LMFDB - Embedded newform 8021.2.a.d.1.14

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:	$174$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.14
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)

$f(q)$	$=$	$q-2.63597 q^{2} -1.22103 q^{3} +4.94831 q^{4} -4.05948 q^{5} +3.21858 q^{6} -2.69195 q^{7} -7.77165 q^{8} -1.50910 q^{9} +O(q^{10})$	\(q-2.63597 q^{2} -1.22103 q^{3} +4.94831 q^{4} -4.05948 q^{5} +3.21858 q^{6} -2.69195 q^{7} -7.77165 q^{8} -1.50910 q^{9} +10.7007 q^{10} -2.72323 q^{11} -6.04201 q^{12} +1.00000 q^{13} +7.09588 q^{14} +4.95673 q^{15} +10.5892 q^{16} -1.72211 q^{17} +3.97793 q^{18} +0.0866039 q^{19} -20.0876 q^{20} +3.28693 q^{21} +7.17835 q^{22} -1.32738 q^{23} +9.48938 q^{24} +11.4794 q^{25} -2.63597 q^{26} +5.50572 q^{27} -13.3206 q^{28} +4.89807 q^{29} -13.0658 q^{30} +9.64439 q^{31} -12.3694 q^{32} +3.32514 q^{33} +4.53943 q^{34} +10.9279 q^{35} -7.46748 q^{36} -6.22935 q^{37} -0.228285 q^{38} -1.22103 q^{39} +31.5489 q^{40} -0.837482 q^{41} -8.66424 q^{42} +0.704741 q^{43} -13.4754 q^{44} +6.12615 q^{45} +3.49892 q^{46} -4.92684 q^{47} -12.9296 q^{48} +0.246573 q^{49} -30.2593 q^{50} +2.10274 q^{51} +4.94831 q^{52} -1.93396 q^{53} -14.5129 q^{54} +11.0549 q^{55} +20.9209 q^{56} -0.105746 q^{57} -12.9111 q^{58} -1.57140 q^{59} +24.5274 q^{60} +10.0158 q^{61} -25.4223 q^{62} +4.06241 q^{63} +11.4269 q^{64} -4.05948 q^{65} -8.76495 q^{66} -7.32271 q^{67} -8.52154 q^{68} +1.62076 q^{69} -28.8056 q^{70} -4.56552 q^{71} +11.7282 q^{72} -8.27407 q^{73} +16.4203 q^{74} -14.0166 q^{75} +0.428543 q^{76} +7.33080 q^{77} +3.21858 q^{78} -14.7330 q^{79} -42.9865 q^{80} -2.19534 q^{81} +2.20757 q^{82} -7.59058 q^{83} +16.2648 q^{84} +6.99088 q^{85} -1.85767 q^{86} -5.98067 q^{87} +21.1640 q^{88} -4.11374 q^{89} -16.1483 q^{90} -2.69195 q^{91} -6.56827 q^{92} -11.7760 q^{93} +12.9870 q^{94} -0.351567 q^{95} +15.1033 q^{96} -8.88940 q^{97} -0.649957 q^{98} +4.10962 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 174 q + 6 q^{2} + 37 q^{3} + 214 q^{4} + 10 q^{5} + 12 q^{6} + 28 q^{7} + 15 q^{8} + 211 q^{9}+O(q^{10}) $ 174 * q + 6 * q^2 + 37 * q^3 + 214 * q^4 + 10 * q^5 + 12 * q^6 + 28 * q^7 + 15 * q^8 + 211 * q^9	\( 174 q + 6 q^{2} + 37 q^{3} + 214 q^{4} + 10 q^{5} + 12 q^{6} + 28 q^{7} + 15 q^{8} + 211 q^{9} + 47 q^{10} + 47 q^{11} + 81 q^{12} + 174 q^{13} + 22 q^{14} + 26 q^{15} + 286 q^{16} + 27 q^{17} + 22 q^{18} + 91 q^{19} + 18 q^{20} + 8 q^{21} + 58 q^{22} + 62 q^{23} + 24 q^{24} + 244 q^{25} + 6 q^{26} + 139 q^{27} + 43 q^{28} + 42 q^{29} + 31 q^{30} + 82 q^{31} + 11 q^{32} + 12 q^{33} + 50 q^{34} + 74 q^{35} + 310 q^{36} + 47 q^{37} + 10 q^{38} + 37 q^{39} + 118 q^{40} + 16 q^{41} + 26 q^{42} + 136 q^{43} + 74 q^{44} + 18 q^{45} + 53 q^{46} + 15 q^{47} + 132 q^{48} + 254 q^{49} - 5 q^{50} + 121 q^{51} + 214 q^{52} + 39 q^{53} + 30 q^{54} + 188 q^{55} + 55 q^{56} + 11 q^{57} + 32 q^{58} + 58 q^{59} + 16 q^{60} + 128 q^{61} + 27 q^{62} + 42 q^{63} + 423 q^{64} + 10 q^{65} + 4 q^{66} + 132 q^{67} + 52 q^{68} + 63 q^{69} - 8 q^{70} + 78 q^{71} + 2 q^{72} + 21 q^{73} - 16 q^{74} + 188 q^{75} + 160 q^{76} + 20 q^{77} + 12 q^{78} + 232 q^{79} + 2 q^{80} + 302 q^{81} + 115 q^{82} + 18 q^{83} - 26 q^{84} + 47 q^{85} + 27 q^{86} + 127 q^{87} + 163 q^{88} + 14 q^{90} + 28 q^{91} + 68 q^{92} + 15 q^{93} + 91 q^{94} + 75 q^{95} - 26 q^{96} + 34 q^{97} - 60 q^{98} + 181 q^{99}+O(q^{100}) \) 174 * q + 6 * q^2 + 37 * q^3 + 214 * q^4 + 10 * q^5 + 12 * q^6 + 28 * q^7 + 15 * q^8 + 211 * q^9 + 47 * q^10 + 47 * q^11 + 81 * q^12 + 174 * q^13 + 22 * q^14 + 26 * q^15 + 286 * q^16 + 27 * q^17 + 22 * q^18 + 91 * q^19 + 18 * q^20 + 8 * q^21 + 58 * q^22 + 62 * q^23 + 24 * q^24 + 244 * q^25 + 6 * q^26 + 139 * q^27 + 43 * q^28 + 42 * q^29 + 31 * q^30 + 82 * q^31 + 11 * q^32 + 12 * q^33 + 50 * q^34 + 74 * q^35 + 310 * q^36 + 47 * q^37 + 10 * q^38 + 37 * q^39 + 118 * q^40 + 16 * q^41 + 26 * q^42 + 136 * q^43 + 74 * q^44 + 18 * q^45 + 53 * q^46 + 15 * q^47 + 132 * q^48 + 254 * q^49 - 5 * q^50 + 121 * q^51 + 214 * q^52 + 39 * q^53 + 30 * q^54 + 188 * q^55 + 55 * q^56 + 11 * q^57 + 32 * q^58 + 58 * q^59 + 16 * q^60 + 128 * q^61 + 27 * q^62 + 42 * q^63 + 423 * q^64 + 10 * q^65 + 4 * q^66 + 132 * q^67 + 52 * q^68 + 63 * q^69 - 8 * q^70 + 78 * q^71 + 2 * q^72 + 21 * q^73 - 16 * q^74 + 188 * q^75 + 160 * q^76 + 20 * q^77 + 12 * q^78 + 232 * q^79 + 2 * q^80 + 302 * q^81 + 115 * q^82 + 18 * q^83 - 26 * q^84 + 47 * q^85 + 27 * q^86 + 127 * q^87 + 163 * q^88 + 14 * q^90 + 28 * q^91 + 68 * q^92 + 15 * q^93 + 91 * q^94 + 75 * q^95 - 26 * q^96 + 34 * q^97 - 60 * q^98 + 181 * 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 $

$2$	−2.63597	−1.86391	−0.931954	−	0.362576i	$-0.881897\pi$
$2$	−2.63597	−1.86391	−0.931954	+	0.362576i	$0.881897\pi$
$3$	−1.22103	−0.704959	−0.352480	−	0.935819i	$-0.614661\pi$
$3$	−1.22103	−0.704959	−0.352480	+	0.935819i	$0.614661\pi$
$4$	4.94831	2.47416
$5$	−4.05948	−1.81546	−0.907728	−	0.419560i	$-0.862184\pi$
$5$	−4.05948	−1.81546	−0.907728	+	0.419560i	$0.862184\pi$
$6$	3.21858	1.31398
$7$	−2.69195	−1.01746	−0.508730	−	0.860926i	$-0.669885\pi$
$7$	−2.69195	−1.01746	−0.508730	+	0.860926i	$0.669885\pi$
$8$	−7.77165	−2.74769
$9$	−1.50910	−0.503032
$10$	10.7007	3.38384
$11$	−2.72323	−0.821086	−0.410543	−	0.911841i	$-0.634661\pi$
$11$	−2.72323	−0.821086	−0.410543	+	0.911841i	$0.634661\pi$
$12$	−6.04201	−1.74418
$13$	1.00000	0.277350
$13$	1.00000	0.277350
$14$	7.09588	1.89645
$15$	4.95673	1.27982
$16$	10.5892	2.64729
$17$	−1.72211	−0.417673	−0.208837	−	0.977951i	$-0.566968\pi$
$17$	−1.72211	−0.417673	−0.208837	+	0.977951i	$0.566968\pi$
$18$	3.97793	0.937606
$19$	0.0866039	0.0198683	0.00993415	−	0.999951i	$-0.496838\pi$
$19$	0.0866039	0.0198683	0.00993415	+	0.999951i	$0.496838\pi$
$20$	−20.0876	−4.49172
$21$	3.28693	0.717268
$22$	7.17835	1.53043
$23$	−1.32738	−0.276777	−0.138388	−	0.990378i	$-0.544192\pi$
$23$	−1.32738	−0.276777	−0.138388	+	0.990378i	$0.544192\pi$
$24$	9.48938	1.93701
$25$	11.4794	2.29588
$26$	−2.63597	−0.516955
$27$	5.50572	1.05958
$28$	−13.3206	−2.51735
$29$	4.89807	0.909548	0.454774	−	0.890607i	$-0.349720\pi$
$29$	4.89807	0.909548	0.454774	+	0.890607i	$0.349720\pi$
