LMFDB - Embedded newform 4021.2.a.b.1.8

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			1.8
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)

$f(q)$	$=$	$q-2.64112 q^{2} +2.33893 q^{3} +4.97551 q^{4} -1.70298 q^{5} -6.17740 q^{6} +0.267464 q^{7} -7.85867 q^{8} +2.47061 q^{9} +O(q^{10})$	\(q-2.64112 q^{2} +2.33893 q^{3} +4.97551 q^{4} -1.70298 q^{5} -6.17740 q^{6} +0.267464 q^{7} -7.85867 q^{8} +2.47061 q^{9} +4.49778 q^{10} -2.86096 q^{11} +11.6374 q^{12} +4.88262 q^{13} -0.706405 q^{14} -3.98316 q^{15} +10.8047 q^{16} -0.337304 q^{17} -6.52517 q^{18} +1.63565 q^{19} -8.47320 q^{20} +0.625581 q^{21} +7.55614 q^{22} +4.18466 q^{23} -18.3809 q^{24} -2.09985 q^{25} -12.8956 q^{26} -1.23821 q^{27} +1.33077 q^{28} -8.63683 q^{29} +10.5200 q^{30} +3.34692 q^{31} -12.8190 q^{32} -6.69160 q^{33} +0.890860 q^{34} -0.455487 q^{35} +12.2925 q^{36} -5.23530 q^{37} -4.31996 q^{38} +11.4201 q^{39} +13.3832 q^{40} +4.38273 q^{41} -1.65223 q^{42} -11.7088 q^{43} -14.2347 q^{44} -4.20740 q^{45} -11.0522 q^{46} -9.72247 q^{47} +25.2714 q^{48} -6.92846 q^{49} +5.54595 q^{50} -0.788931 q^{51} +24.2935 q^{52} -8.61045 q^{53} +3.27026 q^{54} +4.87217 q^{55} -2.10191 q^{56} +3.82569 q^{57} +22.8109 q^{58} +5.00666 q^{59} -19.8183 q^{60} -4.61736 q^{61} -8.83962 q^{62} +0.660800 q^{63} +12.2473 q^{64} -8.31503 q^{65} +17.6733 q^{66} +13.2731 q^{67} -1.67826 q^{68} +9.78764 q^{69} +1.20300 q^{70} +13.4925 q^{71} -19.4157 q^{72} +5.81485 q^{73} +13.8271 q^{74} -4.91141 q^{75} +8.13821 q^{76} -0.765205 q^{77} -30.1619 q^{78} +12.4103 q^{79} -18.4001 q^{80} -10.3079 q^{81} -11.5753 q^{82} -7.91183 q^{83} +3.11258 q^{84} +0.574423 q^{85} +30.9242 q^{86} -20.2010 q^{87} +22.4833 q^{88} -14.0350 q^{89} +11.1123 q^{90} +1.30593 q^{91} +20.8208 q^{92} +7.82823 q^{93} +25.6782 q^{94} -2.78549 q^{95} -29.9829 q^{96} +15.3042 q^{97} +18.2989 q^{98} -7.06832 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	−2.64112	−1.86755	−0.933776	−	0.357857i	$-0.883508\pi$
$2$	−2.64112	−1.86755	−0.933776	+	0.357857i	$0.883508\pi$
$3$	2.33893	1.35038	0.675192	−	0.737642i	$-0.264061\pi$
$3$	2.33893	1.35038	0.675192	+	0.737642i	$0.264061\pi$
$4$	4.97551	2.48775
$5$	−1.70298	−0.761597	−0.380799	−	0.924658i	$-0.624351\pi$
$5$	−1.70298	−0.761597	−0.380799	+	0.924658i	$0.624351\pi$
$6$	−6.17740	−2.52191
$7$	0.267464	0.101092	0.0505460	−	0.998722i	$-0.483904\pi$
$7$	0.267464	0.101092	0.0505460	+	0.998722i	$0.483904\pi$
$8$	−7.85867	−2.77846
$9$	2.47061	0.823536
$10$	4.49778	1.42232
$11$	−2.86096	−0.862612	−0.431306	−	0.902206i	$-0.641947\pi$
$11$	−2.86096	−0.862612	−0.431306	+	0.902206i	$0.641947\pi$
$12$	11.6374	3.35942
$13$	4.88262	1.35420	0.677098	−	0.735893i	$-0.263237\pi$
$13$	4.88262	1.35420	0.677098	+	0.735893i	$0.263237\pi$
$14$	−0.706405	−0.188795
$15$	−3.98316	−1.02845
$16$	10.8047	2.70116
$17$	−0.337304	−0.0818082	−0.0409041	−	0.999163i	$-0.513024\pi$
$17$	−0.337304	−0.0818082	−0.0409041	+	0.999163i	$0.513024\pi$
$18$	−6.52517	−1.53800
$19$	1.63565	0.375245	0.187622	−	0.982241i	$-0.439922\pi$
$19$	1.63565	0.375245	0.187622	+	0.982241i	$0.439922\pi$
$20$	−8.47320	−1.89467
$21$	0.625581	0.136513
$22$	7.55614	1.61097
$23$	4.18466	0.872562	0.436281	−	0.899810i	$-0.356295\pi$
$23$	4.18466	0.872562	0.436281	+	0.899810i	$0.356295\pi$
$24$	−18.3809	−3.75198
$25$	−2.09985	−0.419970
$26$	−12.8956	−2.52903
$27$	−1.23821	−0.238294
$28$	1.33077	0.251492
$29$	−8.63683	−1.60382	−0.801909	−	0.597446i	$-0.796182\pi$
$29$	−8.63683	−1.60382	−0.801909	+	0.597446i	$0.796182\pi$
$30$	10.5200	1.92068
$31$	3.34692	0.601125	0.300563	−	0.953762i	$-0.402826\pi$
$31$	3.34692	0.601125	0.300563	+	0.953762i	$0.402826\pi$
$32$	−12.8190	−2.26611
$33$	−6.69160	−1.16486
$34$	0.890860	0.152781
$35$	−0.455487	−0.0769914
$36$	12.2925	2.04876
$37$	−5.23530	−0.860679	−0.430339	−	0.902667i	$-0.641606\pi$
$37$	−5.23530	−0.860679	−0.430339	+	0.902667i	$0.641606\pi$
$38$	−4.31996	−0.700789
$39$	11.4201	1.82868
$40$	13.3832	2.11607
$41$	4.38273	0.684467	0.342234	−	0.939615i	$-0.388817\pi$
$41$	4.38273	0.684467	0.342234	+	0.939615i	$0.388817\pi$
$42$	−1.65223	−0.254945
$43$	−11.7088	−1.78557	−0.892784	−	0.450485i	$-0.851251\pi$
$43$	−11.7088	−1.78557	−0.892784	+	0.450485i	$0.851251\pi$
$44$	−14.2347	−2.14597
$45$	−4.20740	−0.627203
$46$	−11.0522	−1.62956
$47$	−9.72247	−1.41817	−0.709084	−	0.705124i	$-0.750891\pi$
$47$	−9.72247	−1.41817	−0.709084	+	0.705124i	$0.750891\pi$
$48$	25.2714	3.64761
$49$	−6.92846	−0.989780
$50$	5.54595	0.784316
$51$	−0.788931	−0.110472
$52$	24.2935	3.36891
$53$	−8.61045	−1.18274	−0.591368	−	0.806402i	$-0.701412\pi$
$53$	−8.61045	−1.18274	−0.591368	+	0.806402i	$0.701412\pi$
$54$	3.27026	0.445026
$55$	4.87217	0.656963
$56$	−2.10191	−0.280880
$57$	3.82569	0.506724
$58$	22.8109	2.99522
$59$	5.00666	0.651812	0.325906	−	0.945402i	$-0.394331\pi$
$59$	5.00666	0.651812	0.325906	+	0.945402i	$0.394331\pi$
$60$	−19.8183	−2.55853
$61$	−4.61736	−0.591192	−0.295596	−	0.955313i	$-0.595518\pi$
$61$	−4.61736	−0.591192	−0.295596	+	0.955313i	$0.595518\pi$
$62$	−8.83962	−1.12263
$63$	0.660800	0.0832529
$64$	12.2473	1.53091
$65$	−8.31503	−1.03135
$66$	17.6733	2.17543
$67$	13.2731	1.62157	0.810784	−	0.585345i	$-0.199041\pi$
$67$	13.2731	1.62157	0.810784	+	0.585345i	$0.199041\pi$
$68$	−1.67826	−0.203519
$69$	9.78764	1.17829
$70$	1.20300	0.143785
$71$	13.4925	1.60126	0.800631	−	0.599158i	$-0.204498\pi$
$71$	13.4925	1.60126	0.800631	+	0.599158i	$0.204498\pi$
$72$	−19.4157	−2.28816
$73$	5.81485	0.680577	0.340289	−	0.940321i	$-0.389475\pi$
