LMFDB - Embedded newform 6042.2.a.z.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:	$0$
Dimension:	$9$
Coefficient field:	$\mathbb{Q}[x]/(x^{9} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{9} - 4x^{8} - 11x^{7} + 51x^{6} + 25x^{5} - 180x^{4} + 29x^{3} + 119x^{2} - 8x - 14 $ x^9 - 4x^8 - 11x^7 + 51x^6 + 25x^5 - 180x^4 + 29x^3 + 119x^2 - 8x - 14
Coefficient ring:	$\Z[a_1, \ldots, a_{13}]$
Coefficient ring index:	$ 2 $
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.1
Root			$-0.690250$ 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)

$f(q)$	$=$	$q-1.00000 q^{2} -1.00000 q^{3} +1.00000 q^{4} -4.37472 q^{5} +1.00000 q^{6} -0.773393 q^{7} -1.00000 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q-1.00000 q^{2} -1.00000 q^{3} +1.00000 q^{4} -4.37472 q^{5} +1.00000 q^{6} -0.773393 q^{7} -1.00000 q^{8} +1.00000 q^{9} +4.37472 q^{10} +4.42079 q^{11} -1.00000 q^{12} +0.648462 q^{13} +0.773393 q^{14} +4.37472 q^{15} +1.00000 q^{16} +6.40302 q^{17} -1.00000 q^{18} -1.00000 q^{19} -4.37472 q^{20} +0.773393 q^{21} -4.42079 q^{22} +0.287580 q^{23} +1.00000 q^{24} +14.1381 q^{25} -0.648462 q^{26} -1.00000 q^{27} -0.773393 q^{28} +0.347880 q^{29} -4.37472 q^{30} -3.57302 q^{31} -1.00000 q^{32} -4.42079 q^{33} -6.40302 q^{34} +3.38337 q^{35} +1.00000 q^{36} -8.71669 q^{37} +1.00000 q^{38} -0.648462 q^{39} +4.37472 q^{40} +8.14882 q^{41} -0.773393 q^{42} +8.05514 q^{43} +4.42079 q^{44} -4.37472 q^{45} -0.287580 q^{46} +11.2879 q^{47} -1.00000 q^{48} -6.40186 q^{49} -14.1381 q^{50} -6.40302 q^{51} +0.648462 q^{52} +1.00000 q^{53} +1.00000 q^{54} -19.3397 q^{55} +0.773393 q^{56} +1.00000 q^{57} -0.347880 q^{58} -3.60190 q^{59} +4.37472 q^{60} +6.21492 q^{61} +3.57302 q^{62} -0.773393 q^{63} +1.00000 q^{64} -2.83684 q^{65} +4.42079 q^{66} -1.86347 q^{67} +6.40302 q^{68} -0.287580 q^{69} -3.38337 q^{70} -1.42484 q^{71} -1.00000 q^{72} -8.80129 q^{73} +8.71669 q^{74} -14.1381 q^{75} -1.00000 q^{76} -3.41901 q^{77} +0.648462 q^{78} -7.81384 q^{79} -4.37472 q^{80} +1.00000 q^{81} -8.14882 q^{82} +16.9311 q^{83} +0.773393 q^{84} -28.0114 q^{85} -8.05514 q^{86} -0.347880 q^{87} -4.42079 q^{88} -17.7376 q^{89} +4.37472 q^{90} -0.501516 q^{91} +0.287580 q^{92} +3.57302 q^{93} -11.2879 q^{94} +4.37472 q^{95} +1.00000 q^{96} +9.18686 q^{97} +6.40186 q^{98} +4.42079 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 9 q - 9 q^{2} - 9 q^{3} + 9 q^{4} - q^{5} + 9 q^{6} + 4 q^{7} - 9 q^{8} + 9 q^{9}+O(q^{10}) $ 9 * q - 9 * q^2 - 9 * q^3 + 9 * q^4 - q^5 + 9 * q^6 + 4 * q^7 - 9 * q^8 + 9 * q^9	\( 9 q - 9 q^{2} - 9 q^{3} + 9 q^{4} - q^{5} + 9 q^{6} + 4 q^{7} - 9 q^{8} + 9 q^{9} + q^{10} + 12 q^{11} - 9 q^{12} - q^{13} - 4 q^{14} + q^{15} + 9 q^{16} + 12 q^{17} - 9 q^{18} - 9 q^{19} - q^{20} - 4 q^{21} - 12 q^{22} + 11 q^{23} + 9 q^{24} + 10 q^{25} + q^{26} - 9 q^{27} + 4 q^{28} + 7 q^{29} - q^{30} - 12 q^{31} - 9 q^{32} - 12 q^{33} - 12 q^{34} + 15 q^{35} + 9 q^{36} - 9 q^{37} + 9 q^{38} + q^{39} + q^{40} - 4 q^{41} + 4 q^{42} + 23 q^{43} + 12 q^{44} - q^{45} - 11 q^{46} + 35 q^{47} - 9 q^{48} + 3 q^{49} - 10 q^{50} - 12 q^{51} - q^{52} + 9 q^{53} + 9 q^{54} + 3 q^{55} - 4 q^{56} + 9 q^{57} - 7 q^{58} + 14 q^{59} + q^{60} + 14 q^{61} + 12 q^{62} + 4 q^{63} + 9 q^{64} + 13 q^{65} + 12 q^{66} - 10 q^{67} + 12 q^{68} - 11 q^{69} - 15 q^{70} + 4 q^{71} - 9 q^{72} - 5 q^{73} + 9 q^{74} - 10 q^{75} - 9 q^{76} + 17 q^{77} - q^{78} - 14 q^{79} - q^{80} + 9 q^{81} + 4 q^{82} + 37 q^{83} - 4 q^{84} - 31 q^{85} - 23 q^{86} - 7 q^{87} - 12 q^{88} - 20 q^{89} + q^{90} - 12 q^{91} + 11 q^{92} + 12 q^{93} - 35 q^{94} + q^{95} + 9 q^{96} - 2 q^{97} - 3 q^{98} + 12 q^{99}+O(q^{100}) \) 9 * q - 9 * q^2 - 9 * q^3 + 9 * q^4 - q^5 + 9 * q^6 + 4 * q^7 - 9 * q^8 + 9 * q^9 + q^10 + 12 * q^11 - 9 * q^12 - q^13 - 4 * q^14 + q^15 + 9 * q^16 + 12 * q^17 - 9 * q^18 - 9 * q^19 - q^20 - 4 * q^21 - 12 * q^22 + 11 * q^23 + 9 * q^24 + 10 * q^25 + q^26 - 9 * q^27 + 4 * q^28 + 7 * q^29 - q^30 - 12 * q^31 - 9 * q^32 - 12 * q^33 - 12 * q^34 + 15 * q^35 + 9 * q^36 - 9 * q^37 + 9 * q^38 + q^39 + q^40 - 4 * q^41 + 4 * q^42 + 23 * q^43 + 12 * q^44 - q^45 - 11 * q^46 + 35 * q^47 - 9 * q^48 + 3 * q^49 - 10 * q^50 - 12 * q^51 - q^52 + 9 * q^53 + 9 * q^54 + 3 * q^55 - 4 * q^56 + 9 * q^57 - 7 * q^58 + 14 * q^59 + q^60 + 14 * q^61 + 12 * q^62 + 4 * q^63 + 9 * q^64 + 13 * q^65 + 12 * q^66 - 10 * q^67 + 12 * q^68 - 11 * q^69 - 15 * q^70 + 4 * q^71 - 9 * q^72 - 5 * q^73 + 9 * q^74 - 10 * q^75 - 9 * q^76 + 17 * q^77 - q^78 - 14 * q^79 - q^80 + 9 * q^81 + 4 * q^82 + 37 * q^83 - 4 * q^84 - 31 * q^85 - 23 * q^86 - 7 * q^87 - 12 * q^88 - 20 * q^89 + q^90 - 12 * q^91 + 11 * q^92 + 12 * q^93 - 35 * q^94 + q^95 + 9 * q^96 - 2 * q^97 - 3 * q^98 + 12 * 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
$5$	−4.37472	−1.95643	−0.978216	−	0.207589i	$-0.933438\pi$
$5$	−4.37472	−1.95643	−0.978216	+	0.207589i	$0.933438\pi$
$6$	1.00000	0.408248
$7$	−0.773393	−0.292315	−0.146157	−	0.989261i	$-0.546691\pi$
$7$	−0.773393	−0.292315	−0.146157	+	0.989261i	$0.546691\pi$
$8$	−1.00000	−0.353553
$9$	1.00000	0.333333
$10$	4.37472	1.38341
$11$	4.42079	1.33292	0.666460	−	0.745541i	$-0.267809\pi$
$11$	4.42079	1.33292	0.666460	+	0.745541i	$0.267809\pi$
$12$	−1.00000	−0.288675
$13$	0.648462	0.179851	0.0899255	−	0.995948i	$-0.471337\pi$
$13$	0.648462	0.179851	0.0899255	+	0.995948i	$0.471337\pi$
$14$	0.773393	0.206698
$15$	4.37472	1.12955
$16$	1.00000	0.250000
$17$	6.40302	1.55296	0.776480	−	0.630142i	$-0.217003\pi$
$17$	6.40302	1.55296	0.776480	+	0.630142i	$0.217003\pi$
$18$	−1.00000	−0.235702
$19$	−1.00000	−0.229416
$19$	−1.00000	−0.229416
$20$	−4.37472	−0.978216
$21$	0.773393	0.168768
$22$	−4.42079	−0.942517
$23$	0.287580	0.0599645	0.0299823	−	0.999550i	$-0.490455\pi$
$23$	0.287580	0.0599645	0.0299823	+	0.999550i	$0.490455\pi$
$24$	1.00000	0.204124
$25$	14.1381	2.82763
$26$	−0.648462	−0.127174
$27$	−1.00000	−0.192450
$28$	−0.773393	−0.146157
$29$	0.347880	0.0645998	0.0322999	−	0.999478i	$-0.489717\pi$
$29$	0.347880	0.0645998	0.0322999	+	0.999478i	$0.489717\pi$
$30$	−4.37472	−0.798710
$31$	−3.57302	−0.641733	−0.320867	−	0.947124i	$-0.603974\pi$
