LMFDB - Embedded newform 6046.2.a.e.1.7

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [6046,2,Mod(1,6046)]

mf = mfinit([N,k,chi],0)

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(6046, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([0]))

N = Newforms(chi, 2, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("6046.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 6046 = 2 \cdot 3023 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	6046.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:	$48.2775530621$
Analytic rank:	$1$
Dimension:	$56$
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.7
Character	$\chi$	$=$	6046.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.00000 q^{2} -2.64315 q^{3} +1.00000 q^{4} -1.33957 q^{5} -2.64315 q^{6} +3.06951 q^{7} +1.00000 q^{8} +3.98626 q^{9} +O(q^{10})$	\(q+1.00000 q^{2} -2.64315 q^{3} +1.00000 q^{4} -1.33957 q^{5} -2.64315 q^{6} +3.06951 q^{7} +1.00000 q^{8} +3.98626 q^{9} -1.33957 q^{10} -0.226222 q^{11} -2.64315 q^{12} -2.86347 q^{13} +3.06951 q^{14} +3.54069 q^{15} +1.00000 q^{16} -7.37548 q^{17} +3.98626 q^{18} +3.90348 q^{19} -1.33957 q^{20} -8.11318 q^{21} -0.226222 q^{22} +8.17264 q^{23} -2.64315 q^{24} -3.20555 q^{25} -2.86347 q^{26} -2.60684 q^{27} +3.06951 q^{28} -6.46595 q^{29} +3.54069 q^{30} +10.5352 q^{31} +1.00000 q^{32} +0.597939 q^{33} -7.37548 q^{34} -4.11182 q^{35} +3.98626 q^{36} +2.37336 q^{37} +3.90348 q^{38} +7.56859 q^{39} -1.33957 q^{40} -4.30363 q^{41} -8.11318 q^{42} -12.3357 q^{43} -0.226222 q^{44} -5.33987 q^{45} +8.17264 q^{46} +0.273710 q^{47} -2.64315 q^{48} +2.42188 q^{49} -3.20555 q^{50} +19.4945 q^{51} -2.86347 q^{52} -12.3290 q^{53} -2.60684 q^{54} +0.303040 q^{55} +3.06951 q^{56} -10.3175 q^{57} -6.46595 q^{58} +1.36269 q^{59} +3.54069 q^{60} +1.56062 q^{61} +10.5352 q^{62} +12.2359 q^{63} +1.00000 q^{64} +3.83581 q^{65} +0.597939 q^{66} -7.22566 q^{67} -7.37548 q^{68} -21.6016 q^{69} -4.11182 q^{70} -1.42465 q^{71} +3.98626 q^{72} +15.0562 q^{73} +2.37336 q^{74} +8.47277 q^{75} +3.90348 q^{76} -0.694390 q^{77} +7.56859 q^{78} +4.63774 q^{79} -1.33957 q^{80} -5.06851 q^{81} -4.30363 q^{82} +10.3362 q^{83} -8.11318 q^{84} +9.87997 q^{85} -12.3357 q^{86} +17.0905 q^{87} -0.226222 q^{88} +4.36031 q^{89} -5.33987 q^{90} -8.78944 q^{91} +8.17264 q^{92} -27.8463 q^{93} +0.273710 q^{94} -5.22898 q^{95} -2.64315 q^{96} +9.27070 q^{97} +2.42188 q^{98} -0.901779 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 56 q + 56 q^{2} - 18 q^{3} + 56 q^{4} - 17 q^{5} - 18 q^{6} - 35 q^{7} + 56 q^{8} + 34 q^{9}+O(q^{10}) $ 56 * q + 56 * q^2 - 18 * q^3 + 56 * q^4 - 17 * q^5 - 18 * q^6 - 35 * q^7 + 56 * q^8 + 34 * q^9	\( 56 q + 56 q^{2} - 18 q^{3} + 56 q^{4} - 17 q^{5} - 18 q^{6} - 35 q^{7} + 56 q^{8} + 34 q^{9} - 17 q^{10} - 53 q^{11} - 18 q^{12} - 21 q^{13} - 35 q^{14} - 36 q^{15} + 56 q^{16} - 22 q^{17} + 34 q^{18} - 31 q^{19} - 17 q^{20} - 23 q^{21} - 53 q^{22} - 59 q^{23} - 18 q^{24} + 41 q^{25} - 21 q^{26} - 63 q^{27} - 35 q^{28} - 88 q^{29} - 36 q^{30} - 44 q^{31} + 56 q^{32} + 4 q^{33} - 22 q^{34} - 51 q^{35} + 34 q^{36} - 60 q^{37} - 31 q^{38} - 62 q^{39} - 17 q^{40} - 39 q^{41} - 23 q^{42} - 66 q^{43} - 53 q^{44} - 34 q^{45} - 59 q^{46} - 51 q^{47} - 18 q^{48} + 41 q^{49} + 41 q^{50} - 48 q^{51} - 21 q^{52} - 75 q^{53} - 63 q^{54} - 41 q^{55} - 35 q^{56} - 12 q^{57} - 88 q^{58} - 77 q^{59} - 36 q^{60} - 43 q^{61} - 44 q^{62} - 88 q^{63} + 56 q^{64} - 54 q^{65} + 4 q^{66} - 62 q^{67} - 22 q^{68} - 48 q^{69} - 51 q^{70} - 122 q^{71} + 34 q^{72} - 7 q^{73} - 60 q^{74} - 63 q^{75} - 31 q^{76} - 39 q^{77} - 62 q^{78} - 91 q^{79} - 17 q^{80} + 8 q^{81} - 39 q^{82} - 51 q^{83} - 23 q^{84} - 72 q^{85} - 66 q^{86} - 19 q^{87} - 53 q^{88} - 62 q^{89} - 34 q^{90} - 48 q^{91} - 59 q^{92} - 41 q^{93} - 51 q^{94} - 120 q^{95} - 18 q^{96} + 6 q^{97} + 41 q^{98} - 128 q^{99}+O(q^{100}) \) 56 * q + 56 * q^2 - 18 * q^3 + 56 * q^4 - 17 * q^5 - 18 * q^6 - 35 * q^7 + 56 * q^8 + 34 * q^9 - 17 * q^10 - 53 * q^11 - 18 * q^12 - 21 * q^13 - 35 * q^14 - 36 * q^15 + 56 * q^16 - 22 * q^17 + 34 * q^18 - 31 * q^19 - 17 * q^20 - 23 * q^21 - 53 * q^22 - 59 * q^23 - 18 * q^24 + 41 * q^25 - 21 * q^26 - 63 * q^27 - 35 * q^28 - 88 * q^29 - 36 * q^30 - 44 * q^31 + 56 * q^32 + 4 * q^33 - 22 * q^34 - 51 * q^35 + 34 * q^36 - 60 * q^37 - 31 * q^38 - 62 * q^39 - 17 * q^40 - 39 * q^41 - 23 * q^42 - 66 * q^43 - 53 * q^44 - 34 * q^45 - 59 * q^46 - 51 * q^47 - 18 * q^48 + 41 * q^49 + 41 * q^50 - 48 * q^51 - 21 * q^52 - 75 * q^53 - 63 * q^54 - 41 * q^55 - 35 * q^56 - 12 * q^57 - 88 * q^58 - 77 * q^59 - 36 * q^60 - 43 * q^61 - 44 * q^62 - 88 * q^63 + 56 * q^64 - 54 * q^65 + 4 * q^66 - 62 * q^67 - 22 * q^68 - 48 * q^69 - 51 * q^70 - 122 * q^71 + 34 * q^72 - 7 * q^73 - 60 * q^74 - 63 * q^75 - 31 * q^76 - 39 * q^77 - 62 * q^78 - 91 * q^79 - 17 * q^80 + 8 * q^81 - 39 * q^82 - 51 * q^83 - 23 * q^84 - 72 * q^85 - 66 * q^86 - 19 * q^87 - 53 * q^88 - 62 * q^89 - 34 * q^90 - 48 * q^91 - 59 * q^92 - 41 * q^93 - 51 * q^94 - 120 * q^95 - 18 * q^96 + 6 * q^97 + 41 * q^98 - 128 * 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
$3$	−2.64315	−1.52603	−0.763013	−	0.646384i	$-0.776281\pi$
$3$	−2.64315	−1.52603	−0.763013	+	0.646384i	$0.776281\pi$
$4$	1.00000	0.500000
$5$	−1.33957	−0.599074	−0.299537	−	0.954085i	$-0.596832\pi$
$5$	−1.33957	−0.599074	−0.299537	+	0.954085i	$0.596832\pi$
$6$	−2.64315	−1.07906
$7$	3.06951	1.16016	0.580082	−	0.814558i	$-0.303020\pi$
$7$	3.06951	1.16016	0.580082	+	0.814558i	$0.303020\pi$
$8$	1.00000	0.353553
$9$	3.98626	1.32875
$10$	−1.33957	−0.423609
$11$	−0.226222	−0.0682085	−0.0341042	−	0.999418i	$-0.510858\pi$
$11$	−0.226222	−0.0682085	−0.0341042	+	0.999418i	$0.510858\pi$
$12$	−2.64315	−0.763013
$13$	−2.86347	−0.794183	−0.397092	−	0.917779i	$-0.629981\pi$
$13$	−2.86347	−0.794183	−0.397092	+	0.917779i	$0.629981\pi$
$14$	3.06951	0.820360
$15$	3.54069	0.914201
$16$	1.00000	0.250000
$17$	−7.37548	−1.78882	−0.894408	−	0.447251i	$-0.852403\pi$
$17$	−7.37548	−1.78882	−0.894408	+	0.447251i	$0.852403\pi$
$18$	3.98626	0.939571
$19$	3.90348	0.895520	0.447760	−	0.894154i	$-0.352222\pi$
$19$	3.90348	0.895520	0.447760	+	0.894154i	$0.352222\pi$
$20$	−1.33957	−0.299537
$21$	−8.11318	−1.77044
$22$	−0.226222	−0.0482307
