0.605818i	$-0.207154\pi$
$557$	37.5538	1.59121	0.795604	+	0.605818i	$0.207154\pi$
$558$	21.3643	0.904422
$559$	−16.4062	−0.693908
$560$	−43.9566	−1.85751
$561$	−22.9839	−0.970382
$562$	36.6723	1.54693
$563$	10.8382	0.456777	0.228389	−	0.973570i	$-0.426654\pi$
$563$	10.8382	0.456777	0.228389	+	0.973570i	$0.426654\pi$
$564$	7.25394	0.305446
$565$	−15.9229	−0.669882
$566$	−62.1062	−2.61052
$567$	9.28963	0.390128
$568$	−88.7656	−3.72452
$569$	−21.6790	−0.908829	−0.454415	−	0.890790i	$-0.650152\pi$
$569$	−21.6790	−0.908829	−0.454415	+	0.890790i	$0.650152\pi$
$570$	6.85168	0.286986
$571$	15.3382	0.641882	0.320941	−	0.947099i	$-0.396001\pi$
$571$	15.3382	0.641882	0.320941	+	0.947099i	$0.396001\pi$
$572$	−117.874	−4.92857
$573$	16.6123	0.693990
$574$	1.82243	0.0760669
$575$	0.459944	0.0191810
$576$	−0.371584	−0.0154827
$577$	9.59456	0.399427	0.199713	−	0.979854i	$-0.435999\pi$
$577$	9.59456	0.399427	0.199713	+	0.979854i	$0.435999\pi$
$578$	−23.5521	−0.979637
$579$	14.7048	0.611110
$580$	−68.9215	−2.86181
$581$	−22.1334	−0.918250
$582$	−26.1619	−1.08445
$583$	10.0849	0.417676
$584$	77.0988	3.19037
$585$	25.8194	1.06750
$586$	−6.19550	−0.255934
$587$	−9.87884	−0.407743	−0.203872	−	0.978998i	$-0.565353\pi$
$587$	−9.87884	−0.407743	−0.203872	+	0.978998i	$0.565353\pi$
$588$	1.04385	0.0430476
$589$	−5.08867	−0.209675
$590$	14.2597	0.587061
$591$	−8.99957	−0.370193
$592$	−39.8340	−1.63717
$593$	30.5185	1.25324	0.626622	−	0.779323i	$-0.284437\pi$
$593$	30.5185	1.25324	0.626622	+	0.779323i	$0.284437\pi$
$594$	61.2311	2.51234
$595$	31.0081	1.27121
$596$	−21.3495	−0.874510
$597$	−16.2317	−0.664317
$598$	−11.9806	−0.489922
$599$	8.29791	0.339043	0.169522	−	0.985526i	$-0.445778\pi$
$599$	8.29791	0.339043	0.169522	+	0.985526i	$0.445778\pi$
$600$	2.36219	0.0964361
$601$	42.5008	1.73364	0.866822	−	0.498618i	$-0.166159\pi$
$601$	42.5008	1.73364	0.866822	+	0.498618i	$0.166159\pi$
$602$	23.0662	0.940108
$603$	6.74493	0.274675
$604$	58.2990	2.37215
$605$	−46.8681	−1.90546
$606$	−20.2379	−0.822109
$607$	−18.9333	−0.768479	−0.384240	−	0.923233i	$-0.625536\pi$
$607$	−18.9333	−0.768479	−0.384240	+	0.923233i	$0.625536\pi$
$608$	8.22306	0.333489
$609$	−13.6680	−0.553855
$610$	−24.5434	−0.993732
$611$	−9.40355	−0.380427
$612$	54.2257	2.19194
$613$	−43.7445	−1.76682	−0.883412	−	0.468596i	$-0.844760\pi$
$613$	−43.7445	−1.76682	−0.883412	+	0.468596i	$0.844760\pi$
$614$	19.8587	0.801430
$615$	−0.519031	−0.0209294
$616$	92.0953	3.71062
$617$	−14.3608	−0.578143	−0.289071	−	0.957308i	$-0.593347\pi$
$617$	−14.3608	−0.578143	−0.289071	+	0.957308i	$0.593347\pi$
$618$	−0.760951	−0.0306100
$619$	−15.7406	−0.632667	−0.316333	−	0.948648i	$-0.602452\pi$
$619$	−15.7406	−0.632667	−0.316333	+	0.948648i	$0.602452\pi$
