LMFDB - Embedded newform 6042.2.a.t.1.4

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:	$4$
Coefficient field:	4.4.17609.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} - x^{3} - 7x^{2} + 10x - 1 $ x^4 - x^3 - 7x^2 + 10x - 1
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.4
Root			$1.48539$ of defining polynomial
Character	$\chi$	$=$	6042.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.00000 q^{2} -1.00000 q^{3} +1.00000 q^{4} +3.63500 q^{5} -1.00000 q^{6} -0.793614 q^{7} +1.00000 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q+1.00000 q^{2} -1.00000 q^{3} +1.00000 q^{4} +3.63500 q^{5} -1.00000 q^{6} -0.793614 q^{7} +1.00000 q^{8} +1.00000 q^{9} +3.63500 q^{10} +1.94322 q^{11} -1.00000 q^{12} -6.37184 q^{13} -0.793614 q^{14} -3.63500 q^{15} +1.00000 q^{16} +6.29756 q^{17} +1.00000 q^{18} -1.00000 q^{19} +3.63500 q^{20} +0.793614 q^{21} +1.94322 q^{22} +2.69178 q^{23} -1.00000 q^{24} +8.21322 q^{25} -6.37184 q^{26} -1.00000 q^{27} -0.793614 q^{28} +3.60578 q^{29} -3.63500 q^{30} -1.14961 q^{31} +1.00000 q^{32} -1.94322 q^{33} +6.29756 q^{34} -2.88479 q^{35} +1.00000 q^{36} -1.09283 q^{37} -1.00000 q^{38} +6.37184 q^{39} +3.63500 q^{40} -0.662559 q^{41} +0.793614 q^{42} +12.4647 q^{43} +1.94322 q^{44} +3.63500 q^{45} +2.69178 q^{46} -9.36117 q^{47} -1.00000 q^{48} -6.37018 q^{49} +8.21322 q^{50} -6.29756 q^{51} -6.37184 q^{52} -1.00000 q^{53} -1.00000 q^{54} +7.06361 q^{55} -0.793614 q^{56} +1.00000 q^{57} +3.60578 q^{58} -2.51461 q^{59} -3.63500 q^{60} +12.7622 q^{61} -1.14961 q^{62} -0.793614 q^{63} +1.00000 q^{64} -23.1616 q^{65} -1.94322 q^{66} +8.07262 q^{67} +6.29756 q^{68} -2.69178 q^{69} -2.88479 q^{70} -0.616446 q^{71} +1.00000 q^{72} +1.82283 q^{73} -1.09283 q^{74} -8.21322 q^{75} -1.00000 q^{76} -1.54217 q^{77} +6.37184 q^{78} +5.96178 q^{79} +3.63500 q^{80} +1.00000 q^{81} -0.662559 q^{82} +0.158614 q^{83} +0.793614 q^{84} +22.8916 q^{85} +12.4647 q^{86} -3.60578 q^{87} +1.94322 q^{88} +5.79361 q^{89} +3.63500 q^{90} +5.05678 q^{91} +2.69178 q^{92} +1.14961 q^{93} -9.36117 q^{94} -3.63500 q^{95} -1.00000 q^{96} +17.7898 q^{97} -6.37018 q^{98} +1.94322 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q + 4 q^{2} - 4 q^{3} + 4 q^{4} + 6 q^{5} - 4 q^{6} + 3 q^{7} + 4 q^{8} + 4 q^{9}+O(q^{10}) $ 4 * q + 4 * q^2 - 4 * q^3 + 4 * q^4 + 6 * q^5 - 4 * q^6 + 3 * q^7 + 4 * q^8 + 4 * q^9	\( 4 q + 4 q^{2} - 4 q^{3} + 4 q^{4} + 6 q^{5} - 4 q^{6} + 3 q^{7} + 4 q^{8} + 4 q^{9} + 6 q^{10} - 2 q^{11} - 4 q^{12} - q^{13} + 3 q^{14} - 6 q^{15} + 4 q^{16} + 8 q^{17} + 4 q^{18} - 4 q^{19} + 6 q^{20} - 3 q^{21} - 2 q^{22} + 12 q^{23} - 4 q^{24} + 6 q^{25} - q^{26} - 4 q^{27} + 3 q^{28} - 4 q^{29} - 6 q^{30} - q^{31} + 4 q^{32} + 2 q^{33} + 8 q^{34} + 18 q^{35} + 4 q^{36} + 9 q^{37} - 4 q^{38} + q^{39} + 6 q^{40} + 6 q^{41} - 3 q^{42} + 12 q^{43} - 2 q^{44} + 6 q^{45} + 12 q^{46} + 3 q^{47} - 4 q^{48} + 9 q^{49} + 6 q^{50} - 8 q^{51} - q^{52} - 4 q^{53} - 4 q^{54} + 5 q^{55} + 3 q^{56} + 4 q^{57} - 4 q^{58} - 15 q^{59} - 6 q^{60} - 4 q^{61} - q^{62} + 3 q^{63} + 4 q^{64} - 13 q^{65} + 2 q^{66} + 15 q^{67} + 8 q^{68} - 12 q^{69} + 18 q^{70} + 4 q^{72} + 11 q^{73} + 9 q^{74} - 6 q^{75} - 4 q^{76} - 11 q^{77} + q^{78} + 8 q^{79} + 6 q^{80} + 4 q^{81} + 6 q^{82} + 3 q^{83} - 3 q^{84} + 29 q^{85} + 12 q^{86} + 4 q^{87} - 2 q^{88} + 17 q^{89} + 6 q^{90} + 30 q^{91} + 12 q^{92} + q^{93} + 3 q^{94} - 6 q^{95} - 4 q^{96} + 16 q^{97} + 9 q^{98} - 2 q^{99}+O(q^{100}) \) 4 * q + 4 * q^2 - 4 * q^3 + 4 * q^4 + 6 * q^5 - 4 * q^6 + 3 * q^7 + 4 * q^8 + 4 * q^9 + 6 * q^10 - 2 * q^11 - 4 * q^12 - q^13 + 3 * q^14 - 6 * q^15 + 4 * q^16 + 8 * q^17 + 4 * q^18 - 4 * q^19 + 6 * q^20 - 3 * q^21 - 2 * q^22 + 12 * q^23 - 4 * q^24 + 6 * q^25 - q^26 - 4 * q^27 + 3 * q^28 - 4 * q^29 - 6 * q^30 - q^31 + 4 * q^32 + 2 * q^33 + 8 * q^34 + 18 * q^35 + 4 * q^36 + 9 * q^37 - 4 * q^38 + q^39 + 6 * q^40 + 6 * q^41 - 3 * q^42 + 12 * q^43 - 2 * q^44 + 6 * q^45 + 12 * q^46 + 3 * q^47 - 4 * q^48 + 9 * q^49 + 6 * q^50 - 8 * q^51 - q^52 - 4 * q^53 - 4 * q^54 + 5 * q^55 + 3 * q^56 + 4 * q^57 - 4 * q^58 - 15 * q^59 - 6 * q^60 - 4 * q^61 - q^62 + 3 * q^63 + 4 * q^64 - 13 * q^65 + 2 * q^66 + 15 * q^67 + 8 * q^68 - 12 * q^69 + 18 * q^70 + 4 * q^72 + 11 * q^73 + 9 * q^74 - 6 * q^75 - 4 * q^76 - 11 * q^77 + q^78 + 8 * q^79 + 6 * q^80 + 4 * q^81 + 6 * q^82 + 3 * q^83 - 3 * q^84 + 29 * q^85 + 12 * q^86 + 4 * q^87 - 2 * q^88 + 17 * q^89 + 6 * q^90 + 30 * q^91 + 12 * q^92 + q^93 + 3 * q^94 - 6 * q^95 - 4 * q^96 + 16 * q^97 + 9 * q^98 - 2 * q^99

Display 100 coefficients 10 coefficients

Coefficient data

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

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

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

$2$	1.00000	0.707107
$2$	1.00000	0.707107
$3$	−1.00000	−0.577350
$3$	−1.00000	−0.577350
$4$	1.00000	0.500000
$5$	3.63500	1.62562	0.812811	−	0.582528i	$-0.197936\pi$
$5$	3.63500	1.62562	0.812811	+	0.582528i	$0.197936\pi$
$6$	−1.00000	−0.408248
$7$	−0.793614	−0.299958	−0.149979	−	0.988689i	$-0.547921\pi$
$7$	−0.793614	−0.299958	−0.149979	+	0.988689i	$0.547921\pi$
$8$	1.00000	0.353553
$9$	1.00000	0.333333
$10$	3.63500	1.14949
$11$	1.94322	0.585904	0.292952	−	0.956127i	$-0.405362\pi$
$11$	1.94322	0.585904	0.292952	+	0.956127i	$0.405362\pi$
$12$	−1.00000	−0.288675
$13$	−6.37184	−1.76723	−0.883615	−	0.468215i	$-0.844897\pi$
$13$	−6.37184	−1.76723	−0.883615	+	0.468215i	$0.844897\pi$
$14$	−0.793614	−0.212102
$15$	−3.63500	−0.938553
$16$	1.00000	0.250000
$17$	6.29756	1.52738	0.763691	−	0.645582i	$-0.223385\pi$
$17$	6.29756	1.52738	0.763691	+	0.645582i	$0.223385\pi$
$18$	1.00000	0.235702
$19$	−1.00000	−0.229416
$19$	−1.00000	−0.229416
$20$	3.63500	0.812811
$21$	0.793614	0.173181
$22$	1.94322	0.414296
$23$	2.69178	0.561274	0.280637	−	0.959814i	$-0.409454\pi$
$23$	2.69178	0.561274	0.280637	+	0.959814i	$0.409454\pi$
$24$	−1.00000	−0.204124
$25$	8.21322	1.64264
$26$	−6.37184	−1.24962
$27$	−1.00000	−0.192450
$28$	−0.793614	−0.149979
$29$	3.60578	0.669577	0.334788	−	0.942293i	$-0.391335\pi$
$29$	3.60578	0.669577	0.334788	+	0.942293i	$0.391335\pi$
$30$	−3.63500	−0.663657
