LMFDB - Embedded newform 6042.2.a.bc.1.5

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:	$1$
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} - 3x^{8} - 20x^{7} + 69x^{6} + 27x^{5} - 185x^{4} + 8x^{3} + 109x^{2} - 8x - 14 $ x^9 - 3x^8 - 20x^7 + 69x^6 + 27x^5 - 185x^4 + 8x^3 + 109x^2 - 8x - 14
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.5
Root			$0.487125$ 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)

$f(q)$	$=$	$q+1.00000 q^{2} -1.00000 q^{3} +1.00000 q^{4} -0.487125 q^{5} -1.00000 q^{6} +4.75176 q^{7} +1.00000 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q+1.00000 q^{2} -1.00000 q^{3} +1.00000 q^{4} -0.487125 q^{5} -1.00000 q^{6} +4.75176 q^{7} +1.00000 q^{8} +1.00000 q^{9} -0.487125 q^{10} -5.66565 q^{11} -1.00000 q^{12} +4.03321 q^{13} +4.75176 q^{14} +0.487125 q^{15} +1.00000 q^{16} -4.44432 q^{17} +1.00000 q^{18} +1.00000 q^{19} -0.487125 q^{20} -4.75176 q^{21} -5.66565 q^{22} -5.49160 q^{23} -1.00000 q^{24} -4.76271 q^{25} +4.03321 q^{26} -1.00000 q^{27} +4.75176 q^{28} +0.0939007 q^{29} +0.487125 q^{30} -6.82737 q^{31} +1.00000 q^{32} +5.66565 q^{33} -4.44432 q^{34} -2.31470 q^{35} +1.00000 q^{36} -10.1159 q^{37} +1.00000 q^{38} -4.03321 q^{39} -0.487125 q^{40} -6.52148 q^{41} -4.75176 q^{42} -4.79851 q^{43} -5.66565 q^{44} -0.487125 q^{45} -5.49160 q^{46} +2.63241 q^{47} -1.00000 q^{48} +15.5792 q^{49} -4.76271 q^{50} +4.44432 q^{51} +4.03321 q^{52} -1.00000 q^{53} -1.00000 q^{54} +2.75988 q^{55} +4.75176 q^{56} -1.00000 q^{57} +0.0939007 q^{58} +13.5519 q^{59} +0.487125 q^{60} -0.302849 q^{61} -6.82737 q^{62} +4.75176 q^{63} +1.00000 q^{64} -1.96468 q^{65} +5.66565 q^{66} -9.76859 q^{67} -4.44432 q^{68} +5.49160 q^{69} -2.31470 q^{70} -15.8295 q^{71} +1.00000 q^{72} -12.7465 q^{73} -10.1159 q^{74} +4.76271 q^{75} +1.00000 q^{76} -26.9218 q^{77} -4.03321 q^{78} -0.0301722 q^{79} -0.487125 q^{80} +1.00000 q^{81} -6.52148 q^{82} -5.61820 q^{83} -4.75176 q^{84} +2.16494 q^{85} -4.79851 q^{86} -0.0939007 q^{87} -5.66565 q^{88} -2.07916 q^{89} -0.487125 q^{90} +19.1648 q^{91} -5.49160 q^{92} +6.82737 q^{93} +2.63241 q^{94} -0.487125 q^{95} -1.00000 q^{96} +18.2881 q^{97} +15.5792 q^{98} -5.66565 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 9 q + 9 q^{2} - 9 q^{3} + 9 q^{4} - 3 q^{5} - 9 q^{6} - 7 q^{7} + 9 q^{8} + 9 q^{9}+O(q^{10}) $ 9 * q + 9 * q^2 - 9 * q^3 + 9 * q^4 - 3 * q^5 - 9 * q^6 - 7 * q^7 + 9 * q^8 + 9 * q^9	\( 9 q + 9 q^{2} - 9 q^{3} + 9 q^{4} - 3 q^{5} - 9 q^{6} - 7 q^{7} + 9 q^{8} + 9 q^{9} - 3 q^{10} + 4 q^{11} - 9 q^{12} - 5 q^{13} - 7 q^{14} + 3 q^{15} + 9 q^{16} - 28 q^{17} + 9 q^{18} + 9 q^{19} - 3 q^{20} + 7 q^{21} + 4 q^{22} - 10 q^{23} - 9 q^{24} + 4 q^{25} - 5 q^{26} - 9 q^{27} - 7 q^{28} + 3 q^{30} + 5 q^{31} + 9 q^{32} - 4 q^{33} - 28 q^{34} - 10 q^{35} + 9 q^{36} - 25 q^{37} + 9 q^{38} + 5 q^{39} - 3 q^{40} - 7 q^{41} + 7 q^{42} - 16 q^{43} + 4 q^{44} - 3 q^{45} - 10 q^{46} - 9 q^{47} - 9 q^{48} + 44 q^{49} + 4 q^{50} + 28 q^{51} - 5 q^{52} - 9 q^{53} - 9 q^{54} - 31 q^{55} - 7 q^{56} - 9 q^{57} - 3 q^{59} + 3 q^{60} - 16 q^{61} + 5 q^{62} - 7 q^{63} + 9 q^{64} - 33 q^{65} - 4 q^{66} - 13 q^{67} - 28 q^{68} + 10 q^{69} - 10 q^{70} - 4 q^{71} + 9 q^{72} - 29 q^{73} - 25 q^{74} - 4 q^{75} + 9 q^{76} - 33 q^{77} + 5 q^{78} + 13 q^{79} - 3 q^{80} + 9 q^{81} - 7 q^{82} - 35 q^{83} + 7 q^{84} + 3 q^{85} - 16 q^{86} + 4 q^{88} - 19 q^{89} - 3 q^{90} - 10 q^{92} - 5 q^{93} - 9 q^{94} - 3 q^{95} - 9 q^{96} - 12 q^{97} + 44 q^{98} + 4 q^{99}+O(q^{100}) \) 9 * q + 9 * q^2 - 9 * q^3 + 9 * q^4 - 3 * q^5 - 9 * q^6 - 7 * q^7 + 9 * q^8 + 9 * q^9 - 3 * q^10 + 4 * q^11 - 9 * q^12 - 5 * q^13 - 7 * q^14 + 3 * q^15 + 9 * q^16 - 28 * q^17 + 9 * q^18 + 9 * q^19 - 3 * q^20 + 7 * q^21 + 4 * q^22 - 10 * q^23 - 9 * q^24 + 4 * q^25 - 5 * q^26 - 9 * q^27 - 7 * q^28 + 3 * q^30 + 5 * q^31 + 9 * q^32 - 4 * q^33 - 28 * q^34 - 10 * q^35 + 9 * q^36 - 25 * q^37 + 9 * q^38 + 5 * q^39 - 3 * q^40 - 7 * q^41 + 7 * q^42 - 16 * q^43 + 4 * q^44 - 3 * q^45 - 10 * q^46 - 9 * q^47 - 9 * q^48 + 44 * q^49 + 4 * q^50 + 28 * q^51 - 5 * q^52 - 9 * q^53 - 9 * q^54 - 31 * q^55 - 7 * q^56 - 9 * q^57 - 3 * q^59 + 3 * q^60 - 16 * q^61 + 5 * q^62 - 7 * q^63 + 9 * q^64 - 33 * q^65 - 4 * q^66 - 13 * q^67 - 28 * q^68 + 10 * q^69 - 10 * q^70 - 4 * q^71 + 9 * q^72 - 29 * q^73 - 25 * q^74 - 4 * q^75 + 9 * q^76 - 33 * q^77 + 5 * q^78 + 13 * q^79 - 3 * q^80 + 9 * q^81 - 7 * q^82 - 35 * q^83 + 7 * q^84 + 3 * q^85 - 16 * q^86 + 4 * q^88 - 19 * q^89 - 3 * q^90 - 10 * q^92 - 5 * q^93 - 9 * q^94 - 3 * q^95 - 9 * q^96 - 12 * q^97 + 44 * q^98 + 4 * 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
$5$	−0.487125	−0.217849	−0.108925	−	0.994050i	$-0.534741\pi$
$5$	−0.487125	−0.217849	−0.108925	+	0.994050i	$0.534741\pi$
$6$	−1.00000	−0.408248
$7$	4.75176	1.79599	0.897997	−	0.440001i	$-0.145022\pi$
$7$	4.75176	1.79599	0.897997	+	0.440001i	$0.145022\pi$
$8$	1.00000	0.353553
$9$	1.00000	0.333333
$10$	−0.487125	−0.154043
$11$	−5.66565	−1.70826	−0.854129	−	0.520060i	$-0.825909\pi$
$11$	−5.66565	−1.70826	−0.854129	+	0.520060i	$0.825909\pi$
$12$	−1.00000	−0.288675
$13$	4.03321	1.11861	0.559305	−	0.828962i	$-0.311068\pi$
$13$	4.03321	1.11861	0.559305	+	0.828962i	$0.311068\pi$
$14$	4.75176	1.26996
$15$	0.487125	0.125775
$16$	1.00000	0.250000
$17$	−4.44432	−1.07791	−0.538953	−	0.842336i	$-0.681180\pi$
$17$	−4.44432	−1.07791	−0.538953	+	0.842336i	$0.681180\pi$
$18$	1.00000	0.235702
$19$	1.00000	0.229416
$19$	1.00000	0.229416
$20$	−0.487125	−0.108925
$21$	−4.75176	−1.03692
$22$	−5.66565	−1.20792
$23$	−5.49160	−1.14508	−0.572539	−	0.819878i	$-0.694041\pi$
$23$	−5.49160	−1.14508	−0.572539	+	0.819878i	$0.694041\pi$
$24$	−1.00000	−0.204124
$25$	−4.76271	−0.952542
$26$	4.03321	0.790977
$27$	−1.00000	−0.192450
$28$	4.75176	0.897997
$29$	0.0939007	0.0174369	0.00871846	−	0.999962i	$-0.497225\pi$
$29$	0.0939007	0.0174369	0.00871846	+	0.999962i	$0.497225\pi$
$30$	0.487125	0.0889365
$31$	−6.82737	−1.22623	−0.613116	−	0.789993i	$-0.710084\pi$
$31$	−6.82737	−1.22623	−0.613116	+	0.789993i	$0.710084\pi$
$32$	1.00000	0.176777
$33$	5.66565	0.986264
$34$	−4.44432	−0.762194
$35$	−2.31470	−0.391256
