LMFDB - Embedded newform 6042.2.a.ba.1.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [6042,2,Mod(1,6042)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(6042, 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("6042.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 6042 = 2 \cdot 3 \cdot 19 \cdot 53 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	6042.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:	$48.2456129013$
Analytic rank:	$0$
Dimension:	$9$
Coefficient field:	$\mathbb{Q}[x]/(x^{9} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{9} - x^{8} - 25x^{7} + 62x^{6} + 76x^{5} - 360x^{4} + 182x^{3} + 459x^{2} - 595x + 199 $ x^9 - x^8 - 25x^7 + 62x^6 + 76x^5 - 360x^4 + 182x^3 + 459x^2 - 595*x + 199
Coefficient ring:	$\Z[a_1, \ldots, a_{13}]$
Coefficient ring index:	$ 2^{2} $
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.3
Root			$1.36790$ of defining polynomial
Character	$\chi$	$=$	6042.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.00000 q^{2} +1.00000 q^{3} +1.00000 q^{4} -1.75621 q^{5} -1.00000 q^{6} +2.24076 q^{7} -1.00000 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q-1.00000 q^{2} +1.00000 q^{3} +1.00000 q^{4} -1.75621 q^{5} -1.00000 q^{6} +2.24076 q^{7} -1.00000 q^{8} +1.00000 q^{9} +1.75621 q^{10} -3.18875 q^{11} +1.00000 q^{12} +4.34185 q^{13} -2.24076 q^{14} -1.75621 q^{15} +1.00000 q^{16} +1.72009 q^{17} -1.00000 q^{18} -1.00000 q^{19} -1.75621 q^{20} +2.24076 q^{21} +3.18875 q^{22} +4.06414 q^{23} -1.00000 q^{24} -1.91574 q^{25} -4.34185 q^{26} +1.00000 q^{27} +2.24076 q^{28} +4.17214 q^{29} +1.75621 q^{30} -0.392667 q^{31} -1.00000 q^{32} -3.18875 q^{33} -1.72009 q^{34} -3.93524 q^{35} +1.00000 q^{36} +3.33396 q^{37} +1.00000 q^{38} +4.34185 q^{39} +1.75621 q^{40} -1.43255 q^{41} -2.24076 q^{42} +4.36628 q^{43} -3.18875 q^{44} -1.75621 q^{45} -4.06414 q^{46} +1.18592 q^{47} +1.00000 q^{48} -1.97899 q^{49} +1.91574 q^{50} +1.72009 q^{51} +4.34185 q^{52} -1.00000 q^{53} -1.00000 q^{54} +5.60011 q^{55} -2.24076 q^{56} -1.00000 q^{57} -4.17214 q^{58} -11.6999 q^{59} -1.75621 q^{60} +6.00642 q^{61} +0.392667 q^{62} +2.24076 q^{63} +1.00000 q^{64} -7.62517 q^{65} +3.18875 q^{66} -1.96639 q^{67} +1.72009 q^{68} +4.06414 q^{69} +3.93524 q^{70} +11.8830 q^{71} -1.00000 q^{72} +4.50067 q^{73} -3.33396 q^{74} -1.91574 q^{75} -1.00000 q^{76} -7.14524 q^{77} -4.34185 q^{78} +2.89696 q^{79} -1.75621 q^{80} +1.00000 q^{81} +1.43255 q^{82} -11.8754 q^{83} +2.24076 q^{84} -3.02084 q^{85} -4.36628 q^{86} +4.17214 q^{87} +3.18875 q^{88} +2.01543 q^{89} +1.75621 q^{90} +9.72904 q^{91} +4.06414 q^{92} -0.392667 q^{93} -1.18592 q^{94} +1.75621 q^{95} -1.00000 q^{96} +10.0581 q^{97} +1.97899 q^{98} -3.18875 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 9 q - 9 q^{2} + 9 q^{3} + 9 q^{4} + 2 q^{5} - 9 q^{6} + 10 q^{7} - 9 q^{8} + 9 q^{9}+O(q^{10}) $ 9 * q - 9 * q^2 + 9 * q^3 + 9 * q^4 + 2 * q^5 - 9 * q^6 + 10 * q^7 - 9 * q^8 + 9 * q^9	\( 9 q - 9 q^{2} + 9 q^{3} + 9 q^{4} + 2 q^{5} - 9 q^{6} + 10 q^{7} - 9 q^{8} + 9 q^{9} - 2 q^{10} + 7 q^{11} + 9 q^{12} + 2 q^{13} - 10 q^{14} + 2 q^{15} + 9 q^{16} + 4 q^{17} - 9 q^{18} - 9 q^{19} + 2 q^{20} + 10 q^{21} - 7 q^{22} + 15 q^{23} - 9 q^{24} + 19 q^{25} - 2 q^{26} + 9 q^{27} + 10 q^{28} + 5 q^{29} - 2 q^{30} + q^{31} - 9 q^{32} + 7 q^{33} - 4 q^{34} + 4 q^{35} + 9 q^{36} - 4 q^{37} + 9 q^{38} + 2 q^{39} - 2 q^{40} + 5 q^{41} - 10 q^{42} + 27 q^{43} + 7 q^{44} + 2 q^{45} - 15 q^{46} + 9 q^{48} + 33 q^{49} - 19 q^{50} + 4 q^{51} + 2 q^{52} - 9 q^{53} - 9 q^{54} + 26 q^{55} - 10 q^{56} - 9 q^{57} - 5 q^{58} + 7 q^{59} + 2 q^{60} + 5 q^{61} - q^{62} + 10 q^{63} + 9 q^{64} - 17 q^{65} - 7 q^{66} + 19 q^{67} + 4 q^{68} + 15 q^{69} - 4 q^{70} - 11 q^{71} - 9 q^{72} + 25 q^{73} + 4 q^{74} + 19 q^{75} - 9 q^{76} + 15 q^{77} - 2 q^{78} + 28 q^{79} + 2 q^{80} + 9 q^{81} - 5 q^{82} - 8 q^{83} + 10 q^{84} + 52 q^{85} - 27 q^{86} + 5 q^{87} - 7 q^{88} + 22 q^{89} - 2 q^{90} - 11 q^{91} + 15 q^{92} + q^{93} - 2 q^{95} - 9 q^{96} + 13 q^{97} - 33 q^{98} + 7 q^{99}+O(q^{100}) \) 9 * q - 9 * q^2 + 9 * q^3 + 9 * q^4 + 2 * q^5 - 9 * q^6 + 10 * q^7 - 9 * q^8 + 9 * q^9 - 2 * q^10 + 7 * q^11 + 9 * q^12 + 2 * q^13 - 10 * q^14 + 2 * q^15 + 9 * q^16 + 4 * q^17 - 9 * q^18 - 9 * q^19 + 2 * q^20 + 10 * q^21 - 7 * q^22 + 15 * q^23 - 9 * q^24 + 19 * q^25 - 2 * q^26 + 9 * q^27 + 10 * q^28 + 5 * q^29 - 2 * q^30 + q^31 - 9 * q^32 + 7 * q^33 - 4 * q^34 + 4 * q^35 + 9 * q^36 - 4 * q^37 + 9 * q^38 + 2 * q^39 - 2 * q^40 + 5 * q^41 - 10 * q^42 + 27 * q^43 + 7 * q^44 + 2 * q^45 - 15 * q^46 + 9 * q^48 + 33 * q^49 - 19 * q^50 + 4 * q^51 + 2 * q^52 - 9 * q^53 - 9 * q^54 + 26 * q^55 - 10 * q^56 - 9 * q^57 - 5 * q^58 + 7 * q^59 + 2 * q^60 + 5 * q^61 - q^62 + 10 * q^63 + 9 * q^64 - 17 * q^65 - 7 * q^66 + 19 * q^67 + 4 * q^68 + 15 * q^69 - 4 * q^70 - 11 * q^71 - 9 * q^72 + 25 * q^73 + 4 * q^74 + 19 * q^75 - 9 * q^76 + 15 * q^77 - 2 * q^78 + 28 * q^79 + 2 * q^80 + 9 * q^81 - 5 * q^82 - 8 * q^83 + 10 * q^84 + 52 * q^85 - 27 * q^86 + 5 * q^87 - 7 * q^88 + 22 * q^89 - 2 * q^90 - 11 * q^91 + 15 * q^92 + q^93 - 2 * q^95 - 9 * q^96 + 13 * q^97 - 33 * 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
$5$	−1.75621	−0.785399	−0.392700	−	0.919667i	$-0.628459\pi$
$5$	−1.75621	−0.785399	−0.392700	+	0.919667i	$0.628459\pi$
$6$	−1.00000	−0.408248
$7$	2.24076	0.846928	0.423464	−	0.905913i	$-0.360814\pi$
$7$	2.24076	0.846928	0.423464	+	0.905913i	$0.360814\pi$
$8$	−1.00000	−0.353553
$9$	1.00000	0.333333
$10$	1.75621	0.555361
$11$	−3.18875	−0.961446	−0.480723	−	0.876873i	$-0.659626\pi$
$11$	−3.18875	−0.961446	−0.480723	+	0.876873i	$0.659626\pi$
$12$	1.00000	0.288675
$13$	4.34185	1.20421	0.602106	−	0.798416i	$-0.294329\pi$
$13$	4.34185	1.20421	0.602106	+	0.798416i	$0.294329\pi$
$14$	−2.24076	−0.598869
$15$	−1.75621	−0.453450
$16$	1.00000	0.250000
$17$	1.72009	0.417184	0.208592	−	0.978003i	$-0.433112\pi$
$17$	1.72009	0.417184	0.208592	+	0.978003i	$0.433112\pi$
$18$	−1.00000	−0.235702
$19$	−1.00000	−0.229416
$19$	−1.00000	−0.229416
$20$	−1.75621	−0.392700
$21$	2.24076	0.488974
$22$	3.18875	0.679845
$23$	4.06414	0.847431	0.423716	−	0.905795i	$-0.360726\pi$
$23$	4.06414	0.847431	0.423716	+	0.905795i	$0.360726\pi$
