LMFDB - Embedded newform 8047.2.a.c.1.8

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [8047,2,Mod(1,8047)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(8047, 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("8047.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 8047 = 13 \cdot 619 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	8047.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:	$64.2556185065$
Analytic rank:	$1$
Dimension:	$151$
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.8
Character	$\chi$	$=$	8047.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-2.66015 q^{2} -2.71534 q^{3} +5.07642 q^{4} +1.80330 q^{5} +7.22323 q^{6} -0.0430519 q^{7} -8.18376 q^{8} +4.37308 q^{9} +O(q^{10})$	\(q-2.66015 q^{2} -2.71534 q^{3} +5.07642 q^{4} +1.80330 q^{5} +7.22323 q^{6} -0.0430519 q^{7} -8.18376 q^{8} +4.37308 q^{9} -4.79706 q^{10} +1.58791 q^{11} -13.7842 q^{12} -1.00000 q^{13} +0.114525 q^{14} -4.89658 q^{15} +11.6172 q^{16} +1.31669 q^{17} -11.6331 q^{18} +6.62061 q^{19} +9.15432 q^{20} +0.116901 q^{21} -4.22408 q^{22} -7.01983 q^{23} +22.2217 q^{24} -1.74810 q^{25} +2.66015 q^{26} -3.72838 q^{27} -0.218550 q^{28} -1.51205 q^{29} +13.0257 q^{30} +0.126834 q^{31} -14.5361 q^{32} -4.31171 q^{33} -3.50259 q^{34} -0.0776356 q^{35} +22.1996 q^{36} +6.52958 q^{37} -17.6118 q^{38} +2.71534 q^{39} -14.7578 q^{40} -1.06564 q^{41} -0.310974 q^{42} -0.707771 q^{43} +8.06090 q^{44} +7.88598 q^{45} +18.6738 q^{46} +1.54300 q^{47} -31.5447 q^{48} -6.99815 q^{49} +4.65023 q^{50} -3.57526 q^{51} -5.07642 q^{52} -6.57382 q^{53} +9.91807 q^{54} +2.86348 q^{55} +0.352327 q^{56} -17.9772 q^{57} +4.02228 q^{58} +1.51306 q^{59} -24.8571 q^{60} +10.4527 q^{61} -0.337398 q^{62} -0.188270 q^{63} +15.4338 q^{64} -1.80330 q^{65} +11.4698 q^{66} -10.7746 q^{67} +6.68406 q^{68} +19.0612 q^{69} +0.206523 q^{70} +14.6007 q^{71} -35.7882 q^{72} +3.44914 q^{73} -17.3697 q^{74} +4.74670 q^{75} +33.6090 q^{76} -0.0683625 q^{77} -7.22323 q^{78} +10.1586 q^{79} +20.9494 q^{80} -2.99541 q^{81} +2.83477 q^{82} -4.34868 q^{83} +0.593437 q^{84} +2.37438 q^{85} +1.88278 q^{86} +4.10572 q^{87} -12.9951 q^{88} +5.51183 q^{89} -20.9779 q^{90} +0.0430519 q^{91} -35.6356 q^{92} -0.344398 q^{93} -4.10462 q^{94} +11.9390 q^{95} +39.4704 q^{96} +5.45576 q^{97} +18.6162 q^{98} +6.94405 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 151 q - 13 q^{2} - 16 q^{3} + 151 q^{4} - 43 q^{5} - 17 q^{6} - 18 q^{7} - 39 q^{8} + 135 q^{9}+O(q^{10}) $ 151 * q - 13 * q^2 - 16 * q^3 + 151 * q^4 - 43 * q^5 - 17 * q^6 - 18 * q^7 - 39 * q^8 + 135 * q^9	\( 151 q - 13 q^{2} - 16 q^{3} + 151 q^{4} - 43 q^{5} - 17 q^{6} - 18 q^{7} - 39 q^{8} + 135 q^{9} - 3 q^{10} - 27 q^{11} - 52 q^{12} - 151 q^{13} - 9 q^{14} - 14 q^{15} + 143 q^{16} - 111 q^{17} - 37 q^{18} - 17 q^{19} - 107 q^{20} - 29 q^{21} - 16 q^{22} - 47 q^{23} - 46 q^{24} + 122 q^{25} + 13 q^{26} - 55 q^{27} - 44 q^{28} + 37 q^{29} - 14 q^{30} - 27 q^{31} - 86 q^{32} - 94 q^{33} - 10 q^{34} - 47 q^{35} + 124 q^{36} - 59 q^{37} - 80 q^{38} + 16 q^{39} + 5 q^{40} - 129 q^{41} - 77 q^{42} - 11 q^{43} - 99 q^{44} - 122 q^{45} - 17 q^{46} - 130 q^{47} - 111 q^{48} + 99 q^{49} - 72 q^{50} + 15 q^{51} - 151 q^{52} - 43 q^{53} - 49 q^{54} - 40 q^{55} - 50 q^{56} - 85 q^{57} - 73 q^{58} - 74 q^{59} - 43 q^{60} - 7 q^{61} - 110 q^{62} - 70 q^{63} + 141 q^{64} + 43 q^{65} - 16 q^{66} - 39 q^{67} - 222 q^{68} + 19 q^{69} - 52 q^{70} - 72 q^{71} - 106 q^{72} - 143 q^{73} + 20 q^{74} - 73 q^{75} - 88 q^{76} - 86 q^{77} + 17 q^{78} + 10 q^{79} - 239 q^{80} + 103 q^{81} - 96 q^{82} - 96 q^{83} - 75 q^{84} - 24 q^{85} - 109 q^{86} - 65 q^{87} - 45 q^{88} - 237 q^{89} - 79 q^{90} + 18 q^{91} - 153 q^{92} - 137 q^{93} - 23 q^{94} + 10 q^{95} - 109 q^{96} - 160 q^{97} - 119 q^{98} - 86 q^{99}+O(q^{100}) \) 151 * q - 13 * q^2 - 16 * q^3 + 151 * q^4 - 43 * q^5 - 17 * q^6 - 18 * q^7 - 39 * q^8 + 135 * q^9 - 3 * q^10 - 27 * q^11 - 52 * q^12 - 151 * q^13 - 9 * q^14 - 14 * q^15 + 143 * q^16 - 111 * q^17 - 37 * q^18 - 17 * q^19 - 107 * q^20 - 29 * q^21 - 16 * q^22 - 47 * q^23 - 46 * q^24 + 122 * q^25 + 13 * q^26 - 55 * q^27 - 44 * q^28 + 37 * q^29 - 14 * q^30 - 27 * q^31 - 86 * q^32 - 94 * q^33 - 10 * q^34 - 47 * q^35 + 124 * q^36 - 59 * q^37 - 80 * q^38 + 16 * q^39 + 5 * q^40 - 129 * q^41 - 77 * q^42 - 11 * q^43 - 99 * q^44 - 122 * q^45 - 17 * q^46 - 130 * q^47 - 111 * q^48 + 99 * q^49 - 72 * q^50 + 15 * q^51 - 151 * q^52 - 43 * q^53 - 49 * q^54 - 40 * q^55 - 50 * q^56 - 85 * q^57 - 73 * q^58 - 74 * q^59 - 43 * q^60 - 7 * q^61 - 110 * q^62 - 70 * q^63 + 141 * q^64 + 43 * q^65 - 16 * q^66 - 39 * q^67 - 222 * q^68 + 19 * q^69 - 52 * q^70 - 72 * q^71 - 106 * q^72 - 143 * q^73 + 20 * q^74 - 73 * q^75 - 88 * q^76 - 86 * q^77 + 17 * q^78 + 10 * q^79 - 239 * q^80 + 103 * q^81 - 96 * q^82 - 96 * q^83 - 75 * q^84 - 24 * q^85 - 109 * q^86 - 65 * q^87 - 45 * q^88 - 237 * q^89 - 79 * q^90 + 18 * q^91 - 153 * q^92 - 137 * q^93 - 23 * q^94 + 10 * q^95 - 109 * q^96 - 160 * q^97 - 119 * q^98 - 86 * 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 $

$2$	−2.66015	−1.88101	−0.940507	−	0.339775i	$-0.889649\pi$
$2$	−2.66015	−1.88101	−0.940507	+	0.339775i	$0.889649\pi$
$3$	−2.71534	−1.56770	−0.783852	−	0.620948i	$-0.786748\pi$
$3$	−2.71534	−1.56770	−0.783852	+	0.620948i	$0.786748\pi$
$4$	5.07642	2.53821
$5$	1.80330	0.806461	0.403230	−	0.915098i	$-0.367887\pi$
$5$	1.80330	0.806461	0.403230	+	0.915098i	$0.367887\pi$
$6$	7.22323	2.94887
$7$	−0.0430519	−0.0162721	−0.00813605	−	0.999967i	$-0.502590\pi$
$7$	−0.0430519	−0.0162721	−0.00813605	+	0.999967i	$0.502590\pi$
$8$	−8.18376	−2.89340
$9$	4.37308	1.45769
$10$	−4.79706	−1.51696
$11$	1.58791	0.478772	0.239386	−	0.970924i	$-0.423054\pi$
$11$	1.58791	0.478772	0.239386	+	0.970924i	$0.423054\pi$
$12$	−13.7842	−3.97916
$13$	−1.00000	−0.277350
$13$	−1.00000	−0.277350
$14$	0.114525	0.0306080
$15$	−4.89658	−1.26429
$16$	11.6172	2.90431
$17$	1.31669	0.319344	0.159672	−	0.987170i	$-0.448956\pi$
$17$	1.31669	0.319344	0.159672	+	0.987170i	$0.448956\pi$
$18$	−11.6331	−2.74194
$19$	6.62061	1.51887	0.759436	−	0.650582i	$-0.225475\pi$
$19$	6.62061	1.51887	0.759436	+	0.650582i	$0.225475\pi$
$20$	9.15432	2.04697
$21$	0.116901	0.0255098
$22$	−4.22408	−0.900577
