LMFDB - Embedded newform 4002.2.a.bf.1.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [4002,2,Mod(1,4002)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(4002, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([0, 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("4002.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 4002 = 2 \cdot 3 \cdot 23 \cdot 29 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	4002.a (trivial)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	yes
Analytic conductor:	$31.9561308889$
Analytic rank:	$0$
Dimension:	$6$
Coefficient field:	6.6.61157024.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{6} - 2x^{5} - 8x^{4} + 8x^{3} + 17x^{2} - 4x - 4 $ x^6 - 2x^5 - 8x^4 + 8x^3 + 17x^2 - 4*x - 4
Coefficient ring:	$\Z[a_1, \ldots, a_{11}]$
Coefficient ring index:	$ 2 $
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.1
Root			$-1.82560$ of defining polynomial
Character	$\chi$	$=$	4002.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.00000 q^{2} +1.00000 q^{3} +1.00000 q^{4} -1.56155 q^{5} -1.00000 q^{6} -3.98403 q^{7} -1.00000 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q-1.00000 q^{2} +1.00000 q^{3} +1.00000 q^{4} -1.56155 q^{5} -1.00000 q^{6} -3.98403 q^{7} -1.00000 q^{8} +1.00000 q^{9} +1.56155 q^{10} +2.46602 q^{11} +1.00000 q^{12} +6.11723 q^{13} +3.98403 q^{14} -1.56155 q^{15} +1.00000 q^{16} -3.60607 q^{17} -1.00000 q^{18} -4.79028 q^{19} -1.56155 q^{20} -3.98403 q^{21} -2.46602 q^{22} +1.00000 q^{23} -1.00000 q^{24} -2.56155 q^{25} -6.11723 q^{26} +1.00000 q^{27} -3.98403 q^{28} +1.00000 q^{29} +1.56155 q^{30} -3.90117 q^{31} -1.00000 q^{32} +2.46602 q^{33} +3.60607 q^{34} +6.22127 q^{35} +1.00000 q^{36} +4.61195 q^{37} +4.79028 q^{38} +6.11723 q^{39} +1.56155 q^{40} +3.01426 q^{41} +3.98403 q^{42} -2.59922 q^{43} +2.46602 q^{44} -1.56155 q^{45} -1.00000 q^{46} +8.41233 q^{47} +1.00000 q^{48} +8.87247 q^{49} +2.56155 q^{50} -3.60607 q^{51} +6.11723 q^{52} -2.45746 q^{53} -1.00000 q^{54} -3.85083 q^{55} +3.98403 q^{56} -4.79028 q^{57} -1.00000 q^{58} +9.18776 q^{59} -1.56155 q^{60} -11.3469 q^{61} +3.90117 q^{62} -3.98403 q^{63} +1.00000 q^{64} -9.55237 q^{65} -2.46602 q^{66} +6.45163 q^{67} -3.60607 q^{68} +1.00000 q^{69} -6.22127 q^{70} -10.7005 q^{71} -1.00000 q^{72} +1.24409 q^{73} -4.61195 q^{74} -2.56155 q^{75} -4.79028 q^{76} -9.82471 q^{77} -6.11723 q^{78} +13.5098 q^{79} -1.56155 q^{80} +1.00000 q^{81} -3.01426 q^{82} +8.96121 q^{83} -3.98403 q^{84} +5.63107 q^{85} +2.59922 q^{86} +1.00000 q^{87} -2.46602 q^{88} +3.54725 q^{89} +1.56155 q^{90} -24.3712 q^{91} +1.00000 q^{92} -3.90117 q^{93} -8.41233 q^{94} +7.48028 q^{95} -1.00000 q^{96} -11.3534 q^{97} -8.87247 q^{98} +2.46602 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 6 q - 6 q^{2} + 6 q^{3} + 6 q^{4} + 3 q^{5} - 6 q^{6} + 2 q^{7} - 6 q^{8} + 6 q^{9}+O(q^{10}) $ 6 * q - 6 * q^2 + 6 * q^3 + 6 * q^4 + 3 * q^5 - 6 * q^6 + 2 * q^7 - 6 * q^8 + 6 * q^9	\( 6 q - 6 q^{2} + 6 q^{3} + 6 q^{4} + 3 q^{5} - 6 q^{6} + 2 q^{7} - 6 q^{8} + 6 q^{9} - 3 q^{10} + 7 q^{11} + 6 q^{12} + 3 q^{13} - 2 q^{14} + 3 q^{15} + 6 q^{16} + 8 q^{17} - 6 q^{18} - 4 q^{19} + 3 q^{20} + 2 q^{21} - 7 q^{22} + 6 q^{23} - 6 q^{24} - 3 q^{25} - 3 q^{26} + 6 q^{27} + 2 q^{28} + 6 q^{29} - 3 q^{30} + q^{31} - 6 q^{32} + 7 q^{33} - 8 q^{34} + 18 q^{35} + 6 q^{36} + 7 q^{37} + 4 q^{38} + 3 q^{39} - 3 q^{40} + 13 q^{41} - 2 q^{42} + 7 q^{44} + 3 q^{45} - 6 q^{46} + 22 q^{47} + 6 q^{48} + 8 q^{49} + 3 q^{50} + 8 q^{51} + 3 q^{52} + 10 q^{53} - 6 q^{54} - 5 q^{55} - 2 q^{56} - 4 q^{57} - 6 q^{58} + 17 q^{59} + 3 q^{60} + q^{61} - q^{62} + 2 q^{63} + 6 q^{64} - 7 q^{65} - 7 q^{66} + 3 q^{67} + 8 q^{68} + 6 q^{69} - 18 q^{70} + 11 q^{71} - 6 q^{72} - 7 q^{74} - 3 q^{75} - 4 q^{76} - 3 q^{78} + 2 q^{79} + 3 q^{80} + 6 q^{81} - 13 q^{82} + 16 q^{83} + 2 q^{84} + 4 q^{85} + 6 q^{87} - 7 q^{88} + 16 q^{89} - 3 q^{90} - 28 q^{91} + 6 q^{92} + q^{93} - 22 q^{94} + 32 q^{95} - 6 q^{96} + 2 q^{97} - 8 q^{98} + 7 q^{99}+O(q^{100}) \) 6 * q - 6 * q^2 + 6 * q^3 + 6 * q^4 + 3 * q^5 - 6 * q^6 + 2 * q^7 - 6 * q^8 + 6 * q^9 - 3 * q^10 + 7 * q^11 + 6 * q^12 + 3 * q^13 - 2 * q^14 + 3 * q^15 + 6 * q^16 + 8 * q^17 - 6 * q^18 - 4 * q^19 + 3 * q^20 + 2 * q^21 - 7 * q^22 + 6 * q^23 - 6 * q^24 - 3 * q^25 - 3 * q^26 + 6 * q^27 + 2 * q^28 + 6 * q^29 - 3 * q^30 + q^31 - 6 * q^32 + 7 * q^33 - 8 * q^34 + 18 * q^35 + 6 * q^36 + 7 * q^37 + 4 * q^38 + 3 * q^39 - 3 * q^40 + 13 * q^41 - 2 * q^42 + 7 * q^44 + 3 * q^45 - 6 * q^46 + 22 * q^47 + 6 * q^48 + 8 * q^49 + 3 * q^50 + 8 * q^51 + 3 * q^52 + 10 * q^53 - 6 * q^54 - 5 * q^55 - 2 * q^56 - 4 * q^57 - 6 * q^58 + 17 * q^59 + 3 * q^60 + q^61 - q^62 + 2 * q^63 + 6 * q^64 - 7 * q^65 - 7 * q^66 + 3 * q^67 + 8 * q^68 + 6 * q^69 - 18 * q^70 + 11 * q^71 - 6 * q^72 - 7 * q^74 - 3 * q^75 - 4 * q^76 - 3 * q^78 + 2 * q^79 + 3 * q^80 + 6 * q^81 - 13 * q^82 + 16 * q^83 + 2 * q^84 + 4 * q^85 + 6 * q^87 - 7 * q^88 + 16 * q^89 - 3 * q^90 - 28 * q^91 + 6 * q^92 + q^93 - 22 * q^94 + 32 * q^95 - 6 * q^96 + 2 * q^97 - 8 * q^98 + 7 * 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
$3$	1.00000	0.577350
$3$	1.00000	0.577350
$4$	1.00000	0.500000
$5$	−1.56155	−0.698348	−0.349174	−	0.937058i	$-0.613538\pi$
$5$	−1.56155	−0.698348	−0.349174	+	0.937058i	$0.613538\pi$
$6$	−1.00000	−0.408248
$7$	−3.98403	−1.50582	−0.752910	−	0.658123i	$-0.771351\pi$
$7$	−3.98403	−1.50582	−0.752910	+	0.658123i	$0.771351\pi$
$8$	−1.00000	−0.353553
$9$	1.00000	0.333333
$10$	1.56155	0.493806
$11$	2.46602	0.743534	0.371767	−	0.928326i	$-0.378752\pi$
$11$	2.46602	0.743534	0.371767	+	0.928326i	$0.378752\pi$
$12$	1.00000	0.288675
$13$	6.11723	1.69661	0.848307	−	0.529505i	$-0.177622\pi$
$13$	6.11723	1.69661	0.848307	+	0.529505i	$0.177622\pi$
$14$	3.98403	1.06478
$15$	−1.56155	−0.403191
$16$	1.00000	0.250000
$17$	−3.60607	−0.874601	−0.437300	−	0.899315i	$-0.644065\pi$
$17$	−3.60607	−0.874601	−0.437300	+	0.899315i	$0.644065\pi$
$18$	−1.00000	−0.235702
$19$	−4.79028	−1.09897	−0.549483	−	0.835505i	$-0.685175\pi$
$19$	−4.79028	−1.09897	−0.549483	+	0.835505i	$0.685175\pi$
$20$	−1.56155	−0.349174
$21$	−3.98403	−0.869386
$22$	−2.46602	−0.525758
$23$	1.00000	0.208514
