LMFDB - Embedded newform 6042.2.a.bc.1.1

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			1.1
Root			$3.89305$ 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)

$f(q)$	$=$	$q+1.00000 q^{2} -1.00000 q^{3} +1.00000 q^{4} -3.89305 q^{5} -1.00000 q^{6} -4.93000 q^{7} +1.00000 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q+1.00000 q^{2} -1.00000 q^{3} +1.00000 q^{4} -3.89305 q^{5} -1.00000 q^{6} -4.93000 q^{7} +1.00000 q^{8} +1.00000 q^{9} -3.89305 q^{10} +6.46187 q^{11} -1.00000 q^{12} +1.90103 q^{13} -4.93000 q^{14} +3.89305 q^{15} +1.00000 q^{16} -4.76727 q^{17} +1.00000 q^{18} +1.00000 q^{19} -3.89305 q^{20} +4.93000 q^{21} +6.46187 q^{22} -4.82813 q^{23} -1.00000 q^{24} +10.1558 q^{25} +1.90103 q^{26} -1.00000 q^{27} -4.93000 q^{28} +5.56435 q^{29} +3.89305 q^{30} -3.08814 q^{31} +1.00000 q^{32} -6.46187 q^{33} -4.76727 q^{34} +19.1927 q^{35} +1.00000 q^{36} -0.937169 q^{37} +1.00000 q^{38} -1.90103 q^{39} -3.89305 q^{40} +7.81969 q^{41} +4.93000 q^{42} +7.53454 q^{43} +6.46187 q^{44} -3.89305 q^{45} -4.82813 q^{46} +0.539458 q^{47} -1.00000 q^{48} +17.3049 q^{49} +10.1558 q^{50} +4.76727 q^{51} +1.90103 q^{52} -1.00000 q^{53} -1.00000 q^{54} -25.1564 q^{55} -4.93000 q^{56} -1.00000 q^{57} +5.56435 q^{58} +8.13646 q^{59} +3.89305 q^{60} -11.7666 q^{61} -3.08814 q^{62} -4.93000 q^{63} +1.00000 q^{64} -7.40080 q^{65} -6.46187 q^{66} -6.06996 q^{67} -4.76727 q^{68} +4.82813 q^{69} +19.1927 q^{70} +12.7236 q^{71} +1.00000 q^{72} +4.15462 q^{73} -0.937169 q^{74} -10.1558 q^{75} +1.00000 q^{76} -31.8570 q^{77} -1.90103 q^{78} +1.24021 q^{79} -3.89305 q^{80} +1.00000 q^{81} +7.81969 q^{82} -17.7482 q^{83} +4.93000 q^{84} +18.5592 q^{85} +7.53454 q^{86} -5.56435 q^{87} +6.46187 q^{88} -3.25260 q^{89} -3.89305 q^{90} -9.37208 q^{91} -4.82813 q^{92} +3.08814 q^{93} +0.539458 q^{94} -3.89305 q^{95} -1.00000 q^{96} -3.63330 q^{97} +17.3049 q^{98} +6.46187 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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
$5$	−3.89305	−1.74103	−0.870513	−	0.492146i	$-0.836213\pi$
$5$	−3.89305	−1.74103	−0.870513	+	0.492146i	$0.836213\pi$
$6$	−1.00000	−0.408248
$7$	−4.93000	−1.86337	−0.931683	−	0.363273i	$-0.881659\pi$
$7$	−4.93000	−1.86337	−0.931683	+	0.363273i	$0.881659\pi$
$8$	1.00000	0.353553
$9$	1.00000	0.333333
$10$	−3.89305	−1.23109
$11$	6.46187	1.94833	0.974163	−	0.225845i	$-0.0725144\pi$
$11$	6.46187	1.94833	0.974163	+	0.225845i	$0.0725144\pi$
$12$	−1.00000	−0.288675
$13$	1.90103	0.527251	0.263625	−	0.964625i	$-0.415082\pi$
$13$	1.90103	0.527251	0.263625	+	0.964625i	$0.415082\pi$
$14$	−4.93000	−1.31760
$15$	3.89305	1.00518
$16$	1.00000	0.250000
$17$	−4.76727	−1.15623	−0.578116	−	0.815955i	$-0.696212\pi$
$17$	−4.76727	−1.15623	−0.578116	+	0.815955i	$0.696212\pi$
$18$	1.00000	0.235702
$19$	1.00000	0.229416
$19$	1.00000	0.229416
$20$	−3.89305	−0.870513
$21$	4.93000	1.07581
$22$	6.46187	1.37767
$23$	−4.82813	−1.00673	−0.503367	−	0.864073i	$-0.667906\pi$
$23$	−4.82813	−1.00673	−0.503367	+	0.864073i	$0.667906\pi$
$24$	−1.00000	−0.204124
$25$	10.1558	2.03117
$26$	1.90103	0.372823
$27$	−1.00000	−0.192450
$28$	−4.93000	−0.931683
$29$	5.56435	1.03327	0.516637	−	0.856205i	$-0.327184\pi$
$29$	5.56435	1.03327	0.516637	+	0.856205i	$0.327184\pi$
$30$	3.89305	0.710771
$31$	−3.08814	−0.554645	−0.277323	−	0.960777i	$-0.589447\pi$
$31$	−3.08814	−0.554645	−0.277323	+	0.960777i	$0.589447\pi$
$32$	1.00000	0.176777
$33$	−6.46187	−1.12487
$34$	−4.76727	−0.817579
$35$	19.1927	3.24417
$36$	1.00000	0.166667
$37$	−0.937169	−0.154070	−0.0770348	−	0.997028i	$-0.524545\pi$
$37$	−0.937169	−0.154070	−0.0770348	+	0.997028i	$0.524545\pi$
$38$	1.00000	0.162221
$39$	−1.90103	−0.304408
$40$	−3.89305	−0.615545
$41$	7.81969	1.22123	0.610615	−	0.791928i	$-0.290922\pi$
$41$	7.81969	1.22123	0.610615	+	0.791928i	$0.290922\pi$
$42$	4.93000	0.760716
$43$	7.53454	1.14901	0.574504	−	0.818502i	$-0.305195\pi$
$43$	7.53454	1.14901	0.574504	+	0.818502i	$0.305195\pi$
$44$	6.46187	0.974163
$45$	−3.89305	−0.580342
$46$	−4.82813	−0.711869
$47$	0.539458	0.0786880	0.0393440	−	0.999226i	$-0.487473\pi$
$47$	0.539458	0.0786880	0.0393440	+	0.999226i	$0.487473\pi$
$48$	−1.00000	−0.144338
$49$	17.3049	2.47213
$50$	10.1558	1.43625
$51$	4.76727	0.667551
$52$	1.90103	0.263625
$53$	−1.00000	−0.137361
$53$	−1.00000	−0.137361
$54$	−1.00000	−0.136083
$55$	−25.1564	−3.39209
$56$	−4.93000	−0.658799
$57$	−1.00000	−0.132453
$58$	5.56435	0.730635
$59$	8.13646	1.05928	0.529639	−	0.848223i	$-0.322328\pi$
$59$	8.13646	1.05928	0.529639	+	0.848223i	$0.322328\pi$
$60$	3.89305	0.502591
$61$	−11.7666	−1.50656	−0.753278	−	0.657702i	$-0.771529\pi$
$61$	−11.7666	−1.50656	−0.753278	+	0.657702i	$0.771529\pi$
$62$	−3.08814	−0.392194
$63$	−4.93000	−0.621122
$64$	1.00000	0.125000
$65$	−7.40080	−0.917957
$66$	−6.46187	−0.795401
$67$	−6.06996	−0.741564	−0.370782	−	0.928720i	$-0.620910\pi$
$67$	−6.06996	−0.741564	−0.370782	+	0.928720i	$0.620910\pi$
$68$	−4.76727	−0.578116
$69$	4.82813	0.581238
$70$	19.1927	2.29397
$71$	12.7236	1.51001	0.755005	−	0.655720i	$-0.227635\pi$
$71$	12.7236	1.51001	0.755005	+	0.655720i	$0.227635\pi$
$72$	1.00000	0.117851
$73$	4.15462	0.486262	0.243131	−	0.969993i	$-0.421826\pi$
$73$	4.15462	0.486262	0.243131	+	0.969993i	$0.421826\pi$
$74$	−0.937169	−0.108944
$75$	−10.1558	−1.17270
$76$	1.00000	0.114708
$77$	−31.8570	−3.63044
$78$	−1.90103	−0.215249
$79$	1.24021	0.139535	0.0697675	−	0.997563i	$-0.477774\pi$
$79$	1.24021	0.139535	0.0697675	+	0.997563i	$0.477774\pi$