$23$	−7.01983	−1.46374	−0.731868	−	0.681446i	$-0.761351\pi$
$23$	−7.01983	−1.46374	−0.731868	+	0.681446i	$0.761351\pi$
$24$	22.2217	4.53599
$25$	−1.74810	−0.349621
$26$	2.66015	0.521699
$27$	−3.72838	−0.717527
$28$	−0.218550	−0.0413020
$29$	−1.51205	−0.280780	−0.140390	−	0.990096i	$-0.544836\pi$
$29$	−1.51205	−0.280780	−0.140390	+	0.990096i	$0.544836\pi$
$30$	13.0257	2.37815
$31$	0.126834	0.0227801	0.0113900	−	0.999935i	$-0.496374\pi$
$31$	0.126834	0.0227801	0.0113900	+	0.999935i	$0.496374\pi$
$32$	−14.5361	−2.56964
$33$	−4.31171	−0.750573
$34$	−3.50259	−0.600690
$35$	−0.0776356	−0.0131228
$36$	22.1996	3.69993
$37$	6.52958	1.07346	0.536728	−	0.843755i	$-0.319660\pi$
$37$	6.52958	1.07346	0.536728	+	0.843755i	$0.319660\pi$
$38$	−17.6118	−2.85702
$39$	2.71534	0.434803
$40$	−14.7578	−2.33341
$41$	−1.06564	−0.166425	−0.0832126	−	0.996532i	$-0.526518\pi$
$41$	−1.06564	−0.166425	−0.0832126	+	0.996532i	$0.526518\pi$
$42$	−0.310974	−0.0479843
$43$	−0.707771	−0.107934	−0.0539670	−	0.998543i	$-0.517187\pi$
$43$	−0.707771	−0.107934	−0.0539670	+	0.998543i	$0.517187\pi$
$44$	8.06090	1.21523
$45$	7.88598	1.17557
$46$	18.6738	2.75331
$47$	1.54300	0.225070	0.112535	−	0.993648i	$-0.464103\pi$
$47$	1.54300	0.225070	0.112535	+	0.993648i	$0.464103\pi$
$48$	−31.5447	−4.55309
$49$	−6.99815	−0.999735
$50$	4.65023	0.657642
$51$	−3.57526	−0.500636
$52$	−5.07642	−0.703973
$53$	−6.57382	−0.902983	−0.451492	−	0.892275i	$-0.649108\pi$
$53$	−6.57382	−0.902983	−0.451492	+	0.892275i	$0.649108\pi$
$54$	9.91807	1.34968
$55$	2.86348	0.386111
$56$	0.352327	0.0470816
$57$	−17.9772	−2.38114
$58$	4.02228	0.528151
$59$	1.51306	0.196984	0.0984918	−	0.995138i	$-0.468598\pi$
$59$	1.51306	0.196984	0.0984918	+	0.995138i	$0.468598\pi$
$60$	−24.8571	−3.20904
$61$	10.4527	1.33834	0.669168	−	0.743111i	$-0.266651\pi$
$61$	10.4527	1.33834	0.669168	+	0.743111i	$0.266651\pi$
$62$	−0.337398	−0.0428496
$63$	−0.188270	−0.0237197
$64$	15.4338	1.92922
$65$	−1.80330	−0.223672
$66$	11.4698	1.41184
$67$	−10.7746	−1.31633	−0.658166	−	0.752872i	$-0.728668\pi$
$67$	−10.7746	−1.31633	−0.658166	+	0.752872i	$0.728668\pi$
$68$	6.68406	0.810562
$69$	19.0612	2.29470
$70$	0.206523	0.0246842
$71$	14.6007	1.73278	0.866390	−	0.499368i	$-0.166434\pi$
$71$	14.6007	1.73278	0.866390	+	0.499368i	$0.166434\pi$
$72$	−35.7882	−4.21768
$73$	3.44914	0.403692	0.201846	−	0.979417i	$-0.435306\pi$
$73$	3.44914	0.403692	0.201846	+	0.979417i	$0.435306\pi$
$74$	−17.3697	−2.01919
$75$	4.74670	0.548102
$76$	33.6090	3.85522
$77$	−0.0683625	−0.00779063
$78$	−7.22323	−0.817870
$79$	10.1586	1.14293	0.571464	−	0.820627i	$-0.306376\pi$
$79$	10.1586	1.14293	0.571464	+	0.820627i	$0.306376\pi$
$80$	20.9494	2.34221
$81$	−2.99541	−0.332824
$82$	2.83477	0.313048
$83$	−4.34868	−0.477329	−0.238665	−	0.971102i	$-0.576710\pi$
$83$	−4.34868	−0.477329	−0.238665	+	0.971102i	$0.576710\pi$
$84$	0.593437	0.0647493
$85$	2.37438	0.257538
$86$	1.88278	0.203025
$87$	4.10572	0.440180
$88$	−12.9951	−1.38528
$89$	5.51183	0.584253	0.292127	−	0.956380i	$-0.405637\pi$
$89$	5.51183	0.584253	0.292127	+	0.956380i	$0.405637\pi$
$90$	−20.9779	−2.21127
$91$	0.0430519	0.00451307
$92$	−35.6356	−3.71527
$93$	−0.344398	−0.0357124
$94$	−4.10462	−0.423359
$95$	11.9390	1.22491
$96$	39.4704	4.02844
$97$	5.45576	0.553948	0.276974	−	0.960877i	$-0.410668\pi$
$97$	5.45576	0.553948	0.276974	+	0.960877i	$0.410668\pi$
$98$	18.6162	1.88052
$99$	6.94405	0.697903
$100$	−8.87412	−0.887412
$101$	−14.8178	−1.47442	−0.737212	−	0.675661i	$-0.763858\pi$
$101$	−14.8178	−1.47442	−0.737212	+	0.675661i	$0.763858\pi$
$102$	9.51074	0.941703
$103$	−1.64874	−0.162455	−0.0812273	−	0.996696i	$-0.525884\pi$
$103$	−1.64874	−0.162455	−0.0812273	+	0.996696i	$0.525884\pi$
$104$	8.18376	0.802484
$105$	0.210807	0.0205727
$106$	17.4874	1.69852
$107$	−4.50165	−0.435191	−0.217596	−	0.976039i	$-0.569821\pi$
$107$	−4.50165	−0.435191	−0.217596	+	0.976039i	$0.569821\pi$
$108$	−18.9268	−1.82124
$109$	−7.08120	−0.678256	−0.339128	−	0.940740i	$-0.610132\pi$
$109$	−7.08120	−0.678256	−0.339128	+	0.940740i	$0.610132\pi$
$110$	−7.61729	−0.726280
$111$	−17.7300	−1.68286
$112$	−0.500144	−0.0472592
$113$	−7.64280	−0.718974	−0.359487	−	0.933150i	$-0.617048\pi$
$113$	−7.64280	−0.718974	−0.359487	+	0.933150i	$0.617048\pi$
$114$	47.8222	4.47896
$115$	−12.6589	−1.18045
$116$	−7.67578	−0.712679
$117$	−4.37308	−0.404291
$118$	−4.02497	−0.370529
$119$	−0.0566860	−0.00519639
$120$	40.0724	3.65810
$121$	−8.47855	−0.770777
$122$	−27.8059	−2.51743
$123$	2.89358	0.260905
$124$	0.643863	0.0578206
$125$	−12.1689	−1.08842
$126$	0.500826	0.0446171
$127$	−9.98040	−0.885617	−0.442809	−	0.896616i	$-0.646018\pi$
$127$	−9.98040	−0.885617	−0.442809	+	0.896616i	$0.646018\pi$
$128$	−11.9841	−1.05926
$129$	1.92184	0.169208
$130$	4.79706	0.420730
$131$	−16.8746	−1.47434	−0.737171	−	0.675706i	$-0.763839\pi$
$131$	−16.8746	−1.47434	−0.737171	+	0.675706i	$0.763839\pi$
$132$	−21.8881	−1.90511
$133$	−0.285030	−0.0247152
$134$	28.6622	2.47604
$135$	−6.72339	−0.578657
$136$	−10.7755	−0.923988
$137$	−12.8595	−1.09866	−0.549329	−	0.835606i	$-0.685116\pi$
$137$	−12.8595	−1.09866	−0.549329	+	0.835606i	$0.685116\pi$
$138$	−50.7059	−4.31637
$139$	−18.8323	−1.59733	−0.798665	−	0.601775i	$-0.794460\pi$
$139$	−18.8323	−1.59733	−0.798665	+	0.601775i	$0.794460\pi$
$140$	−0.394111	−0.0333085
$141$	−4.18978	−0.352843
$142$	−38.8400	−3.25938
$143$	−1.58791	−0.132788
$144$	50.8030	4.23359
$145$	−2.72667	−0.226438
$146$	−9.17526	−0.759350
$147$	19.0024	1.56729
$148$	33.1469	2.72466
$149$	−19.3277	−1.58339	−0.791693	−	0.610920i	$-0.790800\pi$
$149$	−19.3277	−1.58339	−0.791693	+	0.610920i	$0.790800\pi$
$150$	−12.6270	−1.03099
$151$	−7.95305	−0.647210	−0.323605	−	0.946192i	$-0.604895\pi$
$151$	−7.95305	−0.647210	−0.323605	+	0.946192i	$0.604895\pi$
$152$	−54.1815	−4.39470
$153$	5.75798	0.465505
$154$	0.181855	0.0146543
$155$	0.228720	0.0183712
$156$	13.7842	1.10362
$157$	−7.33470	−0.585373	−0.292686	−	0.956208i	$-0.594549\pi$
$157$	−7.33470	−0.585373	−0.292686	+	0.956208i	$0.594549\pi$
$158$	−27.0234	−2.14986
$159$	17.8502	1.41561
$160$	−26.2129	−2.07232
$161$	0.302217	0.0238181
$162$	7.96827	0.626046
$163$	10.5792	0.828624	0.414312	−	0.910135i	$-0.364022\pi$
$163$	10.5792	0.828624	0.414312	+	0.910135i	$0.364022\pi$
$164$	−5.40965	−0.422422