$23$	1.00000	0.208514
$24$	−1.00000	−0.204124
$25$	−2.56155	−0.512311
$26$	−6.11723	−1.19969
$27$	1.00000	0.192450
$28$	−3.98403	−0.752910
$29$	1.00000	0.185695
$29$	1.00000	0.185695
$30$	1.56155	0.285099
$31$	−3.90117	−0.700671	−0.350335	−	0.936624i	$-0.613932\pi$
$31$	−3.90117	−0.700671	−0.350335	+	0.936624i	$0.613932\pi$
$32$	−1.00000	−0.176777
$33$	2.46602	0.429280
$34$	3.60607	0.618436
$35$	6.22127	1.05159
$36$	1.00000	0.166667
$37$	4.61195	0.758200	0.379100	−	0.925356i	$-0.376234\pi$
$37$	4.61195	0.758200	0.379100	+	0.925356i	$0.376234\pi$
$38$	4.79028	0.777086
$39$	6.11723	0.979540
$40$	1.56155	0.246903
$41$	3.01426	0.470748	0.235374	−	0.971905i	$-0.424369\pi$
$41$	3.01426	0.470748	0.235374	+	0.971905i	$0.424369\pi$
$42$	3.98403	0.614749
$43$	−2.59922	−0.396378	−0.198189	−	0.980164i	$-0.563506\pi$
$43$	−2.59922	−0.396378	−0.198189	+	0.980164i	$0.563506\pi$
$44$	2.46602	0.371767
$45$	−1.56155	−0.232783
$46$	−1.00000	−0.147442
$47$	8.41233	1.22706	0.613532	−	0.789670i	$-0.289748\pi$
$47$	8.41233	1.22706	0.613532	+	0.789670i	$0.289748\pi$
$48$	1.00000	0.144338
$49$	8.87247	1.26750
$50$	2.56155	0.362258
$51$	−3.60607	−0.504951
$52$	6.11723	0.848307
$53$	−2.45746	−0.337558	−0.168779	−	0.985654i	$-0.553982\pi$
$53$	−2.45746	−0.337558	−0.168779	+	0.985654i	$0.553982\pi$
$54$	−1.00000	−0.136083
$55$	−3.85083	−0.519245
$56$	3.98403	0.532388
$57$	−4.79028	−0.634488
$58$	−1.00000	−0.131306
$59$	9.18776	1.19614	0.598072	−	0.801442i	$-0.295934\pi$
$59$	9.18776	1.19614	0.598072	+	0.801442i	$0.295934\pi$
$60$	−1.56155	−0.201596
$61$	−11.3469	−1.45283	−0.726413	−	0.687259i	$-0.758814\pi$
$61$	−11.3469	−1.45283	−0.726413	+	0.687259i	$0.758814\pi$
$62$	3.90117	0.495449
$63$	−3.98403	−0.501940
$64$	1.00000	0.125000
$65$	−9.55237	−1.18483
$66$	−2.46602	−0.303547
$67$	6.45163	0.788193	0.394096	−	0.919069i	$-0.371058\pi$
$67$	6.45163	0.788193	0.394096	+	0.919069i	$0.371058\pi$
$68$	−3.60607	−0.437300
$69$	1.00000	0.120386
$70$	−6.22127	−0.743584
$71$	−10.7005	−1.26991	−0.634957	−	0.772548i	$-0.718982\pi$
$71$	−10.7005	−1.26991	−0.634957	+	0.772548i	$0.718982\pi$
$72$	−1.00000	−0.117851
$73$	1.24409	0.145610	0.0728048	−	0.997346i	$-0.476805\pi$
$73$	1.24409	0.145610	0.0728048	+	0.997346i	$0.476805\pi$
$74$	−4.61195	−0.536128
$75$	−2.56155	−0.295783
$76$	−4.79028	−0.549483
$77$	−9.82471	−1.11963
$78$	−6.11723	−0.692640
$79$	13.5098	1.51997	0.759985	−	0.649940i	$-0.225206\pi$
$79$	13.5098	1.51997	0.759985	+	0.649940i	$0.225206\pi$
$80$	−1.56155	−0.174587
$81$	1.00000	0.111111
$82$	−3.01426	−0.332869
$83$	8.96121	0.983620	0.491810	−	0.870702i	$-0.336335\pi$
$83$	8.96121	0.983620	0.491810	+	0.870702i	$0.336335\pi$
$84$	−3.98403	−0.434693
$85$	5.63107	0.610775
$86$	2.59922	0.280282
$87$	1.00000	0.107211
$88$	−2.46602	−0.262879
$89$	3.54725	0.376007	0.188004	−	0.982168i	$-0.439798\pi$
$89$	3.54725	0.376007	0.188004	+	0.982168i	$0.439798\pi$
$90$	1.56155	0.164602
$91$	−24.3712	−2.55480
$92$	1.00000	0.104257
$93$	−3.90117	−0.404533
$94$	−8.41233	−0.867665
$95$	7.48028	0.767460
$96$	−1.00000	−0.102062
$97$	−11.3534	−1.15276	−0.576382	−	0.817181i	$-0.695536\pi$
$97$	−11.3534	−1.15276	−0.576382	+	0.817181i	$0.695536\pi$
$98$	−8.87247	−0.896255
$99$	2.46602	0.247845
$100$	−2.56155	−0.256155
$101$	11.8868	1.18278	0.591389	−	0.806386i	$-0.298580\pi$
$101$	11.8868	1.18278	0.591389	+	0.806386i	$0.298580\pi$
$102$	3.60607	0.357054
$103$	−8.14064	−0.802122	−0.401061	−	0.916051i	$-0.631358\pi$
$103$	−8.14064	−0.802122	−0.401061	+	0.916051i	$0.631358\pi$
$104$	−6.11723	−0.599844
$105$	6.22127	0.607134
$106$	2.45746	0.238690
$107$	4.45117	0.430311	0.215156	−	0.976580i	$-0.430974\pi$
$107$	4.45117	0.430311	0.215156	+	0.976580i	$0.430974\pi$
$108$	1.00000	0.0962250
$109$	−5.03655	−0.482414	−0.241207	−	0.970474i	$-0.577543\pi$
$109$	−5.03655	−0.482414	−0.241207	+	0.970474i	$0.577543\pi$
$110$	3.85083	0.367162
$111$	4.61195	0.437747
$112$	−3.98403	−0.376455
$113$	−6.99558	−0.658089	−0.329044	−	0.944314i	$-0.606727\pi$
$113$	−6.99558	−0.658089	−0.329044	+	0.944314i	$0.606727\pi$
$114$	4.79028	0.448651
$115$	−1.56155	−0.145616
$116$	1.00000	0.0928477
$117$	6.11723	0.565538
$118$	−9.18776	−0.845802
$119$	14.3667	1.31699
$120$	1.56155	0.142550
$121$	−4.91873	−0.447157
$122$	11.3469	1.02730
$123$	3.01426	0.271786
$124$	−3.90117	−0.350335
$125$	11.8078	1.05612
$126$	3.98403	0.354925
$127$	−1.63203	−0.144819	−0.0724096	−	0.997375i	$-0.523069\pi$
$127$	−1.63203	−0.144819	−0.0724096	+	0.997375i	$0.523069\pi$
$128$	−1.00000	−0.0883883
$129$	−2.59922	−0.228849
$130$	9.55237	0.837799
$131$	12.4399	1.08688	0.543440	−	0.839448i	$-0.317122\pi$
$131$	12.4399	1.08688	0.543440	+	0.839448i	$0.317122\pi$
$132$	2.46602	0.214640
$133$	19.0846	1.65485
$134$	−6.45163	−0.557336
$135$	−1.56155	−0.134397
$136$	3.60607	0.309218
$137$	6.86995	0.586939	0.293470	−	0.955968i	$-0.405190\pi$
$137$	6.86995	0.586939	0.293470	+	0.955968i	$0.405190\pi$
$138$	−1.00000	−0.0851257
$139$	19.1998	1.62851	0.814254	−	0.580509i	$-0.197146\pi$
$139$	19.1998	1.62851	0.814254	+	0.580509i	$0.197146\pi$
$140$	6.22127	0.525793
$141$	8.41233	0.708446
$142$	10.7005	0.897964
$143$	15.0852	1.26149
$144$	1.00000	0.0833333
$145$	−1.56155	−0.129680
$146$	−1.24409	−0.102962
$147$	8.87247	0.731789
$148$	4.61195	0.379100
$149$	−6.59745	−0.540485	−0.270242	−	0.962792i	$-0.587104\pi$
$149$	−6.59745	−0.540485	−0.270242	+	0.962792i	$0.587104\pi$
$150$	2.56155	0.209150
$151$	9.50264	0.773314	0.386657	−	0.922224i	$-0.373630\pi$
$151$	9.50264	0.773314	0.386657	+	0.922224i	$0.373630\pi$
$152$	4.79028	0.388543
$153$	−3.60607	−0.291534
$154$	9.82471	0.791697
$155$	6.09188	0.489312
$156$	6.11723	0.489770
$157$	21.5613	1.72078	0.860389	−	0.509639i	$-0.170221\pi$
$157$	21.5613	1.72078	0.860389	+	0.509639i	$0.170221\pi$
$158$	−13.5098	−1.07478
$159$	−2.45746	−0.194889
$160$	1.56155	0.123452
$161$	−3.98403	−0.313985
$162$	−1.00000	−0.0785674
$163$	15.6865	1.22867	0.614333	−	0.789047i	$-0.289425\pi$
$163$	15.6865	1.22867	0.614333	+	0.789047i	$0.289425\pi$
$164$	3.01426	0.235374
$165$	−3.85083	−0.299786
$166$	−8.96121	−0.695525
$167$	22.0174	1.70376	0.851878	−	0.523740i	$-0.175464\pi$
$167$	22.0174	1.70376	0.851878	+	0.523740i	$0.175464\pi$