$30$	−13.0658	−2.38547
$31$	9.64439	1.73218	0.866092	−	0.499885i	$-0.166624\pi$
$31$	9.64439	1.73218	0.866092	+	0.499885i	$0.166624\pi$
$32$	−12.3694	−2.18662
$33$	3.32514	0.578832
$34$	4.53943	0.778505
$35$	10.9279	1.84715
$36$	−7.46748	−1.24458
$37$	−6.22935	−1.02410	−0.512049	−	0.858956i	$-0.671113\pi$
$37$	−6.22935	−1.02410	−0.512049	+	0.858956i	$0.671113\pi$
$38$	−0.228285	−0.0370327
$39$	−1.22103	−0.195521
$40$	31.5489	4.98831
$41$	−0.837482	−0.130793	−0.0653964	−	0.997859i	$-0.520831\pi$
$41$	−0.837482	−0.130793	−0.0653964	+	0.997859i	$0.520831\pi$
$42$	−8.66424	−1.33692
$43$	0.704741	0.107472	0.0537360	−	0.998555i	$-0.482887\pi$
$43$	0.704741	0.107472	0.0537360	+	0.998555i	$0.482887\pi$
$44$	−13.4754	−2.03150
$45$	6.12615	0.913233
$46$	3.49892	0.515887
$47$	−4.92684	−0.718653	−0.359326	−	0.933212i	$-0.616994\pi$
$47$	−4.92684	−0.718653	−0.359326	+	0.933212i	$0.616994\pi$
$48$	−12.9296	−1.86623
$49$	0.246573	0.0352247
$50$	−30.2593	−4.27931
$51$	2.10274	0.294443
$52$	4.94831	0.686207
$53$	−1.93396	−0.265650	−0.132825	−	0.991140i	$-0.542405\pi$
$53$	−1.93396	−0.265650	−0.132825	+	0.991140i	$0.542405\pi$
$54$	−14.5129	−1.97495
$55$	11.0549	1.49065
$56$	20.9209	2.79567
$57$	−0.105746	−0.0140064
$58$	−12.9111	−1.69532
$59$	−1.57140	−0.204579	−0.102289	−	0.994755i	$-0.532617\pi$
$59$	−1.57140	−0.204579	−0.102289	+	0.994755i	$0.532617\pi$
$60$	24.5274	3.16648
$61$	10.0158	1.28239	0.641193	−	0.767380i	$-0.278440\pi$
$61$	10.0158	1.28239	0.641193	+	0.767380i	$0.278440\pi$
$62$	−25.4223	−3.22863
$63$	4.06241	0.511815
$64$	11.4269	1.42836
$65$	−4.05948	−0.503517
$66$	−8.76495	−1.07889
$67$	−7.32271	−0.894611	−0.447306	−	0.894381i	$-0.647616\pi$
$67$	−7.32271	−0.894611	−0.447306	+	0.894381i	$0.647616\pi$
$68$	−8.52154	−1.03339
$69$	1.62076	0.195117
$70$	−28.8056	−3.44292
$71$	−4.56552	−0.541828	−0.270914	−	0.962604i	$-0.587326\pi$
$71$	−4.56552	−0.541828	−0.270914	+	0.962604i	$0.587326\pi$
$72$	11.7282	1.38218
$73$	−8.27407	−0.968406	−0.484203	−	0.874956i	$-0.660890\pi$
$73$	−8.27407	−0.968406	−0.484203	+	0.874956i	$0.660890\pi$
$74$	16.4203	1.90883
$75$	−14.0166	−1.61850
$76$	0.428543	0.0491573
$77$	7.33080	0.835422
$78$	3.21858	0.364432
$79$	−14.7330	−1.65759	−0.828796	−	0.559552i	$-0.810973\pi$
$79$	−14.7330	−1.65759	−0.828796	+	0.559552i	$0.810973\pi$
$80$	−42.9865	−4.80604
$81$	−2.19534	−0.243926
$82$	2.20757	0.243786
$83$	−7.59058	−0.833175	−0.416587	−	0.909096i	$-0.636774\pi$
$83$	−7.59058	−0.833175	−0.416587	+	0.909096i	$0.636774\pi$
$84$	16.2648	1.77463
$85$	6.99088	0.758267
$86$	−1.85767	−0.200318
$87$	−5.98067	−0.641195
$88$	21.1640	2.25609
$89$	−4.11374	−0.436056	−0.218028	−	0.975943i	$-0.569962\pi$
$89$	−4.11374	−0.436056	−0.218028	+	0.975943i	$0.569962\pi$
$90$	−16.1483	−1.70218
$91$	−2.69195	−0.282193
$92$	−6.56827	−0.684789
$93$	−11.7760	−1.22112
$94$	12.9870	1.33950
$95$	−0.351567	−0.0360700
$96$	15.1033	1.54148
$97$	−8.88940	−0.902582	−0.451291	−	0.892377i	$-0.649036\pi$
$97$	−8.88940	−0.902582	−0.451291	+	0.892377i	$0.649036\pi$
$98$	−0.649957	−0.0656556
$99$	4.10962	0.413033
$100$	56.8036	5.68036
$101$	−7.85156	−0.781259	−0.390630	−	0.920548i	$-0.627743\pi$
$101$	−7.85156	−0.781259	−0.390630	+	0.920548i	$0.627743\pi$
$102$	−5.54275	−0.548815
$103$	12.5542	1.23700	0.618501	−	0.785784i	$-0.287740\pi$
$103$	12.5542	1.23700	0.618501	+	0.785784i	$0.287740\pi$
$104$	−7.77165	−0.762073
$105$	−13.3432	−1.30217
$106$	5.09785	0.495147
$107$	6.11334	0.590999	0.295500	−	0.955343i	$-0.404514\pi$
$107$	6.11334	0.590999	0.295500	+	0.955343i	$0.404514\pi$
$108$	27.2440	2.62156
$109$	−2.84774	−0.272764	−0.136382	−	0.990656i	$-0.543548\pi$
$109$	−2.84774	−0.272764	−0.136382	+	0.990656i	$0.543548\pi$
$110$	−29.1404	−2.77843
$111$	7.60619	0.721948
$112$	−28.5055	−2.69351
$113$	−13.4589	−1.26611	−0.633055	−	0.774107i	$-0.718199\pi$
$113$	−13.4589	−1.26611	−0.633055	+	0.774107i	$0.718199\pi$
$114$	0.278742	0.0261066
$115$	5.38846	0.502476
$116$	24.2372	2.25036
$117$	−1.50910	−0.139516
$118$	4.14215	0.381316
$119$	4.63583	0.424966
$120$	−38.5220	−3.51656
$121$	−3.58399	−0.325817
$122$	−26.4012	−2.39025
$123$	1.02259	0.0922036
$124$	47.7235	4.28569
$125$	−26.3030	−2.35261
$126$	−10.7084	−0.953977
$127$	−8.17965	−0.725826	−0.362913	−	0.931823i	$-0.618218\pi$
$127$	−8.17965	−0.725826	−0.362913	+	0.931823i	$0.618218\pi$
$128$	−5.38218	−0.475722
$129$	−0.860507	−0.0757634
$130$	10.7007	0.938509
$131$	−12.2211	−1.06776	−0.533882	−	0.845559i	$-0.679267\pi$
$131$	−12.2211	−1.06776	−0.533882	+	0.845559i	$0.679267\pi$
$132$	16.4538	1.43212
$133$	−0.233133	−0.0202152
$134$	19.3024	1.66747
$135$	−22.3504	−1.92361
$136$	13.3836	1.14764
$137$	−2.36418	−0.201986	−0.100993	−	0.994887i	$-0.532202\pi$
$137$	−2.36418	−0.201986	−0.100993	+	0.994887i	$0.532202\pi$
$138$	−4.27227	−0.363679
$139$	−19.7194	−1.67258	−0.836290	−	0.548287i	$-0.815280\pi$
$139$	−19.7194	−1.67258	−0.836290	+	0.548287i	$0.815280\pi$
$140$	54.0747	4.57014
$141$	6.01579	0.506621
$142$	12.0346	1.00992
$143$	−2.72323	−0.227728
$144$	−15.9801	−1.33167
$145$	−19.8836	−1.65124
$146$	21.8102	1.80502
$147$	−0.301071	−0.0248320
$148$	−30.8248	−2.53378
$149$	−16.0668	−1.31624	−0.658120	−	0.752913i	$-0.728648\pi$
$149$	−16.0668	−1.31624	−0.658120	+	0.752913i	$0.728648\pi$
$150$	36.9473	3.01674
$151$	11.7066	0.952668	0.476334	−	0.879264i	$-0.341965\pi$
$151$	11.7066	0.952668	0.476334	+	0.879264i	$0.341965\pi$
$152$	−0.673055	−0.0545920
$153$	2.59883	0.210103
$154$	−19.3237	−1.55715
$155$	−39.1512	−3.14470
$156$	−6.04201	−0.483748
$157$	−5.06673	−0.404369	−0.202185	−	0.979347i	$-0.564804\pi$
$157$	−5.06673	−0.404369	−0.202185	+	0.979347i	$0.564804\pi$
$158$	38.8357	3.08960
$159$	2.36142	0.187272
$160$	50.2132	3.96971
$161$	3.57322	0.281609
$162$	5.78683	0.454656
$163$	−18.4149	−1.44237	−0.721184	−	0.692743i	$-0.756402\pi$
$163$	−18.4149	−1.44237	−0.721184	+	0.692743i	$0.756402\pi$
$164$	−4.14412	−0.323602
$165$	−13.4983	−1.05084
$166$	20.0085	1.55296
$167$	−12.2177	−0.945436	−0.472718	−	0.881214i	$-0.656727\pi$
$167$	−12.2177	−0.945436	−0.472718	+	0.881214i	$0.656727\pi$
$168$	−25.5449	−1.97083
$169$	1.00000	0.0769231
$170$	−18.4277	−1.41334
