LMFDB - Embedded newform 6019.2.a.d.1.14

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [6019,2,Mod(1,6019)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(6019, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([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("6019.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 6019 = 13 \cdot 463 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	6019.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:	$48.0619569766$
Analytic rank:	$0$
Dimension:	$123$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.14
Character	$\chi$	$=$	6019.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-2.25898 q^{2} -0.131578 q^{3} +3.10301 q^{4} +3.21477 q^{5} +0.297232 q^{6} +0.192917 q^{7} -2.49169 q^{8} -2.98269 q^{9} +O(q^{10})$	\(q-2.25898 q^{2} -0.131578 q^{3} +3.10301 q^{4} +3.21477 q^{5} +0.297232 q^{6} +0.192917 q^{7} -2.49169 q^{8} -2.98269 q^{9} -7.26212 q^{10} -5.05709 q^{11} -0.408288 q^{12} -1.00000 q^{13} -0.435797 q^{14} -0.422993 q^{15} -0.577344 q^{16} -0.0387459 q^{17} +6.73784 q^{18} +8.48104 q^{19} +9.97547 q^{20} -0.0253837 q^{21} +11.4239 q^{22} +2.56667 q^{23} +0.327851 q^{24} +5.33475 q^{25} +2.25898 q^{26} +0.787189 q^{27} +0.598625 q^{28} +5.99162 q^{29} +0.955534 q^{30} +1.20710 q^{31} +6.28758 q^{32} +0.665401 q^{33} +0.0875264 q^{34} +0.620185 q^{35} -9.25531 q^{36} -8.04987 q^{37} -19.1585 q^{38} +0.131578 q^{39} -8.01020 q^{40} +3.21278 q^{41} +0.0573413 q^{42} +11.8411 q^{43} -15.6922 q^{44} -9.58866 q^{45} -5.79807 q^{46} +8.08269 q^{47} +0.0759656 q^{48} -6.96278 q^{49} -12.0511 q^{50} +0.00509811 q^{51} -3.10301 q^{52} -4.09202 q^{53} -1.77825 q^{54} -16.2574 q^{55} -0.480689 q^{56} -1.11592 q^{57} -13.5350 q^{58} -0.0159039 q^{59} -1.31255 q^{60} -0.154016 q^{61} -2.72682 q^{62} -0.575412 q^{63} -13.0489 q^{64} -3.21477 q^{65} -1.50313 q^{66} -9.05550 q^{67} -0.120229 q^{68} -0.337717 q^{69} -1.40099 q^{70} -12.0563 q^{71} +7.43192 q^{72} +4.44834 q^{73} +18.1845 q^{74} -0.701935 q^{75} +26.3168 q^{76} -0.975600 q^{77} -0.297232 q^{78} -3.58484 q^{79} -1.85603 q^{80} +8.84449 q^{81} -7.25763 q^{82} +2.38659 q^{83} -0.0787658 q^{84} -0.124559 q^{85} -26.7489 q^{86} -0.788365 q^{87} +12.6007 q^{88} -0.108791 q^{89} +21.6606 q^{90} -0.192917 q^{91} +7.96441 q^{92} -0.158828 q^{93} -18.2587 q^{94} +27.2646 q^{95} -0.827306 q^{96} -13.5477 q^{97} +15.7288 q^{98} +15.0837 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 123 q + 10 q^{2} + q^{3} + 136 q^{4} + 46 q^{5} + 16 q^{6} + 12 q^{7} + 30 q^{8} + 154 q^{9}+O(q^{10}) $ 123 * q + 10 * q^2 + q^3 + 136 * q^4 + 46 * q^5 + 16 * q^6 + 12 * q^7 + 30 * q^8 + 154 * q^9	\( 123 q + 10 q^{2} + q^{3} + 136 q^{4} + 46 q^{5} + 16 q^{6} + 12 q^{7} + 30 q^{8} + 154 q^{9} + 5 q^{10} + 53 q^{11} - 6 q^{12} - 123 q^{13} + 21 q^{14} + 29 q^{15} + 166 q^{16} - 35 q^{17} + 28 q^{18} + 23 q^{19} + 93 q^{20} + 72 q^{21} + 8 q^{22} + 42 q^{23} + 55 q^{24} + 153 q^{25} - 10 q^{26} + 7 q^{27} + 39 q^{28} + 86 q^{29} + 44 q^{30} + 16 q^{31} + 70 q^{32} + 40 q^{33} + 10 q^{34} + 6 q^{35} + 222 q^{36} + 52 q^{37} + 12 q^{38} - q^{39} + 14 q^{40} + 80 q^{41} + 29 q^{42} + 2 q^{43} + 143 q^{44} + 137 q^{45} + 39 q^{46} + 45 q^{47} - 27 q^{48} + 163 q^{49} + 102 q^{50} + 48 q^{51} - 136 q^{52} + 117 q^{53} + 75 q^{54} + 20 q^{55} + 88 q^{56} + 67 q^{57} + 56 q^{58} + 88 q^{59} + 96 q^{60} + 57 q^{61} - 13 q^{62} + 48 q^{63} + 228 q^{64} - 46 q^{65} + 28 q^{66} + 43 q^{67} - 56 q^{68} + 92 q^{69} + 14 q^{70} + 90 q^{71} + 98 q^{72} + 25 q^{73} + 80 q^{74} + 21 q^{75} + 75 q^{76} + 112 q^{77} - 16 q^{78} + 36 q^{79} + 208 q^{80} + 231 q^{81} - 27 q^{82} + 93 q^{83} + 175 q^{84} + 77 q^{85} + 199 q^{86} + 15 q^{87} + 43 q^{88} + 140 q^{89} + 11 q^{90} - 12 q^{91} + 93 q^{92} + 140 q^{93} + 4 q^{94} + 23 q^{95} + 105 q^{96} + 43 q^{97} + 67 q^{98} + 140 q^{99}+O(q^{100}) \) 123 * q + 10 * q^2 + q^3 + 136 * q^4 + 46 * q^5 + 16 * q^6 + 12 * q^7 + 30 * q^8 + 154 * q^9 + 5 * q^10 + 53 * q^11 - 6 * q^12 - 123 * q^13 + 21 * q^14 + 29 * q^15 + 166 * q^16 - 35 * q^17 + 28 * q^18 + 23 * q^19 + 93 * q^20 + 72 * q^21 + 8 * q^22 + 42 * q^23 + 55 * q^24 + 153 * q^25 - 10 * q^26 + 7 * q^27 + 39 * q^28 + 86 * q^29 + 44 * q^30 + 16 * q^31 + 70 * q^32 + 40 * q^33 + 10 * q^34 + 6 * q^35 + 222 * q^36 + 52 * q^37 + 12 * q^38 - q^39 + 14 * q^40 + 80 * q^41 + 29 * q^42 + 2 * q^43 + 143 * q^44 + 137 * q^45 + 39 * q^46 + 45 * q^47 - 27 * q^48 + 163 * q^49 + 102 * q^50 + 48 * q^51 - 136 * q^52 + 117 * q^53 + 75 * q^54 + 20 * q^55 + 88 * q^56 + 67 * q^57 + 56 * q^58 + 88 * q^59 + 96 * q^60 + 57 * q^61 - 13 * q^62 + 48 * q^63 + 228 * q^64 - 46 * q^65 + 28 * q^66 + 43 * q^67 - 56 * q^68 + 92 * q^69 + 14 * q^70 + 90 * q^71 + 98 * q^72 + 25 * q^73 + 80 * q^74 + 21 * q^75 + 75 * q^76 + 112 * q^77 - 16 * q^78 + 36 * q^79 + 208 * q^80 + 231 * q^81 - 27 * q^82 + 93 * q^83 + 175 * q^84 + 77 * q^85 + 199 * q^86 + 15 * q^87 + 43 * q^88 + 140 * q^89 + 11 * q^90 - 12 * q^91 + 93 * q^92 + 140 * q^93 + 4 * q^94 + 23 * q^95 + 105 * q^96 + 43 * q^97 + 67 * q^98 + 140 * 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 $

$2$	−2.25898	−1.59734	−0.798672	−	0.601767i	$-0.794464\pi$
$2$	−2.25898	−1.59734	−0.798672	+	0.601767i	$0.794464\pi$
$3$	−0.131578	−0.0759665	−0.0379833	−	0.999278i	$-0.512093\pi$
$3$	−0.131578	−0.0759665	−0.0379833	+	0.999278i	$0.512093\pi$
$4$	3.10301	1.55151
$5$	3.21477	1.43769	0.718845	−	0.695171i	$-0.244671\pi$
$5$	3.21477	1.43769	0.718845	+	0.695171i	$0.244671\pi$
$6$	0.297232	0.121345
$7$	0.192917	0.0729159	0.0364580	−	0.999335i	$-0.488392\pi$
$7$	0.192917	0.0729159	0.0364580	+	0.999335i	$0.488392\pi$
$8$	−2.49169	−0.880944
$9$	−2.98269	−0.994229
$10$	−7.26212	−2.29648
$11$	−5.05709	−1.52477	−0.762385	−	0.647124i	$-0.775972\pi$
$11$	−5.05709	−1.52477	−0.762385	+	0.647124i	$0.775972\pi$
$12$	−0.408288	−0.117862
$13$	−1.00000	−0.277350
$13$	−1.00000	−0.277350
$14$	−0.435797	−0.116472
$15$	−0.422993	−0.109216
$16$	−0.577344	−0.144336
$17$	−0.0387459	−0.00939727	−0.00469863	−	0.999989i	$-0.501496\pi$
$17$	−0.0387459	−0.00939727	−0.00469863	+	0.999989i	$0.501496\pi$
$18$	6.73784	1.58813