$36$	1.00000	0.166667
$37$	−10.1159	−1.66305	−0.831525	−	0.555487i	$-0.812532\pi$
$37$	−10.1159	−1.66305	−0.831525	+	0.555487i	$0.812532\pi$
$38$	1.00000	0.162221
$39$	−4.03321	−0.645830
$40$	−0.487125	−0.0770213
$41$	−6.52148	−1.01848	−0.509242	−	0.860623i	$-0.670074\pi$
$41$	−6.52148	−1.01848	−0.509242	+	0.860623i	$0.670074\pi$
$42$	−4.75176	−0.733212
$43$	−4.79851	−0.731766	−0.365883	−	0.930661i	$-0.619233\pi$
$43$	−4.79851	−0.731766	−0.365883	+	0.930661i	$0.619233\pi$
$44$	−5.66565	−0.854129
$45$	−0.487125	−0.0726164
$46$	−5.49160	−0.809692
$47$	2.63241	0.383977	0.191989	−	0.981397i	$-0.438506\pi$
$47$	2.63241	0.383977	0.191989	+	0.981397i	$0.438506\pi$
$48$	−1.00000	−0.144338
$49$	15.5792	2.22560
$50$	−4.76271	−0.673549
$51$	4.44432	0.622329
$52$	4.03321	0.559305
$53$	−1.00000	−0.137361
$53$	−1.00000	−0.137361
$54$	−1.00000	−0.136083
$55$	2.75988	0.372143
$56$	4.75176	0.634980
$57$	−1.00000	−0.132453
$58$	0.0939007	0.0123298
$59$	13.5519	1.76430	0.882152	−	0.470965i	$-0.156094\pi$
$59$	13.5519	1.76430	0.882152	+	0.470965i	$0.156094\pi$
$60$	0.487125	0.0628876
$61$	−0.302849	−0.0387758	−0.0193879	−	0.999812i	$-0.506172\pi$
$61$	−0.302849	−0.0387758	−0.0193879	+	0.999812i	$0.506172\pi$
$62$	−6.82737	−0.867077
$63$	4.75176	0.598665
$64$	1.00000	0.125000
$65$	−1.96468	−0.243688
$66$	5.66565	0.697394
$67$	−9.76859	−1.19342	−0.596712	−	0.802456i	$-0.703526\pi$
$67$	−9.76859	−1.19342	−0.596712	+	0.802456i	$0.703526\pi$
$68$	−4.44432	−0.538953
$69$	5.49160	0.661111
$70$	−2.31470	−0.276660
$71$	−15.8295	−1.87862	−0.939308	−	0.343075i	$-0.888532\pi$
$71$	−15.8295	−1.87862	−0.939308	+	0.343075i	$0.888532\pi$
$72$	1.00000	0.117851
$73$	−12.7465	−1.49186	−0.745932	−	0.666023i	$-0.767995\pi$
$73$	−12.7465	−1.49186	−0.745932	+	0.666023i	$0.767995\pi$
$74$	−10.1159	−1.17595
$75$	4.76271	0.549950
$76$	1.00000	0.114708
$77$	−26.9218	−3.06802
$78$	−4.03321	−0.456671
$79$	−0.0301722	−0.00339464	−0.00169732	−	0.999999i	$-0.500540\pi$
$79$	−0.0301722	−0.00339464	−0.00169732	+	0.999999i	$0.500540\pi$
$80$	−0.487125	−0.0544623
$81$	1.00000	0.111111
$82$	−6.52148	−0.720178
$83$	−5.61820	−0.616678	−0.308339	−	0.951277i	$-0.599773\pi$
$83$	−5.61820	−0.616678	−0.308339	+	0.951277i	$0.599773\pi$
$84$	−4.75176	−0.518459
$85$	2.16494	0.234821
$86$	−4.79851	−0.517437
$87$	−0.0939007	−0.0100672
$88$	−5.66565	−0.603961
$89$	−2.07916	−0.220390	−0.110195	−	0.993910i	$-0.535148\pi$
$89$	−2.07916	−0.220390	−0.110195	+	0.993910i	$0.535148\pi$
$90$	−0.487125	−0.0513475
$91$	19.1648	2.00902
$92$	−5.49160	−0.572539
$93$	6.82737	0.707965
$94$	2.63241	0.271513
$95$	−0.487125	−0.0499780
$96$	−1.00000	−0.102062
$97$	18.2881	1.85687	0.928437	−	0.371489i	$-0.121153\pi$
$97$	18.2881	1.85687	0.928437	+	0.371489i	$0.121153\pi$
$98$	15.5792	1.57373
$99$	−5.66565	−0.569420
$100$	−4.76271	−0.476271
$101$	−14.0496	−1.39798	−0.698992	−	0.715130i	$-0.746368\pi$
$101$	−14.0496	−1.39798	−0.698992	+	0.715130i	$0.746368\pi$
$102$	4.44432	0.440053
$103$	13.0731	1.28813	0.644064	−	0.764972i	$-0.277247\pi$
$103$	13.0731	1.28813	0.644064	+	0.764972i	$0.277247\pi$
$104$	4.03321	0.395488
$105$	2.31470	0.225892
$106$	−1.00000	−0.0971286
$107$	9.47189	0.915682	0.457841	−	0.889034i	$-0.348623\pi$
$107$	9.47189	0.915682	0.457841	+	0.889034i	$0.348623\pi$
$108$	−1.00000	−0.0962250
$109$	8.97959	0.860089	0.430044	−	0.902808i	$-0.358498\pi$
$109$	8.97959	0.860089	0.430044	+	0.902808i	$0.358498\pi$
$110$	2.75988	0.263145
$111$	10.1159	0.960163
$112$	4.75176	0.448999
$113$	2.32707	0.218912	0.109456	−	0.993992i	$-0.465089\pi$
$113$	2.32707	0.218912	0.109456	+	0.993992i	$0.465089\pi$
$114$	−1.00000	−0.0936586
$115$	2.67510	0.249454
$116$	0.0939007	0.00871846
$117$	4.03321	0.372870
$118$	13.5519	1.24755
$119$	−21.1183	−1.93591
$120$	0.487125	0.0444683
$121$	21.0996	1.91815
$122$	−0.302849	−0.0274187
$123$	6.52148	0.588022
$124$	−6.82737	−0.613116
$125$	4.75566	0.425359
$126$	4.75176	0.423320
$127$	−8.34098	−0.740142	−0.370071	−	0.929003i	$-0.620667\pi$
$127$	−8.34098	−0.740142	−0.370071	+	0.929003i	$0.620667\pi$
$128$	1.00000	0.0883883
$129$	4.79851	0.422485
$130$	−1.96468	−0.172314
$131$	19.0207	1.66185	0.830924	−	0.556387i	$-0.187813\pi$
$131$	19.0207	1.66185	0.830924	+	0.556387i	$0.187813\pi$
$132$	5.66565	0.493132
$133$	4.75176	0.412029
$134$	−9.76859	−0.843878
$135$	0.487125	0.0419251
$136$	−4.44432	−0.381097
$137$	4.41119	0.376874	0.188437	−	0.982085i	$-0.439658\pi$
$137$	4.41119	0.376874	0.188437	+	0.982085i	$0.439658\pi$
$138$	5.49160	0.467476
$139$	8.16883	0.692871	0.346436	−	0.938074i	$-0.387392\pi$
$139$	8.16883	0.692871	0.346436	+	0.938074i	$0.387392\pi$
$140$	−2.31470	−0.195628
$141$	−2.63241	−0.221689
$142$	−15.8295	−1.32838
$143$	−22.8507	−1.91088
$144$	1.00000	0.0833333
$145$	−0.0457414	−0.00379862
$146$	−12.7465	−1.05491
$147$	−15.5792	−1.28495
$148$	−10.1159	−0.831525
$149$	−15.4193	−1.26320	−0.631599	−	0.775295i	$-0.717601\pi$
$149$	−15.4193	−1.26320	−0.631599	+	0.775295i	$0.717601\pi$
$150$	4.76271	0.388874
$151$	20.3560	1.65654	0.828272	−	0.560326i	$-0.189324\pi$
$151$	20.3560	1.65654	0.828272	+	0.560326i	$0.189324\pi$
$152$	1.00000	0.0811107
$153$	−4.44432	−0.359302
$154$	−26.9218	−2.16942
$155$	3.32578	0.267133
$156$	−4.03321	−0.322915
$157$	−22.3039	−1.78004	−0.890021	−	0.455919i	$-0.849311\pi$
$157$	−22.3039	−1.78004	−0.890021	+	0.455919i	$0.849311\pi$
$158$	−0.0301722	−0.00240037
$159$	1.00000	0.0793052
$160$	−0.487125	−0.0385106
$161$	−26.0947	−2.05655
$162$	1.00000	0.0785674
$163$	2.54460	0.199308	0.0996541	−	0.995022i	$-0.468226\pi$
$163$	2.54460	0.199308	0.0996541	+	0.995022i	$0.468226\pi$
$164$	−6.52148	−0.509242
$165$	−2.75988	−0.214857
$166$	−5.61820	−0.436057
$167$	−18.3031	−1.41634	−0.708169	−	0.706043i	$-0.750479\pi$
$167$	−18.3031	−1.41634	−0.708169	+	0.706043i	$0.750479\pi$
$168$	−4.75176	−0.366606
$169$	3.26675	0.251288
$170$	2.16494	0.166043
$171$	1.00000	0.0764719
$172$	−4.79851	−0.365883
$173$	18.7435	1.42504	0.712521	−	0.701650i	$-0.247553\pi$
$173$	18.7435	1.42504	0.712521	+	0.701650i	$0.247553\pi$
$174$	−0.0939007	−0.00711859
$175$	−22.6312	−1.71076
$176$	−5.66565	−0.427065
$177$	−13.5519	−1.01862