$80$	−3.89305	−0.435256
$81$	1.00000	0.111111
$82$	7.81969	0.863540
$83$	−17.7482	−1.94812	−0.974059	−	0.226293i	$-0.927339\pi$
$83$	−17.7482	−1.94812	−0.974059	+	0.226293i	$0.927339\pi$
$84$	4.93000	0.537907
$85$	18.5592	2.01303
$86$	7.53454	0.812471
$87$	−5.56435	−0.596561
$88$	6.46187	0.688837
$89$	−3.25260	−0.344775	−0.172387	−	0.985029i	$-0.555148\pi$
$89$	−3.25260	−0.344775	−0.172387	+	0.985029i	$0.555148\pi$
$90$	−3.89305	−0.410364
$91$	−9.37208	−0.982461
$92$	−4.82813	−0.503367
$93$	3.08814	0.320225
$94$	0.539458	0.0556408
$95$	−3.89305	−0.399419
$96$	−1.00000	−0.102062
$97$	−3.63330	−0.368905	−0.184453	−	0.982841i	$-0.559051\pi$
$97$	−3.63330	−0.368905	−0.184453	+	0.982841i	$0.559051\pi$
$98$	17.3049	1.74806
$99$	6.46187	0.649442
$100$	10.1558	1.01558
$101$	−17.6442	−1.75567	−0.877833	−	0.478967i	$-0.841011\pi$
$101$	−17.6442	−1.75567	−0.877833	+	0.478967i	$0.841011\pi$
$102$	4.76727	0.472030
$103$	−0.0683706	−0.00673676	−0.00336838	−	0.999994i	$-0.501072\pi$
$103$	−0.0683706	−0.00673676	−0.00336838	+	0.999994i	$0.501072\pi$
$104$	1.90103	0.186411
$105$	−19.1927	−1.87302
$106$	−1.00000	−0.0971286
$107$	3.80678	0.368015	0.184008	−	0.982925i	$-0.441093\pi$
$107$	3.80678	0.368015	0.184008	+	0.982925i	$0.441093\pi$
$108$	−1.00000	−0.0962250
$109$	−16.0285	−1.53525	−0.767627	−	0.640897i	$-0.778562\pi$
$109$	−16.0285	−1.53525	−0.767627	+	0.640897i	$0.778562\pi$
$110$	−25.1564	−2.39857
$111$	0.937169	0.0889521
$112$	−4.93000	−0.465841
$113$	−20.8697	−1.96325	−0.981627	−	0.190811i	$-0.938888\pi$
$113$	−20.8697	−1.96325	−0.981627	+	0.190811i	$0.938888\pi$
$114$	−1.00000	−0.0936586
$115$	18.7962	1.75275
$116$	5.56435	0.516637
$117$	1.90103	0.175750
$118$	8.13646	0.749022
$119$	23.5026	2.15448
$120$	3.89305	0.355385
$121$	30.7557	2.79598
$122$	−11.7666	−1.06530
$123$	−7.81969	−0.705077
$124$	−3.08814	−0.277323
$125$	−20.0720	−1.79529
$126$	−4.93000	−0.439199
$127$	18.3134	1.62506	0.812528	−	0.582922i	$-0.198091\pi$
$127$	18.3134	1.62506	0.812528	+	0.582922i	$0.198091\pi$
$128$	1.00000	0.0883883
$129$	−7.53454	−0.663380
$130$	−7.40080	−0.649094
$131$	−7.56204	−0.660698	−0.330349	−	0.943859i	$-0.607166\pi$
$131$	−7.56204	−0.660698	−0.330349	+	0.943859i	$0.607166\pi$
$132$	−6.46187	−0.562433
$133$	−4.93000	−0.427485
$134$	−6.06996	−0.524365
$135$	3.89305	0.335060
$136$	−4.76727	−0.408790
$137$	5.88812	0.503056	0.251528	−	0.967850i	$-0.419067\pi$
$137$	5.88812	0.503056	0.251528	+	0.967850i	$0.419067\pi$
$138$	4.82813	0.410998
$139$	−9.10598	−0.772359	−0.386180	−	0.922424i	$-0.626206\pi$
$139$	−9.10598	−0.772359	−0.386180	+	0.922424i	$0.626206\pi$
$140$	19.1927	1.62208
$141$	−0.539458	−0.0454305
$142$	12.7236	1.06774
$143$	12.2842	1.02726
$144$	1.00000	0.0833333
$145$	−21.6623	−1.79896
$146$	4.15462	0.343839
$147$	−17.3049	−1.42729
$148$	−0.937169	−0.0770348
$149$	4.68650	0.383933	0.191967	−	0.981401i	$-0.438513\pi$
$149$	4.68650	0.383933	0.191967	+	0.981401i	$0.438513\pi$
$150$	−10.1558	−0.829221
$151$	−8.73342	−0.710715	−0.355358	−	0.934730i	$-0.615641\pi$
$151$	−8.73342	−0.710715	−0.355358	+	0.934730i	$0.615641\pi$
$152$	1.00000	0.0811107
$153$	−4.76727	−0.385411
$154$	−31.8570	−2.56711
$155$	12.0223	0.965652
$156$	−1.90103	−0.152204
$157$	10.5787	0.844273	0.422137	−	0.906532i	$-0.361280\pi$
$157$	10.5787	0.844273	0.422137	+	0.906532i	$0.361280\pi$
$158$	1.24021	0.0986662
$159$	1.00000	0.0793052
$160$	−3.89305	−0.307773
$161$	23.8027	1.87591
$162$	1.00000	0.0785674
$163$	−12.9363	−1.01325	−0.506625	−	0.862167i	$-0.669107\pi$
$163$	−12.9363	−1.01325	−0.506625	+	0.862167i	$0.669107\pi$
$164$	7.81969	0.610615
$165$	25.1564	1.95842
$166$	−17.7482	−1.37753
$167$	−11.5809	−0.896159	−0.448080	−	0.893994i	$-0.647892\pi$
$167$	−11.5809	−0.896159	−0.448080	+	0.893994i	$0.647892\pi$
$168$	4.93000	0.380358
$169$	−9.38609	−0.722007
$170$	18.5592	1.42343
$171$	1.00000	0.0764719
$172$	7.53454	0.574504
$173$	−7.59504	−0.577440	−0.288720	−	0.957414i	$-0.593230\pi$
$173$	−7.59504	−0.577440	−0.288720	+	0.957414i	$0.593230\pi$
$174$	−5.56435	−0.421832
$175$	−50.0683	−3.78481
$176$	6.46187	0.487082
$177$	−8.13646	−0.611574
$178$	−3.25260	−0.243792
$179$	−1.50513	−0.112498	−0.0562492	−	0.998417i	$-0.517914\pi$
$179$	−1.50513	−0.112498	−0.0562492	+	0.998417i	$0.517914\pi$
$180$	−3.89305	−0.290171
$181$	−5.62156	−0.417847	−0.208924	−	0.977932i	$-0.566996\pi$
$181$	−5.62156	−0.417847	−0.208924	+	0.977932i	$0.566996\pi$
$182$	−9.37208	−0.694705
$183$	11.7666	0.869811
$184$	−4.82813	−0.355934
$185$	3.64845	0.268239
$186$	3.08814	0.226433
$187$	−30.8054	−2.25272
$188$	0.539458	0.0393440
$189$	4.93000	0.358605
$190$	−3.89305	−0.282432
$191$	11.2266	0.812327	0.406164	−	0.913800i	$-0.366866\pi$
$191$	11.2266	0.812327	0.406164	+	0.913800i	$0.366866\pi$
$192$	−1.00000	−0.0721688
$193$	5.35893	0.385744	0.192872	−	0.981224i	$-0.438220\pi$
$193$	5.35893	0.385744	0.192872	+	0.981224i	$0.438220\pi$
$194$	−3.63330	−0.260855
$195$	7.40080	0.529983
$196$	17.3049	1.23607
$197$	−18.4553	−1.31488	−0.657442	−	0.753505i	$-0.728362\pi$
$197$	−18.4553	−1.31488	−0.657442	+	0.753505i	$0.728362\pi$
$198$	6.46187	0.459225
$199$	−19.4479	−1.37862	−0.689312	−	0.724464i	$-0.742087\pi$
$199$	−19.4479	−1.37862	−0.689312	+	0.724464i	$0.742087\pi$
$200$	10.1558	0.718127
$201$	6.06996	0.428142
$202$	−17.6442	−1.24144
$203$	−27.4323	−1.92537
$204$	4.76727	0.333775
$205$	−30.4424	−2.12619
$206$	−0.0683706	−0.00476361
$207$	−4.82813	−0.335578
$208$	1.90103	0.131813
$209$	6.46187	0.446977
$210$	−19.1927	−1.32443