$168$	3.98403	0.307374
$169$	24.4205	1.87850
$170$	−5.63107	−0.431883
$171$	−4.79028	−0.366322
$172$	−2.59922	−0.198189
$173$	−12.2503	−0.931371	−0.465686	−	0.884950i	$-0.654192\pi$
$173$	−12.2503	−0.931371	−0.465686	+	0.884950i	$0.654192\pi$
$174$	−1.00000	−0.0758098
$175$	10.2053	0.771448
$176$	2.46602	0.185884
$177$	9.18776	0.690594
$178$	−3.54725	−0.265877
$179$	−20.6015	−1.53983	−0.769916	−	0.638145i	$-0.779702\pi$
$179$	−20.6015	−1.53983	−0.769916	+	0.638145i	$0.779702\pi$
$180$	−1.56155	−0.116391
$181$	0.728822	0.0541729	0.0270864	−	0.999633i	$-0.491377\pi$
$181$	0.728822	0.0541729	0.0270864	+	0.999633i	$0.491377\pi$
$182$	24.3712	1.80651
$183$	−11.3469	−0.838789
$184$	−1.00000	−0.0737210
$185$	−7.20180	−0.529487
$186$	3.90117	0.286048
$187$	−8.89266	−0.650296
$188$	8.41233	0.613532
$189$	−3.98403	−0.289795
$190$	−7.48028	−0.542676
$191$	19.8396	1.43554	0.717770	−	0.696280i	$-0.245163\pi$
$191$	19.8396	1.43554	0.717770	+	0.696280i	$0.245163\pi$
$192$	1.00000	0.0721688
$193$	−9.59953	−0.690989	−0.345495	−	0.938421i	$-0.612289\pi$
$193$	−9.59953	−0.690989	−0.345495	+	0.938421i	$0.612289\pi$
$194$	11.3534	0.815127
$195$	−9.55237	−0.684060
$196$	8.87247	0.633748
$197$	19.1808	1.36658	0.683289	−	0.730148i	$-0.260549\pi$
$197$	19.1808	1.36658	0.683289	+	0.730148i	$0.260549\pi$
$198$	−2.46602	−0.175253
$199$	0.891584	0.0632027	0.0316014	−	0.999501i	$-0.489939\pi$
$199$	0.891584	0.0632027	0.0316014	+	0.999501i	$0.489939\pi$
$200$	2.56155	0.181129
$201$	6.45163	0.455063
$202$	−11.8868	−0.836351
$203$	−3.98403	−0.279624
$204$	−3.60607	−0.252476
$205$	−4.70692	−0.328745
$206$	8.14064	0.567186
$207$	1.00000	0.0695048
$208$	6.11723	0.424153
$209$	−11.8130	−0.817119
$210$	−6.22127	−0.429308
$211$	12.3503	0.850226	0.425113	−	0.905140i	$-0.360234\pi$
$211$	12.3503	0.850226	0.425113	+	0.905140i	$0.360234\pi$
$212$	−2.45746	−0.168779
$213$	−10.7005	−0.733185
$214$	−4.45117	−0.304276
$215$	4.05883	0.276810
$216$	−1.00000	−0.0680414
$217$	15.5424	1.05508
$218$	5.03655	0.341118
$219$	1.24409	0.0840677
$220$	−3.85083	−0.259623
$221$	−22.0592	−1.48386
$222$	−4.61195	−0.309534
$223$	−25.1820	−1.68631	−0.843157	−	0.537668i	$-0.819305\pi$
$223$	−25.1820	−1.68631	−0.843157	+	0.537668i	$0.819305\pi$
$224$	3.98403	0.266194
$225$	−2.56155	−0.170770
$226$	6.99558	0.465339
$227$	24.7427	1.64223	0.821116	−	0.570761i	$-0.193352\pi$
$227$	24.7427	1.64223	0.821116	+	0.570761i	$0.193352\pi$
$228$	−4.79028	−0.317244
$229$	−1.56552	−0.103452	−0.0517262	−	0.998661i	$-0.516472\pi$
$229$	−1.56552	−0.103452	−0.0517262	+	0.998661i	$0.516472\pi$
$230$	1.56155	0.102966
$231$	−9.82471	−0.646418
$232$	−1.00000	−0.0656532
$233$	13.1367	0.860613	0.430307	−	0.902683i	$-0.358405\pi$
$233$	13.1367	0.860613	0.430307	+	0.902683i	$0.358405\pi$
$234$	−6.11723	−0.399896
$235$	−13.1363	−0.856917
$236$	9.18776	0.598072
$237$	13.5098	0.877555
$238$	−14.3667	−0.931254
$239$	17.4521	1.12888	0.564441	−	0.825474i	$-0.309092\pi$
$239$	17.4521	1.12888	0.564441	+	0.825474i	$0.309092\pi$
$240$	−1.56155	−0.100798
$241$	−4.98880	−0.321357	−0.160679	−	0.987007i	$-0.551368\pi$
$241$	−4.98880	−0.321357	−0.160679	+	0.987007i	$0.551368\pi$
$242$	4.91873	0.316188
$243$	1.00000	0.0641500
$244$	−11.3469	−0.726413
$245$	−13.8548	−0.885153
$246$	−3.01426	−0.192182
$247$	−29.3033	−1.86452
$248$	3.90117	0.247725
$249$	8.96121	0.567893
$250$	−11.8078	−0.746789
$251$	14.5773	0.920112	0.460056	−	0.887890i	$-0.347829\pi$
$251$	14.5773	0.920112	0.460056	+	0.887890i	$0.347829\pi$
$252$	−3.98403	−0.250970
$253$	2.46602	0.155038
$254$	1.63203	0.102403
$255$	5.63107	0.352631
$256$	1.00000	0.0625000
$257$	−24.6791	−1.53944	−0.769719	−	0.638383i	$-0.779604\pi$
$257$	−24.6791	−1.53944	−0.769719	+	0.638383i	$0.779604\pi$
$258$	2.59922	0.161821
$259$	−18.3741	−1.14171
$260$	−9.55237	−0.592413
$261$	1.00000	0.0618984
$262$	−12.4399	−0.768540
$263$	14.6606	0.904013	0.452007	−	0.892015i	$-0.350708\pi$
$263$	14.6606	0.904013	0.452007	+	0.892015i	$0.350708\pi$
$264$	−2.46602	−0.151773
$265$	3.83745	0.235733
$266$	−19.0846	−1.17015
$267$	3.54725	0.217088
$268$	6.45163	0.394096
$269$	28.1151	1.71421	0.857104	−	0.515144i	$-0.172262\pi$
$269$	28.1151	1.71421	0.857104	+	0.515144i	$0.172262\pi$
$270$	1.56155	0.0950331
$271$	1.57688	0.0957884	0.0478942	−	0.998852i	$-0.484749\pi$
$271$	1.57688	0.0957884	0.0478942	+	0.998852i	$0.484749\pi$
$272$	−3.60607	−0.218650
$273$	−24.3712	−1.47501
$274$	−6.86995	−0.415029
$275$	−6.31685	−0.380920
$276$	1.00000	0.0601929
$277$	5.99818	0.360396	0.180198	−	0.983630i	$-0.442326\pi$
$277$	5.99818	0.360396	0.180198	+	0.983630i	$0.442326\pi$
$278$	−19.1998	−1.15153
$279$	−3.90117	−0.233557
$280$	−6.22127	−0.371792
$281$	−18.2148	−1.08660	−0.543302	−	0.839537i	$-0.682826\pi$
$281$	−18.2148	−1.08660	−0.543302	+	0.839537i	$0.682826\pi$
$282$	−8.41233	−0.500947
$283$	13.3211	0.791854	0.395927	−	0.918282i	$-0.370423\pi$
$283$	13.3211	0.791854	0.395927	+	0.918282i	$0.370423\pi$
$284$	−10.7005	−0.634957
$285$	7.48028	0.443094
$286$	−15.0852	−0.892008
$287$	−12.0089	−0.708862
$288$	−1.00000	−0.0589256
$289$	−3.99625	−0.235073
$290$	1.56155	0.0916975
$291$	−11.3534	−0.665548
$292$	1.24409	0.0728048
$293$	28.5049	1.66527	0.832637	−	0.553819i	$-0.186830\pi$
$293$	28.5049	1.66527	0.832637	+	0.553819i	$0.186830\pi$
$294$	−8.87247	−0.517453
$295$	−14.3472	−0.835324
$296$	−4.61195	−0.268064
$297$	2.46602	0.143093
$298$	6.59745	0.382180
$299$	6.11723	0.353768
$300$	−2.56155	−0.147891
$301$	10.3554	0.596874
$302$	−9.50264	−0.546816
$303$	11.8868	0.682878
$304$	−4.79028	−0.274742
$305$	17.7188	1.01458
$306$	3.60607	0.206145
$307$	−26.5977	−1.51801	−0.759004	−	0.651086i	$-0.774314\pi$
$307$	−26.5977	−1.51801	−0.759004	+	0.651086i	$0.774314\pi$
$308$	−9.82471	−0.559815
$309$	−8.14064	−0.463105
$310$	−6.09188	−0.345996
$311$	−7.90273	−0.448123	−0.224061	−	0.974575i	$-0.571932\pi$
$311$	−7.90273	−0.448123	−0.224061	+	0.974575i	$0.571932\pi$
$312$	−6.11723	−0.346320
$313$	−13.8283	−0.781620	−0.390810	−	0.920471i	$-0.627805\pi$
$313$	−13.8283	−0.781620	−0.390810	+	0.920471i	$0.627805\pi$
$314$	−21.5613	−1.21677
$315$	6.22127	0.350529
$316$	13.5098	0.759985
$317$	24.3951	1.37016	0.685082	−	0.728466i	$-0.259766\pi$