$165$	−7.77532	−0.605308
$166$	11.5682	0.897863
$167$	24.7666	1.91649	0.958247	−	0.285941i	$-0.0923060\pi$
$167$	24.7666	1.91649	0.958247	+	0.285941i	$0.0923060\pi$
$168$	−0.956687	−0.0738100
$169$	1.00000	0.0769231
$170$	−6.31623	−0.484433
$171$	28.9525	2.21405
$172$	−3.59294	−0.273959
$173$	8.00705	0.608765	0.304382	−	0.952550i	$-0.401550\pi$
$173$	8.00705	0.608765	0.304382	+	0.952550i	$0.401550\pi$
$174$	−10.9219	−0.827984
$175$	0.0752593	0.00568907
$176$	18.4471	1.39050
$177$	−4.10848	−0.308812
$178$	−14.6623	−1.09899
$179$	7.37360	0.551129	0.275564	−	0.961283i	$-0.411135\pi$
$179$	7.37360	0.551129	0.275564	+	0.961283i	$0.411135\pi$
$180$	40.0326	2.98385
$181$	19.5926	1.45631	0.728155	−	0.685413i	$-0.240378\pi$
$181$	19.5926	1.45631	0.728155	+	0.685413i	$0.240378\pi$
$182$	−0.114525	−0.00848914
$183$	−28.3827	−2.09811
$184$	57.4486	4.23517
$185$	11.7748	0.865701
$186$	0.916151	0.0671755
$187$	2.09078	0.152893
$188$	7.83293	0.571275
$189$	0.160514	0.0116757
$190$	−31.7595	−2.30407
$191$	0.0906450	0.00655884	0.00327942	−	0.999995i	$-0.498956\pi$
$191$	0.0906450	0.00655884	0.00327942	+	0.999995i	$0.498956\pi$
$192$	−41.9080	−3.02445
$193$	−21.2083	−1.52661	−0.763303	−	0.646041i	$-0.776423\pi$
$193$	−21.2083	−1.52661	−0.763303	+	0.646041i	$0.776423\pi$
$194$	−14.5132	−1.04198
$195$	4.89658	0.350651
$196$	−35.5256	−2.53754
$197$	−1.92638	−0.137249	−0.0686245	−	0.997643i	$-0.521861\pi$
$197$	−1.92638	−0.137249	−0.0686245	+	0.997643i	$0.521861\pi$
$198$	−18.4722	−1.31277
$199$	8.40791	0.596021	0.298010	−	0.954563i	$-0.403677\pi$
$199$	8.40791	0.596021	0.298010	+	0.954563i	$0.403677\pi$
$200$	14.3061	1.01159
$201$	29.2569	2.06362
$202$	39.4176	2.77341
$203$	0.0650965	0.00456888
$204$	−18.1495	−1.27072
$205$	−1.92167	−0.134215
$206$	4.38589	0.305579
$207$	−30.6983	−2.13368
$208$	−11.6172	−0.805509
$209$	10.5129	0.727194
$210$	−0.560780	−0.0386975
$211$	0.911147	0.0627260	0.0313630	−	0.999508i	$-0.490015\pi$
$211$	0.911147	0.0627260	0.0313630	+	0.999508i	$0.490015\pi$
$212$	−33.3715	−2.29196
$213$	−39.6458	−2.71648
$214$	11.9751	0.818600
$215$	−1.27632	−0.0870445
$216$	30.5122	2.07609
$217$	−0.00546045	−0.000370680 0
$218$	18.8371	1.27581
$219$	−9.36560	−0.632869
$220$	14.5362	0.980032
$221$	−1.31669	−0.0885700
$222$	47.1647	3.16548
$223$	−4.87877	−0.326706	−0.163353	−	0.986568i	$-0.552231\pi$
$223$	−4.87877	−0.326706	−0.163353	+	0.986568i	$0.552231\pi$
$224$	0.625807	0.0418135
$225$	−7.64460	−0.509640
$226$	20.3310	1.35240
$227$	12.3486	0.819605	0.409803	−	0.912174i	$-0.365598\pi$
$227$	12.3486	0.819605	0.409803	+	0.912174i	$0.365598\pi$
$228$	−91.2600	−6.04384
$229$	14.6493	0.968053	0.484026	−	0.875053i	$-0.339174\pi$
$229$	14.6493	0.968053	0.484026	+	0.875053i	$0.339174\pi$
$230$	33.6746	2.22044
$231$	0.185628	0.0122134
$232$	12.3742	0.812407
$233$	1.67422	0.109682	0.0548410	−	0.998495i	$-0.482535\pi$
$233$	1.67422	0.109682	0.0548410	+	0.998495i	$0.482535\pi$
$234$	11.6331	0.760477
$235$	2.78250	0.181510
$236$	7.68093	0.499986
$237$	−27.5840	−1.79177
$238$	0.150793	0.00977448
$239$	−1.84828	−0.119555	−0.0597776	−	0.998212i	$-0.519039\pi$
$239$	−1.84828	−0.119555	−0.0597776	+	0.998212i	$0.519039\pi$
$240$	−56.8846	−3.67189
$241$	−18.2728	−1.17705	−0.588526	−	0.808478i	$-0.700292\pi$
$241$	−18.2728	−1.17705	−0.588526	+	0.808478i	$0.700292\pi$
$242$	22.5542	1.44984
$243$	19.3187	1.23930
$244$	53.0625	3.39698
$245$	−12.6198	−0.806247
$246$	−7.69737	−0.490767
$247$	−6.62061	−0.421259
$248$	−1.03798	−0.0659118
$249$	11.8081	0.748311
$250$	32.3711	2.04733
$251$	−25.7364	−1.62447	−0.812233	−	0.583333i	$-0.801748\pi$
$251$	−25.7364	−1.62447	−0.812233	+	0.583333i	$0.801748\pi$
$252$	−0.955736	−0.0602057
$253$	−11.1469	−0.700797
$254$	26.5494	1.66586
$255$	−6.44727	−0.403743
$256$	1.01200	0.0632499
$257$	23.8973	1.49067	0.745336	−	0.666689i	$-0.232289\pi$
$257$	23.8973	1.49067	0.745336	+	0.666689i	$0.232289\pi$
$258$	−5.11239	−0.318283
$259$	−0.281111	−0.0174674
$260$	−9.15432	−0.567727
$261$	−6.61230	−0.409291
$262$	44.8891	2.77326
$263$	−2.04959	−0.126383	−0.0631917	−	0.998001i	$-0.520128\pi$
$263$	−2.04959	−0.126383	−0.0631917	+	0.998001i	$0.520128\pi$
$264$	35.2860	2.17171
$265$	−11.8546	−0.728221
$266$	0.758224	0.0464897
$267$	−14.9665	−0.915935
$268$	−54.6967	−3.34113
$269$	−13.1031	−0.798911	−0.399456	−	0.916752i	$-0.630801\pi$
$269$	−13.1031	−0.798911	−0.399456	+	0.916752i	$0.630801\pi$
$270$	17.8853	1.08846
$271$	17.0436	1.03532	0.517662	−	0.855585i	$-0.326803\pi$
$271$	17.0436	1.03532	0.517662	+	0.855585i	$0.326803\pi$
$272$	15.2963	0.927472
$273$	−0.116901	−0.00707515
$274$	34.2081	2.06659
$275$	−2.77583	−0.167389
$276$	96.7629	5.82444
$277$	23.4494	1.40894	0.704470	−	0.709734i	$-0.251185\pi$
$277$	23.4494	1.40894	0.704470	+	0.709734i	$0.251185\pi$
$278$	50.0967	3.00460
$279$	0.554655	0.0332064
$280$	0.635351	0.0379695
$281$	−24.9292	−1.48715	−0.743577	−	0.668650i	$-0.766872\pi$
$281$	−24.9292	−1.48715	−0.743577	+	0.668650i	$0.766872\pi$
$282$	11.1455	0.663702
$283$	1.07795	0.0640773	0.0320386	−	0.999487i	$-0.489800\pi$
$283$	1.07795	0.0640773	0.0320386	+	0.999487i	$0.489800\pi$
$284$	74.1191	4.39816
$285$	−32.4183	−1.92030
$286$	4.22408	0.249775
$287$	0.0458779	0.00270809
$288$	−63.5675	−3.74575
$289$	−15.2663	−0.898020
$290$	7.25338	0.425933
$291$	−14.8142	−0.868426
$292$	17.5093	1.02466
$293$	−24.9190	−1.45578	−0.727891	−	0.685693i	$-0.759499\pi$
$293$	−24.9190	−1.45578	−0.727891	+	0.685693i	$0.759499\pi$
$294$	−50.5492	−2.94809
$295$	2.72850	0.158860
$296$	−53.4365	−3.10593
$297$	−5.92033	−0.343532
$298$	51.4146	2.97837
$299$	7.01983	0.405967
$300$	24.0963	1.39120
$301$	0.0304709	0.00175631
$302$	21.1564	1.21741
$303$	40.2354	2.31146
$304$	76.9131	4.41127
$305$	18.8494	1.07932
$306$	−15.3171	−0.875621
$307$	3.07953	0.175758	0.0878792	−	0.996131i	$-0.471991\pi$
$307$	3.07953	0.175758	0.0878792	+	0.996131i	$0.471991\pi$
$308$	−0.347037	−0.0197743
$309$	4.47688	0.254681
$310$	−0.608431	−0.0345565
$311$	9.94499	0.563928	0.281964	−	0.959425i	$-0.409014\pi$
$311$	9.94499	0.563928	0.281964	+	0.959425i	$0.409014\pi$
$312$	−22.2217	−1.25806
$313$	−6.46265	−0.365291	−0.182645	−	0.983179i	$-0.558466\pi$
$313$	−6.46265	−0.365291	−0.182645	+	0.983179i	$0.558466\pi$
$314$	19.5114	1.10109
$315$	−0.339507	−0.0191290