$19$	8.48104	1.94569	0.972843	−	0.231468i	$-0.0743529\pi$
$19$	8.48104	1.94569	0.972843	+	0.231468i	$0.0743529\pi$
$20$	9.97547	2.23058
$21$	−0.0253837	−0.00553917
$22$	11.4239	2.43558
$23$	2.56667	0.535188	0.267594	−	0.963532i	$-0.413771\pi$
$23$	2.56667	0.535188	0.267594	+	0.963532i	$0.413771\pi$
$24$	0.327851	0.0669222
$25$	5.33475	1.06695
$26$	2.25898	0.443023
$27$	0.787189	0.151495
$28$	0.598625	0.113129
$29$	5.99162	1.11262	0.556308	−	0.830976i	$-0.312217\pi$
$29$	5.99162	1.11262	0.556308	+	0.830976i	$0.312217\pi$
$30$	0.955534	0.174456
$31$	1.20710	0.216802	0.108401	−	0.994107i	$-0.465427\pi$
$31$	1.20710	0.216802	0.108401	+	0.994107i	$0.465427\pi$
$32$	6.28758	1.11150
$33$	0.665401	0.115831
$34$	0.0875264	0.0150107
$35$	0.620185	0.104830
$36$	−9.25531	−1.54255
$37$	−8.04987	−1.32339	−0.661695	−	0.749773i	$-0.730163\pi$
$37$	−8.04987	−1.32339	−0.661695	+	0.749773i	$0.730163\pi$
$38$	−19.1585	−3.10793
$39$	0.131578	0.0210693
$40$	−8.01020	−1.26652
$41$	3.21278	0.501752	0.250876	−	0.968019i	$-0.419281\pi$
$41$	3.21278	0.501752	0.250876	+	0.968019i	$0.419281\pi$
$42$	0.0573413	0.00884795
$43$	11.8411	1.80576	0.902878	−	0.429897i	$-0.141450\pi$
$43$	11.8411	1.80576	0.902878	+	0.429897i	$0.141450\pi$
$44$	−15.6922	−2.36569
$45$	−9.58866	−1.42939
$46$	−5.79807	−0.854879
$47$	8.08269	1.17898	0.589491	−	0.807775i	$-0.299328\pi$
$47$	8.08269	1.17898	0.589491	+	0.807775i	$0.299328\pi$
$48$	0.0759656	0.0109647
$49$	−6.96278	−0.994683
$50$	−12.0511	−1.70429
$51$	0.00509811	0.000713878 0
$52$	−3.10301	−0.430310
$53$	−4.09202	−0.562082	−0.281041	−	0.959696i	$-0.590680\pi$
$53$	−4.09202	−0.562082	−0.281041	+	0.959696i	$0.590680\pi$
$54$	−1.77825	−0.241989
$55$	−16.2574	−2.19214
$56$	−0.480689	−0.0642348
$57$	−1.11592	−0.147807
$58$	−13.5350	−1.77723
$59$	−0.0159039	−0.00207051	−0.00103525	−	0.999999i	$-0.500330\pi$
$59$	−0.0159039	−0.00207051	−0.00103525	+	0.999999i	$0.500330\pi$
$60$	−1.31255	−0.169450
$61$	−0.154016	−0.0197197	−0.00985987	−	0.999951i	$-0.503139\pi$
$61$	−0.154016	−0.0197197	−0.00985987	+	0.999951i	$0.503139\pi$
$62$	−2.72682	−0.346307
$63$	−0.575412	−0.0724951
$64$	−13.0489	−1.63111
$65$	−3.21477	−0.398743
$66$	−1.50313	−0.185023
$67$	−9.05550	−1.10630	−0.553152	−	0.833080i	$-0.686575\pi$
$67$	−9.05550	−1.10630	−0.553152	+	0.833080i	$0.686575\pi$
$68$	−0.120229	−0.0145799
$69$	−0.337717	−0.0406564
$70$	−1.40099	−0.167450
$71$	−12.0563	−1.43082	−0.715412	−	0.698702i	$-0.753761\pi$
$71$	−12.0563	−1.43082	−0.715412	+	0.698702i	$0.753761\pi$
$72$	7.43192	0.875860
$73$	4.44834	0.520639	0.260319	−	0.965523i	$-0.416172\pi$
$73$	4.44834	0.520639	0.260319	+	0.965523i	$0.416172\pi$
$74$	18.1845	2.11391
$75$	−0.701935	−0.0810525
$76$	26.3168	3.01874
$77$	−0.975600	−0.111180
$78$	−0.297232	−0.0336549
$79$	−3.58484	−0.403326	−0.201663	−	0.979455i	$-0.564635\pi$
$79$	−3.58484	−0.403326	−0.201663	+	0.979455i	$0.564635\pi$
$80$	−1.85603	−0.207510
$81$	8.84449	0.982721
$82$	−7.25763	−0.801471
$83$	2.38659	0.261962	0.130981	−	0.991385i	$-0.458187\pi$
$83$	2.38659	0.261962	0.130981	+	0.991385i	$0.458187\pi$
$84$	−0.0787658	−0.00859405
$85$	−0.124559	−0.0135103
$86$	−26.7489	−2.88441
$87$	−0.788365	−0.0845216
$88$	12.6007	1.34324
$89$	−0.108791	−0.0115318	−0.00576592	−	0.999983i	$-0.501835\pi$
$89$	−0.108791	−0.0115318	−0.00576592	+	0.999983i	$0.501835\pi$
$90$	21.6606	2.28323
$91$	−0.192917	−0.0202232
$92$	7.96441	0.830348
$93$	−0.158828	−0.0164697
$94$	−18.2587	−1.88324
$95$	27.2646	2.79729
$96$	−0.827306	−0.0844366
$97$	−13.5477	−1.37556	−0.687781	−	0.725918i	$-0.741415\pi$
$97$	−13.5477	−1.37556	−0.687781	+	0.725918i	$0.741415\pi$
$98$	15.7288	1.58885
$99$	15.0837	1.51597
$100$	16.5538	1.65538
$101$	−0.276467	−0.0275095	−0.0137548	−	0.999905i	$-0.504378\pi$
$101$	−0.276467	−0.0275095	−0.0137548	+	0.999905i	$0.504378\pi$
$102$	−0.0115165	−0.00114031
$103$	4.59065	0.452330	0.226165	−	0.974089i	$-0.427381\pi$
$103$	4.59065	0.452330	0.226165	+	0.974089i	$0.427381\pi$
$104$	2.49169	0.244330
$105$	−0.0816026	−0.00796360
$106$	9.24380	0.897837
$107$	−11.3846	−1.10059	−0.550294	−	0.834971i	$-0.685485\pi$
$107$	−11.3846	−1.10059	−0.550294	+	0.834971i	$0.685485\pi$
$108$	2.44266	0.235045
$109$	1.16737	0.111814	0.0559068	−	0.998436i	$-0.482195\pi$
$109$	1.16737	0.111814	0.0559068	+	0.998436i	$0.482195\pi$
$110$	36.7252	3.50161
$111$	1.05918	0.100533
$112$	−0.111380	−0.0105244
$113$	1.84511	0.173574	0.0867869	−	0.996227i	$-0.472340\pi$
$113$	1.84511	0.173574	0.0867869	+	0.996227i	$0.472340\pi$
$114$	2.52084	0.236098
$115$	8.25126	0.769434
$116$	18.5921	1.72623
$117$	2.98269	0.275750
$118$	0.0359266	0.00330731
$119$	−0.00747476	−0.000685210 0
$120$	1.05396	0.0962134
$121$	14.5741	1.32492
$122$	0.347920	0.0314992
$123$	−0.422731	−0.0381164
$124$	3.74565	0.336369
$125$	1.07615	0.0962539
$126$	1.29985	0.115800
$127$	2.30211	0.204279	0.102140	−	0.994770i	$-0.467431\pi$
$127$	2.30211	0.204279	0.102140	+	0.994770i	$0.467431\pi$
$128$	16.9020	1.49394
$129$	−1.55803	−0.137177
$130$	7.26212	0.636930
$131$	5.53665	0.483739	0.241870	−	0.970309i	$-0.422239\pi$
$131$	5.53665	0.483739	0.241870	+	0.970309i	$0.422239\pi$
$132$	2.06475	0.179713
$133$	1.63614	0.141871
$134$	20.4562	1.76715
$135$	2.53063	0.217802
$136$	0.0965426	0.00827846
$137$	15.4406	1.31918	0.659589	−	0.751626i	$-0.270730\pi$
$137$	15.4406	1.31918	0.659589	+	0.751626i	$0.270730\pi$
$138$	0.762898	0.0649422
$139$	−9.86754	−0.836954	−0.418477	−	0.908227i	$-0.637436\pi$
$139$	−9.86754	−0.836954	−0.418477	+	0.908227i	$0.637436\pi$
$140$	1.92444	0.162645
$141$	−1.06350	−0.0895631
$142$	27.2351	2.28552
$143$	5.05709	0.422895
$144$	1.72204	0.143503
$145$	19.2617	1.59960
$146$	−10.0487	−0.831639
$147$	0.916148	0.0755626
$148$	−24.9788	−2.05325
$149$	9.66947	0.792154	0.396077	−	0.918217i	$-0.370371\pi$
$149$	9.66947	0.792154	0.396077	+	0.918217i	$0.370371\pi$
$150$	1.58566	0.129469
$151$	0.455648	0.0370801	0.0185401	−	0.999828i	$-0.494098\pi$
$151$	0.455648	0.0370801	0.0185401	+	0.999828i	$0.494098\pi$
$152$	−21.1321	−1.71404
$153$	0.115567	0.00934304
$154$	2.20387	0.177593
$155$	3.88055	0.311694
$156$	0.408288	0.0326892
$157$	−0.148325	−0.0118376	−0.00591880	−	0.999982i	$-0.501884\pi$
