LMFDB - Embedded newform 4001.2.a.a.1.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [4001,2,Mod(1,4001)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(4001, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("4001.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 4001 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	4001.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:	$31.9481458487$
Analytic rank:	$1$
Dimension:	$149$
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.2
Character	$\chi$	$=$	4001.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-2.68009 q^{2} +1.97360 q^{3} +5.18289 q^{4} +2.92338 q^{5} -5.28944 q^{6} -1.04102 q^{7} -8.53045 q^{8} +0.895108 q^{9} +O(q^{10})$	\(q-2.68009 q^{2} +1.97360 q^{3} +5.18289 q^{4} +2.92338 q^{5} -5.28944 q^{6} -1.04102 q^{7} -8.53045 q^{8} +0.895108 q^{9} -7.83492 q^{10} -1.23466 q^{11} +10.2290 q^{12} +2.97014 q^{13} +2.79004 q^{14} +5.76959 q^{15} +12.4966 q^{16} +0.320191 q^{17} -2.39897 q^{18} -7.24282 q^{19} +15.1516 q^{20} -2.05457 q^{21} +3.30900 q^{22} -6.48684 q^{23} -16.8357 q^{24} +3.54614 q^{25} -7.96024 q^{26} -4.15422 q^{27} -5.39551 q^{28} +2.18400 q^{29} -15.4630 q^{30} -7.15780 q^{31} -16.4311 q^{32} -2.43672 q^{33} -0.858141 q^{34} -3.04331 q^{35} +4.63925 q^{36} -8.70700 q^{37} +19.4114 q^{38} +5.86187 q^{39} -24.9377 q^{40} +4.18105 q^{41} +5.50643 q^{42} +5.42990 q^{43} -6.39910 q^{44} +2.61674 q^{45} +17.3853 q^{46} -7.27969 q^{47} +24.6633 q^{48} -5.91627 q^{49} -9.50398 q^{50} +0.631929 q^{51} +15.3939 q^{52} -9.17430 q^{53} +11.1337 q^{54} -3.60937 q^{55} +8.88040 q^{56} -14.2945 q^{57} -5.85332 q^{58} +2.13326 q^{59} +29.9032 q^{60} -5.33028 q^{61} +19.1836 q^{62} -0.931828 q^{63} +19.0438 q^{64} +8.68283 q^{65} +6.53065 q^{66} +9.41973 q^{67} +1.65951 q^{68} -12.8024 q^{69} +8.15634 q^{70} +0.258870 q^{71} -7.63567 q^{72} +2.76052 q^{73} +23.3356 q^{74} +6.99867 q^{75} -37.5388 q^{76} +1.28531 q^{77} -15.7103 q^{78} -0.315664 q^{79} +36.5323 q^{80} -10.8841 q^{81} -11.2056 q^{82} +13.4221 q^{83} -10.6486 q^{84} +0.936039 q^{85} -14.5526 q^{86} +4.31035 q^{87} +10.5322 q^{88} +3.35259 q^{89} -7.01310 q^{90} -3.09198 q^{91} -33.6206 q^{92} -14.1266 q^{93} +19.5102 q^{94} -21.1735 q^{95} -32.4285 q^{96} -0.557224 q^{97} +15.8561 q^{98} -1.10515 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 149 q - 6 q^{2} - 28 q^{3} + 116 q^{4} - 19 q^{5} - 31 q^{6} - 47 q^{7} - 15 q^{8} + 115 q^{9}+O(q^{10}) $ 149 * q - 6 * q^2 - 28 * q^3 + 116 * q^4 - 19 * q^5 - 31 * q^6 - 47 * q^7 - 15 * q^8 + 115 * q^9	\( 149 q - 6 q^{2} - 28 q^{3} + 116 q^{4} - 19 q^{5} - 31 q^{6} - 47 q^{7} - 15 q^{8} + 115 q^{9} - 48 q^{10} - 31 q^{11} - 61 q^{12} - 54 q^{13} - 44 q^{14} - 65 q^{15} + 58 q^{16} - 26 q^{17} - 23 q^{18} - 86 q^{19} - 52 q^{20} - 30 q^{21} - 56 q^{22} - 63 q^{23} - 90 q^{24} + 92 q^{25} - 38 q^{26} - 103 q^{27} - 77 q^{28} - 51 q^{29} - 22 q^{30} - 256 q^{31} - 21 q^{32} - 36 q^{33} - 124 q^{34} - 50 q^{35} + 45 q^{36} - 42 q^{37} - 14 q^{38} - 119 q^{39} - 131 q^{40} - 55 q^{41} - 5 q^{42} - 55 q^{43} - 54 q^{44} - 68 q^{45} - 59 q^{46} - 82 q^{47} - 89 q^{48} + 30 q^{49} + 13 q^{50} - 83 q^{51} - 126 q^{52} - 23 q^{53} - 83 q^{54} - 244 q^{55} - 94 q^{56} - 14 q^{57} - 60 q^{58} - 93 q^{59} - 70 q^{60} - 139 q^{61} - 10 q^{62} - 120 q^{63} - 45 q^{64} - 37 q^{65} - 28 q^{66} - 110 q^{67} - 27 q^{68} - 79 q^{69} - 78 q^{70} - 123 q^{71} - 74 q^{73} - 25 q^{74} - 146 q^{75} - 192 q^{76} - q^{77} + 26 q^{78} - 273 q^{79} - 51 q^{80} + 41 q^{81} - 120 q^{82} - 27 q^{83} - 14 q^{84} - 71 q^{85} + 3 q^{86} - 98 q^{87} - 143 q^{88} - 70 q^{89} - 24 q^{90} - 256 q^{91} - 47 q^{92} + 16 q^{93} - 151 q^{94} - 83 q^{95} - 137 q^{96} - 108 q^{97} + 17 q^{98} - 131 q^{99}+O(q^{100}) \) 149 * q - 6 * q^2 - 28 * q^3 + 116 * q^4 - 19 * q^5 - 31 * q^6 - 47 * q^7 - 15 * q^8 + 115 * q^9 - 48 * q^10 - 31 * q^11 - 61 * q^12 - 54 * q^13 - 44 * q^14 - 65 * q^15 + 58 * q^16 - 26 * q^17 - 23 * q^18 - 86 * q^19 - 52 * q^20 - 30 * q^21 - 56 * q^22 - 63 * q^23 - 90 * q^24 + 92 * q^25 - 38 * q^26 - 103 * q^27 - 77 * q^28 - 51 * q^29 - 22 * q^30 - 256 * q^31 - 21 * q^32 - 36 * q^33 - 124 * q^34 - 50 * q^35 + 45 * q^36 - 42 * q^37 - 14 * q^38 - 119 * q^39 - 131 * q^40 - 55 * q^41 - 5 * q^42 - 55 * q^43 - 54 * q^44 - 68 * q^45 - 59 * q^46 - 82 * q^47 - 89 * q^48 + 30 * q^49 + 13 * q^50 - 83 * q^51 - 126 * q^52 - 23 * q^53 - 83 * q^54 - 244 * q^55 - 94 * q^56 - 14 * q^57 - 60 * q^58 - 93 * q^59 - 70 * q^60 - 139 * q^61 - 10 * q^62 - 120 * q^63 - 45 * q^64 - 37 * q^65 - 28 * q^66 - 110 * q^67 - 27 * q^68 - 79 * q^69 - 78 * q^70 - 123 * q^71 - 74 * q^73 - 25 * q^74 - 146 * q^75 - 192 * q^76 - q^77 + 26 * q^78 - 273 * q^79 - 51 * q^80 + 41 * q^81 - 120 * q^82 - 27 * q^83 - 14 * q^84 - 71 * q^85 + 3 * q^86 - 98 * q^87 - 143 * q^88 - 70 * q^89 - 24 * q^90 - 256 * q^91 - 47 * q^92 + 16 * q^93 - 151 * q^94 - 83 * q^95 - 137 * q^96 - 108 * q^97 + 17 * q^98 - 131 * 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 $

$2$	−2.68009	−1.89511	−0.947556	−	0.319591i	$-0.896455\pi$
$2$	−2.68009	−1.89511	−0.947556	+	0.319591i	$0.896455\pi$
$3$	1.97360	1.13946	0.569730	−	0.821832i	$-0.307048\pi$
$3$	1.97360	1.13946	0.569730	+	0.821832i	$0.307048\pi$
$4$	5.18289	2.59145
$5$	2.92338	1.30737	0.653687	−	0.756765i	$-0.273221\pi$
$5$	2.92338	1.30737	0.653687	+	0.756765i	$0.273221\pi$
$6$	−5.28944	−2.15940
$7$	−1.04102	−0.393470	−0.196735	−	0.980457i	$-0.563034\pi$
$7$	−1.04102	−0.393470	−0.196735	+	0.980457i	$0.563034\pi$
$8$	−8.53045	−3.01597
$9$	0.895108	0.298369
$10$	−7.83492	−2.47762
$11$	−1.23466	−0.372263	−0.186132	−	0.982525i	$-0.559595\pi$
$11$	−1.23466	−0.372263	−0.186132	+	0.982525i	$0.559595\pi$
$12$	10.2290	2.95285
$13$	2.97014	0.823767	0.411884	−	0.911236i	$-0.364871\pi$
$13$	2.97014	0.823767	0.411884	+	0.911236i	$0.364871\pi$
$14$	2.79004	0.745669
$15$	5.76959	1.48970
$16$	12.4966	3.12415
$17$	0.320191	0.0776577	0.0388288	−	0.999246i	$-0.487637\pi$
$17$	0.320191	0.0776577	0.0388288	+	0.999246i	$0.487637\pi$
$18$	−2.39897	−0.565443
$19$	−7.24282	−1.66162	−0.830809	−	0.556558i	$-0.812122\pi$
$19$	−7.24282	−1.66162	−0.830809	+	0.556558i	$0.812122\pi$
$20$	15.1516	3.38799