$31$	−1.14961	−0.206476	−0.103238	−	0.994657i	$-0.532920\pi$
$31$	−1.14961	−0.206476	−0.103238	+	0.994657i	$0.532920\pi$
$32$	1.00000	0.176777
$33$	−1.94322	−0.338272
$34$	6.29756	1.08002
$35$	−2.88479	−0.487618
$36$	1.00000	0.166667
$37$	−1.09283	−0.179660	−0.0898302	−	0.995957i	$-0.528632\pi$
$37$	−1.09283	−0.179660	−0.0898302	+	0.995957i	$0.528632\pi$
$38$	−1.00000	−0.162221
$39$	6.37184	1.02031
$40$	3.63500	0.574744
$41$	−0.662559	−0.103474	−0.0517372	−	0.998661i	$-0.516476\pi$
$41$	−0.662559	−0.103474	−0.0517372	+	0.998661i	$0.516476\pi$
$42$	0.793614	0.122457
$43$	12.4647	1.90084	0.950422	−	0.310963i	$-0.100652\pi$
$43$	12.4647	1.90084	0.950422	+	0.310963i	$0.100652\pi$
$44$	1.94322	0.292952
$45$	3.63500	0.541874
$46$	2.69178	0.396881
$47$	−9.36117	−1.36547	−0.682734	−	0.730667i	$-0.739209\pi$
$47$	−9.36117	−1.36547	−0.682734	+	0.730667i	$0.739209\pi$
$48$	−1.00000	−0.144338
$49$	−6.37018	−0.910025
$50$	8.21322	1.16152
$51$	−6.29756	−0.881835
$52$	−6.37184	−0.883615
$53$	−1.00000	−0.137361
$53$	−1.00000	−0.137361
$54$	−1.00000	−0.136083
$55$	7.06361	0.952457
$56$	−0.793614	−0.106051
$57$	1.00000	0.132453
$58$	3.60578	0.473462
$59$	−2.51461	−0.327374	−0.163687	−	0.986512i	$-0.552339\pi$
$59$	−2.51461	−0.327374	−0.163687	+	0.986512i	$0.552339\pi$
$60$	−3.63500	−0.469276
$61$	12.7622	1.63404	0.817018	−	0.576613i	$-0.195626\pi$
$61$	12.7622	1.63404	0.817018	+	0.576613i	$0.195626\pi$
$62$	−1.14961	−0.146000
$63$	−0.793614	−0.0999860
$64$	1.00000	0.125000
$65$	−23.1616	−2.87285
$66$	−1.94322	−0.239194
$67$	8.07262	0.986227	0.493114	−	0.869965i	$-0.335859\pi$
$67$	8.07262	0.986227	0.493114	+	0.869965i	$0.335859\pi$
$68$	6.29756	0.763691
$69$	−2.69178	−0.324052
$70$	−2.88479	−0.344798
$71$	−0.616446	−0.0731587	−0.0365793	−	0.999331i	$-0.511646\pi$
$71$	−0.616446	−0.0731587	−0.0365793	+	0.999331i	$0.511646\pi$
$72$	1.00000	0.117851
$73$	1.82283	0.213346	0.106673	−	0.994294i	$-0.465980\pi$
$73$	1.82283	0.213346	0.106673	+	0.994294i	$0.465980\pi$
$74$	−1.09283	−0.127039
$75$	−8.21322	−0.948381
$76$	−1.00000	−0.114708
$77$	−1.54217	−0.175746
$78$	6.37184	0.721468
$79$	5.96178	0.670752	0.335376	−	0.942084i	$-0.391137\pi$
$79$	5.96178	0.670752	0.335376	+	0.942084i	$0.391137\pi$
$80$	3.63500	0.406405
$81$	1.00000	0.111111
$82$	−0.662559	−0.0731674
$83$	0.158614	0.0174102	0.00870509	−	0.999962i	$-0.497229\pi$
$83$	0.158614	0.0174102	0.00870509	+	0.999962i	$0.497229\pi$
$84$	0.793614	0.0865904
$85$	22.8916	2.48294
$86$	12.4647	1.34410
$87$	−3.60578	−0.386580
$88$	1.94322	0.207148
$89$	5.79361	0.614122	0.307061	−	0.951690i	$-0.400654\pi$
$89$	5.79361	0.614122	0.307061	+	0.951690i	$0.400654\pi$
$90$	3.63500	0.383163
$91$	5.05678	0.530094
$92$	2.69178	0.280637
$93$	1.14961	0.119209
$94$	−9.36117	−0.965531
$95$	−3.63500	−0.372943
$96$	−1.00000	−0.102062
$97$	17.7898	1.80628	0.903139	−	0.429347i	$-0.141256\pi$
$97$	17.7898	1.80628	0.903139	+	0.429347i	$0.141256\pi$
$98$	−6.37018	−0.643485
$99$	1.94322	0.195301
$100$	8.21322	0.821322
$101$	4.62816	0.460520	0.230260	−	0.973129i	$-0.426042\pi$
$101$	4.62816	0.460520	0.230260	+	0.973129i	$0.426042\pi$
$102$	−6.29756	−0.623551
$103$	14.4720	1.42597	0.712985	−	0.701179i	$-0.247343\pi$
$103$	14.4720	1.42597	0.712985	+	0.701179i	$0.247343\pi$
$104$	−6.37184	−0.624810
$105$	2.88479	0.281526
$106$	−1.00000	−0.0971286
$107$	4.37184	0.422641	0.211321	−	0.977417i	$-0.432224\pi$
$107$	4.37184	0.422641	0.211321	+	0.977417i	$0.432224\pi$
$108$	−1.00000	−0.0962250
$109$	4.61479	0.442016	0.221008	−	0.975272i	$-0.429065\pi$
$109$	4.61479	0.442016	0.221008	+	0.975272i	$0.429065\pi$
$110$	7.06361	0.673489
$111$	1.09283	0.103727
$112$	−0.793614	−0.0749895
$113$	−2.15644	−0.202861	−0.101431	−	0.994843i	$-0.532342\pi$
$113$	−2.15644	−0.202861	−0.101431	+	0.994843i	$0.532342\pi$
$114$	1.00000	0.0936586
$115$	9.78461	0.912419
$116$	3.60578	0.334788
$117$	−6.37184	−0.589076
$118$	−2.51461	−0.231489
$119$	−4.99783	−0.458150
$120$	−3.63500	−0.331829
$121$	−7.22389	−0.656717
$122$	12.7622	1.15544
$123$	0.662559	0.0597409
$124$	−1.14961	−0.103238
$125$	11.6801	1.04470
$126$	−0.793614	−0.0707007
$127$	−16.7644	−1.48760	−0.743800	−	0.668402i	$-0.766978\pi$
$127$	−16.7644	−1.48760	−0.743800	+	0.668402i	$0.766978\pi$
$128$	1.00000	0.0883883
$129$	−12.4647	−1.09745
$130$	−23.1616	−2.03141
$131$	9.78295	0.854740	0.427370	−	0.904077i	$-0.359440\pi$
$131$	9.78295	0.854740	0.427370	+	0.904077i	$0.359440\pi$
$132$	−1.94322	−0.169136
$133$	0.793614	0.0688151
$134$	8.07262	0.697368
$135$	−3.63500	−0.312851
$136$	6.29756	0.540011
$137$	−4.17611	−0.356790	−0.178395	−	0.983959i	$-0.557090\pi$
$137$	−4.17611	−0.356790	−0.178395	+	0.983959i	$0.557090\pi$
$138$	−2.69178	−0.229139
$139$	−12.4764	−1.05823	−0.529117	−	0.848549i	$-0.677477\pi$
$139$	−12.4764	−1.05823	−0.529117	+	0.848549i	$0.677477\pi$
$140$	−2.88479	−0.243809
$141$	9.36117	0.788353
$142$	−0.616446	−0.0517310
$143$	−12.3819	−1.03543
$144$	1.00000	0.0833333
$145$	13.1070	1.08848
$146$	1.82283	0.150859
$147$	6.37018	0.525403
$148$	−1.09283	−0.0898302
$149$	−5.00684	−0.410176	−0.205088	−	0.978744i	$-0.565748\pi$
$149$	−5.00684	−0.410176	−0.205088	+	0.978744i	$0.565748\pi$
$150$	−8.21322	−0.670607
$151$	−18.0688	−1.47042	−0.735209	−	0.677841i	$-0.762916\pi$
$151$	−18.0688	−1.47042	−0.735209	+	0.677841i	$0.762916\pi$
$152$	−1.00000	−0.0811107
$153$	6.29756	0.509127
$154$	−1.54217	−0.124271
$155$	−4.17883	−0.335651
$156$	6.37184	0.510155
$157$	17.1998	1.37270	0.686349	−	0.727273i	$-0.259212\pi$
$157$	17.1998	1.37270	0.686349	+	0.727273i	$0.259212\pi$
$158$	5.96178	0.474293
$159$	1.00000	0.0793052
$160$	3.63500	0.287372
$161$	−2.13623	−0.168359
$162$	1.00000	0.0785674
$163$	−13.5039	−1.05771	−0.528855	−	0.848712i	$-0.677379\pi$
$163$	−13.5039	−1.05771	−0.528855	+	0.848712i	$0.677379\pi$
$164$	−0.662559	−0.0517372
$165$	−7.06361	−0.549902
$166$	0.158614	0.0123109
$167$	−10.4152	−0.805955	−0.402978	−	0.915210i	$-0.632025\pi$
$167$	−10.4152	−0.805955	−0.402978	+	0.915210i	$0.632025\pi$
$168$	0.793614	0.0612286
$169$	27.6003	2.12310
$170$	22.8916	1.75571
$171$	−1.00000	−0.0764719
$172$	12.4647	0.950422
$173$	−3.16816	−0.240871	−0.120435	−	0.992721i	$-0.538429\pi$