$157$	−0.148325	−0.0118376	−0.00591880	+	0.999982i	$0.501884\pi$
$158$	8.09810	0.644250
$159$	0.538419	0.0426994
$160$	20.2131	1.59799
$161$	0.495156	0.0390237
$162$	−19.9796	−1.56974
$163$	15.3005	1.19842	0.599212	−	0.800590i	$-0.295481\pi$
$163$	15.3005	1.19842	0.599212	+	0.800590i	$0.295481\pi$
$164$	9.96930	0.778472
$165$	2.13911	0.166530
$166$	−5.39127	−0.418444
$167$	−8.39273	−0.649449	−0.324724	−	0.945809i	$-0.605272\pi$
$167$	−8.39273	−0.649449	−0.324724	+	0.945809i	$0.605272\pi$
$168$	0.0632481	0.00487970
$169$	1.00000	0.0769231
$170$	0.281377	0.0215807
$171$	−25.2963	−1.93446
$172$	36.7432	2.80164
$173$	8.52606	0.648224	0.324112	−	0.946019i	$-0.394935\pi$
$173$	8.52606	0.648224	0.324112	+	0.946019i	$0.394935\pi$
$174$	1.78090	0.135010
$175$	1.02917	0.0777977
$176$	2.91968	0.220079
$177$	0.00209260	0.000157289 0
$178$	0.245757	0.0184203
$179$	−1.86874	−0.139676	−0.0698381	−	0.997558i	$-0.522248\pi$
$179$	−1.86874	−0.139676	−0.0698381	+	0.997558i	$0.522248\pi$
$180$	−29.7537	−2.21771
$181$	19.4656	1.44687	0.723435	−	0.690393i	$-0.242562\pi$
$181$	19.4656	1.44687	0.723435	+	0.690393i	$0.242562\pi$
$182$	0.435797	0.0323035
$183$	0.0202651	0.00149804
$184$	−6.39534	−0.471471
$185$	−25.8785	−1.90262
$186$	0.358789	0.0263077
$187$	0.195942	0.0143287
$188$	25.0807	1.82920
$189$	0.151862	0.0110464
$190$	−61.5903	−4.46823
$191$	15.9079	1.15106	0.575529	−	0.817781i	$-0.304796\pi$
$191$	15.9079	1.15106	0.575529	+	0.817781i	$0.304796\pi$
$192$	1.71694	0.123910
$193$	−14.7912	−1.06469	−0.532345	−	0.846527i	$-0.678689\pi$
$193$	−14.7912	−1.06469	−0.532345	+	0.846527i	$0.678689\pi$
$194$	30.6041	2.19725
$195$	0.422993	0.0302911
$196$	−21.6056	−1.54326
$197$	20.9573	1.49314	0.746572	−	0.665305i	$-0.231699\pi$
$197$	20.9573	1.49314	0.746572	+	0.665305i	$0.231699\pi$
$198$	−34.0739	−2.42152
$199$	−12.4505	−0.882595	−0.441298	−	0.897361i	$-0.645482\pi$
$199$	−12.4505	−0.882595	−0.441298	+	0.897361i	$0.645482\pi$
$200$	−13.2925	−0.939923
$201$	1.19150	0.0840421
$202$	0.624535	0.0439422
$203$	1.15589	0.0811274
$204$	0.0158195	0.00110758
$205$	10.3284	0.721364
$206$	−10.3702	−0.722527
$207$	−7.65558	−0.532100
$208$	0.577344	0.0400316
$209$	−42.8894	−2.96672
$210$	0.184339	0.0127206
$211$	8.37912	0.576842	0.288421	−	0.957504i	$-0.406870\pi$
$211$	8.37912	0.576842	0.288421	+	0.957504i	$0.406870\pi$
$212$	−12.6976	−0.872073
$213$	1.58635	0.108695
$214$	25.7176	1.75802
$215$	38.0665	2.59612
$216$	−1.96143	−0.133458
$217$	0.232871	0.0158083
$218$	−2.63707	−0.178605
$219$	−0.585303	−0.0395511
$220$	−50.4468	−3.40112
$221$	0.0387459	0.00260633
$222$	−2.39268	−0.160586
$223$	17.3262	1.16025	0.580124	−	0.814528i	$-0.303004\pi$
$223$	17.3262	1.16025	0.580124	+	0.814528i	$0.303004\pi$
$224$	1.21298	0.0810459
$225$	−15.9119	−1.06079
$226$	−4.16809	−0.277257
$227$	−17.6849	−1.17379	−0.586895	−	0.809663i	$-0.699650\pi$
$227$	−17.6849	−1.17379	−0.586895	+	0.809663i	$0.699650\pi$
$228$	−3.46271	−0.229323
$229$	−26.0368	−1.72056	−0.860280	−	0.509822i	$-0.829711\pi$
$229$	−26.0368	−1.72056	−0.860280	+	0.509822i	$0.829711\pi$
$230$	−18.6395	−1.22905
$231$	0.128367	0.00844595
$232$	−14.9292	−0.980153
$233$	15.4488	1.01209	0.506043	−	0.862508i	$-0.331108\pi$
$233$	15.4488	1.01209	0.506043	+	0.862508i	$0.331108\pi$
$234$	−6.73784	−0.440467
$235$	25.9840	1.69501
$236$	−0.0493499	−0.00321240
$237$	0.471686	0.0306393
$238$	0.0168854	0.00109452
$239$	−9.42161	−0.609433	−0.304717	−	0.952443i	$-0.598562\pi$
$239$	−9.42161	−0.609433	−0.304717	+	0.952443i	$0.598562\pi$
$240$	0.244212	0.0157638
$241$	7.13449	0.459573	0.229786	−	0.973241i	$-0.426197\pi$
$241$	7.13449	0.459573	0.229786	+	0.973241i	$0.426197\pi$
$242$	−32.9228	−2.11635
$243$	−3.52531	−0.226148
$244$	−0.477914	−0.0305953
$245$	−22.3838	−1.43005
$246$	0.954943	0.0608849
$247$	−8.48104	−0.539636
$248$	−3.00772	−0.190990
$249$	−0.314023	−0.0199004
$250$	−2.43101	−0.153751
$251$	2.45135	0.154728	0.0773639	−	0.997003i	$-0.475350\pi$
$251$	2.45135	0.154728	0.0773639	+	0.997003i	$0.475350\pi$
$252$	−1.78551	−0.112477
$253$	−12.9799	−0.816039
$254$	−5.20043	−0.326304
$255$	0.0163892	0.00102633
$256$	−12.0837	−0.755229
$257$	−0.0464000	−0.00289435	−0.00144718	−	0.999999i	$-0.500461\pi$
$257$	−0.0464000	−0.00289435	−0.00144718	+	0.999999i	$0.500461\pi$
$258$	3.51957	0.219119
$259$	−1.55296	−0.0964962
$260$	−9.97547	−0.618652
$261$	−17.8711	−1.10620
$262$	−12.5072	−0.772697
$263$	13.3125	0.820884	0.410442	−	0.911887i	$-0.365374\pi$
$263$	13.3125	0.820884	0.410442	+	0.911887i	$0.365374\pi$
$264$	−1.65797	−0.102041
$265$	−13.1549	−0.808099
$266$	−3.69602	−0.226617
$267$	0.0143145	0.000876033 0
$268$	−28.0993	−1.71644
$269$	16.1308	0.983515	0.491758	−	0.870732i	$-0.336355\pi$
$269$	16.1308	0.983515	0.491758	+	0.870732i	$0.336355\pi$
$270$	−5.71666	−0.347905
$271$	11.9412	0.725379	0.362689	−	0.931910i	$-0.381859\pi$
$271$	11.9412	0.725379	0.362689	+	0.931910i	$0.381859\pi$
$272$	0.0223697	0.00135636
$273$	0.0253837	0.00153629
$274$	−34.8801	−2.10718
$275$	−26.9783	−1.62685
$276$	−1.04794	−0.0630786
$277$	5.66192	0.340192	0.170096	−	0.985428i	$-0.445592\pi$
$277$	5.66192	0.340192	0.170096	+	0.985428i	$0.445592\pi$
$278$	22.2906	1.33690
$279$	−3.60040	−0.215551
$280$	−1.54531	−0.0923497
$281$	20.6278	1.23055	0.615275	−	0.788313i	$-0.289045\pi$
$281$	20.6278	1.23055	0.615275	+	0.788313i	$0.289045\pi$
$282$	2.40244	0.143063
$283$	17.0386	1.01284	0.506421	−	0.862286i	$-0.330968\pi$
$283$	17.0386	1.01284	0.506421	+	0.862286i	$0.330968\pi$
$284$	−37.4110	−2.21993
$285$	−3.58742	−0.212500
$286$	−11.4239	−0.675508
$287$	0.619802	0.0365857
$288$	−18.7539	−1.10508
$289$	−16.9985	−0.999912
$290$	−43.5119	−2.55510
$291$	1.78258	0.104497
$292$	13.8032	0.807774
$293$	14.4149	0.842126	0.421063	−	0.907031i	$-0.361657\pi$
$293$	14.4149	0.842126	0.421063	+	0.907031i	$0.361657\pi$
$294$	−2.06956	−0.120699
$295$	−0.0511273	−0.00297674
$296$	20.0577	1.16583
$297$	−3.98088	−0.230994
$298$	−21.8432	−1.26534
$299$	−2.56667	−0.148435
$300$	−2.17811	−0.125753
$301$	2.28436	0.131668
$302$	−1.02930	−0.0592297
$303$	0.0363770	0.00208980
$304$	−4.89648	−0.280832
$305$	−0.495126	−0.0283508
$306$	−0.261064	−0.0149240