$73$	5.81485	0.680577	0.340289	+	0.940321i	$0.389475\pi$
$74$	13.8271	1.60736
$75$	−4.91141	−0.567120
$76$	8.13821	0.933517
$77$	−0.765205	−0.0872032
$78$	−30.1619	−3.41517
$79$	12.4103	1.39627	0.698134	−	0.715967i	$-0.254014\pi$
$79$	12.4103	1.39627	0.698134	+	0.715967i	$0.254014\pi$
$80$	−18.4001	−2.05720
$81$	−10.3079	−1.14532
$82$	−11.5753	−1.27828
$83$	−7.91183	−0.868437	−0.434218	−	0.900808i	$-0.642975\pi$
$83$	−7.91183	−0.868437	−0.434218	+	0.900808i	$0.642975\pi$
$84$	3.11258	0.339611
$85$	0.574423	0.0623049
$86$	30.9242	3.33464
$87$	−20.2010	−2.16577
$88$	22.4833	2.39673
$89$	−14.0350	−1.48771	−0.743853	−	0.668343i	$-0.767004\pi$
$89$	−14.0350	−1.48771	−0.743853	+	0.668343i	$0.767004\pi$
$90$	11.1123	1.17133
$91$	1.30593	0.136898
$92$	20.8208	2.17072
$93$	7.82823	0.811750
$94$	25.6782	2.64850
$95$	−2.78549	−0.285785
$96$	−29.9829	−3.06011
$97$	15.3042	1.55391	0.776955	−	0.629556i	$-0.216763\pi$
$97$	15.3042	1.55391	0.776955	+	0.629556i	$0.216763\pi$
$98$	18.2989	1.84847
$99$	−7.06832	−0.710393
$100$	−10.4478	−1.04478
$101$	−12.6178	−1.25552	−0.627758	−	0.778409i	$-0.716027\pi$
$101$	−12.6178	−1.25552	−0.627758	+	0.778409i	$0.716027\pi$
$102$	2.08366	0.206313
$103$	−3.02174	−0.297741	−0.148870	−	0.988857i	$-0.547564\pi$
$103$	−3.02174	−0.297741	−0.148870	+	0.988857i	$0.547564\pi$
$104$	−38.3709	−3.76258
$105$	−1.06535	−0.103968
$106$	22.7412	2.20882
$107$	18.9300	1.83004	0.915018	−	0.403413i	$-0.132176\pi$
$107$	18.9300	1.83004	0.915018	+	0.403413i	$0.132176\pi$
$108$	−6.16073	−0.592816
$109$	−19.1737	−1.83651	−0.918253	−	0.395995i	$-0.870400\pi$
$109$	−19.1737	−1.83651	−0.918253	+	0.395995i	$0.870400\pi$
$110$	−12.8680	−1.22691
$111$	−12.2450	−1.16225
$112$	2.88986	0.273066
$113$	−3.82240	−0.359581	−0.179791	−	0.983705i	$-0.557542\pi$
$113$	−3.82240	−0.359581	−0.179791	+	0.983705i	$0.557542\pi$
$114$	−10.1041	−0.946335
$115$	−7.12641	−0.664541
$116$	−42.9726	−3.98990
$117$	12.0631	1.11523
$118$	−13.2232	−1.21729
$119$	−0.0902168	−0.00827016
$120$	31.3023	2.85750
$121$	−2.81490	−0.255900
$122$	12.1950	1.10408
$123$	10.2509	0.924294
$124$	16.6526	1.49545
$125$	12.0909	1.08144
$126$	−1.74525	−0.155479
$127$	−13.4355	−1.19221	−0.596103	−	0.802908i	$-0.703285\pi$
$127$	−13.4355	−1.19221	−0.596103	+	0.802908i	$0.703285\pi$
$128$	−6.70847	−0.592951
$129$	−27.3860	−2.41120
$130$	21.9610	1.92610
$131$	4.77138	0.416877	0.208439	−	0.978035i	$-0.433162\pi$
$131$	4.77138	0.416877	0.208439	+	0.978035i	$0.433162\pi$
$132$	−33.2941	−2.89788
$133$	0.437479	0.0379343
$134$	−35.0558	−3.02836
$135$	2.10865	0.181484
$136$	2.65076	0.227301
$137$	−8.92455	−0.762475	−0.381238	−	0.924477i	$-0.624502\pi$
$137$	−8.92455	−0.762475	−0.381238	+	0.924477i	$0.624502\pi$
$138$	−25.8503	−2.20053
$139$	16.3436	1.38625	0.693123	−	0.720819i	$-0.256234\pi$
$139$	16.3436	1.38625	0.693123	+	0.720819i	$0.256234\pi$
$140$	−2.26628	−0.191536
$141$	−22.7402	−1.91507
$142$	−35.6352	−2.99044
$143$	−13.9690	−1.16815
$144$	26.6941	2.22451
$145$	14.7084	1.22146
$146$	−15.3577	−1.27101
$147$	−16.2052	−1.33658
$148$	−26.0483	−2.14116
$149$	5.12123	0.419547	0.209774	−	0.977750i	$-0.432727\pi$
$149$	5.12123	0.419547	0.209774	+	0.977750i	$0.432727\pi$
$150$	12.9716	1.05913
$151$	12.3814	1.00758	0.503790	−	0.863826i	$-0.331939\pi$
$151$	12.3814	1.00758	0.503790	+	0.863826i	$0.331939\pi$
$152$	−12.8541	−1.04260
$153$	−0.833346	−0.0673720
$154$	2.02100	0.162857
$155$	−5.69975	−0.457815
$156$	56.8210	4.54932
$157$	3.31570	0.264622	0.132311	−	0.991208i	$-0.457760\pi$
$157$	3.31570	0.264622	0.132311	+	0.991208i	$0.457760\pi$
$158$	−32.7771	−2.60760
$159$	−20.1393	−1.59715
$160$	21.8306	1.72586
$161$	1.11925	0.0882091
$162$	27.2244	2.13895
$163$	−10.2509	−0.802909	−0.401455	−	0.915879i	$-0.631495\pi$
$163$	−10.2509	−0.802909	−0.401455	+	0.915879i	$0.631495\pi$
$164$	21.8063	1.70279
$165$	11.3957	0.887152
$166$	20.8961	1.62185
$167$	−17.7836	−1.37614	−0.688069	−	0.725646i	$-0.741541\pi$
$167$	−17.7836	−1.37614	−0.688069	+	0.725646i	$0.741541\pi$
$168$	−4.91623	−0.379296
$169$	10.8400	0.833848
$170$	−1.51712	−0.116358
$171$	4.04106	0.309028
$172$	−58.2570	−4.44205
$173$	−4.60308	−0.349966	−0.174983	−	0.984571i	$-0.555987\pi$
$173$	−4.60308	−0.349966	−0.174983	+	0.984571i	$0.555987\pi$
$174$	53.3531	4.04469
$175$	−0.561635	−0.0424556
$176$	−30.9117	−2.33006
$177$	11.7103	0.880197
$178$	37.0681	2.77837
$179$	−18.5444	−1.38608	−0.693038	−	0.720901i	$-0.743728\pi$
$179$	−18.5444	−1.38608	−0.693038	+	0.720901i	$0.743728\pi$
$180$	−20.9340	−1.56033
$181$	−19.7858	−1.47067	−0.735333	−	0.677706i	$-0.762974\pi$
$181$	−19.7858	−1.47067	−0.735333	+	0.677706i	$0.762974\pi$
$182$	−3.44911	−0.255665
$183$	−10.7997	−0.798336
$184$	−32.8859	−2.42438
$185$	8.91563	0.655490
$186$	−20.6753	−1.51599
$187$	0.965014	0.0705688
$188$	−48.3742	−3.52805
$189$	−0.331177	−0.0240896
$190$	7.35681	0.533719
$191$	−5.14511	−0.372287	−0.186143	−	0.982523i	$-0.559599\pi$
$191$	−5.14511	−0.372287	−0.186143	+	0.982523i	$0.559599\pi$
$192$	28.6456	2.06732
$193$	−22.3158	−1.60633	−0.803163	−	0.595759i	$-0.796851\pi$
$193$	−22.3158	−1.60633	−0.803163	+	0.595759i	$0.796851\pi$
$194$	−40.4203	−2.90201
$195$	−19.4483	−1.39272
$196$	−34.4726	−2.46233
$197$	3.97472	0.283187	0.141594	−	0.989925i	$-0.454777\pi$
$197$	3.97472	0.283187	0.141594	+	0.989925i	$0.454777\pi$
$198$	18.6683	1.32670
$199$	−23.6301	−1.67509	−0.837546	−	0.546367i	$-0.816010\pi$
$199$	−23.6301	−1.67509	−0.837546	+	0.546367i	$0.816010\pi$
$200$	16.5020	1.16687