$171$	−0.130694	−0.00999440
$172$	3.48728	0.265903
$173$	−8.18177	−0.622049	−0.311024	−	0.950402i	$-0.600672\pi$
$173$	−8.18177	−0.622049	−0.311024	+	0.950402i	$0.600672\pi$
$174$	15.7648	1.19513
$175$	−30.9019	−2.33596
$176$	−28.8368	−2.17365
$177$	1.91872	0.144220
$178$	10.8437	0.812768
$179$	−6.17188	−0.461308	−0.230654	−	0.973036i	$-0.574087\pi$
$179$	−6.17188	−0.461308	−0.230654	+	0.973036i	$0.574087\pi$
$180$	30.3141	2.25948
$181$	18.0204	1.33945	0.669723	−	0.742611i	$-0.266413\pi$
$181$	18.0204	1.33945	0.669723	+	0.742611i	$0.266413\pi$
$182$	7.09588	0.525981
$183$	−12.2295	−0.904030
$184$	10.3159	0.760498
$185$	25.2879	1.85921
$186$	31.0413	2.27606
$187$	4.68971	0.342946
$188$	−24.3795	−1.77806
$189$	−14.8211	−1.07808
$190$	0.926719	0.0672312
$191$	5.50295	0.398180	0.199090	−	0.979981i	$-0.436201\pi$
$191$	5.50295	0.398180	0.199090	+	0.979981i	$0.436201\pi$
$192$	−13.9525	−1.00694
$193$	17.4229	1.25413	0.627065	−	0.778967i	$-0.284256\pi$
$193$	17.4229	1.25413	0.627065	+	0.778967i	$0.284256\pi$
$194$	23.4322	1.68233
$195$	4.95673	0.354959
$196$	1.22012	0.0871513
$197$	12.0539	0.858807	0.429404	−	0.903113i	$-0.358724\pi$
$197$	12.0539	0.858807	0.429404	+	0.903113i	$0.358724\pi$
$198$	−10.8328	−0.769856
$199$	10.5896	0.750677	0.375338	−	0.926888i	$-0.377527\pi$
$199$	10.5896	0.750677	0.375338	+	0.926888i	$0.377527\pi$
$200$	−89.2137	−6.30836
$201$	8.94121	0.630665
$202$	20.6964	1.45620
$203$	−13.1853	−0.925429
$204$	10.4050	0.728497
$205$	3.39974	0.237448
$206$	−33.0924	−2.30566
$207$	2.00314	0.139228
$208$	10.5892	0.734226
$209$	−0.235843	−0.0163136
$210$	35.1723	2.42712
$211$	0.296167	0.0203890	0.0101945	−	0.999948i	$-0.496755\pi$
$211$	0.296167	0.0203890	0.0101945	+	0.999948i	$0.496755\pi$
$212$	−9.56984	−0.657259
$213$	5.57462	0.381967
$214$	−16.1146	−1.10157
$215$	−2.86088	−0.195111
$216$	−42.7885	−2.91139
$217$	−25.9622	−1.76243
$218$	7.50655	0.508408
$219$	10.1028	0.682687
$220$	54.7032	3.68809
$221$	−1.72211	−0.115842
$222$	−20.0497	−1.34565
$223$	−9.49211	−0.635639	−0.317819	−	0.948151i	$-0.602951\pi$
$223$	−9.49211	−0.635639	−0.317819	+	0.948151i	$0.602951\pi$
$224$	33.2977	2.22480
$225$	−17.3235	−1.15490
$226$	35.4773	2.35991
$227$	15.3606	1.01952	0.509761	−	0.860316i	$-0.329734\pi$
$227$	15.3606	1.01952	0.509761	+	0.860316i	$0.329734\pi$
$228$	−0.523262	−0.0346539
$229$	25.3230	1.67339	0.836695	−	0.547669i	$-0.184485\pi$
$229$	25.3230	1.67339	0.836695	+	0.547669i	$0.184485\pi$
$230$	−14.2038	−0.936570
$231$	−8.95110	−0.588939
$232$	−38.0661	−2.49916
$233$	21.5931	1.41461	0.707304	−	0.706909i	$-0.249911\pi$
$233$	21.5931	1.41461	0.707304	+	0.706909i	$0.249911\pi$
$234$	3.97793	0.260045
$235$	20.0004	1.30468
$236$	−7.77577	−0.506159
$237$	17.9894	1.16853
$238$	−12.2199	−0.792098
$239$	−14.9130	−0.964644	−0.482322	−	0.875994i	$-0.660207\pi$
$239$	−14.9130	−0.964644	−0.482322	+	0.875994i	$0.660207\pi$
$240$	52.4876	3.38806
$241$	12.7277	0.819862	0.409931	−	0.912117i	$-0.365553\pi$
$241$	12.7277	0.819862	0.409931	+	0.912117i	$0.365553\pi$
$242$	9.44728	0.607294
$243$	−13.8366	−0.887619
$244$	49.5611	3.17282
$245$	−1.00096	−0.0639488
$246$	−2.69550	−0.171859
$247$	0.0866039	0.00551048
$248$	−74.9528	−4.75951
$249$	9.26829	0.587354
$250$	69.3337	4.38505
$251$	8.33940	0.526378	0.263189	−	0.964744i	$-0.415226\pi$
$251$	8.33940	0.526378	0.263189	+	0.964744i	$0.415226\pi$
$252$	20.1021	1.26631
$253$	3.61476	0.227258
$254$	21.5613	1.35287
$255$	−8.53604	−0.534548
$256$	−8.66657	−0.541661
$257$	8.59133	0.535912	0.267956	−	0.963431i	$-0.413652\pi$
$257$	8.59133	0.535912	0.267956	+	0.963431i	$0.413652\pi$
$258$	2.26827	0.141216
$259$	16.7691	1.04198
$260$	−20.0876	−1.24578
$261$	−7.39166	−0.457532
$262$	32.2144	1.99021
$263$	16.0910	0.992214	0.496107	−	0.868261i	$-0.334762\pi$
$263$	16.0910	0.992214	0.496107	+	0.868261i	$0.334762\pi$
$264$	−25.8418	−1.59045
$265$	7.85088	0.482276
$266$	0.614531	0.0376793
$267$	5.02298	0.307402
$268$	−36.2350	−2.21341
$269$	−0.402075	−0.0245149	−0.0122575	−	0.999925i	$-0.503902\pi$
$269$	−0.402075	−0.0245149	−0.0122575	+	0.999925i	$0.503902\pi$
$270$	58.9148	3.58544
$271$	10.3921	0.631275	0.315638	−	0.948880i	$-0.397782\pi$
$271$	10.3921	0.631275	0.315638	+	0.948880i	$0.397782\pi$
$272$	−18.2357	−1.10570
$273$	3.28693	0.198934
$274$	6.23191	0.376483
$275$	−31.2611	−1.88511
$276$	8.02002	0.482749
$277$	−27.0261	−1.62384	−0.811921	−	0.583767i	$-0.801578\pi$
$277$	−27.0261	−1.62384	−0.811921	+	0.583767i	$0.801578\pi$
$278$	51.9797	3.11754
$279$	−14.5543	−0.871344
$280$	−84.9278	−5.07541
$281$	−5.68759	−0.339293	−0.169646	−	0.985505i	$-0.554263\pi$
$281$	−5.68759	−0.339293	−0.169646	+	0.985505i	$0.554263\pi$
$282$	−15.8574	−0.944295
$283$	−18.4594	−1.09730	−0.548648	−	0.836053i	$-0.684857\pi$
$283$	−18.4594	−1.09730	−0.548648	+	0.836053i	$0.684857\pi$
$284$	−22.5916	−1.34057
$285$	0.429272	0.0254279
$286$	7.17835	0.424465
$287$	2.25446	0.133076
$288$	18.6666	1.09994
$289$	−14.0343	−0.825549
$290$	52.4125	3.07777
$291$	10.8542	0.636284
$292$	−40.9427	−2.39599
$293$	−5.27625	−0.308242	−0.154121	−	0.988052i	$-0.549255\pi$
$293$	−5.27625	−0.308242	−0.154121	+	0.988052i	$0.549255\pi$
$294$	0.793614	0.0462845
$295$	6.37906	0.371403
$296$	48.4123	2.81391
$297$	−14.9934	−0.870004
$298$	42.3514	2.45335
$299$	−1.32738	−0.0767641
$300$	−69.3586	−4.00442
$301$	−1.89713	−0.109349
$302$	−30.8581	−1.77569
$303$	9.58695	0.550756
$304$	0.917063	0.0525972
$305$	−40.6588	−2.32811
$306$	−6.85043	−0.391613
$307$	9.37989	0.535339	0.267669	−	0.963511i	$-0.413746\pi$
$307$	9.37989	0.535339	0.267669	+	0.963511i	$0.413746\pi$
$308$	36.2751	2.06696
$309$	−15.3290	−0.872036
$310$	103.201	5.86144
$311$	−0.472681	−0.0268033	−0.0134016	−	0.999910i	$-0.504266\pi$
$311$	−0.472681	−0.0268033	−0.0134016	+	0.999910i	$0.504266\pi$
$312$	9.48938	0.537230
$313$	−30.5365	−1.72603	−0.863013	−	0.505182i	$-0.831425\pi$
$313$	−30.5365	−1.72603	−0.863013	+	0.505182i	$0.831425\pi$
$314$	13.3557	0.753708
$315$	−16.4913	−0.929177
$316$	−72.9034	−4.10114
$317$	−26.7604	−1.50301	−0.751506	−	0.659726i	$-0.770672\pi$
$317$	−26.7604	−1.50301	−0.751506	+	0.659726i	$0.770672\pi$
$318$	−6.22461	−0.349059
