LMFDB - Embedded newform 4021.2.a.b.1.17

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			1.17
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)

$f(q)$	$=$	$q-2.36898 q^{2} +2.54130 q^{3} +3.61208 q^{4} +1.21451 q^{5} -6.02031 q^{6} -1.53479 q^{7} -3.81900 q^{8} +3.45822 q^{9} +O(q^{10})$	\(q-2.36898 q^{2} +2.54130 q^{3} +3.61208 q^{4} +1.21451 q^{5} -6.02031 q^{6} -1.53479 q^{7} -3.81900 q^{8} +3.45822 q^{9} -2.87715 q^{10} +1.14504 q^{11} +9.17940 q^{12} -2.50422 q^{13} +3.63589 q^{14} +3.08643 q^{15} +1.82298 q^{16} -0.901652 q^{17} -8.19247 q^{18} -1.45666 q^{19} +4.38690 q^{20} -3.90036 q^{21} -2.71259 q^{22} -1.33432 q^{23} -9.70524 q^{24} -3.52497 q^{25} +5.93245 q^{26} +1.16448 q^{27} -5.54379 q^{28} +5.28183 q^{29} -7.31170 q^{30} -3.54330 q^{31} +3.31938 q^{32} +2.90990 q^{33} +2.13600 q^{34} -1.86401 q^{35} +12.4914 q^{36} -7.70307 q^{37} +3.45081 q^{38} -6.36397 q^{39} -4.63820 q^{40} -4.23570 q^{41} +9.23990 q^{42} -6.07857 q^{43} +4.13599 q^{44} +4.20003 q^{45} +3.16099 q^{46} -5.97631 q^{47} +4.63276 q^{48} -4.64442 q^{49} +8.35060 q^{50} -2.29137 q^{51} -9.04544 q^{52} +1.18605 q^{53} -2.75863 q^{54} +1.39066 q^{55} +5.86136 q^{56} -3.70183 q^{57} -12.5126 q^{58} -12.1776 q^{59} +11.1484 q^{60} +12.5186 q^{61} +8.39402 q^{62} -5.30764 q^{63} -11.5095 q^{64} -3.04139 q^{65} -6.89351 q^{66} +12.3016 q^{67} -3.25684 q^{68} -3.39092 q^{69} +4.41581 q^{70} -4.16031 q^{71} -13.2070 q^{72} +15.2446 q^{73} +18.2484 q^{74} -8.95802 q^{75} -5.26160 q^{76} -1.75740 q^{77} +15.0761 q^{78} -11.5107 q^{79} +2.21403 q^{80} -7.41537 q^{81} +10.0343 q^{82} -1.83925 q^{83} -14.0884 q^{84} -1.09506 q^{85} +14.4000 q^{86} +13.4227 q^{87} -4.37292 q^{88} +0.591004 q^{89} -9.94981 q^{90} +3.84344 q^{91} -4.81968 q^{92} -9.00460 q^{93} +14.1578 q^{94} -1.76913 q^{95} +8.43556 q^{96} +12.0948 q^{97} +11.0026 q^{98} +3.95981 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	−2.36898	−1.67512	−0.837562	−	0.546342i	$-0.816020\pi$
$2$	−2.36898	−1.67512	−0.837562	+	0.546342i	$0.816020\pi$
$3$	2.54130	1.46722	0.733611	−	0.679570i	$-0.237833\pi$
$3$	2.54130	1.46722	0.733611	+	0.679570i	$0.237833\pi$
$4$	3.61208	1.80604
$5$	1.21451	0.543144	0.271572	−	0.962418i	$-0.412456\pi$
$5$	1.21451	0.543144	0.271572	+	0.962418i	$0.412456\pi$
$6$	−6.02031	−2.45778
$7$	−1.53479	−0.580096	−0.290048	−	0.957012i	$-0.593671\pi$
$7$	−1.53479	−0.580096	−0.290048	+	0.957012i	$0.593671\pi$
$8$	−3.81900	−1.35022
$9$	3.45822	1.15274
$10$	−2.87715	−0.909834
$11$	1.14504	0.345243	0.172622	−	0.984988i	$-0.444776\pi$
$11$	1.14504	0.345243	0.172622	+	0.984988i	$0.444776\pi$
$12$	9.17940	2.64986
$13$	−2.50422	−0.694545	−0.347272	−	0.937764i	$-0.612892\pi$
$13$	−2.50422	−0.694545	−0.347272	+	0.937764i	$0.612892\pi$
$14$	3.63589	0.971733
$15$	3.08643	0.796913
$16$	1.82298	0.455746
$17$	−0.901652	−0.218683	−0.109341	−	0.994004i	$-0.534874\pi$
$17$	−0.901652	−0.218683	−0.109341	+	0.994004i	$0.534874\pi$
$18$	−8.19247	−1.93098
$19$	−1.45666	−0.334182	−0.167091	−	0.985941i	$-0.553437\pi$
$19$	−1.45666	−0.334182	−0.167091	+	0.985941i	$0.553437\pi$
$20$	4.38690	0.980941
$21$	−3.90036	−0.851129
$22$	−2.71259	−0.578326
$23$	−1.33432	−0.278225	−0.139113	−	0.990277i	$-0.544425\pi$
$23$	−1.33432	−0.278225	−0.139113	+	0.990277i	$0.544425\pi$
$24$	−9.70524	−1.98107
$25$	−3.52497	−0.704995
$26$	5.93245	1.16345
$27$	1.16448	0.224104
$28$	−5.54379	−1.04768
$29$	5.28183	0.980810	0.490405	−	0.871495i	$-0.336849\pi$
$29$	5.28183	0.980810	0.490405	+	0.871495i	$0.336849\pi$
$30$	−7.31170	−1.33493
$31$	−3.54330	−0.636395	−0.318198	−	0.948024i	$-0.603078\pi$
$31$	−3.54330	−0.636395	−0.318198	+	0.948024i	$0.603078\pi$
$32$	3.31938	0.586789
$33$	2.90990	0.506549
$34$	2.13600	0.366321
$35$	−1.86401	−0.315076
$36$	12.4914	2.08190
$37$	−7.70307	−1.26638	−0.633188	−	0.773998i	$-0.718254\pi$
$37$	−7.70307	−1.26638	−0.633188	+	0.773998i	$0.718254\pi$
$38$	3.45081	0.559796
$39$	−6.36397	−1.01905
$40$	−4.63820	−0.733364
$41$	−4.23570	−0.661505	−0.330753	−	0.943718i	$-0.607303\pi$
$41$	−4.23570	−0.661505	−0.330753	+	0.943718i	$0.607303\pi$
$42$	9.23990	1.42575
$43$	−6.07857	−0.926973	−0.463486	−	0.886104i	$-0.653402\pi$
$43$	−6.07857	−0.926973	−0.463486	+	0.886104i	$0.653402\pi$
$44$	4.13599	0.623524
$45$	4.20003	0.626104
$46$	3.16099	0.466062
$47$	−5.97631	−0.871734	−0.435867	−	0.900011i	$-0.643558\pi$
$47$	−5.97631	−0.871734	−0.435867	+	0.900011i	$0.643558\pi$
$48$	4.63276	0.668681
$49$	−4.64442	−0.663489
$50$	8.35060	1.18095
$51$	−2.29137	−0.320856
$52$	−9.04544	−1.25438
$53$	1.18605	0.162917	0.0814584	−	0.996677i	$-0.474042\pi$
$53$	1.18605	0.162917	0.0814584	+	0.996677i	$0.474042\pi$
$54$	−2.75863	−0.375402
$55$	1.39066	0.187517
$56$	5.86136	0.783258
$57$	−3.70183	−0.490319
$58$	−12.5126	−1.64298
$59$	−12.1776	−1.58539	−0.792697	−	0.609616i	$-0.791324\pi$
$59$	−12.1776	−1.58539	−0.792697	+	0.609616i	$0.791324\pi$
$60$	11.1484	1.43926
$61$	12.5186	1.60285	0.801423	−	0.598098i	$-0.204077\pi$
$61$	12.5186	1.60285	0.801423	+	0.598098i	$0.204077\pi$
$62$	8.39402	1.06604
$63$	−5.30764	−0.668700
$64$	−11.5095	−1.43869
$65$	−3.04139	−0.377238
$66$	−6.89351	−0.848532
$67$	12.3016	1.50289	0.751443	−	0.659798i	$-0.229358\pi$
$67$	12.3016	1.50289	0.751443	+	0.659798i	$0.229358\pi$
$68$	−3.25684	−0.394950
$69$	−3.39092	−0.408218
$70$	4.41581	0.527791
$71$	−4.16031	−0.493738	−0.246869	−	0.969049i	$-0.579402\pi$
$71$	−4.16031	−0.493738	−0.246869	+	0.969049i	$0.579402\pi$
$72$	−13.2070	−1.55645
$73$	15.2446	1.78424	0.892120	−	0.451798i	$-0.149217\pi$
