LMFDB - Embedded newform 4002.2.a.bf.1.2

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			1.2
Root			$3.25648$ 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)

$f(q)$	$=$	$q-1.00000 q^{2} +1.00000 q^{3} +1.00000 q^{4} -1.56155 q^{5} -1.00000 q^{6} -1.09168 q^{7} -1.00000 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q-1.00000 q^{2} +1.00000 q^{3} +1.00000 q^{4} -1.56155 q^{5} -1.00000 q^{6} -1.09168 q^{7} -1.00000 q^{8} +1.00000 q^{9} +1.56155 q^{10} +4.17571 q^{11} +1.00000 q^{12} -2.33724 q^{13} +1.09168 q^{14} -1.56155 q^{15} +1.00000 q^{16} -0.0496005 q^{17} -1.00000 q^{18} +2.48153 q^{19} -1.56155 q^{20} -1.09168 q^{21} -4.17571 q^{22} +1.00000 q^{23} -1.00000 q^{24} -2.56155 q^{25} +2.33724 q^{26} +1.00000 q^{27} -1.09168 q^{28} +1.00000 q^{29} +1.56155 q^{30} -0.863232 q^{31} -1.00000 q^{32} +4.17571 q^{33} +0.0496005 q^{34} +1.70472 q^{35} +1.00000 q^{36} +9.50994 q^{37} -2.48153 q^{38} -2.33724 q^{39} +1.56155 q^{40} -10.0507 q^{41} +1.09168 q^{42} +1.25320 q^{43} +4.17571 q^{44} -1.56155 q^{45} -1.00000 q^{46} +0.476395 q^{47} +1.00000 q^{48} -5.80823 q^{49} +2.56155 q^{50} -0.0496005 q^{51} -2.33724 q^{52} +12.0862 q^{53} -1.00000 q^{54} -6.52060 q^{55} +1.09168 q^{56} +2.48153 q^{57} -1.00000 q^{58} +1.02075 q^{59} -1.56155 q^{60} +12.5379 q^{61} +0.863232 q^{62} -1.09168 q^{63} +1.00000 q^{64} +3.64972 q^{65} -4.17571 q^{66} -5.94074 q^{67} -0.0496005 q^{68} +1.00000 q^{69} -1.70472 q^{70} +4.49876 q^{71} -1.00000 q^{72} -0.0841599 q^{73} -9.50994 q^{74} -2.56155 q^{75} +2.48153 q^{76} -4.55855 q^{77} +2.33724 q^{78} -12.4528 q^{79} -1.56155 q^{80} +1.00000 q^{81} +10.0507 q^{82} +2.88056 q^{83} -1.09168 q^{84} +0.0774538 q^{85} -1.25320 q^{86} +1.00000 q^{87} -4.17571 q^{88} +6.00654 q^{89} +1.56155 q^{90} +2.55152 q^{91} +1.00000 q^{92} -0.863232 q^{93} -0.476395 q^{94} -3.87503 q^{95} -1.00000 q^{96} -1.94736 q^{97} +5.80823 q^{98} +4.17571 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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
$7$	−1.09168	−0.412616	−0.206308	−	0.978487i	$-0.566145\pi$
$7$	−1.09168	−0.412616	−0.206308	+	0.978487i	$0.566145\pi$
$8$	−1.00000	−0.353553
$9$	1.00000	0.333333
$10$	1.56155	0.493806
$11$	4.17571	1.25903	0.629513	−	0.776990i	$-0.283255\pi$
$11$	4.17571	1.25903	0.629513	+	0.776990i	$0.283255\pi$
$12$	1.00000	0.288675
$13$	−2.33724	−0.648233	−0.324116	−	0.946017i	$-0.605067\pi$
$13$	−2.33724	−0.648233	−0.324116	+	0.946017i	$0.605067\pi$
$14$	1.09168	0.291764
$15$	−1.56155	−0.403191
$16$	1.00000	0.250000
$17$	−0.0496005	−0.0120299	−0.00601495	−	0.999982i	$-0.501915\pi$
$17$	−0.0496005	−0.0120299	−0.00601495	+	0.999982i	$0.501915\pi$
$18$	−1.00000	−0.235702
$19$	2.48153	0.569301	0.284650	−	0.958631i	$-0.408122\pi$
$19$	2.48153	0.569301	0.284650	+	0.958631i	$0.408122\pi$
$20$	−1.56155	−0.349174
$21$	−1.09168	−0.238224
$22$	−4.17571	−0.890265
$23$	1.00000	0.208514
$23$	1.00000	0.208514
$24$	−1.00000	−0.204124
$25$	−2.56155	−0.512311
$26$	2.33724	0.458370
$27$	1.00000	0.192450
$28$	−1.09168	−0.206308
$29$	1.00000	0.185695
$29$	1.00000	0.185695
$30$	1.56155	0.285099
$31$	−0.863232	−0.155041	−0.0775205	−	0.996991i	$-0.524700\pi$
$31$	−0.863232	−0.155041	−0.0775205	+	0.996991i	$0.524700\pi$
$32$	−1.00000	−0.176777
$33$	4.17571	0.726898
$34$	0.0496005	0.00850642
$35$	1.70472	0.288150
$36$	1.00000	0.166667
$37$	9.50994	1.56342	0.781712	−	0.623639i	$-0.214346\pi$
$37$	9.50994	1.56342	0.781712	+	0.623639i	$0.214346\pi$
$38$	−2.48153	−0.402557
$39$	−2.33724	−0.374257
$40$	1.56155	0.246903
$41$	−10.0507	−1.56966	−0.784831	−	0.619709i	$-0.787251\pi$
$41$	−10.0507	−1.56966	−0.784831	+	0.619709i	$0.787251\pi$
$42$	1.09168	0.168450
$43$	1.25320	0.191112	0.0955559	−	0.995424i	$-0.469537\pi$
$43$	1.25320	0.191112	0.0955559	+	0.995424i	$0.469537\pi$
$44$	4.17571	0.629513
$45$	−1.56155	−0.232783
$46$	−1.00000	−0.147442
$47$	0.476395	0.0694893	0.0347447	−	0.999396i	$-0.488938\pi$
$47$	0.476395	0.0694893	0.0347447	+	0.999396i	$0.488938\pi$
$48$	1.00000	0.144338
$49$	−5.80823	−0.829748
$50$	2.56155	0.362258
$51$	−0.0496005	−0.00694546
$52$	−2.33724	−0.324116
$53$	12.0862	1.66016	0.830081	−	0.557643i	$-0.188294\pi$
$53$	12.0862	1.66016	0.830081	+	0.557643i	$0.188294\pi$
$54$	−1.00000	−0.136083
$55$	−6.52060	−0.879237
$56$	1.09168	0.145882
$57$	2.48153	0.328686
$58$	−1.00000	−0.131306
$59$	1.02075	0.132890	0.0664451	−	0.997790i	$-0.478834\pi$
$59$	1.02075	0.132890	0.0664451	+	0.997790i	$0.478834\pi$
$60$	−1.56155	−0.201596
$61$	12.5379	1.60531	0.802654	−	0.596445i	$-0.203421\pi$
$61$	12.5379	1.60531	0.802654	+	0.596445i	$0.203421\pi$
$62$	0.863232	0.109631
$63$	−1.09168	−0.137539
$64$	1.00000	0.125000
$65$	3.64972	0.452692
$66$	−4.17571	−0.513995
$67$	−5.94074	−0.725777	−0.362889	−	0.931833i	$-0.618209\pi$
$67$	−5.94074	−0.725777	−0.362889	+	0.931833i	$0.618209\pi$
$68$	−0.0496005	−0.00601495
$69$	1.00000	0.120386
$70$	−1.70472	−0.203753
$71$	4.49876	0.533905	0.266952	−	0.963710i	$-0.413983\pi$
$71$	4.49876	0.533905	0.266952	+	0.963710i	$0.413983\pi$
$72$	−1.00000	−0.117851
$73$	−0.0841599	−0.00985017	−0.00492508	−	0.999988i	$-0.501568\pi$
$73$	−0.0841599	−0.00985017	−0.00492508	+	0.999988i	$0.501568\pi$
$74$	−9.50994	−1.10551
$75$	−2.56155	−0.295783
$76$	2.48153	0.284650
$77$	−4.55855	−0.519494
$78$	2.33724	0.264640
$79$	−12.4528	−1.40105	−0.700527	−	0.713626i	$-0.747052\pi$
$79$	−12.4528	−1.40105	−0.700527	+	0.713626i	$0.747052\pi$
$80$	−1.56155	−0.174587
$81$	1.00000	0.111111
$82$	10.0507	1.10992
$83$	2.88056	0.316182	0.158091	−	0.987425i	$-0.449466\pi$