$319$	−13.3386	−0.746818
$320$	−46.3873	−2.59313
$321$	−7.46455	−0.416631
$322$	−9.41889	−0.524894
$323$	−0.149142	−0.00829846
$324$	−10.8632	−0.603512
$325$	11.4794	0.636762
$326$	48.5411	2.68844
$327$	3.47717	0.192288
$328$	6.50861	0.359378
$329$	13.2628	0.731200
$330$	35.5812	1.95868
$331$	1.95932	0.107694	0.0538470	−	0.998549i	$-0.482852\pi$
$331$	1.95932	0.107694	0.0538470	+	0.998549i	$0.482852\pi$
$332$	−37.5606	−2.06140
$333$	9.40069	0.515155
$334$	32.2055	1.76221
$335$	29.7264	1.62413
$336$	34.8059	1.89882
$337$	−19.2861	−1.05058	−0.525292	−	0.850922i	$-0.676044\pi$
$337$	−19.2861	−1.05058	−0.525292	+	0.850922i	$0.676044\pi$
$338$	−2.63597	−0.143378
$339$	16.4337	0.892556
$340$	34.5931	1.87607
$341$	−26.2639	−1.42227
$342$	0.344504	0.0186286
$343$	18.1799	0.981620
$344$	−5.47700	−0.295300
$345$	−6.57944	−0.354225
$346$	21.5669	1.15944
$347$	15.7967	0.848011	0.424006	−	0.905660i	$-0.360624\pi$
$347$	15.7967	0.848011	0.424006	+	0.905660i	$0.360624\pi$
$348$	−29.5942	−1.58642
$349$	6.34588	0.339687	0.169844	−	0.985471i	$-0.445674\pi$
$349$	6.34588	0.339687	0.169844	+	0.985471i	$0.445674\pi$
$350$	81.4563	4.35402
$351$	5.50572	0.293874
$352$	33.6847	1.79540
$353$	−22.7655	−1.21168	−0.605841	−	0.795585i	$-0.707163\pi$
$353$	−22.7655	−1.21168	−0.605841	+	0.795585i	$0.707163\pi$
$354$	−5.05767	−0.268812
$355$	18.5337	0.983664
$356$	−20.3561	−1.07887
$357$	−5.66047	−0.299584
$358$	16.2689	0.859836
$359$	1.54995	0.0818033	0.0409016	−	0.999163i	$-0.486977\pi$
$359$	1.54995	0.0818033	0.0409016	+	0.999163i	$0.486977\pi$
$360$	−47.6103	−2.50928
$361$	−18.9925	−0.999605
$362$	−47.5011	−2.49660
$363$	4.37615	0.229688
$364$	−13.3206	−0.698188
$365$	33.5884	1.75810
$366$	32.2365	1.68503
$367$	−1.54250	−0.0805179	−0.0402589	−	0.999189i	$-0.512818\pi$
$367$	−1.54250	−0.0805179	−0.0402589	+	0.999189i	$0.512818\pi$
$368$	−14.0558	−0.732709
$369$	1.26384	0.0657930
$370$	−66.6581	−3.46539
$371$	5.20612	0.270288
$372$	−58.2716	−3.02124
$373$	−30.0047	−1.55359	−0.776793	−	0.629757i	$-0.783155\pi$
$373$	−30.0047	−1.55359	−0.776793	+	0.629757i	$0.783155\pi$
$374$	−12.3619	−0.639220
$375$	32.1166	1.65849
$376$	38.2896	1.97464
$377$	4.89807	0.252263
$378$	39.0679	2.00944
$379$	2.15266	0.110575	0.0552875	−	0.998470i	$-0.482392\pi$
$379$	2.15266	0.110575	0.0552875	+	0.998470i	$0.482392\pi$
$380$	−1.73966	−0.0892429
$381$	9.98756	0.511678
$382$	−14.5056	−0.742171
$383$	−29.9175	−1.52871	−0.764356	−	0.644795i	$-0.776943\pi$
$383$	−29.9175	−1.52871	−0.764356	+	0.644795i	$0.776943\pi$
$384$	6.57178	0.335365
$385$	−29.7593	−1.51667
$386$	−45.9262	−2.33758
$387$	−1.06352	−0.0540619
$388$	−43.9875	−2.23313
$389$	2.60257	0.131956	0.0659778	−	0.997821i	$-0.478983\pi$
$389$	2.60257	0.131956	0.0659778	+	0.997821i	$0.478983\pi$
$390$	−13.0658	−0.661611
$391$	2.28589	0.115602
$392$	−1.91628	−0.0967865
$393$	14.9223	0.752730
$394$	−31.7737	−1.60074
$395$	59.8083	3.00928
$396$	20.3357	1.02191
$397$	31.0587	1.55879	0.779395	−	0.626533i	$-0.215527\pi$
$397$	31.0587	1.55879	0.779395	+	0.626533i	$0.215527\pi$
$398$	−27.9138	−1.39919
$399$	0.284662	0.0142509
$400$	121.557	6.07786
$401$	−4.05477	−0.202485	−0.101243	−	0.994862i	$-0.532282\pi$
$401$	−4.05477	−0.202485	−0.101243	+	0.994862i	$0.532282\pi$
$402$	−23.5687	−1.17550
$403$	9.64439	0.480421
$404$	−38.8520	−1.93296
$405$	8.91193	0.442837
$406$	34.7561	1.72492
$407$	16.9640	0.840873
$408$	−16.3418	−0.809038
$409$	9.16597	0.453228	0.226614	−	0.973985i	$-0.427234\pi$
$409$	9.16597	0.453228	0.226614	+	0.973985i	$0.427234\pi$
$410$	−8.96160	−0.442582
$411$	2.88673	0.142392
$412$	62.1221	3.06053
$413$	4.23012	0.208150
$414$	−5.28020	−0.259508
$415$	30.8138	1.51259
$416$	−12.3694	−0.606458
$417$	24.0779	1.17910
$418$	0.621674	0.0304071
$419$	21.8996	1.06987	0.534934	−	0.844894i	$-0.320337\pi$
$419$	21.8996	1.06987	0.534934	+	0.844894i	$0.320337\pi$
$420$	−66.0266	−3.22177
$421$	2.60372	0.126898	0.0634489	−	0.997985i	$-0.479790\pi$
$421$	2.60372	0.126898	0.0634489	+	0.997985i	$0.479790\pi$
$422$	−0.780686	−0.0380032
$423$	7.43507	0.361506
$424$	15.0301	0.729924
$425$	−19.7688	−0.958927
$426$	−14.6945	−0.711951
$427$	−26.9619	−1.30478
$428$	30.2507	1.46222
$429$	3.32514	0.160539
$430$	7.54119	0.363669
$431$	−4.39834	−0.211861	−0.105930	−	0.994374i	$-0.533782\pi$
$431$	−4.39834	−0.211861	−0.105930	+	0.994374i	$0.533782\pi$
$432$	58.3010	2.80501
$433$	−34.9137	−1.67785	−0.838923	−	0.544251i	$-0.816814\pi$
$433$	−34.9137	−1.67785	−0.838923	+	0.544251i	$0.816814\pi$
$434$	68.4354	3.28500
$435$	24.2784	1.16406
$436$	−14.0915	−0.674862
$437$	−0.114956	−0.00549909
$438$	−26.6308	−1.27247
$439$	−13.7405	−0.655796	−0.327898	−	0.944713i	$-0.606340\pi$
$439$	−13.7405	−0.655796	−0.327898	+	0.944713i	$0.606340\pi$
$440$	−85.9149	−4.09583
$441$	−0.372102	−0.0177191
$442$	4.53943	0.215918
$443$	4.60567	0.218822	0.109411	−	0.993997i	$-0.465104\pi$
$443$	4.60567	0.218822	0.109411	+	0.993997i	$0.465104\pi$
$444$	37.6378	1.78621
$445$	16.6997	0.791640
$446$	25.0209	1.18477
$447$	19.6179	0.927896
$448$	−30.7606	−1.45330
$449$	4.24072	0.200132	0.100066	−	0.994981i	$-0.468095\pi$
$449$	4.24072	0.200132	0.100066	+	0.994981i	$0.468095\pi$
$450$	45.6642	2.15263
$451$	2.28066	0.107392
$452$	−66.5990	−3.13255
$453$	−14.2940	−0.671592
$454$	−40.4901	−1.90029
$455$	10.9279	0.512308
$456$	0.821818	0.0384851
$457$	2.42829	0.113591	0.0567954	−	0.998386i	$-0.481912\pi$
$457$	2.42829	0.113591	0.0567954	+	0.998386i	$0.481912\pi$
$458$	−66.7505	−3.11905
$459$	−9.48147	−0.442557
$460$	26.6638	1.24320
$461$	−29.9240	−1.39370	−0.696850	−	0.717217i	$-0.745416\pi$
$461$	−29.9240	−1.39370	−0.696850	+	0.717217i	$0.745416\pi$
$462$	23.5948	1.09773
$463$	−31.2717	−1.45332	−0.726660	−	0.686997i	$-0.758929\pi$
$463$	−31.2717	−1.45332	−0.726660	+	0.686997i	$0.758929\pi$
$464$	51.8665	2.40784
$465$	47.8046	2.21689
$466$	−56.9186	−2.63670
$467$	−15.2978	−0.707899	−0.353950	−	0.935264i	$-0.615162\pi$
$467$	−15.2978	−0.707899	−0.353950	+	0.935264i	$0.615162\pi$
$468$	−7.46748	−0.345184
$469$	19.7123	0.910231
$470$	−52.7203	−2.43181
$471$	6.18661	0.285064
$472$	12.2123	0.562119
$473$	−1.91918	−0.0882438
$474$	−47.4193	−2.17804