$211$	4.80167	0.330561	0.165280	−	0.986247i	$-0.447147\pi$
$211$	4.80167	0.330561	0.165280	+	0.986247i	$0.447147\pi$
$212$	−1.00000	−0.0686803
$213$	−12.7236	−0.871804
$214$	3.80678	0.260226
$215$	−29.3324	−2.00045
$216$	−1.00000	−0.0680414
$217$	15.2245	1.03351
$218$	−16.0285	−1.08559
$219$	−4.15462	−0.280743
$220$	−25.1564	−1.69604
$221$	−9.06271	−0.609624
$222$	0.937169	0.0628986
$223$	−9.12571	−0.611103	−0.305551	−	0.952176i	$-0.598841\pi$
$223$	−9.12571	−0.611103	−0.305551	+	0.952176i	$0.598841\pi$
$224$	−4.93000	−0.329400
$225$	10.1558	0.677056
$226$	−20.8697	−1.38823
$227$	8.43127	0.559603	0.279801	−	0.960058i	$-0.409731\pi$
$227$	8.43127	0.559603	0.279801	+	0.960058i	$0.409731\pi$
$228$	−1.00000	−0.0662266
$229$	23.8350	1.57506	0.787531	−	0.616274i	$-0.211359\pi$
$229$	23.8350	1.57506	0.787531	+	0.616274i	$0.211359\pi$
$230$	18.7962	1.23938
$231$	31.8570	2.09604
$232$	5.56435	0.365317
$233$	−2.87966	−0.188653	−0.0943265	−	0.995541i	$-0.530070\pi$
$233$	−2.87966	−0.188653	−0.0943265	+	0.995541i	$0.530070\pi$
$234$	1.90103	0.124274
$235$	−2.10014	−0.136998
$236$	8.13646	0.529639
$237$	−1.24021	−0.0805606
$238$	23.5026	1.52345
$239$	−20.1093	−1.30076	−0.650382	−	0.759607i	$-0.725391\pi$
$239$	−20.1093	−1.30076	−0.650382	+	0.759607i	$0.725391\pi$
$240$	3.89305	0.251295
$241$	12.1467	0.782439	0.391220	−	0.920297i	$-0.372053\pi$
$241$	12.1467	0.782439	0.391220	+	0.920297i	$0.372053\pi$
$242$	30.7557	1.97705
$243$	−1.00000	−0.0641500
$244$	−11.7666	−0.753278
$245$	−67.3689	−4.30404
$246$	−7.81969	−0.498565
$247$	1.90103	0.120960
$248$	−3.08814	−0.196097
$249$	17.7482	1.12475
$250$	−20.0720	−1.26946
$251$	−19.7207	−1.24476	−0.622380	−	0.782715i	$-0.713834\pi$
$251$	−19.7207	−1.24476	−0.622380	+	0.782715i	$0.713834\pi$
$252$	−4.93000	−0.310561
$253$	−31.1987	−1.96145
$254$	18.3134	1.14909
$255$	−18.5592	−1.16222
$256$	1.00000	0.0625000
$257$	6.96349	0.434371	0.217185	−	0.976130i	$-0.430312\pi$
$257$	6.96349	0.434371	0.217185	+	0.976130i	$0.430312\pi$
$258$	−7.53454	−0.469080
$259$	4.62024	0.287088
$260$	−7.40080	−0.458978
$261$	5.56435	0.344425
$262$	−7.56204	−0.467184
$263$	−20.6729	−1.27474	−0.637372	−	0.770556i	$-0.719979\pi$
$263$	−20.6729	−1.27474	−0.637372	+	0.770556i	$0.719979\pi$
$264$	−6.46187	−0.397700
$265$	3.89305	0.239148
$266$	−4.93000	−0.302278
$267$	3.25260	0.199056
$268$	−6.06996	−0.370782
$269$	25.9839	1.58427	0.792134	−	0.610347i	$-0.208970\pi$
$269$	25.9839	1.58427	0.792134	+	0.610347i	$0.208970\pi$
$270$	3.89305	0.236924
$271$	−29.6233	−1.79949	−0.899744	−	0.436417i	$-0.856247\pi$
$271$	−29.6233	−1.79949	−0.899744	+	0.436417i	$0.856247\pi$
$272$	−4.76727	−0.289058
$273$	9.37208	0.567224
$274$	5.88812	0.355714
$275$	65.6257	3.95738
$276$	4.82813	0.290619
$277$	11.2934	0.678553	0.339276	−	0.940687i	$-0.389818\pi$
$277$	11.2934	0.678553	0.339276	+	0.940687i	$0.389818\pi$
$278$	−9.10598	−0.546141
$279$	−3.08814	−0.184882
$280$	19.1927	1.14699
$281$	−11.3238	−0.675521	−0.337761	−	0.941232i	$-0.609669\pi$
$281$	−11.3238	−0.675521	−0.337761	+	0.941232i	$0.609669\pi$
$282$	−0.539458	−0.0321242
$283$	16.8728	1.00298	0.501492	−	0.865162i	$-0.332785\pi$
$283$	16.8728	1.00298	0.501492	+	0.865162i	$0.332785\pi$
$284$	12.7236	0.755005
$285$	3.89305	0.230604
$286$	12.2842	0.726380
$287$	−38.5511	−2.27560
$288$	1.00000	0.0589256
$289$	5.72683	0.336872
$290$	−21.6623	−1.27205
$291$	3.63330	0.212988
$292$	4.15462	0.243131
$293$	−2.54100	−0.148447	−0.0742233	−	0.997242i	$-0.523648\pi$
$293$	−2.54100	−0.148447	−0.0742233	+	0.997242i	$0.523648\pi$
$294$	−17.3049	−1.00924
$295$	−31.6757	−1.84423
$296$	−0.937169	−0.0544718
$297$	−6.46187	−0.374956
$298$	4.68650	0.271482
$299$	−9.17841	−0.530801
$300$	−10.1558	−0.586348
$301$	−37.1453	−2.14102
$302$	−8.73342	−0.502552
$303$	17.6442	1.01363
$304$	1.00000	0.0573539
$305$	45.8079	2.62295
$306$	−4.76727	−0.272526
$307$	−13.3763	−0.763428	−0.381714	−	0.924281i	$-0.624666\pi$
$307$	−13.3763	−0.763428	−0.381714	+	0.924281i	$0.624666\pi$
$308$	−31.8570	−1.81522
$309$	0.0683706	0.00388947
$310$	12.0223	0.682819
$311$	17.8610	1.01280	0.506402	−	0.862298i	$-0.330975\pi$
$311$	17.8610	1.01280	0.506402	+	0.862298i	$0.330975\pi$
$312$	−1.90103	−0.107625
$313$	4.74431	0.268164	0.134082	−	0.990970i	$-0.457191\pi$
$313$	4.74431	0.268164	0.134082	+	0.990970i	$0.457191\pi$
$314$	10.5787	0.596991
$315$	19.1927	1.08139
$316$	1.24021	0.0697675
$317$	−9.93702	−0.558118	−0.279059	−	0.960274i	$-0.590023\pi$
$317$	−9.93702	−0.558118	−0.279059	+	0.960274i	$0.590023\pi$
$318$	1.00000	0.0560772
$319$	35.9561	2.01315
$320$	−3.89305	−0.217628
$321$	−3.80678	−0.212474
$322$	23.8027	1.32647
$323$	−4.76727	−0.265258
$324$	1.00000	0.0555556
$325$	19.3066	1.07094
$326$	−12.9363	−0.716475
$327$	16.0285	0.886379
$328$	7.81969	0.431770
$329$	−2.65953	−0.146624
$330$	25.1564	1.38481
$331$	19.8236	1.08960	0.544801	−	0.838565i	$-0.316605\pi$
$331$	19.8236	1.08960	0.544801	+	0.838565i	$0.316605\pi$
$332$	−17.7482	−0.974059
$333$	−0.937169	−0.0513565
$334$	−11.5809	−0.633680
$335$	23.6307	1.29108
$336$	4.93000	0.268954
$337$	−31.4431	−1.71282	−0.856409	−	0.516299i	$-0.827309\pi$
$337$	−31.4431	−1.71282	−0.856409	+	0.516299i	$0.827309\pi$
$338$	−9.38609	−0.510536
$339$	20.8697	1.13349
$340$	18.5592	1.00651
$341$	−19.9551	−1.08063
$342$	1.00000	0.0540738
$343$	−50.8033	−2.74312
$344$	7.53454	0.406235
$345$	−18.7962	−1.01195
$346$	−7.59504	−0.408312
$347$	−14.1869	−0.761595	−0.380797	−	0.924659i	$-0.624350\pi$
$347$	−14.1869	−0.761595	−0.380797	+	0.924659i	$0.624350\pi$