$83$	2.88056	0.316182	0.158091	+	0.987425i	$0.449466\pi$
$84$	−1.09168	−0.119112
$85$	0.0774538	0.00840105
$86$	−1.25320	−0.135136
$87$	1.00000	0.107211
$88$	−4.17571	−0.445133
$89$	6.00654	0.636692	0.318346	−	0.947975i	$-0.396873\pi$
$89$	6.00654	0.636692	0.318346	+	0.947975i	$0.396873\pi$
$90$	1.56155	0.164602
$91$	2.55152	0.267472
$92$	1.00000	0.104257
$93$	−0.863232	−0.0895130
$94$	−0.476395	−0.0491364
$95$	−3.87503	−0.397570
$96$	−1.00000	−0.102062
$97$	−1.94736	−0.197724	−0.0988620	−	0.995101i	$-0.531520\pi$
$97$	−1.94736	−0.197724	−0.0988620	+	0.995101i	$0.531520\pi$
$98$	5.80823	0.586720
$99$	4.17571	0.419675
$100$	−2.56155	−0.256155
$101$	−5.25322	−0.522715	−0.261358	−	0.965242i	$-0.584170\pi$
$101$	−5.25322	−0.522715	−0.261358	+	0.965242i	$0.584170\pi$
$102$	0.0496005	0.00491118
$103$	−8.89875	−0.876820	−0.438410	−	0.898775i	$-0.644458\pi$
$103$	−8.89875	−0.876820	−0.438410	+	0.898775i	$0.644458\pi$
$104$	2.33724	0.229185
$105$	1.70472	0.166363
$106$	−12.0862	−1.17391
$107$	13.2016	1.27625	0.638123	−	0.769934i	$-0.279711\pi$
$107$	13.2016	1.27625	0.638123	+	0.769934i	$0.279711\pi$
$108$	1.00000	0.0962250
$109$	8.74896	0.837998	0.418999	−	0.907987i	$-0.362381\pi$
$109$	8.74896	0.837998	0.418999	+	0.907987i	$0.362381\pi$
$110$	6.52060	0.621715
$111$	9.50994	0.902644
$112$	−1.09168	−0.103154
$113$	7.68513	0.722956	0.361478	−	0.932381i	$-0.382272\pi$
$113$	7.68513	0.722956	0.361478	+	0.932381i	$0.382272\pi$
$114$	−2.48153	−0.232416
$115$	−1.56155	−0.145616
$116$	1.00000	0.0928477
$117$	−2.33724	−0.216078
$118$	−1.02075	−0.0939676
$119$	0.0541479	0.00496373
$120$	1.56155	0.142550
$121$	6.43659	0.585144
$122$	−12.5379	−1.13512
$123$	−10.0507	−0.906245
$124$	−0.863232	−0.0775205
$125$	11.8078	1.05612
$126$	1.09168	0.0972546
$127$	8.68622	0.770777	0.385389	−	0.922754i	$-0.374067\pi$
$127$	8.68622	0.770777	0.385389	+	0.922754i	$0.374067\pi$
$128$	−1.00000	−0.0883883
$129$	1.25320	0.110338
$130$	−3.64972	−0.320101
$131$	6.21366	0.542890	0.271445	−	0.962454i	$-0.412498\pi$
$131$	6.21366	0.542890	0.271445	+	0.962454i	$0.412498\pi$
$132$	4.17571	0.363449
$133$	−2.70903	−0.234903
$134$	5.94074	0.513202
$135$	−1.56155	−0.134397
$136$	0.0496005	0.00425321
$137$	−0.911891	−0.0779081	−0.0389541	−	0.999241i	$-0.512403\pi$
$137$	−0.911891	−0.0779081	−0.0389541	+	0.999241i	$0.512403\pi$
$138$	−1.00000	−0.0851257
$139$	−11.2926	−0.957829	−0.478915	−	0.877861i	$-0.658970\pi$
$139$	−11.2926	−0.957829	−0.478915	+	0.877861i	$0.658970\pi$
$140$	1.70472	0.144075
$141$	0.476395	0.0401197
$142$	−4.49876	−0.377528
$143$	−9.75963	−0.816141
$144$	1.00000	0.0833333
$145$	−1.56155	−0.129680
$146$	0.0841599	0.00696512
$147$	−5.80823	−0.479055
$148$	9.50994	0.781712
$149$	23.8180	1.95125	0.975624	−	0.219447i	$-0.0704254\pi$
$149$	23.8180	1.95125	0.975624	+	0.219447i	$0.0704254\pi$
$150$	2.56155	0.209150
$151$	−1.04295	−0.0848742	−0.0424371	−	0.999099i	$-0.513512\pi$
$151$	−1.04295	−0.0848742	−0.0424371	+	0.999099i	$0.513512\pi$
$152$	−2.48153	−0.201278
$153$	−0.0496005	−0.00400996
$154$	4.55855	0.367338
$155$	1.34798	0.108273
$156$	−2.33724	−0.187129
$157$	8.45317	0.674636	0.337318	−	0.941391i	$-0.390480\pi$
$157$	8.45317	0.674636	0.337318	+	0.941391i	$0.390480\pi$
$158$	12.4528	0.990695
$159$	12.0862	0.958495
$160$	1.56155	0.123452
$161$	−1.09168	−0.0860365
$162$	−1.00000	−0.0785674
$163$	−11.2362	−0.880085	−0.440043	−	0.897977i	$-0.645037\pi$
$163$	−11.2362	−0.880085	−0.440043	+	0.897977i	$0.645037\pi$
$164$	−10.0507	−0.784831
$165$	−6.52060	−0.507628
$166$	−2.88056	−0.223575
$167$	21.8033	1.68719	0.843595	−	0.536979i	$-0.180435\pi$
$167$	21.8033	1.68719	0.843595	+	0.536979i	$0.180435\pi$
$168$	1.09168	0.0842250
$169$	−7.53732	−0.579794
$170$	−0.0774538	−0.00594044
$171$	2.48153	0.189767
$172$	1.25320	0.0955559
$173$	19.8579	1.50977	0.754884	−	0.655859i	$-0.227693\pi$
$173$	19.8579	1.50977	0.754884	+	0.655859i	$0.227693\pi$
$174$	−1.00000	−0.0758098
$175$	2.79640	0.211388
$176$	4.17571	0.314756
$177$	1.02075	0.0767242
$178$	−6.00654	−0.450209
$179$	18.8470	1.40869	0.704347	−	0.709856i	$-0.251240\pi$
$179$	18.8470	1.40869	0.704347	+	0.709856i	$0.251240\pi$
$180$	−1.56155	−0.116391
$181$	2.27965	0.169445	0.0847224	−	0.996405i	$-0.473000\pi$
$181$	2.27965	0.169445	0.0847224	+	0.996405i	$0.473000\pi$
$182$	−2.55152	−0.189131
$183$	12.5379	0.926825
$184$	−1.00000	−0.0737210
$185$	−14.8503	−1.09181
$186$	0.863232	0.0632952
$187$	−0.207118	−0.0151459
$188$	0.476395	0.0347447
$189$	−1.09168	−0.0794081
$190$	3.87503	0.281124
$191$	7.53267	0.545045	0.272522	−	0.962149i	$-0.412142\pi$
$191$	7.53267	0.545045	0.272522	+	0.962149i	$0.412142\pi$
$192$	1.00000	0.0721688
$193$	9.96590	0.717361	0.358681	−	0.933460i	$-0.383227\pi$
$193$	9.96590	0.717361	0.358681	+	0.933460i	$0.383227\pi$
$194$	1.94736	0.139812
$195$	3.64972	0.261362
$196$	−5.80823	−0.414874
$197$	26.3071	1.87430	0.937150	−	0.348927i	$-0.113454\pi$
$197$	26.3071	1.87430	0.937150	+	0.348927i	$0.113454\pi$
$198$	−4.17571	−0.296755
$199$	−20.8469	−1.47779	−0.738897	−	0.673818i	$-0.764653\pi$
$199$	−20.8469	−1.47779	−0.738897	+	0.673818i	$0.764653\pi$
$200$	2.56155	0.181129
$201$	−5.94074	−0.419028
$202$	5.25322	0.369616
$203$	−1.09168	−0.0766209
$204$	−0.0496005	−0.00347273
$205$	15.6948	1.09617
$206$	8.89875	0.620006
$207$	1.00000	0.0695048
$208$	−2.33724	−0.162058
$209$	10.3621	0.716764
$210$	−1.70472	−0.117637
$211$	16.2882	1.12132	0.560662	−	0.828045i	$-0.310547\pi$
$211$	16.2882	1.12132	0.560662	+	0.828045i	$0.310547\pi$
$212$	12.0862	0.830081
$213$	4.49876	0.308250