$73$	15.2446	1.78424	0.892120	+	0.451798i	$0.149217\pi$
$74$	18.2484	2.12134
$75$	−8.95802	−1.03438
$76$	−5.26160	−0.603546
$77$	−1.75740	−0.200274
$78$	15.0761	1.70704
$79$	−11.5107	−1.29505	−0.647525	−	0.762044i	$-0.724196\pi$
$79$	−11.5107	−1.29505	−0.647525	+	0.762044i	$0.724196\pi$
$80$	2.21403	0.247536
$81$	−7.41537	−0.823930
$82$	10.0343	1.10810
$83$	−1.83925	−0.201884	−0.100942	−	0.994892i	$-0.532186\pi$
$83$	−1.83925	−0.201884	−0.100942	+	0.994892i	$0.532186\pi$
$84$	−14.0884	−1.53718
$85$	−1.09506	−0.118776
$86$	14.4000	1.55280
$87$	13.4227	1.43907
$88$	−4.37292	−0.466155
$89$	0.591004	0.0626463	0.0313231	−	0.999509i	$-0.490028\pi$
$89$	0.591004	0.0626463	0.0313231	+	0.999509i	$0.490028\pi$
$90$	−9.94981	−1.04880
$91$	3.84344	0.402902
$92$	−4.81968	−0.502487
$93$	−9.00460	−0.933733
$94$	14.1578	1.46026
$95$	−1.76913	−0.181509
$96$	8.43556	0.860950
$97$	12.0948	1.22804	0.614022	−	0.789289i	$-0.289551\pi$
$97$	12.0948	1.22804	0.614022	+	0.789289i	$0.289551\pi$
$98$	11.0026	1.11143
$99$	3.95981	0.397976
$100$	−12.7325	−1.27325
$101$	0.961592	0.0956820	0.0478410	−	0.998855i	$-0.484766\pi$
$101$	0.961592	0.0956820	0.0478410	+	0.998855i	$0.484766\pi$
$102$	5.42822	0.537474
$103$	−4.55083	−0.448406	−0.224203	−	0.974542i	$-0.571978\pi$
$103$	−4.55083	−0.448406	−0.224203	+	0.974542i	$0.571978\pi$
$104$	9.56361	0.937789
$105$	−4.73702	−0.462286
$106$	−2.80974	−0.272906
$107$	−7.84939	−0.758829	−0.379414	−	0.925227i	$-0.623875\pi$
$107$	−7.84939	−0.758829	−0.379414	+	0.925227i	$0.623875\pi$
$108$	4.20620	0.404742
$109$	−4.40940	−0.422344	−0.211172	−	0.977449i	$-0.567728\pi$
$109$	−4.40940	−0.422344	−0.211172	+	0.977449i	$0.567728\pi$
$110$	−3.29446	−0.314114
$111$	−19.5758	−1.85806
$112$	−2.79790	−0.264376
$113$	−13.2300	−1.24458	−0.622289	−	0.782788i	$-0.713797\pi$
$113$	−13.2300	−1.24458	−0.622289	+	0.782788i	$0.713797\pi$
$114$	8.76957	0.821345
$115$	−1.62054	−0.151116
$116$	19.0784	1.77138
$117$	−8.66013	−0.800630
$118$	28.8486	2.65573
$119$	1.38385	0.126857
$120$	−11.7871	−1.07601
$121$	−9.68888	−0.880807
$122$	−29.6564	−2.68497
$123$	−10.7642	−0.970575
$124$	−12.7987	−1.14936
$125$	−10.3536	−0.926058
$126$	12.5737	1.12016
$127$	12.2568	1.08761	0.543807	−	0.839210i	$-0.316982\pi$
$127$	12.2568	1.08761	0.543807	+	0.839210i	$0.316982\pi$
$128$	20.6271	1.82320
$129$	−15.4475	−1.36008
$130$	7.20500	0.631920
$131$	−3.54024	−0.309312	−0.154656	−	0.987968i	$-0.549427\pi$
$131$	−3.54024	−0.309312	−0.154656	+	0.987968i	$0.549427\pi$
$132$	10.5108	0.914849
$133$	2.23567	0.193857
$134$	−29.1424	−2.51752
$135$	1.41427	0.121721
$136$	3.44341	0.295270
$137$	−7.62419	−0.651379	−0.325689	−	0.945477i	$-0.605596\pi$
$137$	−7.62419	−0.651379	−0.325689	+	0.945477i	$0.605596\pi$
$138$	8.03302	0.683816
$139$	−11.9106	−1.01025	−0.505124	−	0.863047i	$-0.668553\pi$
$139$	−11.9106	−1.01025	−0.505124	+	0.863047i	$0.668553\pi$
$140$	−6.73297	−0.569040
$141$	−15.1876	−1.27903
$142$	9.85571	0.827073
$143$	−2.86744	−0.239787
$144$	6.30429	0.525357
$145$	6.41481	0.532721
$146$	−36.1141	−2.98882
$147$	−11.8029	−0.973485
$148$	−27.8241	−2.28713
$149$	0.718533	0.0588645	0.0294322	−	0.999567i	$-0.490630\pi$
$149$	0.718533	0.0588645	0.0294322	+	0.999567i	$0.490630\pi$
$150$	21.2214	1.73272
$151$	−13.6310	−1.10927	−0.554636	−	0.832093i	$-0.687142\pi$
$151$	−13.6310	−1.10927	−0.554636	+	0.832093i	$0.687142\pi$
$152$	5.56300	0.451219
$153$	−3.11811	−0.252084
$154$	4.16325	0.335484
$155$	−4.30336	−0.345654
$156$	−22.9872	−1.84045
$157$	−6.36543	−0.508017	−0.254009	−	0.967202i	$-0.581749\pi$
$157$	−6.36543	−0.508017	−0.254009	+	0.967202i	$0.581749\pi$
$158$	27.2686	2.16937
$159$	3.01412	0.239035
$160$	4.03141	0.318711
$161$	2.04790	0.161397
$162$	17.5669	1.38019
$163$	19.1975	1.50366	0.751830	−	0.659357i	$-0.229171\pi$
$163$	19.1975	1.50366	0.751830	+	0.659357i	$0.229171\pi$
$164$	−15.2997	−1.19471
$165$	3.53410	0.275129
$166$	4.35716	0.338181
$167$	1.49965	0.116046	0.0580230	−	0.998315i	$-0.481520\pi$
$167$	1.49965	0.116046	0.0580230	+	0.998315i	$0.481520\pi$
$168$	14.8955	1.14921
$169$	−6.72890	−0.517608
$170$	2.59419	0.198965
$171$	−5.03747	−0.385225
$172$	−21.9563	−1.67415
$173$	2.05405	0.156166	0.0780831	−	0.996947i	$-0.475120\pi$
$173$	2.05405	0.156166	0.0780831	+	0.996947i	$0.475120\pi$
$174$	−31.7982	−2.41062
$175$	5.41009	0.408964
$176$	2.08740	0.157343
$177$	−30.9471	−2.32612
$178$	−1.40008	−0.104940
$179$	−16.7674	−1.25326	−0.626628	−	0.779319i	$-0.715565\pi$
$179$	−16.7674	−1.25326	−0.626628	+	0.779319i	$0.715565\pi$
$180$	15.1709	1.13077
$181$	10.3144	0.766665	0.383333	−	0.923610i	$-0.374776\pi$
$181$	10.3144	0.766665	0.383333	+	0.923610i	$0.374776\pi$
$182$	−9.10506	−0.674912
$183$	31.8136	2.35173
$184$	5.09578	0.375666
$185$	−9.35543	−0.687825
$186$	21.3317	1.56412
$187$	−1.03243	−0.0754988
$188$	−21.5869	−1.57439
$189$	−1.78723	−0.130002
$190$	4.19104	0.304050
$191$	4.42860	0.320442	0.160221	−	0.987081i	$-0.448779\pi$
$191$	4.42860	0.320442	0.160221	+	0.987081i	$0.448779\pi$
$192$	−29.2492	−2.11088
$193$	21.4545	1.54433	0.772164	−	0.635424i	$-0.219175\pi$
$193$	21.4545	1.54433	0.772164	+	0.635424i	$0.219175\pi$
$194$	−28.6525	−2.05713
$195$	−7.72909	−0.553491
$196$	−16.7760	−1.19829
$197$	15.2895	1.08933	0.544667	−	0.838652i	$-0.316656\pi$
$197$	15.2895	1.08933	0.544667	+	0.838652i	$0.316656\pi$
$198$	−9.38073	−0.666660
$199$	−19.0050	−1.34723	−0.673616	−	0.739082i	$-0.735260\pi$
$199$	−19.0050	−1.34723	−0.673616	+	0.739082i	$0.735260\pi$
$200$	13.4619	0.951899
$201$	31.2622	2.20507