$620$	−37.4761	−1.50508
$621$	4.30900	0.172914
$622$	−40.9086	−1.64029
$623$	−40.5322	−1.62389
$624$	−27.4698	−1.09967
$625$	−27.0882	−1.08353
$626$	61.6716	2.46489
$627$	−6.40883	−0.255944
$628$	59.0414	2.35601
$629$	28.0999	1.12042
$630$	−36.3006	−1.44625
$631$	38.2252	1.52172	0.760861	−	0.648915i	$-0.224777\pi$
$631$	38.2252	1.52172	0.760861	+	0.648915i	$0.224777\pi$
$632$	27.2324	1.08325
$633$	5.48454	0.217991
$634$	49.5701	1.96868
$635$	7.51721	0.298311
$636$	6.55901	0.260082
$637$	−1.35318	−0.0536150
$638$	93.1087	3.68621
$639$	−32.7268	−1.29465
$640$	−25.9645	−1.02634
$641$	−24.8991	−0.983455	−0.491727	−	0.870749i	$-0.663634\pi$
$641$	−24.8991	−0.983455	−0.491727	+	0.870749i	$0.663634\pi$
$642$	4.01573	0.158488
$643$	21.4669	0.846570	0.423285	−	0.905997i	$-0.360877\pi$
$643$	21.4669	0.846570	0.423285	+	0.905997i	$0.360877\pi$
$644$	11.6625	0.459567
$645$	−6.56928	−0.258665
$646$	−18.6541	−0.733936
$647$	39.2075	1.54141	0.770703	−	0.637195i	$-0.219905\pi$
$647$	39.2075	1.54141	0.770703	+	0.637195i	$0.219905\pi$
$648$	−22.8717	−0.898485
$649$	−13.3380	−0.523562
$650$	−5.51040	−0.216136
$651$	−7.43198	−0.291282
$652$	31.4968	1.23351
$653$	49.2612	1.92774	0.963870	−	0.266375i	$-0.0858259\pi$
$653$	49.2612	1.92774	0.963870	+	0.266375i	$0.0858259\pi$
$654$	40.6272	1.58865
$655$	28.8123	1.12579
$656$	−2.00318	−0.0782110
$657$	28.4254	1.10898
$658$	13.2209	0.515403
$659$	27.2408	1.06115	0.530576	−	0.847638i	$-0.321976\pi$
$659$	27.2408	1.06115	0.530576	+	0.847638i	$0.321976\pi$
$660$	−47.1986	−1.83720
$661$	−32.9619	−1.28207	−0.641034	−	0.767512i	$-0.721494\pi$
$661$	−32.9619	−1.28207	−0.641034	+	0.767512i	$0.721494\pi$
$662$	68.0978	2.64670
$663$	19.3779	0.752575
$664$	54.4940	2.11478
$665$	8.64629	0.335289
$666$	−32.8960	−1.27469
$667$	6.55232	0.253707
$668$	−100.334	−3.88204
$669$	−17.9844	−0.695319
$670$	−17.0882	−0.660176
$671$	22.9570	0.886246
$672$	12.0098	0.463286
$673$	14.2272	0.548419	0.274210	−	0.961670i	$-0.411584\pi$
$673$	14.2272	0.548419	0.274210	+	0.961670i	$0.411584\pi$
$674$	−16.3564	−0.630026
$675$	1.98190	0.0762834
$676$	40.8599	1.57153
$677$	−29.9477	−1.15098	−0.575492	−	0.817807i	$-0.695189\pi$
$677$	−29.9477	−1.15098	−0.575492	+	0.817807i	$0.695189\pi$
$678$	13.9901	0.537288
$679$	−33.0143	−1.26697
$680$	−76.3440	−2.92766
$681$	−3.71289	−0.142278
$682$	50.6279	1.93864
$683$	−10.6699	−0.408271	−0.204136	−	0.978943i	$-0.565438\pi$
$683$	−10.6699	−0.408271	−0.204136	+	0.978943i	$0.565438\pi$
$684$	15.1203	0.578138
$685$	−4.40091	−0.168150
$686$	48.1442	1.83815
$687$	−4.79064	−0.182774
$688$	−25.3539	−0.966607
$689$	−8.50268	−0.323926
$690$	−4.79720	−0.182626
$691$	−19.0115	−0.723232	−0.361616	−	0.932327i	$-0.617775\pi$