$173$	−3.16816	−0.240871	−0.120435	+	0.992721i	$0.538429\pi$
$174$	−3.60578	−0.273354
$175$	−6.51813	−0.492724
$176$	1.94322	0.146476
$177$	2.51461	0.189010
$178$	5.79361	0.434250
$179$	−6.82012	−0.509760	−0.254880	−	0.966973i	$-0.582036\pi$
$179$	−6.82012	−0.509760	−0.254880	+	0.966973i	$0.582036\pi$
$180$	3.63500	0.270937
$181$	16.4169	1.22026	0.610129	−	0.792302i	$-0.291118\pi$
$181$	16.4169	1.22026	0.610129	+	0.792302i	$0.291118\pi$
$182$	5.05678	0.374833
$183$	−12.7622	−0.943411
$184$	2.69178	0.198440
$185$	−3.97244	−0.292060
$186$	1.14961	0.0842934
$187$	12.2376	0.894899
$188$	−9.36117	−0.682734
$189$	0.793614	0.0577269
$190$	−3.63500	−0.263711
$191$	−13.5400	−0.979720	−0.489860	−	0.871801i	$-0.662952\pi$
$191$	−13.5400	−0.979720	−0.489860	+	0.871801i	$0.662952\pi$
$192$	−1.00000	−0.0721688
$193$	−13.4523	−0.968321	−0.484160	−	0.874979i	$-0.660875\pi$
$193$	−13.4523	−0.968321	−0.484160	+	0.874979i	$0.660875\pi$
$194$	17.7898	1.27723
$195$	23.1616	1.65864
$196$	−6.37018	−0.455013
$197$	6.82967	0.486594	0.243297	−	0.969952i	$-0.421771\pi$
$197$	6.82967	0.486594	0.243297	+	0.969952i	$0.421771\pi$
$198$	1.94322	0.138099
$199$	−12.8635	−0.911866	−0.455933	−	0.890014i	$-0.650694\pi$
$199$	−12.8635	−0.911866	−0.455933	+	0.890014i	$0.650694\pi$
$200$	8.21322	0.580762
$201$	−8.07262	−0.569399
$202$	4.62816	0.325636
$203$	−2.86160	−0.200845
$204$	−6.29756	−0.440917
$205$	−2.40840	−0.168210
$206$	14.4720	1.00831
$207$	2.69178	0.187091
$208$	−6.37184	−0.441807
$209$	−1.94322	−0.134416
$210$	2.88479	0.199069
$211$	−19.9028	−1.37017	−0.685084	−	0.728464i	$-0.740234\pi$
$211$	−19.9028	−1.37017	−0.685084	+	0.728464i	$0.740234\pi$
$212$	−1.00000	−0.0686803
$213$	0.616446	0.0422382
$214$	4.37184	0.298853
$215$	45.3091	3.09005
$216$	−1.00000	−0.0680414
$217$	0.912345	0.0619340
$218$	4.61479	0.312553
$219$	−1.82283	−0.123176
$220$	7.06361	0.476229
$221$	−40.1270	−2.69923
$222$	1.09283	0.0733460
$223$	−9.14412	−0.612336	−0.306168	−	0.951978i	$-0.599047\pi$
$223$	−9.14412	−0.612336	−0.306168	+	0.951978i	$0.599047\pi$
$224$	−0.793614	−0.0530256
$225$	8.21322	0.547548
$226$	−2.15644	−0.143445
$227$	16.5081	1.09568	0.547839	−	0.836583i	$-0.315450\pi$
$227$	16.5081	1.09568	0.547839	+	0.836583i	$0.315450\pi$
$228$	1.00000	0.0662266
$229$	24.5761	1.62403	0.812016	−	0.583636i	$-0.198370\pi$
$229$	24.5761	1.62403	0.812016	+	0.583636i	$0.198370\pi$
$230$	9.78461	0.645178
$231$	1.54217	0.101467
$232$	3.60578	0.236731
$233$	9.01584	0.590647	0.295324	−	0.955397i	$-0.404573\pi$
$233$	9.01584	0.590647	0.295324	+	0.955397i	$0.404573\pi$
$234$	−6.37184	−0.416540
$235$	−34.0279	−2.21973
$236$	−2.51461	−0.163687
$237$	−5.96178	−0.387259
$238$	−4.99783	−0.323961
$239$	−9.64867	−0.624121	−0.312060	−	0.950062i	$-0.601019\pi$
$239$	−9.64867	−0.624121	−0.312060	+	0.950062i	$0.601019\pi$
$240$	−3.63500	−0.234638
$241$	−0.850933	−0.0548134	−0.0274067	−	0.999624i	$-0.508725\pi$
$241$	−0.850933	−0.0548134	−0.0274067	+	0.999624i	$0.508725\pi$
$242$	−7.22389	−0.464369
$243$	−1.00000	−0.0641500
$244$	12.7622	0.817018
$245$	−23.1556	−1.47936
$246$	0.662559	0.0422432
$247$	6.37184	0.405430
$248$	−1.14961	−0.0730002
$249$	−0.158614	−0.0100518
$250$	11.6801	0.738712
$251$	−19.1840	−1.21088	−0.605442	−	0.795890i	$-0.707004\pi$
$251$	−19.1840	−1.21088	−0.605442	+	0.795890i	$0.707004\pi$
$252$	−0.793614	−0.0499930
$253$	5.23072	0.328853
$254$	−16.7644	−1.05189
$255$	−22.8916	−1.43353
$256$	1.00000	0.0625000
$257$	11.3650	0.708929	0.354465	−	0.935069i	$-0.384663\pi$
$257$	11.3650	0.708929	0.354465	+	0.935069i	$0.384663\pi$
$258$	−12.4647	−0.776016
$259$	0.867286	0.0538905
$260$	−23.1616	−1.43642
$261$	3.60578	0.223192
$262$	9.78295	0.604393
$263$	17.9085	1.10429	0.552143	−	0.833749i	$-0.313810\pi$
$263$	17.9085	1.10429	0.552143	+	0.833749i	$0.313810\pi$
$264$	−1.94322	−0.119597
$265$	−3.63500	−0.223296
$266$	0.793614	0.0486596
$267$	−5.79361	−0.354563
$268$	8.07262	0.493114
$269$	13.8228	0.842793	0.421396	−	0.906877i	$-0.361540\pi$
$269$	13.8228	0.842793	0.421396	+	0.906877i	$0.361540\pi$
$270$	−3.63500	−0.221219
$271$	10.1002	0.613542	0.306771	−	0.951783i	$-0.400751\pi$
$271$	10.1002	0.613542	0.306771	+	0.951783i	$0.400751\pi$
$272$	6.29756	0.381846
$273$	−5.05678	−0.306050
$274$	−4.17611	−0.252288
$275$	15.9601	0.962431
$276$	−2.69178	−0.162026
$277$	−29.2231	−1.75584	−0.877922	−	0.478804i	$-0.841070\pi$
$277$	−29.2231	−1.75584	−0.877922	+	0.478804i	$0.841070\pi$
$278$	−12.4764	−0.748284
$279$	−1.14961	−0.0688253
$280$	−2.88479	−0.172399
$281$	20.0519	1.19620	0.598098	−	0.801423i	$-0.295923\pi$
$281$	20.0519	1.19620	0.598098	+	0.801423i	$0.295923\pi$
$282$	9.36117	0.557450
$283$	4.63605	0.275585	0.137792	−	0.990461i	$-0.455999\pi$
$283$	4.63605	0.275585	0.137792	+	0.990461i	$0.455999\pi$
$284$	−0.616446	−0.0365793
$285$	3.63500	0.215319
$286$	−12.3819	−0.732157
$287$	0.525816	0.0310379
$288$	1.00000	0.0589256
$289$	22.6592	1.33290
$290$	13.1070	0.769670
$291$	−17.7898	−1.04286
$292$	1.82283	0.106673
$293$	1.76822	0.103301	0.0516504	−	0.998665i	$-0.483552\pi$
$293$	1.76822	0.103301	0.0516504	+	0.998665i	$0.483552\pi$
$294$	6.37018	0.371516
$295$	−9.14060	−0.532186
$296$	−1.09283	−0.0635195
$297$	−1.94322	−0.112757
$298$	−5.00684	−0.290038
$299$	−17.1516	−0.991900
$300$	−8.21322	−0.474191
$301$	−9.89213	−0.570173
$302$	−18.0688	−1.03974
$303$	−4.62816	−0.265881
$304$	−1.00000	−0.0573539
$305$	46.3907	2.65632
$306$	6.29756	0.360007
$307$	−23.8387	−1.36054	−0.680272	−	0.732959i	$-0.738139\pi$
$307$	−23.8387	−1.36054	−0.680272	+	0.732959i	$0.738139\pi$
$308$	−1.54217	−0.0878732
$309$	−14.4720	−0.823284
$310$	−4.17883	−0.237341
$311$	6.92985	0.392955	0.196478	−	0.980508i	$-0.437050\pi$
$311$	6.92985	0.392955	0.196478	+	0.980508i	$0.437050\pi$
$312$	6.37184	0.360734
$313$	24.5812	1.38941	0.694707	−	0.719293i	$-0.255534\pi$
$313$	24.5812	1.38941	0.694707	+	0.719293i	$0.255534\pi$
$314$	17.1998	0.970643
$315$	−2.88479	−0.162539
$316$	5.96178	0.335376
$317$	3.25039	0.182560	0.0912801	−	0.995825i	$-0.470904\pi$
$317$	3.25039	0.182560	0.0912801	+	0.995825i	$0.470904\pi$
$318$	1.00000	0.0560772
$319$	7.00684	0.392307
$320$	3.63500	0.203203
$321$	−4.37184	−0.244012
$322$	−2.13623	−0.119048