$316$	51.5692	2.90099
$317$	−5.49282	−0.308507	−0.154254	−	0.988031i	$-0.549297\pi$
$317$	−5.49282	−0.308507	−0.154254	+	0.988031i	$0.549297\pi$
$318$	−47.4842	−2.66278
$319$	−2.40099	−0.134430
$320$	27.8318	1.55584
$321$	12.2235	0.682250
$322$	−0.803945	−0.0448021
$323$	8.71728	0.485042
$324$	−15.2060	−0.844777
$325$	1.74810	0.0969674
$326$	−28.1422	−1.55865
$327$	19.2279	1.06330
$328$	8.72096	0.481534
$329$	−0.0664292	−0.00366236
$330$	20.6836	1.13859
$331$	16.8661	0.927043	0.463521	−	0.886086i	$-0.346586\pi$
$331$	16.8661	0.927043	0.463521	+	0.886086i	$0.346586\pi$
$332$	−22.0757	−1.21156
$333$	28.5544	1.56477
$334$	−65.8829	−3.60495
$335$	−19.4299	−1.06157
$336$	1.35806	0.0740883
$337$	26.7279	1.45596	0.727982	−	0.685596i	$-0.240458\pi$
$337$	26.7279	1.45596	0.727982	+	0.685596i	$0.240458\pi$
$338$	−2.66015	−0.144693
$339$	20.7528	1.12714
$340$	12.0534	0.653686
$341$	0.201401	0.0109065
$342$	−77.0180	−4.16466
$343$	0.602647	0.0325399
$344$	5.79222	0.312296
$345$	34.3732	1.85059
$346$	−21.3000	−1.14509
$347$	28.9648	1.55491	0.777455	−	0.628938i	$-0.216510\pi$
$347$	28.9648	1.55491	0.777455	+	0.628938i	$0.216510\pi$
$348$	20.8424	1.11727
$349$	23.6671	1.26687	0.633435	−	0.773796i	$-0.281644\pi$
$349$	23.6671	1.26687	0.633435	+	0.773796i	$0.281644\pi$
$350$	−0.200201	−0.0107012
$351$	3.72838	0.199006
$352$	−23.0820	−1.23027
$353$	−6.30131	−0.335385	−0.167692	−	0.985839i	$-0.553632\pi$
$353$	−6.30131	−0.335385	−0.167692	+	0.985839i	$0.553632\pi$
$354$	10.9292	0.580879
$355$	26.3294	1.39742
$356$	27.9804	1.48296
$357$	0.153922	0.00814640
$358$	−19.6149	−1.03668
$359$	−29.7337	−1.56928	−0.784641	−	0.619950i	$-0.787153\pi$
$359$	−29.7337	−1.56928	−0.784641	+	0.619950i	$0.787153\pi$
$360$	−64.5370	−3.40140
$361$	24.8325	1.30697
$362$	−52.1195	−2.73934
$363$	23.0221	1.20835
$364$	0.218550	0.0114551
$365$	6.21985	0.325562
$366$	75.5025	3.94658
$367$	−3.93344	−0.205324	−0.102662	−	0.994716i	$-0.532736\pi$
$367$	−3.93344	−0.205324	−0.102662	+	0.994716i	$0.532736\pi$
$368$	−81.5510	−4.25114
$369$	−4.66014	−0.242597
$370$	−31.3228	−1.62839
$371$	0.283016	0.0146934
$372$	−1.74831	−0.0906456
$373$	−22.0046	−1.13935	−0.569677	−	0.821868i	$-0.692932\pi$
$373$	−22.0046	−1.13935	−0.569677	+	0.821868i	$0.692932\pi$
$374$	−5.56180	−0.287594
$375$	33.0426	1.70631
$376$	−12.6276	−0.651216
$377$	1.51205	0.0778743
$378$	−0.426992	−0.0219621
$379$	15.1281	0.777079	0.388539	−	0.921432i	$-0.372980\pi$
$379$	15.1281	0.777079	0.388539	+	0.921432i	$0.372980\pi$
$380$	60.6072	3.10908
$381$	27.1002	1.38839
$382$	−0.241130	−0.0123373
$383$	−10.9681	−0.560442	−0.280221	−	0.959935i	$-0.590408\pi$
$383$	−10.9681	−0.560442	−0.280221	+	0.959935i	$0.590408\pi$
$384$	32.5410	1.66060
$385$	−0.123278	−0.00628284
$386$	56.4173	2.87156
$387$	−3.09514	−0.157335
$388$	27.6957	1.40604
$389$	−38.2793	−1.94084	−0.970419	−	0.241428i	$-0.922384\pi$
$389$	−38.2793	−1.94084	−0.970419	+	0.241428i	$0.922384\pi$
$390$	−13.0257	−0.659580
$391$	−9.24293	−0.467435
$392$	57.2712	2.89263
$393$	45.8203	2.31133
$394$	5.12448	0.258167
$395$	18.3190	0.921727
$396$	35.2509	1.77143
$397$	16.2747	0.816803	0.408401	−	0.912802i	$-0.366086\pi$
$397$	16.2747	0.816803	0.408401	+	0.912802i	$0.366086\pi$
$398$	−22.3663	−1.12112
$399$	0.773954	0.0387462
$400$	−20.3081	−1.01541
$401$	−11.6517	−0.581858	−0.290929	−	0.956745i	$-0.593964\pi$
$401$	−11.6517	−0.581858	−0.290929	+	0.956745i	$0.593964\pi$
$402$	−77.8277	−3.88170
$403$	−0.126834	−0.00631806
$404$	−75.2213	−3.74240
$405$	−5.40163	−0.268409
$406$	−0.173167	−0.00859412
$407$	10.3684	0.513941
$408$	29.2590	1.44854
$409$	27.3477	1.35225	0.676127	−	0.736785i	$-0.263657\pi$
$409$	27.3477	1.35225	0.676127	+	0.736785i	$0.263657\pi$
$410$	5.11195	0.252461
$411$	34.9178	1.72237
$412$	−8.36968	−0.412344
$413$	−0.0651402	−0.00320534
$414$	81.6622	4.01348
$415$	−7.84198	−0.384948
$416$	14.5361	0.712690
$417$	51.1360	2.50414
$418$	−27.9660	−1.36786
$419$	29.9952	1.46536	0.732682	−	0.680571i	$-0.238268\pi$
$419$	29.9952	1.46536	0.732682	+	0.680571i	$0.238268\pi$
$420$	1.07015	0.0522178
$421$	20.4360	0.995992	0.497996	−	0.867179i	$-0.334069\pi$
$421$	20.4360	0.995992	0.497996	+	0.867179i	$0.334069\pi$
$422$	−2.42379	−0.117988
$423$	6.74767	0.328083
$424$	53.7986	2.61269
$425$	−2.30171	−0.111649
$426$	105.464	5.10974
$427$	−0.450010	−0.0217775
$428$	−22.8523	−1.10461
$429$	4.31171	0.208172
$430$	3.39522	0.163732
$431$	−3.03123	−0.146009	−0.0730046	−	0.997332i	$-0.523259\pi$
$431$	−3.03123	−0.146009	−0.0730046	+	0.997332i	$0.523259\pi$
$432$	−43.3134	−2.08392
$433$	−1.25157	−0.0601468	−0.0300734	−	0.999548i	$-0.509574\pi$
$433$	−1.25157	−0.0601468	−0.0300734	+	0.999548i	$0.509574\pi$
$434$	0.0145256	0.000697253 0
$435$	7.40385	0.354988
$436$	−35.9472	−1.72156
$437$	−46.4756	−2.22323
$438$	24.9140	1.19043
$439$	6.31584	0.301439	0.150719	−	0.988577i	$-0.451841\pi$
$439$	6.31584	0.301439	0.150719	+	0.988577i	$0.451841\pi$
$440$	−23.4340	−1.11717
$441$	−30.6035	−1.45731
$442$	3.50259	0.166601
$443$	−28.4580	−1.35208	−0.676040	−	0.736865i	$-0.736305\pi$
$443$	−28.4580	−1.35208	−0.676040	+	0.736865i	$0.736305\pi$
$444$	−90.0052	−4.27146
$445$	9.93950	0.471177
$446$	12.9783	0.614539
$447$	52.4812	2.48228
$448$	−0.664455	−0.0313925
$449$	32.5941	1.53821	0.769106	−	0.639121i	$-0.220702\pi$
$449$	32.5941	1.53821	0.769106	+	0.639121i	$0.220702\pi$
$450$	20.3358	0.958640
$451$	−1.69214	−0.0796798
$452$	−38.7981	−1.82491
$453$	21.5953	1.01463
$454$	−32.8492	−1.54169
$455$	0.0776356	0.00363961
$456$	147.121	6.88958
$457$	−3.25131	−0.152090	−0.0760449	−	0.997104i	$-0.524229\pi$
$457$	−3.25131	−0.152090	−0.0760449	+	0.997104i	$0.524229\pi$
$458$	−38.9694	−1.82092
$459$	−4.90911	−0.229138
$460$	−64.2618	−2.99622
$461$	−33.0674	−1.54010	−0.770051	−	0.637982i	$-0.779769\pi$
$461$	−33.0674	−1.54010	−0.770051	+	0.637982i	$0.779769\pi$
$462$	−0.493798	−0.0229736
$463$	26.0422	1.21028	0.605142	−	0.796117i	$-0.293116\pi$
$463$	26.0422	1.21028	0.605142	+	0.796117i	$0.293116\pi$
$464$	−17.5658	−0.815471
$465$	−0.621053	−0.0288006
$466$	−4.45369	−0.206313
$467$	3.24179	0.150012	0.0750060	−	0.997183i	$-0.476102\pi$
$467$	3.24179	0.150012	0.0750060	+	0.997183i	$0.476102\pi$
$468$	−22.1996	−1.02618
$469$	0.463869	0.0214195
$470$	−7.40187	−0.341423