$691$	−19.0115	−0.723232	−0.361616	+	0.932327i	$0.617775\pi$
$692$	−87.7979	−3.33757
$693$	33.9544	1.28982
$694$	−18.9833	−0.720597
$695$	33.3249	1.26408
$696$	33.6515	1.27556
$697$	1.41309	0.0535247
$698$	2.54982	0.0965122
$699$	−7.70864	−0.291567
$700$	5.36411	0.202744
$701$	−20.3595	−0.768969	−0.384485	−	0.923131i	$-0.625621\pi$
$701$	−20.3595	−0.768969	−0.384485	+	0.923131i	$0.625621\pi$
$702$	−51.6243	−1.94843
$703$	7.83536	0.295516
$704$	−0.880559	−0.0331873
$705$	−3.76532	−0.141810
$706$	16.4763	0.620094
$707$	−25.5386	−0.960480
$708$	−8.67471	−0.326016
$709$	−36.2782	−1.36246	−0.681229	−	0.732071i	$-0.738554\pi$
$709$	−36.2782	−1.36246	−0.681229	+	0.732071i	$0.738554\pi$
$710$	82.9130	3.11167
$711$	10.0402	0.376538
$712$	99.7929	3.73990
$713$	3.56282	0.133429
$714$	−27.2442	−1.01959
$715$	61.1853	2.28820
$716$	5.51301	0.206031
$717$	4.97967	0.185969
$718$	−44.8265	−1.67291
$719$	−26.0520	−0.971575	−0.485788	−	0.874077i	$-0.661467\pi$
$719$	−26.0520	−0.971575	−0.485788	+	0.874077i	$0.661467\pi$
$720$	39.9009	1.48702
$721$	−0.960261	−0.0357620
$722$	43.2451	1.60942
$723$	14.8715	0.553077
$724$	−39.4598	−1.46651
$725$	3.01370	0.111926
$726$	41.1791	1.52830
$727$	−9.00115	−0.333834	−0.166917	−	0.985971i	$-0.553381\pi$
$727$	−9.00115	−0.333834	−0.166917	+	0.985971i	$0.553381\pi$
$728$	−77.6461	−2.87776
$729$	1.97584	0.0731794
$730$	−72.0155	−2.66541
$731$	17.8853	0.661510
$732$	14.9307	0.551855
$733$	40.7487	1.50509	0.752545	−	0.658541i	$-0.228826\pi$
$733$	40.7487	1.50509	0.752545	+	0.658541i	$0.228826\pi$
$734$	71.3426	2.63330
$735$	−0.541834	−0.0199858
$736$	−5.75737	−0.212219
$737$	15.9837	0.588769
$738$	−1.65428	−0.0608950
$739$	−2.41253	−0.0887465	−0.0443732	−	0.999015i	$-0.514129\pi$
$739$	−2.41253	−0.0887465	−0.0443732	+	0.999015i	$0.514129\pi$
$740$	57.7044	2.12126
$741$	5.40333	0.198496
$742$	11.9543	0.438856
$743$	32.1410	1.17914	0.589570	−	0.807718i	$-0.299297\pi$
$743$	32.1410	1.17914	0.589570	+	0.807718i	$0.299297\pi$
$744$	18.2980	0.670838
$745$	11.0819	0.406011
$746$	36.6528	1.34195
$747$	20.0913	0.735100
$748$	128.501	4.69846
$749$	5.06754	0.185164
$750$	21.7796	0.795277
$751$	−8.05404	−0.293896	−0.146948	−	0.989144i	$-0.546945\pi$
$751$	−8.05404	−0.293896	−0.146948	+	0.989144i	$0.546945\pi$
$752$	−14.5321	−0.529931
$753$	14.8639	0.541670
$754$	−78.5005	−2.85882
$755$	−30.2614	−1.10133
$756$	50.2538	1.82771
$757$	−31.4687	−1.14375	−0.571875	−	0.820341i	$-0.693784\pi$
$757$	−31.4687	−1.14375	−0.571875	+	0.820341i	$0.693784\pi$
$758$	76.5017	2.77867
$759$	4.48714	0.162873
$760$	−21.2877	−0.772187
$761$	−37.4118	−1.35618	−0.678088	−	0.734981i	$-0.737191\pi$
$761$	−37.4118	−1.35618	−0.678088	+	0.734981i	$0.737191\pi$
$762$	−6.60475	−0.239265