$23$	8.17264	1.70411	0.852057	−	0.523449i	$-0.175355\pi$
$23$	8.17264	1.70411	0.852057	+	0.523449i	$0.175355\pi$
$24$	−2.64315	−0.539531
$25$	−3.20555	−0.641111
$26$	−2.86347	−0.561572
$27$	−2.60684	−0.501686
$28$	3.06951	0.580082
$29$	−6.46595	−1.20070	−0.600349	−	0.799738i	$-0.704972\pi$
$29$	−6.46595	−1.20070	−0.600349	+	0.799738i	$0.704972\pi$
$30$	3.54069	0.646438
$31$	10.5352	1.89219	0.946093	−	0.323896i	$-0.104993\pi$
$31$	10.5352	1.89219	0.946093	+	0.323896i	$0.104993\pi$
$32$	1.00000	0.176777
$33$	0.597939	0.104088
$34$	−7.37548	−1.26488
$35$	−4.11182	−0.695024
$36$	3.98626	0.664377
$37$	2.37336	0.390178	0.195089	−	0.980786i	$-0.437500\pi$
$37$	2.37336	0.390178	0.195089	+	0.980786i	$0.437500\pi$
$38$	3.90348	0.633228
$39$	7.56859	1.21194
$40$	−1.33957	−0.211804
$41$	−4.30363	−0.672113	−0.336057	−	0.941842i	$-0.609093\pi$
$41$	−4.30363	−0.672113	−0.336057	+	0.941842i	$0.609093\pi$
$42$	−8.11318	−1.25189
$43$	−12.3357	−1.88117	−0.940587	−	0.339553i	$-0.889724\pi$
$43$	−12.3357	−1.88117	−0.940587	+	0.339553i	$0.889724\pi$
$44$	−0.226222	−0.0341042
$45$	−5.33987	−0.796021
$46$	8.17264	1.20499
$47$	0.273710	0.0399248	0.0199624	−	0.999801i	$-0.493645\pi$
$47$	0.273710	0.0399248	0.0199624	+	0.999801i	$0.493645\pi$
$48$	−2.64315	−0.381506
$49$	2.42188	0.345982
$50$	−3.20555	−0.453334
$51$	19.4945	2.72978
$52$	−2.86347	−0.397092
$53$	−12.3290	−1.69352	−0.846758	−	0.531979i	$-0.821449\pi$
$53$	−12.3290	−1.69352	−0.846758	+	0.531979i	$0.821449\pi$
$54$	−2.60684	−0.354746
$55$	0.303040	0.0408619
$56$	3.06951	0.410180
$57$	−10.3175	−1.36659
$58$	−6.46595	−0.849021
$59$	1.36269	0.177407	0.0887034	−	0.996058i	$-0.471728\pi$
$59$	1.36269	0.177407	0.0887034	+	0.996058i	$0.471728\pi$
$60$	3.54069	0.457101
$61$	1.56062	0.199816	0.0999082	−	0.994997i	$-0.468145\pi$
$61$	1.56062	0.199816	0.0999082	+	0.994997i	$0.468145\pi$
$62$	10.5352	1.33798
$63$	12.2359	1.54157
$64$	1.00000	0.125000
$65$	3.83581	0.475774
$66$	0.597939	0.0736012
$67$	−7.22566	−0.882755	−0.441378	−	0.897321i	$-0.645510\pi$
$67$	−7.22566	−0.882755	−0.441378	+	0.897321i	$0.645510\pi$
$68$	−7.37548	−0.894408
$69$	−21.6016	−2.60052
$70$	−4.11182	−0.491456
$71$	−1.42465	−0.169075	−0.0845377	−	0.996420i	$-0.526941\pi$
$71$	−1.42465	−0.169075	−0.0845377	+	0.996420i	$0.526941\pi$
$72$	3.98626	0.469785
$73$	15.0562	1.76220	0.881100	−	0.472930i	$-0.156804\pi$
$73$	15.0562	1.76220	0.881100	+	0.472930i	$0.156804\pi$
$74$	2.37336	0.275898
$75$	8.47277	0.978352
$76$	3.90348	0.447760
$77$	−0.694390	−0.0791331
$78$	7.56859	0.856974
$79$	4.63774	0.521787	0.260893	−	0.965368i	$-0.415983\pi$
$79$	4.63774	0.521787	0.260893	+	0.965368i	$0.415983\pi$
$80$	−1.33957	−0.149768
$81$	−5.06851	−0.563168
$82$	−4.30363	−0.475256
$83$	10.3362	1.13455	0.567273	−	0.823530i	$-0.307998\pi$
$83$	10.3362	1.13455	0.567273	+	0.823530i	$0.307998\pi$
$84$	−8.11318	−0.885220
$85$	9.87997	1.07163
$86$	−12.3357	−1.33019
$87$	17.0905	1.83229
$88$	−0.226222	−0.0241153
$89$	4.36031	0.462192	0.231096	−	0.972931i	$-0.425769\pi$
$89$	4.36031	0.462192	0.231096	+	0.972931i	$0.425769\pi$
$90$	−5.33987	−0.562872
$91$	−8.78944	−0.921384
$92$	8.17264	0.852057
$93$	−27.8463	−2.88752
$94$	0.273710	0.0282311
$95$	−5.22898	−0.536482
$96$	−2.64315	−0.269766
$97$	9.27070	0.941297	0.470648	−	0.882321i	$-0.344020\pi$
$97$	9.27070	0.941297	0.470648	+	0.882321i	$0.344020\pi$
$98$	2.42188	0.244646
$99$	−0.901779	−0.0906322
$100$	−3.20555	−0.320555
$101$	−9.01063	−0.896591	−0.448296	−	0.893885i	$-0.647969\pi$
$101$	−9.01063	−0.896591	−0.448296	+	0.893885i	$0.647969\pi$
$102$	19.4945	1.93025
$103$	1.76001	0.173419	0.0867095	−	0.996234i	$-0.472365\pi$
$103$	1.76001	0.173419	0.0867095	+	0.996234i	$0.472365\pi$
$104$	−2.86347	−0.280786
$105$	10.8682	1.06062
$106$	−12.3290	−1.19750
$107$	14.7515	1.42608	0.713040	−	0.701123i	$-0.247318\pi$
$107$	14.7515	1.42608	0.713040	+	0.701123i	$0.247318\pi$
$108$	−2.60684	−0.250843
$109$	5.31491	0.509076	0.254538	−	0.967063i	$-0.418077\pi$
$109$	5.31491	0.509076	0.254538	+	0.967063i	$0.418077\pi$
$110$	0.303040	0.0288937
$111$	−6.27316	−0.595422
$112$	3.06951	0.290041
$113$	−12.6595	−1.19091	−0.595453	−	0.803390i	$-0.703027\pi$
$113$	−12.6595	−1.19091	−0.595453	+	0.803390i	$0.703027\pi$
$114$	−10.3175	−0.966323
$115$	−10.9478	−1.02089
$116$	−6.46595	−0.600349
$117$	−11.4145	−1.05527
$118$	1.36269	0.125446
$119$	−22.6391	−2.07532
$120$	3.54069	0.323219
$121$	−10.9488	−0.995348
$122$	1.56062	0.141292
$123$	11.3751	1.02566
$124$	10.5352	0.946093
$125$	10.9919	0.983146
$126$	12.2359	1.09006
$127$	3.79920	0.337124	0.168562	−	0.985691i	$-0.446088\pi$
$127$	3.79920	0.337124	0.168562	+	0.985691i	$0.446088\pi$
$128$	1.00000	0.0883883
$129$	32.6051	2.87072
$130$	3.83581	0.336423
$131$	−8.19712	−0.716186	−0.358093	−	0.933686i	$-0.616573\pi$
$131$	−8.19712	−0.716186	−0.358093	+	0.933686i	$0.616573\pi$
$132$	0.597939	0.0520439
$133$	11.9818	1.03895
$134$	−7.22566	−0.624202
$135$	3.49204	0.300547
$136$	−7.37548	−0.632442
$137$	−16.1023	−1.37572	−0.687858	−	0.725845i	$-0.741449\pi$
$137$	−16.1023	−1.37572	−0.687858	+	0.725845i	$0.741449\pi$
$138$	−21.6016	−1.83885
$139$	−18.6630	−1.58298	−0.791490	−	0.611183i	$-0.790694\pi$
$139$	−18.6630	−1.58298	−0.791490	+	0.611183i	$0.790694\pi$
$140$	−4.11182	−0.347512
$141$	−0.723459	−0.0609262
$142$	−1.42465	−0.119554
$143$	0.647779	0.0541700
$144$	3.98626	0.332188
$145$	8.66159	0.719306
$146$	15.0562	1.24606
$147$	−6.40139	−0.527978
$148$	2.37336	0.195089
$149$	−12.5994	−1.03218	−0.516090	−	0.856534i	$-0.672613\pi$
$149$	−12.5994	−1.03218	−0.516090	+	0.856534i	$0.672613\pi$
$150$	8.47277	0.691799
$151$	−5.41711	−0.440838	−0.220419	−	0.975405i	$-0.570742\pi$
$151$	−5.41711	−0.440838	−0.220419	+	0.975405i	$0.570742\pi$
$152$	3.90348	0.316614
$153$	−29.4006	−2.37690
$154$	−0.694390	−0.0559555
$155$	−14.1127	−1.13356
$156$	7.56859	0.605972
$157$	−6.12987	−0.489217	−0.244608	−	0.969622i	$-0.578659\pi$
$157$	−6.12987	−0.489217	−0.244608	+	0.969622i	$0.578659\pi$
$158$	4.63774	0.368959
$159$	32.5874	2.58435
$160$	−1.33957	−0.105902
$161$	25.0860	1.97705
$162$	−5.06851	−0.398220
$163$	24.0337	1.88247	0.941233	−	0.337757i	$-0.109668\pi$
$163$	24.0337	1.88247	0.941233	+	0.337757i	$0.109668\pi$
$164$	−4.30363	−0.336057
$165$	−0.800981	−0.0623563