$471$	19.9162	0.917691
$472$	−12.3825	−0.569952
$473$	−1.12388	−0.0516758
$474$	73.3777	3.37035
$475$	−11.5735	−0.531029
$476$	−0.287762	−0.0131895
$477$	−28.7478	−1.31627
$478$	4.91671	0.224885
$479$	−4.68465	−0.214047	−0.107024	−	0.994256i	$-0.534132\pi$
$479$	−4.68465	−0.214047	−0.107024	+	0.994256i	$0.534132\pi$
$480$	71.1771	3.24878
$481$	−6.52958	−0.297723
$482$	48.6084	2.21405
$483$	−0.820623	−0.0373397
$484$	−43.0407	−1.95639
$485$	9.83837	0.446738
$486$	−51.3908	−2.33113
$487$	2.31170	0.104753	0.0523765	−	0.998627i	$-0.483320\pi$
$487$	2.31170	0.104753	0.0523765	+	0.998627i	$0.483320\pi$
$488$	−85.5427	−3.87234
$489$	−28.7260	−1.29904
$490$	33.5705	1.51656
$491$	6.99848	0.315837	0.157918	−	0.987452i	$-0.449522\pi$
$491$	6.99848	0.315837	0.157918	+	0.987452i	$0.449522\pi$
$492$	14.6890	0.662233
$493$	−1.99089	−0.0896653
$494$	17.6118	0.792394
$495$	12.5222	0.562832
$496$	1.47346	0.0661603
$497$	−0.628587	−0.0281960
$498$	−31.4115	−1.40758
$499$	−21.6983	−0.971351	−0.485676	−	0.874139i	$-0.661426\pi$
$499$	−21.6983	−0.971351	−0.485676	+	0.874139i	$0.661426\pi$
$500$	−61.7743	−2.76263
$501$	−67.2497	−3.00449
$502$	68.4628	3.05564
$503$	0.0104346	0.000465257 0	0.000232629	−	1.00000i	$-0.499926\pi$
$503$	0.0104346	0.000465257 0	0.000232629		1.00000i	$0.499926\pi$
$504$	1.54075	0.0686306
$505$	−26.7209	−1.18907
$506$	29.6524	1.31821
$507$	−2.71534	−0.120593
$508$	−50.6647	−2.24788
$509$	15.6005	0.691479	0.345740	−	0.938331i	$-0.387628\pi$
$509$	15.6005	0.691479	0.345740	+	0.938331i	$0.387628\pi$
$510$	17.1507	0.759447
$511$	−0.148492	−0.00656891
$512$	21.2762	0.940282
$513$	−24.6841	−1.08983
$514$	−63.5705	−2.80397
$515$	−2.97317	−0.131013
$516$	9.75607	0.429487
$517$	2.45015	0.107757
$518$	0.747799	0.0328564
$519$	−21.7419	−0.954362
$520$	14.7578	0.647172
$521$	29.6089	1.29719	0.648595	−	0.761134i	$-0.275357\pi$
$521$	29.6089	1.29719	0.648595	+	0.761134i	$0.275357\pi$
$522$	17.5897	0.769882
$523$	−5.59410	−0.244613	−0.122306	−	0.992492i	$-0.539029\pi$
$523$	−5.59410	−0.244613	−0.122306	+	0.992492i	$0.539029\pi$
$524$	−85.6627	−3.74219
$525$	−0.204355	−0.00891877
$526$	5.45224	0.237729
$527$	0.167001	0.00727467
$528$	−50.0901	−2.17989
$529$	26.2781	1.14252
$530$	31.5350	1.36979
$531$	6.61673	0.287142
$532$	−1.44693	−0.0627325
$533$	1.06564	0.0461581
$534$	39.8132	1.72289
$535$	−8.11783	−0.350965
$536$	88.1771	3.80867
$537$	−20.0218	−0.864006
$538$	34.8563	1.50276
$539$	−11.1124	−0.478646
$540$	−34.1308	−1.46875
$541$	−19.3128	−0.830322	−0.415161	−	0.909748i	$-0.636275\pi$
$541$	−19.3128	−0.830322	−0.415161	+	0.909748i	$0.636275\pi$
$542$	−45.3385	−1.94746
$543$	−53.2007	−2.28306
$544$	−19.1395	−0.820599
$545$	−12.7695	−0.546987
$546$	0.310974	0.0133085
$547$	37.7251	1.61301	0.806504	−	0.591229i	$-0.201357\pi$
$547$	37.7251	1.61301	0.806504	+	0.591229i	$0.201357\pi$
$548$	−65.2800	−2.78862
$549$	45.7106	1.95088
$550$	7.38414	0.314861
$551$	−10.0107	−0.426469
$552$	−155.993	−6.63949
$553$	−0.437346	−0.0185978
$554$	−62.3791	−2.65023
$555$	−31.9726	−1.35716
$556$	−95.6005	−4.05436
$557$	−40.4847	−1.71539	−0.857697	−	0.514156i	$-0.828105\pi$
$557$	−40.4847	−1.71539	−0.857697	+	0.514156i	$0.828105\pi$
$558$	−1.47547	−0.0624616
$559$	0.707771	0.0299355
$560$	−0.901910	−0.0381127
$561$	−5.67718	−0.239691
$562$	66.3156	2.79736
$563$	9.11666	0.384222	0.192111	−	0.981373i	$-0.438467\pi$
$563$	9.11666	0.384222	0.192111	+	0.981373i	$0.438467\pi$
$564$	−21.2691	−0.895590
$565$	−13.7823	−0.579825
$566$	−2.86750	−0.120530
$567$	0.128958	0.00541574
$568$	−119.488	−5.01362
$569$	−3.88361	−0.162809	−0.0814047	−	0.996681i	$-0.525941\pi$
$569$	−3.88361	−0.162809	−0.0814047	+	0.996681i	$0.525941\pi$
$570$	86.2378	3.61210
$571$	29.0078	1.21394	0.606970	−	0.794725i	$-0.292385\pi$
$571$	29.0078	1.21394	0.606970	+	0.794725i	$0.292385\pi$
$572$	−8.06090	−0.337043
$573$	−0.246132	−0.0102823
$574$	−0.122042	−0.00509395
$575$	12.2714	0.511753
$576$	67.4932	2.81222
$577$	11.5192	0.479549	0.239774	−	0.970829i	$-0.422927\pi$
$577$	11.5192	0.479549	0.239774	+	0.970829i	$0.422927\pi$
$578$	40.6108	1.68919
$579$	57.5877	2.39326
$580$	−13.8418	−0.574747
$581$	0.187219	0.00776715
$582$	39.4082	1.63352
$583$	−10.4386	−0.432324
$584$	−28.2270	−1.16804
$585$	−7.88598	−0.326045
$586$	66.2883	2.73835
$587$	22.6674	0.935583	0.467792	−	0.883839i	$-0.345050\pi$
$587$	22.6674	0.935583	0.467792	+	0.883839i	$0.345050\pi$
$588$	96.4640	3.97811
$589$	0.839719	0.0346000
$590$	−7.25824	−0.298817
$591$	5.23079	0.215166
$592$	75.8556	3.11765
$593$	−1.69240	−0.0694986	−0.0347493	−	0.999396i	$-0.511063\pi$
$593$	−1.69240	−0.0694986	−0.0347493	+	0.999396i	$0.511063\pi$
$594$	15.7490	0.646189
$595$	−0.102222	−0.00419069
$596$	−98.1155	−4.01897
$597$	−22.8303	−0.934384
$598$	−18.6738	−0.763630
$599$	12.7208	0.519757	0.259878	−	0.965641i	$-0.416318\pi$
$599$	12.7208	0.519757	0.259878	+	0.965641i	$0.416318\pi$
$600$	−38.8459	−1.58588
$601$	−3.56408	−0.145382	−0.0726909	−	0.997355i	$-0.523159\pi$
$601$	−3.56408	−0.145382	−0.0726909	+	0.997355i	$0.523159\pi$
$602$	−0.0810573	−0.00330365
$603$	−47.1184	−1.91881
$604$	−40.3731	−1.64276
$605$	−15.2894	−0.621601
$606$	−107.032	−4.34789
$607$	−8.48165	−0.344259	−0.172130	−	0.985074i	$-0.555065\pi$
$607$	−8.48165	−0.344259	−0.172130	+	0.985074i	$0.555065\pi$
$608$	−96.2378	−3.90296
$609$	−0.176759	−0.00716265
$610$	−50.1424	−2.03021
$611$	−1.54300	−0.0624232
$612$	29.2299	1.18155
$613$	−37.5668	−1.51731	−0.758654	−	0.651494i	$-0.774143\pi$
$613$	−37.5668	−1.51731	−0.758654	+	0.651494i	$0.774143\pi$
$614$	−8.19204	−0.330604
$615$	5.21800	0.210410
$616$	0.559463	0.0225414
$617$	−20.0034	−0.805308	−0.402654	−	0.915352i	$-0.631912\pi$
$617$	−20.0034	−0.805308	−0.402654	+	0.915352i	$0.631912\pi$
$618$	−11.9092	−0.479058
$619$	−1.00000	−0.0401934
$619$	−1.00000	−0.0401934
$620$	1.16108	0.0466301
$621$	26.1726	1.05027
$622$	−26.4552	−1.06076
$623$	−0.237295	−0.00950703
$624$	31.5447	1.26280
$625$	−13.2036	−0.528144
$626$	17.1916	0.687116
$627$	−28.5462	−1.14002
$628$	−37.2340	−1.48580
$629$	8.59742	0.342802
$630$	0.903140	0.0359820
$631$	−15.2845	−0.608466	−0.304233	−	0.952598i	$-0.598400\pi$
$631$	−15.2845	−0.608466	−0.304233	+	0.952598i	$0.598400\pi$
$632$	−83.1353	−3.30694
$633$	−2.47408	−0.0983357
$634$	14.6117	0.580307