$763$	51.2684	1.85604
$764$	−92.8779	−3.36020
$765$	−28.1471	−1.01766
$766$	21.8116	0.788084
$767$	11.2453	0.406046
$768$	23.0673	0.832370
$769$	47.1971	1.70197	0.850985	−	0.525190i	$-0.176006\pi$
$769$	47.1971	1.70197	0.850985	+	0.525190i	$0.176006\pi$
$770$	−86.0231	−3.10006
$771$	−6.36790	−0.229334
$772$	−82.2130	−2.95891
$773$	49.5916	1.78369	0.891843	−	0.452346i	$-0.149413\pi$
$773$	49.5916	1.78369	0.891843	+	0.452346i	$0.149413\pi$
$774$	−20.9379	−0.752599
$775$	1.63870	0.0588639
$776$	81.2835	2.91791
$777$	11.4435	0.410534
$778$	−37.9193	−1.35947
$779$	0.394026	0.0141175
$780$	39.7935	1.42483
$781$	−77.5540	−2.77510
$782$	13.0607	0.467048
$783$	28.2339	1.00900
$784$	−2.09118	−0.0746851
$785$	−30.6468	−1.09383
$786$	−25.3150	−0.902955
$787$	44.2238	1.57641	0.788205	−	0.615413i	$-0.211011\pi$
$787$	44.2238	1.57641	0.788205	+	0.615413i	$0.211011\pi$
$788$	50.3157	1.79242
$789$	−16.9140	−0.602154
$790$	−25.4369	−0.905004
$791$	17.6545	0.627721
$792$	−83.5979	−2.97052
$793$	−19.3552	−0.687324
$794$	−19.1310	−0.678935
$795$	−3.40460	−0.120749
$796$	90.7496	3.21653
$797$	47.6432	1.68761	0.843804	−	0.536651i	$-0.180311\pi$
$797$	47.6432	1.68761	0.843804	+	0.536651i	$0.180311\pi$
$798$	−7.59678	−0.268923
$799$	10.2513	0.362665
$800$	−2.64807	−0.0936234
$801$	36.7924	1.29999
$802$	−99.0923	−3.49907
$803$	67.3608	2.37711
$804$	10.3954	0.366619
$805$	−6.05369	−0.213365
$806$	−42.6847	−1.50350
$807$	14.9816	0.527376
$808$	62.8778	2.21203
$809$	9.01054	0.316794	0.158397	−	0.987376i	$-0.449367\pi$
$809$	9.01054	0.316794	0.158397	+	0.987376i	$0.449367\pi$
$810$	21.3637	0.750644
$811$	3.10712	0.109106	0.0545529	−	0.998511i	$-0.482627\pi$
$811$	3.10712	0.109106	0.0545529	+	0.998511i	$0.482627\pi$
$812$	76.4165	2.68169
$813$	−20.3523	−0.713786
$814$	−77.9551	−2.73232
$815$	−16.3491	−0.572684
$816$	29.9463	1.04833
$817$	4.98712	0.174477
$818$	−51.0856	−1.78617
$819$	−28.6271	−1.00031
$820$	2.90185	0.101337
$821$	38.8613	1.35627	0.678134	−	0.734938i	$-0.262789\pi$
$821$	38.8613	1.35627	0.678134	+	0.734938i	$0.262789\pi$
$822$	3.86672	0.134867
$823$	25.6819	0.895216	0.447608	−	0.894230i	$-0.352276\pi$
$823$	25.6819	0.895216	0.447608	+	0.894230i	$0.352276\pi$
$824$	2.36423	0.0823617
$825$	2.06383	0.0718535
$826$	−15.8103	−0.550112
$827$	48.6896	1.69310	0.846552	−	0.532307i	$-0.178675\pi$
$827$	48.6896	1.69310	0.846552	+	0.532307i	$0.178675\pi$
$828$	−10.5864	−0.367904
$829$	21.9659	0.762906	0.381453	−	0.924388i	$-0.375424\pi$
$829$	21.9659	0.762906	0.381453	+	0.924388i	$0.375424\pi$
$830$	−50.9010	−1.76680
$831$	−22.9725	−0.796907
$832$	0.742405	0.0257383
$833$	1.47517	0.0511117
$834$	−29.2798	−1.01388
$835$	52.0806	1.80232
$836$	35.8312	1.23925
$837$	15.3522	0.530650