$317$	24.3951	1.37016	0.685082	+	0.728466i	$0.259766\pi$
$318$	2.45746	0.137807
$319$	2.46602	0.138071
$320$	−1.56155	−0.0872935
$321$	4.45117	0.248440
$322$	3.98403	0.222021
$323$	17.2741	0.961157
$324$	1.00000	0.0555556
$325$	−15.6696	−0.869193
$326$	−15.6865	−0.868797
$327$	−5.03655	−0.278522
$328$	−3.01426	−0.166434
$329$	−33.5149	−1.84774
$330$	3.85083	0.211981
$331$	16.8570	0.926547	0.463273	−	0.886215i	$-0.346675\pi$
$331$	16.8570	0.926547	0.463273	+	0.886215i	$0.346675\pi$
$332$	8.96121	0.491810
$333$	4.61195	0.252733
$334$	−22.0174	−1.20474
$335$	−10.0746	−0.550432
$336$	−3.98403	−0.217347
$337$	−12.9874	−0.707467	−0.353734	−	0.935346i	$-0.615088\pi$
$337$	−12.9874	−0.707467	−0.353734	+	0.935346i	$0.615088\pi$
$338$	−24.4205	−1.32830
$339$	−6.99558	−0.379948
$340$	5.63107	0.305388
$341$	−9.62038	−0.520973
$342$	4.79028	0.259029
$343$	−7.45998	−0.402801
$344$	2.59922	0.140141
$345$	−1.56155	−0.0840712
$346$	12.2503	0.658579
$347$	19.0057	1.02028	0.510139	−	0.860092i	$-0.329594\pi$
$347$	19.0057	1.02028	0.510139	+	0.860092i	$0.329594\pi$
$348$	1.00000	0.0536056
$349$	21.4442	1.14788	0.573941	−	0.818897i	$-0.305414\pi$
$349$	21.4442	1.14788	0.573941	+	0.818897i	$0.305414\pi$
$350$	−10.2053	−0.545496
$351$	6.11723	0.326513
$352$	−2.46602	−0.131440
$353$	9.07736	0.483139	0.241570	−	0.970383i	$-0.422338\pi$
$353$	9.07736	0.483139	0.241570	+	0.970383i	$0.422338\pi$
$354$	−9.18776	−0.488324
$355$	16.7094	0.886841
$356$	3.54725	0.188004
$357$	14.3667	0.760366
$358$	20.6015	1.08883
$359$	−2.54614	−0.134380	−0.0671901	−	0.997740i	$-0.521403\pi$
$359$	−2.54614	−0.134380	−0.0671901	+	0.997740i	$0.521403\pi$
$360$	1.56155	0.0823011
$361$	3.94681	0.207727
$362$	−0.728822	−0.0383060
$363$	−4.91873	−0.258166
$364$	−24.3712	−1.27740
$365$	−1.94271	−0.101686
$366$	11.3469	0.593113
$367$	18.2051	0.950301	0.475150	−	0.879905i	$-0.342394\pi$
$367$	18.2051	0.950301	0.475150	+	0.879905i	$0.342394\pi$
$368$	1.00000	0.0521286
$369$	3.01426	0.156916
$370$	7.20180	0.374404
$371$	9.79059	0.508302
$372$	−3.90117	−0.202266
$373$	−11.9674	−0.619649	−0.309824	−	0.950794i	$-0.600270\pi$
$373$	−11.9674	−0.619649	−0.309824	+	0.950794i	$0.600270\pi$
$374$	8.89266	0.459828
$375$	11.8078	0.609750
$376$	−8.41233	−0.433833
$377$	6.11723	0.315053
$378$	3.98403	0.204916
$379$	−34.2672	−1.76019	−0.880094	−	0.474800i	$-0.842520\pi$
$379$	−34.2672	−1.76019	−0.880094	+	0.474800i	$0.842520\pi$
$380$	7.48028	0.383730
$381$	−1.63203	−0.0836114
$382$	−19.8396	−1.01508
$383$	18.4988	0.945244	0.472622	−	0.881265i	$-0.343308\pi$
$383$	18.4988	0.945244	0.472622	+	0.881265i	$0.343308\pi$
$384$	−1.00000	−0.0510310
$385$	15.3418	0.781890
$386$	9.59953	0.488603
$387$	−2.59922	−0.132126
$388$	−11.3534	−0.576382
$389$	0.589309	0.0298791	0.0149396	−	0.999888i	$-0.495244\pi$
$389$	0.589309	0.0298791	0.0149396	+	0.999888i	$0.495244\pi$
$390$	9.55237	0.483703
$391$	−3.60607	−0.182367
$392$	−8.87247	−0.448128
$393$	12.4399	0.627510
$394$	−19.1808	−0.966317
$395$	−21.0963	−1.06147
$396$	2.46602	0.123922
$397$	−8.81840	−0.442583	−0.221291	−	0.975208i	$-0.571027\pi$
$397$	−8.81840	−0.442583	−0.221291	+	0.975208i	$0.571027\pi$
$398$	−0.891584	−0.0446911
$399$	19.0846	0.955426
$400$	−2.56155	−0.128078
$401$	17.6187	0.879835	0.439918	−	0.898038i	$-0.355008\pi$
$401$	17.6187	0.879835	0.439918	+	0.898038i	$0.355008\pi$
$402$	−6.45163	−0.321778
$403$	−23.8643	−1.18877
$404$	11.8868	0.591389
$405$	−1.56155	−0.0775942
$406$	3.98403	0.197724
$407$	11.3732	0.563747
$408$	3.60607	0.178527
$409$	−2.65150	−0.131108	−0.0655540	−	0.997849i	$-0.520881\pi$
$409$	−2.65150	−0.131108	−0.0655540	+	0.997849i	$0.520881\pi$
$410$	4.70692	0.232458
$411$	6.86995	0.338870
$412$	−8.14064	−0.401061
$413$	−36.6043	−1.80118
$414$	−1.00000	−0.0491473
$415$	−13.9934	−0.686909
$416$	−6.11723	−0.299922
$417$	19.1998	0.940219
$418$	11.8130	0.577790
$419$	3.97648	0.194264	0.0971319	−	0.995272i	$-0.469033\pi$
$419$	3.97648	0.194264	0.0971319	+	0.995272i	$0.469033\pi$
$420$	6.22127	0.303567
$421$	−0.106378	−0.00518454	−0.00259227	−	0.999997i	$-0.500825\pi$
$421$	−0.106378	−0.00518454	−0.00259227	+	0.999997i	$0.500825\pi$
$422$	−12.3503	−0.601201
$423$	8.41233	0.409021
$424$	2.45746	0.119345
$425$	9.23714	0.448067
$426$	10.7005	0.518440
$427$	45.2065	2.18769
$428$	4.45117	0.215156
$429$	15.0852	0.728322
$430$	−4.05883	−0.195734
$431$	8.67626	0.417921	0.208960	−	0.977924i	$-0.432992\pi$
$431$	8.67626	0.417921	0.208960	+	0.977924i	$0.432992\pi$
$432$	1.00000	0.0481125
$433$	−19.3099	−0.927973	−0.463987	−	0.885842i	$-0.653581\pi$
$433$	−19.3099	−0.927973	−0.463987	+	0.885842i	$0.653581\pi$
$434$	−15.5424	−0.746058
$435$	−1.56155	−0.0748707
$436$	−5.03655	−0.241207
$437$	−4.79028	−0.229150
$438$	−1.24409	−0.0594449
$439$	−29.3015	−1.39849	−0.699243	−	0.714885i	$-0.746479\pi$
$439$	−29.3015	−1.39849	−0.699243	+	0.714885i	$0.746479\pi$
$440$	3.85083	0.183581
$441$	8.87247	0.422499
$442$	22.0592	1.04925
$443$	3.00917	0.142970	0.0714851	−	0.997442i	$-0.477226\pi$
$443$	3.00917	0.142970	0.0714851	+	0.997442i	$0.477226\pi$
$444$	4.61195	0.218873
$445$	−5.53921	−0.262584
$446$	25.1820	1.19240
$447$	−6.59745	−0.312049
$448$	−3.98403	−0.188228
$449$	−28.8480	−1.36142	−0.680711	−	0.732552i	$-0.738329\pi$
$449$	−28.8480	−1.36142	−0.680711	+	0.732552i	$0.738329\pi$
$450$	2.56155	0.120753
$451$	7.43323	0.350017
$452$	−6.99558	−0.329044
$453$	9.50264	0.446473
$454$	−24.7427	−1.16123
$455$	38.0569	1.78414
$456$	4.79028	0.224326
$457$	26.6362	1.24599	0.622994	−	0.782227i	$-0.285916\pi$
$457$	26.6362	1.24599	0.622994	+	0.782227i	$0.285916\pi$
$458$	1.56552	0.0731519
$459$	−3.60607	−0.168317
$460$	−1.56155	−0.0728078
$461$	10.7787	0.502014	0.251007	−	0.967985i	$-0.419238\pi$
$461$	10.7787	0.502014	0.251007	+	0.967985i	$0.419238\pi$
$462$	9.82471	0.457087
$463$	−28.5069	−1.32483	−0.662415	−	0.749137i	$-0.730468\pi$
$463$	−28.5069	−1.32483	−0.662415	+	0.749137i	$0.730468\pi$
$464$	1.00000	0.0464238
$465$	6.09188	0.282504
$466$	−13.1367	−0.608546
$467$	−0.546521	−0.0252900	−0.0126450	−	0.999920i	$-0.504025\pi$
$467$	−0.546521	−0.0252900	−0.0126450	+	0.999920i	$0.504025\pi$
$468$	6.11723	0.282769
$469$	−25.7035	−1.18688
$470$	13.1363	0.605932