$475$	0.994160	0.0456152
$476$	22.9395	1.05143
$477$	2.91853	0.133630
$478$	39.3103	1.79801
$479$	−29.8257	−1.36277	−0.681387	−	0.731924i	$-0.738623\pi$
$479$	−29.8257	−1.36277	−0.681387	+	0.731924i	$0.738623\pi$
$480$	−61.3116	−2.79848
$481$	−6.22935	−0.284034
$482$	−33.5497	−1.52815
$483$	−4.36300	−0.198523
$484$	−17.7347	−0.806123
$485$	36.0864	1.63860
$486$	36.4728	1.65444
$487$	15.9463	0.722596	0.361298	−	0.932450i	$-0.382334\pi$
$487$	15.9463	0.722596	0.361298	+	0.932450i	$0.382334\pi$
$488$	−77.8389	−3.52360
$489$	22.4851	1.01681
$490$	2.63849	0.119195
$491$	−28.0282	−1.26490	−0.632448	−	0.774602i	$-0.717950\pi$
$491$	−28.0282	−1.26490	−0.632448	+	0.774602i	$0.717950\pi$
$492$	5.06008	0.228126
$493$	−8.43502	−0.379894
$494$	−0.228285	−0.0102710
$495$	−16.6829	−0.749843
$496$	102.126	4.58559
$497$	12.2901	0.551288
$498$	−24.4309	−1.09477
$499$	−39.9235	−1.78722	−0.893612	−	0.448841i	$-0.851837\pi$
$499$	−39.9235	−1.78722	−0.893612	+	0.448841i	$0.851837\pi$
$500$	−130.155	−5.82072
$501$	14.9182	0.666494
$502$	−21.9824	−0.981121
$503$	−42.8372	−1.91001	−0.955007	−	0.296582i	$-0.904153\pi$
$503$	−42.8372	−1.91001	−0.955007	+	0.296582i	$0.904153\pi$
$504$	−31.5716	−1.40631
$505$	31.8733	1.41834
$506$	−9.52837	−0.423588
$507$	−1.22103	−0.0542276
$508$	−40.4754	−1.79581
$509$	−2.60255	−0.115356	−0.0576780	−	0.998335i	$-0.518370\pi$
$509$	−2.60255	−0.115356	−0.0576780	+	0.998335i	$0.518370\pi$
$510$	22.5007	0.996348
$511$	22.2733	0.985315
$512$	33.6091	1.48533
$513$	0.476817	0.0210520
$514$	−22.6464	−0.998891
$515$	−50.9635	−2.24572
$516$	−4.25806	−0.187451
$517$	13.4169	0.590076
$518$	−44.2027	−1.94215
$519$	9.99015	0.438519
$520$	31.5489	1.38351
$521$	7.53227	0.329995	0.164997	−	0.986294i	$-0.447238\pi$
$521$	7.53227	0.329995	0.164997	+	0.986294i	$0.447238\pi$
$522$	19.4842	0.852798
$523$	−10.3918	−0.454401	−0.227200	−	0.973848i	$-0.572957\pi$
$523$	−10.3918	−0.454401	−0.227200	+	0.973848i	$0.572957\pi$
$524$	−60.4739	−2.64181
$525$	37.7320	1.64676
$526$	−42.4153	−1.84940
$527$	−16.6087	−0.723487
$528$	35.2104	1.53234
$529$	−21.2381	−0.923394
$530$	−20.6946	−0.898918
$531$	2.37139	0.102910
$532$	−1.15362	−0.0500156
$533$	−0.837482	−0.0362754
$534$	−13.2404	−0.572969
$535$	−24.8170	−1.07293
$536$	56.9095	2.45812
$537$	7.53603	0.325204
$538$	1.05985	0.0456936
$539$	−0.671475	−0.0289225
$540$	−110.597	−4.75932
$541$	3.65856	0.157294	0.0786470	−	0.996903i	$-0.474940\pi$
$541$	3.65856	0.157294	0.0786470	+	0.996903i	$0.474940\pi$
$542$	−27.3932	−1.17664
$543$	−22.0034	−0.944254
$544$	21.3014	0.913292
$545$	11.5604	0.495192
$546$	−8.66424	−0.370795
$547$	12.1109	0.517826	0.258913	−	0.965901i	$-0.416636\pi$
$547$	12.1109	0.517826	0.258913	+	0.965901i	$0.416636\pi$
$548$	−11.6987	−0.499745
$549$	−15.1147	−0.645082
$550$	82.4031	3.51368
$551$	0.424192	0.0180712
$552$	−12.5960	−0.536120
$553$	39.6604	1.68653
$554$	71.2399	3.02669
$555$	−30.8772	−1.31066
$556$	−97.5779	−4.13822
$557$	−11.7612	−0.498336	−0.249168	−	0.968460i	$-0.580157\pi$
$557$	−11.7612	−0.498336	−0.249168	+	0.968460i	$0.580157\pi$
$558$	38.3647	1.62411
$559$	0.704741	0.0298074
$560$	115.717	4.88995
$561$	−5.72626	−0.241763
$562$	14.9923	0.632411
$563$	−11.5303	−0.485944	−0.242972	−	0.970033i	$-0.578122\pi$
$563$	−11.5303	−0.485944	−0.242972	+	0.970033i	$0.578122\pi$
$564$	29.7680	1.25346
$565$	54.6363	2.29857
$566$	48.6583	2.04526
$567$	5.90973	0.248185
$568$	35.4816	1.48878
$569$	24.2414	1.01625	0.508127	−	0.861282i	$-0.330338\pi$
$569$	24.2414	1.01625	0.508127	+	0.861282i	$0.330338\pi$
$570$	−1.13155	−0.0473953
$571$	1.67954	0.0702866	0.0351433	−	0.999382i	$-0.488811\pi$
$571$	1.67954	0.0702866	0.0351433	+	0.999382i	$0.488811\pi$
$572$	−13.4754	−0.563435
$573$	−6.71925	−0.280701
$574$	−5.94267	−0.248042
$575$	−15.2375	−0.635446
$576$	−17.2443	−0.718513
$577$	−40.8356	−1.70001	−0.850005	−	0.526775i	$-0.823401\pi$
$577$	−40.8356	−1.70001	−0.850005	+	0.526775i	$0.823401\pi$
$578$	36.9940	1.53875
$579$	−21.2738	−0.884110
$580$	−98.3903	−4.08544
$581$	20.4334	0.847722
$582$	−28.6113	−1.18597
$583$	5.26663	0.218121
$584$	64.3031	2.66088
$585$	6.12615	0.253285
$586$	13.9080	0.574535
$587$	6.49484	0.268071	0.134035	−	0.990977i	$-0.457206\pi$
$587$	6.49484	0.268071	0.134035	+	0.990977i	$0.457206\pi$
$588$	−1.48980	−0.0614381
$589$	0.835242	0.0344156
$590$	−16.8150	−0.692262
$591$	−14.7182	−0.605424
$592$	−65.9636	−2.71109
$593$	−1.89926	−0.0779933	−0.0389966	−	0.999239i	$-0.512416\pi$
$593$	−1.89926	−0.0779933	−0.0389966	+	0.999239i	$0.512416\pi$
$594$	39.5220	1.62161
$595$	−18.8191	−0.771507
$596$	−79.5033	−3.25658
$597$	−12.9302	−0.529197
$598$	3.49892	0.143081
$599$	1.71612	0.0701188	0.0350594	−	0.999385i	$-0.488838\pi$
$599$	1.71612	0.0701188	0.0350594	+	0.999385i	$0.488838\pi$
$600$	108.932	4.44714
$601$	15.0378	0.613406	0.306703	−	0.951805i	$-0.400774\pi$
$601$	15.0378	0.613406	0.306703	+	0.951805i	$0.400774\pi$
$602$	5.00076	0.203816
$603$	11.0507	0.450018
$604$	57.9278	2.35705
$605$	14.5491	0.591507
$606$	−25.2709	−1.02656
$607$	−9.15642	−0.371647	−0.185824	−	0.982583i	$-0.559495\pi$
$607$	−9.15642	−0.371647	−0.185824	+	0.982583i	$0.559495\pi$
$608$	−1.07124	−0.0434444
$609$	16.0996	0.652390
$610$	107.175	4.33939
$611$	−4.92684	−0.199318
$612$	12.8598	0.519828
$613$	−22.1665	−0.895297	−0.447649	−	0.894209i	$-0.647738\pi$
$613$	−22.1665	−0.895297	−0.447649	+	0.894209i	$0.647738\pi$
$614$	−24.7251	−0.997823
$615$	−4.15117	−0.167391
$616$	−56.9724	−2.29548
$617$	−1.00000	−0.0402585
$617$	−1.00000	−0.0402585
$618$	40.4067	1.62540
$619$	26.7150	1.07377	0.536883	−	0.843657i	$-0.319602\pi$
$619$	26.7150	1.07377	0.536883	+	0.843657i	$0.319602\pi$
$620$	−193.732	−7.78048
$621$	−7.30816	−0.293266
$622$	1.24597	0.0499589
$623$	11.0740	0.443669
$624$	−12.9296	−0.517600
$625$	49.3794	1.97518
$626$	80.4932	3.21715
$627$	0.287970	0.0115004
$628$	−25.0718	−1.00047
$629$	10.7276	0.427739
$630$	43.4704	1.73190
$631$	23.0815	0.918862	0.459431	−	0.888214i	$-0.348053\pi$
$631$	23.0815	0.918862	0.459431	+	0.888214i	$0.348053\pi$
$632$	114.500	4.55455
$633$	−0.361627	−0.0143734
$634$	70.5394	2.80148
$635$	33.2051	1.31771
$636$	11.6850	0.463341
