LMFDB - Embedded newform 8026.2.a.b.1.8

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [8026,2,Mod(1,8026)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(8026, 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("8026.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 8026 = 2 \cdot 4013 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	8026.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:	$64.0879326623$
Analytic rank:	$1$
Dimension:	$81$
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.8
Character	$\chi$	$=$	8026.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.00000 q^{2} -2.77693 q^{3} +1.00000 q^{4} +2.15661 q^{5} +2.77693 q^{6} +3.32117 q^{7} -1.00000 q^{8} +4.71136 q^{9} +O(q^{10})$	\(q-1.00000 q^{2} -2.77693 q^{3} +1.00000 q^{4} +2.15661 q^{5} +2.77693 q^{6} +3.32117 q^{7} -1.00000 q^{8} +4.71136 q^{9} -2.15661 q^{10} -1.55320 q^{11} -2.77693 q^{12} -5.45896 q^{13} -3.32117 q^{14} -5.98877 q^{15} +1.00000 q^{16} -2.23032 q^{17} -4.71136 q^{18} -4.92047 q^{19} +2.15661 q^{20} -9.22267 q^{21} +1.55320 q^{22} +3.83366 q^{23} +2.77693 q^{24} -0.349019 q^{25} +5.45896 q^{26} -4.75234 q^{27} +3.32117 q^{28} -1.49081 q^{29} +5.98877 q^{30} +8.42545 q^{31} -1.00000 q^{32} +4.31314 q^{33} +2.23032 q^{34} +7.16248 q^{35} +4.71136 q^{36} +6.95298 q^{37} +4.92047 q^{38} +15.1592 q^{39} -2.15661 q^{40} +0.843499 q^{41} +9.22267 q^{42} +2.75008 q^{43} -1.55320 q^{44} +10.1606 q^{45} -3.83366 q^{46} -5.54606 q^{47} -2.77693 q^{48} +4.03018 q^{49} +0.349019 q^{50} +6.19346 q^{51} -5.45896 q^{52} +3.17078 q^{53} +4.75234 q^{54} -3.34965 q^{55} -3.32117 q^{56} +13.6638 q^{57} +1.49081 q^{58} -10.8188 q^{59} -5.98877 q^{60} -6.24278 q^{61} -8.42545 q^{62} +15.6472 q^{63} +1.00000 q^{64} -11.7729 q^{65} -4.31314 q^{66} -3.87553 q^{67} -2.23032 q^{68} -10.6458 q^{69} -7.16248 q^{70} +10.2541 q^{71} -4.71136 q^{72} +15.1668 q^{73} -6.95298 q^{74} +0.969203 q^{75} -4.92047 q^{76} -5.15845 q^{77} -15.1592 q^{78} +8.30703 q^{79} +2.15661 q^{80} -0.937149 q^{81} -0.843499 q^{82} -8.98766 q^{83} -9.22267 q^{84} -4.80995 q^{85} -2.75008 q^{86} +4.13988 q^{87} +1.55320 q^{88} -4.24398 q^{89} -10.1606 q^{90} -18.1301 q^{91} +3.83366 q^{92} -23.3969 q^{93} +5.54606 q^{94} -10.6115 q^{95} +2.77693 q^{96} -0.647693 q^{97} -4.03018 q^{98} -7.31769 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 81 q - 81 q^{2} - 10 q^{3} + 81 q^{4} - 26 q^{5} + 10 q^{6} + 3 q^{7} - 81 q^{8} + 59 q^{9}+O(q^{10}) $ 81 * q - 81 * q^2 - 10 * q^3 + 81 * q^4 - 26 * q^5 + 10 * q^6 + 3 * q^7 - 81 * q^8 + 59 * q^9	\( 81 q - 81 q^{2} - 10 q^{3} + 81 q^{4} - 26 q^{5} + 10 q^{6} + 3 q^{7} - 81 q^{8} + 59 q^{9} + 26 q^{10} - 41 q^{11} - 10 q^{12} + 33 q^{13} - 3 q^{14} - 7 q^{15} + 81 q^{16} - 9 q^{17} - 59 q^{18} - 32 q^{19} - 26 q^{20} - 23 q^{21} + 41 q^{22} - 28 q^{23} + 10 q^{24} + 81 q^{25} - 33 q^{26} - 37 q^{27} + 3 q^{28} - 35 q^{29} + 7 q^{30} - 29 q^{31} - 81 q^{32} - 7 q^{33} + 9 q^{34} - 67 q^{35} + 59 q^{36} + 13 q^{37} + 32 q^{38} - 42 q^{39} + 26 q^{40} - 66 q^{41} + 23 q^{42} - 22 q^{43} - 41 q^{44} - 65 q^{45} + 28 q^{46} - 71 q^{47} - 10 q^{48} + 64 q^{49} - 81 q^{50} - 43 q^{51} + 33 q^{52} - 37 q^{53} + 37 q^{54} + 12 q^{55} - 3 q^{56} - q^{57} + 35 q^{58} - 162 q^{59} - 7 q^{60} + 19 q^{61} + 29 q^{62} - 16 q^{63} + 81 q^{64} - 45 q^{65} + 7 q^{66} - 43 q^{67} - 9 q^{68} - 21 q^{69} + 67 q^{70} - 99 q^{71} - 59 q^{72} + 53 q^{73} - 13 q^{74} - 61 q^{75} - 32 q^{76} - 31 q^{77} + 42 q^{78} + 4 q^{79} - 26 q^{80} + q^{81} + 66 q^{82} - 112 q^{83} - 23 q^{84} + 17 q^{85} + 22 q^{86} - 15 q^{87} + 41 q^{88} - 111 q^{89} + 65 q^{90} - 49 q^{91} - 28 q^{92} - 19 q^{93} + 71 q^{94} - 53 q^{95} + 10 q^{96} + 50 q^{97} - 64 q^{98} - 97 q^{99}+O(q^{100}) \) 81 * q - 81 * q^2 - 10 * q^3 + 81 * q^4 - 26 * q^5 + 10 * q^6 + 3 * q^7 - 81 * q^8 + 59 * q^9 + 26 * q^10 - 41 * q^11 - 10 * q^12 + 33 * q^13 - 3 * q^14 - 7 * q^15 + 81 * q^16 - 9 * q^17 - 59 * q^18 - 32 * q^19 - 26 * q^20 - 23 * q^21 + 41 * q^22 - 28 * q^23 + 10 * q^24 + 81 * q^25 - 33 * q^26 - 37 * q^27 + 3 * q^28 - 35 * q^29 + 7 * q^30 - 29 * q^31 - 81 * q^32 - 7 * q^33 + 9 * q^34 - 67 * q^35 + 59 * q^36 + 13 * q^37 + 32 * q^38 - 42 * q^39 + 26 * q^40 - 66 * q^41 + 23 * q^42 - 22 * q^43 - 41 * q^44 - 65 * q^45 + 28 * q^46 - 71 * q^47 - 10 * q^48 + 64 * q^49 - 81 * q^50 - 43 * q^51 + 33 * q^52 - 37 * q^53 + 37 * q^54 + 12 * q^55 - 3 * q^56 - q^57 + 35 * q^58 - 162 * q^59 - 7 * q^60 + 19 * q^61 + 29 * q^62 - 16 * q^63 + 81 * q^64 - 45 * q^65 + 7 * q^66 - 43 * q^67 - 9 * q^68 - 21 * q^69 + 67 * q^70 - 99 * q^71 - 59 * q^72 + 53 * q^73 - 13 * q^74 - 61 * q^75 - 32 * q^76 - 31 * q^77 + 42 * q^78 + 4 * q^79 - 26 * q^80 + q^81 + 66 * q^82 - 112 * q^83 - 23 * q^84 + 17 * q^85 + 22 * q^86 - 15 * q^87 + 41 * q^88 - 111 * q^89 + 65 * q^90 - 49 * q^91 - 28 * q^92 - 19 * q^93 + 71 * q^94 - 53 * q^95 + 10 * q^96 + 50 * q^97 - 64 * q^98 - 97 * 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 $

$2$	−1.00000	−0.707107
$2$	−1.00000	−0.707107
$3$	−2.77693	−1.60326	−0.801632	−	0.597818i	$-0.796035\pi$
$3$	−2.77693	−1.60326	−0.801632	+	0.597818i	$0.796035\pi$
$4$	1.00000	0.500000
$5$	2.15661	0.964467	0.482233	−	0.876043i	$-0.339826\pi$
$5$	2.15661	0.964467	0.482233	+	0.876043i	$0.339826\pi$
$6$	2.77693	1.13368
$7$	3.32117	1.25528	0.627642	−	0.778502i	$-0.284020\pi$
$7$	3.32117	1.25528	0.627642	+	0.778502i	$0.284020\pi$
$8$	−1.00000	−0.353553
$9$	4.71136	1.57045
$10$	−2.15661	−0.681981
$11$	−1.55320	−0.468308	−0.234154	−	0.972200i	$-0.575232\pi$
$11$	−1.55320	−0.468308	−0.234154	+	0.972200i	$0.575232\pi$
$12$	−2.77693	−0.801632
$13$	−5.45896	−1.51404	−0.757021	−	0.653391i	$-0.773346\pi$
$13$	−5.45896	−1.51404	−0.757021	+	0.653391i	$0.773346\pi$
$14$	−3.32117	−0.887620
$15$	−5.98877	−1.54629
$16$	1.00000	0.250000
$17$	−2.23032	−0.540933	−0.270467	−	0.962729i	$-0.587178\pi$
$17$	−2.23032	−0.540933	−0.270467	+	0.962729i	$0.587178\pi$
$18$	−4.71136	−1.11048
$19$	−4.92047	−1.12883	−0.564416	−	0.825490i	$-0.690899\pi$
$19$	−4.92047	−1.12883	−0.564416	+	0.825490i	$0.690899\pi$
$20$	2.15661	0.482233
$21$	−9.22267	−2.01255
$22$	1.55320	0.331143
$23$	3.83366	0.799374	0.399687	−	0.916652i	$-0.369119\pi$