$166$	10.3362	0.802245
$167$	6.66384	0.515664	0.257832	−	0.966190i	$-0.416992\pi$
$167$	6.66384	0.515664	0.257832	+	0.966190i	$0.416992\pi$
$168$	−8.11318	−0.625945
$169$	−4.80055	−0.369273
$170$	9.87997	0.757759
$171$	15.5603	1.18993
$172$	−12.3357	−0.940587
$173$	12.9725	0.986277	0.493139	−	0.869951i	$-0.335850\pi$
$173$	12.9725	0.986277	0.493139	+	0.869951i	$0.335850\pi$
$174$	17.0905	1.29563
$175$	−9.83947	−0.743794
$176$	−0.226222	−0.0170521
$177$	−3.60179	−0.270727
$178$	4.36031	0.326819
$179$	−17.7139	−1.32400	−0.661998	−	0.749506i	$-0.730291\pi$
$179$	−17.7139	−1.32400	−0.661998	+	0.749506i	$0.730291\pi$
$180$	−5.33987	−0.398010
$181$	−7.65478	−0.568975	−0.284488	−	0.958680i	$-0.591823\pi$
$181$	−7.65478	−0.568975	−0.284488	+	0.958680i	$0.591823\pi$
$182$	−8.78944	−0.651517
$183$	−4.12495	−0.304925
$184$	8.17264	0.602495
$185$	−3.17928	−0.233746
$186$	−27.8463	−2.04179
$187$	1.66850	0.122012
$188$	0.273710	0.0199624
$189$	−8.00171	−0.582039
$190$	−5.22898	−0.379350
$191$	−25.2446	−1.82664	−0.913319	−	0.407245i	$-0.866490\pi$
$191$	−25.2446	−1.82664	−0.913319	+	0.407245i	$0.866490\pi$
$192$	−2.64315	−0.190753
$193$	2.90126	0.208838	0.104419	−	0.994533i	$-0.466702\pi$
$193$	2.90126	0.208838	0.104419	+	0.994533i	$0.466702\pi$
$194$	9.27070	0.665597
$195$	−10.1386	−0.726044
$196$	2.42188	0.172991
$197$	6.63732	0.472889	0.236445	−	0.971645i	$-0.424018\pi$
$197$	6.63732	0.472889	0.236445	+	0.971645i	$0.424018\pi$
$198$	−0.901779	−0.0640867
$199$	−11.3750	−0.806353	−0.403177	−	0.915122i	$-0.632094\pi$
$199$	−11.3750	−0.806353	−0.403177	+	0.915122i	$0.632094\pi$
$200$	−3.20555	−0.226667
$201$	19.0985	1.34711
$202$	−9.01063	−0.633986
$203$	−19.8473	−1.39301
$204$	19.4945	1.36489
$205$	5.76500	0.402645
$206$	1.76001	0.122626
$207$	32.5783	2.26435
$208$	−2.86347	−0.198546
$209$	−0.883053	−0.0610821
$210$	10.8682	0.749975
$211$	−21.3476	−1.46963	−0.734813	−	0.678270i	$-0.762730\pi$
$211$	−21.3476	−1.46963	−0.734813	+	0.678270i	$0.762730\pi$
$212$	−12.3290	−0.846758
$213$	3.76558	0.258013
$214$	14.7515	1.00839
$215$	16.5245	1.12696
$216$	−2.60684	−0.177373
$217$	32.3380	2.19525
$218$	5.31491	0.359971
$219$	−39.7960	−2.68916
$220$	0.303040	0.0204309
$221$	21.1195	1.42065
$222$	−6.27316	−0.421027
$223$	−9.20853	−0.616649	−0.308324	−	0.951281i	$-0.599768\pi$
$223$	−9.20853	−0.616649	−0.308324	+	0.951281i	$0.599768\pi$
$224$	3.06951	0.205090
$225$	−12.7782	−0.851878
$226$	−12.6595	−0.842097
$227$	11.8369	0.785645	0.392823	−	0.919614i	$-0.371499\pi$
$227$	11.8369	0.785645	0.392823	+	0.919614i	$0.371499\pi$
$228$	−10.3175	−0.683293
$229$	−5.98251	−0.395336	−0.197668	−	0.980269i	$-0.563337\pi$
$229$	−5.98251	−0.395336	−0.197668	+	0.980269i	$0.563337\pi$
$230$	−10.9478	−0.721878
$231$	1.83538	0.120759
$232$	−6.46595	−0.424511
$233$	−24.5341	−1.60728	−0.803641	−	0.595115i	$-0.797107\pi$
$233$	−24.5341	−1.60728	−0.803641	+	0.595115i	$0.797107\pi$
$234$	−11.4145	−0.746191
$235$	−0.366654	−0.0239179
$236$	1.36269	0.0887034
$237$	−12.2583	−0.796260
$238$	−22.6391	−1.46747
$239$	17.7068	1.14536	0.572679	−	0.819780i	$-0.305904\pi$
$239$	17.7068	1.14536	0.572679	+	0.819780i	$0.305904\pi$
$240$	3.54069	0.228550
$241$	−6.04324	−0.389280	−0.194640	−	0.980875i	$-0.562354\pi$
$241$	−6.04324	−0.389280	−0.194640	+	0.980875i	$0.562354\pi$
$242$	−10.9488	−0.703817
$243$	21.2174	1.36109
$244$	1.56062	0.0999082
$245$	−3.24427	−0.207269
$246$	11.3751	0.725253
$247$	−11.1775	−0.711207
$248$	10.5352	0.668988
$249$	−27.3202	−1.73135
$250$	10.9919	0.695189
$251$	−22.9189	−1.44663	−0.723314	−	0.690520i	$-0.757382\pi$
$251$	−22.9189	−1.44663	−0.723314	+	0.690520i	$0.757382\pi$
$252$	12.2359	0.770786
$253$	−1.84883	−0.116235
$254$	3.79920	0.238383
$255$	−26.1143	−1.63534
$256$	1.00000	0.0625000
$257$	5.17169	0.322601	0.161301	−	0.986905i	$-0.448431\pi$
$257$	5.17169	0.322601	0.161301	+	0.986905i	$0.448431\pi$
$258$	32.6051	2.02991
$259$	7.28505	0.452671
$260$	3.83581	0.237887
$261$	−25.7750	−1.59543
$262$	−8.19712	−0.506420
$263$	−30.3571	−1.87190	−0.935951	−	0.352130i	$-0.885457\pi$
$263$	−30.3571	−1.87190	−0.935951	+	0.352130i	$0.885457\pi$
$264$	0.597939	0.0368006
$265$	16.5155	1.01454
$266$	11.9818	0.734649
$267$	−11.5250	−0.705317
$268$	−7.22566	−0.441378
$269$	−26.8116	−1.63473	−0.817365	−	0.576120i	$-0.804566\pi$
$269$	−26.8116	−1.63473	−0.817365	+	0.576120i	$0.804566\pi$
$270$	3.49204	0.212519
$271$	10.7303	0.651818	0.325909	−	0.945401i	$-0.394330\pi$
$271$	10.7303	0.651818	0.325909	+	0.945401i	$0.394330\pi$
$272$	−7.37548	−0.447204
$273$	23.2318	1.40605
$274$	−16.1023	−0.972778
$275$	0.725167	0.0437292
$276$	−21.6016	−1.30026
$277$	8.57036	0.514943	0.257471	−	0.966286i	$-0.417111\pi$
$277$	8.57036	0.514943	0.257471	+	0.966286i	$0.417111\pi$
$278$	−18.6630	−1.11934
$279$	41.9962	2.51425
$280$	−4.11182	−0.245728
$281$	−23.1992	−1.38395	−0.691973	−	0.721923i	$-0.743258\pi$
$281$	−23.1992	−1.38395	−0.691973	+	0.721923i	$0.743258\pi$
$282$	−0.723459	−0.0430813
$283$	−2.22668	−0.132363	−0.0661813	−	0.997808i	$-0.521082\pi$
$283$	−2.22668	−0.132363	−0.0661813	+	0.997808i	$0.521082\pi$
$284$	−1.42465	−0.0845377
$285$	13.8210	0.818686
$286$	0.647779	0.0383040
$287$	−13.2100	−0.779762
$288$	3.98626	0.234893
$289$	37.3977	2.19987
$290$	8.66159	0.508626
$291$	−24.5039	−1.43644
$292$	15.0562	0.881100
$293$	−8.69125	−0.507748	−0.253874	−	0.967237i	$-0.581705\pi$
$293$	−8.69125	−0.507748	−0.253874	+	0.967237i	$0.581705\pi$
$294$	−6.40139	−0.373337
$295$	−1.82541	−0.106280
$296$	2.37336	0.137949
$297$	0.589724	0.0342192
$298$	−12.5994	−0.729862
$299$	−23.4021	−1.35338
$300$	8.47277	0.489176
$301$	−37.8645	−2.18247
$302$	−5.41711	−0.311720
$303$	23.8165	1.36822
$304$	3.90348	0.223880
$305$	−2.09055	−0.119705
$306$	−29.4006	−1.68072
$307$	−31.2188	−1.78175	−0.890874	−	0.454250i	$-0.849907\pi$
$307$	−31.2188	−1.78175	−0.890874	+	0.454250i	$0.849907\pi$
$308$	−0.694390	−0.0395665
$309$	−4.65198	−0.264642
$310$	−14.1127	−0.801547
$311$	2.60464	0.147695	0.0738477	−	0.997270i	$-0.476472\pi$
$311$	2.60464	0.147695	0.0738477	+	0.997270i	$0.476472\pi$
$312$	7.56859	0.428487
$313$	25.8000	1.45830	0.729151	−	0.684353i	$-0.239915\pi$
$313$	25.8000	1.45830	0.729151	+	0.684353i	$0.239915\pi$
$314$	−6.12987	−0.345929
$315$	−16.3908	−0.923516
