LMFDB - Embedded newform 8021.2.a.b.1.16

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:	$1$
Dimension:	$140$
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.16
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)

$f(q)$	$=$	$q-2.33878 q^{2} -3.04534 q^{3} +3.46990 q^{4} -1.89662 q^{5} +7.12240 q^{6} +2.91891 q^{7} -3.43778 q^{8} +6.27412 q^{9} +O(q^{10})$	\(q-2.33878 q^{2} -3.04534 q^{3} +3.46990 q^{4} -1.89662 q^{5} +7.12240 q^{6} +2.91891 q^{7} -3.43778 q^{8} +6.27412 q^{9} +4.43579 q^{10} -1.92526 q^{11} -10.5670 q^{12} -1.00000 q^{13} -6.82668 q^{14} +5.77587 q^{15} +1.10041 q^{16} +4.67431 q^{17} -14.6738 q^{18} +1.41552 q^{19} -6.58110 q^{20} -8.88907 q^{21} +4.50276 q^{22} +4.03821 q^{23} +10.4692 q^{24} -1.40282 q^{25} +2.33878 q^{26} -9.97083 q^{27} +10.1283 q^{28} +6.76529 q^{29} -13.5085 q^{30} -2.72234 q^{31} +4.30193 q^{32} +5.86307 q^{33} -10.9322 q^{34} -5.53606 q^{35} +21.7706 q^{36} +1.13728 q^{37} -3.31060 q^{38} +3.04534 q^{39} +6.52017 q^{40} +9.03305 q^{41} +20.7896 q^{42} -8.21911 q^{43} -6.68046 q^{44} -11.8996 q^{45} -9.44450 q^{46} +0.161733 q^{47} -3.35113 q^{48} +1.52001 q^{49} +3.28089 q^{50} -14.2349 q^{51} -3.46990 q^{52} +5.54370 q^{53} +23.3196 q^{54} +3.65149 q^{55} -10.0345 q^{56} -4.31076 q^{57} -15.8225 q^{58} +1.22240 q^{59} +20.0417 q^{60} +2.56000 q^{61} +6.36696 q^{62} +18.3136 q^{63} -12.2621 q^{64} +1.89662 q^{65} -13.7125 q^{66} -12.5350 q^{67} +16.2194 q^{68} -12.2978 q^{69} +12.9476 q^{70} -12.9407 q^{71} -21.5690 q^{72} +6.58929 q^{73} -2.65984 q^{74} +4.27207 q^{75} +4.91173 q^{76} -5.61965 q^{77} -7.12240 q^{78} +4.87198 q^{79} -2.08707 q^{80} +11.5422 q^{81} -21.1263 q^{82} -7.89412 q^{83} -30.8442 q^{84} -8.86541 q^{85} +19.2227 q^{86} -20.6026 q^{87} +6.61861 q^{88} -11.5310 q^{89} +27.8307 q^{90} -2.91891 q^{91} +14.0122 q^{92} +8.29046 q^{93} -0.378258 q^{94} -2.68472 q^{95} -13.1009 q^{96} -10.4405 q^{97} -3.55497 q^{98} -12.0793 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 140 q - 6 q^{2} - 9 q^{3} + 112 q^{4} - 12 q^{5} - 18 q^{6} - 32 q^{7} - 15 q^{8} + 111 q^{9}+O(q^{10}) $ 140 * q - 6 * q^2 - 9 * q^3 + 112 * q^4 - 12 * q^5 - 18 * q^6 - 32 * q^7 - 15 * q^8 + 111 * q^9	\( 140 q - 6 q^{2} - 9 q^{3} + 112 q^{4} - 12 q^{5} - 18 q^{6} - 32 q^{7} - 15 q^{8} + 111 q^{9} - q^{10} - 47 q^{11} - 11 q^{12} - 140 q^{13} - 12 q^{14} - 30 q^{15} + 64 q^{16} + 3 q^{17} - 22 q^{18} - 91 q^{19} - 24 q^{20} - 28 q^{21} - 12 q^{22} - 10 q^{23} - 42 q^{24} + 84 q^{25} + 6 q^{26} - 33 q^{27} - 71 q^{28} - 32 q^{29} - 45 q^{30} - 90 q^{31} - 31 q^{32} - 32 q^{33} - 78 q^{34} - 50 q^{35} + 10 q^{36} - 67 q^{37} - 8 q^{38} + 9 q^{39} - 10 q^{40} - 22 q^{41} - 30 q^{42} - 40 q^{43} - 88 q^{44} - 36 q^{45} - 77 q^{46} - 29 q^{47} - 4 q^{48} + 66 q^{49} - 45 q^{50} - 87 q^{51} - 112 q^{52} - 19 q^{53} - 82 q^{54} - 28 q^{55} - 63 q^{56} - 41 q^{57} - 96 q^{58} - 84 q^{59} - 106 q^{60} - 58 q^{61} - 3 q^{62} - 76 q^{63} - 55 q^{64} + 12 q^{65} - 56 q^{66} - 140 q^{67} - 4 q^{68} - 41 q^{69} - 106 q^{70} - 104 q^{71} - 52 q^{72} - 57 q^{73} - 24 q^{74} - 62 q^{75} - 184 q^{76} + 8 q^{77} + 18 q^{78} - 104 q^{79} - 102 q^{80} + 4 q^{81} - 37 q^{82} - 52 q^{83} - 94 q^{84} - 93 q^{85} - 79 q^{86} + 51 q^{87} - 47 q^{88} - 64 q^{89} + 22 q^{90} + 32 q^{91} - 42 q^{92} - 115 q^{93} - 43 q^{94} - 25 q^{95} - 116 q^{96} - 92 q^{97} - 36 q^{98} - 223 q^{99}+O(q^{100}) \) 140 * q - 6 * q^2 - 9 * q^3 + 112 * q^4 - 12 * q^5 - 18 * q^6 - 32 * q^7 - 15 * q^8 + 111 * q^9 - q^10 - 47 * q^11 - 11 * q^12 - 140 * q^13 - 12 * q^14 - 30 * q^15 + 64 * q^16 + 3 * q^17 - 22 * q^18 - 91 * q^19 - 24 * q^20 - 28 * q^21 - 12 * q^22 - 10 * q^23 - 42 * q^24 + 84 * q^25 + 6 * q^26 - 33 * q^27 - 71 * q^28 - 32 * q^29 - 45 * q^30 - 90 * q^31 - 31 * q^32 - 32 * q^33 - 78 * q^34 - 50 * q^35 + 10 * q^36 - 67 * q^37 - 8 * q^38 + 9 * q^39 - 10 * q^40 - 22 * q^41 - 30 * q^42 - 40 * q^43 - 88 * q^44 - 36 * q^45 - 77 * q^46 - 29 * q^47 - 4 * q^48 + 66 * q^49 - 45 * q^50 - 87 * q^51 - 112 * q^52 - 19 * q^53 - 82 * q^54 - 28 * q^55 - 63 * q^56 - 41 * q^57 - 96 * q^58 - 84 * q^59 - 106 * q^60 - 58 * q^61 - 3 * q^62 - 76 * q^63 - 55 * q^64 + 12 * q^65 - 56 * q^66 - 140 * q^67 - 4 * q^68 - 41 * q^69 - 106 * q^70 - 104 * q^71 - 52 * q^72 - 57 * q^73 - 24 * q^74 - 62 * q^75 - 184 * q^76 + 8 * q^77 + 18 * q^78 - 104 * q^79 - 102 * q^80 + 4 * q^81 - 37 * q^82 - 52 * q^83 - 94 * q^84 - 93 * q^85 - 79 * q^86 + 51 * q^87 - 47 * q^88 - 64 * q^89 + 22 * q^90 + 32 * q^91 - 42 * q^92 - 115 * q^93 - 43 * q^94 - 25 * q^95 - 116 * q^96 - 92 * q^97 - 36 * q^98 - 223 * 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 $

$2$	−2.33878	−1.65377	−0.826884	−	0.562372i	$-0.809889\pi$
$2$	−2.33878	−1.65377	−0.826884	+	0.562372i	$0.809889\pi$
$3$	−3.04534	−1.75823	−0.879115	−	0.476609i	$-0.841866\pi$
$3$	−3.04534	−1.75823	−0.879115	+	0.476609i	$0.841866\pi$
$4$	3.46990	1.73495
$5$	−1.89662	−0.848196	−0.424098	−	0.905616i	$-0.639409\pi$
$5$	−1.89662	−0.848196	−0.424098	+	0.905616i	$0.639409\pi$
$6$	7.12240	2.90771
$7$	2.91891	1.10324	0.551621	−	0.834095i	$-0.314009\pi$
$7$	2.91891	1.10324	0.551621	+	0.834095i	$0.314009\pi$
$8$	−3.43778	−1.21544
$9$	6.27412	2.09137
$10$	4.43579	1.40272
$11$	−1.92526	−0.580487	−0.290244	−	0.956953i	$-0.593736\pi$
$11$	−1.92526	−0.580487	−0.290244	+	0.956953i	$0.593736\pi$
$12$	−10.5670	−3.05044
$13$	−1.00000	−0.277350
$13$	−1.00000	−0.277350
$14$	−6.82668	−1.82451
$15$	5.77587	1.49132
$16$	1.10041	0.275103
$17$	4.67431	1.13369	0.566844	−	0.823825i	$-0.308164\pi$
$17$	4.67431	1.13369	0.566844	+	0.823825i	$0.308164\pi$
$18$	−14.6738	−3.45865
$19$	1.41552	0.324743	0.162372	−	0.986730i	$-0.448086\pi$
$19$	1.41552	0.324743	0.162372	+	0.986730i	$0.448086\pi$
$20$	−6.58110	−1.47158
$21$	−8.88907	−1.93975
$22$	4.50276	0.959992
$23$	4.03821	0.842026	0.421013	−	0.907055i	$-0.361675\pi$
$23$	4.03821	0.842026	0.421013	+	0.907055i	$0.361675\pi$
$24$	10.4692	2.13702
$25$	−1.40282	−0.280564
$26$	2.33878	0.458673
$27$	−9.97083	−1.91889
$28$	10.1283	1.91407
$29$	6.76529	1.25628	0.628142	−	0.778099i	$-0.283816\pi$
$29$	6.76529	1.25628	0.628142	+	0.778099i	$0.283816\pi$