$24$	−1.00000	−0.204124
$25$	−1.91574	−0.383148
$26$	−4.34185	−0.851506
$27$	1.00000	0.192450
$28$	2.24076	0.423464
$29$	4.17214	0.774747	0.387373	−	0.921923i	$-0.373382\pi$
$29$	4.17214	0.774747	0.387373	+	0.921923i	$0.373382\pi$
$30$	1.75621	0.320638
$31$	−0.392667	−0.0705250	−0.0352625	−	0.999378i	$-0.511227\pi$
$31$	−0.392667	−0.0705250	−0.0352625	+	0.999378i	$0.511227\pi$
$32$	−1.00000	−0.176777
$33$	−3.18875	−0.555091
$34$	−1.72009	−0.294994
$35$	−3.93524	−0.665177
$36$	1.00000	0.166667
$37$	3.33396	0.548100	0.274050	−	0.961715i	$-0.411637\pi$
$37$	3.33396	0.548100	0.274050	+	0.961715i	$0.411637\pi$
$38$	1.00000	0.162221
$39$	4.34185	0.695252
$40$	1.75621	0.277680
$41$	−1.43255	−0.223726	−0.111863	−	0.993724i	$-0.535682\pi$
$41$	−1.43255	−0.223726	−0.111863	+	0.993724i	$0.535682\pi$
$42$	−2.24076	−0.345757
$43$	4.36628	0.665851	0.332926	−	0.942953i	$-0.391964\pi$
$43$	4.36628	0.665851	0.332926	+	0.942953i	$0.391964\pi$
$44$	−3.18875	−0.480723
$45$	−1.75621	−0.261800
$46$	−4.06414	−0.599224
$47$	1.18592	0.172985	0.0864924	−	0.996253i	$-0.472434\pi$
$47$	1.18592	0.172985	0.0864924	+	0.996253i	$0.472434\pi$
$48$	1.00000	0.144338
$49$	−1.97899	−0.282713
$50$	1.91574	0.270927
$51$	1.72009	0.240861
$52$	4.34185	0.602106
$53$	−1.00000	−0.137361
$53$	−1.00000	−0.137361
$54$	−1.00000	−0.136083
$55$	5.60011	0.755118
$56$	−2.24076	−0.299434
$57$	−1.00000	−0.132453
$58$	−4.17214	−0.547829
$59$	−11.6999	−1.52320	−0.761598	−	0.648050i	$-0.775585\pi$
$59$	−11.6999	−1.52320	−0.761598	+	0.648050i	$0.775585\pi$
$60$	−1.75621	−0.226725
$61$	6.00642	0.769044	0.384522	−	0.923116i	$-0.374366\pi$
$61$	6.00642	0.769044	0.384522	+	0.923116i	$0.374366\pi$
$62$	0.392667	0.0498687
$63$	2.24076	0.282309
$64$	1.00000	0.125000
$65$	−7.62517	−0.945786
$66$	3.18875	0.392508
$67$	−1.96639	−0.240232	−0.120116	−	0.992760i	$-0.538327\pi$
$67$	−1.96639	−0.240232	−0.120116	+	0.992760i	$0.538327\pi$
$68$	1.72009	0.208592
$69$	4.06414	0.489265
$70$	3.93524	0.470351
$71$	11.8830	1.41025	0.705124	−	0.709084i	$-0.250891\pi$
$71$	11.8830	1.41025	0.705124	+	0.709084i	$0.250891\pi$
$72$	−1.00000	−0.117851
$73$	4.50067	0.526763	0.263382	−	0.964692i	$-0.415162\pi$
$73$	4.50067	0.526763	0.263382	+	0.964692i	$0.415162\pi$
$74$	−3.33396	−0.387565
$75$	−1.91574	−0.221211
$76$	−1.00000	−0.114708
$77$	−7.14524	−0.814275
$78$	−4.34185	−0.491617
$79$	2.89696	0.325934	0.162967	−	0.986632i	$-0.447894\pi$
$79$	2.89696	0.325934	0.162967	+	0.986632i	$0.447894\pi$
$80$	−1.75621	−0.196350
$81$	1.00000	0.111111
$82$	1.43255	0.158199
$83$	−11.8754	−1.30349	−0.651747	−	0.758437i	$-0.725963\pi$
$83$	−11.8754	−1.30349	−0.651747	+	0.758437i	$0.725963\pi$
$84$	2.24076	0.244487
$85$	−3.02084	−0.327656
$86$	−4.36628	−0.470828
$87$	4.17214	0.447300
$88$	3.18875	0.339922
$89$	2.01543	0.213635	0.106818	−	0.994279i	$-0.465934\pi$
$89$	2.01543	0.213635	0.106818	+	0.994279i	$0.465934\pi$
$90$	1.75621	0.185120
$91$	9.72904	1.01988
$92$	4.06414	0.423716
$93$	−0.392667	−0.0407177
$94$	−1.18592	−0.122319
$95$	1.75621	0.180183
$96$	−1.00000	−0.102062
$97$	10.0581	1.02124	0.510621	−	0.859806i	$-0.329415\pi$
$97$	10.0581	1.02124	0.510621	+	0.859806i	$0.329415\pi$
$98$	1.97899	0.199908
$99$	−3.18875	−0.320482
$100$	−1.91574	−0.191574
$101$	−1.99513	−0.198523	−0.0992613	−	0.995061i	$-0.531648\pi$
$101$	−1.99513	−0.198523	−0.0992613	+	0.995061i	$0.531648\pi$
$102$	−1.72009	−0.170315
$103$	10.6447	1.04885	0.524425	−	0.851457i	$-0.324280\pi$
$103$	10.6447	1.04885	0.524425	+	0.851457i	$0.324280\pi$
$104$	−4.34185	−0.425753
$105$	−3.93524	−0.384040
$106$	1.00000	0.0971286
$107$	3.72787	0.360387	0.180193	−	0.983631i	$-0.442328\pi$
$107$	3.72787	0.360387	0.180193	+	0.983631i	$0.442328\pi$
$108$	1.00000	0.0962250
$109$	2.28269	0.218642	0.109321	−	0.994007i	$-0.465132\pi$
$109$	2.28269	0.218642	0.109321	+	0.994007i	$0.465132\pi$
$110$	−5.60011	−0.533949
$111$	3.33396	0.316446
$112$	2.24076	0.211732
$113$	−19.0320	−1.79038	−0.895190	−	0.445685i	$-0.852960\pi$
$113$	−19.0320	−1.79038	−0.895190	+	0.445685i	$0.852960\pi$
$114$	1.00000	0.0936586
$115$	−7.13746	−0.665572
$116$	4.17214	0.387373
$117$	4.34185	0.401404
$118$	11.6999	1.07706
$119$	3.85432	0.353325
$120$	1.75621	0.160319
$121$	−0.831848	−0.0756225
$122$	−6.00642	−0.543796
$123$	−1.43255	−0.129169
$124$	−0.392667	−0.0352625
$125$	12.1455	1.08632
$126$	−2.24076	−0.199623
$127$	4.81549	0.427306	0.213653	−	0.976910i	$-0.431464\pi$
$127$	4.81549	0.427306	0.213653	+	0.976910i	$0.431464\pi$
$128$	−1.00000	−0.0883883
$129$	4.36628	0.384429
$130$	7.62517	0.668772
$131$	6.84749	0.598268	0.299134	−	0.954211i	$-0.403302\pi$
$131$	6.84749	0.598268	0.299134	+	0.954211i	$0.403302\pi$
$132$	−3.18875	−0.277545
$133$	−2.24076	−0.194299
$134$	1.96639	0.169870
$135$	−1.75621	−0.151150
$136$	−1.72009	−0.147497
$137$	−22.8052	−1.94838	−0.974190	−	0.225729i	$-0.927524\pi$
$137$	−22.8052	−1.94838	−0.974190	+	0.225729i	$0.927524\pi$
$138$	−4.06414	−0.345962
$139$	11.7959	1.00052	0.500259	−	0.865876i	$-0.333238\pi$
$139$	11.7959	1.00052	0.500259	+	0.865876i	$0.333238\pi$
$140$	−3.93524	−0.332588
$141$	1.18592	0.0998729
$142$	−11.8830	−0.997195
$143$	−13.8451	−1.15778
$144$	1.00000	0.0833333
$145$	−7.32713	−0.608485
$146$	−4.50067	−0.372478
$147$	−1.97899	−0.163224
$148$	3.33396	0.274050
$149$	15.4726	1.26756	0.633780	−	0.773513i	$-0.281502\pi$
$149$	15.4726	1.26756	0.633780	+	0.773513i	$0.281502\pi$
$150$	1.91574	0.156420
$151$	8.61221	0.700852	0.350426	−	0.936590i	$-0.386037\pi$
$151$	8.61221	0.700852	0.350426	+	0.936590i	$0.386037\pi$
$152$	1.00000	0.0811107
$153$	1.72009	0.139061
$154$	7.14524	0.575780
$155$	0.689604	0.0553903
$156$	4.34185	0.347626
$157$	11.8156	0.942990	0.471495	−	0.881869i	$-0.343715\pi$
$157$	11.8156	0.942990	0.471495	+	0.881869i	$0.343715\pi$
$158$	−2.89696	−0.230470
$159$	−1.00000	−0.0793052
$160$	1.75621	0.138840
$161$	9.10676	0.717713
$162$	−1.00000	−0.0785674
$163$	2.73682	0.214364	0.107182	−	0.994239i	$-0.465817\pi$
$163$	2.73682	0.214364	0.107182	+	0.994239i	$0.465817\pi$
$164$	−1.43255	−0.111863
$165$	5.60011	0.435968
$166$	11.8754	0.921709
$167$	−25.1262	−1.94433	−0.972163	−	0.234306i	$-0.924718\pi$
$167$	−25.1262	−1.94433	−0.972163	+	0.234306i	$0.924718\pi$