$178$	−2.07916	−0.155840
$179$	−13.3885	−1.00070	−0.500350	−	0.865823i	$-0.666795\pi$
$179$	−13.3885	−1.00070	−0.500350	+	0.865823i	$0.666795\pi$
$180$	−0.487125	−0.0363082
$181$	−3.48926	−0.259355	−0.129677	−	0.991556i	$-0.541394\pi$
$181$	−3.48926	−0.259355	−0.129677	+	0.991556i	$0.541394\pi$
$182$	19.1648	1.42059
$183$	0.302849	0.0223872
$184$	−5.49160	−0.404846
$185$	4.92773	0.362294
$186$	6.82737	0.500607
$187$	25.1800	1.84134
$188$	2.63241	0.191989
$189$	−4.75176	−0.345639
$190$	−0.487125	−0.0353398
$191$	10.5522	0.763529	0.381765	−	0.924260i	$-0.375316\pi$
$191$	10.5522	0.763529	0.381765	+	0.924260i	$0.375316\pi$
$192$	−1.00000	−0.0721688
$193$	17.7885	1.28044	0.640221	−	0.768191i	$-0.278843\pi$
$193$	17.7885	1.28044	0.640221	+	0.768191i	$0.278843\pi$
$194$	18.2881	1.31301
$195$	1.96468	0.140693
$196$	15.5792	1.11280
$197$	−4.13339	−0.294492	−0.147246	−	0.989100i	$-0.547041\pi$
$197$	−4.13339	−0.294492	−0.147246	+	0.989100i	$0.547041\pi$
$198$	−5.66565	−0.402640
$199$	7.92032	0.561457	0.280728	−	0.959787i	$-0.409424\pi$
$199$	7.92032	0.561457	0.280728	+	0.959787i	$0.409424\pi$
$200$	−4.76271	−0.336774
$201$	9.76859	0.689023
$202$	−14.0496	−0.988524
$203$	0.446193	0.0313166
$204$	4.44432	0.311164
$205$	3.17678	0.221876
$206$	13.0731	0.910843
$207$	−5.49160	−0.381693
$208$	4.03321	0.279653
$209$	−5.66565	−0.391901
$210$	2.31470	0.159730
$211$	−2.76651	−0.190454	−0.0952272	−	0.995456i	$-0.530358\pi$
$211$	−2.76651	−0.190454	−0.0952272	+	0.995456i	$0.530358\pi$
$212$	−1.00000	−0.0686803
$213$	15.8295	1.08462
$214$	9.47189	0.647485
$215$	2.33748	0.159415
$216$	−1.00000	−0.0680414
$217$	−32.4420	−2.20231
$218$	8.97959	0.608174
$219$	12.7465	0.861328
$220$	2.75988	0.186071
$221$	−17.9248	−1.20576
$222$	10.1159	0.678938
$223$	2.42443	0.162352	0.0811759	−	0.996700i	$-0.474132\pi$
$223$	2.42443	0.162352	0.0811759	+	0.996700i	$0.474132\pi$
$224$	4.75176	0.317490
$225$	−4.76271	−0.317514
$226$	2.32707	0.154794
$227$	−2.19407	−0.145626	−0.0728129	−	0.997346i	$-0.523198\pi$
$227$	−2.19407	−0.145626	−0.0728129	+	0.997346i	$0.523198\pi$
$228$	−1.00000	−0.0662266
$229$	−10.8574	−0.717475	−0.358737	−	0.933439i	$-0.616793\pi$
$229$	−10.8574	−0.717475	−0.358737	+	0.933439i	$0.616793\pi$
$230$	2.67510	0.176391
$231$	26.9218	1.77132
$232$	0.0939007	0.00616488
$233$	−25.1962	−1.65066	−0.825328	−	0.564654i	$-0.809010\pi$
$233$	−25.1962	−1.65066	−0.825328	+	0.564654i	$0.809010\pi$
$234$	4.03321	0.263659
$235$	−1.28232	−0.0836491
$236$	13.5519	0.882152
$237$	0.0301722	0.00195990
$238$	−21.1183	−1.36890
$239$	−27.8108	−1.79893	−0.899466	−	0.436991i	$-0.856044\pi$
$239$	−27.8108	−1.79893	−0.899466	+	0.436991i	$0.856044\pi$
$240$	0.487125	0.0314438
$241$	−23.6235	−1.52172	−0.760861	−	0.648915i	$-0.775223\pi$
$241$	−23.6235	−1.52172	−0.760861	+	0.648915i	$0.775223\pi$
$242$	21.0996	1.35634
$243$	−1.00000	−0.0641500
$244$	−0.302849	−0.0193879
$245$	−7.58901	−0.484844
$246$	6.52148	0.415795
$247$	4.03321	0.256627
$248$	−6.82737	−0.433538
$249$	5.61820	0.356039
$250$	4.75566	0.300775
$251$	9.89187	0.624369	0.312185	−	0.950021i	$-0.398939\pi$
$251$	9.89187	0.624369	0.312185	+	0.950021i	$0.398939\pi$
$252$	4.75176	0.299332
$253$	31.1135	1.95609
$254$	−8.34098	−0.523359
$255$	−2.16494	−0.135574
$256$	1.00000	0.0625000
$257$	−23.9620	−1.49471	−0.747355	−	0.664425i	$-0.768677\pi$
$257$	−23.9620	−1.49471	−0.747355	+	0.664425i	$0.768677\pi$
$258$	4.79851	0.298742
$259$	−48.0685	−2.98683
$260$	−1.96468	−0.121844
$261$	0.0939007	0.00581231
$262$	19.0207	1.17510
$263$	1.73672	0.107091	0.0535453	−	0.998565i	$-0.482948\pi$
$263$	1.73672	0.107091	0.0535453	+	0.998565i	$0.482948\pi$
$264$	5.66565	0.348697
$265$	0.487125	0.0299239
$266$	4.75176	0.291349
$267$	2.07916	0.127242
$268$	−9.76859	−0.596712
$269$	29.3801	1.79134	0.895668	−	0.444723i	$-0.146698\pi$
$269$	29.3801	1.79134	0.895668	+	0.444723i	$0.146698\pi$
$270$	0.487125	0.0296455
$271$	7.27393	0.441860	0.220930	−	0.975290i	$-0.429091\pi$
$271$	7.27393	0.441860	0.220930	+	0.975290i	$0.429091\pi$
$272$	−4.44432	−0.269476
$273$	−19.1648	−1.15991
$274$	4.41119	0.266490
$275$	26.9839	1.62719
$276$	5.49160	0.330556
$277$	23.4399	1.40837	0.704185	−	0.710017i	$-0.251313\pi$
$277$	23.4399	1.40837	0.704185	+	0.710017i	$0.251313\pi$
$278$	8.16883	0.489934
$279$	−6.82737	−0.408744
$280$	−2.31470	−0.138330
$281$	4.17808	0.249244	0.124622	−	0.992204i	$-0.460228\pi$
$281$	4.17808	0.249244	0.124622	+	0.992204i	$0.460228\pi$
$282$	−2.63241	−0.156758
$283$	4.67717	0.278029	0.139015	−	0.990290i	$-0.455607\pi$
$283$	4.67717	0.278029	0.139015	+	0.990290i	$0.455607\pi$
$284$	−15.8295	−0.939308
$285$	0.487125	0.0288548
$286$	−22.8507	−1.35119
$287$	−30.9885	−1.82919
$288$	1.00000	0.0589256
$289$	2.75196	0.161880
$290$	−0.0457414	−0.00268603
$291$	−18.2881	−1.07207
$292$	−12.7465	−0.745932
$293$	16.9749	0.991685	0.495843	−	0.868412i	$-0.334859\pi$
$293$	16.9749	0.991685	0.495843	+	0.868412i	$0.334859\pi$
$294$	−15.5792	−0.908596
$295$	−6.60146	−0.384352
$296$	−10.1159	−0.587977
$297$	5.66565	0.328755
$298$	−15.4193	−0.893216
$299$	−22.1488	−1.28090
$300$	4.76271	0.274975
$301$	−22.8014	−1.31425
$302$	20.3560	1.17135
$303$	14.0496	0.807126
$304$	1.00000	0.0573539
$305$	0.147525	0.00844728
$306$	−4.44432	−0.254065
$307$	−27.3937	−1.56344	−0.781720	−	0.623629i	$-0.785657\pi$
$307$	−27.3937	−1.56344	−0.781720	+	0.623629i	$0.785657\pi$
$308$	−26.9218	−1.53401
$309$	−13.0731	−0.743701
$310$	3.32578	0.188892
$311$	−5.83899	−0.331099	−0.165549	−	0.986201i	$-0.552940\pi$
$311$	−5.83899	−0.331099	−0.165549	+	0.986201i	$0.552940\pi$
$312$	−4.03321	−0.228335
$313$	−9.97016	−0.563547	−0.281773	−	0.959481i	$-0.590923\pi$
$313$	−9.97016	−0.563547	−0.281773	+	0.959481i	$0.590923\pi$
$314$	−22.3039	−1.25868
$315$	−2.31470	−0.130419
$316$	−0.0301722	−0.00169732
$317$	−4.26401	−0.239491	−0.119745	−	0.992805i	$-0.538208\pi$
$317$	−4.26401	−0.239491	−0.119745	+	0.992805i	$0.538208\pi$
$318$	1.00000	0.0560772
$319$	−0.532009	−0.0297868
$320$	−0.487125	−0.0272311
$321$	−9.47189	−0.528669
$322$	−26.0947	−1.45420
$323$	−4.44432	−0.247288
$324$	1.00000	0.0555556
$325$	−19.2090	−1.06552