$323$	−6.29756	−0.350406
$324$	1.00000	0.0555556
$325$	−52.3333	−2.90293
$326$	−13.5039	−0.747914
$327$	−4.61479	−0.255198
$328$	−0.662559	−0.0365837
$329$	7.42916	0.409583
$330$	−7.06361	−0.388839
$331$	−6.30717	−0.346673	−0.173337	−	0.984863i	$-0.555455\pi$
$331$	−6.30717	−0.346673	−0.173337	+	0.984863i	$0.555455\pi$
$332$	0.158614	0.00870509
$333$	−1.09283	−0.0598868
$334$	−10.4152	−0.569896
$335$	29.3440	1.60323
$336$	0.793614	0.0432952
$337$	−33.3102	−1.81452	−0.907260	−	0.420569i	$-0.861830\pi$
$337$	−33.3102	−1.81452	−0.907260	+	0.420569i	$0.861830\pi$
$338$	27.6003	1.50126
$339$	2.15644	0.117122
$340$	22.8916	1.24147
$341$	−2.23395	−0.120975
$342$	−1.00000	−0.0540738
$343$	10.6108	0.572927
$344$	12.4647	0.672050
$345$	−9.78461	−0.526786
$346$	−3.16816	−0.170321
$347$	−24.7202	−1.32705	−0.663524	−	0.748155i	$-0.730940\pi$
$347$	−24.7202	−1.32705	−0.663524	+	0.748155i	$0.730940\pi$
$348$	−3.60578	−0.193290
$349$	2.52799	0.135320	0.0676600	−	0.997708i	$-0.478447\pi$
$349$	2.52799	0.135320	0.0676600	+	0.997708i	$0.478447\pi$
$350$	−6.51813	−0.348409
$351$	6.37184	0.340103
$352$	1.94322	0.103574
$353$	13.1739	0.701178	0.350589	−	0.936529i	$-0.385981\pi$
$353$	13.1739	0.701178	0.350589	+	0.936529i	$0.385981\pi$
$354$	2.51461	0.133650
$355$	−2.24078	−0.118928
$356$	5.79361	0.307061
$357$	4.99783	0.264513
$358$	−6.82012	−0.360455
$359$	20.2201	1.06717	0.533587	−	0.845745i	$-0.320844\pi$
$359$	20.2201	1.06717	0.533587	+	0.845745i	$0.320844\pi$
$360$	3.63500	0.191581
$361$	1.00000	0.0526316
$362$	16.4169	0.862853
$363$	7.22389	0.379156
$364$	5.05678	0.265047
$365$	6.62599	0.346820
$366$	−12.7622	−0.667092
$367$	24.5817	1.28316	0.641578	−	0.767058i	$-0.278280\pi$
$367$	24.5817	1.28316	0.641578	+	0.767058i	$0.278280\pi$
$368$	2.69178	0.140319
$369$	−0.662559	−0.0344914
$370$	−3.97244	−0.206517
$371$	0.793614	0.0412024
$372$	1.14961	0.0596044
$373$	16.5430	0.856564	0.428282	−	0.903645i	$-0.359119\pi$
$373$	16.5430	0.856564	0.428282	+	0.903645i	$0.359119\pi$
$374$	12.2376	0.632789
$375$	−11.6801	−0.603156
$376$	−9.36117	−0.482766
$377$	−22.9754	−1.18330
$378$	0.793614	0.0408191
$379$	6.65738	0.341967	0.170983	−	0.985274i	$-0.445306\pi$
$379$	6.65738	0.341967	0.170983	+	0.985274i	$0.445306\pi$
$380$	−3.63500	−0.186472
$381$	16.7644	0.858866
$382$	−13.5400	−0.692767
$383$	16.8507	0.861030	0.430515	−	0.902583i	$-0.358332\pi$
$383$	16.8507	0.861030	0.430515	+	0.902583i	$0.358332\pi$
$384$	−1.00000	−0.0510310
$385$	−5.60578	−0.285697
$386$	−13.4523	−0.684706
$387$	12.4647	0.633615
$388$	17.7898	0.903139
$389$	5.79084	0.293607	0.146804	−	0.989166i	$-0.453101\pi$
$389$	5.79084	0.293607	0.146804	+	0.989166i	$0.453101\pi$
$390$	23.1616	1.17283
$391$	16.9516	0.857280
$392$	−6.37018	−0.321743
$393$	−9.78295	−0.493485
$394$	6.82967	0.344074
$395$	21.6711	1.09039
$396$	1.94322	0.0976506
$397$	33.1595	1.66423	0.832113	−	0.554607i	$-0.187131\pi$
$397$	33.1595	1.66423	0.832113	+	0.554607i	$0.187131\pi$
$398$	−12.8635	−0.644787
$399$	−0.793614	−0.0397304
$400$	8.21322	0.410661
$401$	−22.0915	−1.10320	−0.551598	−	0.834110i	$-0.685982\pi$
$401$	−22.0915	−1.10320	−0.551598	+	0.834110i	$0.685982\pi$
$402$	−8.07262	−0.402626
$403$	7.32512	0.364890
$404$	4.62816	0.230260
$405$	3.63500	0.180625
$406$	−2.86160	−0.142019
$407$	−2.12361	−0.105264
$408$	−6.29756	−0.311776
$409$	9.63500	0.476420	0.238210	−	0.971214i	$-0.423439\pi$
$409$	9.63500	0.476420	0.238210	+	0.971214i	$0.423439\pi$
$410$	−2.40840	−0.118942
$411$	4.17611	0.205993
$412$	14.4720	0.712985
$413$	1.99563	0.0981985
$414$	2.69178	0.132294
$415$	0.576563	0.0283024
$416$	−6.37184	−0.312405
$417$	12.4764	0.610971
$418$	−1.94322	−0.0950461
$419$	−17.6959	−0.864501	−0.432251	−	0.901754i	$-0.642280\pi$
$419$	−17.6959	−0.864501	−0.432251	+	0.901754i	$0.642280\pi$
$420$	2.88479	0.140763
$421$	−3.54434	−0.172740	−0.0863702	−	0.996263i	$-0.527527\pi$
$421$	−3.54434	−0.172740	−0.0863702	+	0.996263i	$0.527527\pi$
$422$	−19.9028	−0.968855
$423$	−9.36117	−0.455156
$424$	−1.00000	−0.0485643
$425$	51.7232	2.50895
$426$	0.616446	0.0298669
$427$	−10.1283	−0.490142
$428$	4.37184	0.211321
$429$	12.3819	0.597804
$430$	45.3091	2.18500
$431$	−19.1878	−0.924245	−0.462123	−	0.886816i	$-0.652912\pi$
$431$	−19.1878	−0.924245	−0.462123	+	0.886816i	$0.652912\pi$
$432$	−1.00000	−0.0481125
$433$	−13.4114	−0.644511	−0.322256	−	0.946653i	$-0.604441\pi$
$433$	−13.4114	−0.644511	−0.322256	+	0.946653i	$0.604441\pi$
$434$	0.912345	0.0437940
$435$	−13.1070	−0.628433
$436$	4.61479	0.221008
$437$	−2.69178	−0.128765
$438$	−1.82283	−0.0870983
$439$	11.9648	0.571048	0.285524	−	0.958372i	$-0.407832\pi$
$439$	11.9648	0.571048	0.285524	+	0.958372i	$0.407832\pi$
$440$	7.06361	0.336745
$441$	−6.37018	−0.303342
$442$	−40.1270	−1.90865
$443$	−15.4253	−0.732878	−0.366439	−	0.930442i	$-0.619423\pi$
$443$	−15.4253	−0.732878	−0.366439	+	0.930442i	$0.619423\pi$
$444$	1.09283	0.0518635
$445$	21.0598	0.998329
$446$	−9.14412	−0.432987
$447$	5.00684	0.236815
$448$	−0.793614	−0.0374947
$449$	−13.2178	−0.623786	−0.311893	−	0.950117i	$-0.600963\pi$
$449$	−13.2178	−0.623786	−0.311893	+	0.950117i	$0.600963\pi$
$450$	8.21322	0.387175
$451$	−1.28750	−0.0606260
$452$	−2.15644	−0.101431
$453$	18.0688	0.848946
$454$	16.5081	0.774762
$455$	18.3814	0.861733
$456$	1.00000	0.0468293
$457$	−3.04394	−0.142390	−0.0711948	−	0.997462i	$-0.522681\pi$
$457$	−3.04394	−0.142390	−0.0711948	+	0.997462i	$0.522681\pi$
$458$	24.5761	1.14836
$459$	−6.29756	−0.293945
$460$	9.78461	0.456210
$461$	−5.69695	−0.265334	−0.132667	−	0.991161i	$-0.542354\pi$
$461$	−5.69695	−0.265334	−0.132667	+	0.991161i	$0.542354\pi$
$462$	1.54217	0.0717482
$463$	33.5954	1.56131	0.780656	−	0.624962i	$-0.214885\pi$
$463$	33.5954	1.56131	0.780656	+	0.624962i	$0.214885\pi$
$464$	3.60578	0.167394
$465$	4.17883	0.193788
$466$	9.01584	0.417651
$467$	−32.0502	−1.48311	−0.741554	−	0.670893i	$-0.765911\pi$
$467$	−32.0502	−1.48311	−0.741554	+	0.670893i	$0.765911\pi$
$468$	−6.37184	−0.294538
$469$	−6.40654	−0.295827
$470$	−34.0279	−1.56959
$471$	−17.1998	−0.792527
$472$	−2.51461	−0.115744
$473$	24.2216	1.11371
$474$	−5.96178	−0.273833
$475$	−8.21322	−0.376848
$476$	−4.99783	−0.229075