$168$	−2.24076	−0.172878
$169$	5.85162	0.450125
$170$	3.02084	0.231688
$171$	−1.00000	−0.0764719
$172$	4.36628	0.332926
$173$	14.1664	1.07705	0.538525	−	0.842610i	$-0.318982\pi$
$173$	14.1664	1.07705	0.538525	+	0.842610i	$0.318982\pi$
$174$	−4.17214	−0.316289
$175$	−4.29272	−0.324499
$176$	−3.18875	−0.240361
$177$	−11.6999	−0.879417
$178$	−2.01543	−0.151063
$179$	16.1040	1.20367	0.601836	−	0.798620i	$-0.294436\pi$
$179$	16.1040	1.20367	0.601836	+	0.798620i	$0.294436\pi$
$180$	−1.75621	−0.130900
$181$	2.58886	0.192428	0.0962142	−	0.995361i	$-0.469327\pi$
$181$	2.58886	0.192428	0.0962142	+	0.995361i	$0.469327\pi$
$182$	−9.72904	−0.721164
$183$	6.00642	0.444008
$184$	−4.06414	−0.299612
$185$	−5.85512	−0.430477
$186$	0.392667	0.0287917
$187$	−5.48496	−0.401100
$188$	1.18592	0.0864924
$189$	2.24076	0.162991
$190$	−1.75621	−0.127409
$191$	26.5086	1.91810	0.959048	−	0.283244i	$-0.0914105\pi$
$191$	26.5086	1.91810	0.959048	+	0.283244i	$0.0914105\pi$
$192$	1.00000	0.0721688
$193$	−4.15856	−0.299340	−0.149670	−	0.988736i	$-0.547821\pi$
$193$	−4.15856	−0.299340	−0.149670	+	0.988736i	$0.547821\pi$
$194$	−10.0581	−0.722127
$195$	−7.62517	−0.546050
$196$	−1.97899	−0.141356
$197$	−27.3139	−1.94604	−0.973018	−	0.230731i	$-0.925888\pi$
$197$	−27.3139	−1.94604	−0.973018	+	0.230731i	$0.925888\pi$
$198$	3.18875	0.226615
$199$	11.0136	0.780732	0.390366	−	0.920660i	$-0.372349\pi$
$199$	11.0136	0.780732	0.390366	+	0.920660i	$0.372349\pi$
$200$	1.91574	0.135463
$201$	−1.96639	−0.138698
$202$	1.99513	0.140377
$203$	9.34877	0.656155
$204$	1.72009	0.120431
$205$	2.51585	0.175715
$206$	−10.6447	−0.741649
$207$	4.06414	0.282477
$208$	4.34185	0.301053
$209$	3.18875	0.220571
$210$	3.93524	0.271557
$211$	9.16082	0.630657	0.315328	−	0.948983i	$-0.397885\pi$
$211$	9.16082	0.630657	0.315328	+	0.948983i	$0.397885\pi$
$212$	−1.00000	−0.0686803
$213$	11.8830	0.814207
$214$	−3.72787	−0.254832
$215$	−7.66808	−0.522959
$216$	−1.00000	−0.0680414
$217$	−0.879873	−0.0597296
$218$	−2.28269	−0.154603
$219$	4.50067	0.304127
$220$	5.60011	0.377559
$221$	7.46838	0.502378
$222$	−3.33396	−0.223761
$223$	8.86289	0.593503	0.296751	−	0.954955i	$-0.404097\pi$
$223$	8.86289	0.593503	0.296751	+	0.954955i	$0.404097\pi$
$224$	−2.24076	−0.149717
$225$	−1.91574	−0.127716
$226$	19.0320	1.26599
$227$	11.9694	0.794440	0.397220	−	0.917723i	$-0.369975\pi$
$227$	11.9694	0.794440	0.397220	+	0.917723i	$0.369975\pi$
$228$	−1.00000	−0.0662266
$229$	13.8310	0.913976	0.456988	−	0.889473i	$-0.348928\pi$
$229$	13.8310	0.913976	0.456988	+	0.889473i	$0.348928\pi$
$230$	7.13746	0.470630
$231$	−7.14524	−0.470122
$232$	−4.17214	−0.273914
$233$	−21.4540	−1.40550	−0.702749	−	0.711438i	$-0.748044\pi$
$233$	−21.4540	−1.40550	−0.702749	+	0.711438i	$0.748044\pi$
$234$	−4.34185	−0.283835
$235$	−2.08273	−0.135862
$236$	−11.6999	−0.761598
$237$	2.89696	0.188178
$238$	−3.85432	−0.249839
$239$	25.2498	1.63327	0.816636	−	0.577153i	$-0.195836\pi$
$239$	25.2498	1.63327	0.816636	+	0.577153i	$0.195836\pi$
$240$	−1.75621	−0.113363
$241$	−30.5643	−1.96882	−0.984410	−	0.175888i	$-0.943720\pi$
$241$	−30.5643	−1.96882	−0.984410	+	0.175888i	$0.943720\pi$
$242$	0.831848	0.0534732
$243$	1.00000	0.0641500
$244$	6.00642	0.384522
$245$	3.47551	0.222042
$246$	1.43255	0.0913360
$247$	−4.34185	−0.276265
$248$	0.392667	0.0249344
$249$	−11.8754	−0.752572
$250$	−12.1455	−0.768147
$251$	−1.08279	−0.0683449	−0.0341725	−	0.999416i	$-0.510880\pi$
$251$	−1.08279	−0.0683449	−0.0341725	+	0.999416i	$0.510880\pi$
$252$	2.24076	0.141155
$253$	−12.9595	−0.814759
$254$	−4.81549	−0.302151
$255$	−3.02084	−0.189172
$256$	1.00000	0.0625000
$257$	25.1196	1.56692	0.783460	−	0.621442i	$-0.213453\pi$
$257$	25.1196	1.56692	0.783460	+	0.621442i	$0.213453\pi$
$258$	−4.36628	−0.271833
$259$	7.47061	0.464201
$260$	−7.62517	−0.472893
$261$	4.17214	0.258249
$262$	−6.84749	−0.423039
$263$	−19.5854	−1.20769	−0.603845	−	0.797102i	$-0.706365\pi$
$263$	−19.5854	−1.20769	−0.603845	+	0.797102i	$0.706365\pi$
$264$	3.18875	0.196254
$265$	1.75621	0.107883
$266$	2.24076	0.137390
$267$	2.01543	0.123342
$268$	−1.96639	−0.120116
$269$	0.233901	0.0142612	0.00713061	−	0.999975i	$-0.497730\pi$
$269$	0.233901	0.0142612	0.00713061	+	0.999975i	$0.497730\pi$
$270$	1.75621	0.106879
$271$	−18.7274	−1.13761	−0.568804	−	0.822473i	$-0.692594\pi$
$271$	−18.7274	−1.13761	−0.568804	+	0.822473i	$0.692594\pi$
$272$	1.72009	0.104296
$273$	9.72904	0.588828
$274$	22.8052	1.37771
$275$	6.10883	0.368376
$276$	4.06414	0.244632
$277$	30.0063	1.80290	0.901451	−	0.432881i	$-0.142503\pi$
$277$	30.0063	1.80290	0.901451	+	0.432881i	$0.142503\pi$
$278$	−11.7959	−0.707473
$279$	−0.392667	−0.0235083
$280$	3.93524	0.235175
$281$	29.0055	1.73032	0.865162	−	0.501493i	$-0.167216\pi$
$281$	29.0055	1.73032	0.865162	+	0.501493i	$0.167216\pi$
$282$	−1.18592	−0.0706208
$283$	−3.74906	−0.222858	−0.111429	−	0.993772i	$-0.535543\pi$
$283$	−3.74906	−0.222858	−0.111429	+	0.993772i	$0.535543\pi$
$284$	11.8830	0.705124
$285$	1.75621	0.104029
$286$	13.8451	0.818677
$287$	−3.21000	−0.189480
$288$	−1.00000	−0.0589256
$289$	−14.0413	−0.825957
$290$	7.32713	0.430264
$291$	10.0581	0.589615
$292$	4.50067	0.263382
$293$	1.12786	0.0658901	0.0329451	−	0.999457i	$-0.489511\pi$
$293$	1.12786	0.0658901	0.0329451	+	0.999457i	$0.489511\pi$
$294$	1.97899	0.115417
$295$	20.5474	1.19632
$296$	−3.33396	−0.193783
$297$	−3.18875	−0.185030
$298$	−15.4726	−0.896301
$299$	17.6459	1.02049
$300$	−1.91574	−0.110605
$301$	9.78379	0.563928
$302$	−8.61221	−0.495577
$303$	−1.99513	−0.114617
$304$	−1.00000	−0.0573539
$305$	−10.5485	−0.604006
$306$	−1.72009	−0.0983313
$307$	4.28719	0.244683	0.122341	−	0.992488i	$-0.460960\pi$
$307$	4.28719	0.244683	0.122341	+	0.992488i	$0.460960\pi$
$308$	−7.14524	−0.407138
$309$	10.6447	0.605554
$310$	−0.689604	−0.0391669
$311$	−28.1817	−1.59804	−0.799020	−	0.601304i	$-0.794648\pi$
$311$	−28.1817	−1.59804	−0.799020	+	0.601304i	$0.794648\pi$
$312$	−4.34185	−0.245809
$313$	23.5454	1.33086	0.665431	−	0.746459i	$-0.268248\pi$
$313$	23.5454	1.33086	0.665431	+	0.746459i	$0.268248\pi$
$314$	−11.8156	−0.666794
$315$	−3.93524	−0.221726
$316$	2.89696	0.162967
$317$	−1.16000	−0.0651520	−0.0325760	−	0.999469i	$-0.510371\pi$
$317$	−1.16000	−0.0651520	−0.0325760	+	0.999469i	$0.510371\pi$
