LMFDB - Embedded newform 4021.2.a.b.1.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [4021,2,Mod(1,4021)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(4021, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([0]))

N = Newforms(chi, 2, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("4021.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 4021 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	4021.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:	$32.1078466528$
Analytic rank:	$1$
Dimension:	$151$
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.3
Character	$\chi$	$=$	4021.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-2.70449 q^{2} -0.271185 q^{3} +5.31424 q^{4} -1.63010 q^{5} +0.733417 q^{6} -2.12965 q^{7} -8.96332 q^{8} -2.92646 q^{9} +O(q^{10})$	\(q-2.70449 q^{2} -0.271185 q^{3} +5.31424 q^{4} -1.63010 q^{5} +0.733417 q^{6} -2.12965 q^{7} -8.96332 q^{8} -2.92646 q^{9} +4.40858 q^{10} -6.23527 q^{11} -1.44114 q^{12} +4.36501 q^{13} +5.75960 q^{14} +0.442060 q^{15} +13.6127 q^{16} +1.81989 q^{17} +7.91456 q^{18} -0.176629 q^{19} -8.66275 q^{20} +0.577529 q^{21} +16.8632 q^{22} -8.40411 q^{23} +2.43072 q^{24} -2.34277 q^{25} -11.8051 q^{26} +1.60717 q^{27} -11.3175 q^{28} +7.89677 q^{29} -1.19554 q^{30} +6.05530 q^{31} -18.8887 q^{32} +1.69091 q^{33} -4.92188 q^{34} +3.47154 q^{35} -15.5519 q^{36} +6.05738 q^{37} +0.477690 q^{38} -1.18373 q^{39} +14.6111 q^{40} +3.06792 q^{41} -1.56192 q^{42} +5.07956 q^{43} -33.1357 q^{44} +4.77042 q^{45} +22.7288 q^{46} +6.40908 q^{47} -3.69156 q^{48} -2.46460 q^{49} +6.33599 q^{50} -0.493529 q^{51} +23.1967 q^{52} +3.93397 q^{53} -4.34656 q^{54} +10.1641 q^{55} +19.0887 q^{56} +0.0478992 q^{57} -21.3567 q^{58} +9.04918 q^{59} +2.34921 q^{60} +1.65322 q^{61} -16.3765 q^{62} +6.23232 q^{63} +23.8587 q^{64} -7.11541 q^{65} -4.57305 q^{66} +13.1221 q^{67} +9.67136 q^{68} +2.27907 q^{69} -9.38873 q^{70} -2.78236 q^{71} +26.2308 q^{72} -3.16988 q^{73} -16.3821 q^{74} +0.635325 q^{75} -0.938648 q^{76} +13.2789 q^{77} +3.20137 q^{78} -10.1845 q^{79} -22.1900 q^{80} +8.34353 q^{81} -8.29715 q^{82} -5.25216 q^{83} +3.06913 q^{84} -2.96661 q^{85} -13.7376 q^{86} -2.14149 q^{87} +55.8887 q^{88} +5.26503 q^{89} -12.9015 q^{90} -9.29593 q^{91} -44.6615 q^{92} -1.64211 q^{93} -17.3333 q^{94} +0.287923 q^{95} +5.12233 q^{96} +5.69410 q^{97} +6.66549 q^{98} +18.2473 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 151 q - 16 q^{2} - 29 q^{3} + 120 q^{4} - 27 q^{5} - 18 q^{6} - 18 q^{7} - 48 q^{8} + 98 q^{9}+O(q^{10}) $ 151 * q - 16 * q^2 - 29 * q^3 + 120 * q^4 - 27 * q^5 - 18 * q^6 - 18 * q^7 - 48 * q^8 + 98 * q^9	\( 151 q - 16 q^{2} - 29 q^{3} + 120 q^{4} - 27 q^{5} - 18 q^{6} - 18 q^{7} - 48 q^{8} + 98 q^{9} - 7 q^{10} - 126 q^{11} - 47 q^{12} - 10 q^{13} - 58 q^{14} - 50 q^{15} + 74 q^{16} - 39 q^{17} - 47 q^{18} - 48 q^{19} - 64 q^{20} - 50 q^{21} - 7 q^{22} - 91 q^{23} - 44 q^{24} + 102 q^{25} - 94 q^{26} - 92 q^{27} - 27 q^{28} - 79 q^{29} - 12 q^{30} - 33 q^{31} - 102 q^{32} - 7 q^{33} - 17 q^{34} - 183 q^{35} - 6 q^{36} - 24 q^{37} - 77 q^{38} - 81 q^{39} - 37 q^{40} - 62 q^{41} + 4 q^{42} - 74 q^{43} - 209 q^{44} - 35 q^{45} - 37 q^{46} - 127 q^{47} - 59 q^{48} + 75 q^{49} - 79 q^{50} - 138 q^{51} - 12 q^{52} - 104 q^{53} - 43 q^{54} - 49 q^{55} - 167 q^{56} - 19 q^{57} - 32 q^{58} - 207 q^{59} - 94 q^{60} - 57 q^{61} - 69 q^{62} - 49 q^{63} - 4 q^{64} - 78 q^{65} - 51 q^{66} - 92 q^{67} - 80 q^{68} - 84 q^{69} + 5 q^{70} - 217 q^{71} - 79 q^{72} + 2 q^{73} - 113 q^{74} - 173 q^{75} - 70 q^{76} - 85 q^{77} - 46 q^{78} - 70 q^{79} - 95 q^{80} - 49 q^{81} - 12 q^{82} - 109 q^{83} - 114 q^{84} - 25 q^{85} - 136 q^{86} - 60 q^{87} - 2 q^{88} - 144 q^{89} - 55 q^{90} - 62 q^{91} - 175 q^{92} - 42 q^{93} - 15 q^{94} - 189 q^{95} - 64 q^{96} - 24 q^{97} - 37 q^{98} - 293 q^{99}+O(q^{100}) \) 151 * q - 16 * q^2 - 29 * q^3 + 120 * q^4 - 27 * q^5 - 18 * q^6 - 18 * q^7 - 48 * q^8 + 98 * q^9 - 7 * q^10 - 126 * q^11 - 47 * q^12 - 10 * q^13 - 58 * q^14 - 50 * q^15 + 74 * q^16 - 39 * q^17 - 47 * q^18 - 48 * q^19 - 64 * q^20 - 50 * q^21 - 7 * q^22 - 91 * q^23 - 44 * q^24 + 102 * q^25 - 94 * q^26 - 92 * q^27 - 27 * q^28 - 79 * q^29 - 12 * q^30 - 33 * q^31 - 102 * q^32 - 7 * q^33 - 17 * q^34 - 183 * q^35 - 6 * q^36 - 24 * q^37 - 77 * q^38 - 81 * q^39 - 37 * q^40 - 62 * q^41 + 4 * q^42 - 74 * q^43 - 209 * q^44 - 35 * q^45 - 37 * q^46 - 127 * q^47 - 59 * q^48 + 75 * q^49 - 79 * q^50 - 138 * q^51 - 12 * q^52 - 104 * q^53 - 43 * q^54 - 49 * q^55 - 167 * q^56 - 19 * q^57 - 32 * q^58 - 207 * q^59 - 94 * q^60 - 57 * q^61 - 69 * q^62 - 49 * q^63 - 4 * q^64 - 78 * q^65 - 51 * q^66 - 92 * q^67 - 80 * q^68 - 84 * q^69 + 5 * q^70 - 217 * q^71 - 79 * q^72 + 2 * q^73 - 113 * q^74 - 173 * q^75 - 70 * q^76 - 85 * q^77 - 46 * q^78 - 70 * q^79 - 95 * q^80 - 49 * q^81 - 12 * q^82 - 109 * q^83 - 114 * q^84 - 25 * q^85 - 136 * q^86 - 60 * q^87 - 2 * q^88 - 144 * q^89 - 55 * q^90 - 62 * q^91 - 175 * q^92 - 42 * q^93 - 15 * q^94 - 189 * q^95 - 64 * q^96 - 24 * q^97 - 37 * q^98 - 293 * 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 $

$2$	−2.70449	−1.91236	−0.956180	−	0.292779i	$-0.905420\pi$
$2$	−2.70449	−1.91236	−0.956180	+	0.292779i	$0.905420\pi$
$3$	−0.271185	−0.156569	−0.0782845	−	0.996931i	$-0.524944\pi$
$3$	−0.271185	−0.156569	−0.0782845	+	0.996931i	$0.524944\pi$
$4$	5.31424	2.65712
$5$	−1.63010	−0.729003	−0.364502	−	0.931203i	$-0.618761\pi$
$5$	−1.63010	−0.729003	−0.364502	+	0.931203i	$0.618761\pi$
$6$	0.733417	0.299416
$7$	−2.12965	−0.804931	−0.402465	−	0.915435i	$-0.631847\pi$
$7$	−2.12965	−0.804931	−0.402465	+	0.915435i	$0.631847\pi$
$8$	−8.96332	−3.16901
$9$	−2.92646	−0.975486
$10$	4.40858	1.39412
$11$	−6.23527	−1.88001	−0.940003	−	0.341167i	$-0.889178\pi$
$11$	−6.23527	−1.88001	−0.940003	+	0.341167i	$0.889178\pi$
$12$	−1.44114	−0.416023
$13$	4.36501	1.21064	0.605318	−	0.795984i	$-0.293046\pi$
$13$	4.36501	1.21064	0.605318	+	0.795984i	$0.293046\pi$
$14$	5.75960	1.53932
$15$	0.442060	0.114139
$16$	13.6127	3.40317
$17$	1.81989	0.441389	0.220695	−	0.975343i	$-0.429168\pi$
$17$	1.81989	0.441389	0.220695	+	0.975343i	$0.429168\pi$
$18$	7.91456	1.86548
$19$	−0.176629	−0.0405214	−0.0202607	−	0.999795i	$-0.506450\pi$