$637$	0.246573	0.00976956
$638$	35.1601	1.39200
$639$	6.88982	0.272557
$640$	21.8489	0.863652
$641$	8.44055	0.333382	0.166691	−	0.986009i	$-0.446692\pi$
$641$	8.44055	0.333382	0.166691	+	0.986009i	$0.446692\pi$
$642$	19.6763	0.776561
$643$	−37.6563	−1.48502	−0.742510	−	0.669835i	$-0.766365\pi$
$643$	−37.6563	−1.48502	−0.742510	+	0.669835i	$0.766365\pi$
$644$	17.6814	0.696746
$645$	3.49321	0.137545
$646$	0.393132	0.0154676
$647$	16.7156	0.657160	0.328580	−	0.944476i	$-0.393430\pi$
$647$	16.7156	0.657160	0.328580	+	0.944476i	$0.393430\pi$
$648$	17.0614	0.670234
$649$	4.27929	0.167977
$650$	−30.2593	−1.18687
$651$	31.7005	1.24244
$652$	−91.1228	−3.56865
$653$	42.0684	1.64626	0.823131	−	0.567851i	$-0.192225\pi$
$653$	42.0684	1.64626	0.823131	+	0.567851i	$0.192225\pi$
$654$	−9.16569	−0.358407
$655$	49.6114	1.93848
$656$	−8.86824	−0.346246
$657$	12.4864	0.487140
$658$	−34.9602	−1.36289
$659$	32.8897	1.28120	0.640601	−	0.767874i	$-0.278685\pi$
$659$	32.8897	1.28120	0.640601	+	0.767874i	$0.278685\pi$
$660$	−66.7940	−2.59995
$661$	−18.7326	−0.728612	−0.364306	−	0.931279i	$-0.618694\pi$
$661$	−18.7326	−0.728612	−0.364306	+	0.931279i	$0.618694\pi$
$662$	−5.16470	−0.200732
$663$	2.10274	0.0816637
$664$	58.9913	2.28931
$665$	0.946400	0.0366998
$666$	−24.7799	−0.960201
$667$	−6.50158	−0.251742
$668$	−60.4571	−2.33916
$669$	11.5901	0.448100
$670$	−78.3577	−3.02722
$671$	−27.2753	−1.05295
$672$	−40.6573	−1.56839
$673$	27.4995	1.06003	0.530015	−	0.847988i	$-0.322186\pi$
$673$	27.4995	1.06003	0.530015	+	0.847988i	$0.322186\pi$
$674$	50.8376	1.95819
$675$	63.2023	2.43266
$676$	4.94831	0.190320
$677$	20.6451	0.793454	0.396727	−	0.917937i	$-0.370146\pi$
$677$	20.6451	0.793454	0.396727	+	0.917937i	$0.370146\pi$
$678$	−43.3187	−1.66364
$679$	23.9298	0.918341
$680$	−54.3306	−2.08349
$681$	−18.7557	−0.718721
$682$	69.2308	2.65099
$683$	39.7910	1.52256	0.761280	−	0.648423i	$-0.224571\pi$
$683$	39.7910	1.52256	0.761280	+	0.648423i	$0.224571\pi$
$684$	−0.646713	−0.0247277
$685$	9.59736	0.366696
$686$	−47.9215	−1.82965
$687$	−30.9200	−1.17967
$688$	7.46262	0.284510
$689$	−1.93396	−0.0736780
$690$	17.3432	0.660244
$691$	−24.8833	−0.946606	−0.473303	−	0.880900i	$-0.656938\pi$
$691$	−24.8833	−0.946606	−0.473303	+	0.880900i	$0.656938\pi$
$692$	−40.4860	−1.53905
$693$	−11.0629	−0.420244
$694$	−41.6395	−1.58062
$695$	80.0507	3.03649
$696$	46.4796	1.76181
$697$	1.44224	0.0546286
$698$	−16.7275	−0.633146
$699$	−26.3657	−0.997242
$700$	−152.912	−5.77954
$701$	−41.2443	−1.55778	−0.778888	−	0.627164i	$-0.784216\pi$
$701$	−41.2443	−1.55778	−0.778888	+	0.627164i	$0.784216\pi$
$702$	−14.5129	−0.547754
$703$	−0.539486	−0.0203471
$704$	−31.1182	−1.17281
$705$	−24.4210	−0.919748
$706$	60.0089	2.25847
$707$	21.1360	0.794900
$708$	9.49441	0.356822
$709$	−27.7477	−1.04209	−0.521044	−	0.853530i	$-0.674457\pi$
$709$	−27.7477	−1.04209	−0.521044	+	0.853530i	$0.674457\pi$
$710$	−48.8541	−1.83346
$711$	22.2335	0.833822
$712$	31.9705	1.19815
$713$	−12.8017	−0.479429
$714$	14.9208	0.558397
$715$	11.0549	0.413431
$716$	−30.5404	−1.14135
$717$	18.2092	0.680035
$718$	−4.08562	−0.152474
$719$	−16.6786	−0.622008	−0.311004	−	0.950409i	$-0.600665\pi$
$719$	−16.6786	−0.622008	−0.311004	+	0.950409i	$0.600665\pi$
$720$	64.8708	2.41759
$721$	−33.7952	−1.25860
$722$	50.0636	1.86317
$723$	−15.5408	−0.577969
$724$	89.1705	3.31400
$725$	56.2268	2.08821
$726$	−11.5354	−0.428118
$727$	−13.8657	−0.514249	−0.257125	−	0.966378i	$-0.582775\pi$
$727$	−13.8657	−0.514249	−0.257125	+	0.966378i	$0.582775\pi$
$728$	20.9209	0.775378
$729$	23.4809	0.869661
$730$	−88.5379	−3.27693
$731$	−1.21364	−0.0448882
$732$	−60.5153	−2.23671
$733$	−27.5291	−1.01681	−0.508406	−	0.861118i	$-0.669765\pi$
$733$	−27.5291	−1.01681	−0.508406	+	0.861118i	$0.669765\pi$
$734$	4.06598	0.150078
$735$	1.22219	0.0450813
$736$	16.4188	0.605205
$737$	19.9415	0.734553
$738$	−3.33144	−0.122632
$739$	−11.8694	−0.436624	−0.218312	−	0.975879i	$-0.570055\pi$
$739$	−11.8694	−0.436624	−0.218312	+	0.975879i	$0.570055\pi$
$740$	125.133	4.59996
$741$	−0.105746	−0.00388466
$742$	−13.7231	−0.503792
$743$	−45.4923	−1.66895	−0.834475	−	0.551046i	$-0.814229\pi$
$743$	−45.4923	−1.66895	−0.834475	+	0.551046i	$0.814229\pi$
$744$	91.5193	3.35526
$745$	65.2227	2.38957
$746$	79.0914	2.89574
$747$	11.4549	0.419114
$748$	23.2062	0.848502
$749$	−16.4568	−0.601318
$750$	−84.6582	−3.09128
$751$	48.7531	1.77903	0.889513	−	0.456910i	$-0.151044\pi$
$751$	48.7531	1.77903	0.889513	+	0.456910i	$0.151044\pi$
$752$	−52.1711	−1.90248
$753$	−10.1826	−0.371075
$754$	−12.9111	−0.470196
$755$	−47.5226	−1.72953
$756$	−73.3394	−2.66733
$757$	−49.2135	−1.78869	−0.894347	−	0.447374i	$-0.852359\pi$
$757$	−49.2135	−1.78869	−0.894347	+	0.447374i	$0.852359\pi$
$758$	−5.67435	−0.206102
$759$	−4.41371	−0.160208
$760$	2.73226	0.0991093
$761$	−7.25299	−0.262921	−0.131460	−	0.991321i	$-0.541967\pi$
$761$	−7.25299	−0.262921	−0.131460	+	0.991321i	$0.541967\pi$
$762$	−26.3269	−0.953721
$763$	7.66597	0.277527
$764$	27.2303	0.985159
$765$	−10.5499	−0.381433
$766$	78.8614	2.84938
$767$	−1.57140	−0.0567399
$768$	10.5821	0.381849
$769$	−1.67203	−0.0602951	−0.0301475	−	0.999545i	$-0.509598\pi$
$769$	−1.67203	−0.0602951	−0.0301475	+	0.999545i	$0.509598\pi$
$770$	78.4443	2.82694
$771$	−10.4902	−0.377796
$772$	86.2140	3.10291
$773$	49.7425	1.78911	0.894557	−	0.446954i	$-0.147491\pi$
$773$	49.7425	1.78911	0.894557	+	0.446954i	$0.147491\pi$
$774$	2.80341	0.100766
$775$	110.712	3.97688
$776$	69.0853	2.48002
$777$	−20.4755	−0.734553
$778$	−6.86029	−0.245953
$779$	−0.0725293	−0.00259863
$780$	24.5274	0.878223
$781$	12.4330	0.444887
$782$	−6.02552	−0.215472
$783$	26.9674	0.963736
$784$	2.61100	0.0932499
$785$	20.5683	0.734115
$786$	−39.3346	−1.40302
$787$	−37.5307	−1.33782	−0.668912	−	0.743342i	$-0.733240\pi$
$787$	−37.5307	−1.33782	−0.668912	+	0.743342i	$0.733240\pi$
$788$	59.6466	2.12482
$789$	−19.6475	−0.699470
$790$	−157.653	−5.60903
$791$	36.2307	1.28822
$792$	−31.9385	−1.13489
$793$	10.0158	0.355670
$794$	−81.8696	−2.90544
$795$	−9.58612	−0.339985
$796$	52.4006	1.85729
$797$	−24.9388	−0.883377	−0.441689	−	0.897168i	$-0.645620\pi$
$797$	−24.9388	−0.883377	−0.441689	+	0.897168i	$0.645620\pi$