$318$	1.00000	0.0560772
$319$	−13.3039	−0.744877
$320$	−1.75621	−0.0981749
$321$	3.72787	0.208070
$322$	−9.10676	−0.507500
$323$	−1.72009	−0.0957086
$324$	1.00000	0.0555556
$325$	−8.31785	−0.461392
$326$	−2.73682	−0.151579
$327$	2.28269	0.126233
$328$	1.43255	0.0790993
$329$	2.65737	0.146506
$330$	−5.60011	−0.308276
$331$	2.39325	0.131545	0.0657724	−	0.997835i	$-0.479049\pi$
$331$	2.39325	0.131545	0.0657724	+	0.997835i	$0.479049\pi$
$332$	−11.8754	−0.651747
$333$	3.33396	0.182700
$334$	25.1262	1.37485
$335$	3.45338	0.188678
$336$	2.24076	0.122244
$337$	−1.92829	−0.105041	−0.0525203	−	0.998620i	$-0.516725\pi$
$337$	−1.92829	−0.105041	−0.0525203	+	0.998620i	$0.516725\pi$
$338$	−5.85162	−0.318286
$339$	−19.0320	−1.03368
$340$	−3.02084	−0.163828
$341$	1.25212	0.0678060
$342$	1.00000	0.0540738
$343$	−20.1198	−1.08637
$344$	−4.36628	−0.235414
$345$	−7.13746	−0.384268
$346$	−14.1664	−0.761589
$347$	32.1065	1.72357	0.861783	−	0.507276i	$-0.169348\pi$
$347$	32.1065	1.72357	0.861783	+	0.507276i	$0.169348\pi$
$348$	4.17214	0.223650
$349$	−9.06648	−0.485318	−0.242659	−	0.970112i	$-0.578020\pi$
$349$	−9.06648	−0.485318	−0.242659	+	0.970112i	$0.578020\pi$
$350$	4.29272	0.229456
$351$	4.34185	0.231751
$352$	3.18875	0.169961
$353$	22.7091	1.20868	0.604341	−	0.796725i	$-0.293436\pi$
$353$	22.7091	1.20868	0.604341	+	0.796725i	$0.293436\pi$
$354$	11.6999	0.621842
$355$	−20.8689	−1.10761
$356$	2.01543	0.106818
$357$	3.85432	0.203992
$358$	−16.1040	−0.851124
$359$	9.45746	0.499146	0.249573	−	0.968356i	$-0.419710\pi$
$359$	9.45746	0.499146	0.249573	+	0.968356i	$0.419710\pi$
$360$	1.75621	0.0925602
$361$	1.00000	0.0526316
$362$	−2.58886	−0.136067
$363$	−0.831848	−0.0436607
$364$	9.72904	0.509940
$365$	−7.90410	−0.413719
$366$	−6.00642	−0.313961
$367$	12.6122	0.658351	0.329176	−	0.944269i	$-0.393229\pi$
$367$	12.6122	0.658351	0.329176	+	0.944269i	$0.393229\pi$
$368$	4.06414	0.211858
$369$	−1.43255	−0.0745755
$370$	5.85512	0.304393
$371$	−2.24076	−0.116335
$372$	−0.392667	−0.0203588
$373$	−4.29516	−0.222395	−0.111197	−	0.993798i	$-0.535469\pi$
$373$	−4.29516	−0.222395	−0.111197	+	0.993798i	$0.535469\pi$
$374$	5.48496	0.283620
$375$	12.1455	0.627189
$376$	−1.18592	−0.0611594
$377$	18.1148	0.932959
$378$	−2.24076	−0.115252
$379$	−2.96675	−0.152392	−0.0761958	−	0.997093i	$-0.524277\pi$
$379$	−2.96675	−0.152392	−0.0761958	+	0.997093i	$0.524277\pi$
$380$	1.75621	0.0900914
$381$	4.81549	0.246705
$382$	−26.5086	−1.35630
$383$	28.5671	1.45971	0.729855	−	0.683602i	$-0.239588\pi$
$383$	28.5671	1.45971	0.729855	+	0.683602i	$0.239588\pi$
$384$	−1.00000	−0.0510310
$385$	12.5485	0.639531
$386$	4.15856	0.211665
$387$	4.36628	0.221950
$388$	10.0581	0.510621
$389$	10.0212	0.508095	0.254047	−	0.967192i	$-0.418238\pi$
$389$	10.0212	0.508095	0.254047	+	0.967192i	$0.418238\pi$
$390$	7.62517	0.386116
$391$	6.99070	0.353535
$392$	1.97899	0.0999540
$393$	6.84749	0.345410
$394$	27.3139	1.37605
$395$	−5.08766	−0.255988
$396$	−3.18875	−0.160241
$397$	−5.70403	−0.286277	−0.143139	−	0.989703i	$-0.545719\pi$
$397$	−5.70403	−0.286277	−0.143139	+	0.989703i	$0.545719\pi$
$398$	−11.0136	−0.552061
$399$	−2.24076	−0.112178
$400$	−1.91574	−0.0957871
$401$	29.2636	1.46136	0.730678	−	0.682722i	$-0.239204\pi$
$401$	29.2636	1.46136	0.730678	+	0.682722i	$0.239204\pi$
$402$	1.96639	0.0980744
$403$	−1.70490	−0.0849270
$404$	−1.99513	−0.0992613
$405$	−1.75621	−0.0872666
$406$	−9.34877	−0.463972
$407$	−10.6312	−0.526968
$408$	−1.72009	−0.0851574
$409$	−6.60479	−0.326586	−0.163293	−	0.986578i	$-0.552212\pi$
$409$	−6.60479	−0.326586	−0.163293	+	0.986578i	$0.552212\pi$
$410$	−2.51585	−0.124249
$411$	−22.8052	−1.12490
$412$	10.6447	0.524425
$413$	−26.2167	−1.29004
$414$	−4.06414	−0.199741
$415$	20.8556	1.02376
$416$	−4.34185	−0.212876
$417$	11.7959	0.577649
$418$	−3.18875	−0.155967
$419$	−19.5869	−0.956885	−0.478442	−	0.878119i	$-0.658798\pi$
$419$	−19.5869	−0.956885	−0.478442	+	0.878119i	$0.658798\pi$
$420$	−3.93524	−0.192020
$421$	3.41496	0.166435	0.0832175	−	0.996531i	$-0.473480\pi$
$421$	3.41496	0.166435	0.0832175	+	0.996531i	$0.473480\pi$
$422$	−9.16082	−0.445942
$423$	1.18592	0.0576616
$424$	1.00000	0.0485643
$425$	−3.29526	−0.159843
$426$	−11.8830	−0.575731
$427$	13.4590	0.651325
$428$	3.72787	0.180193
$429$	−13.8451	−0.668447
$430$	7.66808	0.369788
$431$	4.21748	0.203149	0.101575	−	0.994828i	$-0.467612\pi$
$431$	4.21748	0.203149	0.101575	+	0.994828i	$0.467612\pi$
$432$	1.00000	0.0481125
$433$	9.15900	0.440154	0.220077	−	0.975483i	$-0.429369\pi$
$433$	9.15900	0.440154	0.220077	+	0.975483i	$0.429369\pi$
$434$	0.879873	0.0422352
$435$	−7.32713	−0.351309
$436$	2.28269	0.109321
$437$	−4.06414	−0.194414
$438$	−4.50067	−0.215050
$439$	19.8991	0.949730	0.474865	−	0.880059i	$-0.342497\pi$
$439$	19.8991	0.949730	0.474865	+	0.880059i	$0.342497\pi$
$440$	−5.60011	−0.266975
$441$	−1.97899	−0.0942376
$442$	−7.46838	−0.355235
$443$	0.723754	0.0343866	0.0171933	−	0.999852i	$-0.494527\pi$
$443$	0.723754	0.0343866	0.0171933	+	0.999852i	$0.494527\pi$
$444$	3.33396	0.158223
$445$	−3.53951	−0.167789
$446$	−8.86289	−0.419670
$447$	15.4726	0.731827
$448$	2.24076	0.105866
$449$	17.5898	0.830113	0.415057	−	0.909796i	$-0.363762\pi$
$449$	17.5898	0.830113	0.415057	+	0.909796i	$0.363762\pi$
$450$	1.91574	0.0903089
$451$	4.56804	0.215101
$452$	−19.0320	−0.895190
$453$	8.61221	0.404637
$454$	−11.9694	−0.561754
$455$	−17.0862	−0.801013
$456$	1.00000	0.0468293
$457$	−19.1059	−0.893735	−0.446868	−	0.894600i	$-0.647461\pi$
$457$	−19.1059	−0.893735	−0.446868	+	0.894600i	$0.647461\pi$
$458$	−13.8310	−0.646279
$459$	1.72009	0.0802871
$460$	−7.13746	−0.332786
$461$	−5.45570	−0.254097	−0.127049	−	0.991896i	$-0.540550\pi$
$461$	−5.45570	−0.254097	−0.127049	+	0.991896i	$0.540550\pi$
$462$	7.14524	0.332426
$463$	−6.93546	−0.322318	−0.161159	−	0.986928i	$-0.551523\pi$
$463$	−6.93546	−0.322318	−0.161159	+	0.986928i	$0.551523\pi$
$464$	4.17214	0.193687
$465$	0.689604	0.0319796
$466$	21.4540	0.993837
$467$	27.9222	1.29209	0.646043	−	0.763301i	$-0.276423\pi$
$467$	27.9222	1.29209	0.646043	+	0.763301i	$0.276423\pi$
$468$	4.34185	0.200702
$469$	−4.40620	−0.203460
$470$	2.08273	0.0960690
$471$	11.8156	0.544435
$472$	11.6999	0.538531