$21$	−2.05457	−0.448343
$22$	3.30900	0.705481
$23$	−6.48684	−1.35260	−0.676300	−	0.736626i	$-0.736418\pi$
$23$	−6.48684	−1.35260	−0.676300	+	0.736626i	$0.736418\pi$
$24$	−16.8357	−3.43658
$25$	3.54614	0.709228
$26$	−7.96024	−1.56113
$27$	−4.15422	−0.799480
$28$	−5.39551	−1.01966
$29$	2.18400	0.405559	0.202779	−	0.979224i	$-0.435003\pi$
$29$	2.18400	0.405559	0.202779	+	0.979224i	$0.435003\pi$
$30$	−15.4630	−2.82315
$31$	−7.15780	−1.28558	−0.642789	−	0.766043i	$-0.722223\pi$
$31$	−7.15780	−1.28558	−0.642789	+	0.766043i	$0.722223\pi$
$32$	−16.4311	−2.90464
$33$	−2.43672	−0.424179
$34$	−0.858141	−0.147170
$35$	−3.04331	−0.514413
$36$	4.63925	0.773208
$37$	−8.70700	−1.43142	−0.715711	−	0.698396i	$-0.753897\pi$
$37$	−8.70700	−1.43142	−0.715711	+	0.698396i	$0.753897\pi$
$38$	19.4114	3.14895
$39$	5.86187	0.938650
$40$	−24.9377	−3.94300
$41$	4.18105	0.652971	0.326485	−	0.945202i	$-0.394136\pi$
$41$	4.18105	0.652971	0.326485	+	0.945202i	$0.394136\pi$
$42$	5.50643	0.849660
$43$	5.42990	0.828051	0.414026	−	0.910265i	$-0.364122\pi$
$43$	5.42990	0.828051	0.414026	+	0.910265i	$0.364122\pi$
$44$	−6.39910	−0.964701
$45$	2.61674	0.390080
$46$	17.3853	2.56333
$47$	−7.27969	−1.06185	−0.530926	−	0.847418i	$-0.678156\pi$
$47$	−7.27969	−1.06185	−0.530926	+	0.847418i	$0.678156\pi$
$48$	24.6633	3.55984
$49$	−5.91627	−0.845181
$50$	−9.50398	−1.34407
$51$	0.631929	0.0884878
$52$	15.3939	2.13475
$53$	−9.17430	−1.26019	−0.630093	−	0.776520i	$-0.716983\pi$
$53$	−9.17430	−1.26019	−0.630093	+	0.776520i	$0.716983\pi$
$54$	11.1337	1.51510
$55$	−3.60937	−0.486688
$56$	8.88040	1.18669
$57$	−14.2945	−1.89335
$58$	−5.85332	−0.768579
$59$	2.13326	0.277727	0.138863	−	0.990312i	$-0.455655\pi$
$59$	2.13326	0.277727	0.138863	+	0.990312i	$0.455655\pi$
$60$	29.9032	3.86048
$61$	−5.33028	−0.682472	−0.341236	−	0.939978i	$-0.610846\pi$
$61$	−5.33028	−0.682472	−0.341236	+	0.939978i	$0.610846\pi$
$62$	19.1836	2.43631
$63$	−0.931828	−0.117399
$64$	19.0438	2.38047
$65$	8.68283	1.07697
$66$	6.53065	0.803867
$67$	9.41973	1.15080	0.575402	−	0.817871i	$-0.304846\pi$
$67$	9.41973	1.15080	0.575402	+	0.817871i	$0.304846\pi$
$68$	1.65951	0.201246
$69$	−12.8024	−1.54123
$70$	8.15634	0.974869
$71$	0.258870	0.0307222	0.0153611	−	0.999882i	$-0.495110\pi$
$71$	0.258870	0.0307222	0.0153611	+	0.999882i	$0.495110\pi$
$72$	−7.63567	−0.899872
$73$	2.76052	0.323094	0.161547	−	0.986865i	$-0.448352\pi$
$73$	2.76052	0.323094	0.161547	+	0.986865i	$0.448352\pi$
$74$	23.3356	2.71270
$75$	6.99867	0.808137
$76$	−37.5388	−4.30599
$77$	1.28531	0.146474
$78$	−15.7103	−1.77885
$79$	−0.315664	−0.0355150	−0.0177575	−	0.999842i	$-0.505653\pi$
$79$	−0.315664	−0.0355150	−0.0177575	+	0.999842i	$0.505653\pi$
$80$	36.5323	4.08443
$81$	−10.8841	−1.20935
$82$	−11.2056	−1.23745
$83$	13.4221	1.47326	0.736632	−	0.676294i	$-0.236415\pi$
$83$	13.4221	1.47326	0.736632	+	0.676294i	$0.236415\pi$
$84$	−10.6486	−1.16186
$85$	0.936039	0.101528
$86$	−14.5526	−1.56925
$87$	4.31035	0.462118
$88$	10.5322	1.12274
$89$	3.35259	0.355374	0.177687	−	0.984087i	$-0.443139\pi$
$89$	3.35259	0.355374	0.177687	+	0.984087i	$0.443139\pi$
$90$	−7.01310	−0.739246
$91$	−3.09198	−0.324128
$92$	−33.6206	−3.50519
$93$	−14.1266	−1.46487
$94$	19.5102	2.01233
$95$	−21.1735	−2.17236
$96$	−32.4285	−3.30972
$97$	−0.557224	−0.0565775	−0.0282888	−	0.999600i	$-0.509006\pi$
$97$	−0.557224	−0.0565775	−0.0282888	+	0.999600i	$0.509006\pi$
$98$	15.8561	1.60171
$99$	−1.10515	−0.111072
$100$	18.3793	1.83793
$101$	4.40478	0.438292	0.219146	−	0.975692i	$-0.429673\pi$
$101$	4.40478	0.438292	0.219146	+	0.975692i	$0.429673\pi$
$102$	−1.69363	−0.167694
$103$	−15.9213	−1.56877	−0.784384	−	0.620275i	$-0.787021\pi$
$103$	−15.9213	−1.56877	−0.784384	+	0.620275i	$0.787021\pi$
$104$	−25.3366	−2.48446
$105$	−6.00628	−0.586153
$106$	24.5880	2.38819
$107$	−11.9364	−1.15393	−0.576966	−	0.816768i	$-0.695763\pi$
$107$	−11.9364	−1.15393	−0.576966	+	0.816768i	$0.695763\pi$
$108$	−21.5309	−2.07181
$109$	−17.4122	−1.66778	−0.833892	−	0.551927i	$-0.813893\pi$
$109$	−17.4122	−1.66778	−0.833892	+	0.551927i	$0.813893\pi$
$110$	9.67345	0.922327
$111$	−17.1842	−1.63105
$112$	−13.0093	−1.22926
$113$	−7.76455	−0.730427	−0.365213	−	0.930924i	$-0.619004\pi$
$113$	−7.76455	−0.730427	−0.365213	+	0.930924i	$0.619004\pi$
$114$	38.3105	3.58810
$115$	−18.9635	−1.76835
$116$	11.3194	1.05098
$117$	2.65859	0.245787
$118$	−5.71733	−0.526323
$119$	−0.333326	−0.0305560
$120$	−49.2172	−4.49289
$121$	−9.47562	−0.861420
$122$	14.2856	1.29336
$123$	8.25173	0.744034
$124$	−37.0981	−3.33151
$125$	−4.25018	−0.380148
$126$	2.49739	0.222485
$127$	−7.92612	−0.703330	−0.351665	−	0.936126i	$-0.614384\pi$
$127$	−7.92612	−0.703330	−0.351665	+	0.936126i	$0.614384\pi$
$128$	−18.1768	−1.60662
$129$	10.7165	0.943532
$130$	−23.2708	−2.04098
$131$	7.10454	0.620726	0.310363	−	0.950618i	$-0.399549\pi$
$131$	7.10454	0.620726	0.310363	+	0.950618i	$0.399549\pi$
$132$	−12.6293	−1.09924
$133$	7.53995	0.653797
$134$	−25.2457	−2.18090
$135$	−12.1444	−1.04522
$136$	−2.73137	−0.234213
$137$	22.3715	1.91132	0.955662	−	0.294465i	$-0.0951414\pi$
$137$	22.3715	1.91132	0.955662	+	0.294465i	$0.0951414\pi$
$138$	34.3117	2.92081
$139$	−1.70796	−0.144867	−0.0724337	−	0.997373i	$-0.523077\pi$
$139$	−1.70796	−0.144867	−0.0724337	+	0.997373i	$0.523077\pi$
$140$	−15.7731	−1.33307
$141$	−14.3672	−1.20994
$142$	−0.693796	−0.0582221
$143$	−3.66710	−0.306658
$144$	11.1858	0.932150
$145$	6.38466	0.530217
$146$	−7.39845	−0.612300
$147$	−11.6764	−0.963050
$148$	−45.1275	−3.70945
$149$	−2.28535	−0.187223	−0.0936117	−	0.995609i	$-0.529841\pi$
$149$	−2.28535	−0.187223	−0.0936117	+	0.995609i	$0.529841\pi$
$150$	−18.7571	−1.53151
$151$	16.5382	1.34586	0.672930	−	0.739706i	$-0.265036\pi$
$151$	16.5382	1.34586	0.672930	+	0.739706i	$0.265036\pi$
$152$	61.7845	5.01139
$153$	0.286605	0.0231707
$154$	−3.44474	−0.277585
$155$	−20.9249	−1.68073
$156$	30.3814	2.43246
$157$	13.4074	1.07003	0.535013	−	0.844844i	$-0.320307\pi$
$157$	13.4074	1.07003	0.535013	+	0.844844i	$0.320307\pi$
$158$	0.846010	0.0673049
$159$	−18.1064	−1.43593
$160$	−48.0344	−3.79746
$161$	6.75296	0.532207
$162$	29.1704	2.29184
$163$	−14.7821	−1.15782	−0.578911	−	0.815391i	$-0.696522\pi$
$163$	−14.7821	−1.15782	−0.578911	+	0.815391i	$0.696522\pi$