$23$	3.83366	0.799374	0.399687	+	0.916652i	$0.369119\pi$
$24$	2.77693	0.566839
$25$	−0.349019	−0.0698038
$26$	5.45896	1.07059
$27$	−4.75234	−0.914589
$28$	3.32117	0.627642
$29$	−1.49081	−0.276837	−0.138418	−	0.990374i	$-0.544202\pi$
$29$	−1.49081	−0.276837	−0.138418	+	0.990374i	$0.544202\pi$
$30$	5.98877	1.09340
$31$	8.42545	1.51326	0.756628	−	0.653846i	$-0.226846\pi$
$31$	8.42545	1.51326	0.756628	+	0.653846i	$0.226846\pi$
$32$	−1.00000	−0.176777
$33$	4.31314	0.750820
$34$	2.23032	0.382497
$35$	7.16248	1.21068
$36$	4.71136	0.785227
$37$	6.95298	1.14306	0.571531	−	0.820580i	$-0.306350\pi$
$37$	6.95298	1.14306	0.571531	+	0.820580i	$0.306350\pi$
$38$	4.92047	0.798205
$39$	15.1592	2.42741
$40$	−2.15661	−0.340991
$41$	0.843499	0.131732	0.0658662	−	0.997828i	$-0.479019\pi$
$41$	0.843499	0.131732	0.0658662	+	0.997828i	$0.479019\pi$
$42$	9.22267	1.42309
$43$	2.75008	0.419383	0.209692	−	0.977768i	$-0.432754\pi$
$43$	2.75008	0.419383	0.209692	+	0.977768i	$0.432754\pi$
$44$	−1.55320	−0.234154
$45$	10.1606	1.51465
$46$	−3.83366	−0.565243
$47$	−5.54606	−0.808976	−0.404488	−	0.914543i	$-0.632550\pi$
$47$	−5.54606	−0.808976	−0.404488	+	0.914543i	$0.632550\pi$
$48$	−2.77693	−0.400816
$49$	4.03018	0.575740
$50$	0.349019	0.0493588
$51$	6.19346	0.867258
$52$	−5.45896	−0.757021
$53$	3.17078	0.435540	0.217770	−	0.976000i	$-0.430122\pi$
$53$	3.17078	0.435540	0.217770	+	0.976000i	$0.430122\pi$
$54$	4.75234	0.646712
$55$	−3.34965	−0.451667
$56$	−3.32117	−0.443810
$57$	13.6638	1.80982
$58$	1.49081	0.195753
$59$	−10.8188	−1.40848	−0.704241	−	0.709961i	$-0.748713\pi$
$59$	−10.8188	−1.40848	−0.704241	+	0.709961i	$0.748713\pi$
$60$	−5.98877	−0.773147
$61$	−6.24278	−0.799306	−0.399653	−	0.916667i	$-0.630869\pi$
$61$	−6.24278	−0.799306	−0.399653	+	0.916667i	$0.630869\pi$
$62$	−8.42545	−1.07003
$63$	15.6472	1.97137
$64$	1.00000	0.125000
$65$	−11.7729	−1.46024
$66$	−4.31314	−0.530910
$67$	−3.87553	−0.473472	−0.236736	−	0.971574i	$-0.576078\pi$
$67$	−3.87553	−0.473472	−0.236736	+	0.971574i	$0.576078\pi$
$68$	−2.23032	−0.270467
$69$	−10.6458	−1.28161
$70$	−7.16248	−0.856080
$71$	10.2541	1.21693	0.608467	−	0.793579i	$-0.291785\pi$
$71$	10.2541	1.21693	0.608467	+	0.793579i	$0.291785\pi$
$72$	−4.71136	−0.555239
$73$	15.1668	1.77514	0.887569	−	0.460674i	$-0.152392\pi$
$73$	15.1668	1.77514	0.887569	+	0.460674i	$0.152392\pi$
$74$	−6.95298	−0.808267
$75$	0.969203	0.111914
$76$	−4.92047	−0.564416
$77$	−5.15845	−0.587859
$78$	−15.1592	−1.71644
$79$	8.30703	0.934614	0.467307	−	0.884095i	$-0.345224\pi$
$79$	8.30703	0.934614	0.467307	+	0.884095i	$0.345224\pi$
$80$	2.15661	0.241117
$81$	−0.937149	−0.104128
$82$	−0.843499	−0.0931489
$83$	−8.98766	−0.986524	−0.493262	−	0.869881i	$-0.664196\pi$
$83$	−8.98766	−0.986524	−0.493262	+	0.869881i	$0.664196\pi$
$84$	−9.22267	−1.00628
$85$	−4.80995	−0.521712
$86$	−2.75008	−0.296549
$87$	4.13988	0.443842
$88$	1.55320	0.165572
$89$	−4.24398	−0.449861	−0.224931	−	0.974375i	$-0.572216\pi$
$89$	−4.24398	−0.449861	−0.224931	+	0.974375i	$0.572216\pi$
$90$	−10.1606	−1.07102
$91$	−18.1301	−1.90055
$92$	3.83366	0.399687
$93$	−23.3969	−2.42615
$94$	5.54606	0.572033
$95$	−10.6115	−1.08872
$96$	2.77693	0.283420
$97$	−0.647693	−0.0657633	−0.0328816	−	0.999459i	$-0.510468\pi$
$97$	−0.647693	−0.0657633	−0.0328816	+	0.999459i	$0.510468\pi$
$98$	−4.03018	−0.407110
$99$	−7.31769	−0.735456
$100$	−0.349019	−0.0349019
$101$	12.4416	1.23799	0.618993	−	0.785397i	$-0.287541\pi$
$101$	12.4416	1.23799	0.618993	+	0.785397i	$0.287541\pi$
$102$	−6.19346	−0.613244
$103$	−11.7076	−1.15358	−0.576791	−	0.816892i	$-0.695695\pi$
$103$	−11.7076	−1.15358	−0.576791	+	0.816892i	$0.695695\pi$
$104$	5.45896	0.535295
$105$	−19.8897	−1.94104
$106$	−3.17078	−0.307973
$107$	1.29630	0.125319	0.0626593	−	0.998035i	$-0.480042\pi$
$107$	1.29630	0.125319	0.0626593	+	0.998035i	$0.480042\pi$
$108$	−4.75234	−0.457294
$109$	5.85943	0.561232	0.280616	−	0.959820i	$-0.409461\pi$
$109$	5.85943	0.561232	0.280616	+	0.959820i	$0.409461\pi$
$110$	3.34965	0.319377
$111$	−19.3080	−1.83263
$112$	3.32117	0.313821
$113$	8.38327	0.788631	0.394316	−	0.918975i	$-0.370982\pi$
$113$	8.38327	0.788631	0.394316	+	0.918975i	$0.370982\pi$
$114$	−13.6638	−1.27973
$115$	8.26773	0.770970
$116$	−1.49081	−0.138418
$117$	−25.7191	−2.37773
$118$	10.8188	0.995947
$119$	−7.40729	−0.679025
$120$	5.98877	0.546698
$121$	−8.58757	−0.780688
$122$	6.24278	0.565195
$123$	−2.34234	−0.211202
$124$	8.42545	0.756628
$125$	−11.5358	−1.03179
$126$	−15.6472	−1.39397
$127$	3.86034	0.342549	0.171275	−	0.985223i	$-0.445211\pi$
$127$	3.86034	0.342549	0.171275	+	0.985223i	$0.445211\pi$
$128$	−1.00000	−0.0883883
$129$	−7.63679	−0.672382
$130$	11.7729	1.03255
$131$	−14.4049	−1.25857	−0.629283	−	0.777176i	$-0.716651\pi$
$131$	−14.4049	−1.25857	−0.629283	+	0.777176i	$0.716651\pi$
$132$	4.31314	0.375410
$133$	−16.3417	−1.41701
$134$	3.87553	0.334795
$135$	−10.2490	−0.882090
$136$	2.23032	0.191249
$137$	−7.40120	−0.632327	−0.316164	−	0.948705i	$-0.602395\pi$
$137$	−7.40120	−0.632327	−0.316164	+	0.948705i	$0.602395\pi$
$138$	10.6458	0.906233
$139$	−13.7951	−1.17008	−0.585041	−	0.811004i	$-0.698921\pi$
$139$	−13.7951	−1.17008	−0.585041	+	0.811004i	$0.698921\pi$
$140$	7.16248	0.605340
$141$	15.4011	1.29700
$142$	−10.2541	−0.860503
$143$	8.47885	0.709037
$144$	4.71136	0.392614
$145$	−3.21510	−0.267000
$146$	−15.1668	−1.25521
$147$	−11.1915	−0.923063
$148$	6.95298	0.571531
$149$	9.88936	0.810168	0.405084	−	0.914279i	$-0.367242\pi$
$149$	9.88936	0.810168	0.405084	+	0.914279i	$0.367242\pi$
$150$	−0.969203	−0.0791351
$151$	2.68059	0.218143	0.109072	−	0.994034i	$-0.465212\pi$
$151$	2.68059	0.218143	0.109072	+	0.994034i	$0.465212\pi$
$152$	4.92047	0.399103
$153$	−10.5079	−0.849511
$154$	5.15845	0.415679
$155$	18.1704	1.45948
$156$	15.1592	1.21370
$157$	−23.3802	−1.86595	−0.932973	−	0.359946i	$-0.882795\pi$
$157$	−23.3802	−1.86595	−0.932973	+	0.359946i	$0.882795\pi$
$158$	−8.30703	−0.660872
$159$	−8.80505	−0.698286
$160$	−2.15661	−0.170495
$161$	12.7323	1.00344
$162$	0.937149	0.0736293
$163$	−10.1006	−0.791137	−0.395569	−	0.918436i	$-0.629452\pi$
$163$	−10.1006	−0.791137	−0.395569	+	0.918436i	$0.629452\pi$
$164$	0.843499	0.0658662
$165$	9.30176	0.724141
$166$	8.98766	0.697578