$473$	−13.9230	−0.640180
$474$	−2.89696	−0.133062
$475$	1.91574	0.0879003
$476$	3.85432	0.176663
$477$	−1.00000	−0.0457869
$478$	−25.2498	−1.15490
$479$	−6.19035	−0.282844	−0.141422	−	0.989949i	$-0.545168\pi$
$479$	−6.19035	−0.282844	−0.141422	+	0.989949i	$0.545168\pi$
$480$	1.75621	0.0801595
$481$	14.4755	0.660028
$482$	30.5643	1.39217
$483$	9.10676	0.414372
$484$	−0.831848	−0.0378113
$485$	−17.6640	−0.802083
$486$	−1.00000	−0.0453609
$487$	3.21412	0.145645	0.0728227	−	0.997345i	$-0.476799\pi$
$487$	3.21412	0.145645	0.0728227	+	0.997345i	$0.476799\pi$
$488$	−6.00642	−0.271898
$489$	2.73682	0.123763
$490$	−3.47551	−0.157008
$491$	8.88951	0.401178	0.200589	−	0.979675i	$-0.435714\pi$
$491$	8.88951	0.401178	0.200589	+	0.979675i	$0.435714\pi$
$492$	−1.43255	−0.0645843
$493$	7.17647	0.323212
$494$	4.34185	0.195349
$495$	5.60011	0.251706
$496$	−0.392667	−0.0176313
$497$	26.6269	1.19438
$498$	11.8754	0.532149
$499$	−29.9822	−1.34219	−0.671094	−	0.741373i	$-0.734175\pi$
$499$	−29.9822	−1.34219	−0.671094	+	0.741373i	$0.734175\pi$
$500$	12.1455	0.543162
$501$	−25.1262	−1.12256
$502$	1.08279	0.0483272
$503$	4.99159	0.222564	0.111282	−	0.993789i	$-0.464504\pi$
$503$	4.99159	0.222564	0.111282	+	0.993789i	$0.464504\pi$
$504$	−2.24076	−0.0998114
$505$	3.50386	0.155920
$506$	12.9595	0.576122
$507$	5.85162	0.259880
$508$	4.81549	0.213653
$509$	30.9050	1.36984	0.684921	−	0.728618i	$-0.259837\pi$
$509$	30.9050	1.36984	0.684921	+	0.728618i	$0.259837\pi$
$510$	3.02084	0.133765
$511$	10.0849	0.446131
$512$	−1.00000	−0.0441942
$513$	−1.00000	−0.0441511
$514$	−25.1196	−1.10798
$515$	−18.6942	−0.823766
$516$	4.36628	0.192215
$517$	−3.78162	−0.166316
$518$	−7.47061	−0.328240
$519$	14.1664	0.621835
$520$	7.62517	0.334386
$521$	−32.1167	−1.40706	−0.703530	−	0.710666i	$-0.748394\pi$
$521$	−32.1167	−1.40706	−0.703530	+	0.710666i	$0.748394\pi$
$522$	−4.17214	−0.182610
$523$	−25.2994	−1.10627	−0.553133	−	0.833093i	$-0.686568\pi$
$523$	−25.2994	−1.10627	−0.553133	+	0.833093i	$0.686568\pi$
$524$	6.84749	0.299134
$525$	−4.29272	−0.187350
$526$	19.5854	0.853966
$527$	−0.675424	−0.0294219
$528$	−3.18875	−0.138773
$529$	−6.48278	−0.281860
$530$	−1.75621	−0.0762847
$531$	−11.6999	−0.507732
$532$	−2.24076	−0.0971493
$533$	−6.21990	−0.269414
$534$	−2.01543	−0.0872162
$535$	−6.54691	−0.283048
$536$	1.96639	0.0849350
$537$	16.1040	0.694940
$538$	−0.233901	−0.0100842
$539$	6.31051	0.271813
$540$	−1.75621	−0.0755751
$541$	−6.70117	−0.288106	−0.144053	−	0.989570i	$-0.546014\pi$
$541$	−6.70117	−0.288106	−0.144053	+	0.989570i	$0.546014\pi$
$542$	18.7274	0.804410
$543$	2.58886	0.111099
$544$	−1.72009	−0.0737484
$545$	−4.00887	−0.171721
$546$	−9.72904	−0.416364
$547$	−41.9220	−1.79245	−0.896227	−	0.443596i	$-0.853703\pi$
$547$	−41.9220	−1.79245	−0.896227	+	0.443596i	$0.853703\pi$
$548$	−22.8052	−0.974190
$549$	6.00642	0.256348
$550$	−6.10883	−0.260481
$551$	−4.17214	−0.177739
$552$	−4.06414	−0.172981
$553$	6.49140	0.276042
$554$	−30.0063	−1.27484
$555$	−5.85512	−0.248536
$556$	11.7959	0.500259
$557$	37.6716	1.59620	0.798099	−	0.602526i	$-0.205839\pi$
$557$	37.6716	1.59620	0.798099	+	0.602526i	$0.205839\pi$
$558$	0.392667	0.0166229
$559$	18.9577	0.801825
$560$	−3.93524	−0.166294
$561$	−5.48496	−0.231575
$562$	−29.0055	−1.22352
$563$	−34.2549	−1.44367	−0.721836	−	0.692065i	$-0.756701\pi$
$563$	−34.2549	−1.44367	−0.721836	+	0.692065i	$0.756701\pi$
$564$	1.18592	0.0499364
$565$	33.4241	1.40616
$566$	3.74906	0.157585
$567$	2.24076	0.0941031
$568$	−11.8830	−0.498598
$569$	−30.4354	−1.27592	−0.637959	−	0.770071i	$-0.720221\pi$
$569$	−30.4354	−1.27592	−0.637959	+	0.770071i	$0.720221\pi$
$570$	−1.75621	−0.0735594
$571$	20.8625	0.873069	0.436534	−	0.899688i	$-0.356206\pi$
$571$	20.8625	0.873069	0.436534	+	0.899688i	$0.356206\pi$
$572$	−13.8451	−0.578892
$573$	26.5086	1.10741
$574$	3.21000	0.133983
$575$	−7.78584	−0.324692
$576$	1.00000	0.0416667
$577$	6.81087	0.283540	0.141770	−	0.989900i	$-0.454721\pi$
$577$	6.81087	0.283540	0.141770	+	0.989900i	$0.454721\pi$
$578$	14.0413	0.584040
$579$	−4.15856	−0.172824
$580$	−7.32713	−0.304243
$581$	−26.6099	−1.10397
$582$	−10.0581	−0.416920
$583$	3.18875	0.132065
$584$	−4.50067	−0.186239
$585$	−7.62517	−0.315262
$586$	−1.12786	−0.0465913
$587$	6.14142	0.253483	0.126742	−	0.991936i	$-0.459548\pi$
$587$	6.14142	0.253483	0.126742	+	0.991936i	$0.459548\pi$
$588$	−1.97899	−0.0816121
$589$	0.392667	0.0161796
$590$	−20.5474	−0.845923
$591$	−27.3139	−1.12354
$592$	3.33396	0.137025
$593$	10.3964	0.426928	0.213464	−	0.976951i	$-0.431525\pi$
$593$	10.3964	0.426928	0.213464	+	0.976951i	$0.431525\pi$
$594$	3.18875	0.130836
$595$	−6.76898	−0.277501
$596$	15.4726	0.633780
$597$	11.0136	0.450756
$598$	−17.6459	−0.721593
$599$	−27.7716	−1.13472	−0.567358	−	0.823471i	$-0.692035\pi$
$599$	−27.7716	−1.13472	−0.567358	+	0.823471i	$0.692035\pi$
$600$	1.91574	0.0782098
$601$	24.1432	0.984821	0.492410	−	0.870363i	$-0.336116\pi$
$601$	24.1432	0.984821	0.492410	+	0.870363i	$0.336116\pi$
$602$	−9.78379	−0.398757
$603$	−1.96639	−0.0800774
$604$	8.61221	0.350426
$605$	1.46090	0.0593939
$606$	1.99513	0.0810465
$607$	9.06951	0.368120	0.184060	−	0.982915i	$-0.441076\pi$
$607$	9.06951	0.368120	0.184060	+	0.982915i	$0.441076\pi$
$608$	1.00000	0.0405554
$609$	9.34877	0.378831
$610$	10.5485	0.427097
$611$	5.14910	0.208310
$612$	1.72009	0.0695307
$613$	23.4706	0.947968	0.473984	−	0.880534i	$-0.342815\pi$
$613$	23.4706	0.947968	0.473984	+	0.880534i	$0.342815\pi$
$614$	−4.28719	−0.173017
$615$	2.51585	0.101449
$616$	7.14524	0.287890
$617$	−16.4705	−0.663079	−0.331540	−	0.943441i	$-0.607568\pi$
$617$	−16.4705	−0.663079	−0.331540	+	0.943441i	$0.607568\pi$
$618$	−10.6447	−0.428191
$619$	29.9776	1.20490	0.602451	−	0.798156i	$-0.294191\pi$
$619$	29.9776	1.20490	0.602451	+	0.798156i	$0.294191\pi$
$620$	0.689604	0.0276952
$621$	4.06414	0.163088
$622$	28.1817	1.12999
$623$	4.51610	0.180934
$624$	4.34185	0.173813
$625$	−11.7512	−0.470049
$626$	−23.5454	−0.941062
$627$	3.18875	0.127347
$628$	11.8156	0.471495
$629$	5.73473	0.228659
$630$	3.93524	0.156784
$631$	−49.7858	−1.98194	−0.990970	−	0.134084i	$-0.957191\pi$
$631$	−49.7858	−1.98194	−0.990970	+	0.134084i	$0.957191\pi$
$632$	−2.89696	−0.115235
$633$	9.16082	0.364110
