LMFDB - Embedded newform 6042.2.a.bf.1.8

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:	$12$
Coefficient field:	$\mathbb{Q}[x]/(x^{12} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{12} - 5 x^{11} - 27 x^{10} + 134 x^{9} + 294 x^{8} - 1313 x^{7} - 1685 x^{6} + 5910 x^{5} + \cdots + 4048 $ x^12 - 5x^11 - 27x^10 + 134x^9 + 294x^8 - 1313x^7 - 1685x^6 + 5910x^5 + 5237x^4 - 12206x^3 - 7876x^2 + 9264*x + 4048
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			1.8
Root			$1.70127$ of defining polynomial
Character	$\chi$	$=$	6042.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.00000 q^{2} +1.00000 q^{3} +1.00000 q^{4} +0.701272 q^{5} -1.00000 q^{6} +5.18729 q^{7} -1.00000 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q-1.00000 q^{2} +1.00000 q^{3} +1.00000 q^{4} +0.701272 q^{5} -1.00000 q^{6} +5.18729 q^{7} -1.00000 q^{8} +1.00000 q^{9} -0.701272 q^{10} +1.24662 q^{11} +1.00000 q^{12} +6.30123 q^{13} -5.18729 q^{14} +0.701272 q^{15} +1.00000 q^{16} -3.07769 q^{17} -1.00000 q^{18} +1.00000 q^{19} +0.701272 q^{20} +5.18729 q^{21} -1.24662 q^{22} -4.62675 q^{23} -1.00000 q^{24} -4.50822 q^{25} -6.30123 q^{26} +1.00000 q^{27} +5.18729 q^{28} +5.88814 q^{29} -0.701272 q^{30} -4.72744 q^{31} -1.00000 q^{32} +1.24662 q^{33} +3.07769 q^{34} +3.63770 q^{35} +1.00000 q^{36} -3.54295 q^{37} -1.00000 q^{38} +6.30123 q^{39} -0.701272 q^{40} -3.03959 q^{41} -5.18729 q^{42} +6.62675 q^{43} +1.24662 q^{44} +0.701272 q^{45} +4.62675 q^{46} +7.00081 q^{47} +1.00000 q^{48} +19.9080 q^{49} +4.50822 q^{50} -3.07769 q^{51} +6.30123 q^{52} +1.00000 q^{53} -1.00000 q^{54} +0.874218 q^{55} -5.18729 q^{56} +1.00000 q^{57} -5.88814 q^{58} +1.31166 q^{59} +0.701272 q^{60} +4.84496 q^{61} +4.72744 q^{62} +5.18729 q^{63} +1.00000 q^{64} +4.41887 q^{65} -1.24662 q^{66} -2.94658 q^{67} -3.07769 q^{68} -4.62675 q^{69} -3.63770 q^{70} +2.79745 q^{71} -1.00000 q^{72} +12.9071 q^{73} +3.54295 q^{74} -4.50822 q^{75} +1.00000 q^{76} +6.46657 q^{77} -6.30123 q^{78} +13.4739 q^{79} +0.701272 q^{80} +1.00000 q^{81} +3.03959 q^{82} -15.4069 q^{83} +5.18729 q^{84} -2.15829 q^{85} -6.62675 q^{86} +5.88814 q^{87} -1.24662 q^{88} -5.69340 q^{89} -0.701272 q^{90} +32.6863 q^{91} -4.62675 q^{92} -4.72744 q^{93} -7.00081 q^{94} +0.701272 q^{95} -1.00000 q^{96} -18.6821 q^{97} -19.9080 q^{98} +1.24662 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q - 12 q^{2} + 12 q^{3} + 12 q^{4} - 7 q^{5} - 12 q^{6} + 5 q^{7} - 12 q^{8} + 12 q^{9}+O(q^{10}) $ 12 * q - 12 * q^2 + 12 * q^3 + 12 * q^4 - 7 * q^5 - 12 * q^6 + 5 * q^7 - 12 * q^8 + 12 * q^9	\( 12 q - 12 q^{2} + 12 q^{3} + 12 q^{4} - 7 q^{5} - 12 q^{6} + 5 q^{7} - 12 q^{8} + 12 q^{9} + 7 q^{10} - 5 q^{11} + 12 q^{12} + 10 q^{13} - 5 q^{14} - 7 q^{15} + 12 q^{16} + 6 q^{17} - 12 q^{18} + 12 q^{19} - 7 q^{20} + 5 q^{21} + 5 q^{22} - 12 q^{24} + 21 q^{25} - 10 q^{26} + 12 q^{27} + 5 q^{28} + 7 q^{30} + 2 q^{31} - 12 q^{32} - 5 q^{33} - 6 q^{34} - 17 q^{35} + 12 q^{36} + 16 q^{37} - 12 q^{38} + 10 q^{39} + 7 q^{40} + 7 q^{41} - 5 q^{42} + 24 q^{43} - 5 q^{44} - 7 q^{45} + 4 q^{47} + 12 q^{48} + 29 q^{49} - 21 q^{50} + 6 q^{51} + 10 q^{52} + 12 q^{53} - 12 q^{54} - 2 q^{55} - 5 q^{56} + 12 q^{57} + 2 q^{59} - 7 q^{60} + 29 q^{61} - 2 q^{62} + 5 q^{63} + 12 q^{64} - 17 q^{65} + 5 q^{66} + 36 q^{67} + 6 q^{68} + 17 q^{70} - 3 q^{71} - 12 q^{72} + 7 q^{73} - 16 q^{74} + 21 q^{75} + 12 q^{76} - 35 q^{77} - 10 q^{78} + 40 q^{79} - 7 q^{80} + 12 q^{81} - 7 q^{82} + 24 q^{83} + 5 q^{84} - 22 q^{85} - 24 q^{86} + 5 q^{88} - 45 q^{89} + 7 q^{90} + 71 q^{91} + 2 q^{93} - 4 q^{94} - 7 q^{95} - 12 q^{96} + q^{97} - 29 q^{98} - 5 q^{99}+O(q^{100}) \) 12 * q - 12 * q^2 + 12 * q^3 + 12 * q^4 - 7 * q^5 - 12 * q^6 + 5 * q^7 - 12 * q^8 + 12 * q^9 + 7 * q^10 - 5 * q^11 + 12 * q^12 + 10 * q^13 - 5 * q^14 - 7 * q^15 + 12 * q^16 + 6 * q^17 - 12 * q^18 + 12 * q^19 - 7 * q^20 + 5 * q^21 + 5 * q^22 - 12 * q^24 + 21 * q^25 - 10 * q^26 + 12 * q^27 + 5 * q^28 + 7 * q^30 + 2 * q^31 - 12 * q^32 - 5 * q^33 - 6 * q^34 - 17 * q^35 + 12 * q^36 + 16 * q^37 - 12 * q^38 + 10 * q^39 + 7 * q^40 + 7 * q^41 - 5 * q^42 + 24 * q^43 - 5 * q^44 - 7 * q^45 + 4 * q^47 + 12 * q^48 + 29 * q^49 - 21 * q^50 + 6 * q^51 + 10 * q^52 + 12 * q^53 - 12 * q^54 - 2 * q^55 - 5 * q^56 + 12 * q^57 + 2 * q^59 - 7 * q^60 + 29 * q^61 - 2 * q^62 + 5 * q^63 + 12 * q^64 - 17 * q^65 + 5 * q^66 + 36 * q^67 + 6 * q^68 + 17 * q^70 - 3 * q^71 - 12 * q^72 + 7 * q^73 - 16 * q^74 + 21 * q^75 + 12 * q^76 - 35 * q^77 - 10 * q^78 + 40 * q^79 - 7 * q^80 + 12 * q^81 - 7 * q^82 + 24 * q^83 + 5 * q^84 - 22 * q^85 - 24 * q^86 + 5 * q^88 - 45 * q^89 + 7 * q^90 + 71 * q^91 + 2 * q^93 - 4 * q^94 - 7 * q^95 - 12 * q^96 + q^97 - 29 * q^98 - 5 * q^99

Display 100 coefficients 10 coefficients

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$	$a_n / n^{(k-1)/2}$	$ \alpha_n $			$ \theta_n $
$p$	$a_p$	$a_p / p^{(k-1)/2}$	$ \alpha_p$			$ \theta_p $

$2$	−1.00000	−0.707107
$2$	−1.00000	−0.707107
$3$	1.00000	0.577350
$3$	1.00000	0.577350
$4$	1.00000	0.500000
$5$	0.701272	0.313618	0.156809	−	0.987629i	$-0.449879\pi$
$5$	0.701272	0.313618	0.156809	+	0.987629i	$0.449879\pi$
$6$	−1.00000	−0.408248
$7$	5.18729	1.96061	0.980306	−	0.197483i	$-0.0632768\pi$
$7$	5.18729	1.96061	0.980306	+	0.197483i	$0.0632768\pi$
$8$	−1.00000	−0.353553
$9$	1.00000	0.333333
$10$	−0.701272	−0.221762
$11$	1.24662	0.375870	0.187935	−	0.982182i	$-0.439821\pi$
$11$	1.24662	0.375870	0.187935	+	0.982182i	$0.439821\pi$
$12$	1.00000	0.288675
$13$	6.30123	1.74765	0.873823	−	0.486245i	$-0.161634\pi$
$13$	6.30123	1.74765	0.873823	+	0.486245i	$0.161634\pi$
$14$	−5.18729	−1.38636
$15$	0.701272	0.181068
$16$	1.00000	0.250000
$17$	−3.07769	−0.746448	−0.373224	−	0.927741i	$-0.621748\pi$
$17$	−3.07769	−0.746448	−0.373224	+	0.927741i	$0.621748\pi$
$18$	−1.00000	−0.235702
$19$	1.00000	0.229416
$19$	1.00000	0.229416
$20$	0.701272	0.156809
$21$	5.18729	1.13196
$22$	−1.24662	−0.265780
$23$	−4.62675	−0.964744	−0.482372	−	0.875966i	$-0.660225\pi$
$23$	−4.62675	−0.964744	−0.482372	+	0.875966i	$0.660225\pi$
$24$	−1.00000	−0.204124
$25$	−4.50822	−0.901644
$26$	−6.30123	−1.23577
$27$	1.00000	0.192450
$28$	5.18729	0.980306