$214$	−13.2016	−0.902442
$215$	−1.95694	−0.133462
$216$	−1.00000	−0.0680414
$217$	0.942373	0.0639725
$218$	−8.74896	−0.592554
$219$	−0.0841599	−0.00568700
$220$	−6.52060	−0.439619
$221$	0.115928	0.00779817
$222$	−9.50994	−0.638266
$223$	25.2440	1.69047	0.845233	−	0.534399i	$-0.179462\pi$
$223$	25.2440	1.69047	0.845233	+	0.534399i	$0.179462\pi$
$224$	1.09168	0.0729410
$225$	−2.56155	−0.170770
$226$	−7.68513	−0.511207
$227$	3.68658	0.244687	0.122343	−	0.992488i	$-0.460959\pi$
$227$	3.68658	0.244687	0.122343	+	0.992488i	$0.460959\pi$
$228$	2.48153	0.164343
$229$	−13.8676	−0.916399	−0.458200	−	0.888849i	$-0.651506\pi$
$229$	−13.8676	−0.916399	−0.458200	+	0.888849i	$0.651506\pi$
$230$	1.56155	0.102966
$231$	−4.55855	−0.299930
$232$	−1.00000	−0.0656532
$233$	−7.48280	−0.490214	−0.245107	−	0.969496i	$-0.578823\pi$
$233$	−7.48280	−0.490214	−0.245107	+	0.969496i	$0.578823\pi$
$234$	2.33724	0.152790
$235$	−0.743916	−0.0485277
$236$	1.02075	0.0664451
$237$	−12.4528	−0.808899
$238$	−0.0541479	−0.00350989
$239$	−7.00761	−0.453285	−0.226642	−	0.973978i	$-0.572775\pi$
$239$	−7.00761	−0.453285	−0.226642	+	0.973978i	$0.572775\pi$
$240$	−1.56155	−0.100798
$241$	−11.6699	−0.751722	−0.375861	−	0.926676i	$-0.622653\pi$
$241$	−11.6699	−0.751722	−0.375861	+	0.926676i	$0.622653\pi$
$242$	−6.43659	−0.413759
$243$	1.00000	0.0641500
$244$	12.5379	0.802654
$245$	9.06986	0.579452
$246$	10.0507	0.640812
$247$	−5.79991	−0.369040
$248$	0.863232	0.0548153
$249$	2.88056	0.182548
$250$	−11.8078	−0.746789
$251$	−11.2276	−0.708681	−0.354341	−	0.935116i	$-0.615295\pi$
$251$	−11.2276	−0.708681	−0.354341	+	0.935116i	$0.615295\pi$
$252$	−1.09168	−0.0687694
$253$	4.17571	0.262525
$254$	−8.68622	−0.545022
$255$	0.0774538	0.00485035
$256$	1.00000	0.0625000
$257$	10.5404	0.657494	0.328747	−	0.944418i	$-0.393374\pi$
$257$	10.5404	0.657494	0.328747	+	0.944418i	$0.393374\pi$
$258$	−1.25320	−0.0780210
$259$	−10.3818	−0.645095
$260$	3.64972	0.226346
$261$	1.00000	0.0618984
$262$	−6.21366	−0.383881
$263$	8.49927	0.524087	0.262044	−	0.965056i	$-0.415604\pi$
$263$	8.49927	0.524087	0.262044	+	0.965056i	$0.415604\pi$
$264$	−4.17571	−0.256997
$265$	−18.8732	−1.15937
$266$	2.70903	0.166101
$267$	6.00654	0.367595
$268$	−5.94074	−0.362889
$269$	21.0059	1.28075	0.640375	−	0.768062i	$-0.278779\pi$
$269$	21.0059	1.28075	0.640375	+	0.768062i	$0.278779\pi$
$270$	1.56155	0.0950331
$271$	−12.1608	−0.738713	−0.369356	−	0.929288i	$-0.620422\pi$
$271$	−12.1608	−0.738713	−0.369356	+	0.929288i	$0.620422\pi$
$272$	−0.0496005	−0.00300747
$273$	2.55152	0.154425
$274$	0.911891	0.0550894
$275$	−10.6963	−0.645012
$276$	1.00000	0.0601929
$277$	−17.4450	−1.04817	−0.524086	−	0.851666i	$-0.675593\pi$
$277$	−17.4450	−1.04817	−0.524086	+	0.851666i	$0.675593\pi$
$278$	11.2926	0.677288
$279$	−0.863232	−0.0516803
$280$	−1.70472	−0.101876
$281$	−7.84868	−0.468213	−0.234107	−	0.972211i	$-0.575216\pi$
$281$	−7.84868	−0.468213	−0.234107	+	0.972211i	$0.575216\pi$
$282$	−0.476395	−0.0283689
$283$	12.7594	0.758468	0.379234	−	0.925301i	$-0.376187\pi$
$283$	12.7594	0.758468	0.379234	+	0.925301i	$0.376187\pi$
$284$	4.49876	0.266952
$285$	−3.87503	−0.229537
$286$	9.75963	0.577099
$287$	10.9722	0.647669
$288$	−1.00000	−0.0589256
$289$	−16.9975	−0.999855
$290$	1.56155	0.0916975
$291$	−1.94736	−0.114156
$292$	−0.0841599	−0.00492508
$293$	−28.2425	−1.64995	−0.824973	−	0.565171i	$-0.808810\pi$
$293$	−28.2425	−1.64995	−0.824973	+	0.565171i	$0.808810\pi$
$294$	5.80823	0.338743
$295$	−1.59395	−0.0928036
$296$	−9.50994	−0.552754
$297$	4.17571	0.242299
$298$	−23.8180	−1.37974
$299$	−2.33724	−0.135166
$300$	−2.56155	−0.147891
$301$	−1.36810	−0.0788558
$302$	1.04295	0.0600151
$303$	−5.25322	−0.301790
$304$	2.48153	0.142325
$305$	−19.5785	−1.12106
$306$	0.0496005	0.00283547
$307$	27.0167	1.54192	0.770962	−	0.636881i	$-0.219776\pi$
$307$	27.0167	1.54192	0.770962	+	0.636881i	$0.219776\pi$
$308$	−4.55855	−0.259747
$309$	−8.89875	−0.506232
$310$	−1.34798	−0.0765602
$311$	−19.8500	−1.12559	−0.562794	−	0.826597i	$-0.690274\pi$
$311$	−19.8500	−1.12559	−0.562794	+	0.826597i	$0.690274\pi$
$312$	2.33724	0.132320
$313$	22.0844	1.24829	0.624143	−	0.781310i	$-0.285448\pi$
$313$	22.0844	1.24829	0.624143	+	0.781310i	$0.285448\pi$
$314$	−8.45317	−0.477040
$315$	1.70472	0.0960499
$316$	−12.4528	−0.700527
$317$	−14.4579	−0.812034	−0.406017	−	0.913865i	$-0.633083\pi$
$317$	−14.4579	−0.812034	−0.406017	+	0.913865i	$0.633083\pi$
$318$	−12.0862	−0.677758
$319$	4.17571	0.233795
$320$	−1.56155	−0.0872935
$321$	13.2016	0.736841
$322$	1.09168	0.0608370
$323$	−0.123085	−0.00684863
$324$	1.00000	0.0555556
$325$	5.98696	0.332097
$326$	11.2362	0.622314
$327$	8.74896	0.483818
$328$	10.0507	0.554960
$329$	−0.520071	−0.0286724
$330$	6.52060	0.358947
$331$	11.8220	0.649793	0.324897	−	0.945750i	$-0.394670\pi$
$331$	11.8220	0.649793	0.324897	+	0.945750i	$0.394670\pi$
$332$	2.88056	0.158091
$333$	9.50994	0.521142
$334$	−21.8033	−1.19302
$335$	9.27678	0.506845
$336$	−1.09168	−0.0595561
$337$	23.0539	1.25583	0.627914	−	0.778283i	$-0.283909\pi$
$337$	23.0539	1.25583	0.627914	+	0.778283i	$0.283909\pi$
$338$	7.53732	0.409976
$339$	7.68513	0.417399
$340$	0.0774538	0.00420052
$341$	−3.60461	−0.195201
$342$	−2.48153	−0.134186
$343$	13.9825	0.754984
$344$	−1.25320	−0.0675682
$345$	−1.56155	−0.0840712
$346$	−19.8579	−1.06757
$347$	7.83831	0.420783	0.210391	−	0.977617i	$-0.432526\pi$
$347$	7.83831	0.420783	0.210391	+	0.977617i	$0.432526\pi$
$348$	1.00000	0.0536056
$349$	31.4883	1.68553	0.842764	−	0.538283i	$-0.180927\pi$
$349$	31.4883	1.68553	0.842764	+	0.538283i	$0.180927\pi$