$634$	1.16000	0.0460694
$635$	−8.45700	−0.335606
$636$	−1.00000	−0.0396526
$637$	−8.59246	−0.340446
$638$	13.3039	0.526707
$639$	11.8830	0.470082
$640$	1.75621	0.0694201
$641$	4.96674	0.196174	0.0980872	−	0.995178i	$-0.468728\pi$
$641$	4.96674	0.196174	0.0980872	+	0.995178i	$0.468728\pi$
$642$	−3.72787	−0.147127
$643$	−24.2213	−0.955196	−0.477598	−	0.878578i	$-0.658492\pi$
$643$	−24.2213	−0.955196	−0.477598	+	0.878578i	$0.658492\pi$
$644$	9.10676	0.358857
$645$	−7.66808	−0.301930
$646$	1.72009	0.0676762
$647$	−0.945070	−0.0371545	−0.0185773	−	0.999827i	$-0.505914\pi$
$647$	−0.945070	−0.0371545	−0.0185773	+	0.999827i	$0.505914\pi$
$648$	−1.00000	−0.0392837
$649$	37.3081	1.46447
$650$	8.31785	0.326253
$651$	−0.879873	−0.0344849
$652$	2.73682	0.107182
$653$	23.1138	0.904515	0.452257	−	0.891887i	$-0.350619\pi$
$653$	23.1138	0.904515	0.452257	+	0.891887i	$0.350619\pi$
$654$	−2.28269	−0.0892601
$655$	−12.0256	−0.469879
$656$	−1.43255	−0.0559316
$657$	4.50067	0.175588
$658$	−2.65737	−0.103595
$659$	−0.207239	−0.00807287	−0.00403644	−	0.999992i	$-0.501285\pi$
$659$	−0.207239	−0.00807287	−0.00403644	+	0.999992i	$0.501285\pi$
$660$	5.60011	0.217984
$661$	−41.1392	−1.60013	−0.800064	−	0.599914i	$-0.795201\pi$
$661$	−41.1392	−1.60013	−0.800064	+	0.599914i	$0.795201\pi$
$662$	−2.39325	−0.0930162
$663$	7.46838	0.290048
$664$	11.8754	0.460855
$665$	3.93524	0.152602
$666$	−3.33396	−0.129188
$667$	16.9561	0.656545
$668$	−25.1262	−0.972163
$669$	8.86289	0.342659
$670$	−3.45338	−0.133416
$671$	−19.1530	−0.739394
$672$	−2.24076	−0.0864392
$673$	16.2171	0.625122	0.312561	−	0.949898i	$-0.398813\pi$
$673$	16.2171	0.625122	0.312561	+	0.949898i	$0.398813\pi$
$674$	1.92829	0.0742750
$675$	−1.91574	−0.0737369
$676$	5.85162	0.225062
$677$	−14.9836	−0.575865	−0.287933	−	0.957651i	$-0.592968\pi$
$677$	−14.9836	−0.575865	−0.287933	+	0.957651i	$0.592968\pi$
$678$	19.0320	0.730919
$679$	22.5377	0.864919
$680$	3.02084	0.115844
$681$	11.9694	0.458670
$682$	−1.25212	−0.0479461
$683$	46.5062	1.77951	0.889754	−	0.456440i	$-0.150876\pi$
$683$	46.5062	1.77951	0.889754	+	0.456440i	$0.150876\pi$
$684$	−1.00000	−0.0382360
$685$	40.0506	1.53026
$686$	20.1198	0.768176
$687$	13.8310	0.527684
$688$	4.36628	0.166463
$689$	−4.34185	−0.165411
$690$	7.13746	0.271719
$691$	−2.01462	−0.0766396	−0.0383198	−	0.999266i	$-0.512201\pi$
$691$	−2.01462	−0.0766396	−0.0383198	+	0.999266i	$0.512201\pi$
$692$	14.1664	0.538525
$693$	−7.14524	−0.271425
$694$	−32.1065	−1.21875
$695$	−20.7161	−0.785805
$696$	−4.17214	−0.158145
$697$	−2.46412	−0.0933352
$698$	9.06648	0.343171
$699$	−21.4540	−0.811464
$700$	−4.29272	−0.162250
$701$	38.6584	1.46011	0.730055	−	0.683389i	$-0.239495\pi$
$701$	38.6584	1.46011	0.730055	+	0.683389i	$0.239495\pi$
$702$	−4.34185	−0.163872
$703$	−3.33396	−0.125743
$704$	−3.18875	−0.120181
$705$	−2.08273	−0.0784400
$706$	−22.7091	−0.854668
$707$	−4.47061	−0.168134
$708$	−11.6999	−0.439709
$709$	10.1738	0.382087	0.191043	−	0.981582i	$-0.438813\pi$
$709$	10.1738	0.382087	0.191043	+	0.981582i	$0.438813\pi$
$710$	20.8689	0.783196
$711$	2.89696	0.108645
$712$	−2.01543	−0.0755314
$713$	−1.59585	−0.0597651
$714$	−3.85432	−0.144244
$715$	24.3148	0.909322
$716$	16.1040	0.601836
$717$	25.2498	0.942970
$718$	−9.45746	−0.352949
$719$	−21.4304	−0.799218	−0.399609	−	0.916686i	$-0.630854\pi$
$719$	−21.4304	−0.799218	−0.399609	+	0.916686i	$0.630854\pi$
$720$	−1.75621	−0.0654499
$721$	23.8522	0.888301
$722$	−1.00000	−0.0372161
$723$	−30.5643	−1.13670
$724$	2.58886	0.0962142
$725$	−7.99274	−0.296843
$726$	0.831848	0.0308728
$727$	−13.2692	−0.492127	−0.246063	−	0.969254i	$-0.579137\pi$
$727$	−13.2692	−0.492127	−0.246063	+	0.969254i	$0.579137\pi$
$728$	−9.72904	−0.360582
$729$	1.00000	0.0370370
$730$	7.90410	0.292544
$731$	7.51041	0.277783
$732$	6.00642	0.222004
$733$	1.95735	0.0722965	0.0361483	−	0.999346i	$-0.488491\pi$
$733$	1.95735	0.0722965	0.0361483	+	0.999346i	$0.488491\pi$
$734$	−12.6122	−0.465525
$735$	3.47551	0.128196
$736$	−4.06414	−0.149806
$737$	6.27032	0.230970
$738$	1.43255	0.0527328
$739$	10.1970	0.375101	0.187551	−	0.982255i	$-0.439945\pi$
$739$	10.1970	0.375101	0.187551	+	0.982255i	$0.439945\pi$
$740$	−5.85512	−0.215239
$741$	−4.34185	−0.159502
$742$	2.24076	0.0822609
$743$	−37.9209	−1.39118	−0.695592	−	0.718437i	$-0.744858\pi$
$743$	−37.9209	−1.39118	−0.695592	+	0.718437i	$0.744858\pi$
$744$	0.392667	0.0143959
$745$	−27.1730	−0.995541
$746$	4.29516	0.157257
$747$	−11.8754	−0.434498
$748$	−5.48496	−0.200550
$749$	8.35327	0.305222
$750$	−12.1455	−0.443490
$751$	40.8584	1.49094	0.745472	−	0.666537i	$-0.232224\pi$
$751$	40.8584	1.49094	0.745472	+	0.666537i	$0.232224\pi$
$752$	1.18592	0.0432462
$753$	−1.08279	−0.0394590
$754$	−18.1148	−0.659701
$755$	−15.1248	−0.550448
$756$	2.24076	0.0814957
$757$	−37.3882	−1.35890	−0.679449	−	0.733723i	$-0.737781\pi$
$757$	−37.3882	−1.35890	−0.679449	+	0.733723i	$0.737781\pi$
$758$	2.96675	0.107757
$759$	−12.9595	−0.470401
$760$	−1.75621	−0.0637043
$761$	7.20558	0.261202	0.130601	−	0.991435i	$-0.458309\pi$
$761$	7.20558	0.261202	0.130601	+	0.991435i	$0.458309\pi$
$762$	−4.81549	−0.174447
$763$	5.11495	0.185174
$764$	26.5086	0.959048
$765$	−3.02084	−0.109219
$766$	−28.5671	−1.03217
$767$	−50.7991	−1.83425
$768$	1.00000	0.0360844
$769$	26.0259	0.938519	0.469259	−	0.883060i	$-0.344521\pi$
$769$	26.0259	0.938519	0.469259	+	0.883060i	$0.344521\pi$
$770$	−12.5485	−0.452217
$771$	25.1196	0.904662
$772$	−4.15856	−0.149670
$773$	44.3733	1.59600	0.797998	−	0.602661i	$-0.205893\pi$
$773$	44.3733	1.59600	0.797998	+	0.602661i	$0.205893\pi$
$774$	−4.36628	−0.156943
$775$	0.752248	0.0270216
$776$	−10.0581	−0.361064
$777$	7.47061	0.268007
$778$	−10.0212	−0.359277
$779$	1.43255	0.0513264
$780$	−7.62517	−0.273025
$781$	−37.8918	−1.35588
$782$	−6.99070	−0.249987
$783$	4.17214	0.149100
$784$	−1.97899	−0.0706782
$785$	−20.7507	−0.740623
$786$	−6.84749	−0.244242
$787$	12.3184	0.439102	0.219551	−	0.975601i	$-0.429541\pi$
$787$	12.3184	0.439102	0.219551	+	0.975601i	$0.429541\pi$
$788$	−27.3139	−0.973018
$789$	−19.5854	−0.697260
$790$	5.08766	0.181011
$791$	−42.6462	−1.51632
$792$	3.18875	0.113307
$793$	26.0790	0.926091
$794$	5.70403	0.202428
$795$	1.75621	0.0622862
$796$	11.0136	0.390366