$30$	−13.5085	−2.46630
$31$	−2.72234	−0.488947	−0.244473	−	0.969656i	$-0.578615\pi$
$31$	−2.72234	−0.488947	−0.244473	+	0.969656i	$0.578615\pi$
$32$	4.30193	0.760482
$33$	5.86307	1.02063
$34$	−10.9322	−1.87486
$35$	−5.53606	−0.935766
$36$	21.7706	3.62843
$37$	1.13728	0.186967	0.0934837	−	0.995621i	$-0.470200\pi$
$37$	1.13728	0.186967	0.0934837	+	0.995621i	$0.470200\pi$
$38$	−3.31060	−0.537051
$39$	3.04534	0.487645
$40$	6.52017	1.03093
$41$	9.03305	1.41073	0.705363	−	0.708847i	$-0.250784\pi$
$41$	9.03305	1.41073	0.705363	+	0.708847i	$0.250784\pi$
$42$	20.7896	3.20791
$43$	−8.21911	−1.25340	−0.626701	−	0.779260i	$-0.715595\pi$
$43$	−8.21911	−1.25340	−0.626701	+	0.779260i	$0.715595\pi$
$44$	−6.68046	−1.00712
$45$	−11.8996	−1.77389
$46$	−9.44450	−1.39252
$47$	0.161733	0.0235912	0.0117956	−	0.999930i	$-0.496245\pi$
$47$	0.161733	0.0235912	0.0117956	+	0.999930i	$0.496245\pi$
$48$	−3.35113	−0.483694
$49$	1.52001	0.217144
$50$	3.28089	0.463988
$51$	−14.2349	−1.99328
$52$	−3.46990	−0.481189
$53$	5.54370	0.761486	0.380743	−	0.924681i	$-0.375668\pi$
$53$	5.54370	0.761486	0.380743	+	0.924681i	$0.375668\pi$
$54$	23.3196	3.17340
$55$	3.65149	0.492367
$56$	−10.0345	−1.34092
$57$	−4.31076	−0.570974
$58$	−15.8225	−2.07760
$59$	1.22240	0.159144	0.0795718	−	0.996829i	$-0.474645\pi$
$59$	1.22240	0.159144	0.0795718	+	0.996829i	$0.474645\pi$
$60$	20.0417	2.58737
$61$	2.56000	0.327774	0.163887	−	0.986479i	$-0.447597\pi$
$61$	2.56000	0.327774	0.163887	+	0.986479i	$0.447597\pi$
$62$	6.36696	0.808605
$63$	18.3136	2.30729
$64$	−12.2621	−1.53276
$65$	1.89662	0.235247
$66$	−13.7125	−1.68789
$67$	−12.5350	−1.53139	−0.765694	−	0.643205i	$-0.777604\pi$
$67$	−12.5350	−1.53139	−0.765694	+	0.643205i	$0.777604\pi$
$68$	16.2194	1.96689
$69$	−12.2978	−1.48048
$70$	12.9476	1.54754
$71$	−12.9407	−1.53578	−0.767889	−	0.640583i	$-0.778693\pi$
$71$	−12.9407	−1.53578	−0.767889	+	0.640583i	$0.778693\pi$
$72$	−21.5690	−2.54194
$73$	6.58929	0.771218	0.385609	−	0.922662i	$-0.373991\pi$
$73$	6.58929	0.771218	0.385609	+	0.922662i	$0.373991\pi$
$74$	−2.65984	−0.309201
$75$	4.27207	0.493296
$76$	4.91173	0.563414
$77$	−5.61965	−0.640418
$78$	−7.12240	−0.806453
$79$	4.87198	0.548141	0.274071	−	0.961710i	$-0.411630\pi$
$79$	4.87198	0.548141	0.274071	+	0.961710i	$0.411630\pi$
$80$	−2.08707	−0.233341
$81$	11.5422	1.28247
$82$	−21.1263	−2.33301
$83$	−7.89412	−0.866493	−0.433246	−	0.901276i	$-0.642632\pi$
$83$	−7.89412	−0.866493	−0.433246	+	0.901276i	$0.642632\pi$
$84$	−30.8442	−3.36538
$85$	−8.86541	−0.961589
$86$	19.2227	2.07284
$87$	−20.6026	−2.20884
$88$	6.61861	0.705546
$89$	−11.5310	−1.22228	−0.611141	−	0.791522i	$-0.709289\pi$
$89$	−11.5310	−1.22228	−0.611141	+	0.791522i	$0.709289\pi$
$90$	27.8307	2.93361
$91$	−2.91891	−0.305984
$92$	14.0122	1.46087
$93$	8.29046	0.859681
$94$	−0.378258	−0.0390143
$95$	−2.68472	−0.275446
$96$	−13.1009	−1.33710
$97$	−10.4405	−1.06007	−0.530035	−	0.847976i	$-0.677821\pi$
$97$	−10.4405	−1.06007	−0.530035	+	0.847976i	$0.677821\pi$
$98$	−3.55497	−0.359106
$99$	−12.0793	−1.21402
$100$	−4.86764	−0.486764
$101$	−5.45274	−0.542568	−0.271284	−	0.962499i	$-0.587448\pi$
$101$	−5.45274	−0.542568	−0.271284	+	0.962499i	$0.587448\pi$
$102$	33.2923	3.29643
$103$	10.9570	1.07962	0.539811	−	0.841786i	$-0.318496\pi$
$103$	10.9570	1.07962	0.539811	+	0.841786i	$0.318496\pi$
$104$	3.43778	0.337102
$105$	16.8592	1.64529
$106$	−12.9655	−1.25932
$107$	−5.60836	−0.542181	−0.271091	−	0.962554i	$-0.587384\pi$
$107$	−5.60836	−0.542181	−0.271091	+	0.962554i	$0.587384\pi$
$108$	−34.5978	−3.32917
$109$	0.938728	0.0899139	0.0449569	−	0.998989i	$-0.485685\pi$
$109$	0.938728	0.0899139	0.0449569	+	0.998989i	$0.485685\pi$
$110$	−8.54004	−0.814261
$111$	−3.46340	−0.328732
$112$	3.21200	0.303505
$113$	−3.07474	−0.289247	−0.144624	−	0.989487i	$-0.546197\pi$
$113$	−3.07474	−0.289247	−0.144624	+	0.989487i	$0.546197\pi$
$114$	10.0819	0.944259
$115$	−7.65897	−0.714203
$116$	23.4749	2.17959
$117$	−6.27412	−0.580043
$118$	−2.85894	−0.263187
$119$	13.6439	1.25073
$120$	−19.8562	−1.81261
$121$	−7.29338	−0.663035
$122$	−5.98727	−0.542062
$123$	−27.5087	−2.48038
$124$	−9.44625	−0.848299
$125$	12.1437	1.08617
$126$	−42.8314	−3.81573
$127$	−0.587582	−0.0521395	−0.0260698	−	0.999660i	$-0.508299\pi$
$127$	−0.587582	−0.0521395	−0.0260698	+	0.999660i	$0.508299\pi$
$128$	20.0745	1.77435
$129$	25.0300	2.20377
$130$	−4.43579	−0.389044
$131$	−10.2414	−0.894794	−0.447397	−	0.894336i	$-0.647649\pi$
$131$	−10.2414	−0.894794	−0.447397	+	0.894336i	$0.647649\pi$
$132$	20.3443	1.77074
$133$	4.13178	0.358271
$134$	29.3165	2.53256
$135$	18.9109	1.62759
$136$	−16.0693	−1.37793
$137$	4.52314	0.386438	0.193219	−	0.981156i	$-0.438107\pi$
$137$	4.52314	0.386438	0.193219	+	0.981156i	$0.438107\pi$
$138$	28.7618	2.44836
$139$	−7.75921	−0.658128	−0.329064	−	0.944308i	$-0.606733\pi$
$139$	−7.75921	−0.658128	−0.329064	+	0.944308i	$0.606733\pi$
$140$	−19.2096	−1.62351
$141$	−0.492533	−0.0414787
$142$	30.2655	2.53982
$143$	1.92526	0.160998
$144$	6.90411	0.575343
$145$	−12.8312	−1.06557
$146$	−15.4109	−1.27542
$147$	−4.62895	−0.381789
$148$	3.94624	0.324379
$149$	−8.60390	−0.704859	−0.352429	−	0.935838i	$-0.614644\pi$
$149$	−8.60390	−0.704859	−0.352429	+	0.935838i	$0.614644\pi$
$150$	−9.99144	−0.815797
$151$	−3.27214	−0.266283	−0.133141	−	0.991097i	$-0.542506\pi$
$151$	−3.27214	−0.266283	−0.133141	+	0.991097i	$0.542506\pi$
$152$	−4.86626	−0.394706
$153$	29.3272	2.37097
$154$	13.1431	1.05910
$155$	5.16325	0.414723
$156$	10.5670	0.846041
$157$	−3.86068	−0.308116	−0.154058	−	0.988062i	$-0.549234\pi$
$157$	−3.86068	−0.308116	−0.154058	+	0.988062i	$0.549234\pi$
$158$	−11.3945	−0.906499
$159$	−16.8825	−1.33887
$160$	−8.15915	−0.645037
$161$	11.7872	0.928959
$162$	−26.9948	−2.12091
$163$	−2.53546	−0.198593	−0.0992964	−	0.995058i	$-0.531659\pi$
$163$	−2.53546	−0.198593	−0.0992964	+	0.995058i	$0.531659\pi$
$164$	31.3438	2.44754
$165$	−11.1200	−0.865694
$166$	18.4626	1.43298
$167$	−9.99238	−0.773233	−0.386617	−	0.922240i	$-0.626356\pi$
$167$	−9.99238	−0.773233	−0.386617	+	0.922240i	$0.626356\pi$
$168$	30.5587	2.35765
$169$	1.00000	0.0769231
$170$	20.7343	1.59025
$171$	8.88117	0.679160