$477$	−1.00000	−0.0457869
$478$	−9.64867	−0.441320
$479$	40.6904	1.85919	0.929596	−	0.368580i	$-0.120156\pi$
$479$	40.6904	1.85919	0.929596	+	0.368580i	$0.120156\pi$
$480$	−3.63500	−0.165914
$481$	6.96334	0.317501
$482$	−0.850933	−0.0387590
$483$	2.13623	0.0972019
$484$	−7.22389	−0.328358
$485$	64.6659	2.93633
$486$	−1.00000	−0.0453609
$487$	33.0221	1.49637	0.748186	−	0.663489i	$-0.230925\pi$
$487$	33.0221	1.49637	0.748186	+	0.663489i	$0.230925\pi$
$488$	12.7622	0.577719
$489$	13.5039	0.610669
$490$	−23.1556	−1.04606
$491$	−5.10078	−0.230195	−0.115098	−	0.993354i	$-0.536718\pi$
$491$	−5.10078	−0.230195	−0.115098	+	0.993354i	$0.536718\pi$
$492$	0.662559	0.0298705
$493$	22.7076	1.02270
$494$	6.37184	0.286682
$495$	7.06361	0.317486
$496$	−1.14961	−0.0516190
$497$	0.489220	0.0219445
$498$	−0.158614	−0.00710768
$499$	−25.8955	−1.15924	−0.579620	−	0.814887i	$-0.696799\pi$
$499$	−25.8955	−1.15924	−0.579620	+	0.814887i	$0.696799\pi$
$500$	11.6801	0.522348
$501$	10.4152	0.465318
$502$	−19.1840	−0.856224
$503$	26.5091	1.18198	0.590992	−	0.806678i	$-0.298737\pi$
$503$	26.5091	1.18198	0.590992	+	0.806678i	$0.298737\pi$
$504$	−0.793614	−0.0353504
$505$	16.8234	0.748630
$506$	5.23072	0.232534
$507$	−27.6003	−1.22577
$508$	−16.7644	−0.743800
$509$	−4.75810	−0.210899	−0.105450	−	0.994425i	$-0.533628\pi$
$509$	−4.75810	−0.210899	−0.105450	+	0.994425i	$0.533628\pi$
$510$	−22.8916	−1.01366
$511$	−1.44662	−0.0639949
$512$	1.00000	0.0441942
$513$	1.00000	0.0441511
$514$	11.3650	0.501289
$515$	52.6058	2.31809
$516$	−12.4647	−0.548726
$517$	−18.1908	−0.800032
$518$	0.867286	0.0381064
$519$	3.16816	0.139067
$520$	−23.1616	−1.01570
$521$	−42.1482	−1.84655	−0.923274	−	0.384142i	$-0.874497\pi$
$521$	−42.1482	−1.84655	−0.923274	+	0.384142i	$0.874497\pi$
$522$	3.60578	0.157821
$523$	−27.5899	−1.20642	−0.603212	−	0.797581i	$-0.706113\pi$
$523$	−27.5899	−1.20642	−0.603212	+	0.797581i	$0.706113\pi$
$524$	9.78295	0.427370
$525$	6.51813	0.284474
$526$	17.9085	0.780848
$527$	−7.23973	−0.315367
$528$	−1.94322	−0.0845679
$529$	−15.7543	−0.684971
$530$	−3.63500	−0.157894
$531$	−2.51461	−0.109125
$532$	0.793614	0.0344075
$533$	4.22172	0.182863
$534$	−5.79361	−0.250714
$535$	15.8916	0.687055
$536$	8.07262	0.348684
$537$	6.82012	0.294310
$538$	13.8228	0.595945
$539$	−12.3787	−0.533187
$540$	−3.63500	−0.156425
$541$	6.88759	0.296121	0.148060	−	0.988978i	$-0.452697\pi$
$541$	6.88759	0.296121	0.148060	+	0.988978i	$0.452697\pi$
$542$	10.1002	0.433840
$543$	−16.4169	−0.704516
$544$	6.29756	0.270006
$545$	16.7747	0.718551
$546$	−5.05678	−0.216410
$547$	30.1015	1.28705	0.643524	−	0.765426i	$-0.277472\pi$
$547$	30.1015	1.28705	0.643524	+	0.765426i	$0.277472\pi$
$548$	−4.17611	−0.178395
$549$	12.7622	0.544679
$550$	15.9601	0.680542
$551$	−3.60578	−0.153611
$552$	−2.69178	−0.114570
$553$	−4.73135	−0.201197
$554$	−29.2231	−1.24157
$555$	3.97244	0.168621
$556$	−12.4764	−0.529117
$557$	−32.3164	−1.36929	−0.684645	−	0.728877i	$-0.740043\pi$
$557$	−32.3164	−1.36929	−0.684645	+	0.728877i	$0.740043\pi$
$558$	−1.14961	−0.0486668
$559$	−79.4228	−3.35923
$560$	−2.88479	−0.121904
$561$	−12.2376	−0.516670
$562$	20.0519	0.845838
$563$	−27.2448	−1.14823	−0.574117	−	0.818774i	$-0.694654\pi$
$563$	−27.2448	−1.14823	−0.574117	+	0.818774i	$0.694654\pi$
$564$	9.36117	0.394176
$565$	−7.83867	−0.329775
$566$	4.63605	0.194868
$567$	−0.793614	−0.0333287
$568$	−0.616446	−0.0258655
$569$	17.9315	0.751728	0.375864	−	0.926675i	$-0.377346\pi$
$569$	17.9315	0.751728	0.375864	+	0.926675i	$0.377346\pi$
$570$	3.63500	0.152253
$571$	−13.3156	−0.557239	−0.278620	−	0.960402i	$-0.589877\pi$
$571$	−13.3156	−0.557239	−0.278620	+	0.960402i	$0.589877\pi$
$572$	−12.3819	−0.517713
$573$	13.5400	0.565642
$574$	0.525816	0.0219471
$575$	22.1082	0.921974
$576$	1.00000	0.0416667
$577$	−22.4598	−0.935013	−0.467507	−	0.883990i	$-0.654848\pi$
$577$	−22.4598	−0.935013	−0.467507	+	0.883990i	$0.654848\pi$
$578$	22.6592	0.942500
$579$	13.4523	0.559060
$580$	13.1070	0.544239
$581$	−0.125879	−0.00522232
$582$	−17.7898	−0.737410
$583$	−1.94322	−0.0804801
$584$	1.82283	0.0754293
$585$	−23.1616	−0.957615
$586$	1.76822	0.0730447
$587$	0.792466	0.0327086	0.0163543	−	0.999866i	$-0.494794\pi$
$587$	0.792466	0.0327086	0.0163543	+	0.999866i	$0.494794\pi$
$588$	6.37018	0.262702
$589$	1.14961	0.0473688
$590$	−9.14060	−0.376313
$591$	−6.82967	−0.280935
$592$	−1.09283	−0.0449151
$593$	9.63388	0.395616	0.197808	−	0.980241i	$-0.436618\pi$
$593$	9.63388	0.395616	0.197808	+	0.980241i	$0.436618\pi$
$594$	−1.94322	−0.0797314
$595$	−18.1671	−0.744779
$596$	−5.00684	−0.205088
$597$	12.8635	0.526466
$598$	−17.1516	−0.701380
$599$	−28.1641	−1.15075	−0.575377	−	0.817889i	$-0.695145\pi$
$599$	−28.1641	−1.15075	−0.575377	+	0.817889i	$0.695145\pi$
$600$	−8.21322	−0.335303
$601$	−31.9918	−1.30497	−0.652486	−	0.757800i	$-0.726274\pi$
$601$	−31.9918	−1.30497	−0.652486	+	0.757800i	$0.726274\pi$
$602$	−9.89213	−0.403173
$603$	8.07262	0.328742
$604$	−18.0688	−0.735209
$605$	−26.2588	−1.06757
$606$	−4.62816	−0.188006
$607$	−9.10011	−0.369362	−0.184681	−	0.982798i	$-0.559125\pi$
$607$	−9.10011	−0.369362	−0.184681	+	0.982798i	$0.559125\pi$
$608$	−1.00000	−0.0405554
$609$	2.86160	0.115958
$610$	46.3907	1.87830
$611$	59.6478	2.41309
$612$	6.29756	0.254564
$613$	−5.62931	−0.227366	−0.113683	−	0.993517i	$-0.536265\pi$
$613$	−5.62931	−0.227366	−0.113683	+	0.993517i	$0.536265\pi$
$614$	−23.8387	−0.962051
$615$	2.40840	0.0971161
$616$	−1.54217	−0.0621357
$617$	−28.8215	−1.16031	−0.580154	−	0.814507i	$-0.697008\pi$
$617$	−28.8215	−1.16031	−0.580154	+	0.814507i	$0.697008\pi$
$618$	−14.4720	−0.582150
$619$	−24.5605	−0.987169	−0.493584	−	0.869698i	$-0.664314\pi$
$619$	−24.5605	−0.987169	−0.493584	+	0.869698i	$0.664314\pi$
$620$	−4.17883	−0.167826
$621$	−2.69178	−0.108017
$622$	6.92985	0.277861
$623$	−4.59789	−0.184211
$624$	6.37184	0.255078
$625$	1.39090	0.0556360
$626$	24.5812	0.982463
$627$	1.94322	0.0776048
$628$	17.1998	0.686349
$629$	−6.88217	−0.274410
$630$	−2.88479	−0.114933
$631$	−35.1521	−1.39938	−0.699691	−	0.714446i	$-0.746679\pi$
$631$	−35.1521	−1.39938	−0.699691	+	0.714446i	$0.746679\pi$
$632$	5.96178	0.237147
$633$	19.9028	0.791066