$471$	21.5613	0.993491
$472$	−9.18776	−0.422901
$473$	−6.40975	−0.294721
$474$	−13.5098	−0.620525
$475$	12.2706	0.563012
$476$	14.3667	0.658496
$477$	−2.45746	−0.112519
$478$	−17.4521	−0.798240
$479$	−7.27567	−0.332434	−0.166217	−	0.986089i	$-0.553155\pi$
$479$	−7.27567	−0.332434	−0.166217	+	0.986089i	$0.553155\pi$
$480$	1.56155	0.0712748
$481$	28.2123	1.28637
$482$	4.98880	0.227234
$483$	−3.98403	−0.181280
$484$	−4.91873	−0.223578
$485$	17.7289	0.805030
$486$	−1.00000	−0.0453609
$487$	37.1498	1.68342	0.841709	−	0.539931i	$-0.181550\pi$
$487$	37.1498	1.68342	0.841709	+	0.539931i	$0.181550\pi$
$488$	11.3469	0.513651
$489$	15.6865	0.709370
$490$	13.8548	0.625898
$491$	−24.7646	−1.11761	−0.558806	−	0.829298i	$-0.688740\pi$
$491$	−24.7646	−1.11761	−0.558806	+	0.829298i	$0.688740\pi$
$492$	3.01426	0.135893
$493$	−3.60607	−0.162409
$494$	29.3033	1.31842
$495$	−3.85083	−0.173082
$496$	−3.90117	−0.175168
$497$	42.6310	1.91226
$498$	−8.96121	−0.401561
$499$	35.3334	1.58174	0.790870	−	0.611984i	$-0.209628\pi$
$499$	35.3334	1.58174	0.790870	+	0.611984i	$0.209628\pi$
$500$	11.8078	0.528059
$501$	22.0174	0.983664
$502$	−14.5773	−0.650618
$503$	13.1214	0.585055	0.292528	−	0.956257i	$-0.405504\pi$
$503$	13.1214	0.585055	0.292528	+	0.956257i	$0.405504\pi$
$504$	3.98403	0.177463
$505$	−18.5618	−0.825991
$506$	−2.46602	−0.109628
$507$	24.4205	1.08455
$508$	−1.63203	−0.0724096
$509$	−24.5656	−1.08885	−0.544426	−	0.838809i	$-0.683253\pi$
$509$	−24.5656	−1.08885	−0.544426	+	0.838809i	$0.683253\pi$
$510$	−5.63107	−0.249348
$511$	−4.95648	−0.219262
$512$	−1.00000	−0.0441942
$513$	−4.79028	−0.211496
$514$	24.6791	1.08855
$515$	12.7120	0.560160
$516$	−2.59922	−0.114424
$517$	20.7450	0.912364
$518$	18.3741	0.807313
$519$	−12.2503	−0.537728
$520$	9.55237	0.418899
$521$	−40.6931	−1.78280	−0.891399	−	0.453219i	$-0.850276\pi$
$521$	−40.6931	−1.78280	−0.891399	+	0.453219i	$0.850276\pi$
$522$	−1.00000	−0.0437688
$523$	3.31034	0.144751	0.0723754	−	0.997377i	$-0.476942\pi$
$523$	3.31034	0.144751	0.0723754	+	0.997377i	$0.476942\pi$
$524$	12.4399	0.543440
$525$	10.2053	0.445396
$526$	−14.6606	−0.639234
$527$	14.0679	0.612807
$528$	2.46602	0.107320
$529$	1.00000	0.0434783
$530$	−3.83745	−0.166688
$531$	9.18776	0.398715
$532$	19.0846	0.827423
$533$	18.4389	0.798677
$534$	−3.54725	−0.153504
$535$	−6.95074	−0.300507
$536$	−6.45163	−0.278668
$537$	−20.6015	−0.889022
$538$	−28.1151	−1.21213
$539$	21.8797	0.942427
$540$	−1.56155	−0.0671985
$541$	33.7808	1.45235	0.726175	−	0.687510i	$-0.241296\pi$
$541$	33.7808	1.45235	0.726175	+	0.687510i	$0.241296\pi$
$542$	−1.57688	−0.0677326
$543$	0.728822	0.0312767
$544$	3.60607	0.154609
$545$	7.86484	0.336893
$546$	24.3712	1.04299
$547$	35.8388	1.53236	0.766178	−	0.642628i	$-0.222156\pi$
$547$	35.8388	1.53236	0.766178	+	0.642628i	$0.222156\pi$
$548$	6.86995	0.293470
$549$	−11.3469	−0.484275
$550$	6.31685	0.269351
$551$	−4.79028	−0.204073
$552$	−1.00000	−0.0425628
$553$	−53.8234	−2.28880
$554$	−5.99818	−0.254838
$555$	−7.20180	−0.305699
$556$	19.1998	0.814254
$557$	27.6262	1.17056	0.585280	−	0.810831i	$-0.300984\pi$
$557$	27.6262	1.17056	0.585280	+	0.810831i	$0.300984\pi$
$558$	3.90117	0.165150
$559$	−15.9000	−0.672500
$560$	6.22127	0.262897
$561$	−8.89266	−0.375448
$562$	18.2148	0.768345
$563$	−10.8025	−0.455272	−0.227636	−	0.973746i	$-0.573100\pi$
$563$	−10.8025	−0.455272	−0.227636	+	0.973746i	$0.573100\pi$
$564$	8.41233	0.354223
$565$	10.9240	0.459575
$566$	−13.3211	−0.559926
$567$	−3.98403	−0.167313
$568$	10.7005	0.448982
$569$	−3.49695	−0.146600	−0.0732999	−	0.997310i	$-0.523353\pi$
$569$	−3.49695	−0.146600	−0.0732999	+	0.997310i	$0.523353\pi$
$570$	−7.48028	−0.313314
$571$	−27.0279	−1.13108	−0.565541	−	0.824720i	$-0.691333\pi$
$571$	−27.0279	−1.13108	−0.565541	+	0.824720i	$0.691333\pi$
$572$	15.0852	0.630745
$573$	19.8396	0.828809
$574$	12.0089	0.501241
$575$	−2.56155	−0.106824
$576$	1.00000	0.0416667
$577$	24.0253	1.00019	0.500093	−	0.865972i	$-0.333299\pi$
$577$	24.0253	1.00019	0.500093	+	0.865972i	$0.333299\pi$
$578$	3.99625	0.166222
$579$	−9.59953	−0.398943
$580$	−1.56155	−0.0648400
$581$	−35.7017	−1.48116
$582$	11.3534	0.470614
$583$	−6.06015	−0.250986
$584$	−1.24409	−0.0514808
$585$	−9.55237	−0.394942
$586$	−28.5049	−1.17753
$587$	−1.14177	−0.0471259	−0.0235630	−	0.999722i	$-0.507501\pi$
$587$	−1.14177	−0.0471259	−0.0235630	+	0.999722i	$0.507501\pi$
$588$	8.87247	0.365895
$589$	18.6877	0.770014
$590$	14.3472	0.590664
$591$	19.1808	0.788994
$592$	4.61195	0.189550
$593$	−17.0145	−0.698701	−0.349351	−	0.936992i	$-0.613598\pi$
$593$	−17.0145	−0.698701	−0.349351	+	0.936992i	$0.613598\pi$
$594$	−2.46602	−0.101182
$595$	−22.4343	−0.919718
$596$	−6.59745	−0.270242
$597$	0.891584	0.0364901
$598$	−6.11723	−0.250152
$599$	−37.0994	−1.51584	−0.757920	−	0.652347i	$-0.773784\pi$
$599$	−37.0994	−1.51584	−0.757920	+	0.652347i	$0.773784\pi$
$600$	2.56155	0.104575
$601$	−34.2490	−1.39705	−0.698523	−	0.715587i	$-0.746159\pi$
$601$	−34.2490	−1.39705	−0.698523	+	0.715587i	$0.746159\pi$
$602$	−10.3554	−0.422054
$603$	6.45163	0.262731
$604$	9.50264	0.386657
$605$	7.68085	0.312271
$606$	−11.8868	−0.482867
$607$	−7.66171	−0.310979	−0.155490	−	0.987838i	$-0.549696\pi$
$607$	−7.66171	−0.310979	−0.155490	+	0.987838i	$0.549696\pi$
$608$	4.79028	0.194272
$609$	−3.98403	−0.161441
$610$	−17.7188	−0.717414
$611$	51.4601	2.08185
$612$	−3.60607	−0.145767
$613$	−10.1617	−0.410427	−0.205214	−	0.978717i	$-0.565789\pi$
$613$	−10.1617	−0.410427	−0.205214	+	0.978717i	$0.565789\pi$
$614$	26.5977	1.07339
$615$	−4.70692	−0.189801
$616$	9.82471	0.395849
$617$	−2.64671	−0.106552	−0.0532762	−	0.998580i	$-0.516966\pi$
$617$	−2.64671	−0.106552	−0.0532762	+	0.998580i	$0.516966\pi$
$618$	8.14064	0.327465
$619$	−48.1008	−1.93333	−0.966666	−	0.256039i	$-0.917582\pi$
$619$	−48.1008	−1.93333	−0.966666	+	0.256039i	$0.917582\pi$
$620$	6.09188	0.244656
$621$	1.00000	0.0401286
$622$	7.90273	0.316871
$623$	−14.1323	−0.566199
$624$	6.11723	0.244885
$625$	−5.63068	−0.225227
$626$	13.8283	0.552689
$627$	−11.8130	−0.471764
$628$	21.5613	0.860389
$629$	−16.6310	−0.663122
$630$	−6.22127	−0.247861
$631$	−29.2335	−1.16377	−0.581883	−	0.813272i	$-0.697684\pi$