$172$	−28.5195	−2.17459
$173$	−7.22963	−0.549658	−0.274829	−	0.961493i	$-0.588621\pi$
$173$	−7.22963	−0.549658	−0.274829	+	0.961493i	$0.588621\pi$
$174$	48.1851	3.65290
$175$	−4.09470	−0.309530
$176$	−2.11858	−0.159694
$177$	−3.72264	−0.279811
$178$	26.9685	2.02137
$179$	−13.6431	−1.01973	−0.509867	−	0.860253i	$-0.670306\pi$
$179$	−13.6431	−1.01973	−0.509867	+	0.860253i	$0.670306\pi$
$180$	−41.2906	−3.07762
$181$	−14.5261	−1.07972	−0.539858	−	0.841756i	$-0.681522\pi$
$181$	−14.5261	−1.07972	−0.539858	+	0.841756i	$0.681522\pi$
$182$	6.82668	0.506027
$183$	−7.79607	−0.576302
$184$	−13.8825	−1.02343
$185$	−2.15699	−0.158585
$186$	−19.3896	−1.42171
$187$	−8.99926	−0.658091
$188$	0.561197	0.0409295
$189$	−29.1039	−2.11700
$190$	6.27896	0.455524
$191$	16.8117	1.21645	0.608226	−	0.793764i	$-0.291881\pi$
$191$	16.8117	1.21645	0.608226	+	0.793764i	$0.291881\pi$
$192$	37.3423	2.69495
$193$	6.11376	0.440078	0.220039	−	0.975491i	$-0.429382\pi$
$193$	6.11376	0.440078	0.220039	+	0.975491i	$0.429382\pi$
$194$	24.4180	1.75311
$195$	−5.77587	−0.413619
$196$	5.27428	0.376734
$197$	18.5724	1.32323	0.661613	−	0.749845i	$-0.269872\pi$
$197$	18.5724	1.32323	0.661613	+	0.749845i	$0.269872\pi$
$198$	28.2509	2.00770
$199$	12.3787	0.877503	0.438752	−	0.898608i	$-0.355421\pi$
$199$	12.3787	0.877503	0.438752	+	0.898608i	$0.355421\pi$
$200$	4.82258	0.341008
$201$	38.1732	2.69253
$202$	12.7528	0.897281
$203$	19.7472	1.38599
$204$	−49.3937	−3.45825
$205$	−17.1323	−1.19657
$206$	−25.6260	−1.78545
$207$	25.3362	1.76099
$208$	−1.10041	−0.0762998
$209$	−2.72525	−0.188509
$210$	−39.4300	−2.72093
$211$	16.6846	1.14861	0.574306	−	0.818640i	$-0.305272\pi$
$211$	16.6846	1.14861	0.574306	+	0.818640i	$0.305272\pi$
$212$	19.2361	1.32114
$213$	39.4089	2.70025
$214$	13.1167	0.896642
$215$	15.5886	1.06313
$216$	34.2775	2.33229
$217$	−7.94625	−0.539427
$218$	−2.19548	−0.148697
$219$	−20.0667	−1.35598
$220$	12.6703	0.854232
$221$	−4.67431	−0.314428
$222$	8.10014	0.543646
$223$	−8.58890	−0.575156	−0.287578	−	0.957757i	$-0.592850\pi$
$223$	−8.58890	−0.575156	−0.287578	+	0.957757i	$0.592850\pi$
$224$	12.5569	0.838996
$225$	−8.80146	−0.586764
$226$	7.19115	0.478348
$227$	27.7974	1.84498	0.922490	−	0.386021i	$-0.126151\pi$
$227$	27.7974	1.84498	0.922490	+	0.386021i	$0.126151\pi$
$228$	−14.9579	−0.990611
$229$	−24.7493	−1.63548	−0.817740	−	0.575587i	$-0.804773\pi$
$229$	−24.7493	−1.63548	−0.817740	+	0.575587i	$0.804773\pi$
$230$	17.9127	1.18113
$231$	17.1138	1.12600
$232$	−23.2576	−1.52693
$233$	−4.10977	−0.269240	−0.134620	−	0.990897i	$-0.542981\pi$
$233$	−4.10977	−0.269240	−0.134620	+	0.990897i	$0.542981\pi$
$234$	14.6738	0.959257
$235$	−0.306747	−0.0200099
$236$	4.24162	0.276106
$237$	−14.8369	−0.963758
$238$	−31.9101	−2.06842
$239$	2.85179	0.184467	0.0922335	−	0.995737i	$-0.470599\pi$
$239$	2.85179	0.184467	0.0922335	+	0.995737i	$0.470599\pi$
$240$	6.35583	0.410267
$241$	−9.79863	−0.631185	−0.315593	−	0.948895i	$-0.602203\pi$
$241$	−9.79863	−0.631185	−0.315593	+	0.948895i	$0.602203\pi$
$242$	17.0576	1.09651
$243$	−5.23761	−0.335993
$244$	8.88293	0.568671
$245$	−2.88288	−0.184181
$246$	64.3369	4.10197
$247$	−1.41552	−0.0900676
$248$	9.35880	0.594285
$249$	24.0403	1.52349
$250$	−28.4016	−1.79627
$251$	−17.8445	−1.12633	−0.563166	−	0.826344i	$-0.690417\pi$
$251$	−17.8445	−1.12633	−0.563166	+	0.826344i	$0.690417\pi$
$252$	63.5463	4.00304
$253$	−7.77460	−0.488785
$254$	1.37423	0.0862267
$255$	26.9982	1.69070
$256$	−22.4257	−1.40161
$257$	28.9817	1.80783	0.903915	−	0.427712i	$-0.140680\pi$
$257$	28.9817	1.80783	0.903915	+	0.427712i	$0.140680\pi$
$258$	−58.5397	−3.64453
$259$	3.31961	0.206270
$260$	6.58110	0.408142
$261$	42.4463	2.62736
$262$	23.9524	1.47978
$263$	31.6176	1.94963	0.974814	−	0.223020i	$-0.0715915\pi$
$263$	31.6176	1.94963	0.974814	+	0.223020i	$0.0715915\pi$
$264$	−20.1559	−1.24051
$265$	−10.5143	−0.645889
$266$	−9.66333	−0.592497
$267$	35.1158	2.14905
$268$	−43.4950	−2.65688
$269$	4.45850	0.271839	0.135920	−	0.990720i	$-0.456601\pi$
$269$	4.45850	0.271839	0.135920	+	0.990720i	$0.456601\pi$
$270$	−44.2285	−2.69166
$271$	−16.1761	−0.982625	−0.491313	−	0.870983i	$-0.663483\pi$
$271$	−16.1761	−0.982625	−0.491313	+	0.870983i	$0.663483\pi$
$272$	5.14367	0.311881
$273$	8.88907	0.537991
$274$	−10.5786	−0.639079
$275$	2.70079	0.162864
$276$	−42.6720	−2.56855
$277$	−0.0334023	−0.00200695	−0.00100347	−	0.999999i	$-0.500319\pi$
$277$	−0.0334023	−0.00200695	−0.00100347	+	0.999999i	$0.500319\pi$
$278$	18.1471	1.08839
$279$	−17.0803	−1.02257
$280$	19.0318	1.13737
$281$	19.4235	1.15871	0.579353	−	0.815076i	$-0.303305\pi$
$281$	19.4235	1.15871	0.579353	+	0.815076i	$0.303305\pi$
$282$	1.15193	0.0685962
$283$	24.4086	1.45094	0.725470	−	0.688254i	$-0.241623\pi$
$283$	24.4086	1.45094	0.725470	+	0.688254i	$0.241623\pi$
$284$	−44.9029	−2.66450
$285$	8.17588	0.484298
$286$	−4.50276	−0.266254
$287$	26.3666	1.55637
$288$	26.9909	1.59045
$289$	4.84922	0.285248
$290$	30.0094	1.76221
$291$	31.7949	1.86385
$292$	22.8642	1.33803
$293$	20.8089	1.21567	0.607836	−	0.794063i	$-0.292038\pi$
$293$	20.8089	1.21567	0.607836	+	0.794063i	$0.292038\pi$
$294$	10.8261	0.631391
$295$	−2.31844	−0.134985
$296$	−3.90971	−0.227247
$297$	19.1964	1.11389
$298$	20.1226	1.16567
$299$	−4.03821	−0.233536
$300$	14.8237	0.855844
$301$	−23.9908	−1.38281
$302$	7.65281	0.440370
$303$	16.6055	0.953959
$304$	1.55766	0.0893378
$305$	−4.85535	−0.278016
$306$	−68.5900	−3.92103
$307$	−5.55832	−0.317230	−0.158615	−	0.987340i	$-0.550703\pi$
$307$	−5.55832	−0.317230	−0.158615	+	0.987340i	$0.550703\pi$
$308$	−19.4996	−1.11109
$309$	−33.3678	−1.89823
$310$	−12.0757	−0.685855
$311$	3.21663	0.182399	0.0911993	−	0.995833i	$-0.470930\pi$
$311$	3.21663	0.182399	0.0911993	+	0.995833i	$0.470930\pi$
$312$	−10.4692	−0.592703
$313$	−5.29438	−0.299256	−0.149628	−	0.988742i	$-0.547808\pi$
$313$	−5.29438	−0.299256	−0.149628	+	0.988742i	$0.547808\pi$
$314$	9.02929	0.509553
$315$	−34.7339	−1.95704
$316$	16.9053	0.950998
$317$	−7.37582	−0.414267	−0.207134	−	0.978313i	$-0.566413\pi$
$317$	−7.37582	−0.414267	−0.207134	+	0.978313i	$0.566413\pi$
$318$	39.4844	2.21418
$319$	−13.0249	−0.729256
