LMFDB - Embedded newform 8021.2.a.c.1.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [8021,2,Mod(1,8021)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(8021, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("8021.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 8021 = 13 \cdot 617 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	8021.a (trivial)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	yes
Analytic conductor:	$64.0480074613$
Analytic rank:	$0$
Dimension:	$169$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.4
Character	$\chi$	$=$	8021.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-2.77986 q^{2} +1.10062 q^{3} +5.72762 q^{4} -3.35511 q^{5} -3.05957 q^{6} +3.90263 q^{7} -10.3623 q^{8} -1.78864 q^{9} +O(q^{10})$	\(q-2.77986 q^{2} +1.10062 q^{3} +5.72762 q^{4} -3.35511 q^{5} -3.05957 q^{6} +3.90263 q^{7} -10.3623 q^{8} -1.78864 q^{9} +9.32675 q^{10} +0.510462 q^{11} +6.30393 q^{12} -1.00000 q^{13} -10.8488 q^{14} -3.69270 q^{15} +17.3504 q^{16} -2.35075 q^{17} +4.97217 q^{18} +4.74703 q^{19} -19.2168 q^{20} +4.29530 q^{21} -1.41901 q^{22} -1.89089 q^{23} -11.4049 q^{24} +6.25679 q^{25} +2.77986 q^{26} -5.27046 q^{27} +22.3528 q^{28} +9.43905 q^{29} +10.2652 q^{30} +9.29081 q^{31} -27.5072 q^{32} +0.561824 q^{33} +6.53475 q^{34} -13.0938 q^{35} -10.2446 q^{36} -3.90115 q^{37} -13.1961 q^{38} -1.10062 q^{39} +34.7666 q^{40} +7.79664 q^{41} -11.9403 q^{42} +0.706506 q^{43} +2.92373 q^{44} +6.00109 q^{45} +5.25641 q^{46} +7.53859 q^{47} +19.0962 q^{48} +8.23050 q^{49} -17.3930 q^{50} -2.58728 q^{51} -5.72762 q^{52} -13.6239 q^{53} +14.6512 q^{54} -1.71266 q^{55} -40.4400 q^{56} +5.22467 q^{57} -26.2392 q^{58} +6.43593 q^{59} -21.1504 q^{60} -6.88806 q^{61} -25.8271 q^{62} -6.98039 q^{63} +41.7652 q^{64} +3.35511 q^{65} -1.56179 q^{66} -7.53424 q^{67} -13.4642 q^{68} -2.08115 q^{69} +36.3988 q^{70} -5.57212 q^{71} +18.5343 q^{72} -6.93942 q^{73} +10.8446 q^{74} +6.88634 q^{75} +27.1892 q^{76} +1.99214 q^{77} +3.05957 q^{78} +11.3519 q^{79} -58.2126 q^{80} -0.434853 q^{81} -21.6736 q^{82} +14.6325 q^{83} +24.6019 q^{84} +7.88703 q^{85} -1.96399 q^{86} +10.3888 q^{87} -5.28954 q^{88} +10.2796 q^{89} -16.6822 q^{90} -3.90263 q^{91} -10.8303 q^{92} +10.2256 q^{93} -20.9562 q^{94} -15.9268 q^{95} -30.2749 q^{96} -8.02934 q^{97} -22.8796 q^{98} -0.913032 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 169 q + 9 q^{2} + 9 q^{3} + 199 q^{4} + 12 q^{5} + 22 q^{6} + 36 q^{7} + 30 q^{8} + 198 q^{9}+O(q^{10}) $ 169 * q + 9 * q^2 + 9 * q^3 + 199 * q^4 + 12 * q^5 + 22 * q^6 + 36 * q^7 + 30 * q^8 + 198 * q^9	\( 169 q + 9 q^{2} + 9 q^{3} + 199 q^{4} + 12 q^{5} + 22 q^{6} + 36 q^{7} + 30 q^{8} + 198 q^{9} - 3 q^{10} + 59 q^{11} + 11 q^{12} - 169 q^{13} + 30 q^{14} + 50 q^{15} + 267 q^{16} + q^{17} + 53 q^{18} + 107 q^{19} + 48 q^{20} + 36 q^{21} + 14 q^{22} + 12 q^{23} + 78 q^{24} + 217 q^{25} - 9 q^{26} + 39 q^{27} + 99 q^{28} + 30 q^{29} - q^{30} + 106 q^{31} + 74 q^{32} + 16 q^{33} + 56 q^{34} + 46 q^{35} + 271 q^{36} + 73 q^{37} + 2 q^{38} - 9 q^{39} - 16 q^{40} + 52 q^{41} - 2 q^{42} + 64 q^{43} + 124 q^{44} + 84 q^{45} + 105 q^{46} + 55 q^{47} + 26 q^{48} + 257 q^{49} + 60 q^{50} + 117 q^{51} - 199 q^{52} + 7 q^{53} + 78 q^{54} - 4 q^{55} + 63 q^{56} + 51 q^{57} + 84 q^{58} + 98 q^{59} + 94 q^{60} + 32 q^{61} - 25 q^{62} + 128 q^{63} + 380 q^{64} - 12 q^{65} + 16 q^{66} + 170 q^{67} - 10 q^{68} + 55 q^{69} + 70 q^{70} + 124 q^{71} + 173 q^{72} + 81 q^{73} + 54 q^{74} + 120 q^{75} + 212 q^{76} + 20 q^{77} - 22 q^{78} + 92 q^{79} + 66 q^{80} + 265 q^{81} + 21 q^{82} + 62 q^{83} + 98 q^{84} + 139 q^{85} + 51 q^{86} - 33 q^{87} + 31 q^{88} + 58 q^{89} + 16 q^{90} - 36 q^{91} + 40 q^{92} + 37 q^{93} + 55 q^{94} + 23 q^{95} + 164 q^{96} + 78 q^{97} + 69 q^{98} + 307 q^{99}+O(q^{100}) \) 169 * q + 9 * q^2 + 9 * q^3 + 199 * q^4 + 12 * q^5 + 22 * q^6 + 36 * q^7 + 30 * q^8 + 198 * q^9 - 3 * q^10 + 59 * q^11 + 11 * q^12 - 169 * q^13 + 30 * q^14 + 50 * q^15 + 267 * q^16 + q^17 + 53 * q^18 + 107 * q^19 + 48 * q^20 + 36 * q^21 + 14 * q^22 + 12 * q^23 + 78 * q^24 + 217 * q^25 - 9 * q^26 + 39 * q^27 + 99 * q^28 + 30 * q^29 - q^30 + 106 * q^31 + 74 * q^32 + 16 * q^33 + 56 * q^34 + 46 * q^35 + 271 * q^36 + 73 * q^37 + 2 * q^38 - 9 * q^39 - 16 * q^40 + 52 * q^41 - 2 * q^42 + 64 * q^43 + 124 * q^44 + 84 * q^45 + 105 * q^46 + 55 * q^47 + 26 * q^48 + 257 * q^49 + 60 * q^50 + 117 * q^51 - 199 * q^52 + 7 * q^53 + 78 * q^54 - 4 * q^55 + 63 * q^56 + 51 * q^57 + 84 * q^58 + 98 * q^59 + 94 * q^60 + 32 * q^61 - 25 * q^62 + 128 * q^63 + 380 * q^64 - 12 * q^65 + 16 * q^66 + 170 * q^67 - 10 * q^68 + 55 * q^69 + 70 * q^70 + 124 * q^71 + 173 * q^72 + 81 * q^73 + 54 * q^74 + 120 * q^75 + 212 * q^76 + 20 * q^77 - 22 * q^78 + 92 * q^79 + 66 * q^80 + 265 * q^81 + 21 * q^82 + 62 * q^83 + 98 * q^84 + 139 * q^85 + 51 * q^86 - 33 * q^87 + 31 * q^88 + 58 * q^89 + 16 * q^90 - 36 * q^91 + 40 * q^92 + 37 * q^93 + 55 * q^94 + 23 * q^95 + 164 * q^96 + 78 * q^97 + 69 * q^98 + 307 * 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 $

$2$	−2.77986	−1.96566	−0.982829	−	0.184519i	$-0.940927\pi$
$2$	−2.77986	−1.96566	−0.982829	+	0.184519i	$0.940927\pi$
$3$	1.10062	0.635442	0.317721	−	0.948184i	$-0.397082\pi$
$3$	1.10062	0.635442	0.317721	+	0.948184i	$0.397082\pi$
$4$	5.72762	2.86381
$5$	−3.35511	−1.50045	−0.750226	−	0.661181i	$-0.770056\pi$
$5$	−3.35511	−1.50045	−0.750226	+	0.661181i	$0.770056\pi$
$6$	−3.05957	−1.24906
$7$	3.90263	1.47505	0.737527	−	0.675317i	$-0.235993\pi$
$7$	3.90263	1.47505	0.737527	+	0.675317i	$0.235993\pi$
$8$	−10.3623	−3.66361
$9$	−1.78864	−0.596213
$10$	9.32675	2.94938
$11$	0.510462	0.153910	0.0769550	−	0.997035i	$-0.475480\pi$
$11$	0.510462	0.153910	0.0769550	+	0.997035i	$0.475480\pi$
$12$	6.30393	1.81979
$13$	−1.00000	−0.277350
$13$	−1.00000	−0.277350
$14$	−10.8488	−2.89945
$15$	−3.69270	−0.953451
$16$	17.3504	4.33760
$17$	−2.35075	−0.570141	−0.285070	−	0.958507i	$-0.592017\pi$
$17$	−2.35075	−0.570141	−0.285070	+	0.958507i	$0.592017\pi$
$18$	4.97217	1.17195
$19$	4.74703	1.08904	0.544521	−	0.838747i	$-0.316711\pi$
$19$	4.74703	1.08904	0.544521	+	0.838747i	$0.316711\pi$
$20$	−19.2168	−4.29701
