LMFDB - Embedded newform 4002.2.a.bf.1.5

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			1.5
Root			$1.85969$ 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)

$f(q)$	$=$	$q-1.00000 q^{2} +1.00000 q^{3} +1.00000 q^{4} +2.56155 q^{5} -1.00000 q^{6} +3.26093 q^{7} -1.00000 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q-1.00000 q^{2} +1.00000 q^{3} +1.00000 q^{4} +2.56155 q^{5} -1.00000 q^{6} +3.26093 q^{7} -1.00000 q^{8} +1.00000 q^{9} -2.56155 q^{10} +0.513894 q^{11} +1.00000 q^{12} -3.20549 q^{13} -3.26093 q^{14} +2.56155 q^{15} +1.00000 q^{16} -2.52278 q^{17} -1.00000 q^{18} +3.58156 q^{19} +2.56155 q^{20} +3.26093 q^{21} -0.513894 q^{22} +1.00000 q^{23} -1.00000 q^{24} +1.56155 q^{25} +3.20549 q^{26} +1.00000 q^{27} +3.26093 q^{28} +1.00000 q^{29} -2.56155 q^{30} -9.93042 q^{31} -1.00000 q^{32} +0.513894 q^{33} +2.52278 q^{34} +8.35304 q^{35} +1.00000 q^{36} +4.60517 q^{37} -3.58156 q^{38} -3.20549 q^{39} -2.56155 q^{40} +6.66047 q^{41} -3.26093 q^{42} +1.43067 q^{43} +0.513894 q^{44} +2.56155 q^{45} -1.00000 q^{46} +6.20215 q^{47} +1.00000 q^{48} +3.63366 q^{49} -1.56155 q^{50} -2.52278 q^{51} -3.20549 q^{52} +6.04002 q^{53} -1.00000 q^{54} +1.31637 q^{55} -3.26093 q^{56} +3.58156 q^{57} -1.00000 q^{58} +8.70408 q^{59} +2.56155 q^{60} +0.354436 q^{61} +9.93042 q^{62} +3.26093 q^{63} +1.00000 q^{64} -8.21104 q^{65} -0.513894 q^{66} -10.2025 q^{67} -2.52278 q^{68} +1.00000 q^{69} -8.35304 q^{70} +9.89709 q^{71} -1.00000 q^{72} +13.5674 q^{73} -4.60517 q^{74} +1.56155 q^{75} +3.58156 q^{76} +1.67577 q^{77} +3.20549 q^{78} +12.8688 q^{79} +2.56155 q^{80} +1.00000 q^{81} -6.66047 q^{82} -8.47531 q^{83} +3.26093 q^{84} -6.46224 q^{85} -1.43067 q^{86} +1.00000 q^{87} -0.513894 q^{88} +2.85805 q^{89} -2.56155 q^{90} -10.4529 q^{91} +1.00000 q^{92} -9.93042 q^{93} -6.20215 q^{94} +9.17436 q^{95} -1.00000 q^{96} +13.0160 q^{97} -3.63366 q^{98} +0.513894 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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
$5$	2.56155	1.14556	0.572781	−	0.819709i	$-0.305865\pi$
$5$	2.56155	1.14556	0.572781	+	0.819709i	$0.305865\pi$
$6$	−1.00000	−0.408248
$7$	3.26093	1.23252	0.616258	−	0.787545i	$-0.288648\pi$
$7$	3.26093	1.23252	0.616258	+	0.787545i	$0.288648\pi$
$8$	−1.00000	−0.353553
$9$	1.00000	0.333333
$10$	−2.56155	−0.810034
$11$	0.513894	0.154945	0.0774724	−	0.996994i	$-0.475315\pi$
$11$	0.513894	0.154945	0.0774724	+	0.996994i	$0.475315\pi$
$12$	1.00000	0.288675
$13$	−3.20549	−0.889043	−0.444522	−	0.895768i	$-0.646626\pi$
$13$	−3.20549	−0.889043	−0.444522	+	0.895768i	$0.646626\pi$
$14$	−3.26093	−0.871520
$15$	2.56155	0.661390
$16$	1.00000	0.250000
$17$	−2.52278	−0.611864	−0.305932	−	0.952053i	$-0.598968\pi$
$17$	−2.52278	−0.611864	−0.305932	+	0.952053i	$0.598968\pi$
$18$	−1.00000	−0.235702
$19$	3.58156	0.821667	0.410833	−	0.911710i	$-0.365238\pi$
$19$	3.58156	0.821667	0.410833	+	0.911710i	$0.365238\pi$
$20$	2.56155	0.572781
$21$	3.26093	0.711593
$22$	−0.513894	−0.109563
$23$	1.00000	0.208514
$23$	1.00000	0.208514
$24$	−1.00000	−0.204124
$25$	1.56155	0.312311
$26$	3.20549	0.628649
$27$	1.00000	0.192450
$28$	3.26093	0.616258
$29$	1.00000	0.185695
$29$	1.00000	0.185695
$30$	−2.56155	−0.467673
$31$	−9.93042	−1.78356	−0.891778	−	0.452473i	$-0.850542\pi$
$31$	−9.93042	−1.78356	−0.891778	+	0.452473i	$0.850542\pi$
$32$	−1.00000	−0.176777
$33$	0.513894	0.0894574
$34$	2.52278	0.432653
$35$	8.35304	1.41192
$36$	1.00000	0.166667
$37$	4.60517	0.757085	0.378542	−	0.925584i	$-0.376425\pi$
$37$	4.60517	0.757085	0.378542	+	0.925584i	$0.376425\pi$
$38$	−3.58156	−0.581006
$39$	−3.20549	−0.513289
$40$	−2.56155	−0.405017
$41$	6.66047	1.04019	0.520095	−	0.854108i	$-0.325897\pi$
$41$	6.66047	1.04019	0.520095	+	0.854108i	$0.325897\pi$
$42$	−3.26093	−0.503172
$43$	1.43067	0.218175	0.109087	−	0.994032i	$-0.465207\pi$
$43$	1.43067	0.218175	0.109087	+	0.994032i	$0.465207\pi$
$44$	0.513894	0.0774724
$45$	2.56155	0.381854
$46$	−1.00000	−0.147442
$47$	6.20215	0.904676	0.452338	−	0.891847i	$-0.350590\pi$
$47$	6.20215	0.904676	0.452338	+	0.891847i	$0.350590\pi$
$48$	1.00000	0.144338
$49$	3.63366	0.519094
$50$	−1.56155	−0.220837
$51$	−2.52278	−0.353260
$52$	−3.20549	−0.444522
$53$	6.04002	0.829660	0.414830	−	0.909899i	$-0.363841\pi$
$53$	6.04002	0.829660	0.414830	+	0.909899i	$0.363841\pi$
$54$	−1.00000	−0.136083
$55$	1.31637	0.177499
$56$	−3.26093	−0.435760
$57$	3.58156	0.474389
$58$	−1.00000	−0.131306
$59$	8.70408	1.13317	0.566587	−	0.824002i	$-0.308263\pi$
$59$	8.70408	1.13317	0.566587	+	0.824002i	$0.308263\pi$
$60$	2.56155	0.330695
$61$	0.354436	0.0453809	0.0226905	−	0.999743i	$-0.492777\pi$
$61$	0.354436	0.0453809	0.0226905	+	0.999743i	$0.492777\pi$
$62$	9.93042	1.26116
$63$	3.26093	0.410838
$64$	1.00000	0.125000
$65$	−8.21104	−1.01845
$66$	−0.513894	−0.0632559
$67$	−10.2025	−1.24643	−0.623215	−	0.782050i	$-0.714174\pi$
$67$	−10.2025	−1.24643	−0.623215	+	0.782050i	$0.714174\pi$
$68$	−2.52278	−0.305932
$69$	1.00000	0.120386
$70$	−8.35304	−0.998379
$71$	9.89709	1.17457	0.587284	−	0.809381i	$-0.300197\pi$
$71$	9.89709	1.17457	0.587284	+	0.809381i	$0.300197\pi$
$72$	−1.00000	−0.117851
$73$	13.5674	1.58795	0.793973	−	0.607953i	$-0.208009\pi$
$73$	13.5674	1.58795	0.793973	+	0.607953i	$0.208009\pi$
$74$	−4.60517	−0.535340
$75$	1.56155	0.180313
$76$	3.58156	0.410833
$77$	1.67577	0.190972
$78$	3.20549	0.362950
$79$	12.8688	1.44786	0.723928	−	0.689875i	$-0.242335\pi$
$79$	12.8688	1.44786	0.723928	+	0.689875i	$0.242335\pi$
$80$	2.56155	0.286390