$167$	−6.08456	−0.470837	−0.235419	−	0.971894i	$-0.575646\pi$
$167$	−6.08456	−0.470837	−0.235419	+	0.971894i	$0.575646\pi$
$168$	9.22267	0.711545
$169$	16.8002	1.29232
$170$	4.80995	0.368906
$171$	−23.1821	−1.77278
$172$	2.75008	0.209692
$173$	4.97513	0.378252	0.189126	−	0.981953i	$-0.439435\pi$
$173$	4.97513	0.378252	0.189126	+	0.981953i	$0.439435\pi$
$174$	−4.13988	−0.313844
$175$	−1.15915	−0.0876237
$176$	−1.55320	−0.117077
$177$	30.0430	2.25817
$178$	4.24398	0.318100
$179$	−6.22605	−0.465357	−0.232679	−	0.972554i	$-0.574749\pi$
$179$	−6.22605	−0.465357	−0.232679	+	0.972554i	$0.574749\pi$
$180$	10.1606	0.757325
$181$	13.5566	1.00766	0.503829	−	0.863804i	$-0.331924\pi$
$181$	13.5566	1.00766	0.503829	+	0.863804i	$0.331924\pi$
$182$	18.1301	1.34389
$183$	17.3358	1.28150
$184$	−3.83366	−0.282621
$185$	14.9949	1.10245
$186$	23.3969	1.71555
$187$	3.46414	0.253323
$188$	−5.54606	−0.404488
$189$	−15.7833	−1.14807
$190$	10.6115	0.769843
$191$	−6.67728	−0.483151	−0.241575	−	0.970382i	$-0.577664\pi$
$191$	−6.67728	−0.483151	−0.241575	+	0.970382i	$0.577664\pi$
$192$	−2.77693	−0.200408
$193$	14.0795	1.01346	0.506731	−	0.862104i	$-0.330854\pi$
$193$	14.0795	1.01346	0.506731	+	0.862104i	$0.330854\pi$
$194$	0.647693	0.0465017
$195$	32.6924	2.34115
$196$	4.03018	0.287870
$197$	2.22662	0.158640	0.0793201	−	0.996849i	$-0.474725\pi$
$197$	2.22662	0.158640	0.0793201	+	0.996849i	$0.474725\pi$
$198$	7.31769	0.520046
$199$	3.97736	0.281947	0.140974	−	0.990013i	$-0.454977\pi$
$199$	3.97736	0.281947	0.140974	+	0.990013i	$0.454977\pi$
$200$	0.349019	0.0246794
$201$	10.7621	0.759100
$202$	−12.4416	−0.875388
$203$	−4.95124	−0.347509
$204$	6.19346	0.433629
$205$	1.81910	0.127052
$206$	11.7076	0.815706
$207$	18.0618	1.25538
$208$	−5.45896	−0.378510
$209$	7.64247	0.528641
$210$	19.8897	1.37252
$211$	−20.7908	−1.43130	−0.715649	−	0.698460i	$-0.753869\pi$
$211$	−20.7908	−1.43130	−0.715649	+	0.698460i	$0.753869\pi$
$212$	3.17078	0.217770
$213$	−28.4749	−1.95107
$214$	−1.29630	−0.0886136
$215$	5.93086	0.404481
$216$	4.75234	0.323356
$217$	27.9824	1.89957
$218$	−5.85943	−0.396851
$219$	−42.1172	−2.84601
$220$	−3.34965	−0.225834
$221$	12.1752	0.818995
$222$	19.3080	1.29587
$223$	−0.185548	−0.0124252	−0.00621262	−	0.999981i	$-0.501978\pi$
$223$	−0.185548	−0.0124252	−0.00621262	+	0.999981i	$0.501978\pi$
$224$	−3.32117	−0.221905
$225$	−1.64436	−0.109624
$226$	−8.38327	−0.557647
$227$	19.7975	1.31401	0.657004	−	0.753887i	$-0.271823\pi$
$227$	19.7975	1.31401	0.657004	+	0.753887i	$0.271823\pi$
$228$	13.6638	0.904908
$229$	−0.287303	−0.0189855	−0.00949276	−	0.999955i	$-0.503022\pi$
$229$	−0.287303	−0.0189855	−0.00949276	+	0.999955i	$0.503022\pi$
$230$	−8.26773	−0.545158
$231$	14.3247	0.942494
$232$	1.49081	0.0978765
$233$	17.5813	1.15179	0.575894	−	0.817524i	$-0.304654\pi$
$233$	17.5813	1.15179	0.575894	+	0.817524i	$0.304654\pi$
$234$	25.7191	1.68131
$235$	−11.9607	−0.780231
$236$	−10.8188	−0.704241
$237$	−23.0681	−1.49843
$238$	7.40729	0.480143
$239$	−13.2093	−0.854437	−0.427218	−	0.904148i	$-0.640506\pi$
$239$	−13.2093	−0.854437	−0.427218	+	0.904148i	$0.640506\pi$
$240$	−5.98877	−0.386574
$241$	4.13484	0.266349	0.133174	−	0.991093i	$-0.457483\pi$
$241$	4.13484	0.266349	0.133174	+	0.991093i	$0.457483\pi$
$242$	8.58757	0.552030
$243$	16.8594	1.08153
$244$	−6.24278	−0.399653
$245$	8.69154	0.555282
$246$	2.34234	0.149342
$247$	26.8606	1.70910
$248$	−8.42545	−0.535017
$249$	24.9581	1.58166
$250$	11.5358	0.729586
$251$	−7.23351	−0.456575	−0.228288	−	0.973594i	$-0.573313\pi$
$251$	−7.23351	−0.456575	−0.228288	+	0.973594i	$0.573313\pi$
$252$	15.6472	0.985684
$253$	−5.95445	−0.374353
$254$	−3.86034	−0.242219
$255$	13.3569	0.836442
$256$	1.00000	0.0625000
$257$	10.8490	0.676742	0.338371	−	0.941013i	$-0.390124\pi$
$257$	10.8490	0.676742	0.338371	+	0.941013i	$0.390124\pi$
$258$	7.63679	0.475446
$259$	23.0920	1.43487
$260$	−11.7729	−0.730121
$261$	−7.02375	−0.434759
$262$	14.4049	0.889941
$263$	7.57649	0.467186	0.233593	−	0.972334i	$-0.424952\pi$
$263$	7.57649	0.467186	0.233593	+	0.972334i	$0.424952\pi$
$264$	−4.31314	−0.265455
$265$	6.83815	0.420064
$266$	16.3417	1.00198
$267$	11.7853	0.721246
$268$	−3.87553	−0.236736
$269$	−1.09782	−0.0669353	−0.0334677	−	0.999440i	$-0.510655\pi$
$269$	−1.09782	−0.0669353	−0.0334677	+	0.999440i	$0.510655\pi$
$270$	10.2490	0.623732
$271$	−18.5265	−1.12540	−0.562702	−	0.826660i	$-0.690238\pi$
$271$	−18.5265	−1.12540	−0.562702	+	0.826660i	$0.690238\pi$
$272$	−2.23032	−0.135233
$273$	50.3462	3.04709
$274$	7.40120	0.447123
$275$	0.542097	0.0326897
$276$	−10.6458	−0.640804
$277$	−16.7272	−1.00504	−0.502521	−	0.864565i	$-0.667594\pi$
$277$	−16.7272	−1.00504	−0.502521	+	0.864565i	$0.667594\pi$
$278$	13.7951	0.827372
$279$	39.6953	2.37650
$280$	−7.16248	−0.428040
$281$	−20.9778	−1.25143	−0.625715	−	0.780052i	$-0.715193\pi$
$281$	−20.9778	−1.25143	−0.625715	+	0.780052i	$0.715193\pi$
$282$	−15.4011	−0.917119
$283$	19.6423	1.16761	0.583807	−	0.811892i	$-0.301562\pi$
$283$	19.6423	1.16761	0.583807	+	0.811892i	$0.301562\pi$
$284$	10.2541	0.608467
$285$	29.4676	1.74551
$286$	−8.47885	−0.501365
$287$	2.80141	0.165362
$288$	−4.71136	−0.277620
$289$	−12.0257	−0.707391
$290$	3.21510	0.188797
$291$	1.79860	0.105436
$292$	15.1668	0.887569
$293$	−27.3271	−1.59646	−0.798232	−	0.602350i	$-0.794231\pi$
$293$	−27.3271	−1.59646	−0.798232	+	0.602350i	$0.794231\pi$
$294$	11.1915	0.652704
$295$	−23.3319	−1.35843
$296$	−6.95298	−0.404134
$297$	7.38134	0.428309
$298$	−9.88936	−0.572876
$299$	−20.9278	−1.21029
$300$	0.969203	0.0559570
$301$	9.13348	0.526445
$302$	−2.68059	−0.154250
$303$	−34.5495	−1.98482
$304$	−4.92047	−0.282208
$305$	−13.4633	−0.770904
$306$	10.5079	0.600695
$307$	−23.8300	−1.36005	−0.680024	−	0.733190i	$-0.738031\pi$
$307$	−23.8300	−1.36005	−0.680024	+	0.733190i	$0.738031\pi$
$308$	−5.15845	−0.293930
$309$	32.5112	1.84950
$310$	−18.1704	−1.03201
$311$	−20.8363	−1.18152	−0.590760	−	0.806848i	$-0.701172\pi$
$311$	−20.8363	−1.18152	−0.590760	+	0.806848i	$0.701172\pi$
$312$	−15.1592	−0.858218
$313$	−27.1987	−1.53736	−0.768681	−	0.639632i	$-0.779087\pi$
$313$	−27.1987	−1.53736	−0.768681	+	0.639632i	$0.779087\pi$
$314$	23.3802	1.31942
$315$	33.7451	1.90132
$316$	8.30703	0.467307
$317$	25.7323	1.44527	0.722636	−	0.691229i	$-0.242930\pi$