$202$	−2.27800	−0.160279
$203$	−8.10649	−0.568964
$204$	−8.27663	−0.579480
$205$	−5.14429	−0.359293
$206$	10.7808	0.751137
$207$	−4.61438	−0.320722
$208$	−4.56515	−0.316536
$209$	−1.66794	−0.115374
$210$	11.2219	0.774386
$211$	27.7498	1.91037	0.955187	−	0.296004i	$-0.0956543\pi$
$211$	27.7498	1.91037	0.955187	+	0.296004i	$0.0956543\pi$
$212$	4.28412	0.294235
$213$	−10.5726	−0.724423
$214$	18.5951	1.27113
$215$	−7.38246	−0.503480
$216$	−4.44715	−0.302590
$217$	5.43822	0.369170
$218$	10.4458	0.707478
$219$	38.7410	2.61788
$220$	5.02319	0.338663
$221$	2.25793	0.151885
$222$	46.3748	3.11247
$223$	4.64382	0.310973	0.155487	−	0.987838i	$-0.450305\pi$
$223$	4.64382	0.310973	0.155487	+	0.987838i	$0.450305\pi$
$224$	−5.09455	−0.340394
$225$	−12.1901	−0.812676
$226$	31.3418	2.08482
$227$	−12.6438	−0.839199	−0.419599	−	0.907709i	$-0.637829\pi$
$227$	−12.6438	−0.839199	−0.419599	+	0.907709i	$0.637829\pi$
$228$	−13.3713	−0.885537
$229$	15.7359	1.03985	0.519927	−	0.854211i	$-0.325959\pi$
$229$	15.7359	1.03985	0.519927	+	0.854211i	$0.325959\pi$
$230$	3.83904	0.253139
$231$	−4.46609	−0.293847
$232$	−20.1713	−1.32431
$233$	−21.1513	−1.38567	−0.692835	−	0.721096i	$-0.743639\pi$
$233$	−21.1513	−1.38567	−0.692835	+	0.721096i	$0.743639\pi$
$234$	20.5157	1.34115
$235$	−7.25827	−0.473477
$236$	−43.9867	−2.86329
$237$	−29.2521	−1.90013
$238$	−3.27831	−0.212501
$239$	22.5342	1.45762	0.728808	−	0.684718i	$-0.240075\pi$
$239$	22.5342	1.45762	0.728808	+	0.684718i	$0.240075\pi$
$240$	5.62652	0.363190
$241$	10.3345	0.665704	0.332852	−	0.942979i	$-0.391989\pi$
$241$	10.3345	0.665704	0.332852	+	0.942979i	$0.391989\pi$
$242$	22.9528	1.47546
$243$	−22.3381	−1.43299
$244$	45.2183	2.89481
$245$	−5.64068	−0.360370
$246$	25.5002	1.62583
$247$	3.64780	0.232104
$248$	13.5319	0.859275
$249$	−4.67410	−0.296209
$250$	24.5276	1.55126
$251$	20.3103	1.28197	0.640986	−	0.767553i	$-0.278526\pi$
$251$	20.3103	1.28197	0.640986	+	0.767553i	$0.278526\pi$
$252$	−19.1716	−1.20770
$253$	−1.52786	−0.0960555
$254$	−29.0361	−1.82189
$255$	−2.78289	−0.174271
$256$	−25.8463	−1.61539
$257$	14.7128	0.917757	0.458878	−	0.888499i	$-0.348251\pi$
$257$	14.7128	0.917757	0.458878	+	0.888499i	$0.348251\pi$
$258$	36.5948	2.27830
$259$	11.8226	0.734620
$260$	−10.9857	−0.681307
$261$	18.2657	1.13062
$262$	8.38677	0.518136
$263$	13.0984	0.807683	0.403841	−	0.914829i	$-0.367675\pi$
$263$	13.0984	0.807683	0.403841	+	0.914829i	$0.367675\pi$
$264$	−11.1129	−0.683953
$265$	1.44047	0.0884873
$266$	−5.29627	−0.324735
$267$	1.50192	0.0919160
$268$	44.4346	2.71428
$269$	−14.6140	−0.891031	−0.445516	−	0.895274i	$-0.646980\pi$
$269$	−14.6140	−0.891031	−0.445516	+	0.895274i	$0.646980\pi$
$270$	−3.35038	−0.203898
$271$	−9.38899	−0.570340	−0.285170	−	0.958477i	$-0.592050\pi$
$271$	−9.38899	−0.570340	−0.285170	+	0.958477i	$0.592050\pi$
$272$	−1.64370	−0.0996639
$273$	9.76736	0.591147
$274$	18.0616	1.09114
$275$	−4.03625	−0.243395
$276$	−12.2483	−0.737259
$277$	−8.32542	−0.500226	−0.250113	−	0.968217i	$-0.580468\pi$
$277$	−8.32542	−0.500226	−0.250113	+	0.968217i	$0.580468\pi$
$278$	28.2161	1.69229
$279$	−12.2535	−0.733599
$280$	7.11867	0.425422
$281$	−28.9775	−1.72865	−0.864325	−	0.502934i	$-0.832254\pi$
$281$	−28.9775	−1.72865	−0.864325	+	0.502934i	$0.832254\pi$
$282$	35.9792	2.14253
$283$	−0.349043	−0.0207485	−0.0103742	−	0.999946i	$-0.503302\pi$
$283$	−0.349043	−0.0207485	−0.0103742	+	0.999946i	$0.503302\pi$
$284$	−15.0274	−0.891712
$285$	−4.49589	−0.266314
$286$	6.79291	0.401673
$287$	6.50091	0.383736
$288$	11.4792	0.676416
$289$	−16.1870	−0.952178
$290$	−15.1966	−0.892374
$291$	30.7366	1.80181
$292$	55.0646	3.22241
$293$	5.09473	0.297637	0.148819	−	0.988865i	$-0.452453\pi$
$293$	5.09473	0.297637	0.148819	+	0.988865i	$0.452453\pi$
$294$	27.9608	1.63071
$295$	−14.7898	−0.861097
$296$	29.4180	1.70989
$297$	1.33338	0.0773705
$298$	−1.70219	−0.0986053
$299$	3.34143	0.193240
$300$	−32.3571	−1.86814
$301$	9.32932	0.537733
$302$	32.2915	1.85817
$303$	2.44370	0.140387
$304$	−2.65548	−0.152302
$305$	15.2040	0.870576
$306$	7.38676	0.422273
$307$	2.31488	0.132117	0.0660585	−	0.997816i	$-0.478958\pi$
$307$	2.31488	0.132117	0.0660585	+	0.997816i	$0.478958\pi$
$308$	−6.34788	−0.361704
$309$	−11.5650	−0.657912
$310$	10.1946	0.579014
$311$	−8.10408	−0.459540	−0.229770	−	0.973245i	$-0.573797\pi$
$311$	−8.10408	−0.459540	−0.229770	+	0.973245i	$0.573797\pi$
$312$	24.3040	1.37594
$313$	18.7873	1.06192	0.530961	−	0.847396i	$-0.321831\pi$
$313$	18.7873	1.06192	0.530961	+	0.847396i	$0.321831\pi$
$314$	15.0796	0.850992
$315$	−6.44617	−0.363200
$316$	−41.5775	−2.33892
$317$	16.6126	0.933055	0.466528	−	0.884507i	$-0.345505\pi$
$317$	16.6126	0.933055	0.466528	+	0.884507i	$0.345505\pi$
$318$	−7.14040	−0.400414
$319$	6.04792	0.338618
$320$	−13.9784	−0.781417
$321$	−19.9477	−1.11337
$322$	−4.85145	−0.270361
$323$	1.31340	0.0730798
$324$	−26.7849	−1.48805
$325$	8.82729	0.489650
$326$	−45.4785	−2.51882
$327$	−11.2056	−0.619672
$328$	16.1761	0.893178
$329$	9.17237	0.505689
$330$	−8.37221	−0.460875
$331$	17.0310	0.936108	0.468054	−	0.883700i	$-0.344955\pi$
$331$	17.0310	0.936108	0.468054	+	0.883700i	$0.344955\pi$
$332$	−6.64353	−0.364611
$333$	−26.6389	−1.45980
$334$	−3.55264	−0.194392
$335$	14.9404	0.816283
$336$	−7.11031	−0.387899
$337$	−3.04067	−0.165636	−0.0828179	−	0.996565i	$-0.526392\pi$
$337$	−3.04067	−0.165636	−0.0828179	+	0.996565i	$0.526392\pi$
$338$	15.9407	0.867058
$339$	−33.6215	−1.82607
$340$	−3.95546	−0.214515
$341$	−4.05723	−0.219711
$342$	11.9337	0.645300
$343$	17.8717	0.964983