$31$	−3.57302	−0.641733	−0.320867	+	0.947124i	$0.603974\pi$
$32$	−1.00000	−0.176777
$33$	−4.42079	−0.769562
$34$	−6.40302	−1.09811
$35$	3.38337	0.571894
$36$	1.00000	0.166667
$37$	−8.71669	−1.43301	−0.716507	−	0.697580i	$-0.754260\pi$
$37$	−8.71669	−1.43301	−0.716507	+	0.697580i	$0.754260\pi$
$38$	1.00000	0.162221
$39$	−0.648462	−0.103837
$40$	4.37472	0.691703
$41$	8.14882	1.27263	0.636316	−	0.771429i	$-0.280458\pi$
$41$	8.14882	1.27263	0.636316	+	0.771429i	$0.280458\pi$
$42$	−0.773393	−0.119337
$43$	8.05514	1.22840	0.614199	−	0.789151i	$-0.289479\pi$
$43$	8.05514	1.22840	0.614199	+	0.789151i	$0.289479\pi$
$44$	4.42079	0.666460
$45$	−4.37472	−0.652144
$46$	−0.287580	−0.0424013
$47$	11.2879	1.64650	0.823252	−	0.567676i	$-0.192157\pi$
$47$	11.2879	1.64650	0.823252	+	0.567676i	$0.192157\pi$
$48$	−1.00000	−0.144338
$49$	−6.40186	−0.914552
$50$	−14.1381	−1.99943
$51$	−6.40302	−0.896602
$52$	0.648462	0.0899255
$53$	1.00000	0.137361
$53$	1.00000	0.137361
$54$	1.00000	0.136083
$55$	−19.3397	−2.60777
$56$	0.773393	0.103349
$57$	1.00000	0.132453
$58$	−0.347880	−0.0456789
$59$	−3.60190	−0.468927	−0.234463	−	0.972125i	$-0.575333\pi$
$59$	−3.60190	−0.468927	−0.234463	+	0.972125i	$0.575333\pi$
$60$	4.37472	0.564773
$61$	6.21492	0.795738	0.397869	−	0.917442i	$-0.369750\pi$
$61$	6.21492	0.795738	0.397869	+	0.917442i	$0.369750\pi$
$62$	3.57302	0.453774
$63$	−0.773393	−0.0974383
$64$	1.00000	0.125000
$65$	−2.83684	−0.351866
$66$	4.42079	0.544162
$67$	−1.86347	−0.227659	−0.113830	−	0.993500i	$-0.536312\pi$
$67$	−1.86347	−0.227659	−0.113830	+	0.993500i	$0.536312\pi$
$68$	6.40302	0.776480
$69$	−0.287580	−0.0346205
$70$	−3.38337	−0.404390
$71$	−1.42484	−0.169097	−0.0845487	−	0.996419i	$-0.526945\pi$
$71$	−1.42484	−0.169097	−0.0845487	+	0.996419i	$0.526945\pi$
$72$	−1.00000	−0.117851
$73$	−8.80129	−1.03011	−0.515056	−	0.857156i	$-0.672229\pi$
$73$	−8.80129	−1.03011	−0.515056	+	0.857156i	$0.672229\pi$
$74$	8.71669	1.01329
$75$	−14.1381	−1.63253
$76$	−1.00000	−0.114708
$77$	−3.41901	−0.389632
$78$	0.648462	0.0734238
$79$	−7.81384	−0.879126	−0.439563	−	0.898212i	$-0.644867\pi$
$79$	−7.81384	−0.879126	−0.439563	+	0.898212i	$0.644867\pi$
$80$	−4.37472	−0.489108
$81$	1.00000	0.111111
$82$	−8.14882	−0.899886
$83$	16.9311	1.85843	0.929216	−	0.369537i	$-0.120484\pi$
$83$	16.9311	1.85843	0.929216	+	0.369537i	$0.120484\pi$
$84$	0.773393	0.0843841
$85$	−28.0114	−3.03826
$86$	−8.05514	−0.868608
$87$	−0.347880	−0.0372967
$88$	−4.42079	−0.471258
$89$	−17.7376	−1.88019	−0.940094	−	0.340917i	$-0.889263\pi$
$89$	−17.7376	−1.88019	−0.940094	+	0.340917i	$0.889263\pi$
$90$	4.37472	0.461136
$91$	−0.501516	−0.0525731
$92$	0.287580	0.0299823
$93$	3.57302	0.370505
$94$	−11.2879	−1.16425
$95$	4.37472	0.448836
$96$	1.00000	0.102062
$97$	9.18686	0.932785	0.466392	−	0.884578i	$-0.345553\pi$
$97$	9.18686	0.932785	0.466392	+	0.884578i	$0.345553\pi$
$98$	6.40186	0.646686
$99$	4.42079	0.444307
$100$	14.1381	1.41381
$101$	16.2939	1.62131	0.810654	−	0.585526i	$-0.199112\pi$
$101$	16.2939	1.62131	0.810654	+	0.585526i	$0.199112\pi$
$102$	6.40302	0.633994
$103$	−8.42044	−0.829690	−0.414845	−	0.909892i	$-0.636164\pi$
$103$	−8.42044	−0.829690	−0.414845	+	0.909892i	$0.636164\pi$
$104$	−0.648462	−0.0635869
$105$	−3.38337	−0.330183
$106$	−1.00000	−0.0971286
$107$	0.329410	0.0318452	0.0159226	−	0.999873i	$-0.494931\pi$
$107$	0.329410	0.0318452	0.0159226	+	0.999873i	$0.494931\pi$
$108$	−1.00000	−0.0962250
$109$	−0.493136	−0.0472338	−0.0236169	−	0.999721i	$-0.507518\pi$
$109$	−0.493136	−0.0472338	−0.0236169	+	0.999721i	$0.507518\pi$
$110$	19.3397	1.84397
$111$	8.71669	0.827351
$112$	−0.773393	−0.0730787
$113$	−17.2506	−1.62280	−0.811400	−	0.584492i	$-0.801294\pi$
$113$	−17.2506	−1.62280	−0.811400	+	0.584492i	$0.801294\pi$
$114$	−1.00000	−0.0936586
$115$	−1.25808	−0.117317
$116$	0.347880	0.0322999
$117$	0.648462	0.0599503
$118$	3.60190	0.331581
$119$	−4.95205	−0.453954
$120$	−4.37472	−0.399355
$121$	8.54342	0.776675
$122$	−6.21492	−0.562672
$123$	−8.14882	−0.734754
$124$	−3.57302	−0.320867
$125$	−39.9768	−3.57563
$126$	0.773393	0.0688993
$127$	−10.8921	−0.966521	−0.483261	−	0.875476i	$-0.660548\pi$
$127$	−10.8921	−0.966521	−0.483261	+	0.875476i	$0.660548\pi$
$128$	−1.00000	−0.0883883
$129$	−8.05514	−0.709216
$130$	2.83684	0.248807
$131$	4.64018	0.405414	0.202707	−	0.979239i	$-0.435026\pi$
$131$	4.64018	0.405414	0.202707	+	0.979239i	$0.435026\pi$
$132$	−4.42079	−0.384781
$133$	0.773393	0.0670617
$134$	1.86347	0.160979
$135$	4.37472	0.376516
$136$	−6.40302	−0.549054
$137$	−18.5932	−1.58853	−0.794263	−	0.607574i	$-0.792143\pi$
$137$	−18.5932	−1.58853	−0.794263	+	0.607574i	$0.792143\pi$
$138$	0.287580	0.0244804
$139$	−20.2541	−1.71793	−0.858965	−	0.512035i	$-0.828892\pi$
$139$	−20.2541	−1.71793	−0.858965	+	0.512035i	$0.828892\pi$
$140$	3.38337	0.285947
$141$	−11.2879	−0.950610
$142$	1.42484	0.119570
$143$	2.86672	0.239727
$144$	1.00000	0.0833333
$145$	−1.52188	−0.126385
$146$	8.80129	0.728400
$147$	6.40186	0.528017
$148$	−8.71669	−0.716507
$149$	3.94550	0.323228	0.161614	−	0.986854i	$-0.448330\pi$
$149$	3.94550	0.323228	0.161614	+	0.986854i	$0.448330\pi$
$150$	14.1381	1.15437
$151$	−6.27644	−0.510770	−0.255385	−	0.966839i	$-0.582202\pi$
$151$	−6.27644	−0.510770	−0.255385	+	0.966839i	$0.582202\pi$
$152$	1.00000	0.0811107
$153$	6.40302	0.517654
$154$	3.41901	0.275512
$155$	15.6309	1.25551
$156$	−0.648462	−0.0519185
$157$	9.71418	0.775276	0.387638	−	0.921812i	$-0.373291\pi$
$157$	9.71418	0.775276	0.387638	+	0.921812i	$0.373291\pi$
$158$	7.81384	0.621636
$159$	−1.00000	−0.0793052
$160$	4.37472	0.345852
$161$	−0.222412	−0.0175285
$162$	−1.00000	−0.0785674
$163$	19.7130	1.54404	0.772021	−	0.635597i	$-0.219246\pi$
$163$	19.7130	1.54404	0.772021	+	0.635597i	$0.219246\pi$
$164$	8.14882	0.636316
$165$	19.3397	1.50560
$166$	−16.9311	−1.31411
$167$	−12.8412	−0.993683	−0.496842	−	0.867841i	$-0.665507\pi$
$167$	−12.8412	−0.993683	−0.496842	+	0.867841i	$0.665507\pi$
$168$	−0.773393	−0.0596685
$169$	−12.5795	−0.967654
$170$	28.0114	2.14838
$171$	−1.00000	−0.0764719
$172$	8.05514	0.614199
$173$	10.3472	0.786683	0.393341	−	0.919393i	$-0.371319\pi$
$173$	10.3472	0.786683	0.393341	+	0.919393i	$0.371319\pi$