$81$	1.00000	0.111111
$82$	−6.66047	−0.735525
$83$	−8.47531	−0.930286	−0.465143	−	0.885236i	$-0.653997\pi$
$83$	−8.47531	−0.930286	−0.465143	+	0.885236i	$0.653997\pi$
$84$	3.26093	0.355796
$85$	−6.46224	−0.700928
$86$	−1.43067	−0.154273
$87$	1.00000	0.107211
$88$	−0.513894	−0.0547813
$89$	2.85805	0.302952	0.151476	−	0.988461i	$-0.451597\pi$
$89$	2.85805	0.302952	0.151476	+	0.988461i	$0.451597\pi$
$90$	−2.56155	−0.270011
$91$	−10.4529	−1.09576
$92$	1.00000	0.104257
$93$	−9.93042	−1.02974
$94$	−6.20215	−0.639703
$95$	9.17436	0.941270
$96$	−1.00000	−0.102062
$97$	13.0160	1.32158	0.660788	−	0.750573i	$-0.270222\pi$
$97$	13.0160	1.32158	0.660788	+	0.750573i	$0.270222\pi$
$98$	−3.63366	−0.367055
$99$	0.513894	0.0516483
$100$	1.56155	0.156155
$101$	3.21406	0.319811	0.159905	−	0.987132i	$-0.448881\pi$
$101$	3.21406	0.319811	0.159905	+	0.987132i	$0.448881\pi$
$102$	2.52278	0.249793
$103$	4.73507	0.466561	0.233280	−	0.972410i	$-0.425054\pi$
$103$	4.73507	0.466561	0.233280	+	0.972410i	$0.425054\pi$
$104$	3.20549	0.314324
$105$	8.35304	0.815173
$106$	−6.04002	−0.586658
$107$	12.5974	1.21784	0.608918	−	0.793233i	$-0.291604\pi$
$107$	12.5974	1.21784	0.608918	+	0.793233i	$0.291604\pi$
$108$	1.00000	0.0962250
$109$	12.2135	1.16984	0.584922	−	0.811089i	$-0.301125\pi$
$109$	12.2135	1.16984	0.584922	+	0.811089i	$0.301125\pi$
$110$	−1.31637	−0.125511
$111$	4.60517	0.437103
$112$	3.26093	0.308129
$113$	6.48945	0.610476	0.305238	−	0.952276i	$-0.401264\pi$
$113$	6.48945	0.610476	0.305238	+	0.952276i	$0.401264\pi$
$114$	−3.58156	−0.335444
$115$	2.56155	0.238866
$116$	1.00000	0.0928477
$117$	−3.20549	−0.296348
$118$	−8.70408	−0.801276
$119$	−8.22661	−0.754132
$120$	−2.56155	−0.233837
$121$	−10.7359	−0.975992
$122$	−0.354436	−0.0320891
$123$	6.66047	0.600554
$124$	−9.93042	−0.891778
$125$	−8.80776	−0.787790
$126$	−3.26093	−0.290507
$127$	−13.4281	−1.19155	−0.595775	−	0.803151i	$-0.703155\pi$
$127$	−13.4281	−1.19155	−0.595775	+	0.803151i	$0.703155\pi$
$128$	−1.00000	−0.0883883
$129$	1.43067	0.125963
$130$	8.21104	0.720155
$131$	4.15449	0.362979	0.181490	−	0.983393i	$-0.441908\pi$
$131$	4.15449	0.362979	0.181490	+	0.983393i	$0.441908\pi$
$132$	0.513894	0.0447287
$133$	11.6792	1.01272
$134$	10.2025	0.881359
$135$	2.56155	0.220463
$136$	2.52278	0.216327
$137$	−10.3838	−0.887145	−0.443573	−	0.896238i	$-0.646289\pi$
$137$	−10.3838	−0.887145	−0.443573	+	0.896238i	$0.646289\pi$
$138$	−1.00000	−0.0851257
$139$	−19.4044	−1.64586	−0.822928	−	0.568145i	$-0.807661\pi$
$139$	−19.4044	−1.64586	−0.822928	+	0.568145i	$0.807661\pi$
$140$	8.35304	0.705961
$141$	6.20215	0.522315
$142$	−9.89709	−0.830545
$143$	−1.64728	−0.137753
$144$	1.00000	0.0833333
$145$	2.56155	0.212725
$146$	−13.5674	−1.12285
$147$	3.63366	0.299699
$148$	4.60517	0.378542
$149$	−6.04894	−0.495548	−0.247774	−	0.968818i	$-0.579699\pi$
$149$	−6.04894	−0.495548	−0.247774	+	0.968818i	$0.579699\pi$
$150$	−1.56155	−0.127500
$151$	−12.3623	−1.00603	−0.503013	−	0.864279i	$-0.667775\pi$
$151$	−12.3623	−1.00603	−0.503013	+	0.864279i	$0.667775\pi$
$152$	−3.58156	−0.290503
$153$	−2.52278	−0.203955
$154$	−1.67577	−0.135037
$155$	−25.4373	−2.04317
$156$	−3.20549	−0.256645
$157$	−2.98654	−0.238352	−0.119176	−	0.992873i	$-0.538025\pi$
$157$	−2.98654	−0.238352	−0.119176	+	0.992873i	$0.538025\pi$
$158$	−12.8688	−1.02379
$159$	6.04002	0.479005
$160$	−2.56155	−0.202509
$161$	3.26093	0.256997
$162$	−1.00000	−0.0785674
$163$	14.1375	1.10734	0.553669	−	0.832737i	$-0.313227\pi$
$163$	14.1375	1.10734	0.553669	+	0.832737i	$0.313227\pi$
$164$	6.66047	0.520095
$165$	1.31637	0.102479
$166$	8.47531	0.657811
$167$	−12.7796	−0.988917	−0.494459	−	0.869201i	$-0.664634\pi$
$167$	−12.7796	−0.988917	−0.494459	+	0.869201i	$0.664634\pi$
$168$	−3.26093	−0.251586
$169$	−2.72483	−0.209602
$170$	6.46224	0.495631
$171$	3.58156	0.273889
$172$	1.43067	0.109087
$173$	14.6234	1.11180	0.555899	−	0.831250i	$-0.312374\pi$
$173$	14.6234	1.11180	0.555899	+	0.831250i	$0.312374\pi$
$174$	−1.00000	−0.0758098
$175$	5.09211	0.384928
$176$	0.513894	0.0387362
$177$	8.70408	0.654239
$178$	−2.85805	−0.214220
$179$	−20.1935	−1.50933	−0.754665	−	0.656110i	$-0.772201\pi$
$179$	−20.1935	−1.50933	−0.754665	+	0.656110i	$0.772201\pi$
$180$	2.56155	0.190927
$181$	−19.7979	−1.47157	−0.735783	−	0.677218i	$-0.763186\pi$
$181$	−19.7979	−1.47157	−0.735783	+	0.677218i	$0.763186\pi$
$182$	10.4529	0.774819
$183$	0.354436	0.0262007
$184$	−1.00000	−0.0737210
$185$	11.7964	0.867287
$186$	9.93042	0.728134
$187$	−1.29644	−0.0948052
$188$	6.20215	0.452338
$189$	3.26093	0.237198
$190$	−9.17436	−0.665578
$191$	−1.75927	−0.127296	−0.0636480	−	0.997972i	$-0.520273\pi$
$191$	−1.75927	−0.127296	−0.0636480	+	0.997972i	$0.520273\pi$
$192$	1.00000	0.0721688
$193$	−23.8470	−1.71654	−0.858271	−	0.513197i	$-0.828461\pi$
$193$	−23.8470	−1.71654	−0.858271	+	0.513197i	$0.828461\pi$
$194$	−13.0160	−0.934495
$195$	−8.21104	−0.588004
$196$	3.63366	0.259547
$197$	3.71894	0.264963	0.132482	−	0.991185i	$-0.457705\pi$
$197$	3.71894	0.264963	0.132482	+	0.991185i	$0.457705\pi$
$198$	−0.513894	−0.0365208
$199$	5.58551	0.395946	0.197973	−	0.980207i	$-0.436564\pi$
$199$	5.58551	0.395946	0.197973	+	0.980207i	$0.436564\pi$
$200$	−1.56155	−0.110418
$201$	−10.2025	−0.719627
$202$	−3.21406	−0.226140
$203$	3.26093	0.228872
$204$	−2.52278	−0.176630
$205$	17.0611	1.19160
$206$	−4.73507	−0.329908
$207$	1.00000	0.0695048
$208$	−3.20549	−0.222261
$209$	1.84054	0.127313
$210$	−8.35304	−0.576415
$211$	7.31232	0.503401	0.251700	−	0.967805i	$-0.419010\pi$