$344$	23.2141	1.25162
$345$	−4.11829	−0.221721
$346$	−4.86600	−0.261598
$347$	21.8114	1.17090	0.585449	−	0.810709i	$-0.300918\pi$
$347$	21.8114	1.17090	0.585449	+	0.810709i	$0.300918\pi$
$348$	48.4840	2.59901
$349$	−1.99700	−0.106897	−0.0534485	−	0.998571i	$-0.517021\pi$
$349$	−1.99700	−0.106897	−0.0534485	+	0.998571i	$0.517021\pi$
$350$	−12.8164	−0.685066
$351$	−2.91611	−0.155650
$352$	3.80084	0.202585
$353$	−23.9261	−1.27346	−0.636728	−	0.771089i	$-0.719713\pi$
$353$	−23.9261	−1.27346	−0.636728	+	0.771089i	$0.719713\pi$
$354$	73.3131	3.89655
$355$	−5.05272	−0.268171
$356$	2.13475	0.113142
$357$	3.51677	0.186127
$358$	39.7217	2.09936
$359$	−28.3295	−1.49517	−0.747586	−	0.664165i	$-0.768787\pi$
$359$	−28.3295	−1.49517	−0.747586	+	0.664165i	$0.768787\pi$
$360$	−16.0399	−0.845379
$361$	−16.8781	−0.888323
$362$	−24.4347	−1.28426
$363$	−24.6224	−1.29234
$364$	13.8828	0.727659
$365$	18.5146	0.969099
$366$	−75.3660	−3.93944
$367$	24.3489	1.27100	0.635500	−	0.772101i	$-0.280794\pi$
$367$	24.3489	1.27100	0.635500	+	0.772101i	$0.280794\pi$
$368$	−2.43245	−0.126800
$369$	−14.6480	−0.762544
$370$	22.1629	1.15219
$371$	−1.82034	−0.0945073
$372$	−32.5254	−1.68636
$373$	−19.1294	−0.990484	−0.495242	−	0.868755i	$-0.664921\pi$
$373$	−19.1294	−0.990484	−0.495242	+	0.868755i	$0.664921\pi$
$374$	2.44581	0.126470
$375$	−26.3117	−1.35873
$376$	22.8235	1.17703
$377$	−13.2268	−0.681216
$378$	4.23392	0.217769
$379$	18.5873	0.954763	0.477381	−	0.878696i	$-0.341586\pi$
$379$	18.5873	0.954763	0.477381	+	0.878696i	$0.341586\pi$
$380$	−6.39024	−0.327813
$381$	31.1482	1.59577
$382$	−10.4913	−0.536780
$383$	−13.4678	−0.688171	−0.344085	−	0.938938i	$-0.611811\pi$
$383$	−13.4678	−0.688171	−0.344085	+	0.938938i	$0.611811\pi$
$384$	52.4198	2.67504
$385$	−2.13437	−0.108778
$386$	−50.8253	−2.58694
$387$	−21.0210	−1.06856
$388$	43.6876	2.21790
$389$	21.1216	1.07091	0.535453	−	0.844565i	$-0.320141\pi$
$389$	21.1216	1.07091	0.535453	+	0.844565i	$0.320141\pi$
$390$	18.3101	0.927167
$391$	1.20309	0.0608431
$392$	17.7371	0.895857
$393$	−8.99682	−0.453830
$394$	−36.2207	−1.82477
$395$	−13.9798	−0.703399
$396$	14.3032	0.718762
$397$	−37.1502	−1.86452	−0.932259	−	0.361793i	$-0.882165\pi$
$397$	−37.1502	−1.86452	−0.932259	+	0.361793i	$0.882165\pi$
$398$	45.0226	2.25678
$399$	5.68152	0.284432
$400$	−6.42597	−0.321299
$401$	−1.51446	−0.0756283	−0.0378142	−	0.999285i	$-0.512039\pi$
$401$	−1.51446	−0.0756283	−0.0378142	+	0.999285i	$0.512039\pi$
$402$	−74.0597	−3.69376
$403$	8.87319	0.442005
$404$	3.47335	0.172806
$405$	−9.00602	−0.447513
$406$	19.2041	0.953085
$407$	−8.82034	−0.437208
$408$	8.75075	0.433227
$409$	−3.48422	−0.172284	−0.0861418	−	0.996283i	$-0.527454\pi$
$409$	−3.48422	−0.172284	−0.0861418	+	0.996283i	$0.527454\pi$
$410$	12.1867	0.601860
$411$	−19.3754	−0.955717
$412$	−16.4380	−0.809841
$413$	18.6901	0.919680
$414$	10.9314	0.537249
$415$	−2.23378	−0.109652
$416$	−8.31245	−0.407551
$417$	−30.2686	−1.48226
$418$	3.95133	0.193266
$419$	−8.89702	−0.434648	−0.217324	−	0.976100i	$-0.569733\pi$
$419$	−8.89702	−0.434648	−0.217324	+	0.976100i	$0.569733\pi$
$420$	−17.1105	−0.834908
$421$	25.2101	1.22866	0.614331	−	0.789048i	$-0.289426\pi$
$421$	25.2101	1.22866	0.614331	+	0.789048i	$0.289426\pi$
$422$	−65.7388	−3.20011
$423$	−20.6674	−1.00488
$424$	−4.52954	−0.219974
$425$	3.17830	0.154170
$426$	25.0463	1.21350
$427$	−19.2135	−0.929804
$428$	−28.3526	−1.37048
$429$	−7.28702	−0.351821
$430$	17.4889	0.843391
$431$	−32.0408	−1.54335	−0.771676	−	0.636016i	$-0.780581\pi$
$431$	−32.0408	−1.54335	−0.771676	+	0.636016i	$0.780581\pi$
$432$	2.12283	0.102135
$433$	22.1993	1.06683	0.533415	−	0.845853i	$-0.320908\pi$
$433$	22.1993	1.06683	0.533415	+	0.845853i	$0.320908\pi$
$434$	−12.8831	−0.618406
$435$	16.3020	0.781620
$436$	−15.9271	−0.762770
$437$	1.94366	0.0929778
$438$	−91.7769	−4.38527
$439$	−15.0338	−0.717523	−0.358761	−	0.933429i	$-0.616801\pi$
$439$	−15.0338	−0.717523	−0.358761	+	0.933429i	$0.616801\pi$
$440$	−5.31094	−0.253189
$441$	−16.0614	−0.764830
$442$	−5.34900	−0.254426
$443$	36.8344	1.75005	0.875027	−	0.484073i	$-0.160843\pi$
$443$	36.8344	1.75005	0.875027	+	0.484073i	$0.160843\pi$
$444$	−70.7096	−3.35573
$445$	0.717778	0.0340259
$446$	−11.0011	−0.520919
$447$	1.82601	0.0863673
$448$	17.6647	0.834579
$449$	−12.6014	−0.594697	−0.297348	−	0.954769i	$-0.596102\pi$
$449$	−12.6014	−0.594697	−0.297348	+	0.954769i	$0.596102\pi$
$450$	28.8782	1.36133
$451$	−4.85006	−0.228380
$452$	−47.7880	−2.24776
$453$	−34.6404	−1.62755
$454$	29.9530	1.40576
$455$	4.66789	0.218834
$456$	14.1373	0.662039
$457$	−26.2806	−1.22935	−0.614677	−	0.788779i	$-0.710714\pi$
$457$	−26.2806	−1.22935	−0.614677	+	0.788779i	$0.710714\pi$
$458$	−37.2780	−1.74189
$459$	−1.04996	−0.0490077
$460$	−5.85354	−0.272923
$461$	28.0706	1.30738	0.653689	−	0.756764i	$-0.273221\pi$
$461$	28.0706	1.30738	0.653689	+	0.756764i	$0.273221\pi$
$462$	10.5801	0.492230
$463$	1.49393	0.0694287	0.0347144	−	0.999397i	$-0.488948\pi$
$463$	1.49393	0.0694287	0.0347144	+	0.999397i	$0.488948\pi$
$464$	9.62869	0.447001
$465$	−10.9361	−0.507152
$466$	50.1072	2.32117
$467$	−37.0289	−1.71349	−0.856746	−	0.515738i	$-0.827518\pi$
$467$	−37.0289	−1.71349	−0.856746	+	0.515738i	$0.827518\pi$
$468$	−31.2811	−1.44597
$469$	−18.8804	−0.871818
$470$	17.1947	0.793133
$471$	−16.1765	−0.745374
$472$	46.5064	2.14063
$473$	−6.96022	−0.320031
$474$	69.2977	3.18295
$475$	5.13470	0.235596
$476$	4.99857	0.229109
$477$	4.10163	0.187801
$478$	−53.3832	−2.44169
$479$	5.93238	0.271058	0.135529	−	0.990773i	$-0.456727\pi$