$348$	−5.56435	−0.298280
$349$	−12.9589	−0.693674	−0.346837	−	0.937925i	$-0.612744\pi$
$349$	−12.9589	−0.693674	−0.346837	+	0.937925i	$0.612744\pi$
$350$	−50.0683	−2.67627
$351$	−1.90103	−0.101469
$352$	6.46187	0.344419
$353$	6.12050	0.325761	0.162881	−	0.986646i	$-0.447921\pi$
$353$	6.12050	0.325761	0.162881	+	0.986646i	$0.447921\pi$
$354$	−8.13646	−0.432448
$355$	−49.5335	−2.62896
$356$	−3.25260	−0.172387
$357$	−23.5026	−1.24389
$358$	−1.50513	−0.0795484
$359$	−4.58433	−0.241952	−0.120976	−	0.992655i	$-0.538602\pi$
$359$	−4.58433	−0.241952	−0.120976	+	0.992655i	$0.538602\pi$
$360$	−3.89305	−0.205182
$361$	1.00000	0.0526316
$362$	−5.62156	−0.295463
$363$	−30.7557	−1.61426
$364$	−9.37208	−0.491230
$365$	−16.1742	−0.846594
$366$	11.7666	0.615049
$367$	0.663831	0.0346517	0.0173258	−	0.999850i	$-0.494485\pi$
$367$	0.663831	0.0346517	0.0173258	+	0.999850i	$0.494485\pi$
$368$	−4.82813	−0.251684
$369$	7.81969	0.407077
$370$	3.64845	0.189674
$371$	4.93000	0.255953
$372$	3.08814	0.160112
$373$	−9.68798	−0.501624	−0.250812	−	0.968036i	$-0.580698\pi$
$373$	−9.68798	−0.501624	−0.250812	+	0.968036i	$0.580698\pi$
$374$	−30.8054	−1.59291
$375$	20.0720	1.03651
$376$	0.539458	0.0278204
$377$	10.5780	0.544794
$378$	4.93000	0.253572
$379$	22.7768	1.16997	0.584983	−	0.811045i	$-0.301101\pi$
$379$	22.7768	1.16997	0.584983	+	0.811045i	$0.301101\pi$
$380$	−3.89305	−0.199709
$381$	−18.3134	−0.938226
$382$	11.2266	0.574402
$383$	33.7161	1.72281	0.861407	−	0.507916i	$-0.169584\pi$
$383$	33.7161	1.72281	0.861407	+	0.507916i	$0.169584\pi$
$384$	−1.00000	−0.0510310
$385$	124.021	6.32070
$386$	5.35893	0.272762
$387$	7.53454	0.383002
$388$	−3.63330	−0.184453
$389$	−4.24743	−0.215353	−0.107677	−	0.994186i	$-0.534341\pi$
$389$	−4.24743	−0.215353	−0.107677	+	0.994186i	$0.534341\pi$
$390$	7.40080	0.374754
$391$	23.0170	1.16402
$392$	17.3049	0.874030
$393$	7.56204	0.381454
$394$	−18.4553	−0.929764
$395$	−4.82822	−0.242934
$396$	6.46187	0.324721
$397$	−6.65701	−0.334106	−0.167053	−	0.985948i	$-0.553425\pi$
$397$	−6.65701	−0.334106	−0.167053	+	0.985948i	$0.553425\pi$
$398$	−19.4479	−0.974835
$399$	4.93000	0.246809
$400$	10.1558	0.507792
$401$	−39.4444	−1.96976	−0.984879	−	0.173245i	$-0.944575\pi$
$401$	−39.4444	−1.96976	−0.984879	+	0.173245i	$0.944575\pi$
$402$	6.06996	0.302742
$403$	−5.87064	−0.292437
$404$	−17.6442	−0.877833
$405$	−3.89305	−0.193447
$406$	−27.4323	−1.36144
$407$	−6.05586	−0.300178
$408$	4.76727	0.236015
$409$	17.4171	0.861219	0.430609	−	0.902538i	$-0.358299\pi$
$409$	17.4171	0.861219	0.430609	+	0.902538i	$0.358299\pi$
$410$	−30.4424	−1.50345
$411$	−5.88812	−0.290440
$412$	−0.0683706	−0.00336838
$413$	−40.1128	−1.97382
$414$	−4.82813	−0.237290
$415$	69.0947	3.39172
$416$	1.90103	0.0932056
$417$	9.10598	0.445922
$418$	6.46187	0.316060
$419$	−3.35124	−0.163719	−0.0818594	−	0.996644i	$-0.526086\pi$
$419$	−3.35124	−0.163719	−0.0818594	+	0.996644i	$0.526086\pi$
$420$	−19.1927	−0.936510
$421$	−18.1245	−0.883336	−0.441668	−	0.897178i	$-0.645613\pi$
$421$	−18.1245	−0.883336	−0.441668	+	0.897178i	$0.645613\pi$
$422$	4.80167	0.233742
$423$	0.539458	0.0262293
$424$	−1.00000	−0.0485643
$425$	−48.4156	−2.34850
$426$	−12.7236	−0.616459
$427$	58.0093	2.80726
$428$	3.80678	0.184008
$429$	−12.2842	−0.593087
$430$	−29.3324	−1.41453
$431$	−35.1173	−1.69154	−0.845771	−	0.533546i	$-0.820859\pi$
$431$	−35.1173	−1.69154	−0.845771	+	0.533546i	$0.820859\pi$
$432$	−1.00000	−0.0481125
$433$	2.50925	0.120587	0.0602935	−	0.998181i	$-0.480796\pi$
$433$	2.50925	0.120587	0.0602935	+	0.998181i	$0.480796\pi$
$434$	15.2245	0.730800
$435$	21.6623	1.03863
$436$	−16.0285	−0.767627
$437$	−4.82813	−0.230961
$438$	−4.15462	−0.198516
$439$	22.8809	1.09204	0.546022	−	0.837771i	$-0.316142\pi$
$439$	22.8809	1.09204	0.546022	+	0.837771i	$0.316142\pi$
$440$	−25.1564	−1.19928
$441$	17.3049	0.824044
$442$	−9.06271	−0.431069
$443$	−18.1773	−0.863628	−0.431814	−	0.901963i	$-0.642126\pi$
$443$	−18.1773	−0.863628	−0.431814	+	0.901963i	$0.642126\pi$
$444$	0.937169	0.0444761
$445$	12.6625	0.600261
$446$	−9.12571	−0.432115
$447$	−4.68650	−0.221664
$448$	−4.93000	−0.232921
$449$	22.7824	1.07517	0.537585	−	0.843210i	$-0.319337\pi$
$449$	22.7824	1.07517	0.537585	+	0.843210i	$0.319337\pi$
$450$	10.1558	0.478751
$451$	50.5298	2.37935
$452$	−20.8697	−0.981627
$453$	8.73342	0.410332
$454$	8.43127	0.395699
$455$	36.4860	1.71049
$456$	−1.00000	−0.0468293
$457$	32.1016	1.50165	0.750825	−	0.660501i	$-0.229656\pi$
$457$	32.1016	1.50165	0.750825	+	0.660501i	$0.229656\pi$
$458$	23.8350	1.11374
$459$	4.76727	0.222517
$460$	18.7962	0.876375
$461$	−6.41210	−0.298641	−0.149321	−	0.988789i	$-0.547709\pi$
$461$	−6.41210	−0.298641	−0.149321	+	0.988789i	$0.547709\pi$
$462$	31.8570	1.48212
$463$	−2.62810	−0.122138	−0.0610692	−	0.998134i	$-0.519451\pi$
$463$	−2.62810	−0.122138	−0.0610692	+	0.998134i	$0.519451\pi$
$464$	5.56435	0.258318
$465$	−12.0223	−0.557519
$466$	−2.87966	−0.133398
$467$	−5.37731	−0.248832	−0.124416	−	0.992230i	$-0.539706\pi$
$467$	−5.37731	−0.248832	−0.124416	+	0.992230i	$0.539706\pi$
$468$	1.90103	0.0878751
$469$	29.9249	1.38181
$470$	−2.10014	−0.0968720
$471$	−10.5787	−0.487441
$472$	8.13646	0.374511
$473$	48.6872	2.23864
$474$	−1.24021	−0.0569649
$475$	10.1558	0.465982
$476$	23.5026	1.07724
$477$	−1.00000	−0.0457869
$478$	−20.1093	−0.919779
$479$	−10.0277	−0.458179	−0.229089	−	0.973405i	$-0.573575\pi$
$479$	−10.0277	−0.458179	−0.229089	+	0.973405i	$0.573575\pi$
$480$	3.89305	0.177693
$481$	−1.78159	−0.0812333
$482$	12.1467	0.553268