$19$	−0.176629	−0.0405214	−0.0202607	+	0.999795i	$0.506450\pi$
$20$	−8.66275	−1.93705
$21$	0.577529	0.126027
$22$	16.8632	3.59525
$23$	−8.40411	−1.75238	−0.876189	−	0.481967i	$-0.839922\pi$
$23$	−8.40411	−1.75238	−0.876189	+	0.481967i	$0.839922\pi$
$24$	2.43072	0.496169
$25$	−2.34277	−0.468554
$26$	−11.8051	−2.31517
$27$	1.60717	0.309300
$28$	−11.3175	−2.13880
$29$	7.89677	1.46639	0.733197	−	0.680016i	$-0.238027\pi$
$29$	7.89677	1.46639	0.733197	+	0.680016i	$0.238027\pi$
$30$	−1.19554	−0.218275
$31$	6.05530	1.08756	0.543782	−	0.839226i	$-0.316992\pi$
$31$	6.05530	1.08756	0.543782	+	0.839226i	$0.316992\pi$
$32$	−18.8887	−3.33907
$33$	1.69091	0.294350
$34$	−4.92188	−0.844095
$35$	3.47154	0.586797
$36$	−15.5519	−2.59198
$37$	6.05738	0.995826	0.497913	−	0.867227i	$-0.334100\pi$
$37$	6.05738	0.995826	0.497913	+	0.867227i	$0.334100\pi$
$38$	0.477690	0.0774916
$39$	−1.18373	−0.189548
$40$	14.6111	2.31022
$41$	3.06792	0.479129	0.239564	−	0.970880i	$-0.422995\pi$
$41$	3.06792	0.479129	0.239564	+	0.970880i	$0.422995\pi$
$42$	−1.56192	−0.241009
$43$	5.07956	0.774626	0.387313	−	0.921948i	$-0.373403\pi$
$43$	5.07956	0.774626	0.387313	+	0.921948i	$0.373403\pi$
$44$	−33.1357	−4.99540
$45$	4.77042	0.711133
$46$	22.7288	3.35118
$47$	6.40908	0.934861	0.467430	−	0.884030i	$-0.345180\pi$
$47$	6.40908	0.934861	0.467430	+	0.884030i	$0.345180\pi$
$48$	−3.69156	−0.532831
$49$	−2.46460	−0.352086
$50$	6.33599	0.896044
$51$	−0.493529	−0.0691078
$52$	23.1967	3.21680
$53$	3.93397	0.540373	0.270186	−	0.962808i	$-0.412915\pi$
$53$	3.93397	0.540373	0.270186	+	0.962808i	$0.412915\pi$
$54$	−4.34656	−0.591492
$55$	10.1641	1.37053
$56$	19.0887	2.55083
$57$	0.0478992	0.00634440
$58$	−21.3567	−2.80427
$59$	9.04918	1.17810	0.589052	−	0.808095i	$-0.299501\pi$
$59$	9.04918	1.17810	0.589052	+	0.808095i	$0.299501\pi$
$60$	2.34921	0.303282
$61$	1.65322	0.211673	0.105837	−	0.994384i	$-0.466248\pi$
$61$	1.65322	0.211673	0.105837	+	0.994384i	$0.466248\pi$
$62$	−16.3765	−2.07981
$63$	6.23232	0.785199
$64$	23.8587	2.98234
$65$	−7.11541	−0.882557
$66$	−4.57305	−0.562904
$67$	13.1221	1.60312	0.801559	−	0.597915i	$-0.204004\pi$
$67$	13.1221	1.60312	0.801559	+	0.597915i	$0.204004\pi$
$68$	9.67136	1.17282
$69$	2.27907	0.274368
$70$	−9.38873	−1.12217
$71$	−2.78236	−0.330205	−0.165103	−	0.986276i	$-0.552796\pi$
$71$	−2.78236	−0.330205	−0.165103	+	0.986276i	$0.552796\pi$
$72$	26.2308	3.09133
$73$	−3.16988	−0.371006	−0.185503	−	0.982644i	$-0.559391\pi$
$73$	−3.16988	−0.371006	−0.185503	+	0.982644i	$0.559391\pi$
$74$	−16.3821	−1.90438
$75$	0.635325	0.0733610
$76$	−0.938648	−0.107670
$77$	13.2789	1.51327
$78$	3.20137	0.362484
$79$	−10.1845	−1.14584	−0.572921	−	0.819611i	$-0.694190\pi$
$79$	−10.1845	−1.14584	−0.572921	+	0.819611i	$0.694190\pi$
$80$	−22.1900	−2.48092
$81$	8.34353	0.927059
$82$	−8.29715	−0.916267
$83$	−5.25216	−0.576499	−0.288249	−	0.957555i	$-0.593073\pi$
$83$	−5.25216	−0.576499	−0.288249	+	0.957555i	$0.593073\pi$
$84$	3.06913	0.334869
$85$	−2.96661	−0.321774
$86$	−13.7376	−1.48136
$87$	−2.14149	−0.229592
$88$	55.8887	5.95776
$89$	5.26503	0.558092	0.279046	−	0.960278i	$-0.409982\pi$
$89$	5.26503	0.558092	0.279046	+	0.960278i	$0.409982\pi$
$90$	−12.9015	−1.35994
$91$	−9.29593	−0.974478
$92$	−44.6615	−4.65628
$93$	−1.64211	−0.170279
$94$	−17.3333	−1.78779
$95$	0.287923	0.0295403
$96$	5.12233	0.522795
$97$	5.69410	0.578149	0.289074	−	0.957307i	$-0.406653\pi$
$97$	5.69410	0.578149	0.289074	+	0.957307i	$0.406653\pi$
$98$	6.66549	0.673316
$99$	18.2473	1.83392
$100$	−12.4500	−1.24500
$101$	−14.5906	−1.45182	−0.725908	−	0.687792i	$-0.758580\pi$
$101$	−14.5906	−1.45182	−0.725908	+	0.687792i	$0.758580\pi$
$102$	1.33474	0.132159
$103$	−15.8055	−1.55736	−0.778681	−	0.627421i	$-0.784111\pi$
$103$	−15.8055	−1.55736	−0.778681	+	0.627421i	$0.784111\pi$
$104$	−39.1250	−3.83652
$105$	−0.941431	−0.0918742
$106$	−10.6394	−1.03339
$107$	−13.4255	−1.29789	−0.648945	−	0.760835i	$-0.724790\pi$
$107$	−13.4255	−1.29789	−0.648945	+	0.760835i	$0.724790\pi$
$108$	8.54088	0.821847
$109$	−3.25307	−0.311588	−0.155794	−	0.987790i	$-0.549794\pi$
$109$	−3.25307	−0.311588	−0.155794	+	0.987790i	$0.549794\pi$
$110$	−27.4887	−2.62095
$111$	−1.64267	−0.155915
$112$	−28.9902	−2.73932
$113$	−14.4975	−1.36381	−0.681904	−	0.731441i	$-0.738848\pi$
$113$	−14.4975	−1.36381	−0.681904	+	0.731441i	$0.738848\pi$
$114$	−0.129543	−0.0121328
$115$	13.6996	1.27749
$116$	41.9654	3.89639
$117$	−12.7740	−1.18096
$118$	−24.4734	−2.25296
$119$	−3.87573	−0.355288
$120$	−3.96232	−0.361709
$121$	27.8786	2.53442
$122$	−4.47111	−0.404795
$123$	−0.831975	−0.0750167
$124$	32.1793	2.88979
$125$	11.9695	1.07058
$126$	−16.8552	−1.50158
$127$	−4.51970	−0.401059	−0.200529	−	0.979688i	$-0.564266\pi$
$127$	−4.51970	−0.401059	−0.200529	+	0.979688i	$0.564266\pi$
$128$	−26.7483	−2.36424
$129$	−1.37750	−0.121282
$130$	19.2435	1.68777
$131$	16.4235	1.43493	0.717463	−	0.696596i	$-0.245303\pi$
$131$	16.4235	1.43493	0.717463	+	0.696596i	$0.245303\pi$
$132$	8.98593	0.782125
$133$	0.376157	0.0326170
$134$	−35.4885	−3.06574
$135$	−2.61985	−0.225481
$136$	−16.3123	−1.39877
$137$	−5.75902	−0.492027	−0.246013	−	0.969266i	$-0.579121\pi$
$137$	−5.75902	−0.492027	−0.246013	+	0.969266i	$0.579121\pi$
$138$	−6.16372	−0.524691
$139$	−16.3656	−1.38811	−0.694057	−	0.719920i	$-0.744179\pi$
$139$	−16.3656	−1.38811	−0.694057	+	0.719920i	$0.744179\pi$
$140$	18.4486	1.55919
$141$	−1.73805	−0.146370
$142$	7.52485	0.631472
$143$	−27.2170	−2.27600
$144$	−39.8369	−3.31975
$145$	−12.8725	−1.06901
$146$	8.57289	0.709497
$147$	0.668365	0.0551258
$148$	32.1904	2.64603
$149$	−3.56574	−0.292117	−0.146059	−	0.989276i	$-0.546659\pi$
$149$	−3.56574	−0.292117	−0.146059	+	0.989276i	$0.546659\pi$
$150$	−1.71823	−0.140293
$151$	−14.1852	−1.15438	−0.577189	−	0.816611i	$-0.695850\pi$
$151$	−14.1852	−1.15438	−0.577189	+	0.816611i	$0.695850\pi$
$152$	1.58318	0.128413
$153$	−5.32585	−0.430569
$154$	−35.9127	−2.89392
$155$	−9.87076	−0.792838
$156$	−6.29061	−0.503652
$157$	23.6791	1.88980	0.944898	−	0.327364i	$-0.106160\pi$
$157$	23.6791	1.88980	0.944898	+	0.327364i	$0.106160\pi$
$158$	27.5437	2.19126
$159$	−1.06684	−0.0846056
$160$	30.7904	2.43420
$161$	17.8978	1.41054
$162$	−22.5650	−1.77287
$163$	6.16533	0.482906	0.241453	−	0.970413i	$-0.422376\pi$