$326$	2.54460	0.140932
$327$	−8.97959	−0.496572
$328$	−6.52148	−0.360089
$329$	12.5086	0.689621
$330$	−2.75988	−0.151927
$331$	−9.35569	−0.514235	−0.257118	−	0.966380i	$-0.582773\pi$
$331$	−9.35569	−0.514235	−0.257118	+	0.966380i	$0.582773\pi$
$332$	−5.61820	−0.308339
$333$	−10.1159	−0.554350
$334$	−18.3031	−1.00150
$335$	4.75853	0.259986
$336$	−4.75176	−0.259230
$337$	−28.5407	−1.55471	−0.777354	−	0.629063i	$-0.783439\pi$
$337$	−28.5407	−1.55471	−0.777354	+	0.629063i	$0.783439\pi$
$338$	3.26675	0.177688
$339$	−2.32707	−0.126389
$340$	2.16494	0.117410
$341$	38.6815	2.09472
$342$	1.00000	0.0540738
$343$	40.7662	2.20117
$344$	−4.79851	−0.258718
$345$	−2.67510	−0.144022
$346$	18.7435	1.00766
$347$	−13.7040	−0.735670	−0.367835	−	0.929891i	$-0.619901\pi$
$347$	−13.7040	−0.735670	−0.367835	+	0.929891i	$0.619901\pi$
$348$	−0.0939007	−0.00503360
$349$	24.2081	1.29583	0.647916	−	0.761712i	$-0.275641\pi$
$349$	24.2081	1.29583	0.647916	+	0.761712i	$0.275641\pi$
$350$	−22.6312	−1.20969
$351$	−4.03321	−0.215277
$352$	−5.66565	−0.301980
$353$	15.1457	0.806123	0.403062	−	0.915173i	$-0.367946\pi$
$353$	15.1457	0.806123	0.403062	+	0.915173i	$0.367946\pi$
$354$	−13.5519	−0.720274
$355$	7.71095	0.409255
$356$	−2.07916	−0.110195
$357$	21.1183	1.11770
$358$	−13.3885	−0.707602
$359$	21.1690	1.11726	0.558629	−	0.829418i	$-0.311328\pi$
$359$	21.1690	1.11726	0.558629	+	0.829418i	$0.311328\pi$
$360$	−0.487125	−0.0256738
$361$	1.00000	0.0526316
$362$	−3.48926	−0.183392
$363$	−21.0996	−1.10744
$364$	19.1648	1.00451
$365$	6.20914	0.325001
$366$	0.302849	0.0158302
$367$	4.45105	0.232343	0.116171	−	0.993229i	$-0.462938\pi$
$367$	4.45105	0.232343	0.116171	+	0.993229i	$0.462938\pi$
$368$	−5.49160	−0.286269
$369$	−6.52148	−0.339495
$370$	4.92773	0.256181
$371$	−4.75176	−0.246699
$372$	6.82737	0.353983
$373$	4.41354	0.228524	0.114262	−	0.993451i	$-0.463550\pi$
$373$	4.41354	0.228524	0.114262	+	0.993451i	$0.463550\pi$
$374$	25.1800	1.30203
$375$	−4.75566	−0.245581
$376$	2.63241	0.135756
$377$	0.378721	0.0195051
$378$	−4.75176	−0.244404
$379$	−0.266127	−0.0136700	−0.00683502	−	0.999977i	$-0.502176\pi$
$379$	−0.266127	−0.0136700	−0.00683502	+	0.999977i	$0.502176\pi$
$380$	−0.487125	−0.0249890
$381$	8.34098	0.427321
$382$	10.5522	0.539897
$383$	−5.70301	−0.291410	−0.145705	−	0.989328i	$-0.546545\pi$
$383$	−5.70301	−0.291410	−0.145705	+	0.989328i	$0.546545\pi$
$384$	−1.00000	−0.0510310
$385$	13.1143	0.668366
$386$	17.7885	0.905409
$387$	−4.79851	−0.243922
$388$	18.2881	0.928437
$389$	−24.6343	−1.24901	−0.624505	−	0.781021i	$-0.714699\pi$
$389$	−24.6343	−1.24901	−0.624505	+	0.781021i	$0.714699\pi$
$390$	1.96468	0.0994853
$391$	24.4064	1.23429
$392$	15.5792	0.786867
$393$	−19.0207	−0.959468
$394$	−4.13339	−0.208237
$395$	0.0146977	0.000739520 0
$396$	−5.66565	−0.284710
$397$	4.76630	0.239214	0.119607	−	0.992821i	$-0.461837\pi$
$397$	4.76630	0.239214	0.119607	+	0.992821i	$0.461837\pi$
$398$	7.92032	0.397010
$399$	−4.75176	−0.237885
$400$	−4.76271	−0.238135
$401$	2.95448	0.147540	0.0737698	−	0.997275i	$-0.476497\pi$
$401$	2.95448	0.147540	0.0737698	+	0.997275i	$0.476497\pi$
$402$	9.76859	0.487213
$403$	−27.5362	−1.37167
$404$	−14.0496	−0.698992
$405$	−0.487125	−0.0242055
$406$	0.446193	0.0221442
$407$	57.3134	2.84092
$408$	4.44432	0.220027
$409$	4.77300	0.236010	0.118005	−	0.993013i	$-0.462350\pi$
$409$	4.77300	0.236010	0.118005	+	0.993013i	$0.462350\pi$
$410$	3.17678	0.156890
$411$	−4.41119	−0.217588
$412$	13.0731	0.644064
$413$	64.3952	3.16868
$414$	−5.49160	−0.269897
$415$	2.73677	0.134343
$416$	4.03321	0.197744
$417$	−8.16883	−0.400029
$418$	−5.66565	−0.277116
$419$	1.05678	0.0516272	0.0258136	−	0.999667i	$-0.491782\pi$
$419$	1.05678	0.0516272	0.0258136	+	0.999667i	$0.491782\pi$
$420$	2.31470	0.112946
$421$	−15.4595	−0.753448	−0.376724	−	0.926325i	$-0.622950\pi$
$421$	−15.4595	−0.753448	−0.376724	+	0.926325i	$0.622950\pi$
$422$	−2.76651	−0.134672
$423$	2.63241	0.127992
$424$	−1.00000	−0.0485643
$425$	21.1670	1.02675
$426$	15.8295	0.766942
$427$	−1.43906	−0.0696412
$428$	9.47189	0.457841
$429$	22.8507	1.10324
$430$	2.33748	0.112723
$431$	−27.3641	−1.31808	−0.659040	−	0.752108i	$-0.729037\pi$
$431$	−27.3641	−1.31808	−0.659040	+	0.752108i	$0.729037\pi$
$432$	−1.00000	−0.0481125
$433$	16.9495	0.814539	0.407270	−	0.913308i	$-0.366481\pi$
$433$	16.9495	0.814539	0.407270	+	0.913308i	$0.366481\pi$
$434$	−32.4420	−1.55726
$435$	0.0457414	0.00219313
$436$	8.97959	0.430044
$437$	−5.49160	−0.262699
$438$	12.7465	0.609051
$439$	−35.3454	−1.68694	−0.843472	−	0.537173i	$-0.819492\pi$
$439$	−35.3454	−1.68694	−0.843472	+	0.537173i	$0.819492\pi$
$440$	2.75988	0.131572
$441$	15.5792	0.741866
$442$	−17.9248	−0.852598
$443$	22.4089	1.06468	0.532340	−	0.846531i	$-0.321313\pi$
$443$	22.4089	1.06468	0.532340	+	0.846531i	$0.321313\pi$
$444$	10.1159	0.480081
$445$	1.01281	0.0480118
$446$	2.42443	0.114800
$447$	15.4193	0.729308
$448$	4.75176	0.224499
$449$	−15.9697	−0.753657	−0.376828	−	0.926283i	$-0.622985\pi$
$449$	−15.9697	−0.753657	−0.376828	+	0.926283i	$0.622985\pi$
$450$	−4.76271	−0.224516
$451$	36.9485	1.73984
$452$	2.32707	0.109456
$453$	−20.3560	−0.956406
$454$	−2.19407	−0.102973
$455$	−9.33566	−0.437663
$456$	−1.00000	−0.0468293
$457$	−25.4486	−1.19044	−0.595218	−	0.803564i	$-0.702934\pi$
$457$	−25.4486	−1.19044	−0.595218	+	0.803564i	$0.702934\pi$
$458$	−10.8574	−0.507331
$459$	4.44432	0.207443
$460$	2.67510	0.124727
$461$	−27.1701	−1.26544	−0.632719	−	0.774381i	$-0.718061\pi$
$461$	−27.1701	−1.26544	−0.632719	+	0.774381i	$0.718061\pi$
$462$	26.9218	1.25252
$463$	28.3460	1.31735	0.658675	−	0.752427i	$-0.271117\pi$
$463$	28.3460	1.31735	0.658675	+	0.752427i	$0.271117\pi$
$464$	0.0939007	0.00435923
$465$	−3.32578	−0.154230
$466$	−25.1962	−1.16719
$467$	−0.149569	−0.00692123	−0.00346061	−	0.999994i	$-0.501102\pi$
$467$	−0.149569	−0.00692123	−0.00346061	+	0.999994i	$0.501102\pi$
$468$	4.03321	0.186435
$469$	−46.4180	−2.14338
$470$	−1.28232	−0.0591488
$471$	22.3039	1.02771
$472$	13.5519	0.623776
$473$	27.1867	1.25005
$474$	0.0301722	0.00138586
$475$	−4.76271	−0.218528
$476$	−21.1183	−0.967956
$477$	−1.00000	−0.0457869
$478$	−27.8108	−1.27204