$211$	7.31232	0.503401	0.251700	+	0.967805i	$0.419010\pi$
$212$	6.04002	0.414830
$213$	9.89709	0.678137
$214$	−12.5974	−0.861140
$215$	3.66473	0.249933
$216$	−1.00000	−0.0680414
$217$	−32.3824	−2.19826
$218$	−12.2135	−0.827205
$219$	13.5674	0.916801
$220$	1.31637	0.0887494
$221$	8.08675	0.543974
$222$	−4.60517	−0.309079
$223$	−26.4260	−1.76961	−0.884807	−	0.465958i	$-0.845710\pi$
$223$	−26.4260	−1.76961	−0.884807	+	0.465958i	$0.845710\pi$
$224$	−3.26093	−0.217880
$225$	1.56155	0.104104
$226$	−6.48945	−0.431672
$227$	5.83322	0.387164	0.193582	−	0.981084i	$-0.437989\pi$
$227$	5.83322	0.387164	0.193582	+	0.981084i	$0.437989\pi$
$228$	3.58156	0.237195
$229$	22.8231	1.50819	0.754096	−	0.656764i	$-0.228075\pi$
$229$	22.8231	1.50819	0.754096	+	0.656764i	$0.228075\pi$
$230$	−2.56155	−0.168904
$231$	1.67577	0.110258
$232$	−1.00000	−0.0656532
$233$	24.9439	1.63413	0.817066	−	0.576545i	$-0.195599\pi$
$233$	24.9439	1.63413	0.817066	+	0.576545i	$0.195599\pi$
$234$	3.20549	0.209550
$235$	15.8871	1.03636
$236$	8.70408	0.566587
$237$	12.8688	0.835920
$238$	8.22661	0.533252
$239$	−28.4198	−1.83832	−0.919162	−	0.393880i	$-0.871132\pi$
$239$	−28.4198	−1.83832	−0.919162	+	0.393880i	$0.871132\pi$
$240$	2.56155	0.165348
$241$	−22.4261	−1.44459	−0.722296	−	0.691584i	$-0.756913\pi$
$241$	−22.4261	−1.44459	−0.722296	+	0.691584i	$0.756913\pi$
$242$	10.7359	0.690131
$243$	1.00000	0.0641500
$244$	0.354436	0.0226905
$245$	9.30780	0.594654
$246$	−6.66047	−0.424656
$247$	−11.4807	−0.730497
$248$	9.93042	0.630582
$249$	−8.47531	−0.537101
$250$	8.80776	0.557052
$251$	9.30608	0.587395	0.293697	−	0.955898i	$-0.405114\pi$
$251$	9.30608	0.587395	0.293697	+	0.955898i	$0.405114\pi$
$252$	3.26093	0.205419
$253$	0.513894	0.0323082
$254$	13.4281	0.842553
$255$	−6.46224	−0.404681
$256$	1.00000	0.0625000
$257$	11.4385	0.713512	0.356756	−	0.934198i	$-0.383883\pi$
$257$	11.4385	0.713512	0.356756	+	0.934198i	$0.383883\pi$
$258$	−1.43067	−0.0890696
$259$	15.0171	0.933119
$260$	−8.21104	−0.509227
$261$	1.00000	0.0618984
$262$	−4.15449	−0.256665
$263$	15.1714	0.935510	0.467755	−	0.883858i	$-0.345063\pi$
$263$	15.1714	0.935510	0.467755	+	0.883858i	$0.345063\pi$
$264$	−0.513894	−0.0316280
$265$	15.4718	0.950427
$266$	−11.6792	−0.716099
$267$	2.85805	0.174910
$268$	−10.2025	−0.623215
$269$	−30.0545	−1.83245	−0.916227	−	0.400660i	$-0.868781\pi$
$269$	−30.0545	−1.83245	−0.916227	+	0.400660i	$0.868781\pi$
$270$	−2.56155	−0.155891
$271$	25.5234	1.55044	0.775218	−	0.631694i	$-0.217640\pi$
$271$	25.5234	1.55044	0.775218	+	0.631694i	$0.217640\pi$
$272$	−2.52278	−0.152966
$273$	−10.4529	−0.632637
$274$	10.3838	0.627307
$275$	0.802472	0.0483909
$276$	1.00000	0.0601929
$277$	−20.1539	−1.21093	−0.605465	−	0.795872i	$-0.707013\pi$
$277$	−20.1539	−1.21093	−0.605465	+	0.795872i	$0.707013\pi$
$278$	19.4044	1.16380
$279$	−9.93042	−0.594519
$280$	−8.35304	−0.499190
$281$	19.4320	1.15921	0.579607	−	0.814896i	$-0.303206\pi$
$281$	19.4320	1.15921	0.579607	+	0.814896i	$0.303206\pi$
$282$	−6.20215	−0.369333
$283$	6.87622	0.408749	0.204375	−	0.978893i	$-0.434484\pi$
$283$	6.87622	0.408749	0.204375	+	0.978893i	$0.434484\pi$
$284$	9.89709	0.587284
$285$	9.17436	0.543442
$286$	1.64728	0.0974058
$287$	21.7193	1.28205
$288$	−1.00000	−0.0589256
$289$	−10.6356	−0.625622
$290$	−2.56155	−0.150420
$291$	13.0160	0.763012
$292$	13.5674	0.793973
$293$	17.3419	1.01313	0.506564	−	0.862203i	$-0.330915\pi$
$293$	17.3419	1.01313	0.506564	+	0.862203i	$0.330915\pi$
$294$	−3.63366	−0.211919
$295$	22.2960	1.29812
$296$	−4.60517	−0.267670
$297$	0.513894	0.0298191
$298$	6.04894	0.350405
$299$	−3.20549	−0.185378
$300$	1.56155	0.0901563
$301$	4.66531	0.268904
$302$	12.3623	0.711368
$303$	3.21406	0.184643
$304$	3.58156	0.205417
$305$	0.907907	0.0519866
$306$	2.52278	0.144218
$307$	−21.7731	−1.24266	−0.621329	−	0.783549i	$-0.713407\pi$
$307$	−21.7731	−1.24266	−0.621329	+	0.783549i	$0.713407\pi$
$308$	1.67577	0.0954859
$309$	4.73507	0.269369
$310$	25.4373	1.44474
$311$	12.6368	0.716566	0.358283	−	0.933613i	$-0.383362\pi$
$311$	12.6368	0.716566	0.358283	+	0.933613i	$0.383362\pi$
$312$	3.20549	0.181475
$313$	−28.2444	−1.59647	−0.798234	−	0.602347i	$-0.794232\pi$
$313$	−28.2444	−1.59647	−0.798234	+	0.602347i	$0.794232\pi$
$314$	2.98654	0.168540
$315$	8.35304	0.470641
$316$	12.8688	0.723928
$317$	−17.8766	−1.00405	−0.502024	−	0.864854i	$-0.667411\pi$
$317$	−17.8766	−1.00405	−0.502024	+	0.864854i	$0.667411\pi$
$318$	−6.04002	−0.338707
$319$	0.513894	0.0287725
$320$	2.56155	0.143195
$321$	12.5974	0.703118
$322$	−3.26093	−0.181724
$323$	−9.03550	−0.502749
$324$	1.00000	0.0555556
$325$	−5.00554	−0.277658
$326$	−14.1375	−0.783006
$327$	12.2135	0.675410
$328$	−6.66047	−0.367763
$329$	20.2248	1.11503
$330$	−1.31637	−0.0724636
$331$	−16.9855	−0.933606	−0.466803	−	0.884361i	$-0.654594\pi$
$331$	−16.9855	−0.933606	−0.466803	+	0.884361i	$0.654594\pi$
$332$	−8.47531	−0.465143
$333$	4.60517	0.252362
$334$	12.7796	0.699270
$335$	−26.1342	−1.42786
$336$	3.26093	0.177898
$337$	−4.15420	−0.226294	−0.113147	−	0.993578i	$-0.536093\pi$
$337$	−4.15420	−0.226294	−0.113147	+	0.993578i	$0.536093\pi$
$338$	2.72483	0.148211
$339$	6.48945	0.352459
$340$	−6.46224	−0.350464
$341$	−5.10318	−0.276353
$342$	−3.58156	−0.193669
$343$	−10.9774	−0.592724
$344$	−1.43067	−0.0771365
$345$	2.56155	0.137909
$346$	−14.6234	−0.786160
$347$	7.27163	0.390362	0.195181	−	0.980767i	$-0.437471\pi$
$347$	7.27163	0.390362	0.195181	+	0.980767i	$0.437471\pi$
$348$	1.00000	0.0536056
$349$	−0.326949	−0.0175012	−0.00875058	−	0.999962i	$-0.502785\pi$