$320$	23.2566	1.30008
$321$	17.0794	0.953279
$322$	−27.5676	−1.53628
$323$	6.61660	0.368158
$324$	40.0504	2.22502
$325$	1.40282	0.0778144
$326$	5.92990	0.328427
$327$	−2.85875	−0.158089
$328$	−31.0536	−1.71465
$329$	0.472083	0.0260268
$330$	26.0074	1.43166
$331$	5.21255	0.286508	0.143254	−	0.989686i	$-0.454243\pi$
$331$	5.21255	0.286508	0.143254	+	0.989686i	$0.454243\pi$
$332$	−27.3918	−1.50332
$333$	7.13542	0.391019
$334$	23.3700	1.27875
$335$	23.7741	1.29892
$336$	−9.78163	−0.533632
$337$	3.42934	0.186808	0.0934040	−	0.995628i	$-0.470225\pi$
$337$	3.42934	0.186808	0.0934040	+	0.995628i	$0.470225\pi$
$338$	−2.33878	−0.127213
$339$	9.36365	0.508564
$340$	−30.7621	−1.66831
$341$	5.24121	0.283827
$342$	−20.7711	−1.12317
$343$	−15.9956	−0.863680
$344$	28.2555	1.52343
$345$	23.3242	1.25573
$346$	16.9085	0.909008
$347$	16.2779	0.873845	0.436923	−	0.899499i	$-0.356068\pi$
$347$	16.2779	0.873845	0.436923	+	0.899499i	$0.356068\pi$
$348$	−71.4891	−3.83222
$349$	−19.1130	−1.02310	−0.511549	−	0.859254i	$-0.670928\pi$
$349$	−19.1130	−1.02310	−0.511549	+	0.859254i	$0.670928\pi$
$350$	9.57660	0.511891
$351$	9.97083	0.532203
$352$	−8.28233	−0.441450
$353$	34.9390	1.85962	0.929809	−	0.368043i	$-0.119972\pi$
$353$	34.9390	1.85962	0.929809	+	0.368043i	$0.119972\pi$
$354$	8.70645	0.462743
$355$	24.5436	1.30264
$356$	−40.0114	−2.12060
$357$	−41.5503	−2.19908
$358$	31.9083	1.68641
$359$	−25.0863	−1.32400	−0.662001	−	0.749503i	$-0.730293\pi$
$359$	−25.0863	−1.32400	−0.662001	+	0.749503i	$0.730293\pi$
$360$	40.9083	2.15606
$361$	−16.9963	−0.894542
$362$	33.9733	1.78560
$363$	22.2109	1.16577
$364$	−10.1283	−0.530868
$365$	−12.4974	−0.654144
$366$	18.2333	0.953070
$367$	3.80018	0.198368	0.0991839	−	0.995069i	$-0.468377\pi$
$367$	3.80018	0.198368	0.0991839	+	0.995069i	$0.468377\pi$
$368$	4.44370	0.231644
$369$	56.6744	2.95035
$370$	5.04472	0.262263
$371$	16.1815	0.840103
$372$	28.7671	1.49150
$373$	−10.0507	−0.520407	−0.260203	−	0.965554i	$-0.583790\pi$
$373$	−10.0507	−0.520407	−0.260203	+	0.965554i	$0.583790\pi$
$374$	21.0473	1.08833
$375$	−36.9819	−1.90974
$376$	−0.556002	−0.0286736
$377$	−6.76529	−0.348430
$378$	68.0677	3.50102
$379$	−9.58462	−0.492329	−0.246165	−	0.969228i	$-0.579170\pi$
$379$	−9.58462	−0.492329	−0.246165	+	0.969228i	$0.579170\pi$
$380$	−9.31570	−0.477885
$381$	1.78939	0.0916733
$382$	−39.3189	−2.01173
$383$	−28.3130	−1.44673	−0.723364	−	0.690467i	$-0.757405\pi$
$383$	−28.3130	−1.44673	−0.723364	+	0.690467i	$0.757405\pi$
$384$	−61.1339	−3.11972
$385$	10.6584	0.543200
$386$	−14.2988	−0.727787
$387$	−51.5677	−2.62133
$388$	−36.2274	−1.83917
$389$	−30.5846	−1.55070	−0.775350	−	0.631532i	$-0.782426\pi$
$389$	−30.5846	−1.55070	−0.775350	+	0.631532i	$0.782426\pi$
$390$	13.5085	0.684030
$391$	18.8759	0.954594
$392$	−5.22545	−0.263925
$393$	31.1885	1.57325
$394$	−43.4367	−2.18831
$395$	−9.24032	−0.464931
$396$	−41.9140	−2.10626
$397$	−31.0104	−1.55636	−0.778182	−	0.628038i	$-0.783858\pi$
$397$	−31.0104	−1.55636	−0.778182	+	0.628038i	$0.783858\pi$
$398$	−28.9511	−1.45119
$399$	−12.5827	−0.629923
$400$	−1.54368	−0.0771839
$401$	26.5831	1.32750	0.663748	−	0.747956i	$-0.268965\pi$
$401$	26.5831	1.32750	0.663748	+	0.747956i	$0.268965\pi$
$402$	−89.2789	−4.45283
$403$	2.72234	0.135609
$404$	−18.9205	−0.941328
$405$	−21.8913	−1.08779
$406$	−46.1845	−2.29210
$407$	−2.18955	−0.108532
$408$	48.9364	2.42271
$409$	−39.5329	−1.95478	−0.977388	−	0.211452i	$-0.932181\pi$
$409$	−39.5329	−1.95478	−0.977388	+	0.211452i	$0.932181\pi$
$410$	40.0687	1.97885
$411$	−13.7745	−0.679447
$412$	38.0196	1.87309
$413$	3.56808	0.175574
$414$	−59.2560	−2.91227
$415$	14.9722	0.734956
$416$	−4.30193	−0.210920
$417$	23.6295	1.15714
$418$	6.37376	0.311751
$419$	12.7965	0.625148	0.312574	−	0.949893i	$-0.398809\pi$
$419$	12.7965	0.625148	0.312574	+	0.949893i	$0.398809\pi$
$420$	58.4998	2.85450
$421$	39.3313	1.91689	0.958445	−	0.285276i	$-0.0920854\pi$
$421$	39.3313	1.91689	0.958445	+	0.285276i	$0.0920854\pi$
$422$	−39.0216	−1.89954
$423$	1.01473	0.0493380
$424$	−19.0580	−0.925539
$425$	−6.55722	−0.318072
$426$	−92.1687	−4.46559
$427$	7.47238	0.361614
$428$	−19.4605	−0.940657
$429$	−5.86307	−0.283072
$430$	−36.4582	−1.75817
$431$	8.71710	0.419888	0.209944	−	0.977713i	$-0.432672\pi$
$431$	8.71710	0.419888	0.209944	+	0.977713i	$0.432672\pi$
$432$	−10.9720	−0.527891
$433$	27.6351	1.32806	0.664029	−	0.747707i	$-0.268845\pi$
$433$	27.6351	1.32806	0.664029	+	0.747707i	$0.268845\pi$
$434$	18.5846	0.892087
$435$	39.0755	1.87352
$436$	3.25729	0.155996
$437$	5.71619	0.273442
$438$	46.9315	2.24248
$439$	36.2468	1.72996	0.864982	−	0.501804i	$-0.167330\pi$
$439$	36.2468	1.72996	0.864982	+	0.501804i	$0.167330\pi$
$440$	−12.5530	−0.598441
$441$	9.53672	0.454130
$442$	10.9322	0.519992
$443$	−37.9086	−1.80109	−0.900545	−	0.434763i	$-0.856832\pi$
$443$	−37.9086	−1.80109	−0.900545	+	0.434763i	$0.856832\pi$
$444$	−12.0177	−0.570333
$445$	21.8699	1.03673
$446$	20.0876	0.951174
$447$	26.2018	1.23930
$448$	−35.7919	−1.69101
$449$	−7.72951	−0.364778	−0.182389	−	0.983226i	$-0.558383\pi$
$449$	−7.72951	−0.364778	−0.182389	+	0.983226i	$0.558383\pi$
$450$	20.5847	0.970372
$451$	−17.3910	−0.818908
$452$	−10.6691	−0.501830
$453$	9.96478	0.468186
$454$	−65.0121	−3.05117
$455$	5.53606	0.259535
$456$	14.8194	0.693983
$457$	4.30453	0.201358	0.100679	−	0.994919i	$-0.467899\pi$
$457$	4.30453	0.201358	0.100679	+	0.994919i	$0.467899\pi$
$458$	57.8832	2.70471
$459$	−46.6068	−2.17542
$460$	−26.5759	−1.23911
$461$	1.89282	0.0881572	0.0440786	−	0.999028i	$-0.485965\pi$
$461$	1.89282	0.0881572	0.0440786	+	0.999028i	$0.485965\pi$
$462$	−40.0254	−1.86215
$463$	−6.33837	−0.294569	−0.147285	−	0.989094i	$-0.547053\pi$
$463$	−6.33837	−0.294569	−0.147285	+	0.989094i	$0.547053\pi$
$464$	7.44460	0.345607
$465$	−15.7239	−0.729178
$466$	9.61187	0.445261
$467$	12.1096	0.560365	0.280182	−	0.959947i	$-0.409605\pi$
$467$	12.1096	0.560365	0.280182	+	0.959947i	$0.409605\pi$
$468$	−21.7706	−1.00635
$469$	−36.5883	−1.68949
$470$	0.717413	0.0330918
$471$	11.7571	0.541739
$472$	−4.20236	−0.193429
$473$	15.8239	0.727584
$474$	34.7002	1.59383
$475$	−1.98572	−0.0911113
$476$	47.3429	2.16996