$174$	0.347880	0.0263727
$175$	−10.9343	−0.826558
$176$	4.42079	0.333230
$177$	3.60190	0.270735
$178$	17.7376	1.32949
$179$	9.63680	0.720288	0.360144	−	0.932897i	$-0.382728\pi$
$179$	9.63680	0.720288	0.360144	+	0.932897i	$0.382728\pi$
$180$	−4.37472	−0.326072
$181$	20.7568	1.54284	0.771420	−	0.636326i	$-0.219547\pi$
$181$	20.7568	1.54284	0.771420	+	0.636326i	$0.219547\pi$
$182$	0.501516	0.0371748
$183$	−6.21492	−0.459420
$184$	−0.287580	−0.0212007
$185$	38.1330	2.80360
$186$	−3.57302	−0.261986
$187$	28.3064	2.06997
$188$	11.2879	0.823252
$189$	0.773393	0.0562560
$190$	−4.37472	−0.317375
$191$	2.13393	0.154406	0.0772030	−	0.997015i	$-0.475401\pi$
$191$	2.13393	0.154406	0.0772030	+	0.997015i	$0.475401\pi$
$192$	−1.00000	−0.0721688
$193$	5.01259	0.360814	0.180407	−	0.983592i	$-0.442259\pi$
$193$	5.01259	0.360814	0.180407	+	0.983592i	$0.442259\pi$
$194$	−9.18686	−0.659578
$195$	2.83684	0.203150
$196$	−6.40186	−0.457276
$197$	16.1361	1.14965	0.574825	−	0.818276i	$-0.305070\pi$
$197$	16.1361	1.14965	0.574825	+	0.818276i	$0.305070\pi$
$198$	−4.42079	−0.314172
$199$	13.0215	0.923069	0.461535	−	0.887122i	$-0.347299\pi$
$199$	13.0215	0.923069	0.461535	+	0.887122i	$0.347299\pi$
$200$	−14.1381	−0.999717
$201$	1.86347	0.131439
$202$	−16.2939	−1.14644
$203$	−0.269048	−0.0188835
$204$	−6.40302	−0.448301
$205$	−35.6488	−2.48982
$206$	8.42044	0.586680
$207$	0.287580	0.0199882
$208$	0.648462	0.0449627
$209$	−4.42079	−0.305793
$210$	3.38337	0.233475
$211$	−4.52168	−0.311285	−0.155643	−	0.987813i	$-0.549745\pi$
$211$	−4.52168	−0.311285	−0.155643	+	0.987813i	$0.549745\pi$
$212$	1.00000	0.0686803
$213$	1.42484	0.0976285
$214$	−0.329410	−0.0225180
$215$	−35.2389	−2.40328
$216$	1.00000	0.0680414
$217$	2.76335	0.187588
$218$	0.493136	0.0333994
$219$	8.80129	0.594736
$220$	−19.3397	−1.30388
$221$	4.15211	0.279301
$222$	−8.71669	−0.585026
$223$	−20.1908	−1.35207	−0.676037	−	0.736868i	$-0.736304\pi$
$223$	−20.1908	−1.35207	−0.676037	+	0.736868i	$0.736304\pi$
$224$	0.773393	0.0516745
$225$	14.1381	0.942543
$226$	17.2506	1.14749
$227$	17.1876	1.14078	0.570392	−	0.821373i	$-0.306791\pi$
$227$	17.1876	1.14078	0.570392	+	0.821373i	$0.306791\pi$
$228$	1.00000	0.0662266
$229$	19.9182	1.31623	0.658114	−	0.752918i	$-0.271354\pi$
$229$	19.9182	1.31623	0.658114	+	0.752918i	$0.271354\pi$
$230$	1.25808	0.0829553
$231$	3.41901	0.224954
$232$	−0.347880	−0.0228395
$233$	21.1819	1.38767	0.693836	−	0.720133i	$-0.255919\pi$
$233$	21.1819	1.38767	0.693836	+	0.720133i	$0.255919\pi$
$234$	−0.648462	−0.0423913
$235$	−49.3812	−3.22127
$236$	−3.60190	−0.234463
$237$	7.81384	0.507564
$238$	4.95205	0.320994
$239$	−1.90069	−0.122945	−0.0614727	−	0.998109i	$-0.519580\pi$
$239$	−1.90069	−0.122945	−0.0614727	+	0.998109i	$0.519580\pi$
$240$	4.37472	0.282387
$241$	−0.815676	−0.0525423	−0.0262712	−	0.999655i	$-0.508363\pi$
$241$	−0.815676	−0.0525423	−0.0262712	+	0.999655i	$0.508363\pi$
$242$	−8.54342	−0.549192
$243$	−1.00000	−0.0641500
$244$	6.21492	0.397869
$245$	28.0063	1.78926
$246$	8.14882	0.519550
$247$	−0.648462	−0.0412606
$248$	3.57302	0.226887
$249$	−16.9311	−1.07297
$250$	39.9768	2.52835
$251$	−24.0194	−1.51609	−0.758045	−	0.652202i	$-0.773845\pi$
$251$	−24.0194	−1.51609	−0.758045	+	0.652202i	$0.773845\pi$
$252$	−0.773393	−0.0487192
$253$	1.27133	0.0799279
$254$	10.8921	0.683434
$255$	28.0114	1.75414
$256$	1.00000	0.0625000
$257$	29.0813	1.81404	0.907020	−	0.421088i	$-0.138352\pi$
$257$	29.0813	1.81404	0.907020	+	0.421088i	$0.138352\pi$
$258$	8.05514	0.501491
$259$	6.74142	0.418892
$260$	−2.83684	−0.175933
$261$	0.347880	0.0215333
$262$	−4.64018	−0.286671
$263$	2.58074	0.159135	0.0795676	−	0.996829i	$-0.474646\pi$
$263$	2.58074	0.159135	0.0795676	+	0.996829i	$0.474646\pi$
$264$	4.42079	0.272081
$265$	−4.37472	−0.268737
$266$	−0.773393	−0.0474197
$267$	17.7376	1.08553
$268$	−1.86347	−0.113830
$269$	9.69784	0.591288	0.295644	−	0.955298i	$-0.404466\pi$
$269$	9.69784	0.591288	0.295644	+	0.955298i	$0.404466\pi$
$270$	−4.37472	−0.266237
$271$	−24.3884	−1.48149	−0.740745	−	0.671786i	$-0.765527\pi$
$271$	−24.3884	−1.48149	−0.740745	+	0.671786i	$0.765527\pi$
$272$	6.40302	0.388240
$273$	0.501516	0.0303531
$274$	18.5932	1.12326
$275$	62.5018	3.76900
$276$	−0.287580	−0.0173103
$277$	−10.8414	−0.651399	−0.325700	−	0.945473i	$-0.605600\pi$
$277$	−10.8414	−0.651399	−0.325700	+	0.945473i	$0.605600\pi$
$278$	20.2541	1.21476
$279$	−3.57302	−0.213911
$280$	−3.38337	−0.202195
$281$	−9.00314	−0.537082	−0.268541	−	0.963268i	$-0.586542\pi$
$281$	−9.00314	−0.537082	−0.268541	+	0.963268i	$0.586542\pi$
$282$	11.2879	0.672182
$283$	18.4920	1.09924	0.549619	−	0.835416i	$-0.314773\pi$
$283$	18.4920	1.09924	0.549619	+	0.835416i	$0.314773\pi$
$284$	−1.42484	−0.0845487
$285$	−4.37472	−0.259136
$286$	−2.86672	−0.169512
$287$	−6.30223	−0.372009
$288$	−1.00000	−0.0589256
$289$	23.9987	1.41169
$290$	1.52188	0.0893678
$291$	−9.18686	−0.538544
$292$	−8.80129	−0.515056
$293$	6.56376	0.383459	0.191729	−	0.981448i	$-0.438590\pi$
$293$	6.56376	0.383459	0.191729	+	0.981448i	$0.438590\pi$
$294$	−6.40186	−0.373364
$295$	15.7573	0.917424
$296$	8.71669	0.506647
$297$	−4.42079	−0.256521
$298$	−3.94550	−0.228557
$299$	0.186484	0.0107847
$300$	−14.1381	−0.816266
$301$	−6.22979	−0.359079
$302$	6.27644	0.361169
$303$	−16.2939	−0.936062
$304$	−1.00000	−0.0573539
$305$	−27.1885	−1.55681
$306$	−6.40302	−0.366036
$307$	19.0958	1.08986	0.544928	−	0.838483i	$-0.316557\pi$
$307$	19.0958	1.08986	0.544928	+	0.838483i	$0.316557\pi$
$308$	−3.41901	−0.194816
$309$	8.42044	0.479022
$310$	−15.6309	−0.887778
$311$	22.8539	1.29593	0.647964	−	0.761671i	$-0.275621\pi$
$311$	22.8539	1.29593	0.647964	+	0.761671i	$0.275621\pi$
$312$	0.648462	0.0367119
$313$	28.4846	1.61004	0.805022	−	0.593244i	$-0.202153\pi$
$313$	28.4846	1.61004	0.805022	+	0.593244i	$0.202153\pi$
$314$	−9.71418	−0.548203
$315$	3.38337	0.190631
$316$	−7.81384	−0.439563
$317$	20.1541	1.13197	0.565983	−	0.824417i	$-0.308497\pi$
$317$	20.1541	1.13197	0.565983	+	0.824417i	$0.308497\pi$
$318$	1.00000	0.0560772
$319$	1.53791	0.0861063
$320$	−4.37472	−0.244554
$321$	−0.329410	−0.0183858
$322$	0.222412	0.0123945