$350$	−2.79640	−0.149474
$351$	−2.33724	−0.124752
$352$	−4.17571	−0.222566
$353$	−18.5107	−0.985223	−0.492611	−	0.870249i	$-0.663958\pi$
$353$	−18.5107	−0.985223	−0.492611	+	0.870249i	$0.663958\pi$
$354$	−1.02075	−0.0542522
$355$	−7.02505	−0.372851
$356$	6.00654	0.318346
$357$	0.0541479	0.00286581
$358$	−18.8470	−0.996097
$359$	14.0031	0.739056	0.369528	−	0.929220i	$-0.379519\pi$
$359$	14.0031	0.739056	0.369528	+	0.929220i	$0.379519\pi$
$360$	1.56155	0.0823011
$361$	−12.8420	−0.675896
$362$	−2.27965	−0.119816
$363$	6.43659	0.337833
$364$	2.55152	0.133736
$365$	0.131420	0.00687884
$366$	−12.5379	−0.655364
$367$	−7.29534	−0.380814	−0.190407	−	0.981705i	$-0.560981\pi$
$367$	−7.29534	−0.380814	−0.190407	+	0.981705i	$0.560981\pi$
$368$	1.00000	0.0521286
$369$	−10.0507	−0.523221
$370$	14.8503	0.772029
$371$	−13.1942	−0.685010
$372$	−0.863232	−0.0447565
$373$	10.4473	0.540939	0.270469	−	0.962729i	$-0.412821\pi$
$373$	10.4473	0.540939	0.270469	+	0.962729i	$0.412821\pi$
$374$	0.207118	0.0107098
$375$	11.8078	0.609750
$376$	−0.476395	−0.0245682
$377$	−2.33724	−0.120374
$378$	1.09168	0.0561500
$379$	−23.0878	−1.18594	−0.592969	−	0.805225i	$-0.702044\pi$
$379$	−23.0878	−1.18594	−0.592969	+	0.805225i	$0.702044\pi$
$380$	−3.87503	−0.198785
$381$	8.68622	0.445008
$382$	−7.53267	−0.385405
$383$	−0.256923	−0.0131282	−0.00656408	−	0.999978i	$-0.502089\pi$
$383$	−0.256923	−0.0131282	−0.00656408	+	0.999978i	$0.502089\pi$
$384$	−1.00000	−0.0510310
$385$	7.11841	0.362788
$386$	−9.96590	−0.507251
$387$	1.25320	0.0637039
$388$	−1.94736	−0.0988620
$389$	7.92122	0.401622	0.200811	−	0.979630i	$-0.435642\pi$
$389$	7.92122	0.401622	0.200811	+	0.979630i	$0.435642\pi$
$390$	−3.64972	−0.184811
$391$	−0.0496005	−0.00250841
$392$	5.80823	0.293360
$393$	6.21366	0.313438
$394$	−26.3071	−1.32533
$395$	19.4458	0.978423
$396$	4.17571	0.209838
$397$	1.32515	0.0665072	0.0332536	−	0.999447i	$-0.489413\pi$
$397$	1.32515	0.0665072	0.0332536	+	0.999447i	$0.489413\pi$
$398$	20.8469	1.04496
$399$	−2.70903	−0.135621
$400$	−2.56155	−0.128078
$401$	−12.8447	−0.641433	−0.320716	−	0.947175i	$-0.603924\pi$
$401$	−12.8447	−0.641433	−0.320716	+	0.947175i	$0.603924\pi$
$402$	5.94074	0.296297
$403$	2.01758	0.100503
$404$	−5.25322	−0.261358
$405$	−1.56155	−0.0775942
$406$	1.09168	0.0541792
$407$	39.7108	1.96839
$408$	0.0496005	0.00245559
$409$	19.8318	0.980618	0.490309	−	0.871549i	$-0.336884\pi$
$409$	19.8318	0.980618	0.490309	+	0.871549i	$0.336884\pi$
$410$	−15.6948	−0.775110
$411$	−0.911891	−0.0449803
$412$	−8.89875	−0.438410
$413$	−1.11433	−0.0548327
$414$	−1.00000	−0.0491473
$415$	−4.49814	−0.220805
$416$	2.33724	0.114592
$417$	−11.2926	−0.553003
$418$	−10.3621	−0.506829
$419$	−26.4475	−1.29205	−0.646023	−	0.763318i	$-0.723569\pi$
$419$	−26.4475	−1.29205	−0.646023	+	0.763318i	$0.723569\pi$
$420$	1.70472	0.0831817
$421$	−30.6760	−1.49505	−0.747527	−	0.664231i	$-0.768759\pi$
$421$	−30.6760	−1.49505	−0.747527	+	0.664231i	$0.768759\pi$
$422$	−16.2882	−0.792895
$423$	0.476395	0.0231631
$424$	−12.0862	−0.586956
$425$	0.127054	0.00616304
$426$	−4.49876	−0.217966
$427$	−13.6873	−0.662376
$428$	13.2016	0.638123
$429$	−9.75963	−0.471199
$430$	1.95694	0.0943722
$431$	7.12066	0.342990	0.171495	−	0.985185i	$-0.445140\pi$
$431$	7.12066	0.342990	0.171495	+	0.985185i	$0.445140\pi$
$432$	1.00000	0.0481125
$433$	−16.3538	−0.785914	−0.392957	−	0.919557i	$-0.628548\pi$
$433$	−16.3538	−0.785914	−0.392957	+	0.919557i	$0.628548\pi$
$434$	−0.942373	−0.0452354
$435$	−1.56155	−0.0748707
$436$	8.74896	0.418999
$437$	2.48153	0.118707
$438$	0.0841599	0.00402131
$439$	1.08369	0.0517216	0.0258608	−	0.999666i	$-0.491767\pi$
$439$	1.08369	0.0517216	0.0258608	+	0.999666i	$0.491767\pi$
$440$	6.52060	0.310857
$441$	−5.80823	−0.276583
$442$	−0.115928	−0.00551414
$443$	33.3307	1.58359	0.791794	−	0.610788i	$-0.209147\pi$
$443$	33.3307	1.58359	0.791794	+	0.610788i	$0.209147\pi$
$444$	9.50994	0.451322
$445$	−9.37954	−0.444633
$446$	−25.2440	−1.19534
$447$	23.8180	1.12655
$448$	−1.09168	−0.0515771
$449$	28.8753	1.36271	0.681356	−	0.731952i	$-0.261391\pi$
$449$	28.8753	1.36271	0.681356	+	0.731952i	$0.261391\pi$
$450$	2.56155	0.120753
$451$	−41.9690	−1.97624
$452$	7.68513	0.361478
$453$	−1.04295	−0.0490021
$454$	−3.68658	−0.173020
$455$	−3.98433	−0.186788
$456$	−2.48153	−0.116208
$457$	17.8905	0.836883	0.418442	−	0.908244i	$-0.362576\pi$
$457$	17.8905	0.836883	0.418442	+	0.908244i	$0.362576\pi$
$458$	13.8676	0.647992
$459$	−0.0496005	−0.00231515
$460$	−1.56155	−0.0728078
$461$	13.3187	0.620314	0.310157	−	0.950685i	$-0.399618\pi$
$461$	13.3187	0.620314	0.310157	+	0.950685i	$0.399618\pi$
$462$	4.55855	0.212083
$463$	34.3982	1.59862	0.799309	−	0.600920i	$-0.205199\pi$
$463$	34.3982	1.59862	0.799309	+	0.600920i	$0.205199\pi$
$464$	1.00000	0.0464238
$465$	1.34798	0.0625112
$466$	7.48280	0.346634
$467$	−1.96503	−0.0909307	−0.0454653	−	0.998966i	$-0.514477\pi$
$467$	−1.96503	−0.0909307	−0.0454653	+	0.998966i	$0.514477\pi$
$468$	−2.33724	−0.108039
$469$	6.48539	0.299468
$470$	0.743916	0.0343143
$471$	8.45317	0.389501
$472$	−1.02075	−0.0469838
$473$	5.23302	0.240614
$474$	12.4528	0.571978
$475$	−6.35656	−0.291659
$476$	0.0541479	0.00248187
$477$	12.0862	0.553387
$478$	7.00761	0.320521
$479$	−39.6404	−1.81122	−0.905608	−	0.424115i	$-0.860585\pi$
$479$	−39.6404	−1.81122	−0.905608	+	0.424115i	$0.860585\pi$
$480$	1.56155	0.0712748
$481$	−22.2270	−1.01346
$482$	11.6699	0.531548
$483$	−1.09168	−0.0496732
$484$	6.43659	0.292572
$485$	3.04090	0.138080
$486$	−1.00000	−0.0453609
$487$	−3.79426	−0.171934	−0.0859672	−	0.996298i	$-0.527398\pi$