$164$	21.6699	1.69214
$165$	−7.12347	−0.554561
$166$	−35.9724	−2.79200
$167$	6.82196	0.527899	0.263950	−	0.964536i	$-0.414975\pi$
$167$	6.82196	0.527899	0.263950	+	0.964536i	$0.414975\pi$
$168$	17.5264	1.35219
$169$	−4.17830	−0.321407
$170$	−2.50867	−0.192406
$171$	−6.48311	−0.495776
$172$	28.1426	2.14585
$173$	13.6763	1.03979	0.519895	−	0.854230i	$-0.325971\pi$
$173$	13.6763	1.03979	0.519895	+	0.854230i	$0.325971\pi$
$174$	−11.5521	−0.875765
$175$	−3.69162	−0.279060
$176$	−15.4290	−1.16301
$177$	4.21021	0.316459
$178$	−8.98526	−0.673474
$179$	−16.6484	−1.24436	−0.622180	−	0.782874i	$-0.713753\pi$
$179$	−16.6484	−1.24436	−0.622180	+	0.782874i	$0.713753\pi$
$180$	13.5623	1.01087
$181$	19.2758	1.43276	0.716378	−	0.697712i	$-0.245798\pi$
$181$	19.2758	1.43276	0.716378	+	0.697712i	$0.245798\pi$
$182$	8.28679	0.614258
$183$	−10.5199	−0.777650
$184$	55.3357	4.07940
$185$	−25.4539	−1.87140
$186$	37.8607	2.77608
$187$	−0.395326	−0.0289091
$188$	−37.7298	−2.75173
$189$	4.32464	0.314571
$190$	56.7470	4.11686
$191$	−3.02704	−0.219029	−0.109514	−	0.993985i	$-0.534930\pi$
$191$	−3.02704	−0.219029	−0.109514	+	0.993985i	$0.534930\pi$
$192$	37.5848	2.71245
$193$	17.3490	1.24881	0.624406	−	0.781100i	$-0.285341\pi$
$193$	17.3490	1.24881	0.624406	+	0.781100i	$0.285341\pi$
$194$	1.49341	0.107221
$195$	17.1365	1.22717
$196$	−30.6634	−2.19024
$197$	4.74699	0.338209	0.169105	−	0.985598i	$-0.445912\pi$
$197$	4.74699	0.338209	0.169105	+	0.985598i	$0.445912\pi$
$198$	2.96191	0.210494
$199$	−18.2201	−1.29159	−0.645793	−	0.763512i	$-0.723473\pi$
$199$	−18.2201	−1.29159	−0.645793	+	0.763512i	$0.723473\pi$
$200$	−30.2502	−2.13901
$201$	18.5908	1.31129
$202$	−11.8052	−0.830611
$203$	−2.27360	−0.159575
$204$	3.27522	0.229311
$205$	12.2228	0.853677
$206$	42.6705	2.97299
$207$	−5.80642	−0.403574
$208$	37.1166	2.57357
$209$	8.94241	0.618560
$210$	16.0974	1.11082
$211$	−10.9675	−0.755034	−0.377517	−	0.926003i	$-0.623222\pi$
$211$	−10.9675	−0.755034	−0.377517	+	0.926003i	$0.623222\pi$
$212$	−47.5494	−3.26571
$213$	0.510907	0.0350068
$214$	31.9905	2.18683
$215$	15.8736	1.08257
$216$	35.4374	2.41121
$217$	7.45144	0.505836
$218$	46.6663	3.16064
$219$	5.44817	0.368153
$220$	−18.7070	−1.26123
$221$	0.951010	0.0639719
$222$	46.0551	3.09102
$223$	22.0534	1.47680	0.738401	−	0.674362i	$-0.235581\pi$
$223$	22.0534	1.47680	0.738401	+	0.674362i	$0.235581\pi$
$224$	17.1052	1.14289
$225$	3.17418	0.211612
$226$	20.8097	1.38424
$227$	−21.7779	−1.44545	−0.722724	−	0.691137i	$-0.757110\pi$
$227$	−21.7779	−1.44545	−0.722724	+	0.691137i	$0.757110\pi$
$228$	−74.0866	−4.90651
$229$	11.6802	0.771848	0.385924	−	0.922530i	$-0.373883\pi$
$229$	11.6802	0.771848	0.385924	+	0.922530i	$0.373883\pi$
$230$	50.8239	3.35123
$231$	2.53669	0.166902
$232$	−18.6305	−1.22315
$233$	27.3393	1.79106	0.895529	−	0.445003i	$-0.146797\pi$
$233$	27.3393	1.79106	0.895529	+	0.445003i	$0.146797\pi$
$234$	−7.12527	−0.465793
$235$	−21.2813	−1.38824
$236$	11.0565	0.719714
$237$	−0.622996	−0.0404679
$238$	0.893345	0.0579069
$239$	10.7959	0.698328	0.349164	−	0.937062i	$-0.386466\pi$
$239$	10.7959	0.698328	0.349164	+	0.937062i	$0.386466\pi$
$240$	72.1002	4.65405
$241$	20.2507	1.30446	0.652230	−	0.758021i	$-0.273833\pi$
$241$	20.2507	1.30446	0.652230	+	0.758021i	$0.273833\pi$
$242$	25.3955	1.63249
$243$	−9.01824	−0.578520
$244$	−27.6263	−1.76859
$245$	−17.2955	−1.10497
$246$	−22.1154	−1.41003
$247$	−21.5122	−1.36879
$248$	61.0592	3.87726
$249$	26.4898	1.67873
$250$	11.3909	0.720423
$251$	16.8966	1.06651	0.533253	−	0.845956i	$-0.320969\pi$
$251$	16.8966	1.06651	0.533253	+	0.845956i	$0.320969\pi$
$252$	−4.82957	−0.304234
$253$	8.00903	0.503524
$254$	21.2427	1.33289
$255$	1.84737	0.115687
$256$	10.6279	0.664244
$257$	7.98055	0.497813	0.248907	−	0.968528i	$-0.419929\pi$
$257$	7.98055	0.497813	0.248907	+	0.968528i	$0.419929\pi$
$258$	−28.7211	−1.78810
$259$	9.06420	0.563222
$260$	45.0022	2.79092
$261$	1.95492	0.121006
$262$	−19.0408	−1.17635
$263$	−10.7953	−0.665665	−0.332833	−	0.942986i	$-0.608004\pi$
$263$	−10.7953	−0.665665	−0.332833	+	0.942986i	$0.608004\pi$
$264$	20.7864	1.27931
$265$	−26.8199	−1.64754
$266$	−20.2078	−1.23902
$267$	6.61669	0.404935
$268$	48.8215	2.98224
$269$	14.1980	0.865664	0.432832	−	0.901474i	$-0.357514\pi$
$269$	14.1980	0.865664	0.432832	+	0.901474i	$0.357514\pi$
$270$	32.5480	1.98081
$271$	−6.30275	−0.382865	−0.191432	−	0.981506i	$-0.561313\pi$
$271$	−6.30275	−0.382865	−0.191432	+	0.981506i	$0.561313\pi$
$272$	4.00130	0.242614
$273$	−6.10234	−0.369331
$274$	−59.9576	−3.62217
$275$	−4.37827	−0.264020
$276$	−66.3537	−3.99403
$277$	−23.6392	−1.42034	−0.710170	−	0.704030i	$-0.751382\pi$
$277$	−23.6392	−1.42034	−0.710170	+	0.704030i	$0.751382\pi$
$278$	4.57749	0.274540
$279$	−6.40700	−0.383577
$280$	25.9608	1.55145
$281$	3.14996	0.187911	0.0939555	−	0.995576i	$-0.470049\pi$
$281$	3.14996	0.187911	0.0939555	+	0.995576i	$0.470049\pi$
$282$	38.5054	2.29297
$283$	−27.7671	−1.65059	−0.825293	−	0.564705i	$-0.808990\pi$
$283$	−27.7671	−1.65059	−0.825293	+	0.564705i	$0.808990\pi$
$284$	1.34170	0.0796151
$285$	−41.7881	−2.47531
$286$	9.82817	0.581152
$287$	−4.35257	−0.256924
$288$	−14.7076	−0.866656
$289$	−16.8975	−0.993969
$290$	−17.1115	−1.00482
$291$	−1.09974	−0.0644678
$292$	14.3075	0.837282
$293$	13.8797	0.810864	0.405432	−	0.914125i	$-0.367121\pi$
$293$	13.8797	0.810864	0.405432	+	0.914125i	$0.367121\pi$
$294$	31.2937	1.82509
$295$	6.23633	0.363093
$296$	74.2746	4.31713
$297$	5.12904	0.297617
$298$	6.12496	0.354809
$299$	−19.2668	−1.11423
$300$	36.2734	2.09424
$301$	−5.65265	−0.325813
$302$	−44.3239	−2.55055
$303$	8.69328	0.499416
$304$	−90.5107	−5.19114
$305$	−15.5824	−0.892247
$306$	−0.768128	−0.0439110
$307$	28.2419	1.61185	0.805925	−	0.592018i	$-0.201668\pi$
$307$	28.2419	1.61185	0.805925	+	0.592018i	$0.201668\pi$
$308$	6.66162	0.379581
$309$	−31.4223	−1.78755
$310$	56.0808	3.18517
$311$	−7.54544	−0.427863	−0.213931	−	0.976849i	$-0.568627\pi$
$311$	−7.54544	−0.427863	−0.213931	+	0.976849i	$0.568627\pi$
$312$	−50.0044	−2.83094
$313$	−17.1788	−0.971004	−0.485502	−	0.874236i	$-0.661363\pi$
$313$	−17.1788	−0.971004	−0.485502	+	0.874236i	$0.661363\pi$
$314$	−35.9330	−2.02782
$315$	−2.72409	−0.153485