$635$	−17.9977	−0.714216
$636$	90.6150	3.59312
$637$	6.99815	0.277277
$638$	6.38701	0.252864
$639$	63.8499	2.52586
$640$	−21.6110	−0.854248
$641$	−4.37711	−0.172885	−0.0864427	−	0.996257i	$-0.527550\pi$
$641$	−4.37711	−0.172885	−0.0864427	+	0.996257i	$0.527550\pi$
$642$	−32.5165	−1.28332
$643$	−31.6069	−1.24645	−0.623227	−	0.782041i	$-0.714179\pi$
$643$	−31.6069	−1.24645	−0.623227	+	0.782041i	$0.714179\pi$
$644$	1.53418	0.0604553
$645$	3.46565	0.136460
$646$	−23.1893	−0.912371
$647$	−34.5657	−1.35892	−0.679459	−	0.733713i	$-0.737785\pi$
$647$	−34.5657	−1.35892	−0.679459	+	0.733713i	$0.737785\pi$
$648$	24.5138	0.962991
$649$	2.40260	0.0943104
$650$	−4.65023	−0.182397
$651$	0.0148270	0.000581116 0
$652$	53.7043	2.10322
$653$	−35.8372	−1.40242	−0.701208	−	0.712956i	$-0.747356\pi$
$653$	−35.8372	−1.40242	−0.701208	+	0.712956i	$0.747356\pi$
$654$	−51.1492	−2.00009
$655$	−30.4300	−1.18900
$656$	−12.3798	−0.483350
$657$	15.0834	0.588459
$658$	0.176712	0.00688895
$659$	−23.5990	−0.919287	−0.459643	−	0.888104i	$-0.652023\pi$
$659$	−23.5990	−0.919287	−0.459643	+	0.888104i	$0.652023\pi$
$660$	−39.4708	−1.53640
$661$	3.54783	0.137995	0.0689973	−	0.997617i	$-0.478020\pi$
$661$	3.54783	0.137995	0.0689973	+	0.997617i	$0.478020\pi$
$662$	−44.8663	−1.74378
$663$	3.57526	0.138851
$664$	35.5885	1.38110
$665$	−0.513995	−0.0199319
$666$	−75.9591	−2.94335
$667$	10.6143	0.410988
$668$	125.726	4.86447
$669$	13.2475	0.512179
$670$	51.6866	1.99683
$671$	16.5980	0.640758
$672$	−1.69928	−0.0655511
$673$	−13.9537	−0.537876	−0.268938	−	0.963158i	$-0.586673\pi$
$673$	−13.9537	−0.537876	−0.268938	+	0.963158i	$0.586673\pi$
$674$	−71.1005	−2.73869
$675$	6.51760	0.250862
$676$	5.07642	0.195247
$677$	−16.0779	−0.617925	−0.308962	−	0.951074i	$-0.599982\pi$
$677$	−16.0779	−0.617925	−0.308962	+	0.951074i	$0.599982\pi$
$678$	−55.2057	−2.12016
$679$	−0.234881	−0.00901390
$680$	−19.4314	−0.745160
$681$	−33.5307	−1.28490
$682$	−0.535758	−0.0205152
$683$	18.6031	0.711830	0.355915	−	0.934518i	$-0.384169\pi$
$683$	18.6031	0.711830	0.355915	+	0.934518i	$0.384169\pi$
$684$	146.975	5.61973
$685$	−23.1895	−0.886024
$686$	−1.60313	−0.0612080
$687$	−39.7778	−1.51762
$688$	−8.22233	−0.313473
$689$	6.57382	0.250443
$690$	−91.4379	−3.48098
$691$	21.9264	0.834121	0.417061	−	0.908879i	$-0.363060\pi$
$691$	21.9264	0.834121	0.417061	+	0.908879i	$0.363060\pi$
$692$	40.6472	1.54517
$693$	−0.298955	−0.0113564
$694$	−77.0508	−2.92481
$695$	−33.9602	−1.28818
$696$	−33.6002	−1.27361
$697$	−1.40312	−0.0531469
$698$	−62.9581	−2.38300
$699$	−4.54608	−0.171949
$700$	0.382048	0.0144401
$701$	12.0078	0.453530	0.226765	−	0.973949i	$-0.427185\pi$
$701$	12.0078	0.453530	0.226765	+	0.973949i	$0.427185\pi$
$702$	−9.91807	−0.374333
$703$	43.2298	1.63044
$704$	24.5075	0.923660
$705$	−7.55543	−0.284554
$706$	16.7625	0.630863
$707$	0.637934	0.0239920
$708$	−20.8564	−0.783830
$709$	−10.3121	−0.387278	−0.193639	−	0.981073i	$-0.562029\pi$
$709$	−10.3121	−0.387278	−0.193639	+	0.981073i	$0.562029\pi$
$710$	−70.0403	−2.62856
$711$	44.4242	1.66604
$712$	−45.1075	−1.69048
$713$	−0.890354	−0.0333440
$714$	−0.409456	−0.0153235
$715$	−2.86348	−0.107088
$716$	37.4315	1.39888
$717$	5.01871	0.187427
$718$	79.0961	2.95184
$719$	17.7194	0.660823	0.330412	−	0.943837i	$-0.392812\pi$
$719$	17.7194	0.660823	0.330412	+	0.943837i	$0.392812\pi$
$720$	91.6132	3.41422
$721$	0.0709812	0.00264348
$722$	−66.0582	−2.45843
$723$	49.6168	1.84527
$724$	99.4605	3.69642
$725$	2.64321	0.0981665
$726$	−61.2425	−2.27292
$727$	6.35886	0.235837	0.117919	−	0.993023i	$-0.462378\pi$
$727$	6.35886	0.235837	0.117919	+	0.993023i	$0.462378\pi$
$728$	−0.352327	−0.0130581
$729$	−43.4707	−1.61002
$730$	−16.5458	−0.612386
$731$	−0.931913	−0.0344680
$732$	−144.083	−5.32545
$733$	9.73270	0.359485	0.179743	−	0.983714i	$-0.442473\pi$
$733$	9.73270	0.359485	0.179743	+	0.983714i	$0.442473\pi$
$734$	10.4636	0.386217
$735$	34.2670	1.26396
$736$	102.041	3.76128
$737$	−17.1092	−0.630224
$738$	12.3967	0.456328
$739$	−48.1466	−1.77110	−0.885550	−	0.464544i	$-0.846218\pi$
$739$	−48.1466	−1.77110	−0.885550	+	0.464544i	$0.846218\pi$
$740$	59.7739	2.19733
$741$	17.9772	0.660410
$742$	−0.752865	−0.0276386
$743$	−3.24291	−0.118971	−0.0594855	−	0.998229i	$-0.518946\pi$
$743$	−3.24291	−0.118971	−0.0594855	+	0.998229i	$0.518946\pi$
$744$	2.81847	0.103330
$745$	−34.8536	−1.27694
$746$	58.5356	2.14314
$747$	−19.0171	−0.695800
$748$	10.6137	0.388075
$749$	0.193805	0.00708147
$750$	−87.8985	−3.20960
$751$	−27.7030	−1.01090	−0.505449	−	0.862857i	$-0.668673\pi$
$751$	−27.7030	−1.01090	−0.505449	+	0.862857i	$0.668673\pi$
$752$	17.9254	0.653672
$753$	69.8831	2.54668
$754$	−4.02228	−0.146483
$755$	−14.3418	−0.521950
$756$	0.814837	0.0296353
$757$	−6.26587	−0.227737	−0.113869	−	0.993496i	$-0.536324\pi$
$757$	−6.26587	−0.227737	−0.113869	+	0.993496i	$0.536324\pi$
$758$	−40.2431	−1.46170
$759$	30.2675	1.09864
$760$	−97.7055	−3.54415
$761$	42.0121	1.52294	0.761468	−	0.648202i	$-0.224479\pi$
$761$	42.0121	1.52294	0.761468	+	0.648202i	$0.224479\pi$
$762$	−72.0907	−2.61157
$763$	0.304860	0.0110367
$764$	0.460153	0.0166477
$765$	10.3834	0.375412
$766$	29.1768	1.05420
$767$	−1.51306	−0.0546334
$768$	−2.74792	−0.0991570
$769$	32.1932	1.16092	0.580458	−	0.814290i	$-0.302873\pi$
$769$	32.1932	1.16092	0.580458	+	0.814290i	$0.302873\pi$
$770$	0.327939	0.0118181
$771$	−64.8893	−2.33693
$772$	−107.662	−3.87485
$773$	−30.3023	−1.08990	−0.544949	−	0.838469i	$-0.683451\pi$
$773$	−30.3023	−1.08990	−0.544949	+	0.838469i	$0.683451\pi$
$774$	8.23354	0.295949
$775$	−0.221719	−0.00796439
$776$	−44.6486	−1.60279
$777$	0.763312	0.0273837
$778$	101.829	3.65074
$779$	−7.05520	−0.252779
$780$	24.8571	0.890027
$781$	23.1845	0.829607
$782$	24.5876	0.879252
$783$	5.63748	0.201467
$784$	−81.2990	−2.90354
$785$	−13.2267	−0.472080
$786$	−121.889	−4.34764
$787$	0.478639	0.0170616	0.00853082	−	0.999964i	$-0.497285\pi$
$787$	0.478639	0.0170616	0.00853082	+	0.999964i	$0.497285\pi$
$788$	−9.77913	−0.348367
$789$	5.56535	0.198132
$790$	−48.7313	−1.73378
$791$	0.329037	0.0116992
$792$	−56.8285	−2.01931
$793$	−10.4527	−0.371188
$794$	−43.2932	−1.53642
$795$	32.1892	1.14163
$796$	42.6821	1.51283
$797$	−49.4979	−1.75330	−0.876652	−	0.481125i	$-0.840228\pi$
$797$	−49.4979	−1.75330	−0.876652	+	0.481125i	$0.840228\pi$