$838$	−33.0100	−1.14031
$839$	36.1803	1.24908	0.624541	−	0.780992i	$-0.285286\pi$
$839$	36.1803	1.24908	0.624541	+	0.780992i	$0.285286\pi$
$840$	−31.0907	−1.07273
$841$	13.9329	0.480443
$842$	74.6145	2.57139
$843$	11.5801	0.398840
$844$	−30.6635	−1.05548
$845$	−21.2092	−0.729620
$846$	−12.0010	−0.412603
$847$	51.9648	1.78553
$848$	−13.1399	−0.451226
$849$	−19.6114	−0.673063
$850$	6.00717	0.206044
$851$	−5.48592	−0.188055
$852$	−50.4393	−1.72802
$853$	−11.5104	−0.394108	−0.197054	−	0.980393i	$-0.563137\pi$
$853$	−11.5104	−0.394108	−0.197054	+	0.980393i	$0.563137\pi$
$854$	27.2124	0.931188
$855$	−7.84852	−0.268414
$856$	−12.4766	−0.426442
$857$	−42.9683	−1.46777	−0.733885	−	0.679273i	$-0.762295\pi$
$857$	−42.9683	−1.46777	−0.733885	+	0.679273i	$0.762295\pi$
$858$	−53.7585	−1.83528
$859$	−22.5726	−0.770166	−0.385083	−	0.922882i	$-0.625827\pi$
$859$	−22.5726	−0.770166	−0.385083	+	0.922882i	$0.625827\pi$
$860$	36.7282	1.25242
$861$	0.575474	0.0196121
$862$	9.69429	0.330189
$863$	6.42580	0.218737	0.109368	−	0.994001i	$-0.465117\pi$
$863$	6.42580	0.218737	0.109368	+	0.994001i	$0.465117\pi$
$864$	−24.8085	−0.844003
$865$	45.5735	1.54955
$866$	−92.6838	−3.14952
$867$	−7.43709	−0.252577
$868$	41.5515	1.41035
$869$	23.7928	0.807115
$870$	−31.4328	−1.06567
$871$	−13.4760	−0.456617
$872$	−126.226	−4.27456
$873$	29.9682	1.01427
$874$	3.64183	0.123187
$875$	27.4841	0.929132
$876$	43.8099	1.48020
$877$	48.7007	1.64451	0.822253	−	0.569123i	$-0.192717\pi$
$877$	48.7007	1.64451	0.822253	+	0.569123i	$0.192717\pi$
$878$	83.4517	2.81636
$879$	−1.95637	−0.0659867
$880$	94.5548	3.18744
$881$	−6.67843	−0.225002	−0.112501	−	0.993652i	$-0.535886\pi$
$881$	−6.67843	−0.225002	−0.112501	+	0.993652i	$0.535886\pi$
$882$	−1.72696	−0.0581497
$883$	43.7705	1.47299	0.736497	−	0.676441i	$-0.236479\pi$
$883$	43.7705	1.47299	0.736497	+	0.676441i	$0.236479\pi$
$884$	−108.340	−3.64387
$885$	4.50281	0.151360
$886$	57.4081	1.92866
$887$	40.1543	1.34825	0.674125	−	0.738617i	$-0.264521\pi$
$887$	40.1543	1.34825	0.674125	+	0.738617i	$0.264521\pi$
$888$	−28.1747	−0.945480
$889$	−8.33467	−0.279536
$890$	−93.2132	−3.12451
$891$	−19.9829	−0.669451
$892$	100.549	3.36664
$893$	2.85847	0.0956550
$894$	−9.73679	−0.325647
$895$	−2.86165	−0.0956544
$896$	28.7881	0.961742
$897$	−3.78313	−0.126315
$898$	−11.0216	−0.367794
$899$	23.3448	0.778591
$900$	−4.86918	−0.162306
$901$	9.26922	0.308803
$902$	−3.92022	−0.130529
$903$	7.28367	0.242385
$904$	−43.4665	−1.44567
$905$	20.4825	0.680862
$906$	26.5882	0.883334
$907$	−16.5618	−0.549926	−0.274963	−	0.961455i	$-0.588666\pi$
$907$	−16.5618	−0.549926	−0.274963	+	0.961455i	$0.588666\pi$
$908$	20.7584	0.688893
$909$	23.1823	0.768907
$910$	72.5267	2.40424