$21$	4.29530	0.937312
$22$	−1.41901	−0.302535
$23$	−1.89089	−0.394278	−0.197139	−	0.980376i	$-0.563165\pi$
$23$	−1.89089	−0.394278	−0.197139	+	0.980376i	$0.563165\pi$
$24$	−11.4049	−2.32802
$25$	6.25679	1.25136
$26$	2.77986	0.545175
$27$	−5.27046	−1.01430
$28$	22.3528	4.22428
$29$	9.43905	1.75279	0.876394	−	0.481596i	$-0.159943\pi$
$29$	9.43905	1.75279	0.876394	+	0.481596i	$0.159943\pi$
$30$	10.2652	1.87416
$31$	9.29081	1.66868	0.834339	−	0.551252i	$-0.185850\pi$
$31$	9.29081	1.66868	0.834339	+	0.551252i	$0.185850\pi$
$32$	−27.5072	−4.86262
$33$	0.561824	0.0978010
$34$	6.53475	1.12070
$35$	−13.0938	−2.21325
$36$	−10.2446	−1.70744
$37$	−3.90115	−0.641345	−0.320672	−	0.947190i	$-0.603909\pi$
$37$	−3.90115	−0.641345	−0.320672	+	0.947190i	$0.603909\pi$
$38$	−13.1961	−2.14069
$39$	−1.10062	−0.176240
$40$	34.7666	5.49708
$41$	7.79664	1.21763	0.608815	−	0.793312i	$-0.291645\pi$
$41$	7.79664	1.21763	0.608815	+	0.793312i	$0.291645\pi$
$42$	−11.9403	−1.84243
$43$	0.706506	0.107741	0.0538706	−	0.998548i	$-0.482844\pi$
$43$	0.706506	0.107741	0.0538706	+	0.998548i	$0.482844\pi$
$44$	2.92373	0.440769
$45$	6.00109	0.894590
$46$	5.25641	0.775016
$47$	7.53859	1.09962	0.549808	−	0.835291i	$-0.314701\pi$
$47$	7.53859	1.09962	0.549808	+	0.835291i	$0.314701\pi$
$48$	19.0962	2.75629
$49$	8.23050	1.17579
$50$	−17.3930	−2.45974
$51$	−2.58728	−0.362291
$52$	−5.72762	−0.794278
$53$	−13.6239	−1.87138	−0.935691	−	0.352819i	$-0.885223\pi$
$53$	−13.6239	−1.87138	−0.935691	+	0.352819i	$0.885223\pi$
$54$	14.6512	1.99377
$55$	−1.71266	−0.230935
$56$	−40.4400	−5.40403
$57$	5.22467	0.692024
$58$	−26.2392	−3.44538
$59$	6.43593	0.837886	0.418943	−	0.908012i	$-0.362401\pi$
$59$	6.43593	0.837886	0.418943	+	0.908012i	$0.362401\pi$
$60$	−21.1504	−2.73050
$61$	−6.88806	−0.881926	−0.440963	−	0.897525i	$-0.645363\pi$
$61$	−6.88806	−0.881926	−0.440963	+	0.897525i	$0.645363\pi$
$62$	−25.8271	−3.28005
$63$	−6.98039	−0.879447
$64$	41.7652	5.22065
$65$	3.35511	0.416151
$66$	−1.56179	−0.192243
$67$	−7.53424	−0.920454	−0.460227	−	0.887801i	$-0.652232\pi$
$67$	−7.53424	−0.920454	−0.460227	+	0.887801i	$0.652232\pi$
$68$	−13.4642	−1.63277
$69$	−2.08115	−0.250541
$70$	36.3988	4.35049
$71$	−5.57212	−0.661289	−0.330645	−	0.943755i	$-0.607266\pi$
$71$	−5.57212	−0.661289	−0.330645	+	0.943755i	$0.607266\pi$
$72$	18.5343	2.18429
$73$	−6.93942	−0.812198	−0.406099	−	0.913829i	$-0.633111\pi$
$73$	−6.93942	−0.812198	−0.406099	+	0.913829i	$0.633111\pi$
$74$	10.8446	1.26066
$75$	6.88634	0.795166
$76$	27.1892	3.11881
$77$	1.99214	0.227026
$78$	3.05957	0.346428
$79$	11.3519	1.27719	0.638596	−	0.769542i	$-0.279515\pi$
$79$	11.3519	1.27719	0.638596	+	0.769542i	$0.279515\pi$
$80$	−58.2126	−6.50836
$81$	−0.434853	−0.0483170
$82$	−21.6736	−2.39344
$83$	14.6325	1.60613	0.803064	−	0.595893i	$-0.203202\pi$
$83$	14.6325	1.60613	0.803064	+	0.595893i	$0.203202\pi$
$84$	24.6019	2.68428
$85$	7.88703	0.855469
$86$	−1.96399	−0.211782
$87$	10.3888	1.11380
$88$	−5.28954	−0.563867
$89$	10.2796	1.08963	0.544816	−	0.838555i	$-0.316599\pi$
$89$	10.2796	1.08963	0.544816	+	0.838555i	$0.316599\pi$
$90$	−16.6822	−1.75846
$91$	−3.90263	−0.409106
$92$	−10.8303	−1.12914
$93$	10.2256	1.06035
$94$	−20.9562	−2.16147
$95$	−15.9268	−1.63406
$96$	−30.2749	−3.08992
$97$	−8.02934	−0.815255	−0.407628	−	0.913148i	$-0.633644\pi$
$97$	−8.02934	−0.815255	−0.407628	+	0.913148i	$0.633644\pi$
$98$	−22.8796	−2.31119
$99$	−0.913032	−0.0917632
$100$	35.8365	3.58365
$101$	−4.41235	−0.439046	−0.219523	−	0.975607i	$-0.570450\pi$
$101$	−4.41235	−0.439046	−0.219523	+	0.975607i	$0.570450\pi$
$102$	7.19227	0.712141
$103$	−12.7615	−1.25743	−0.628716	−	0.777635i	$-0.716419\pi$
$103$	−12.7615	−1.25743	−0.628716	+	0.777635i	$0.716419\pi$
$104$	10.3623	1.01610
$105$	−14.4112	−1.40639
$106$	37.8725	3.67850
$107$	−3.94529	−0.381405	−0.190703	−	0.981648i	$-0.561077\pi$
$107$	−3.94529	−0.381405	−0.190703	+	0.981648i	$0.561077\pi$
$108$	−30.1872	−2.90477
$109$	−10.6711	−1.02210	−0.511052	−	0.859550i	$-0.670744\pi$
$109$	−10.6711	−1.02210	−0.511052	+	0.859550i	$0.670744\pi$
$110$	4.76095	0.453939
$111$	−4.29368	−0.407538
$112$	67.7121	6.39820
$113$	−11.3898	−1.07146	−0.535731	−	0.844389i	$-0.679964\pi$
$113$	−11.3898	−1.07146	−0.535731	+	0.844389i	$0.679964\pi$
$114$	−14.5238	−1.36028
$115$	6.34416	0.591596
$116$	54.0633	5.01965
$117$	1.78864	0.165360
$118$	−17.8910	−1.64700
$119$	−9.17410	−0.840988
$120$	38.2647	3.49308
$121$	−10.7394	−0.976312
$122$	19.1478	1.73356
$123$	8.58112	0.773734
$124$	53.2142	4.77878
$125$	−4.21669	−0.377152
$126$	19.4045	1.72869
$127$	−12.2310	−1.08532	−0.542662	−	0.839951i	$-0.682584\pi$
$127$	−12.2310	−1.08532	−0.542662	+	0.839951i	$0.682584\pi$
$128$	−61.0872	−5.39939
$129$	0.777594	0.0684633
$130$	−9.32675	−0.818010
$131$	13.6038	1.18857	0.594283	−	0.804256i	$-0.297436\pi$
$131$	13.6038	1.18857	0.594283	+	0.804256i	$0.297436\pi$
$132$	3.21791	0.280083
$133$	18.5259	1.60640
$134$	20.9441	1.80930
$135$	17.6830	1.52191
$136$	24.3591	2.08877
$137$	−4.49901	−0.384377	−0.192188	−	0.981358i	$-0.561558\pi$
$137$	−4.49901	−0.384377	−0.192188	+	0.981358i	$0.561558\pi$
$138$	5.78531	0.492478
$139$	9.35522	0.793499	0.396750	−	0.917927i	$-0.370138\pi$
$139$	9.35522	0.793499	0.396750	+	0.917927i	$0.370138\pi$
$140$	−74.9961	−6.33833
$141$	8.29712	0.698743
$142$	15.4897	1.29987
$143$	−0.510462	−0.0426870
$144$	−31.0336	−2.58613
$145$	−31.6691	−2.62997
$146$	19.2906	1.59650
$147$	9.05864	0.747144
$148$	−22.3443	−1.83669
$149$	−16.1205	−1.32065	−0.660323	−	0.750981i	$-0.729581\pi$
$149$	−16.1205	−1.32065	−0.660323	+	0.750981i	$0.729581\pi$
$150$	−19.1431	−1.56302
$151$	13.1716	1.07189	0.535946	−	0.844252i	$-0.319955\pi$
$151$	13.1716	1.07189	0.535946	+	0.844252i	$0.319955\pi$
$152$	−49.1900	−3.98983
$153$	4.20464	0.339925
$154$	−5.53788	−0.446255
$155$	−31.1717	−2.50377
$156$	−6.30393	−0.504718
$157$	8.13415	0.649176	0.324588	−	0.945856i	$-0.394774\pi$
$157$	8.13415	0.649176	0.324588	+	0.945856i	$0.394774\pi$
$158$	−31.5568	−2.51052
$159$	−14.9947	−1.18916
$160$	92.2896	7.29614
$161$	−7.37945	−0.581582
$162$	1.20883	0.0949747
$163$	9.70937	0.760496	0.380248	−	0.924884i	$-0.375839\pi$
$163$	9.70937	0.760496	0.380248	+	0.924884i	$0.375839\pi$