$163$	6.16533	0.482906	0.241453	+	0.970413i	$0.422376\pi$
$164$	16.3037	1.27310
$165$	−2.75636	−0.214582
$166$	14.2044	1.10247
$167$	3.16606	0.244997	0.122499	−	0.992469i	$-0.460909\pi$
$167$	3.16606	0.244997	0.122499	+	0.992469i	$0.460909\pi$
$168$	−5.17658	−0.399381
$169$	6.05330	0.465639
$170$	8.02316	0.615348
$171$	0.516897	0.0395281
$172$	26.9940	2.05827
$173$	13.6640	1.03886	0.519429	−	0.854514i	$-0.326145\pi$
$173$	13.6640	1.03886	0.519429	+	0.854514i	$0.326145\pi$
$174$	5.79163	0.439062
$175$	4.98927	0.377154
$176$	−84.8787	−6.39798
$177$	−2.45401	−0.184454
$178$	−14.2392	−1.06727
$179$	0.132345	0.00989195	0.00494597	−	0.999988i	$-0.498426\pi$
$179$	0.132345	0.00989195	0.00494597	+	0.999988i	$0.498426\pi$
$180$	25.3512	1.88957
$181$	0.785353	0.0583748	0.0291874	−	0.999574i	$-0.490708\pi$
$181$	0.785353	0.0583748	0.0291874	+	0.999574i	$0.490708\pi$
$182$	25.1407	1.86355
$183$	−0.448329	−0.0331414
$184$	75.3287	5.55331
$185$	−9.87414	−0.725961
$186$	4.44106	0.325634
$187$	−11.3475	−0.829814
$188$	34.0594	2.48404
$189$	−3.42270	−0.248965
$190$	−0.778683	−0.0564916
$191$	−2.63857	−0.190920	−0.0954600	−	0.995433i	$-0.530432\pi$
$191$	−2.63857	−0.190920	−0.0954600	+	0.995433i	$0.530432\pi$
$192$	−6.47014	−0.466942
$193$	12.2264	0.880073	0.440036	−	0.897980i	$-0.354966\pi$
$193$	12.2264	0.880073	0.440036	+	0.897980i	$0.354966\pi$
$194$	−15.3996	−1.10563
$195$	1.92959	0.138181
$196$	−13.0975	−0.935536
$197$	7.42826	0.529242	0.264621	−	0.964353i	$-0.414753\pi$
$197$	7.42826	0.529242	0.264621	+	0.964353i	$0.414753\pi$
$198$	−49.3495	−3.50711
$199$	−15.2049	−1.07785	−0.538923	−	0.842355i	$-0.681169\pi$
$199$	−15.2049	−1.07785	−0.538923	+	0.842355i	$0.681169\pi$
$200$	20.9990	1.48485
$201$	−3.55852	−0.250999
$202$	39.4600	2.77639
$203$	−16.8173	−1.18035
$204$	−2.62273	−0.183628
$205$	−5.00102	−0.349287
$206$	42.7457	2.97824
$207$	24.5943	1.70942
$208$	59.4195	4.12000
$209$	1.10133	0.0761805
$210$	2.54609	0.175697
$211$	−25.2006	−1.73488	−0.867442	−	0.497539i	$-0.834237\pi$
$211$	−25.2006	−1.73488	−0.867442	+	0.497539i	$0.834237\pi$
$212$	20.9061	1.43584
$213$	0.754535	0.0516999
$214$	36.3090	2.48203
$215$	−8.28020	−0.564705
$216$	−14.4056	−0.980174
$217$	−12.8957	−0.875414
$218$	8.79789	0.595868
$219$	0.859624	0.0580880
$220$	54.0146	3.64166
$221$	7.94385	0.534362
$222$	4.44258	0.298167
$223$	−13.7020	−0.917551	−0.458775	−	0.888552i	$-0.651712\pi$
$223$	−13.7020	−0.917551	−0.458775	+	0.888552i	$0.651712\pi$
$224$	40.2262	2.68772
$225$	6.85602	0.457068
$226$	39.2082	2.60809
$227$	10.8662	0.721217	0.360609	−	0.932717i	$-0.382569\pi$
$227$	10.8662	0.721217	0.360609	+	0.932717i	$0.382569\pi$
$228$	0.254548	0.0168578
$229$	−0.0623647	−0.00412117	−0.00206059	−	0.999998i	$-0.500656\pi$
$229$	−0.0623647	−0.00412117	−0.00206059	+	0.999998i	$0.500656\pi$
$230$	−37.0502	−2.44302
$231$	−3.60105	−0.236932
$232$	−70.7813	−4.64702
$233$	−4.33584	−0.284050	−0.142025	−	0.989863i	$-0.545361\pi$
$233$	−4.33584	−0.284050	−0.142025	+	0.989863i	$0.545361\pi$
$234$	34.5471	2.25842
$235$	−10.4475	−0.681517
$236$	48.0895	3.13036
$237$	2.76188	0.179403
$238$	10.4819	0.679438
$239$	8.34926	0.540069	0.270034	−	0.962851i	$-0.412965\pi$
$239$	8.34926	0.540069	0.270034	+	0.962851i	$0.412965\pi$
$240$	6.01761	0.388435
$241$	−5.25026	−0.338199	−0.169100	−	0.985599i	$-0.554086\pi$
$241$	−5.25026	−0.338199	−0.169100	+	0.985599i	$0.554086\pi$
$242$	−75.3973	−4.84672
$243$	−7.08415	−0.454448
$244$	8.78561	0.562441
$245$	4.01756	0.256672
$246$	2.25006	0.143459
$247$	−0.770986	−0.0490567
$248$	−54.2756	−3.44650
$249$	1.42431	0.0902618
$250$	−32.3712	−2.04734
$251$	−17.4199	−1.09953	−0.549766	−	0.835319i	$-0.685283\pi$
$251$	−17.4199	−1.09953	−0.549766	+	0.835319i	$0.685283\pi$
$252$	33.1201	2.08637
$253$	52.4019	3.29448
$254$	12.2235	0.766969
$255$	0.804502	0.0503799
$256$	24.6229	1.53893
$257$	6.21874	0.387914	0.193957	−	0.981010i	$-0.437868\pi$
$257$	6.21874	0.387914	0.193957	+	0.981010i	$0.437868\pi$
$258$	3.72544	0.231935
$259$	−12.9001	−0.801571
$260$	−37.8130	−2.34506
$261$	−23.1096	−1.43045
$262$	−44.4171	−2.74410
$263$	18.1431	1.11875	0.559376	−	0.828914i	$-0.311041\pi$
$263$	18.1431	1.11875	0.559376	+	0.828914i	$0.311041\pi$
$264$	−15.1562	−0.932800
$265$	−6.41277	−0.393933
$266$	−1.01731	−0.0623754
$267$	−1.42780	−0.0873799
$268$	69.7340	4.25968
$269$	−5.16225	−0.314748	−0.157374	−	0.987539i	$-0.550303\pi$
$269$	−5.16225	−0.314748	−0.157374	+	0.987539i	$0.550303\pi$
$270$	7.08534	0.431200
$271$	−1.82094	−0.110615	−0.0553073	−	0.998469i	$-0.517614\pi$
$271$	−1.82094	−0.110615	−0.0553073	+	0.998469i	$0.517614\pi$
$272$	24.7736	1.50212
$273$	2.52092	0.152573
$274$	15.5752	0.940932
$275$	14.6078	0.880884
$276$	12.1115	0.729029
$277$	−17.5231	−1.05286	−0.526430	−	0.850219i	$-0.676470\pi$
$277$	−17.5231	−1.05286	−0.526430	+	0.850219i	$0.676470\pi$
$278$	44.2606	2.65457
$279$	−17.7206	−1.06090
$280$	−31.1165	−1.85957
$281$	−18.8288	−1.12323	−0.561616	−	0.827398i	$-0.689820\pi$
$281$	−18.8288	−1.12323	−0.561616	+	0.827398i	$0.689820\pi$
$282$	4.70053	0.279912
$283$	33.3705	1.98367	0.991834	−	0.127533i	$-0.0407058\pi$
$283$	33.3705	1.98367	0.991834	+	0.127533i	$0.0407058\pi$
$284$	−14.7861	−0.877396
$285$	−0.0780805	−0.00462509
$286$	73.6080	4.35253
$287$	−6.53359	−0.385666
$288$	55.2769	3.25722
$289$	−13.6880	−0.805176
$290$	34.8136	2.04432
$291$	−1.54416	−0.0905201
$292$	−16.8455	−0.985808
$293$	31.0999	1.81687	0.908437	−	0.418021i	$-0.137276\pi$
$293$	31.0999	1.81687	0.908437	+	0.418021i	$0.137276\pi$
$294$	−1.80758	−0.105420
$295$	−14.7511	−0.858841
$296$	−54.2942	−3.15579
$297$	−10.0211	−0.581485
$298$	9.64350	0.558633
$299$	−36.6840	−2.12149
$300$	3.37627	0.194929
$301$	−10.8177	−0.623520
$302$	38.3637	2.20759
$303$	3.95675	0.227309
$304$	−2.40439	−0.137901
$305$	−2.69492	−0.154310
$306$	14.4037	0.823403
$307$	−0.179128	−0.0102234	−0.00511170	−	0.999987i	$-0.501627\pi$
$307$	−0.179128	−0.0102234	−0.00511170	+	0.999987i	$0.501627\pi$
$308$	70.5674	4.02095
$309$	4.28622	0.243834
$310$	26.6953	1.51619
$311$	−9.40073	−0.533067	−0.266533	−	0.963826i	$-0.585878\pi$
$311$	−9.40073	−0.533067	−0.266533	+	0.963826i	$0.585878\pi$
$312$	10.6101	0.600680
$313$	−2.12002	−0.119831	−0.0599154	−	0.998203i	$-0.519083\pi$