$483$	−23.8027	−1.08306
$484$	30.7557	1.39799
$485$	14.1446	0.642273
$486$	−1.00000	−0.0453609
$487$	36.3830	1.64867	0.824335	−	0.566102i	$-0.191549\pi$
$487$	36.3830	1.64867	0.824335	+	0.566102i	$0.191549\pi$
$488$	−11.7666	−0.532648
$489$	12.9363	0.585000
$490$	−67.3689	−3.04342
$491$	−27.4917	−1.24068	−0.620341	−	0.784333i	$-0.713006\pi$
$491$	−27.4917	−1.24068	−0.620341	+	0.784333i	$0.713006\pi$
$492$	−7.81969	−0.352539
$493$	−26.5267	−1.19470
$494$	1.90103	0.0855314
$495$	−25.1564	−1.13070
$496$	−3.08814	−0.138661
$497$	−62.7272	−2.81370
$498$	17.7482	0.795316
$499$	23.5463	1.05408	0.527039	−	0.849841i	$-0.323302\pi$
$499$	23.5463	1.05408	0.527039	+	0.849841i	$0.323302\pi$
$500$	−20.0720	−0.897646
$501$	11.5809	0.517398
$502$	−19.7207	−0.880178
$503$	14.2073	0.633472	0.316736	−	0.948514i	$-0.397413\pi$
$503$	14.2073	0.633472	0.316736	+	0.948514i	$0.397413\pi$
$504$	−4.93000	−0.219600
$505$	68.6899	3.05666
$506$	−31.1987	−1.38695
$507$	9.38609	0.416851
$508$	18.3134	0.812528
$509$	35.3437	1.56658	0.783292	−	0.621654i	$-0.213539\pi$
$509$	35.3437	1.56658	0.783292	+	0.621654i	$0.213539\pi$
$510$	−18.5592	−0.821816
$511$	−20.4823	−0.906084
$512$	1.00000	0.0441942
$513$	−1.00000	−0.0441511
$514$	6.96349	0.307146
$515$	0.266170	0.0117289
$516$	−7.53454	−0.331690
$517$	3.48590	0.153310
$518$	4.62024	0.203002
$519$	7.59504	0.333385
$520$	−7.40080	−0.324547
$521$	−20.7671	−0.909825	−0.454913	−	0.890536i	$-0.650330\pi$
$521$	−20.7671	−0.909825	−0.454913	+	0.890536i	$0.650330\pi$
$522$	5.56435	0.243545
$523$	8.80081	0.384833	0.192416	−	0.981313i	$-0.438368\pi$
$523$	8.80081	0.384833	0.192416	+	0.981313i	$0.438368\pi$
$524$	−7.56204	−0.330349
$525$	50.0683	2.18516
$526$	−20.6729	−0.901381
$527$	14.7220	0.641299
$528$	−6.46187	−0.281217
$529$	0.310823	0.0135141
$530$	3.89305	0.169103
$531$	8.13646	0.353092
$532$	−4.93000	−0.213743
$533$	14.8655	0.643894
$534$	3.25260	0.140754
$535$	−14.8200	−0.640724
$536$	−6.06996	−0.262182
$537$	1.50513	0.0649510
$538$	25.9839	1.12025
$539$	111.822	4.81652
$540$	3.89305	0.167530
$541$	−35.6037	−1.53072	−0.765361	−	0.643602i	$-0.777439\pi$
$541$	−35.6037	−1.53072	−0.765361	+	0.643602i	$0.777439\pi$
$542$	−29.6233	−1.27243
$543$	5.62156	0.241244
$544$	−4.76727	−0.204395
$545$	62.3998	2.67291
$546$	9.37208	0.401088
$547$	29.4013	1.25711	0.628554	−	0.777766i	$-0.283647\pi$
$547$	29.4013	1.25711	0.628554	+	0.777766i	$0.283647\pi$
$548$	5.88812	0.251528
$549$	−11.7666	−0.502185
$550$	65.6257	2.79829
$551$	5.56435	0.237049
$552$	4.82813	0.205499
$553$	−6.11426	−0.260005
$554$	11.2934	0.479809
$555$	−3.64845	−0.154868
$556$	−9.10598	−0.386180
$557$	2.09694	0.0888501	0.0444250	−	0.999013i	$-0.485854\pi$
$557$	2.09694	0.0888501	0.0444250	+	0.999013i	$0.485854\pi$
$558$	−3.08814	−0.130731
$559$	14.3234	0.605815
$560$	19.1927	0.811042
$561$	30.8054	1.30061
$562$	−11.3238	−0.477666
$563$	5.05057	0.212856	0.106428	−	0.994320i	$-0.466059\pi$
$563$	5.05057	0.212856	0.106428	+	0.994320i	$0.466059\pi$
$564$	−0.539458	−0.0227153
$565$	81.2467	3.41807
$566$	16.8728	0.709217
$567$	−4.93000	−0.207041
$568$	12.7236	0.533869
$569$	−45.8499	−1.92213	−0.961064	−	0.276326i	$-0.910883\pi$
$569$	−45.8499	−1.92213	−0.961064	+	0.276326i	$0.910883\pi$
$570$	3.89305	0.163062
$571$	−1.53722	−0.0643306	−0.0321653	−	0.999483i	$-0.510240\pi$
$571$	−1.53722	−0.0643306	−0.0321653	+	0.999483i	$0.510240\pi$
$572$	12.2842	0.513628
$573$	−11.2266	−0.468997
$574$	−38.5511	−1.60909
$575$	−49.0337	−2.04485
$576$	1.00000	0.0416667
$577$	25.9157	1.07888	0.539442	−	0.842023i	$-0.318635\pi$
$577$	25.9157	1.07888	0.539442	+	0.842023i	$0.318635\pi$
$578$	5.72683	0.238205
$579$	−5.35893	−0.222709
$580$	−21.6623	−0.899478
$581$	87.4987	3.63006
$582$	3.63330	0.150605
$583$	−6.46187	−0.267623
$584$	4.15462	0.171920
$585$	−7.40080	−0.305986
$586$	−2.54100	−0.104968
$587$	6.89719	0.284678	0.142339	−	0.989818i	$-0.454538\pi$
$587$	6.89719	0.284678	0.142339	+	0.989818i	$0.454538\pi$
$588$	−17.3049	−0.713643
$589$	−3.08814	−0.127244
$590$	−31.6757	−1.30407
$591$	18.4553	0.759149
$592$	−0.937169	−0.0385174
$593$	−20.0950	−0.825205	−0.412602	−	0.910911i	$-0.635380\pi$
$593$	−20.0950	−0.825205	−0.412602	+	0.910911i	$0.635380\pi$
$594$	−6.46187	−0.265134
$595$	−91.4970	−3.75101
$596$	4.68650	0.191967
$597$	19.4479	0.795949
$598$	−9.17841	−0.375333
$599$	28.5245	1.16548	0.582741	−	0.812658i	$-0.301980\pi$
$599$	28.5245	1.16548	0.582741	+	0.812658i	$0.301980\pi$
$600$	−10.1558	−0.414611
$601$	0.797701	0.0325389	0.0162695	−	0.999868i	$-0.494821\pi$
$601$	0.797701	0.0325389	0.0162695	+	0.999868i	$0.494821\pi$
$602$	−37.1453	−1.51393
$603$	−6.06996	−0.247188
$604$	−8.73342	−0.355358
$605$	−119.734	−4.86786
$606$	17.6442	0.716748
$607$	41.7961	1.69645	0.848226	−	0.529634i	$-0.177671\pi$
$607$	41.7961	1.69645	0.848226	+	0.529634i	$0.177671\pi$
$608$	1.00000	0.0405554
$609$	27.4323	1.11161
$610$	45.8079	1.85471
$611$	1.02552	0.0414883
$612$	−4.76727	−0.192705
$613$	−12.3022	−0.496881	−0.248441	−	0.968647i	$-0.579918\pi$
$613$	−12.3022	−0.496881	−0.248441	+	0.968647i	$0.579918\pi$
$614$	−13.3763	−0.539825
$615$	30.4424	1.22756
$616$	−31.8570	−1.28356
$617$	−2.65967	−0.107074	−0.0535371	−	0.998566i	$-0.517050\pi$
$617$	−2.65967	−0.107074	−0.0535371	+	0.998566i	$0.517050\pi$
$618$	0.0683706	0.00275027
$619$	−28.3345	−1.13886	−0.569430	−	0.822040i	$-0.692836\pi$
$619$	−28.3345	−1.13886	−0.569430	+	0.822040i	$0.692836\pi$
$620$	12.0223	0.482826
$621$	4.82813	0.193746
$622$	17.8610	0.716160
$623$	16.0353	0.642441