$487$	−3.79426	−0.171934	−0.0859672	+	0.996298i	$0.527398\pi$
$488$	−12.5379	−0.567562
$489$	−11.2362	−0.508117
$490$	−9.06986	−0.409735
$491$	11.5859	0.522865	0.261432	−	0.965222i	$-0.415805\pi$
$491$	11.5859	0.522865	0.261432	+	0.965222i	$0.415805\pi$
$492$	−10.0507	−0.453123
$493$	−0.0496005	−0.00223390
$494$	5.79991	0.260950
$495$	−6.52060	−0.293079
$496$	−0.863232	−0.0387603
$497$	−4.91121	−0.220298
$498$	−2.88056	−0.129081
$499$	17.2466	0.772063	0.386032	−	0.922485i	$-0.373846\pi$
$499$	17.2466	0.772063	0.386032	+	0.922485i	$0.373846\pi$
$500$	11.8078	0.528059
$501$	21.8033	0.974100
$502$	11.2276	0.501113
$503$	3.11973	0.139102	0.0695510	−	0.997578i	$-0.477843\pi$
$503$	3.11973	0.139102	0.0695510	+	0.997578i	$0.477843\pi$
$504$	1.09168	0.0486273
$505$	8.20319	0.365037
$506$	−4.17571	−0.185633
$507$	−7.53732	−0.334744
$508$	8.68622	0.385389
$509$	−32.6519	−1.44727	−0.723636	−	0.690182i	$-0.757530\pi$
$509$	−32.6519	−1.44727	−0.723636	+	0.690182i	$0.757530\pi$
$510$	−0.0774538	−0.00342971
$511$	0.0918757	0.00406434
$512$	−1.00000	−0.0441942
$513$	2.48153	0.109562
$514$	−10.5404	−0.464918
$515$	13.8959	0.612325
$516$	1.25320	0.0551692
$517$	1.98929	0.0874888
$518$	10.3818	0.456151
$519$	19.8579	0.871665
$520$	−3.64972	−0.160051
$521$	31.6386	1.38611	0.693056	−	0.720884i	$-0.256264\pi$
$521$	31.6386	1.38611	0.693056	+	0.720884i	$0.256264\pi$
$522$	−1.00000	−0.0437688
$523$	−2.36350	−0.103348	−0.0516742	−	0.998664i	$-0.516456\pi$
$523$	−2.36350	−0.103348	−0.0516742	+	0.998664i	$0.516456\pi$
$524$	6.21366	0.271445
$525$	2.79640	0.122045
$526$	−8.49927	−0.370586
$527$	0.0428168	0.00186513
$528$	4.17571	0.181725
$529$	1.00000	0.0434783
$530$	18.8732	0.819798
$531$	1.02075	0.0442967
$532$	−2.70903	−0.117451
$533$	23.4910	1.01751
$534$	−6.00654	−0.259929
$535$	−20.6150	−0.891264
$536$	5.94074	0.256601
$537$	18.8470	0.813310
$538$	−21.0059	−0.905628
$539$	−24.2535	−1.04467
$540$	−1.56155	−0.0671985
$541$	5.29517	0.227657	0.113829	−	0.993500i	$-0.463689\pi$
$541$	5.29517	0.227657	0.113829	+	0.993500i	$0.463689\pi$
$542$	12.1608	0.522349
$543$	2.27965	0.0978290
$544$	0.0496005	0.00212661
$545$	−13.6620	−0.585214
$546$	−2.55152	−0.109195
$547$	8.49153	0.363071	0.181536	−	0.983384i	$-0.441893\pi$
$547$	8.49153	0.363071	0.181536	+	0.983384i	$0.441893\pi$
$548$	−0.911891	−0.0389541
$549$	12.5379	0.535103
$550$	10.6963	0.456092
$551$	2.48153	0.105717
$552$	−1.00000	−0.0425628
$553$	13.5945	0.578098
$554$	17.4450	0.741169
$555$	−14.8503	−0.630359
$556$	−11.2926	−0.478915
$557$	28.0884	1.19014	0.595071	−	0.803673i	$-0.297124\pi$
$557$	28.0884	1.19014	0.595071	+	0.803673i	$0.297124\pi$
$558$	0.863232	0.0365435
$559$	−2.92903	−0.123885
$560$	1.70472	0.0720374
$561$	−0.207118	−0.00874451
$562$	7.84868	0.331077
$563$	−25.3800	−1.06964	−0.534820	−	0.844966i	$-0.679621\pi$
$563$	−25.3800	−1.06964	−0.534820	+	0.844966i	$0.679621\pi$
$564$	0.476395	0.0200598
$565$	−12.0007	−0.504875
$566$	−12.7594	−0.536318
$567$	−1.09168	−0.0458463
$568$	−4.49876	−0.188764
$569$	−39.3891	−1.65128	−0.825638	−	0.564201i	$-0.809184\pi$
$569$	−39.3891	−1.65128	−0.825638	+	0.564201i	$0.809184\pi$
$570$	3.87503	0.162307
$571$	−21.0685	−0.881689	−0.440845	−	0.897583i	$-0.645321\pi$
$571$	−21.0685	−0.881689	−0.440845	+	0.897583i	$0.645321\pi$
$572$	−9.75963	−0.408071
$573$	7.53267	0.314682
$574$	−10.9722	−0.457971
$575$	−2.56155	−0.106824
$576$	1.00000	0.0416667
$577$	12.3825	0.515491	0.257745	−	0.966213i	$-0.417020\pi$
$577$	12.3825	0.515491	0.257745	+	0.966213i	$0.417020\pi$
$578$	16.9975	0.707004
$579$	9.96590	0.414169
$580$	−1.56155	−0.0648400
$581$	−3.14465	−0.130462
$582$	1.94736	0.0807205
$583$	50.4683	2.09018
$584$	0.0841599	0.00348256
$585$	3.64972	0.150897
$586$	28.2425	1.16669
$587$	−25.5585	−1.05491	−0.527456	−	0.849583i	$-0.676854\pi$
$587$	−25.5585	−1.05491	−0.527456	+	0.849583i	$0.676854\pi$
$588$	−5.80823	−0.239528
$589$	−2.14213	−0.0882650
$590$	1.59395	0.0656220
$591$	26.3071	1.08213
$592$	9.50994	0.390856
$593$	−3.82566	−0.157101	−0.0785506	−	0.996910i	$-0.525029\pi$
$593$	−3.82566	−0.157101	−0.0785506	+	0.996910i	$0.525029\pi$
$594$	−4.17571	−0.171332
$595$	−0.0845548	−0.00346641
$596$	23.8180	0.975624
$597$	−20.8469	−0.853205
$598$	2.33724	0.0955767
$599$	11.6902	0.477650	0.238825	−	0.971063i	$-0.423238\pi$
$599$	11.6902	0.477650	0.238825	+	0.971063i	$0.423238\pi$
$600$	2.56155	0.104575
$601$	−0.585128	−0.0238679	−0.0119339	−	0.999929i	$-0.503799\pi$
$601$	−0.585128	−0.0238679	−0.0119339	+	0.999929i	$0.503799\pi$
$602$	1.36810	0.0557595
$603$	−5.94074	−0.241926
$604$	−1.04295	−0.0424371
$605$	−10.0511	−0.408634
$606$	5.25322	0.213398
$607$	39.8131	1.61596	0.807981	−	0.589208i	$-0.200560\pi$
$607$	39.8131	1.61596	0.807981	+	0.589208i	$0.200560\pi$
$608$	−2.48153	−0.100639
$609$	−1.09168	−0.0442371
$610$	19.5785	0.792711
$611$	−1.11345	−0.0450453
$612$	−0.0496005	−0.00200498
$613$	−1.27058	−0.0513184	−0.0256592	−	0.999671i	$-0.508168\pi$
$613$	−1.27058	−0.0513184	−0.0256592	+	0.999671i	$0.508168\pi$
$614$	−27.0167	−1.09031
$615$	15.6948	0.632874
$616$	4.55855	0.183669
$617$	−33.8494	−1.36273	−0.681363	−	0.731946i	$-0.738612\pi$
$617$	−33.8494	−1.36273	−0.681363	+	0.731946i	$0.738612\pi$
$618$	8.89875	0.357960
$619$	−15.4618	−0.621463	−0.310732	−	0.950498i	$-0.600574\pi$
$619$	−15.4618	−0.621463	−0.310732	+	0.950498i	$0.600574\pi$
$620$	1.34798	0.0541363
$621$	1.00000	0.0401286
$622$	19.8500	0.795911
$623$	−6.55723	−0.262710
$624$	−2.33724	−0.0935643
$625$	−5.63068	−0.225227
$626$	−22.0844	−0.882672