$201$	31.0449	2.18974
$202$	33.3250	2.34474
$203$	−2.31004	−0.162133
$204$	−3.92533	−0.274828
$205$	−7.46371	−0.521288
$206$	7.98077	0.556047
$207$	10.3387	0.718587
$208$	52.7551	3.65791
$209$	−4.67954	−0.323691
$210$	2.81373	0.194166
$211$	−6.03251	−0.415295	−0.207647	−	0.978204i	$-0.566581\pi$
$211$	−6.03251	−0.415295	−0.207647	+	0.978204i	$0.566581\pi$
$212$	−42.8413	−2.94236
$213$	31.5580	2.16232
$214$	−49.9965	−3.41769
$215$	19.9398	1.35988
$216$	9.73069	0.662089
$217$	0.895183	0.0607690
$218$	50.6400	3.42977
$219$	13.6006	0.919040
$220$	24.2415	1.63436
$221$	−1.64693	−0.110784
$222$	32.3406	2.17056
$223$	11.1544	0.746951	0.373476	−	0.927640i	$-0.378166\pi$
$223$	11.1544	0.746951	0.373476	+	0.927640i	$0.378166\pi$
$224$	−3.42864	−0.229085
$225$	−5.18791	−0.345860
$226$	10.0954	0.671537
$227$	−27.2502	−1.80866	−0.904330	−	0.426833i	$-0.859629\pi$
$227$	−27.2502	−1.80866	−0.904330	+	0.426833i	$0.859629\pi$
$228$	19.0347	1.26061
$229$	18.0641	1.19371	0.596855	−	0.802349i	$-0.296417\pi$
$229$	18.0641	1.19371	0.596855	+	0.802349i	$0.296417\pi$
$230$	18.8217	1.24106
$231$	−1.78976	−0.117758
$232$	67.8739	4.45614
$233$	10.6154	0.695439	0.347719	−	0.937599i	$-0.386956\pi$
$233$	10.6154	0.695439	0.347719	+	0.937599i	$0.386956\pi$
$234$	−31.8600	−2.08275
$235$	16.5572	1.08007
$236$	24.9107	1.62155
$237$	29.0269	1.88550
$238$	0.238273	0.0154450
$239$	9.76298	0.631514	0.315757	−	0.948840i	$-0.397741\pi$
$239$	9.76298	0.631514	0.315757	+	0.948840i	$0.397741\pi$
$240$	−43.0367	−2.77801
$241$	−6.16498	−0.397121	−0.198561	−	0.980089i	$-0.563627\pi$
$241$	−6.16498	−0.397121	−0.198561	+	0.980089i	$0.563627\pi$
$242$	7.43448	0.477907
$243$	−20.3949	−1.30833
$244$	−22.9737	−1.47074
$245$	11.7991	0.753814
$246$	−27.0739	−1.72617
$247$	7.98629	0.508155
$248$	−26.3023	−1.67020
$249$	−18.5053	−1.17272
$250$	−31.9336	−2.01966
$251$	13.9356	0.879610	0.439805	−	0.898093i	$-0.355048\pi$
$251$	13.9356	0.879610	0.439805	+	0.898093i	$0.355048\pi$
$252$	3.28781	0.207113
$253$	−11.9722	−0.752683
$254$	35.4847	2.22651
$255$	1.34354	0.0841355
$256$	−6.77671	−0.423545
$257$	6.94030	0.432924	0.216462	−	0.976291i	$-0.430548\pi$
$257$	6.94030	0.432924	0.216462	+	0.976291i	$0.430548\pi$
$258$	72.3296	4.50305
$259$	−1.40026	−0.0870077
$260$	−41.3715	−2.56575
$261$	−21.3382	−1.32080
$262$	−12.6018	−0.778541
$263$	3.40226	0.209792	0.104896	−	0.994483i	$-0.466549\pi$
$263$	3.40226	0.209792	0.104896	+	0.994483i	$0.466549\pi$
$264$	52.5870	3.23651
$265$	14.6634	0.900768
$266$	−1.15543	−0.0708442
$267$	−32.8269	−2.00898
$268$	66.0404	4.03406
$269$	−14.2170	−0.866826	−0.433413	−	0.901196i	$-0.642691\pi$
$269$	−14.2170	−0.866826	−0.433413	+	0.901196i	$0.642691\pi$
$270$	−5.56920	−0.338931
$271$	15.8685	0.963944	0.481972	−	0.876187i	$-0.339921\pi$
$271$	15.8685	0.963944	0.481972	+	0.876187i	$0.339921\pi$
$272$	−3.64445	−0.220977
$273$	3.05448	0.184865
$274$	23.5708	1.42396
$275$	6.00759	0.362271
$276$	48.6985	2.93130
$277$	8.36505	0.502607	0.251304	−	0.967908i	$-0.419141\pi$
$277$	8.36505	0.502607	0.251304	+	0.967908i	$0.419141\pi$
$278$	−43.1654	−2.58889
$279$	8.26894	0.495048
$280$	3.57952	0.213917
$281$	13.6395	0.813662	0.406831	−	0.913503i	$-0.366634\pi$
$281$	13.6395	0.813662	0.406831	+	0.913503i	$0.366634\pi$
$282$	60.0596	3.57650
$283$	2.52262	0.149954	0.0749771	−	0.997185i	$-0.476112\pi$
$283$	2.52262	0.149954	0.0749771	+	0.997185i	$0.476112\pi$
$284$	67.1319	3.98354
$285$	−6.51508	−0.385920
$286$	36.8938	2.18158
$287$	1.17222	0.0691942
$288$	−31.6708	−1.86622
$289$	−16.8862	−0.993307
$290$	−38.8465	−2.28115
$291$	35.7956	2.09837
$292$	28.9318	1.69311
$293$	20.4132	1.19255	0.596276	−	0.802780i	$-0.296647\pi$
$293$	20.4132	1.19255	0.596276	+	0.802780i	$0.296647\pi$
$294$	42.7999	2.49614
$295$	−8.52626	−0.496418
$296$	41.1425	2.39136
$297$	3.54247	0.205555
$298$	−13.5258	−0.783526
$299$	20.4321	1.18162
$300$	−24.4367	−1.41086
$301$	−3.13167	−0.180507
$302$	−32.7006	−1.88171
$303$	−29.5121	−1.69543
$304$	17.6727	1.01360
$305$	7.86328	0.450250
$306$	2.20097	0.125821
$307$	−26.0388	−1.48611	−0.743055	−	0.669230i	$-0.766624\pi$
$307$	−26.0388	−1.48611	−0.743055	+	0.669230i	$0.766624\pi$
$308$	−3.80728	−0.216940
$309$	−7.06765	−0.402064
$310$	15.0537	0.854994
$311$	25.0633	1.42121	0.710605	−	0.703591i	$-0.248421\pi$
$311$	25.0633	1.42121	0.710605	+	0.703591i	$0.248421\pi$
$312$	−89.7470	−5.08092
$313$	−21.9581	−1.24115	−0.620573	−	0.784148i	$-0.713100\pi$
$313$	−21.9581	−1.24115	−0.620573	+	0.784148i	$0.713100\pi$
$314$	−8.75717	−0.494195
$315$	−1.12533	−0.0634052
$316$	61.7475	3.47357
$317$	−32.6405	−1.83327	−0.916637	−	0.399720i	$-0.869107\pi$
$317$	−32.6405	−1.83327	−0.916637	+	0.399720i	$0.869107\pi$
$318$	53.1902	2.98276
$319$	24.7096	1.38347
$320$	−20.8569	−1.16594
$321$	44.2761	2.47125
$322$	−2.95607	−0.164735
$323$	−0.551713	−0.0306981
$324$	−51.2871	−2.84928
$325$	−10.2528	−0.568722
$326$	27.0737	1.49948
$327$	−44.8460	−2.47999
$328$	−34.4424	−1.90176
$329$	−2.60041	−0.143365
$330$	−30.0973	−1.65680
$331$	−21.9473	−1.20633	−0.603167	−	0.797615i	$-0.706095\pi$
$331$	−21.9473	−1.20633	−0.603167	+	0.797615i	$0.706095\pi$
$332$	−39.3654	−2.16046
$333$	−12.9344	−0.708800
$334$	46.9686	2.57001
$335$	−22.6039	−1.23498
$336$	6.75919	0.368744
$337$	−4.83194	−0.263213	−0.131606	−	0.991302i	$-0.542013\pi$
$337$	−4.83194	−0.263213	−0.131606	+	0.991302i	$0.542013\pi$
$338$	−28.6298	−1.55726
$339$	−8.94034	−0.485572
$340$	2.85804	0.154999
$341$	−9.57542	−0.518538
$342$	−10.6729	−0.577126