$316$	4.63774	0.260893
$317$	−20.4134	−1.14653	−0.573264	−	0.819371i	$-0.694323\pi$
$317$	−20.4134	−1.14653	−0.573264	+	0.819371i	$0.694323\pi$
$318$	32.5874	1.82741
$319$	1.46274	0.0818977
$320$	−1.33957	−0.0748842
$321$	−38.9905	−2.17623
$322$	25.0860	1.39799
$323$	−28.7901	−1.60192
$324$	−5.06851	−0.281584
$325$	9.17901	0.509160
$326$	24.0337	1.33111
$327$	−14.0481	−0.776862
$328$	−4.30363	−0.237628
$329$	0.840156	0.0463193
$330$	−0.800981	−0.0440925
$331$	−14.1568	−0.778128	−0.389064	−	0.921211i	$-0.627201\pi$
$331$	−14.1568	−0.778128	−0.389064	+	0.921211i	$0.627201\pi$
$332$	10.3362	0.567273
$333$	9.46084	0.518451
$334$	6.66384	0.364629
$335$	9.67927	0.528835
$336$	−8.11318	−0.442610
$337$	−26.1171	−1.42269	−0.711346	−	0.702842i	$-0.751914\pi$
$337$	−26.1171	−1.42269	−0.711346	+	0.702842i	$0.751914\pi$
$338$	−4.80055	−0.261115
$339$	33.4610	1.81735
$340$	9.87997	0.535816
$341$	−2.38330	−0.129063
$342$	15.5603	0.841404
$343$	−14.0526	−0.758768
$344$	−12.3357	−0.665095
$345$	28.9368	1.55790
$346$	12.9725	0.697403
$347$	0.128707	0.00690937	0.00345469	−	0.999994i	$-0.498900\pi$
$347$	0.128707	0.00690937	0.00345469	+	0.999994i	$0.498900\pi$
$348$	17.0905	0.916147
$349$	−19.6544	−1.05208	−0.526038	−	0.850461i	$-0.676323\pi$
$349$	−19.6544	−1.05208	−0.526038	+	0.850461i	$0.676323\pi$
$350$	−9.83947	−0.525942
$351$	7.46460	0.398431
$352$	−0.226222	−0.0120577
$353$	−8.50246	−0.452540	−0.226270	−	0.974065i	$-0.572653\pi$
$353$	−8.50246	−0.452540	−0.226270	+	0.974065i	$0.572653\pi$
$354$	−3.60179	−0.191433
$355$	1.90842	0.101289
$356$	4.36031	0.231096
$357$	59.8386	3.16699
$358$	−17.7139	−0.936206
$359$	27.6901	1.46143	0.730713	−	0.682685i	$-0.239188\pi$
$359$	27.6901	1.46143	0.730713	+	0.682685i	$0.239188\pi$
$360$	−5.33987	−0.281436
$361$	−3.76283	−0.198044
$362$	−7.65478	−0.402326
$363$	28.9394	1.51893
$364$	−8.78944	−0.460692
$365$	−20.1689	−1.05569
$366$	−4.12495	−0.215615
$367$	−0.00112933	−5.89503e−5 0	−2.94752e−5	−	1.00000i	$-0.500009\pi$
$367$	−0.00112933	−5.89503e−5 0	−2.94752e−5		1.00000i	$0.500009\pi$
$368$	8.17264	0.426028
$369$	−17.1554	−0.893073
$370$	−3.17928	−0.165283
$371$	−37.8439	−1.96476
$372$	−27.8463	−1.44376
$373$	−0.905695	−0.0468951	−0.0234475	−	0.999725i	$-0.507464\pi$
$373$	−0.905695	−0.0468951	−0.0234475	+	0.999725i	$0.507464\pi$
$374$	1.66850	0.0862758
$375$	−29.0533	−1.50031
$376$	0.273710	0.0141155
$377$	18.5151	0.953574
$378$	−8.00171	−0.411563
$379$	−23.9019	−1.22776	−0.613880	−	0.789399i	$-0.710392\pi$
$379$	−23.9019	−1.22776	−0.613880	+	0.789399i	$0.710392\pi$
$380$	−5.22898	−0.268241
$381$	−10.0419	−0.514460
$382$	−25.2446	−1.29163
$383$	30.1957	1.54293	0.771463	−	0.636274i	$-0.219525\pi$
$383$	30.1957	1.54293	0.771463	+	0.636274i	$0.219525\pi$
$384$	−2.64315	−0.134883
$385$	0.930183	0.0474065
$386$	2.90126	0.147670
$387$	−49.1732	−2.49962
$388$	9.27070	0.470648
$389$	18.8211	0.954268	0.477134	−	0.878831i	$-0.341676\pi$
$389$	18.8211	0.954268	0.477134	+	0.878831i	$0.341676\pi$
$390$	−10.1386	−0.513390
$391$	−60.2772	−3.04835
$392$	2.42188	0.122323
$393$	21.6663	1.09292
$394$	6.63732	0.334383
$395$	−6.21258	−0.312589
$396$	−0.901779	−0.0453161
$397$	1.85190	0.0929443	0.0464721	−	0.998920i	$-0.485202\pi$
$397$	1.85190	0.0929443	0.0464721	+	0.998920i	$0.485202\pi$
$398$	−11.3750	−0.570178
$399$	−31.6697	−1.58547
$400$	−3.20555	−0.160278
$401$	−23.8957	−1.19329	−0.596647	−	0.802504i	$-0.703501\pi$
$401$	−23.8957	−1.19329	−0.596647	+	0.802504i	$0.703501\pi$
$402$	19.0985	0.952548
$403$	−30.1673	−1.50274
$404$	−9.01063	−0.448296
$405$	6.78962	0.337379
$406$	−19.8473	−0.985004
$407$	−0.536907	−0.0266135
$408$	19.4945	0.965123
$409$	−7.77300	−0.384350	−0.192175	−	0.981361i	$-0.561554\pi$
$409$	−7.77300	−0.384350	−0.192175	+	0.981361i	$0.561554\pi$
$410$	5.76500	0.284713
$411$	42.5610	2.09938
$412$	1.76001	0.0867095
$413$	4.18278	0.205821
$414$	32.5783	1.60114
$415$	−13.8461	−0.679677
$416$	−2.86347	−0.140393
$417$	49.3293	2.41567
$418$	−0.883053	−0.0431915
$419$	−8.70430	−0.425233	−0.212616	−	0.977136i	$-0.568198\pi$
$419$	−8.70430	−0.425233	−0.212616	+	0.977136i	$0.568198\pi$
$420$	10.8682	0.530312
$421$	28.7314	1.40028	0.700141	−	0.714005i	$-0.253121\pi$
$421$	28.7314	1.40028	0.700141	+	0.714005i	$0.253121\pi$
$422$	−21.3476	−1.03918
$423$	1.09108	0.0530502
$424$	−12.3290	−0.598748
$425$	23.6425	1.14683
$426$	3.76558	0.182443
$427$	4.79032	0.231820
$428$	14.7515	0.713040
$429$	−1.71218	−0.0826648
$430$	16.5245	0.796882
$431$	14.8532	0.715455	0.357727	−	0.933826i	$-0.383552\pi$
$431$	14.8532	0.715455	0.357727	+	0.933826i	$0.383552\pi$
$432$	−2.60684	−0.125422
$433$	−17.6376	−0.847611	−0.423805	−	0.905753i	$-0.639306\pi$
$433$	−17.6376	−0.847611	−0.423805	+	0.905753i	$0.639306\pi$
$434$	32.3380	1.55227
$435$	−22.8939	−1.09768
$436$	5.31491	0.254538
$437$	31.9018	1.52607
$438$	−39.7960	−1.90152
$439$	25.4784	1.21602	0.608009	−	0.793930i	$-0.291968\pi$
$439$	25.4784	1.21602	0.608009	+	0.793930i	$0.291968\pi$
$440$	0.303040	0.0144469
$441$	9.65423	0.459725
$442$	21.1195	1.00455
$443$	−22.6603	−1.07662	−0.538311	−	0.842746i	$-0.680937\pi$
$443$	−22.6603	−1.07662	−0.538311	+	0.842746i	$0.680937\pi$
$444$	−6.27316	−0.297711
$445$	−5.84094	−0.276887
$446$	−9.20853	−0.436036
$447$	33.3021	1.57513
$448$	3.06951	0.145021
$449$	−2.81060	−0.132641	−0.0663203	−	0.997798i	$-0.521126\pi$
$449$	−2.81060	−0.132641	−0.0663203	+	0.997798i	$0.521126\pi$
$450$	−12.7782	−0.602369
$451$	0.973574	0.0458438
$452$	−12.6595	−0.595453
$453$	14.3182	0.672730
$454$	11.8369	0.555535
$455$	11.7741	0.551976
$456$	−10.3175	−0.483161
$457$	−20.4997	−0.958935	−0.479467	−	0.877560i	$-0.659170\pi$
$457$	−20.4997	−0.958935	−0.479467	+	0.877560i	$0.659170\pi$
$458$	−5.98251	−0.279544
$459$	19.2267	0.897424
$460$	−10.9478	−0.510445
$461$	−7.93356	−0.369503	−0.184751	−	0.982785i	$-0.559148\pi$
$461$	−7.93356	−0.369503	−0.184751	+	0.982785i	$0.559148\pi$
$462$	1.83538	0.0853896
$463$	17.8804	0.830974	0.415487	−	0.909599i	$-0.363611\pi$
$463$	17.8804	0.830974	0.415487	+	0.909599i	$0.363611\pi$
$464$	−6.46595	−0.300174
$465$	37.3020	1.72984
$466$	−24.5341	−1.13652
$467$	23.2912	1.07779	0.538895	−	0.842373i	$-0.318842\pi$
$467$	23.2912	1.07779	0.538895	+	0.842373i	$0.318842\pi$
$468$	−11.4145	−0.527637