$316$	−1.63606	−0.0920353
$317$	6.49527	0.364811	0.182405	−	0.983223i	$-0.441612\pi$
$317$	6.49527	0.364811	0.182405	+	0.983223i	$0.441612\pi$
$318$	48.5269	2.72125
$319$	−2.69649	−0.150975
$320$	55.6721	3.11217
$321$	−23.5576	−1.31486
$322$	−18.0985	−1.00859
$323$	−2.31909	−0.129037
$324$	−56.4112	−3.13395
$325$	10.5325	0.584239
$326$	39.6173	2.19420
$327$	−34.3647	−1.90037
$328$	−35.6662	−1.96934
$329$	7.57833	0.417807
$330$	19.0916	1.05096
$331$	10.0658	0.553266	0.276633	−	0.960976i	$-0.410781\pi$
$331$	10.0658	0.553266	0.276633	+	0.960976i	$0.410781\pi$
$332$	69.5652	3.81788
$333$	−7.79370	−0.427092
$334$	−18.2835	−1.00043
$335$	27.5374	1.50453
$336$	−25.6751	−1.40069
$337$	−27.1342	−1.47809	−0.739046	−	0.673654i	$-0.764724\pi$
$337$	−27.1342	−1.47809	−0.739046	+	0.673654i	$0.764724\pi$
$338$	11.1982	0.609103
$339$	−15.3241	−0.832292
$340$	4.85139	0.263104
$341$	8.83743	0.478574
$342$	17.3753	0.939550
$343$	13.4461	0.726023
$344$	−46.3194	−2.49738
$345$	−37.4264	−2.01497
$346$	−36.6538	−1.97052
$347$	−12.9539	−0.695403	−0.347701	−	0.937605i	$-0.613038\pi$
$347$	−12.9539	−0.695403	−0.347701	+	0.937605i	$0.613038\pi$
$348$	22.3401	1.19755
$349$	−5.77072	−0.308899	−0.154450	−	0.988001i	$-0.549360\pi$
$349$	−5.77072	−0.308899	−0.154450	+	0.988001i	$0.549360\pi$
$350$	9.89387	0.528850
$351$	−12.3386	−0.658586
$352$	20.2868	1.08129
$353$	24.7140	1.31539	0.657696	−	0.753283i	$-0.271531\pi$
$353$	24.7140	1.31539	0.657696	+	0.753283i	$0.271531\pi$
$354$	−11.2837	−0.599724
$355$	0.756776	0.0401655
$356$	17.3761	0.920933
$357$	−0.657853	−0.0348173
$358$	44.6193	2.35820
$359$	−22.3095	−1.17745	−0.588725	−	0.808334i	$-0.700370\pi$
$359$	−22.3095	−1.17745	−0.588725	+	0.808334i	$0.700370\pi$
$360$	−22.3219	−1.17647
$361$	33.4585	1.76097
$362$	−51.6608	−2.71523
$363$	−18.7011	−0.981554
$364$	−16.0254	−0.839960
$365$	8.07004	0.422405
$366$	28.1942	1.47373
$367$	18.2664	0.953500	0.476750	−	0.879039i	$-0.341815\pi$
$367$	18.2664	0.953500	0.476750	+	0.879039i	$0.341815\pi$
$368$	−81.0635	−4.22573
$369$	3.74249	0.194826
$370$	68.2187	3.54652
$371$	9.55066	0.495845
$372$	−73.2169	−3.79612
$373$	0.934972	0.0484110	0.0242055	−	0.999707i	$-0.492294\pi$
$373$	0.934972	0.0484110	0.0242055	+	0.999707i	$0.492294\pi$
$374$	1.05951	0.0547860
$375$	−8.38817	−0.433163
$376$	62.0990	3.20251
$377$	6.48678	0.334086
$378$	−11.5904	−0.596148
$379$	9.73548	0.500078	0.250039	−	0.968236i	$-0.419557\pi$
$379$	9.73548	0.500078	0.250039	+	0.968236i	$0.419557\pi$
$380$	−109.740	−5.62955
$381$	−15.6430	−0.801416
$382$	8.11274	0.415084
$383$	−5.43775	−0.277856	−0.138928	−	0.990302i	$-0.544366\pi$
$383$	−5.43775	−0.277856	−0.138928	+	0.990302i	$0.544366\pi$
$384$	−35.8737	−1.83067
$385$	3.75744	0.191497
$386$	−46.4970	−2.36664
$387$	4.86034	0.247065
$388$	−2.88803	−0.146618
$389$	−6.65280	−0.337310	−0.168655	−	0.985675i	$-0.553942\pi$
$389$	−6.65280	−0.337310	−0.168655	+	0.985675i	$0.553942\pi$
$390$	−45.9273	−2.32562
$391$	−2.07703	−0.105040
$392$	50.4684	2.54904
$393$	14.0215	0.707293
$394$	−12.7224	−0.640944
$395$	−0.922806	−0.0464314
$396$	−5.72789	−0.287837
$397$	−15.2934	−0.767553	−0.383776	−	0.923426i	$-0.625377\pi$
$397$	−15.2934	−0.767553	−0.383776	+	0.923426i	$0.625377\pi$
$398$	48.8315	2.44770
$399$	14.8809	0.744975
$400$	44.3147	2.21573
$401$	9.13990	0.456425	0.228212	−	0.973611i	$-0.426712\pi$
$401$	9.13990	0.456425	0.228212	+	0.973611i	$0.426712\pi$
$402$	−49.8251	−2.48505
$403$	−21.2596	−1.05902
$404$	22.8295	1.13581
$405$	−31.8184	−1.58107
$406$	6.09345	0.302413
$407$	10.7502	0.532866
$408$	−5.39064	−0.266877
$409$	1.33006	0.0657672	0.0328836	−	0.999459i	$-0.489531\pi$
$409$	1.33006	0.0657672	0.0328836	+	0.999459i	$0.489531\pi$
$410$	−32.7582	−1.61781
$411$	44.1524	2.17788
$412$	−82.5182	−4.06538
$413$	−2.22077	−0.109277
$414$	15.5617	0.764818
$415$	39.2378	1.92611
$416$	−48.8027	−2.39275
$417$	−3.37084	−0.165071
$418$	−23.9665	−1.17224
$419$	28.1488	1.37516	0.687579	−	0.726110i	$-0.258674\pi$
$419$	28.1488	1.37516	0.687579	+	0.726110i	$0.258674\pi$
$420$	−31.1299	−1.51898
$421$	5.95657	0.290305	0.145153	−	0.989409i	$-0.453633\pi$
$421$	5.95657	0.290305	0.145153	+	0.989409i	$0.453633\pi$
$422$	29.3939	1.43087
$423$	−6.51610	−0.316824
$424$	78.2609	3.80068
$425$	1.13544	0.0550770
$426$	−1.36928	−0.0663417
$427$	5.54895	0.268532
$428$	−61.8649	−2.99035
$429$	−7.23740	−0.349425
$430$	−42.5428	−2.05160
$431$	−10.8141	−0.520897	−0.260448	−	0.965488i	$-0.583870\pi$
$431$	−10.8141	−0.520897	−0.260448	+	0.965488i	$0.583870\pi$
$432$	−51.9136	−2.49770
$433$	−5.91426	−0.284221	−0.142111	−	0.989851i	$-0.545389\pi$
$433$	−5.91426	−0.284221	−0.142111	+	0.989851i	$0.545389\pi$
$434$	−19.9705	−0.958616
$435$	12.6008	0.604161
$436$	−90.2455	−4.32198
$437$	46.9830	2.24750
$438$	−14.6016	−0.697691
$439$	−35.7493	−1.70622	−0.853111	−	0.521730i	$-0.825287\pi$
$439$	−35.7493	−1.70622	−0.853111	+	0.521730i	$0.825287\pi$
$440$	30.7896	1.46784
$441$	−5.29570	−0.252176
$442$	−2.54879	−0.121234
$443$	36.8851	1.75246	0.876231	−	0.481891i	$-0.160050\pi$
$443$	36.8851	1.75246	0.876231	+	0.481891i	$0.160050\pi$
$444$	−89.0637	−4.22678
$445$	9.80090	0.464607
$446$	−59.1051	−2.79871
$447$	−4.51038	−0.213334
$448$	−19.8250	−0.936644
$449$	2.68873	0.126889	0.0634445	−	0.997985i	$-0.479791\pi$
$449$	2.68873	0.126889	0.0634445	+	0.997985i	$0.479791\pi$
$450$	−8.50709	−0.401028
$451$	−5.16217	−0.243077
$452$	−40.2428	−1.89286
$453$	32.6398	1.53355
$454$	58.3667	2.73928
$455$	−9.03903	−0.423756
$456$	121.938	5.71027
$457$	9.13987	0.427545	0.213772	−	0.976883i	$-0.431425\pi$
$457$	9.13987	0.427545	0.213772	+	0.976883i	$0.431425\pi$
$458$	−31.3040	−1.46274
$459$	−1.33014	−0.0620858
$460$	−98.2858	−4.58260
$461$	36.6705	1.70791	0.853957	−	0.520344i	$-0.174196\pi$
$461$	36.6705	1.70791	0.853957	+	0.520344i	$0.174196\pi$
$462$	−6.79856	−0.316298
$463$	−8.91373	−0.414256	−0.207128	−	0.978314i	$-0.566412\pi$
$463$	−8.91373	−0.414256	−0.207128	+	0.978314i	$0.566412\pi$
$464$	27.2926	1.26703
$465$	−41.2975	−1.91513
$466$	−73.2719	−3.39425
$467$	1.22991	0.0569135	0.0284567	−	0.999595i	$-0.490941\pi$
$467$	1.22991	0.0569135	0.0284567	+	0.999595i	$0.490941\pi$
$468$	13.7792	0.636943
$469$	−9.80616	−0.452806