$479$	14.1230	0.645297	0.322649	−	0.946519i	$-0.395427\pi$
$479$	14.1230	0.645297	0.322649	+	0.946519i	$0.395427\pi$
$480$	0.487125	0.0222341
$481$	−40.7997	−1.86031
$482$	−23.6235	−1.07602
$483$	26.0947	1.18735
$484$	21.0996	0.959074
$485$	−8.90860	−0.404518
$486$	−1.00000	−0.0453609
$487$	4.46835	0.202480	0.101240	−	0.994862i	$-0.467719\pi$
$487$	4.46835	0.202480	0.101240	+	0.994862i	$0.467719\pi$
$488$	−0.302849	−0.0137093
$489$	−2.54460	−0.115071
$490$	−7.58901	−0.342837
$491$	−37.6681	−1.69994	−0.849968	−	0.526834i	$-0.823379\pi$
$491$	−37.6681	−1.69994	−0.849968	+	0.526834i	$0.823379\pi$
$492$	6.52148	0.294011
$493$	−0.417324	−0.0187953
$494$	4.03321	0.181463
$495$	2.75988	0.124048
$496$	−6.82737	−0.306558
$497$	−75.2179	−3.37398
$498$	5.61820	0.251758
$499$	35.8395	1.60440	0.802198	−	0.597058i	$-0.203664\pi$
$499$	35.8395	1.60440	0.802198	+	0.597058i	$0.203664\pi$
$500$	4.75566	0.212680
$501$	18.3031	0.817723
$502$	9.89187	0.441496
$503$	−32.6701	−1.45669	−0.728343	−	0.685213i	$-0.759709\pi$
$503$	−32.6701	−1.45669	−0.728343	+	0.685213i	$0.759709\pi$
$504$	4.75176	0.211660
$505$	6.84390	0.304550
$506$	31.1135	1.38316
$507$	−3.26675	−0.145081
$508$	−8.34098	−0.370071
$509$	21.7325	0.963274	0.481637	−	0.876371i	$-0.340042\pi$
$509$	21.7325	0.963274	0.481637	+	0.876371i	$0.340042\pi$
$510$	−2.16494	−0.0958652
$511$	−60.5682	−2.67938
$512$	1.00000	0.0441942
$513$	−1.00000	−0.0441511
$514$	−23.9620	−1.05692
$515$	−6.36822	−0.280617
$516$	4.79851	0.211243
$517$	−14.9144	−0.655932
$518$	−48.0685	−2.11201
$519$	−18.7435	−0.822749
$520$	−1.96468	−0.0861568
$521$	3.73636	0.163693	0.0818464	−	0.996645i	$-0.473918\pi$
$521$	3.73636	0.163693	0.0818464	+	0.996645i	$0.473918\pi$
$522$	0.0939007	0.00410992
$523$	18.3155	0.800881	0.400441	−	0.916323i	$-0.368857\pi$
$523$	18.3155	0.800881	0.400441	+	0.916323i	$0.368857\pi$
$524$	19.0207	0.830924
$525$	22.6312	0.987708
$526$	1.73672	0.0757245
$527$	30.3430	1.32176
$528$	5.66565	0.246566
$529$	7.15768	0.311203
$530$	0.487125	0.0211594
$531$	13.5519	0.588101
$532$	4.75176	0.206015
$533$	−26.3025	−1.13929
$534$	2.07916	0.0899740
$535$	−4.61400	−0.199481
$536$	−9.76859	−0.421939
$537$	13.3885	0.577755
$538$	29.3801	1.26667
$539$	−88.2662	−3.80190
$540$	0.487125	0.0209625
$541$	−22.2295	−0.955721	−0.477861	−	0.878436i	$-0.658588\pi$
$541$	−22.2295	−0.955721	−0.477861	+	0.878436i	$0.658588\pi$
$542$	7.27393	0.312442
$543$	3.48926	0.149739
$544$	−4.44432	−0.190549
$545$	−4.37419	−0.187370
$546$	−19.1648	−0.820178
$547$	5.27411	0.225505	0.112752	−	0.993623i	$-0.464033\pi$
$547$	5.27411	0.225505	0.112752	+	0.993623i	$0.464033\pi$
$548$	4.41119	0.188437
$549$	−0.302849	−0.0129253
$550$	26.9839	1.15060
$551$	0.0939007	0.00400030
$552$	5.49160	0.233738
$553$	−0.143371	−0.00609676
$554$	23.4399	0.995868
$555$	−4.92773	−0.209171
$556$	8.16883	0.346436
$557$	2.28322	0.0967433	0.0483717	−	0.998829i	$-0.484597\pi$
$557$	2.28322	0.0967433	0.0483717	+	0.998829i	$0.484597\pi$
$558$	−6.82737	−0.289026
$559$	−19.3534	−0.818561
$560$	−2.31470	−0.0978140
$561$	−25.1800	−1.06310
$562$	4.17808	0.176242
$563$	−20.4096	−0.860160	−0.430080	−	0.902791i	$-0.641515\pi$
$563$	−20.4096	−0.860160	−0.430080	+	0.902791i	$0.641515\pi$
$564$	−2.63241	−0.110845
$565$	−1.13357	−0.0476898
$566$	4.67717	0.196596
$567$	4.75176	0.199555
$568$	−15.8295	−0.664191
$569$	29.2673	1.22695	0.613474	−	0.789715i	$-0.289772\pi$
$569$	29.2673	1.22695	0.613474	+	0.789715i	$0.289772\pi$
$570$	0.487125	0.0204034
$571$	2.24417	0.0939154	0.0469577	−	0.998897i	$-0.485047\pi$
$571$	2.24417	0.0939154	0.0469577	+	0.998897i	$0.485047\pi$
$572$	−22.8507	−0.955438
$573$	−10.5522	−0.440824
$574$	−30.9885	−1.29344
$575$	26.1549	1.09073
$576$	1.00000	0.0416667
$577$	2.49969	0.104064	0.0520318	−	0.998645i	$-0.483430\pi$
$577$	2.49969	0.104064	0.0520318	+	0.998645i	$0.483430\pi$
$578$	2.75196	0.114466
$579$	−17.7885	−0.739263
$580$	−0.0457414	−0.00189931
$581$	−26.6963	−1.10755
$582$	−18.2881	−0.758066
$583$	5.66565	0.234647
$584$	−12.7465	−0.527453
$585$	−1.96468	−0.0812294
$586$	16.9749	0.701227
$587$	27.8017	1.14750	0.573750	−	0.819031i	$-0.305488\pi$
$587$	27.8017	1.14750	0.573750	+	0.819031i	$0.305488\pi$
$588$	−15.5792	−0.642475
$589$	−6.82737	−0.281317
$590$	−6.60146	−0.271778
$591$	4.13339	0.170025
$592$	−10.1159	−0.415763
$593$	8.38198	0.344207	0.172103	−	0.985079i	$-0.444944\pi$
$593$	8.38198	0.344207	0.172103	+	0.985079i	$0.444944\pi$
$594$	5.66565	0.232465
$595$	10.2873	0.421737
$596$	−15.4193	−0.631599
$597$	−7.92032	−0.324157
$598$	−22.1488	−0.905730
$599$	8.13015	0.332189	0.166094	−	0.986110i	$-0.446884\pi$
$599$	8.13015	0.332189	0.166094	+	0.986110i	$0.446884\pi$
$600$	4.76271	0.194437
$601$	−25.5538	−1.04236	−0.521181	−	0.853446i	$-0.674509\pi$
$601$	−25.5538	−1.04236	−0.521181	+	0.853446i	$0.674509\pi$
$602$	−22.8014	−0.929314
$603$	−9.76859	−0.397808
$604$	20.3560	0.828272
$605$	−10.2782	−0.417867
$606$	14.0496	0.570725
$607$	30.7211	1.24693	0.623466	−	0.781850i	$-0.285724\pi$
$607$	30.7211	1.24693	0.623466	+	0.781850i	$0.285724\pi$
$608$	1.00000	0.0405554
$609$	−0.446193	−0.0180807
$610$	0.147525	0.00597313
$611$	10.6171	0.429521
$612$	−4.44432	−0.179651
$613$	41.0740	1.65896	0.829481	−	0.558535i	$-0.188636\pi$
$613$	41.0740	1.65896	0.829481	+	0.558535i	$0.188636\pi$
$614$	−27.3937	−1.10552
$615$	−3.17678	−0.128100
$616$	−26.9218	−1.08471
$617$	−7.49633	−0.301791	−0.150896	−	0.988550i	$-0.548216\pi$
$617$	−7.49633	−0.301791	−0.150896	+	0.988550i	$0.548216\pi$
$618$	−13.0731	−0.525876
$619$	11.0405	0.443756	0.221878	−	0.975074i	$-0.428781\pi$
$619$	11.0405	0.443756	0.221878	+	0.975074i	$0.428781\pi$
$620$	3.32578	0.133567
$621$	5.49160	0.220370
$622$	−5.83899	−0.234122
$623$	−9.87965	−0.395820
$624$	−4.03321	−0.161457
$625$	21.4969	0.859878
$626$	−9.97016	−0.398488
$627$	5.66565	0.226264
$628$	−22.3039	−0.890021
$629$	44.9585	1.79261
$630$	−2.31470	−0.0922199
$631$	−2.13982	−0.0851848	−0.0425924	−	0.999093i	$-0.513562\pi$
$631$	−2.13982	−0.0851848	−0.0425924	+	0.999093i	$0.513562\pi$
$632$	−0.0301722	−0.00120019
$633$	2.76651	0.109959
$634$	−4.26401	−0.169345
$635$	4.06310	0.161239