$911$	−31.5857	−1.04648	−0.523240	−	0.852186i	$-0.675277\pi$
$911$	−31.5857	−1.04648	−0.523240	+	0.852186i	$0.675277\pi$
$912$	8.35021	0.276503
$913$	47.6111	1.57570
$914$	21.5283	0.712092
$915$	−7.75012	−0.256211
$916$	26.7840	0.884969
$917$	−31.9455	−1.05493
$918$	56.2784	1.85746
$919$	−4.06181	−0.133987	−0.0669933	−	0.997753i	$-0.521341\pi$
$919$	−4.06181	−0.133987	−0.0669933	+	0.997753i	$0.521341\pi$
$920$	14.9046	0.491390
$921$	6.27082	0.206630
$922$	62.0025	2.04194
$923$	65.3863	2.15222
$924$	52.3313	1.72157
$925$	−2.52322	−0.0829629
$926$	21.7962	0.716269
$927$	0.871661	0.0286291
$928$	−37.7241	−1.23835
$929$	20.2801	0.665368	0.332684	−	0.943038i	$-0.392046\pi$
$929$	20.2801	0.665368	0.332684	+	0.943038i	$0.392046\pi$
$930$	−17.0916	−0.560455
$931$	0.411337	0.0134810
$932$	43.0982	1.41173
$933$	−12.9178	−0.422910
$934$	−28.3411	−0.927348
$935$	−66.7013	−2.18137
$936$	70.4819	2.30377
$937$	−8.95649	−0.292596	−0.146298	−	0.989241i	$-0.546736\pi$
$937$	−8.95649	−0.292596	−0.146298	+	0.989241i	$0.546736\pi$
$938$	18.9465	0.618625
$939$	19.4742	0.635516
$940$	21.0515	0.686626
$941$	−3.82069	−0.124551	−0.0622754	−	0.998059i	$-0.519836\pi$
$941$	−3.82069	−0.124551	−0.0622754	+	0.998059i	$0.519836\pi$
$942$	26.9268	0.877321
$943$	−0.275877	−0.00898379
$944$	17.3784	0.565618
$945$	−26.0854	−0.848557
$946$	−49.6175	−1.61321
$947$	60.7367	1.97368	0.986839	−	0.161703i	$-0.0516987\pi$
$947$	60.7367	1.97368	0.986839	+	0.161703i	$0.0516987\pi$
$948$	15.4743	0.502580
$949$	−56.7923	−1.84356
$950$	1.67504	0.0543454
$951$	15.6529	0.507579
$952$	84.6461	2.74340
$953$	12.5508	0.406562	0.203281	−	0.979120i	$-0.434840\pi$
$953$	12.5508	0.406562	0.203281	+	0.979120i	$0.434840\pi$
$954$	−10.8513	−0.351324
$955$	48.2104	1.56005
$956$	−27.8409	−0.900438
$957$	29.4011	0.950404
$958$	11.1859	0.361401
$959$	4.87949	0.157567
$960$	0.297270	0.00959435
$961$	−18.3063	−0.590525
$962$	65.7244	2.11904
$963$	−4.59997	−0.148232
$964$	−83.1452	−2.67793
$965$	42.6745	1.37374
$966$	5.31887	0.171132
$967$	−4.98598	−0.160338	−0.0801692	−	0.996781i	$-0.525546\pi$
$967$	−4.98598	−0.160338	−0.0801692	+	0.996781i	$0.525546\pi$
$968$	−127.941	−4.11217
$969$	−5.89045	−0.189229
$970$	−75.9242	−2.43778
$971$	39.4529	1.26610	0.633051	−	0.774110i	$-0.281802\pi$
$971$	39.4529	1.26610	0.633051	+	0.774110i	$0.281802\pi$
$972$	−71.1884	−2.28337
$973$	−36.9488	−1.18452
$974$	6.27015	0.200909
$975$	−1.74003	−0.0557256
$976$	−29.9112	−0.957436
$977$	9.47862	0.303248	0.151624	−	0.988438i	$-0.451550\pi$
$977$	9.47862	0.303248	0.151624	+	0.988438i	$0.451550\pi$
$978$	14.3646	0.459329
$979$	87.1885	2.78656
$980$	3.02934	0.0967687
$981$	−46.5380	−1.48584
$982$	−41.9412	−1.33840
$983$	−33.2045	−1.05906	−0.529530	−	0.848291i	$-0.677632\pi$