$477$	34.7818	1.59255
$478$	−6.66971	−0.305066
$479$	−22.7024	−1.03730	−0.518649	−	0.854987i	$-0.673565\pi$
$479$	−22.7024	−1.03730	−0.518649	+	0.854987i	$0.673565\pi$
$480$	24.8474	1.13412
$481$	−1.13728	−0.0518554
$482$	22.9169	1.04383
$483$	−35.8960	−1.63332
$484$	−25.3073	−1.15033
$485$	19.8017	0.899147
$486$	12.2496	0.555655
$487$	7.77266	0.352213	0.176106	−	0.984371i	$-0.443650\pi$
$487$	7.77266	0.352213	0.176106	+	0.984371i	$0.443650\pi$
$488$	−8.80070	−0.398389
$489$	7.72136	0.349172
$490$	6.74244	0.304592
$491$	−32.1522	−1.45101	−0.725503	−	0.688219i	$-0.758393\pi$
$491$	−32.1522	−1.45101	−0.725503	+	0.688219i	$0.758393\pi$
$492$	−95.4526	−4.30334
$493$	31.6231	1.42423
$494$	3.31060	0.148951
$495$	22.9099	1.02972
$496$	−2.99569	−0.134511
$497$	−37.7727	−1.69434
$498$	−56.2251	−2.51951
$499$	22.3370	0.999941	0.499970	−	0.866042i	$-0.333344\pi$
$499$	22.3370	0.999941	0.499970	+	0.866042i	$0.333344\pi$
$500$	42.1376	1.88445
$501$	30.4302	1.35952
$502$	41.7343	1.86269
$503$	−15.5071	−0.691427	−0.345713	−	0.938340i	$-0.612363\pi$
$503$	−15.5071	−0.691427	−0.345713	+	0.938340i	$0.612363\pi$
$504$	−62.9580	−2.80437
$505$	10.3418	0.460204
$506$	18.1831	0.808338
$507$	−3.04534	−0.135248
$508$	−2.03885	−0.0904595
$509$	15.1380	0.670981	0.335491	−	0.942044i	$-0.391098\pi$
$509$	15.1380	0.670981	0.335491	+	0.942044i	$0.391098\pi$
$510$	−63.1430	−2.79602
$511$	19.2335	0.850840
$512$	12.2998	0.543581
$513$	−14.1139	−0.623146
$514$	−67.7819	−2.98973
$515$	−20.7813	−0.915732
$516$	86.8517	3.82343
$517$	−0.311378	−0.0136944
$518$	−7.76383	−0.341123
$519$	22.0167	0.966426
$520$	−6.52017	−0.285928
$521$	10.9061	0.477805	0.238903	−	0.971043i	$-0.423212\pi$
$521$	10.9061	0.477805	0.238903	+	0.971043i	$0.423212\pi$
$522$	−99.2726	−4.34504
$523$	−26.5658	−1.16164	−0.580820	−	0.814032i	$-0.697268\pi$
$523$	−26.5658	−1.16164	−0.580820	+	0.814032i	$0.697268\pi$
$524$	−35.5366	−1.55242
$525$	12.4698	0.544225
$526$	−73.9468	−3.22423
$527$	−12.7251	−0.554313
$528$	6.45179	0.280778
$529$	−6.69283	−0.290993
$530$	24.5907	1.06815
$531$	7.66951	0.332829
$532$	14.3369	0.621582
$533$	−9.03305	−0.391265
$534$	−82.1283	−3.55404
$535$	10.6370	0.459876
$536$	43.0924	1.86131
$537$	41.5480	1.79293
$538$	−10.4275	−0.449559
$539$	−2.92641	−0.126049
$540$	65.6190	2.82379
$541$	−15.4235	−0.663110	−0.331555	−	0.943436i	$-0.607573\pi$
$541$	−15.4235	−0.663110	−0.331555	+	0.943436i	$0.607573\pi$
$542$	37.8323	1.62503
$543$	44.2369	1.89839
$544$	20.1086	0.862149
$545$	−1.78041	−0.0762646
$546$	−20.7896	−0.889713
$547$	20.2397	0.865388	0.432694	−	0.901541i	$-0.357563\pi$
$547$	20.2397	0.865388	0.432694	+	0.901541i	$0.357563\pi$
$548$	15.6948	0.670451
$549$	16.0617	0.685498
$550$	−6.31656	−0.269339
$551$	9.57643	0.407970
$552$	42.2769	1.79943
$553$	14.2209	0.604733
$554$	0.0781207	0.00331903
$555$	6.56877	0.278829
$556$	−26.9237	−1.14182
$557$	−34.9119	−1.47927	−0.739633	−	0.673010i	$-0.765001\pi$
$557$	−34.9119	−1.47927	−0.739633	+	0.673010i	$0.765001\pi$
$558$	39.9471	1.69110
$559$	8.21911	0.347631
$560$	−6.09195	−0.257432
$561$	27.4059	1.15708
$562$	−45.4273	−1.91623
$563$	15.4624	0.651661	0.325831	−	0.945428i	$-0.394356\pi$
$563$	15.4624	0.651661	0.325831	+	0.945428i	$0.394356\pi$
$564$	−1.70904	−0.0719635
$565$	5.83163	0.245338
$566$	−57.0863	−2.39952
$567$	33.6907	1.41488
$568$	44.4872	1.86664
$569$	−1.83833	−0.0770666	−0.0385333	−	0.999257i	$-0.512269\pi$
$569$	−1.83833	−0.0770666	−0.0385333	+	0.999257i	$0.512269\pi$
$570$	−19.1216	−0.800916
$571$	−34.1658	−1.42980	−0.714898	−	0.699229i	$-0.753527\pi$
$571$	−34.1658	−1.42980	−0.714898	+	0.699229i	$0.753527\pi$
$572$	6.68046	0.279324
$573$	−51.1974	−2.13880
$574$	−61.6658	−2.57388
$575$	−5.66488	−0.236242
$576$	−76.9340	−3.20558
$577$	−2.63782	−0.109814	−0.0549070	−	0.998491i	$-0.517486\pi$
$577$	−2.63782	−0.109814	−0.0549070	+	0.998491i	$0.517486\pi$
$578$	−11.3413	−0.471734
$579$	−18.6185	−0.773759
$580$	−44.5230	−1.84872
$581$	−23.0422	−0.955952
$582$	−74.3612	−3.08237
$583$	−10.6731	−0.442033
$584$	−22.6525	−0.937368
$585$	11.8996	0.491990
$586$	−48.6676	−2.01044
$587$	42.7975	1.76644	0.883220	−	0.468958i	$-0.155371\pi$
$587$	42.7975	1.76644	0.883220	+	0.468958i	$0.155371\pi$
$588$	−16.0620	−0.662386
$589$	−3.85354	−0.158782
$590$	5.42233	0.223234
$591$	−56.5593	−2.32654
$592$	1.25147	0.0514352
$593$	−10.9474	−0.449555	−0.224777	−	0.974410i	$-0.572165\pi$
$593$	−10.9474	−0.449555	−0.224777	+	0.974410i	$0.572165\pi$
$594$	−44.8962	−1.84212
$595$	−25.8773	−1.06087
$596$	−29.8547	−1.22290
$597$	−37.6974	−1.54285
$598$	9.44450	0.386214
$599$	−21.9379	−0.896357	−0.448179	−	0.893944i	$-0.647927\pi$
$599$	−21.9379	−0.896357	−0.448179	+	0.893944i	$0.647927\pi$
$600$	−14.6864	−0.599571
$601$	43.2737	1.76517	0.882585	−	0.470152i	$-0.155801\pi$
$601$	43.2737	1.76517	0.882585	+	0.470152i	$0.155801\pi$
$602$	56.1092	2.28684
$603$	−78.6458	−3.20271
$604$	−11.3540	−0.461987
$605$	13.8328	0.562383
$606$	−38.8366	−1.57763
$607$	−48.5329	−1.96989	−0.984946	−	0.172864i	$-0.944698\pi$
$607$	−48.5329	−1.96989	−0.984946	+	0.172864i	$0.944698\pi$
$608$	6.08949	0.246961
$609$	−60.1372	−2.43688
$610$	11.3556	0.459775
$611$	−0.161733	−0.00654302
$612$	101.763	4.11351
$613$	16.2942	0.658116	0.329058	−	0.944310i	$-0.393269\pi$
$613$	16.2942	0.658116	0.329058	+	0.944310i	$0.393269\pi$
$614$	12.9997	0.524625
$615$	52.1737	2.10385
$616$	19.3191	0.778389
$617$	−1.00000	−0.0402585
$617$	−1.00000	−0.0402585
$618$	78.0399	3.13923
$619$	12.4936	0.502161	0.251080	−	0.967966i	$-0.419214\pi$
$619$	12.4936	0.502161	0.251080	+	0.967966i	$0.419214\pi$
$620$	17.9160	0.719523
$621$	−40.2643	−1.61575
$622$	−7.52301	−0.301645
$623$	−33.6579	−1.34847
$624$	3.35113	0.134153
$625$	−16.0180	−0.640720
$626$	12.3824	0.494900
$627$	8.29932	0.331443
$628$	−13.3962	−0.534566
$629$	5.31599	0.211963
$630$	81.2351	3.23648
$631$	−19.2749	−0.767321	−0.383661	−	0.923474i	$-0.625337\pi$
$631$	−19.2749	−0.767321	−0.383661	+	0.923474i	$0.625337\pi$
$632$	−16.7488	−0.666232
$633$	−50.8102	−2.01953
$634$	17.2504	0.685102
$635$	1.11442	0.0442245
$636$	−58.5805	−2.32287
$637$	−1.52001	−0.0602249
$638$	30.4625	1.20602