$164$	44.6562	3.48706
$165$	−1.88498	−0.146746
$166$	−40.6763	−3.15710
$167$	5.92313	0.458346	0.229173	−	0.973386i	$-0.426398\pi$
$167$	5.92313	0.458346	0.229173	+	0.973386i	$0.426398\pi$
$168$	−44.5091	−3.43395
$169$	1.00000	0.0769231
$170$	−21.9249	−1.68156
$171$	−8.49072	−0.649302
$172$	4.04660	0.308550
$173$	6.49071	0.493479	0.246740	−	0.969082i	$-0.420641\pi$
$173$	6.49071	0.493479	0.246740	+	0.969082i	$0.420641\pi$
$174$	−28.8794	−2.18934
$175$	24.4179	1.84582
$176$	8.85672	0.667600
$177$	7.08350	0.532429
$178$	−28.5758	−2.14185
$179$	9.51038	0.710839	0.355419	−	0.934707i	$-0.384338\pi$
$179$	9.51038	0.710839	0.355419	+	0.934707i	$0.384338\pi$
$180$	34.3720	2.56193
$181$	6.70609	0.498460	0.249230	−	0.968444i	$-0.419823\pi$
$181$	6.70609	0.498460	0.249230	+	0.968444i	$0.419823\pi$
$182$	10.8488	0.804163
$183$	−7.58113	−0.560413
$184$	19.5939	1.44448
$185$	13.0888	0.962308
$186$	−28.4258	−2.08428
$187$	−1.19997	−0.0877504
$188$	43.1782	3.14909
$189$	−20.5687	−1.49615
$190$	44.2743	3.21200
$191$	−10.8022	−0.781623	−0.390811	−	0.920471i	$-0.627806\pi$
$191$	−10.8022	−0.781623	−0.390811	+	0.920471i	$0.627806\pi$
$192$	45.9676	3.31742
$193$	1.63654	0.117801	0.0589005	−	0.998264i	$-0.481241\pi$
$193$	1.63654	0.117801	0.0589005	+	0.998264i	$0.481241\pi$
$194$	22.3204	1.60251
$195$	3.69270	0.264440
$196$	47.1412	3.36723
$197$	−2.36889	−0.168776	−0.0843880	−	0.996433i	$-0.526894\pi$
$197$	−2.36889	−0.168776	−0.0843880	+	0.996433i	$0.526894\pi$
$198$	2.53810	0.180375
$199$	−14.9180	−1.05751	−0.528755	−	0.848775i	$-0.677341\pi$
$199$	−14.9180	−1.05751	−0.528755	+	0.848775i	$0.677341\pi$
$200$	−64.8345	−4.58449
$201$	−8.29233	−0.584896
$202$	12.2657	0.863013
$203$	36.8371	2.58546
$204$	−14.8190	−1.03753
$205$	−26.1586	−1.82700
$206$	35.4753	2.47168
$207$	3.38212	0.235074
$208$	−17.3504	−1.20303
$209$	2.42318	0.167615
$210$	40.0612	2.76449
$211$	−8.04471	−0.553821	−0.276910	−	0.960896i	$-0.589311\pi$
$211$	−8.04471	−0.553821	−0.276910	+	0.960896i	$0.589311\pi$
$212$	−78.0324	−5.35929
$213$	−6.13278	−0.420211
$214$	10.9674	0.749713
$215$	−2.37041	−0.161661
$216$	54.6139	3.71601
$217$	36.2585	2.46139
$218$	29.6641	2.00911
$219$	−7.63766	−0.516105
$220$	−9.80946	−0.661354
$221$	2.35075	0.158129
$222$	11.9358	0.801080
$223$	20.9176	1.40075	0.700373	−	0.713777i	$-0.253017\pi$
$223$	20.9176	1.40075	0.700373	+	0.713777i	$0.253017\pi$
$224$	−107.350	−7.17263
$225$	−11.1911	−0.746076
$226$	31.6620	2.10613
$227$	21.0190	1.39508	0.697538	−	0.716547i	$-0.254279\pi$
$227$	21.0190	1.39508	0.697538	+	0.716547i	$0.254279\pi$
$228$	29.9249	1.98183
$229$	−22.1722	−1.46518	−0.732589	−	0.680671i	$-0.761688\pi$
$229$	−22.1722	−1.46518	−0.732589	+	0.680671i	$0.761688\pi$
$230$	−17.6359	−1.16288
$231$	2.19259	0.144262
$232$	−97.8099	−6.42153
$233$	−23.2323	−1.52200	−0.761000	−	0.648752i	$-0.775291\pi$
$233$	−23.2323	−1.52200	−0.761000	+	0.648752i	$0.775291\pi$
$234$	−4.97217	−0.325041
$235$	−25.2928	−1.64992
$236$	36.8626	2.39955
$237$	12.4941	0.811582
$238$	25.5027	1.65310
$239$	5.63915	0.364766	0.182383	−	0.983228i	$-0.441619\pi$
$239$	5.63915	0.364766	0.182383	+	0.983228i	$0.441619\pi$
$240$	−64.0698	−4.13569
$241$	13.3429	0.859492	0.429746	−	0.902950i	$-0.358603\pi$
$241$	13.3429	0.859492	0.429746	+	0.902950i	$0.358603\pi$
$242$	29.8541	1.91909
$243$	15.3328	0.983599
$244$	−39.4522	−2.52567
$245$	−27.6143	−1.76421
$246$	−23.8543	−1.52090
$247$	−4.74703	−0.302046
$248$	−96.2738	−6.11339
$249$	16.1048	1.02060
$250$	11.7218	0.741352
$251$	19.6427	1.23984	0.619918	−	0.784667i	$-0.287166\pi$
$251$	19.6427	1.23984	0.619918	+	0.784667i	$0.287166\pi$
$252$	−39.9810	−2.51857
$253$	−0.965228	−0.0606834
$254$	34.0004	2.13338
$255$	8.68062	0.543601
$256$	86.2833	5.39271
$257$	−8.86288	−0.552851	−0.276426	−	0.961035i	$-0.589150\pi$
$257$	−8.86288	−0.552851	−0.276426	+	0.961035i	$0.589150\pi$
$258$	−2.16160	−0.134575
$259$	−15.2247	−0.946018
$260$	19.2168	1.19178
$261$	−16.8830	−1.04503
$262$	−37.8166	−2.33631
$263$	11.1782	0.689278	0.344639	−	0.938735i	$-0.388001\pi$
$263$	11.1782	0.689278	0.344639	+	0.938735i	$0.388001\pi$
$264$	−5.82177	−0.358305
$265$	45.7097	2.80792
$266$	−51.4993	−3.15763
$267$	11.3139	0.692399
$268$	−43.1533	−2.63601
$269$	27.0710	1.65055	0.825273	−	0.564734i	$-0.191021\pi$
$269$	27.0710	1.65055	0.825273	+	0.564734i	$0.191021\pi$
$270$	−49.1563	−2.99156
$271$	−18.4185	−1.11885	−0.559423	−	0.828882i	$-0.688977\pi$
$271$	−18.4185	−1.11885	−0.559423	+	0.828882i	$0.688977\pi$
$272$	−40.7864	−2.47304
$273$	−4.29530	−0.259964
$274$	12.5066	0.755553
$275$	3.19386	0.192597
$276$	−11.9200	−0.717502
$277$	9.68139	0.581698	0.290849	−	0.956769i	$-0.406062\pi$
$277$	9.68139	0.581698	0.290849	+	0.956769i	$0.406062\pi$
$278$	−26.0062	−1.55975
$279$	−16.6179	−0.994888
$280$	135.681	8.10849
$281$	28.5983	1.70603	0.853016	−	0.521884i	$-0.174771\pi$
$281$	28.5983	1.70603	0.853016	+	0.521884i	$0.174771\pi$
$282$	−23.0648	−1.37349
$283$	21.9363	1.30398	0.651988	−	0.758229i	$-0.273935\pi$
$283$	21.9363	1.30398	0.651988	+	0.758229i	$0.273935\pi$
$284$	−31.9150	−1.89381
$285$	−17.5294	−1.03835
$286$	1.41901	0.0839080
$287$	30.4274	1.79607
$288$	49.2004	2.89916
$289$	−11.4740	−0.674940
$290$	88.0356	5.16963
$291$	−8.83723	−0.518048
$292$	−39.7464	−2.32598
$293$	29.2776	1.71042	0.855209	−	0.518284i	$-0.173429\pi$
$293$	29.2776	1.71042	0.855209	+	0.518284i	$0.173429\pi$
$294$	−25.1817	−1.46863
$295$	−21.5933	−1.25721
$296$	40.4247	2.34964
$297$	−2.69037	−0.156111
$298$	44.8129	2.59594
$299$	1.89089	0.109353
$300$	39.4424	2.27721
$301$	2.75723	0.158924
$302$	−36.6153	−2.10697
$303$	−4.85632	−0.278988
$304$	82.3628	4.72383
$305$	23.1102	1.32329
$306$	−11.6883	−0.668177
$307$	14.6294	0.834942	0.417471	−	0.908690i	$-0.362916\pi$
$307$	14.6294	0.834942	0.417471	+	0.908690i	$0.362916\pi$
$308$	11.4102	0.650159
$309$	−14.0456	−0.799025
$310$	86.6530	4.92156
$311$	−23.0153	−1.30508	−0.652539	−	0.757755i	$-0.726296\pi$
$311$	−23.0153	−1.30508	−0.652539	+	0.757755i	$0.726296\pi$
$312$	11.4049	0.645675
$313$	31.2839	1.76827	0.884136	−	0.467229i	$-0.154748\pi$
$313$	31.2839	1.76827	0.884136	+	0.467229i	$0.154748\pi$
$314$	−22.6118	−1.27606