$349$	−0.326949	−0.0175012	−0.00875058	+	0.999962i	$0.502785\pi$
$350$	−5.09211	−0.272185
$351$	−3.20549	−0.171096
$352$	−0.513894	−0.0273906
$353$	−5.39173	−0.286973	−0.143486	−	0.989652i	$-0.545831\pi$
$353$	−5.39173	−0.286973	−0.143486	+	0.989652i	$0.545831\pi$
$354$	−8.70408	−0.462617
$355$	25.3519	1.34554
$356$	2.85805	0.151476
$357$	−8.22661	−0.435398
$358$	20.1935	1.06726
$359$	11.0689	0.584195	0.292098	−	0.956389i	$-0.405647\pi$
$359$	11.0689	0.584195	0.292098	+	0.956389i	$0.405647\pi$
$360$	−2.56155	−0.135006
$361$	−6.17241	−0.324864
$362$	19.7979	1.04055
$363$	−10.7359	−0.563489
$364$	−10.4529	−0.547880
$365$	34.7537	1.81909
$366$	−0.354436	−0.0185267
$367$	−2.38125	−0.124300	−0.0621500	−	0.998067i	$-0.519796\pi$
$367$	−2.38125	−0.124300	−0.0621500	+	0.998067i	$0.519796\pi$
$368$	1.00000	0.0521286
$369$	6.66047	0.346730
$370$	−11.7964	−0.613265
$371$	19.6961	1.02257
$372$	−9.93042	−0.514868
$373$	−18.3022	−0.947650	−0.473825	−	0.880619i	$-0.657127\pi$
$373$	−18.3022	−0.947650	−0.473825	+	0.880619i	$0.657127\pi$
$374$	1.29644	0.0670374
$375$	−8.80776	−0.454831
$376$	−6.20215	−0.319851
$377$	−3.20549	−0.165091
$378$	−3.26093	−0.167724
$379$	2.60318	0.133716	0.0668582	−	0.997762i	$-0.478702\pi$
$379$	2.60318	0.133716	0.0668582	+	0.997762i	$0.478702\pi$
$380$	9.17436	0.470635
$381$	−13.4281	−0.687942
$382$	1.75927	0.0900119
$383$	17.4335	0.890808	0.445404	−	0.895330i	$-0.353060\pi$
$383$	17.4335	0.890808	0.445404	+	0.895330i	$0.353060\pi$
$384$	−1.00000	−0.0510310
$385$	4.29258	0.218770
$386$	23.8470	1.21378
$387$	1.43067	0.0727250
$388$	13.0160	0.660788
$389$	−11.7377	−0.595123	−0.297561	−	0.954703i	$-0.596173\pi$
$389$	−11.7377	−0.595123	−0.297561	+	0.954703i	$0.596173\pi$
$390$	8.21104	0.415782
$391$	−2.52278	−0.127583
$392$	−3.63366	−0.183527
$393$	4.15449	0.209566
$394$	−3.71894	−0.187357
$395$	32.9642	1.65861
$396$	0.513894	0.0258241
$397$	12.2931	0.616974	0.308487	−	0.951229i	$-0.400177\pi$
$397$	12.2931	0.616974	0.308487	+	0.951229i	$0.400177\pi$
$398$	−5.58551	−0.279976
$399$	11.6792	0.584692
$400$	1.56155	0.0780776
$401$	−28.2496	−1.41072	−0.705358	−	0.708851i	$-0.749214\pi$
$401$	−28.2496	−1.41072	−0.705358	+	0.708851i	$0.749214\pi$
$402$	10.2025	0.508853
$403$	31.8319	1.58566
$404$	3.21406	0.159905
$405$	2.56155	0.127285
$406$	−3.26093	−0.161837
$407$	2.36657	0.117306
$408$	2.52278	0.124896
$409$	−35.5775	−1.75919	−0.879597	−	0.475719i	$-0.842188\pi$
$409$	−35.5775	−1.75919	−0.879597	+	0.475719i	$0.842188\pi$
$410$	−17.0611	−0.842589
$411$	−10.3838	−0.512194
$412$	4.73507	0.233280
$413$	28.3834	1.39666
$414$	−1.00000	−0.0491473
$415$	−21.7099	−1.06570
$416$	3.20549	0.157162
$417$	−19.4044	−0.950236
$418$	−1.84054	−0.0900239
$419$	21.6897	1.05961	0.529806	−	0.848119i	$-0.322265\pi$
$419$	21.6897	1.05961	0.529806	+	0.848119i	$0.322265\pi$
$420$	8.35304	0.407587
$421$	30.8811	1.50505	0.752526	−	0.658563i	$-0.228835\pi$
$421$	30.8811	1.50505	0.752526	+	0.658563i	$0.228835\pi$
$422$	−7.31232	−0.355958
$423$	6.20215	0.301559
$424$	−6.04002	−0.293329
$425$	−3.93946	−0.191092
$426$	−9.89709	−0.479516
$427$	1.15579	0.0559326
$428$	12.5974	0.608918
$429$	−1.64728	−0.0795315
$430$	−3.66473	−0.176729
$431$	−16.7845	−0.808480	−0.404240	−	0.914653i	$-0.632464\pi$
$431$	−16.7845	−0.808480	−0.404240	+	0.914653i	$0.632464\pi$
$432$	1.00000	0.0481125
$433$	−34.7198	−1.66853	−0.834263	−	0.551367i	$-0.814106\pi$
$433$	−34.7198	−1.66853	−0.834263	+	0.551367i	$0.814106\pi$
$434$	32.3824	1.55440
$435$	2.56155	0.122817
$436$	12.2135	0.584922
$437$	3.58156	0.171329
$438$	−13.5674	−0.648276
$439$	−3.46274	−0.165268	−0.0826339	−	0.996580i	$-0.526333\pi$
$439$	−3.46274	−0.165268	−0.0826339	+	0.996580i	$0.526333\pi$
$440$	−1.31637	−0.0627553
$441$	3.63366	0.173031
$442$	−8.08675	−0.384648
$443$	−14.4669	−0.687343	−0.343671	−	0.939090i	$-0.611671\pi$
$443$	−14.4669	−0.687343	−0.343671	+	0.939090i	$0.611671\pi$
$444$	4.60517	0.218552
$445$	7.32104	0.347051
$446$	26.4260	1.25131
$447$	−6.04894	−0.286105
$448$	3.26093	0.154064
$449$	−27.0281	−1.27554	−0.637768	−	0.770229i	$-0.720142\pi$
$449$	−27.0281	−1.27554	−0.637768	+	0.770229i	$0.720142\pi$
$450$	−1.56155	−0.0736123
$451$	3.42277	0.161172
$452$	6.48945	0.305238
$453$	−12.3623	−0.580829
$454$	−5.83322	−0.273766
$455$	−26.7756	−1.25526
$456$	−3.58156	−0.167722
$457$	31.4925	1.47316	0.736580	−	0.676351i	$-0.236440\pi$
$457$	31.4925	1.47316	0.736580	+	0.676351i	$0.236440\pi$
$458$	−22.8231	−1.06645
$459$	−2.52278	−0.117753
$460$	2.56155	0.119433
$461$	−36.7196	−1.71020	−0.855100	−	0.518463i	$-0.826504\pi$
$461$	−36.7196	−1.71020	−0.855100	+	0.518463i	$0.826504\pi$
$462$	−1.67577	−0.0779639
$463$	34.0251	1.58128	0.790640	−	0.612281i	$-0.209748\pi$
$463$	34.0251	1.58128	0.790640	+	0.612281i	$0.209748\pi$
$464$	1.00000	0.0464238
$465$	−25.4373	−1.17963
$466$	−24.9439	−1.15551
$467$	−8.65038	−0.400292	−0.200146	−	0.979766i	$-0.564142\pi$
$467$	−8.65038	−0.400292	−0.200146	+	0.979766i	$0.564142\pi$
$468$	−3.20549	−0.148174
$469$	−33.2695	−1.53624
$470$	−15.8871	−0.732819
$471$	−2.98654	−0.137612
$472$	−8.70408	−0.400638
$473$	0.735212	0.0338051
$474$	−12.8688	−0.591085
$475$	5.59280	0.256615
$476$	−8.22661	−0.377066
$477$	6.04002	0.276553
$478$	28.4198	1.29989
$479$	18.2393	0.833375	0.416688	−	0.909050i	$-0.363191\pi$
$479$	18.2393	0.833375	0.416688	+	0.909050i	$0.363191\pi$
$480$	−2.56155	−0.116918
$481$	−14.7618	−0.673081
$482$	22.4261	1.02148
$483$	3.26093	0.148377
$484$	−10.7359	−0.487996