$307$	−2.59611	−0.148168	−0.0740840	−	0.997252i	$-0.523603\pi$
$307$	−2.59611	−0.148168	−0.0740840	+	0.997252i	$0.523603\pi$
$308$	−3.02730	−0.172496
$309$	−0.604028	−0.0343620
$310$	−8.76611	−0.497882
$311$	−8.36318	−0.474232	−0.237116	−	0.971481i	$-0.576202\pi$
$311$	−8.36318	−0.474232	−0.237116	+	0.971481i	$0.576202\pi$
$312$	−0.327851	−0.0185609
$313$	−3.57500	−0.202071	−0.101035	−	0.994883i	$-0.532216\pi$
$313$	−3.57500	−0.202071	−0.101035	+	0.994883i	$0.532216\pi$
$314$	0.335063	0.0189087
$315$	−1.84982	−0.104225
$316$	−11.1238	−0.625763
$317$	8.97640	0.504165	0.252082	−	0.967706i	$-0.418885\pi$
$317$	8.97640	0.504165	0.252082	+	0.967706i	$0.418885\pi$
$318$	−1.21628	−0.0682056
$319$	−30.3002	−1.69648
$320$	−41.9491	−2.34503
$321$	1.49796	0.0836079
$322$	−1.11855	−0.0623343
$323$	−0.328606	−0.0182841
$324$	27.4445	1.52470
$325$	−5.33475	−0.295919
$326$	−34.5635	−1.91430
$327$	−0.153600	−0.00849409
$328$	−8.00524	−0.442016
$329$	1.55929	0.0859665
$330$	−4.83222	−0.266005
$331$	3.47337	0.190913	0.0954567	−	0.995434i	$-0.469569\pi$
$331$	3.47337	0.190913	0.0954567	+	0.995434i	$0.469569\pi$
$332$	7.40562	0.406436
$333$	24.0102	1.31575
$334$	18.9590	1.03739
$335$	−29.1113	−1.59052
$336$	0.0146551	0.000799501 0
$337$	28.8367	1.57084	0.785419	−	0.618965i	$-0.212448\pi$
$337$	28.8367	1.57084	0.785419	+	0.618965i	$0.212448\pi$
$338$	−2.25898	−0.122873
$339$	−0.242776	−0.0131858
$340$	−0.386509	−0.0209614
$341$	−6.10442	−0.330573
$342$	57.1440	3.08999
$343$	−2.69366	−0.145444
$344$	−29.5044	−1.59077
$345$	−1.08568	−0.0584512
$346$	−19.2602	−1.03544
$347$	−12.3232	−0.661542	−0.330771	−	0.943711i	$-0.607309\pi$
$347$	−12.3232	−0.661542	−0.330771	+	0.943711i	$0.607309\pi$
$348$	−2.44631	−0.131136
$349$	34.5802	1.85103	0.925517	−	0.378705i	$-0.123631\pi$
$349$	34.5802	1.85103	0.925517	+	0.378705i	$0.123631\pi$
$350$	−2.32487	−0.124270
$351$	−0.787189	−0.0420171
$352$	−31.7969	−1.69478
$353$	16.8095	0.894681	0.447340	−	0.894364i	$-0.352371\pi$
$353$	16.8095	0.894681	0.447340	+	0.894364i	$0.352371\pi$
$354$	−0.00472714	−0.000251245 0
$355$	−38.7584	−2.05708
$356$	−0.337580	−0.0178917
$357$	0.000983513 0	5.20530e−5 0
$358$	4.22145	0.223111
$359$	19.7331	1.04147	0.520735	−	0.853718i	$-0.325658\pi$
$359$	19.7331	1.04147	0.520735	+	0.853718i	$0.325658\pi$
$360$	23.8919	1.25921
$361$	52.9281	2.78569
$362$	−43.9726	−2.31115
$363$	−1.91763	−0.100650
$364$	−0.598625	−0.0313765
$365$	14.3004	0.748517
$366$	−0.0457786	−0.00239288
$367$	−14.8356	−0.774414	−0.387207	−	0.921993i	$-0.626560\pi$
$367$	−14.8356	−0.774414	−0.387207	+	0.921993i	$0.626560\pi$
$368$	−1.48185	−0.0772469
$369$	−9.58272	−0.498857
$370$	58.4591	3.03914
$371$	−0.789421	−0.0409847
$372$	−0.492844	−0.0255528
$373$	15.2003	0.787044	0.393522	−	0.919315i	$-0.371257\pi$
$373$	15.2003	0.787044	0.393522	+	0.919315i	$0.371257\pi$
$374$	−0.442629	−0.0228878
$375$	−0.141598	−0.00731207
$376$	−20.1395	−1.03862
$377$	−5.99162	−0.308584
$378$	−0.343055	−0.0176448
$379$	30.4940	1.56637	0.783186	−	0.621788i	$-0.213593\pi$
$379$	30.4940	1.56637	0.783186	+	0.621788i	$0.213593\pi$
$380$	84.6024	4.34001
$381$	−0.302907	−0.0155184
$382$	−35.9358	−1.83863
$383$	34.7663	1.77648	0.888238	−	0.459383i	$-0.151929\pi$
$383$	34.7663	1.77648	0.888238	+	0.459383i	$0.151929\pi$
$384$	−2.22393	−0.113489
$385$	−3.13633	−0.159842
$386$	33.4130	1.70068
$387$	−35.3184	−1.79534
$388$	−42.0387	−2.13419
$389$	−4.00421	−0.203021	−0.101511	−	0.994834i	$-0.532368\pi$
$389$	−4.00421	−0.203021	−0.101511	+	0.994834i	$0.532368\pi$
$390$	−0.955534	−0.0483853
$391$	−0.0994481	−0.00502931
$392$	17.3491	0.876260
$393$	−0.728500	−0.0367480
$394$	−47.3421	−2.38506
$395$	−11.5244	−0.579858
$396$	46.8049	2.35204
$397$	4.78396	0.240100	0.120050	−	0.992768i	$-0.461695\pi$
$397$	4.78396	0.240100	0.120050	+	0.992768i	$0.461695\pi$
$398$	28.1256	1.40981
$399$	−0.215280	−0.0107775
$400$	−3.07999	−0.153999
$401$	7.85287	0.392153	0.196077	−	0.980589i	$-0.437180\pi$
$401$	7.85287	0.392153	0.196077	+	0.980589i	$0.437180\pi$
$402$	−2.69159	−0.134244
$403$	−1.20710	−0.0601300
$404$	−0.857881	−0.0426812
$405$	28.4330	1.41285
$406$	−2.61113	−0.129588
$407$	40.7089	2.01786
$408$	−0.0127029	−0.000628886 0
$409$	−7.18679	−0.355364	−0.177682	−	0.984088i	$-0.556860\pi$
$409$	−7.18679	−0.355364	−0.177682	+	0.984088i	$0.556860\pi$
$410$	−23.3316	−1.15227
$411$	−2.03164	−0.100213
$412$	14.2448	0.701793
$413$	−0.00306813	−0.000150973 0
$414$	17.2938	0.849946
$415$	7.67234	0.376621
$416$	−6.28758	−0.308274
$417$	1.29835	0.0635805
$418$	96.8865	4.73887
$419$	16.4555	0.803904	0.401952	−	0.915661i	$-0.368332\pi$
$419$	16.4555	0.803904	0.401952	+	0.915661i	$0.368332\pi$
$420$	−0.253214	−0.0123556
$421$	−5.90630	−0.287856	−0.143928	−	0.989588i	$-0.545973\pi$
$421$	−5.90630	−0.287856	−0.143928	+	0.989588i	$0.545973\pi$
$422$	−18.9283	−0.921415
$423$	−24.1081	−1.17218
$424$	10.1960	0.495162
$425$	−0.206700	−0.0100264
$426$	−3.58354	−0.173623
$427$	−0.0297124	−0.00143788
$428$	−35.3265	−1.70757
$429$	−0.665401	−0.0321259
$430$	−85.9917	−4.14689
$431$	−12.4811	−0.601195	−0.300597	−	0.953751i	$-0.597186\pi$
$431$	−12.4811	−0.601195	−0.300597	+	0.953751i	$0.597186\pi$
$432$	−0.454479	−0.0218661
$433$	38.2655	1.83892	0.919460	−	0.393183i	$-0.128626\pi$
$433$	38.2655	1.83892	0.919460	+	0.393183i	$0.128626\pi$
$434$	−0.526051	−0.0252513
$435$	−2.53441	−0.121516
$436$	3.62236	0.173479
$437$	21.7681	1.04131
$438$	1.32219	0.0631767
$439$	−3.02320	−0.144289	−0.0721447	−	0.997394i	$-0.522984\pi$
$439$	−3.02320	−0.144289	−0.0721447	+	0.997394i	$0.522984\pi$
$440$	40.5083	1.93116
$441$	20.7678	0.988943
$442$	−0.0875264	−0.00416321
$443$	−11.1473	−0.529624	−0.264812	−	0.964300i	$-0.585310\pi$
$443$	−11.1473	−0.529624	−0.264812	+	0.964300i	$0.585310\pi$
$444$	3.28666	0.155978
$445$	−0.349738	−0.0165792
$446$	−39.1396	−1.85331
$447$	−1.27229	−0.0601772
$448$	−2.51735	−0.118934
$449$	39.0460	1.84269	0.921347	−	0.388741i	$-0.127090\pi$
$449$	39.0460	1.84269	0.921347	+	0.388741i	$0.127090\pi$
$450$	35.9447	1.69445
$451$	−16.2473	−0.765057
$452$	5.72541	0.269301
$453$	−0.0599532	−0.00281685
$454$	39.9500	1.87494
$455$	−0.620185	−0.0290747