$639$	−81.1915	−3.21189
$640$	−38.0738	−1.50500
$641$	11.9318	0.471277	0.235639	−	0.971841i	$-0.424282\pi$
$641$	11.9318	0.471277	0.235639	+	0.971841i	$0.424282\pi$
$642$	−39.9450	−1.57650
$643$	−16.6278	−0.655738	−0.327869	−	0.944723i	$-0.606330\pi$
$643$	−16.6278	−0.655738	−0.327869	+	0.944723i	$0.606330\pi$
$644$	40.9003	1.61170
$645$	−47.4725	−1.86923
$646$	−15.4748	−0.608848
$647$	−9.03135	−0.355059	−0.177529	−	0.984115i	$-0.556810\pi$
$647$	−9.03135	−0.355059	−0.177529	+	0.984115i	$0.556810\pi$
$648$	−39.6797	−1.55876
$649$	−2.35344	−0.0923808
$650$	−3.28089	−0.128687
$651$	24.1991	0.948437
$652$	−8.79781	−0.344549
$653$	−11.3731	−0.445065	−0.222533	−	0.974925i	$-0.571432\pi$
$653$	−11.3731	−0.445065	−0.222533	+	0.974925i	$0.571432\pi$
$654$	6.68600	0.261443
$655$	19.4240	0.758960
$656$	9.94007	0.388094
$657$	41.3420	1.61291
$658$	−1.10410	−0.0430423
$659$	−24.9066	−0.970223	−0.485112	−	0.874452i	$-0.661221\pi$
$659$	−24.9066	−0.970223	−0.485112	+	0.874452i	$0.661221\pi$
$660$	−38.5855	−1.50194
$661$	−29.8198	−1.15985	−0.579927	−	0.814668i	$-0.696919\pi$
$661$	−29.8198	−1.15985	−0.579927	+	0.814668i	$0.696919\pi$
$662$	−12.1910	−0.473817
$663$	14.2349	0.552838
$664$	27.1382	1.05317
$665$	−7.83643	−0.303884
$666$	−16.6882	−0.646654
$667$	27.3197	1.05782
$668$	−34.6726	−1.34152
$669$	26.1562	1.01126
$670$	−55.6024	−2.14811
$671$	−4.92865	−0.190269
$672$	−38.2402	−1.47515
$673$	32.0217	1.23435	0.617173	−	0.786828i	$-0.288278\pi$
$673$	32.0217	1.23435	0.617173	+	0.786828i	$0.288278\pi$
$674$	−8.02048	−0.308937
$675$	13.9873	0.538370
$676$	3.46990	0.133458
$677$	−3.98927	−0.153320	−0.0766600	−	0.997057i	$-0.524426\pi$
$677$	−3.98927	−0.153320	−0.0766600	+	0.997057i	$0.524426\pi$
$678$	−21.8995	−0.841047
$679$	−30.4748	−1.16951
$680$	30.4773	1.16875
$681$	−84.6528	−3.24390
$682$	−12.2580	−0.469385
$683$	30.1538	1.15380	0.576901	−	0.816814i	$-0.304262\pi$
$683$	30.1538	1.15380	0.576901	+	0.816814i	$0.304262\pi$
$684$	30.8168	1.17831
$685$	−8.57869	−0.327775
$686$	37.4102	1.42833
$687$	75.3702	2.87555
$688$	−9.04440	−0.344814
$689$	−5.54370	−0.211198
$690$	−54.5502	−2.07669
$691$	6.71658	0.255511	0.127755	−	0.991806i	$-0.459223\pi$
$691$	6.71658	0.255511	0.127755	+	0.991806i	$0.459223\pi$
$692$	−25.0861	−0.953630
$693$	−35.2584	−1.33935
$694$	−38.0705	−1.44514
$695$	14.7163	0.558221
$696$	70.8273	2.68470
$697$	42.2233	1.59932
$698$	44.7012	1.69197
$699$	12.5157	0.473386
$700$	−14.2082	−0.537019
$701$	33.7971	1.27650	0.638249	−	0.769830i	$-0.279659\pi$
$701$	33.7971	1.27650	0.638249	+	0.769830i	$0.279659\pi$
$702$	−23.3196	−0.880141
$703$	1.60984	0.0607164
$704$	23.6077	0.889750
$705$	0.934149	0.0351821
$706$	−81.7148	−3.07538
$707$	−15.9160	−0.598584
$708$	−12.9172	−0.485458
$709$	−22.8952	−0.859849	−0.429924	−	0.902865i	$-0.641460\pi$
$709$	−22.8952	−0.859849	−0.429924	+	0.902865i	$0.641460\pi$
$710$	−57.4022	−2.15427
$711$	30.5674	1.14637
$712$	39.6410	1.48561
$713$	−10.9934	−0.411706
$714$	97.1771	3.63676
$715$	−3.65149	−0.136558
$716$	−47.3403	−1.76919
$717$	−8.68468	−0.324335
$718$	58.6713	2.18959
$719$	11.7611	0.438617	0.219308	−	0.975656i	$-0.429620\pi$
$719$	11.7611	0.438617	0.219308	+	0.975656i	$0.429620\pi$
$720$	−13.0945	−0.488003
$721$	31.9824	1.19109
$722$	39.7506	1.47936
$723$	29.8402	1.10977
$724$	−50.4041	−1.87325
$725$	−9.49048	−0.352468
$726$	−51.9463	−1.92791
$727$	34.7656	1.28939	0.644693	−	0.764442i	$-0.276985\pi$
$727$	34.7656	1.28939	0.644693	+	0.764442i	$0.276985\pi$
$728$	10.0345	0.371905
$729$	−18.6764	−0.691718
$730$	29.2287	1.08180
$731$	−38.4187	−1.42097
$732$	−27.0516	−0.999855
$733$	29.2600	1.08074	0.540372	−	0.841426i	$-0.318284\pi$
$733$	29.2600	1.08074	0.540372	+	0.841426i	$0.318284\pi$
$734$	−8.88779	−0.328054
$735$	8.77938	0.323832
$736$	17.3721	0.640345
$737$	24.1330	0.888951
$738$	−132.549	−4.87920
$739$	−22.0867	−0.812473	−0.406236	−	0.913768i	$-0.633159\pi$
$739$	−22.0867	−0.812473	−0.406236	+	0.913768i	$0.633159\pi$
$740$	−7.48453	−0.275137
$741$	4.31076	0.158360
$742$	−37.8451	−1.38934
$743$	−11.4478	−0.419979	−0.209990	−	0.977704i	$-0.567343\pi$
$743$	−11.4478	−0.419979	−0.209990	+	0.977704i	$0.567343\pi$
$744$	−28.5008	−1.04489
$745$	16.3184	0.597858
$746$	23.5065	0.860633
$747$	−49.5287	−1.81216
$748$	−31.2266	−1.14176
$749$	−16.3703	−0.598157
$750$	86.4925	3.15826
$751$	−34.3814	−1.25459	−0.627297	−	0.778780i	$-0.715839\pi$
$751$	−34.3814	−1.25459	−0.627297	+	0.778780i	$0.715839\pi$
$752$	0.177973	0.00649000
$753$	54.3425	1.98035
$754$	15.8225	0.576223
$755$	6.20601	0.225860
$756$	−100.988	−3.67289
$757$	24.1382	0.877317	0.438659	−	0.898654i	$-0.355454\pi$
$757$	24.1382	0.877317	0.438659	+	0.898654i	$0.355454\pi$
$758$	22.4163	0.814198
$759$	23.6763	0.859397
$760$	9.22946	0.334788
$761$	−5.22839	−0.189529	−0.0947645	−	0.995500i	$-0.530210\pi$
$761$	−5.22839	−0.189529	−0.0947645	+	0.995500i	$0.530210\pi$
$762$	−4.18499	−0.151606
$763$	2.74006	0.0991968
$764$	58.3349	2.11048
$765$	−55.6227	−2.01104
$766$	66.2180	2.39255
$767$	−1.22240	−0.0441385
$768$	68.2941	2.46435
$769$	−20.1052	−0.725013	−0.362506	−	0.931981i	$-0.618079\pi$
$769$	−20.1052	−0.725013	−0.362506	+	0.931981i	$0.618079\pi$
$770$	−24.9276	−0.898327
$771$	−88.2593	−3.17858
$772$	21.2141	0.763514
$773$	15.9372	0.573220	0.286610	−	0.958047i	$-0.407472\pi$
$773$	15.9372	0.573220	0.286610	+	0.958047i	$0.407472\pi$
$774$	120.606	4.33508
$775$	3.81895	0.137181
$776$	35.8920	1.28845
$777$	−10.1093	−0.362671
$778$	71.5306	2.56450
$779$	12.7865	0.458124
$780$	−20.0417	−0.717608
$781$	24.9142	0.891499
$782$	−44.1466	−1.57868
$783$	−67.4556	−2.41067
$784$	1.67263	0.0597370
$785$	7.32226	0.261343
$786$	−72.9432	−2.60180
$787$	−21.8521	−0.778944	−0.389472	−	0.921038i	$-0.627342\pi$
$787$	−21.8521	−0.778944	−0.389472	+	0.921038i	$0.627342\pi$
$788$	64.4443	2.29573
$789$	−96.2866	−3.42789
$790$	21.6111	0.768888
$791$	−8.97488	−0.319110
$792$	41.5260	1.47556
$793$	−2.56000	−0.0909081
$794$	72.5264	2.57387
$795$	32.0197	1.13562
$796$	42.9529	1.52243
$797$	−38.9901	−1.38110	−0.690550	−	0.723285i	$-0.742631\pi$
$797$	−38.9901	−1.38110	−0.690550	+	0.723285i	$0.742631\pi$