$485$	33.3412	1.51395
$486$	−1.00000	−0.0453609
$487$	−42.4026	−1.92145	−0.960724	−	0.277507i	$-0.910492\pi$
$487$	−42.4026	−1.92145	−0.960724	+	0.277507i	$0.910492\pi$
$488$	−0.354436	−0.0160446
$489$	14.1375	0.639322
$490$	−9.30780	−0.420484
$491$	14.7408	0.665244	0.332622	−	0.943060i	$-0.392067\pi$
$491$	14.7408	0.665244	0.332622	+	0.943060i	$0.392067\pi$
$492$	6.66047	0.300277
$493$	−2.52278	−0.113620
$494$	11.4807	0.516540
$495$	1.31637	0.0591663
$496$	−9.93042	−0.445889
$497$	32.2737	1.44767
$498$	8.47531	0.379788
$499$	16.3704	0.732838	0.366419	−	0.930450i	$-0.380584\pi$
$499$	16.3704	0.732838	0.366419	+	0.930450i	$0.380584\pi$
$500$	−8.80776	−0.393895
$501$	−12.7796	−0.570952
$502$	−9.30608	−0.415351
$503$	26.4925	1.18124	0.590620	−	0.806950i	$-0.298883\pi$
$503$	26.4925	1.18124	0.590620	+	0.806950i	$0.298883\pi$
$504$	−3.26093	−0.145253
$505$	8.23297	0.366363
$506$	−0.513894	−0.0228454
$507$	−2.72483	−0.121014
$508$	−13.4281	−0.595775
$509$	−5.88868	−0.261011	−0.130505	−	0.991448i	$-0.541660\pi$
$509$	−5.88868	−0.261011	−0.130505	+	0.991448i	$0.541660\pi$
$510$	6.46224	0.286153
$511$	44.2424	1.95717
$512$	−1.00000	−0.0441942
$513$	3.58156	0.158130
$514$	−11.4385	−0.504529
$515$	12.1291	0.534474
$516$	1.43067	0.0629817
$517$	3.18725	0.140175
$518$	−15.0171	−0.659814
$519$	14.6234	0.641897
$520$	8.21104	0.360078
$521$	32.4674	1.42242	0.711211	−	0.702979i	$-0.248147\pi$
$521$	32.4674	1.42242	0.711211	+	0.702979i	$0.248147\pi$
$522$	−1.00000	−0.0437688
$523$	36.7377	1.60643	0.803215	−	0.595690i	$-0.203121\pi$
$523$	36.7377	1.60643	0.803215	+	0.595690i	$0.203121\pi$
$524$	4.15449	0.181490
$525$	5.09211	0.222238
$526$	−15.1714	−0.661506
$527$	25.0523	1.09129
$528$	0.513894	0.0223644
$529$	1.00000	0.0434783
$530$	−15.4718	−0.672053
$531$	8.70408	0.377725
$532$	11.6792	0.506358
$533$	−21.3501	−0.924774
$534$	−2.85805	−0.123680
$535$	32.2689	1.39511
$536$	10.2025	0.440680
$537$	−20.1935	−0.871412
$538$	30.0545	1.29574
$539$	1.86731	0.0804309
$540$	2.56155	0.110232
$541$	23.4991	1.01030	0.505152	−	0.863031i	$-0.331437\pi$
$541$	23.4991	1.01030	0.505152	+	0.863031i	$0.331437\pi$
$542$	−25.5234	−1.09632
$543$	−19.7979	−0.849609
$544$	2.52278	0.108163
$545$	31.2856	1.34013
$546$	10.4529	0.447342
$547$	8.09388	0.346069	0.173035	−	0.984916i	$-0.444643\pi$
$547$	8.09388	0.346069	0.173035	+	0.984916i	$0.444643\pi$
$548$	−10.3838	−0.443573
$549$	0.354436	0.0151270
$550$	−0.802472	−0.0342175
$551$	3.58156	0.152580
$552$	−1.00000	−0.0425628
$553$	41.9643	1.78451
$554$	20.1539	0.856257
$555$	11.7964	0.500728
$556$	−19.4044	−0.822928
$557$	−21.1809	−0.897466	−0.448733	−	0.893666i	$-0.648124\pi$
$557$	−21.1809	−0.897466	−0.448733	+	0.893666i	$0.648124\pi$
$558$	9.93042	0.420388
$559$	−4.58600	−0.193967
$560$	8.35304	0.352980
$561$	−1.29644	−0.0547358
$562$	−19.4320	−0.819688
$563$	−41.5310	−1.75032	−0.875161	−	0.483832i	$-0.839245\pi$
$563$	−41.5310	−1.75032	−0.875161	+	0.483832i	$0.839245\pi$
$564$	6.20215	0.261158
$565$	16.6231	0.699338
$566$	−6.87622	−0.289029
$567$	3.26093	0.136946
$568$	−9.89709	−0.415273
$569$	30.1631	1.26450	0.632252	−	0.774763i	$-0.282131\pi$
$569$	30.1631	1.26450	0.632252	+	0.774763i	$0.282131\pi$
$570$	−9.17436	−0.384272
$571$	−28.9531	−1.21165	−0.605825	−	0.795598i	$-0.707157\pi$
$571$	−28.9531	−1.21165	−0.605825	+	0.795598i	$0.707157\pi$
$572$	−1.64728	−0.0688763
$573$	−1.75927	−0.0734944
$574$	−21.7193	−0.906546
$575$	1.56155	0.0651213
$576$	1.00000	0.0416667
$577$	−24.3507	−1.01373	−0.506867	−	0.862024i	$-0.669197\pi$
$577$	−24.3507	−1.01373	−0.506867	+	0.862024i	$0.669197\pi$
$578$	10.6356	0.442382
$579$	−23.8470	−0.991046
$580$	2.56155	0.106363
$581$	−27.6374	−1.14659
$582$	−13.0160	−0.539531
$583$	3.10393	0.128552
$584$	−13.5674	−0.561424
$585$	−8.21104	−0.339485
$586$	−17.3419	−0.716389
$587$	31.1042	1.28381	0.641904	−	0.766785i	$-0.278145\pi$
$587$	31.1042	1.28381	0.641904	+	0.766785i	$0.278145\pi$
$588$	3.63366	0.149849
$589$	−35.5664	−1.46549
$590$	−22.2960	−0.917910
$591$	3.71894	0.152977
$592$	4.60517	0.189271
$593$	−26.9064	−1.10491	−0.552457	−	0.833542i	$-0.686310\pi$
$593$	−26.9064	−1.10491	−0.552457	+	0.833542i	$0.686310\pi$
$594$	−0.513894	−0.0210853
$595$	−21.0729	−0.863904
$596$	−6.04894	−0.247774
$597$	5.58551	0.228600
$598$	3.20549	0.131082
$599$	20.5595	0.840038	0.420019	−	0.907515i	$-0.362023\pi$
$599$	20.5595	0.840038	0.420019	+	0.907515i	$0.362023\pi$
$600$	−1.56155	−0.0637501
$601$	−7.09979	−0.289607	−0.144803	−	0.989460i	$-0.546255\pi$
$601$	−7.09979	−0.289607	−0.144803	+	0.989460i	$0.546255\pi$
$602$	−4.66531	−0.190144
$603$	−10.2025	−0.415477
$604$	−12.3623	−0.503013
$605$	−27.5006	−1.11806
$606$	−3.21406	−0.130562
$607$	11.2606	0.457055	0.228528	−	0.973537i	$-0.426609\pi$
$607$	11.2606	0.457055	0.228528	+	0.973537i	$0.426609\pi$
$608$	−3.58156	−0.145252
$609$	3.26093	0.132139
$610$	−0.907907	−0.0367601
$611$	−19.8809	−0.804296
$612$	−2.52278	−0.101977
$613$	25.7546	1.04022	0.520110	−	0.854099i	$-0.325891\pi$
$613$	25.7546	1.04022	0.520110	+	0.854099i	$0.325891\pi$
$614$	21.7731	0.878692
$615$	17.0611	0.687971
$616$	−1.67577	−0.0675187
$617$	29.3139	1.18013	0.590066	−	0.807355i	$-0.299102\pi$
$617$	29.3139	1.18013	0.590066	+	0.807355i	$0.299102\pi$
$618$	−4.73507	−0.190473
$619$	−10.0403	−0.403552	−0.201776	−	0.979432i	$-0.564671\pi$
$619$	−10.0403	−0.403552	−0.201776	+	0.979432i	$0.564671\pi$
$620$	−25.4373	−1.02159
$621$	1.00000	0.0401286
$622$	−12.6368	−0.506689
$623$	9.31989	0.373393
$624$	−3.20549	−0.128322