$343$	−3.72537	−0.201151
$344$	92.0152	4.96113
$345$	−16.6682	−0.897385
$346$	12.1573	0.653580
$347$	−7.36643	−0.395451	−0.197725	−	0.980257i	$-0.563355\pi$
$347$	−7.36643	−0.395451	−0.197725	+	0.980257i	$0.563355\pi$
$348$	−100.510	−5.38790
$349$	8.63639	0.462296	0.231148	−	0.972919i	$-0.425752\pi$
$349$	8.63639	0.462296	0.231148	+	0.972919i	$0.425752\pi$
$350$	1.48334	0.0792881
$351$	−6.04572	−0.322697
$352$	36.6748	1.95477
$353$	4.94688	0.263296	0.131648	−	0.991297i	$-0.457973\pi$
$353$	4.94688	0.263296	0.131648	+	0.991297i	$0.457973\pi$
$354$	−30.9282	−1.64381
$355$	−22.9774	−1.21952
$356$	−69.8312	−3.70105
$357$	−0.211011	−0.0111679
$358$	48.9780	2.58857
$359$	−9.61296	−0.507353	−0.253676	−	0.967289i	$-0.581640\pi$
$359$	−9.61296	−0.507353	−0.253676	+	0.967289i	$0.581640\pi$
$360$	33.0646	1.74266
$361$	−16.3246	−0.859191
$362$	52.2566	2.74655
$363$	−6.58386	−0.345563
$364$	6.49765	0.340570
$365$	−9.90260	−0.518326
$366$	28.5233	1.49094
$367$	9.33132	0.487091	0.243545	−	0.969890i	$-0.421690\pi$
$367$	9.33132	0.487091	0.243545	+	0.969890i	$0.421690\pi$
$368$	45.2138	2.35693
$369$	10.8280	0.563684
$370$	−23.5472	−1.22416
$371$	−2.30299	−0.119565
$372$	38.9494	2.01943
$373$	−5.93939	−0.307530	−0.153765	−	0.988107i	$-0.549140\pi$
$373$	−5.93939	−0.307530	−0.153765	+	0.988107i	$0.549140\pi$
$374$	−2.54872	−0.131791
$375$	28.2799	1.46037
$376$	76.4056	3.94032
$377$	−42.1704	−2.17189
$378$	0.874678	0.0449886
$379$	−17.3767	−0.892580	−0.446290	−	0.894889i	$-0.647255\pi$
$379$	−17.3767	−0.892580	−0.446290	+	0.894889i	$0.647255\pi$
$380$	−13.8592	−0.710963
$381$	−31.4247	−1.60993
$382$	13.5888	0.695266
$383$	−14.7730	−0.754865	−0.377433	−	0.926037i	$-0.623193\pi$
$383$	−14.7730	−0.754865	−0.377433	+	0.926037i	$0.623193\pi$
$384$	−15.6907	−0.800711
$385$	1.30313	0.0664137
$386$	58.9387	2.99990
$387$	−28.9277	−1.47048
$388$	76.1463	3.86574
$389$	−10.5599	−0.535406	−0.267703	−	0.963501i	$-0.586265\pi$
$389$	−10.5599	−0.535406	−0.267703	+	0.963501i	$0.586265\pi$
$390$	51.3652	2.60098
$391$	−1.41150	−0.0713828
$392$	54.4485	2.75006
$393$	11.1599	0.562945
$394$	−10.4977	−0.528867
$395$	−21.1345	−1.06339
$396$	−35.1685	−1.76728
$397$	−35.3349	−1.77341	−0.886705	−	0.462336i	$-0.847011\pi$
$397$	−35.3349	−1.77341	−0.886705	+	0.462336i	$0.847011\pi$
$398$	62.4098	3.12832
$399$	1.02323	0.0512258
$400$	−22.6881	−1.13441
$401$	10.6929	0.533977	0.266989	−	0.963700i	$-0.413971\pi$
$401$	10.6929	0.533977	0.266989	+	0.963700i	$0.413971\pi$
$402$	−81.9933	−4.08945
$403$	16.3418	0.814042
$404$	−62.7798	−3.12341
$405$	17.5542	0.872276
$406$	6.10110	0.302792
$407$	14.9780	0.742432
$408$	6.19995	0.306943
$409$	−10.1707	−0.502910	−0.251455	−	0.967869i	$-0.580909\pi$
$409$	−10.1707	−0.502910	−0.251455	+	0.967869i	$0.580909\pi$
$410$	19.7126	0.973534
$411$	−20.8739	−1.02963
$412$	−15.0347	−0.740706
$413$	1.33910	0.0658930
$414$	−27.3056	−1.34200
$415$	13.4737	0.661399
$416$	−62.5906	−3.06875
$417$	38.2266	1.87196
$418$	12.3592	0.604510
$419$	−18.8354	−0.920172	−0.460086	−	0.887874i	$-0.652181\pi$
$419$	−18.8354	−0.920172	−0.460086	+	0.887874i	$0.652181\pi$
$420$	−5.30068	−0.258647
$421$	−16.7718	−0.817409	−0.408704	−	0.912667i	$-0.634019\pi$
$421$	−16.7718	−0.817409	−0.408704	+	0.912667i	$0.634019\pi$
$422$	15.9326	0.775585
$423$	−24.0204	−1.16791
$424$	67.6666	3.28618
$425$	0.708287	0.0343570
$426$	−83.3484	−4.03824
$427$	−1.23498	−0.0597648
$428$	94.1865	4.55268
$429$	−32.6726	−1.57745
$430$	−52.6634	−2.53965
$431$	40.7032	1.96060	0.980301	−	0.197508i	$-0.0632848\pi$
$431$	40.7032	1.96060	0.980301	+	0.197508i	$0.0632848\pi$
$432$	−13.3784	−0.643671
$433$	39.7982	1.91258	0.956290	−	0.292419i	$-0.0944603\pi$
$433$	39.7982	1.91258	0.956290	+	0.292419i	$0.0944603\pi$
$434$	−2.36428	−0.113489
$435$	34.4019	1.64944
$436$	−95.3988	−4.56877
$437$	6.84466	0.327424
$438$	−35.9207	−1.71636
$439$	−27.7113	−1.32259	−0.661293	−	0.750128i	$-0.729992\pi$
$439$	−27.7113	−1.32259	−0.661293	+	0.750128i	$0.729992\pi$
$440$	−38.2887	−1.82534
$441$	−17.1175	−0.815120
$442$	4.34973	0.206896
$443$	−32.1845	−1.52913	−0.764567	−	0.644544i	$-0.777047\pi$
$443$	−32.1845	−1.52913	−0.764567	+	0.644544i	$0.777047\pi$
$444$	−60.9252	−2.89138
$445$	23.9014	1.13303
$446$	−29.4600	−1.39497
$447$	11.9782	0.566550
$448$	3.27571	0.154763
$449$	16.2208	0.765509	0.382755	−	0.923850i	$-0.374975\pi$
$449$	16.2208	0.765509	0.382755	+	0.923850i	$0.374975\pi$
$450$	13.7019	0.645913
$451$	−12.5388	−0.590430
$452$	−19.0184	−0.894549
$453$	28.9592	1.36062
$454$	71.9711	3.37777
$455$	−2.22397	−0.104261
$456$	−30.0648	−1.40791
$457$	22.9789	1.07491	0.537454	−	0.843293i	$-0.319386\pi$
$457$	22.9789	1.07491	0.537454	+	0.843293i	$0.319386\pi$
$458$	−47.7095	−2.22932
$459$	0.417653	0.0194944
$460$	−35.4575	−1.65321
$461$	16.1193	0.750749	0.375375	−	0.926873i	$-0.377514\pi$
$461$	16.1193	0.750749	0.375375	+	0.926873i	$0.377514\pi$
$462$	4.72698	0.219919
$463$	27.4352	1.27502	0.637511	−	0.770441i	$-0.279964\pi$
$463$	27.4352	1.27502	0.637511	+	0.770441i	$0.279964\pi$
$464$	−93.3179	−4.33218
$465$	−13.3313	−0.618226
$466$	−28.0366	−1.29877
$467$	−13.7631	−0.636881	−0.318441	−	0.947943i	$-0.603159\pi$
$467$	−13.7631	−0.636881	−0.318441	+	0.947943i	$0.603159\pi$
$468$	60.0198	2.77442
$469$	3.55008	0.163928
$470$	−43.7295	−2.01709
$471$	7.75521	0.357341
$472$	−39.3457	−1.81103
$473$	33.4983	1.54025
$474$	−76.6634	−3.52126
$475$	−3.43463	−0.157592
$476$	−0.448874	−0.0205741
$477$	−21.2730	−0.974026
$478$	−25.7852	−1.17939