$470$	57.0358	2.63086
$471$	26.4608	1.21925
$472$	−18.1977	−0.837615
$473$	−6.70407	−0.308253
$474$	1.66969	0.0766913
$475$	−25.6841	−1.17847
$476$	−1.72759	−0.0791842
$477$	−8.21198	−0.376001
$478$	−28.9340	−1.32341
$479$	1.54723	0.0706946	0.0353473	−	0.999375i	$-0.488746\pi$
$479$	1.54723	0.0706946	0.0353473	+	0.999375i	$0.488746\pi$
$480$	−94.8009	−4.32705
$481$	−25.8610	−1.17916
$482$	−54.2737	−2.47210
$483$	13.3277	0.606429
$484$	−49.1111	−2.23232
$485$	−1.62898	−0.0739680
$486$	24.1697	1.09636
$487$	−28.7026	−1.30064	−0.650319	−	0.759661i	$-0.725365\pi$
$487$	−28.7026	−1.30064	−0.650319	+	0.759661i	$0.725365\pi$
$488$	45.4697	2.05831
$489$	−29.1739	−1.31929
$490$	46.3535	2.09404
$491$	16.2592	0.733766	0.366883	−	0.930267i	$-0.380425\pi$
$491$	16.2592	0.733766	0.366883	+	0.930267i	$0.380425\pi$
$492$	42.7679	1.92812
$493$	0.699297	0.0314947
$494$	57.6546	2.59400
$495$	−3.23078	−0.145213
$496$	−89.4481	−4.01634
$497$	−0.269490	−0.0120883
$498$	−70.9952	−3.18137
$499$	−1.09140	−0.0488577	−0.0244288	−	0.999702i	$-0.507777\pi$
$499$	−1.09140	−0.0488577	−0.0244288	+	0.999702i	$0.507777\pi$
$500$	−22.0283	−0.985133
$501$	13.4638	0.601520
$502$	−45.2845	−2.02115
$503$	31.7426	1.41533	0.707667	−	0.706546i	$-0.249748\pi$
$503$	31.7426	1.41533	0.707667	+	0.706546i	$0.249748\pi$
$504$	7.94891	0.354073
$505$	12.8768	0.573011
$506$	−21.4649	−0.954233
$507$	−8.24630	−0.366231
$508$	−41.0803	−1.82264
$509$	−27.9176	−1.23743	−0.618713	−	0.785617i	$-0.712345\pi$
$509$	−27.9176	−1.23743	−0.618713	+	0.785617i	$0.712345\pi$
$510$	−4.95112	−0.219239
$511$	−2.87377	−0.127128
$512$	7.86980	0.347800
$513$	30.0883	1.32843
$514$	−21.3886	−0.943411
$515$	−46.5439	−2.05097
$516$	55.5423	2.44511
$517$	8.98793	0.395289
$518$	−24.2929	−1.06737
$519$	26.9916	1.18480
$520$	−74.0684	−3.24812
$521$	−38.2706	−1.67667	−0.838333	−	0.545159i	$-0.816469\pi$
$521$	−38.2706	−1.67667	−0.838333	+	0.545159i	$0.816469\pi$
$522$	−5.23935	−0.229320
$523$	16.4704	0.720202	0.360101	−	0.932913i	$-0.382742\pi$
$523$	16.4704	0.720202	0.360101	+	0.932913i	$0.382742\pi$
$524$	36.8220	1.60858
$525$	−7.28578	−0.317978
$526$	28.9323	1.26151
$527$	−2.29186	−0.0998350
$528$	−30.4508	−1.32520
$529$	19.0791	0.829527
$530$	71.8799	3.12226
$531$	1.90950	0.0828651
$532$	39.0788	1.69428
$533$	12.4183	0.537896
$534$	−17.7333	−0.767396
$535$	−34.8945	−1.50862
$536$	−80.3545	−3.47079
$537$	−32.8574	−1.41790
$538$	−38.0518	−1.64053
$539$	7.30457	0.314630
$540$	−62.9429	−2.70863
$541$	8.13658	0.349819	0.174909	−	0.984585i	$-0.444037\pi$
$541$	8.13658	0.349819	0.174909	+	0.984585i	$0.444037\pi$
$542$	16.8919	0.725571
$543$	38.0427	1.63257
$544$	−5.26110	−0.225568
$545$	−50.9024	−2.18042
$546$	16.3548	0.699923
$547$	10.7638	0.460226	0.230113	−	0.973164i	$-0.426090\pi$
$547$	10.7638	0.460226	0.230113	+	0.973164i	$0.426090\pi$
$548$	115.949	4.95310
$549$	−4.77117	−0.203629
$550$	11.7342	0.500347
$551$	−15.8183	−0.673883
$552$	109.211	4.64831
$553$	0.328614	0.0139741
$554$	63.3552	2.69170
$555$	−50.2358	−2.13239
$556$	−8.85218	−0.375416
$557$	1.98725	0.0842023	0.0421011	−	0.999113i	$-0.486595\pi$
$557$	1.98725	0.0842023	0.0421011	+	0.999113i	$0.486595\pi$
$558$	17.1713	0.726921
$559$	16.1275	0.682122
$560$	−38.0310	−1.60710
$561$	−0.780217	−0.0329408
$562$	−8.44219	−0.356112
$563$	33.6899	1.41986	0.709930	−	0.704272i	$-0.248727\pi$
$563$	33.6899	1.41986	0.709930	+	0.704272i	$0.248727\pi$
$564$	−74.4637	−3.13549
$565$	−22.6987	−0.954942
$566$	74.4185	3.12804
$567$	11.3306	0.475841
$568$	−2.20828	−0.0926573
$569$	−27.5444	−1.15472	−0.577360	−	0.816490i	$-0.695917\pi$
$569$	−27.5444	−1.15472	−0.577360	+	0.816490i	$0.695917\pi$
$570$	111.996	4.69099
$571$	−20.1321	−0.842504	−0.421252	−	0.906944i	$-0.638409\pi$
$571$	−20.1321	−0.842504	−0.421252	+	0.906944i	$0.638409\pi$
$572$	−19.0062	−0.794689
$573$	−5.97417	−0.249575
$574$	11.6653	0.486900
$575$	−23.0032	−0.959302
$576$	17.0462	0.710259
$577$	15.8026	0.657871	0.328936	−	0.944352i	$-0.393310\pi$
$577$	15.8026	0.657871	0.328936	+	0.944352i	$0.393310\pi$
$578$	45.2868	1.88368
$579$	34.2401	1.42297
$580$	33.0910	1.37403
$581$	−13.9727	−0.579685
$582$	2.94740	0.122174
$583$	11.3271	0.469121
$584$	−23.5485	−0.974442
$585$	7.77207	0.321335
$586$	−37.1990	−1.53668
$587$	−23.6332	−0.975446	−0.487723	−	0.872998i	$-0.662172\pi$
$587$	−23.6332	−0.975446	−0.487723	+	0.872998i	$0.662172\pi$
$588$	−60.5174	−2.49569
$589$	51.8427	2.13614
$590$	−16.7139	−0.688102
$591$	9.36867	0.385376
$592$	−108.808	−4.47198
$593$	−24.8862	−1.02196	−0.510978	−	0.859594i	$-0.670716\pi$
$593$	−24.8862	−1.02196	−0.510978	+	0.859594i	$0.670716\pi$
$594$	−13.7463	−0.564018
$595$	−0.974438	−0.0399481
$596$	−11.8447	−0.485179
$597$	−35.9592	−1.47171
$598$	51.6368	2.11159
$599$	−38.7047	−1.58143	−0.790716	−	0.612183i	$-0.790292\pi$
$599$	−38.7047	−1.58143	−0.790716	+	0.612183i	$0.790292\pi$
$600$	−59.7018	−2.43732
$601$	−36.8193	−1.50189	−0.750945	−	0.660365i	$-0.770401\pi$
$601$	−36.8193	−1.50189	−0.750945	+	0.660365i	$0.770401\pi$
$602$	15.1496	0.617453
$603$	8.43167	0.343364
$604$	85.7157	3.48772
$605$	−27.7008	−1.12620
$606$	−23.2988	−0.946448
$607$	3.98739	0.161843	0.0809216	−	0.996720i	$-0.474214\pi$
$607$	3.98739	0.161843	0.0809216	+	0.996720i	$0.474214\pi$
$608$	119.008	4.82641
$609$	−4.48717	−0.181829
$610$	41.7623	1.69091
$611$	−21.6217	−0.874719
$612$	1.48544	0.0600455
$613$	−13.2567	−0.535434	−0.267717	−	0.963498i	$-0.586269\pi$
$613$	−13.2567	−0.535434	−0.267717	+	0.963498i	$0.586269\pi$
$614$	−75.6909	−3.05464
$615$	24.1229	0.972731
$616$	−10.9643	−0.441762
$617$	−21.0666	−0.848109	−0.424055	−	0.905637i	$-0.639394\pi$
$617$	−21.0666	−0.848109	−0.424055	+	0.905637i	$0.639394\pi$
$618$	84.2145	3.38761
$619$	−26.1661	−1.05170	−0.525852	−	0.850576i	$-0.676253\pi$
$619$	−26.1661	−1.05170	−0.525852	+	0.850576i	$0.676253\pi$
$620$	−108.452	−4.35553
$621$	26.9478	1.08138
$622$	20.2225	0.810847
$623$	−3.49013	−0.139829
$624$	73.2534	2.93248
$625$	−30.1556	−1.20622
$626$	46.0408	1.84016
$627$	17.6488	0.704824
$628$	69.4890	2.77291
$629$	−2.78790	−0.111161
$630$	7.30080	0.290871
$631$	−11.8430	−0.471464	−0.235732	−	0.971818i	$-0.575749\pi$
$631$	−11.8430	−0.471464	−0.235732	+	0.971818i	$0.575749\pi$