$317$	25.7323	1.44527	0.722636	+	0.691229i	$0.242930\pi$
$318$	8.80505	0.493763
$319$	2.31553	0.129645
$320$	2.15661	0.120558
$321$	−3.59975	−0.200919
$322$	−12.7323	−0.709541
$323$	10.9742	0.610623
$324$	−0.937149	−0.0520638
$325$	1.90528	0.105686
$326$	10.1006	0.559419
$327$	−16.2713	−0.899803
$328$	−0.843499	−0.0465745
$329$	−18.4194	−1.01550
$330$	−9.30176	−0.512045
$331$	−0.417145	−0.0229283	−0.0114642	−	0.999934i	$-0.503649\pi$
$331$	−0.417145	−0.0229283	−0.0114642	+	0.999934i	$0.503649\pi$
$332$	−8.98766	−0.493262
$333$	32.7580	1.79513
$334$	6.08456	0.332932
$335$	−8.35803	−0.456648
$336$	−9.22267	−0.503138
$337$	−7.25189	−0.395036	−0.197518	−	0.980299i	$-0.563288\pi$
$337$	−7.25189	−0.395036	−0.197518	+	0.980299i	$0.563288\pi$
$338$	−16.8002	−0.913810
$339$	−23.2798	−1.26438
$340$	−4.80995	−0.260856
$341$	−13.0864	−0.708669
$342$	23.1821	1.25354
$343$	−9.86328	−0.532567
$344$	−2.75008	−0.148274
$345$	−22.9589	−1.23607
$346$	−4.97513	−0.267465
$347$	−13.4874	−0.724044	−0.362022	−	0.932170i	$-0.617913\pi$
$347$	−13.4874	−0.724044	−0.362022	+	0.932170i	$0.617913\pi$
$348$	4.13988	0.221921
$349$	−2.96719	−0.158830	−0.0794151	−	0.996842i	$-0.525305\pi$
$349$	−2.96719	−0.158830	−0.0794151	+	0.996842i	$0.525305\pi$
$350$	1.15915	0.0619593
$351$	25.9428	1.38473
$352$	1.55320	0.0827859
$353$	13.0493	0.694546	0.347273	−	0.937764i	$-0.387108\pi$
$353$	13.0493	0.694546	0.347273	+	0.937764i	$0.387108\pi$
$354$	−30.0430	−1.59677
$355$	22.1141	1.17369
$356$	−4.24398	−0.224931
$357$	20.5696	1.08866
$358$	6.22605	0.329057
$359$	−12.0619	−0.636603	−0.318301	−	0.947990i	$-0.603112\pi$
$359$	−12.0619	−0.636603	−0.318301	+	0.947990i	$0.603112\pi$
$360$	−10.1606	−0.535510
$361$	5.21101	0.274263
$362$	−13.5566	−0.712521
$363$	23.8471	1.25165
$364$	−18.1301	−0.950277
$365$	32.7089	1.71206
$366$	−17.3358	−0.906156
$367$	−37.3889	−1.95168	−0.975842	−	0.218480i	$-0.929890\pi$
$367$	−37.3889	−1.95168	−0.975842	+	0.218480i	$0.929890\pi$
$368$	3.83366	0.199844
$369$	3.97403	0.206880
$370$	−14.9949	−0.779547
$371$	10.5307	0.546727
$372$	−23.3969	−1.21307
$373$	35.4078	1.83335	0.916674	−	0.399636i	$-0.130864\pi$
$373$	35.4078	1.83335	0.916674	+	0.399636i	$0.130864\pi$
$374$	−3.46414	−0.179126
$375$	32.0341	1.65423
$376$	5.54606	0.286016
$377$	8.13827	0.419142
$378$	15.7833	0.811808
$379$	36.1932	1.85912	0.929560	−	0.368672i	$-0.120187\pi$
$379$	36.1932	1.85912	0.929560	+	0.368672i	$0.120187\pi$
$380$	−10.6115	−0.544361
$381$	−10.7199	−0.549197
$382$	6.67728	0.341639
$383$	−11.7935	−0.602621	−0.301311	−	0.953526i	$-0.597424\pi$
$383$	−11.7935	−0.602621	−0.301311	+	0.953526i	$0.597424\pi$
$384$	2.77693	0.141710
$385$	−11.1248	−0.566971
$386$	−14.0795	−0.716626
$387$	12.9566	0.658622
$388$	−0.647693	−0.0328816
$389$	−22.5729	−1.14449	−0.572245	−	0.820083i	$-0.693927\pi$
$389$	−22.5729	−1.14449	−0.572245	+	0.820083i	$0.693927\pi$
$390$	−32.6924	−1.65545
$391$	−8.55031	−0.432408
$392$	−4.03018	−0.203555
$393$	40.0016	2.01781
$394$	−2.22662	−0.112176
$395$	17.9151	0.901404
$396$	−7.31769	−0.367728
$397$	1.11349	0.0558844	0.0279422	−	0.999610i	$-0.491105\pi$
$397$	1.11349	0.0558844	0.0279422	+	0.999610i	$0.491105\pi$
$398$	−3.97736	−0.199367
$399$	45.3799	2.27184
$400$	−0.349019	−0.0174510
$401$	−28.4318	−1.41982	−0.709908	−	0.704294i	$-0.751264\pi$
$401$	−28.4318	−1.41982	−0.709908	+	0.704294i	$0.751264\pi$
$402$	−10.7621	−0.536765
$403$	−45.9941	−2.29113
$404$	12.4416	0.618993
$405$	−2.02107	−0.100428
$406$	4.95124	0.245726
$407$	−10.7994	−0.535305
$408$	−6.19346	−0.306622
$409$	−3.33936	−0.165121	−0.0825603	−	0.996586i	$-0.526310\pi$
$409$	−3.33936	−0.165121	−0.0825603	+	0.996586i	$0.526310\pi$
$410$	−1.81910	−0.0898390
$411$	20.5526	1.01379
$412$	−11.7076	−0.576791
$413$	−35.9309	−1.76805
$414$	−18.0618	−0.887688
$415$	−19.3829	−0.951469
$416$	5.45896	0.267647
$417$	38.3080	1.87595
$418$	−7.64247	−0.373806
$419$	−30.4571	−1.48793	−0.743963	−	0.668221i	$-0.767056\pi$
$419$	−30.4571	−1.48793	−0.743963	+	0.668221i	$0.767056\pi$
$420$	−19.8897	−0.970520
$421$	29.2355	1.42485	0.712425	−	0.701748i	$-0.247597\pi$
$421$	29.2355	1.42485	0.712425	+	0.701748i	$0.247597\pi$
$422$	20.7908	1.01208
$423$	−26.1295	−1.27046
$424$	−3.17078	−0.153987
$425$	0.778426	0.0377592
$426$	28.4749	1.37961
$427$	−20.7333	−1.00336
$428$	1.29630	0.0626593
$429$	−23.5452	−1.13677
$430$	−5.93086	−0.286011
$431$	−21.5252	−1.03683	−0.518415	−	0.855129i	$-0.673478\pi$
$431$	−21.5252	−1.03683	−0.518415	+	0.855129i	$0.673478\pi$
$432$	−4.75234	−0.228647
$433$	25.2201	1.21200	0.606002	−	0.795463i	$-0.292773\pi$
$433$	25.2201	1.21200	0.606002	+	0.795463i	$0.292773\pi$
$434$	−27.9824	−1.34320
$435$	8.92813	0.428071
$436$	5.85943	0.280616
$437$	−18.8634	−0.902360
$438$	42.1172	2.01244
$439$	27.0325	1.29019	0.645095	−	0.764102i	$-0.276818\pi$
$439$	27.0325	1.29019	0.645095	+	0.764102i	$0.276818\pi$
$440$	3.34965	0.159688
$441$	18.9876	0.904174
$442$	−12.1752	−0.579117
$443$	7.51560	0.357077	0.178538	−	0.983933i	$-0.442863\pi$
$443$	7.51560	0.357077	0.178538	+	0.983933i	$0.442863\pi$
$444$	−19.3080	−0.916315
$445$	−9.15263	−0.433876
$446$	0.185548	0.00878597
$447$	−27.4621	−1.29891
$448$	3.32117	0.156911
$449$	−7.51061	−0.354448	−0.177224	−	0.984171i	$-0.556712\pi$
$449$	−7.51061	−0.354448	−0.177224	+	0.984171i	$0.556712\pi$
$450$	1.64436	0.0775157
$451$	−1.31012	−0.0616913
$452$	8.38327	0.394316
$453$	−7.44381	−0.349741
$454$	−19.7975	−0.929145
$455$	−39.0997	−1.83302
$456$	−13.6638	−0.639867
$457$	3.83154	0.179232	0.0896159	−	0.995976i	$-0.471436\pi$
$457$	3.83154	0.179232	0.0896159	+	0.995976i	$0.471436\pi$
$458$	0.287303	0.0134248
$459$	10.5993	0.494731
$460$	8.26773	0.385485
$461$	12.2934	0.572560	0.286280	−	0.958146i	$-0.407581\pi$
$461$	12.2934	0.572560	0.286280	+	0.958146i	$0.407581\pi$
$462$	−14.3247	−0.666444
$463$	17.1507	0.797062	0.398531	−	0.917155i	$-0.369520\pi$
$463$	17.1507	0.797062	0.398531	+	0.917155i	$0.369520\pi$
$464$	−1.49081	−0.0692092
$465$	−50.4581	−2.33994
$466$	−17.5813	−0.814438
$467$	−36.4013	−1.68445	−0.842226	−	0.539124i	$-0.818755\pi$
$467$	−36.4013	−1.68445	−0.842226	+	0.539124i	$0.818755\pi$
$468$	−25.7191	−1.18887
$469$	−12.8713	−0.594342
$470$	11.9607	0.551707
$471$	64.9254	2.99160