$456$	2.78052	0.130210
$457$	−21.0032	−0.982487	−0.491244	−	0.871022i	$-0.663458\pi$
$457$	−21.0032	−0.982487	−0.491244	+	0.871022i	$0.663458\pi$
$458$	58.8167	2.74833
$459$	−0.0305004	−0.00142364
$460$	25.6038	1.19378
$461$	30.9235	1.44025	0.720126	−	0.693843i	$-0.244084\pi$
$461$	30.9235	1.44025	0.720126	+	0.693843i	$0.244084\pi$
$462$	−0.289980	−0.0134911
$463$	1.00000	0.0464739
$463$	1.00000	0.0464739
$464$	−3.45923	−0.160591
$465$	−0.510595	−0.0236783
$466$	−34.8987	−1.61665
$467$	17.5922	0.814071	0.407036	−	0.913412i	$-0.366562\pi$
$467$	17.5922	0.814071	0.407036	+	0.913412i	$0.366562\pi$
$468$	9.25531	0.427827
$469$	−1.74696	−0.0806672
$470$	−58.6974	−2.70751
$471$	0.0195162	0.000899261 0
$472$	0.0396274	0.00182400
$473$	−59.8817	−2.75336
$474$	−1.06553	−0.0489414
$475$	45.2443	2.07595
$476$	−0.0231943	−0.00106311
$477$	12.2052	0.558838
$478$	21.2833	0.973474
$479$	24.8217	1.13413	0.567065	−	0.823673i	$-0.308079\pi$
$479$	24.8217	1.13413	0.567065	+	0.823673i	$0.308079\pi$
$480$	−2.65960	−0.121394
$481$	8.04987	0.367042
$482$	−16.1167	−0.734095
$483$	−0.0651515	−0.00296450
$484$	45.2237	2.05562
$485$	−43.5528	−1.97763
$486$	7.96361	0.361237
$487$	−37.8950	−1.71719	−0.858593	−	0.512658i	$-0.828661\pi$
$487$	−37.8950	−1.71719	−0.858593	+	0.512658i	$0.828661\pi$
$488$	0.383760	0.0173720
$489$	−2.01320	−0.0910402
$490$	50.5646	2.28427
$491$	−18.9898	−0.857000	−0.428500	−	0.903542i	$-0.640958\pi$
$491$	−18.9898	−0.857000	−0.428500	+	0.903542i	$0.640958\pi$
$492$	−1.31174	−0.0591378
$493$	−0.232151	−0.0104556
$494$	19.1585	0.861984
$495$	48.4907	2.17949
$496$	−0.696912	−0.0312923
$497$	−2.32588	−0.104330
$498$	0.709372	0.0317877
$499$	−8.66300	−0.387809	−0.193905	−	0.981020i	$-0.562115\pi$
$499$	−8.66300	−0.387809	−0.193905	+	0.981020i	$0.562115\pi$
$500$	3.33931	0.149338
$501$	1.10430	0.0493364
$502$	−5.53756	−0.247154
$503$	−29.7561	−1.32676	−0.663380	−	0.748282i	$-0.730879\pi$
$503$	−29.7561	−1.32676	−0.663380	+	0.748282i	$0.730879\pi$
$504$	1.43375	0.0638641
$505$	−0.888779	−0.0395501
$506$	29.3214	1.30349
$507$	−0.131578	−0.00584358
$508$	7.14347	0.316940
$509$	41.9896	1.86115	0.930577	−	0.366095i	$-0.119306\pi$
$509$	41.9896	1.86115	0.930577	+	0.366095i	$0.119306\pi$
$510$	−0.0370230	−0.00163941
$511$	0.858162	0.0379629
$512$	−6.50721	−0.287581
$513$	6.67619	0.294761
$514$	0.104817	0.00462328
$515$	14.7579	0.650311
$516$	−4.83459	−0.212831
$517$	−40.8749	−1.79767
$518$	3.50811	0.154138
$519$	−1.12184	−0.0492433
$520$	8.01020	0.351270
$521$	17.9565	0.786687	0.393343	−	0.919392i	$-0.371318\pi$
$521$	17.9565	0.786687	0.393343	+	0.919392i	$0.371318\pi$
$522$	40.3706	1.76697
$523$	−17.1030	−0.747863	−0.373931	−	0.927456i	$-0.621990\pi$
$523$	−17.1030	−0.747863	−0.373931	+	0.927456i	$0.621990\pi$
$524$	17.1803	0.750524
$525$	−0.135416	−0.00591002
$526$	−30.0727	−1.31123
$527$	−0.0467702	−0.00203734
$528$	−0.384165	−0.0167186
$529$	−16.4122	−0.713574
$530$	29.7167	1.29081
$531$	0.0474362	0.00205856
$532$	5.07696	0.220114
$533$	−3.21278	−0.139161
$534$	−0.0323362	−0.00139933
$535$	−36.5988	−1.58230
$536$	22.5634	0.974592
$537$	0.245885	0.0106107
$538$	−36.4393	−1.57101
$539$	35.2114	1.51666
$540$	7.85258	0.337921
$541$	39.1551	1.68341	0.841704	−	0.539939i	$-0.181553\pi$
$541$	39.1551	1.68341	0.841704	+	0.539939i	$0.181553\pi$
$542$	−26.9751	−1.15868
$543$	−2.56125	−0.109914
$544$	−0.243618	−0.0104450
$545$	3.75282	0.160753
$546$	−0.0573413	−0.00245398
$547$	−20.2704	−0.866698	−0.433349	−	0.901226i	$-0.642668\pi$
$547$	−20.2704	−0.866698	−0.433349	+	0.901226i	$0.642668\pi$
$548$	47.9123	2.04671
$549$	0.459382	0.0196059
$550$	60.9436	2.59864
$551$	50.8152	2.16480
$552$	0.841485	0.0358160
$553$	−0.691578	−0.0294089
$554$	−12.7902	−0.543403
$555$	3.40503	0.144536
$556$	−30.6191	−1.29854
$557$	−26.6888	−1.13084	−0.565419	−	0.824803i	$-0.691286\pi$
$557$	−26.6888	−1.13084	−0.565419	+	0.824803i	$0.691286\pi$
$558$	8.13326	0.344308
$559$	−11.8411	−0.500827
$560$	−0.358060	−0.0151308
$561$	−0.0257816	−0.00108850
$562$	−46.5978	−1.96561
$563$	−20.8933	−0.880549	−0.440274	−	0.897863i	$-0.645119\pi$
$563$	−20.8933	−0.880549	−0.440274	+	0.897863i	$0.645119\pi$
$564$	−3.30006	−0.138958
$565$	5.93162	0.249545
$566$	−38.4900	−1.61786
$567$	1.70626	0.0716560
$568$	30.0406	1.26048
$569$	23.3944	0.980745	0.490373	−	0.871513i	$-0.336861\pi$
$569$	23.3944	0.980745	0.490373	+	0.871513i	$0.336861\pi$
$570$	8.10393	0.339436
$571$	4.37013	0.182884	0.0914421	−	0.995810i	$-0.470852\pi$
$571$	4.37013	0.182884	0.0914421	+	0.995810i	$0.470852\pi$
$572$	15.6922	0.656124
$573$	−2.09313	−0.0874419
$574$	−1.40012	−0.0584400
$575$	13.6926	0.571019
$576$	38.9207	1.62169
$577$	27.4143	1.14127	0.570637	−	0.821203i	$-0.306696\pi$
$577$	27.4143	1.14127	0.570637	+	0.821203i	$0.306696\pi$
$578$	38.3993	1.59720
$579$	1.94619	0.0808808
$580$	59.7693	2.48178
$581$	0.460415	0.0191012
$582$	−4.02682	−0.166917
$583$	20.6937	0.857045
$584$	−11.0839	−0.458654
$585$	9.58866	0.396442
$586$	−32.5630	−1.34516
$587$	−1.78061	−0.0734937	−0.0367468	−	0.999325i	$-0.511700\pi$
$587$	−1.78061	−0.0734937	−0.0367468	+	0.999325i	$0.511700\pi$
$588$	2.84282	0.117236
$589$	10.2375	0.421828
$590$	0.115496	0.00475488
$591$	−2.75751	−0.113429
$592$	4.64754	0.191013
$593$	11.7839	0.483906	0.241953	−	0.970288i	$-0.422212\pi$
$593$	11.7839	0.483906	0.241953	+	0.970288i	$0.422212\pi$
$594$	8.99276	0.368977
$595$	−0.0240296	−0.000985120 0
$596$	30.0045	1.22903
$597$	1.63822	0.0670477
$598$	5.79807	0.237101
$599$	28.5445	1.16630	0.583148	−	0.812366i	$-0.301821\pi$
$599$	28.5445	1.16630	0.583148	+	0.812366i	$0.301821\pi$
$600$	1.74900	0.0714027
$601$	−33.0428	−1.34785	−0.673923	−	0.738802i	$-0.735392\pi$
$601$	−33.0428	−1.34785	−0.673923	+	0.738802i	$0.735392\pi$
$602$	−5.16034	−0.210320
$603$	27.0097	1.09992
$604$	1.41388	0.0575300
$605$	46.8525	1.90483
$606$	−0.0821750	−0.00333813
$607$	43.1747	1.75241	0.876203	−	0.481942i	$-0.160068\pi$
$607$	43.1747	1.75241	0.876203	+	0.481942i	$0.160068\pi$
$608$	53.3253	2.16262
$609$	−0.152089	−0.00616297
$610$	1.11848	0.0452860
$611$	−8.08269	−0.326991
$612$	0.358606	0.0144958
$613$	8.32941	0.336422	0.168211	−	0.985751i	$-0.446201\pi$