$323$	−6.40302	−0.356274
$324$	1.00000	0.0555556
$325$	9.16804	0.508551
$326$	−19.7130	−1.09180
$327$	0.493136	0.0272705
$328$	−8.14882	−0.449943
$329$	−8.72995	−0.481298
$330$	−19.3397	−1.06462
$331$	25.8195	1.41917	0.709584	−	0.704621i	$-0.248883\pi$
$331$	25.8195	1.41917	0.709584	+	0.704621i	$0.248883\pi$
$332$	16.9311	0.929216
$333$	−8.71669	−0.477672
$334$	12.8412	0.702640
$335$	8.15216	0.445400
$336$	0.773393	0.0421920
$337$	19.8224	1.07980	0.539899	−	0.841730i	$-0.318463\pi$
$337$	19.8224	1.07980	0.539899	+	0.841730i	$0.318463\pi$
$338$	12.5795	0.684234
$339$	17.2506	0.936924
$340$	−28.0114	−1.51913
$341$	−15.7956	−0.855379
$342$	1.00000	0.0540738
$343$	10.3649	0.559652
$344$	−8.05514	−0.434304
$345$	1.25808	0.0677327
$346$	−10.3472	−0.556269
$347$	−21.0397	−1.12947	−0.564735	−	0.825272i	$-0.691022\pi$
$347$	−21.0397	−1.12947	−0.564735	+	0.825272i	$0.691022\pi$
$348$	−0.347880	−0.0186483
$349$	−22.1208	−1.18410	−0.592049	−	0.805902i	$-0.701681\pi$
$349$	−22.1208	−1.18410	−0.592049	+	0.805902i	$0.701681\pi$
$350$	10.9343	0.584465
$351$	−0.648462	−0.0346123
$352$	−4.42079	−0.235629
$353$	−35.6025	−1.89493	−0.947466	−	0.319857i	$-0.896365\pi$
$353$	−35.6025	−1.89493	−0.947466	+	0.319857i	$0.896365\pi$
$354$	−3.60190	−0.191439
$355$	6.23327	0.330828
$356$	−17.7376	−0.940094
$357$	4.95205	0.262090
$358$	−9.63680	−0.509321
$359$	2.14270	0.113087	0.0565437	−	0.998400i	$-0.481992\pi$
$359$	2.14270	0.113087	0.0565437	+	0.998400i	$0.481992\pi$
$360$	4.37472	0.230568
$361$	1.00000	0.0526316
$362$	−20.7568	−1.09095
$363$	−8.54342	−0.448413
$364$	−0.501516	−0.0262866
$365$	38.5031	2.01535
$366$	6.21492	0.324859
$367$	−20.6265	−1.07670	−0.538349	−	0.842722i	$-0.680952\pi$
$367$	−20.6265	−1.07670	−0.538349	+	0.842722i	$0.680952\pi$
$368$	0.287580	0.0149911
$369$	8.14882	0.424210
$370$	−38.1330	−1.98244
$371$	−0.773393	−0.0401525
$372$	3.57302	0.185252
$373$	−31.0811	−1.60932	−0.804660	−	0.593735i	$-0.797653\pi$
$373$	−31.0811	−1.60932	−0.804660	+	0.593735i	$0.797653\pi$
$374$	−28.3064	−1.46369
$375$	39.9768	2.06439
$376$	−11.2879	−0.582127
$377$	0.225587	0.0116183
$378$	−0.773393	−0.0397790
$379$	20.7497	1.06584	0.532920	−	0.846165i	$-0.321095\pi$
$379$	20.7497	1.06584	0.532920	+	0.846165i	$0.321095\pi$
$380$	4.37472	0.224418
$381$	10.8921	0.558021
$382$	−2.13393	−0.109182
$383$	29.8122	1.52333	0.761667	−	0.647969i	$-0.224381\pi$
$383$	29.8122	1.52333	0.761667	+	0.647969i	$0.224381\pi$
$384$	1.00000	0.0510310
$385$	14.9572	0.762289
$386$	−5.01259	−0.255134
$387$	8.05514	0.409466
$388$	9.18686	0.466392
$389$	6.58436	0.333841	0.166920	−	0.985970i	$-0.446618\pi$
$389$	6.58436	0.333841	0.166920	+	0.985970i	$0.446618\pi$
$390$	−2.83684	−0.143649
$391$	1.84138	0.0931225
$392$	6.40186	0.323343
$393$	−4.64018	−0.234066
$394$	−16.1361	−0.812926
$395$	34.1833	1.71995
$396$	4.42079	0.222153
$397$	8.13941	0.408505	0.204253	−	0.978918i	$-0.434524\pi$
$397$	8.13941	0.408505	0.204253	+	0.978918i	$0.434524\pi$
$398$	−13.0215	−0.652709
$399$	−0.773393	−0.0387181
$400$	14.1381	0.706907
$401$	13.6896	0.683627	0.341813	−	0.939768i	$-0.388959\pi$
$401$	13.6896	0.683627	0.341813	+	0.939768i	$0.388959\pi$
$402$	−1.86347	−0.0929415
$403$	−2.31697	−0.115416
$404$	16.2939	0.810654
$405$	−4.37472	−0.217381
$406$	0.269048	0.0133526
$407$	−38.5347	−1.91009
$408$	6.40302	0.316997
$409$	−16.8342	−0.832397	−0.416199	−	0.909274i	$-0.636638\pi$
$409$	−16.8342	−0.832397	−0.416199	+	0.909274i	$0.636638\pi$
$410$	35.6488	1.76057
$411$	18.5932	0.917136
$412$	−8.42044	−0.414845
$413$	2.78568	0.137074
$414$	−0.287580	−0.0141338
$415$	−74.0688	−3.63590
$416$	−0.648462	−0.0317934
$417$	20.2541	0.991847
$418$	4.42079	0.216228
$419$	17.1176	0.836248	0.418124	−	0.908390i	$-0.362688\pi$
$419$	17.1176	0.836248	0.418124	+	0.908390i	$0.362688\pi$
$420$	−3.38337	−0.165092
$421$	−5.89560	−0.287334	−0.143667	−	0.989626i	$-0.545889\pi$
$421$	−5.89560	−0.287334	−0.143667	+	0.989626i	$0.545889\pi$
$422$	4.52168	0.220112
$423$	11.2879	0.548835
$424$	−1.00000	−0.0485643
$425$	90.5268	4.39119
$426$	−1.42484	−0.0690337
$427$	−4.80657	−0.232606
$428$	0.329410	0.0159226
$429$	−2.86672	−0.138406
$430$	35.2389	1.69937
$431$	1.84910	0.0890681	0.0445341	−	0.999008i	$-0.485820\pi$
$431$	1.84910	0.0890681	0.0445341	+	0.999008i	$0.485820\pi$
$432$	−1.00000	−0.0481125
$433$	18.0909	0.869394	0.434697	−	0.900577i	$-0.356856\pi$
$433$	18.0909	0.869394	0.434697	+	0.900577i	$0.356856\pi$
$434$	−2.76335	−0.132645
$435$	1.52188	0.0729685
$436$	−0.493136	−0.0236169
$437$	−0.287580	−0.0137568
$438$	−8.80129	−0.420542
$439$	−8.56484	−0.408778	−0.204389	−	0.978890i	$-0.565521\pi$
$439$	−8.56484	−0.408778	−0.204389	+	0.978890i	$0.565521\pi$
$440$	19.3397	0.921985
$441$	−6.40186	−0.304851
$442$	−4.15211	−0.197496
$443$	28.8514	1.37077	0.685385	−	0.728181i	$-0.259634\pi$
$443$	28.8514	1.37077	0.685385	+	0.728181i	$0.259634\pi$
$444$	8.71669	0.413676
$445$	77.5972	3.67846
$446$	20.1908	0.956060
$447$	−3.94550	−0.186616
$448$	−0.773393	−0.0365394
$449$	−11.8345	−0.558505	−0.279253	−	0.960218i	$-0.590087\pi$
$449$	−11.8345	−0.558505	−0.279253	+	0.960218i	$0.590087\pi$
$450$	−14.1381	−0.666478
$451$	36.0242	1.69632
$452$	−17.2506	−0.811400
$453$	6.27644	0.294893
$454$	−17.1876	−0.806656
$455$	2.19399	0.102856
$456$	−1.00000	−0.0468293
$457$	6.35020	0.297050	0.148525	−	0.988909i	$-0.452547\pi$
$457$	6.35020	0.297050	0.148525	+	0.988909i	$0.452547\pi$
$458$	−19.9182	−0.930714
$459$	−6.40302	−0.298867
$460$	−1.25808	−0.0586583
$461$	9.51641	0.443223	0.221612	−	0.975135i	$-0.428868\pi$
$461$	9.51641	0.443223	0.221612	+	0.975135i	$0.428868\pi$
$462$	−3.41901	−0.159067
$463$	−26.8266	−1.24674	−0.623369	−	0.781927i	$-0.714237\pi$
$463$	−26.8266	−1.24674	−0.623369	+	0.781927i	$0.714237\pi$
$464$	0.347880	0.0161499
$465$	−15.6309	−0.724868
$466$	−21.1819	−0.981232
$467$	−9.63770	−0.445980	−0.222990	−	0.974821i	$-0.571582\pi$
$467$	−9.63770	−0.445980	−0.222990	+	0.974821i	$0.571582\pi$
$468$	0.648462	0.0299752
$469$	1.44120	0.0665482
$470$	49.3812	2.27778
$471$	−9.71418	−0.447606
$472$	3.60190	0.165791
$473$	35.6101	1.63735
$474$	−7.81384	−0.358902
$475$	−14.1381	−0.648702