$634$	3.25039	0.129090
$635$	−60.9386	−2.41827
$636$	1.00000	0.0396526
$637$	40.5897	1.60822
$638$	7.00684	0.277403
$639$	−0.616446	−0.0243862
$640$	3.63500	0.143686
$641$	−48.2383	−1.90530	−0.952649	−	0.304072i	$-0.901654\pi$
$641$	−48.2383	−1.90530	−0.952649	+	0.304072i	$0.901654\pi$
$642$	−4.37184	−0.172543
$643$	12.6588	0.499214	0.249607	−	0.968347i	$-0.419699\pi$
$643$	12.6588	0.499214	0.249607	+	0.968347i	$0.419699\pi$
$644$	−2.13623	−0.0841793
$645$	−45.3091	−1.78404
$646$	−6.29756	−0.247774
$647$	−14.2635	−0.560754	−0.280377	−	0.959890i	$-0.590460\pi$
$647$	−14.2635	−0.560754	−0.280377	+	0.959890i	$0.590460\pi$
$648$	1.00000	0.0392837
$649$	−4.88645	−0.191810
$650$	−52.3333	−2.05268
$651$	−0.912345	−0.0357576
$652$	−13.5039	−0.528855
$653$	−41.0306	−1.60565	−0.802825	−	0.596215i	$-0.796671\pi$
$653$	−41.0306	−1.60565	−0.802825	+	0.596215i	$0.796671\pi$
$654$	−4.61479	−0.180452
$655$	35.5610	1.38948
$656$	−0.662559	−0.0258686
$657$	1.82283	0.0711155
$658$	7.42916	0.289619
$659$	27.0985	1.05561	0.527804	−	0.849366i	$-0.323015\pi$
$659$	27.0985	1.05561	0.527804	+	0.849366i	$0.323015\pi$
$660$	−7.06361	−0.274951
$661$	−11.3887	−0.442969	−0.221485	−	0.975164i	$-0.571090\pi$
$661$	−11.3887	−0.442969	−0.221485	+	0.975164i	$0.571090\pi$
$662$	−6.30717	−0.245135
$663$	40.1270	1.55840
$664$	0.158614	0.00615543
$665$	2.88479	0.111867
$666$	−1.09283	−0.0423463
$667$	9.70596	0.375816
$668$	−10.4152	−0.402978
$669$	9.14412	0.353532
$670$	29.3440	1.13366
$671$	24.7998	0.957387
$672$	0.793614	0.0306143
$673$	−12.9691	−0.499923	−0.249961	−	0.968256i	$-0.580418\pi$
$673$	−12.9691	−0.499923	−0.249961	+	0.968256i	$0.580418\pi$
$674$	−33.3102	−1.28306
$675$	−8.21322	−0.316127
$676$	27.6003	1.06155
$677$	−27.8693	−1.07110	−0.535552	−	0.844503i	$-0.679896\pi$
$677$	−27.8693	−1.07110	−0.535552	+	0.844503i	$0.679896\pi$
$678$	2.15644	0.0828177
$679$	−14.1182	−0.541808
$680$	22.8916	0.877854
$681$	−16.5081	−0.632591
$682$	−2.23395	−0.0855422
$683$	4.01916	0.153789	0.0768944	−	0.997039i	$-0.475500\pi$
$683$	4.01916	0.153789	0.0768944	+	0.997039i	$0.475500\pi$
$684$	−1.00000	−0.0382360
$685$	−15.1802	−0.580005
$686$	10.6108	0.405121
$687$	−24.5761	−0.937635
$688$	12.4647	0.475211
$689$	6.37184	0.242748
$690$	−9.78461	−0.372494
$691$	−11.0933	−0.422011	−0.211005	−	0.977485i	$-0.567674\pi$
$691$	−11.0933	−0.422011	−0.211005	+	0.977485i	$0.567674\pi$
$692$	−3.16816	−0.120435
$693$	−1.54217	−0.0585821
$694$	−24.7202	−0.938365
$695$	−45.3517	−1.72029
$696$	−3.60578	−0.136677
$697$	−4.17250	−0.158045
$698$	2.52799	0.0956857
$699$	−9.01584	−0.341010
$700$	−6.51813	−0.246362
$701$	14.3123	0.540570	0.270285	−	0.962780i	$-0.412882\pi$
$701$	14.3123	0.540570	0.270285	+	0.962780i	$0.412882\pi$
$702$	6.37184	0.240489
$703$	1.09283	0.0412169
$704$	1.94322	0.0732380
$705$	34.0279	1.28156
$706$	13.1739	0.495808
$707$	−3.67298	−0.138136
$708$	2.51461	0.0945048
$709$	6.31892	0.237312	0.118656	−	0.992935i	$-0.462141\pi$
$709$	6.31892	0.237312	0.118656	+	0.992935i	$0.462141\pi$
$710$	−2.24078	−0.0840950
$711$	5.96178	0.223584
$712$	5.79361	0.217125
$713$	−3.09449	−0.115890
$714$	4.99783	0.187039
$715$	−45.0082	−1.68321
$716$	−6.82012	−0.254880
$717$	9.64867	0.360336
$718$	20.2201	0.754606
$719$	−0.570333	−0.0212698	−0.0106349	−	0.999943i	$-0.503385\pi$
$719$	−0.570333	−0.0212698	−0.0106349	+	0.999943i	$0.503385\pi$
$720$	3.63500	0.135468
$721$	−11.4852	−0.427731
$722$	1.00000	0.0372161
$723$	0.850933	0.0316466
$724$	16.4169	0.610129
$725$	29.6151	1.09988
$726$	7.22389	0.268104
$727$	−3.36503	−0.124802	−0.0624011	−	0.998051i	$-0.519876\pi$
$727$	−3.36503	−0.124802	−0.0624011	+	0.998051i	$0.519876\pi$
$728$	5.05678	0.187417
$729$	1.00000	0.0370370
$730$	6.62599	0.245239
$731$	78.4970	2.90332
$732$	−12.7622	−0.471705
$733$	10.8354	0.400213	0.200106	−	0.979774i	$-0.435871\pi$
$733$	10.8354	0.400213	0.200106	+	0.979774i	$0.435871\pi$
$734$	24.5817	0.907329
$735$	23.1556	0.854107
$736$	2.69178	0.0992202
$737$	15.6869	0.577834
$738$	−0.662559	−0.0243891
$739$	−21.8713	−0.804550	−0.402275	−	0.915519i	$-0.631781\pi$
$739$	−21.8713	−0.804550	−0.402275	+	0.915519i	$0.631781\pi$
$740$	−3.97244	−0.146030
$741$	−6.37184	−0.234075
$742$	0.793614	0.0291345
$743$	15.2504	0.559484	0.279742	−	0.960075i	$-0.409751\pi$
$743$	15.2504	0.559484	0.279742	+	0.960075i	$0.409751\pi$
$744$	1.14961	0.0421467
$745$	−18.1998	−0.666791
$746$	16.5430	0.605682
$747$	0.158614	0.00580340
$748$	12.2376	0.447449
$749$	−3.46955	−0.126775
$750$	−11.6801	−0.426495
$751$	0.468185	0.0170843	0.00854215	−	0.999964i	$-0.497281\pi$
$751$	0.468185	0.0170843	0.00854215	+	0.999964i	$0.497281\pi$
$752$	−9.36117	−0.341367
$753$	19.1840	0.699104
$754$	−22.9754	−0.836716
$755$	−65.6800	−2.39034
$756$	0.793614	0.0288635
$757$	35.2394	1.28080	0.640399	−	0.768042i	$-0.278769\pi$
$757$	35.2394	1.28080	0.640399	+	0.768042i	$0.278769\pi$
$758$	6.65738	0.241807
$759$	−5.23072	−0.189863
$760$	−3.63500	−0.131855
$761$	30.1370	1.09247	0.546233	−	0.837633i	$-0.316061\pi$
$761$	30.1370	1.09247	0.546233	+	0.837633i	$0.316061\pi$
$762$	16.7644	0.607310
$763$	−3.66236	−0.132586
$764$	−13.5400	−0.489860
$765$	22.8916	0.827648
$766$	16.8507	0.608840
$767$	16.0227	0.578545
$768$	−1.00000	−0.0360844
$769$	18.2251	0.657215	0.328608	−	0.944467i	$-0.393421\pi$
$769$	18.2251	0.657215	0.328608	+	0.944467i	$0.393421\pi$
$770$	−5.60578	−0.202018
$771$	−11.3650	−0.409300
$772$	−13.4523	−0.484160
$773$	−2.54786	−0.0916400	−0.0458200	−	0.998950i	$-0.514590\pi$
$773$	−2.54786	−0.0916400	−0.0458200	+	0.998950i	$0.514590\pi$
$774$	12.4647	0.448033
$775$	−9.44199	−0.339166
$776$	17.7898	0.638616
$777$	−0.867286	−0.0311137
$778$	5.79084	0.207612
$779$	0.662559	0.0237386
$780$	23.1616	0.829319
$781$	−1.19789	−0.0428639
$782$	16.9516	0.606189
$783$	−3.60578	−0.128860
$784$	−6.37018	−0.227506
$785$	62.5214	2.23149
$786$	−9.78295	−0.348946
$787$	25.3506	0.903651	0.451826	−	0.892106i	$-0.350773\pi$
$787$	25.3506	0.903651	0.451826	+	0.892106i	$0.350773\pi$
$788$	6.82967	0.243297
$789$	−17.9085	−0.637560
$790$	21.6711	0.771021
$791$	1.71138	0.0608498
$792$	1.94322	0.0690494
$793$	−81.3188	−2.88772
$794$	33.1595	1.17678
$795$	3.63500	0.128920