$469$	−22.1792	−1.02414
$470$	−0.366654	−0.0169125
$471$	16.2022	0.746557
$472$	1.36269	0.0627228
$473$	2.79060	0.128312
$474$	−12.2583	−0.563041
$475$	−12.5128	−0.574128
$476$	−22.6391	−1.03766
$477$	−49.1465	−2.25026
$478$	17.7068	0.809891
$479$	2.41781	0.110473	0.0552363	−	0.998473i	$-0.482409\pi$
$479$	2.41781	0.110473	0.0552363	+	0.998473i	$0.482409\pi$
$480$	3.54069	0.161609
$481$	−6.79605	−0.309873
$482$	−6.04324	−0.275262
$483$	−66.3061	−3.01703
$484$	−10.9488	−0.497674
$485$	−12.4187	−0.563906
$486$	21.2174	0.962439
$487$	7.48769	0.339299	0.169650	−	0.985504i	$-0.445736\pi$
$487$	7.48769	0.339299	0.169650	+	0.985504i	$0.445736\pi$
$488$	1.56062	0.0706458
$489$	−63.5248	−2.87269
$490$	−3.24427	−0.146561
$491$	12.4573	0.562190	0.281095	−	0.959680i	$-0.409302\pi$
$491$	12.4573	0.562190	0.281095	+	0.959680i	$0.409302\pi$
$492$	11.3751	0.512831
$493$	47.6895	2.14783
$494$	−11.1775	−0.502899
$495$	1.20800	0.0542954
$496$	10.5352	0.473046
$497$	−4.37299	−0.196155
$498$	−27.3202	−1.22425
$499$	−7.86042	−0.351881	−0.175940	−	0.984401i	$-0.556297\pi$
$499$	−7.86042	−0.351881	−0.175940	+	0.984401i	$0.556297\pi$
$500$	10.9919	0.491573
$501$	−17.6136	−0.786916
$502$	−22.9189	−1.02292
$503$	16.4498	0.733460	0.366730	−	0.930327i	$-0.380477\pi$
$503$	16.4498	0.733460	0.366730	+	0.930327i	$0.380477\pi$
$504$	12.2359	0.545028
$505$	12.0704	0.537124
$506$	−1.84883	−0.0821906
$507$	12.6886	0.563520
$508$	3.79920	0.168562
$509$	−27.7451	−1.22978	−0.614891	−	0.788612i	$-0.710800\pi$
$509$	−27.7451	−1.22978	−0.614891	+	0.788612i	$0.710800\pi$
$510$	−26.1143	−1.15636
$511$	46.2153	2.04444
$512$	1.00000	0.0441942
$513$	−10.1757	−0.449270
$514$	5.17169	0.228114
$515$	−2.35766	−0.103891
$516$	32.6051	1.43536
$517$	−0.0619193	−0.00272321
$518$	7.28505	0.320087
$519$	−34.2882	−1.50508
$520$	3.83581	0.168212
$521$	−38.0187	−1.66563	−0.832816	−	0.553550i	$-0.813273\pi$
$521$	−38.0187	−1.66563	−0.832816	+	0.553550i	$0.813273\pi$
$522$	−25.7750	−1.12814
$523$	−14.6403	−0.640177	−0.320088	−	0.947388i	$-0.603713\pi$
$523$	−14.6403	−0.640177	−0.320088	+	0.947388i	$0.603713\pi$
$524$	−8.19712	−0.358093
$525$	26.0072	1.13505
$526$	−30.3571	−1.32363
$527$	−77.7025	−3.38477
$528$	0.597939	0.0260220
$529$	43.7921	1.90400
$530$	16.5155	0.717388
$531$	5.43203	0.235730
$532$	11.9818	0.519476
$533$	12.3233	0.533781
$534$	−11.5250	−0.498735
$535$	−19.7606	−0.854327
$536$	−7.22566	−0.312101
$537$	46.8204	2.02045
$538$	−26.8116	−1.15593
$539$	−0.547882	−0.0235989
$540$	3.49204	0.150273
$541$	8.44764	0.363193	0.181596	−	0.983373i	$-0.441874\pi$
$541$	8.44764	0.363193	0.181596	+	0.983373i	$0.441874\pi$
$542$	10.7303	0.460905
$543$	20.2328	0.868271
$544$	−7.37548	−0.316221
$545$	−7.11968	−0.304974
$546$	23.2318	0.994231
$547$	−28.0142	−1.19780	−0.598901	−	0.800823i	$-0.704396\pi$
$547$	−28.0142	−1.19780	−0.598901	+	0.800823i	$0.704396\pi$
$548$	−16.1023	−0.687858
$549$	6.22102	0.265507
$550$	0.725167	0.0309212
$551$	−25.2397	−1.07525
$552$	−21.6016	−0.919423
$553$	14.2356	0.605359
$554$	8.57036	0.364120
$555$	8.40333	0.356702
$556$	−18.6630	−0.791490
$557$	5.01913	0.212667	0.106334	−	0.994331i	$-0.466089\pi$
$557$	5.01913	0.212667	0.106334	+	0.994331i	$0.466089\pi$
$558$	41.9962	1.77784
$559$	35.3228	1.49400
$560$	−4.11182	−0.173756
$561$	−4.41009	−0.186194
$562$	−23.1992	−0.978598
$563$	20.9785	0.884139	0.442069	−	0.896981i	$-0.354245\pi$
$563$	20.9785	0.884139	0.442069	+	0.896981i	$0.354245\pi$
$564$	−0.723459	−0.0304631
$565$	16.9583	0.713440
$566$	−2.22668	−0.0935945
$567$	−15.5578	−0.653367
$568$	−1.42465	−0.0597772
$569$	−28.3704	−1.18935	−0.594675	−	0.803966i	$-0.702719\pi$
$569$	−28.3704	−1.18935	−0.594675	+	0.803966i	$0.702719\pi$
$570$	13.8210	0.578898
$571$	−20.4157	−0.854372	−0.427186	−	0.904164i	$-0.640495\pi$
$571$	−20.4157	−0.854372	−0.427186	+	0.904164i	$0.640495\pi$
$572$	0.647779	0.0270850
$573$	66.7255	2.78750
$574$	−13.2100	−0.551375
$575$	−26.1979	−1.09253
$576$	3.98626	0.166094
$577$	−5.33467	−0.222085	−0.111043	−	0.993816i	$-0.535419\pi$
$577$	−5.33467	−0.222085	−0.111043	+	0.993816i	$0.535419\pi$
$578$	37.3977	1.55554
$579$	−7.66849	−0.318691
$580$	8.66159	0.359653
$581$	31.7271	1.31626
$582$	−24.5039	−1.01572
$583$	2.78909	0.115512
$584$	15.0562	0.623032
$585$	15.2906	0.632187
$586$	−8.69125	−0.359032
$587$	−20.6365	−0.851758	−0.425879	−	0.904780i	$-0.640035\pi$
$587$	−20.6365	−0.851758	−0.425879	+	0.904780i	$0.640035\pi$
$588$	−6.40139	−0.263989
$589$	41.1241	1.69449
$590$	−1.82541	−0.0751511
$591$	−17.5434	−0.721641
$592$	2.37336	0.0975446
$593$	17.9110	0.735517	0.367759	−	0.929921i	$-0.380125\pi$
$593$	17.9110	0.735517	0.367759	+	0.929921i	$0.380125\pi$
$594$	0.589724	0.0241967
$595$	30.3266	1.24327
$596$	−12.5994	−0.516090
$597$	30.0659	1.23052
$598$	−23.4021	−0.956983
$599$	41.4996	1.69563	0.847814	−	0.530293i	$-0.177918\pi$
$599$	41.4996	1.69563	0.847814	+	0.530293i	$0.177918\pi$
$600$	8.47277	0.345900
$601$	25.6675	1.04700	0.523499	−	0.852026i	$-0.324626\pi$
$601$	25.6675	1.04700	0.523499	+	0.852026i	$0.324626\pi$
$602$	−37.8645	−1.54324
$603$	−28.8034	−1.17296
$604$	−5.41711	−0.220419
$605$	14.6667	0.596286
$606$	23.8165	0.967478
$607$	5.81514	0.236029	0.118015	−	0.993012i	$-0.462347\pi$
$607$	5.81514	0.236029	0.118015	+	0.993012i	$0.462347\pi$
$608$	3.90348	0.158307
$609$	52.4594	2.12576
$610$	−2.09055	−0.0846441
$611$	−0.783761	−0.0317076
$612$	−29.4006	−1.18845
$613$	7.92505	0.320090	0.160045	−	0.987110i	$-0.448836\pi$
$613$	7.92505	0.320090	0.160045	+	0.987110i	$0.448836\pi$
$614$	−31.2188	−1.25989
$615$	−15.2378	−0.614447
$616$	−0.694390	−0.0279778
$617$	−32.7592	−1.31884	−0.659418	−	0.751776i	$-0.729197\pi$
$617$	−32.7592	−1.31884	−0.659418	+	0.751776i	$0.729197\pi$
$618$	−4.65198	−0.187130
$619$	−9.14883	−0.367723	−0.183861	−	0.982952i	$-0.558860\pi$
$619$	−9.14883	−0.367723	−0.183861	+	0.982952i	$0.558860\pi$
$620$	−14.1127	−0.566779
$621$	−21.3048	−0.854930
$622$	2.60464	0.104436
$623$	13.3840	0.536219
$624$	7.56859	0.302986
$625$	1.30335	0.0521342
$626$	25.8000	1.03118
$627$	2.33404	0.0932128
$628$	−6.12987	−0.244608
$629$	−17.5047	−0.697958
$630$	−16.3908	−0.653024
$631$	30.9557	1.23233	0.616163	−	0.787619i	$-0.288686\pi$
$631$	30.9557	1.23233	0.616163	+	0.787619i	$0.288686\pi$