$476$	−4.95205	−0.226977
$477$	1.00000	0.0457869
$478$	1.90069	0.0869355
$479$	−20.1735	−0.921750	−0.460875	−	0.887465i	$-0.652464\pi$
$479$	−20.1735	−0.921750	−0.460875	+	0.887465i	$0.652464\pi$
$480$	−4.37472	−0.199678
$481$	−5.65244	−0.257729
$482$	0.815676	0.0371530
$483$	0.222412	0.0101201
$484$	8.54342	0.388337
$485$	−40.1899	−1.82493
$486$	1.00000	0.0453609
$487$	−3.00738	−0.136277	−0.0681386	−	0.997676i	$-0.521706\pi$
$487$	−3.00738	−0.136277	−0.0681386	+	0.997676i	$0.521706\pi$
$488$	−6.21492	−0.281336
$489$	−19.7130	−0.891453
$490$	−28.0063	−1.26520
$491$	−18.0303	−0.813695	−0.406847	−	0.913496i	$-0.633372\pi$
$491$	−18.0303	−0.813695	−0.406847	+	0.913496i	$0.633372\pi$
$492$	−8.14882	−0.367377
$493$	2.22749	0.100321
$494$	0.648462	0.0291757
$495$	−19.3397	−0.869256
$496$	−3.57302	−0.160433
$497$	1.10196	0.0494297
$498$	16.9311	0.758702
$499$	22.9499	1.02738	0.513689	−	0.857976i	$-0.328278\pi$
$499$	22.9499	1.02738	0.513689	+	0.857976i	$0.328278\pi$
$500$	−39.9768	−1.78782
$501$	12.8412	0.573703
$502$	24.0194	1.07204
$503$	19.0086	0.847551	0.423775	−	0.905767i	$-0.360705\pi$
$503$	19.0086	0.847551	0.423775	+	0.905767i	$0.360705\pi$
$504$	0.773393	0.0344496
$505$	−71.2813	−3.17198
$506$	−1.27133	−0.0565176
$507$	12.5795	0.558675
$508$	−10.8921	−0.483261
$509$	−44.7135	−1.98189	−0.990945	−	0.134270i	$-0.957131\pi$
$509$	−44.7135	−1.98189	−0.990945	+	0.134270i	$0.957131\pi$
$510$	−28.0114	−1.24037
$511$	6.80685	0.301117
$512$	−1.00000	−0.0441942
$513$	1.00000	0.0441511
$514$	−29.0813	−1.28272
$515$	36.8370	1.62323
$516$	−8.05514	−0.354608
$517$	49.9013	2.19466
$518$	−6.74142	−0.296201
$519$	−10.3472	−0.454191
$520$	2.83684	0.124403
$521$	−15.0524	−0.659457	−0.329728	−	0.944076i	$-0.606957\pi$
$521$	−15.0524	−0.659457	−0.329728	+	0.944076i	$0.606957\pi$
$522$	−0.347880	−0.0152263
$523$	10.8505	0.474458	0.237229	−	0.971454i	$-0.423761\pi$
$523$	10.8505	0.474458	0.237229	+	0.971454i	$0.423761\pi$
$524$	4.64018	0.202707
$525$	10.9343	0.477213
$526$	−2.58074	−0.112526
$527$	−22.8781	−0.996586
$528$	−4.42079	−0.192390
$529$	−22.9173	−0.996404
$530$	4.37472	0.190026
$531$	−3.60190	−0.156309
$532$	0.773393	0.0335308
$533$	5.28419	0.228884
$534$	−17.7376	−0.767583
$535$	−1.44107	−0.0623030
$536$	1.86347	0.0804897
$537$	−9.63680	−0.415859
$538$	−9.69784	−0.418104
$539$	−28.3013	−1.21902
$540$	4.37472	0.188258
$541$	−29.4066	−1.26429	−0.632144	−	0.774851i	$-0.717825\pi$
$541$	−29.4066	−1.26429	−0.632144	+	0.774851i	$0.717825\pi$
$542$	24.3884	1.04757
$543$	−20.7568	−0.890760
$544$	−6.40302	−0.274527
$545$	2.15733	0.0924098
$546$	−0.501516	−0.0214629
$547$	−24.1790	−1.03382	−0.516910	−	0.856039i	$-0.672918\pi$
$547$	−24.1790	−1.03382	−0.516910	+	0.856039i	$0.672918\pi$
$548$	−18.5932	−0.794263
$549$	6.21492	0.265246
$550$	−62.5018	−2.66509
$551$	−0.347880	−0.0148202
$552$	0.287580	0.0122402
$553$	6.04317	0.256982
$554$	10.8414	0.460609
$555$	−38.1330	−1.61866
$556$	−20.2541	−0.858965
$557$	−17.8091	−0.754596	−0.377298	−	0.926092i	$-0.623147\pi$
$557$	−17.8091	−0.754596	−0.377298	+	0.926092i	$0.623147\pi$
$558$	3.57302	0.151258
$559$	5.22345	0.220928
$560$	3.38337	0.142974
$561$	−28.3064	−1.19510
$562$	9.00314	0.379775
$563$	3.25383	0.137132	0.0685662	−	0.997647i	$-0.478158\pi$
$563$	3.25383	0.137132	0.0685662	+	0.997647i	$0.478158\pi$
$564$	−11.2879	−0.475305
$565$	75.4664	3.17490
$566$	−18.4920	−0.777278
$567$	−0.773393	−0.0324794
$568$	1.42484	0.0597850
$569$	−13.8182	−0.579290	−0.289645	−	0.957134i	$-0.593537\pi$
$569$	−13.8182	−0.579290	−0.289645	+	0.957134i	$0.593537\pi$
$570$	4.37472	0.183237
$571$	21.5278	0.900911	0.450455	−	0.892799i	$-0.351262\pi$
$571$	21.5278	0.900911	0.450455	+	0.892799i	$0.351262\pi$
$572$	2.86672	0.119863
$573$	−2.13393	−0.0891463
$574$	6.30223	0.263050
$575$	4.06584	0.169557
$576$	1.00000	0.0416667
$577$	37.9416	1.57953	0.789765	−	0.613409i	$-0.210202\pi$
$577$	37.9416	1.57953	0.789765	+	0.613409i	$0.210202\pi$
$578$	−23.9987	−0.998213
$579$	−5.01259	−0.208316
$580$	−1.52188	−0.0631925
$581$	−13.0944	−0.543247
$582$	9.18686	0.380808
$583$	4.42079	0.183091
$584$	8.80129	0.364200
$585$	−2.83684	−0.117289
$586$	−6.56376	−0.271146
$587$	−26.4655	−1.09235	−0.546174	−	0.837672i	$-0.683916\pi$
$587$	−26.4655	−1.09235	−0.546174	+	0.837672i	$0.683916\pi$
$588$	6.40186	0.264008
$589$	3.57302	0.147224
$590$	−15.7573	−0.648717
$591$	−16.1361	−0.663751
$592$	−8.71669	−0.358254
$593$	14.7251	0.604685	0.302343	−	0.953199i	$-0.402231\pi$
$593$	14.7251	0.604685	0.302343	+	0.953199i	$0.402231\pi$
$594$	4.42079	0.181387
$595$	21.6638	0.888130
$596$	3.94550	0.161614
$597$	−13.0215	−0.532934
$598$	−0.186484	−0.00762592
$599$	45.3990	1.85495	0.927476	−	0.373882i	$-0.121974\pi$
$599$	45.3990	1.85495	0.927476	+	0.373882i	$0.121974\pi$
$600$	14.1381	0.577187
$601$	18.4301	0.751781	0.375891	−	0.926664i	$-0.377337\pi$
$601$	18.4301	0.751781	0.375891	+	0.926664i	$0.377337\pi$
$602$	6.22979	0.253907
$603$	−1.86347	−0.0758864
$604$	−6.27644	−0.255385
$605$	−37.3751	−1.51951
$606$	16.2939	0.661896
$607$	10.8395	0.439960	0.219980	−	0.975504i	$-0.429401\pi$
$607$	10.8395	0.439960	0.219980	+	0.975504i	$0.429401\pi$
$608$	1.00000	0.0405554
$609$	0.269048	0.0109024
$610$	27.1885	1.10083
$611$	7.31975	0.296125
$612$	6.40302	0.258827
$613$	−9.40916	−0.380033	−0.190016	−	0.981781i	$-0.560854\pi$
$613$	−9.40916	−0.380033	−0.190016	+	0.981781i	$0.560854\pi$
$614$	−19.0958	−0.770645
$615$	35.6488	1.43750
$616$	3.41901	0.137756
$617$	1.80538	0.0726820	0.0363410	−	0.999339i	$-0.488430\pi$
$617$	1.80538	0.0726820	0.0363410	+	0.999339i	$0.488430\pi$
$618$	−8.42044	−0.338720
$619$	−17.1871	−0.690807	−0.345403	−	0.938454i	$-0.612258\pi$
$619$	−17.1871	−0.690807	−0.345403	+	0.938454i	$0.612258\pi$
$620$	15.6309	0.627754
$621$	−0.287580	−0.0115402
$622$	−22.8539	−0.916359
$623$	13.7182	0.549607
$624$	−0.648462	−0.0259592
$625$	104.196	4.16785
$626$	−28.4846	−1.13847
$627$	4.42079	0.176550
$628$	9.71418	0.387638
$629$	−55.8131	−2.22542
$630$	−3.38337	−0.134797
$631$	−35.7059	−1.42143	−0.710715	−	0.703480i	$-0.751628\pi$
$631$	−35.7059	−1.42143	−0.710715	+	0.703480i	$0.751628\pi$
$632$	7.81384	0.310818