$797$	−30.2116	−1.07015	−0.535076	−	0.844804i	$-0.679717\pi$
$797$	−30.2116	−1.07015	−0.535076	+	0.844804i	$0.679717\pi$
$798$	2.24076	0.0793221
$799$	2.03990	0.0721666
$800$	1.91574	0.0677317
$801$	2.01543	0.0712117
$802$	−29.2636	−1.03334
$803$	−14.3515	−0.506454
$804$	−1.96639	−0.0693491
$805$	−15.9933	−0.563691
$806$	1.70490	0.0600525
$807$	0.233901	0.00823372
$808$	1.99513	0.0701884
$809$	43.0910	1.51500	0.757499	−	0.652836i	$-0.226421\pi$
$809$	43.0910	1.51500	0.757499	+	0.652836i	$0.226421\pi$
$810$	1.75621	0.0617068
$811$	−8.34392	−0.292995	−0.146497	−	0.989211i	$-0.546800\pi$
$811$	−8.34392	−0.292995	−0.146497	+	0.989211i	$0.546800\pi$
$812$	9.34877	0.328077
$813$	−18.7274	−0.656798
$814$	10.6312	0.372623
$815$	−4.80642	−0.168362
$816$	1.72009	0.0602154
$817$	−4.36628	−0.152757
$818$	6.60479	0.230931
$819$	9.72904	0.339960
$820$	2.51585	0.0878573
$821$	12.5033	0.436368	0.218184	−	0.975908i	$-0.429987\pi$
$821$	12.5033	0.436368	0.218184	+	0.975908i	$0.429987\pi$
$822$	22.8052	0.795423
$823$	25.3916	0.885096	0.442548	−	0.896745i	$-0.354075\pi$
$823$	25.3916	0.885096	0.442548	+	0.896745i	$0.354075\pi$
$824$	−10.6447	−0.370825
$825$	6.10883	0.212682
$826$	26.2167	0.912194
$827$	−25.4543	−0.885134	−0.442567	−	0.896735i	$-0.645932\pi$
$827$	−25.4543	−0.885134	−0.442567	+	0.896735i	$0.645932\pi$
$828$	4.06414	0.141239
$829$	31.0975	1.08006	0.540030	−	0.841646i	$-0.318413\pi$
$829$	31.0975	1.08006	0.540030	+	0.841646i	$0.318413\pi$
$830$	−20.8556	−0.723909
$831$	30.0063	1.04091
$832$	4.34185	0.150526
$833$	−3.40405	−0.117943
$834$	−11.7959	−0.408459
$835$	44.1268	1.52707
$836$	3.18875	0.110285
$837$	−0.392667	−0.0135726
$838$	19.5869	0.676620
$839$	48.7353	1.68253	0.841265	−	0.540624i	$-0.181812\pi$
$839$	48.7353	1.68253	0.841265	+	0.540624i	$0.181812\pi$
$840$	3.93524	0.135779
$841$	−11.5933	−0.399768
$842$	−3.41496	−0.117687
$843$	29.0055	0.999003
$844$	9.16082	0.315328
$845$	−10.2766	−0.353527
$846$	−1.18592	−0.0407729
$847$	−1.86397	−0.0640468
$848$	−1.00000	−0.0343401
$849$	−3.74906	−0.128667
$850$	3.29526	0.113026
$851$	13.5497	0.464477
$852$	11.8830	0.407103
$853$	37.8023	1.29433	0.647163	−	0.762352i	$-0.275955\pi$
$853$	37.8023	1.29433	0.647163	+	0.762352i	$0.275955\pi$
$854$	−13.4590	−0.460556
$855$	1.75621	0.0600610
$856$	−3.72787	−0.127416
$857$	−17.1879	−0.587128	−0.293564	−	0.955939i	$-0.594841\pi$
$857$	−17.1879	−0.587128	−0.293564	+	0.955939i	$0.594841\pi$
$858$	13.8451	0.472663
$859$	34.6895	1.18359	0.591795	−	0.806089i	$-0.298420\pi$
$859$	34.6895	1.18359	0.591795	+	0.806089i	$0.298420\pi$
$860$	−7.66808	−0.261479
$861$	−3.21000	−0.109396
$862$	−4.21748	−0.143648
$863$	−17.8754	−0.608485	−0.304242	−	0.952595i	$-0.598403\pi$
$863$	−17.8754	−0.608485	−0.304242	+	0.952595i	$0.598403\pi$
$864$	−1.00000	−0.0340207
$865$	−24.8791	−0.845913
$866$	−9.15900	−0.311236
$867$	−14.0413	−0.476867
$868$	−0.879873	−0.0298648
$869$	−9.23769	−0.313367
$870$	7.32713	0.248413
$871$	−8.53774	−0.289290
$872$	−2.28269	−0.0773015
$873$	10.0581	0.340414
$874$	4.06414	0.137472
$875$	27.2151	0.920038
$876$	4.50067	0.152063
$877$	−25.3790	−0.856988	−0.428494	−	0.903545i	$-0.640956\pi$
$877$	−25.3790	−0.856988	−0.428494	+	0.903545i	$0.640956\pi$
$878$	−19.8991	−0.671561
$879$	1.12786	0.0380417
$880$	5.60011	0.188780
$881$	−31.7501	−1.06969	−0.534843	−	0.844951i	$-0.679629\pi$
$881$	−31.7501	−1.06969	−0.534843	+	0.844951i	$0.679629\pi$
$882$	1.97899	0.0666360
$883$	−2.60363	−0.0876193	−0.0438096	−	0.999040i	$-0.513950\pi$
$883$	−2.60363	−0.0876193	−0.0438096	+	0.999040i	$0.513950\pi$
$884$	7.46838	0.251189
$885$	20.5474	0.690693
$886$	−0.723754	−0.0243150
$887$	43.4202	1.45791	0.728954	−	0.684563i	$-0.240007\pi$
$887$	43.4202	1.45791	0.728954	+	0.684563i	$0.240007\pi$
$888$	−3.33396	−0.111880
$889$	10.7904	0.361897
$890$	3.53951	0.118645
$891$	−3.18875	−0.106827
$892$	8.86289	0.296751
$893$	−1.18592	−0.0396855
$894$	−15.4726	−0.517480
$895$	−28.2820	−0.945362
$896$	−2.24076	−0.0748586
$897$	17.6459	0.589178
$898$	−17.5898	−0.586979
$899$	−1.63826	−0.0546390
$900$	−1.91574	−0.0638581
$901$	−1.72009	−0.0573047
$902$	−4.56804	−0.152099
$903$	9.78379	0.325584
$904$	19.0320	0.632995
$905$	−4.54657	−0.151133
$906$	−8.61221	−0.286122
$907$	32.8373	1.09035	0.545173	−	0.838324i	$-0.316464\pi$
$907$	32.8373	1.09035	0.545173	+	0.838324i	$0.316464\pi$
$908$	11.9694	0.397220
$909$	−1.99513	−0.0661742
$910$	17.0862	0.566402
$911$	14.1816	0.469858	0.234929	−	0.972013i	$-0.424514\pi$
$911$	14.1816	0.469858	0.234929	+	0.972013i	$0.424514\pi$
$912$	−1.00000	−0.0331133
$913$	37.8677	1.25324
$914$	19.1059	0.631966
$915$	−10.5485	−0.348723
$916$	13.8310	0.456988
$917$	15.3436	0.506690
$918$	−1.72009	−0.0567716
$919$	8.27675	0.273025	0.136512	−	0.990638i	$-0.456411\pi$
$919$	8.27675	0.273025	0.136512	+	0.990638i	$0.456411\pi$
$920$	7.13746	0.235315
$921$	4.28719	0.141268
$922$	5.45570	0.179674
$923$	51.5939	1.69824
$924$	−7.14524	−0.235061
$925$	−6.38701	−0.210004
$926$	6.93546	0.227913
$927$	10.6447	0.349617
$928$	−4.17214	−0.136957
$929$	−42.4202	−1.39176	−0.695881	−	0.718158i	$-0.744986\pi$
$929$	−42.4202	−1.39176	−0.695881	+	0.718158i	$0.744986\pi$
$930$	−0.689604	−0.0226130
$931$	1.97899	0.0648587
$932$	−21.4540	−0.702749
$933$	−28.1817	−0.922629
$934$	−27.9222	−0.913643
$935$	9.63272	0.315023
$936$	−4.34185	−0.141918
$937$	11.2837	0.368621	0.184310	−	0.982868i	$-0.440995\pi$
$937$	11.2837	0.368621	0.184310	+	0.982868i	$0.440995\pi$
$938$	4.40620	0.143868
$939$	23.5454	0.768374
$940$	−2.08273	−0.0679311
$941$	−10.8467	−0.353594	−0.176797	−	0.984247i	$-0.556574\pi$
$941$	−10.8467	−0.353594	−0.176797	+	0.984247i	$0.556574\pi$
$942$	−11.8156	−0.384974
$943$	−5.82207	−0.189593
$944$	−11.6999	−0.380799
$945$	−3.93524	−0.128013
$946$	13.9230	0.452675
$947$	2.21778	0.0720683	0.0360342	−	0.999351i	$-0.488527\pi$
$947$	2.21778	0.0720683	0.0360342	+	0.999351i	$0.488527\pi$
$948$	2.89696	0.0940889
$949$	19.5412	0.634334
$950$	−1.91574	−0.0621549
$951$	−1.16000	−0.0376155
$952$	−3.85432	−0.124919
$953$	−24.7318	−0.801142	−0.400571	−	0.916266i	$-0.631188\pi$
$953$	−24.7318	−0.801142	−0.400571	+	0.916266i	$0.631188\pi$
$954$	1.00000	0.0323762
$955$	−46.5546	−1.50647
$956$	25.2498	0.816636