$983$	−33.2045	−1.05906	−0.529530	+	0.848291i	$0.677632\pi$
$984$	−1.41685	−0.0451677
$985$	−26.1175	−0.832174
$986$	85.5775	2.72534
$987$	4.17478	0.132885
$988$	−30.2095	−0.961092
$989$	−3.49173	−0.111030
$990$	78.0860	2.48174
$991$	−11.4925	−0.365071	−0.182536	−	0.983199i	$-0.558430\pi$
$991$	−11.4925	−0.365071	−0.182536	+	0.983199i	$0.558430\pi$
$992$	−20.5125	−0.651272
$993$	21.5034	0.682390
$994$	−91.9295	−2.91583
$995$	−47.1057	−1.49335
$996$	30.9651	0.981167
$997$	6.98474	0.221209	0.110604	−	0.993865i	$-0.464721\pi$
$997$	6.98474	0.221209	0.110604	+	0.993865i	$0.464721\pi$
$998$	−78.1261	−2.47304
$999$	−23.6388	−0.747899

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	8027.2.a.f.1.12	✓	176

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
8027.2.a.f.1.12	✓	176	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:	\( N \)	\(=\)	\( 8027 = 23 \cdot 349 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	8027.a (trivial)

\(f(q)\)	\(=\)	\(q-2.54982 q^{2} -0.805163 q^{3} +4.50159 q^{4} -2.33665 q^{5} +2.05302 q^{6} +2.59075 q^{7} -6.37861 q^{8} -2.35171 q^{9} +O(q^{10})\)	\(q-2.54982 q^{2} -0.805163 q^{3} +4.50159 q^{4} -2.33665 q^{5} +2.05302 q^{6} +2.59075 q^{7} -6.37861 q^{8} -2.35171 q^{9} +5.95805 q^{10} -5.57295 q^{11} -3.62451 q^{12} +4.69859 q^{13} -6.60596 q^{14} +1.88139 q^{15} +7.26113 q^{16} -5.12218 q^{17} +5.99645 q^{18} -1.42827 q^{19} -10.5186 q^{20} -2.08598 q^{21} +14.2100 q^{22} +1.00000 q^{23} +5.13582 q^{24} +0.459944 q^{25} -11.9806 q^{26} +4.30900 q^{27} +11.6625 q^{28} +6.55232 q^{29} -4.79720 q^{30} +3.56282 q^{31} -5.75737 q^{32} +4.48714 q^{33} +13.0607 q^{34} -6.05369 q^{35} -10.5864 q^{36} -5.48592 q^{37} +3.64183 q^{38} -3.78313 q^{39} +14.9046 q^{40} -0.275877 q^{41} +5.31887 q^{42} -3.49173 q^{43} -25.0871 q^{44} +5.49513 q^{45} -2.54982 q^{46} -2.00135 q^{47} -5.84639 q^{48} -0.287997 q^{49} -1.17278 q^{50} +4.12419 q^{51} +21.1511 q^{52} -1.80962 q^{53} -10.9872 q^{54} +13.0221 q^{55} -16.5254 q^{56} +1.14999 q^{57} -16.7072 q^{58} +2.39334 q^{59} +8.46923 q^{60} -4.11937 q^{61} -9.08457 q^{62} -6.09271 q^{63} +0.158006 q^{64} -10.9790 q^{65} -11.4414 q^{66} -2.86809 q^{67} -23.0580 q^{68} -0.805163 q^{69} +15.4358 q^{70} +13.9161 q^{71} +15.0006 q^{72} -12.0871 q^{73} +13.9881 q^{74} -0.370330 q^{75} -6.42947 q^{76} -14.4381 q^{77} +9.64631 q^{78} -4.26933 q^{79} -16.9667 q^{80} +3.58569 q^{81} +0.703437 q^{82} -8.54324 q^{83} -9.39022 q^{84} +11.9688 q^{85} +8.90328 q^{86} -5.27568 q^{87} +35.5477 q^{88} -15.6449 q^{89} -14.0116 q^{90} +12.1729 q^{91} +4.50159 q^{92} -2.86866 q^{93} +5.10310 q^{94} +3.33736 q^{95} +4.63562 q^{96} -12.7431 q^{97} +0.734341 q^{98} +13.1060 