$632$	2.69276	0.107112
$633$	−21.6455	−0.860331
$634$	−17.4079	−0.691357
$635$	−23.1711	−0.919515
$636$	−93.8436	−3.72114
$637$	−17.5721	−0.696233
$638$	7.22685	0.286114
$639$	0.231717	0.00916657
$640$	−53.1376	−2.10045
$641$	24.7064	0.975845	0.487923	−	0.872887i	$-0.337755\pi$
$641$	24.7064	0.975845	0.487923	+	0.872887i	$0.337755\pi$
$642$	63.1366	2.49180
$643$	14.2634	0.562495	0.281248	−	0.959635i	$-0.409252\pi$
$643$	14.2634	0.562495	0.281248	+	0.959635i	$0.409252\pi$
$644$	34.9999	1.37919
$645$	31.3283	1.23355
$646$	6.21536	0.244540
$647$	13.1168	0.515675	0.257837	−	0.966188i	$-0.416990\pi$
$647$	13.1168	0.515675	0.257837	+	0.966188i	$0.416990\pi$
$648$	92.8463	3.64735
$649$	−2.63385	−0.103388
$650$	−28.2281	−1.10720
$651$	14.7062	0.576380
$652$	−76.6139	−3.00043
$653$	33.8031	1.32282	0.661409	−	0.750026i	$-0.269959\pi$
$653$	33.8031	1.32282	0.661409	+	0.750026i	$0.269959\pi$
$654$	92.1007	3.60142
$655$	20.7692	0.811521
$656$	52.2489	2.03998
$657$	2.47096	0.0964014
$658$	−20.3106	−0.791790
$659$	−19.5538	−0.761709	−0.380855	−	0.924635i	$-0.624370\pi$
$659$	−19.5538	−0.761709	−0.380855	+	0.924635i	$0.624370\pi$
$660$	−36.9202	−1.43712
$661$	−37.4050	−1.45489	−0.727443	−	0.686168i	$-0.759292\pi$
$661$	−37.4050	−1.45489	−0.727443	+	0.686168i	$0.759292\pi$
$662$	−26.9773	−1.04850
$663$	1.87692	0.0728934
$664$	−114.496	−4.44332
$665$	22.0421	0.854757
$666$	20.8878	0.809388
$667$	−14.1673	−0.548559
$668$	35.3575	1.36802
$669$	43.5246	1.68276
$670$	−73.8028	−2.85125
$671$	6.58107	0.254059
$672$	33.7589	1.30228
$673$	−34.8659	−1.34398	−0.671990	−	0.740560i	$-0.734560\pi$
$673$	−34.8659	−1.34398	−0.671990	+	0.740560i	$0.734560\pi$
$674$	72.7221	2.80115
$675$	−14.7314	−0.567014
$676$	−21.6557	−0.832910
$677$	−5.89325	−0.226496	−0.113248	−	0.993567i	$-0.536125\pi$
$677$	−5.89325	−0.226496	−0.113248	+	0.993567i	$0.536125\pi$
$678$	41.0701	1.57729
$679$	0.580083	0.0222615
$680$	−7.98483	−0.306204
$681$	−42.9808	−1.64703
$682$	−23.6851	−0.906951
$683$	−42.6082	−1.63036	−0.815179	−	0.579209i	$-0.803361\pi$
$683$	−42.6082	−1.63036	−0.815179	+	0.579209i	$0.803361\pi$
$684$	−33.6013	−1.28478
$685$	65.4003	2.49882
$686$	−36.0369	−1.37590
$687$	23.0520	0.879490
$688$	67.8552	2.58696
$689$	−27.2489	−1.03810
$690$	100.306	3.81859
$691$	−35.8998	−1.36569	−0.682846	−	0.730563i	$-0.739258\pi$
$691$	−35.8998	−1.36569	−0.682846	+	0.730563i	$0.739258\pi$
$692$	70.8828	2.69456
$693$	1.15049	0.0437035
$694$	34.7177	1.31787
$695$	−4.99301	−0.189396
$696$	−36.7692	−1.39373
$697$	1.33873	0.0507082
$698$	15.4661	0.585399
$699$	53.9569	2.04084
$700$	−19.1332	−0.723169
$701$	−31.9884	−1.20819	−0.604093	−	0.796913i	$-0.706465\pi$
$701$	−31.9884	−1.20819	−0.604093	+	0.796913i	$0.706465\pi$
$702$	33.0686	1.24809
$703$	63.0633	2.37848
$704$	−23.5125	−0.886163
$705$	−42.0008	−1.58184
$706$	−66.2358	−2.49282
$707$	−4.58548	−0.172455
$708$	21.8211	0.820086
$709$	11.9617	0.449230	0.224615	−	0.974448i	$-0.427888\pi$
$709$	11.9617	0.449230	0.224615	+	0.974448i	$0.427888\pi$
$710$	−2.02823	−0.0761180
$711$	−0.282554	−0.0105966
$712$	−28.5991	−1.07180
$713$	46.4315	1.73887
$714$	1.76311	0.0659827
$715$	−10.7203	−0.400917
$716$	−86.2870	−3.22470
$717$	21.3068	0.795717
$718$	59.7915	2.23140
$719$	−11.2484	−0.419494	−0.209747	−	0.977756i	$-0.567264\pi$
$719$	−11.2484	−0.419494	−0.209747	+	0.977756i	$0.567264\pi$
$720$	32.7003	1.21867
$721$	16.5744	0.617263
$722$	−89.6718	−3.33724
$723$	39.9668	1.48638
$724$	99.9043	3.71291
$725$	7.74477	0.287633
$726$	50.1207	1.86015
$727$	18.8892	0.700563	0.350282	−	0.936644i	$-0.386086\pi$
$727$	18.8892	0.700563	0.350282	+	0.936644i	$0.386086\pi$
$728$	26.3760	0.977559
$729$	14.8539	0.550144
$730$	−21.6285	−0.800505
$731$	1.73860	0.0643045
$732$	−54.5233	−2.01524
$733$	16.2296	0.599455	0.299727	−	0.954025i	$-0.403104\pi$
$733$	16.2296	0.599455	0.299727	+	0.954025i	$0.403104\pi$
$734$	−48.9557	−1.80699
$735$	−34.1344	−1.25907
$736$	106.586	3.92882
$737$	−11.6301	−0.428402
$738$	−10.0302	−0.369218
$739$	−17.6223	−0.648248	−0.324124	−	0.946015i	$-0.605069\pi$
$739$	−17.6223	−0.648248	−0.324124	+	0.946015i	$0.605069\pi$
$740$	−131.925	−4.84965
$741$	−42.4565	−1.55968
$742$	−25.5966	−0.939682
$743$	16.8808	0.619296	0.309648	−	0.950851i	$-0.399789\pi$
$743$	16.8808	0.619296	0.309648	+	0.950851i	$0.399789\pi$
$744$	120.507	4.41799
$745$	−6.68095	−0.244771
$746$	−2.50581	−0.0917442
$747$	12.0142	0.439577
$748$	−2.04893	−0.0749164
$749$	12.4260	0.454037
$750$	22.4811	0.820893
$751$	25.0207	0.913019	0.456509	−	0.889719i	$-0.349099\pi$
$751$	25.0207	0.913019	0.456509	+	0.889719i	$0.349099\pi$
$752$	−90.9713	−3.31738
$753$	33.3472	1.21524
$754$	−17.3852	−0.633130
$755$	48.3474	1.75954
$756$	22.4142	0.815195
$757$	25.4965	0.926685	0.463343	−	0.886179i	$-0.346650\pi$
$757$	25.4965	0.926685	0.463343	+	0.886179i	$0.346650\pi$
$758$	−26.0920	−0.947704
$759$	15.8066	0.573745
$760$	180.620	6.55176
$761$	34.1056	1.23633	0.618164	−	0.786049i	$-0.287877\pi$
$761$	34.1056	1.23633	0.618164	+	0.786049i	$0.287877\pi$
$762$	41.9247	1.51877
$763$	18.1265	0.656223
$764$	−15.6888	−0.567601
$765$	0.837855	0.0302927
$766$	14.5737	0.526568
$767$	6.33607	0.228782
$768$	20.9753	0.756879
$769$	24.1727	0.871691	0.435846	−	0.900021i	$-0.356449\pi$
$769$	24.1727	0.871691	0.435846	+	0.900021i	$0.356449\pi$
$770$	−10.0703	−0.362908
$771$	15.7504	0.567238
$772$	89.9182	3.23623
$773$	29.7604	1.07041	0.535204	−	0.844723i	$-0.320235\pi$
$773$	29.7604	1.07041	0.535204	+	0.844723i	$0.320235\pi$
$774$	−13.0262	−0.468216
$775$	−25.3825	−0.911768
$776$	4.75337	0.170636
$777$	17.8891	0.641769
$778$	17.8301	0.639241
$779$	−30.2826	−1.08499
$780$	88.8164	3.18014
$781$	−0.319616	−0.0114368
$782$	5.56662	0.199062
$783$	−9.07282	−0.324236
$784$	−73.9333	−2.64047
$785$	39.1948	1.39892
$786$	−37.5790	−1.34040
$787$	35.9043	1.27985	0.639926	−	0.768437i	$-0.278965\pi$
$787$	35.9043	1.27985	0.639926	+	0.768437i	$0.278965\pi$
$788$	24.6032	0.876451
$789$	−21.3056	−0.758499
$790$	2.47321	0.0879927
$791$	8.08308	0.287401
$792$	9.42744	0.334990
$793$	−15.8316	−0.562198
$794$	40.9877	1.45460
$795$	−52.9319	−1.87730
$796$	−94.4327	−3.34708
$797$	41.4141	1.46696	0.733482	−	0.679709i	$-0.237894\pi$
$797$	41.4141	1.46696	0.733482	+	0.679709i	$0.237894\pi$