$315$	23.4200	1.31957
$316$	65.0196	3.65764
$317$	−6.83065	−0.383647	−0.191824	−	0.981429i	$-0.561440\pi$
$317$	−6.83065	−0.383647	−0.191824	+	0.981429i	$0.561440\pi$
$318$	41.6831	2.33747
$319$	4.81828	0.269772
$320$	−140.127	−7.83334
$321$	−4.34226	−0.242361
$322$	20.5138	1.14319
$323$	−11.1591	−0.620908
$324$	−2.49067	−0.138371
$325$	−6.25679	−0.347064
$326$	−26.9907	−1.49488
$327$	−11.7448	−0.649489
$328$	−80.7908	−4.46093
$329$	29.4203	1.62199
$330$	5.23999	0.288452
$331$	−13.0401	−0.716749	−0.358374	−	0.933578i	$-0.616669\pi$
$331$	−13.0401	−0.716749	−0.358374	+	0.933578i	$0.616669\pi$
$332$	83.8095	4.59964
$333$	6.97775	0.382378
$334$	−16.4655	−0.900951
$335$	25.2783	1.38110
$336$	74.5252	4.06568
$337$	−3.95776	−0.215593	−0.107796	−	0.994173i	$-0.534379\pi$
$337$	−3.95776	−0.215593	−0.107796	+	0.994173i	$0.534379\pi$
$338$	−2.77986	−0.151204
$339$	−12.5358	−0.680852
$340$	45.1739	2.44990
$341$	4.74260	0.256826
$342$	23.6030	1.27630
$343$	4.80217	0.259293
$344$	−7.32101	−0.394722
$345$	6.98250	0.375925
$346$	−18.0433	−0.970012
$347$	11.7608	0.631354	0.315677	−	0.948867i	$-0.397768\pi$
$347$	11.7608	0.631354	0.315677	+	0.948867i	$0.397768\pi$
$348$	59.5030	3.18970
$349$	21.8844	1.17144	0.585722	−	0.810512i	$-0.300811\pi$
$349$	21.8844	1.17144	0.585722	+	0.810512i	$0.300811\pi$
$350$	−67.8784	−3.62825
$351$	5.27046	0.281317
$352$	−14.0414	−0.748407
$353$	13.2282	0.704065	0.352033	−	0.935988i	$-0.385491\pi$
$353$	13.2282	0.704065	0.352033	+	0.935988i	$0.385491\pi$
$354$	−19.6911	−1.04657
$355$	18.6951	0.992233
$356$	58.8775	3.12050
$357$	−10.0972	−0.534400
$358$	−26.4375	−1.39727
$359$	26.3714	1.39183	0.695915	−	0.718124i	$-0.254999\pi$
$359$	26.3714	1.39183	0.695915	+	0.718124i	$0.254999\pi$
$360$	−62.1849	−3.27743
$361$	3.53428	0.186015
$362$	−18.6420	−0.979801
$363$	−11.8200	−0.620390
$364$	−22.3528	−1.17160
$365$	23.2826	1.21867
$366$	21.0745	1.10158
$367$	20.5670	1.07359	0.536794	−	0.843713i	$-0.319635\pi$
$367$	20.5670	1.07359	0.536794	+	0.843713i	$0.319635\pi$
$368$	−32.8077	−1.71022
$369$	−13.9454	−0.725967
$370$	−36.3850	−1.89157
$371$	−53.1689	−2.76039
$372$	58.5685	3.03664
$373$	27.8117	1.44004	0.720018	−	0.693955i	$-0.244134\pi$
$373$	27.8117	1.44004	0.720018	+	0.693955i	$0.244134\pi$
$374$	3.33574	0.172487
$375$	−4.64096	−0.239658
$376$	−78.1169	−4.02857
$377$	−9.43905	−0.486136
$378$	57.1780	2.94092
$379$	−26.6013	−1.36642	−0.683210	−	0.730222i	$-0.739416\pi$
$379$	−26.6013	−1.36642	−0.683210	+	0.730222i	$0.739416\pi$
$380$	−91.2228	−4.67963
$381$	−13.4616	−0.689661
$382$	30.0287	1.53640
$383$	0.942053	0.0481366	0.0240683	−	0.999710i	$-0.492338\pi$
$383$	0.942053	0.0481366	0.0240683	+	0.999710i	$0.492338\pi$
$384$	−67.2337	−3.43100
$385$	−6.68387	−0.340641
$386$	−4.54936	−0.231556
$387$	−1.26368	−0.0642367
$388$	−45.9890	−2.33474
$389$	−9.17847	−0.465367	−0.232683	−	0.972553i	$-0.574751\pi$
$389$	−9.17847	−0.465367	−0.232683	+	0.972553i	$0.574751\pi$
$390$	−10.2652	−0.519798
$391$	4.44501	0.224794
$392$	−85.2866	−4.30762
$393$	14.9726	0.755265
$394$	6.58517	0.331756
$395$	−38.0870	−1.91637
$396$	−5.22950	−0.262792
$397$	9.47590	0.475582	0.237791	−	0.971316i	$-0.423577\pi$
$397$	9.47590	0.475582	0.237791	+	0.971316i	$0.423577\pi$
$398$	41.4700	2.07870
$399$	20.3899	1.02077
$400$	108.558	5.42789
$401$	−21.2268	−1.06002	−0.530009	−	0.847992i	$-0.677811\pi$
$401$	−21.2268	−1.06002	−0.530009	+	0.847992i	$0.677811\pi$
$402$	23.0515	1.14970
$403$	−9.29081	−0.462808
$404$	−25.2723	−1.25734
$405$	1.45898	0.0724974
$406$	−102.402	−5.08212
$407$	−1.99139	−0.0987094
$408$	26.8101	1.32730
$409$	−36.4313	−1.80141	−0.900706	−	0.434430i	$-0.856950\pi$
$409$	−36.4313	−1.80141	−0.900706	+	0.434430i	$0.856950\pi$
$410$	72.7173	3.59125
$411$	−4.95170	−0.244249
$412$	−73.0932	−3.60104
$413$	25.1170	1.23593
$414$	−9.40183	−0.462075
$415$	−49.0938	−2.40992
$416$	27.5072	1.34865
$417$	10.2965	0.504223
$418$	−6.73609	−0.329473
$419$	−8.17665	−0.399455	−0.199728	−	0.979851i	$-0.564006\pi$
$419$	−8.17665	−0.399455	−0.199728	+	0.979851i	$0.564006\pi$
$420$	−82.5421	−4.02764
$421$	22.7116	1.10690	0.553448	−	0.832884i	$-0.313312\pi$
$421$	22.7116	1.10690	0.553448	+	0.832884i	$0.313312\pi$
$422$	22.3632	1.08862
$423$	−13.4838	−0.655606
$424$	141.174	6.85602
$425$	−14.7082	−0.713450
$426$	17.0483	0.825991
$427$	−26.8815	−1.30089
$428$	−22.5971	−1.09227
$429$	−0.561824	−0.0271251
$430$	6.58941	0.317769
$431$	26.3756	1.27047	0.635234	−	0.772320i	$-0.280904\pi$
$431$	26.3756	1.27047	0.635234	+	0.772320i	$0.280904\pi$
$432$	−91.4447	−4.39963
$433$	25.6947	1.23481	0.617404	−	0.786647i	$-0.288185\pi$
$433$	25.6947	1.23481	0.617404	+	0.786647i	$0.288185\pi$
$434$	−100.794	−4.83825
$435$	−34.8556	−1.67120
$436$	−61.1199	−2.92711
$437$	−8.97612	−0.429386
$438$	21.2316	1.01449
$439$	−12.0190	−0.573633	−0.286817	−	0.957985i	$-0.592597\pi$
$439$	−12.0190	−0.573633	−0.286817	+	0.957985i	$0.592597\pi$
$440$	17.7470	0.846056
$441$	−14.7214	−0.701018
$442$	−6.53475	−0.310827
$443$	−33.0481	−1.57016	−0.785081	−	0.619393i	$-0.787379\pi$
$443$	−33.0481	−1.57016	−0.785081	+	0.619393i	$0.787379\pi$
$444$	−24.5925	−1.16711
$445$	−34.4892	−1.63494
$446$	−58.1480	−2.75339
$447$	−17.7426	−0.839195
$448$	162.994	7.70075
$449$	−3.57419	−0.168676	−0.0843382	−	0.996437i	$-0.526878\pi$
$449$	−3.57419	−0.168676	−0.0843382	+	0.996437i	$0.526878\pi$
$450$	31.1098	1.46653
$451$	3.97989	0.187406
$452$	−65.2364	−3.06846
$453$	14.4969	0.681126
$454$	−58.4297	−2.74224
$455$	13.0938	0.613845
$456$	−54.1394	−2.53531
$457$	−0.827453	−0.0387066	−0.0193533	−	0.999813i	$-0.506161\pi$
$457$	−0.827453	−0.0387066	−0.0193533	+	0.999813i	$0.506161\pi$
$458$	61.6355	2.88004
$459$	12.3895	0.578294
$460$	36.3369	1.69422
$461$	29.9995	1.39722	0.698608	−	0.715505i	$-0.253803\pi$
$461$	29.9995	1.39722	0.698608	+	0.715505i	$0.253803\pi$
$462$	−6.09509	−0.283569
$463$	22.2500	1.03405	0.517023	−	0.855972i	$-0.327040\pi$
$463$	22.2500	1.03405	0.517023	+	0.855972i	$0.327040\pi$
$464$	163.771	7.60289
$465$	−34.3082	−1.59100
$466$	64.5826	2.99173
$467$	−35.4104	−1.63860	−0.819299	−	0.573366i	$-0.805637\pi$
$467$	−35.4104	−1.63860	−0.819299	+	0.573366i	$0.805637\pi$
$468$	10.2446	0.473559