$479$	−13.9083	−0.635485	−0.317743	−	0.948177i	$-0.602925\pi$
$479$	−13.9083	−0.635485	−0.317743	+	0.948177i	$0.602925\pi$
$480$	51.0603	2.33057
$481$	−25.5620	−1.16553
$482$	16.2824	0.741645
$483$	2.61785	0.119116
$484$	−14.0055	−0.636616
$485$	−26.0629	−1.18345
$486$	53.8653	2.44338
$487$	−34.2597	−1.55246	−0.776228	−	0.630453i	$-0.782869\pi$
$487$	−34.2597	−1.55246	−0.776228	+	0.630453i	$0.782869\pi$
$488$	36.2863	1.64260
$489$	−23.9761	−1.08424
$490$	−31.1627	−1.40779
$491$	−28.9897	−1.30829	−0.654143	−	0.756371i	$-0.726971\pi$
$491$	−28.9897	−1.30829	−0.654143	+	0.756371i	$0.726971\pi$
$492$	51.0035	2.29941
$493$	2.91324	0.131206
$494$	−21.0927	−0.949007
$495$	12.0372	0.541033
$496$	36.1623	1.62374
$497$	3.60875	0.161875
$498$	48.8746	2.19012
$499$	−10.0796	−0.451224	−0.225612	−	0.974217i	$-0.572438\pi$
$499$	−10.0796	−0.451224	−0.225612	+	0.974217i	$0.572438\pi$
$500$	60.1585	2.69037
$501$	−41.5947	−1.85831
$502$	−36.8057	−1.64272
$503$	−1.05108	−0.0468651	−0.0234326	−	0.999725i	$-0.507459\pi$
$503$	−1.05108	−0.0468651	−0.0234326	+	0.999725i	$0.507459\pi$
$504$	−5.19300	−0.231315
$505$	21.4878	0.956197
$506$	31.6199	1.40567
$507$	25.3541	1.12602
$508$	−66.8483	−2.96591
$509$	−29.0047	−1.28561	−0.642806	−	0.766029i	$-0.722230\pi$
$509$	−29.0047	−1.28561	−0.642806	+	0.766029i	$0.722230\pi$
$510$	−3.54844	−0.157128
$511$	1.55527	0.0688009
$512$	31.3150	1.38394
$513$	−2.02528	−0.0894185
$514$	−18.3302	−0.808509
$515$	5.14597	0.226759
$516$	−136.259	−5.99848
$517$	27.8156	1.22333
$518$	3.69824	0.162492
$519$	−10.7663	−0.472588
$520$	65.3450	2.86557
$521$	41.6282	1.82376	0.911881	−	0.410454i	$-0.134630\pi$
$521$	41.6282	1.82376	0.911881	+	0.410454i	$0.134630\pi$
$522$	56.3568	2.46667
$523$	27.9116	1.22049	0.610244	−	0.792214i	$-0.291071\pi$
$523$	27.9116	1.22049	0.610244	+	0.792214i	$0.291071\pi$
$524$	23.7400	1.03709
$525$	−1.31363	−0.0573314
$526$	−8.98578	−0.391798
$527$	−1.12893	−0.0491770
$528$	−72.3004	−3.14647
$529$	−5.48861	−0.238635
$530$	−38.7279	−1.68223
$531$	12.3695	0.536791
$532$	2.17668	0.0943711
$533$	21.3992	0.926903
$534$	86.6998	3.75187
$535$	−32.2375	−1.39375
$536$	−104.309	−4.50546
$537$	−43.3742	−1.87173
$538$	37.5488	1.61884
$539$	19.8221	0.853797
$540$	10.4916	0.451487
$541$	−5.94083	−0.255416	−0.127708	−	0.991812i	$-0.540762\pi$
$541$	−5.94083	−0.255416	−0.127708	+	0.991812i	$0.540762\pi$
$542$	−41.9107	−1.80022
$543$	−46.2777	−1.98596
$544$	4.32391	0.185386
$545$	32.6524	1.39868
$546$	−8.06724	−0.345246
$547$	25.5240	1.09133	0.545664	−	0.838004i	$-0.316277\pi$
$547$	25.5240	1.09133	0.545664	+	0.838004i	$0.316277\pi$
$548$	−44.4041	−1.89685
$549$	−11.4077	−0.486868
$550$	−15.8668	−0.676561
$551$	−14.1269	−0.601825
$552$	−76.9178	−3.27384
$553$	3.31931	0.141152
$554$	−22.0931	−0.938646
$555$	20.8531	0.885163
$556$	81.3177	3.44864
$557$	−15.2909	−0.647897	−0.323948	−	0.946075i	$-0.605010\pi$
$557$	−15.2909	−0.647897	−0.323948	+	0.946075i	$0.605010\pi$
$558$	−21.8392	−0.924529
$559$	−57.1694	−2.41801
$560$	−4.92138	−0.207966
$561$	2.25710	0.0952949
$562$	−36.0234	−1.51956
$563$	12.3900	0.522178	0.261089	−	0.965315i	$-0.415918\pi$
$563$	12.3900	0.522178	0.261089	+	0.965315i	$0.415918\pi$
$564$	−113.144	−4.76422
$565$	6.50948	0.273856
$566$	−6.66254	−0.280047
$567$	−2.75700	−0.115783
$568$	−106.033	−4.44904
$569$	5.97251	0.250381	0.125190	−	0.992133i	$-0.460046\pi$
$569$	5.97251	0.250381	0.125190	+	0.992133i	$0.460046\pi$
$570$	17.2071	0.720726
$571$	−5.40962	−0.226385	−0.113193	−	0.993573i	$-0.536108\pi$
$571$	−5.40962	−0.226385	−0.113193	+	0.993573i	$0.536108\pi$
$572$	−69.5029	−2.90606
$573$	−12.0341	−0.502730
$574$	−3.09598	−0.129224
$575$	−8.78716	−0.366450
$576$	30.2583	1.26076
$577$	34.1927	1.42346	0.711730	−	0.702453i	$-0.247912\pi$
$577$	34.1927	1.42346	0.711730	+	0.702453i	$0.247912\pi$
$578$	44.5985	1.85505
$579$	−52.1952	−2.16916
$580$	73.1816	3.03870
$581$	−2.11613	−0.0877920
$582$	−94.5404	−3.91883
$583$	24.6342	1.02024
$584$	−45.6970	−1.89095
$585$	−20.5432	−0.849356
$586$	−53.9137	−2.22715
$587$	12.5459	0.517826	0.258913	−	0.965901i	$-0.416636\pi$
$587$	12.5459	0.517826	0.258913	+	0.965901i	$0.416636\pi$
$588$	−80.6291	−3.32509
$589$	5.47441	0.225569
$590$	22.5189	0.927087
$591$	9.29661	0.382412
$592$	−56.5656	−2.32483
$593$	29.7457	1.22151	0.610755	−	0.791819i	$-0.290866\pi$
$593$	29.7457	1.22151	0.610755	+	0.791819i	$0.290866\pi$
$594$	−9.35609	−0.383885
$595$	0.153638	0.00629853
$596$	25.4807	1.04373
$597$	−55.2692	−2.26202
$598$	−53.9637	−2.20674
$599$	−25.7454	−1.05193	−0.525964	−	0.850507i	$-0.676295\pi$
$599$	−25.7454	−1.05193	−0.525964	+	0.850507i	$0.676295\pi$
$600$	38.5971	1.57572
$601$	−27.3917	−1.11733	−0.558665	−	0.829393i	$-0.688686\pi$
$601$	−27.3917	−1.11733	−0.558665	+	0.829393i	$0.688686\pi$
$602$	8.27112	0.337106
$603$	32.7927	1.33542
$604$	61.6035	2.50661
$605$	4.79372	0.194893
$606$	77.9450	3.16630
$607$	−5.05230	−0.205067	−0.102533	−	0.994730i	$-0.532695\pi$
$607$	−5.05230	−0.205067	−0.102533	+	0.994730i	$0.532695\pi$
$608$	−20.9675	−0.850345
$609$	−5.40304	−0.218942
$610$	−20.7679	−0.840866
$611$	−47.4712	−1.92048
$612$	−4.14632	−0.167605
$613$	3.00832	0.121505	0.0607524	−	0.998153i	$-0.480650\pi$
$613$	3.00832	0.121505	0.0607524	+	0.998153i	$0.480650\pi$
$614$	68.7715	2.77539
$615$	−17.4571	−0.703939
$616$	6.01349	0.242291
$617$	−17.1507	−0.690463	−0.345231	−	0.938518i	$-0.612200\pi$
$617$	−17.1507	−0.690463	−0.345231	+	0.938518i	$0.612200\pi$
$618$	18.6665	0.750876
$619$	2.42975	0.0976599	0.0488299	−	0.998807i	$-0.484451\pi$