$798$	−0.750358	−0.0265624
$799$	8.48456	0.300162
$800$	−141.993	−5.02021
$801$	6.20804	0.219350
$802$	10.6882	0.377414
$803$	22.5322	0.795145
$804$	44.2439	1.56036
$805$	−14.5054	−0.511249
$806$	−25.4223	−0.895462
$807$	0.490943	0.0172820
$808$	61.0195	2.14666
$809$	10.8787	0.382474	0.191237	−	0.981544i	$-0.438750\pi$
$809$	10.8787	0.382474	0.191237	+	0.981544i	$0.438750\pi$
$810$	−23.4915	−0.825408
$811$	48.5769	1.70576	0.852882	−	0.522104i	$-0.174853\pi$
$811$	48.5769	1.70576	0.852882	+	0.522104i	$0.174853\pi$
$812$	−65.2451	−2.28966
$813$	−12.6890	−0.445023
$814$	−44.7165	−1.56731
$815$	74.7551	2.61856
$816$	22.2663	0.779476
$817$	0.0610334	0.00213529
$818$	−24.1612	−0.844775
$819$	4.06241	0.141952
$820$	16.8230	0.587484
$821$	−30.8281	−1.07591	−0.537954	−	0.842974i	$-0.680803\pi$
$821$	−30.8281	−1.07591	−0.537954	+	0.842974i	$0.680803\pi$
$822$	−7.60932	−0.265405
$823$	−6.83149	−0.238131	−0.119065	−	0.992886i	$-0.537990\pi$
$823$	−6.83149	−0.238131	−0.119065	+	0.992886i	$0.537990\pi$
$824$	−97.5668	−3.39890
$825$	38.1706	1.32893
$826$	−11.1504	−0.387974
$827$	−12.7492	−0.443332	−0.221666	−	0.975123i	$-0.571150\pi$
$827$	−12.7492	−0.443332	−0.221666	+	0.975123i	$0.571150\pi$
$828$	9.91215	0.344471
$829$	5.68097	0.197308	0.0986541	−	0.995122i	$-0.468546\pi$
$829$	5.68097	0.197308	0.0986541	+	0.995122i	$0.468546\pi$
$830$	−81.2242	−2.81933
$831$	32.9996	1.14474
$832$	11.4269	0.396157
$833$	−0.424626	−0.0147124
$834$	−63.4686	−2.19774
$835$	49.5976	1.71640
$836$	−1.16702	−0.0403624
$837$	53.0993	1.83538
$838$	−57.7267	−1.99414
$839$	−40.6605	−1.40376	−0.701878	−	0.712297i	$-0.747655\pi$
$839$	−40.6605	−1.40376	−0.701878	+	0.712297i	$0.747655\pi$
$840$	103.699	3.57796
$841$	−5.00893	−0.172722
$842$	−6.86332	−0.236526
$843$	6.94469	0.239188
$844$	1.46553	0.0504455
$845$	−4.05948	−0.139650
$846$	−19.5986	−0.673813
$847$	9.64791	0.331506
$848$	−20.4790	−0.703253
$849$	22.5394	0.773549
$850$	52.1098	1.78735
$851$	8.26869	0.283447
$852$	27.5850	0.945045
$853$	−13.9344	−0.477105	−0.238552	−	0.971130i	$-0.576673\pi$
$853$	−13.9344	−0.477105	−0.238552	+	0.971130i	$0.576673\pi$
$854$	71.0706	2.43198
$855$	0.530549	0.0181444
$856$	−47.5108	−1.62388
$857$	22.1491	0.756599	0.378300	−	0.925683i	$-0.376509\pi$
$857$	22.1491	0.756599	0.378300	+	0.925683i	$0.376509\pi$
$858$	−8.76495	−0.299230
$859$	31.1784	1.06379	0.531897	−	0.846809i	$-0.321479\pi$
$859$	31.1784	1.06379	0.531897	+	0.846809i	$0.321479\pi$
$860$	−14.1565	−0.482734
$861$	−2.75275	−0.0938134
$862$	11.5939	0.394889
$863$	46.8621	1.59520	0.797602	−	0.603184i	$-0.206102\pi$
$863$	46.8621	1.59520	0.797602	+	0.603184i	$0.206102\pi$
$864$	−68.1023	−2.31689
$865$	33.2138	1.12930
$866$	92.0313	3.12735
$867$	17.1363	0.581978
$868$	−128.469	−4.36052
$869$	40.1214	1.36103
$870$	−63.9970	−2.16970
$871$	−7.32271	−0.248120
$872$	22.1317	0.749473
$873$	13.4150	0.454028
$874$	0.303020	0.0102498
$875$	70.8061	2.39368
$876$	49.9920	1.68907
$877$	33.5518	1.13296	0.566481	−	0.824075i	$-0.308304\pi$
$877$	33.5518	1.13296	0.566481	+	0.824075i	$0.308304\pi$
$878$	36.2194	1.22234
$879$	6.44244	0.217298
$880$	117.062	3.94617
$881$	13.2615	0.446791	0.223396	−	0.974728i	$-0.428286\pi$
$881$	13.2615	0.446791	0.223396	+	0.974728i	$0.428286\pi$
$882$	0.980848	0.0330269
$883$	−25.8177	−0.868836	−0.434418	−	0.900711i	$-0.643046\pi$
$883$	−25.8177	−0.868836	−0.434418	+	0.900711i	$0.643046\pi$
$884$	−8.52154	−0.286611
$885$	−7.78900	−0.261824
$886$	−12.1404	−0.407864
$887$	29.1463	0.978636	0.489318	−	0.872105i	$-0.337246\pi$
$887$	29.1463	0.978636	0.489318	+	0.872105i	$0.337246\pi$
$888$	−59.1126	−1.98369
$889$	22.0192	0.738499
$890$	−44.0197	−1.47554
$891$	5.97842	0.200285
$892$	−46.9699	−1.57267
$893$	−0.426683	−0.0142784
$894$	−51.7122	−1.72951
$895$	25.0546	0.837484
$896$	14.4885	0.484028
$897$	1.62076	0.0541156
$898$	−11.1784	−0.373028
$899$	47.2389	1.57551
$900$	−85.7221	−2.85740
$901$	3.33050	0.110955
$902$	−6.01174	−0.200169
$903$	2.31644	0.0770863
$904$	104.598	3.47888
$905$	−73.1534	−2.43170
$906$	37.6786	1.25179
$907$	13.0633	0.433758	0.216879	−	0.976198i	$-0.430412\pi$
$907$	13.0633	0.433758	0.216879	+	0.976198i	$0.430412\pi$
$908$	76.0092	2.52245
$909$	11.8488	0.392999
$910$	−28.8056	−0.954895
$911$	−10.6675	−0.353430	−0.176715	−	0.984262i	$-0.556547\pi$
$911$	−10.6675	−0.353430	−0.176715	+	0.984262i	$0.556547\pi$
$912$	−1.11976	−0.0370789
$913$	20.6709	0.684108
$914$	−6.40090	−0.211723
$915$	49.6454	1.64123
$916$	125.306	4.14023
$917$	32.8986	1.08641
$918$	24.9928	0.824886
$919$	−51.1583	−1.68756	−0.843779	−	0.536691i	$-0.819674\pi$
$919$	−51.1583	−1.68756	−0.843779	+	0.536691i	$0.819674\pi$
$920$	−41.8772	−1.38065
$921$	−11.4531	−0.377392
$922$	78.8787	2.59773
$923$	−4.56552	−0.150276
$924$	−44.2928	−1.45713
$925$	−71.5091	−2.35121
$926$	82.4312	2.70886
$927$	−18.9455	−0.622252
$928$	−60.5860	−1.98883
$929$	−36.8341	−1.20849	−0.604244	−	0.796799i	$-0.706525\pi$
$929$	−36.8341	−1.20849	−0.604244	+	0.796799i	$0.706525\pi$
$930$	−126.011	−4.13208
$931$	0.0213542	0.000699855 0
$932$	106.849	3.49996
$933$	0.577156	0.0188952
$934$	40.3246	1.31946
$935$	−19.0378	−0.622603
$936$	11.7282	0.383347
$937$	−6.05191	−0.197707	−0.0988536	−	0.995102i	$-0.531518\pi$
$937$	−6.05191	−0.197707	−0.0988536	+	0.995102i	$0.531518\pi$
$938$	−51.9610	−1.69659
$939$	37.2859	1.21678
$940$	98.9682	3.22799
$941$	57.6069	1.87793	0.938966	−	0.344009i	$-0.111785\pi$
$941$	57.6069	1.87793	0.938966	+	0.344009i	$0.111785\pi$
$942$	−16.3077	−0.531333
$943$	1.11165	0.0362004
$944$	−16.6398	−0.541579
$945$	60.1660	1.95720
$946$	5.05888	0.164478
$947$	−8.42493	−0.273773	−0.136887	−	0.990587i	$-0.543710\pi$
$947$	−8.42493	−0.273773	−0.136887	+	0.990587i	$0.543710\pi$
$948$	89.0170	2.89114
$949$	−8.27407	−0.268588
$950$	−2.62057	−0.0850226
$951$	32.6751	1.05956
$952$	−36.0280	−1.16768
$953$	−26.4238	−0.855950	−0.427975	−	0.903791i	$-0.640773\pi$
$953$	−26.4238	−0.855950	−0.427975	+	0.903791i	$0.640773\pi$
$954$	−7.69315	−0.249075
$955$	−22.3391	−0.722878
$956$	−73.7944	−2.38668
$957$	16.2868	0.526476
$958$	78.6196	2.54008
$959$	6.36426	0.205513
$960$	56.6401	1.82805
$961$	62.0143	2.00046