$633$	4.52168	0.179721
$634$	−20.1541	−0.800421
$635$	47.6500	1.89093
$636$	−1.00000	−0.0396526
$637$	−4.15136	−0.164483
$638$	−1.53791	−0.0608864
$639$	−1.42484	−0.0563658
$640$	4.37472	0.172926
$641$	15.0696	0.595214	0.297607	−	0.954688i	$-0.403811\pi$
$641$	15.0696	0.595214	0.297607	+	0.954688i	$0.403811\pi$
$642$	0.329410	0.0130008
$643$	32.5585	1.28398	0.641992	−	0.766712i	$-0.278108\pi$
$643$	32.5585	1.28398	0.641992	+	0.766712i	$0.278108\pi$
$644$	−0.222412	−0.00876426
$645$	35.2389	1.38753
$646$	6.40302	0.251923
$647$	−12.3081	−0.483883	−0.241942	−	0.970291i	$-0.577784\pi$
$647$	−12.3081	−0.483883	−0.241942	+	0.970291i	$0.577784\pi$
$648$	−1.00000	−0.0392837
$649$	−15.9232	−0.625042
$650$	−9.16804	−0.359600
$651$	−2.76335	−0.108304
$652$	19.7130	0.772021
$653$	−19.4383	−0.760678	−0.380339	−	0.924847i	$-0.624193\pi$
$653$	−19.4383	−0.760678	−0.380339	+	0.924847i	$0.624193\pi$
$654$	−0.493136	−0.0192831
$655$	−20.2995	−0.793166
$656$	8.14882	0.318158
$657$	−8.80129	−0.343371
$658$	8.72995	0.340329
$659$	−35.5229	−1.38378	−0.691888	−	0.722005i	$-0.743221\pi$
$659$	−35.5229	−1.38378	−0.691888	+	0.722005i	$0.743221\pi$
$660$	19.3397	0.752798
$661$	−41.9544	−1.63184	−0.815918	−	0.578168i	$-0.803768\pi$
$661$	−41.9544	−1.63184	−0.815918	+	0.578168i	$0.803768\pi$
$662$	−25.8195	−1.00350
$663$	−4.15211	−0.161255
$664$	−16.9311	−0.657055
$665$	−3.38337	−0.131202
$666$	8.71669	0.337765
$667$	0.100043	0.00387369
$668$	−12.8412	−0.496842
$669$	20.1908	0.780620
$670$	−8.15216	−0.314945
$671$	27.4749	1.06066
$672$	−0.773393	−0.0298343
$673$	48.8542	1.88319	0.941596	−	0.336745i	$-0.109326\pi$
$673$	48.8542	1.88319	0.941596	+	0.336745i	$0.109326\pi$
$674$	−19.8224	−0.763532
$675$	−14.1381	−0.544177
$676$	−12.5795	−0.483827
$677$	−24.5972	−0.945349	−0.472674	−	0.881237i	$-0.656711\pi$
$677$	−24.5972	−0.945349	−0.472674	+	0.881237i	$0.656711\pi$
$678$	−17.2506	−0.662505
$679$	−7.10505	−0.272667
$680$	28.0114	1.07419
$681$	−17.1876	−0.658632
$682$	15.7956	0.604844
$683$	32.6023	1.24749	0.623746	−	0.781627i	$-0.285610\pi$
$683$	32.6023	1.24749	0.623746	+	0.781627i	$0.285610\pi$
$684$	−1.00000	−0.0382360
$685$	81.3400	3.10784
$686$	−10.3649	−0.395734
$687$	−19.9182	−0.759925
$688$	8.05514	0.307099
$689$	0.648462	0.0247044
$690$	−1.25808	−0.0478943
$691$	12.1284	0.461385	0.230692	−	0.973027i	$-0.425901\pi$
$691$	12.1284	0.461385	0.230692	+	0.973027i	$0.425901\pi$
$692$	10.3472	0.393341
$693$	−3.41901	−0.129877
$694$	21.0397	0.798656
$695$	88.6059	3.36101
$696$	0.347880	0.0131864
$697$	52.1770	1.97635
$698$	22.1208	0.837284
$699$	−21.1819	−0.801173
$700$	−10.9343	−0.413279
$701$	−0.917740	−0.0346625	−0.0173313	−	0.999850i	$-0.505517\pi$
$701$	−0.917740	−0.0346625	−0.0173313	+	0.999850i	$0.505517\pi$
$702$	0.648462	0.0244746
$703$	8.71669	0.328756
$704$	4.42079	0.166615
$705$	49.3812	1.85980
$706$	35.6025	1.33992
$707$	−12.6016	−0.473932
$708$	3.60190	0.135368
$709$	−13.7581	−0.516696	−0.258348	−	0.966052i	$-0.583178\pi$
$709$	−13.7581	−0.516696	−0.258348	+	0.966052i	$0.583178\pi$
$710$	−6.23327	−0.233931
$711$	−7.81384	−0.293042
$712$	17.7376	0.664747
$713$	−1.02753	−0.0384812
$714$	−4.95205	−0.185326
$715$	−12.5411	−0.469009
$716$	9.63680	0.360144
$717$	1.90069	0.0709825
$718$	−2.14270	−0.0799648
$719$	8.42431	0.314174	0.157087	−	0.987585i	$-0.449790\pi$
$719$	8.42431	0.314174	0.157087	+	0.987585i	$0.449790\pi$
$720$	−4.37472	−0.163036
$721$	6.51230	0.242531
$722$	−1.00000	−0.0372161
$723$	0.815676	0.0303353
$724$	20.7568	0.771420
$725$	4.91838	0.182664
$726$	8.54342	0.317076
$727$	11.6726	0.432911	0.216456	−	0.976292i	$-0.430550\pi$
$727$	11.6726	0.432911	0.216456	+	0.976292i	$0.430550\pi$
$728$	0.501516	0.0185874
$729$	1.00000	0.0370370
$730$	−38.5031	−1.42506
$731$	51.5772	1.90765
$732$	−6.21492	−0.229710
$733$	45.1855	1.66896	0.834482	−	0.551036i	$-0.185767\pi$
$733$	45.1855	1.66896	0.834482	+	0.551036i	$0.185767\pi$
$734$	20.6265	0.761340
$735$	−28.0063	−1.03303
$736$	−0.287580	−0.0106003
$737$	−8.23803	−0.303452
$738$	−8.14882	−0.299962
$739$	29.9073	1.10016	0.550080	−	0.835112i	$-0.314597\pi$
$739$	29.9073	1.10016	0.550080	+	0.835112i	$0.314597\pi$
$740$	38.1330	1.40180
$741$	0.648462	0.0238218
$742$	0.773393	0.0283921
$743$	−26.4670	−0.970978	−0.485489	−	0.874243i	$-0.661358\pi$
$743$	−26.4670	−0.970978	−0.485489	+	0.874243i	$0.661358\pi$
$744$	−3.57302	−0.130993
$745$	−17.2604	−0.632373
$746$	31.0811	1.13796
$747$	16.9311	0.619477
$748$	28.3064	1.03499
$749$	−0.254763	−0.00930884
$750$	−39.9768	−1.45975
$751$	−33.5132	−1.22291	−0.611457	−	0.791277i	$-0.709416\pi$
$751$	−33.5132	−1.22291	−0.611457	+	0.791277i	$0.709416\pi$
$752$	11.2879	0.411626
$753$	24.0194	0.875315
$754$	−0.225587	−0.00821540
$755$	27.4577	0.999286
$756$	0.773393	0.0281280
$757$	−33.1757	−1.20579	−0.602896	−	0.797820i	$-0.705987\pi$
$757$	−33.1757	−1.20579	−0.602896	+	0.797820i	$0.705987\pi$
$758$	−20.7497	−0.753663
$759$	−1.27133	−0.0461464
$760$	−4.37472	−0.158688
$761$	−13.1685	−0.477357	−0.238678	−	0.971099i	$-0.576714\pi$
$761$	−13.1685	−0.477357	−0.238678	+	0.971099i	$0.576714\pi$
$762$	−10.8921	−0.394581
$763$	0.381388	0.0138072
$764$	2.13393	0.0772030
$765$	−28.0114	−1.01275
$766$	−29.8122	−1.07716
$767$	−2.33569	−0.0843369
$768$	−1.00000	−0.0360844
$769$	37.5952	1.35572	0.677860	−	0.735191i	$-0.262908\pi$
$769$	37.5952	1.35572	0.677860	+	0.735191i	$0.262908\pi$
$770$	−14.9572	−0.539020
$771$	−29.0813	−1.04734
$772$	5.01259	0.180407
$773$	15.8778	0.571084	0.285542	−	0.958366i	$-0.407826\pi$
$773$	15.8778	0.571084	0.285542	+	0.958366i	$0.407826\pi$
$774$	−8.05514	−0.289536
$775$	−50.5158	−1.81458
$776$	−9.18686	−0.329789
$777$	−6.74142	−0.241847
$778$	−6.58436	−0.236061
$779$	−8.14882	−0.291962
$780$	2.83684	0.101575
$781$	−6.29893	−0.225393
$782$	−1.84138	−0.0658476
$783$	−0.347880	−0.0124322
$784$	−6.40186	−0.228638
$785$	−42.4968	−1.51677
$786$	4.64018	0.165510
$787$	32.1823	1.14718	0.573588	−	0.819144i	$-0.305551\pi$
$787$	32.1823	1.14718	0.573588	+	0.819144i	$0.305551\pi$
$788$	16.1361	0.574825
$789$	−2.58074	−0.0918768
$790$	−34.1833	−1.21619
$791$	13.3415	0.474369
$792$	−4.42079	−0.157086
$793$	4.03013	0.143114