$627$	10.3621	0.413824
$628$	8.45317	0.337318
$629$	−0.471698	−0.0188078
$630$	−1.70472	−0.0679175
$631$	46.4443	1.84892	0.924458	−	0.381283i	$-0.124518\pi$
$631$	46.4443	1.84892	0.924458	+	0.381283i	$0.124518\pi$
$632$	12.4528	0.495348
$633$	16.2882	0.647396
$634$	14.4579	0.574195
$635$	−13.5640	−0.538270
$636$	12.0862	0.479247
$637$	13.5752	0.537870
$638$	−4.17571	−0.165318
$639$	4.49876	0.177968
$640$	1.56155	0.0617258
$641$	−22.8093	−0.900913	−0.450456	−	0.892798i	$-0.648739\pi$
$641$	−22.8093	−0.900913	−0.450456	+	0.892798i	$0.648739\pi$
$642$	−13.2016	−0.521025
$643$	−24.7068	−0.974341	−0.487170	−	0.873307i	$-0.661971\pi$
$643$	−24.7068	−0.974341	−0.487170	+	0.873307i	$0.661971\pi$
$644$	−1.09168	−0.0430182
$645$	−1.95694	−0.0770546
$646$	0.123085	0.00484271
$647$	45.9049	1.80471	0.902354	−	0.430997i	$-0.141838\pi$
$647$	45.9049	1.80471	0.902354	+	0.430997i	$0.141838\pi$
$648$	−1.00000	−0.0392837
$649$	4.26236	0.167312
$650$	−5.98696	−0.234828
$651$	0.942373	0.0369345
$652$	−11.2362	−0.440043
$653$	5.69081	0.222699	0.111349	−	0.993781i	$-0.464483\pi$
$653$	5.69081	0.222699	0.111349	+	0.993781i	$0.464483\pi$
$654$	−8.74896	−0.342111
$655$	−9.70296	−0.379126
$656$	−10.0507	−0.392416
$657$	−0.0841599	−0.00328339
$658$	0.520071	0.0202745
$659$	27.7285	1.08015	0.540074	−	0.841617i	$-0.318396\pi$
$659$	27.7285	1.08015	0.540074	+	0.841617i	$0.318396\pi$
$660$	−6.52060	−0.253814
$661$	33.7073	1.31106	0.655532	−	0.755168i	$-0.272444\pi$
$661$	33.7073	1.31106	0.655532	+	0.755168i	$0.272444\pi$
$662$	−11.8220	−0.459473
$663$	0.115928	0.00450228
$664$	−2.88056	−0.111787
$665$	4.23030	0.164044
$666$	−9.50994	−0.368503
$667$	1.00000	0.0387202
$668$	21.8033	0.843595
$669$	25.2440	0.975990
$670$	−9.27678	−0.358393
$671$	52.3545	2.02112
$672$	1.09168	0.0421125
$673$	−45.6883	−1.76116	−0.880578	−	0.473902i	$-0.842845\pi$
$673$	−45.6883	−1.76116	−0.880578	+	0.473902i	$0.842845\pi$
$674$	−23.0539	−0.888005
$675$	−2.56155	−0.0985942
$676$	−7.53732	−0.289897
$677$	−20.8448	−0.801133	−0.400566	−	0.916268i	$-0.631187\pi$
$677$	−20.8448	−0.801133	−0.400566	+	0.916268i	$0.631187\pi$
$678$	−7.68513	−0.295146
$679$	2.12589	0.0815842
$680$	−0.0774538	−0.00297022
$681$	3.68658	0.141270
$682$	3.60461	0.138028
$683$	−13.1760	−0.504167	−0.252083	−	0.967706i	$-0.581116\pi$
$683$	−13.1760	−0.504167	−0.252083	+	0.967706i	$0.581116\pi$
$684$	2.48153	0.0948835
$685$	1.42397	0.0544070
$686$	−13.9825	−0.533854
$687$	−13.8676	−0.529083
$688$	1.25320	0.0477779
$689$	−28.2482	−1.07617
$690$	1.56155	0.0594473
$691$	−7.77578	−0.295804	−0.147902	−	0.989002i	$-0.547252\pi$
$691$	−7.77578	−0.295804	−0.147902	+	0.989002i	$0.547252\pi$
$692$	19.8579	0.754884
$693$	−4.55855	−0.173165
$694$	−7.83831	−0.297538
$695$	17.6341	0.668898
$696$	−1.00000	−0.0379049
$697$	0.498522	0.0188829
$698$	−31.4883	−1.19185
$699$	−7.48280	−0.283025
$700$	2.79640	0.105694
$701$	−17.8604	−0.674578	−0.337289	−	0.941401i	$-0.609510\pi$
$701$	−17.8604	−0.674578	−0.337289	+	0.941401i	$0.609510\pi$
$702$	2.33724	0.0882133
$703$	23.5992	0.890059
$704$	4.17571	0.157378
$705$	−0.743916	−0.0280175
$706$	18.5107	0.696658
$707$	5.73484	0.215681
$708$	1.02075	0.0383621
$709$	22.5614	0.847312	0.423656	−	0.905823i	$-0.360747\pi$
$709$	22.5614	0.847312	0.423656	+	0.905823i	$0.360747\pi$
$710$	7.02505	0.263645
$711$	−12.4528	−0.467018
$712$	−6.00654	−0.225105
$713$	−0.863232	−0.0323283
$714$	−0.0541479	−0.00202644
$715$	15.2402	0.569950
$716$	18.8470	0.704347
$717$	−7.00761	−0.261704
$718$	−14.0031	−0.522592
$719$	−33.2124	−1.23861	−0.619306	−	0.785150i	$-0.712586\pi$
$719$	−33.2124	−1.23861	−0.619306	+	0.785150i	$0.712586\pi$
$720$	−1.56155	−0.0581956
$721$	9.71460	0.361790
$722$	12.8420	0.477931
$723$	−11.6699	−0.434007
$724$	2.27965	0.0847224
$725$	−2.56155	−0.0951337
$726$	−6.43659	−0.238884
$727$	−22.1393	−0.821100	−0.410550	−	0.911838i	$-0.634663\pi$
$727$	−22.1393	−0.821100	−0.410550	+	0.911838i	$0.634663\pi$
$728$	−2.55152	−0.0945655
$729$	1.00000	0.0370370
$730$	−0.131420	−0.00486408
$731$	−0.0621595	−0.00229905
$732$	12.5379	0.463412
$733$	5.72493	0.211455	0.105728	−	0.994395i	$-0.466283\pi$
$733$	5.72493	0.211455	0.105728	+	0.994395i	$0.466283\pi$
$734$	7.29534	0.269276
$735$	9.06986	0.334547
$736$	−1.00000	−0.0368605
$737$	−24.8068	−0.913772
$738$	10.0507	0.369973
$739$	−44.3614	−1.63186	−0.815931	−	0.578149i	$-0.803775\pi$
$739$	−44.3614	−1.63186	−0.815931	+	0.578149i	$0.803775\pi$
$740$	−14.8503	−0.545907
$741$	−5.79991	−0.213065
$742$	13.1942	0.484375
$743$	−7.11662	−0.261083	−0.130542	−	0.991443i	$-0.541672\pi$
$743$	−7.11662	−0.261083	−0.130542	+	0.991443i	$0.541672\pi$
$744$	0.863232	0.0316476
$745$	−37.1931	−1.36265
$746$	−10.4473	−0.382501
$747$	2.88056	0.105394
$748$	−0.207118	−0.00757297
$749$	−14.4119	−0.526600
$750$	−11.8078	−0.431159
$751$	13.2716	0.484289	0.242144	−	0.970240i	$-0.422149\pi$
$751$	13.2716	0.484289	0.242144	+	0.970240i	$0.422149\pi$
$752$	0.476395	0.0173723
$753$	−11.2276	−0.409157
$754$	2.33724	0.0851171
$755$	1.62862	0.0592717
$756$	−1.09168	−0.0397040
$757$	−18.2769	−0.664285	−0.332142	−	0.943229i	$-0.607771\pi$
$757$	−18.2769	−0.664285	−0.332142	+	0.943229i	$0.607771\pi$
$758$	23.0878	0.838585
$759$	4.17571	0.151569
$760$	3.87503	0.140562
$761$	−13.2747	−0.481207	−0.240604	−	0.970623i	$-0.577345\pi$
$761$	−13.2747	−0.481207	−0.240604	+	0.970623i	$0.577345\pi$
$762$	−8.68622	−0.314668
$763$	−9.55106	−0.345772
$764$	7.53267	0.272522
$765$	0.0774538	0.00280035
$766$	0.256923	0.00928301
$767$	−2.38573	−0.0861438
$768$	1.00000	0.0360844