$636$	1.00000	0.0396526
$637$	62.8340	2.48958
$638$	−0.532009	−0.0210624
$639$	−15.8295	−0.626205
$640$	−0.487125	−0.0192553
$641$	12.9863	0.512927	0.256463	−	0.966554i	$-0.417443\pi$
$641$	12.9863	0.512927	0.256463	+	0.966554i	$0.417443\pi$
$642$	−9.47189	−0.373826
$643$	25.9504	1.02338	0.511692	−	0.859169i	$-0.329019\pi$
$643$	25.9504	1.02338	0.511692	+	0.859169i	$0.329019\pi$
$644$	−26.0947	−1.02828
$645$	−2.33748	−0.0920381
$646$	−4.44432	−0.174859
$647$	7.19062	0.282692	0.141346	−	0.989960i	$-0.454857\pi$
$647$	7.19062	0.282692	0.141346	+	0.989960i	$0.454857\pi$
$648$	1.00000	0.0392837
$649$	−76.7802	−3.01389
$650$	−19.2090	−0.753438
$651$	32.4420	1.27150
$652$	2.54460	0.0996541
$653$	16.3244	0.638824	0.319412	−	0.947616i	$-0.396515\pi$
$653$	16.3244	0.638824	0.319412	+	0.947616i	$0.396515\pi$
$654$	−8.97959	−0.351130
$655$	−9.26547	−0.362032
$656$	−6.52148	−0.254621
$657$	−12.7465	−0.497288
$658$	12.5086	0.487636
$659$	46.3475	1.80544	0.902722	−	0.430225i	$-0.141566\pi$
$659$	46.3475	1.80544	0.902722	+	0.430225i	$0.141566\pi$
$660$	−2.75988	−0.107428
$661$	−32.8696	−1.27848	−0.639241	−	0.769007i	$-0.720751\pi$
$661$	−32.8696	−1.27848	−0.639241	+	0.769007i	$0.720751\pi$
$662$	−9.35569	−0.363619
$663$	17.9248	0.696143
$664$	−5.61820	−0.218029
$665$	−2.31470	−0.0897602
$666$	−10.1159	−0.391985
$667$	−0.515665	−0.0199666
$668$	−18.3031	−0.708169
$669$	−2.42443	−0.0937339
$670$	4.75853	0.183838
$671$	1.71584	0.0662392
$672$	−4.75176	−0.183303
$673$	−33.1156	−1.27651	−0.638256	−	0.769824i	$-0.720344\pi$
$673$	−33.1156	−1.27651	−0.638256	+	0.769824i	$0.720344\pi$
$674$	−28.5407	−1.09935
$675$	4.76271	0.183317
$676$	3.26675	0.125644
$677$	−12.8832	−0.495142	−0.247571	−	0.968870i	$-0.579632\pi$
$677$	−12.8832	−0.495142	−0.247571	+	0.968870i	$0.579632\pi$
$678$	−2.32707	−0.0893705
$679$	86.9006	3.33494
$680$	2.16494	0.0830217
$681$	2.19407	0.0840771
$682$	38.6815	1.48119
$683$	−14.9061	−0.570366	−0.285183	−	0.958473i	$-0.592054\pi$
$683$	−14.9061	−0.570366	−0.285183	+	0.958473i	$0.592054\pi$
$684$	1.00000	0.0382360
$685$	−2.14880	−0.0821016
$686$	40.7662	1.55646
$687$	10.8574	0.414234
$688$	−4.79851	−0.182942
$689$	−4.03321	−0.153653
$690$	−2.67510	−0.101839
$691$	28.7303	1.09295	0.546476	−	0.837475i	$-0.315969\pi$
$691$	28.7303	1.09295	0.546476	+	0.837475i	$0.315969\pi$
$692$	18.7435	0.712521
$693$	−26.9218	−1.02267
$694$	−13.7040	−0.520197
$695$	−3.97925	−0.150941
$696$	−0.0939007	−0.00355930
$697$	28.9836	1.09783
$698$	24.2081	0.916291
$699$	25.1962	0.953007
$700$	−22.6312	−0.855380
$701$	−27.5148	−1.03922	−0.519611	−	0.854403i	$-0.673923\pi$
$701$	−27.5148	−1.03922	−0.519611	+	0.854403i	$0.673923\pi$
$702$	−4.03321	−0.152224
$703$	−10.1159	−0.381530
$704$	−5.66565	−0.213532
$705$	1.28232	0.0482948
$706$	15.1457	0.570015
$707$	−66.7601	−2.51077
$708$	−13.5519	−0.509311
$709$	6.11772	0.229756	0.114878	−	0.993380i	$-0.463352\pi$
$709$	6.11772	0.229756	0.114878	+	0.993380i	$0.463352\pi$
$710$	7.71095	0.289387
$711$	−0.0301722	−0.00113155
$712$	−2.07916	−0.0779198
$713$	37.4932	1.40413
$714$	21.1183	0.790333
$715$	11.1312	0.416283
$716$	−13.3885	−0.500350
$717$	27.8108	1.03861
$718$	21.1690	0.790020
$719$	−14.4564	−0.539134	−0.269567	−	0.962982i	$-0.586881\pi$
$719$	−14.4564	−0.539134	−0.269567	+	0.962982i	$0.586881\pi$
$720$	−0.487125	−0.0181541
$721$	62.1200	2.31347
$722$	1.00000	0.0372161
$723$	23.6235	0.878566
$724$	−3.48926	−0.129677
$725$	−0.447222	−0.0166094
$726$	−21.0996	−0.783081
$727$	−9.34070	−0.346427	−0.173214	−	0.984884i	$-0.555415\pi$
$727$	−9.34070	−0.346427	−0.173214	+	0.984884i	$0.555415\pi$
$728$	19.1648	0.710295
$729$	1.00000	0.0370370
$730$	6.20914	0.229810
$731$	21.3261	0.788775
$732$	0.302849	0.0111936
$733$	−5.51697	−0.203774	−0.101887	−	0.994796i	$-0.532488\pi$
$733$	−5.51697	−0.203774	−0.101887	+	0.994796i	$0.532488\pi$
$734$	4.45105	0.164291
$735$	7.58901	0.279925
$736$	−5.49160	−0.202423
$737$	55.3455	2.03868
$738$	−6.52148	−0.240059
$739$	−53.9930	−1.98616	−0.993082	−	0.117420i	$-0.962538\pi$
$739$	−53.9930	−1.98616	−0.993082	+	0.117420i	$0.962538\pi$
$740$	4.92773	0.181147
$741$	−4.03321	−0.148164
$742$	−4.75176	−0.174442
$743$	11.8625	0.435194	0.217597	−	0.976039i	$-0.430178\pi$
$743$	11.8625	0.435194	0.217597	+	0.976039i	$0.430178\pi$
$744$	6.82737	0.250303
$745$	7.51114	0.275187
$746$	4.41354	0.161591
$747$	−5.61820	−0.205559
$748$	25.1800	0.920671
$749$	45.0081	1.64456
$750$	−4.75566	−0.173652
$751$	−37.4190	−1.36544	−0.682719	−	0.730681i	$-0.739203\pi$
$751$	−37.4190	−1.36544	−0.682719	+	0.730681i	$0.739203\pi$
$752$	2.63241	0.0959943
$753$	−9.89187	−0.360480
$754$	0.378721	0.0137922
$755$	−9.91590	−0.360877
$756$	−4.75176	−0.172820
$757$	−2.48212	−0.0902143	−0.0451071	−	0.998982i	$-0.514363\pi$
$757$	−2.48212	−0.0902143	−0.0451071	+	0.998982i	$0.514363\pi$
$758$	−0.266127	−0.00966617
$759$	−31.1135	−1.12935
$760$	−0.487125	−0.0176699
$761$	−19.6979	−0.714048	−0.357024	−	0.934095i	$-0.616208\pi$
$761$	−19.6979	−0.714048	−0.357024	+	0.934095i	$0.616208\pi$
$762$	8.34098	0.302162
$763$	42.6688	1.54471
$764$	10.5522	0.381765
$765$	2.16494	0.0782736
$766$	−5.70301	−0.206058
$767$	54.6575	1.97357
$768$	−1.00000	−0.0360844
$769$	1.97441	0.0711992	0.0355996	−	0.999366i	$-0.488666\pi$
$769$	1.97441	0.0711992	0.0355996	+	0.999366i	$0.488666\pi$
$770$	13.1143	0.472606
$771$	23.9620	0.862971
$772$	17.7885	0.640221
$773$	13.8262	0.497292	0.248646	−	0.968594i	$-0.420014\pi$
$773$	13.8262	0.497292	0.248646	+	0.968594i	$0.420014\pi$
$774$	−4.79851	−0.172479
$775$	32.5168	1.16804
$776$	18.2881	0.656504
$777$	48.0685	1.72445
$778$	−24.6343	−0.883183
$779$	−6.52148	−0.233656
$780$	1.96468	0.0703467
$781$	89.6845	3.20916
$782$	24.4064	0.872772
$783$	−0.0939007	−0.00335574
$784$	15.5792	0.556399
$785$	10.8648	0.387781
$786$	−19.0207	−0.678446
$787$	−41.4015	−1.47581	−0.737903	−	0.674907i	$-0.764184\pi$
$787$	−41.4015	−1.47581	−0.737903	+	0.674907i	$0.764184\pi$
$788$	−4.13339	−0.147246
$789$	−1.73672	−0.0618288
$790$	0.0146977	0.000522919 0
$791$	11.0577	0.393165
$792$	−5.66565	−0.201320
$793$	−1.22145	−0.0433750
$794$	4.76630	0.169150
$795$	−0.487125	−0.0172766