$479$	5.93238	0.271058	0.135529	+	0.990773i	$0.456727\pi$
$480$	10.2450	0.467620
$481$	19.2901	0.879555
$482$	−24.4823	−1.11514
$483$	5.20434	0.236806
$484$	−34.9970	−1.59077
$485$	14.6893	0.667005
$486$	52.9187	2.40044
$487$	−9.91555	−0.449316	−0.224658	−	0.974438i	$-0.572127\pi$
$487$	−9.91555	−0.449316	−0.224658	+	0.974438i	$0.572127\pi$
$488$	−47.8087	−2.16420
$489$	48.7866	2.20620
$490$	13.3627	0.603665
$491$	−11.6969	−0.527875	−0.263938	−	0.964540i	$-0.585021\pi$
$491$	−11.6969	−0.527875	−0.263938	+	0.964540i	$0.585021\pi$
$492$	−38.8812	−1.75290
$493$	−4.76237	−0.214486
$494$	−8.64159	−0.388803
$495$	4.80922	0.216158
$496$	−6.45938	−0.290035
$497$	6.38520	0.286415
$498$	11.0729	0.496187
$499$	−11.7576	−0.526342	−0.263171	−	0.964749i	$-0.584768\pi$
$499$	−11.7576	−0.526342	−0.263171	+	0.964749i	$0.584768\pi$
$500$	−37.3982	−1.67250
$501$	3.81105	0.170265
$502$	−48.1147	−2.14746
$503$	42.1578	1.87972	0.939862	−	0.341553i	$-0.110953\pi$
$503$	42.1578	1.87972	0.939862	+	0.341553i	$0.110953\pi$
$504$	20.2699	0.902893
$505$	1.16786	0.0519691
$506$	3.61947	0.160905
$507$	−17.1002	−0.759446
$508$	44.2726	1.96428
$509$	8.70885	0.386013	0.193007	−	0.981197i	$-0.438176\pi$
$509$	8.70885	0.386013	0.193007	+	0.981197i	$0.438176\pi$
$510$	6.59261	0.291926
$511$	−23.3972	−1.03503
$512$	19.9751	0.882785
$513$	−1.69626	−0.0748915
$514$	−34.8543	−1.53736
$515$	−5.52701	−0.243549
$516$	−55.7976	−2.45635
$517$	−6.84313	−0.300961
$518$	−28.0075	−1.23058
$519$	5.21996	0.229131
$520$	11.6151	0.509354
$521$	−5.37241	−0.235370	−0.117685	−	0.993051i	$-0.537547\pi$
$521$	−5.37241	−0.235370	−0.117685	+	0.993051i	$0.537547\pi$
$522$	−43.2712	−1.89393
$523$	−10.1091	−0.442041	−0.221021	−	0.975269i	$-0.570939\pi$
$523$	−10.1091	−0.442041	−0.221021	+	0.975269i	$0.570939\pi$
$524$	−12.7876	−0.558631
$525$	13.7487	0.600042
$526$	−31.0299	−1.35297
$527$	3.19482	0.139169
$528$	5.30471	0.230858
$529$	−21.2196	−0.922591
$530$	−3.41245	−0.148227
$531$	−42.1130	−1.82755
$532$	8.07544	0.350115
$533$	10.6071	0.459445
$534$	−3.55802	−0.153971
$535$	−9.53314	−0.412153
$536$	−46.9800	−2.02923
$537$	−42.6111	−1.83880
$538$	34.6203	1.49259
$539$	−5.31806	−0.229065
$540$	5.10846	0.219833
$541$	28.4726	1.22413	0.612067	−	0.790806i	$-0.290338\pi$
$541$	28.4726	1.22413	0.612067	+	0.790806i	$0.290338\pi$
$542$	22.2424	0.955391
$543$	26.2121	1.12487
$544$	−2.99293	−0.128321
$545$	−5.35524	−0.229393
$546$	−23.1387	−0.990245
$547$	−15.2314	−0.651248	−0.325624	−	0.945499i	$-0.605574\pi$
$547$	−15.2314	−0.651248	−0.325624	+	0.945499i	$0.605574\pi$
$548$	−27.5392	−1.17642
$549$	43.2922	1.84767
$550$	9.56180	0.407717
$551$	−7.69385	−0.327769
$552$	12.9499	0.551185
$553$	17.6664	0.751253
$554$	19.7228	0.837941
$555$	−23.7750	−1.00919
$556$	−43.0223	−1.82455
$557$	3.47562	0.147267	0.0736335	−	0.997285i	$-0.476541\pi$
$557$	3.47562	0.147267	0.0736335	+	0.997285i	$0.476541\pi$
$558$	29.0284	1.22887
$559$	15.2220	0.643824
$560$	−3.39807	−0.143595
$561$	−2.62372	−0.110773
$562$	68.6471	2.89570
$563$	−36.7617	−1.54932	−0.774661	−	0.632376i	$-0.782080\pi$
$563$	−36.7617	−1.54932	−0.774661	+	0.632376i	$0.782080\pi$
$564$	−54.8589	−2.30998
$565$	−16.0680	−0.675985
$566$	0.826878	0.0347563
$567$	11.3810	0.477958
$568$	15.8882	0.666655
$569$	7.89244	0.330868	0.165434	−	0.986221i	$-0.447097\pi$
$569$	7.89244	0.330868	0.165434	+	0.986221i	$0.447097\pi$
$570$	10.6507	0.446109
$571$	−28.1417	−1.17769	−0.588846	−	0.808245i	$-0.700418\pi$
$571$	−28.1417	−1.17769	−0.588846	+	0.808245i	$0.700418\pi$
$572$	−10.3574	−0.433065
$573$	11.2544	0.470160
$574$	−15.4005	−0.642806
$575$	4.70345	0.196147
$576$	−39.8025	−1.65844
$577$	−34.9164	−1.45359	−0.726794	−	0.686855i	$-0.758991\pi$
$577$	−34.9164	−1.45359	−0.726794	+	0.686855i	$0.758991\pi$
$578$	38.3468	1.59502
$579$	54.5223	2.26587
$580$	23.1708	0.962117
$581$	2.82286	0.117112
$582$	−72.8146	−3.01826
$583$	1.35808	0.0562460
$584$	−58.2190	−2.40912
$585$	−10.5178	−0.434857
$586$	−12.0693	−0.498579
$587$	−33.0944	−1.36595	−0.682976	−	0.730441i	$-0.739314\pi$
$587$	−33.0944	−1.36595	−0.682976	+	0.730441i	$0.739314\pi$
$588$	−42.6330	−1.75816
$589$	5.16140	0.212672
$590$	35.0369	1.44244
$591$	38.8553	1.59830
$592$	−14.0426	−0.577146
$593$	23.5974	0.969030	0.484515	−	0.874783i	$-0.338996\pi$
$593$	23.5974	0.969030	0.484515	+	0.874783i	$0.338996\pi$
$594$	−3.15875	−0.129605
$595$	1.68069	0.0689016
$596$	2.59540	0.106312
$597$	−48.2976	−1.97669
$598$	−7.91579	−0.323701
$599$	12.8738	0.526009	0.263004	−	0.964795i	$-0.415287\pi$
$599$	12.8738	0.526009	0.263004	+	0.964795i	$0.415287\pi$
$600$	34.2107	1.39665
$601$	11.5052	0.469305	0.234653	−	0.972079i	$-0.424605\pi$
$601$	11.5052	0.469305	0.234653	+	0.972079i	$0.424605\pi$
$602$	−22.1010	−0.900770
$603$	42.5418	1.73244
$604$	−49.2362	−2.00339
$605$	−11.7672	−0.478405
$606$	−5.78908	−0.235165
$607$	0.531848	0.0215870	0.0107935	−	0.999942i	$-0.496564\pi$
$607$	0.531848	0.0215870	0.0107935	+	0.999942i	$0.496564\pi$
$608$	−4.83523	−0.196094
$609$	−20.6010	−0.834796
$610$	−36.0179	−1.45832
$611$	14.9660	0.605458
$612$	−11.2629	−0.455275
$613$	38.3809	1.55019	0.775094	−	0.631846i	$-0.217702\pi$
$613$	38.3809	1.55019	0.775094	+	0.631846i	$0.217702\pi$
$614$	−5.48391	−0.221312
$615$	−13.0732	−0.527162
$616$	6.71151	0.270415
$617$	−13.8099	−0.555967	−0.277984	−	0.960586i	$-0.589666\pi$
$617$	−13.8099	−0.555967	−0.277984	+	0.960586i	$0.589666\pi$
$618$	27.3974	1.10208
$619$	−49.3499	−1.98354	−0.991770	−	0.128032i	$-0.959134\pi$