$472$	10.8188	0.497974
$473$	−4.27142	−0.196400
$474$	23.0681	1.05955
$475$	1.71734	0.0787969
$476$	−7.40729	−0.339513
$477$	14.9387	0.683996
$478$	13.2093	0.604178
$479$	−11.2479	−0.513932	−0.256966	−	0.966420i	$-0.582723\pi$
$479$	−11.2479	−0.513932	−0.256966	+	0.966420i	$0.582723\pi$
$480$	5.98877	0.273349
$481$	−37.9560	−1.73064
$482$	−4.13484	−0.188337
$483$	−35.3566	−1.60878
$484$	−8.58757	−0.390344
$485$	−1.39682	−0.0634265
$486$	−16.8594	−0.764759
$487$	−3.94271	−0.178661	−0.0893306	−	0.996002i	$-0.528473\pi$
$487$	−3.94271	−0.178661	−0.0893306	+	0.996002i	$0.528473\pi$
$488$	6.24278	0.282597
$489$	28.0486	1.26840
$490$	−8.69154	−0.392644
$491$	16.8873	0.762114	0.381057	−	0.924551i	$-0.375560\pi$
$491$	16.8873	0.762114	0.381057	+	0.924551i	$0.375560\pi$
$492$	−2.34234	−0.105601
$493$	3.32499	0.149750
$494$	−26.8606	−1.20852
$495$	−15.7814	−0.709323
$496$	8.42545	0.378314
$497$	34.0555	1.52760
$498$	−24.9581	−1.11840
$499$	−34.6841	−1.55267	−0.776336	−	0.630319i	$-0.782924\pi$
$499$	−34.6841	−1.55267	−0.776336	+	0.630319i	$0.782924\pi$
$500$	−11.5358	−0.515895
$501$	16.8964	0.754876
$502$	7.23351	0.322847
$503$	39.3625	1.75509	0.877543	−	0.479499i	$-0.159181\pi$
$503$	39.3625	1.75509	0.877543	+	0.479499i	$0.159181\pi$
$504$	−15.6472	−0.696984
$505$	26.8317	1.19400
$506$	5.95445	0.264708
$507$	−46.6530	−2.07193
$508$	3.86034	0.171275
$509$	−7.60205	−0.336955	−0.168477	−	0.985706i	$-0.553885\pi$
$509$	−7.60205	−0.336955	−0.168477	+	0.985706i	$0.553885\pi$
$510$	−13.3569	−0.591454
$511$	50.3715	2.22830
$512$	−1.00000	−0.0441942
$513$	23.3837	1.03242
$514$	−10.8490	−0.478529
$515$	−25.2487	−1.11259
$516$	−7.63679	−0.336191
$517$	8.61415	0.378850
$518$	−23.0920	−1.01461
$519$	−13.8156	−0.606438
$520$	11.7729	0.516274
$521$	−27.6783	−1.21261	−0.606305	−	0.795232i	$-0.707349\pi$
$521$	−27.6783	−1.21261	−0.606305	+	0.795232i	$0.707349\pi$
$522$	7.02375	0.307421
$523$	3.76553	0.164655	0.0823275	−	0.996605i	$-0.473765\pi$
$523$	3.76553	0.164655	0.0823275	+	0.996605i	$0.473765\pi$
$524$	−14.4049	−0.629283
$525$	3.21889	0.140484
$526$	−7.57649	−0.330351
$527$	−18.7915	−0.818570
$528$	4.31314	0.187705
$529$	−8.30302	−0.361001
$530$	−6.83815	−0.297030
$531$	−50.9711	−2.21196
$532$	−16.3417	−0.708503
$533$	−4.60462	−0.199448
$534$	−11.7853	−0.509998
$535$	2.79563	0.120866
$536$	3.87553	0.167398
$537$	17.2893	0.746090
$538$	1.09782	0.0473304
$539$	−6.25968	−0.269623
$540$	−10.2490	−0.441045
$541$	21.6076	0.928983	0.464491	−	0.885578i	$-0.346237\pi$
$541$	21.6076	0.928983	0.464491	+	0.885578i	$0.346237\pi$
$542$	18.5265	0.795781
$543$	−37.6459	−1.61554
$544$	2.23032	0.0956243
$545$	12.6365	0.541290
$546$	−50.3462	−2.15462
$547$	−13.5169	−0.577943	−0.288971	−	0.957338i	$-0.593313\pi$
$547$	−13.5169	−0.577943	−0.288971	+	0.957338i	$0.593313\pi$
$548$	−7.40120	−0.316164
$549$	−29.4120	−1.25527
$550$	−0.542097	−0.0231151
$551$	7.33549	0.312502
$552$	10.6458	0.453117
$553$	27.5891	1.17321
$554$	16.7272	0.710672
$555$	−41.6398	−1.76751
$556$	−13.7951	−0.585041
$557$	27.1872	1.15196	0.575980	−	0.817464i	$-0.304620\pi$
$557$	27.1872	1.15196	0.575980	+	0.817464i	$0.304620\pi$
$558$	−39.6953	−1.68044
$559$	−15.0126	−0.634963
$560$	7.16248	0.302670
$561$	−9.61969	−0.406144
$562$	20.9778	0.884894
$563$	−14.2164	−0.599149	−0.299574	−	0.954073i	$-0.596845\pi$
$563$	−14.2164	−0.599149	−0.299574	+	0.954073i	$0.596845\pi$
$564$	15.4011	0.648501
$565$	18.0795	0.760609
$566$	−19.6423	−0.825628
$567$	−3.11243	−0.130710
$568$	−10.2541	−0.430251
$569$	−32.3805	−1.35746	−0.678731	−	0.734387i	$-0.737470\pi$
$569$	−32.3805	−1.35746	−0.678731	+	0.734387i	$0.737470\pi$
$570$	−29.4676	−1.23426
$571$	13.9112	0.582167	0.291083	−	0.956698i	$-0.405984\pi$
$571$	13.9112	0.582167	0.291083	+	0.956698i	$0.405984\pi$
$572$	8.47885	0.354519
$573$	18.5424	0.774618
$574$	−2.80141	−0.116928
$575$	−1.33802	−0.0557994
$576$	4.71136	0.196307
$577$	21.9646	0.914397	0.457198	−	0.889365i	$-0.348853\pi$
$577$	21.9646	0.914397	0.457198	+	0.889365i	$0.348853\pi$
$578$	12.0257	0.500201
$579$	−39.0977	−1.62485
$580$	−3.21510	−0.133500
$581$	−29.8496	−1.23837
$582$	−1.79860	−0.0745544
$583$	−4.92486	−0.203967
$584$	−15.1668	−0.627606
$585$	−55.4662	−2.29324
$586$	27.3271	1.12887
$587$	−18.4813	−0.762806	−0.381403	−	0.924409i	$-0.624559\pi$
$587$	−18.4813	−0.762806	−0.381403	+	0.924409i	$0.624559\pi$
$588$	−11.1915	−0.461532
$589$	−41.4572	−1.70821
$590$	23.3319	0.960558
$591$	−6.18318	−0.254342
$592$	6.95298	0.285766
$593$	−7.19591	−0.295501	−0.147750	−	0.989025i	$-0.547203\pi$
$593$	−7.19591	−0.295501	−0.147750	+	0.989025i	$0.547203\pi$
$594$	−7.38134	−0.302860
$595$	−15.9747	−0.654897
$596$	9.88936	0.405084
$597$	−11.0449	−0.452036
$598$	20.9278	0.855801
$599$	−26.6900	−1.09052	−0.545261	−	0.838266i	$-0.683570\pi$
$599$	−26.6900	−1.09052	−0.545261	+	0.838266i	$0.683570\pi$
$600$	−0.969203	−0.0395676
$601$	24.8539	1.01381	0.506905	−	0.862002i	$-0.330789\pi$
$601$	24.8539	1.01381	0.506905	+	0.862002i	$0.330789\pi$
$602$	−9.13348	−0.372253
$603$	−18.2591	−0.743566
$604$	2.68059	0.109072
$605$	−18.5201	−0.752948
$606$	34.5495	1.40348
$607$	−33.6778	−1.36694	−0.683471	−	0.729978i	$-0.739530\pi$
$607$	−33.6778	−1.36694	−0.683471	+	0.729978i	$0.739530\pi$
$608$	4.92047	0.199551
$609$	13.7493	0.557148
$610$	13.4633	0.545111
$611$	30.2757	1.22482
$612$	−10.5079	−0.424755
$613$	−37.5018	−1.51468	−0.757341	−	0.653020i	$-0.773502\pi$
$613$	−37.5018	−1.51468	−0.757341	+	0.653020i	$0.773502\pi$
$614$	23.8300	0.961699
$615$	−5.05153	−0.203697
$616$	5.15845	0.207840
$617$	22.2961	0.897608	0.448804	−	0.893630i	$-0.351850\pi$
$617$	22.2961	0.897608	0.448804	+	0.893630i	$0.351850\pi$
$618$	−32.5112	−1.30779
$619$	−32.7285	−1.31547	−0.657734	−	0.753250i	$-0.728485\pi$
$619$	−32.7285	−1.31547	−0.657734	+	0.753250i	$0.728485\pi$
$620$	18.1704	0.729742
$621$	−18.2189	−0.731098
$622$	20.8363	0.835460
$623$	−14.0950	−0.564704
$624$	15.1592	0.606852
$625$	−23.1331	−0.925324
$626$	27.1987	1.08708
$627$	−21.2226	−0.847551
$628$	−23.3802	−0.932973
$629$	−15.5074	−0.618320
$630$	−33.7451	−1.34444
$631$	18.2998	0.728504	0.364252	−	0.931300i	$-0.381325\pi$
$631$	18.2998	0.728504	0.364252	+	0.931300i	$0.381325\pi$
$632$	−8.30703	−0.330436