$29$	5.88814	1.09340	0.546700	−	0.837328i	$-0.315884\pi$
$29$	5.88814	1.09340	0.546700	+	0.837328i	$0.315884\pi$
$30$	−0.701272	−0.128034
$31$	−4.72744	−0.849073	−0.424537	−	0.905411i	$-0.639563\pi$
$31$	−4.72744	−0.849073	−0.424537	+	0.905411i	$0.639563\pi$
$32$	−1.00000	−0.176777
$33$	1.24662	0.217008
$34$	3.07769	0.527819
$35$	3.63770	0.614884
$36$	1.00000	0.166667
$37$	−3.54295	−0.582458	−0.291229	−	0.956653i	$-0.594064\pi$
$37$	−3.54295	−0.582458	−0.291229	+	0.956653i	$0.594064\pi$
$38$	−1.00000	−0.162221
$39$	6.30123	1.00900
$40$	−0.701272	−0.110881
$41$	−3.03959	−0.474705	−0.237352	−	0.971424i	$-0.576280\pi$
$41$	−3.03959	−0.474705	−0.237352	+	0.971424i	$0.576280\pi$
$42$	−5.18729	−0.800417
$43$	6.62675	1.01057	0.505285	−	0.862952i	$-0.331387\pi$
$43$	6.62675	1.01057	0.505285	+	0.862952i	$0.331387\pi$
$44$	1.24662	0.187935
$45$	0.701272	0.104539
$46$	4.62675	0.682177
$47$	7.00081	1.02117	0.510587	−	0.859826i	$-0.329428\pi$
$47$	7.00081	1.02117	0.510587	+	0.859826i	$0.329428\pi$
$48$	1.00000	0.144338
$49$	19.9080	2.84400
$50$	4.50822	0.637558
$51$	−3.07769	−0.430962
$52$	6.30123	0.873823
$53$	1.00000	0.137361
$53$	1.00000	0.137361
$54$	−1.00000	−0.136083
$55$	0.874218	0.117880
$56$	−5.18729	−0.693181
$57$	1.00000	0.132453
$58$	−5.88814	−0.773151
$59$	1.31166	0.170764	0.0853819	−	0.996348i	$-0.472789\pi$
$59$	1.31166	0.170764	0.0853819	+	0.996348i	$0.472789\pi$
$60$	0.701272	0.0905338
$61$	4.84496	0.620334	0.310167	−	0.950682i	$-0.399615\pi$
$61$	4.84496	0.620334	0.310167	+	0.950682i	$0.399615\pi$
$62$	4.72744	0.600385
$63$	5.18729	0.653538
$64$	1.00000	0.125000
$65$	4.41887	0.548093
$66$	−1.24662	−0.153448
$67$	−2.94658	−0.359983	−0.179991	−	0.983668i	$-0.557607\pi$
$67$	−2.94658	−0.359983	−0.179991	+	0.983668i	$0.557607\pi$
$68$	−3.07769	−0.373224
$69$	−4.62675	−0.556995
$70$	−3.63770	−0.434788
$71$	2.79745	0.331996	0.165998	−	0.986126i	$-0.446915\pi$
$71$	2.79745	0.331996	0.165998	+	0.986126i	$0.446915\pi$
$72$	−1.00000	−0.117851
$73$	12.9071	1.51066	0.755331	−	0.655344i	$-0.227476\pi$
$73$	12.9071	1.51066	0.755331	+	0.655344i	$0.227476\pi$
$74$	3.54295	0.411860
$75$	−4.50822	−0.520564
$76$	1.00000	0.114708
$77$	6.46657	0.736935
$78$	−6.30123	−0.713473
$79$	13.4739	1.51594	0.757968	−	0.652291i	$-0.226192\pi$
$79$	13.4739	1.51594	0.757968	+	0.652291i	$0.226192\pi$
$80$	0.701272	0.0784045
$81$	1.00000	0.111111
$82$	3.03959	0.335667
$83$	−15.4069	−1.69112	−0.845561	−	0.533879i	$-0.820734\pi$
$83$	−15.4069	−1.69112	−0.845561	+	0.533879i	$0.820734\pi$
$84$	5.18729	0.565980
$85$	−2.15829	−0.234100
$86$	−6.62675	−0.714581
$87$	5.88814	0.631275
$88$	−1.24662	−0.132890
$89$	−5.69340	−0.603499	−0.301750	−	0.953387i	$-0.597571\pi$
$89$	−5.69340	−0.603499	−0.301750	+	0.953387i	$0.597571\pi$
$90$	−0.701272	−0.0739205
$91$	32.6863	3.42646
$92$	−4.62675	−0.482372
$93$	−4.72744	−0.490213
$94$	−7.00081	−0.722079
$95$	0.701272	0.0719489
$96$	−1.00000	−0.102062
$97$	−18.6821	−1.89688	−0.948442	−	0.316950i	$-0.897341\pi$
$97$	−18.6821	−1.89688	−0.948442	+	0.316950i	$0.897341\pi$
$98$	−19.9080	−2.01101
$99$	1.24662	0.125290
$100$	−4.50822	−0.450822
$101$	−16.4976	−1.64157	−0.820786	−	0.571235i	$-0.806464\pi$
$101$	−16.4976	−1.64157	−0.820786	+	0.571235i	$0.806464\pi$
$102$	3.07769	0.304736
$103$	15.1782	1.49555	0.747777	−	0.663949i	$-0.231121\pi$
$103$	15.1782	1.49555	0.747777	+	0.663949i	$0.231121\pi$
$104$	−6.30123	−0.617886
$105$	3.63770	0.355003
$106$	−1.00000	−0.0971286
$107$	5.95866	0.576045	0.288023	−	0.957624i	$-0.407002\pi$
$107$	5.95866	0.576045	0.288023	+	0.957624i	$0.407002\pi$
$108$	1.00000	0.0962250
$109$	4.94374	0.473524	0.236762	−	0.971568i	$-0.423914\pi$
$109$	4.94374	0.473524	0.236762	+	0.971568i	$0.423914\pi$
$110$	−0.874218	−0.0833534
$111$	−3.54295	−0.336282
$112$	5.18729	0.490153
$113$	10.7315	1.00953	0.504766	−	0.863256i	$-0.331579\pi$
$113$	10.7315	1.00953	0.504766	+	0.863256i	$0.331579\pi$
$114$	−1.00000	−0.0936586
$115$	−3.24461	−0.302561
$116$	5.88814	0.546700
$117$	6.30123	0.582548
$118$	−1.31166	−0.120748
$119$	−15.9649	−1.46350
$120$	−0.701272	−0.0640170
$121$	−9.44594	−0.858722
$122$	−4.84496	−0.438642
$123$	−3.03959	−0.274071
$124$	−4.72744	−0.424537
$125$	−6.66784	−0.596390
$126$	−5.18729	−0.462121
$127$	−0.0537738	−0.00477165	−0.00238582	−	0.999997i	$-0.500759\pi$
$127$	−0.0537738	−0.00477165	−0.00238582	+	0.999997i	$0.500759\pi$
$128$	−1.00000	−0.0883883
$129$	6.62675	0.583453
$130$	−4.41887	−0.387561
$131$	−14.0769	−1.22990	−0.614951	−	0.788566i	$-0.710824\pi$
$131$	−14.0769	−1.22990	−0.614951	+	0.788566i	$0.710824\pi$
$132$	1.24662	0.108504
$133$	5.18729	0.449795
$134$	2.94658	0.254546
$135$	0.701272	0.0603558
$136$	3.07769	0.263909
$137$	5.67522	0.484867	0.242434	−	0.970168i	$-0.422054\pi$
$137$	5.67522	0.484867	0.242434	+	0.970168i	$0.422054\pi$
$138$	4.62675	0.393855
$139$	−4.65908	−0.395178	−0.197589	−	0.980285i	$-0.563311\pi$
$139$	−4.65908	−0.395178	−0.197589	+	0.980285i	$0.563311\pi$
$140$	3.63770	0.307442
$141$	7.00081	0.589575
$142$	−2.79745	−0.234757
$143$	7.85522	0.656887
$144$	1.00000	0.0833333
$145$	4.12919	0.342910
$146$	−12.9071	−1.06820
$147$	19.9080	1.64199
$148$	−3.54295	−0.291229
$149$	−0.621309	−0.0508996	−0.0254498	−	0.999676i	$-0.508102\pi$
$149$	−0.621309	−0.0508996	−0.0254498	+	0.999676i	$0.508102\pi$
$150$	4.50822	0.368094
$151$	−21.9318	−1.78479	−0.892393	−	0.451259i	$-0.850975\pi$
$151$	−21.9318	−1.78479	−0.892393	+	0.451259i	$0.850975\pi$
$152$	−1.00000	−0.0811107
$153$	−3.07769	−0.248816
$154$	−6.46657	−0.521091
$155$	−3.31522	−0.266285
$156$	6.30123	0.504502
$157$	12.0131	0.958749	0.479374	−	0.877611i	$-0.340864\pi$
$157$	12.0131	0.958749	0.479374	+	0.877611i	$0.340864\pi$
$158$	−13.4739	−1.07193
$159$	1.00000	0.0793052
$160$	−0.701272	−0.0554404
$161$	−24.0003	−1.89149
$162$	−1.00000	−0.0785674
$163$	−19.1031	−1.49627	−0.748135	−	0.663547i	$-0.769050\pi$
$163$	−19.1031	−1.49627	−0.748135	+	0.663547i	$0.769050\pi$
$164$	−3.03959	−0.237352
$165$	0.874218	0.0680578
$166$	15.4069	1.19580
$167$	18.0988	1.40053	0.700263	−	0.713885i	$-0.253066\pi$
$167$	18.0988	1.40053	0.700263	+	0.713885i	$0.253066\pi$
$168$	−5.18729	−0.400208
$169$	26.7054	2.05426
$170$	2.15829	0.165534