$632$	4.63774	0.184479
$633$	56.4249	2.24269
$634$	−20.4134	−0.810718
$635$	−5.08929	−0.201962
$636$	32.5874	1.29217
$637$	−6.93497	−0.274773
$638$	1.46274	0.0579104
$639$	−5.67904	−0.224659
$640$	−1.33957	−0.0529511
$641$	3.17837	0.125538	0.0627690	−	0.998028i	$-0.480007\pi$
$641$	3.17837	0.125538	0.0627690	+	0.998028i	$0.480007\pi$
$642$	−38.9905	−1.53883
$643$	6.51740	0.257021	0.128511	−	0.991708i	$-0.458980\pi$
$643$	6.51740	0.257021	0.128511	+	0.991708i	$0.458980\pi$
$644$	25.0860	0.988527
$645$	−43.6768	−1.71977
$646$	−28.7901	−1.13273
$647$	−26.2371	−1.03148	−0.515742	−	0.856744i	$-0.672484\pi$
$647$	−26.2371	−1.03148	−0.515742	+	0.856744i	$0.672484\pi$
$648$	−5.06851	−0.199110
$649$	−0.308270	−0.0121007
$650$	9.17901	0.360030
$651$	−85.4743	−3.35000
$652$	24.0337	0.941233
$653$	25.9962	1.01731	0.508654	−	0.860971i	$-0.330143\pi$
$653$	25.9962	1.01731	0.508654	+	0.860971i	$0.330143\pi$
$654$	−14.0481	−0.549325
$655$	10.9806	0.429048
$656$	−4.30363	−0.168028
$657$	60.0181	2.34153
$658$	0.840156	0.0327527
$659$	34.1525	1.33039	0.665196	−	0.746669i	$-0.268348\pi$
$659$	34.1525	1.33039	0.665196	+	0.746669i	$0.268348\pi$
$660$	−0.800981	−0.0311781
$661$	21.5468	0.838075	0.419037	−	0.907969i	$-0.362368\pi$
$661$	21.5468	0.838075	0.419037	+	0.907969i	$0.362368\pi$
$662$	−14.1568	−0.550219
$663$	−55.8220	−2.16795
$664$	10.3362	0.401123
$665$	−16.0504	−0.622408
$666$	9.46084	0.366600
$667$	−52.8439	−2.04612
$668$	6.66384	0.257832
$669$	24.3396	0.941021
$670$	9.67927	0.373943
$671$	−0.353046	−0.0136292
$672$	−8.11318	−0.312973
$673$	11.7379	0.452462	0.226231	−	0.974074i	$-0.427360\pi$
$673$	11.7379	0.452462	0.226231	+	0.974074i	$0.427360\pi$
$674$	−26.1171	−1.00599
$675$	8.35636	0.321636
$676$	−4.80055	−0.184636
$677$	−8.98182	−0.345199	−0.172600	−	0.984992i	$-0.555217\pi$
$677$	−8.98182	−0.345199	−0.172600	+	0.984992i	$0.555217\pi$
$678$	33.4610	1.28506
$679$	28.4565	1.09206
$680$	9.87997	0.378879
$681$	−31.2868	−1.19891
$682$	−2.38330	−0.0912614
$683$	1.40069	0.0535958	0.0267979	−	0.999641i	$-0.491469\pi$
$683$	1.40069	0.0535958	0.0267979	+	0.999641i	$0.491469\pi$
$684$	15.5603	0.594963
$685$	21.5702	0.824155
$686$	−14.0526	−0.536530
$687$	15.8127	0.603292
$688$	−12.3357	−0.470294
$689$	35.3036	1.34496
$690$	28.9368	1.10160
$691$	−7.62129	−0.289927	−0.144964	−	0.989437i	$-0.546307\pi$
$691$	−7.62129	−0.289927	−0.144964	+	0.989437i	$0.546307\pi$
$692$	12.9725	0.493139
$693$	−2.76802	−0.105148
$694$	0.128707	0.00488566
$695$	25.0004	0.948321
$696$	17.0905	0.647814
$697$	31.7413	1.20229
$698$	−19.6544	−0.743930
$699$	64.8474	2.45275
$700$	−9.83947	−0.371897
$701$	4.46287	0.168560	0.0842802	−	0.996442i	$-0.473141\pi$
$701$	4.46287	0.168560	0.0842802	+	0.996442i	$0.473141\pi$
$702$	7.46460	0.281733
$703$	9.26438	0.349413
$704$	−0.226222	−0.00852606
$705$	0.969123	0.0364993
$706$	−8.50246	−0.319994
$707$	−27.6582	−1.04019
$708$	−3.60179	−0.135364
$709$	43.6989	1.64115	0.820574	−	0.571541i	$-0.193654\pi$
$709$	43.6989	1.64115	0.820574	+	0.571541i	$0.193654\pi$
$710$	1.90842	0.0716218
$711$	18.4872	0.693326
$712$	4.36031	0.163410
$713$	86.1008	3.22450
$714$	59.8386	2.23940
$715$	−0.867745	−0.0324518
$716$	−17.7139	−0.661998
$717$	−46.8018	−1.74785
$718$	27.6901	1.03338
$719$	37.4023	1.39487	0.697436	−	0.716647i	$-0.254324\pi$
$719$	37.4023	1.39487	0.697436	+	0.716647i	$0.254324\pi$
$720$	−5.33987	−0.199005
$721$	5.40237	0.201195
$722$	−3.76283	−0.140038
$723$	15.9732	0.594050
$724$	−7.65478	−0.284488
$725$	20.7270	0.769780
$726$	28.9394	1.07404
$727$	−11.0708	−0.410595	−0.205298	−	0.978700i	$-0.565816\pi$
$727$	−11.0708	−0.410595	−0.205298	+	0.978700i	$0.565816\pi$
$728$	−8.78944	−0.325758
$729$	−40.8752	−1.51390
$730$	−20.1689	−0.746484
$731$	90.9816	3.36508
$732$	−4.12495	−0.152463
$733$	34.6239	1.27886	0.639431	−	0.768849i	$-0.279170\pi$
$733$	34.6239	1.27886	0.639431	+	0.768849i	$0.279170\pi$
$734$	−0.00112933	−4.16842e−5 0
$735$	8.57511	0.316298
$736$	8.17264	0.301248
$737$	1.63460	0.0602114
$738$	−17.1554	−0.631498
$739$	33.0684	1.21644	0.608220	−	0.793768i	$-0.291884\pi$
$739$	33.0684	1.21644	0.608220	+	0.793768i	$0.291884\pi$
$740$	−3.17928	−0.116873
$741$	29.5438	1.08532
$742$	−37.8439	−1.38929
$743$	7.00994	0.257170	0.128585	−	0.991699i	$-0.458957\pi$
$743$	7.00994	0.257170	0.128585	+	0.991699i	$0.458957\pi$
$744$	−27.8463	−1.02089
$745$	16.8777	0.618352
$746$	−0.905695	−0.0331598
$747$	41.2028	1.50753
$748$	1.66850	0.0610062
$749$	45.2798	1.65449
$750$	−29.0533	−1.06088
$751$	39.9834	1.45902	0.729508	−	0.683972i	$-0.239749\pi$
$751$	39.9834	1.45902	0.729508	+	0.683972i	$0.239749\pi$
$752$	0.273710	0.00998119
$753$	60.5781	2.20759
$754$	18.5151	0.674278
$755$	7.25659	0.264094
$756$	−8.00171	−0.291019
$757$	−30.5031	−1.10866	−0.554328	−	0.832299i	$-0.687025\pi$
$757$	−30.5031	−1.10866	−0.554328	+	0.832299i	$0.687025\pi$
$758$	−23.9019	−0.868158
$759$	4.88674	0.177378
$760$	−5.22898	−0.189675
$761$	26.5775	0.963432	0.481716	−	0.876327i	$-0.340014\pi$
$761$	26.5775	0.963432	0.481716	+	0.876327i	$0.340014\pi$
$762$	−10.0419	−0.363778
$763$	16.3141	0.590612
$764$	−25.2446	−0.913319
$765$	39.3841	1.42394
$766$	30.1957	1.09101
$767$	−3.90202	−0.140894
$768$	−2.64315	−0.0953766
$769$	−44.1010	−1.59032	−0.795162	−	0.606397i	$-0.792614\pi$
$769$	−44.1010	−1.59032	−0.795162	+	0.606397i	$0.792614\pi$
$770$	0.930183	0.0335215
$771$	−13.6696	−0.492298
$772$	2.90126	0.104419
$773$	−7.71595	−0.277523	−0.138762	−	0.990326i	$-0.544312\pi$
$773$	−7.71595	−0.277523	−0.138762	+	0.990326i	$0.544312\pi$
$774$	−49.1732	−1.76750
$775$	−33.7713	−1.21310
$776$	9.27070	0.332799
$777$	−19.2555	−0.690788
$778$	18.8211	0.674769
$779$	−16.7991	−0.601891
$780$	−10.1386	−0.363022
$781$	0.322288	0.0115324
$782$	−60.2772	−2.15551
$783$	16.8557	0.602373
$784$	2.42188	0.0864956
$785$	8.21138	0.293077
$786$	21.6663	0.772810
$787$	−1.65235	−0.0589000	−0.0294500	−	0.999566i	$-0.509376\pi$
$787$	−1.65235	−0.0589000	−0.0294500	+	0.999566i	$0.509376\pi$
$788$	6.63732	0.236445
$789$	80.2386	2.85657
$790$	−6.21258	−0.221034
$791$	−38.8584	−1.38165
$792$	−0.901779	−0.0320433
$793$	−4.46878	−0.158691
$794$	1.85190	0.0657215
$795$	−43.6531	−1.54821
$796$	−11.3750	−0.403177
$797$	27.1173	0.960545	0.480272	−	0.877119i	$-0.340538\pi$