$633$	57.7347	2.29475
$634$	−25.7323	−1.02196
$635$	8.32525	0.330378
$636$	−8.80505	−0.349143
$637$	−22.0006	−0.871695
$638$	−2.31553	−0.0916726
$639$	48.3107	1.91114
$640$	−2.15661	−0.0852476
$641$	2.21361	0.0874322	0.0437161	−	0.999044i	$-0.486080\pi$
$641$	2.21361	0.0874322	0.0437161	+	0.999044i	$0.486080\pi$
$642$	3.59975	0.142071
$643$	41.9377	1.65386	0.826930	−	0.562304i	$-0.190085\pi$
$643$	41.9377	1.65386	0.826930	+	0.562304i	$0.190085\pi$
$644$	12.7323	0.501721
$645$	−16.4696	−0.648490
$646$	−10.9742	−0.431776
$647$	6.31833	0.248399	0.124200	−	0.992257i	$-0.460364\pi$
$647$	6.31833	0.248399	0.124200	+	0.992257i	$0.460364\pi$
$648$	0.937149	0.0368147
$649$	16.8037	0.659603
$650$	−1.90528	−0.0747312
$651$	−77.7052	−3.04551
$652$	−10.1006	−0.395569
$653$	−27.1677	−1.06315	−0.531577	−	0.847010i	$-0.678400\pi$
$653$	−27.1677	−1.06315	−0.531577	+	0.847010i	$0.678400\pi$
$654$	16.2713	0.636257
$655$	−31.0659	−1.21385
$656$	0.843499	0.0329331
$657$	71.4562	2.78777
$658$	18.4194	0.718064
$659$	−24.9384	−0.971463	−0.485732	−	0.874108i	$-0.661447\pi$
$659$	−24.9384	−0.971463	−0.485732	+	0.874108i	$0.661447\pi$
$660$	9.30176	0.362071
$661$	32.7065	1.27214	0.636068	−	0.771633i	$-0.280560\pi$
$661$	32.7065	1.27214	0.636068	+	0.771633i	$0.280560\pi$
$662$	0.417145	0.0162128
$663$	−33.8098	−1.31307
$664$	8.98766	0.348789
$665$	−35.2428	−1.36666
$666$	−32.7580	−1.26935
$667$	−5.71527	−0.221296
$668$	−6.08456	−0.235419
$669$	0.515256	0.0199209
$670$	8.35803	0.322899
$671$	9.69629	0.374321
$672$	9.22267	0.355772
$673$	13.2434	0.510494	0.255247	−	0.966876i	$-0.417843\pi$
$673$	13.2434	0.510494	0.255247	+	0.966876i	$0.417843\pi$
$674$	7.25189	0.279333
$675$	1.65866	0.0638418
$676$	16.8002	0.646161
$677$	−11.1951	−0.430263	−0.215131	−	0.976585i	$-0.569018\pi$
$677$	−11.1951	−0.430263	−0.215131	+	0.976585i	$0.569018\pi$
$678$	23.2798	0.894054
$679$	−2.15110	−0.0825517
$680$	4.80995	0.184453
$681$	−54.9765	−2.10670
$682$	13.0864	0.501105
$683$	−25.9023	−0.991125	−0.495563	−	0.868572i	$-0.665038\pi$
$683$	−25.9023	−0.991125	−0.495563	+	0.868572i	$0.665038\pi$
$684$	−23.1821	−0.886390
$685$	−15.9615	−0.609859
$686$	9.86328	0.376582
$687$	0.797821	0.0304388
$688$	2.75008	0.104846
$689$	−17.3091	−0.659426
$690$	22.9589	0.874032
$691$	0.451380	0.0171713	0.00858566	−	0.999963i	$-0.497267\pi$
$691$	0.451380	0.0171713	0.00858566	+	0.999963i	$0.497267\pi$
$692$	4.97513	0.189126
$693$	−24.3033	−0.923206
$694$	13.4874	0.511976
$695$	−29.7506	−1.12850
$696$	−4.13988	−0.156922
$697$	−1.88128	−0.0712584
$698$	2.96719	0.112310
$699$	−48.8221	−1.84662
$700$	−1.15915	−0.0438118
$701$	−24.2695	−0.916645	−0.458322	−	0.888786i	$-0.651549\pi$
$701$	−24.2695	−0.916645	−0.458322	+	0.888786i	$0.651549\pi$
$702$	−25.9428	−0.979149
$703$	−34.2119	−1.29033
$704$	−1.55320	−0.0585384
$705$	33.2141	1.25092
$706$	−13.0493	−0.491118
$707$	41.3207	1.55402
$708$	30.0430	1.12908
$709$	−1.61409	−0.0606185	−0.0303092	−	0.999541i	$-0.509649\pi$
$709$	−1.61409	−0.0606185	−0.0303092	+	0.999541i	$0.509649\pi$
$710$	−22.1141	−0.829926
$711$	39.1374	1.46777
$712$	4.24398	0.159050
$713$	32.3003	1.20966
$714$	−20.5696	−0.769796
$715$	18.2856	0.683843
$716$	−6.22605	−0.232679
$717$	36.6813	1.36989
$718$	12.0619	0.450146
$719$	−21.5975	−0.805449	−0.402725	−	0.915321i	$-0.631937\pi$
$719$	−21.5975	−0.805449	−0.402725	+	0.915321i	$0.631937\pi$
$720$	10.1606	0.378663
$721$	−38.8829	−1.44807
$722$	−5.21101	−0.193934
$723$	−11.4822	−0.427027
$724$	13.5566	0.503829
$725$	0.520322	0.0193243
$726$	−23.8471	−0.885049
$727$	37.5227	1.39164	0.695820	−	0.718216i	$-0.255041\pi$
$727$	37.5227	1.39164	0.695820	+	0.718216i	$0.255041\pi$
$728$	18.1301	0.671947
$729$	−44.0061	−1.62985
$730$	−32.7089	−1.21061
$731$	−6.13357	−0.226858
$732$	17.3358	0.640749
$733$	10.6844	0.394639	0.197319	−	0.980339i	$-0.436776\pi$
$733$	10.6844	0.394639	0.197319	+	0.980339i	$0.436776\pi$
$734$	37.3889	1.38005
$735$	−24.1358	−0.890264
$736$	−3.83366	−0.141311
$737$	6.01948	0.221730
$738$	−3.97403	−0.146286
$739$	−2.81189	−0.103437	−0.0517185	−	0.998662i	$-0.516470\pi$
$739$	−2.81189	−0.103437	−0.0517185	+	0.998662i	$0.516470\pi$
$740$	14.9949	0.551223
$741$	−74.5902	−2.74014
$742$	−10.5307	−0.386594
$743$	−48.0123	−1.76140	−0.880701	−	0.473673i	$-0.842928\pi$
$743$	−48.0123	−1.76140	−0.880701	+	0.473673i	$0.842928\pi$
$744$	23.3969	0.857773
$745$	21.3275	0.781380
$746$	−35.4078	−1.29637
$747$	−42.3441	−1.54929
$748$	3.46414	0.126662
$749$	4.30525	0.157310
$750$	−32.0341	−1.16972
$751$	16.6751	0.608484	0.304242	−	0.952595i	$-0.401597\pi$
$751$	16.6751	0.608484	0.304242	+	0.952595i	$0.401597\pi$
$752$	−5.54606	−0.202244
$753$	20.0870	0.732010
$754$	−8.13827	−0.296378
$755$	5.78099	0.210392
$756$	−15.7833	−0.574035
$757$	25.0656	0.911023	0.455512	−	0.890230i	$-0.349456\pi$
$757$	25.0656	0.911023	0.455512	+	0.890230i	$0.349456\pi$
$758$	−36.1932	−1.31460
$759$	16.5351	0.600186
$760$	10.6115	0.384921
$761$	18.7490	0.679652	0.339826	−	0.940488i	$-0.389632\pi$
$761$	18.7490	0.679652	0.339826	+	0.940488i	$0.389632\pi$
$762$	10.7199	0.388341
$763$	19.4602	0.704506
$764$	−6.67728	−0.241575
$765$	−22.6614	−0.819325
$766$	11.7935	0.426118
$767$	59.0591	2.13250
$768$	−2.77693	−0.100204
$769$	41.2480	1.48744	0.743721	−	0.668490i	$-0.233059\pi$
$769$	41.2480	1.48744	0.743721	+	0.668490i	$0.233059\pi$
$770$	11.1248	0.400909
$771$	−30.1269	−1.08500
$772$	14.0795	0.506731
$773$	17.5037	0.629563	0.314782	−	0.949164i	$-0.398069\pi$
$773$	17.5037	0.629563	0.314782	+	0.949164i	$0.398069\pi$
$774$	−12.9566	−0.465716
$775$	−2.94064	−0.105631
$776$	0.647693	0.0232508
$777$	−64.1251	−2.30047
$778$	22.5729	0.809276
$779$	−4.15041	−0.148704
$780$	32.6924	1.17058
$781$	−15.9266	−0.569900
$782$	8.55031	0.305759
$783$	7.08484	0.253192
$784$	4.03018	0.143935
$785$	−50.4221	−1.79964
$786$	−40.0016	−1.42681
$787$	−6.02118	−0.214632	−0.107316	−	0.994225i	$-0.534226\pi$
$787$	−6.02118	−0.214632	−0.107316	+	0.994225i	$0.534226\pi$
$788$	2.22662	0.0793201
$789$	−21.0394	−0.749023
$790$	−17.9151	−0.637389
$791$	27.8423	0.989957
$792$	7.31769	0.260023
$793$	34.0790	1.21018
$794$	−1.11349	−0.0395162
$795$	−18.9891	−0.673473
$796$	3.97736	0.140974
$797$	−7.00739	−0.248214	−0.124107	−	0.992269i	$-0.539607\pi$