$794$	−8.13941	−0.288857
$795$	4.37472	0.155155
$796$	13.0215	0.461535
$797$	−4.13282	−0.146392	−0.0731961	−	0.997318i	$-0.523320\pi$
$797$	−4.13282	−0.146392	−0.0731961	+	0.997318i	$0.523320\pi$
$798$	0.773393	0.0273778
$799$	72.2764	2.55696
$800$	−14.1381	−0.499859
$801$	−17.7376	−0.626729
$802$	−13.6896	−0.483397
$803$	−38.9087	−1.37306
$804$	1.86347	0.0657196
$805$	0.972990	0.0342934
$806$	2.31697	0.0816116
$807$	−9.69784	−0.341380
$808$	−16.2939	−0.573219
$809$	−30.8579	−1.08491	−0.542454	−	0.840086i	$-0.682505\pi$
$809$	−30.8579	−1.08491	−0.542454	+	0.840086i	$0.682505\pi$
$810$	4.37472	0.153712
$811$	10.5909	0.371896	0.185948	−	0.982560i	$-0.440464\pi$
$811$	10.5909	0.371896	0.185948	+	0.982560i	$0.440464\pi$
$812$	−0.269048	−0.00944174
$813$	24.3884	0.855339
$814$	38.5347	1.35064
$815$	−86.2388	−3.02081
$816$	−6.40302	−0.224151
$817$	−8.05514	−0.281814
$818$	16.8342	0.588594
$819$	−0.501516	−0.0175244
$820$	−35.6488	−1.24491
$821$	47.3101	1.65114	0.825568	−	0.564303i	$-0.190855\pi$
$821$	47.3101	1.65114	0.825568	+	0.564303i	$0.190855\pi$
$822$	−18.5932	−0.648513
$823$	6.83735	0.238335	0.119168	−	0.992874i	$-0.461977\pi$
$823$	6.83735	0.238335	0.119168	+	0.992874i	$0.461977\pi$
$824$	8.42044	0.293340
$825$	−62.5018	−2.17603
$826$	−2.78568	−0.0969262
$827$	18.7924	0.653474	0.326737	−	0.945115i	$-0.394051\pi$
$827$	18.7924	0.653474	0.326737	+	0.945115i	$0.394051\pi$
$828$	0.287580	0.00999409
$829$	40.4699	1.40558	0.702789	−	0.711398i	$-0.251938\pi$
$829$	40.4699	1.40558	0.702789	+	0.711398i	$0.251938\pi$
$830$	74.0688	2.57097
$831$	10.8414	0.376086
$832$	0.648462	0.0224814
$833$	−40.9913	−1.42026
$834$	−20.2541	−0.701342
$835$	56.1767	1.94407
$836$	−4.42079	−0.152896
$837$	3.57302	0.123502
$838$	−17.1176	−0.591317
$839$	−45.6022	−1.57436	−0.787182	−	0.616721i	$-0.788461\pi$
$839$	−45.6022	−1.57436	−0.787182	+	0.616721i	$0.788461\pi$
$840$	3.38337	0.116737
$841$	−28.8790	−0.995827
$842$	5.89560	0.203176
$843$	9.00314	0.310085
$844$	−4.52168	−0.155643
$845$	55.0317	1.89315
$846$	−11.2879	−0.388085
$847$	−6.60742	−0.227034
$848$	1.00000	0.0343401
$849$	−18.4920	−0.634645
$850$	−90.5268	−3.10504
$851$	−2.50674	−0.0859300
$852$	1.42484	0.0488142
$853$	−32.1482	−1.10073	−0.550367	−	0.834923i	$-0.685512\pi$
$853$	−32.1482	−1.10073	−0.550367	+	0.834923i	$0.685512\pi$
$854$	4.80657	0.164477
$855$	4.37472	0.149612
$856$	−0.329410	−0.0112590
$857$	21.1875	0.723750	0.361875	−	0.932227i	$-0.382137\pi$
$857$	21.1875	0.723750	0.361875	+	0.932227i	$0.382137\pi$
$858$	2.86672	0.0978681
$859$	12.7865	0.436270	0.218135	−	0.975919i	$-0.430003\pi$
$859$	12.7865	0.436270	0.218135	+	0.975919i	$0.430003\pi$
$860$	−35.2389	−1.20164
$861$	6.30223	0.214780
$862$	−1.84910	−0.0629807
$863$	40.3087	1.37213	0.686063	−	0.727542i	$-0.259338\pi$
$863$	40.3087	1.37213	0.686063	+	0.727542i	$0.259338\pi$
$864$	1.00000	0.0340207
$865$	−45.2660	−1.53909
$866$	−18.0909	−0.614754
$867$	−23.9987	−0.815038
$868$	2.76335	0.0937941
$869$	−34.5434	−1.17180
$870$	−1.52188	−0.0515965
$871$	−1.20839	−0.0409447
$872$	0.493136	0.0166997
$873$	9.18686	0.310928
$874$	0.287580	0.00972753
$875$	30.9177	1.04521
$876$	8.80129	0.297368
$877$	38.1296	1.28754	0.643772	−	0.765217i	$-0.277369\pi$
$877$	38.1296	1.28754	0.643772	+	0.765217i	$0.277369\pi$
$878$	8.56484	0.289049
$879$	−6.56376	−0.221390
$880$	−19.3397	−0.651942
$881$	−4.82124	−0.162432	−0.0812159	−	0.996697i	$-0.525880\pi$
$881$	−4.82124	−0.162432	−0.0812159	+	0.996697i	$0.525880\pi$
$882$	6.40186	0.215562
$883$	−10.2507	−0.344964	−0.172482	−	0.985013i	$-0.555179\pi$
$883$	−10.2507	−0.344964	−0.172482	+	0.985013i	$0.555179\pi$
$884$	4.15211	0.139651
$885$	−15.7573	−0.529675
$886$	−28.8514	−0.969281
$887$	23.8066	0.799346	0.399673	−	0.916658i	$-0.369124\pi$
$887$	23.8066	0.799346	0.399673	+	0.916658i	$0.369124\pi$
$888$	−8.71669	−0.292513
$889$	8.42390	0.282529
$890$	−77.5972	−2.60106
$891$	4.42079	0.148102
$892$	−20.1908	−0.676037
$893$	−11.2879	−0.377734
$894$	3.94550	0.131957
$895$	−42.1583	−1.40920
$896$	0.773393	0.0258372
$897$	−0.186484	−0.00622653
$898$	11.8345	0.394923
$899$	−1.24298	−0.0414558
$900$	14.1381	0.471271
$901$	6.40302	0.213316
$902$	−36.0242	−1.19948
$903$	6.22979	0.207314
$904$	17.2506	0.573746
$905$	−90.8051	−3.01846
$906$	−6.27644	−0.208521
$907$	51.8686	1.72227	0.861134	−	0.508378i	$-0.169755\pi$
$907$	51.8686	1.72227	0.861134	+	0.508378i	$0.169755\pi$
$908$	17.1876	0.570392
$909$	16.2939	0.540436
$910$	−2.19399	−0.0727300
$911$	21.0121	0.696162	0.348081	−	0.937464i	$-0.386833\pi$
$911$	21.0121	0.696162	0.348081	+	0.937464i	$0.386833\pi$
$912$	1.00000	0.0331133
$913$	74.8490	2.47714
$914$	−6.35020	−0.210046
$915$	27.1885	0.898824
$916$	19.9182	0.658114
$917$	−3.58868	−0.118509
$918$	6.40302	0.211331
$919$	29.2886	0.966142	0.483071	−	0.875581i	$-0.339521\pi$
$919$	29.2886	0.966142	0.483071	+	0.875581i	$0.339521\pi$
$920$	1.25808	0.0414777
$921$	−19.0958	−0.629229
$922$	−9.51641	−0.313406
$923$	−0.923954	−0.0304123
$924$	3.41901	0.112477
$925$	−123.238	−4.05203
$926$	26.8266	0.881578
$927$	−8.42044	−0.276563
$928$	−0.347880	−0.0114197
$929$	28.6935	0.941404	0.470702	−	0.882292i	$-0.344001\pi$
$929$	28.6935	0.941404	0.470702	+	0.882292i	$0.344001\pi$
$930$	15.6309	0.512559
$931$	6.40186	0.209813
$932$	21.1819	0.693836
$933$	−22.8539	−0.748204
$934$	9.63770	0.315355
$935$	−123.833	−4.04976
$936$	−0.648462	−0.0211956
$937$	15.0827	0.492730	0.246365	−	0.969177i	$-0.420764\pi$
$937$	15.0827	0.492730	0.246365	+	0.969177i	$0.420764\pi$
$938$	−1.44120	−0.0470567
$939$	−28.4846	−0.929560
$940$	−49.3812	−1.61064
$941$	−8.37048	−0.272870	−0.136435	−	0.990649i	$-0.543564\pi$
$941$	−8.37048	−0.272870	−0.136435	+	0.990649i	$0.543564\pi$
$942$	9.71418	0.316505
$943$	2.34343	0.0763127
$944$	−3.60190	−0.117232
$945$	−3.38337	−0.110061
$946$	−35.6101	−1.15778
$947$	20.9380	0.680394	0.340197	−	0.940354i	$-0.389506\pi$
$947$	20.9380	0.680394	0.340197	+	0.940354i	$0.389506\pi$
$948$	7.81384	0.253782
$949$	−5.70730	−0.185267
$950$	14.1381	0.458702
$951$	−20.1541	−0.653541
$952$	4.95205	0.160497
$953$	8.10083	0.262412	0.131206	−	0.991355i	$-0.458115\pi$