$962$	16.4203	0.529413
$963$	−9.22563	−0.297292
$964$	62.9805	2.02847
$965$	−70.7280	−2.27682
$966$	11.5007	0.370029
$967$	15.6308	0.502652	0.251326	−	0.967902i	$-0.419133\pi$
$967$	15.6308	0.502652	0.251326	+	0.967902i	$0.419133\pi$
$968$	27.8535	0.895246
$969$	0.182106	0.00585008
$970$	−95.1224	−3.05420
$971$	39.3402	1.26249	0.631244	−	0.775584i	$-0.282545\pi$
$971$	39.3402	1.26249	0.631244	+	0.775584i	$0.282545\pi$
$972$	−68.4678	−2.19611
$973$	53.0836	1.70178
$974$	−42.0339	−1.34685
$975$	−14.0166	−0.448891
$976$	106.058	3.39485
$977$	11.0849	0.354638	0.177319	−	0.984153i	$-0.443258\pi$
$977$	11.0849	0.354638	0.177319	+	0.984153i	$0.443258\pi$
$978$	−59.2699	−1.89524
$979$	11.2027	0.358039
$980$	−4.95305	−0.158219
$981$	4.29752	0.137209
$982$	73.8815	2.35765
$983$	−53.1440	−1.69503	−0.847515	−	0.530772i	$-0.821902\pi$
$983$	−53.1440	−1.69503	−0.847515	+	0.530772i	$0.821902\pi$
$984$	−7.94718	−0.253347
$985$	−48.9327	−1.55913
$986$	22.2344	0.708088
$987$	−16.1942	−0.515467
$988$	0.428543	0.0136338
$989$	−0.935457	−0.0297458
$990$	43.9757	1.39764
$991$	−2.10378	−0.0668287	−0.0334144	−	0.999442i	$-0.510638\pi$
$991$	−2.10378	−0.0668287	−0.0334144	+	0.999442i	$0.510638\pi$
$992$	−119.295	−3.78762
$993$	−2.39238	−0.0759200
$994$	−32.3964	−1.02755
$995$	−42.9883	−1.36282
$996$	45.8624	1.45321
$997$	57.2012	1.81158	0.905790	−	0.423727i	$-0.139279\pi$
$997$	57.2012	1.81158	0.905790	+	0.423727i	$0.139279\pi$
$998$	105.237	3.33122
$999$	−34.2971	−1.08511

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	8021.2.a.d.1.14	✓	174

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
8021.2.a.d.1.14	✓	174	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)

\(f(q)\)	\(=\)	\(q-2.63597 q^{2} -1.22103 q^{3} +4.94831 q^{4} -4.05948 q^{5} +3.21858 q^{6} -2.69195 q^{7} -7.77165 q^{8} -1.50910 q^{9} +O(q^{10})\)	\(q-2.63597 q^{2} -1.22103 q^{3} +4.94831 q^{4} -4.05948 q^{5} +3.21858 q^{6} -2.69195 q^{7} -7.77165 q^{8} -1.50910 q^{9} +10.7007 q^{10} -2.72323 q^{11} -6.04201 q^{12} +1.00000 q^{13} +7.09588 q^{14} +4.95673 q^{15} +10.5892 q^{16} -1.72211 q^{17} +3.97793 q^{18} +0.0866039 q^{19} -20.0876 q^{20} +3.28693 q^{21} +7.17835 q^{22} -1.32738 q^{23} +9.48938 q^{24} +11.4794 q^{25} -2.63597 q^{26} +5.50572 q^{27} -13.3206 q^{28} +4.89807 q^{29} -13.0658 q^{30} +9.64439 q^{31} -12.3694 q^{32} +3.32514 q^{33} +4.53943 q^{34} +10.9279 q^{35} -7.46748 q^{36} -6.22935 q^{37} -0.228285 q^{38} -1.22103 q^{39} +31.5489 q^{40} -0.837482 q^{41} -8.66424 q^{42} +0.704741 q^{43} -13.4754 q^{44} +6.12615 q^{45} +3.49892 q^{46} -4.92684 q^{47} -12.9296 q^{48} +0.246573 q^{49} -30.2593 q^{50} +2.10274 q^{51} +4.94831 q^{52} -1.93396 q^{53} -14.5129 q^{54} +11.0549 q^{55} +20.9209 q^{56} -0.105746 q^{57} -12.9111 q^{58} -1.57140 q^{59} +24.5274 q^{60} +10.0158 q^{61} -25.4223 q^{62} +4.06241 q^{63} +11.4269 q^{64} -4.05948 q^{65} -8.76495 q^{66} -7.32271 q^{67} -8.52154 q^{68} +1.62076 q^{69} -28.8056 q^{70} -4.56552 q^{71} +11.7282 q^{72} -8.27407 q^{73} +16.4203 q^{74} -14.0166 q^{75} +0.428543 q^{76} +7.33080 q^{77} +3.21858 q^{78} -14.7330 q^{79} -42.9865 q^{80} -2.19534 q^{81} +2.20757 q^{82} -7.59058 q^{83} +16.2648 q^{84} +6.99088 q^{85} -1.85767 q^{86} -5.98067 q^{87} +21.1640 q^{88} -4.11374 q^{89} -16.1483 q^{90} -2.69195 q^{91} -6.56827 q^{92} -11.7760 q^{93} +12.9870 q^{94} -0.351567 q^{95} +15.1033 q^{96} -8.88940 q^{97} -0.649957 q^{98} +4.10962 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 174 q + 6 q^{2} + 37 q^{3} + 214 q^{4} + 10 q^{5} + 12 q^{6} + 28 q^{7} + 15 q^{8} + 211 q^{9}+O(q^{10}) \) 174 * q + 6 * q^2 + 37 * q^3 + 214 * q^4 + 10 * q^5 + 12 * q^6 + 28 * q^7 + 15 * q^8 + 211 * q^9	\( 174 q + 6 q^{2} + 37 q^{3} + 214 q^{4} + 10 q^{5} + 12 q^{6} + 28 q^{7} + 15 q^{8} + 211 q^{9} + 47 q^{10} + 47 q^{11} + 81 q^{12} + 174 q^{13} + 22 q^{14} + 26 q^{15} + 286 q^{16} + 27 q^{17} + 22 q^{18} + 91 q^{19} + 18 q^{20} + 8 q^{21} + 58 q^{22} + 62 q^{23} + 24 q^{24} + 244 q^{25} + 6 q^{26} + 139 q^{27} + 43 q^{28} + 42 q^{29} + 31 q^{30} + 82 q^{31} + 11 q^{32} + 12 q^{33} + 50 q^{34} + 74 q^{35} + 310 q^{36} + 47 q^{37} + 10 q^{38} + 37 q^{39} + 118 q^{40} + 16 q^{41} + 26 q^{42} + 136 q^{43} + 74 q^{44} + 18 q^{45} + 53 q^{46} + 15 q^{47} + 132 q^{48} + 254 q^{49} - 5 q^{50} + 121 q^{51} + 214 q^{52} + 39 q^{53} + 30 q^{54} + 188 q^{55} + 55 q^{56} + 11 q^{57} + 32 q^{58} + 58 q^{59} + 16 q^{60} + 128 q^{61} + 27 q^{62} + 42 q^{63} + 423 q^{64} + 10 q^{65} + 4 q^{66} + 132 q^{67} + 52 q^{68} + 63 q^{69} - 8 q^{70} + 78 q^{71} + 2 q^{72} + 21 q^{73} - 16 q^{74} + 188 q^{75} + 160 q^{76} + 20 q^{77} + 12 q^{78} + 232 q^{79} + 2 q^{80} + 302 q^{81} + 115 q^{82} + 18 q^{83} - 26 q^{84} + 47 q^{85} + 27 q^{86} + 127 q^{87} + 163 q^{88} + 14 q^{90} + 28 q^{91} + 68 q^{92} + 15 q^{93} + 91 q^{94} + 75 q^{95} - 26 q^{96} + 34 q^{97} - 60 q^{98} + 181 q^{99}+O(q^{100}) \) 174 * q + 6 * q^2 + 37 * q^3 + 214 * q^4 + 10 * q^5 + 12 * q^6 + 28 * q^7 + 15 * q^8 + 211 * q^9 + 47 * q^10 + 47 * q^11 + 81 * q^12 + 174 * q^13 + 22 * q^14 + 26 * q^15 + 286 * q^16 + 27 * q^17 + 22 * q^18 + 91 * q^19 + 18 * q^20 + 8 * q^21 + 58 * q^22 + 62 * q^23 + 24 * q^24 + 244 * q^25 + 6 * q^26 + 139 * q^27 + 43 * q^28 + 42 * q^29 + 31 * q^30 + 82 * q^31 + 11 * q^32 + 12 * q^33 + 50 * q^34 + 74 * q^35 + 310 * q^36 + 47 * q^37 + 10 * q^38 + 37 * q^39 + 118 * q^40 + 16 * q^41 + 26 * q^42 + 136 * q^43 + 74 * q^44 + 18 * q^45 + 53 * q^46 + 15 * q^47 + 132 * q^48 + 254 * q^49 - 5 * q^50 + 121 * q^51 + 214 * q^52 + 39 * q^53 + 30 * q^54 + 188 * q^55 + 55 * q^56 + 11 * q^57 + 32 * q^58 + 58 * q^59 + 16 * q^60 + 128 * q^61 + 27 * q^62 + 42 * q^63 + 423 * q^64 + 10 * q^65 + 4 * q^66 + 132 * q^67 + 52 * q^68 + 63 * q^69 - 8 * q^70 + 78 * q^71 + 2 * q^72 + 21 * q^73 - 16 * q^74 + 188 * q^75 + 160 * q^76 + 20 * q^77 + 12 * q^78 + 232 * q^79 + 2 * q^80 + 302 * q^81 + 115 * q^82 + 18 * q^83 - 26 * q^84 + 47 * q^85 + 27 * q^86 + 127 * q^87 + 163 * q^88 + 14 * q^90 + 28 * q^91 + 68 * q^92 + 15 * q^93 + 91 * q^94 + 75 * q^95 - 26 * q^96 + 34 * q^97 - 60 * q^98 + 181 * q^99

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