$171$	1.00000	0.0764719
$172$	6.62675	0.505285
$173$	7.14565	0.543274	0.271637	−	0.962400i	$-0.412435\pi$
$173$	7.14565	0.543274	0.271637	+	0.962400i	$0.412435\pi$
$174$	−5.88814	−0.446379
$175$	−23.3855	−1.76777
$176$	1.24662	0.0939674
$177$	1.31166	0.0985905
$178$	5.69340	0.426738
$179$	3.35208	0.250546	0.125273	−	0.992122i	$-0.460019\pi$
$179$	3.35208	0.250546	0.125273	+	0.992122i	$0.460019\pi$
$180$	0.701272	0.0522697
$181$	−7.75521	−0.576440	−0.288220	−	0.957564i	$-0.593064\pi$
$181$	−7.75521	−0.576440	−0.288220	+	0.957564i	$0.593064\pi$
$182$	−32.6863	−2.42287
$183$	4.84496	0.358150
$184$	4.62675	0.341089
$185$	−2.48457	−0.182669
$186$	4.72744	0.346633
$187$	−3.83670	−0.280567
$188$	7.00081	0.510587
$189$	5.18729	0.377320
$190$	−0.701272	−0.0508756
$191$	9.85024	0.712738	0.356369	−	0.934345i	$-0.384015\pi$
$191$	9.85024	0.712738	0.356369	+	0.934345i	$0.384015\pi$
$192$	1.00000	0.0721688
$193$	−18.8273	−1.35522	−0.677611	−	0.735421i	$-0.736985\pi$
$193$	−18.8273	−1.35522	−0.677611	+	0.735421i	$0.736985\pi$
$194$	18.6821	1.34130
$195$	4.41887	0.316442
$196$	19.9080	1.42200
$197$	−1.21702	−0.0867091	−0.0433546	−	0.999060i	$-0.513805\pi$
$197$	−1.21702	−0.0867091	−0.0433546	+	0.999060i	$0.513805\pi$
$198$	−1.24662	−0.0885933
$199$	−3.76777	−0.267090	−0.133545	−	0.991043i	$-0.542636\pi$
$199$	−3.76777	−0.267090	−0.133545	+	0.991043i	$0.542636\pi$
$200$	4.50822	0.318779
$201$	−2.94658	−0.207836
$202$	16.4976	1.16077
$203$	30.5435	2.14373
$204$	−3.07769	−0.215481
$205$	−2.13158	−0.148876
$206$	−15.1782	−1.05752
$207$	−4.62675	−0.321581
$208$	6.30123	0.436911
$209$	1.24662	0.0862304
$210$	−3.63770	−0.251025
$211$	0.115274	0.00793579	0.00396790	−	0.999992i	$-0.498737\pi$
$211$	0.115274	0.00793579	0.00396790	+	0.999992i	$0.498737\pi$
$212$	1.00000	0.0686803
$213$	2.79745	0.191678
$214$	−5.95866	−0.407326
$215$	4.64715	0.316933
$216$	−1.00000	−0.0680414
$217$	−24.5226	−1.66470
$218$	−4.94374	−0.334832
$219$	12.9071	0.872181
$220$	0.874218	0.0589398
$221$	−19.3932	−1.30453
$222$	3.54295	0.237788
$223$	−3.08662	−0.206696	−0.103348	−	0.994645i	$-0.532955\pi$
$223$	−3.08662	−0.206696	−0.103348	+	0.994645i	$0.532955\pi$
$224$	−5.18729	−0.346591
$225$	−4.50822	−0.300548
$226$	−10.7315	−0.713848
$227$	0.953680	0.0632980	0.0316490	−	0.999499i	$-0.489924\pi$
$227$	0.953680	0.0632980	0.0316490	+	0.999499i	$0.489924\pi$
$228$	1.00000	0.0662266
$229$	4.18755	0.276721	0.138361	−	0.990382i	$-0.455817\pi$
$229$	4.18755	0.276721	0.138361	+	0.990382i	$0.455817\pi$
$230$	3.24461	0.213943
$231$	6.46657	0.425469
$232$	−5.88814	−0.386575
$233$	1.56870	0.102769	0.0513845	−	0.998679i	$-0.483637\pi$
$233$	1.56870	0.102769	0.0513845	+	0.998679i	$0.483637\pi$
$234$	−6.30123	−0.411924
$235$	4.90947	0.320258
$236$	1.31166	0.0853819
$237$	13.4739	0.875226
$238$	15.9649	1.03485
$239$	−20.6049	−1.33282	−0.666411	−	0.745585i	$-0.732170\pi$
$239$	−20.6049	−1.33282	−0.666411	+	0.745585i	$0.732170\pi$
$240$	0.701272	0.0452669
$241$	22.2208	1.43137	0.715685	−	0.698424i	$-0.246115\pi$
$241$	22.2208	1.43137	0.715685	+	0.698424i	$0.246115\pi$
$242$	9.44594	0.607208
$243$	1.00000	0.0641500
$244$	4.84496	0.310167
$245$	13.9609	0.891931
$246$	3.03959	0.193797
$247$	6.30123	0.400937
$248$	4.72744	0.300193
$249$	−15.4069	−0.976370
$250$	6.66784	0.421711
$251$	6.16833	0.389341	0.194671	−	0.980869i	$-0.437636\pi$
$251$	6.16833	0.389341	0.194671	+	0.980869i	$0.437636\pi$
$252$	5.18729	0.326769
$253$	−5.76779	−0.362618
$254$	0.0537738	0.00337407
$255$	−2.15829	−0.135158
$256$	1.00000	0.0625000
$257$	23.1181	1.44207	0.721035	−	0.692899i	$-0.243667\pi$
$257$	23.1181	1.44207	0.721035	+	0.692899i	$0.243667\pi$
$258$	−6.62675	−0.412564
$259$	−18.3783	−1.14197
$260$	4.41887	0.274047
$261$	5.88814	0.364467
$262$	14.0769	0.869672
$263$	−22.6620	−1.39740	−0.698700	−	0.715414i	$-0.746238\pi$
$263$	−22.6620	−1.39740	−0.698700	+	0.715414i	$0.746238\pi$
$264$	−1.24662	−0.0767240
$265$	0.701272	0.0430788
$266$	−5.18729	−0.318053
$267$	−5.69340	−0.348430
$268$	−2.94658	−0.179991
$269$	2.32845	0.141968	0.0709839	−	0.997477i	$-0.477386\pi$
$269$	2.32845	0.141968	0.0709839	+	0.997477i	$0.477386\pi$
$270$	−0.701272	−0.0426780
$271$	17.4776	1.06169	0.530845	−	0.847469i	$-0.321874\pi$
$271$	17.4776	1.06169	0.530845	+	0.847469i	$0.321874\pi$
$272$	−3.07769	−0.186612
$273$	32.6863	1.97827
$274$	−5.67522	−0.342853
$275$	−5.62003	−0.338900
$276$	−4.62675	−0.278498
$277$	−7.39635	−0.444404	−0.222202	−	0.975001i	$-0.571324\pi$
$277$	−7.39635	−0.444404	−0.222202	+	0.975001i	$0.571324\pi$
$278$	4.65908	0.279433
$279$	−4.72744	−0.283024
$280$	−3.63770	−0.217394
$281$	−27.3880	−1.63383	−0.816915	−	0.576758i	$-0.804318\pi$
$281$	−27.3880	−1.63383	−0.816915	+	0.576758i	$0.804318\pi$
$282$	−7.00081	−0.416892
$283$	−20.0439	−1.19149	−0.595743	−	0.803175i	$-0.703142\pi$
$283$	−20.0439	−1.19149	−0.595743	+	0.803175i	$0.703142\pi$
$284$	2.79745	0.165998
$285$	0.701272	0.0415397
$286$	−7.85522	−0.464489
$287$	−15.7673	−0.930712
$288$	−1.00000	−0.0589256
$289$	−7.52785	−0.442815
$290$	−4.12919	−0.242474
$291$	−18.6821	−1.09517
$292$	12.9071	0.755331
$293$	5.38919	0.314840	0.157420	−	0.987532i	$-0.449682\pi$
$293$	5.38919	0.314840	0.157420	+	0.987532i	$0.449682\pi$
$294$	−19.9080	−1.16106
$295$	0.919831	0.0535546
$296$	3.54295	0.205930
$297$	1.24662	0.0723361
$298$	0.621309	0.0359915
$299$	−29.1542	−1.68603
$300$	−4.50822	−0.260282
$301$	34.3749	1.98134
$302$	21.9318	1.26203
$303$	−16.4976	−0.947762
$304$	1.00000	0.0573539
$305$	3.39763	0.194548
$306$	3.07769	0.175940
$307$	−19.0989	−1.09003	−0.545015	−	0.838427i	$-0.683476\pi$
$307$	−19.0989	−1.09003	−0.545015	+	0.838427i	$0.683476\pi$
$308$	6.46657	0.368467
$309$	15.1782	0.863459
$310$	3.31522	0.188292
$311$	29.9034	1.69567	0.847835	−	0.530261i	$-0.177906\pi$
$311$	29.9034	1.69567	0.847835	+	0.530261i	$0.177906\pi$
$312$	−6.30123	−0.356737
$313$	−11.4546	−0.647455	−0.323727	−	0.946150i	$-0.604936\pi$
$313$	−11.4546	−0.647455	−0.323727	+	0.946150i	$0.604936\pi$
$314$	−12.0131	−0.677938
$315$	3.63770	0.204961
$316$	13.4739	0.757968
$317$	20.4887	1.15076	0.575381	−	0.817885i	$-0.304854\pi$
$317$	20.4887	1.15076	0.575381	+	0.817885i	$0.304854\pi$