$797$	27.1173	0.960545	0.480272	+	0.877119i	$0.340538\pi$
$798$	−31.6697	−1.12109
$799$	−2.01875	−0.0714181
$800$	−3.20555	−0.113333
$801$	17.3813	0.614140
$802$	−23.8957	−0.843786
$803$	−3.40605	−0.120197
$804$	19.0985	0.673553
$805$	−33.6044	−1.18440
$806$	−30.1673	−1.06260
$807$	70.8671	2.49464
$808$	−9.01063	−0.316993
$809$	−48.2987	−1.69809	−0.849046	−	0.528319i	$-0.822822\pi$
$809$	−48.2987	−1.69809	−0.849046	+	0.528319i	$0.822822\pi$
$810$	6.78962	0.238563
$811$	43.8107	1.53840	0.769202	−	0.639006i	$-0.220654\pi$
$811$	43.8107	1.53840	0.769202	+	0.639006i	$0.220654\pi$
$812$	−19.8473	−0.696503
$813$	−28.3618	−0.994691
$814$	−0.536907	−0.0188186
$815$	−32.1948	−1.12774
$816$	19.4945	0.682445
$817$	−48.1521	−1.68463
$818$	−7.77300	−0.271777
$819$	−35.0370	−1.22429
$820$	5.76500	0.201323
$821$	−47.4787	−1.65702	−0.828508	−	0.559977i	$-0.810810\pi$
$821$	−47.4787	−1.65702	−0.828508	+	0.559977i	$0.810810\pi$
$822$	42.5610	1.48448
$823$	−39.8479	−1.38901	−0.694506	−	0.719487i	$-0.744377\pi$
$823$	−39.8479	−1.38901	−0.694506	+	0.719487i	$0.744377\pi$
$824$	1.76001	0.0613129
$825$	−1.91673	−0.0667319
$826$	4.18278	0.145538
$827$	−9.83197	−0.341891	−0.170946	−	0.985280i	$-0.554682\pi$
$827$	−9.83197	−0.341891	−0.170946	+	0.985280i	$0.554682\pi$
$828$	32.5783	1.13217
$829$	38.0575	1.32179	0.660896	−	0.750478i	$-0.270177\pi$
$829$	38.0575	1.32179	0.660896	+	0.750478i	$0.270177\pi$
$830$	−13.8461	−0.480604
$831$	−22.6528	−0.785816
$832$	−2.86347	−0.0992729
$833$	−17.8625	−0.618899
$834$	49.3293	1.70813
$835$	−8.92668	−0.308920
$836$	−0.883053	−0.0305410
$837$	−27.4637	−0.949283
$838$	−8.70430	−0.300685
$839$	−33.4352	−1.15431	−0.577155	−	0.816634i	$-0.695837\pi$
$839$	−33.4352	−1.15431	−0.577155	+	0.816634i	$0.695837\pi$
$840$	10.8682	0.374987
$841$	12.8085	0.441674
$842$	28.7314	0.990149
$843$	61.3190	2.11194
$844$	−21.3476	−0.734813
$845$	6.43066	0.221222
$846$	1.09108	0.0375121
$847$	−33.6075	−1.15477
$848$	−12.3290	−0.423379
$849$	5.88547	0.201989
$850$	23.6425	0.810931
$851$	19.3966	0.664908
$852$	3.76558	0.129007
$853$	−31.7502	−1.08711	−0.543553	−	0.839375i	$-0.682921\pi$
$853$	−31.7502	−1.08711	−0.543553	+	0.839375i	$0.682921\pi$
$854$	4.79032	0.163922
$855$	−20.8441	−0.712853
$856$	14.7515	0.504196
$857$	−0.722789	−0.0246900	−0.0123450	−	0.999924i	$-0.503930\pi$
$857$	−0.722789	−0.0246900	−0.0123450	+	0.999924i	$0.503930\pi$
$858$	−1.71218	−0.0584529
$859$	37.2631	1.27140	0.635700	−	0.771936i	$-0.280711\pi$
$859$	37.2631	1.27140	0.635700	+	0.771936i	$0.280711\pi$
$860$	16.5245	0.563481
$861$	34.9161	1.18994
$862$	14.8532	0.505903
$863$	25.5348	0.869216	0.434608	−	0.900620i	$-0.356887\pi$
$863$	25.5348	0.869216	0.434608	+	0.900620i	$0.356887\pi$
$864$	−2.60684	−0.0886864
$865$	−17.3775	−0.590853
$866$	−17.6376	−0.599351
$867$	−98.8479	−3.35705
$868$	32.3380	1.09762
$869$	−1.04916	−0.0355903
$870$	−22.8939	−0.776176
$871$	20.6905	0.701069
$872$	5.31491	0.179985
$873$	36.9554	1.25075
$874$	31.9018	1.07909
$875$	33.7397	1.14061
$876$	−39.7960	−1.34458
$877$	−24.5773	−0.829916	−0.414958	−	0.909841i	$-0.636204\pi$
$877$	−24.5773	−0.829916	−0.414958	+	0.909841i	$0.636204\pi$
$878$	25.4784	0.859855
$879$	22.9723	0.774837
$880$	0.303040	0.0102155
$881$	−32.4019	−1.09165	−0.545824	−	0.837900i	$-0.683783\pi$
$881$	−32.4019	−1.09165	−0.545824	+	0.837900i	$0.683783\pi$
$882$	9.65423	0.325075
$883$	11.7700	0.396091	0.198045	−	0.980193i	$-0.436541\pi$
$883$	11.7700	0.396091	0.198045	+	0.980193i	$0.436541\pi$
$884$	21.1195	0.710324
$885$	4.82485	0.162186
$886$	−22.6603	−0.761286
$887$	−16.4224	−0.551410	−0.275705	−	0.961242i	$-0.588911\pi$
$887$	−16.4224	−0.551410	−0.275705	+	0.961242i	$0.588911\pi$
$888$	−6.27316	−0.210514
$889$	11.6617	0.391120
$890$	−5.84094	−0.195789
$891$	1.14661	0.0384128
$892$	−9.20853	−0.308324
$893$	1.06842	0.0357534
$894$	33.3021	1.11379
$895$	23.7289	0.793171
$896$	3.06951	0.102545
$897$	61.8554	2.06529
$898$	−2.81060	−0.0937910
$899$	−68.1204	−2.27194
$900$	−12.7782	−0.425939
$901$	90.9321	3.02939
$902$	0.973574	0.0324165
$903$	100.082	3.33051
$904$	−12.6595	−0.421049
$905$	10.2541	0.340858
$906$	14.3182	0.475692
$907$	−18.4908	−0.613977	−0.306989	−	0.951713i	$-0.599321\pi$
$907$	−18.4908	−0.613977	−0.306989	+	0.951713i	$0.599321\pi$
$908$	11.8369	0.392823
$909$	−35.9187	−1.19135
$910$	11.7741	0.390306
$911$	−13.4319	−0.445018	−0.222509	−	0.974931i	$-0.571425\pi$
$911$	−13.4319	−0.445018	−0.222509	+	0.974931i	$0.571425\pi$
$912$	−10.3175	−0.341647
$913$	−2.33828	−0.0773857
$914$	−20.4997	−0.678069
$915$	5.52565	0.182673
$916$	−5.98251	−0.197668
$917$	−25.1611	−0.830894
$918$	19.2267	0.634575
$919$	41.6827	1.37499	0.687493	−	0.726191i	$-0.258711\pi$
$919$	41.6827	1.37499	0.687493	+	0.726191i	$0.258711\pi$
$920$	−10.9478	−0.360939
$921$	82.5160	2.71899
$922$	−7.93356	−0.261278
$923$	4.07945	0.134277
$924$	1.83538	0.0603795
$925$	−7.60794	−0.250148
$926$	17.8804	0.587587
$927$	7.01586	0.230431
$928$	−6.46595	−0.212255
$929$	−14.7848	−0.485072	−0.242536	−	0.970142i	$-0.577979\pi$
$929$	−14.7848	−0.485072	−0.242536	+	0.970142i	$0.577979\pi$
$930$	37.3020	1.22318
$931$	9.45375	0.309834
$932$	−24.5341	−0.803641
$933$	−6.88445	−0.225387
$934$	23.2912	0.762113
$935$	−2.23506	−0.0730944
$936$	−11.4145	−0.373096
$937$	−12.0394	−0.393309	−0.196654	−	0.980473i	$-0.563008\pi$
$937$	−12.0394	−0.393309	−0.196654	+	0.980473i	$0.563008\pi$
$938$	−22.1792	−0.724177
$939$	−68.1934	−2.22541
$940$	−0.366654	−0.0119589
$941$	22.9552	0.748319	0.374160	−	0.927364i	$-0.377931\pi$
$941$	22.9552	0.748319	0.374160	+	0.927364i	$0.377931\pi$
$942$	16.2022	0.527896
$943$	−35.1720	−1.14536
$944$	1.36269	0.0443517
$945$	10.7188	0.348684
$946$	2.79060	0.0907303
$947$	50.1238	1.62880	0.814402	−	0.580301i	$-0.197065\pi$
$947$	50.1238	1.62880	0.814402	+	0.580301i	$0.197065\pi$
$948$	−12.2583	−0.398130
$949$	−43.1131	−1.39951
$950$	−12.5128	−0.405970
$951$	53.9556	1.74963
$952$	−22.6391	−0.733737
$953$	13.4788	0.436622	0.218311	−	0.975879i	$-0.429945\pi$
$953$	13.4788	0.436622	0.218311	+	0.975879i	$0.429945\pi$
$954$	−49.1465	−1.59118
$955$	33.8169	1.09429
$956$	17.7068	0.572679
$957$	−3.86625	−0.124978
$958$	2.41781	0.0781160
$959$	−49.4263	−1.59606
$960$	3.54069	0.114275