$619$	−49.3499	−1.98354	−0.991770	+	0.128032i	$0.959134\pi$
$620$	−15.5441	−0.624266
$621$	−1.55379	−0.0623515
$622$	19.1984	0.769787
$623$	−0.907066	−0.0363408
$624$	−11.6014	−0.464429
$625$	5.05030	0.202012
$626$	−44.5069	−1.77885
$627$	−4.23875	−0.169279
$628$	−22.9925	−0.917500
$629$	6.94549	0.276935
$630$	15.2709	0.608406
$631$	−38.3533	−1.52682	−0.763411	−	0.645913i	$-0.776477\pi$
$631$	−38.3533	−1.52682	−0.763411	+	0.645913i	$0.776477\pi$
$632$	43.9592	1.74860
$633$	70.5206	2.80294
$634$	−39.3549	−1.56298
$635$	14.8860	0.590731
$636$	10.8872	0.431707
$637$	11.6306	0.460823
$638$	−14.3274	−0.567228
$639$	−14.3873	−0.569152
$640$	25.0518	0.990259
$641$	26.2162	1.03548	0.517738	−	0.855539i	$-0.326774\pi$
$641$	26.2162	1.03548	0.517738	+	0.855539i	$0.326774\pi$
$642$	47.2557	1.86503
$643$	2.45368	0.0967638	0.0483819	−	0.998829i	$-0.484594\pi$
$643$	2.45368	0.0967638	0.0483819	+	0.998829i	$0.484594\pi$
$644$	7.39720	0.291490
$645$	−18.7611	−0.738717
$646$	−3.11143	−0.122418
$647$	3.99228	0.156953	0.0784764	−	0.996916i	$-0.474994\pi$
$647$	3.99228	0.156953	0.0784764	+	0.996916i	$0.474994\pi$
$648$	28.3193	1.11249
$649$	−13.9439	−0.547347
$650$	−20.9117	−0.820225
$651$	13.8202	0.541655
$652$	69.3428	2.71567
$653$	−37.6861	−1.47477	−0.737385	−	0.675473i	$-0.763940\pi$
$653$	−37.6861	−1.47477	−0.737385	+	0.675473i	$0.763940\pi$
$654$	26.5459	1.03803
$655$	−4.29965	−0.168001
$656$	−7.72162	−0.301478
$657$	52.7190	2.05677
$658$	−21.7292	−0.847093
$659$	11.1405	0.433972	0.216986	−	0.976175i	$-0.430377\pi$
$659$	11.1405	0.433972	0.216986	+	0.976175i	$0.430377\pi$
$660$	12.7655	0.496894
$661$	−8.61300	−0.335007	−0.167503	−	0.985871i	$-0.553571\pi$
$661$	−8.61300	−0.335007	−0.167503	+	0.985871i	$0.553571\pi$
$662$	−40.3462	−1.56810
$663$	5.73809	0.222849
$664$	7.02411	0.272588
$665$	2.71524	0.105293
$666$	63.1072	2.44535
$667$	−7.04765	−0.272886
$668$	5.41685	0.209584
$669$	11.8014	0.456267
$670$	−35.3937	−1.36738
$671$	14.3344	0.553372
$672$	−12.9468	−0.499434
$673$	46.2408	1.78245	0.891227	−	0.453558i	$-0.149846\pi$
$673$	46.2408	1.78245	0.891227	+	0.453558i	$0.149846\pi$
$674$	7.20330	0.277461
$675$	−4.10476	−0.157992
$676$	−24.3054	−0.934822
$677$	−38.4051	−1.47603	−0.738013	−	0.674786i	$-0.764236\pi$
$677$	−38.4051	−1.47603	−0.738013	+	0.674786i	$0.764236\pi$
$678$	79.6489	3.05890
$679$	−18.5630	−0.712383
$680$	4.18205	0.160374
$681$	−32.1317	−1.23129
$682$	9.61151	0.368044
$683$	−11.1107	−0.425140	−0.212570	−	0.977146i	$-0.568183\pi$
$683$	−11.1107	−0.425140	−0.212570	+	0.977146i	$0.568183\pi$
$684$	−18.1958	−0.695732
$685$	−9.25963	−0.353792
$686$	−42.3378	−1.61647
$687$	39.9896	1.52570
$688$	−11.0811	−0.422464
$689$	−2.97013	−0.113153
$690$	9.75616	0.371411
$691$	30.8409	1.17324	0.586621	−	0.809861i	$-0.300458\pi$
$691$	30.8409	1.17324	0.586621	+	0.809861i	$0.300458\pi$
$692$	7.41939	0.282043
$693$	−6.07748	−0.230864
$694$	−51.6709	−1.96140
$695$	−14.4656	−0.548710
$696$	−51.2614	−1.94306
$697$	3.81913	0.144660
$698$	4.73087	0.179066
$699$	−53.7519	−2.03309
$700$	19.5417	0.738607
$701$	−29.0874	−1.09862	−0.549308	−	0.835620i	$-0.685108\pi$
$701$	−29.0874	−1.09862	−0.549308	+	0.835620i	$0.685108\pi$
$702$	6.90821	0.260734
$703$	11.2208	0.423200
$704$	−13.1789	−0.496699
$705$	−18.4455	−0.694696
$706$	56.6805	2.13320
$707$	−1.47584	−0.0555047
$708$	−111.783	−4.20108
$709$	21.9548	0.824528	0.412264	−	0.911064i	$-0.364738\pi$
$709$	21.9548	0.824528	0.412264	+	0.911064i	$0.364738\pi$
$710$	11.9698	0.449219
$711$	−39.8064	−1.49286
$712$	−2.25704	−0.0845863
$713$	4.72790	0.177061
$714$	−8.33118	−0.311786
$715$	−3.48252	−0.130239
$716$	−60.5653	−2.26343
$717$	57.2662	2.13865
$718$	67.1120	2.50460
$719$	24.7340	0.922424	0.461212	−	0.887290i	$-0.347415\pi$
$719$	24.7340	0.922424	0.461212	+	0.887290i	$0.347415\pi$
$720$	7.65660	0.285345
$721$	6.98456	0.260119
$722$	39.9840	1.48805
$723$	26.2631	0.976736
$724$	37.2566	1.38463
$725$	−18.6183	−0.691466
$726$	58.3300	2.16483
$727$	−40.3533	−1.49662	−0.748310	−	0.663349i	$-0.769134\pi$
$727$	−40.3533	−1.49662	−0.748310	+	0.663349i	$0.769134\pi$
$728$	−14.6781	−0.544007
$729$	−34.5219	−1.27859
$730$	−43.8608	−1.62336
$731$	5.48075	0.202713
$732$	114.913	4.24733
$733$	16.7283	0.617873	0.308937	−	0.951083i	$-0.400027\pi$
$733$	16.7283	0.617873	0.308937	+	0.951083i	$0.400027\pi$
$734$	−57.6820	−2.12908
$735$	−14.3347	−0.528743
$736$	−4.42912	−0.163260
$737$	14.0859	0.518861
$738$	34.7008	1.27736
$739$	18.8431	0.693156	0.346578	−	0.938021i	$-0.387344\pi$
$739$	18.8431	0.693156	0.346578	+	0.938021i	$0.387344\pi$
$740$	−33.7926	−1.24224
$741$	9.27017	0.340548
$742$	4.31236	0.158312
$743$	37.8809	1.38972	0.694858	−	0.719147i	$-0.255467\pi$
$743$	37.8809	1.38972	0.694858	+	0.719147i	$0.255467\pi$
$744$	34.3886	1.26075
$745$	0.872663	0.0319719
$746$	45.3173	1.65918
$747$	−6.36054	−0.232720
$748$	−3.72923	−0.136354
$749$	12.0472	0.440193
$750$	62.3321	2.27605
$751$	−10.0134	−0.365394	−0.182697	−	0.983169i	$-0.558483\pi$
$751$	−10.0134	−0.365394	−0.182697	+	0.983169i	$0.558483\pi$
$752$	−10.8947	−0.397290
$753$	51.6145	1.88094
$754$	31.3341	1.14112
$755$	−16.5549	−0.602494
$756$	−6.45563	−0.234789
$757$	17.3647	0.631130	0.315565	−	0.948904i	$-0.397806\pi$
$757$	17.3647	0.631130	0.315565	+	0.948904i	$0.397806\pi$
$758$	−44.0329	−1.59935
$759$	−3.88274	−0.140935
$760$	6.75631	0.245077
$761$	−13.6710	−0.495574	−0.247787	−	0.968815i	$-0.579703\pi$
$761$	−13.6710	−0.495574	−0.247787	+	0.968815i	$0.579703\pi$
$762$	−73.7896	−2.67312
$763$	6.76749	0.245000
$764$	15.9965	0.578732