$798$	29.4282	1.04175
$799$	0.755991	0.0267450
$800$	−6.03484	−0.213364
$801$	−72.3468	−2.55625
$802$	−62.1720	−2.19537
$803$	−12.6861	−0.447682
$804$	132.457	4.67141
$805$	−22.3558	−0.787939
$806$	−6.36696	−0.224267
$807$	−13.5777	−0.477956
$808$	18.7453	0.659457
$809$	36.2356	1.27397	0.636987	−	0.770874i	$-0.280180\pi$
$809$	36.2356	1.27397	0.636987	+	0.770874i	$0.280180\pi$
$810$	51.1989	1.79895
$811$	−20.7794	−0.729663	−0.364832	−	0.931074i	$-0.618873\pi$
$811$	−20.7794	−0.729663	−0.364832	+	0.931074i	$0.618873\pi$
$812$	68.5210	2.40462
$813$	49.2617	1.72768
$814$	5.12089	0.179487
$815$	4.80882	0.168446
$816$	−15.6642	−0.548358
$817$	−11.6343	−0.407034
$818$	92.4589	3.23275
$819$	−18.3136	−0.639928
$820$	−59.4474	−2.07599
$821$	−6.48973	−0.226493	−0.113247	−	0.993567i	$-0.536125\pi$
$821$	−6.48973	−0.226493	−0.113247	+	0.993567i	$0.536125\pi$
$822$	32.2156	1.12365
$823$	30.6510	1.06843	0.534213	−	0.845350i	$-0.320608\pi$
$823$	30.6510	1.06843	0.534213	+	0.845350i	$0.320608\pi$
$824$	−37.6676	−1.31221
$825$	−8.22484	−0.286352
$826$	−8.34497	−0.290359
$827$	−22.9665	−0.798623	−0.399312	−	0.916815i	$-0.630751\pi$
$827$	−22.9665	−0.798623	−0.399312	+	0.916815i	$0.630751\pi$
$828$	87.9143	3.05523
$829$	6.97176	0.242139	0.121070	−	0.992644i	$-0.461368\pi$
$829$	6.97176	0.242139	0.121070	+	0.992644i	$0.461368\pi$
$830$	−35.0167	−1.21545
$831$	0.101721	0.00352868
$832$	12.2621	0.425112
$833$	7.10500	0.246174
$834$	−55.2642	−1.91364
$835$	18.9518	0.655853
$836$	−9.45634	−0.327055
$837$	27.1440	0.938234
$838$	−29.9281	−1.03385
$839$	25.4438	0.878417	0.439209	−	0.898385i	$-0.355259\pi$
$839$	25.4438	0.878417	0.439209	+	0.898385i	$0.355259\pi$
$840$	−57.9583	−1.99975
$841$	16.7692	0.578247
$842$	−91.9873	−3.17009
$843$	−59.1511	−2.03727
$844$	57.8938	1.99279
$845$	−1.89662	−0.0652458
$846$	−2.37324	−0.0815936
$847$	−21.2887	−0.731488
$848$	6.10035	0.209487
$849$	−74.3325	−2.55109
$850$	15.3359	0.526017
$851$	4.59257	0.157431
$852$	136.745	4.68480
$853$	8.05029	0.275637	0.137818	−	0.990458i	$-0.455991\pi$
$853$	8.05029	0.275637	0.137818	+	0.990458i	$0.455991\pi$
$854$	−17.4763	−0.598026
$855$	−16.8442	−0.576061
$856$	19.2803	0.658987
$857$	8.12453	0.277529	0.138764	−	0.990325i	$-0.455687\pi$
$857$	8.12453	0.277529	0.138764	+	0.990325i	$0.455687\pi$
$858$	13.7125	0.468135
$859$	−9.34550	−0.318864	−0.159432	−	0.987209i	$-0.550966\pi$
$859$	−9.34550	−0.318864	−0.159432	+	0.987209i	$0.550966\pi$
$860$	54.0907	1.84448
$861$	−80.2954	−2.73646
$862$	−20.3874	−0.694398
$863$	−23.5879	−0.802943	−0.401471	−	0.915872i	$-0.631501\pi$
$863$	−23.5879	−0.802943	−0.401471	+	0.915872i	$0.631501\pi$
$864$	−42.8939	−1.45928
$865$	13.7119	0.466218
$866$	−64.6325	−2.19630
$867$	−14.7675	−0.501532
$868$	−27.5727	−0.935879
$869$	−9.37983	−0.318189
$870$	−91.3890	−3.09838
$871$	12.5350	0.424731
$872$	−3.22714	−0.109285
$873$	−65.5048	−2.21700
$874$	−13.3689	−0.452210
$875$	35.4464	1.19831
$876$	−69.6293	−2.35256
$877$	14.4179	0.486857	0.243429	−	0.969919i	$-0.421728\pi$
$877$	14.4179	0.486857	0.243429	+	0.969919i	$0.421728\pi$
$878$	−84.7733	−2.86096
$879$	−63.3704	−2.13743
$880$	4.01814	0.135452
$881$	−8.37512	−0.282165	−0.141082	−	0.989998i	$-0.545058\pi$
$881$	−8.37512	−0.282165	−0.141082	+	0.989998i	$0.545058\pi$
$882$	−22.3043	−0.751025
$883$	19.8470	0.667904	0.333952	−	0.942590i	$-0.391618\pi$
$883$	19.8470	0.667904	0.333952	+	0.942590i	$0.391618\pi$
$884$	−16.2194	−0.545518
$885$	7.06045	0.237334
$886$	88.6598	2.97859
$887$	−27.7092	−0.930383	−0.465192	−	0.885210i	$-0.654015\pi$
$887$	−27.7092	−0.930383	−0.465192	+	0.885210i	$0.654015\pi$
$888$	11.9064	0.399553
$889$	−1.71510	−0.0575225
$890$	−51.1490	−1.71452
$891$	−22.2218	−0.744458
$892$	−29.8026	−0.997867
$893$	0.228937	0.00766108
$894$	−61.2804	−2.04952
$895$	25.8759	0.864935
$896$	58.5957	1.95754
$897$	12.2978	0.410610
$898$	18.0776	0.603259
$899$	−18.4174	−0.614256
$900$	−30.5402	−1.01801
$901$	25.9130	0.863287
$902$	40.6736	1.35428
$903$	73.0602	2.43129
$904$	10.5703	0.351562
$905$	27.5505	0.915810
$906$	−23.3054	−0.774272
$907$	23.8512	0.791968	0.395984	−	0.918257i	$-0.370404\pi$
$907$	23.8512	0.791968	0.395984	+	0.918257i	$0.370404\pi$
$908$	96.4543	3.20095
$909$	−34.2111	−1.13471
$910$	−12.9476	−0.429210
$911$	−11.7065	−0.387854	−0.193927	−	0.981016i	$-0.562122\pi$
$911$	−11.7065	−0.387854	−0.193927	+	0.981016i	$0.562122\pi$
$912$	−4.74361	−0.157076
$913$	15.1982	0.502988
$914$	−10.0674	−0.332999
$915$	14.7862	0.488817
$916$	−85.8777	−2.83748
$917$	−29.8936	−0.987174
$918$	109.003	3.59764
$919$	−18.3882	−0.606570	−0.303285	−	0.952900i	$-0.598083\pi$
$919$	−18.3882	−0.606570	−0.303285	+	0.952900i	$0.598083\pi$
$920$	26.3298	0.868069
$921$	16.9270	0.557764
$922$	−4.42688	−0.145792
$923$	12.9407	0.425948
$924$	59.3831	1.95356
$925$	−1.59540	−0.0524563
$926$	14.8241	0.487149
$927$	68.7454	2.25790
$928$	29.1038	0.955380
$929$	−14.7322	−0.483347	−0.241673	−	0.970358i	$-0.577696\pi$
$929$	−14.7322	−0.483347	−0.241673	+	0.970358i	$0.577696\pi$
$930$	36.7747	1.20589
$931$	2.15161	0.0705161
$932$	−14.2605	−0.467119
$933$	−9.79576	−0.320699
$934$	−28.3217	−0.926714
$935$	17.0682	0.558190
$936$	21.5690	0.705006
$937$	35.7937	1.16933	0.584664	−	0.811276i	$-0.301226\pi$
$937$	35.7937	1.16933	0.584664	+	0.811276i	$0.301226\pi$
$938$	85.5721	2.79403
$939$	16.1232	0.526161
$940$	−1.06438	−0.0347162
$941$	42.0299	1.37014	0.685068	−	0.728479i	$-0.259772\pi$
$941$	42.0299	1.37014	0.685068	+	0.728479i	$0.259772\pi$
$942$	−27.4973	−0.895911
$943$	36.4774	1.18787
$944$	1.34515	0.0437808
$945$	55.1992	1.79563
$946$	−37.0087	−1.20326
$947$	−17.6649	−0.574032	−0.287016	−	0.957926i	$-0.592663\pi$
$947$	−17.6649	−0.574032	−0.287016	+	0.957926i	$0.592663\pi$
$948$	−51.4825	−1.67207
$949$	−6.58929	−0.213897
$950$	4.64418	0.150677
$951$	22.4619	0.728377
$952$	−46.9046	−1.52019
$953$	−13.1036	−0.424467	−0.212233	−	0.977219i	$-0.568074\pi$
$953$	−13.1036	−0.424467	−0.212233	+	0.977219i	$0.568074\pi$
$954$	−81.3472	−2.63371
$955$	−31.8855	−1.03179
$956$	9.89543	0.320041
$957$	39.6654	1.28220
$958$	53.0959	1.71545
$959$	13.2026	0.426335
$960$	−70.8244	−2.28585
$961$	−23.5889	−0.760931