$796$	−12.8635	−0.455933
$797$	14.7186	0.521359	0.260679	−	0.965425i	$-0.416053\pi$
$797$	14.7186	0.521359	0.260679	+	0.965425i	$0.416053\pi$
$798$	−0.793614	−0.0280936
$799$	−58.9525	−2.08559
$800$	8.21322	0.290381
$801$	5.79361	0.204707
$802$	−22.0915	−0.780077
$803$	3.54217	0.125000
$804$	−8.07262	−0.284699
$805$	−7.76520	−0.273687
$806$	7.32512	0.258016
$807$	−13.8228	−0.486587
$808$	4.62816	0.162818
$809$	31.3828	1.10336	0.551680	−	0.834056i	$-0.313987\pi$
$809$	31.3828	1.10336	0.551680	+	0.834056i	$0.313987\pi$
$810$	3.63500	0.127721
$811$	−20.0068	−0.702535	−0.351268	−	0.936275i	$-0.614249\pi$
$811$	−20.0068	−0.702535	−0.351268	+	0.936275i	$0.614249\pi$
$812$	−2.86160	−0.100422
$813$	−10.1002	−0.354229
$814$	−2.12361	−0.0744326
$815$	−49.0868	−1.71944
$816$	−6.29756	−0.220459
$817$	−12.4647	−0.436084
$818$	9.63500	0.336880
$819$	5.05678	0.176698
$820$	−2.40840	−0.0841050
$821$	16.9915	0.593008	0.296504	−	0.955032i	$-0.404179\pi$
$821$	16.9915	0.593008	0.296504	+	0.955032i	$0.404179\pi$
$822$	4.17611	0.145659
$823$	22.4816	0.783658	0.391829	−	0.920038i	$-0.371842\pi$
$823$	22.4816	0.783658	0.391829	+	0.920038i	$0.371842\pi$
$824$	14.4720	0.504156
$825$	−15.9601	−0.555660
$826$	1.99563	0.0694368
$827$	−53.7011	−1.86737	−0.933685	−	0.358095i	$-0.883426\pi$
$827$	−53.7011	−1.86737	−0.933685	+	0.358095i	$0.883426\pi$
$828$	2.69178	0.0935457
$829$	25.0005	0.868305	0.434152	−	0.900839i	$-0.357048\pi$
$829$	25.0005	0.868305	0.434152	+	0.900839i	$0.357048\pi$
$830$	0.576563	0.0200128
$831$	29.2231	1.01374
$832$	−6.37184	−0.220904
$833$	−40.1166	−1.38996
$834$	12.4764	0.432022
$835$	−37.8594	−1.31018
$836$	−1.94322	−0.0672078
$837$	1.14961	0.0397363
$838$	−17.6959	−0.611295
$839$	−27.1307	−0.936657	−0.468329	−	0.883554i	$-0.655144\pi$
$839$	−27.1307	−0.936657	−0.468329	+	0.883554i	$0.655144\pi$
$840$	2.88479	0.0995346
$841$	−15.9983	−0.551667
$842$	−3.54434	−0.122146
$843$	−20.0519	−0.690624
$844$	−19.9028	−0.685084
$845$	100.327	3.45136
$846$	−9.36117	−0.321844
$847$	5.73298	0.196987
$848$	−1.00000	−0.0343401
$849$	−4.63605	−0.159109
$850$	51.7232	1.77409
$851$	−2.94166	−0.100839
$852$	0.616446	0.0211191
$853$	50.4177	1.72627	0.863135	−	0.504974i	$-0.168498\pi$
$853$	50.4177	1.72627	0.863135	+	0.504974i	$0.168498\pi$
$854$	−10.1283	−0.346583
$855$	−3.63500	−0.124314
$856$	4.37184	0.149426
$857$	1.32320	0.0451995	0.0225997	−	0.999745i	$-0.492806\pi$
$857$	1.32320	0.0451995	0.0225997	+	0.999745i	$0.492806\pi$
$858$	12.3819	0.422711
$859$	−14.9534	−0.510203	−0.255101	−	0.966914i	$-0.582109\pi$
$859$	−14.9534	−0.510203	−0.255101	+	0.966914i	$0.582109\pi$
$860$	45.3091	1.54503
$861$	−0.525816	−0.0179198
$862$	−19.1878	−0.653540
$863$	9.93693	0.338257	0.169129	−	0.985594i	$-0.445905\pi$
$863$	9.93693	0.338257	0.169129	+	0.985594i	$0.445905\pi$
$864$	−1.00000	−0.0340207
$865$	−11.5163	−0.391565
$866$	−13.4114	−0.455738
$867$	−22.6592	−0.769548
$868$	0.912345	0.0309670
$869$	11.5851	0.392996
$870$	−13.1070	−0.444369
$871$	−51.4374	−1.74289
$872$	4.61479	0.156276
$873$	17.7898	0.602093
$874$	−2.69178	−0.0910507
$875$	−9.26946	−0.313365
$876$	−1.82283	−0.0615878
$877$	19.2520	0.650092	0.325046	−	0.945698i	$-0.394620\pi$
$877$	19.2520	0.650092	0.325046	+	0.945698i	$0.394620\pi$
$878$	11.9648	0.403792
$879$	−1.76822	−0.0596407
$880$	7.06361	0.238114
$881$	−51.7841	−1.74465	−0.872325	−	0.488927i	$-0.837389\pi$
$881$	−51.7841	−1.74465	−0.872325	+	0.488927i	$0.837389\pi$
$882$	−6.37018	−0.214495
$883$	−38.8331	−1.30684	−0.653419	−	0.756996i	$-0.726666\pi$
$883$	−38.8331	−1.30684	−0.653419	+	0.756996i	$0.726666\pi$
$884$	−40.1270	−1.34962
$885$	9.14060	0.307258
$886$	−15.4253	−0.518223
$887$	−37.9579	−1.27450	−0.637252	−	0.770656i	$-0.719929\pi$
$887$	−37.9579	−1.27450	−0.637252	+	0.770656i	$0.719929\pi$
$888$	1.09283	0.0366730
$889$	13.3045	0.446217
$890$	21.0598	0.705926
$891$	1.94322	0.0651004
$892$	−9.14412	−0.306168
$893$	9.36117	0.313260
$894$	5.00684	0.167454
$895$	−24.7911	−0.828676
$896$	−0.793614	−0.0265128
$897$	17.1516	0.572674
$898$	−13.2178	−0.441083
$899$	−4.14524	−0.138251
$900$	8.21322	0.273774
$901$	−6.29756	−0.209802
$902$	−1.28750	−0.0428690
$903$	9.89213	0.329190
$904$	−2.15644	−0.0717223
$905$	59.6754	1.98368
$906$	18.0688	0.600295
$907$	−48.6768	−1.61629	−0.808144	−	0.588985i	$-0.799528\pi$
$907$	−48.6768	−1.61629	−0.808144	+	0.588985i	$0.799528\pi$
$908$	16.5081	0.547839
$909$	4.62816	0.153507
$910$	18.3814	0.609337
$911$	5.02455	0.166471	0.0832354	−	0.996530i	$-0.473475\pi$
$911$	5.02455	0.166471	0.0832354	+	0.996530i	$0.473475\pi$
$912$	1.00000	0.0331133
$913$	0.308223	0.0102007
$914$	−3.04394	−0.100685
$915$	−46.3907	−1.53363
$916$	24.5761	0.812016
$917$	−7.76388	−0.256386
$918$	−6.29756	−0.207850
$919$	6.26773	0.206753	0.103377	−	0.994642i	$-0.467035\pi$
$919$	6.26773	0.206753	0.103377	+	0.994642i	$0.467035\pi$
$920$	9.78461	0.322589
$921$	23.8387	0.785511
$922$	−5.69695	−0.187619
$923$	3.92789	0.129288
$924$	1.54217	0.0507336
$925$	−8.97566	−0.295118
$926$	33.5954	1.10401
$927$	14.4720	0.475323
$928$	3.60578	0.118366
$929$	12.3738	0.405971	0.202985	−	0.979182i	$-0.434936\pi$
$929$	12.3738	0.405971	0.202985	+	0.979182i	$0.434936\pi$
$930$	4.17883	0.137029
$931$	6.37018	0.208774
$932$	9.01584	0.295324
$933$	−6.92985	−0.226873
$934$	−32.0502	−1.04872
$935$	44.4835	1.45477
$936$	−6.37184	−0.208270
$937$	0.288553	0.00942660	0.00471330	−	0.999989i	$-0.498500\pi$
$937$	0.288553	0.00942660	0.00471330	+	0.999989i	$0.498500\pi$
$938$	−6.40654	−0.209181
$939$	−24.5812	−0.802178
$940$	−34.0279	−1.10987
$941$	−40.8045	−1.33019	−0.665094	−	0.746759i	$-0.731609\pi$
$941$	−40.8045	−1.33019	−0.665094	+	0.746759i	$0.731609\pi$
$942$	−17.1998	−0.560401
$943$	−1.78346	−0.0580775
$944$	−2.51461	−0.0818436
$945$	2.88479	0.0938421
$946$	24.2216	0.787513
$947$	28.0852	0.912648	0.456324	−	0.889814i	$-0.349166\pi$
$947$	28.0852	0.912648	0.456324	+	0.889814i	$0.349166\pi$
$948$	−5.96178	−0.193629
$949$	−11.6148	−0.377032
$950$	−8.21322	−0.266472
$951$	−3.25039	−0.105401
$952$	−4.99783	−0.161981
$953$	−30.6745	−0.993645	−0.496822	−	0.867852i	$-0.665500\pi$
$953$	−30.6745	−0.993645	−0.496822	+	0.867852i	$0.665500\pi$