$625$	−30.3693	−1.21477
$626$	28.2444	1.12887
$627$	1.84054	0.0735042
$628$	−2.98654	−0.119176
$629$	−11.6178	−0.463233
$630$	−8.35304	−0.332793
$631$	24.7497	0.985270	0.492635	−	0.870236i	$-0.336034\pi$
$631$	24.7497	0.985270	0.492635	+	0.870236i	$0.336034\pi$
$632$	−12.8688	−0.511895
$633$	7.31232	0.290639
$634$	17.8766	0.709969
$635$	−34.3968	−1.36499
$636$	6.04002	0.239502
$637$	−11.6477	−0.461497
$638$	−0.513894	−0.0203452
$639$	9.89709	0.391523
$640$	−2.56155	−0.101254
$641$	1.37443	0.0542869	0.0271434	−	0.999632i	$-0.491359\pi$
$641$	1.37443	0.0542869	0.0271434	+	0.999632i	$0.491359\pi$
$642$	−12.5974	−0.497179
$643$	26.5933	1.04874	0.524368	−	0.851492i	$-0.324302\pi$
$643$	26.5933	1.04874	0.524368	+	0.851492i	$0.324302\pi$
$644$	3.26093	0.128499
$645$	3.66473	0.144299
$646$	9.03550	0.355497
$647$	−20.4971	−0.805825	−0.402912	−	0.915239i	$-0.632002\pi$
$647$	−20.4971	−0.805825	−0.402912	+	0.915239i	$0.632002\pi$
$648$	−1.00000	−0.0392837
$649$	4.47297	0.175580
$650$	5.00554	0.196334
$651$	−32.3824	−1.26917
$652$	14.1375	0.553669
$653$	−16.1462	−0.631852	−0.315926	−	0.948784i	$-0.602315\pi$
$653$	−16.1462	−0.631852	−0.315926	+	0.948784i	$0.602315\pi$
$654$	−12.2135	−0.477587
$655$	10.6419	0.415815
$656$	6.66047	0.260048
$657$	13.5674	0.529315
$658$	−20.2248	−0.788443
$659$	−13.8198	−0.538341	−0.269171	−	0.963093i	$-0.586750\pi$
$659$	−13.8198	−0.538341	−0.269171	+	0.963093i	$0.586750\pi$
$660$	1.31637	0.0512395
$661$	−25.5665	−0.994421	−0.497210	−	0.867630i	$-0.665642\pi$
$661$	−25.5665	−0.994421	−0.497210	+	0.867630i	$0.665642\pi$
$662$	16.9855	0.660159
$663$	8.08675	0.314063
$664$	8.47531	0.328906
$665$	29.9169	1.16013
$666$	−4.60517	−0.178447
$667$	1.00000	0.0387202
$668$	−12.7796	−0.494459
$669$	−26.4260	−1.02169
$670$	26.1342	1.00965
$671$	0.182143	0.00703153
$672$	−3.26093	−0.125793
$673$	26.4633	1.02009	0.510043	−	0.860149i	$-0.329629\pi$
$673$	26.4633	1.02009	0.510043	+	0.860149i	$0.329629\pi$
$674$	4.15420	0.160014
$675$	1.56155	0.0601042
$676$	−2.72483	−0.104801
$677$	7.14704	0.274683	0.137341	−	0.990524i	$-0.456144\pi$
$677$	7.14704	0.274683	0.137341	+	0.990524i	$0.456144\pi$
$678$	−6.48945	−0.249226
$679$	42.4443	1.62886
$680$	6.46224	0.247815
$681$	5.83322	0.223529
$682$	5.10318	0.195411
$683$	17.4363	0.667182	0.333591	−	0.942718i	$-0.391740\pi$
$683$	17.4363	0.667182	0.333591	+	0.942718i	$0.391740\pi$
$684$	3.58156	0.136944
$685$	−26.5986	−1.01628
$686$	10.9774	0.419119
$687$	22.8231	0.870755
$688$	1.43067	0.0545437
$689$	−19.3612	−0.737604
$690$	−2.56155	−0.0975166
$691$	−16.3665	−0.622610	−0.311305	−	0.950310i	$-0.600766\pi$
$691$	−16.3665	−0.622610	−0.311305	+	0.950310i	$0.600766\pi$
$692$	14.6234	0.555899
$693$	1.67577	0.0636573
$694$	−7.27163	−0.276027
$695$	−49.7053	−1.88543
$696$	−1.00000	−0.0379049
$697$	−16.8029	−0.636455
$698$	0.326949	0.0123752
$699$	24.9439	0.943466
$700$	5.09211	0.192464
$701$	−4.94942	−0.186937	−0.0934684	−	0.995622i	$-0.529795\pi$
$701$	−4.94942	−0.186937	−0.0934684	+	0.995622i	$0.529795\pi$
$702$	3.20549	0.120983
$703$	16.4937	0.622071
$704$	0.513894	0.0193681
$705$	15.8871	0.598344
$706$	5.39173	0.202920
$707$	10.4808	0.394171
$708$	8.70408	0.327119
$709$	−15.9135	−0.597643	−0.298821	−	0.954309i	$-0.596593\pi$
$709$	−15.9135	−0.597643	−0.298821	+	0.954309i	$0.596593\pi$
$710$	−25.3519	−0.951440
$711$	12.8688	0.482619
$712$	−2.85805	−0.107110
$713$	−9.93042	−0.371897
$714$	8.22661	0.307873
$715$	−4.21960	−0.157804
$716$	−20.1935	−0.754665
$717$	−28.4198	−1.06136
$718$	−11.0689	−0.413088
$719$	−24.6306	−0.918565	−0.459282	−	0.888290i	$-0.651893\pi$
$719$	−24.6306	−0.918565	−0.459282	+	0.888290i	$0.651893\pi$
$720$	2.56155	0.0954634
$721$	15.4407	0.575043
$722$	6.17241	0.229713
$723$	−22.4261	−0.834035
$724$	−19.7979	−0.735783
$725$	1.56155	0.0579946
$726$	10.7359	0.398447
$727$	−10.1864	−0.377794	−0.188897	−	0.981997i	$-0.560491\pi$
$727$	−10.1864	−0.377794	−0.188897	+	0.981997i	$0.560491\pi$
$728$	10.4529	0.387409
$729$	1.00000	0.0370370
$730$	−34.7537	−1.28629
$731$	−3.60926	−0.133493
$732$	0.354436	0.0131003
$733$	−49.5873	−1.83155	−0.915775	−	0.401692i	$-0.868422\pi$
$733$	−49.5873	−1.83155	−0.915775	+	0.401692i	$0.868422\pi$
$734$	2.38125	0.0878934
$735$	9.30780	0.343323
$736$	−1.00000	−0.0368605
$737$	−5.24299	−0.193128
$738$	−6.66047	−0.245175
$739$	21.7988	0.801881	0.400940	−	0.916104i	$-0.368683\pi$
$739$	21.7988	0.801881	0.400940	+	0.916104i	$0.368683\pi$
$740$	11.7964	0.433644
$741$	−11.4807	−0.421753
$742$	−19.6961	−0.723065
$743$	4.76074	0.174655	0.0873274	−	0.996180i	$-0.472167\pi$
$743$	4.76074	0.174655	0.0873274	+	0.996180i	$0.472167\pi$
$744$	9.93042	0.364067
$745$	−15.4947	−0.567681
$746$	18.3022	0.670090
$747$	−8.47531	−0.310095
$748$	−1.29644	−0.0474026
$749$	41.0792	1.50100
$750$	8.80776	0.321614
$751$	−18.7265	−0.683340	−0.341670	−	0.939820i	$-0.610992\pi$
$751$	−18.7265	−0.683340	−0.341670	+	0.939820i	$0.610992\pi$
$752$	6.20215	0.226169
$753$	9.30608	0.339133
$754$	3.20549	0.116737
$755$	−31.6666	−1.15246
$756$	3.26093	0.118599
$757$	32.6893	1.18811	0.594057	−	0.804423i	$-0.297525\pi$
$757$	32.6893	1.18811	0.594057	+	0.804423i	$0.297525\pi$
$758$	−2.60318	−0.0945518
$759$	0.513894	0.0186532
$760$	−9.17436	−0.332789
$761$	25.2991	0.917093	0.458546	−	0.888670i	$-0.348370\pi$
$761$	25.2991	0.917093	0.458546	+	0.888670i	$0.348370\pi$
$762$	13.4281	0.486448
$763$	39.8275	1.44185
$764$	−1.75927	−0.0636480
$765$	−6.46224	−0.233643
$766$	−17.4335	−0.629896
$767$	−27.9009	−1.00744
$768$	1.00000	0.0360844