$469$	−29.4033	−1.35772
$470$	70.3106	3.24318
$471$	8.95259	0.412514
$472$	−66.6908	−3.06969
$473$	0.360645	0.0165825
$474$	−34.7320	−1.59529
$475$	29.7012	1.36278
$476$	−52.5458	−2.40843
$477$	24.3682	1.11574
$478$	−15.6760	−0.717005
$479$	2.32415	0.106193	0.0530965	−	0.998589i	$-0.483091\pi$
$479$	2.32415	0.106193	0.0530965	+	0.998589i	$0.483091\pi$
$480$	101.576	4.63627
$481$	3.90115	0.177877
$482$	−37.0914	−1.68947
$483$	−8.12195	−0.369562
$484$	−61.5114	−2.79597
$485$	26.9393	1.22325
$486$	−42.6230	−1.93342
$487$	5.78156	0.261987	0.130994	−	0.991383i	$-0.458183\pi$
$487$	5.78156	0.261987	0.130994	+	0.991383i	$0.458183\pi$
$488$	71.3759	3.23103
$489$	10.6863	0.483252
$490$	76.7638	3.46783
$491$	38.3355	1.73005	0.865027	−	0.501725i	$-0.167301\pi$
$491$	38.3355	1.73005	0.865027	+	0.501725i	$0.167301\pi$
$492$	49.1494	2.21583
$493$	−22.1888	−0.999335
$494$	13.1961	0.593719
$495$	3.06333	0.137686
$496$	161.199	7.23806
$497$	−21.7459	−0.975438
$498$	−44.7691	−2.00615
$499$	−7.46669	−0.334255	−0.167128	−	0.985935i	$-0.553449\pi$
$499$	−7.46669	−0.334255	−0.167128	+	0.985935i	$0.553449\pi$
$500$	−24.1516	−1.08009
$501$	6.51911	0.291252
$502$	−54.6039	−2.43709
$503$	−0.750703	−0.0334722	−0.0167361	−	0.999860i	$-0.505328\pi$
$503$	−0.750703	−0.0334722	−0.0167361	+	0.999860i	$0.505328\pi$
$504$	72.3327	3.22195
$505$	14.8040	0.658767
$506$	2.68320	0.119283
$507$	1.10062	0.0488802
$508$	−70.0544	−3.10816
$509$	7.82076	0.346649	0.173325	−	0.984865i	$-0.444549\pi$
$509$	7.82076	0.346649	0.173325	+	0.984865i	$0.444549\pi$
$510$	−24.1309	−1.06853
$511$	−27.0820	−1.19804
$512$	−117.681	−5.20082
$513$	−25.0190	−1.10462
$514$	24.6376	1.08672
$515$	42.8164	1.88672
$516$	4.45376	0.196066
$517$	3.84817	0.169242
$518$	42.3226	1.85955
$519$	7.14379	0.313578
$520$	−34.7666	−1.52462
$521$	−7.47187	−0.327349	−0.163674	−	0.986514i	$-0.552335\pi$
$521$	−7.47187	−0.327349	−0.163674	+	0.986514i	$0.552335\pi$
$522$	46.9325	2.05418
$523$	−10.1533	−0.443973	−0.221986	−	0.975050i	$-0.571254\pi$
$523$	−10.1533	−0.443973	−0.221986	+	0.975050i	$0.571254\pi$
$524$	77.9172	3.40383
$525$	26.8748	1.17291
$526$	−31.0739	−1.35489
$527$	−21.8404	−0.951381
$528$	9.74787	0.424222
$529$	−19.4245	−0.844545
$530$	−127.066	−5.51941
$531$	−11.5116	−0.499559
$532$	106.109	4.60042
$533$	−7.79664	−0.337710
$534$	−31.4510	−1.36102
$535$	13.2369	0.572281
$536$	78.0718	3.37219
$537$	10.4673	0.451697
$538$	−75.2535	−3.24441
$539$	4.20136	0.180965
$540$	101.282	4.35847
$541$	−34.8402	−1.49790	−0.748949	−	0.662627i	$-0.769441\pi$
$541$	−34.8402	−1.49790	−0.748949	+	0.662627i	$0.769441\pi$
$542$	51.2009	2.19927
$543$	7.38085	0.316742
$544$	64.6624	2.77238
$545$	35.8027	1.53362
$546$	11.9403	0.510999
$547$	−15.7533	−0.673560	−0.336780	−	0.941583i	$-0.609338\pi$
$547$	−15.7533	−0.673560	−0.336780	+	0.941583i	$0.609338\pi$
$548$	−25.7686	−1.10078
$549$	12.3203	0.525816
$550$	−8.87847	−0.378579
$551$	44.8074	1.90886
$552$	21.5654	0.917886
$553$	44.3024	1.88393
$554$	−26.9129	−1.14342
$555$	14.4058	0.611491
$556$	53.5831	2.27243
$557$	−9.37524	−0.397242	−0.198621	−	0.980076i	$-0.563646\pi$
$557$	−9.37524	−0.397242	−0.198621	+	0.980076i	$0.563646\pi$
$558$	46.1954	1.95561
$559$	−0.706506	−0.0298820
$560$	−227.182	−9.60019
$561$	−1.32071	−0.0557603
$562$	−79.4993	−3.35348
$563$	−13.6037	−0.573327	−0.286663	−	0.958031i	$-0.592546\pi$
$563$	−13.6037	−0.573327	−0.286663	+	0.958031i	$0.592546\pi$
$564$	47.5227	2.00107
$565$	38.2141	1.60768
$566$	−60.9798	−2.56317
$567$	−1.69707	−0.0712702
$568$	57.7398	2.42271
$569$	32.4509	1.36041	0.680207	−	0.733020i	$-0.261890\pi$
$569$	32.4509	1.36041	0.680207	+	0.733020i	$0.261890\pi$
$570$	48.7292	2.04104
$571$	21.2231	0.888159	0.444080	−	0.895987i	$-0.353531\pi$
$571$	21.2231	0.888159	0.444080	+	0.895987i	$0.353531\pi$
$572$	−2.92373	−0.122247
$573$	−11.8891	−0.496676
$574$	−84.5838	−3.53046
$575$	−11.8309	−0.493383
$576$	−74.7029	−3.11262
$577$	−32.1999	−1.34050	−0.670250	−	0.742136i	$-0.733813\pi$
$577$	−32.1999	−1.34050	−0.670250	+	0.742136i	$0.733813\pi$
$578$	31.8960	1.32670
$579$	1.80121	0.0748558
$580$	−181.389	−7.53175
$581$	57.1052	2.36912
$582$	24.5663	1.01830
$583$	−6.95447	−0.288025
$584$	71.9081	2.97558
$585$	−6.00109	−0.248114
$586$	−81.3877	−3.36209
$587$	11.8213	0.487916	0.243958	−	0.969786i	$-0.421554\pi$
$587$	11.8213	0.487916	0.243958	+	0.969786i	$0.421554\pi$
$588$	51.8844	2.13968
$589$	44.1037	1.81726
$590$	60.0263	2.47124
$591$	−2.60724	−0.107247
$592$	−67.6865	−2.78190
$593$	−0.688725	−0.0282825	−0.0141413	−	0.999900i	$-0.504501\pi$
$593$	−0.688725	−0.0282825	−0.0141413	+	0.999900i	$0.504501\pi$
$594$	7.47886	0.306861
$595$	30.7802	1.26186
$596$	−92.3324	−3.78208
$597$	−16.4190	−0.671986
$598$	−5.25641	−0.214951
$599$	−13.1623	−0.537796	−0.268898	−	0.963169i	$-0.586659\pi$
$599$	−13.1623	−0.537796	−0.268898	+	0.963169i	$0.586659\pi$
$600$	−71.3581	−2.91318
$601$	−19.0526	−0.777170	−0.388585	−	0.921413i	$-0.627036\pi$
$601$	−19.0526	−0.777170	−0.388585	+	0.921413i	$0.627036\pi$
$602$	−7.66472	−0.312390
$603$	13.4760	0.548787
$604$	75.4422	3.06970
$605$	36.0320	1.46491
$606$	13.4999	0.548395
$607$	−1.26975	−0.0515374	−0.0257687	−	0.999668i	$-0.508203\pi$
$607$	−1.26975	−0.0515374	−0.0257687	+	0.999668i	$0.508203\pi$
$608$	−130.577	−5.29561
$609$	40.5436	1.64291
$610$	−64.2432	−2.60113
$611$	−7.53859	−0.304979
$612$	24.0826	0.973481
$613$	15.9229	0.643121	0.321561	−	0.946889i	$-0.395793\pi$
$613$	15.9229	0.643121	0.321561	+	0.946889i	$0.395793\pi$
$614$	−40.6676	−1.64121
$615$	−28.7907	−1.16095
$616$	−20.6431	−0.831735
$617$	1.00000	0.0402585
$617$	1.00000	0.0402585
$618$	39.0447	1.57061
$619$	20.1890	0.811463	0.405732	−	0.913992i	$-0.367017\pi$
$619$	20.1890	0.811463	0.405732	+	0.913992i	$0.367017\pi$
$620$	−178.540	−7.17033
$621$	9.96588	0.399917
$622$	63.9793	2.56534
$623$	40.1173	1.60727
$624$	−19.0962	−0.764459
$625$	−17.1365	−0.685460
$626$	−86.9650	−3.47582
$627$	2.66699	0.106509
$628$	46.5893	1.85912
$629$	9.17062	0.365657
$630$	−65.1043	−2.59382
$631$	16.9259	0.673810	0.336905	−	0.941539i	$-0.390620\pi$
$631$	16.9259	0.673810	0.336905	+	0.941539i	$0.390620\pi$
$632$	−117.632	−4.67914
$633$	−8.85416	−0.351921