$796$	7.92032	0.280728
$797$	6.89671	0.244294	0.122147	−	0.992512i	$-0.461022\pi$
$797$	6.89671	0.244294	0.122147	+	0.992512i	$0.461022\pi$
$798$	−4.75176	−0.168210
$799$	−11.6993	−0.413891
$800$	−4.76271	−0.168387
$801$	−2.07916	−0.0734635
$802$	2.95448	0.104326
$803$	72.2172	2.54849
$804$	9.76859	0.344512
$805$	12.7114	0.448018
$806$	−27.5362	−0.969920
$807$	−29.3801	−1.03423
$808$	−14.0496	−0.494262
$809$	12.3056	0.432642	0.216321	−	0.976322i	$-0.430594\pi$
$809$	12.3056	0.432642	0.216321	+	0.976322i	$0.430594\pi$
$810$	−0.487125	−0.0171158
$811$	−21.7690	−0.764414	−0.382207	−	0.924077i	$-0.624836\pi$
$811$	−21.7690	−0.764414	−0.382207	+	0.924077i	$0.624836\pi$
$812$	0.446193	0.0156583
$813$	−7.27393	−0.255108
$814$	57.3134	2.00883
$815$	−1.23954	−0.0434191
$816$	4.44432	0.155582
$817$	−4.79851	−0.167879
$818$	4.77300	0.166884
$819$	19.1648	0.669673
$820$	3.17678	0.110938
$821$	51.9045	1.81148	0.905739	−	0.423836i	$-0.139317\pi$
$821$	51.9045	1.81148	0.905739	+	0.423836i	$0.139317\pi$
$822$	−4.41119	−0.153858
$823$	−3.30753	−0.115293	−0.0576466	−	0.998337i	$-0.518360\pi$
$823$	−3.30753	−0.115293	−0.0576466	+	0.998337i	$0.518360\pi$
$824$	13.0731	0.455422
$825$	−26.9839	−0.939457
$826$	64.3952	2.24060
$827$	46.3116	1.61041	0.805207	−	0.592994i	$-0.202054\pi$
$827$	46.3116	1.61041	0.805207	+	0.592994i	$0.202054\pi$
$828$	−5.49160	−0.190846
$829$	−41.5095	−1.44169	−0.720843	−	0.693099i	$-0.756245\pi$
$829$	−41.5095	−1.44169	−0.720843	+	0.693099i	$0.756245\pi$
$830$	2.73677	0.0949947
$831$	−23.4399	−0.813122
$832$	4.03321	0.139826
$833$	−69.2388	−2.39898
$834$	−8.16883	−0.282864
$835$	8.91592	0.308548
$836$	−5.66565	−0.195951
$837$	6.82737	0.235988
$838$	1.05678	0.0365059
$839$	4.92928	0.170178	0.0850889	−	0.996373i	$-0.472883\pi$
$839$	4.92928	0.170178	0.0850889	+	0.996373i	$0.472883\pi$
$840$	2.31470	0.0798648
$841$	−28.9912	−0.999696
$842$	−15.4595	−0.532768
$843$	−4.17808	−0.143901
$844$	−2.76651	−0.0952272
$845$	−1.59132	−0.0547429
$846$	2.63241	0.0905043
$847$	100.260	3.44498
$848$	−1.00000	−0.0343401
$849$	−4.67717	−0.160520
$850$	21.1670	0.726022
$851$	55.5527	1.90432
$852$	15.8295	0.542310
$853$	−14.1964	−0.486076	−0.243038	−	0.970017i	$-0.578144\pi$
$853$	−14.1964	−0.486076	−0.243038	+	0.970017i	$0.578144\pi$
$854$	−1.43906	−0.0492438
$855$	−0.487125	−0.0166593
$856$	9.47189	0.323743
$857$	−39.8180	−1.36016	−0.680078	−	0.733139i	$-0.738054\pi$
$857$	−39.8180	−1.36016	−0.680078	+	0.733139i	$0.738054\pi$
$858$	22.8507	0.780112
$859$	7.70511	0.262895	0.131447	−	0.991323i	$-0.458038\pi$
$859$	7.70511	0.262895	0.131447	+	0.991323i	$0.458038\pi$
$860$	2.33748	0.0797073
$861$	30.9885	1.05609
$862$	−27.3641	−0.932023
$863$	20.3963	0.694298	0.347149	−	0.937810i	$-0.387150\pi$
$863$	20.3963	0.694298	0.347149	+	0.937810i	$0.387150\pi$
$864$	−1.00000	−0.0340207
$865$	−9.13044	−0.310444
$866$	16.9495	0.575966
$867$	−2.75196	−0.0934614
$868$	−32.4420	−1.10115
$869$	0.170945	0.00579893
$870$	0.0457414	0.00155078
$871$	−39.3987	−1.33498
$872$	8.97959	0.304087
$873$	18.2881	0.618958
$874$	−5.49160	−0.185756
$875$	22.5977	0.763943
$876$	12.7465	0.430664
$877$	11.4239	0.385756	0.192878	−	0.981223i	$-0.438218\pi$
$877$	11.4239	0.385756	0.192878	+	0.981223i	$0.438218\pi$
$878$	−35.3454	−1.19285
$879$	−16.9749	−0.572550
$880$	2.75988	0.0930357
$881$	−49.6601	−1.67309	−0.836546	−	0.547897i	$-0.815429\pi$
$881$	−49.6601	−1.67309	−0.836546	+	0.547897i	$0.815429\pi$
$882$	15.5792	0.524578
$883$	24.6966	0.831108	0.415554	−	0.909569i	$-0.363588\pi$
$883$	24.6966	0.831108	0.415554	+	0.909569i	$0.363588\pi$
$884$	−17.9248	−0.602878
$885$	6.60146	0.221906
$886$	22.4089	0.752842
$887$	−6.57316	−0.220705	−0.110353	−	0.993892i	$-0.535198\pi$
$887$	−6.57316	−0.220705	−0.110353	+	0.993892i	$0.535198\pi$
$888$	10.1159	0.339469
$889$	−39.6343	−1.32929
$890$	1.01281	0.0339495
$891$	−5.66565	−0.189807
$892$	2.42443	0.0811759
$893$	2.63241	0.0880904
$894$	15.4193	0.515699
$895$	6.52186	0.218002
$896$	4.75176	0.158745
$897$	22.1488	0.739525
$898$	−15.9697	−0.532916
$899$	−0.641094	−0.0213817
$900$	−4.76271	−0.158757
$901$	4.44432	0.148062
$902$	36.9485	1.23025
$903$	22.8014	0.758782
$904$	2.32707	0.0773971
$905$	1.69971	0.0565002
$906$	−20.3560	−0.676281
$907$	−18.8889	−0.627194	−0.313597	−	0.949556i	$-0.601534\pi$
$907$	−18.8889	−0.627194	−0.313597	+	0.949556i	$0.601534\pi$
$908$	−2.19407	−0.0728129
$909$	−14.0496	−0.465995
$910$	−9.33566	−0.309474
$911$	−12.6025	−0.417540	−0.208770	−	0.977965i	$-0.566946\pi$
$911$	−12.6025	−0.417540	−0.208770	+	0.977965i	$0.566946\pi$
$912$	−1.00000	−0.0331133
$913$	31.8308	1.05345
$914$	−25.4486	−0.841765
$915$	−0.147525	−0.00487704
$916$	−10.8574	−0.358737
$917$	90.3818	2.98467
$918$	4.44432	0.146684
$919$	18.3634	0.605751	0.302876	−	0.953030i	$-0.402053\pi$
$919$	18.3634	0.605751	0.302876	+	0.953030i	$0.402053\pi$
$920$	2.67510	0.0881954
$921$	27.3937	0.902653
$922$	−27.1701	−0.894800
$923$	−63.8436	−2.10144
$924$	26.9218	0.885662
$925$	48.1793	1.58413
$926$	28.3460	0.931508
$927$	13.0731	0.429376
$928$	0.0939007	0.00308244
$929$	−26.7839	−0.878752	−0.439376	−	0.898303i	$-0.644800\pi$
$929$	−26.7839	−0.878752	−0.439376	+	0.898303i	$0.644800\pi$
$930$	−3.32578	−0.109057
$931$	15.5792	0.510587
$932$	−25.1962	−0.825328
$933$	5.83899	0.191160
$934$	−0.149569	−0.00489405
$935$	−12.2658	−0.401135
$936$	4.03321	0.131829
$937$	3.74746	0.122424	0.0612121	−	0.998125i	$-0.480503\pi$
$937$	3.74746	0.122424	0.0612121	+	0.998125i	$0.480503\pi$
$938$	−46.4180	−1.51560
$939$	9.97016	0.325364
$940$	−1.28232	−0.0418245
$941$	35.1464	1.14574	0.572871	−	0.819646i	$-0.305830\pi$
$941$	35.1464	1.14574	0.572871	+	0.819646i	$0.305830\pi$
$942$	22.3039	0.726699
$943$	35.8134	1.16624
$944$	13.5519	0.441076
$945$	2.31470	0.0752972
$946$	27.1867	0.883916
$947$	42.4325	1.37887	0.689436	−	0.724347i	$-0.257859\pi$
$947$	42.4325	1.37887	0.689436	+	0.724347i	$0.257859\pi$
$948$	0.0301722	0.000979949 0
$949$	−51.4092	−1.66881
$950$	−4.76271	−0.154523
$951$	4.26401	0.138270
$952$	−21.1183	−0.684448
$953$	−16.3932	−0.531029	−0.265514	−	0.964107i	$-0.585542\pi$