$769$	−29.2220	−1.05377	−0.526887	−	0.849935i	$-0.676641\pi$
$769$	−29.2220	−1.05377	−0.526887	+	0.849935i	$0.676641\pi$
$770$	−4.29258	−0.154694
$771$	11.4385	0.411946
$772$	−23.8470	−0.858271
$773$	−49.5948	−1.78380	−0.891900	−	0.452233i	$-0.850628\pi$
$773$	−49.5948	−1.78380	−0.891900	+	0.452233i	$0.850628\pi$
$774$	−1.43067	−0.0514243
$775$	−15.5069	−0.557023
$776$	−13.0160	−0.467248
$777$	15.0171	0.538736
$778$	11.7377	0.420815
$779$	23.8549	0.854690
$780$	−8.21104	−0.294002
$781$	5.08605	0.181993
$782$	2.52278	0.0902145
$783$	1.00000	0.0357371
$784$	3.63366	0.129773
$785$	−7.65018	−0.273047
$786$	−4.15449	−0.148186
$787$	−46.2909	−1.65009	−0.825046	−	0.565065i	$-0.808851\pi$
$787$	−46.2909	−1.65009	−0.825046	+	0.565065i	$0.808851\pi$
$788$	3.71894	0.132482
$789$	15.1714	0.540117
$790$	−32.9642	−1.17281
$791$	21.1616	0.752421
$792$	−0.513894	−0.0182604
$793$	−1.13614	−0.0403456
$794$	−12.2931	−0.436266
$795$	15.4718	0.548729
$796$	5.58551	0.197973
$797$	35.2597	1.24896	0.624482	−	0.781039i	$-0.285310\pi$
$797$	35.2597	1.24896	0.624482	+	0.781039i	$0.285310\pi$
$798$	−11.6792	−0.413440
$799$	−15.6467	−0.553539
$800$	−1.56155	−0.0552092
$801$	2.85805	0.100984
$802$	28.2496	0.997527
$803$	6.97221	0.246044
$804$	−10.2025	−0.359813
$805$	8.35304	0.294406
$806$	−31.8319	−1.12123
$807$	−30.0545	−1.05797
$808$	−3.21406	−0.113070
$809$	12.8762	0.452704	0.226352	−	0.974046i	$-0.427320\pi$
$809$	12.8762	0.452704	0.226352	+	0.974046i	$0.427320\pi$
$810$	−2.56155	−0.0900038
$811$	−30.0527	−1.05529	−0.527647	−	0.849464i	$-0.676926\pi$
$811$	−30.0527	−1.05529	−0.527647	+	0.849464i	$0.676926\pi$
$812$	3.26093	0.114436
$813$	25.5234	0.895145
$814$	−2.36657	−0.0829481
$815$	36.2140	1.26852
$816$	−2.52278	−0.0883150
$817$	5.12403	0.179267
$818$	35.5775	1.24394
$819$	−10.4529	−0.365253
$820$	17.0611	0.595801
$821$	−36.4669	−1.27270	−0.636352	−	0.771399i	$-0.719557\pi$
$821$	−36.4669	−1.27270	−0.636352	+	0.771399i	$0.719557\pi$
$822$	10.3838	0.362176
$823$	−10.3311	−0.360120	−0.180060	−	0.983656i	$-0.557629\pi$
$823$	−10.3311	−0.360120	−0.180060	+	0.983656i	$0.557629\pi$
$824$	−4.73507	−0.164954
$825$	0.802472	0.0279385
$826$	−28.3834	−0.987584
$827$	−19.3997	−0.674594	−0.337297	−	0.941398i	$-0.609513\pi$
$827$	−19.3997	−0.674594	−0.337297	+	0.941398i	$0.609513\pi$
$828$	1.00000	0.0347524
$829$	−15.9866	−0.555239	−0.277619	−	0.960691i	$-0.589545\pi$
$829$	−15.9866	−0.555239	−0.277619	+	0.960691i	$0.589545\pi$
$830$	21.7099	0.753563
$831$	−20.1539	−0.699131
$832$	−3.20549	−0.111130
$833$	−9.16692	−0.317615
$834$	19.4044	0.671918
$835$	−32.7357	−1.13287
$836$	1.84054	0.0636565
$837$	−9.93042	−0.343246
$838$	−21.6897	−0.749259
$839$	−32.5826	−1.12488	−0.562439	−	0.826839i	$-0.690137\pi$
$839$	−32.5826	−1.12488	−0.562439	+	0.826839i	$0.690137\pi$
$840$	−8.35304	−0.288207
$841$	1.00000	0.0344828
$842$	−30.8811	−1.06423
$843$	19.4320	0.669272
$844$	7.31232	0.251700
$845$	−6.97978	−0.240112
$846$	−6.20215	−0.213234
$847$	−35.0090	−1.20293
$848$	6.04002	0.207415
$849$	6.87622	0.235991
$850$	3.93946	0.135122
$851$	4.60517	0.157863
$852$	9.89709	0.339069
$853$	−45.9769	−1.57422	−0.787110	−	0.616812i	$-0.788424\pi$
$853$	−45.9769	−1.57422	−0.787110	+	0.616812i	$0.788424\pi$
$854$	−1.15579	−0.0395504
$855$	9.17436	0.313757
$856$	−12.5974	−0.430570
$857$	44.4844	1.51956	0.759780	−	0.650181i	$-0.225307\pi$
$857$	44.4844	1.51956	0.759780	+	0.650181i	$0.225307\pi$
$858$	1.64728	0.0562373
$859$	18.6495	0.636313	0.318157	−	0.948038i	$-0.396936\pi$
$859$	18.6495	0.636313	0.318157	+	0.948038i	$0.396936\pi$
$860$	3.66473	0.124966
$861$	21.7193	0.740192
$862$	16.7845	0.571681
$863$	−8.00602	−0.272528	−0.136264	−	0.990673i	$-0.543510\pi$
$863$	−8.00602	−0.272528	−0.136264	+	0.990673i	$0.543510\pi$
$864$	−1.00000	−0.0340207
$865$	37.4586	1.27363
$866$	34.7198	1.17983
$867$	−10.6356	−0.361203
$868$	−32.3824	−1.09913
$869$	6.61321	0.224338
$870$	−2.56155	−0.0868448
$871$	32.7039	1.10813
$872$	−12.2135	−0.413603
$873$	13.0160	0.440525
$874$	−3.58156	−0.121148
$875$	−28.7215	−0.970964
$876$	13.5674	0.458401
$877$	−17.1696	−0.579776	−0.289888	−	0.957061i	$-0.593618\pi$
$877$	−17.1696	−0.579776	−0.289888	+	0.957061i	$0.593618\pi$
$878$	3.46274	0.116862
$879$	17.3419	0.584929
$880$	1.31637	0.0443747
$881$	−32.9558	−1.11031	−0.555155	−	0.831747i	$-0.687341\pi$
$881$	−32.9558	−1.11031	−0.555155	+	0.831747i	$0.687341\pi$
$882$	−3.63366	−0.122352
$883$	−45.9615	−1.54673	−0.773363	−	0.633963i	$-0.781427\pi$
$883$	−45.9615	−1.54673	−0.773363	+	0.633963i	$0.781427\pi$
$884$	8.08675	0.271987
$885$	22.2960	0.749471
$886$	14.4669	0.486025
$887$	−0.352247	−0.0118273	−0.00591364	−	0.999983i	$-0.501882\pi$
$887$	−0.352247	−0.0118273	−0.00591364	+	0.999983i	$0.501882\pi$
$888$	−4.60517	−0.154539
$889$	−43.7880	−1.46860
$890$	−7.32104	−0.245402
$891$	0.513894	0.0172161
$892$	−26.4260	−0.884807
$893$	22.2134	0.743342
$894$	6.04894	0.202307
$895$	−51.7266	−1.72903
$896$	−3.26093	−0.108940
$897$	−3.20549	−0.107028
$898$	27.0281	0.901940
$899$	−9.93042	−0.331198
$900$	1.56155	0.0520518
$901$	−15.2376	−0.507640
$902$	−3.42277	−0.113966
$903$	4.66531	0.155252
$904$	−6.48945	−0.215836
$905$	−50.7133	−1.68577
$906$	12.3623	0.410708
$907$	56.8694	1.88832	0.944158	−	0.329492i	$-0.106877\pi$
$907$	56.8694	1.88832	0.944158	+	0.329492i	$0.106877\pi$
$908$	5.83322	0.193582
$909$	3.21406	0.106604
$910$	26.7756	0.887603
$911$	−43.3244	−1.43540	−0.717700	−	0.696352i	$-0.754805\pi$
$911$	−43.3244	−1.43540	−0.717700	+	0.696352i	$0.754805\pi$