$634$	18.9882	0.754120
$635$	41.0363	1.62848
$636$	−85.8839	−3.40552
$637$	−8.23050	−0.326104
$638$	−13.3941	−0.530279
$639$	9.96652	0.394269
$640$	204.954	8.10154
$641$	−30.7747	−1.21553	−0.607764	−	0.794118i	$-0.707933\pi$
$641$	−30.7747	−1.21553	−0.607764	+	0.794118i	$0.707933\pi$
$642$	12.0709	0.476399
$643$	−29.7285	−1.17238	−0.586189	−	0.810175i	$-0.699372\pi$
$643$	−29.7285	−1.17238	−0.586189	+	0.810175i	$0.699372\pi$
$644$	−42.2667	−1.66554
$645$	−2.60892	−0.102726
$646$	31.0207	1.22049
$647$	−37.4913	−1.47394	−0.736968	−	0.675928i	$-0.763743\pi$
$647$	−37.4913	−1.47394	−0.736968	+	0.675928i	$0.763743\pi$
$648$	4.50606	0.177015
$649$	3.28530	0.128959
$650$	17.3930	0.682210
$651$	39.9068	1.56407
$652$	55.6116	2.17792
$653$	14.8862	0.582542	0.291271	−	0.956641i	$-0.405922\pi$
$653$	14.8862	0.582542	0.291271	+	0.956641i	$0.405922\pi$
$654$	32.6489	1.27667
$655$	−45.6422	−1.78339
$656$	135.275	5.28159
$657$	12.4121	0.484243
$658$	−81.7844	−3.18829
$659$	−12.2004	−0.475260	−0.237630	−	0.971356i	$-0.576371\pi$
$659$	−12.2004	−0.475260	−0.237630	+	0.971356i	$0.576371\pi$
$660$	−10.7965	−0.420252
$661$	−0.631852	−0.0245762	−0.0122881	−	0.999924i	$-0.503912\pi$
$661$	−0.631852	−0.0245762	−0.0122881	+	0.999924i	$0.503912\pi$
$662$	36.2496	1.40888
$663$	2.58728	0.100482
$664$	−151.626	−5.88423
$665$	−62.1564	−2.41032
$666$	−19.3972	−0.751625
$667$	−17.8482	−0.691086
$668$	33.9255	1.31262
$669$	23.0223	0.890094
$670$	−70.2700	−2.71477
$671$	−3.51609	−0.135737
$672$	−118.152	−4.55780
$673$	12.9212	0.498077	0.249039	−	0.968494i	$-0.419885\pi$
$673$	12.9212	0.498077	0.249039	+	0.968494i	$0.419885\pi$
$674$	11.0020	0.423782
$675$	−32.9762	−1.26925
$676$	5.72762	0.220293
$677$	36.6707	1.40937	0.704685	−	0.709520i	$-0.251088\pi$
$677$	36.6707	1.40937	0.704685	+	0.709520i	$0.251088\pi$
$678$	34.8478	1.33832
$679$	−31.3355	−1.20255
$680$	−81.7275	−3.13411
$681$	23.1338	0.886491
$682$	−13.1838	−0.504833
$683$	4.29503	0.164345	0.0821724	−	0.996618i	$-0.473814\pi$
$683$	4.29503	0.164345	0.0821724	+	0.996618i	$0.473814\pi$
$684$	−48.6316	−1.85948
$685$	15.0947	0.576739
$686$	−13.3494	−0.509681
$687$	−24.4031	−0.931036
$688$	12.2582	0.467338
$689$	13.6239	0.519028
$690$	−19.4104	−0.738940
$691$	24.0127	0.913487	0.456744	−	0.889598i	$-0.349016\pi$
$691$	24.0127	0.913487	0.456744	+	0.889598i	$0.349016\pi$
$692$	37.1763	1.41323
$693$	−3.56322	−0.135356
$694$	−32.6934	−1.24103
$695$	−31.3878	−1.19061
$696$	−107.651	−4.08051
$697$	−18.3279	−0.694220
$698$	−60.8355	−2.30266
$699$	−25.5699	−0.967144
$700$	139.857	5.28608
$701$	−27.1272	−1.02458	−0.512290	−	0.858812i	$-0.671203\pi$
$701$	−27.1272	−1.02458	−0.512290	+	0.858812i	$0.671203\pi$
$702$	−14.6512	−0.552972
$703$	−18.5189	−0.698452
$704$	21.3196	0.803511
$705$	−27.8378	−1.04843
$706$	−36.7725	−1.38395
$707$	−17.2198	−0.647616
$708$	40.5716	1.52477
$709$	40.4817	1.52032	0.760161	−	0.649735i	$-0.225120\pi$
$709$	40.4817	1.52032	0.760161	+	0.649735i	$0.225120\pi$
$710$	−51.9698	−1.95039
$711$	−20.3045	−0.761479
$712$	−106.520	−3.99199
$713$	−17.5679	−0.657923
$714$	28.0688	1.05045
$715$	1.71266	0.0640498
$716$	54.4718	2.03571
$717$	6.20655	0.231788
$718$	−73.3088	−2.73586
$719$	25.5223	0.951823	0.475911	−	0.879493i	$-0.342118\pi$
$719$	25.5223	0.951823	0.475911	+	0.879493i	$0.342118\pi$
$720$	104.121	3.88037
$721$	−49.8035	−1.85478
$722$	−9.82479	−0.365641
$723$	14.6854	0.546157
$724$	38.4099	1.42749
$725$	59.0582	2.19337
$726$	32.8580	1.21947
$727$	23.0951	0.856551	0.428275	−	0.903648i	$-0.359121\pi$
$727$	23.0951	0.856551	0.428275	+	0.903648i	$0.359121\pi$
$728$	40.4400	1.49881
$729$	18.1801	0.673337
$730$	−64.7223	−2.39548
$731$	−1.66082	−0.0614276
$732$	−43.4218	−1.60492
$733$	33.4169	1.23428	0.617140	−	0.786853i	$-0.288291\pi$
$733$	33.4169	1.23428	0.617140	+	0.786853i	$0.288291\pi$
$734$	−57.1734	−2.11031
$735$	−30.3928	−1.12105
$736$	52.0130	1.91723
$737$	−3.84595	−0.141667
$738$	38.7662	1.42700
$739$	1.20758	0.0444214	0.0222107	−	0.999753i	$-0.492930\pi$
$739$	1.20758	0.0444214	0.0222107	+	0.999753i	$0.492930\pi$
$740$	74.9677	2.75587
$741$	−5.22467	−0.191933
$742$	147.802	5.42598
$743$	−6.69692	−0.245686	−0.122843	−	0.992426i	$-0.539201\pi$
$743$	−6.69692	−0.245686	−0.122843	+	0.992426i	$0.539201\pi$
$744$	−105.961	−3.88471
$745$	54.0863	1.98157
$746$	−77.3127	−2.83062
$747$	−26.1723	−0.957594
$748$	−6.87296	−0.251300
$749$	−15.3970	−0.562594
$750$	12.9012	0.471086
$751$	−12.4051	−0.452667	−0.226334	−	0.974050i	$-0.572674\pi$
$751$	−12.4051	−0.452667	−0.226334	+	0.974050i	$0.572674\pi$
$752$	130.798	4.76970
$753$	21.6191	0.787844
$754$	26.2392	0.955576
$755$	−44.1924	−1.60832
$756$	−117.809	−4.28469
$757$	28.5128	1.03631	0.518157	−	0.855285i	$-0.326618\pi$
$757$	28.5128	1.03631	0.518157	+	0.855285i	$0.326618\pi$
$758$	73.9480	2.68591
$759$	−1.06235	−0.0385608
$760$	165.038	5.98656
$761$	−8.59666	−0.311629	−0.155814	−	0.987786i	$-0.549800\pi$
$761$	−8.59666	−0.311629	−0.155814	+	0.987786i	$0.549800\pi$
$762$	37.4215	1.35564
$763$	−41.6453	−1.50766
$764$	−61.8711	−2.23842
$765$	−14.1071	−0.510042
$766$	−2.61877	−0.0946202
$767$	−6.43593	−0.232388
$768$	94.9650	3.42676
$769$	38.5035	1.38847	0.694236	−	0.719748i	$-0.255743\pi$
$769$	38.5035	1.38847	0.694236	+	0.719748i	$0.255743\pi$
$770$	18.5802	0.669584
$771$	−9.75465	−0.351305
$772$	9.37350	0.337360
$773$	−49.8084	−1.79148	−0.895742	−	0.444573i	$-0.853355\pi$
$773$	−49.8084	−1.79148	−0.895742	+	0.444573i	$0.853355\pi$
$774$	3.51287	0.126267
$775$	58.1307	2.08811
$776$	83.2021	2.98678
$777$	−16.7566	−0.601140
$778$	25.5149	0.914752
$779$	37.0109	1.32605
$780$	21.1504	0.757305
$781$	−2.84436	−0.101779
$782$	−12.3565	−0.441868
$783$	−49.7482	−1.77785
$784$	142.802	5.10009
$785$	−27.2910	−0.974058
$786$	−41.6216	−1.48459
$787$	−42.7682	−1.52452	−0.762262	−	0.647269i	$-0.775911\pi$
$787$	−42.7682	−1.52452	−0.762262	+	0.647269i	$0.775911\pi$
$788$	−13.5681	−0.483343
$789$	12.3030	0.437997
$790$	105.877	3.76692
$791$	−44.4501	−1.58046
$792$	9.46108	0.336185
$793$	6.88806	0.244602
$794$	−26.3417	−0.934831
$795$	50.3089	1.78427
$796$	−85.4447	−3.02851
$797$	51.8793	1.83766	0.918829	−	0.394655i	$-0.129136\pi$