$318$	−1.00000	−0.0560772
$319$	7.34026	0.410976
$320$	0.701272	0.0392023
$321$	5.95866	0.332580
$322$	24.0003	1.33749
$323$	−3.07769	−0.171247
$324$	1.00000	0.0555556
$325$	−28.4073	−1.57575
$326$	19.1031	1.05802
$327$	4.94374	0.273389
$328$	3.03959	0.167833
$329$	36.3153	2.00213
$330$	−0.874218	−0.0481241
$331$	13.8987	0.763940	0.381970	−	0.924175i	$-0.375246\pi$
$331$	13.8987	0.763940	0.381970	+	0.924175i	$0.375246\pi$
$332$	−15.4069	−0.845561
$333$	−3.54295	−0.194153
$334$	−18.0988	−0.990322
$335$	−2.06636	−0.112897
$336$	5.18729	0.282990
$337$	−23.7124	−1.29170	−0.645849	−	0.763465i	$-0.723496\pi$
$337$	−23.7124	−1.29170	−0.645849	+	0.763465i	$0.723496\pi$
$338$	−26.7054	−1.45258
$339$	10.7315	0.582854
$340$	−2.15829	−0.117050
$341$	−5.89331	−0.319141
$342$	−1.00000	−0.0540738
$343$	66.9576	3.61537
$344$	−6.62675	−0.357291
$345$	−3.24461	−0.174684
$346$	−7.14565	−0.384153
$347$	−22.5693	−1.21158	−0.605792	−	0.795623i	$-0.707144\pi$
$347$	−22.5693	−1.21158	−0.605792	+	0.795623i	$0.707144\pi$
$348$	5.88814	0.315637
$349$	1.74512	0.0934140	0.0467070	−	0.998909i	$-0.485127\pi$
$349$	1.74512	0.0934140	0.0467070	+	0.998909i	$0.485127\pi$
$350$	23.3855	1.25000
$351$	6.30123	0.336335
$352$	−1.24662	−0.0664450
$353$	−34.3128	−1.82629	−0.913143	−	0.407640i	$-0.866352\pi$
$353$	−34.3128	−1.82629	−0.913143	+	0.407640i	$0.866352\pi$
$354$	−1.31166	−0.0697140
$355$	1.96177	0.104120
$356$	−5.69340	−0.301750
$357$	−15.9649	−0.844950
$358$	−3.35208	−0.177163
$359$	21.3822	1.12851	0.564255	−	0.825601i	$-0.309164\pi$
$359$	21.3822	1.12851	0.564255	+	0.825601i	$0.309164\pi$
$360$	−0.701272	−0.0369603
$361$	1.00000	0.0526316
$362$	7.75521	0.407605
$363$	−9.44594	−0.495783
$364$	32.6863	1.71323
$365$	9.05138	0.473771
$366$	−4.84496	−0.253250
$367$	12.9240	0.674627	0.337313	−	0.941392i	$-0.390482\pi$
$367$	12.9240	0.674627	0.337313	+	0.941392i	$0.390482\pi$
$368$	−4.62675	−0.241186
$369$	−3.03959	−0.158235
$370$	2.48457	0.129167
$371$	5.18729	0.269311
$372$	−4.72744	−0.245106
$373$	18.9713	0.982297	0.491149	−	0.871076i	$-0.336577\pi$
$373$	18.9713	0.982297	0.491149	+	0.871076i	$0.336577\pi$
$374$	3.83670	0.198391
$375$	−6.66784	−0.344326
$376$	−7.00081	−0.361039
$377$	37.1025	1.91088
$378$	−5.18729	−0.266806
$379$	−28.5821	−1.46817	−0.734083	−	0.679060i	$-0.762388\pi$
$379$	−28.5821	−1.46817	−0.734083	+	0.679060i	$0.762388\pi$
$380$	0.701272	0.0359745
$381$	−0.0537738	−0.00275491
$382$	−9.85024	−0.503982
$383$	−23.5856	−1.20517	−0.602584	−	0.798055i	$-0.705862\pi$
$383$	−23.5856	−1.20517	−0.602584	+	0.798055i	$0.705862\pi$
$384$	−1.00000	−0.0510310
$385$	4.53482	0.231116
$386$	18.8273	0.958287
$387$	6.62675	0.336857
$388$	−18.6821	−0.948442
$389$	23.8295	1.20821	0.604103	−	0.796906i	$-0.293532\pi$
$389$	23.8295	1.20821	0.604103	+	0.796906i	$0.293532\pi$
$390$	−4.41887	−0.223758
$391$	14.2397	0.720132
$392$	−19.9080	−1.00551
$393$	−14.0769	−0.710084
$394$	1.21702	0.0613126
$395$	9.44889	0.475425
$396$	1.24662	0.0626449
$397$	−16.1069	−0.808380	−0.404190	−	0.914675i	$-0.632447\pi$
$397$	−16.1069	−0.808380	−0.404190	+	0.914675i	$0.632447\pi$
$398$	3.76777	0.188861
$399$	5.18729	0.259689
$400$	−4.50822	−0.225411
$401$	35.8090	1.78822	0.894108	−	0.447851i	$-0.147811\pi$
$401$	35.8090	1.78822	0.894108	+	0.447851i	$0.147811\pi$
$402$	2.94658	0.146962
$403$	−29.7887	−1.48388
$404$	−16.4976	−0.820786
$405$	0.701272	0.0348465
$406$	−30.5435	−1.51585
$407$	−4.41671	−0.218928
$408$	3.07769	0.152368
$409$	30.2286	1.49471	0.747354	−	0.664427i	$-0.231324\pi$
$409$	30.2286	1.49471	0.747354	+	0.664427i	$0.231324\pi$
$410$	2.13158	0.105271
$411$	5.67522	0.279938
$412$	15.1782	0.747777
$413$	6.80397	0.334802
$414$	4.62675	0.227392
$415$	−10.8044	−0.530366
$416$	−6.30123	−0.308943
$417$	−4.65908	−0.228156
$418$	−1.24662	−0.0609741
$419$	22.6876	1.10836	0.554182	−	0.832395i	$-0.313031\pi$
$419$	22.6876	1.10836	0.554182	+	0.832395i	$0.313031\pi$
$420$	3.63770	0.177502
$421$	−7.39925	−0.360618	−0.180309	−	0.983610i	$-0.557710\pi$
$421$	−7.39925	−0.360618	−0.180309	+	0.983610i	$0.557710\pi$
$422$	−0.115274	−0.00561145
$423$	7.00081	0.340391
$424$	−1.00000	−0.0485643
$425$	13.8749	0.673030
$426$	−2.79745	−0.135537
$427$	25.1322	1.21623
$428$	5.95866	0.288023
$429$	7.85522	0.379254
$430$	−4.64715	−0.224106
$431$	−19.3952	−0.934233	−0.467117	−	0.884196i	$-0.654707\pi$
$431$	−19.3952	−0.934233	−0.467117	+	0.884196i	$0.654707\pi$
$432$	1.00000	0.0481125
$433$	18.6674	0.897100	0.448550	−	0.893758i	$-0.351941\pi$
$433$	18.6674	0.897100	0.448550	+	0.893758i	$0.351941\pi$
$434$	24.5226	1.17712
$435$	4.12919	0.197979
$436$	4.94374	0.236762
$437$	−4.62675	−0.221328
$438$	−12.9071	−0.616725
$439$	24.4352	1.16623	0.583114	−	0.812390i	$-0.301834\pi$
$439$	24.4352	1.16623	0.583114	+	0.812390i	$0.301834\pi$
$440$	−0.874218	−0.0416767
$441$	19.9080	0.948001
$442$	19.3932	0.922440
$443$	−29.1869	−1.38671	−0.693356	−	0.720595i	$-0.743869\pi$
$443$	−29.1869	−1.38671	−0.693356	+	0.720595i	$0.743869\pi$
$444$	−3.54295	−0.168141
$445$	−3.99262	−0.189268
$446$	3.08662	0.146156
$447$	−0.621309	−0.0293869
$448$	5.18729	0.245077
$449$	−0.182753	−0.00862465	−0.00431233	−	0.999991i	$-0.501373\pi$
$449$	−0.182753	−0.00862465	−0.00431233	+	0.999991i	$0.501373\pi$
$450$	4.50822	0.212519
$451$	−3.78921	−0.178427
$452$	10.7315	0.504766
$453$	−21.9318	−1.03045
$454$	−0.953680	−0.0447584
$455$	22.9220	1.07460
$456$	−1.00000	−0.0468293
$457$	−13.0092	−0.608544	−0.304272	−	0.952585i	$-0.598413\pi$
$457$	−13.0092	−0.608544	−0.304272	+	0.952585i	$0.598413\pi$
$458$	−4.18755	−0.195672
$459$	−3.07769	−0.143654
$460$	−3.24461	−0.151281
$461$	−22.1031	−1.02944	−0.514721	−	0.857358i	$-0.672105\pi$
$461$	−22.1031	−1.02944	−0.514721	+	0.857358i	$0.672105\pi$
$462$	−6.46657	−0.300852
$463$	0.962969	0.0447530	0.0223765	−	0.999750i	$-0.492877\pi$
$463$	0.962969	0.0447530	0.0223765	+	0.999750i	$0.492877\pi$
$464$	5.88814	0.273350
$465$	−3.31522	−0.153740
$466$	−1.56870	−0.0726687
$467$	−32.7136	−1.51380	−0.756902	−	0.653528i	$-0.773288\pi$
$467$	−32.7136	−1.51380	−0.756902	+	0.653528i	$0.773288\pi$
$468$	6.30123	0.291274
$469$	−15.2848	−0.705786
$470$	−4.90947	−0.226457
$471$	12.0131	0.553534
$472$	−1.31166	−0.0603741