$954$	−1.00000	−0.0323762
$955$	−49.2179	−1.59265
$956$	−9.64867	−0.312060
$957$	−7.00684	−0.226499
$958$	40.6904	1.31465
$959$	3.31422	0.107022
$960$	−3.63500	−0.117319
$961$	−29.6784	−0.957368
$962$	6.96334	0.224507
$963$	4.37184	0.140880
$964$	−0.850933	−0.0274067
$965$	−48.8993	−1.57412
$966$	2.13623	0.0687321
$967$	13.6336	0.438428	0.219214	−	0.975677i	$-0.429651\pi$
$967$	13.6336	0.438428	0.219214	+	0.975677i	$0.429651\pi$
$968$	−7.22389	−0.232184
$969$	6.29756	0.202307
$970$	64.6659	2.07630
$971$	−3.81600	−0.122461	−0.0612306	−	0.998124i	$-0.519502\pi$
$971$	−3.81600	−0.122461	−0.0612306	+	0.998124i	$0.519502\pi$
$972$	−1.00000	−0.0320750
$973$	9.90143	0.317425
$974$	33.0221	1.05810
$975$	52.3333	1.67601
$976$	12.7622	0.408509
$977$	20.7136	0.662688	0.331344	−	0.943510i	$-0.392498\pi$
$977$	20.7136	0.662688	0.331344	+	0.943510i	$0.392498\pi$
$978$	13.5039	0.431809
$979$	11.2583	0.359816
$980$	−23.1556	−0.739678
$981$	4.61479	0.147339
$982$	−5.10078	−0.162773
$983$	24.9309	0.795172	0.397586	−	0.917565i	$-0.369848\pi$
$983$	24.9309	0.795172	0.397586	+	0.917565i	$0.369848\pi$
$984$	0.662559	0.0211216
$985$	24.8258	0.791017
$986$	22.7076	0.723158
$987$	−7.42916	−0.236473
$988$	6.37184	0.202715
$989$	33.5521	1.06689
$990$	7.06361	0.224496
$991$	−17.2118	−0.546751	−0.273376	−	0.961907i	$-0.588140\pi$
$991$	−17.2118	−0.546751	−0.273376	+	0.961907i	$0.588140\pi$
$992$	−1.14961	−0.0365001
$993$	6.30717	0.200152
$994$	0.489220	0.0155171
$995$	−46.7587	−1.48235
$996$	−0.158614	−0.00502589
$997$	−25.5623	−0.809567	−0.404783	−	0.914413i	$-0.632653\pi$
$997$	−25.5623	−0.809567	−0.404783	+	0.914413i	$0.632653\pi$
$998$	−25.8955	−0.819706
$999$	1.09283	0.0345756

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	6042.2.a.t.1.4	✓	4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
6042.2.a.t.1.4	✓	4	1.1	even	1	trivial

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

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

\(f(q)\)	\(=\)	\(q+1.00000 q^{2} -1.00000 q^{3} +1.00000 q^{4} +3.63500 q^{5} -1.00000 q^{6} -0.793614 q^{7} +1.00000 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q+1.00000 q^{2} -1.00000 q^{3} +1.00000 q^{4} +3.63500 q^{5} -1.00000 q^{6} -0.793614 q^{7} +1.00000 q^{8} +1.00000 q^{9} +3.63500 q^{10} +1.94322 q^{11} -1.00000 q^{12} -6.37184 q^{13} -0.793614 q^{14} -3.63500 q^{15} +1.00000 q^{16} +6.29756 q^{17} +1.00000 q^{18} -1.00000 q^{19} +3.63500 q^{20} +0.793614 q^{21} +1.94322 q^{22} +2.69178 q^{23} -1.00000 q^{24} +8.21322 q^{25} -6.37184 q^{26} -1.00000 q^{27} -0.793614 q^{28} +3.60578 q^{29} -3.63500 q^{30} -1.14961 q^{31} +1.00000 q^{32} -1.94322 q^{33} +6.29756 q^{34} -2.88479 q^{35} +1.00000 q^{36} -1.09283 q^{37} -1.00000 q^{38} +6.37184 q^{39} +3.63500 q^{40} -0.662559 q^{41} +0.793614 q^{42} +12.4647 q^{43} +1.94322 q^{44} +3.63500 q^{45} +2.69178 q^{46} -9.36117 q^{47} -1.00000 q^{48} -6.37018 q^{49} +8.21322 q^{50} -6.29756 q^{51} -6.37184 q^{52} -1.00000 q^{53} -1.00000 q^{54} +7.06361 q^{55} -0.793614 q^{56} +1.00000 q^{57} +3.60578 q^{58} -2.51461 q^{59} -3.63500 q^{60} +12.7622 q^{61} -1.14961 q^{62} -0.793614 q^{63} +1.00000 q^{64} -23.1616 q^{65} -1.94322 q^{66} +8.07262 q^{67} +6.29756 q^{68} -2.69178 q^{69} -2.88479 q^{70} -0.616446 q^{71} +1.00000 q^{72} +1.82283 q^{73} -1.09283 q^{74} -8.21322 q^{75} -1.00000 q^{76} -1.54217 q^{77} +6.37184 q^{78} +5.96178 q^{79} +3.63500 q^{80} +1.00000 q^{81} -0.662559 q^{82} +0.158614 q^{83} +0.793614 q^{84} +22.8916 q^{85} +12.4647 q^{86} -3.60578 q^{87} +1.94322 q^{88} +5.79361 q^{89} +3.63500 q^{90} +5.05678 q^{91} +2.69178 q^{92} +1.14961 q^{93} -9.36117 q^{94} -3.63500 q^{95} -1.00000 q^{96} +17.7898 q^{97} -6.37018 q^{98} +1.94322 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q + 4 q^{2} - 4 q^{3} + 4 q^{4} + 6 q^{5} - 4 q^{6} + 3 q^{7} + 4 q^{8} + 4 q^{9}+O(q^{10}) \) 4 * q + 4 * q^2 - 4 * q^3 + 4 * q^4 + 6 * q^5 - 4 * q^6 + 3 * q^7 + 4 * q^8 + 4 * q^9	\( 4 q + 4 q^{2} - 4 q^{3} + 4 q^{4} + 6 q^{5} - 4 q^{6} + 3 q^{7} + 4 q^{8} + 4 q^{9} + 6 q^{10} - 2 q^{11} - 4 q^{12} - q^{13} + 3 q^{14} - 6 q^{15} + 4 q^{16} + 8 q^{17} + 4 q^{18} - 4 q^{19} + 6 q^{20} - 3 q^{21} - 2 q^{22} + 12 q^{23} - 4 q^{24} + 6 q^{25} - q^{26} - 4 q^{27} + 3 q^{28} - 4 q^{29} - 6 q^{30} - q^{31} + 4 q^{32} + 2 q^{33} + 8 q^{34} + 18 q^{35} + 4 q^{36} + 9 q^{37} - 4 q^{38} + q^{39} + 6 q^{40} + 6 q^{41} - 3 q^{42} + 12 q^{43} - 2 q^{44} + 6 q^{45} + 12 q^{46} + 3 q^{47} - 4 q^{48} + 9 q^{49} + 6 q^{50} - 8 q^{51} - q^{52} - 4 q^{53} - 4 q^{54} + 5 q^{55} + 3 q^{56} + 4 q^{57} - 4 q^{58} - 15 q^{59} - 6 q^{60} - 4 q^{61} - q^{62} + 3 q^{63} + 4 q^{64} - 13 q^{65} + 2 q^{66} + 15 q^{67} + 8 q^{68} - 12 q^{69} + 18 q^{70} + 4 q^{72} + 11 q^{73} + 9 q^{74} - 6 q^{75} - 4 q^{76} - 11 q^{77} + q^{78} + 8 q^{79} + 6 q^{80} + 4 q^{81} + 6 q^{82} + 3 q^{83} - 3 q^{84} + 29 q^{85} + 12 q^{86} + 4 q^{87} - 2 q^{88} + 17 q^{89} + 6 q^{90} + 30 q^{91} + 12 q^{92} + q^{93} + 3 q^{94} - 6 q^{95} - 4 q^{96} + 16 q^{97} + 9 q^{98} - 2 q^{99}+O(q^{100}) \) 4 * q + 4 * q^2 - 4 * q^3 + 4 * q^4 + 6 * q^5 - 4 * q^6 + 3 * q^7 + 4 * q^8 + 4 * q^9 + 6 * q^10 - 2 * q^11 - 4 * q^12 - q^13 + 3 * q^14 - 6 * q^15 + 4 * q^16 + 8 * q^17 + 4 * q^18 - 4 * q^19 + 6 * q^20 - 3 * q^21 - 2 * q^22 + 12 * q^23 - 4 * q^24 + 6 * q^25 - q^26 - 4 * q^27 + 3 * q^28 - 4 * q^29 - 6 * q^30 - q^31 + 4 * q^32 + 2 * q^33 + 8 * q^34 + 18 * q^35 + 4 * q^36 + 9 * q^37 - 4 * q^38 + q^39 + 6 * q^40 + 6 * q^41 - 3 * q^42 + 12 * q^43 - 2 * q^44 + 6 * q^45 + 12 * q^46 + 3 * q^47 - 4 * q^48 + 9 * q^49 + 6 * q^50 - 8 * q^51 - q^52 - 4 * q^53 - 4 * q^54 + 5 * q^55 + 3 * q^56 + 4 * q^57 - 4 * q^58 - 15 * q^59 - 6 * q^60 - 4 * q^61 - q^62 + 3 * q^63 + 4 * q^64 - 13 * q^65 + 2 * q^66 + 15 * q^67 + 8 * q^68 - 12 * q^69 + 18 * q^70 + 4 * q^72 + 11 * q^73 + 9 * q^74 - 6 * q^75 - 4 * q^76 - 11 * q^77 + q^78 + 8 * q^79 + 6 * q^80 + 4 * q^81 + 6 * q^82 + 3 * q^83 - 3 * q^84 + 29 * q^85 + 12 * q^86 + 4 * q^87 - 2 * q^88 + 17 * q^89 + 6 * q^90 + 30 * q^91 + 12 * q^92 + q^93 + 3 * q^94 - 6 * q^95 - 4 * q^96 + 16 * q^97 + 9 * q^98 - 2 * q^99

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