$769$	14.3944	0.519076	0.259538	−	0.965733i	$-0.416430\pi$
$769$	14.3944	0.519076	0.259538	+	0.965733i	$0.416430\pi$
$770$	−7.11841	−0.256530
$771$	10.5404	0.379604
$772$	9.96590	0.358681
$773$	−16.6515	−0.598911	−0.299456	−	0.954110i	$-0.596805\pi$
$773$	−16.6515	−0.598911	−0.299456	+	0.954110i	$0.596805\pi$
$774$	−1.25320	−0.0450455
$775$	2.21121	0.0794292
$776$	1.94736	0.0699060
$777$	−10.3818	−0.372446
$778$	−7.92122	−0.283990
$779$	−24.9412	−0.893611
$780$	3.64972	0.130681
$781$	18.7855	0.672199
$782$	0.0496005	0.00177371
$783$	1.00000	0.0357371
$784$	−5.80823	−0.207437
$785$	−13.2001	−0.471131
$786$	−6.21366	−0.221634
$787$	−19.4411	−0.693000	−0.346500	−	0.938050i	$-0.612630\pi$
$787$	−19.4411	−0.693000	−0.346500	+	0.938050i	$0.612630\pi$
$788$	26.3071	0.937150
$789$	8.49927	0.302582
$790$	−19.4458	−0.691850
$791$	−8.38970	−0.298304
$792$	−4.17571	−0.148378
$793$	−29.3039	−1.04061
$794$	−1.32515	−0.0470277
$795$	−18.8732	−0.669362
$796$	−20.8469	−0.738897
$797$	−27.3744	−0.969650	−0.484825	−	0.874611i	$-0.661117\pi$
$797$	−27.3744	−0.969650	−0.484825	+	0.874611i	$0.661117\pi$
$798$	2.70903	0.0958987
$799$	−0.0236294	−0.000835949 0
$800$	2.56155	0.0905646
$801$	6.00654	0.212231
$802$	12.8447	0.453561
$803$	−0.351428	−0.0124016
$804$	−5.94074	−0.209514
$805$	1.70472	0.0600834
$806$	−2.01758	−0.0710661
$807$	21.0059	0.739442
$808$	5.25322	0.184808
$809$	−45.9317	−1.61487	−0.807436	−	0.589955i	$-0.799146\pi$
$809$	−45.9317	−1.61487	−0.807436	+	0.589955i	$0.799146\pi$
$810$	1.56155	0.0548674
$811$	−17.6878	−0.621102	−0.310551	−	0.950557i	$-0.600514\pi$
$811$	−17.6878	−0.621102	−0.310551	+	0.950557i	$0.600514\pi$
$812$	−1.09168	−0.0383105
$813$	−12.1608	−0.426496
$814$	−39.7108	−1.39186
$815$	17.5459	0.614605
$816$	−0.0496005	−0.00173637
$817$	3.10986	0.108800
$818$	−19.8318	−0.693402
$819$	2.55152	0.0891572
$820$	15.6948	0.548085
$821$	11.3307	0.395443	0.197722	−	0.980258i	$-0.436646\pi$
$821$	11.3307	0.395443	0.197722	+	0.980258i	$0.436646\pi$
$822$	0.911891	0.0318059
$823$	−2.61686	−0.0912180	−0.0456090	−	0.998959i	$-0.514523\pi$
$823$	−2.61686	−0.0912180	−0.0456090	+	0.998959i	$0.514523\pi$
$824$	8.89875	0.310003
$825$	−10.6963	−0.372398
$826$	1.11433	0.0387726
$827$	9.62649	0.334746	0.167373	−	0.985894i	$-0.446472\pi$
$827$	9.62649	0.334746	0.167373	+	0.985894i	$0.446472\pi$
$828$	1.00000	0.0347524
$829$	21.8914	0.760319	0.380160	−	0.924921i	$-0.375869\pi$
$829$	21.8914	0.760319	0.380160	+	0.924921i	$0.375869\pi$
$830$	4.49814	0.156133
$831$	−17.4450	−0.605162
$832$	−2.33724	−0.0810291
$833$	0.288091	0.00998178
$834$	11.2926	0.391032
$835$	−34.0470	−1.17825
$836$	10.3621	0.358382
$837$	−0.863232	−0.0298377
$838$	26.4475	0.913614
$839$	23.5229	0.812102	0.406051	−	0.913850i	$-0.366906\pi$
$839$	23.5229	0.812102	0.406051	+	0.913850i	$0.366906\pi$
$840$	−1.70472	−0.0588183
$841$	1.00000	0.0344828
$842$	30.6760	1.05716
$843$	−7.84868	−0.270323
$844$	16.2882	0.560662
$845$	11.7699	0.404898
$846$	−0.476395	−0.0163788
$847$	−7.02669	−0.241440
$848$	12.0862	0.415040
$849$	12.7594	0.437902
$850$	−0.127054	−0.00435793
$851$	9.50994	0.325997
$852$	4.49876	0.154125
$853$	6.80470	0.232988	0.116494	−	0.993191i	$-0.462834\pi$
$853$	6.80470	0.232988	0.116494	+	0.993191i	$0.462834\pi$
$854$	13.6873	0.468371
$855$	−3.87503	−0.132523
$856$	−13.2016	−0.451221
$857$	−40.2595	−1.37524	−0.687619	−	0.726072i	$-0.741344\pi$
$857$	−40.2595	−1.37524	−0.687619	+	0.726072i	$0.741344\pi$
$858$	9.75963	0.333188
$859$	−13.1215	−0.447699	−0.223849	−	0.974624i	$-0.571862\pi$
$859$	−13.1215	−0.447699	−0.223849	+	0.974624i	$0.571862\pi$
$860$	−1.95694	−0.0667312
$861$	10.9722	0.373932
$862$	−7.12066	−0.242531
$863$	−15.3580	−0.522792	−0.261396	−	0.965232i	$-0.584183\pi$
$863$	−15.3580	−0.522792	−0.261396	+	0.965232i	$0.584183\pi$
$864$	−1.00000	−0.0340207
$865$	−31.0091	−1.05434
$866$	16.3538	0.555725
$867$	−16.9975	−0.577267
$868$	0.942373	0.0319862
$869$	−51.9995	−1.76396
$870$	1.56155	0.0529416
$871$	13.8849	0.470473
$872$	−8.74896	−0.296277
$873$	−1.94736	−0.0659080
$874$	−2.48153	−0.0839388
$875$	−12.8903	−0.435772
$876$	−0.0841599	−0.00284350
$877$	−37.4236	−1.26370	−0.631852	−	0.775089i	$-0.717705\pi$
$877$	−37.4236	−1.26370	−0.631852	+	0.775089i	$0.717705\pi$
$878$	−1.08369	−0.0365727
$879$	−28.2425	−0.952597
$880$	−6.52060	−0.219809
$881$	40.3515	1.35948	0.679738	−	0.733455i	$-0.262094\pi$
$881$	40.3515	1.35948	0.679738	+	0.733455i	$0.262094\pi$
$882$	5.80823	0.195573
$883$	−35.5348	−1.19584	−0.597920	−	0.801556i	$-0.704006\pi$
$883$	−35.5348	−1.19584	−0.597920	+	0.801556i	$0.704006\pi$
$884$	0.115928	0.00389909
$885$	−1.59395	−0.0535802
$886$	−33.3307	−1.11977
$887$	20.3598	0.683615	0.341808	−	0.939770i	$-0.388961\pi$
$887$	20.3598	0.683615	0.341808	+	0.939770i	$0.388961\pi$
$888$	−9.50994	−0.319133
$889$	−9.48257	−0.318035
$890$	9.37954	0.314403
$891$	4.17571	0.139892
$892$	25.2440	0.845233
$893$	1.18219	0.0395603
$894$	−23.8180	−0.796594
$895$	−29.4306	−0.983758
$896$	1.09168	0.0364705
$897$	−2.33724	−0.0780381
$898$	−28.8753	−0.963583
$899$	−0.863232	−0.0287904
$900$	−2.56155	−0.0853851
$901$	−0.599480	−0.0199716
$902$	41.9690	1.39742
$903$	−1.36810	−0.0455274
$904$	−7.68513	−0.255604
$905$	−3.55979	−0.118331
$906$	1.04295	0.0346497
$907$	−18.4551	−0.612792	−0.306396	−	0.951904i	$-0.599123\pi$
$907$	−18.4551	−0.612792	−0.306396	+	0.951904i	$0.599123\pi$
$908$	3.68658	0.122343
$909$	−5.25322	−0.174238
$910$	3.98433	0.132079
$911$	9.70405	0.321510	0.160755	−	0.986994i	$-0.448607\pi$
$911$	9.70405	0.321510	0.160755	+	0.986994i	$0.448607\pi$