$619$	2.42975	0.0976599	0.0488299	+	0.998807i	$0.484451\pi$
$620$	−28.3592	−1.13893
$621$	−5.18149	−0.207926
$622$	−66.1952	−2.65419
$623$	−3.75386	−0.150395
$624$	123.391	4.93958
$625$	−10.0914	−0.403655
$626$	57.9940	2.31791
$627$	−10.9451	−0.437107
$628$	16.4973	0.658314
$629$	1.76589	0.0704106
$630$	2.97213	0.118413
$631$	6.28134	0.250056	0.125028	−	0.992153i	$-0.460098\pi$
$631$	6.28134	0.250056	0.125028	+	0.992153i	$0.460098\pi$
$632$	−97.5284	−3.87947
$633$	−14.1096	−0.560808
$634$	86.2075	3.42374
$635$	22.8804	0.907980
$636$	−100.203	−3.97331
$637$	−33.8291	−1.34036
$638$	−65.2611	−2.58371
$639$	33.3346	1.31870
$640$	11.4244	0.451590
$641$	−35.3547	−1.39643	−0.698213	−	0.715890i	$-0.746021\pi$
$641$	−35.3547	−1.39643	−0.698213	+	0.715890i	$0.746021\pi$
$642$	−116.938	−4.61519
$643$	34.4155	1.35721	0.678607	−	0.734502i	$-0.262584\pi$
$643$	34.4155	1.35721	0.678607	+	0.734502i	$0.262584\pi$
$644$	5.56882	0.219442
$645$	46.6379	1.83636
$646$	1.45714	0.0573303
$647$	44.5702	1.75224	0.876119	−	0.482096i	$-0.160124\pi$
$647$	44.5702	1.75224	0.876119	+	0.482096i	$0.160124\pi$
$648$	81.0065	3.18224
$649$	−14.3239	−0.562261
$650$	27.0788	1.06212
$651$	2.09377	0.0820614
$652$	−51.0032	−1.99744
$653$	31.7477	1.24238	0.621191	−	0.783659i	$-0.286649\pi$
$653$	31.7477	1.24238	0.621191	+	0.783659i	$0.286649\pi$
$654$	118.443	4.63151
$655$	−8.12558	−0.317493
$656$	47.3539	1.84886
$657$	14.3662	0.560480
$658$	6.86800	0.267743
$659$	−24.1129	−0.939307	−0.469653	−	0.882851i	$-0.655621\pi$
$659$	−24.1129	−0.939307	−0.469653	+	0.882851i	$0.655621\pi$
$660$	56.6993	2.20702
$661$	−46.9027	−1.82431	−0.912153	−	0.409851i	$-0.865581\pi$
$661$	−46.9027	−1.82431	−0.912153	+	0.409851i	$0.865581\pi$
$662$	57.9655	2.25289
$663$	−3.85206	−0.149601
$664$	62.1765	2.41291
$665$	−0.745020	−0.0288906
$666$	34.1612	1.32372
$667$	−36.1422	−1.39943
$668$	−88.4825	−3.42349
$669$	26.0893	1.00867
$670$	59.6995	2.30639
$671$	13.2101	0.509970
$672$	−8.01935	−0.309353
$673$	−23.1970	−0.894181	−0.447090	−	0.894489i	$-0.647540\pi$
$673$	−23.1970	−0.894181	−0.447090	+	0.894489i	$0.647540\pi$
$674$	12.7617	0.491563
$675$	2.60006	0.100076
$676$	53.9346	2.07441
$677$	14.5459	0.559043	0.279521	−	0.960139i	$-0.409824\pi$
$677$	14.5459	0.559043	0.279521	+	0.960139i	$0.409824\pi$
$678$	23.6125	0.906832
$679$	4.09334	0.157088
$680$	−4.51420	−0.173112
$681$	−63.7365	−2.44239
$682$	25.2898	0.968397
$683$	−10.8061	−0.413486	−0.206743	−	0.978395i	$-0.566286\pi$
$683$	−10.8061	−0.413486	−0.206743	+	0.978395i	$0.566286\pi$
$684$	20.1063	0.768785
$685$	15.1983	0.580699
$686$	9.83914	0.375660
$687$	42.2508	1.61197
$688$	−126.509	−4.82311
$689$	−42.0416	−1.60166
$690$	44.0227	1.67591
$691$	9.31655	0.354418	0.177209	−	0.984173i	$-0.443293\pi$
$691$	9.31655	0.354418	0.177209	+	0.984173i	$0.443293\pi$
$692$	−22.9027	−0.870629
$693$	−1.89052	−0.0718150
$694$	19.4556	0.738525
$695$	−27.8329	−1.05576
$696$	158.753	6.01750
$697$	−1.47831	−0.0559951
$698$	−22.8097	−0.863361
$699$	24.8287	0.939109
$700$	−2.79442	−0.105619
$701$	21.9624	0.829510	0.414755	−	0.909933i	$-0.363867\pi$
$701$	21.9624	0.829510	0.414755	+	0.909933i	$0.363867\pi$
$702$	15.9675	0.602653
$703$	−8.56315	−0.322965
$704$	−35.0390	−1.32058
$705$	38.7262	1.45851
$706$	−13.0653	−0.491719
$707$	−3.37480	−0.126923
$708$	58.2645	2.18971
$709$	−8.27727	−0.310859	−0.155430	−	0.987847i	$-0.549676\pi$
$709$	−8.27727	−0.310859	−0.155430	+	0.987847i	$0.549676\pi$
$710$	60.6861	2.27751
$711$	30.6610	1.14988
$712$	110.296	4.13353
$713$	14.0057	0.524519
$714$	0.557305	0.0208566
$715$	23.7890	0.889657
$716$	−92.2679	−3.44821
$717$	22.8349	0.852787
$718$	25.3890	0.947508
$719$	12.5935	0.469658	0.234829	−	0.972037i	$-0.424547\pi$
$719$	12.5935	0.469658	0.234829	+	0.972037i	$0.424547\pi$
$720$	−45.4595	−1.69418
$721$	−0.808208	−0.0300992
$722$	43.1153	1.60459
$723$	−14.4195	−0.536266
$724$	−98.4444	−3.65866
$725$	18.1360	0.673555
$726$	17.3888	0.645357
$727$	6.49434	0.240862	0.120431	−	0.992722i	$-0.461572\pi$
$727$	6.49434	0.240862	0.120431	+	0.992722i	$0.461572\pi$
$728$	−10.2629	−0.380367
$729$	−16.7786	−0.621428
$730$	26.1539	0.968000
$731$	3.94941	0.146074
$732$	−53.7339	−1.98606
$733$	7.63817	0.282122	0.141061	−	0.990001i	$-0.454949\pi$
$733$	7.63817	0.282122	0.141061	+	0.990001i	$0.454949\pi$
$734$	−24.6451	−0.909668
$735$	27.5972	1.01794
$736$	−53.6433	−1.97732
$737$	−37.9738	−1.39878
$738$	−28.5981	−1.05271
$739$	34.6881	1.27602	0.638011	−	0.770027i	$-0.279757\pi$
$739$	34.6881	1.27602	0.638011	+	0.770027i	$0.279757\pi$
$740$	44.3598	1.63070
$741$	18.6794	0.686205
$742$	6.08246	0.223294
$743$	50.3036	1.84546	0.922731	−	0.385445i	$-0.125952\pi$
$743$	50.3036	1.84546	0.922731	+	0.385445i	$0.125952\pi$
$744$	−61.5194	−2.25541
$745$	−8.72136	−0.319526
$746$	15.6866	0.574328
$747$	−19.5470	−0.715189
$748$	4.80143	0.175558
$749$	5.06311	0.185002
$750$	−74.6905	−2.72731
$751$	44.8471	1.63649	0.818246	−	0.574868i	$-0.194946\pi$
$751$	44.8471	1.63649	0.818246	+	0.574868i	$0.194946\pi$
$752$	−105.048	−3.83070
$753$	32.5945	1.18781
$754$	111.377	4.05611
$755$	−21.0852	−0.767370
$756$	−1.64777	−0.0599290
$757$	9.81328	0.356670	0.178335	−	0.983970i	$-0.442929\pi$
$757$	9.81328	0.356670	0.178335	+	0.983970i	$0.442929\pi$
$758$	45.8938	1.66694
$759$	−28.0021	−1.01641
$760$	21.8902	0.794043
$761$	−48.8754	−1.77173	−0.885865	−	0.463942i	$-0.846434\pi$
$761$	−48.8754	−1.77173	−0.885865	+	0.463942i	$0.846434\pi$
$762$	82.9963	3.00664
$763$	−5.12828	−0.185656