$765$	−3.78697	−0.136918
$766$	31.9049	1.15277
$767$	30.4954	1.10113
$768$	−65.6832	−2.37014
$769$	46.6592	1.68258	0.841288	−	0.540588i	$-0.181798\pi$
$769$	46.6592	1.68258	0.841288	+	0.540588i	$0.181798\pi$
$770$	5.05630	0.182216
$771$	37.3896	1.34655
$772$	77.4954	2.78912
$773$	−28.3104	−1.01825	−0.509127	−	0.860691i	$-0.670032\pi$
$773$	−28.3104	−1.01825	−0.509127	+	0.860691i	$0.670032\pi$
$774$	49.7985	1.78997
$775$	12.4900	0.448655
$776$	−46.1902	−1.65813
$777$	30.0448	1.07785
$778$	−50.0367	−1.79390
$779$	6.16999	0.221063
$780$	−27.9181	−0.999629
$781$	−4.76373	−0.170460
$782$	−2.85011	−0.101920
$783$	6.15058	0.219804
$784$	−8.46671	−0.302383
$785$	−7.73086	−0.275926
$786$	21.3133	0.760221
$787$	21.1195	0.752827	0.376414	−	0.926452i	$-0.377157\pi$
$787$	21.1195	0.752827	0.376414	+	0.926452i	$0.377157\pi$
$788$	55.2271	1.96738
$789$	33.2870	1.18505
$790$	33.1179	1.17828
$791$	20.3053	0.721974
$792$	−15.1225	−0.537356
$793$	−31.3493	−1.11325
$794$	88.0083	3.12330
$795$	3.66067	0.129830
$796$	−68.6478	−2.43316
$797$	−20.4792	−0.725412	−0.362706	−	0.931904i	$-0.618147\pi$
$797$	−20.4792	−0.725412	−0.362706	+	0.931904i	$0.618147\pi$
$798$	−13.4594	−0.476459
$799$	5.38855	0.190633
$800$	−11.7007	−0.413683
$801$	2.04382	0.0722149
$802$	3.58772	0.126687
$803$	17.4557	0.615997
$804$	112.922	3.98244
$805$	2.48719	0.0876620
$806$	−21.0204	−0.740413
$807$	−37.1386	−1.30734
$808$	−3.67232	−0.129192
$809$	−45.6659	−1.60553	−0.802764	−	0.596296i	$-0.796638\pi$
$809$	−45.6659	−1.60553	−0.802764	+	0.596296i	$0.796638\pi$
$810$	21.3351	0.749639
$811$	−23.7583	−0.834268	−0.417134	−	0.908845i	$-0.636965\pi$
$811$	−23.7583	−0.834268	−0.417134	+	0.908845i	$0.636965\pi$
$812$	−29.2813	−1.02757
$813$	−23.8603	−0.836816
$814$	20.8953	0.732378
$815$	23.3154	0.816704
$816$	−4.17714	−0.146229
$817$	8.85444	0.309777
$818$	8.25406	0.288596
$819$	13.2915	0.464442
$820$	−18.5816	−0.648898
$821$	−14.8034	−0.516641	−0.258321	−	0.966059i	$-0.583169\pi$
$821$	−14.8034	−0.516641	−0.258321	+	0.966059i	$0.583169\pi$
$822$	45.9000	1.60095
$823$	−25.7734	−0.898406	−0.449203	−	0.893430i	$-0.648292\pi$
$823$	−25.7734	−0.898406	−0.449203	+	0.893430i	$0.648292\pi$
$824$	17.3796	0.605448
$825$	−10.2573	−0.357114
$826$	−44.2766	−1.54058
$827$	21.5843	0.750560	0.375280	−	0.926911i	$-0.377547\pi$
$827$	21.5843	0.750560	0.375280	+	0.926911i	$0.377547\pi$
$828$	−16.6675	−0.579237
$829$	−52.9760	−1.83993	−0.919967	−	0.391996i	$-0.871785\pi$
$829$	−52.9760	−1.83993	−0.919967	+	0.391996i	$0.871785\pi$
$830$	5.29180	0.183681
$831$	−21.1574	−0.733943
$832$	28.8224	0.999235
$833$	4.18765	0.145094
$834$	71.7057	2.48297
$835$	1.82133	0.0630297
$836$	−6.02475	−0.208370
$837$	−4.12610	−0.142619
$838$	21.0769	0.728089
$839$	−0.0848679	−0.00292997	−0.00146498	−	0.999999i	$-0.500466\pi$
$839$	−0.0848679	−0.00292997	−0.00146498	+	0.999999i	$0.500466\pi$
$840$	18.0907	0.624188
$841$	−1.10232	−0.0380112
$842$	−59.7222	−2.05816
$843$	−73.6405	−2.53631
$844$	100.235	3.45021
$845$	−8.17230	−0.281136
$846$	48.9607	1.68330
$847$	14.8704	0.510952
$848$	2.16216	0.0742487
$849$	−0.887024	−0.0304426
$850$	−7.52934	−0.258254
$851$	10.2784	0.352338
$852$	−38.1892	−1.30834
$853$	12.5621	0.430117	0.215059	−	0.976601i	$-0.431006\pi$
$853$	12.5621	0.430117	0.215059	+	0.976601i	$0.431006\pi$
$854$	45.5164	1.55754
$855$	−6.11804	−0.209233
$856$	29.9768	1.02459
$857$	−1.47124	−0.0502566	−0.0251283	−	0.999684i	$-0.507999\pi$
$857$	−1.47124	−0.0502566	−0.0251283	+	0.999684i	$0.507999\pi$
$858$	17.2628	0.589344
$859$	−21.2399	−0.724696	−0.362348	−	0.932043i	$-0.618025\pi$
$859$	−21.2399	−0.724696	−0.362348	+	0.932043i	$0.618025\pi$
$860$	−26.6661	−0.909306
$861$	16.5208	0.563026
$862$	75.9042	2.58531
$863$	−12.6219	−0.429654	−0.214827	−	0.976652i	$-0.568919\pi$
$863$	−12.6219	−0.429654	−0.214827	+	0.976652i	$0.568919\pi$
$864$	3.86535	0.131502
$865$	2.49465	0.0848208
$866$	−52.5898	−1.78707
$867$	−41.1361	−1.39706
$868$	19.6433	0.666737
$869$	−13.1802	−0.447108
$870$	−38.6191	−1.30931
$871$	−30.8060	−1.04382
$872$	16.8395	0.570257
$873$	41.8266	1.41562
$874$	−4.60450	−0.155749
$875$	15.8907	0.537202
$876$	139.936	4.72800
$877$	51.6150	1.74292	0.871458	−	0.490470i	$-0.163175\pi$
$877$	51.6150	1.74292	0.871458	+	0.490470i	$0.163175\pi$
$878$	35.6148	1.20194
$879$	12.9472	0.436700
$880$	2.53516	0.0854601
$881$	−46.9346	−1.58127	−0.790633	−	0.612290i	$-0.790249\pi$
$881$	−46.9346	−1.58127	−0.790633	+	0.612290i	$0.790249\pi$
$882$	38.0493	1.28119
$883$	40.1623	1.35157	0.675785	−	0.737099i	$-0.263805\pi$
$883$	40.1623	1.35157	0.675785	+	0.737099i	$0.263805\pi$
$884$	8.15584	0.274311
$885$	−37.5854	−1.26342
$886$	−87.2601	−2.93156
$887$	−33.0229	−1.10880	−0.554401	−	0.832250i	$-0.687053\pi$
$887$	−33.0229	−1.10880	−0.554401	+	0.832250i	$0.687053\pi$
$888$	74.7601	2.50879
$889$	−18.8116	−0.630921
$890$	−1.70040	−0.0569977
$891$	−8.49092	−0.284456
$892$	16.7739	0.561631
$893$	8.70548	0.291318
$894$	−4.32579	−0.144676
$895$	−20.3641	−0.680698
$896$	−31.6583	−1.05763
$897$	8.49159	0.283526
$898$	29.8525	0.996191
$899$	−18.7151	−0.624183
$900$	−44.0318	−1.46773
$901$	−1.06941	−0.0356271
$902$	11.4897	0.382565
$903$	23.7086	0.788974
$904$	50.5255	1.68045
$905$	12.5269	0.416410
$906$	82.0625	2.72634
$907$	−34.3118	−1.13930	−0.569652	−	0.821886i	$-0.692922\pi$
$907$	−34.3118	−1.13930	−0.569652	+	0.821886i	$0.692922\pi$
$908$	−45.6705	−1.51563
$909$	3.32540	0.110297
$910$	−11.0582	−0.366574
$911$	7.67120	0.254158	0.127079	−	0.991893i	$-0.459440\pi$