$473$	8.26103	0.379843
$474$	−13.4739	−0.618879
$475$	−4.50822	−0.206851
$476$	−15.9649	−0.731748
$477$	1.00000	0.0457869
$478$	20.6049	0.942447
$479$	13.7663	0.629000	0.314500	−	0.949257i	$-0.398163\pi$
$479$	13.7663	0.629000	0.314500	+	0.949257i	$0.398163\pi$
$480$	−0.701272	−0.0320085
$481$	−22.3250	−1.01793
$482$	−22.2208	−1.01213
$483$	−24.0003	−1.09205
$484$	−9.44594	−0.429361
$485$	−13.1013	−0.594897
$486$	−1.00000	−0.0453609
$487$	−24.7380	−1.12099	−0.560494	−	0.828159i	$-0.689389\pi$
$487$	−24.7380	−1.12099	−0.560494	+	0.828159i	$0.689389\pi$
$488$	−4.84496	−0.219321
$489$	−19.1031	−0.863871
$490$	−13.9609	−0.630690
$491$	6.27664	0.283261	0.141630	−	0.989920i	$-0.454766\pi$
$491$	6.27664	0.283261	0.141630	+	0.989920i	$0.454766\pi$
$492$	−3.03959	−0.137035
$493$	−18.1218	−0.816167
$494$	−6.30123	−0.283506
$495$	0.874218	0.0392932
$496$	−4.72744	−0.212268
$497$	14.5112	0.650916
$498$	15.4069	0.690398
$499$	6.73574	0.301533	0.150767	−	0.988569i	$-0.451826\pi$
$499$	6.73574	0.301533	0.150767	+	0.988569i	$0.451826\pi$
$500$	−6.66784	−0.298195
$501$	18.0988	0.808594
$502$	−6.16833	−0.275306
$503$	−17.5762	−0.783685	−0.391842	−	0.920032i	$-0.628162\pi$
$503$	−17.5762	−0.783685	−0.391842	+	0.920032i	$0.628162\pi$
$504$	−5.18729	−0.231060
$505$	−11.5693	−0.514827
$506$	5.76779	0.256410
$507$	26.7054	1.18603
$508$	−0.0537738	−0.00238582
$509$	2.50006	0.110813	0.0554067	−	0.998464i	$-0.482354\pi$
$509$	2.50006	0.110813	0.0554067	+	0.998464i	$0.482354\pi$
$510$	2.15829	0.0955708
$511$	66.9529	2.96182
$512$	−1.00000	−0.0441942
$513$	1.00000	0.0441511
$514$	−23.1181	−1.01970
$515$	10.6441	0.469033
$516$	6.62675	0.291726
$517$	8.72734	0.383828
$518$	18.3783	0.807498
$519$	7.14565	0.313659
$520$	−4.41887	−0.193780
$521$	−40.7496	−1.78527	−0.892636	−	0.450777i	$-0.851147\pi$
$521$	−40.7496	−1.78527	−0.892636	+	0.450777i	$0.851147\pi$
$522$	−5.88814	−0.257717
$523$	32.2951	1.41217	0.706084	−	0.708128i	$-0.250460\pi$
$523$	32.2951	1.41217	0.706084	+	0.708128i	$0.250460\pi$
$524$	−14.0769	−0.614951
$525$	−23.3855	−1.02062
$526$	22.6620	0.988112
$527$	14.5496	0.633789
$528$	1.24662	0.0542521
$529$	−1.59317	−0.0692681
$530$	−0.701272	−0.0304613
$531$	1.31166	0.0569213
$532$	5.18729	0.224898
$533$	−19.1532	−0.829615
$534$	5.69340	0.246377
$535$	4.17864	0.180658
$536$	2.94658	0.127273
$537$	3.35208	0.144653
$538$	−2.32845	−0.100386
$539$	24.8177	1.06897
$540$	0.701272	0.0301779
$541$	23.5642	1.01310	0.506552	−	0.862209i	$-0.330920\pi$
$541$	23.5642	1.01310	0.506552	+	0.862209i	$0.330920\pi$
$542$	−17.4776	−0.750729
$543$	−7.75521	−0.332808
$544$	3.07769	0.131955
$545$	3.46690	0.148506
$546$	−32.6863	−1.39884
$547$	35.8586	1.53320	0.766602	−	0.642123i	$-0.221946\pi$
$547$	35.8586	1.53320	0.766602	+	0.642123i	$0.221946\pi$
$548$	5.67522	0.242434
$549$	4.84496	0.206778
$550$	5.62003	0.239639
$551$	5.88814	0.250843
$552$	4.62675	0.196928
$553$	69.8933	2.97216
$554$	7.39635	0.314241
$555$	−2.48457	−0.105464
$556$	−4.65908	−0.197589
$557$	−43.5751	−1.84633	−0.923167	−	0.384399i	$-0.874409\pi$
$557$	−43.5751	−1.84633	−0.923167	+	0.384399i	$0.874409\pi$
$558$	4.72744	0.200128
$559$	41.7567	1.76612
$560$	3.63770	0.153721
$561$	−3.83670	−0.161986
$562$	27.3880	1.15529
$563$	−8.61440	−0.363054	−0.181527	−	0.983386i	$-0.558104\pi$
$563$	−8.61440	−0.363054	−0.181527	+	0.983386i	$0.558104\pi$
$564$	7.00081	0.294787
$565$	7.52568	0.316608
$566$	20.0439	0.842508
$567$	5.18729	0.217846
$568$	−2.79745	−0.117378
$569$	−30.4702	−1.27738	−0.638689	−	0.769465i	$-0.720523\pi$
$569$	−30.4702	−1.27738	−0.638689	+	0.769465i	$0.720523\pi$
$570$	−0.701272	−0.0293730
$571$	−3.37708	−0.141326	−0.0706632	−	0.997500i	$-0.522512\pi$
$571$	−3.37708	−0.141326	−0.0706632	+	0.997500i	$0.522512\pi$
$572$	7.85522	0.328443
$573$	9.85024	0.411500
$574$	15.7673	0.658113
$575$	20.8584	0.869856
$576$	1.00000	0.0416667
$577$	11.7892	0.490791	0.245395	−	0.969423i	$-0.421082\pi$
$577$	11.7892	0.490791	0.245395	+	0.969423i	$0.421082\pi$
$578$	7.52785	0.313117
$579$	−18.8273	−0.782438
$580$	4.12919	0.171455
$581$	−79.9199	−3.31563
$582$	18.6821	0.774400
$583$	1.24662	0.0516297
$584$	−12.9071	−0.534100
$585$	4.41887	0.182698
$586$	−5.38919	−0.222626
$587$	−24.2417	−1.00056	−0.500281	−	0.865863i	$-0.666770\pi$
$587$	−24.2417	−1.00056	−0.500281	+	0.865863i	$0.666770\pi$
$588$	19.9080	0.820993
$589$	−4.72744	−0.194791
$590$	−0.919831	−0.0378688
$591$	−1.21702	−0.0500615
$592$	−3.54295	−0.145615
$593$	15.2785	0.627414	0.313707	−	0.949520i	$-0.398429\pi$
$593$	15.2785	0.627414	0.313707	+	0.949520i	$0.398429\pi$
$594$	−1.24662	−0.0511494
$595$	−11.1957	−0.458979
$596$	−0.621309	−0.0254498
$597$	−3.76777	−0.154205
$598$	29.1542	1.19220
$599$	31.9247	1.30441	0.652204	−	0.758044i	$-0.273845\pi$
$599$	31.9247	1.30441	0.652204	+	0.758044i	$0.273845\pi$
$600$	4.50822	0.184047
$601$	12.0740	0.492509	0.246255	−	0.969205i	$-0.420800\pi$
$601$	12.0740	0.492509	0.246255	+	0.969205i	$0.420800\pi$
$602$	−34.3749	−1.40102
$603$	−2.94658	−0.119994
$604$	−21.9318	−0.892393
$605$	−6.62417	−0.269311
$606$	16.4976	0.670169
$607$	−18.5519	−0.752999	−0.376500	−	0.926417i	$-0.622872\pi$
$607$	−18.5519	−0.752999	−0.376500	+	0.926417i	$0.622872\pi$
$608$	−1.00000	−0.0405554
$609$	30.5435	1.23769
$610$	−3.39763	−0.137566
$611$	44.1137	1.78465
$612$	−3.07769	−0.124408
$613$	5.41952	0.218892	0.109446	−	0.993993i	$-0.465092\pi$
$613$	5.41952	0.218892	0.109446	+	0.993993i	$0.465092\pi$
$614$	19.0989	0.770767
$615$	−2.13158	−0.0859536
$616$	−6.46657	−0.260546
$617$	11.8089	0.475409	0.237704	−	0.971338i	$-0.423605\pi$
$617$	11.8089	0.475409	0.237704	+	0.971338i	$0.423605\pi$
$618$	−15.1782	−0.610558
$619$	−28.9240	−1.16255	−0.581277	−	0.813706i	$-0.697447\pi$
$619$	−28.9240	−1.16255	−0.581277	+	0.813706i	$0.697447\pi$
$620$	−3.31522	−0.133142
$621$	−4.62675	−0.185665
$622$	−29.9034	−1.19902
$623$	−29.5333	−1.18323
$624$	6.30123	0.252251
$625$	17.8651	0.714605
$626$	11.4546	0.457820
$627$	1.24662	0.0497851
$628$	12.0131	0.479374
$629$	10.9041	0.434775
$630$	−3.63770	−0.144929
$631$	23.7780	0.946585	0.473293	−	0.880905i	$-0.343065\pi$
$631$	23.7780	0.946585	0.473293	+	0.880905i	$0.343065\pi$
$632$	−13.4739	−0.535965