$797$	−7.00739	−0.248214	−0.124107	+	0.992269i	$0.539607\pi$
$798$	−45.3799	−1.60643
$799$	12.3695	0.437602
$800$	0.349019	0.0123397
$801$	−19.9949	−0.706486
$802$	28.4318	1.00396
$803$	−23.5571	−0.831311
$804$	10.7621	0.379550
$805$	27.4585	0.967787
$806$	45.9941	1.62007
$807$	3.04858	0.107315
$808$	−12.4416	−0.437694
$809$	−3.43766	−0.120862	−0.0604308	−	0.998172i	$-0.519247\pi$
$809$	−3.43766	−0.120862	−0.0604308	+	0.998172i	$0.519247\pi$
$810$	2.02107	0.0710131
$811$	−30.9964	−1.08843	−0.544215	−	0.838946i	$-0.683172\pi$
$811$	−30.9964	−1.08843	−0.544215	+	0.838946i	$0.683172\pi$
$812$	−4.95124	−0.173754
$813$	51.4468	1.80432
$814$	10.7994	0.378518
$815$	−21.7830	−0.763026
$816$	6.19346	0.216815
$817$	−13.5317	−0.473413
$818$	3.33936	0.116758
$819$	−85.4176	−2.98473
$820$	1.81910	0.0635258
$821$	2.67824	0.0934711	0.0467356	−	0.998907i	$-0.485118\pi$
$821$	2.67824	0.0934711	0.0467356	+	0.998907i	$0.485118\pi$
$822$	−20.5526	−0.716856
$823$	34.7444	1.21111	0.605556	−	0.795802i	$-0.292951\pi$
$823$	34.7444	1.21111	0.605556	+	0.795802i	$0.292951\pi$
$824$	11.7076	0.407853
$825$	−1.50537	−0.0524101
$826$	35.9309	1.25020
$827$	−0.990216	−0.0344332	−0.0172166	−	0.999852i	$-0.505480\pi$
$827$	−0.990216	−0.0344332	−0.0172166	+	0.999852i	$0.505480\pi$
$828$	18.0618	0.627690
$829$	−34.1111	−1.18473	−0.592365	−	0.805670i	$-0.701805\pi$
$829$	−34.1111	−1.18473	−0.592365	+	0.805670i	$0.701805\pi$
$830$	19.3829	0.672790
$831$	46.4504	1.61135
$832$	−5.45896	−0.189255
$833$	−8.98861	−0.311437
$834$	−38.3080	−1.32650
$835$	−13.1220	−0.454107
$836$	7.64247	0.264320
$837$	−40.0406	−1.38401
$838$	30.4571	1.05212
$839$	2.73855	0.0945452	0.0472726	−	0.998882i	$-0.484947\pi$
$839$	2.73855	0.0945452	0.0472726	+	0.998882i	$0.484947\pi$
$840$	19.8897	0.686261
$841$	−26.7775	−0.923361
$842$	−29.2355	−1.00752
$843$	58.2539	2.00637
$844$	−20.7908	−0.715649
$845$	36.2315	1.24640
$846$	26.1295	0.898351
$847$	−28.5208	−0.979986
$848$	3.17078	0.108885
$849$	−54.5454	−1.87199
$850$	−0.778426	−0.0266998
$851$	26.6554	0.913735
$852$	−28.4749	−0.975534
$853$	38.4126	1.31522	0.657611	−	0.753358i	$-0.271567\pi$
$853$	38.4126	1.31522	0.657611	+	0.753358i	$0.271567\pi$
$854$	20.7333	0.709480
$855$	−49.9948	−1.70979
$856$	−1.29630	−0.0443068
$857$	33.2560	1.13600	0.568001	−	0.823028i	$-0.307717\pi$
$857$	33.2560	1.13600	0.568001	+	0.823028i	$0.307717\pi$
$858$	23.5452	0.803820
$859$	−38.0499	−1.29824	−0.649122	−	0.760684i	$-0.724864\pi$
$859$	−38.0499	−1.29824	−0.649122	+	0.760684i	$0.724864\pi$
$860$	5.93086	0.202241
$861$	−7.77932	−0.265118
$862$	21.5252	0.733150
$863$	23.0316	0.784006	0.392003	−	0.919964i	$-0.371782\pi$
$863$	23.0316	0.784006	0.392003	+	0.919964i	$0.371782\pi$
$864$	4.75234	0.161678
$865$	10.7294	0.364812
$866$	−25.2201	−0.857016
$867$	33.3945	1.13414
$868$	27.9824	0.949783
$869$	−12.9025	−0.437687
$870$	−8.92813	−0.302692
$871$	21.1564	0.716856
$872$	−5.85943	−0.198425
$873$	−3.05152	−0.103278
$874$	18.8634	0.638065
$875$	−38.3123	−1.29519
$876$	−42.1172	−1.42301
$877$	5.92251	0.199989	0.0999945	−	0.994988i	$-0.468117\pi$
$877$	5.92251	0.199989	0.0999945	+	0.994988i	$0.468117\pi$
$878$	−27.0325	−0.912302
$879$	75.8855	2.55955
$880$	−3.34965	−0.112917
$881$	49.0165	1.65141	0.825704	−	0.564103i	$-0.190778\pi$
$881$	49.0165	1.65141	0.825704	+	0.564103i	$0.190778\pi$
$882$	−18.9876	−0.639347
$883$	2.84114	0.0956121	0.0478061	−	0.998857i	$-0.484777\pi$
$883$	2.84114	0.0956121	0.0478061	+	0.998857i	$0.484777\pi$
$884$	12.1752	0.409498
$885$	64.7911	2.17793
$886$	−7.51560	−0.252491
$887$	−36.8994	−1.23896	−0.619480	−	0.785013i	$-0.712656\pi$
$887$	−36.8994	−1.23896	−0.619480	+	0.785013i	$0.712656\pi$
$888$	19.3080	0.647933
$889$	12.8208	0.429997
$890$	9.15263	0.306797
$891$	1.45558	0.0487638
$892$	−0.185548	−0.00621262
$893$	27.2892	0.913199
$894$	27.4621	0.918471
$895$	−13.4272	−0.448821
$896$	−3.32117	−0.110953
$897$	58.1151	1.94041
$898$	7.51061	0.250632
$899$	−12.5607	−0.418924
$900$	−1.64436	−0.0548119
$901$	−7.07187	−0.235598
$902$	1.31012	0.0436223
$903$	−25.3631	−0.844031
$904$	−8.38327	−0.278823
$905$	29.2364	0.971852
$906$	7.44381	0.247304
$907$	16.5696	0.550185	0.275092	−	0.961418i	$-0.411292\pi$
$907$	16.5696	0.550185	0.275092	+	0.961418i	$0.411292\pi$
$908$	19.7975	0.657004
$909$	58.6169	1.94420
$910$	39.0997	1.29614
$911$	−27.4801	−0.910457	−0.455229	−	0.890375i	$-0.650442\pi$
$911$	−27.4801	−0.910457	−0.455229	+	0.890375i	$0.650442\pi$
$912$	13.6638	0.452454
$913$	13.9596	0.461996
$914$	−3.83154	−0.126736
$915$	37.3866	1.23596
$916$	−0.287303	−0.00949276
$917$	−47.8413	−1.57986
$918$	−10.5993	−0.349828
$919$	5.29874	0.174789	0.0873947	−	0.996174i	$-0.472146\pi$
$919$	5.29874	0.174789	0.0873947	+	0.996174i	$0.472146\pi$
$920$	−8.26773	−0.272579
$921$	66.1743	2.18052
$922$	−12.2934	−0.404861
$923$	−55.9765	−1.84249
$924$	14.3247	0.471247
$925$	−2.42672	−0.0797902
$926$	−17.1507	−0.563608
$927$	−55.1586	−1.81165
$928$	1.49081	0.0489383
$929$	−30.3046	−0.994263	−0.497132	−	0.867675i	$-0.665613\pi$
$929$	−30.3046	−0.994263	−0.497132	+	0.867675i	$0.665613\pi$
$930$	50.4581	1.65459
$931$	−19.8304	−0.649914
$932$	17.5813	0.575894
$933$	57.8611	1.89429
$934$	36.4013	1.19109
$935$	7.47081	0.244322
$936$	25.7191	0.840656
$937$	−32.1459	−1.05016	−0.525080	−	0.851053i	$-0.675965\pi$
$937$	−32.1459	−1.05016	−0.525080	+	0.851053i	$0.675965\pi$
$938$	12.8713	0.420263
$939$	75.5290	2.46480
$940$	−11.9607	−0.390115
$941$	−51.0743	−1.66497	−0.832487	−	0.554045i	$-0.813083\pi$
$941$	−51.0743	−1.66497	−0.832487	+	0.554045i	$0.813083\pi$
$942$	−64.9254	−2.11538
$943$	3.23369	0.105304
$944$	−10.8188	−0.352120
$945$	−34.0386	−1.10727
$946$	4.27142	0.138876
$947$	8.69091	0.282417	0.141208	−	0.989980i	$-0.454901\pi$
$947$	8.69091	0.282417	0.141208	+	0.989980i	$0.454901\pi$
$948$	−23.0681	−0.749216
$949$	−82.7948	−2.68763
$950$	−1.71734	−0.0557178
$951$	−71.4570	−2.31715
$952$	7.40729	0.240072
$953$	−32.0021	−1.03665	−0.518325	−	0.855184i	$-0.673444\pi$
$953$	−32.0021	−1.03665	−0.518325	+	0.855184i	$0.673444\pi$
$954$	−14.9387	−0.483658
$955$	−14.4003	−0.465983
$956$	−13.2093	−0.427218
$957$	−6.43007	−0.207855
$958$	11.2479	0.363405
$959$	−24.5807	−0.793751
$960$	−5.98877	−0.193287