$631$	−29.2335	−1.16377	−0.581883	+	0.813272i	$0.697684\pi$
$632$	−13.5098	−0.537391
$633$	12.3503	0.490878
$634$	−24.3951	−0.968852
$635$	2.54850	0.101134
$636$	−2.45746	−0.0974446
$637$	54.2749	2.15045
$638$	−2.46602	−0.0976308
$639$	−10.7005	−0.423304
$640$	1.56155	0.0617258
$641$	−24.2746	−0.958790	−0.479395	−	0.877599i	$-0.659144\pi$
$641$	−24.2746	−0.958790	−0.479395	+	0.877599i	$0.659144\pi$
$642$	−4.45117	−0.175674
$643$	26.5290	1.04620	0.523100	−	0.852271i	$-0.324775\pi$
$643$	26.5290	1.04620	0.523100	+	0.852271i	$0.324775\pi$
$644$	−3.98403	−0.156993
$645$	4.05883	0.159816
$646$	−17.2741	−0.679640
$647$	−44.9673	−1.76785	−0.883924	−	0.467631i	$-0.845108\pi$
$647$	−44.9673	−1.76785	−0.883924	+	0.467631i	$0.845108\pi$
$648$	−1.00000	−0.0392837
$649$	22.6572	0.889374
$650$	15.6696	0.614612
$651$	15.5424	0.609153
$652$	15.6865	0.614333
$653$	−29.4122	−1.15099	−0.575494	−	0.817806i	$-0.695190\pi$
$653$	−29.4122	−1.15099	−0.575494	+	0.817806i	$0.695190\pi$
$654$	5.03655	0.196945
$655$	−19.4256	−0.759020
$656$	3.01426	0.117687
$657$	1.24409	0.0485365
$658$	33.5149	1.30655
$659$	−0.964035	−0.0375535	−0.0187767	−	0.999824i	$-0.505977\pi$
$659$	−0.964035	−0.0375535	−0.0187767	+	0.999824i	$0.505977\pi$
$660$	−3.85083	−0.149893
$661$	12.0290	0.467874	0.233937	−	0.972252i	$-0.424839\pi$
$661$	12.0290	0.467874	0.233937	+	0.972252i	$0.424839\pi$
$662$	−16.8570	−0.655167
$663$	−22.0592	−0.856707
$664$	−8.96121	−0.347762
$665$	−29.8016	−1.15566
$666$	−4.61195	−0.178709
$667$	1.00000	0.0387202
$668$	22.0174	0.851878
$669$	−25.1820	−0.973594
$670$	10.0746	0.389215
$671$	−27.9818	−1.08023
$672$	3.98403	0.153687
$673$	29.5826	1.14033	0.570163	−	0.821532i	$-0.306880\pi$
$673$	29.5826	1.14033	0.570163	+	0.821532i	$0.306880\pi$
$674$	12.9874	0.500255
$675$	−2.56155	−0.0985942
$676$	24.4205	0.939249
$677$	19.8670	0.763550	0.381775	−	0.924255i	$-0.375313\pi$
$677$	19.8670	0.763550	0.381775	+	0.924255i	$0.375313\pi$
$678$	6.99558	0.268664
$679$	45.2323	1.73585
$680$	−5.63107	−0.215942
$681$	24.7427	0.948143
$682$	9.62038	0.368383
$683$	2.97002	0.113645	0.0568224	−	0.998384i	$-0.481903\pi$
$683$	2.97002	0.113645	0.0568224	+	0.998384i	$0.481903\pi$
$684$	−4.79028	−0.183161
$685$	−10.7278	−0.409888
$686$	7.45998	0.284824
$687$	−1.56552	−0.0597283
$688$	−2.59922	−0.0990945
$689$	−15.0328	−0.572706
$690$	1.56155	0.0594473
$691$	−1.32579	−0.0504353	−0.0252177	−	0.999682i	$-0.508028\pi$
$691$	−1.32579	−0.0504353	−0.0252177	+	0.999682i	$0.508028\pi$
$692$	−12.2503	−0.465686
$693$	−9.82471	−0.373210
$694$	−19.0057	−0.721445
$695$	−29.9815	−1.13726
$696$	−1.00000	−0.0379049
$697$	−10.8696	−0.411716
$698$	−21.4442	−0.811675
$699$	13.1367	0.496875
$700$	10.2053	0.385724
$701$	10.1898	0.384862	0.192431	−	0.981310i	$-0.438363\pi$
$701$	10.1898	0.384862	0.192431	+	0.981310i	$0.438363\pi$
$702$	−6.11723	−0.230880
$703$	−22.0925	−0.833236
$704$	2.46602	0.0929418
$705$	−13.1363	−0.494741
$706$	−9.07736	−0.341631
$707$	−47.3573	−1.78105
$708$	9.18776	0.345297
$709$	−31.3792	−1.17847	−0.589235	−	0.807962i	$-0.700571\pi$
$709$	−31.3792	−1.17847	−0.589235	+	0.807962i	$0.700571\pi$
$710$	−16.7094	−0.627091
$711$	13.5098	0.506657
$712$	−3.54725	−0.132939
$713$	−3.90117	−0.146100
$714$	−14.3667	−0.537660
$715$	−23.5564	−0.880959
$716$	−20.6015	−0.769916
$717$	17.4521	0.651760
$718$	2.54614	0.0950212
$719$	−15.4071	−0.574586	−0.287293	−	0.957843i	$-0.592755\pi$
$719$	−15.4071	−0.574586	−0.287293	+	0.957843i	$0.592755\pi$
$720$	−1.56155	−0.0581956
$721$	32.4325	1.20785
$722$	−3.94681	−0.146885
$723$	−4.98880	−0.185536
$724$	0.728822	0.0270864
$725$	−2.56155	−0.0951337
$726$	4.91873	0.182551
$727$	−40.2995	−1.49462	−0.747312	−	0.664473i	$-0.768656\pi$
$727$	−40.2995	−1.49462	−0.747312	+	0.664473i	$0.768656\pi$
$728$	24.3712	0.903257
$729$	1.00000	0.0370370
$730$	1.94271	0.0719029
$731$	9.37299	0.346673
$732$	−11.3469	−0.419394
$733$	−31.3657	−1.15852	−0.579259	−	0.815144i	$-0.696658\pi$
$733$	−31.3657	−1.15852	−0.579259	+	0.815144i	$0.696658\pi$
$734$	−18.2051	−0.671964
$735$	−13.8548	−0.511043
$736$	−1.00000	−0.0368605
$737$	15.9099	0.586048
$738$	−3.01426	−0.110956
$739$	−11.6068	−0.426961	−0.213481	−	0.976947i	$-0.568480\pi$
$739$	−11.6068	−0.426961	−0.213481	+	0.976947i	$0.568480\pi$
$740$	−7.20180	−0.264744
$741$	−29.3033	−1.07648
$742$	−9.79059	−0.359424
$743$	−19.2767	−0.707195	−0.353598	−	0.935398i	$-0.615042\pi$
$743$	−19.2767	−0.707195	−0.353598	+	0.935398i	$0.615042\pi$
$744$	3.90117	0.143024
$745$	10.3023	0.377446
$746$	11.9674	0.438158
$747$	8.96121	0.327873
$748$	−8.89266	−0.325148
$749$	−17.7336	−0.647971
$750$	−11.8078	−0.431159
$751$	−41.7049	−1.52183	−0.760916	−	0.648850i	$-0.775250\pi$
$751$	−41.7049	−1.52183	−0.760916	+	0.648850i	$0.775250\pi$
$752$	8.41233	0.306766
$753$	14.5773	0.531227
$754$	−6.11723	−0.222776
$755$	−14.8389	−0.540042
$756$	−3.98403	−0.144898
$757$	48.6336	1.76762	0.883808	−	0.467849i	$-0.154971\pi$
$757$	48.6336	1.76762	0.883808	+	0.467849i	$0.154971\pi$
$758$	34.2672	1.24464
$759$	2.46602	0.0895110
$760$	−7.48028	−0.271338
$761$	−39.9062	−1.44660	−0.723300	−	0.690534i	$-0.757376\pi$
$761$	−39.9062	−1.44660	−0.723300	+	0.690534i	$0.757376\pi$
$762$	1.63203	0.0591222
$763$	20.0658	0.726429
$764$	19.8396	0.717770
$765$	5.63107	0.203592
$766$	−18.4988	−0.668388
$767$	56.2036	2.02939
$768$	1.00000	0.0360844
$769$	−43.3768	−1.56421	−0.782104	−	0.623148i	$-0.785854\pi$
$769$	−43.3768	−1.56421	−0.782104	+	0.623148i	$0.785854\pi$
$770$	−15.3418	−0.552880
$771$	−24.6791	−0.888795
$772$	−9.59953	−0.345495
$773$	46.9983	1.69041	0.845206	−	0.534440i	$-0.179477\pi$
$773$	46.9983	1.69041	0.845206	+	0.534440i	$0.179477\pi$
$774$	2.59922	0.0934272
$775$	9.99305	0.358961
$776$	11.3534	0.407563
$777$	−18.3741	−0.659168
$778$	−0.589309	−0.0211277
$779$	−14.4391	−0.517336
$780$	−9.55237	−0.342030
$781$	−26.3876	−0.944224
$782$	3.60607	0.128953
$783$	1.00000	0.0357371
$784$	8.87247	0.316874
$785$	−33.6691	−1.20170
$786$	−12.4399	−0.443717
$787$	22.0779	0.786992	0.393496	−	0.919326i	$-0.371266\pi$
$787$	22.0779	0.786992	0.393496	+	0.919326i	$0.371266\pi$
$788$	19.1808	0.683289
$789$	14.6606	0.521932
$790$	21.0963	0.750571
$791$	27.8706	0.990964
$792$	−2.46602	−0.0876263