$624$	−1.90103	−0.0761021
$625$	27.3620	1.09448
$626$	4.74431	0.189621
$627$	−6.46187	−0.258062
$628$	10.5787	0.422137
$629$	4.46773	0.178140
$630$	19.1927	0.764657
$631$	1.74598	0.0695065	0.0347532	−	0.999396i	$-0.488935\pi$
$631$	1.74598	0.0695065	0.0347532	+	0.999396i	$0.488935\pi$
$632$	1.24021	0.0493331
$633$	−4.80167	−0.190849
$634$	−9.93702	−0.394649
$635$	−71.2952	−2.82926
$636$	1.00000	0.0396526
$637$	32.8972	1.30343
$638$	35.9561	1.42351
$639$	12.7236	0.503336
$640$	−3.89305	−0.153886
$641$	−46.5429	−1.83833	−0.919166	−	0.393870i	$-0.871136\pi$
$641$	−46.5429	−1.83833	−0.919166	+	0.393870i	$0.871136\pi$
$642$	−3.80678	−0.150242
$643$	−9.94265	−0.392100	−0.196050	−	0.980594i	$-0.562811\pi$
$643$	−9.94265	−0.392100	−0.196050	+	0.980594i	$0.562811\pi$
$644$	23.8027	0.937957
$645$	29.3324	1.15496
$646$	−4.76727	−0.187566
$647$	−3.78828	−0.148933	−0.0744664	−	0.997224i	$-0.523725\pi$
$647$	−3.78828	−0.148933	−0.0744664	+	0.997224i	$0.523725\pi$
$648$	1.00000	0.0392837
$649$	52.5767	2.06382
$650$	19.3066	0.757266
$651$	−15.2245	−0.596696
$652$	−12.9363	−0.506625
$653$	25.2836	0.989425	0.494712	−	0.869057i	$-0.335273\pi$
$653$	25.2836	0.989425	0.494712	+	0.869057i	$0.335273\pi$
$654$	16.0285	0.626764
$655$	29.4394	1.15029
$656$	7.81969	0.305307
$657$	4.15462	0.162087
$658$	−2.65953	−0.103679
$659$	−0.707422	−0.0275573	−0.0137786	−	0.999905i	$-0.504386\pi$
$659$	−0.707422	−0.0275573	−0.0137786	+	0.999905i	$0.504386\pi$
$660$	25.1564	0.979211
$661$	30.3501	1.18048	0.590242	−	0.807226i	$-0.299032\pi$
$661$	30.3501	1.18048	0.590242	+	0.807226i	$0.299032\pi$
$662$	19.8236	0.770465
$663$	9.06271	0.351967
$664$	−17.7482	−0.688764
$665$	19.1927	0.744263
$666$	−0.937169	−0.0363145
$667$	−26.8654	−1.04023
$668$	−11.5809	−0.448080
$669$	9.12571	0.352820
$670$	23.6307	0.912933
$671$	−76.0341	−2.93526
$672$	4.93000	0.190179
$673$	−28.5185	−1.09931	−0.549653	−	0.835393i	$-0.685240\pi$
$673$	−28.5185	−1.09931	−0.549653	+	0.835393i	$0.685240\pi$
$674$	−31.4431	−1.21114
$675$	−10.1558	−0.390899
$676$	−9.38609	−0.361003
$677$	−8.29037	−0.318625	−0.159312	−	0.987228i	$-0.550928\pi$
$677$	−8.29037	−0.318625	−0.159312	+	0.987228i	$0.550928\pi$
$678$	20.8697	0.801495
$679$	17.9122	0.687405
$680$	18.5592	0.711713
$681$	−8.43127	−0.323087
$682$	−19.9551	−0.764121
$683$	17.0609	0.652819	0.326409	−	0.945229i	$-0.394161\pi$
$683$	17.0609	0.652819	0.326409	+	0.945229i	$0.394161\pi$
$684$	1.00000	0.0382360
$685$	−22.9228	−0.875834
$686$	−50.8033	−1.93968
$687$	−23.8350	−0.909363
$688$	7.53454	0.287252
$689$	−1.90103	−0.0724235
$690$	−18.7962	−0.715557
$691$	4.10212	0.156052	0.0780260	−	0.996951i	$-0.475138\pi$
$691$	4.10212	0.156052	0.0780260	+	0.996951i	$0.475138\pi$
$692$	−7.59504	−0.288720
$693$	−31.8570	−1.21015
$694$	−14.1869	−0.538529
$695$	35.4501	1.34470
$696$	−5.56435	−0.210916
$697$	−37.2785	−1.41203
$698$	−12.9589	−0.490501
$699$	2.87966	0.108919
$700$	−50.0683	−1.89241
$701$	−29.3095	−1.10701	−0.553503	−	0.832847i	$-0.686709\pi$
$701$	−29.3095	−1.10701	−0.553503	+	0.832847i	$0.686709\pi$
$702$	−1.90103	−0.0717497
$703$	−0.937169	−0.0353460
$704$	6.46187	0.243541
$705$	2.10014	0.0790957
$706$	6.12050	0.230348
$707$	86.9861	3.27145
$708$	−8.13646	−0.305787
$709$	−51.9113	−1.94957	−0.974786	−	0.223143i	$-0.928368\pi$
$709$	−51.9113	−1.94957	−0.974786	+	0.223143i	$0.928368\pi$
$710$	−49.5335	−1.85896
$711$	1.24021	0.0465117
$712$	−3.25260	−0.121896
$713$	14.9099	0.558381
$714$	−23.5026	−0.879564
$715$	−47.8230	−1.78848
$716$	−1.50513	−0.0562492
$717$	20.1093	0.750997
$718$	−4.58433	−0.171086
$719$	−10.2411	−0.381928	−0.190964	−	0.981597i	$-0.561161\pi$
$719$	−10.2411	−0.381928	−0.190964	+	0.981597i	$0.561161\pi$
$720$	−3.89305	−0.145085
$721$	0.337067	0.0125530
$722$	1.00000	0.0372161
$723$	−12.1467	−0.451741
$724$	−5.62156	−0.208924
$725$	56.5107	2.09875
$726$	−30.7557	−1.14145
$727$	−34.5644	−1.28192	−0.640962	−	0.767573i	$-0.721464\pi$
$727$	−34.5644	−1.28192	−0.640962	+	0.767573i	$0.721464\pi$
$728$	−9.37208	−0.347352
$729$	1.00000	0.0370370
$730$	−16.1742	−0.598633
$731$	−35.9192	−1.32852
$732$	11.7666	0.434905
$733$	−10.3986	−0.384081	−0.192040	−	0.981387i	$-0.561510\pi$
$733$	−10.3986	−0.384081	−0.192040	+	0.981387i	$0.561510\pi$
$734$	0.663831	0.0245024
$735$	67.3689	2.48494
$736$	−4.82813	−0.177967
$737$	−39.2233	−1.44481
$738$	7.81969	0.287847
$739$	34.1422	1.25594	0.627970	−	0.778237i	$-0.283886\pi$
$739$	34.1422	1.25594	0.627970	+	0.778237i	$0.283886\pi$
$740$	3.64845	0.134120
$741$	−1.90103	−0.0698361
$742$	4.93000	0.180986
$743$	−37.9514	−1.39230	−0.696151	−	0.717895i	$-0.745106\pi$
$743$	−37.9514	−1.39230	−0.696151	+	0.717895i	$0.745106\pi$
$744$	3.08814	0.113217
$745$	−18.2448	−0.668437
$746$	−9.68798	−0.354702
$747$	−17.7482	−0.649373
$748$	−30.8054	−1.12636
$749$	−18.7674	−0.685747
$750$	20.0720	0.732925
$751$	26.9676	0.984063	0.492031	−	0.870577i	$-0.336255\pi$
$751$	26.9676	0.984063	0.492031	+	0.870577i	$0.336255\pi$
$752$	0.539458	0.0196720
$753$	19.7207	0.718663
$754$	10.5780	0.385228
$755$	33.9996	1.23737
$756$	4.93000	0.179302
$757$	41.1525	1.49571	0.747857	−	0.663860i	$-0.231083\pi$
$757$	41.1525	1.49571	0.747857	+	0.663860i	$0.231083\pi$
$758$	22.7768	0.827291
$759$	31.1987	1.13244
$760$	−3.89305	−0.141216
$761$	−33.2981	−1.20705	−0.603527	−	0.797343i	$-0.706238\pi$
$761$	−33.2981	−1.20705	−0.603527	+	0.797343i	$0.706238\pi$
$762$	−18.3134	−0.663426
$763$	79.0206	2.86074
$764$	11.2266	0.406164
$765$	18.5592	0.671010
$766$	33.7161	1.21821
$767$	15.4677	0.558505