$961$	39.9882	1.28994
$962$	37.9560	1.22375
$963$	6.10736	0.196807
$964$	4.13484	0.133174
$965$	30.3640	0.977450
$966$	35.3566	1.13758
$967$	10.4638	0.336495	0.168247	−	0.985745i	$-0.446189\pi$
$967$	10.4638	0.336495	0.168247	+	0.985745i	$0.446189\pi$
$968$	8.58757	0.276015
$969$	−30.4747	−0.978990
$970$	1.39682	0.0448493
$971$	21.4573	0.688597	0.344298	−	0.938860i	$-0.388117\pi$
$971$	21.4573	0.688597	0.344298	+	0.938860i	$0.388117\pi$
$972$	16.8594	0.540766
$973$	−45.8157	−1.46879
$974$	3.94271	0.126332
$975$	−5.29084	−0.169442
$976$	−6.24278	−0.199826
$977$	−20.1359	−0.644204	−0.322102	−	0.946705i	$-0.604389\pi$
$977$	−20.1359	−0.644204	−0.322102	+	0.946705i	$0.604389\pi$
$978$	−28.0486	−0.896896
$979$	6.59175	0.210673
$980$	8.69154	0.277641
$981$	27.6059	0.881389
$982$	−16.8873	−0.538896
$983$	−52.0734	−1.66088	−0.830441	−	0.557106i	$-0.811912\pi$
$983$	−52.0734	−1.66088	−0.830441	+	0.557106i	$0.811912\pi$
$984$	2.34234	0.0746711
$985$	4.80196	0.153003
$986$	−3.32499	−0.105889
$987$	51.1495	1.62811
$988$	26.8606	0.854550
$989$	10.5429	0.335244
$990$	15.7814	0.501567
$991$	−23.4351	−0.744440	−0.372220	−	0.928144i	$-0.621403\pi$
$991$	−23.4351	−0.744440	−0.372220	+	0.928144i	$0.621403\pi$
$992$	−8.42545	−0.267508
$993$	1.15838	0.0367602
$994$	−34.0555	−1.08018
$995$	8.57762	0.271929
$996$	24.9581	0.790829
$997$	−26.0215	−0.824109	−0.412055	−	0.911159i	$-0.635189\pi$
$997$	−26.0215	−0.824109	−0.412055	+	0.911159i	$0.635189\pi$
$998$	34.6841	1.09791
$999$	−33.0429	−1.04543

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	8026.2.a.b.1.8	✓	81

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
8026.2.a.b.1.8	✓	81	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:	\( N \)	\(=\)	\( 8026 = 2 \cdot 4013 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	8026.a (trivial)

\(f(q)\)	\(=\)	\(q-1.00000 q^{2} -2.77693 q^{3} +1.00000 q^{4} +2.15661 q^{5} +2.77693 q^{6} +3.32117 q^{7} -1.00000 q^{8} +4.71136 q^{9} +O(q^{10})\)	\(q-1.00000 q^{2} -2.77693 q^{3} +1.00000 q^{4} +2.15661 q^{5} +2.77693 q^{6} +3.32117 q^{7} -1.00000 q^{8} +4.71136 q^{9} -2.15661 q^{10} -1.55320 q^{11} -2.77693 q^{12} -5.45896 q^{13} -3.32117 q^{14} -5.98877 q^{15} +1.00000 q^{16} -2.23032 q^{17} -4.71136 q^{18} -4.92047 q^{19} +2.15661 q^{20} -9.22267 q^{21} +1.55320 q^{22} +3.83366 q^{23} +2.77693 q^{24} -0.349019 q^{25} +5.45896 q^{26} -4.75234 q^{27} +3.32117 q^{28} -1.49081 q^{29} +5.98877 q^{30} +8.42545 q^{31} -1.00000 q^{32} +4.31314 q^{33} +2.23032 q^{34} +7.16248 q^{35} +4.71136 q^{36} +6.95298 q^{37} +4.92047 q^{38} +15.1592 q^{39} -2.15661 q^{40} +0.843499 q^{41} +9.22267 q^{42} +2.75008 q^{43} -1.55320 q^{44} +10.1606 q^{45} -3.83366 q^{46} -5.54606 q^{47} -2.77693 q^{48} +4.03018 q^{49} +0.349019 q^{50} +6.19346 q^{51} -5.45896 q^{52} +3.17078 q^{53} +4.75234 q^{54} -3.34965 q^{55} -3.32117 q^{56} +13.6638 q^{57} +1.49081 q^{58} -10.8188 q^{59} -5.98877 q^{60} -6.24278 q^{61} -8.42545 q^{62} +15.6472 q^{63} +1.00000 q^{64} -11.7729 q^{65} -4.31314 q^{66} -3.87553 q^{67} -2.23032 q^{68} -10.6458 q^{69} -7.16248 q^{70} +10.2541 q^{71} -4.71136 q^{72} +15.1668 q^{73} -6.95298 q^{74} +0.969203 q^{75} -4.92047 q^{76} -5.15845 q^{77} -15.1592 q^{78} +8.30703 q^{79} +2.15661 q^{80} -0.937149 q^{81} -0.843499 q^{82} -8.98766 q^{83} -9.22267 q^{84} -4.80995 q^{85} -2.75008 q^{86} +4.13988 q^{87} +1.55320 q^{88} -4.24398 q^{89} -10.1606 q^{90} -18.1301 q^{91} +3.83366 q^{92} -23.3969 q^{93} +5.54606 q^{94} -10.6115 q^{95} +2.77693 q^{96} -0.647693 q^{97} -4.03018 q^{98} -7.31769 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 81 q - 81 q^{2} - 10 q^{3} + 81 q^{4} - 26 q^{5} + 10 q^{6} + 3 q^{7} - 81 q^{8} + 59 q^{9}+O(q^{10}) \) 81 * q - 81 * q^2 - 10 * q^3 + 81 * q^4 - 26 * q^5 + 10 * q^6 + 3 * q^7 - 81 * q^8 + 59 * q^9	\( 81 q - 81 q^{2} - 10 q^{3} + 81 q^{4} - 26 q^{5} + 10 q^{6} + 3 q^{7} - 81 q^{8} + 59 q^{9} + 26 q^{10} - 41 q^{11} - 10 q^{12} + 33 q^{13} - 3 q^{14} - 7 q^{15} + 81 q^{16} - 9 q^{17} - 59 q^{18} - 32 q^{19} - 26 q^{20} - 23 q^{21} + 41 q^{22} - 28 q^{23} + 10 q^{24} + 81 q^{25} - 33 q^{26} - 37 q^{27} + 3 q^{28} - 35 q^{29} + 7 q^{30} - 29 q^{31} - 81 q^{32} - 7 q^{33} + 9 q^{34} - 67 q^{35} + 59 q^{36} + 13 q^{37} + 32 q^{38} - 42 q^{39} + 26 q^{40} - 66 q^{41} + 23 q^{42} - 22 q^{43} - 41 q^{44} - 65 q^{45} + 28 q^{46} - 71 q^{47} - 10 q^{48} + 64 q^{49} - 81 q^{50} - 43 q^{51} + 33 q^{52} - 37 q^{53} + 37 q^{54} + 12 q^{55} - 3 q^{56} - q^{57} + 35 q^{58} - 162 q^{59} - 7 q^{60} + 19 q^{61} + 29 q^{62} - 16 q^{63} + 81 q^{64} - 45 q^{65} + 7 q^{66} - 43 q^{67} - 9 q^{68} - 21 q^{69} + 67 q^{70} - 99 q^{71} - 59 q^{72} + 53 q^{73} - 13 q^{74} - 61 q^{75} - 32 q^{76} - 31 q^{77} + 42 q^{78} + 4 q^{79} - 26 q^{80} + q^{81} + 66 q^{82} - 112 q^{83} - 23 q^{84} + 17 q^{85} + 22 q^{86} - 15 q^{87} + 41 q^{88} - 111 q^{89} + 65 q^{90} - 49 q^{91} - 28 q^{92} - 19 q^{93} + 71 q^{94} - 53 q^{95} + 10 q^{96} + 50 q^{97} - 64 q^{98} - 97 q^{99}+O(q^{100}) \) 81 * q - 81 * q^2 - 10 * q^3 + 81 * q^4 - 26 * q^5 + 10 * q^6 + 3 * q^7 - 81 * q^8 + 59 * q^9 + 26 * q^10 - 41 * q^11 - 10 * q^12 + 33 * q^13 - 3 * q^14 - 7 * q^15 + 81 * q^16 - 9 * q^17 - 59 * q^18 - 32 * q^19 - 26 * q^20 - 23 * q^21 + 41 * q^22 - 28 * q^23 + 10 * q^24 + 81 * q^25 - 33 * q^26 - 37 * q^27 + 3 * q^28 - 35 * q^29 + 7 * q^30 - 29 * q^31 - 81 * q^32 - 7 * q^33 + 9 * q^34 - 67 * q^35 + 59 * q^36 + 13 * q^37 + 32 * q^38 - 42 * q^39 + 26 * q^40 - 66 * q^41 + 23 * q^42 - 22 * q^43 - 41 * q^44 - 65 * q^45 + 28 * q^46 - 71 * q^47 - 10 * q^48 + 64 * q^49 - 81 * q^50 - 43 * q^51 + 33 * q^52 - 37 * q^53 + 37 * q^54 + 12 * q^55 - 3 * q^56 - q^57 + 35 * q^58 - 162 * q^59 - 7 * q^60 + 19 * q^61 + 29 * q^62 - 16 * q^63 + 81 * q^64 - 45 * q^65 + 7 * q^66 - 43 * q^67 - 9 * q^68 - 21 * q^69 + 67 * q^70 - 99 * q^71 - 59 * q^72 + 53 * q^73 - 13 * q^74 - 61 * q^75 - 32 * q^76 - 31 * q^77 + 42 * q^78 + 4 * q^79 - 26 * q^80 + q^81 + 66 * q^82 - 112 * q^83 - 23 * q^84 + 17 * q^85 + 22 * q^86 - 15 * q^87 + 41 * q^88 - 111 * q^89 + 65 * q^90 - 49 * q^91 - 28 * q^92 - 19 * q^93 + 71 * q^94 - 53 * q^95 + 10 * q^96 + 50 * q^97 - 64 * q^98 - 97 * q^99

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