$798$	−2.05884	−0.0728820
$799$	2.03165	0.0718746
$800$	25.4106	0.898400
$801$	24.1037	0.851662
$802$	30.9953	1.09448
$803$	5.47693	0.193277
$804$	148.520	5.23790
$805$	0.544989	0.0192083
$806$	0.337398	0.0118843
$807$	35.5795	1.25246
$808$	121.265	4.26610
$809$	15.2112	0.534797	0.267398	−	0.963586i	$-0.413836\pi$
$809$	15.2112	0.534797	0.267398	+	0.963586i	$0.413836\pi$
$810$	14.3692	0.504882
$811$	−15.8259	−0.555723	−0.277861	−	0.960621i	$-0.589626\pi$
$811$	−15.8259	−0.555723	−0.277861	+	0.960621i	$0.589626\pi$
$812$	0.330457	0.0115968
$813$	−46.2791	−1.62308
$814$	−27.5815	−0.966731
$815$	19.0774	0.668253
$816$	−41.5346	−1.45400
$817$	−4.68587	−0.163938
$818$	−72.7490	−2.54361
$819$	0.188270	0.00657867
$820$	−9.75522	−0.340667
$821$	1.82326	0.0636322	0.0318161	−	0.999494i	$-0.489871\pi$
$821$	1.82326	0.0636322	0.0318161	+	0.999494i	$0.489871\pi$
$822$	−92.8868	−3.23980
$823$	−21.8151	−0.760425	−0.380213	−	0.924899i	$-0.624149\pi$
$823$	−21.8151	−0.760425	−0.380213	+	0.924899i	$0.624149\pi$
$824$	13.4929	0.470046
$825$	7.53733	0.262416
$826$	0.173283	0.00602928
$827$	−16.3725	−0.569329	−0.284664	−	0.958627i	$-0.591882\pi$
$827$	−16.3725	−0.569329	−0.284664	+	0.958627i	$0.591882\pi$
$828$	−155.838	−5.41573
$829$	−41.8480	−1.45344	−0.726720	−	0.686934i	$-0.758956\pi$
$829$	−41.8480	−1.45344	−0.726720	+	0.686934i	$0.758956\pi$
$830$	20.8609	0.724091
$831$	−63.6732	−2.20880
$832$	−15.4338	−0.535071
$833$	−9.21437	−0.319259
$834$	−136.030	−4.71032
$835$	44.6616	1.54558
$836$	53.3681	1.84577
$837$	−0.472886	−0.0163453
$838$	−79.7920	−2.75637
$839$	10.0360	0.346483	0.173241	−	0.984879i	$-0.444576\pi$
$839$	10.0360	0.346483	0.173241	+	0.984879i	$0.444576\pi$
$840$	−1.72520	−0.0595249
$841$	−26.7137	−0.921163
$842$	−54.3630	−1.87347
$843$	67.6914	2.33142
$844$	4.62537	0.159212
$845$	1.80330	0.0620354
$846$	−17.9498	−0.617128
$847$	0.365018	0.0125422
$848$	−76.3695	−2.62254
$849$	−2.92699	−0.100454
$850$	6.12290	0.210014
$851$	−45.8366	−1.57126
$852$	−201.259	−6.89501
$853$	27.8516	0.953619	0.476809	−	0.879007i	$-0.341793\pi$
$853$	27.8516	0.953619	0.476809	+	0.879007i	$0.341793\pi$
$854$	1.19710	0.0409638
$855$	52.2100	1.78554
$856$	36.8404	1.25918
$857$	−27.9308	−0.954096	−0.477048	−	0.878877i	$-0.658293\pi$
$857$	−27.9308	−0.954096	−0.477048	+	0.878877i	$0.658293\pi$
$858$	−11.4698	−0.391573
$859$	16.0856	0.548833	0.274417	−	0.961611i	$-0.411515\pi$
$859$	16.0856	0.548833	0.274417	+	0.961611i	$0.411515\pi$
$860$	−6.47916	−0.220937
$861$	−0.124574	−0.00424548
$862$	8.06354	0.274645
$863$	−0.726489	−0.0247300	−0.0123650	−	0.999924i	$-0.503936\pi$
$863$	−0.726489	−0.0247300	−0.0123650	+	0.999924i	$0.503936\pi$
$864$	54.1961	1.84379
$865$	14.4391	0.490945
$866$	3.32938	0.113137
$867$	41.4533	1.40783
$868$	−0.0277196	−0.000940863 0
$869$	16.1309	0.547203
$870$	−19.6954	−0.667736
$871$	10.7746	0.365085
$872$	57.9509	1.96246
$873$	23.8585	0.807486
$874$	123.632	4.18192
$875$	0.523893	0.0177108
$876$	−47.5438	−1.60635
$877$	26.0644	0.880131	0.440065	−	0.897966i	$-0.354955\pi$
$877$	26.0644	0.880131	0.440065	+	0.897966i	$0.354955\pi$
$878$	−16.8011	−0.567010
$879$	67.6635	2.28223
$880$	33.2657	1.12139
$881$	−5.82078	−0.196107	−0.0980535	−	0.995181i	$-0.531262\pi$
$881$	−5.82078	−0.196107	−0.0980535	+	0.995181i	$0.531262\pi$
$882$	81.4099	2.74121
$883$	14.5785	0.490605	0.245303	−	0.969447i	$-0.421113\pi$
$883$	14.5785	0.490605	0.245303	+	0.969447i	$0.421113\pi$
$884$	−6.68406	−0.224809
$885$	−7.40882	−0.249045
$886$	75.7027	2.54328
$887$	−42.8540	−1.43890	−0.719448	−	0.694546i	$-0.755605\pi$
$887$	−42.8540	−1.43890	−0.719448	+	0.694546i	$0.755605\pi$
$888$	145.098	4.86918
$889$	0.429676	0.0144109
$890$	−26.4406	−0.886291
$891$	−4.75644	−0.159347
$892$	−24.7667	−0.829250
$893$	10.2156	0.341852
$894$	−139.608	−4.66920
$895$	13.2968	0.444464
$896$	0.515939	0.0172363
$897$	−19.0612	−0.636436
$898$	−86.7054	−2.89340
$899$	−0.191779	−0.00639619
$900$	−38.8072	−1.29357
$901$	−8.65567	−0.288362
$902$	4.50136	0.149879
$903$	−0.0827389	−0.00275338
$904$	62.5469	2.08028
$905$	35.3314	1.17446
$906$	−57.4467	−1.90854
$907$	4.30160	0.142832	0.0714161	−	0.997447i	$-0.477248\pi$
$907$	4.30160	0.142832	0.0714161	+	0.997447i	$0.477248\pi$
$908$	62.6867	2.08033
$909$	−64.7994	−2.14926
$910$	−0.206523	−0.00684616
$911$	48.7966	1.61670	0.808352	−	0.588700i	$-0.200360\pi$
$911$	48.7966	1.61670	0.808352	+	0.588700i	$0.200360\pi$
$912$	−208.845	−6.91556
$913$	−6.90530	−0.228532
$914$	8.64899	0.286083
$915$	−51.1826	−1.69205
$916$	74.3660	2.45712
$917$	0.726485	0.0239906
$918$	13.0590	0.431011
$919$	−37.6038	−1.24043	−0.620217	−	0.784430i	$-0.712956\pi$
$919$	−37.6038	−1.24043	−0.620217	+	0.784430i	$0.712956\pi$
$920$	103.597	3.41550
$921$	−8.36199	−0.275537
$922$	87.9644	2.89695
$923$	−14.6007	−0.480587
$924$	0.942324	0.0310002
$925$	−11.4144	−0.375303
$926$	−69.2763	−2.27656
$927$	−7.21005	−0.236809
$928$	21.9792	0.721504
$929$	1.15312	0.0378328	0.0189164	−	0.999821i	$-0.493978\pi$
$929$	1.15312	0.0378328	0.0189164	+	0.999821i	$0.493978\pi$
$930$	1.65210	0.0541744
$931$	−46.3320	−1.51847
$932$	8.49906	0.278396
$933$	−27.0040	−0.884072
$934$	−8.62366	−0.282175
$935$	3.77031	0.123302
$936$	35.7882	1.16978
$937$	25.3637	0.828598	0.414299	−	0.910141i	$-0.364027\pi$
$937$	25.3637	0.828598	0.414299	+	0.910141i	$0.364027\pi$
$938$	−1.23396	−0.0402904
$939$	17.5483	0.572667
$940$	14.1251	0.460711
$941$	−50.2299	−1.63745	−0.818725	−	0.574187i	$-0.805318\pi$
$941$	−50.2299	−1.63745	−0.818725	+	0.574187i	$0.805318\pi$
$942$	−52.9802	−1.72619
$943$	7.48063	0.243603
$944$	17.5776	0.572101
$945$	0.289455	0.00941597
$946$	2.98968	0.0972029
$947$	35.8302	1.16432	0.582162	−	0.813073i	$-0.302207\pi$
$947$	35.8302	1.16432	0.582162	+	0.813073i	$0.302207\pi$
$948$	−140.028	−4.54790
$949$	−3.44914	−0.111964
$950$	30.7874	0.998874
$951$	14.9149	0.483648
$952$	0.463904	0.0150352
$953$	15.3057	0.495800	0.247900	−	0.968786i	$-0.420260\pi$
$953$	15.3057	0.495800	0.247900	+	0.968786i	$0.420260\pi$
$954$	76.4737	2.47593
$955$	0.163460	0.00528945
$956$	−9.38265	−0.303457
$957$	6.51951	0.210746
$958$	12.4619	0.402626
$959$	0.553624	0.0178775
$960$	−75.5728	−2.43910
$961$	−30.9839	−0.999481
$962$	17.3697	0.560021
$963$	−19.6861	−0.634375