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 176 q + 19 q^{2} + 22 q^{3} + 203 q^{4} + 28 q^{5} + 9 q^{6} + 30 q^{7} + 51 q^{8} + 204 q^{9}+O(q^{10}) \) 176 * q + 19 * q^2 + 22 * q^3 + 203 * q^4 + 28 * q^5 + 9 * q^6 + 30 * q^7 + 51 * q^8 + 204 * q^9	\( 176 q + 19 q^{2} + 22 q^{3} + 203 q^{4} + 28 q^{5} + 9 q^{6} + 30 q^{7} + 51 q^{8} + 204 q^{9} + 18 q^{10} + 11 q^{11} + 46 q^{12} + 87 q^{13} - 6 q^{14} + 29 q^{15} + 257 q^{16} + 14 q^{17} + 72 q^{18} + 34 q^{19} + 45 q^{20} + 23 q^{21} + 62 q^{22} + 176 q^{23} + 33 q^{24} + 272 q^{25} + 31 q^{26} + 82 q^{27} + 80 q^{28} + 75 q^{29} - 30 q^{30} + 73 q^{31} + 71 q^{32} + 30 q^{33} + 23 q^{34} + 44 q^{35} + 264 q^{36} + 236 q^{37} - 21 q^{38} + 17 q^{39} + 43 q^{40} + 51 q^{41} + 38 q^{42} + 51 q^{43} + 12 q^{44} + 127 q^{45} + 19 q^{46} + 45 q^{47} + 61 q^{48} + 268 q^{49} + 55 q^{50} - 3 q^{51} + 166 q^{52} + 63 q^{53} - 32 q^{54} + 11 q^{55} - 9 q^{56} + 72 q^{57} + 98 q^{58} + 95 q^{59} - 7 q^{60} + 73 q^{61} + 12 q^{62} + 19 q^{63} + 365 q^{64} + 19 q^{65} - 28 q^{66} + 138 q^{67} + 16 q^{68} + 22 q^{69} + 100 q^{70} + 85 q^{71} + 129 q^{72} + 118 q^{73} - 21 q^{74} - 12 q^{75} + 52 q^{76} + 75 q^{77} + 97 q^{78} + 74 q^{79} + 8 q^{80} + 280 q^{81} + 67 q^{82} + 10 q^{83} - 51 q^{84} + 169 q^{85} - 39 q^{86} - 6 q^{87} + 159 q^{88} + 38 q^{89} + 22 q^{90} + 90 q^{91} + 203 q^{92} + 230 q^{93} + 63 q^{94} + 30 q^{95} + 107 q^{96} + 161 q^{97} + 58 q^{98} + 7 q^{99}+O(q^{100}) \) 176 * q + 19 * q^2 + 22 * q^3 + 203 * q^4 + 28 * q^5 + 9 * q^6 + 30 * q^7 + 51 * q^8 + 204 * q^9 + 18 * q^10 + 11 * q^11 + 46 * q^12 + 87 * q^13 - 6 * q^14 + 29 * q^15 + 257 * q^16 + 14 * q^17 + 72 * q^18 + 34 * q^19 + 45 * q^20 + 23 * q^21 + 62 * q^22 + 176 * q^23 + 33 * q^24 + 272 * q^25 + 31 * q^26 + 82 * q^27 + 80 * q^28 + 75 * q^29 - 30 * q^30 + 73 * q^31 + 71 * q^32 + 30 * q^33 + 23 * q^34 + 44 * q^35 + 264 * q^36 + 236 * q^37 - 21 * q^38 + 17 * q^39 + 43 * q^40 + 51 * q^41 + 38 * q^42 + 51 * q^43 + 12 * q^44 + 127 * q^45 + 19 * q^46 + 45 * q^47 + 61 * q^48 + 268 * q^49 + 55 * q^50 - 3 * q^51 + 166 * q^52 + 63 * q^53 - 32 * q^54 + 11 * q^55 - 9 * q^56 + 72 * q^57 + 98 * q^58 + 95 * q^59 - 7 * q^60 + 73 * q^61 + 12 * q^62 + 19 * q^63 + 365 * q^64 + 19 * q^65 - 28 * q^66 + 138 * q^67 + 16 * q^68 + 22 * q^69 + 100 * q^70 + 85 * q^71 + 129 * q^72 + 118 * q^73 - 21 * q^74 - 12 * q^75 + 52 * q^76 + 75 * q^77 + 97 * q^78 + 74 * q^79 + 8 * q^80 + 280 * q^81 + 67 * q^82 + 10 * q^83 - 51 * q^84 + 169 * q^85 - 39 * q^86 - 6 * q^87 + 159 * q^88 + 38 * q^89 + 22 * q^90 + 90 * q^91 + 203 * q^92 + 230 * q^93 + 63 * q^94 + 30 * q^95 + 107 * q^96 + 161 * q^97 + 58 * q^98 + 7 * q^99

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