$633$	0.115274	0.00458173
$634$	−20.4887	−0.813712
$635$	−0.0377100	−0.00149648
$636$	1.00000	0.0396526
$637$	125.445	4.97031
$638$	−7.34026	−0.290604
$639$	2.79745	0.110665
$640$	−0.701272	−0.0277202
$641$	27.7539	1.09621	0.548107	−	0.836408i	$-0.315349\pi$
$641$	27.7539	1.09621	0.548107	+	0.836408i	$0.315349\pi$
$642$	−5.95866	−0.235170
$643$	1.22306	0.0482330	0.0241165	−	0.999709i	$-0.492323\pi$
$643$	1.22306	0.0482330	0.0241165	+	0.999709i	$0.492323\pi$
$644$	−24.0003	−0.945745
$645$	4.64715	0.182981
$646$	3.07769	0.121090
$647$	2.21964	0.0872629	0.0436314	−	0.999048i	$-0.486107\pi$
$647$	2.21964	0.0872629	0.0436314	+	0.999048i	$0.486107\pi$
$648$	−1.00000	−0.0392837
$649$	1.63514	0.0641849
$650$	28.4073	1.11423
$651$	−24.5226	−0.961117
$652$	−19.1031	−0.748135
$653$	30.0182	1.17470	0.587351	−	0.809333i	$-0.300171\pi$
$653$	30.0182	1.17470	0.587351	+	0.809333i	$0.300171\pi$
$654$	−4.94374	−0.193315
$655$	−9.87170	−0.385719
$656$	−3.03959	−0.118676
$657$	12.9071	0.503554
$658$	−36.3153	−1.41572
$659$	−21.8815	−0.852382	−0.426191	−	0.904633i	$-0.640145\pi$
$659$	−21.8815	−0.852382	−0.426191	+	0.904633i	$0.640145\pi$
$660$	0.874218	0.0340289
$661$	9.17635	0.356919	0.178459	−	0.983947i	$-0.442889\pi$
$661$	9.17635	0.356919	0.178459	+	0.983947i	$0.442889\pi$
$662$	−13.8987	−0.540187
$663$	−19.3932	−0.753169
$664$	15.4069	0.597902
$665$	3.63770	0.141064
$666$	3.54295	0.137287
$667$	−27.2430	−1.05485
$668$	18.0988	0.700263
$669$	−3.08662	−0.119336
$670$	2.06636	0.0798303
$671$	6.03982	0.233165
$672$	−5.18729	−0.200104
$673$	−25.8126	−0.995003	−0.497501	−	0.867463i	$-0.665749\pi$
$673$	−25.8126	−0.995003	−0.497501	+	0.867463i	$0.665749\pi$
$674$	23.7124	0.913369
$675$	−4.50822	−0.173521
$676$	26.7054	1.02713
$677$	−28.4295	−1.09264	−0.546318	−	0.837578i	$-0.683971\pi$
$677$	−28.4295	−1.09264	−0.546318	+	0.837578i	$0.683971\pi$
$678$	−10.7315	−0.412140
$679$	−96.9098	−3.71906
$680$	2.15829	0.0827668
$681$	0.953680	0.0365451
$682$	5.89331	0.225667
$683$	−17.9173	−0.685585	−0.342792	−	0.939411i	$-0.611373\pi$
$683$	−17.9173	−0.685585	−0.342792	+	0.939411i	$0.611373\pi$
$684$	1.00000	0.0382360
$685$	3.97987	0.152063
$686$	−66.9576	−2.55645
$687$	4.18755	0.159765
$688$	6.62675	0.252643
$689$	6.30123	0.240058
$690$	3.24461	0.123520
$691$	−32.7861	−1.24724	−0.623621	−	0.781727i	$-0.714339\pi$
$691$	−32.7861	−1.24724	−0.623621	+	0.781727i	$0.714339\pi$
$692$	7.14565	0.271637
$693$	6.46657	0.245645
$694$	22.5693	0.856720
$695$	−3.26728	−0.123935
$696$	−5.88814	−0.223189
$697$	9.35491	0.354343
$698$	−1.74512	−0.0660537
$699$	1.56870	0.0593338
$700$	−23.3855	−0.883887
$701$	50.4807	1.90663	0.953314	−	0.301980i	$-0.0976476\pi$
$701$	50.4807	1.90663	0.953314	+	0.301980i	$0.0976476\pi$
$702$	−6.30123	−0.237824
$703$	−3.54295	−0.133625
$704$	1.24662	0.0469837
$705$	4.90947	0.184901
$706$	34.3128	1.29138
$707$	−85.5779	−3.21849
$708$	1.31166	0.0492953
$709$	8.59274	0.322707	0.161353	−	0.986897i	$-0.448414\pi$
$709$	8.59274	0.322707	0.161353	+	0.986897i	$0.448414\pi$
$710$	−1.96177	−0.0736240
$711$	13.4739	0.505312
$712$	5.69340	0.213369
$713$	21.8727	0.819139
$714$	15.9649	0.597470
$715$	5.50864	0.206012
$716$	3.35208	0.125273
$717$	−20.6049	−0.769505
$718$	−21.3822	−0.797977
$719$	4.38673	0.163597	0.0817987	−	0.996649i	$-0.473934\pi$
$719$	4.38673	0.163597	0.0817987	+	0.996649i	$0.473934\pi$
$720$	0.701272	0.0261348
$721$	78.7339	2.93220
$722$	−1.00000	−0.0372161
$723$	22.2208	0.826401
$724$	−7.75521	−0.288220
$725$	−26.5450	−0.985857
$726$	9.44594	0.350572
$727$	−1.13695	−0.0421671	−0.0210835	−	0.999778i	$-0.506712\pi$
$727$	−1.13695	−0.0421671	−0.0210835	+	0.999778i	$0.506712\pi$
$728$	−32.6863	−1.21144
$729$	1.00000	0.0370370
$730$	−9.05138	−0.335007
$731$	−20.3951	−0.754339
$732$	4.84496	0.179075
$733$	16.4341	0.607008	0.303504	−	0.952830i	$-0.401843\pi$
$733$	16.4341	0.607008	0.303504	+	0.952830i	$0.401843\pi$
$734$	−12.9240	−0.477033
$735$	13.9609	0.514956
$736$	4.62675	0.170544
$737$	−3.67327	−0.135306
$738$	3.03959	0.111889
$739$	1.35604	0.0498827	0.0249413	−	0.999689i	$-0.492060\pi$
$739$	1.35604	0.0498827	0.0249413	+	0.999689i	$0.492060\pi$
$740$	−2.48457	−0.0913347
$741$	6.30123	0.231481
$742$	−5.18729	−0.190432
$743$	31.0483	1.13905	0.569525	−	0.821974i	$-0.307127\pi$
$743$	31.0483	1.13905	0.569525	+	0.821974i	$0.307127\pi$
$744$	4.72744	0.173316
$745$	−0.435706	−0.0159630
$746$	−18.9713	−0.694589
$747$	−15.4069	−0.563707
$748$	−3.83670	−0.140284
$749$	30.9093	1.12940
$750$	6.66784	0.243475
$751$	−23.0232	−0.840127	−0.420063	−	0.907495i	$-0.637992\pi$
$751$	−23.0232	−0.840127	−0.420063	+	0.907495i	$0.637992\pi$
$752$	7.00081	0.255293
$753$	6.16833	0.224786
$754$	−37.1025	−1.35119
$755$	−15.3802	−0.559741
$756$	5.18729	0.188660
$757$	−30.0017	−1.09043	−0.545215	−	0.838296i	$-0.683552\pi$
$757$	−30.0017	−1.09043	−0.545215	+	0.838296i	$0.683552\pi$
$758$	28.5821	1.03815
$759$	−5.76779	−0.209358
$760$	−0.701272	−0.0254378
$761$	−40.8282	−1.48002	−0.740011	−	0.672595i	$-0.765180\pi$
$761$	−40.8282	−1.48002	−0.740011	+	0.672595i	$0.765180\pi$
$762$	0.0537738	0.00194802
$763$	25.6446	0.928397
$764$	9.85024	0.356369
$765$	−2.15829	−0.0780333
$766$	23.5856	0.852182
$767$	8.26507	0.298435
$768$	1.00000	0.0360844
$769$	−35.0234	−1.26298	−0.631489	−	0.775385i	$-0.717556\pi$
$769$	−35.0234	−1.26298	−0.631489	+	0.775385i	$0.717556\pi$
$770$	−4.53482	−0.163424
$771$	23.1181	0.832579
$772$	−18.8273	−0.677611
$773$	25.3942	0.913365	0.456682	−	0.889630i	$-0.349038\pi$
$773$	25.3942	0.913365	0.456682	+	0.889630i	$0.349038\pi$
$774$	−6.62675	−0.238194
$775$	21.3123	0.765562
$776$	18.6821	0.670650
$777$	−18.3783	−0.659319
$778$	−23.8295	−0.854331
$779$	−3.03959	−0.108905
$780$	4.41887	0.158221
$781$	3.48735	0.124787
$782$	−14.2397	−0.509210
$783$	5.88814	0.210425
$784$	19.9080	0.711000
$785$	8.42443	0.300681
$786$	14.0769	0.502105
$787$	−43.5749	−1.55328	−0.776639	−	0.629946i	$-0.783077\pi$
$787$	−43.5749	−1.55328	−0.776639	+	0.629946i	$0.783077\pi$
$788$	−1.21702	−0.0433546
$789$	−22.6620	−0.806790
$790$	−9.44889	−0.336176
$791$	55.6673	1.97930
$792$	−1.24662	−0.0442966
$793$	30.5292	1.08412
$794$	16.1069	0.571611