$964$	−92.7603	−2.98761
$965$	−38.2449	−1.23115
$966$	2.18299	0.0702364
$967$	1.03094	0.0331526	0.0165763	−	0.999863i	$-0.494723\pi$
$967$	1.03094	0.0331526	0.0165763	+	0.999863i	$0.494723\pi$
$968$	69.3864	2.23016
$969$	−23.6704	−0.760402
$970$	−26.1716	−0.840319
$971$	−1.68856	−0.0541885	−0.0270942	−	0.999633i	$-0.508625\pi$
$971$	−1.68856	−0.0541885	−0.0270942	+	0.999633i	$0.508625\pi$
$972$	98.0699	3.14560
$973$	0.810765	0.0259919
$974$	−6.14947	−0.197042
$975$	−4.74670	−0.152016
$976$	121.432	3.88694
$977$	−35.7510	−1.14377	−0.571887	−	0.820332i	$-0.693789\pi$
$977$	−35.7510	−1.14377	−0.571887	+	0.820332i	$0.693789\pi$
$978$	76.4157	2.44350
$979$	8.75229	0.279724
$980$	−64.0633	−2.04643
$981$	−30.9667	−0.988690
$982$	−18.6170	−0.594094
$983$	−48.4231	−1.54446	−0.772229	−	0.635345i	$-0.780858\pi$
$983$	−48.4231	−1.54446	−0.772229	+	0.635345i	$0.780858\pi$
$984$	−23.6804	−0.754903
$985$	−3.47385	−0.110686
$986$	5.29608	0.168662
$987$	0.180378	0.00574149
$988$	−33.6090	−1.06925
$989$	4.96843	0.157987
$990$	−33.3110	−1.05869
$991$	−34.3495	−1.09115	−0.545575	−	0.838062i	$-0.683689\pi$
$991$	−34.3495	−1.09115	−0.545575	+	0.838062i	$0.683689\pi$
$992$	−1.84367	−0.0585366
$993$	−45.7971	−1.45333
$994$	1.67214	0.0530370
$995$	15.1620	0.480668
$996$	59.9431	1.89937
$997$	29.1110	0.921954	0.460977	−	0.887412i	$-0.347499\pi$
$997$	29.1110	0.921954	0.460977	+	0.887412i	$0.347499\pi$
$998$	57.7209	1.82712
$999$	−24.3448	−0.770234

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	8047.2.a.c.1.8	✓	151

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
8047.2.a.c.1.8	✓	151	1.1	even	1	trivial

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 8047 = 13 \cdot 619 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	8047.a (trivial)

\(f(q)\)	\(=\)	\(q-2.66015 q^{2} -2.71534 q^{3} +5.07642 q^{4} +1.80330 q^{5} +7.22323 q^{6} -0.0430519 q^{7} -8.18376 q^{8} +4.37308 q^{9} +O(q^{10})\)	\(q-2.66015 q^{2} -2.71534 q^{3} +5.07642 q^{4} +1.80330 q^{5} +7.22323 q^{6} -0.0430519 q^{7} -8.18376 q^{8} +4.37308 q^{9} -4.79706 q^{10} +1.58791 q^{11} -13.7842 q^{12} -1.00000 q^{13} +0.114525 q^{14} -4.89658 q^{15} +11.6172 q^{16} +1.31669 q^{17} -11.6331 q^{18} +6.62061 q^{19} +9.15432 q^{20} +0.116901 q^{21} -4.22408 q^{22} -7.01983 q^{23} +22.2217 q^{24} -1.74810 q^{25} +2.66015 q^{26} -3.72838 q^{27} -0.218550 q^{28} -1.51205 q^{29} +13.0257 q^{30} +0.126834 q^{31} -14.5361 q^{32} -4.31171 q^{33} -3.50259 q^{34} -0.0776356 q^{35} +22.1996 q^{36} +6.52958 q^{37} -17.6118 q^{38} +2.71534 q^{39} -14.7578 q^{40} -1.06564 q^{41} -0.310974 q^{42} -0.707771 q^{43} +8.06090 q^{44} +7.88598 q^{45} +18.6738 q^{46} +1.54300 q^{47} -31.5447 q^{48} -6.99815 q^{49} +4.65023 q^{50} -3.57526 q^{51} -5.07642 q^{52} -6.57382 q^{53} +9.91807 q^{54} +2.86348 q^{55} +0.352327 q^{56} -17.9772 q^{57} +4.02228 q^{58} +1.51306 q^{59} -24.8571 q^{60} +10.4527 q^{61} -0.337398 q^{62} -0.188270 q^{63} +15.4338 q^{64} -1.80330 q^{65} +11.4698 q^{66} -10.7746 q^{67} +6.68406 q^{68} +19.0612 q^{69} +0.206523 q^{70} +14.6007 q^{71} -35.7882 q^{72} +3.44914 q^{73} -17.3697 q^{74} +4.74670 q^{75} +33.6090 q^{76} -0.0683625 q^{77} -7.22323 q^{78} +10.1586 q^{79} +20.9494 q^{80} -2.99541 q^{81} +2.83477 q^{82} -4.34868 q^{83} +0.593437 q^{84} +2.37438 q^{85} +1.88278 q^{86} +4.10572 q^{87} -12.9951 q^{88} +5.51183 q^{89} -20.9779 q^{90} +0.0430519 q^{91} -35.6356 q^{92} -0.344398 q^{93} -4.10462 q^{94} +11.9390 q^{95} +39.4704 q^{96} +5.45576 q^{97} +18.6162 q^{98} +6.94405 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 151 q - 13 q^{2} - 16 q^{3} + 151 q^{4} - 43 q^{5} - 17 q^{6} - 18 q^{7} - 39 q^{8} + 135 q^{9}+O(q^{10}) \) 151 * q - 13 * q^2 - 16 * q^3 + 151 * q^4 - 43 * q^5 - 17 * q^6 - 18 * q^7 - 39 * q^8 + 135 * q^9	\( 151 q - 13 q^{2} - 16 q^{3} + 151 q^{4} - 43 q^{5} - 17 q^{6} - 18 q^{7} - 39 q^{8} + 135 q^{9} - 3 q^{10} - 27 q^{11} - 52 q^{12} - 151 q^{13} - 9 q^{14} - 14 q^{15} + 143 q^{16} - 111 q^{17} - 37 q^{18} - 17 q^{19} - 107 q^{20} - 29 q^{21} - 16 q^{22} - 47 q^{23} - 46 q^{24} + 122 q^{25} + 13 q^{26} - 55 q^{27} - 44 q^{28} + 37 q^{29} - 14 q^{30} - 27 q^{31} - 86 q^{32} - 94 q^{33} - 10 q^{34} - 47 q^{35} + 124 q^{36} - 59 q^{37} - 80 q^{38} + 16 q^{39} + 5 q^{40} - 129 q^{41} - 77 q^{42} - 11 q^{43} - 99 q^{44} - 122 q^{45} - 17 q^{46} - 130 q^{47} - 111 q^{48} + 99 q^{49} - 72 q^{50} + 15 q^{51} - 151 q^{52} - 43 q^{53} - 49 q^{54} - 40 q^{55} - 50 q^{56} - 85 q^{57} - 73 q^{58} - 74 q^{59} - 43 q^{60} - 7 q^{61} - 110 q^{62} - 70 q^{63} + 141 q^{64} + 43 q^{65} - 16 q^{66} - 39 q^{67} - 222 q^{68} + 19 q^{69} - 52 q^{70} - 72 q^{71} - 106 q^{72} - 143 q^{73} + 20 q^{74} - 73 q^{75} - 88 q^{76} - 86 q^{77} + 17 q^{78} + 10 q^{79} - 239 q^{80} + 103 q^{81} - 96 q^{82} - 96 q^{83} - 75 q^{84} - 24 q^{85} - 109 q^{86} - 65 q^{87} - 45 q^{88} - 237 q^{89} - 79 q^{90} + 18 q^{91} - 153 q^{92} - 137 q^{93} - 23 q^{94} + 10 q^{95} - 109 q^{96} - 160 q^{97} - 119 q^{98} - 86 q^{99}+O(q^{100}) \) 151 * q - 13 * q^2 - 16 * q^3 + 151 * q^4 - 43 * q^5 - 17 * q^6 - 18 * q^7 - 39 * q^8 + 135 * q^9 - 3 * q^10 - 27 * q^11 - 52 * q^12 - 151 * q^13 - 9 * q^14 - 14 * q^15 + 143 * q^16 - 111 * q^17 - 37 * q^18 - 17 * q^19 - 107 * q^20 - 29 * q^21 - 16 * q^22 - 47 * q^23 - 46 * q^24 + 122 * q^25 + 13 * q^26 - 55 * q^27 - 44 * q^28 + 37 * q^29 - 14 * q^30 - 27 * q^31 - 86 * q^32 - 94 * q^33 - 10 * q^34 - 47 * q^35 + 124 * q^36 - 59 * q^37 - 80 * q^38 + 16 * q^39 + 5 * q^40 - 129 * q^41 - 77 * q^42 - 11 * q^43 - 99 * q^44 - 122 * q^45 - 17 * q^46 - 130 * q^47 - 111 * q^48 + 99 * q^49 - 72 * q^50 + 15 * q^51 - 151 * q^52 - 43 * q^53 - 49 * q^54 - 40 * q^55 - 50 * q^56 - 85 * q^57 - 73 * q^58 - 74 * q^59 - 43 * q^60 - 7 * q^61 - 110 * q^62 - 70 * q^63 + 141 * q^64 + 43 * q^65 - 16 * q^66 - 39 * q^67 - 222 * q^68 + 19 * q^69 - 52 * q^70 - 72 * q^71 - 106 * q^72 - 143 * q^73 + 20 * q^74 - 73 * q^75 - 88 * q^76 - 86 * q^77 + 17 * q^78 + 10 * q^79 - 239 * q^80 + 103 * q^81 - 96 * q^82 - 96 * q^83 - 75 * q^84 - 24 * q^85 - 109 * q^86 - 65 * q^87 - 45 * q^88 - 237 * q^89 - 79 * q^90 + 18 * q^91 - 153 * q^92 - 137 * q^93 - 23 * q^94 + 10 * q^95 - 109 * q^96 - 160 * q^97 - 119 * q^98 - 86 * q^99

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