$953$	8.10083	0.262412	0.131206	+	0.991355i	$0.458115\pi$
$954$	−1.00000	−0.0323762
$955$	−9.33535	−0.302085
$956$	−1.90069	−0.0614727
$957$	−1.53791	−0.0497135
$958$	20.1735	0.651776
$959$	14.3799	0.464350
$960$	4.37472	0.141193
$961$	−18.2335	−0.588179
$962$	5.65244	0.182242
$963$	0.329410	0.0106151
$964$	−0.815676	−0.0262712
$965$	−21.9286	−0.705908
$966$	−0.222412	−0.00715599
$967$	−14.2848	−0.459370	−0.229685	−	0.973265i	$-0.573770\pi$
$967$	−14.2848	−0.459370	−0.229685	+	0.973265i	$0.573770\pi$
$968$	−8.54342	−0.274596
$969$	6.40302	0.205695
$970$	40.1899	1.29042
$971$	38.9676	1.25053	0.625266	−	0.780412i	$-0.284991\pi$
$971$	38.9676	1.25053	0.625266	+	0.780412i	$0.284991\pi$
$972$	−1.00000	−0.0320750
$973$	15.6644	0.502176
$974$	3.00738	0.0963626
$975$	−9.16804	−0.293612
$976$	6.21492	0.198935
$977$	−44.3004	−1.41729	−0.708647	−	0.705563i	$-0.750694\pi$
$977$	−44.3004	−1.41729	−0.708647	+	0.705563i	$0.750694\pi$
$978$	19.7130	0.630352
$979$	−78.4145	−2.50614
$980$	28.0063	0.894630
$981$	−0.493136	−0.0157446
$982$	18.0303	0.575369
$983$	51.2218	1.63372	0.816861	−	0.576834i	$-0.195712\pi$
$983$	51.2218	1.63372	0.816861	+	0.576834i	$0.195712\pi$
$984$	8.14882	0.259775
$985$	−70.5909	−2.24921
$986$	−2.22749	−0.0709376
$987$	8.72995	0.277877
$988$	−0.648462	−0.0206303
$989$	2.31650	0.0736603
$990$	19.3397	0.614657
$991$	43.4662	1.38075	0.690375	−	0.723452i	$-0.257446\pi$
$991$	43.4662	1.38075	0.690375	+	0.723452i	$0.257446\pi$
$992$	3.57302	0.113443
$993$	−25.8195	−0.819357
$994$	−1.10196	−0.0349521
$995$	−56.9653	−1.80592
$996$	−16.9311	−0.536483
$997$	29.5124	0.934668	0.467334	−	0.884081i	$-0.345215\pi$
$997$	29.5124	0.934668	0.467334	+	0.884081i	$0.345215\pi$
$998$	−22.9499	−0.726466
$999$	8.71669	0.275784

Twists

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

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
6042.2.a.z.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)

\(f(q)\)	\(=\)	\(q-1.00000 q^{2} -1.00000 q^{3} +1.00000 q^{4} -4.37472 q^{5} +1.00000 q^{6} -0.773393 q^{7} -1.00000 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q-1.00000 q^{2} -1.00000 q^{3} +1.00000 q^{4} -4.37472 q^{5} +1.00000 q^{6} -0.773393 q^{7} -1.00000 q^{8} +1.00000 q^{9} +4.37472 q^{10} +4.42079 q^{11} -1.00000 q^{12} +0.648462 q^{13} +0.773393 q^{14} +4.37472 q^{15} +1.00000 q^{16} +6.40302 q^{17} -1.00000 q^{18} -1.00000 q^{19} -4.37472 q^{20} +0.773393 q^{21} -4.42079 q^{22} +0.287580 q^{23} +1.00000 q^{24} +14.1381 q^{25} -0.648462 q^{26} -1.00000 q^{27} -0.773393 q^{28} +0.347880 q^{29} -4.37472 q^{30} -3.57302 q^{31} -1.00000 q^{32} -4.42079 q^{33} -6.40302 q^{34} +3.38337 q^{35} +1.00000 q^{36} -8.71669 q^{37} +1.00000 q^{38} -0.648462 q^{39} +4.37472 q^{40} +8.14882 q^{41} -0.773393 q^{42} +8.05514 q^{43} +4.42079 q^{44} -4.37472 q^{45} -0.287580 q^{46} +11.2879 q^{47} -1.00000 q^{48} -6.40186 q^{49} -14.1381 q^{50} -6.40302 q^{51} +0.648462 q^{52} +1.00000 q^{53} +1.00000 q^{54} -19.3397 q^{55} +0.773393 q^{56} +1.00000 q^{57} -0.347880 q^{58} -3.60190 q^{59} +4.37472 q^{60} +6.21492 q^{61} +3.57302 q^{62} -0.773393 q^{63} +1.00000 q^{64} -2.83684 q^{65} +4.42079 q^{66} -1.86347 q^{67} +6.40302 q^{68} -0.287580 q^{69} -3.38337 q^{70} -1.42484 q^{71} -1.00000 q^{72} -8.80129 q^{73} +8.71669 q^{74} -14.1381 q^{75} -1.00000 q^{76} -3.41901 q^{77} +0.648462 q^{78} -7.81384 q^{79} -4.37472 q^{80} +1.00000 q^{81} -8.14882 q^{82} +16.9311 q^{83} +0.773393 q^{84} -28.0114 q^{85} -8.05514 q^{86} -0.347880 q^{87} -4.42079 q^{88} -17.7376 q^{89} +4.37472 q^{90} -0.501516 q^{91} +0.287580 q^{92} +3.57302 q^{93} -11.2879 q^{94} +4.37472 q^{95} +1.00000 q^{96} +9.18686 q^{97} +6.40186 q^{98} +4.42079 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 9 q - 9 q^{2} - 9 q^{3} + 9 q^{4} - q^{5} + 9 q^{6} + 4 q^{7} - 9 q^{8} + 9 q^{9}+O(q^{10}) \) 9 * q - 9 * q^2 - 9 * q^3 + 9 * q^4 - q^5 + 9 * q^6 + 4 * q^7 - 9 * q^8 + 9 * q^9	\( 9 q - 9 q^{2} - 9 q^{3} + 9 q^{4} - q^{5} + 9 q^{6} + 4 q^{7} - 9 q^{8} + 9 q^{9} + q^{10} + 12 q^{11} - 9 q^{12} - q^{13} - 4 q^{14} + q^{15} + 9 q^{16} + 12 q^{17} - 9 q^{18} - 9 q^{19} - q^{20} - 4 q^{21} - 12 q^{22} + 11 q^{23} + 9 q^{24} + 10 q^{25} + q^{26} - 9 q^{27} + 4 q^{28} + 7 q^{29} - q^{30} - 12 q^{31} - 9 q^{32} - 12 q^{33} - 12 q^{34} + 15 q^{35} + 9 q^{36} - 9 q^{37} + 9 q^{38} + q^{39} + q^{40} - 4 q^{41} + 4 q^{42} + 23 q^{43} + 12 q^{44} - q^{45} - 11 q^{46} + 35 q^{47} - 9 q^{48} + 3 q^{49} - 10 q^{50} - 12 q^{51} - q^{52} + 9 q^{53} + 9 q^{54} + 3 q^{55} - 4 q^{56} + 9 q^{57} - 7 q^{58} + 14 q^{59} + q^{60} + 14 q^{61} + 12 q^{62} + 4 q^{63} + 9 q^{64} + 13 q^{65} + 12 q^{66} - 10 q^{67} + 12 q^{68} - 11 q^{69} - 15 q^{70} + 4 q^{71} - 9 q^{72} - 5 q^{73} + 9 q^{74} - 10 q^{75} - 9 q^{76} + 17 q^{77} - q^{78} - 14 q^{79} - q^{80} + 9 q^{81} + 4 q^{82} + 37 q^{83} - 4 q^{84} - 31 q^{85} - 23 q^{86} - 7 q^{87} - 12 q^{88} - 20 q^{89} + q^{90} - 12 q^{91} + 11 q^{92} + 12 q^{93} - 35 q^{94} + q^{95} + 9 q^{96} - 2 q^{97} - 3 q^{98} + 12 q^{99}+O(q^{100}) \) 9 * q - 9 * q^2 - 9 * q^3 + 9 * q^4 - q^5 + 9 * q^6 + 4 * q^7 - 9 * q^8 + 9 * q^9 + q^10 + 12 * q^11 - 9 * q^12 - q^13 - 4 * q^14 + q^15 + 9 * q^16 + 12 * q^17 - 9 * q^18 - 9 * q^19 - q^20 - 4 * q^21 - 12 * q^22 + 11 * q^23 + 9 * q^24 + 10 * q^25 + q^26 - 9 * q^27 + 4 * q^28 + 7 * q^29 - q^30 - 12 * q^31 - 9 * q^32 - 12 * q^33 - 12 * q^34 + 15 * q^35 + 9 * q^36 - 9 * q^37 + 9 * q^38 + q^39 + q^40 - 4 * q^41 + 4 * q^42 + 23 * q^43 + 12 * q^44 - q^45 - 11 * q^46 + 35 * q^47 - 9 * q^48 + 3 * q^49 - 10 * q^50 - 12 * q^51 - q^52 + 9 * q^53 + 9 * q^54 + 3 * q^55 - 4 * q^56 + 9 * q^57 - 7 * q^58 + 14 * q^59 + q^60 + 14 * q^61 + 12 * q^62 + 4 * q^63 + 9 * q^64 + 13 * q^65 + 12 * q^66 - 10 * q^67 + 12 * q^68 - 11 * q^69 - 15 * q^70 + 4 * q^71 - 9 * q^72 - 5 * q^73 + 9 * q^74 - 10 * q^75 - 9 * q^76 + 17 * q^77 - q^78 - 14 * q^79 - q^80 + 9 * q^81 + 4 * q^82 + 37 * q^83 - 4 * q^84 - 31 * q^85 - 23 * q^86 - 7 * q^87 - 12 * q^88 - 20 * q^89 + q^90 - 12 * q^91 + 11 * q^92 + 12 * q^93 - 35 * q^94 + q^95 + 9 * q^96 - 2 * q^97 - 3 * q^98 + 12 * q^99

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