$961$	79.9913	2.58036
$962$	−6.79605	−0.219113
$963$	58.8033	1.89491
$964$	−6.04324	−0.194640
$965$	−3.88644	−0.125109
$966$	−66.3061	−2.13336
$967$	39.4358	1.26817	0.634085	−	0.773263i	$-0.281377\pi$
$967$	39.4358	1.26817	0.634085	+	0.773263i	$0.281377\pi$
$968$	−10.9488	−0.351909
$969$	76.0965	2.44457
$970$	−12.4187	−0.398742
$971$	1.91928	0.0615925	0.0307963	−	0.999526i	$-0.490196\pi$
$971$	1.91928	0.0615925	0.0307963	+	0.999526i	$0.490196\pi$
$972$	21.2174	0.680547
$973$	−57.2864	−1.83652
$974$	7.48769	0.239921
$975$	−24.2615	−0.776991
$976$	1.56062	0.0499541
$977$	10.2084	0.326597	0.163299	−	0.986577i	$-0.447787\pi$
$977$	10.2084	0.326597	0.163299	+	0.986577i	$0.447787\pi$
$978$	−63.5248	−2.03130
$979$	−0.986398	−0.0315254
$980$	−3.24427	−0.103634
$981$	21.1866	0.676436
$982$	12.4573	0.397528
$983$	51.7207	1.64963	0.824817	−	0.565400i	$-0.191278\pi$
$983$	51.7207	1.64963	0.824817	+	0.565400i	$0.191278\pi$
$984$	11.3751	0.362626
$985$	−8.89114	−0.283295
$986$	47.6895	1.51874
$987$	−2.22066	−0.0706844
$988$	−11.1775	−0.355604
$989$	−100.815	−3.20573
$990$	1.20800	0.0383926
$991$	−52.0553	−1.65359	−0.826796	−	0.562502i	$-0.809839\pi$
$991$	−52.0553	−1.65359	−0.826796	+	0.562502i	$0.809839\pi$
$992$	10.5352	0.334494
$993$	37.4186	1.18744
$994$	−4.37299	−0.138703
$995$	15.2376	0.483065
$996$	−27.3202	−0.865673
$997$	−50.5935	−1.60231	−0.801156	−	0.598456i	$-0.795781\pi$
$997$	−50.5935	−1.60231	−0.801156	+	0.598456i	$0.795781\pi$
$998$	−7.86042	−0.248817
$999$	−6.18697	−0.195747

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	6046.2.a.e.1.7	✓	56

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
6046.2.a.e.1.7	✓	56	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:	\( N \)	\(=\)	\( 6046 = 2 \cdot 3023 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	6046.a (trivial)

\(f(q)\)	\(=\)	\(q+1.00000 q^{2} -2.64315 q^{3} +1.00000 q^{4} -1.33957 q^{5} -2.64315 q^{6} +3.06951 q^{7} +1.00000 q^{8} +3.98626 q^{9} +O(q^{10})\)	\(q+1.00000 q^{2} -2.64315 q^{3} +1.00000 q^{4} -1.33957 q^{5} -2.64315 q^{6} +3.06951 q^{7} +1.00000 q^{8} +3.98626 q^{9} -1.33957 q^{10} -0.226222 q^{11} -2.64315 q^{12} -2.86347 q^{13} +3.06951 q^{14} +3.54069 q^{15} +1.00000 q^{16} -7.37548 q^{17} +3.98626 q^{18} +3.90348 q^{19} -1.33957 q^{20} -8.11318 q^{21} -0.226222 q^{22} +8.17264 q^{23} -2.64315 q^{24} -3.20555 q^{25} -2.86347 q^{26} -2.60684 q^{27} +3.06951 q^{28} -6.46595 q^{29} +3.54069 q^{30} +10.5352 q^{31} +1.00000 q^{32} +0.597939 q^{33} -7.37548 q^{34} -4.11182 q^{35} +3.98626 q^{36} +2.37336 q^{37} +3.90348 q^{38} +7.56859 q^{39} -1.33957 q^{40} -4.30363 q^{41} -8.11318 q^{42} -12.3357 q^{43} -0.226222 q^{44} -5.33987 q^{45} +8.17264 q^{46} +0.273710 q^{47} -2.64315 q^{48} +2.42188 q^{49} -3.20555 q^{50} +19.4945 q^{51} -2.86347 q^{52} -12.3290 q^{53} -2.60684 q^{54} +0.303040 q^{55} +3.06951 q^{56} -10.3175 q^{57} -6.46595 q^{58} +1.36269 q^{59} +3.54069 q^{60} +1.56062 q^{61} +10.5352 q^{62} +12.2359 q^{63} +1.00000 q^{64} +3.83581 q^{65} +0.597939 q^{66} -7.22566 q^{67} -7.37548 q^{68} -21.6016 q^{69} -4.11182 q^{70} -1.42465 q^{71} +3.98626 q^{72} +15.0562 q^{73} +2.37336 q^{74} +8.47277 q^{75} +3.90348 q^{76} -0.694390 q^{77} +7.56859 q^{78} +4.63774 q^{79} -1.33957 q^{80} -5.06851 q^{81} -4.30363 q^{82} +10.3362 q^{83} -8.11318 q^{84} +9.87997 q^{85} -12.3357 q^{86} +17.0905 q^{87} -0.226222 q^{88} +4.36031 q^{89} -5.33987 q^{90} -8.78944 q^{91} +8.17264 q^{92} -27.8463 q^{93} +0.273710 q^{94} -5.22898 q^{95} -2.64315 q^{96} +9.27070 q^{97} +2.42188 q^{98} -0.901779 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 56 q + 56 q^{2} - 18 q^{3} + 56 q^{4} - 17 q^{5} - 18 q^{6} - 35 q^{7} + 56 q^{8} + 34 q^{9}+O(q^{10}) \) 56 * q + 56 * q^2 - 18 * q^3 + 56 * q^4 - 17 * q^5 - 18 * q^6 - 35 * q^7 + 56 * q^8 + 34 * q^9	\( 56 q + 56 q^{2} - 18 q^{3} + 56 q^{4} - 17 q^{5} - 18 q^{6} - 35 q^{7} + 56 q^{8} + 34 q^{9} - 17 q^{10} - 53 q^{11} - 18 q^{12} - 21 q^{13} - 35 q^{14} - 36 q^{15} + 56 q^{16} - 22 q^{17} + 34 q^{18} - 31 q^{19} - 17 q^{20} - 23 q^{21} - 53 q^{22} - 59 q^{23} - 18 q^{24} + 41 q^{25} - 21 q^{26} - 63 q^{27} - 35 q^{28} - 88 q^{29} - 36 q^{30} - 44 q^{31} + 56 q^{32} + 4 q^{33} - 22 q^{34} - 51 q^{35} + 34 q^{36} - 60 q^{37} - 31 q^{38} - 62 q^{39} - 17 q^{40} - 39 q^{41} - 23 q^{42} - 66 q^{43} - 53 q^{44} - 34 q^{45} - 59 q^{46} - 51 q^{47} - 18 q^{48} + 41 q^{49} + 41 q^{50} - 48 q^{51} - 21 q^{52} - 75 q^{53} - 63 q^{54} - 41 q^{55} - 35 q^{56} - 12 q^{57} - 88 q^{58} - 77 q^{59} - 36 q^{60} - 43 q^{61} - 44 q^{62} - 88 q^{63} + 56 q^{64} - 54 q^{65} + 4 q^{66} - 62 q^{67} - 22 q^{68} - 48 q^{69} - 51 q^{70} - 122 q^{71} + 34 q^{72} - 7 q^{73} - 60 q^{74} - 63 q^{75} - 31 q^{76} - 39 q^{77} - 62 q^{78} - 91 q^{79} - 17 q^{80} + 8 q^{81} - 39 q^{82} - 51 q^{83} - 23 q^{84} - 72 q^{85} - 66 q^{86} - 19 q^{87} - 53 q^{88} - 62 q^{89} - 34 q^{90} - 48 q^{91} - 59 q^{92} - 41 q^{93} - 51 q^{94} - 120 q^{95} - 18 q^{96} + 6 q^{97} + 41 q^{98} - 128 q^{99}+O(q^{100}) \) 56 * q + 56 * q^2 - 18 * q^3 + 56 * q^4 - 17 * q^5 - 18 * q^6 - 35 * q^7 + 56 * q^8 + 34 * q^9 - 17 * q^10 - 53 * q^11 - 18 * q^12 - 21 * q^13 - 35 * q^14 - 36 * q^15 + 56 * q^16 - 22 * q^17 + 34 * q^18 - 31 * q^19 - 17 * q^20 - 23 * q^21 - 53 * q^22 - 59 * q^23 - 18 * q^24 + 41 * q^25 - 21 * q^26 - 63 * q^27 - 35 * q^28 - 88 * q^29 - 36 * q^30 - 44 * q^31 + 56 * q^32 + 4 * q^33 - 22 * q^34 - 51 * q^35 + 34 * q^36 - 60 * q^37 - 31 * q^38 - 62 * q^39 - 17 * q^40 - 39 * q^41 - 23 * q^42 - 66 * q^43 - 53 * q^44 - 34 * q^45 - 59 * q^46 - 51 * q^47 - 18 * q^48 + 41 * q^49 + 41 * q^50 - 48 * q^51 - 21 * q^52 - 75 * q^53 - 63 * q^54 - 41 * q^55 - 35 * q^56 - 12 * q^57 - 88 * q^58 - 77 * q^59 - 36 * q^60 - 43 * q^61 - 44 * q^62 - 88 * q^63 + 56 * q^64 - 54 * q^65 + 4 * q^66 - 62 * q^67 - 22 * q^68 - 48 * q^69 - 51 * q^70 - 122 * q^71 + 34 * q^72 - 7 * q^73 - 60 * q^74 - 63 * q^75 - 31 * q^76 - 39 * q^77 - 62 * q^78 - 91 * q^79 - 17 * q^80 + 8 * q^81 - 39 * q^82 - 51 * q^83 - 23 * q^84 - 72 * q^85 - 66 * q^86 - 19 * q^87 - 53 * q^88 - 62 * q^89 - 34 * q^90 - 48 * q^91 - 59 * q^92 - 41 * q^93 - 51 * q^94 - 120 * q^95 - 18 * q^96 + 6 * q^97 + 41 * q^98 - 128 * q^99

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