$798$	−39.8821	−1.41181
$799$	−2.33089	−0.0824609
$800$	−58.2671	−2.06005
$801$	3.00093	0.106033
$802$	−24.4958	−0.864976
$803$	−3.40830	−0.120276
$804$	96.3541	3.39815
$805$	19.7414	0.695794
$806$	56.9778	2.00696
$807$	28.0211	0.986390
$808$	−37.5747	−1.32187
$809$	6.02731	0.211909	0.105954	−	0.994371i	$-0.466210\pi$
$809$	6.02731	0.211909	0.105954	+	0.994371i	$0.466210\pi$
$810$	85.2761	2.99630
$811$	−47.5049	−1.66812	−0.834061	−	0.551673i	$-0.813990\pi$
$811$	−47.5049	−1.66812	−0.834061	+	0.551673i	$0.813990\pi$
$812$	−11.7838	−0.413530
$813$	−12.4391	−0.436259
$814$	−28.8115	−1.00984
$815$	−43.2136	−1.51371
$816$	7.89697	0.276449
$817$	−39.3278	−1.37590
$818$	−3.56468	−0.124636
$819$	−2.76766	−0.0967097
$820$	63.3494	2.21226
$821$	−20.1234	−0.702311	−0.351155	−	0.936317i	$-0.614211\pi$
$821$	−20.1234	−0.702311	−0.351155	+	0.936317i	$0.614211\pi$
$822$	−118.333	−4.12732
$823$	25.3482	0.883584	0.441792	−	0.897117i	$-0.354343\pi$
$823$	25.3482	0.883584	0.441792	+	0.897117i	$0.354343\pi$
$824$	135.816	4.73136
$825$	−8.64097	−0.300840
$826$	5.95188	0.207092
$827$	−15.2321	−0.529673	−0.264837	−	0.964293i	$-0.585318\pi$
$827$	−15.2321	−0.529673	−0.264837	+	0.964293i	$0.585318\pi$
$828$	−30.0941	−1.04584
$829$	−23.4686	−0.815098	−0.407549	−	0.913183i	$-0.633616\pi$
$829$	−23.4686	−0.815098	−0.407549	+	0.913183i	$0.633616\pi$
$830$	−105.161	−3.65019
$831$	−46.6544	−1.61842
$832$	56.5626	1.96095
$833$	−1.89434	−0.0656348
$834$	9.03415	0.312827
$835$	19.9432	0.690162
$836$	46.3476	1.60296
$837$	29.7351	1.02779
$838$	−75.4413	−2.60608
$839$	−54.2903	−1.87431	−0.937155	−	0.348913i	$-0.886551\pi$
$839$	−54.2903	−1.87431	−0.937155	+	0.348913i	$0.886551\pi$
$840$	51.2362	1.76782
$841$	−24.2301	−0.835522
$842$	−15.9641	−0.550161
$843$	6.21678	0.214117
$844$	−56.8434	−1.95663
$845$	−12.2147	−0.420200
$846$	17.4638	0.600416
$847$	9.86434	0.338943
$848$	−114.647	−3.93701
$849$	−54.8013	−1.88078
$850$	−3.04309	−0.104377
$851$	56.4809	1.93614
$852$	2.64798	0.0907182
$853$	−7.43569	−0.254593	−0.127297	−	0.991865i	$-0.540630\pi$
$853$	−7.43569	−0.254593	−0.127297	+	0.991865i	$0.540630\pi$
$854$	−14.8717	−0.508899
$855$	−18.9526	−0.648164
$856$	101.822	3.48022
$857$	−34.2947	−1.17148	−0.585742	−	0.810498i	$-0.699197\pi$
$857$	−34.2947	−1.17148	−0.585742	+	0.810498i	$0.699197\pi$
$858$	19.3969	0.662199
$859$	−43.5429	−1.48566	−0.742832	−	0.669478i	$-0.766518\pi$
$859$	−43.5429	−1.48566	−0.742832	+	0.669478i	$0.766518\pi$
$860$	82.2714	2.80543
$861$	−8.59025	−0.292755
$862$	28.9828	0.987157
$863$	−38.2758	−1.30292	−0.651462	−	0.758681i	$-0.725844\pi$
$863$	−38.2758	−1.30292	−0.651462	+	0.758681i	$0.725844\pi$
$864$	68.2586	2.32220
$865$	39.9810	1.35940
$866$	15.8508	0.538631
$867$	−33.3489	−1.13259
$868$	38.6200	1.31085
$869$	0.389738	0.0132209
$870$	−33.7712	−1.14495
$871$	27.9779	0.947994
$872$	148.534	5.02999
$873$	−0.498775	−0.0168810
$874$	−125.919	−4.25927
$875$	4.42454	0.149577
$876$	28.2373	0.954049
$877$	−29.4815	−0.995519	−0.497760	−	0.867315i	$-0.665844\pi$
$877$	−29.4815	−0.995519	−0.497760	+	0.867315i	$0.665844\pi$
$878$	95.8115	3.23348
$879$	27.3931	0.923947
$880$	−45.1049	−1.52049
$881$	9.37636	0.315898	0.157949	−	0.987447i	$-0.449512\pi$
$881$	9.37636	0.315898	0.157949	+	0.987447i	$0.449512\pi$
$882$	14.1930	0.477902
$883$	9.07955	0.305551	0.152776	−	0.988261i	$-0.451179\pi$
$883$	9.07955	0.305551	0.152776	+	0.988261i	$0.451179\pi$
$884$	4.92898	0.165780
$885$	12.3080	0.413730
$886$	−98.8554	−3.32111
$887$	−8.65659	−0.290660	−0.145330	−	0.989383i	$-0.546424\pi$
$887$	−8.65659	−0.290660	−0.145330	+	0.989383i	$0.546424\pi$
$888$	146.589	4.91919
$889$	8.25128	0.276739
$890$	−26.2673	−0.880482
$891$	13.4382	0.450195
$892$	114.300	3.82706
$893$	52.7255	1.76439
$894$	12.0882	0.404291
$895$	−48.6696	−1.62685
$896$	18.9225	0.632155
$897$	−38.0250	−1.26962
$898$	−7.20605	−0.240469
$899$	−15.6326	−0.521377
$900$	16.4514	0.548381
$901$	−2.93753	−0.0978631
$902$	13.8351	0.460658
$903$	−11.1561	−0.371251
$904$	66.2351	2.20295
$905$	56.3504	1.87315
$906$	−87.4778	−2.90625
$907$	−3.09196	−0.102667	−0.0513334	−	0.998682i	$-0.516347\pi$
$907$	−3.09196	−0.102667	−0.0513334	+	0.998682i	$0.516347\pi$
$908$	−112.872	−3.74580
$909$	3.94275	0.130773
$910$	24.2254	0.803065
$911$	51.6549	1.71140	0.855702	−	0.517469i	$-0.173126\pi$
$911$	51.6549	1.71140	0.855702	+	0.517469i	$0.173126\pi$
$912$	−178.632	−5.91510
$913$	−16.5717	−0.548442
$914$	−24.4957	−0.810245
$915$	−30.7535	−1.01668
$916$	60.5372	2.00020
$917$	−7.39599	−0.244237
$918$	3.56491	0.117659
$919$	−30.9395	−1.02060	−0.510300	−	0.859997i	$-0.670466\pi$
$919$	−30.9395	−1.02060	−0.510300	+	0.859997i	$0.670466\pi$
$920$	161.767	5.33330
$921$	55.7383	1.83664
$922$	−98.2802	−3.23669
$923$	0.768880	0.0253080
$924$	13.1474	0.432517
$925$	−30.8762	−1.01520
$926$	23.8896	0.785062
$927$	−14.2512	−0.468072
$928$	−35.8856	−1.17800
$929$	−51.2239	−1.68060	−0.840301	−	0.542120i	$-0.817622\pi$
$929$	−51.2239	−1.68060	−0.840301	+	0.542120i	$0.817622\pi$
$930$	110.681	3.62938
$931$	42.8505	1.40437
$932$	141.697	4.64143
$933$	−14.8917	−0.487532
$934$	−3.29627	−0.107857
$935$	−1.15569	−0.0377950
$936$	−22.6790	−0.741285
$937$	8.66676	0.283131	0.141565	−	0.989929i	$-0.454786\pi$
$937$	8.66676	0.283131	0.141565	+	0.989929i	$0.454786\pi$
$938$	26.2814	0.858119
$939$	−33.9041	−1.10642
$940$	−110.299	−3.59754
$941$	−15.0789	−0.491557	−0.245778	−	0.969326i	$-0.579044\pi$
$941$	−15.0789	−0.491557	−0.245778	+	0.969326i	$0.579044\pi$
$942$	−70.9175	−2.31062
$943$	−27.1218	−0.883208
$944$	26.6585	0.867660
$945$	12.6426	0.411263
$946$	17.9675	0.584174
$947$	−53.9050	−1.75168	−0.875838	−	0.482604i	$-0.839691\pi$
$947$	−53.9050	−1.75168	−0.875838	+	0.482604i	$0.839691\pi$
$948$	−3.22892	−0.104871
$949$	8.19912	0.266155
$950$	68.8356	2.23332
$951$	12.8191	0.415687
$952$	2.84342	0.0921558
$953$	−11.4714	−0.371595	−0.185797	−	0.982588i	$-0.559487\pi$
$953$	−11.4714	−0.371595	−0.185797	+	0.982588i	$0.559487\pi$
$954$	22.0089	0.712563
$955$	−8.84918	−0.286353
$956$	55.9540	1.80968
$957$	−5.32181	−0.172030
$958$	−4.14671	−0.133974
$959$	−23.2892	−0.752049
$960$	109.875	3.54619
$961$	20.2341	0.652712
$962$	69.3098	2.23464