$764$	−25.5995	−0.926158
$765$	1.41917	0.0513103
$766$	39.0173	1.40975
$767$	24.4457	0.882682
$768$	−15.8503	−0.571948
$769$	13.3725	0.482226	0.241113	−	0.970497i	$-0.422488\pi$
$769$	13.3725	0.482226	0.241113	+	0.970497i	$0.422488\pi$
$770$	−3.44172	−0.124031
$771$	16.2329	0.584614
$772$	−111.032	−3.99614
$773$	21.6634	0.779180	0.389590	−	0.920988i	$-0.372617\pi$
$773$	21.6634	0.779180	0.389590	+	0.920988i	$0.372617\pi$
$774$	76.4016	2.74620
$775$	−7.02803	−0.252454
$776$	−120.271	−4.31747
$777$	−3.27511	−0.117494
$778$	27.8898	0.999899
$779$	7.16863	0.256843
$780$	−96.7651	−3.46475
$781$	−38.6014	−1.38127
$782$	3.72795	0.133311
$783$	10.6942	0.382180
$784$	−74.8596	−2.67356
$785$	−5.64659	−0.201535
$786$	−29.4747	−1.05133
$787$	−28.5884	−1.01907	−0.509534	−	0.860451i	$-0.670182\pi$
$787$	−28.5884	−1.01907	−0.509534	+	0.860451i	$0.670182\pi$
$788$	19.7763	0.704500
$789$	7.95766	0.283300
$790$	55.8188	1.98594
$791$	−1.02236	−0.0363508
$792$	55.5475	1.97380
$793$	−22.5448	−0.800590
$794$	93.3237	3.31194
$795$	34.2968	1.21638
$796$	−117.572	−4.16721
$797$	−4.77363	−0.169091	−0.0845453	−	0.996420i	$-0.526944\pi$
$797$	−4.77363	−0.169091	−0.0845453	+	0.996420i	$0.526944\pi$
$798$	−2.70248	−0.0956669
$799$	3.27943	0.116018
$800$	26.9181	0.951697
$801$	−34.6750	−1.22518
$802$	−28.2412	−0.997231
$803$	−16.6361	−0.587074
$804$	154.464	5.44753
$805$	−1.90606	−0.0671798
$806$	−43.1605	−1.52027
$807$	−33.2526	−1.17055
$808$	99.1588	3.48840
$809$	8.03851	0.282619	0.141309	−	0.989965i	$-0.454869\pi$
$809$	8.03851	0.282619	0.141309	+	0.989965i	$0.454869\pi$
$810$	−46.3627	−1.62902
$811$	9.94254	0.349130	0.174565	−	0.984646i	$-0.444148\pi$
$811$	9.94254	0.349130	0.174565	+	0.984646i	$0.444148\pi$
$812$	−11.4936	−0.403348
$813$	37.1154	1.30169
$814$	−39.5587	−1.38653
$815$	17.4570	0.611493
$816$	−8.52413	−0.298404
$817$	−19.1515	−0.670025
$818$	26.8621	0.939211
$819$	3.22644	0.112741
$820$	−37.1358	−1.29684
$821$	−38.1712	−1.33218	−0.666092	−	0.745870i	$-0.732034\pi$
$821$	−38.1712	−1.33218	−0.666092	+	0.745870i	$0.732034\pi$
$822$	55.1305	1.92290
$823$	52.7505	1.83877	0.919384	−	0.393361i	$-0.128688\pi$
$823$	52.7505	1.83877	0.919384	+	0.393361i	$0.128688\pi$
$824$	23.7468	0.827260
$825$	14.0513	0.489205
$826$	−3.53673	−0.123059
$827$	12.9968	0.451941	0.225971	−	0.974134i	$-0.427445\pi$
$827$	12.9968	0.451941	0.225971	+	0.974134i	$0.427445\pi$
$828$	51.4401	1.78767
$829$	−21.8443	−0.758685	−0.379343	−	0.925256i	$-0.623850\pi$
$829$	−21.8443	−0.758685	−0.379343	+	0.925256i	$0.623850\pi$
$830$	−35.5857	−1.23520
$831$	19.5653	0.678713
$832$	59.7989	2.07316
$833$	2.33700	0.0809722
$834$	−100.961	−3.49599
$835$	30.2852	1.04806
$836$	−23.2831	−0.805263
$837$	−4.14420	−0.143244
$838$	49.7466	1.71847
$839$	−12.6404	−0.436395	−0.218198	−	0.975905i	$-0.570018\pi$
$839$	−12.6404	−0.436395	−0.218198	+	0.975905i	$0.570018\pi$
$840$	8.37226	0.288871
$841$	45.5948	1.57223
$842$	44.2964	1.52655
$843$	31.9018	1.09876
$844$	−30.0148	−1.03315
$845$	−18.4604	−0.635056
$846$	63.4408	2.18114
$847$	−0.752885	−0.0258694
$848$	−93.0329	−3.19476
$849$	5.90024	0.202496
$850$	−1.87067	−0.0641635
$851$	−21.9080	−0.750995
$852$	157.017	5.37931
$853$	37.5133	1.28443	0.642216	−	0.766524i	$-0.278015\pi$
$853$	37.5133	1.28443	0.642216	+	0.766524i	$0.278015\pi$
$854$	3.26173	0.111614
$855$	−6.88186	−0.235355
$856$	−148.765	−5.08468
$857$	3.29329	0.112497	0.0562484	−	0.998417i	$-0.482086\pi$
$857$	3.29329	0.112497	0.0562484	+	0.998417i	$0.482086\pi$
$858$	86.2921	2.94596
$859$	−29.1209	−0.993593	−0.496797	−	0.867867i	$-0.665490\pi$
$859$	−29.1209	−0.993593	−0.496797	+	0.867867i	$0.665490\pi$
$860$	99.2106	3.38305
$861$	2.74175	0.0934387
$862$	−107.502	−3.66153
$863$	−0.990407	−0.0337138	−0.0168569	−	0.999858i	$-0.505366\pi$
$863$	−0.990407	−0.0337138	−0.0168569	+	0.999858i	$0.505366\pi$
$864$	15.8727	0.539999
$865$	7.83897	0.266533
$866$	−105.112	−3.57184
$867$	−39.4958	−1.34135
$868$	4.45399	0.151178
$869$	−35.5054	−1.20444
$870$	−90.8595	−3.08042
$871$	64.8076	2.19592
$872$	150.680	5.10265
$873$	37.8108	1.27970
$874$	−18.0776	−0.611482
$875$	3.23389	0.109325
$876$	67.6697	2.28635
$877$	42.7481	1.44350	0.721750	−	0.692154i	$-0.243338\pi$
$877$	42.7481	1.44350	0.721750	+	0.692154i	$0.243338\pi$
$878$	73.1887	2.47000
$879$	47.7451	1.61040
$880$	52.6421	1.77456
$881$	−24.1021	−0.812020	−0.406010	−	0.913869i	$-0.633080\pi$
$881$	−24.1021	−0.812020	−0.406010	+	0.913869i	$0.633080\pi$
$882$	45.2094	1.52228
$883$	37.5224	1.26273	0.631365	−	0.775486i	$-0.282495\pi$
$883$	37.5224	1.26273	0.631365	+	0.775486i	$0.282495\pi$
$884$	−8.19430	−0.275604
$885$	−19.9424	−0.670355
$886$	85.0032	2.85574
$887$	29.2879	0.983392	0.491696	−	0.870767i	$-0.336377\pi$
$887$	29.2879	0.983392	0.491696	+	0.870767i	$0.336377\pi$
$888$	96.2296	3.22925
$889$	−3.59351	−0.120522
$890$	−63.1263	−2.11600
$891$	29.4906	0.987971
$892$	55.4986	1.85823
$893$	−15.9026	−0.532160
$894$	−31.6359	−1.05806
$895$	31.5808	1.05563
$896$	−1.79428	−0.0599426
$897$	47.7894	1.59564
$898$	−42.8412	−1.42963
$899$	−28.9068	−0.964095
$900$	−25.8125	−0.860415
$901$	2.90434	0.0967575
$902$	33.1165	1.10266
$903$	−7.32478	−0.243753
$904$	30.0390	0.999081
$905$	33.6949	1.12006
$906$	−76.4846	−2.54103
$907$	−24.1930	−0.803317	−0.401658	−	0.915790i	$-0.631566\pi$
$907$	−24.1930	−0.803317	−0.401658	+	0.915790i	$0.631566\pi$
$908$	−135.584	−4.49950
$909$	−31.1736	−1.03396
$910$	5.87378	0.194714
$911$	−1.06313	−0.0352232	−0.0176116	−	0.999845i	$-0.505606\pi$