$613$	8.32941	0.336422	0.168211	+	0.985751i	$0.446201\pi$
$614$	5.86458	0.236675
$615$	−1.35898	−0.0547995
$616$	2.43089	0.0979433
$617$	−23.6556	−0.952338	−0.476169	−	0.879354i	$-0.657975\pi$
$617$	−23.6556	−0.952338	−0.476169	+	0.879354i	$0.657975\pi$
$618$	1.36449	0.0548879
$619$	−37.1375	−1.49268	−0.746342	−	0.665563i	$-0.768192\pi$
$619$	−37.1375	−1.49268	−0.746342	+	0.665563i	$0.768192\pi$
$620$	12.0414	0.483594
$621$	2.02046	0.0810781
$622$	18.8923	0.757512
$623$	−0.0209877	−0.000840854 0
$624$	−0.0759656	−0.00304106
$625$	−23.2142	−0.928567
$626$	8.07587	0.322777
$627$	5.64329	0.225371
$628$	−0.460253	−0.0183661
$629$	0.311899	0.0124362
$630$	4.17871	0.166484
$631$	5.24821	0.208928	0.104464	−	0.994529i	$-0.466687\pi$
$631$	5.24821	0.208928	0.104464	+	0.994529i	$0.466687\pi$
$632$	8.93229	0.355308
$633$	−1.10251	−0.0438207
$634$	−20.2775	−0.805324
$635$	7.40076	0.293690
$636$	1.67072	0.0662483
$637$	6.96278	0.275876
$638$	68.4476	2.70987
$639$	35.9603	1.42257
$640$	54.3361	2.14782
$641$	−1.95011	−0.0770247	−0.0385124	−	0.999258i	$-0.512262\pi$
$641$	−1.95011	−0.0770247	−0.0385124	+	0.999258i	$0.512262\pi$
$642$	−3.38387	−0.133551
$643$	−30.1556	−1.18922	−0.594611	−	0.804014i	$-0.702694\pi$
$643$	−30.1556	−1.18922	−0.594611	+	0.804014i	$0.702694\pi$
$644$	1.53647	0.0605456
$645$	−5.00871	−0.197218
$646$	0.742316	0.0292060
$647$	−3.15931	−0.124205	−0.0621026	−	0.998070i	$-0.519781\pi$
$647$	−3.15931	−0.124205	−0.0621026	+	0.998070i	$0.519781\pi$
$648$	−22.0377	−0.865722
$649$	0.0804272	0.00315704
$650$	12.0511	0.472684
$651$	−0.0306406	−0.00120090
$652$	47.4775	1.85936
$653$	18.5765	0.726953	0.363477	−	0.931603i	$-0.381590\pi$
$653$	18.5765	0.726953	0.363477	+	0.931603i	$0.381590\pi$
$654$	0.346980	0.0135680
$655$	17.7991	0.695466
$656$	−1.85488	−0.0724209
$657$	−13.2680	−0.517634
$658$	−3.52242	−0.137318
$659$	−5.94408	−0.231548	−0.115774	−	0.993276i	$-0.536935\pi$
$659$	−5.94408	−0.231548	−0.115774	+	0.993276i	$0.536935\pi$
$660$	6.63769	0.258372
$661$	38.5205	1.49828	0.749138	−	0.662414i	$-0.230468\pi$
$661$	38.5205	1.49828	0.749138	+	0.662414i	$0.230468\pi$
$662$	−7.84628	−0.304954
$663$	−0.00509811	−0.000197994 0
$664$	−5.94663	−0.230774
$665$	5.25982	0.203967
$666$	−54.2387	−2.10171
$667$	15.3785	0.595459
$668$	−26.0427	−1.00762
$669$	−2.27974	−0.0881399
$670$	65.7621	2.54061
$671$	0.778873	0.0300680
$672$	−0.159602	−0.00615677
$673$	−43.2649	−1.66774	−0.833869	−	0.551963i	$-0.813879\pi$
$673$	−43.2649	−1.66774	−0.833869	+	0.551963i	$0.813879\pi$
$674$	−65.1418	−2.50917
$675$	4.19946	0.161637
$676$	3.10301	0.119347
$677$	−27.8803	−1.07153	−0.535763	−	0.844368i	$-0.679976\pi$
$677$	−27.8803	−1.07153	−0.535763	+	0.844368i	$0.679976\pi$
$678$	0.548428	0.0210622
$679$	−2.61359	−0.100300
$680$	0.310362	0.0119019
$681$	2.32694	0.0891687
$682$	13.7898	0.528038
$683$	14.1099	0.539899	0.269949	−	0.962874i	$-0.412993\pi$
$683$	14.1099	0.539899	0.269949	+	0.962874i	$0.412993\pi$
$684$	−78.4947	−3.00132
$685$	49.6380	1.89657
$686$	6.08494	0.232324
$687$	3.42587	0.130705
$688$	−6.83640	−0.260635
$689$	4.09202	0.155893
$690$	2.45254	0.0933667
$691$	38.8178	1.47670	0.738349	−	0.674419i	$-0.235606\pi$
$691$	38.8178	1.47670	0.738349	+	0.674419i	$0.235606\pi$
$692$	26.4564	1.00572
$693$	2.90991	0.110538
$694$	27.8378	1.05671
$695$	−31.7219	−1.20328
$696$	1.96436	0.0744588
$697$	−0.124482	−0.00471510
$698$	−78.1161	−2.95674
$699$	−2.03272	−0.0768847
$700$	3.19352	0.120704
$701$	−45.2414	−1.70874	−0.854371	−	0.519663i	$-0.826058\pi$
$701$	−45.2414	−1.70874	−0.854371	+	0.519663i	$0.826058\pi$
$702$	1.77825	0.0671157
$703$	−68.2713	−2.57490
$704$	65.9892	2.48706
$705$	−3.41892	−0.128764
$706$	−37.9725	−1.42911
$707$	−0.0533354	−0.00200588
$708$	0.00649335	0.000244035 0
$709$	−8.37447	−0.314510	−0.157255	−	0.987558i	$-0.550264\pi$
$709$	−8.37447	−0.314510	−0.157255	+	0.987558i	$0.550264\pi$
$710$	87.5546	3.28587
$711$	10.6925	0.400999
$712$	0.271073	0.0101589
$713$	3.09823	0.116030
$714$	−0.00222174	−8.31466e−5 0
$715$	16.2574	0.607991
$716$	−5.79872	−0.216708
$717$	1.23967	0.0462965
$718$	−44.5767	−1.66359
$719$	−15.3089	−0.570927	−0.285464	−	0.958390i	$-0.592148\pi$
$719$	−15.3089	−0.570927	−0.285464	+	0.958390i	$0.592148\pi$
$720$	5.53595	0.206313
$721$	0.885617	0.0329821
$722$	−119.564	−4.44970
$723$	−0.938741	−0.0349121
$724$	60.4021	2.24483
$725$	31.9638	1.18711
$726$	4.33191	0.160772
$727$	5.76797	0.213922	0.106961	−	0.994263i	$-0.465888\pi$
$727$	5.76797	0.213922	0.106961	+	0.994263i	$0.465888\pi$
$728$	0.480689	0.0178155
$729$	−26.0696	−0.965541
$730$	−32.3044	−1.19564
$731$	−0.458796	−0.0169692
$732$	0.0628828	0.00232422
$733$	−33.7148	−1.24528	−0.622642	−	0.782506i	$-0.713941\pi$
$733$	−33.7148	−1.24528	−0.622642	+	0.782506i	$0.713941\pi$
$734$	33.5135	1.23700
$735$	2.94521	0.108636
$736$	16.1382	0.594861
$737$	45.7944	1.68686
$738$	21.6472	0.796845
$739$	−4.27138	−0.157125	−0.0785627	−	0.996909i	$-0.525033\pi$
$739$	−4.27138	−0.157125	−0.0785627	+	0.996909i	$0.525033\pi$
$740$	−80.3012	−2.95193
$741$	1.11592	0.0409943
$742$	1.78329	0.0654666
$743$	−10.6336	−0.390110	−0.195055	−	0.980792i	$-0.562489\pi$
$743$	−10.6336	−0.390110	−0.195055	+	0.980792i	$0.562489\pi$
$744$	0.395749	0.0145089
$745$	31.0851	1.13887
$746$	−34.3373	−1.25718
$747$	−7.11845	−0.260451
$748$	0.608009	0.0222310
$749$	−2.19628	−0.0802505
$750$	0.319867	0.0116799
$751$	−50.2261	−1.83278	−0.916389	−	0.400290i	$-0.868909\pi$
$751$	−50.2261	−1.83278	−0.916389	+	0.400290i	$0.868909\pi$
$752$	−4.66649	−0.170169
$753$	−0.322543	−0.0117541
$754$	13.5350	0.492915
$755$	1.46480	0.0533097
$756$	0.471231	0.0171385
$757$	−0.728347	−0.0264722	−0.0132361	−	0.999912i	$-0.504213\pi$
$757$	−0.728347	−0.0264722	−0.0132361	+	0.999912i	$0.504213\pi$
$758$	−68.8855	−2.50203
$759$	1.70787	0.0619916
$760$	−67.9348	−2.46426
$761$	37.2553	1.35051	0.675253	−	0.737587i	$-0.264035\pi$
$761$	37.2553	1.35051	0.675253	+	0.737587i	$0.264035\pi$
$762$	0.684262	0.0247882
$763$	0.225206	0.00815299
$764$	49.3625	1.78587
$765$	0.371521	0.0134324
$766$	−78.5366	−2.83764
$767$	0.0159039	0.000574255 0
$768$	1.58994	0.0573721
$769$	11.7613	0.424123	0.212061	−	0.977256i	$-0.431982\pi$