$797$	51.8793	1.83766	0.918829	+	0.394655i	$0.129136\pi$
$798$	−56.6811	−2.00649
$799$	−17.7213	−0.626936
$800$	−172.107	−6.08489
$801$	−18.3865	−0.649653
$802$	59.0076	2.08363
$803$	−3.54231	−0.125005
$804$	−47.4953	−1.67503
$805$	24.7589	0.872636
$806$	25.8271	0.909722
$807$	29.7948	1.04883
$808$	45.7220	1.60849
$809$	24.2579	0.852861	0.426430	−	0.904520i	$-0.359771\pi$
$809$	24.2579	0.852861	0.426430	+	0.904520i	$0.359771\pi$
$810$	−4.05577	−0.142505
$811$	7.93604	0.278672	0.139336	−	0.990245i	$-0.455503\pi$
$811$	7.93604	0.278672	0.139336	+	0.990245i	$0.455503\pi$
$812$	210.989	7.40426
$813$	−20.2718	−0.710962
$814$	5.53578	0.194029
$815$	−32.5760	−1.14109
$816$	−44.8903	−1.57148
$817$	3.35381	0.117335
$818$	101.274	3.54096
$819$	6.98039	0.243915
$820$	−149.827	−5.23217
$821$	−43.8958	−1.53197	−0.765987	−	0.642856i	$-0.777749\pi$
$821$	−43.8958	−1.53197	−0.765987	+	0.642856i	$0.777749\pi$
$822$	13.7650	0.480110
$823$	−1.66931	−0.0581884	−0.0290942	−	0.999577i	$-0.509262\pi$
$823$	−1.66931	−0.0581884	−0.0290942	+	0.999577i	$0.509262\pi$
$824$	132.238	4.60674
$825$	3.51522	0.122384
$826$	−69.8218	−2.42941
$827$	−5.80992	−0.202031	−0.101015	−	0.994885i	$-0.532209\pi$
$827$	−5.80992	−0.202031	−0.101015	+	0.994885i	$0.532209\pi$
$828$	19.3715	0.673207
$829$	29.4673	1.02344	0.511721	−	0.859152i	$-0.329008\pi$
$829$	29.4673	1.02344	0.511721	+	0.859152i	$0.329008\pi$
$830$	136.474	4.73707
$831$	10.6555	0.369636
$832$	−41.7652	−1.44795
$833$	−19.3478	−0.670363
$834$	−28.6229	−0.991130
$835$	−19.8728	−0.687726
$836$	13.8790	0.480017
$837$	−48.9669	−1.69254
$838$	22.7299	0.785193
$839$	19.1311	0.660477	0.330239	−	0.943897i	$-0.392871\pi$
$839$	19.1311	0.660477	0.330239	+	0.943897i	$0.392871\pi$
$840$	149.333	5.15248
$841$	60.0956	2.07226
$842$	−63.1351	−2.17578
$843$	31.4758	1.08409
$844$	−46.0771	−1.58604
$845$	−3.35511	−0.115419
$846$	37.4831	1.28870
$847$	−41.9120	−1.44011
$848$	−236.380	−8.11731
$849$	24.1435	0.828602
$850$	40.8866	1.40240
$851$	7.37665	0.252868
$852$	−35.1262	−1.20341
$853$	53.2674	1.82384	0.911920	−	0.410369i	$-0.134600\pi$
$853$	53.2674	1.82384	0.911920	+	0.410369i	$0.134600\pi$
$854$	74.7269	2.55710
$855$	28.4873	0.974246
$856$	40.8821	1.39732
$857$	47.6367	1.62724	0.813619	−	0.581398i	$-0.197494\pi$
$857$	47.6367	1.62724	0.813619	+	0.581398i	$0.197494\pi$
$858$	1.56179	0.0533187
$859$	32.0947	1.09506	0.547528	−	0.836788i	$-0.315569\pi$
$859$	32.0947	1.09506	0.547528	+	0.836788i	$0.315569\pi$
$860$	−13.5768	−0.462965
$861$	33.4889	1.14130
$862$	−73.3205	−2.49731
$863$	−47.0662	−1.60215	−0.801075	−	0.598563i	$-0.795738\pi$
$863$	−47.0662	−1.60215	−0.801075	+	0.598563i	$0.795738\pi$
$864$	144.975	4.93217
$865$	−21.7771	−0.740443
$866$	−71.4276	−2.42721
$867$	−12.6285	−0.428885
$868$	207.675	7.04896
$869$	5.79473	0.196573
$870$	96.8936	3.28500
$871$	7.53424	0.255288
$872$	110.577	3.74460
$873$	14.3616	0.486066
$874$	24.9523	0.844026
$875$	−16.4562	−0.556320
$876$	−43.7456	−1.47803
$877$	24.3282	0.821506	0.410753	−	0.911747i	$-0.365266\pi$
$877$	24.3282	0.821506	0.410753	+	0.911747i	$0.365266\pi$
$878$	33.4110	1.12757
$879$	32.2235	1.08687
$880$	−29.7153	−1.00170
$881$	43.3996	1.46217	0.731085	−	0.682286i	$-0.239014\pi$
$881$	43.3996	1.46217	0.731085	+	0.682286i	$0.239014\pi$
$882$	40.9234	1.37796
$883$	53.4142	1.79753	0.898765	−	0.438431i	$-0.144466\pi$
$883$	53.4142	1.79753	0.898765	+	0.438431i	$0.144466\pi$
$884$	13.4642	0.452850
$885$	−23.7660	−0.798884
$886$	91.8691	3.08640
$887$	12.2810	0.412356	0.206178	−	0.978515i	$-0.433897\pi$
$887$	12.2810	0.412356	0.206178	+	0.978515i	$0.433897\pi$
$888$	44.4922	1.49306
$889$	−47.7330	−1.60091
$890$	95.8750	3.21374
$891$	−0.221976	−0.00743648
$892$	119.808	4.01147
$893$	35.7859	1.19753
$894$	49.3219	1.64957
$895$	−31.9084	−1.06658
$896$	−238.400	−7.96440
$897$	2.08115	0.0694876
$898$	9.93575	0.331560
$899$	87.6964	2.92484
$900$	−64.0986	−2.13662
$901$	32.0263	1.06695
$902$	−11.0635	−0.368375
$903$	3.03466	0.100987
$904$	118.024	3.92542
$905$	−22.4997	−0.747915
$906$	−40.2995	−1.33886
$907$	49.6727	1.64935	0.824677	−	0.565604i	$-0.191357\pi$
$907$	49.6727	1.64935	0.824677	+	0.565604i	$0.191357\pi$
$908$	120.389	3.99524
$909$	7.89211	0.261765
$910$	−36.3988	−1.20661
$911$	10.1663	0.336825	0.168412	−	0.985717i	$-0.446136\pi$
$911$	10.1663	0.336825	0.168412	+	0.985717i	$0.446136\pi$
$912$	90.6501	3.00172
$913$	7.46934	0.247199
$914$	2.30020	0.0760840
$915$	25.4355	0.840873
$916$	−126.994	−4.19599
$917$	53.0904	1.75320
$918$	−34.4412	−1.13673
$919$	2.33787	0.0771191	0.0385596	−	0.999256i	$-0.487723\pi$
$919$	2.33787	0.0771191	0.0385596	+	0.999256i	$0.487723\pi$
$920$	−65.7398	−2.16738
$921$	16.1014	0.530558
$922$	−83.3944	−2.74645
$923$	5.57212	0.183409
$924$	12.5583	0.413138
$925$	−24.4087	−0.802552
$926$	−61.8519	−2.03258
$927$	22.8258	0.749697
$928$	−259.641	−8.52314
$929$	35.6263	1.16886	0.584431	−	0.811443i	$-0.301318\pi$
$929$	35.6263	1.16886	0.584431	+	0.811443i	$0.301318\pi$
$930$	95.3719	3.12737
$931$	39.0704	1.28048
$932$	−133.066	−4.35872
$933$	−25.3311	−0.829301
$934$	98.4360	3.22092
$935$	4.02603	0.131665
$936$	−18.5343	−0.605814
$937$	−24.9352	−0.814597	−0.407298	−	0.913295i	$-0.633529\pi$
$937$	−24.9352	−0.814597	−0.407298	+	0.913295i	$0.633529\pi$
$938$	81.7372	2.66881
$939$	34.4317	1.12364
$940$	−144.868	−4.72507
$941$	42.8165	1.39578	0.697890	−	0.716205i	$-0.254123\pi$
$941$	42.8165	1.39578	0.697890	+	0.716205i	$0.254123\pi$
$942$	−24.8870	−0.810861
$943$	−14.7426	−0.480085
$944$	111.666	3.63442
$945$	69.0102	2.24490
$946$	−1.00254	−0.0325954
$947$	14.3222	0.465408	0.232704	−	0.972548i	$-0.425243\pi$
$947$	14.3222	0.465408	0.232704	+	0.972548i	$0.425243\pi$
$948$	71.5617	2.32422
$949$	6.93942	0.225263
$950$	−82.5651	−2.67877
$951$	−7.51794	−0.243786
$952$	95.0644	3.08106
$953$	−6.36073	−0.206044	−0.103022	−	0.994679i	$-0.532851\pi$
$953$	−6.36073	−0.206044	−0.103022	+	0.994679i	$0.532851\pi$
$954$	−67.7402	−2.19317
$955$	36.2428	1.17279
$956$	32.2989	1.04462
$957$	5.30308	0.171424
$958$	−6.46080	−0.208739
$959$	−17.5580	−0.566976
$960$	−154.226	−4.97764
$961$	55.3191	1.78449
$962$	−10.8446	−0.349645
$963$	7.05670	0.227399
$964$	76.4231	2.46142