$313$	−2.12002	−0.119831	−0.0599154	+	0.998203i	$0.519083\pi$
$314$	−64.0397	−3.61397
$315$	−10.1593	−0.572413
$316$	−54.1227	−3.04464
$317$	−0.706006	−0.0396533	−0.0198266	−	0.999803i	$-0.506311\pi$
$317$	−0.706006	−0.0396533	−0.0198266	+	0.999803i	$0.506311\pi$
$318$	2.88524	0.161796
$319$	−49.2385	−2.75683
$320$	−38.8922	−2.17414
$321$	3.64079	0.203209
$322$	−48.4043	−2.69747
$323$	−0.321446	−0.0178857
$324$	44.3396	2.46331
$325$	−10.2262	−0.567248
$326$	−16.6740	−0.923490
$327$	0.882186	0.0487850
$328$	−27.4988	−1.51836
$329$	−13.6491	−0.752498
$330$	7.45454	0.410359
$331$	−23.2180	−1.27618	−0.638088	−	0.769963i	$-0.720274\pi$
$331$	−23.2180	−1.27618	−0.638088	+	0.769963i	$0.720274\pi$
$332$	−27.9112	−1.53183
$333$	−17.7267	−0.971415
$334$	−8.56256	−0.468522
$335$	−21.3903	−1.16868
$336$	7.86172	0.428892
$337$	34.2565	1.86607	0.933036	−	0.359783i	$-0.117149\pi$
$337$	34.2565	1.86607	0.933036	+	0.359783i	$0.117149\pi$
$338$	−16.3711	−0.890469
$339$	3.93151	0.213530
$340$	−15.7653	−0.854993
$341$	−37.7565	−2.04463
$342$	−1.39794	−0.0755920
$343$	20.1563	1.08834
$344$	−45.5297	−2.45480
$345$	−3.71512	−0.200015
$346$	−36.9542	−1.98667
$347$	8.19742	0.440061	0.220030	−	0.975493i	$-0.429384\pi$
$347$	8.19742	0.440061	0.220030	+	0.975493i	$0.429384\pi$
$348$	−11.3804	−0.610053
$349$	2.00100	0.107111	0.0535556	−	0.998565i	$-0.482945\pi$
$349$	2.00100	0.107111	0.0535556	+	0.998565i	$0.482945\pi$
$350$	−13.4934	−0.721253
$351$	7.01531	0.374449
$352$	117.776	6.27748
$353$	22.0398	1.17306	0.586530	−	0.809927i	$-0.300493\pi$
$353$	22.0398	1.17306	0.586530	+	0.809927i	$0.300493\pi$
$354$	6.63682	0.352743
$355$	4.53553	0.240721
$356$	27.9796	1.48292
$357$	1.05104	0.0556270
$358$	−0.357926	−0.0189170
$359$	11.6372	0.614188	0.307094	−	0.951679i	$-0.400643\pi$
$359$	11.6372	0.614188	0.307094	+	0.951679i	$0.400643\pi$
$360$	−42.7588	−2.25359
$361$	−18.9688	−0.998358
$362$	−2.12398	−0.111634
$363$	−7.56027	−0.396811
$364$	−49.4008	−2.58931
$365$	5.16722	0.270465
$366$	1.21250	0.0633784
$367$	−3.32571	−0.173601	−0.0868003	−	0.996226i	$-0.527664\pi$
$367$	−3.32571	−0.173601	−0.0868003	+	0.996226i	$0.527664\pi$
$368$	−114.402	−5.96364
$369$	−8.97814	−0.467384
$370$	26.7045	1.38830
$371$	−8.37797	−0.434963
$372$	−8.72657	−0.452451
$373$	−6.94512	−0.359605	−0.179802	−	0.983703i	$-0.557546\pi$
$373$	−6.94512	−0.359605	−0.179802	+	0.983703i	$0.557546\pi$
$374$	30.6892	1.58690
$375$	−3.24594	−0.167620
$376$	−57.4466	−2.96258
$377$	34.4695	1.77527
$378$	9.25665	0.476111
$379$	34.4727	1.77075	0.885373	−	0.464881i	$-0.153903\pi$
$379$	34.4727	1.77075	0.885373	+	0.464881i	$0.153903\pi$
$380$	1.53009	0.0784921
$381$	1.22568	0.0627934
$382$	7.13596	0.365108
$383$	−29.5114	−1.50796	−0.753980	−	0.656897i	$-0.771868\pi$
$383$	−29.5114	−1.50796	−0.753980	+	0.656897i	$0.771868\pi$
$384$	7.25375	0.370166
$385$	−21.6460	−1.10318
$386$	−33.0660	−1.68302
$387$	−14.8651	−0.755637
$388$	30.2598	1.53621
$389$	4.10346	0.208054	0.104027	−	0.994574i	$-0.466827\pi$
$389$	4.10346	0.208054	0.104027	+	0.994574i	$0.466827\pi$
$390$	−5.21856	−0.264252
$391$	−15.2946	−0.773481
$392$	22.0910	1.11577
$393$	−4.45381	−0.224665
$394$	−20.0896	−1.01210
$395$	16.6017	0.835322
$396$	96.9704	4.87294
$397$	−10.9177	−0.547943	−0.273971	−	0.961738i	$-0.588337\pi$
$397$	−10.9177	−0.547943	−0.273971	+	0.961738i	$0.588337\pi$
$398$	41.1214	2.06123
$399$	−0.102008	−0.00510680
$400$	−31.8914	−1.59457
$401$	20.0604	1.00177	0.500884	−	0.865514i	$-0.333008\pi$
$401$	20.0604	1.00177	0.500884	+	0.865514i	$0.333008\pi$
$402$	9.62396	0.480000
$403$	26.4314	1.31664
$404$	−77.5378	−3.85765
$405$	−13.6008	−0.675829
$406$	45.4822	2.25725
$407$	−37.7694	−1.87216
$408$	4.42365	0.219004
$409$	−23.5312	−1.16355	−0.581773	−	0.813351i	$-0.697641\pi$
$409$	−23.5312	−1.16355	−0.581773	+	0.813351i	$0.697641\pi$
$410$	13.5252	0.667962
$411$	1.56176	0.0770361
$412$	−83.9942	−4.13810
$413$	−19.2716	−0.948291
$414$	−66.5149	−3.26903
$415$	8.56154	0.420270
$416$	−82.4492	−4.04240
$417$	4.43812	0.217336
$418$	−2.97853	−0.145685
$419$	22.7654	1.11216	0.556080	−	0.831128i	$-0.312305\pi$
$419$	22.7654	1.11216	0.556080	+	0.831128i	$0.312305\pi$
$420$	−5.00299	−0.244121
$421$	23.1595	1.12872	0.564362	−	0.825527i	$-0.309122\pi$
$421$	23.1595	1.12872	0.564362	+	0.825527i	$0.309122\pi$
$422$	68.1547	3.31772
$423$	−18.7559	−0.911944
$424$	−35.2614	−1.71245
$425$	−4.26359	−0.206815
$426$	−2.04063	−0.0988688
$427$	−3.52078	−0.170382
$428$	−71.3463	−3.44865
$429$	7.38086	0.356351
$430$	22.3937	1.07992
$431$	27.8829	1.34307	0.671536	−	0.740972i	$-0.265635\pi$
$431$	27.8829	1.34307	0.671536	+	0.740972i	$0.265635\pi$
$432$	21.8779	1.05260
$433$	11.2787	0.542021	0.271010	−	0.962576i	$-0.412642\pi$
$433$	11.2787	0.542021	0.271010	+	0.962576i	$0.412642\pi$
$434$	34.8761	1.67411
$435$	3.49084	0.167373
$436$	−17.2876	−0.827927
$437$	1.48441	0.0710089
$438$	−2.32484	−0.111085
$439$	−39.8877	−1.90374	−0.951868	−	0.306508i	$-0.900839\pi$
$439$	−39.8877	−1.90374	−0.951868	+	0.306508i	$0.900839\pi$
$440$	−91.1043	−4.34323
$441$	7.21256	0.343455
$442$	−21.4840	−1.02189
$443$	22.5438	1.07109	0.535545	−	0.844507i	$-0.320106\pi$
$443$	22.5438	1.07109	0.535545	+	0.844507i	$0.320106\pi$
$444$	−8.72955	−0.414286
$445$	−8.58253	−0.406851
$446$	37.0567	1.75469
$447$	0.966978	0.0457365
$448$	−50.8107	−2.40058
$449$	−18.6748	−0.881318	−0.440659	−	0.897675i	$-0.645255\pi$
$449$	−18.6748	−0.881318	−0.440659	+	0.897675i	$0.645255\pi$
$450$	−18.5420	−0.874078
$451$	−19.1293	−0.900765
$452$	−77.0431	−3.62380
$453$	3.84683	0.180740
$454$	−29.3876	−1.37923
$455$	15.1533	0.710398
$456$	−0.429335	−0.0201055
$457$	−20.6098	−0.964085	−0.482043	−	0.876148i	$-0.660105\pi$
$457$	−20.6098	−0.964085	−0.482043	+	0.876148i	$0.660105\pi$
$458$	0.168664	0.00788117
$459$	2.92488	0.136522
$460$	72.8027	3.39445
$461$	−31.3892	−1.46194	−0.730971	−	0.682408i	$-0.760933\pi$
$461$	−31.3892	−1.46194	−0.730971	+	0.682408i	$0.760933\pi$
$462$	9.73899	0.453099
$463$	−5.62581	−0.261453	−0.130727	−	0.991418i	$-0.541731\pi$
$463$	−5.62581	−0.261453	−0.130727	+	0.991418i	$0.541731\pi$
$464$	107.496	4.99039
$465$	2.67680	0.124134
$466$	11.7262	0.543206
$467$	−13.8306	−0.640005	−0.320002	−	0.947417i	$-0.603684\pi$
$467$	−13.8306	−0.640005	−0.320002	+	0.947417i	$0.603684\pi$