$793$	−69.4117	−2.46488
$794$	8.81840	0.312953
$795$	3.83745	0.136100
$796$	0.891584	0.0316014
$797$	34.9134	1.23670	0.618349	−	0.785904i	$-0.287802\pi$
$797$	34.9134	1.23670	0.618349	+	0.785904i	$0.287802\pi$
$798$	−19.0846	−0.675588
$799$	−30.3355	−1.07319
$800$	2.56155	0.0905646
$801$	3.54725	0.125336
$802$	−17.6187	−0.622137
$803$	3.06795	0.108266
$804$	6.45163	0.227532
$805$	6.22127	0.219271
$806$	23.8643	0.840586
$807$	28.1151	0.989698
$808$	−11.8868	−0.418175
$809$	36.1010	1.26924	0.634622	−	0.772823i	$-0.281156\pi$
$809$	36.1010	1.26924	0.634622	+	0.772823i	$0.281156\pi$
$810$	1.56155	0.0548674
$811$	−20.0173	−0.702903	−0.351451	−	0.936206i	$-0.614312\pi$
$811$	−20.0173	−0.702903	−0.351451	+	0.936206i	$0.614312\pi$
$812$	−3.98403	−0.139812
$813$	1.57688	0.0553035
$814$	−11.3732	−0.398630
$815$	−24.4954	−0.858035
$816$	−3.60607	−0.126238
$817$	12.4510	0.435606
$818$	2.65150	0.0927074
$819$	−24.3712	−0.851599
$820$	−4.70692	−0.164373
$821$	−18.9908	−0.662784	−0.331392	−	0.943493i	$-0.607518\pi$
$821$	−18.9908	−0.662784	−0.331392	+	0.943493i	$0.607518\pi$
$822$	−6.86995	−0.239617
$823$	37.8385	1.31897	0.659484	−	0.751719i	$-0.270775\pi$
$823$	37.8385	1.31897	0.659484	+	0.751719i	$0.270775\pi$
$824$	8.14064	0.283593
$825$	−6.31685	−0.219924
$826$	36.6043	1.27363
$827$	1.59657	0.0555183	0.0277591	−	0.999615i	$-0.491163\pi$
$827$	1.59657	0.0555183	0.0277591	+	0.999615i	$0.491163\pi$
$828$	1.00000	0.0347524
$829$	41.6709	1.44729	0.723645	−	0.690173i	$-0.242465\pi$
$829$	41.6709	1.44729	0.723645	+	0.690173i	$0.242465\pi$
$830$	13.9934	0.485718
$831$	5.99818	0.208075
$832$	6.11723	0.212077
$833$	−31.9948	−1.10855
$834$	−19.1998	−0.664836
$835$	−34.3813	−1.18981
$836$	−11.8130	−0.408559
$837$	−3.90117	−0.134844
$838$	−3.97648	−0.137365
$839$	23.6515	0.816541	0.408271	−	0.912861i	$-0.366132\pi$
$839$	23.6515	0.816541	0.408271	+	0.912861i	$0.366132\pi$
$840$	−6.22127	−0.214654
$841$	1.00000	0.0344828
$842$	0.106378	0.00366603
$843$	−18.2148	−0.627351
$844$	12.3503	0.425113
$845$	−38.1339	−1.31184
$846$	−8.41233	−0.289222
$847$	19.5963	0.673338
$848$	−2.45746	−0.0843895
$849$	13.3211	0.457177
$850$	−9.23714	−0.316831
$851$	4.61195	0.158096
$852$	−10.7005	−0.366592
$853$	42.0205	1.43875	0.719377	−	0.694620i	$-0.244428\pi$
$853$	42.0205	1.43875	0.719377	+	0.694620i	$0.244428\pi$
$854$	−45.2065	−1.54693
$855$	7.48028	0.255820
$856$	−4.45117	−0.152138
$857$	5.19161	0.177342	0.0886710	−	0.996061i	$-0.471738\pi$
$857$	5.19161	0.177342	0.0886710	+	0.996061i	$0.471738\pi$
$858$	−15.0852	−0.515001
$859$	23.6403	0.806598	0.403299	−	0.915068i	$-0.367863\pi$
$859$	23.6403	0.806598	0.403299	+	0.915068i	$0.367863\pi$
$860$	4.05883	0.138405
$861$	−12.0089	−0.409261
$862$	−8.67626	−0.295514
$863$	16.8612	0.573961	0.286980	−	0.957936i	$-0.407349\pi$
$863$	16.8612	0.573961	0.286980	+	0.957936i	$0.407349\pi$
$864$	−1.00000	−0.0340207
$865$	19.1295	0.650421
$866$	19.3099	0.656176
$867$	−3.99625	−0.135720
$868$	15.5424	0.527542
$869$	33.3155	1.13015
$870$	1.56155	0.0529416
$871$	39.4661	1.33726
$872$	5.03655	0.170559
$873$	−11.3534	−0.384254
$874$	4.79028	0.162034
$875$	−47.0425	−1.59033
$876$	1.24409	0.0420339
$877$	4.78865	0.161701	0.0808506	−	0.996726i	$-0.474236\pi$
$877$	4.78865	0.161701	0.0808506	+	0.996726i	$0.474236\pi$
$878$	29.3015	0.988878
$879$	28.5049	0.961447
$880$	−3.85083	−0.129811
$881$	−40.3099	−1.35807	−0.679037	−	0.734104i	$-0.737602\pi$
$881$	−40.3099	−1.35807	−0.679037	+	0.734104i	$0.737602\pi$
$882$	−8.87247	−0.298752
$883$	−5.94599	−0.200099	−0.100049	−	0.994982i	$-0.531900\pi$
$883$	−5.94599	−0.200099	−0.100049	+	0.994982i	$0.531900\pi$
$884$	−22.0592	−0.741930
$885$	−14.3472	−0.482275
$886$	−3.00917	−0.101095
$887$	−42.2276	−1.41786	−0.708931	−	0.705278i	$-0.750822\pi$
$887$	−42.2276	−1.41786	−0.708931	+	0.705278i	$0.750822\pi$
$888$	−4.61195	−0.154767
$889$	6.50205	0.218072
$890$	5.53921	0.185675
$891$	2.46602	0.0826149
$892$	−25.1820	−0.843157
$893$	−40.2974	−1.34850
$894$	6.59745	0.220652
$895$	32.1704	1.07534
$896$	3.98403	0.133097
$897$	6.11723	0.204248
$898$	28.8480	0.962671
$899$	−3.90117	−0.130111
$900$	−2.56155	−0.0853851
$901$	8.86178	0.295229
$902$	−7.43323	−0.247499
$903$	10.3554	0.344606
$904$	6.99558	0.232669
$905$	−1.13809	−0.0378315
$906$	−9.50264	−0.315704
$907$	−16.2748	−0.540395	−0.270197	−	0.962805i	$-0.587089\pi$
$907$	−16.2748	−0.540395	−0.270197	+	0.962805i	$0.587089\pi$
$908$	24.7427	0.821116
$909$	11.8868	0.394260
$910$	−38.0569	−1.26157
$911$	36.8420	1.22063	0.610315	−	0.792159i	$-0.291043\pi$
$911$	36.8420	1.22063	0.610315	+	0.792159i	$0.291043\pi$
$912$	−4.79028	−0.158622
$913$	22.0986	0.731355
$914$	−26.6362	−0.881046
$915$	17.7188	0.585766
$916$	−1.56552	−0.0517262
$917$	−49.5609	−1.63665
$918$	3.60607	0.119018
$919$	46.9635	1.54918	0.774592	−	0.632461i	$-0.217955\pi$
$919$	46.9635	1.54918	0.774592	+	0.632461i	$0.217955\pi$
$920$	1.56155	0.0514829
$921$	−26.5977	−0.876423
$922$	−10.7787	−0.354977
$923$	−65.4573	−2.15455
$924$	−9.82471	−0.323209
$925$	−11.8138	−0.388434
$926$	28.5069	0.936796
$927$	−8.14064	−0.267374
$928$	−1.00000	−0.0328266
$929$	−2.96083	−0.0971416	−0.0485708	−	0.998820i	$-0.515467\pi$
$929$	−2.96083	−0.0971416	−0.0485708	+	0.998820i	$0.515467\pi$
$930$	−6.09188	−0.199761
$931$	−42.5017	−1.39294
$932$	13.1367	0.430307
$933$	−7.90273	−0.258724
$934$	0.546521	0.0178827
$935$	13.8864	0.454132
$936$	−6.11723	−0.199948
$937$	−36.5398	−1.19370	−0.596852	−	0.802351i	$-0.703582\pi$
$937$	−36.5398	−1.19370	−0.596852	+	0.802351i	$0.703582\pi$
$938$	25.7035	0.839249
$939$	−13.8283	−0.451269
$940$	−13.1363	−0.428459
$941$	−6.92391	−0.225713	−0.112857	−	0.993611i	$-0.536000\pi$
$941$	−6.92391	−0.225713	−0.112857	+	0.993611i	$0.536000\pi$
$942$	−21.5613	−0.702504
$943$	3.01426	0.0981577
$944$	9.18776	0.299036
$945$	6.22127	0.202378
$946$	6.40975	0.208399
$947$	−12.2236	−0.397215	−0.198607	−	0.980079i	$-0.563642\pi$
$947$	−12.2236	−0.397215	−0.198607	+	0.980079i	$0.563642\pi$
$948$	13.5098	0.438778
$949$	7.61037	0.247043
$950$	−12.2706	−0.398110
$951$	24.3951	0.791065
$952$	−14.3667	−0.465627
$953$	−5.40405	−0.175054	−0.0875271	−	0.996162i	$-0.527896\pi$