$912$	3.58156	0.118597
$913$	−4.35541	−0.144143
$914$	−31.4925	−1.04168
$915$	0.907907	0.0300145
$916$	22.8231	0.754096
$917$	13.5475	0.447378
$918$	2.52278	0.0832642
$919$	16.3072	0.537924	0.268962	−	0.963151i	$-0.413319\pi$
$919$	16.3072	0.537924	0.268962	+	0.963151i	$0.413319\pi$
$920$	−2.56155	−0.0844519
$921$	−21.7731	−0.717449
$922$	36.7196	1.20929
$923$	−31.7250	−1.04424
$924$	1.67577	0.0551288
$925$	7.19121	0.236446
$926$	−34.0251	−1.11813
$927$	4.73507	0.155520
$928$	−1.00000	−0.0328266
$929$	−28.4605	−0.933759	−0.466880	−	0.884321i	$-0.654622\pi$
$929$	−28.4605	−0.933759	−0.466880	+	0.884321i	$0.654622\pi$
$930$	25.4373	0.834122
$931$	13.0142	0.426522
$932$	24.9439	0.817066
$933$	12.6368	0.413710
$934$	8.65038	0.283049
$935$	−3.32090	−0.108605
$936$	3.20549	0.104775
$937$	23.3998	0.764439	0.382219	−	0.924072i	$-0.375160\pi$
$937$	23.3998	0.764439	0.382219	+	0.924072i	$0.375160\pi$
$938$	33.2695	1.08629
$939$	−28.2444	−0.921722
$940$	15.8871	0.518181
$941$	16.8285	0.548592	0.274296	−	0.961645i	$-0.411555\pi$
$941$	16.8285	0.548592	0.274296	+	0.961645i	$0.411555\pi$
$942$	2.98654	0.0973067
$943$	6.66047	0.216895
$944$	8.70408	0.283294
$945$	8.35304	0.271724
$946$	−0.735212	−0.0239038
$947$	19.2516	0.625594	0.312797	−	0.949820i	$-0.398734\pi$
$947$	19.2516	0.625594	0.312797	+	0.949820i	$0.398734\pi$
$948$	12.8688	0.417960
$949$	−43.4902	−1.41175
$950$	−5.59280	−0.181454
$951$	−17.8766	−0.579687
$952$	8.22661	0.266626
$953$	−23.1775	−0.750793	−0.375396	−	0.926864i	$-0.622493\pi$
$953$	−23.1775	−0.750793	−0.375396	+	0.926864i	$0.622493\pi$
$954$	−6.04002	−0.195553
$955$	−4.50645	−0.145825
$956$	−28.4198	−0.919162
$957$	0.513894	0.0166118
$958$	−18.2393	−0.589285
$959$	−33.8607	−1.09342
$960$	2.56155	0.0826738
$961$	67.6133	2.18107
$962$	14.7618	0.475940
$963$	12.5974	0.405945
$964$	−22.4261	−0.722296
$965$	−61.0853	−1.96640
$966$	−3.26093	−0.104919
$967$	12.2462	0.393813	0.196906	−	0.980422i	$-0.436911\pi$
$967$	12.2462	0.393813	0.196906	+	0.980422i	$0.436911\pi$
$968$	10.7359	0.345065
$969$	−9.03550	−0.290262
$970$	−33.3412	−1.07052
$971$	29.9414	0.960864	0.480432	−	0.877032i	$-0.340480\pi$
$971$	29.9414	0.960864	0.480432	+	0.877032i	$0.340480\pi$
$972$	1.00000	0.0320750
$973$	−63.2763	−2.02854
$974$	42.4026	1.35867
$975$	−5.00554	−0.160306
$976$	0.354436	0.0113452
$977$	−34.3769	−1.09982	−0.549908	−	0.835226i	$-0.685337\pi$
$977$	−34.3769	−1.09982	−0.549908	+	0.835226i	$0.685337\pi$
$978$	−14.1375	−0.452069
$979$	1.46873	0.0469409
$980$	9.30780	0.297327
$981$	12.2135	0.389948
$982$	−14.7408	−0.470399
$983$	−4.39564	−0.140199	−0.0700996	−	0.997540i	$-0.522332\pi$
$983$	−4.39564	−0.140199	−0.0700996	+	0.997540i	$0.522332\pi$
$984$	−6.66047	−0.212328
$985$	9.52625	0.303532
$986$	2.52278	0.0803417
$987$	20.2248	0.643761
$988$	−11.4807	−0.365249
$989$	1.43067	0.0454926
$990$	−1.31637	−0.0418369
$991$	2.49351	0.0792088	0.0396044	−	0.999215i	$-0.487390\pi$
$991$	2.49351	0.0792088	0.0396044	+	0.999215i	$0.487390\pi$
$992$	9.93042	0.315291
$993$	−16.9855	−0.539018
$994$	−32.2737	−1.02366
$995$	14.3076	0.453581
$996$	−8.47531	−0.268550
$997$	−19.5166	−0.618098	−0.309049	−	0.951046i	$-0.600011\pi$
$997$	−19.5166	−0.618098	−0.309049	+	0.951046i	$0.600011\pi$
$998$	−16.3704	−0.518195
$999$	4.60517	0.145701

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	4002.2.a.bf.1.5	✓	6

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
4002.2.a.bf.1.5	✓	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)

\(f(q)\)	\(=\)	\(q-1.00000 q^{2} +1.00000 q^{3} +1.00000 q^{4} +2.56155 q^{5} -1.00000 q^{6} +3.26093 q^{7} -1.00000 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q-1.00000 q^{2} +1.00000 q^{3} +1.00000 q^{4} +2.56155 q^{5} -1.00000 q^{6} +3.26093 q^{7} -1.00000 q^{8} +1.00000 q^{9} -2.56155 q^{10} +0.513894 q^{11} +1.00000 q^{12} -3.20549 q^{13} -3.26093 q^{14} +2.56155 q^{15} +1.00000 q^{16} -2.52278 q^{17} -1.00000 q^{18} +3.58156 q^{19} +2.56155 q^{20} +3.26093 q^{21} -0.513894 q^{22} +1.00000 q^{23} -1.00000 q^{24} +1.56155 q^{25} +3.20549 q^{26} +1.00000 q^{27} +3.26093 q^{28} +1.00000 q^{29} -2.56155 q^{30} -9.93042 q^{31} -1.00000 q^{32} +0.513894 q^{33} +2.52278 q^{34} +8.35304 q^{35} +1.00000 q^{36} +4.60517 q^{37} -3.58156 q^{38} -3.20549 q^{39} -2.56155 q^{40} +6.66047 q^{41} -3.26093 q^{42} +1.43067 q^{43} +0.513894 q^{44} +2.56155 q^{45} -1.00000 q^{46} +6.20215 q^{47} +1.00000 q^{48} +3.63366 q^{49} -1.56155 q^{50} -2.52278 q^{51} -3.20549 q^{52} +6.04002 q^{53} -1.00000 q^{54} +1.31637 q^{55} -3.26093 q^{56} +3.58156 q^{57} -1.00000 q^{58} +8.70408 q^{59} +2.56155 q^{60} +0.354436 q^{61} +9.93042 q^{62} +3.26093 q^{63} +1.00000 q^{64} -8.21104 q^{65} -0.513894 q^{66} -10.2025 q^{67} -2.52278 q^{68} +1.00000 q^{69} -8.35304 q^{70} +9.89709 q^{71} -1.00000 q^{72} +13.5674 q^{73} -4.60517 q^{74} +1.56155 q^{75} +3.58156 q^{76} +1.67577 q^{77} +3.20549 q^{78} +12.8688 q^{79} +2.56155 q^{80} +1.00000 q^{81} -6.66047 q^{82} -8.47531 q^{83} +3.26093 q^{84} -6.46224 q^{85} -1.43067 q^{86} +1.00000 q^{87} -0.513894 q^{88} +2.85805 q^{89} -2.56155 q^{90} -10.4529 q^{91} +1.00000 q^{92} -9.93042 q^{93} -6.20215 q^{94} +9.17436 q^{95} -1.00000 q^{96} +13.0160 q^{97} -3.63366 q^{98} +0.513894 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 6 q - 6 q^{2} + 6 q^{3} + 6 q^{4} + 3 q^{5} - 6 q^{6} + 2 q^{7} - 6 q^{8} + 6 q^{9}+O(q^{10}) \) 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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