$768$	−1.00000	−0.0360844
$769$	35.8793	1.29384	0.646920	−	0.762558i	$-0.276057\pi$
$769$	35.8793	1.29384	0.646920	+	0.762558i	$0.276057\pi$
$770$	124.021	4.46941
$771$	−6.96349	−0.250784
$772$	5.35893	0.192872
$773$	45.3020	1.62940	0.814699	−	0.579884i	$-0.196902\pi$
$773$	45.3020	1.62940	0.814699	+	0.579884i	$0.196902\pi$
$774$	7.53454	0.270824
$775$	−31.3626	−1.12658
$776$	−3.63330	−0.130428
$777$	−4.62024	−0.165750
$778$	−4.24743	−0.152278
$779$	7.81969	0.280169
$780$	7.40080	0.264991
$781$	82.2180	2.94199
$782$	23.0170	0.823085
$783$	−5.56435	−0.198854
$784$	17.3049	0.618033
$785$	−41.1835	−1.46990
$786$	7.56204	0.269729
$787$	8.99264	0.320553	0.160276	−	0.987072i	$-0.448761\pi$
$787$	8.99264	0.320553	0.160276	+	0.987072i	$0.448761\pi$
$788$	−18.4553	−0.657442
$789$	20.6729	0.735974
$790$	−4.82822	−0.171780
$791$	102.888	3.65826
$792$	6.46187	0.229612
$793$	−22.3686	−0.794333
$794$	−6.65701	−0.236248
$795$	−3.89305	−0.138072
$796$	−19.4479	−0.689312
$797$	−7.34865	−0.260303	−0.130151	−	0.991494i	$-0.541546\pi$
$797$	−7.34865	−0.260303	−0.130151	+	0.991494i	$0.541546\pi$
$798$	4.93000	0.174520
$799$	−2.57174	−0.0909816
$800$	10.1558	0.359063
$801$	−3.25260	−0.114925
$802$	−39.4444	−1.39283
$803$	26.8466	0.947397
$804$	6.06996	0.214071
$805$	−92.6651	−3.26601
$806$	−5.87064	−0.206784
$807$	−25.9839	−0.914678
$808$	−17.6442	−0.620722
$809$	−15.3780	−0.540661	−0.270330	−	0.962768i	$-0.587133\pi$
$809$	−15.3780	−0.540661	−0.270330	+	0.962768i	$0.587133\pi$
$810$	−3.89305	−0.136788
$811$	31.3696	1.10154	0.550768	−	0.834659i	$-0.314335\pi$
$811$	31.3696	1.10154	0.550768	+	0.834659i	$0.314335\pi$
$812$	−27.4323	−0.962683
$813$	29.6233	1.03894
$814$	−6.05586	−0.212258
$815$	50.3617	1.76409
$816$	4.76727	0.166888
$817$	7.53454	0.263600
$818$	17.4171	0.608974
$819$	−9.37208	−0.327487
$820$	−30.4424	−1.06310
$821$	−40.3299	−1.40752	−0.703761	−	0.710437i	$-0.748497\pi$
$821$	−40.3299	−1.40752	−0.703761	+	0.710437i	$0.748497\pi$
$822$	−5.88812	−0.205372
$823$	10.0474	0.350230	0.175115	−	0.984548i	$-0.443970\pi$
$823$	10.0474	0.350230	0.175115	+	0.984548i	$0.443970\pi$
$824$	−0.0683706	−0.00238180
$825$	−65.6257	−2.28479
$826$	−40.1128	−1.39570
$827$	−48.8668	−1.69927	−0.849633	−	0.527374i	$-0.823177\pi$
$827$	−48.8668	−1.69927	−0.849633	+	0.527374i	$0.823177\pi$
$828$	−4.82813	−0.167789
$829$	−20.5224	−0.712774	−0.356387	−	0.934338i	$-0.615992\pi$
$829$	−20.5224	−0.712774	−0.356387	+	0.934338i	$0.615992\pi$
$830$	69.0947	2.39831
$831$	−11.2934	−0.391763
$832$	1.90103	0.0659063
$833$	−82.4972	−2.85836
$834$	9.10598	0.315314
$835$	45.0852	1.56024
$836$	6.46187	0.223488
$837$	3.08814	0.106742
$838$	−3.35124	−0.115767
$839$	36.6864	1.26655	0.633277	−	0.773925i	$-0.281709\pi$
$839$	36.6864	1.26655	0.633277	+	0.773925i	$0.281709\pi$
$840$	−19.1927	−0.662213
$841$	1.96198	0.0676544
$842$	−18.1245	−0.624613
$843$	11.3238	0.390012
$844$	4.80167	0.165280
$845$	36.5405	1.25703
$846$	0.539458	0.0185469
$847$	−151.626	−5.20992
$848$	−1.00000	−0.0343401
$849$	−16.8728	−0.579073
$850$	−48.4156	−1.66064
$851$	4.52477	0.155107
$852$	−12.7236	−0.435902
$853$	−20.4626	−0.700627	−0.350313	−	0.936633i	$-0.613925\pi$
$853$	−20.4626	−0.700627	−0.350313	+	0.936633i	$0.613925\pi$
$854$	58.0093	1.98504
$855$	−3.89305	−0.133140
$856$	3.80678	0.130113
$857$	−27.3749	−0.935108	−0.467554	−	0.883964i	$-0.654865\pi$
$857$	−27.3749	−0.935108	−0.467554	+	0.883964i	$0.654865\pi$
$858$	−12.2842	−0.419376
$859$	−53.3635	−1.82074	−0.910369	−	0.413797i	$-0.864202\pi$
$859$	−53.3635	−1.82074	−0.910369	+	0.413797i	$0.864202\pi$
$860$	−29.3324	−1.00023
$861$	38.5511	1.31382
$862$	−35.1173	−1.19610
$863$	−38.5120	−1.31096	−0.655482	−	0.755211i	$-0.727534\pi$
$863$	−38.5120	−1.31096	−0.655482	+	0.755211i	$0.727534\pi$
$864$	−1.00000	−0.0340207
$865$	29.5679	1.00534
$866$	2.50925	0.0852679
$867$	−5.72683	−0.194493
$868$	15.2245	0.516754
$869$	8.01410	0.271860
$870$	21.6623	0.734421
$871$	−11.5392	−0.390990
$872$	−16.0285	−0.542794
$873$	−3.63330	−0.122968
$874$	−4.82813	−0.163314
$875$	98.9549	3.34529
$876$	−4.15462	−0.140372
$877$	−51.4880	−1.73863	−0.869314	−	0.494261i	$-0.835439\pi$
$877$	−51.4880	−1.73863	−0.869314	+	0.494261i	$0.835439\pi$
$878$	22.8809	0.772191
$879$	2.54100	0.0857057
$880$	−25.1564	−0.848021
$881$	10.1637	0.342425	0.171213	−	0.985234i	$-0.445231\pi$
$881$	10.1637	0.342425	0.171213	+	0.985234i	$0.445231\pi$
$882$	17.3049	0.582687
$883$	−47.0466	−1.58324	−0.791621	−	0.611012i	$-0.790763\pi$
$883$	−47.0466	−1.58324	−0.791621	+	0.611012i	$0.790763\pi$
$884$	−9.06271	−0.304812
$885$	31.6757	1.06477
$886$	−18.1773	−0.610677
$887$	−3.78342	−0.127035	−0.0635174	−	0.997981i	$-0.520232\pi$
$887$	−3.78342	−0.127035	−0.0635174	+	0.997981i	$0.520232\pi$
$888$	0.937169	0.0314493
$889$	−90.2853	−3.02807
$890$	12.6625	0.424449
$891$	6.46187	0.216481
$892$	−9.12571	−0.305551
$893$	0.539458	0.0180523
$894$	−4.68650	−0.156740
$895$	5.85953	0.195863
$896$	−4.93000	−0.164700
$897$	9.17841	0.306458
$898$	22.7824	0.760259
$899$	−17.1835	−0.573101
$900$	10.1558	0.338528
$901$	4.76727	0.158821
$902$	50.5298	1.68246
$903$	37.1453	1.23612
$904$	−20.8697	−0.694115
$905$	21.8850	0.727483
$906$	8.73342	0.290148
$907$	18.4628	0.613047	0.306523	−	0.951863i	$-0.400834\pi$
$907$	18.4628	0.613047	0.306523	+	0.951863i	$0.400834\pi$
$908$	8.43127	0.279801
$909$	−17.6442	−0.585222
$910$	36.4860	1.20950
$911$	−18.5157	−0.613454	−0.306727	−	0.951798i	$-0.599234\pi$
$911$	−18.5157	−0.613454	−0.306727	+	0.951798i	$0.599234\pi$