$911$	−1.06313	−0.0352232	−0.0176116	+	0.999845i	$0.505606\pi$
$912$	41.3352	1.36875
$913$	22.6355	0.749124
$914$	−60.6901	−2.00745
$915$	18.3917	0.608011
$916$	89.8781	2.96966
$917$	1.27617	0.0421430
$918$	−1.10307	−0.0364068
$919$	29.7338	0.980828	0.490414	−	0.871490i	$-0.336846\pi$
$919$	29.7338	0.980828	0.490414	+	0.871490i	$0.336846\pi$
$920$	56.0040	1.84640
$921$	−60.9029	−2.00682
$922$	−42.5729	−1.40206
$923$	65.8787	2.16842
$924$	−8.90498	−0.292952
$925$	10.9933	0.361459
$926$	−72.4596	−2.38117
$927$	−7.46554	−0.245200
$928$	110.716	3.63442
$929$	11.0469	0.362436	0.181218	−	0.983443i	$-0.441996\pi$
$929$	11.0469	0.362436	0.181218	+	0.983443i	$0.441996\pi$
$930$	35.2096	1.15457
$931$	−11.3326	−0.371410
$932$	52.8171	1.73008
$933$	58.6214	1.91918
$934$	36.3500	1.18941
$935$	−1.64340	−0.0537450
$936$	−94.7995	−3.09862
$937$	−10.0589	−0.328609	−0.164305	−	0.986410i	$-0.552538\pi$
$937$	−10.0589	−0.328609	−0.164305	+	0.986410i	$0.552538\pi$
$938$	−9.37619	−0.306143
$939$	−51.3586	−1.67602
$940$	82.3804	2.68695
$941$	60.1076	1.95945	0.979726	−	0.200344i	$-0.0642061\pi$
$941$	60.1076	1.95945	0.979726	+	0.200344i	$0.0642061\pi$
$942$	−20.4824	−0.667354
$943$	18.3402	0.597240
$944$	54.0953	1.76065
$945$	0.563989	0.0183466
$946$	−88.4730	−2.87650
$947$	−22.8505	−0.742543	−0.371271	−	0.928524i	$-0.621078\pi$
$947$	−22.8505	−0.742543	−0.371271	+	0.928524i	$0.621078\pi$
$948$	144.423	4.69065
$949$	28.3917	0.921635
$950$	9.07126	0.294310
$951$	−76.3440	−2.47562
$952$	0.708984	0.0229783
$953$	18.0456	0.584555	0.292277	−	0.956334i	$-0.405587\pi$
$953$	18.0456	0.584555	0.292277	+	0.956334i	$0.405587\pi$
$954$	56.1846	1.81904
$955$	8.76203	0.283533
$956$	48.5758	1.57105
$957$	57.7942	1.86822
$958$	36.7334	1.18680
$959$	−2.38700	−0.0770802
$960$	−48.7830	−1.57446
$961$	−19.7981	−0.638649
$962$	67.5123	2.17668
$963$	46.7687	1.50710
$964$	−30.6739	−0.987939
$965$	38.0034	1.22337
$966$	−6.91404	−0.222456
$967$	−16.7459	−0.538512	−0.269256	−	0.963069i	$-0.586778\pi$
$967$	−16.7459	−0.538512	−0.269256	+	0.963069i	$0.586778\pi$
$968$	22.1213	0.711007
$969$	−1.29042	−0.0414542
$970$	68.8351	2.21016
$971$	11.2931	0.362413	0.181206	−	0.983445i	$-0.442000\pi$
$971$	11.2931	0.362413	0.181206	+	0.983445i	$0.442000\pi$
$972$	−101.475	−3.25481
$973$	4.37133	0.140138
$974$	90.4839	2.89929
$975$	−23.9806	−0.767993
$976$	−49.8890	−1.59691
$977$	6.41747	0.205313	0.102657	−	0.994717i	$-0.467266\pi$
$977$	6.41747	0.205313	0.102657	+	0.994717i	$0.467266\pi$
$978$	63.3236	2.02487
$979$	40.1536	1.28331
$980$	58.7063	1.87530
$981$	−47.3707	−1.51243
$982$	76.5652	2.44329
$983$	−38.9566	−1.24252	−0.621261	−	0.783604i	$-0.713379\pi$
$983$	−38.9566	−1.24252	−0.621261	+	0.783604i	$0.713379\pi$
$984$	−80.5585	−2.56811
$985$	−6.76889	−0.215675
$986$	−7.69420	−0.245033
$987$	−6.08219	−0.193598
$988$	39.7358	1.26416
$989$	−48.9972	−1.55802
$990$	−31.7917	−1.01041
$991$	48.9310	1.55434	0.777172	−	0.629288i	$-0.216653\pi$
$991$	48.9310	1.55434	0.777172	+	0.629288i	$0.216653\pi$
$992$	−42.9043	−1.36221
$993$	−51.3333	−1.62901
$994$	−9.53115	−0.302310
$995$	40.2416	1.27574
$996$	−92.0730	−2.91744
$997$	−21.7518	−0.688887	−0.344443	−	0.938807i	$-0.611932\pi$
$997$	−21.7518	−0.688887	−0.344443	+	0.938807i	$0.611932\pi$
$998$	26.6214	0.842684
$999$	6.48241	0.205094

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	4021.2.a.b.1.8	✓	151

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
4021.2.a.b.1.8	✓	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)

\(f(q)\)	\(=\)	\(q-2.64112 q^{2} +2.33893 q^{3} +4.97551 q^{4} -1.70298 q^{5} -6.17740 q^{6} +0.267464 q^{7} -7.85867 q^{8} +2.47061 q^{9} +O(q^{10})\)	\(q-2.64112 q^{2} +2.33893 q^{3} +4.97551 q^{4} -1.70298 q^{5} -6.17740 q^{6} +0.267464 q^{7} -7.85867 q^{8} +2.47061 q^{9} +4.49778 q^{10} -2.86096 q^{11} +11.6374 q^{12} +4.88262 q^{13} -0.706405 q^{14} -3.98316 q^{15} +10.8047 q^{16} -0.337304 q^{17} -6.52517 q^{18} +1.63565 q^{19} -8.47320 q^{20} +0.625581 q^{21} +7.55614 q^{22} +4.18466 q^{23} -18.3809 q^{24} -2.09985 q^{25} -12.8956 q^{26} -1.23821 q^{27} +1.33077 q^{28} -8.63683 q^{29} +10.5200 q^{30} +3.34692 q^{31} -12.8190 q^{32} -6.69160 q^{33} +0.890860 q^{34} -0.455487 q^{35} +12.2925 q^{36} -5.23530 q^{37} -4.31996 q^{38} +11.4201 q^{39} +13.3832 q^{40} +4.38273 q^{41} -1.65223 q^{42} -11.7088 q^{43} -14.2347 q^{44} -4.20740 q^{45} -11.0522 q^{46} -9.72247 q^{47} +25.2714 q^{48} -6.92846 q^{49} +5.54595 q^{50} -0.788931 q^{51} +24.2935 q^{52} -8.61045 q^{53} +3.27026 q^{54} +4.87217 q^{55} -2.10191 q^{56} +3.82569 q^{57} +22.8109 q^{58} +5.00666 q^{59} -19.8183 q^{60} -4.61736 q^{61} -8.83962 q^{62} +0.660800 q^{63} +12.2473 q^{64} -8.31503 q^{65} +17.6733 q^{66} +13.2731 q^{67} -1.67826 q^{68} +9.78764 q^{69} +1.20300 q^{70} +13.4925 q^{71} -19.4157 q^{72} +5.81485 q^{73} +13.8271 q^{74} -4.91141 q^{75} +8.13821 q^{76} -0.765205 q^{77} -30.1619 q^{78} +12.4103 q^{79} -18.4001 q^{80} -10.3079 q^{81} -11.5753 q^{82} -7.91183 q^{83} +3.11258 q^{84} +0.574423 q^{85} +30.9242 q^{86} -20.2010 q^{87} +22.4833 q^{88} -14.0350 q^{89} +11.1123 q^{90} +1.30593 q^{91} +20.8208 q^{92} +7.82823 q^{93} +25.6782 q^{94} -2.78549 q^{95} -29.9829 q^{96} +15.3042 q^{97} +18.2989 q^{98} -7.06832 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 151 q - 16 q^{2} - 29 q^{3} + 120 q^{4} - 27 q^{5} - 18 q^{6} - 18 q^{7} - 48 q^{8} + 98 q^{9}+O(q^{10}) \) 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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