$769$	11.7613	0.424123	0.212061	+	0.977256i	$0.431982\pi$
$770$	7.08492	0.255323
$771$	0.00610521	0.000219874 0
$772$	−45.8971	−1.65187
$773$	−13.9545	−0.501910	−0.250955	−	0.967999i	$-0.580745\pi$
$773$	−13.9545	−0.501910	−0.250955	+	0.967999i	$0.580745\pi$
$774$	79.7837	2.86777
$775$	6.43958	0.231317
$776$	33.7567	1.21179
$777$	0.204335	0.00733048
$778$	9.04544	0.324295
$779$	27.2477	0.976252
$780$	1.31255	0.0469969
$781$	60.9700	2.18168
$782$	0.224652	0.00803353
$783$	4.71654	0.168555
$784$	4.01992	0.143569
$785$	−0.476830	−0.0170188
$786$	1.64567	0.0586991
$787$	21.2259	0.756621	0.378310	−	0.925679i	$-0.376505\pi$
$787$	21.2259	0.756621	0.378310	+	0.925679i	$0.376505\pi$
$788$	65.0306	2.31662
$789$	−1.75163	−0.0623597
$790$	26.0335	0.926232
$791$	0.355955	0.0126563
$792$	−37.5839	−1.33548
$793$	0.154016	0.00546927
$794$	−10.8069	−0.383522
$795$	1.73089	0.0613884
$796$	−38.6342	−1.36935
$797$	24.6056	0.871577	0.435788	−	0.900049i	$-0.356470\pi$
$797$	24.6056	0.871577	0.435788	+	0.900049i	$0.356470\pi$
$798$	0.486314	0.0172153
$799$	−0.313171	−0.0110792
$800$	33.5427	1.18591
$801$	0.324490	0.0114653
$802$	−17.7395	−0.626404
$803$	−22.4956	−0.793854
$804$	3.69725	0.130392
$805$	1.59181	0.0561040
$806$	2.72682	0.0960482
$807$	−2.12246	−0.0747142
$808$	0.688870	0.0242343
$809$	41.9986	1.47659	0.738295	−	0.674478i	$-0.235631\pi$
$809$	41.9986	1.47659	0.738295	+	0.674478i	$0.235631\pi$
$810$	−64.2297	−2.25680
$811$	−18.8153	−0.660693	−0.330347	−	0.943860i	$-0.607166\pi$
$811$	−18.8153	−0.660693	−0.330347	+	0.943860i	$0.607166\pi$
$812$	3.58673	0.125870
$813$	−1.57120	−0.0551045
$814$	−91.9607	−3.22322
$815$	49.1875	1.72296
$816$	−0.00294336	−0.000103038 0
$817$	100.425	3.51343
$818$	16.2349	0.567639
$819$	0.575412	0.0201065
$820$	32.0490	1.11920
$821$	54.2022	1.89167	0.945834	−	0.324650i	$-0.105246\pi$
$821$	54.2022	1.89167	0.945834	+	0.324650i	$0.105246\pi$
$822$	4.58944	0.160075
$823$	−22.6796	−0.790562	−0.395281	−	0.918560i	$-0.629353\pi$
$823$	−22.6796	−0.790562	−0.395281	+	0.918560i	$0.629353\pi$
$824$	−11.4385	−0.398478
$825$	3.54975	0.123586
$826$	0.00693086	0.000241156 0
$827$	0.991041	0.0344619	0.0172309	−	0.999852i	$-0.494515\pi$
$827$	0.991041	0.0344619	0.0172309	+	0.999852i	$0.494515\pi$
$828$	−23.7554	−0.825556
$829$	−32.5284	−1.12976	−0.564879	−	0.825174i	$-0.691077\pi$
$829$	−32.5284	−1.12976	−0.564879	+	0.825174i	$0.691077\pi$
$830$	−17.3317	−0.601592
$831$	−0.744984	−0.0258432
$832$	13.0489	0.452388
$833$	0.269779	0.00934730
$834$	−2.93295	−0.101560
$835$	−26.9807	−0.933705
$836$	−133.086	−4.60288
$837$	0.950217	0.0328443
$838$	−37.1727	−1.28411
$839$	−23.6657	−0.817032	−0.408516	−	0.912751i	$-0.633954\pi$
$839$	−23.6657	−0.817032	−0.408516	+	0.912751i	$0.633954\pi$
$840$	0.203328	0.00701549
$841$	6.89954	0.237915
$842$	13.3422	0.459804
$843$	−2.71416	−0.0934806
$844$	26.0005	0.894974
$845$	3.21477	0.110591
$846$	54.4599	1.87237
$847$	2.81160	0.0966079
$848$	2.36250	0.0811286
$849$	−2.24191	−0.0769421
$850$	0.466932	0.0160156
$851$	−20.6614	−0.708263
$852$	4.92246	0.168641
$853$	−37.0798	−1.26959	−0.634794	−	0.772681i	$-0.718915\pi$
$853$	−37.0798	−1.26959	−0.634794	+	0.772681i	$0.718915\pi$
$854$	0.0671198	0.00229679
$855$	−81.3218	−2.78115
$856$	28.3668	0.969557
$857$	−15.5247	−0.530314	−0.265157	−	0.964205i	$-0.585424\pi$
$857$	−15.5247	−0.530314	−0.265157	+	0.964205i	$0.585424\pi$
$858$	1.50313	0.0513160
$859$	38.4010	1.31022	0.655112	−	0.755532i	$-0.272621\pi$
$859$	38.4010	1.31022	0.655112	+	0.755532i	$0.272621\pi$
$860$	118.121	4.02789
$861$	−0.0815522	−0.00277929
$862$	28.1947	0.960314
$863$	27.5650	0.938322	0.469161	−	0.883113i	$-0.344556\pi$
$863$	27.5650	0.938322	0.469161	+	0.883113i	$0.344556\pi$
$864$	4.94952	0.168386
$865$	27.4093	0.931945
$866$	−86.4411	−2.93739
$867$	2.23663	0.0759598
$868$	0.722601	0.0245267
$869$	18.1289	0.614979
$870$	5.72520	0.194102
$871$	9.05550	0.306834
$872$	−2.90871	−0.0985015
$873$	40.4086	1.36762
$874$	−49.1737	−1.66333
$875$	0.207608	0.00701844
$876$	−1.81620	−0.0613638
$877$	−24.1563	−0.815702	−0.407851	−	0.913049i	$-0.633722\pi$
$877$	−24.1563	−0.815702	−0.407851	+	0.913049i	$0.633722\pi$
$878$	6.82936	0.230480
$879$	−1.89668	−0.0639734
$880$	9.38609	0.316405
$881$	57.6986	1.94391	0.971957	−	0.235159i	$-0.0755609\pi$
$881$	57.6986	1.94391	0.971957	+	0.235159i	$0.0755609\pi$
$882$	−46.9141	−1.57968
$883$	−24.2765	−0.816969	−0.408485	−	0.912765i	$-0.633943\pi$
$883$	−24.2765	−0.816969	−0.408485	+	0.912765i	$0.633943\pi$
$884$	0.120229	0.00404374
$885$	0.00672722	0.000226133 0
$886$	25.1816	0.845991
$887$	−0.233391	−0.00783651	−0.00391826	−	0.999992i	$-0.501247\pi$
$887$	−0.233391	−0.00783651	−0.00391826	+	0.999992i	$0.501247\pi$
$888$	−2.63915	−0.0885642
$889$	0.444117	0.0148952
$890$	0.790054	0.0264827
$891$	−44.7273	−1.49842
$892$	53.7633	1.80013
$893$	68.5496	2.29393
$894$	2.87408	0.0961236
$895$	−6.00757	−0.200811
$896$	3.26069	0.108932
$897$	0.337717	0.0112761
$898$	−88.2043	−2.94342
$899$	7.23249	0.241217
$900$	−49.3748	−1.64583
$901$	0.158549	0.00528203
$902$	36.7024	1.22206
$903$	−0.300571	−0.0100024
$904$	−4.59745	−0.152909
$905$	62.5776	2.08015
$906$	0.135433	0.00449947
$907$	−35.5135	−1.17921	−0.589603	−	0.807693i	$-0.700716\pi$
$907$	−35.5135	−1.17921	−0.589603	+	0.807693i	$0.700716\pi$
$908$	−54.8765	−1.82114
$909$	0.824616	0.0273508
$910$	1.40099	0.0464423
$911$	56.7791	1.88117	0.940587	−	0.339552i	$-0.110275\pi$
$911$	56.7791	1.88117	0.940587	+	0.339552i	$0.110275\pi$
$912$	0.644268	0.0213338
$913$	−12.0692	−0.399432
$914$	47.4459	1.56937
$915$	0.0651477	0.00215372
$916$	−80.7925	−2.66946
$917$	1.06812	0.0352723
$918$	0.0688999	0.00227403
$919$	39.2282	1.29402	0.647009	−	0.762483i	$-0.276020\pi$
$919$	39.2282	1.29402	0.647009	+	0.762483i	$0.276020\pi$
$920$	−20.5596	−0.677828
$921$	0.341591	0.0112558
$922$	−69.8558	−2.30058
$923$	12.0563	0.396839
$924$	0.398325	0.0131039
$925$	−42.9440	−1.41199
$926$	−2.25898	−0.0742348
$927$	−13.6925	−0.449720
$928$	37.6728	1.23667
$929$	−8.18959	−0.268692	−0.134346	−	0.990935i	$-0.542893\pi$
$929$	−8.18959	−0.268692	−0.134346	+	0.990935i	$0.542893\pi$
$930$	1.15343	0.0378223