$795$	0.701272	0.0248715
$796$	−3.76777	−0.133545
$797$	−4.98996	−0.176754	−0.0883768	−	0.996087i	$-0.528168\pi$
$797$	−4.98996	−0.176754	−0.0883768	+	0.996087i	$0.528168\pi$
$798$	−5.18729	−0.183628
$799$	−21.5463	−0.762253
$800$	4.50822	0.159390
$801$	−5.69340	−0.201166
$802$	−35.8090	−1.26446
$803$	16.0902	0.567812
$804$	−2.94658	−0.103918
$805$	−16.8307	−0.593206
$806$	29.7887	1.04926
$807$	2.32845	0.0819652
$808$	16.4976	0.580384
$809$	−52.5587	−1.84787	−0.923933	−	0.382555i	$-0.875044\pi$
$809$	−52.5587	−1.84787	−0.923933	+	0.382555i	$0.875044\pi$
$810$	−0.701272	−0.0246402
$811$	1.71978	0.0603897	0.0301948	−	0.999544i	$-0.490387\pi$
$811$	1.71978	0.0603897	0.0301948	+	0.999544i	$0.490387\pi$
$812$	30.5435	1.07187
$813$	17.4776	0.612968
$814$	4.41671	0.154806
$815$	−13.3964	−0.469257
$816$	−3.07769	−0.107741
$817$	6.62675	0.231841
$818$	−30.2286	−1.05692
$819$	32.6863	1.14215
$820$	−2.13158	−0.0744380
$821$	43.2623	1.50987	0.754933	−	0.655802i	$-0.227669\pi$
$821$	43.2623	1.50987	0.754933	+	0.655802i	$0.227669\pi$
$822$	−5.67522	−0.197946
$823$	25.1067	0.875166	0.437583	−	0.899178i	$-0.355835\pi$
$823$	25.1067	0.875166	0.437583	+	0.899178i	$0.355835\pi$
$824$	−15.1782	−0.528758
$825$	−5.62003	−0.195664
$826$	−6.80397	−0.236740
$827$	31.3826	1.09128	0.545641	−	0.838019i	$-0.316286\pi$
$827$	31.3826	1.09128	0.545641	+	0.838019i	$0.316286\pi$
$828$	−4.62675	−0.160791
$829$	21.0080	0.729639	0.364820	−	0.931078i	$-0.381131\pi$
$829$	21.0080	0.729639	0.364820	+	0.931078i	$0.381131\pi$
$830$	10.8044	0.375026
$831$	−7.39635	−0.256577
$832$	6.30123	0.218456
$833$	−61.2706	−2.12290
$834$	4.65908	0.161331
$835$	12.6922	0.439230
$836$	1.24662	0.0431152
$837$	−4.72744	−0.163404
$838$	−22.6876	−0.783732
$839$	−12.2572	−0.423164	−0.211582	−	0.977360i	$-0.567862\pi$
$839$	−12.2572	−0.423164	−0.211582	+	0.977360i	$0.567862\pi$
$840$	−3.63770	−0.125513
$841$	5.67020	0.195524
$842$	7.39925	0.254995
$843$	−27.3880	−0.943293
$844$	0.115274	0.00396790
$845$	18.7278	0.644255
$846$	−7.00081	−0.240693
$847$	−48.9989	−1.68362
$848$	1.00000	0.0343401
$849$	−20.0439	−0.687905
$850$	−13.8749	−0.475904
$851$	16.3924	0.561923
$852$	2.79745	0.0958391
$853$	10.4876	0.359089	0.179544	−	0.983750i	$-0.442538\pi$
$853$	10.4876	0.359089	0.179544	+	0.983750i	$0.442538\pi$
$854$	−25.1322	−0.860007
$855$	0.701272	0.0239830
$856$	−5.95866	−0.203663
$857$	13.2610	0.452989	0.226494	−	0.974012i	$-0.427274\pi$
$857$	13.2610	0.452989	0.226494	+	0.974012i	$0.427274\pi$
$858$	−7.85522	−0.268173
$859$	9.87484	0.336925	0.168463	−	0.985708i	$-0.446120\pi$
$859$	9.87484	0.336925	0.168463	+	0.985708i	$0.446120\pi$
$860$	4.64715	0.158467
$861$	−15.7673	−0.537347
$862$	19.3952	0.660603
$863$	19.7343	0.671765	0.335882	−	0.941904i	$-0.390965\pi$
$863$	19.7343	0.671765	0.335882	+	0.941904i	$0.390965\pi$
$864$	−1.00000	−0.0340207
$865$	5.01104	0.170381
$866$	−18.6674	−0.634345
$867$	−7.52785	−0.255659
$868$	−24.5226	−0.832352
$869$	16.7969	0.569794
$870$	−4.12919	−0.139992
$871$	−18.5671	−0.629122
$872$	−4.94374	−0.167416
$873$	−18.6821	−0.632295
$874$	4.62675	0.156502
$875$	−34.5881	−1.16929
$876$	12.9071	0.436091
$877$	2.53833	0.0857134	0.0428567	−	0.999081i	$-0.486354\pi$
$877$	2.53833	0.0857134	0.0428567	+	0.999081i	$0.486354\pi$
$878$	−24.4352	−0.824647
$879$	5.38919	0.181773
$880$	0.874218	0.0294699
$881$	28.5707	0.962573	0.481286	−	0.876563i	$-0.340170\pi$
$881$	28.5707	0.962573	0.481286	+	0.876563i	$0.340170\pi$
$882$	−19.9080	−0.670338
$883$	52.4957	1.76662	0.883311	−	0.468788i	$-0.155309\pi$
$883$	52.4957	1.76662	0.883311	+	0.468788i	$0.155309\pi$
$884$	−19.3932	−0.652264
$885$	0.919831	0.0309198
$886$	29.1869	0.980553
$887$	29.2940	0.983595	0.491797	−	0.870710i	$-0.336340\pi$
$887$	29.2940	0.983595	0.491797	+	0.870710i	$0.336340\pi$
$888$	3.54295	0.118894
$889$	−0.278940	−0.00935536
$890$	3.99262	0.133833
$891$	1.24662	0.0417633
$892$	−3.08662	−0.103348
$893$	7.00081	0.234273
$894$	0.621309	0.0207797
$895$	2.35072	0.0785758
$896$	−5.18729	−0.173295
$897$	−29.1542	−0.973431
$898$	0.182753	0.00609855
$899$	−27.8358	−0.928377
$900$	−4.50822	−0.150274
$901$	−3.07769	−0.102533
$902$	3.78921	0.126167
$903$	34.3749	1.14393
$904$	−10.7315	−0.356924
$905$	−5.43851	−0.180782
$906$	21.9318	0.728636
$907$	−26.5998	−0.883232	−0.441616	−	0.897204i	$-0.645595\pi$
$907$	−26.5998	−0.883232	−0.441616	+	0.897204i	$0.645595\pi$
$908$	0.953680	0.0316490
$909$	−16.4976	−0.547191
$910$	−22.9220	−0.759856
$911$	44.1366	1.46231	0.731156	−	0.682210i	$-0.238981\pi$
$911$	44.1366	1.46231	0.731156	+	0.682210i	$0.238981\pi$
$912$	1.00000	0.0331133
$913$	−19.2065	−0.635641
$914$	13.0092	0.430306
$915$	3.39763	0.112322
$916$	4.18755	0.138361
$917$	−73.0208	−2.41136
$918$	3.07769	0.101579
$919$	−21.7740	−0.718260	−0.359130	−	0.933288i	$-0.616926\pi$
$919$	−21.7740	−0.718260	−0.359130	+	0.933288i	$0.616926\pi$
$920$	3.24461	0.106972
$921$	−19.0989	−0.629329
$922$	22.1031	0.727926
$923$	17.6274	0.580212
$924$	6.46657	0.212735
$925$	15.9724	0.525170
$926$	−0.962969	−0.0316451
$927$	15.1782	0.498518
$928$	−5.88814	−0.193288
$929$	−24.3143	−0.797725	−0.398862	−	0.917011i	$-0.630595\pi$
$929$	−24.3143	−0.797725	−0.398862	+	0.917011i	$0.630595\pi$
$930$	3.31522	0.108710
$931$	19.9080	0.652459
$932$	1.56870	0.0513845
$933$	29.9034	0.978995
$934$	32.7136	1.07042
$935$	−2.69057	−0.0879910
$936$	−6.30123	−0.205962
$937$	7.06902	0.230935	0.115467	−	0.993311i	$-0.463163\pi$
$937$	7.06902	0.230935	0.115467	+	0.993311i	$0.463163\pi$
$938$	15.2848	0.499066
$939$	−11.4546	−0.373808
$940$	4.90947	0.160129
$941$	−40.0077	−1.30421	−0.652107	−	0.758127i	$-0.726115\pi$
$941$	−40.0077	−1.30421	−0.652107	+	0.758127i	$0.726115\pi$
$942$	−12.0131	−0.391407
$943$	14.0634	0.457969
$944$	1.31166	0.0426909
$945$	3.63770	0.118334
$946$	−8.26103	−0.268589
$947$	17.3165	0.562709	0.281355	−	0.959604i	$-0.409216\pi$
$947$	17.3165	0.562709	0.281355	+	0.959604i	$0.409216\pi$
$948$	13.4739	0.437613
$949$	81.3305	2.64010
$950$	4.50822	0.146266
$951$	20.4887	0.664393
$952$	15.9649	0.517424
$953$	−23.5805	−0.763848	−0.381924	−	0.924194i	$-0.624738\pi$
$953$	−23.5805	−0.763848	−0.381924	+	0.924194i	$0.624738\pi$
$954$	−1.00000	−0.0323762