$468$	−67.8842	−3.13795
$469$	−27.9454	−1.29040
$470$	28.2550	1.30331
$471$	−6.42142	−0.295883
$472$	−81.1107	−3.73342
$473$	−31.6724	−1.45630
$474$	−7.46946	−0.343084
$475$	0.413801	0.0189865
$476$	−20.5966	−0.944043
$477$	−11.5126	−0.527126
$478$	−22.5804	−1.03281
$479$	4.11177	0.187872	0.0939358	−	0.995578i	$-0.470055\pi$
$479$	4.11177	0.187872	0.0939358	+	0.995578i	$0.470055\pi$
$480$	−8.34991	−0.381120
$481$	26.4405	1.20558
$482$	14.1993	0.646759
$483$	−4.85362	−0.220847
$484$	148.154	6.73426
$485$	−9.28196	−0.421472
$486$	19.1590	0.869069
$487$	33.5692	1.52117	0.760583	−	0.649240i	$-0.224913\pi$
$487$	33.5692	1.52117	0.760583	+	0.649240i	$0.224913\pi$
$488$	−14.8183	−0.670795
$489$	−1.67195	−0.0756080
$490$	−10.8654	−0.490850
$491$	−33.7505	−1.52314	−0.761569	−	0.648084i	$-0.775571\pi$
$491$	−33.7505	−1.52314	−0.761569	+	0.648084i	$0.775571\pi$
$492$	−4.42132	−0.199328
$493$	14.3713	0.647251
$494$	2.08512	0.0938141
$495$	−29.7449	−1.33693
$496$	82.4289	3.70117
$497$	5.92545	0.265793
$498$	−3.85202	−0.172613
$499$	6.28487	0.281349	0.140675	−	0.990056i	$-0.455073\pi$
$499$	6.28487	0.281349	0.140675	+	0.990056i	$0.455073\pi$
$500$	63.6086	2.84466
$501$	−0.858589	−0.0383589
$502$	47.1118	2.10270
$503$	−37.3118	−1.66365	−0.831826	−	0.555036i	$-0.812704\pi$
$503$	−37.3118	−1.66365	−0.831826	+	0.555036i	$0.812704\pi$
$504$	−55.8623	−2.48830
$505$	23.7841	1.05838
$506$	−141.720	−6.30023
$507$	−1.64157	−0.0729045
$508$	−24.0188	−1.06566
$509$	−7.07888	−0.313766	−0.156883	−	0.987617i	$-0.550145\pi$
$509$	−7.07888	−0.313766	−0.156883	+	0.987617i	$0.550145\pi$
$510$	−2.17576	−0.0963444
$511$	6.75072	0.298634
$512$	−13.0957	−0.578753
$513$	−0.283872	−0.0125333
$514$	−16.8185	−0.741832
$515$	25.7645	1.13532
$516$	−7.32038	−0.322262
$517$	−39.9624	−1.75754
$518$	34.8881	1.53289
$519$	−3.70548	−0.162653
$520$	63.7776	2.79683
$521$	−27.3902	−1.19999	−0.599994	−	0.800005i	$-0.704830\pi$
$521$	−27.3902	−1.19999	−0.599994	+	0.800005i	$0.704830\pi$
$522$	62.4995	2.73553
$523$	−24.5863	−1.07508	−0.537542	−	0.843237i	$-0.680647\pi$
$523$	−24.5863	−1.07508	−0.537542	+	0.843237i	$0.680647\pi$
$524$	87.2784	3.81277
$525$	−1.35302	−0.0590505
$526$	−49.0678	−2.13946
$527$	11.0200	0.480039
$528$	23.0179	1.00172
$529$	47.6291	2.07083
$530$	17.3432	0.753343
$531$	−26.4821	−1.14922
$532$	1.99899	0.0866672
$533$	13.3915	0.580050
$534$	3.86146	0.167102
$535$	21.8849	0.946167
$536$	−117.617	−5.08030
$537$	−0.0358901	−0.00154877
$538$	13.9612	0.601911
$539$	15.3675	0.661924
$540$	−13.9225	−0.599129
$541$	−0.768457	−0.0330386	−0.0165193	−	0.999864i	$-0.505258\pi$
$541$	−0.768457	−0.0330386	−0.0165193	+	0.999864i	$0.505258\pi$
$542$	4.92472	0.211535
$543$	−0.212976	−0.00913968
$544$	−34.3754	−1.47383
$545$	5.30284	0.227149
$546$	−6.81779	−0.291774
$547$	37.8236	1.61722	0.808610	−	0.588345i	$-0.200220\pi$
$547$	37.8236	1.61722	0.808610	+	0.588345i	$0.200220\pi$
$548$	−30.6048	−1.30737
$549$	−4.83808	−0.206484
$550$	−39.5066	−1.68457
$551$	−1.39480	−0.0594204
$552$	−20.4280	−0.869476
$553$	21.6893	0.922323
$554$	47.3909	2.01345
$555$	2.67772	0.113663
$556$	−86.9709	−3.68839
$557$	10.4236	0.441664	0.220832	−	0.975312i	$-0.429123\pi$
$557$	10.4236	0.441664	0.220832	+	0.975312i	$0.429123\pi$
$558$	47.9251	2.02883
$559$	22.1723	0.937790
$560$	47.2570	1.99697
$561$	3.07729	0.129923
$562$	50.9223	2.14803
$563$	41.8950	1.76566	0.882832	−	0.469690i	$-0.155634\pi$
$563$	41.8950	1.76566	0.882832	+	0.469690i	$0.155634\pi$
$564$	−9.23641	−0.388923
$565$	23.6324	0.994221
$566$	−90.2500	−3.79349
$567$	−17.7688	−0.746219
$568$	24.9392	1.04642
$569$	−21.9400	−0.919773	−0.459887	−	0.887978i	$-0.652110\pi$
$569$	−21.9400	−0.919773	−0.459887	+	0.887978i	$0.652110\pi$
$570$	0.211167	0.00884483
$571$	38.6217	1.61627	0.808133	−	0.589000i	$-0.200478\pi$
$571$	38.6217	1.61627	0.808133	+	0.589000i	$0.200478\pi$
$572$	−144.638	−6.04761
$573$	0.715541	0.0298921
$574$	17.6700	0.737531
$575$	19.6889	0.821084
$576$	−69.8216	−2.90923
$577$	3.34146	0.139107	0.0695533	−	0.997578i	$-0.477843\pi$
$577$	3.34146	0.139107	0.0695533	+	0.997578i	$0.477843\pi$
$578$	37.0190	1.53979
$579$	−3.31561	−0.137792
$580$	−68.4078	−2.84048
$581$	11.1852	0.464042
$582$	4.17615	0.173107
$583$	−24.5294	−1.01590
$584$	28.4126	1.17572
$585$	20.8229	0.860923
$586$	−84.1092	−3.47452
$587$	−15.5640	−0.642394	−0.321197	−	0.947012i	$-0.604085\pi$
$587$	−15.5640	−0.642394	−0.321197	+	0.947012i	$0.604085\pi$
$588$	3.55185	0.146476
$589$	−1.06954	−0.0440697
$590$	39.8941	1.64241
$591$	−2.01444	−0.0828628
$592$	82.4571	3.38897
$593$	−27.3827	−1.12447	−0.562235	−	0.826977i	$-0.690059\pi$
$593$	−27.3827	−1.12447	−0.562235	+	0.826977i	$0.690059\pi$
$594$	27.1020	1.11201
$595$	6.31784	0.259006
$596$	−18.9492	−0.776191
$597$	4.12334	0.168757
$598$	99.2114	4.05706
$599$	−23.5450	−0.962022	−0.481011	−	0.876715i	$-0.659730\pi$
$599$	−23.5450	−0.962022	−0.481011	+	0.876715i	$0.659730\pi$
$600$	−5.69462	−0.232482
$601$	−12.8601	−0.524573	−0.262286	−	0.964990i	$-0.584477\pi$
$601$	−12.8601	−0.524573	−0.262286	+	0.964990i	$0.584477\pi$
$602$	29.2562	1.19240
$603$	−38.4013	−1.56382
$604$	−75.3837	−3.06732
$605$	−45.4450	−1.84760
$606$	−10.7010	−0.434697
$607$	5.48330	0.222560	0.111280	−	0.993789i	$-0.464505\pi$
$607$	5.48330	0.222560	0.111280	+	0.993789i	$0.464505\pi$
$608$	3.33628	0.135304
$609$	4.56062	0.184805
$610$	7.28836	0.295097
$611$	27.9757	1.13178
$612$	−28.3028	−1.14407
$613$	−21.9389	−0.886103	−0.443051	−	0.896496i	$-0.646104\pi$
$613$	−21.9389	−0.886103	−0.443051	+	0.896496i	$0.646104\pi$
$614$	0.484450	0.0195508
$615$	1.35620	0.0546874
$616$	−119.023	−4.79558
$617$	−6.61523	−0.266319	−0.133160	−	0.991095i	$-0.542512\pi$
$617$	−6.61523	−0.266319	−0.133160	+	0.991095i	$0.542512\pi$
$618$	−11.5920	−0.466299
$619$	−6.38203	−0.256515	−0.128258	−	0.991741i	$-0.540938\pi$
$619$	−6.38203	−0.256515	−0.128258	+	0.991741i	$0.540938\pi$
$620$	−52.4556	−2.10667
$621$	−13.5068	−0.542010
$622$	25.4241	1.01942
$623$	−11.2127	−0.449225
$624$	−16.1137	−0.645064
$625$	−7.79758	−0.311903
$626$	5.73358	0.229160
$627$	−0.298664	−0.0119275
$628$	125.836	5.02142
$629$	11.0238	0.439547
$630$	27.4757	1.09466
$631$	−5.90721	−0.235162	−0.117581	−	0.993063i	$-0.537514\pi$