$953$	−5.40405	−0.175054	−0.0875271	+	0.996162i	$0.527896\pi$
$954$	2.45746	0.0795632
$955$	−30.9805	−1.00251
$956$	17.4521	0.564441
$957$	2.46602	0.0797152
$958$	7.27567	0.235066
$959$	−27.3701	−0.883825
$960$	−1.56155	−0.0503989
$961$	−15.7809	−0.509060
$962$	−28.2123	−0.909603
$963$	4.45117	0.143437
$964$	−4.98880	−0.160679
$965$	14.9902	0.482551
$966$	3.98403	0.128184
$967$	5.66866	0.182292	0.0911458	−	0.995838i	$-0.470947\pi$
$967$	5.66866	0.182292	0.0911458	+	0.995838i	$0.470947\pi$
$968$	4.91873	0.158094
$969$	17.2741	0.554924
$970$	−17.7289	−0.569242
$971$	−52.2704	−1.67744	−0.838718	−	0.544566i	$-0.816694\pi$
$971$	−52.2704	−1.67744	−0.838718	+	0.544566i	$0.816694\pi$
$972$	1.00000	0.0320750
$973$	−76.4926	−2.45224
$974$	−37.1498	−1.19036
$975$	−15.6696	−0.501829
$976$	−11.3469	−0.363206
$977$	26.7799	0.856766	0.428383	−	0.903597i	$-0.359083\pi$
$977$	26.7799	0.856766	0.428383	+	0.903597i	$0.359083\pi$
$978$	−15.6865	−0.501600
$979$	8.74759	0.279574
$980$	−13.8548	−0.442576
$981$	−5.03655	−0.160805
$982$	24.7646	0.790271
$983$	−1.53256	−0.0488809	−0.0244405	−	0.999701i	$-0.507780\pi$
$983$	−1.53256	−0.0488809	−0.0244405	+	0.999701i	$0.507780\pi$
$984$	−3.01426	−0.0960910
$985$	−29.9519	−0.954347
$986$	3.60607	0.114841
$987$	−33.5149	−1.06679
$988$	−29.3033	−0.932261
$989$	−2.59922	−0.0826505
$990$	3.85083	0.122387
$991$	54.5770	1.73369	0.866847	−	0.498573i	$-0.166143\pi$
$991$	54.5770	1.73369	0.866847	+	0.498573i	$0.166143\pi$
$992$	3.90117	0.123862
$993$	16.8570	0.534942
$994$	−42.6310	−1.35217
$995$	−1.39226	−0.0441375
$996$	8.96121	0.283947
$997$	54.1167	1.71389	0.856947	−	0.515405i	$-0.172358\pi$
$997$	54.1167	1.71389	0.856947	+	0.515405i	$0.172358\pi$
$998$	−35.3334	−1.11846
$999$	4.61195	0.145916

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	4002.2.a.bf.1.1	✓	6

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
4002.2.a.bf.1.1	✓	6	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:	\( N \)	\(=\)	\( 4002 = 2 \cdot 3 \cdot 23 \cdot 29 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	4002.a (trivial)

\(f(q)\)	\(=\)	\(q-1.00000 q^{2} +1.00000 q^{3} +1.00000 q^{4} -1.56155 q^{5} -1.00000 q^{6} -3.98403 q^{7} -1.00000 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q-1.00000 q^{2} +1.00000 q^{3} +1.00000 q^{4} -1.56155 q^{5} -1.00000 q^{6} -3.98403 q^{7} -1.00000 q^{8} +1.00000 q^{9} +1.56155 q^{10} +2.46602 q^{11} +1.00000 q^{12} +6.11723 q^{13} +3.98403 q^{14} -1.56155 q^{15} +1.00000 q^{16} -3.60607 q^{17} -1.00000 q^{18} -4.79028 q^{19} -1.56155 q^{20} -3.98403 q^{21} -2.46602 q^{22} +1.00000 q^{23} -1.00000 q^{24} -2.56155 q^{25} -6.11723 q^{26} +1.00000 q^{27} -3.98403 q^{28} +1.00000 q^{29} +1.56155 q^{30} -3.90117 q^{31} -1.00000 q^{32} +2.46602 q^{33} +3.60607 q^{34} +6.22127 q^{35} +1.00000 q^{36} +4.61195 q^{37} +4.79028 q^{38} +6.11723 q^{39} +1.56155 q^{40} +3.01426 q^{41} +3.98403 q^{42} -2.59922 q^{43} +2.46602 q^{44} -1.56155 q^{45} -1.00000 q^{46} +8.41233 q^{47} +1.00000 q^{48} +8.87247 q^{49} +2.56155 q^{50} -3.60607 q^{51} +6.11723 q^{52} -2.45746 q^{53} -1.00000 q^{54} -3.85083 q^{55} +3.98403 q^{56} -4.79028 q^{57} -1.00000 q^{58} +9.18776 q^{59} -1.56155 q^{60} -11.3469 q^{61} +3.90117 q^{62} -3.98403 q^{63} +1.00000 q^{64} -9.55237 q^{65} -2.46602 q^{66} +6.45163 q^{67} -3.60607 q^{68} +1.00000 q^{69} -6.22127 q^{70} -10.7005 q^{71} -1.00000 q^{72} +1.24409 q^{73} -4.61195 q^{74} -2.56155 q^{75} -4.79028 q^{76} -9.82471 q^{77} -6.11723 q^{78} +13.5098 q^{79} -1.56155 q^{80} +1.00000 q^{81} -3.01426 q^{82} +8.96121 q^{83} -3.98403 q^{84} +5.63107 q^{85} +2.59922 q^{86} +1.00000 q^{87} -2.46602 q^{88} +3.54725 q^{89} +1.56155 q^{90} -24.3712 q^{91} +1.00000 q^{92} -3.90117 q^{93} -8.41233 q^{94} +7.48028 q^{95} -1.00000 q^{96} -11.3534 q^{97} -8.87247 q^{98} +2.46602 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 6 q - 6 q^{2} + 6 q^{3} + 6 q^{4} + 3 q^{5} - 6 q^{6} + 2 q^{7} - 6 q^{8} + 6 q^{9}+O(q^{10}) \) 6 * q - 6 * q^2 + 6 * q^3 + 6 * q^4 + 3 * q^5 - 6 * q^6 + 2 * q^7 - 6 * q^8 + 6 * q^9	\( 6 q - 6 q^{2} + 6 q^{3} + 6 q^{4} + 3 q^{5} - 6 q^{6} + 2 q^{7} - 6 q^{8} + 6 q^{9} - 3 q^{10} + 7 q^{11} + 6 q^{12} + 3 q^{13} - 2 q^{14} + 3 q^{15} + 6 q^{16} + 8 q^{17} - 6 q^{18} - 4 q^{19} + 3 q^{20} + 2 q^{21} - 7 q^{22} + 6 q^{23} - 6 q^{24} - 3 q^{25} - 3 q^{26} + 6 q^{27} + 2 q^{28} + 6 q^{29} - 3 q^{30} + q^{31} - 6 q^{32} + 7 q^{33} - 8 q^{34} + 18 q^{35} + 6 q^{36} + 7 q^{37} + 4 q^{38} + 3 q^{39} - 3 q^{40} + 13 q^{41} - 2 q^{42} + 7 q^{44} + 3 q^{45} - 6 q^{46} + 22 q^{47} + 6 q^{48} + 8 q^{49} + 3 q^{50} + 8 q^{51} + 3 q^{52} + 10 q^{53} - 6 q^{54} - 5 q^{55} - 2 q^{56} - 4 q^{57} - 6 q^{58} + 17 q^{59} + 3 q^{60} + q^{61} - q^{62} + 2 q^{63} + 6 q^{64} - 7 q^{65} - 7 q^{66} + 3 q^{67} + 8 q^{68} + 6 q^{69} - 18 q^{70} + 11 q^{71} - 6 q^{72} - 7 q^{74} - 3 q^{75} - 4 q^{76} - 3 q^{78} + 2 q^{79} + 3 q^{80} + 6 q^{81} - 13 q^{82} + 16 q^{83} + 2 q^{84} + 4 q^{85} + 6 q^{87} - 7 q^{88} + 16 q^{89} - 3 q^{90} - 28 q^{91} + 6 q^{92} + q^{93} - 22 q^{94} + 32 q^{95} - 6 q^{96} + 2 q^{97} - 8 q^{98} + 7 q^{99}+O(q^{100}) \) 6 * q - 6 * q^2 + 6 * q^3 + 6 * q^4 + 3 * q^5 - 6 * q^6 + 2 * q^7 - 6 * q^8 + 6 * q^9 - 3 * q^10 + 7 * q^11 + 6 * q^12 + 3 * q^13 - 2 * q^14 + 3 * q^15 + 6 * q^16 + 8 * q^17 - 6 * q^18 - 4 * q^19 + 3 * q^20 + 2 * q^21 - 7 * q^22 + 6 * q^23 - 6 * q^24 - 3 * q^25 - 3 * q^26 + 6 * q^27 + 2 * q^28 + 6 * q^29 - 3 * q^30 + q^31 - 6 * q^32 + 7 * q^33 - 8 * q^34 + 18 * q^35 + 6 * q^36 + 7 * q^37 + 4 * q^38 + 3 * q^39 - 3 * q^40 + 13 * q^41 - 2 * q^42 + 7 * q^44 + 3 * q^45 - 6 * q^46 + 22 * q^47 + 6 * q^48 + 8 * q^49 + 3 * q^50 + 8 * q^51 + 3 * q^52 + 10 * q^53 - 6 * q^54 - 5 * q^55 - 2 * q^56 - 4 * q^57 - 6 * q^58 + 17 * q^59 + 3 * q^60 + q^61 - q^62 + 2 * q^63 + 6 * q^64 - 7 * q^65 - 7 * q^66 + 3 * q^67 + 8 * q^68 + 6 * q^69 - 18 * q^70 + 11 * q^71 - 6 * q^72 - 7 * q^74 - 3 * q^75 - 4 * q^76 - 3 * q^78 + 2 * q^79 + 3 * q^80 + 6 * q^81 - 13 * q^82 + 16 * q^83 + 2 * q^84 + 4 * q^85 + 6 * q^87 - 7 * q^88 + 16 * q^89 - 3 * q^90 - 28 * q^91 + 6 * q^92 + q^93 - 22 * q^94 + 32 * q^95 - 6 * q^96 + 2 * q^97 - 8 * q^98 + 7 * q^99

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