$953$	−16.3932	−0.531029	−0.265514	+	0.964107i	$0.585542\pi$
$954$	−1.00000	−0.0323762
$955$	−5.14024	−0.166334
$956$	−27.8108	−0.899466
$957$	0.532009	0.0171974
$958$	14.1230	0.456294
$959$	20.9609	0.676863
$960$	0.487125	0.0157219
$961$	15.6129	0.503643
$962$	−40.7997	−1.31543
$963$	9.47189	0.305227
$964$	−23.6235	−0.760861
$965$	−8.66521	−0.278943
$966$	26.0947	0.839585
$967$	−58.4717	−1.88032	−0.940162	−	0.340728i	$-0.889326\pi$
$967$	−58.4717	−1.88032	−0.940162	+	0.340728i	$0.889326\pi$
$968$	21.0996	0.678168
$969$	4.44432	0.142772
$970$	−8.90860	−0.286038
$971$	21.8486	0.701155	0.350577	−	0.936534i	$-0.385985\pi$
$971$	21.8486	0.701155	0.350577	+	0.936534i	$0.385985\pi$
$972$	−1.00000	−0.0320750
$973$	38.8163	1.24439
$974$	4.46835	0.143175
$975$	19.2090	0.615180
$976$	−0.302849	−0.00969396
$977$	16.5584	0.529751	0.264875	−	0.964283i	$-0.414669\pi$
$977$	16.5584	0.529751	0.264875	+	0.964283i	$0.414669\pi$
$978$	−2.54460	−0.0813672
$979$	11.7798	0.376484
$980$	−7.58901	−0.242422
$981$	8.97959	0.286696
$982$	−37.6681	−1.20204
$983$	−10.1789	−0.324655	−0.162328	−	0.986737i	$-0.551900\pi$
$983$	−10.1789	−0.324655	−0.162328	+	0.986737i	$0.551900\pi$
$984$	6.52148	0.207897
$985$	2.01348	0.0641549
$986$	−0.417324	−0.0132903
$987$	−12.5086	−0.398153
$988$	4.03321	0.128313
$989$	26.3515	0.837929
$990$	2.75988	0.0877149
$991$	17.3240	0.550314	0.275157	−	0.961399i	$-0.411270\pi$
$991$	17.3240	0.550314	0.275157	+	0.961399i	$0.411270\pi$
$992$	−6.82737	−0.216769
$993$	9.35569	0.296894
$994$	−75.2179	−2.38577
$995$	−3.85819	−0.122313
$996$	5.61820	0.178020
$997$	16.3037	0.516343	0.258171	−	0.966099i	$-0.416880\pi$
$997$	16.3037	0.516343	0.258171	+	0.966099i	$0.416880\pi$
$998$	35.8395	1.13448
$999$	10.1159	0.320054

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	6042.2.a.bc.1.5	✓	9

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
6042.2.a.bc.1.5	✓	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)

\(f(q)\)	\(=\)	\(q+1.00000 q^{2} -1.00000 q^{3} +1.00000 q^{4} -0.487125 q^{5} -1.00000 q^{6} +4.75176 q^{7} +1.00000 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q+1.00000 q^{2} -1.00000 q^{3} +1.00000 q^{4} -0.487125 q^{5} -1.00000 q^{6} +4.75176 q^{7} +1.00000 q^{8} +1.00000 q^{9} -0.487125 q^{10} -5.66565 q^{11} -1.00000 q^{12} +4.03321 q^{13} +4.75176 q^{14} +0.487125 q^{15} +1.00000 q^{16} -4.44432 q^{17} +1.00000 q^{18} +1.00000 q^{19} -0.487125 q^{20} -4.75176 q^{21} -5.66565 q^{22} -5.49160 q^{23} -1.00000 q^{24} -4.76271 q^{25} +4.03321 q^{26} -1.00000 q^{27} +4.75176 q^{28} +0.0939007 q^{29} +0.487125 q^{30} -6.82737 q^{31} +1.00000 q^{32} +5.66565 q^{33} -4.44432 q^{34} -2.31470 q^{35} +1.00000 q^{36} -10.1159 q^{37} +1.00000 q^{38} -4.03321 q^{39} -0.487125 q^{40} -6.52148 q^{41} -4.75176 q^{42} -4.79851 q^{43} -5.66565 q^{44} -0.487125 q^{45} -5.49160 q^{46} +2.63241 q^{47} -1.00000 q^{48} +15.5792 q^{49} -4.76271 q^{50} +4.44432 q^{51} +4.03321 q^{52} -1.00000 q^{53} -1.00000 q^{54} +2.75988 q^{55} +4.75176 q^{56} -1.00000 q^{57} +0.0939007 q^{58} +13.5519 q^{59} +0.487125 q^{60} -0.302849 q^{61} -6.82737 q^{62} +4.75176 q^{63} +1.00000 q^{64} -1.96468 q^{65} +5.66565 q^{66} -9.76859 q^{67} -4.44432 q^{68} +5.49160 q^{69} -2.31470 q^{70} -15.8295 q^{71} +1.00000 q^{72} -12.7465 q^{73} -10.1159 q^{74} +4.76271 q^{75} +1.00000 q^{76} -26.9218 q^{77} -4.03321 q^{78} -0.0301722 q^{79} -0.487125 q^{80} +1.00000 q^{81} -6.52148 q^{82} -5.61820 q^{83} -4.75176 q^{84} +2.16494 q^{85} -4.79851 q^{86} -0.0939007 q^{87} -5.66565 q^{88} -2.07916 q^{89} -0.487125 q^{90} +19.1648 q^{91} -5.49160 q^{92} +6.82737 q^{93} +2.63241 q^{94} -0.487125 q^{95} -1.00000 q^{96} +18.2881 q^{97} +15.5792 q^{98} -5.66565 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 9 q + 9 q^{2} - 9 q^{3} + 9 q^{4} - 3 q^{5} - 9 q^{6} - 7 q^{7} + 9 q^{8} + 9 q^{9}+O(q^{10}) \) 9 * q + 9 * q^2 - 9 * q^3 + 9 * q^4 - 3 * q^5 - 9 * q^6 - 7 * q^7 + 9 * q^8 + 9 * q^9	\( 9 q + 9 q^{2} - 9 q^{3} + 9 q^{4} - 3 q^{5} - 9 q^{6} - 7 q^{7} + 9 q^{8} + 9 q^{9} - 3 q^{10} + 4 q^{11} - 9 q^{12} - 5 q^{13} - 7 q^{14} + 3 q^{15} + 9 q^{16} - 28 q^{17} + 9 q^{18} + 9 q^{19} - 3 q^{20} + 7 q^{21} + 4 q^{22} - 10 q^{23} - 9 q^{24} + 4 q^{25} - 5 q^{26} - 9 q^{27} - 7 q^{28} + 3 q^{30} + 5 q^{31} + 9 q^{32} - 4 q^{33} - 28 q^{34} - 10 q^{35} + 9 q^{36} - 25 q^{37} + 9 q^{38} + 5 q^{39} - 3 q^{40} - 7 q^{41} + 7 q^{42} - 16 q^{43} + 4 q^{44} - 3 q^{45} - 10 q^{46} - 9 q^{47} - 9 q^{48} + 44 q^{49} + 4 q^{50} + 28 q^{51} - 5 q^{52} - 9 q^{53} - 9 q^{54} - 31 q^{55} - 7 q^{56} - 9 q^{57} - 3 q^{59} + 3 q^{60} - 16 q^{61} + 5 q^{62} - 7 q^{63} + 9 q^{64} - 33 q^{65} - 4 q^{66} - 13 q^{67} - 28 q^{68} + 10 q^{69} - 10 q^{70} - 4 q^{71} + 9 q^{72} - 29 q^{73} - 25 q^{74} - 4 q^{75} + 9 q^{76} - 33 q^{77} + 5 q^{78} + 13 q^{79} - 3 q^{80} + 9 q^{81} - 7 q^{82} - 35 q^{83} + 7 q^{84} + 3 q^{85} - 16 q^{86} + 4 q^{88} - 19 q^{89} - 3 q^{90} - 10 q^{92} - 5 q^{93} - 9 q^{94} - 3 q^{95} - 9 q^{96} - 12 q^{97} + 44 q^{98} + 4 q^{99}+O(q^{100}) \) 9 * q + 9 * q^2 - 9 * q^3 + 9 * q^4 - 3 * q^5 - 9 * q^6 - 7 * q^7 + 9 * q^8 + 9 * q^9 - 3 * q^10 + 4 * q^11 - 9 * q^12 - 5 * q^13 - 7 * q^14 + 3 * q^15 + 9 * q^16 - 28 * q^17 + 9 * q^18 + 9 * q^19 - 3 * q^20 + 7 * q^21 + 4 * q^22 - 10 * q^23 - 9 * q^24 + 4 * q^25 - 5 * q^26 - 9 * q^27 - 7 * q^28 + 3 * q^30 + 5 * q^31 + 9 * q^32 - 4 * q^33 - 28 * q^34 - 10 * q^35 + 9 * q^36 - 25 * q^37 + 9 * q^38 + 5 * q^39 - 3 * q^40 - 7 * q^41 + 7 * q^42 - 16 * q^43 + 4 * q^44 - 3 * q^45 - 10 * q^46 - 9 * q^47 - 9 * q^48 + 44 * q^49 + 4 * q^50 + 28 * q^51 - 5 * q^52 - 9 * q^53 - 9 * q^54 - 31 * q^55 - 7 * q^56 - 9 * q^57 - 3 * q^59 + 3 * q^60 - 16 * q^61 + 5 * q^62 - 7 * q^63 + 9 * q^64 - 33 * q^65 - 4 * q^66 - 13 * q^67 - 28 * q^68 + 10 * q^69 - 10 * q^70 - 4 * q^71 + 9 * q^72 - 29 * q^73 - 25 * q^74 - 4 * q^75 + 9 * q^76 - 33 * q^77 + 5 * q^78 + 13 * q^79 - 3 * q^80 + 9 * q^81 - 7 * q^82 - 35 * q^83 + 7 * q^84 + 3 * q^85 - 16 * q^86 + 4 * q^88 - 19 * q^89 - 3 * q^90 - 10 * q^92 - 5 * q^93 - 9 * q^94 - 3 * q^95 - 9 * q^96 - 12 * q^97 + 44 * q^98 + 4 * q^99

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