$965$	−5.49079	−0.176755
$966$	22.5779	0.726432
$967$	−16.7394	−0.538301	−0.269151	−	0.963098i	$-0.586743\pi$
$967$	−16.7394	−0.538301	−0.269151	+	0.963098i	$0.586743\pi$
$968$	111.285	3.57683
$969$	−12.2819	−0.394551
$970$	−74.8876	−2.40450
$971$	−28.3916	−0.911131	−0.455566	−	0.890202i	$-0.650563\pi$
$971$	−28.3916	−0.911131	−0.455566	+	0.890202i	$0.650563\pi$
$972$	87.8204	2.81684
$973$	36.5099	1.17045
$974$	−16.0719	−0.514978
$975$	−6.88634	−0.220539
$976$	−119.511	−3.82544
$977$	−4.63337	−0.148235	−0.0741174	−	0.997250i	$-0.523614\pi$
$977$	−4.63337	−0.148235	−0.0741174	+	0.997250i	$0.523614\pi$
$978$	−29.7064	−0.949907
$979$	5.24733	0.167705
$980$	−158.164	−5.05236
$981$	19.0867	0.609392
$982$	−106.567	−3.40070
$983$	28.4426	0.907177	0.453588	−	0.891211i	$-0.350144\pi$
$983$	28.4426	0.907177	0.453588	+	0.891211i	$0.350144\pi$
$984$	−88.9199	−2.83466
$985$	7.94788	0.253241
$986$	61.6819	1.96435
$987$	32.3805	1.03068
$988$	−27.1892	−0.865003
$989$	−1.33593	−0.0424800
$990$	−8.51562	−0.270644
$991$	−21.2018	−0.673499	−0.336749	−	0.941594i	$-0.609327\pi$
$991$	−21.2018	−0.673499	−0.336749	+	0.941594i	$0.609327\pi$
$992$	−255.564	−8.11415
$993$	−14.3522	−0.455452
$994$	60.4506	1.91738
$995$	50.0516	1.58674
$996$	92.2423	2.92281
$997$	53.9612	1.70897	0.854485	−	0.519476i	$-0.173873\pi$
$997$	53.9612	1.70897	0.854485	+	0.519476i	$0.173873\pi$
$998$	20.7564	0.657031
$999$	20.5609	0.650517

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	8021.2.a.c.1.4	✓	169

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
8021.2.a.c.1.4	✓	169	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:	\( N \)	\(=\)	\( 8021 = 13 \cdot 617 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	8021.a (trivial)

\(f(q)\)	\(=\)	\(q-2.77986 q^{2} +1.10062 q^{3} +5.72762 q^{4} -3.35511 q^{5} -3.05957 q^{6} +3.90263 q^{7} -10.3623 q^{8} -1.78864 q^{9} +O(q^{10})\)	\(q-2.77986 q^{2} +1.10062 q^{3} +5.72762 q^{4} -3.35511 q^{5} -3.05957 q^{6} +3.90263 q^{7} -10.3623 q^{8} -1.78864 q^{9} +9.32675 q^{10} +0.510462 q^{11} +6.30393 q^{12} -1.00000 q^{13} -10.8488 q^{14} -3.69270 q^{15} +17.3504 q^{16} -2.35075 q^{17} +4.97217 q^{18} +4.74703 q^{19} -19.2168 q^{20} +4.29530 q^{21} -1.41901 q^{22} -1.89089 q^{23} -11.4049 q^{24} +6.25679 q^{25} +2.77986 q^{26} -5.27046 q^{27} +22.3528 q^{28} +9.43905 q^{29} +10.2652 q^{30} +9.29081 q^{31} -27.5072 q^{32} +0.561824 q^{33} +6.53475 q^{34} -13.0938 q^{35} -10.2446 q^{36} -3.90115 q^{37} -13.1961 q^{38} -1.10062 q^{39} +34.7666 q^{40} +7.79664 q^{41} -11.9403 q^{42} +0.706506 q^{43} +2.92373 q^{44} +6.00109 q^{45} +5.25641 q^{46} +7.53859 q^{47} +19.0962 q^{48} +8.23050 q^{49} -17.3930 q^{50} -2.58728 q^{51} -5.72762 q^{52} -13.6239 q^{53} +14.6512 q^{54} -1.71266 q^{55} -40.4400 q^{56} +5.22467 q^{57} -26.2392 q^{58} +6.43593 q^{59} -21.1504 q^{60} -6.88806 q^{61} -25.8271 q^{62} -6.98039 q^{63} +41.7652 q^{64} +3.35511 q^{65} -1.56179 q^{66} -7.53424 q^{67} -13.4642 q^{68} -2.08115 q^{69} +36.3988 q^{70} -5.57212 q^{71} +18.5343 q^{72} -6.93942 q^{73} +10.8446 q^{74} +6.88634 q^{75} +27.1892 q^{76} +1.99214 q^{77} +3.05957 q^{78} +11.3519 q^{79} -58.2126 q^{80} -0.434853 q^{81} -21.6736 q^{82} +14.6325 q^{83} +24.6019 q^{84} +7.88703 q^{85} -1.96399 q^{86} +10.3888 q^{87} -5.28954 q^{88} +10.2796 q^{89} -16.6822 q^{90} -3.90263 q^{91} -10.8303 q^{92} +10.2256 q^{93} -20.9562 q^{94} -15.9268 q^{95} -30.2749 q^{96} -8.02934 q^{97} -22.8796 q^{98} -0.913032 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 169 q + 9 q^{2} + 9 q^{3} + 199 q^{4} + 12 q^{5} + 22 q^{6} + 36 q^{7} + 30 q^{8} + 198 q^{9}+O(q^{10}) \) 169 * q + 9 * q^2 + 9 * q^3 + 199 * q^4 + 12 * q^5 + 22 * q^6 + 36 * q^7 + 30 * q^8 + 198 * q^9	\( 169 q + 9 q^{2} + 9 q^{3} + 199 q^{4} + 12 q^{5} + 22 q^{6} + 36 q^{7} + 30 q^{8} + 198 q^{9} - 3 q^{10} + 59 q^{11} + 11 q^{12} - 169 q^{13} + 30 q^{14} + 50 q^{15} + 267 q^{16} + q^{17} + 53 q^{18} + 107 q^{19} + 48 q^{20} + 36 q^{21} + 14 q^{22} + 12 q^{23} + 78 q^{24} + 217 q^{25} - 9 q^{26} + 39 q^{27} + 99 q^{28} + 30 q^{29} - q^{30} + 106 q^{31} + 74 q^{32} + 16 q^{33} + 56 q^{34} + 46 q^{35} + 271 q^{36} + 73 q^{37} + 2 q^{38} - 9 q^{39} - 16 q^{40} + 52 q^{41} - 2 q^{42} + 64 q^{43} + 124 q^{44} + 84 q^{45} + 105 q^{46} + 55 q^{47} + 26 q^{48} + 257 q^{49} + 60 q^{50} + 117 q^{51} - 199 q^{52} + 7 q^{53} + 78 q^{54} - 4 q^{55} + 63 q^{56} + 51 q^{57} + 84 q^{58} + 98 q^{59} + 94 q^{60} + 32 q^{61} - 25 q^{62} + 128 q^{63} + 380 q^{64} - 12 q^{65} + 16 q^{66} + 170 q^{67} - 10 q^{68} + 55 q^{69} + 70 q^{70} + 124 q^{71} + 173 q^{72} + 81 q^{73} + 54 q^{74} + 120 q^{75} + 212 q^{76} + 20 q^{77} - 22 q^{78} + 92 q^{79} + 66 q^{80} + 265 q^{81} + 21 q^{82} + 62 q^{83} + 98 q^{84} + 139 q^{85} + 51 q^{86} - 33 q^{87} + 31 q^{88} + 58 q^{89} + 16 q^{90} - 36 q^{91} + 40 q^{92} + 37 q^{93} + 55 q^{94} + 23 q^{95} + 164 q^{96} + 78 q^{97} + 69 q^{98} + 307 q^{99}+O(q^{100}) \) 169 * q + 9 * q^2 + 9 * q^3 + 199 * q^4 + 12 * q^5 + 22 * q^6 + 36 * q^7 + 30 * q^8 + 198 * q^9 - 3 * q^10 + 59 * q^11 + 11 * q^12 - 169 * q^13 + 30 * q^14 + 50 * q^15 + 267 * q^16 + q^17 + 53 * q^18 + 107 * q^19 + 48 * q^20 + 36 * q^21 + 14 * q^22 + 12 * q^23 + 78 * q^24 + 217 * q^25 - 9 * q^26 + 39 * q^27 + 99 * q^28 + 30 * q^29 - q^30 + 106 * q^31 + 74 * q^32 + 16 * q^33 + 56 * q^34 + 46 * q^35 + 271 * q^36 + 73 * q^37 + 2 * q^38 - 9 * q^39 - 16 * q^40 + 52 * q^41 - 2 * q^42 + 64 * q^43 + 124 * q^44 + 84 * q^45 + 105 * q^46 + 55 * q^47 + 26 * q^48 + 257 * q^49 + 60 * q^50 + 117 * q^51 - 199 * q^52 + 7 * q^53 + 78 * q^54 - 4 * q^55 + 63 * q^56 + 51 * q^57 + 84 * q^58 + 98 * q^59 + 94 * q^60 + 32 * q^61 - 25 * q^62 + 128 * q^63 + 380 * q^64 - 12 * q^65 + 16 * q^66 + 170 * q^67 - 10 * q^68 + 55 * q^69 + 70 * q^70 + 124 * q^71 + 173 * q^72 + 81 * q^73 + 54 * q^74 + 120 * q^75 + 212 * q^76 + 20 * q^77 - 22 * q^78 + 92 * q^79 + 66 * q^80 + 265 * q^81 + 21 * q^82 + 62 * q^83 + 98 * q^84 + 139 * q^85 + 51 * q^86 - 33 * q^87 + 31 * q^88 + 58 * q^89 + 16 * q^90 - 36 * q^91 + 40 * q^92 + 37 * q^93 + 55 * q^94 + 23 * q^95 + 164 * q^96 + 78 * q^97 + 69 * q^98 + 307 * q^99

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