$912$	−1.00000	−0.0331133
$913$	−114.687	−3.79557
$914$	32.1016	1.06183
$915$	−45.8079	−1.51436
$916$	23.8350	0.787531
$917$	37.2809	1.23112
$918$	4.76727	0.157343
$919$	47.8056	1.57696	0.788481	−	0.615059i	$-0.210868\pi$
$919$	47.8056	1.57696	0.788481	+	0.615059i	$0.210868\pi$
$920$	18.7962	0.619691
$921$	13.3763	0.440765
$922$	−6.41210	−0.211171
$923$	24.1879	0.796153
$924$	31.8570	1.04802
$925$	−9.51774	−0.312941
$926$	−2.62810	−0.0863649
$927$	−0.0683706	−0.00224559
$928$	5.56435	0.182659
$929$	−32.7800	−1.07548	−0.537738	−	0.843112i	$-0.680721\pi$
$929$	−32.7800	−1.07548	−0.537738	+	0.843112i	$0.680721\pi$
$930$	−12.0223	−0.394226
$931$	17.3049	0.567146
$932$	−2.87966	−0.0943265
$933$	−17.8610	−0.584742
$934$	−5.37731	−0.175951
$935$	119.927	3.92204
$936$	1.90103	0.0621371
$937$	−30.6173	−1.00022	−0.500111	−	0.865961i	$-0.666708\pi$
$937$	−30.6173	−1.00022	−0.500111	+	0.865961i	$0.666708\pi$
$938$	29.9249	0.977084
$939$	−4.74431	−0.154825
$940$	−2.10014	−0.0684989
$941$	−25.1379	−0.819472	−0.409736	−	0.912204i	$-0.634379\pi$
$941$	−25.1379	−0.819472	−0.409736	+	0.912204i	$0.634379\pi$
$942$	−10.5787	−0.344673
$943$	−37.7545	−1.22945
$944$	8.13646	0.264819
$945$	−19.1927	−0.624340
$946$	48.6872	1.58296
$947$	−7.92224	−0.257438	−0.128719	−	0.991681i	$-0.541087\pi$
$947$	−7.92224	−0.257438	−0.128719	+	0.991681i	$0.541087\pi$
$948$	−1.24021	−0.0402803
$949$	7.89806	0.256382
$950$	10.1558	0.329499
$951$	9.93702	0.322230
$952$	23.5026	0.761725
$953$	21.0674	0.682440	0.341220	−	0.939983i	$-0.389160\pi$
$953$	21.0674	0.682440	0.341220	+	0.939983i	$0.389160\pi$
$954$	−1.00000	−0.0323762
$955$	−43.7057	−1.41428
$956$	−20.1093	−0.650382
$957$	−35.9561	−1.16230
$958$	−10.0277	−0.323981
$959$	−29.0285	−0.937378
$960$	3.89305	0.125648
$961$	−21.4634	−0.692368
$962$	−1.78159	−0.0574406
$963$	3.80678	0.122672
$964$	12.1467	0.391220
$965$	−20.8626	−0.671590
$966$	−23.8027	−0.765839
$967$	−1.16351	−0.0374160	−0.0187080	−	0.999825i	$-0.505955\pi$
$967$	−1.16351	−0.0374160	−0.0187080	+	0.999825i	$0.505955\pi$
$968$	30.7557	0.988527
$969$	4.76727	0.153147
$970$	14.1446	0.454156
$971$	12.9820	0.416613	0.208307	−	0.978064i	$-0.433205\pi$
$971$	12.9820	0.416613	0.208307	+	0.978064i	$0.433205\pi$
$972$	−1.00000	−0.0320750
$973$	44.8925	1.43919
$974$	36.3830	1.16579
$975$	−19.3066	−0.618305
$976$	−11.7666	−0.376639
$977$	−10.5845	−0.338630	−0.169315	−	0.985562i	$-0.554155\pi$
$977$	−10.5845	−0.338630	−0.169315	+	0.985562i	$0.554155\pi$
$978$	12.9363	0.413657
$979$	−21.0178	−0.671733
$980$	−67.3689	−2.15202
$981$	−16.0285	−0.511751
$982$	−27.4917	−0.877294
$983$	−13.7815	−0.439562	−0.219781	−	0.975549i	$-0.570534\pi$
$983$	−13.7815	−0.439562	−0.219781	+	0.975549i	$0.570534\pi$
$984$	−7.81969	−0.249283
$985$	71.8474	2.28925
$986$	−26.5267	−0.844783
$987$	2.65953	0.0846537
$988$	1.90103	0.0604798
$989$	−36.3777	−1.15674
$990$	−25.1564	−0.799522
$991$	10.5464	0.335017	0.167509	−	0.985871i	$-0.446428\pi$
$991$	10.5464	0.335017	0.167509	+	0.985871i	$0.446428\pi$
$992$	−3.08814	−0.0980484
$993$	−19.8236	−0.629082
$994$	−62.7272	−1.98959
$995$	75.7116	2.40022
$996$	17.7482	0.562373
$997$	−9.03686	−0.286200	−0.143100	−	0.989708i	$-0.545707\pi$
$997$	−9.03686	−0.286200	−0.143100	+	0.989708i	$0.545707\pi$
$998$	23.5463	0.745345
$999$	0.937169	0.0296507

Twists

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

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
6042.2.a.bc.1.1	✓	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)

\(f(q)\)	\(=\)	\(q+1.00000 q^{2} -1.00000 q^{3} +1.00000 q^{4} -3.89305 q^{5} -1.00000 q^{6} -4.93000 q^{7} +1.00000 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q+1.00000 q^{2} -1.00000 q^{3} +1.00000 q^{4} -3.89305 q^{5} -1.00000 q^{6} -4.93000 q^{7} +1.00000 q^{8} +1.00000 q^{9} -3.89305 q^{10} +6.46187 q^{11} -1.00000 q^{12} +1.90103 q^{13} -4.93000 q^{14} +3.89305 q^{15} +1.00000 q^{16} -4.76727 q^{17} +1.00000 q^{18} +1.00000 q^{19} -3.89305 q^{20} +4.93000 q^{21} +6.46187 q^{22} -4.82813 q^{23} -1.00000 q^{24} +10.1558 q^{25} +1.90103 q^{26} -1.00000 q^{27} -4.93000 q^{28} +5.56435 q^{29} +3.89305 q^{30} -3.08814 q^{31} +1.00000 q^{32} -6.46187 q^{33} -4.76727 q^{34} +19.1927 q^{35} +1.00000 q^{36} -0.937169 q^{37} +1.00000 q^{38} -1.90103 q^{39} -3.89305 q^{40} +7.81969 q^{41} +4.93000 q^{42} +7.53454 q^{43} +6.46187 q^{44} -3.89305 q^{45} -4.82813 q^{46} +0.539458 q^{47} -1.00000 q^{48} +17.3049 q^{49} +10.1558 q^{50} +4.76727 q^{51} +1.90103 q^{52} -1.00000 q^{53} -1.00000 q^{54} -25.1564 q^{55} -4.93000 q^{56} -1.00000 q^{57} +5.56435 q^{58} +8.13646 q^{59} +3.89305 q^{60} -11.7666 q^{61} -3.08814 q^{62} -4.93000 q^{63} +1.00000 q^{64} -7.40080 q^{65} -6.46187 q^{66} -6.06996 q^{67} -4.76727 q^{68} +4.82813 q^{69} +19.1927 q^{70} +12.7236 q^{71} +1.00000 q^{72} +4.15462 q^{73} -0.937169 q^{74} -10.1558 q^{75} +1.00000 q^{76} -31.8570 q^{77} -1.90103 q^{78} +1.24021 q^{79} -3.89305 q^{80} +1.00000 q^{81} +7.81969 q^{82} -17.7482 q^{83} +4.93000 q^{84} +18.5592 q^{85} +7.53454 q^{86} -5.56435 q^{87} +6.46187 q^{88} -3.25260 q^{89} -3.89305 q^{90} -9.37208 q^{91} -4.82813 q^{92} +3.08814 q^{93} +0.539458 q^{94} -3.89305 q^{95} -1.00000 q^{96} -3.63330 q^{97} +17.3049 q^{98} +6.46187 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 9 q + 9 q^{2} - 9 q^{3} + 9 q^{4} - 3 q^{5} - 9 q^{6} - 7 q^{7} + 9 q^{8} + 9 q^{9}+O(q^{10}) \) 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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