$957$	−13.3039	−0.430055
$958$	6.19035	0.200001
$959$	−51.1010	−1.65014
$960$	−1.75621	−0.0566813
$961$	−30.8458	−0.995026
$962$	−14.4755	−0.466710
$963$	3.72787	0.120129
$964$	−30.5643	−0.984410
$965$	7.30329	0.235101
$966$	−9.10676	−0.293005
$967$	−23.0861	−0.742398	−0.371199	−	0.928553i	$-0.621053\pi$
$967$	−23.0861	−0.742398	−0.371199	+	0.928553i	$0.621053\pi$
$968$	0.831848	0.0267366
$969$	−1.72009	−0.0552574
$970$	17.6640	0.567158
$971$	−29.7089	−0.953403	−0.476702	−	0.879065i	$-0.658168\pi$
$971$	−29.7089	−0.953403	−0.476702	+	0.879065i	$0.658168\pi$
$972$	1.00000	0.0320750
$973$	26.4318	0.847366
$974$	−3.21412	−0.102987
$975$	−8.31785	−0.266385
$976$	6.00642	0.192261
$977$	−14.1132	−0.451520	−0.225760	−	0.974183i	$-0.572487\pi$
$977$	−14.1132	−0.451520	−0.225760	+	0.974183i	$0.572487\pi$
$978$	−2.73682	−0.0875139
$979$	−6.42671	−0.205399
$980$	3.47551	0.111021
$981$	2.28269	0.0728806
$982$	−8.88951	−0.283676
$983$	−0.362179	−0.0115517	−0.00577585	−	0.999983i	$-0.501839\pi$
$983$	−0.362179	−0.0115517	−0.00577585	+	0.999983i	$0.501839\pi$
$984$	1.43255	0.0456680
$985$	47.9688	1.52841
$986$	−7.17647	−0.228545
$987$	2.65737	0.0845851
$988$	−4.34185	−0.138132
$989$	17.7452	0.564263
$990$	−5.60011	−0.177983
$991$	50.5169	1.60472	0.802360	−	0.596840i	$-0.203577\pi$
$991$	50.5169	1.60472	0.802360	+	0.596840i	$0.203577\pi$
$992$	0.392667	0.0124672
$993$	2.39325	0.0759474
$994$	−26.6269	−0.844553
$995$	−19.3421	−0.613186
$996$	−11.8754	−0.376286
$997$	−45.7208	−1.44799	−0.723997	−	0.689803i	$-0.757697\pi$
$997$	−45.7208	−1.44799	−0.723997	+	0.689803i	$0.757697\pi$
$998$	29.9822	0.949070
$999$	3.33396	0.105482

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	6042.2.a.ba.1.3	✓	9

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
6042.2.a.ba.1.3	✓	9	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:	\( N \)	\(=\)	\( 6042 = 2 \cdot 3 \cdot 19 \cdot 53 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	6042.a (trivial)

\(f(q)\)	\(=\)	\(q-1.00000 q^{2} +1.00000 q^{3} +1.00000 q^{4} -1.75621 q^{5} -1.00000 q^{6} +2.24076 q^{7} -1.00000 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q-1.00000 q^{2} +1.00000 q^{3} +1.00000 q^{4} -1.75621 q^{5} -1.00000 q^{6} +2.24076 q^{7} -1.00000 q^{8} +1.00000 q^{9} +1.75621 q^{10} -3.18875 q^{11} +1.00000 q^{12} +4.34185 q^{13} -2.24076 q^{14} -1.75621 q^{15} +1.00000 q^{16} +1.72009 q^{17} -1.00000 q^{18} -1.00000 q^{19} -1.75621 q^{20} +2.24076 q^{21} +3.18875 q^{22} +4.06414 q^{23} -1.00000 q^{24} -1.91574 q^{25} -4.34185 q^{26} +1.00000 q^{27} +2.24076 q^{28} +4.17214 q^{29} +1.75621 q^{30} -0.392667 q^{31} -1.00000 q^{32} -3.18875 q^{33} -1.72009 q^{34} -3.93524 q^{35} +1.00000 q^{36} +3.33396 q^{37} +1.00000 q^{38} +4.34185 q^{39} +1.75621 q^{40} -1.43255 q^{41} -2.24076 q^{42} +4.36628 q^{43} -3.18875 q^{44} -1.75621 q^{45} -4.06414 q^{46} +1.18592 q^{47} +1.00000 q^{48} -1.97899 q^{49} +1.91574 q^{50} +1.72009 q^{51} +4.34185 q^{52} -1.00000 q^{53} -1.00000 q^{54} +5.60011 q^{55} -2.24076 q^{56} -1.00000 q^{57} -4.17214 q^{58} -11.6999 q^{59} -1.75621 q^{60} +6.00642 q^{61} +0.392667 q^{62} +2.24076 q^{63} +1.00000 q^{64} -7.62517 q^{65} +3.18875 q^{66} -1.96639 q^{67} +1.72009 q^{68} +4.06414 q^{69} +3.93524 q^{70} +11.8830 q^{71} -1.00000 q^{72} +4.50067 q^{73} -3.33396 q^{74} -1.91574 q^{75} -1.00000 q^{76} -7.14524 q^{77} -4.34185 q^{78} +2.89696 q^{79} -1.75621 q^{80} +1.00000 q^{81} +1.43255 q^{82} -11.8754 q^{83} +2.24076 q^{84} -3.02084 q^{85} -4.36628 q^{86} +4.17214 q^{87} +3.18875 q^{88} +2.01543 q^{89} +1.75621 q^{90} +9.72904 q^{91} +4.06414 q^{92} -0.392667 q^{93} -1.18592 q^{94} +1.75621 q^{95} -1.00000 q^{96} +10.0581 q^{97} +1.97899 q^{98} -3.18875 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 9 q - 9 q^{2} + 9 q^{3} + 9 q^{4} + 2 q^{5} - 9 q^{6} + 10 q^{7} - 9 q^{8} + 9 q^{9}+O(q^{10}) \) 9 * q - 9 * q^2 + 9 * q^3 + 9 * q^4 + 2 * q^5 - 9 * q^6 + 10 * q^7 - 9 * q^8 + 9 * q^9	\( 9 q - 9 q^{2} + 9 q^{3} + 9 q^{4} + 2 q^{5} - 9 q^{6} + 10 q^{7} - 9 q^{8} + 9 q^{9} - 2 q^{10} + 7 q^{11} + 9 q^{12} + 2 q^{13} - 10 q^{14} + 2 q^{15} + 9 q^{16} + 4 q^{17} - 9 q^{18} - 9 q^{19} + 2 q^{20} + 10 q^{21} - 7 q^{22} + 15 q^{23} - 9 q^{24} + 19 q^{25} - 2 q^{26} + 9 q^{27} + 10 q^{28} + 5 q^{29} - 2 q^{30} + q^{31} - 9 q^{32} + 7 q^{33} - 4 q^{34} + 4 q^{35} + 9 q^{36} - 4 q^{37} + 9 q^{38} + 2 q^{39} - 2 q^{40} + 5 q^{41} - 10 q^{42} + 27 q^{43} + 7 q^{44} + 2 q^{45} - 15 q^{46} + 9 q^{48} + 33 q^{49} - 19 q^{50} + 4 q^{51} + 2 q^{52} - 9 q^{53} - 9 q^{54} + 26 q^{55} - 10 q^{56} - 9 q^{57} - 5 q^{58} + 7 q^{59} + 2 q^{60} + 5 q^{61} - q^{62} + 10 q^{63} + 9 q^{64} - 17 q^{65} - 7 q^{66} + 19 q^{67} + 4 q^{68} + 15 q^{69} - 4 q^{70} - 11 q^{71} - 9 q^{72} + 25 q^{73} + 4 q^{74} + 19 q^{75} - 9 q^{76} + 15 q^{77} - 2 q^{78} + 28 q^{79} + 2 q^{80} + 9 q^{81} - 5 q^{82} - 8 q^{83} + 10 q^{84} + 52 q^{85} - 27 q^{86} + 5 q^{87} - 7 q^{88} + 22 q^{89} - 2 q^{90} - 11 q^{91} + 15 q^{92} + q^{93} - 2 q^{95} - 9 q^{96} + 13 q^{97} - 33 q^{98} + 7 q^{99}+O(q^{100}) \) 9 * q - 9 * q^2 + 9 * q^3 + 9 * q^4 + 2 * q^5 - 9 * q^6 + 10 * q^7 - 9 * q^8 + 9 * q^9 - 2 * q^10 + 7 * q^11 + 9 * q^12 + 2 * q^13 - 10 * q^14 + 2 * q^15 + 9 * q^16 + 4 * q^17 - 9 * q^18 - 9 * q^19 + 2 * q^20 + 10 * q^21 - 7 * q^22 + 15 * q^23 - 9 * q^24 + 19 * q^25 - 2 * q^26 + 9 * q^27 + 10 * q^28 + 5 * q^29 - 2 * q^30 + q^31 - 9 * q^32 + 7 * q^33 - 4 * q^34 + 4 * q^35 + 9 * q^36 - 4 * q^37 + 9 * q^38 + 2 * q^39 - 2 * q^40 + 5 * q^41 - 10 * q^42 + 27 * q^43 + 7 * q^44 + 2 * q^45 - 15 * q^46 + 9 * q^48 + 33 * q^49 - 19 * q^50 + 4 * q^51 + 2 * q^52 - 9 * q^53 - 9 * q^54 + 26 * q^55 - 10 * q^56 - 9 * q^57 - 5 * q^58 + 7 * q^59 + 2 * q^60 + 5 * q^61 - q^62 + 10 * q^63 + 9 * q^64 - 17 * q^65 - 7 * q^66 + 19 * q^67 + 4 * q^68 + 15 * q^69 - 4 * q^70 - 11 * q^71 - 9 * q^72 + 25 * q^73 + 4 * q^74 + 19 * q^75 - 9 * q^76 + 15 * q^77 - 2 * q^78 + 28 * q^79 + 2 * q^80 + 9 * q^81 - 5 * q^82 - 8 * q^83 + 10 * q^84 + 52 * q^85 - 27 * q^86 + 5 * q^87 - 7 * q^88 + 22 * q^89 - 2 * q^90 - 11 * q^91 + 15 * q^92 + q^93 - 2 * q^95 - 9 * q^96 + 13 * q^97 - 33 * q^98 + 7 * q^99

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