$963$	−10.6843	−0.344298
$964$	104.957	3.38044
$965$	50.7178	1.63266
$966$	−35.7193	−1.14925
$967$	−5.49117	−0.176584	−0.0882920	−	0.996095i	$-0.528141\pi$
$967$	−5.49117	−0.176584	−0.0882920	+	0.996095i	$0.528141\pi$
$968$	80.8313	2.59802
$969$	−4.57695	−0.147033
$970$	4.36581	0.140178
$971$	17.6973	0.567935	0.283967	−	0.958834i	$-0.408349\pi$
$971$	17.6973	0.567935	0.283967	+	0.958834i	$0.408349\pi$
$972$	−46.7406	−1.49920
$973$	1.77803	0.0570009
$974$	76.9255	2.46485
$975$	20.7870	0.665717
$976$	−66.6103	−2.13215
$977$	4.52726	0.144840	0.0724199	−	0.997374i	$-0.476928\pi$
$977$	4.52726	0.144840	0.0724199	+	0.997374i	$0.476928\pi$
$978$	78.1888	2.50020
$979$	−4.13931	−0.132293
$980$	−89.6407	−2.86347
$981$	−15.5858	−0.497616
$982$	−43.5761	−1.39057
$983$	−20.2505	−0.645891	−0.322945	−	0.946418i	$-0.604673\pi$
$983$	−20.2505	−0.645891	−0.322945	+	0.946418i	$0.604673\pi$
$984$	−70.3910	−2.24398
$985$	13.8773	0.442166
$986$	−1.87418	−0.0596860
$987$	14.9566	0.476074
$988$	−111.495	−3.54714
$989$	−35.2229	−1.12002
$990$	8.65878	0.275194
$991$	36.2767	1.15237	0.576184	−	0.817320i	$-0.304541\pi$
$991$	36.2767	1.15237	0.576184	+	0.817320i	$0.304541\pi$
$992$	117.611	3.73415
$993$	19.8659	0.630425
$994$	0.722258	0.0229086
$995$	−53.2642	−1.68859
$996$	137.294	4.35033
$997$	−22.3735	−0.708575	−0.354287	−	0.935137i	$-0.615277\pi$
$997$	−22.3735	−0.708575	−0.354287	+	0.935137i	$0.615277\pi$
$998$	2.92505	0.0925908
$999$	36.1708	1.14439

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	4001.2.a.a.1.2	✓	149

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
4001.2.a.a.1.2	✓	149	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:	\( N \)	\(=\)	\( 4001 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	4001.a (trivial)

\(f(q)\)	\(=\)	\(q-2.68009 q^{2} +1.97360 q^{3} +5.18289 q^{4} +2.92338 q^{5} -5.28944 q^{6} -1.04102 q^{7} -8.53045 q^{8} +0.895108 q^{9} +O(q^{10})\)	\(q-2.68009 q^{2} +1.97360 q^{3} +5.18289 q^{4} +2.92338 q^{5} -5.28944 q^{6} -1.04102 q^{7} -8.53045 q^{8} +0.895108 q^{9} -7.83492 q^{10} -1.23466 q^{11} +10.2290 q^{12} +2.97014 q^{13} +2.79004 q^{14} +5.76959 q^{15} +12.4966 q^{16} +0.320191 q^{17} -2.39897 q^{18} -7.24282 q^{19} +15.1516 q^{20} -2.05457 q^{21} +3.30900 q^{22} -6.48684 q^{23} -16.8357 q^{24} +3.54614 q^{25} -7.96024 q^{26} -4.15422 q^{27} -5.39551 q^{28} +2.18400 q^{29} -15.4630 q^{30} -7.15780 q^{31} -16.4311 q^{32} -2.43672 q^{33} -0.858141 q^{34} -3.04331 q^{35} +4.63925 q^{36} -8.70700 q^{37} +19.4114 q^{38} +5.86187 q^{39} -24.9377 q^{40} +4.18105 q^{41} +5.50643 q^{42} +5.42990 q^{43} -6.39910 q^{44} +2.61674 q^{45} +17.3853 q^{46} -7.27969 q^{47} +24.6633 q^{48} -5.91627 q^{49} -9.50398 q^{50} +0.631929 q^{51} +15.3939 q^{52} -9.17430 q^{53} +11.1337 q^{54} -3.60937 q^{55} +8.88040 q^{56} -14.2945 q^{57} -5.85332 q^{58} +2.13326 q^{59} +29.9032 q^{60} -5.33028 q^{61} +19.1836 q^{62} -0.931828 q^{63} +19.0438 q^{64} +8.68283 q^{65} +6.53065 q^{66} +9.41973 q^{67} +1.65951 q^{68} -12.8024 q^{69} +8.15634 q^{70} +0.258870 q^{71} -7.63567 q^{72} +2.76052 q^{73} +23.3356 q^{74} +6.99867 q^{75} -37.5388 q^{76} +1.28531 q^{77} -15.7103 q^{78} -0.315664 q^{79} +36.5323 q^{80} -10.8841 q^{81} -11.2056 q^{82} +13.4221 q^{83} -10.6486 q^{84} +0.936039 q^{85} -14.5526 q^{86} +4.31035 q^{87} +10.5322 q^{88} +3.35259 q^{89} -7.01310 q^{90} -3.09198 q^{91} -33.6206 q^{92} -14.1266 q^{93} +19.5102 q^{94} -21.1735 q^{95} -32.4285 q^{96} -0.557224 q^{97} +15.8561 q^{98} -1.10515 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 149 q - 6 q^{2} - 28 q^{3} + 116 q^{4} - 19 q^{5} - 31 q^{6} - 47 q^{7} - 15 q^{8} + 115 q^{9}+O(q^{10}) \) 149 * q - 6 * q^2 - 28 * q^3 + 116 * q^4 - 19 * q^5 - 31 * q^6 - 47 * q^7 - 15 * q^8 + 115 * q^9	\( 149 q - 6 q^{2} - 28 q^{3} + 116 q^{4} - 19 q^{5} - 31 q^{6} - 47 q^{7} - 15 q^{8} + 115 q^{9} - 48 q^{10} - 31 q^{11} - 61 q^{12} - 54 q^{13} - 44 q^{14} - 65 q^{15} + 58 q^{16} - 26 q^{17} - 23 q^{18} - 86 q^{19} - 52 q^{20} - 30 q^{21} - 56 q^{22} - 63 q^{23} - 90 q^{24} + 92 q^{25} - 38 q^{26} - 103 q^{27} - 77 q^{28} - 51 q^{29} - 22 q^{30} - 256 q^{31} - 21 q^{32} - 36 q^{33} - 124 q^{34} - 50 q^{35} + 45 q^{36} - 42 q^{37} - 14 q^{38} - 119 q^{39} - 131 q^{40} - 55 q^{41} - 5 q^{42} - 55 q^{43} - 54 q^{44} - 68 q^{45} - 59 q^{46} - 82 q^{47} - 89 q^{48} + 30 q^{49} + 13 q^{50} - 83 q^{51} - 126 q^{52} - 23 q^{53} - 83 q^{54} - 244 q^{55} - 94 q^{56} - 14 q^{57} - 60 q^{58} - 93 q^{59} - 70 q^{60} - 139 q^{61} - 10 q^{62} - 120 q^{63} - 45 q^{64} - 37 q^{65} - 28 q^{66} - 110 q^{67} - 27 q^{68} - 79 q^{69} - 78 q^{70} - 123 q^{71} - 74 q^{73} - 25 q^{74} - 146 q^{75} - 192 q^{76} - q^{77} + 26 q^{78} - 273 q^{79} - 51 q^{80} + 41 q^{81} - 120 q^{82} - 27 q^{83} - 14 q^{84} - 71 q^{85} + 3 q^{86} - 98 q^{87} - 143 q^{88} - 70 q^{89} - 24 q^{90} - 256 q^{91} - 47 q^{92} + 16 q^{93} - 151 q^{94} - 83 q^{95} - 137 q^{96} - 108 q^{97} + 17 q^{98} - 131 q^{99}+O(q^{100}) \) 149 * q - 6 * q^2 - 28 * q^3 + 116 * q^4 - 19 * q^5 - 31 * q^6 - 47 * q^7 - 15 * q^8 + 115 * q^9 - 48 * q^10 - 31 * q^11 - 61 * q^12 - 54 * q^13 - 44 * q^14 - 65 * q^15 + 58 * q^16 - 26 * q^17 - 23 * q^18 - 86 * q^19 - 52 * q^20 - 30 * q^21 - 56 * q^22 - 63 * q^23 - 90 * q^24 + 92 * q^25 - 38 * q^26 - 103 * q^27 - 77 * q^28 - 51 * q^29 - 22 * q^30 - 256 * q^31 - 21 * q^32 - 36 * q^33 - 124 * q^34 - 50 * q^35 + 45 * q^36 - 42 * q^37 - 14 * q^38 - 119 * q^39 - 131 * q^40 - 55 * q^41 - 5 * q^42 - 55 * q^43 - 54 * q^44 - 68 * q^45 - 59 * q^46 - 82 * q^47 - 89 * q^48 + 30 * q^49 + 13 * q^50 - 83 * q^51 - 126 * q^52 - 23 * q^53 - 83 * q^54 - 244 * q^55 - 94 * q^56 - 14 * q^57 - 60 * q^58 - 93 * q^59 - 70 * q^60 - 139 * q^61 - 10 * q^62 - 120 * q^63 - 45 * q^64 - 37 * q^65 - 28 * q^66 - 110 * q^67 - 27 * q^68 - 79 * q^69 - 78 * q^70 - 123 * q^71 - 74 * q^73 - 25 * q^74 - 146 * q^75 - 192 * q^76 - q^77 + 26 * q^78 - 273 * q^79 - 51 * q^80 + 41 * q^81 - 120 * q^82 - 27 * q^83 - 14 * q^84 - 71 * q^85 + 3 * q^86 - 98 * q^87 - 143 * q^88 - 70 * q^89 - 24 * q^90 - 256 * q^91 - 47 * q^92 + 16 * q^93 - 151 * q^94 - 83 * q^95 - 137 * q^96 - 108 * q^97 + 17 * q^98 - 131 * q^99

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