$631$	−5.90721	−0.235162	−0.117581	+	0.993063i	$0.537514\pi$
$632$	91.2866	3.63119
$633$	6.83404	0.271629
$634$	1.90938	0.0758313
$635$	7.36758	0.292373
$636$	−5.66942	−0.224807
$637$	−10.7580	−0.426248
$638$	133.165	5.27205
$639$	8.14246	0.322111
$640$	43.6024	1.72354
$641$	31.7919	1.25570	0.627852	−	0.778332i	$-0.283934\pi$
$641$	31.7919	1.25570	0.627852	+	0.778332i	$0.283934\pi$
$642$	−9.84648	−0.388609
$643$	7.78753	0.307110	0.153555	−	0.988140i	$-0.450928\pi$
$643$	7.78753	0.307110	0.153555	+	0.988140i	$0.450928\pi$
$644$	95.1132	3.74798
$645$	2.24547	0.0884152
$646$	0.869346	0.0342039
$647$	−22.9976	−0.904128	−0.452064	−	0.891985i	$-0.649312\pi$
$647$	−22.9976	−0.904128	−0.452064	+	0.891985i	$0.649312\pi$
$648$	−74.7858	−2.93786
$649$	−56.4241	−2.21484
$650$	27.6566	1.08478
$651$	3.49711	0.137063
$652$	32.7640	1.28314
$653$	−36.3529	−1.42260	−0.711299	−	0.702890i	$-0.751893\pi$
$653$	−36.3529	−1.42260	−0.711299	+	0.702890i	$0.751893\pi$
$654$	−2.38586	−0.0932945
$655$	−26.7719	−1.04607
$656$	41.7626	1.63056
$657$	9.27651	0.361911
$658$	36.9137	1.43905
$659$	1.31734	0.0513163	0.0256582	−	0.999671i	$-0.491832\pi$
$659$	1.31734	0.0513163	0.0256582	+	0.999671i	$0.491832\pi$
$660$	−14.6480	−0.570171
$661$	−41.1915	−1.60216	−0.801081	−	0.598555i	$-0.795742\pi$
$661$	−41.1915	−1.60216	−0.801081	+	0.598555i	$0.795742\pi$
$662$	62.7927	2.44051
$663$	−2.15426	−0.0836644
$664$	47.0767	1.82693
$665$	−0.613174	−0.0237779
$666$	47.9415	1.85769
$667$	−66.3654	−2.56968
$668$	16.8252	0.650987
$669$	3.71577	0.143660
$670$	57.8499	2.23494
$671$	−10.3083	−0.397947
$672$	−10.9087	−0.420814
$673$	48.2785	1.86100	0.930500	−	0.366293i	$-0.119373\pi$
$673$	48.2785	1.86100	0.930500	+	0.366293i	$0.119373\pi$
$674$	−92.6463	−3.56860
$675$	−3.76523	−0.144924
$676$	32.1687	1.23726
$677$	−30.8140	−1.18428	−0.592140	−	0.805835i	$-0.701717\pi$
$677$	−30.8140	−1.18428	−0.592140	+	0.805835i	$0.701717\pi$
$678$	−10.6327	−0.408346
$679$	−12.1264	−0.465370
$680$	26.5907	1.01971
$681$	−2.94676	−0.112920
$682$	102.112	3.91006
$683$	−44.8045	−1.71440	−0.857198	−	0.514986i	$-0.827797\pi$
$683$	−44.8045	−1.71440	−0.857198	+	0.514986i	$0.827797\pi$
$684$	2.74692	0.105031
$685$	9.38779	0.358689
$686$	−54.5123	−2.08129
$687$	0.0169124	0.000645248 0
$688$	69.1464	2.63618
$689$	17.1718	0.654194
$690$	10.0475	0.382501
$691$	27.1711	1.03364	0.516819	−	0.856095i	$-0.327116\pi$
$691$	27.1711	1.03364	0.516819	+	0.856095i	$0.327116\pi$
$692$	72.6140	2.76037
$693$	−38.8602	−1.47618
$694$	−22.1698	−0.841554
$695$	26.6776	1.01194
$696$	19.1949	0.727579
$697$	5.58329	0.211482
$698$	−5.41168	−0.204835
$699$	1.17582	0.0444735
$700$	26.5142	1.00214
$701$	−39.9151	−1.50757	−0.753787	−	0.657119i	$-0.771775\pi$
$701$	−39.9151	−1.50757	−0.753787	+	0.657119i	$0.771775\pi$
$702$	−18.9728	−0.716082
$703$	−1.06991	−0.0403523
$704$	−148.766	−5.60682
$705$	2.83320	0.106704
$706$	−59.6064	−2.24331
$707$	31.0728	1.16861
$708$	−13.0412	−0.490117
$709$	8.98975	0.337617	0.168809	−	0.985649i	$-0.446008\pi$
$709$	8.98975	0.337617	0.168809	+	0.985649i	$0.446008\pi$
$710$	−12.2663	−0.460345
$711$	29.8044	1.11775
$712$	−47.1921	−1.76860
$713$	−50.8894	−1.90582
$714$	−2.84253	−0.106379
$715$	44.3665	1.65921
$716$	0.703315	0.0262841
$717$	−2.26420	−0.0845580
$718$	−31.4727	−1.17455
$719$	−21.6910	−0.808938	−0.404469	−	0.914552i	$-0.632544\pi$
$719$	−21.6910	−0.808938	−0.404469	+	0.914552i	$0.632544\pi$
$720$	64.9382	2.42011
$721$	33.6601	1.25357
$722$	51.3008	1.90922
$723$	1.42379	0.0529515
$724$	4.17355	0.155109
$725$	−18.5003	−0.687085
$726$	20.4466	0.758846
$727$	−24.8243	−0.920681	−0.460340	−	0.887742i	$-0.652273\pi$
$727$	−24.8243	−0.920681	−0.460340	+	0.887742i	$0.652273\pi$
$728$	83.3223	3.08813
$729$	−23.1095	−0.855907
$730$	−13.9747	−0.517226
$731$	9.24427	0.341912
$732$	−2.38253	−0.0880608
$733$	6.35619	0.234771	0.117386	−	0.993086i	$-0.462549\pi$
$733$	6.35619	0.234771	0.117386	+	0.993086i	$0.462549\pi$
$734$	8.99433	0.331987
$735$	−1.08950	−0.0401869
$736$	158.742	5.85132
$737$	−81.8198	−3.01387
$738$	24.2813	0.893806
$739$	−27.3411	−1.00576	−0.502880	−	0.864356i	$-0.667726\pi$
$739$	−27.3411	−1.00576	−0.502880	+	0.864356i	$0.667726\pi$
$740$	−52.4735	−1.92897
$741$	0.209080	0.00768075
$742$	22.6581	0.831805
$743$	17.2642	0.633363	0.316682	−	0.948532i	$-0.397431\pi$
$743$	17.2642	0.633363	0.316682	+	0.948532i	$0.397431\pi$
$744$	14.7187	0.539615
$745$	5.81252	0.212954
$746$	18.7830	0.687694
$747$	15.3702	0.562367
$748$	−60.3035	−2.20492
$749$	28.5915	1.04471
$750$	8.77860	0.320549
$751$	−30.3766	−1.10846	−0.554229	−	0.832365i	$-0.686987\pi$
$751$	−30.3766	−1.10846	−0.554229	+	0.832365i	$0.686987\pi$
$752$	87.2448	3.18149
$753$	4.72401	0.172153
$754$	−93.2222	−3.39495
$755$	23.1234	0.841545
$756$	−18.1891	−0.661530
$757$	−0.471450	−0.0171351	−0.00856756	−	0.999963i	$-0.502727\pi$
$757$	−0.471450	−0.0171351	−0.00856756	+	0.999963i	$0.502727\pi$
$758$	−93.2310	−3.38630
$759$	−14.2106	−0.515813
$760$	−2.58074	−0.0936134
$761$	45.0281	1.63227	0.816134	−	0.577862i	$-0.196113\pi$
$761$	45.0281	1.63227	0.816134	+	0.577862i	$0.196113\pi$
$762$	−3.31483	−0.120084
$763$	6.92790	0.250807
$764$	−14.0220	−0.507297
$765$	8.68167	0.313886
$766$	79.8130	2.88376
$767$	39.4998	1.42625
$768$	−6.67737	−0.240949
$769$	−39.6319	−1.42916	−0.714582	−	0.699551i	$-0.753383\pi$
$769$	−39.6319	−1.42916	−0.714582	+	0.699551i	$0.753383\pi$
$770$	58.5413	2.10968
$771$	−1.68643	−0.0607353
$772$	64.9738	2.33846
$773$	9.14708	0.328998	0.164499	−	0.986377i	$-0.447399\pi$
$773$	9.14708	0.328998	0.164499	+	0.986377i	$0.447399\pi$
$774$	40.2025	1.44505
$775$	−14.1862	−0.509583
$776$	−51.0380	−1.83216
$777$	3.49831	0.125501
$778$	−11.0977	−0.397873
$779$	−0.541883	−0.0194150
$780$	10.2543	0.367164
$781$	17.3488	0.620788
$782$	41.3640	1.47917
$783$	12.6914	0.453555
$784$	−33.5499	−1.19821
$785$	−38.5993	−1.37767
$786$	12.0453	0.429640
$787$	−50.2199	−1.79015	−0.895073	−	0.445920i	$-0.852877\pi$
$787$	−50.2199	−1.79015	−0.895073	+	0.445920i	$0.852877\pi$
$788$	39.4756	1.40626
$789$	−4.92015	−0.175162
$790$	−44.8991	−1.59744
$791$	30.8745	1.09777
$792$	−163.556	−5.81171
$793$	7.21632	0.256259
$794$	29.5267	1.04786
$795$	1.73905	0.0616777
$796$	−80.8025	−2.86397