$911$	7.67120	0.254158	0.127079	+	0.991893i	$0.459440\pi$
$912$	−6.74837	−0.223461
$913$	−2.10602	−0.0696992
$914$	62.2583	2.05932
$915$	38.6379	1.27733
$916$	56.8392	1.87802
$917$	5.43352	0.179431
$918$	2.48733	0.0820940
$919$	7.53013	0.248396	0.124198	−	0.992257i	$-0.460364\pi$
$919$	7.53013	0.248396	0.124198	+	0.992257i	$0.460364\pi$
$920$	6.18886	0.204041
$921$	5.88281	0.193845
$922$	−66.4987	−2.19002
$923$	10.4183	0.342923
$924$	−16.1319	−0.530700
$925$	27.1531	0.892789
$926$	−3.53909	−0.116302
$927$	−15.7378	−0.516896
$928$	17.5324	0.575529
$929$	−15.7263	−0.515963	−0.257982	−	0.966150i	$-0.583057\pi$
$929$	−15.7263	−0.515963	−0.257982	+	0.966150i	$0.583057\pi$
$930$	25.9076	0.849542
$931$	6.76536	0.221726
$932$	−76.4004	−2.50258
$933$	−20.5949	−0.674248
$934$	87.7208	2.87031
$935$	−1.25389	−0.0410067
$936$	33.0731	1.08103
$937$	−1.74741	−0.0570853	−0.0285427	−	0.999593i	$-0.509087\pi$
$937$	−1.74741	−0.0570853	−0.0285427	+	0.999593i	$0.509087\pi$
$938$	44.7275	1.46040
$939$	47.7443	1.55808
$940$	−26.2175	−0.855120
$941$	52.6406	1.71604	0.858018	−	0.513620i	$-0.171696\pi$
$941$	52.6406	1.71604	0.858018	+	0.513620i	$0.171696\pi$
$942$	38.3219	1.24859
$943$	5.65179	0.184047
$944$	−22.1997	−0.722537
$945$	−2.17060	−0.0706098
$946$	16.4887	0.536092
$947$	−30.3669	−0.986792	−0.493396	−	0.869805i	$-0.664245\pi$
$947$	−30.3669	−0.986792	−0.493396	+	0.869805i	$0.664245\pi$
$948$	−105.661	−3.43171
$949$	−38.1757	−1.23923
$950$	−12.1640	−0.394653
$951$	42.2176	1.36900
$952$	−5.28491	−0.171285
$953$	−0.105640	−0.00342203	−0.00171101	−	0.999999i	$-0.500545\pi$
$953$	−0.105640	−0.00342203	−0.00171101	+	0.999999i	$0.500545\pi$
$954$	−9.71670	−0.314590
$955$	5.37856	0.174046
$956$	81.3954	2.63252
$957$	15.3696	0.496828
$958$	−14.0537	−0.454055
$959$	11.7015	0.377862
$960$	−35.5234	−1.14651
$961$	−18.4450	−0.595001
$962$	−45.6980	−1.47336
$963$	−27.1449	−0.874733
$964$	37.3291	1.20229
$965$	26.0566	0.838792
$966$	−12.3290	−0.396679
$967$	17.2105	0.553451	0.276725	−	0.960949i	$-0.410751\pi$
$967$	17.2105	0.553451	0.276725	+	0.960949i	$0.410751\pi$
$968$	37.0018	1.18928
$969$	3.33776	0.107224
$970$	−34.7986	−1.11732
$971$	−29.0333	−0.931722	−0.465861	−	0.884858i	$-0.654255\pi$
$971$	−29.0333	−0.931722	−0.465861	+	0.884858i	$0.654255\pi$
$972$	−80.6872	−2.58804
$973$	18.2803	0.586041
$974$	23.4898	0.752661
$975$	22.4328	0.718426
$976$	22.8213	0.730491
$977$	16.9752	0.543084	0.271542	−	0.962427i	$-0.412466\pi$
$977$	16.9752	0.543084	0.271542	+	0.962427i	$0.412466\pi$
$978$	−115.575	−3.69567
$979$	0.676725	0.0216282
$980$	−20.3746	−0.650843
$981$	−15.2487	−0.486853
$982$	27.7098	0.884257
$983$	−13.5187	−0.431179	−0.215589	−	0.976484i	$-0.569167\pi$
$983$	−13.5187	−0.431179	−0.215589	+	0.976484i	$0.569167\pi$
$984$	41.1085	1.31049
$985$	18.5692	0.591665
$986$	11.2820	0.359291
$987$	23.3098	0.741959
$988$	13.1762	0.419190
$989$	8.11077	0.257907
$990$	−11.3930	−0.362092
$991$	4.35433	0.138320	0.0691599	−	0.997606i	$-0.477968\pi$
$991$	4.35433	0.138320	0.0691599	+	0.997606i	$0.477968\pi$
$992$	−11.7616	−0.373430
$993$	43.2809	1.37348
$994$	−15.1264	−0.479781
$995$	−23.0818	−0.731741
$996$	−16.8832	−0.534966
$997$	8.61019	0.272688	0.136344	−	0.990662i	$-0.456465\pi$
$997$	8.61019	0.272688	0.136344	+	0.990662i	$0.456465\pi$
$998$	27.8535	0.881688
$999$	−8.97007	−0.283800

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	4021.2.a.b.1.17	✓	151

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
4021.2.a.b.1.17	✓	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)

\(f(q)\)	\(=\)	\(q-2.36898 q^{2} +2.54130 q^{3} +3.61208 q^{4} +1.21451 q^{5} -6.02031 q^{6} -1.53479 q^{7} -3.81900 q^{8} +3.45822 q^{9} +O(q^{10})\)	\(q-2.36898 q^{2} +2.54130 q^{3} +3.61208 q^{4} +1.21451 q^{5} -6.02031 q^{6} -1.53479 q^{7} -3.81900 q^{8} +3.45822 q^{9} -2.87715 q^{10} +1.14504 q^{11} +9.17940 q^{12} -2.50422 q^{13} +3.63589 q^{14} +3.08643 q^{15} +1.82298 q^{16} -0.901652 q^{17} -8.19247 q^{18} -1.45666 q^{19} +4.38690 q^{20} -3.90036 q^{21} -2.71259 q^{22} -1.33432 q^{23} -9.70524 q^{24} -3.52497 q^{25} +5.93245 q^{26} +1.16448 q^{27} -5.54379 q^{28} +5.28183 q^{29} -7.31170 q^{30} -3.54330 q^{31} +3.31938 q^{32} +2.90990 q^{33} +2.13600 q^{34} -1.86401 q^{35} +12.4914 q^{36} -7.70307 q^{37} +3.45081 q^{38} -6.36397 q^{39} -4.63820 q^{40} -4.23570 q^{41} +9.23990 q^{42} -6.07857 q^{43} +4.13599 q^{44} +4.20003 q^{45} +3.16099 q^{46} -5.97631 q^{47} +4.63276 q^{48} -4.64442 q^{49} +8.35060 q^{50} -2.29137 q^{51} -9.04544 q^{52} +1.18605 q^{53} -2.75863 q^{54} +1.39066 q^{55} +5.86136 q^{56} -3.70183 q^{57} -12.5126 q^{58} -12.1776 q^{59} +11.1484 q^{60} +12.5186 q^{61} +8.39402 q^{62} -5.30764 q^{63} -11.5095 q^{64} -3.04139 q^{65} -6.89351 q^{66} +12.3016 q^{67} -3.25684 q^{68} -3.39092 q^{69} +4.41581 q^{70} -4.16031 q^{71} -13.2070 q^{72} +15.2446 q^{73} +18.2484 q^{74} -8.95802 q^{75} -5.26160 q^{76} -1.75740 q^{77} +15.0761 q^{78} -11.5107 q^{79} +2.21403 q^{80} -7.41537 q^{81} +10.0343 q^{82} -1.83925 q^{83} -14.0884 q^{84} -1.09506 q^{85} +14.4000 q^{86} +13.4227 q^{87} -4.37292 q^{88} +0.591004 q^{89} -9.94981 q^{90} +3.84344 q^{91} -4.81968 q^{92} -9.00460 q^{93} +14.1578 q^{94} -1.76913 q^{95} +8.43556 q^{96} +12.0948 q^{97} +11.0026 q^{98} +3.95981 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 151 q - 16 q^{2} - 29 q^{3} + 120 q^{4} - 27 q^{5} - 18 q^{6} - 18 q^{7} - 48 q^{8} + 98 q^{9}+O(q^{10}) \) 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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