$962$	2.65984	0.0857568
$963$	−35.1876	−1.13390
$964$	−34.0003	−1.09507
$965$	−11.5955	−0.373272
$966$	83.9528	2.70114
$967$	−19.7658	−0.635625	−0.317813	−	0.948154i	$-0.602948\pi$
$967$	−19.7658	−0.635625	−0.317813	+	0.948154i	$0.602948\pi$
$968$	25.0730	0.805877
$969$	−20.1498	−0.647306
$970$	−46.3118	−1.48698
$971$	34.0102	1.09144	0.545720	−	0.837968i	$-0.316256\pi$
$971$	34.0102	1.09144	0.545720	+	0.837968i	$0.316256\pi$
$972$	−18.1740	−0.582931
$973$	−22.6484	−0.726075
$974$	−18.1786	−0.582479
$975$	−4.27207	−0.136816
$976$	2.81705	0.0901715
$977$	−7.10295	−0.227244	−0.113622	−	0.993524i	$-0.536245\pi$
$977$	−7.10295	−0.227244	−0.113622	+	0.993524i	$0.536245\pi$
$978$	−18.0586	−0.577450
$979$	22.2001	0.709519
$980$	−10.0033	−0.319544
$981$	5.88970	0.188044
$982$	75.1969	2.39963
$983$	19.9739	0.637070	0.318535	−	0.947911i	$-0.396809\pi$
$983$	19.9739	0.637070	0.318535	+	0.947911i	$0.396809\pi$
$984$	94.5689	3.01475
$985$	−35.2248	−1.12236
$986$	−73.9595	−2.35535
$987$	−1.43766	−0.0457611
$988$	−4.91173	−0.156263
$989$	−33.1905	−1.05540
$990$	−53.5813	−1.70292
$991$	14.6225	0.464498	0.232249	−	0.972656i	$-0.425392\pi$
$991$	14.6225	0.464498	0.232249	+	0.972656i	$0.425392\pi$
$992$	−11.7113	−0.371835
$993$	−15.8740	−0.503746
$994$	88.3420	2.80204
$995$	−23.4778	−0.744295
$996$	83.4176	2.64319
$997$	27.7374	0.878451	0.439226	−	0.898377i	$-0.355253\pi$
$997$	27.7374	0.878451	0.439226	+	0.898377i	$0.355253\pi$
$998$	−52.2413	−1.65367
$999$	−11.3396	−0.358769

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	8021.2.a.b.1.16	✓	140

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
8021.2.a.b.1.16	✓	140	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)

\(f(q)\)	\(=\)	\(q-2.33878 q^{2} -3.04534 q^{3} +3.46990 q^{4} -1.89662 q^{5} +7.12240 q^{6} +2.91891 q^{7} -3.43778 q^{8} +6.27412 q^{9} +O(q^{10})\)	\(q-2.33878 q^{2} -3.04534 q^{3} +3.46990 q^{4} -1.89662 q^{5} +7.12240 q^{6} +2.91891 q^{7} -3.43778 q^{8} +6.27412 q^{9} +4.43579 q^{10} -1.92526 q^{11} -10.5670 q^{12} -1.00000 q^{13} -6.82668 q^{14} +5.77587 q^{15} +1.10041 q^{16} +4.67431 q^{17} -14.6738 q^{18} +1.41552 q^{19} -6.58110 q^{20} -8.88907 q^{21} +4.50276 q^{22} +4.03821 q^{23} +10.4692 q^{24} -1.40282 q^{25} +2.33878 q^{26} -9.97083 q^{27} +10.1283 q^{28} +6.76529 q^{29} -13.5085 q^{30} -2.72234 q^{31} +4.30193 q^{32} +5.86307 q^{33} -10.9322 q^{34} -5.53606 q^{35} +21.7706 q^{36} +1.13728 q^{37} -3.31060 q^{38} +3.04534 q^{39} +6.52017 q^{40} +9.03305 q^{41} +20.7896 q^{42} -8.21911 q^{43} -6.68046 q^{44} -11.8996 q^{45} -9.44450 q^{46} +0.161733 q^{47} -3.35113 q^{48} +1.52001 q^{49} +3.28089 q^{50} -14.2349 q^{51} -3.46990 q^{52} +5.54370 q^{53} +23.3196 q^{54} +3.65149 q^{55} -10.0345 q^{56} -4.31076 q^{57} -15.8225 q^{58} +1.22240 q^{59} +20.0417 q^{60} +2.56000 q^{61} +6.36696 q^{62} +18.3136 q^{63} -12.2621 q^{64} +1.89662 q^{65} -13.7125 q^{66} -12.5350 q^{67} +16.2194 q^{68} -12.2978 q^{69} +12.9476 q^{70} -12.9407 q^{71} -21.5690 q^{72} +6.58929 q^{73} -2.65984 q^{74} +4.27207 q^{75} +4.91173 q^{76} -5.61965 q^{77} -7.12240 q^{78} +4.87198 q^{79} -2.08707 q^{80} +11.5422 q^{81} -21.1263 q^{82} -7.89412 q^{83} -30.8442 q^{84} -8.86541 q^{85} +19.2227 q^{86} -20.6026 q^{87} +6.61861 q^{88} -11.5310 q^{89} +27.8307 q^{90} -2.91891 q^{91} +14.0122 q^{92} +8.29046 q^{93} -0.378258 q^{94} -2.68472 q^{95} -13.1009 q^{96} -10.4405 q^{97} -3.55497 q^{98} -12.0793 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 140 q - 6 q^{2} - 9 q^{3} + 112 q^{4} - 12 q^{5} - 18 q^{6} - 32 q^{7} - 15 q^{8} + 111 q^{9}+O(q^{10}) \) 140 * q - 6 * q^2 - 9 * q^3 + 112 * q^4 - 12 * q^5 - 18 * q^6 - 32 * q^7 - 15 * q^8 + 111 * q^9	\( 140 q - 6 q^{2} - 9 q^{3} + 112 q^{4} - 12 q^{5} - 18 q^{6} - 32 q^{7} - 15 q^{8} + 111 q^{9} - q^{10} - 47 q^{11} - 11 q^{12} - 140 q^{13} - 12 q^{14} - 30 q^{15} + 64 q^{16} + 3 q^{17} - 22 q^{18} - 91 q^{19} - 24 q^{20} - 28 q^{21} - 12 q^{22} - 10 q^{23} - 42 q^{24} + 84 q^{25} + 6 q^{26} - 33 q^{27} - 71 q^{28} - 32 q^{29} - 45 q^{30} - 90 q^{31} - 31 q^{32} - 32 q^{33} - 78 q^{34} - 50 q^{35} + 10 q^{36} - 67 q^{37} - 8 q^{38} + 9 q^{39} - 10 q^{40} - 22 q^{41} - 30 q^{42} - 40 q^{43} - 88 q^{44} - 36 q^{45} - 77 q^{46} - 29 q^{47} - 4 q^{48} + 66 q^{49} - 45 q^{50} - 87 q^{51} - 112 q^{52} - 19 q^{53} - 82 q^{54} - 28 q^{55} - 63 q^{56} - 41 q^{57} - 96 q^{58} - 84 q^{59} - 106 q^{60} - 58 q^{61} - 3 q^{62} - 76 q^{63} - 55 q^{64} + 12 q^{65} - 56 q^{66} - 140 q^{67} - 4 q^{68} - 41 q^{69} - 106 q^{70} - 104 q^{71} - 52 q^{72} - 57 q^{73} - 24 q^{74} - 62 q^{75} - 184 q^{76} + 8 q^{77} + 18 q^{78} - 104 q^{79} - 102 q^{80} + 4 q^{81} - 37 q^{82} - 52 q^{83} - 94 q^{84} - 93 q^{85} - 79 q^{86} + 51 q^{87} - 47 q^{88} - 64 q^{89} + 22 q^{90} + 32 q^{91} - 42 q^{92} - 115 q^{93} - 43 q^{94} - 25 q^{95} - 116 q^{96} - 92 q^{97} - 36 q^{98} - 223 q^{99}+O(q^{100}) \) 140 * q - 6 * q^2 - 9 * q^3 + 112 * q^4 - 12 * q^5 - 18 * q^6 - 32 * q^7 - 15 * q^8 + 111 * q^9 - q^10 - 47 * q^11 - 11 * q^12 - 140 * q^13 - 12 * q^14 - 30 * q^15 + 64 * q^16 + 3 * q^17 - 22 * q^18 - 91 * q^19 - 24 * q^20 - 28 * q^21 - 12 * q^22 - 10 * q^23 - 42 * q^24 + 84 * q^25 + 6 * q^26 - 33 * q^27 - 71 * q^28 - 32 * q^29 - 45 * q^30 - 90 * q^31 - 31 * q^32 - 32 * q^33 - 78 * q^34 - 50 * q^35 + 10 * q^36 - 67 * q^37 - 8 * q^38 + 9 * q^39 - 10 * q^40 - 22 * q^41 - 30 * q^42 - 40 * q^43 - 88 * q^44 - 36 * q^45 - 77 * q^46 - 29 * q^47 - 4 * q^48 + 66 * q^49 - 45 * q^50 - 87 * q^51 - 112 * q^52 - 19 * q^53 - 82 * q^54 - 28 * q^55 - 63 * q^56 - 41 * q^57 - 96 * q^58 - 84 * q^59 - 106 * q^60 - 58 * q^61 - 3 * q^62 - 76 * q^63 - 55 * q^64 + 12 * q^65 - 56 * q^66 - 140 * q^67 - 4 * q^68 - 41 * q^69 - 106 * q^70 - 104 * q^71 - 52 * q^72 - 57 * q^73 - 24 * q^74 - 62 * q^75 - 184 * q^76 + 8 * q^77 + 18 * q^78 - 104 * q^79 - 102 * q^80 + 4 * q^81 - 37 * q^82 - 52 * q^83 - 94 * q^84 - 93 * q^85 - 79 * q^86 + 51 * q^87 - 47 * q^88 - 64 * q^89 + 22 * q^90 + 32 * q^91 - 42 * q^92 - 115 * q^93 - 43 * q^94 - 25 * q^95 - 116 * q^96 - 92 * q^97 - 36 * q^98 - 223 * q^99

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