$797$	−46.2071	−1.63674	−0.818369	−	0.574693i	$-0.805121\pi$
$797$	−46.2071	−1.63674	−0.818369	+	0.574693i	$0.805121\pi$
$798$	0.275880	0.00976604
$799$	11.6639	0.412637
$800$	44.2518	1.56454
$801$	−15.4079	−0.544411
$802$	−54.2530	−1.91574
$803$	19.7650	0.697493
$804$	−18.9108	−0.666934
$805$	−29.1752	−1.02829
$806$	−71.4835	−2.51790
$807$	1.39993	0.0492797
$808$	130.780	4.60082
$809$	42.8576	1.50679	0.753397	−	0.657566i	$-0.228414\pi$
$809$	42.8576	1.50679	0.753397	+	0.657566i	$0.228414\pi$
$810$	36.7832	1.29243
$811$	−27.5070	−0.965902	−0.482951	−	0.875647i	$-0.660435\pi$
$811$	−27.5070	−0.965902	−0.482951	+	0.875647i	$0.660435\pi$
$812$	−89.3714	−3.13632
$813$	0.493814	0.0173188
$814$	102.147	3.58024
$815$	−10.0501	−0.352040
$816$	−6.71825	−0.235186
$817$	−0.897197	−0.0313890
$818$	63.6399	2.22512
$819$	27.2041	0.950590
$820$	−26.5766	−0.928096
$821$	22.8127	0.796169	0.398085	−	0.917349i	$-0.369675\pi$
$821$	22.8127	0.796169	0.398085	+	0.917349i	$0.369675\pi$
$822$	−4.22377	−0.147321
$823$	0.210167	0.00732596	0.00366298	−	0.999993i	$-0.498834\pi$
$823$	0.210167	0.00732596	0.00366298	+	0.999993i	$0.498834\pi$
$824$	141.670	4.93530
$825$	−3.96142	−0.137919
$826$	52.1197	1.81347
$827$	9.52649	0.331269	0.165634	−	0.986187i	$-0.447033\pi$
$827$	9.52649	0.331269	0.165634	+	0.986187i	$0.447033\pi$
$828$	130.700	4.54214
$829$	36.3821	1.26360	0.631801	−	0.775131i	$-0.282316\pi$
$829$	36.3821	1.26360	0.631801	+	0.775131i	$0.282316\pi$
$830$	−23.1546	−0.803707
$831$	4.75200	0.164845
$832$	104.144	3.61053
$833$	−4.48532	−0.155407
$834$	−12.0028	−0.415624
$835$	−5.16100	−0.178604
$836$	5.85273	0.202421
$837$	9.73189	0.336383
$838$	−61.5686	−2.12685
$839$	−16.1589	−0.557867	−0.278933	−	0.960310i	$-0.589981\pi$
$839$	−16.1589	−0.557867	−0.278933	+	0.960310i	$0.589981\pi$
$840$	8.43834	0.291150
$841$	33.3590	1.15031
$842$	−62.6345	−2.15853
$843$	5.10610	0.175863
$844$	−133.922	−4.60979
$845$	−9.86749	−0.339452
$846$	50.7251	1.74396
$847$	−59.3716	−2.04003
$848$	53.5519	1.83898
$849$	−9.04958	−0.310581
$850$	11.5308	0.395504
$851$	−50.9069	−1.74506
$852$	4.00978	0.137373
$853$	9.05513	0.310042	0.155021	−	0.987911i	$-0.450456\pi$
$853$	9.05513	0.310042	0.155021	+	0.987911i	$0.450456\pi$
$854$	9.52188	0.325832
$855$	−0.842594	−0.0288161
$856$	120.337	4.11303
$857$	−40.8112	−1.39408	−0.697041	−	0.717031i	$-0.745501\pi$
$857$	−40.8112	−1.39408	−0.697041	+	0.717031i	$0.745501\pi$
$858$	−19.9614	−0.681471
$859$	−20.4848	−0.698934	−0.349467	−	0.936949i	$-0.613637\pi$
$859$	−20.4848	−0.698934	−0.349467	+	0.936949i	$0.613637\pi$
$860$	−44.0030	−1.50049
$861$	1.77181	0.0603832
$862$	−75.4089	−2.56844
$863$	−20.2819	−0.690403	−0.345202	−	0.938529i	$-0.612189\pi$
$863$	−20.2819	−0.690403	−0.345202	+	0.938529i	$0.612189\pi$
$864$	−30.3573	−1.03277
$865$	−22.2738	−0.757330
$866$	−30.5031	−1.03654
$867$	3.71198	0.126065
$868$	−68.5306	−2.32608
$869$	63.5029	2.15419
$870$	−9.44094	−0.320078
$871$	57.2781	1.94079
$872$	29.1583	0.987426
$873$	−16.6636	−0.563976
$874$	−4.01456	−0.135795
$875$	−25.4907	−0.861744
$876$	4.56825	0.154347
$877$	−47.9265	−1.61836	−0.809182	−	0.587558i	$-0.800089\pi$
$877$	−47.9265	−1.61836	−0.809182	+	0.587558i	$0.800089\pi$
$878$	107.876	3.64063
$879$	−8.43383	−0.284466
$880$	138.361	4.66415
$881$	−24.5970	−0.828693	−0.414347	−	0.910119i	$-0.635990\pi$
$881$	−24.5970	−0.828693	−0.414347	+	0.910119i	$0.635990\pi$
$882$	−19.5063	−0.656810
$883$	4.36250	0.146810	0.0734050	−	0.997302i	$-0.476613\pi$
$883$	4.36250	0.146810	0.0734050	+	0.997302i	$0.476613\pi$
$884$	42.2156	1.41986
$885$	4.00028	0.134468
$886$	−60.9695	−2.04831
$887$	53.0643	1.78173	0.890863	−	0.454272i	$-0.150101\pi$
$887$	53.0643	1.78173	0.890863	+	0.454272i	$0.150101\pi$
$888$	14.7238	0.494098
$889$	9.62537	0.322825
$890$	23.2113	0.778046
$891$	−52.0242	−1.74288
$892$	−72.8155	−2.43804
$893$	−1.13203	−0.0378819
$894$	−2.61518	−0.0874646
$895$	−0.215736	−0.00721126
$896$	56.9644	1.90305
$897$	9.94817	0.332160
$898$	50.5057	1.68540
$899$	47.8174	1.59480
$900$	36.4345	1.21448
$901$	7.15941	0.238515
$902$	51.7350	1.72259
$903$	2.93359	0.0976239
$904$	129.946	4.32193
$905$	−1.28020	−0.0425554
$906$	−10.4037	−0.345639
$907$	45.7841	1.52024	0.760118	−	0.649785i	$-0.225141\pi$
$907$	45.7841	1.52024	0.760118	+	0.649785i	$0.225141\pi$
$908$	57.7458	1.91636
$909$	42.6987	1.41623
$910$	−40.9819	−1.35854
$911$	15.4083	0.510499	0.255249	−	0.966875i	$-0.417842\pi$
$911$	15.4083	0.510499	0.255249	+	0.966875i	$0.417842\pi$
$912$	0.652036	0.0215911
$913$	32.7486	1.08382
$914$	55.7389	1.84368
$915$	0.730822	0.0241602
$916$	−0.331421	−0.0109505
$917$	−34.9762	−1.15502
$918$	−7.91029	−0.261078
$919$	29.8716	0.985372	0.492686	−	0.870207i	$-0.336015\pi$
$919$	29.8716	0.985372	0.492686	+	0.870207i	$0.336015\pi$
$920$	−122.793	−4.04838
$921$	0.0485770	0.00160067
$922$	84.8918	2.79576
$923$	−12.1450	−0.399758
$924$	−19.1368	−0.629556
$925$	−14.1910	−0.466598
$926$	15.2149	0.499993
$927$	46.2541	1.51918
$928$	−149.159	−4.89640
$929$	18.8432	0.618224	0.309112	−	0.951026i	$-0.399968\pi$
$929$	18.8432	0.618224	0.309112	+	0.951026i	$0.399968\pi$
$930$	−7.23938	−0.237389
$931$	0.435320	0.0142670
$932$	−23.0417	−0.754756
$933$	2.54934	0.0834617
$934$	37.4047	1.22392
$935$	18.4976	0.604937
$936$	114.498	3.74247
$937$	7.11103	0.232307	0.116154	−	0.993231i	$-0.462943\pi$
$937$	7.11103	0.232307	0.116154	+	0.993231i	$0.462943\pi$
$938$	75.5780	2.46771
$939$	0.574920	0.0187618
$940$	−55.5203	−1.81087
$941$	8.41910	0.274455	0.137227	−	0.990540i	$-0.456181\pi$
$941$	8.41910	0.274455	0.137227	+	0.990540i	$0.456181\pi$
$942$	17.3666	0.565836
$943$	−25.7832	−0.839615
$944$	123.184	4.00928
$945$	5.57935	0.181496
$946$	85.6577	2.78497
$947$	−5.03644	−0.163662	−0.0818311	−	0.996646i	$-0.526077\pi$
$947$	−5.03644	−0.163662	−0.0818311	+	0.996646i	$0.526077\pi$
$948$	14.6773	0.476696
$949$	−13.8365	−0.449153
$950$	−1.11912	−0.0363090
$951$	0.191459	0.00620847
$952$	34.7394	1.12591
$953$	15.3929	0.498624	0.249312	−	0.968423i	$-0.419795\pi$
$953$	15.3929	0.498624	0.249312	+	0.968423i	$0.419795\pi$
$954$	31.1357	1.00805
$955$	4.30113	0.139181
$956$	44.3700	1.43503
$957$	13.3528	0.431634
$958$	−11.1202	−0.359278
$959$	12.2647	0.396047
$960$	10.5470	0.340402
$961$	5.66669	0.182796