$912$	2.48153	0.0821715
$913$	12.0284	0.398081
$914$	−17.8905	−0.591766
$915$	−19.5785	−0.647246
$916$	−13.8676	−0.458200
$917$	−6.78333	−0.224005
$918$	0.0496005	0.00163706
$919$	−6.41496	−0.211610	−0.105805	−	0.994387i	$-0.533742\pi$
$919$	−6.41496	−0.211610	−0.105805	+	0.994387i	$0.533742\pi$
$920$	1.56155	0.0514829
$921$	27.0167	0.890231
$922$	−13.3187	−0.438628
$923$	−10.5147	−0.346094
$924$	−4.55855	−0.149965
$925$	−24.3602	−0.800959
$926$	−34.3982	−1.13039
$927$	−8.89875	−0.292273
$928$	−1.00000	−0.0328266
$929$	−34.5843	−1.13468	−0.567338	−	0.823485i	$-0.692027\pi$
$929$	−34.5843	−1.13468	−0.567338	+	0.823485i	$0.692027\pi$
$930$	−1.34798	−0.0442021
$931$	−14.4133	−0.472376
$932$	−7.48280	−0.245107
$933$	−19.8500	−0.649858
$934$	1.96503	0.0642977
$935$	0.323425	0.0105771
$936$	2.33724	0.0763950
$937$	−28.8387	−0.942120	−0.471060	−	0.882101i	$-0.656128\pi$
$937$	−28.8387	−0.942120	−0.471060	+	0.882101i	$0.656128\pi$
$938$	−6.48539	−0.211756
$939$	22.0844	0.720699
$940$	−0.743916	−0.0242639
$941$	46.7340	1.52348	0.761742	−	0.647880i	$-0.224344\pi$
$941$	46.7340	1.52348	0.761742	+	0.647880i	$0.224344\pi$
$942$	−8.45317	−0.275419
$943$	−10.0507	−0.327297
$944$	1.02075	0.0332226
$945$	1.70472	0.0554544
$946$	−5.23302	−0.170140
$947$	−16.1878	−0.526032	−0.263016	−	0.964791i	$-0.584717\pi$
$947$	−16.1878	−0.526032	−0.263016	+	0.964791i	$0.584717\pi$
$948$	−12.4528	−0.404450
$949$	0.196702	0.00638520
$950$	6.35656	0.206234
$951$	−14.4579	−0.468828
$952$	−0.0541479	−0.00175494
$953$	−26.4735	−0.857560	−0.428780	−	0.903409i	$-0.641056\pi$
$953$	−26.4735	−0.857560	−0.428780	+	0.903409i	$0.641056\pi$
$954$	−12.0862	−0.391304
$955$	−11.7627	−0.380631
$956$	−7.00761	−0.226642
$957$	4.17571	0.134982
$958$	39.6404	1.28072
$959$	0.995494	0.0321462
$960$	−1.56155	−0.0503989
$961$	−30.2548	−0.975962
$962$	22.2270	0.716627
$963$	13.2016	0.425415
$964$	−11.6699	−0.375861
$965$	−15.5623	−0.500967
$966$	1.09168	0.0351242
$967$	−34.0243	−1.09415	−0.547074	−	0.837085i	$-0.684258\pi$
$967$	−34.0243	−1.09415	−0.547074	+	0.837085i	$0.684258\pi$
$968$	−6.43659	−0.206880
$969$	−0.123085	−0.00395406
$970$	−3.04090	−0.0976374
$971$	−30.6945	−0.985034	−0.492517	−	0.870303i	$-0.663923\pi$
$971$	−30.6945	−0.985034	−0.492517	+	0.870303i	$0.663923\pi$
$972$	1.00000	0.0320750
$973$	12.3280	0.395216
$974$	3.79426	0.121576
$975$	5.98696	0.191736
$976$	12.5379	0.401327
$977$	48.7627	1.56006	0.780029	−	0.625743i	$-0.215204\pi$
$977$	48.7627	1.56006	0.780029	+	0.625743i	$0.215204\pi$
$978$	11.2362	0.359293
$979$	25.0816	0.801612
$980$	9.06986	0.289726
$981$	8.74896	0.279333
$982$	−11.5859	−0.369721
$983$	−25.7303	−0.820669	−0.410334	−	0.911935i	$-0.634588\pi$
$983$	−25.7303	−0.820669	−0.410334	+	0.911935i	$0.634588\pi$
$984$	10.0507	0.320406
$985$	−41.0799	−1.30891
$986$	0.0496005	0.00157960
$987$	−0.520071	−0.0165540
$988$	−5.79991	−0.184520
$989$	1.25320	0.0398495
$990$	6.52060	0.207238
$991$	−61.8691	−1.96534	−0.982668	−	0.185373i	$-0.940651\pi$
$991$	−61.8691	−1.96534	−0.982668	+	0.185373i	$0.940651\pi$
$992$	0.863232	0.0274076
$993$	11.8220	0.375158
$994$	4.91121	0.155774
$995$	32.5535	1.03201
$996$	2.88056	0.0912739
$997$	5.94512	0.188284	0.0941420	−	0.995559i	$-0.469989\pi$
$997$	5.94512	0.188284	0.0941420	+	0.995559i	$0.469989\pi$
$998$	−17.2466	−0.545931
$999$	9.50994	0.300881

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	4002.2.a.bf.1.2	✓	6

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
4002.2.a.bf.1.2	✓	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)

\(f(q)\)	\(=\)	\(q-1.00000 q^{2} +1.00000 q^{3} +1.00000 q^{4} -1.56155 q^{5} -1.00000 q^{6} -1.09168 q^{7} -1.00000 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q-1.00000 q^{2} +1.00000 q^{3} +1.00000 q^{4} -1.56155 q^{5} -1.00000 q^{6} -1.09168 q^{7} -1.00000 q^{8} +1.00000 q^{9} +1.56155 q^{10} +4.17571 q^{11} +1.00000 q^{12} -2.33724 q^{13} +1.09168 q^{14} -1.56155 q^{15} +1.00000 q^{16} -0.0496005 q^{17} -1.00000 q^{18} +2.48153 q^{19} -1.56155 q^{20} -1.09168 q^{21} -4.17571 q^{22} +1.00000 q^{23} -1.00000 q^{24} -2.56155 q^{25} +2.33724 q^{26} +1.00000 q^{27} -1.09168 q^{28} +1.00000 q^{29} +1.56155 q^{30} -0.863232 q^{31} -1.00000 q^{32} +4.17571 q^{33} +0.0496005 q^{34} +1.70472 q^{35} +1.00000 q^{36} +9.50994 q^{37} -2.48153 q^{38} -2.33724 q^{39} +1.56155 q^{40} -10.0507 q^{41} +1.09168 q^{42} +1.25320 q^{43} +4.17571 q^{44} -1.56155 q^{45} -1.00000 q^{46} +0.476395 q^{47} +1.00000 q^{48} -5.80823 q^{49} +2.56155 q^{50} -0.0496005 q^{51} -2.33724 q^{52} +12.0862 q^{53} -1.00000 q^{54} -6.52060 q^{55} +1.09168 q^{56} +2.48153 q^{57} -1.00000 q^{58} +1.02075 q^{59} -1.56155 q^{60} +12.5379 q^{61} +0.863232 q^{62} -1.09168 q^{63} +1.00000 q^{64} +3.64972 q^{65} -4.17571 q^{66} -5.94074 q^{67} -0.0496005 q^{68} +1.00000 q^{69} -1.70472 q^{70} +4.49876 q^{71} -1.00000 q^{72} -0.0841599 q^{73} -9.50994 q^{74} -2.56155 q^{75} +2.48153 q^{76} -4.55855 q^{77} +2.33724 q^{78} -12.4528 q^{79} -1.56155 q^{80} +1.00000 q^{81} +10.0507 q^{82} +2.88056 q^{83} -1.09168 q^{84} +0.0774538 q^{85} -1.25320 q^{86} +1.00000 q^{87} -4.17571 q^{88} +6.00654 q^{89} +1.56155 q^{90} +2.55152 q^{91} +1.00000 q^{92} -0.863232 q^{93} -0.476395 q^{94} -3.87503 q^{95} -1.00000 q^{96} -1.94736 q^{97} +5.80823 q^{98} +4.17571 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 6 q - 6 q^{2} + 6 q^{3} + 6 q^{4} + 3 q^{5} - 6 q^{6} + 2 q^{7} - 6 q^{8} + 6 q^{9}+O(q^{10}) \) 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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