$955$	6.90769	0.223528
$956$	−20.6049	−0.666411
$957$	7.34026	0.237277
$958$	−13.7663	−0.444770
$959$	29.4390	0.950636
$960$	0.701272	0.0226334
$961$	−8.65131	−0.279075
$962$	22.3250	0.719786
$963$	5.95866	0.192015
$964$	22.2208	0.715685
$965$	−13.2031	−0.425022
$966$	24.0003	0.772198
$967$	0.0711048	0.00228658	0.00114329	−	0.999999i	$-0.499636\pi$
$967$	0.0711048	0.00228658	0.00114329	+	0.999999i	$0.499636\pi$
$968$	9.44594	0.303604
$969$	−3.07769	−0.0988695
$970$	13.1013	0.420656
$971$	55.6318	1.78531	0.892655	−	0.450741i	$-0.148840\pi$
$971$	55.6318	1.78531	0.892655	+	0.450741i	$0.148840\pi$
$972$	1.00000	0.0320750
$973$	−24.1680	−0.774791
$974$	24.7380	0.792658
$975$	−28.4073	−0.909762
$976$	4.84496	0.155083
$977$	15.2342	0.487384	0.243692	−	0.969853i	$-0.421641\pi$
$977$	15.2342	0.487384	0.243692	+	0.969853i	$0.421641\pi$
$978$	19.1031	0.610849
$979$	−7.09749	−0.226837
$980$	13.9609	0.445965
$981$	4.94374	0.157841
$982$	−6.27664	−0.200296
$983$	34.7231	1.10749	0.553747	−	0.832685i	$-0.313198\pi$
$983$	34.7231	1.10749	0.553747	+	0.832685i	$0.313198\pi$
$984$	3.03959	0.0968987
$985$	−0.853462	−0.0271936
$986$	18.1218	0.577117
$987$	36.3153	1.15593
$988$	6.30123	0.200469
$989$	−30.6603	−0.974942
$990$	−0.874218	−0.0277845
$991$	19.6159	0.623119	0.311559	−	0.950227i	$-0.399149\pi$
$991$	19.6159	0.623119	0.311559	+	0.950227i	$0.399149\pi$
$992$	4.72744	0.150096
$993$	13.8987	0.441061
$994$	−14.5112	−0.460267
$995$	−2.64223	−0.0837643
$996$	−15.4069	−0.488185
$997$	35.9785	1.13945	0.569726	−	0.821835i	$-0.307049\pi$
$997$	35.9785	1.13945	0.569726	+	0.821835i	$0.307049\pi$
$998$	−6.73574	−0.213216
$999$	−3.54295	−0.112094

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	6042.2.a.bf.1.8	✓	12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
6042.2.a.bf.1.8	✓	12	1.1	even	1	trivial

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 6042 = 2 \cdot 3 \cdot 19 \cdot 53 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	6042.a (trivial)

\(f(q)\)	\(=\)	\(q-1.00000 q^{2} +1.00000 q^{3} +1.00000 q^{4} +0.701272 q^{5} -1.00000 q^{6} +5.18729 q^{7} -1.00000 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q-1.00000 q^{2} +1.00000 q^{3} +1.00000 q^{4} +0.701272 q^{5} -1.00000 q^{6} +5.18729 q^{7} -1.00000 q^{8} +1.00000 q^{9} -0.701272 q^{10} +1.24662 q^{11} +1.00000 q^{12} +6.30123 q^{13} -5.18729 q^{14} +0.701272 q^{15} +1.00000 q^{16} -3.07769 q^{17} -1.00000 q^{18} +1.00000 q^{19} +0.701272 q^{20} +5.18729 q^{21} -1.24662 q^{22} -4.62675 q^{23} -1.00000 q^{24} -4.50822 q^{25} -6.30123 q^{26} +1.00000 q^{27} +5.18729 q^{28} +5.88814 q^{29} -0.701272 q^{30} -4.72744 q^{31} -1.00000 q^{32} +1.24662 q^{33} +3.07769 q^{34} +3.63770 q^{35} +1.00000 q^{36} -3.54295 q^{37} -1.00000 q^{38} +6.30123 q^{39} -0.701272 q^{40} -3.03959 q^{41} -5.18729 q^{42} +6.62675 q^{43} +1.24662 q^{44} +0.701272 q^{45} +4.62675 q^{46} +7.00081 q^{47} +1.00000 q^{48} +19.9080 q^{49} +4.50822 q^{50} -3.07769 q^{51} +6.30123 q^{52} +1.00000 q^{53} -1.00000 q^{54} +0.874218 q^{55} -5.18729 q^{56} +1.00000 q^{57} -5.88814 q^{58} +1.31166 q^{59} +0.701272 q^{60} +4.84496 q^{61} +4.72744 q^{62} +5.18729 q^{63} +1.00000 q^{64} +4.41887 q^{65} -1.24662 q^{66} -2.94658 q^{67} -3.07769 q^{68} -4.62675 q^{69} -3.63770 q^{70} +2.79745 q^{71} -1.00000 q^{72} +12.9071 q^{73} +3.54295 q^{74} -4.50822 q^{75} +1.00000 q^{76} +6.46657 q^{77} -6.30123 q^{78} +13.4739 q^{79} +0.701272 q^{80} +1.00000 q^{81} +3.03959 q^{82} -15.4069 q^{83} +5.18729 q^{84} -2.15829 q^{85} -6.62675 q^{86} +5.88814 q^{87} -1.24662 q^{88} -5.69340 q^{89} -0.701272 q^{90} +32.6863 q^{91} -4.62675 q^{92} -4.72744 q^{93} -7.00081 q^{94} +0.701272 q^{95} -1.00000 q^{96} -18.6821 q^{97} -19.9080 q^{98} +1.24662 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q - 12 q^{2} + 12 q^{3} + 12 q^{4} - 7 q^{5} - 12 q^{6} + 5 q^{7} - 12 q^{8} + 12 q^{9}+O(q^{10}) \) 12 * q - 12 * q^2 + 12 * q^3 + 12 * q^4 - 7 * q^5 - 12 * q^6 + 5 * q^7 - 12 * q^8 + 12 * q^9	\( 12 q - 12 q^{2} + 12 q^{3} + 12 q^{4} - 7 q^{5} - 12 q^{6} + 5 q^{7} - 12 q^{8} + 12 q^{9} + 7 q^{10} - 5 q^{11} + 12 q^{12} + 10 q^{13} - 5 q^{14} - 7 q^{15} + 12 q^{16} + 6 q^{17} - 12 q^{18} + 12 q^{19} - 7 q^{20} + 5 q^{21} + 5 q^{22} - 12 q^{24} + 21 q^{25} - 10 q^{26} + 12 q^{27} + 5 q^{28} + 7 q^{30} + 2 q^{31} - 12 q^{32} - 5 q^{33} - 6 q^{34} - 17 q^{35} + 12 q^{36} + 16 q^{37} - 12 q^{38} + 10 q^{39} + 7 q^{40} + 7 q^{41} - 5 q^{42} + 24 q^{43} - 5 q^{44} - 7 q^{45} + 4 q^{47} + 12 q^{48} + 29 q^{49} - 21 q^{50} + 6 q^{51} + 10 q^{52} + 12 q^{53} - 12 q^{54} - 2 q^{55} - 5 q^{56} + 12 q^{57} + 2 q^{59} - 7 q^{60} + 29 q^{61} - 2 q^{62} + 5 q^{63} + 12 q^{64} - 17 q^{65} + 5 q^{66} + 36 q^{67} + 6 q^{68} + 17 q^{70} - 3 q^{71} - 12 q^{72} + 7 q^{73} - 16 q^{74} + 21 q^{75} + 12 q^{76} - 35 q^{77} - 10 q^{78} + 40 q^{79} - 7 q^{80} + 12 q^{81} - 7 q^{82} + 24 q^{83} + 5 q^{84} - 22 q^{85} - 24 q^{86} + 5 q^{88} - 45 q^{89} + 7 q^{90} + 71 q^{91} + 2 q^{93} - 4 q^{94} - 7 q^{95} - 12 q^{96} + q^{97} - 29 q^{98} - 5 q^{99}+O(q^{100}) \) 12 * q - 12 * q^2 + 12 * q^3 + 12 * q^4 - 7 * q^5 - 12 * q^6 + 5 * q^7 - 12 * q^8 + 12 * q^9 + 7 * q^10 - 5 * q^11 + 12 * q^12 + 10 * q^13 - 5 * q^14 - 7 * q^15 + 12 * q^16 + 6 * q^17 - 12 * q^18 + 12 * q^19 - 7 * q^20 + 5 * q^21 + 5 * q^22 - 12 * q^24 + 21 * q^25 - 10 * q^26 + 12 * q^27 + 5 * q^28 + 7 * q^30 + 2 * q^31 - 12 * q^32 - 5 * q^33 - 6 * q^34 - 17 * q^35 + 12 * q^36 + 16 * q^37 - 12 * q^38 + 10 * q^39 + 7 * q^40 + 7 * q^41 - 5 * q^42 + 24 * q^43 - 5 * q^44 - 7 * q^45 + 4 * q^47 + 12 * q^48 + 29 * q^49 - 21 * q^50 + 6 * q^51 + 10 * q^52 + 12 * q^53 - 12 * q^54 - 2 * q^55 - 5 * q^56 + 12 * q^57 + 2 * q^59 - 7 * q^60 + 29 * q^61 - 2 * q^62 + 5 * q^63 + 12 * q^64 - 17 * q^65 + 5 * q^66 + 36 * q^67 + 6 * q^68 + 17 * q^70 - 3 * q^71 - 12 * q^72 + 7 * q^73 - 16 * q^74 + 21 * q^75 + 12 * q^76 - 35 * q^77 - 10 * q^78 + 40 * q^79 - 7 * q^80 + 12 * q^81 - 7 * q^82 + 24 * q^83 + 5 * q^84 - 22 * q^85 - 24 * q^86 + 5 * q^88 - 45 * q^89 + 7 * q^90 + 71 * q^91 + 2 * q^93 - 4 * q^94 - 7 * q^95 - 12 * q^96 + q^97 - 29 * q^98 - 5 * q^99

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