$962$	−71.5079	−2.30551
$963$	39.2891	1.26607
$964$	−27.9012	−0.898636
$965$	−19.9302	−0.641576
$966$	13.1265	0.422340
$967$	−43.8358	−1.40966	−0.704832	−	0.709374i	$-0.748978\pi$
$967$	−43.8358	−1.40966	−0.704832	+	0.709374i	$0.748978\pi$
$968$	−249.885	−8.03160
$969$	0.0871714	0.00280035
$970$	25.1029	0.806007
$971$	−26.6651	−0.855724	−0.427862	−	0.903844i	$-0.640733\pi$
$971$	−26.6651	−0.855724	−0.427862	+	0.903844i	$0.640733\pi$
$972$	−37.6469	−1.20752
$973$	34.8530	1.11734
$974$	−90.7875	−2.90902
$975$	2.77320	0.0888134
$976$	22.5048	0.720360
$977$	17.5673	0.562027	0.281014	−	0.959704i	$-0.409329\pi$
$977$	17.5673	0.562027	0.281014	+	0.959704i	$0.409329\pi$
$978$	4.52176	0.144590
$979$	−32.8289	−1.04922
$980$	21.3503	0.682009
$981$	9.51999	0.303950
$982$	91.2777	2.91279
$983$	22.7148	0.724491	0.362245	−	0.932083i	$-0.382010\pi$
$983$	22.7148	0.724491	0.362245	+	0.932083i	$0.382010\pi$
$984$	7.45726	0.237729
$985$	−12.1088	−0.385819
$986$	−38.8670	−1.23778
$987$	3.70143	0.117818
$988$	−4.09721	−0.130350
$989$	−42.6892	−1.35744
$990$	80.4446	2.55670
$991$	8.99526	0.285744	0.142872	−	0.989741i	$-0.454366\pi$
$991$	8.99526	0.285744	0.142872	+	0.989741i	$0.454366\pi$
$992$	−114.377	−3.63146
$993$	6.29638	0.199809
$994$	−16.0253	−0.508291
$995$	24.7855	0.785753
$996$	7.56911	0.239837
$997$	44.5650	1.41139	0.705695	−	0.708516i	$-0.250635\pi$
$997$	44.5650	1.41139	0.705695	+	0.708516i	$0.250635\pi$
$998$	−16.9973	−0.538041
$999$	9.73522	0.308009

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	4021.2.a.b.1.3	✓	151

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
4021.2.a.b.1.3	✓	151	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:	\( N \)	\(=\)	\( 4021 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	4021.a (trivial)

\(f(q)\)	\(=\)	\(q-2.70449 q^{2} -0.271185 q^{3} +5.31424 q^{4} -1.63010 q^{5} +0.733417 q^{6} -2.12965 q^{7} -8.96332 q^{8} -2.92646 q^{9} +O(q^{10})\)	\(q-2.70449 q^{2} -0.271185 q^{3} +5.31424 q^{4} -1.63010 q^{5} +0.733417 q^{6} -2.12965 q^{7} -8.96332 q^{8} -2.92646 q^{9} +4.40858 q^{10} -6.23527 q^{11} -1.44114 q^{12} +4.36501 q^{13} +5.75960 q^{14} +0.442060 q^{15} +13.6127 q^{16} +1.81989 q^{17} +7.91456 q^{18} -0.176629 q^{19} -8.66275 q^{20} +0.577529 q^{21} +16.8632 q^{22} -8.40411 q^{23} +2.43072 q^{24} -2.34277 q^{25} -11.8051 q^{26} +1.60717 q^{27} -11.3175 q^{28} +7.89677 q^{29} -1.19554 q^{30} +6.05530 q^{31} -18.8887 q^{32} +1.69091 q^{33} -4.92188 q^{34} +3.47154 q^{35} -15.5519 q^{36} +6.05738 q^{37} +0.477690 q^{38} -1.18373 q^{39} +14.6111 q^{40} +3.06792 q^{41} -1.56192 q^{42} +5.07956 q^{43} -33.1357 q^{44} +4.77042 q^{45} +22.7288 q^{46} +6.40908 q^{47} -3.69156 q^{48} -2.46460 q^{49} +6.33599 q^{50} -0.493529 q^{51} +23.1967 q^{52} +3.93397 q^{53} -4.34656 q^{54} +10.1641 q^{55} +19.0887 q^{56} +0.0478992 q^{57} -21.3567 q^{58} +9.04918 q^{59} +2.34921 q^{60} +1.65322 q^{61} -16.3765 q^{62} +6.23232 q^{63} +23.8587 q^{64} -7.11541 q^{65} -4.57305 q^{66} +13.1221 q^{67} +9.67136 q^{68} +2.27907 q^{69} -9.38873 q^{70} -2.78236 q^{71} +26.2308 q^{72} -3.16988 q^{73} -16.3821 q^{74} +0.635325 q^{75} -0.938648 q^{76} +13.2789 q^{77} +3.20137 q^{78} -10.1845 q^{79} -22.1900 q^{80} +8.34353 q^{81} -8.29715 q^{82} -5.25216 q^{83} +3.06913 q^{84} -2.96661 q^{85} -13.7376 q^{86} -2.14149 q^{87} +55.8887 q^{88} +5.26503 q^{89} -12.9015 q^{90} -9.29593 q^{91} -44.6615 q^{92} -1.64211 q^{93} -17.3333 q^{94} +0.287923 q^{95} +5.12233 q^{96} +5.69410 q^{97} +6.66549 q^{98} +18.2473 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 151 q - 16 q^{2} - 29 q^{3} + 120 q^{4} - 27 q^{5} - 18 q^{6} - 18 q^{7} - 48 q^{8} + 98 q^{9}+O(q^{10}) \) 151 * q - 16 * q^2 - 29 * q^3 + 120 * q^4 - 27 * q^5 - 18 * q^6 - 18 * q^7 - 48 * q^8 + 98 * q^9	\( 151 q - 16 q^{2} - 29 q^{3} + 120 q^{4} - 27 q^{5} - 18 q^{6} - 18 q^{7} - 48 q^{8} + 98 q^{9} - 7 q^{10} - 126 q^{11} - 47 q^{12} - 10 q^{13} - 58 q^{14} - 50 q^{15} + 74 q^{16} - 39 q^{17} - 47 q^{18} - 48 q^{19} - 64 q^{20} - 50 q^{21} - 7 q^{22} - 91 q^{23} - 44 q^{24} + 102 q^{25} - 94 q^{26} - 92 q^{27} - 27 q^{28} - 79 q^{29} - 12 q^{30} - 33 q^{31} - 102 q^{32} - 7 q^{33} - 17 q^{34} - 183 q^{35} - 6 q^{36} - 24 q^{37} - 77 q^{38} - 81 q^{39} - 37 q^{40} - 62 q^{41} + 4 q^{42} - 74 q^{43} - 209 q^{44} - 35 q^{45} - 37 q^{46} - 127 q^{47} - 59 q^{48} + 75 q^{49} - 79 q^{50} - 138 q^{51} - 12 q^{52} - 104 q^{53} - 43 q^{54} - 49 q^{55} - 167 q^{56} - 19 q^{57} - 32 q^{58} - 207 q^{59} - 94 q^{60} - 57 q^{61} - 69 q^{62} - 49 q^{63} - 4 q^{64} - 78 q^{65} - 51 q^{66} - 92 q^{67} - 80 q^{68} - 84 q^{69} + 5 q^{70} - 217 q^{71} - 79 q^{72} + 2 q^{73} - 113 q^{74} - 173 q^{75} - 70 q^{76} - 85 q^{77} - 46 q^{78} - 70 q^{79} - 95 q^{80} - 49 q^{81} - 12 q^{82} - 109 q^{83} - 114 q^{84} - 25 q^{85} - 136 q^{86} - 60 q^{87} - 2 q^{88} - 144 q^{89} - 55 q^{90} - 62 q^{91} - 175 q^{92} - 42 q^{93} - 15 q^{94} - 189 q^{95} - 64 q^{96} - 24 q^{97} - 37 q^{98} - 293 q^{99}+O(q^{100}) \) 151 * q - 16 * q^2 - 29 * q^3 + 120 * q^4 - 27 * q^5 - 18 * q^6 - 18 * q^7 - 48 * q^8 + 98 * q^9 - 7 * q^10 - 126 * q^11 - 47 * q^12 - 10 * q^13 - 58 * q^14 - 50 * q^15 + 74 * q^16 - 39 * q^17 - 47 * q^18 - 48 * q^19 - 64 * q^20 - 50 * q^21 - 7 * q^22 - 91 * q^23 - 44 * q^24 + 102 * q^25 - 94 * q^26 - 92 * q^27 - 27 * q^28 - 79 * q^29 - 12 * q^30 - 33 * q^31 - 102 * q^32 - 7 * q^33 - 17 * q^34 - 183 * q^35 - 6 * q^36 - 24 * q^37 - 77 * q^38 - 81 * q^39 - 37 * q^40 - 62 * q^41 + 4 * q^42 - 74 * q^43 - 209 * q^44 - 35 * q^45 - 37 * q^46 - 127 * q^47 - 59 * q^48 + 75 * q^49 - 79 * q^50 - 138 * q^51 - 12 * q^52 - 104 * q^53 - 43 * q^54 - 49 * q^55 - 167 * q^56 - 19 * q^57 - 32 * q^58 - 207 * q^59 - 94 * q^60 - 57 * q^61 - 69 * q^62 - 49 * q^63 - 4 * q^64 - 78 * q^65 - 51 * q^66 - 92 * q^67 - 80 * q^68 - 84 * q^69 + 5 * q^70 - 217 * q^71 - 79 * q^72 + 2 * q^73 - 113 * q^74 - 173 * q^75 - 70 * q^76 - 85 * q^77 - 46 * q^78 - 70 * q^79 - 95 * q^80 - 49 * q^81 - 12 * q^82 - 109 * q^83 - 114 * q^84 - 25 * q^85 - 136 * q^86 - 60 * q^87 - 2 * q^88 - 144 * q^89 - 55 * q^90 - 62 * q^91 - 175 * q^92 - 42 * q^93 - 15 * q^94 - 189 * q^95 - 64 * q^96 - 24 * q^97 - 37 * q^98 - 293 * q^99

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