$931$	−59.0517	−1.93534
$932$	47.9379	1.57026
$933$	1.10041	0.0360258
$934$	−39.7406	−1.30035
$935$	0.629907	0.0206002
$936$	−7.43192	−0.242920
$937$	−1.23204	−0.0402490	−0.0201245	−	0.999797i	$-0.506406\pi$
$937$	−1.23204	−0.0402490	−0.0201245	+	0.999797i	$0.506406\pi$
$938$	3.94636	0.128853
$939$	0.470391	0.0153506
$940$	80.6286	2.62982
$941$	33.6644	1.09743	0.548714	−	0.836010i	$-0.315118\pi$
$941$	33.6644	1.09743	0.548714	+	0.836010i	$0.315118\pi$
$942$	−0.0440869	−0.00143643
$943$	8.24616	0.268532
$944$	0.00918199	0.000298848 0
$945$	0.488203	0.0158812
$946$	135.272	4.39806
$947$	−30.0551	−0.976659	−0.488330	−	0.872659i	$-0.662394\pi$
$947$	−30.0551	−0.976659	−0.488330	+	0.872659i	$0.662394\pi$
$948$	1.46365	0.0475370
$949$	−4.44834	−0.144399
$950$	−102.206	−3.31600
$951$	−1.18110	−0.0382996
$952$	0.0186248	0.000603632 0
$953$	16.7331	0.542039	0.271020	−	0.962574i	$-0.412639\pi$
$953$	16.7331	0.542039	0.271020	+	0.962574i	$0.412639\pi$
$954$	−27.5714	−0.892656
$955$	51.1404	1.65486
$956$	−29.2353	−0.945539
$957$	3.98683	0.128876
$958$	−56.0717	−1.81160
$959$	2.97876	0.0961891
$960$	5.51957	0.178143
$961$	−29.5429	−0.952997
$962$	−18.1845	−0.586293
$963$	33.9566	1.09424
$964$	22.1384	0.713030
$965$	−47.5502	−1.53069
$966$	0.147176	0.00473532
$967$	17.5856	0.565514	0.282757	−	0.959192i	$-0.408751\pi$
$967$	17.5856	0.565514	0.282757	+	0.959192i	$0.408751\pi$
$968$	−36.3142	−1.16718
$969$	0.0432373	0.00138898
$970$	98.3851	3.15896
$971$	−38.4124	−1.23271	−0.616356	−	0.787467i	$-0.711392\pi$
$971$	−38.4124	−1.23271	−0.616356	+	0.787467i	$0.711392\pi$
$972$	−10.9391	−0.350871
$973$	−1.90362	−0.0610273
$974$	85.6042	2.74293
$975$	0.701935	0.0224799
$976$	0.0889202	0.00284627
$977$	−17.5448	−0.561307	−0.280653	−	0.959809i	$-0.590551\pi$
$977$	−17.5448	−0.561307	−0.280653	+	0.959809i	$0.590551\pi$
$978$	4.54779	0.145422
$979$	0.550166	0.0175834
$980$	−69.4570	−2.21872
$981$	−3.48189	−0.111168
$982$	42.8978	1.36892
$983$	18.9543	0.604548	0.302274	−	0.953221i	$-0.402254\pi$
$983$	18.9543	0.604548	0.302274	+	0.953221i	$0.402254\pi$
$984$	1.05331	0.0335784
$985$	67.3728	2.14668
$986$	0.524425	0.0167011
$987$	−0.205168	−0.00653058
$988$	−26.3168	−0.837248
$989$	30.3923	0.966419
$990$	−109.540	−3.48140
$991$	−41.8379	−1.32902	−0.664512	−	0.747277i	$-0.731361\pi$
$991$	−41.8379	−1.32902	−0.664512	+	0.747277i	$0.731361\pi$
$992$	7.58974	0.240975
$993$	−0.457018	−0.0145030
$994$	5.25412	0.166651
$995$	−40.0256	−1.26890
$996$	−0.974415	−0.0308755
$997$	−36.7133	−1.16272	−0.581361	−	0.813646i	$-0.697479\pi$
$997$	−36.7133	−1.16272	−0.581361	+	0.813646i	$0.697479\pi$
$998$	19.5696	0.619464
$999$	−6.33677	−0.200486

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	6019.2.a.d.1.14	✓	123

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
6019.2.a.d.1.14	✓	123	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:	\( N \)	\(=\)	\( 6019 = 13 \cdot 463 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	6019.a (trivial)

\(f(q)\)	\(=\)	\(q-2.25898 q^{2} -0.131578 q^{3} +3.10301 q^{4} +3.21477 q^{5} +0.297232 q^{6} +0.192917 q^{7} -2.49169 q^{8} -2.98269 q^{9} +O(q^{10})\)	\(q-2.25898 q^{2} -0.131578 q^{3} +3.10301 q^{4} +3.21477 q^{5} +0.297232 q^{6} +0.192917 q^{7} -2.49169 q^{8} -2.98269 q^{9} -7.26212 q^{10} -5.05709 q^{11} -0.408288 q^{12} -1.00000 q^{13} -0.435797 q^{14} -0.422993 q^{15} -0.577344 q^{16} -0.0387459 q^{17} +6.73784 q^{18} +8.48104 q^{19} +9.97547 q^{20} -0.0253837 q^{21} +11.4239 q^{22} +2.56667 q^{23} +0.327851 q^{24} +5.33475 q^{25} +2.25898 q^{26} +0.787189 q^{27} +0.598625 q^{28} +5.99162 q^{29} +0.955534 q^{30} +1.20710 q^{31} +6.28758 q^{32} +0.665401 q^{33} +0.0875264 q^{34} +0.620185 q^{35} -9.25531 q^{36} -8.04987 q^{37} -19.1585 q^{38} +0.131578 q^{39} -8.01020 q^{40} +3.21278 q^{41} +0.0573413 q^{42} +11.8411 q^{43} -15.6922 q^{44} -9.58866 q^{45} -5.79807 q^{46} +8.08269 q^{47} +0.0759656 q^{48} -6.96278 q^{49} -12.0511 q^{50} +0.00509811 q^{51} -3.10301 q^{52} -4.09202 q^{53} -1.77825 q^{54} -16.2574 q^{55} -0.480689 q^{56} -1.11592 q^{57} -13.5350 q^{58} -0.0159039 q^{59} -1.31255 q^{60} -0.154016 q^{61} -2.72682 q^{62} -0.575412 q^{63} -13.0489 q^{64} -3.21477 q^{65} -1.50313 q^{66} -9.05550 q^{67} -0.120229 q^{68} -0.337717 q^{69} -1.40099 q^{70} -12.0563 q^{71} +7.43192 q^{72} +4.44834 q^{73} +18.1845 q^{74} -0.701935 q^{75} +26.3168 q^{76} -0.975600 q^{77} -0.297232 q^{78} -3.58484 q^{79} -1.85603 q^{80} +8.84449 q^{81} -7.25763 q^{82} +2.38659 q^{83} -0.0787658 q^{84} -0.124559 q^{85} -26.7489 q^{86} -0.788365 q^{87} +12.6007 q^{88} -0.108791 q^{89} +21.6606 q^{90} -0.192917 q^{91} +7.96441 q^{92} -0.158828 q^{93} -18.2587 q^{94} +27.2646 q^{95} -0.827306 q^{96} -13.5477 q^{97} +15.7288 q^{98} +15.0837 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 123 q + 10 q^{2} + q^{3} + 136 q^{4} + 46 q^{5} + 16 q^{6} + 12 q^{7} + 30 q^{8} + 154 q^{9}+O(q^{10}) \) 123 * q + 10 * q^2 + q^3 + 136 * q^4 + 46 * q^5 + 16 * q^6 + 12 * q^7 + 30 * q^8 + 154 * q^9	\( 123 q + 10 q^{2} + q^{3} + 136 q^{4} + 46 q^{5} + 16 q^{6} + 12 q^{7} + 30 q^{8} + 154 q^{9} + 5 q^{10} + 53 q^{11} - 6 q^{12} - 123 q^{13} + 21 q^{14} + 29 q^{15} + 166 q^{16} - 35 q^{17} + 28 q^{18} + 23 q^{19} + 93 q^{20} + 72 q^{21} + 8 q^{22} + 42 q^{23} + 55 q^{24} + 153 q^{25} - 10 q^{26} + 7 q^{27} + 39 q^{28} + 86 q^{29} + 44 q^{30} + 16 q^{31} + 70 q^{32} + 40 q^{33} + 10 q^{34} + 6 q^{35} + 222 q^{36} + 52 q^{37} + 12 q^{38} - q^{39} + 14 q^{40} + 80 q^{41} + 29 q^{42} + 2 q^{43} + 143 q^{44} + 137 q^{45} + 39 q^{46} + 45 q^{47} - 27 q^{48} + 163 q^{49} + 102 q^{50} + 48 q^{51} - 136 q^{52} + 117 q^{53} + 75 q^{54} + 20 q^{55} + 88 q^{56} + 67 q^{57} + 56 q^{58} + 88 q^{59} + 96 q^{60} + 57 q^{61} - 13 q^{62} + 48 q^{63} + 228 q^{64} - 46 q^{65} + 28 q^{66} + 43 q^{67} - 56 q^{68} + 92 q^{69} + 14 q^{70} + 90 q^{71} + 98 q^{72} + 25 q^{73} + 80 q^{74} + 21 q^{75} + 75 q^{76} + 112 q^{77} - 16 q^{78} + 36 q^{79} + 208 q^{80} + 231 q^{81} - 27 q^{82} + 93 q^{83} + 175 q^{84} + 77 q^{85} + 199 q^{86} + 15 q^{87} + 43 q^{88} + 140 q^{89} + 11 q^{90} - 12 q^{91} + 93 q^{92} + 140 q^{93} + 4 q^{94} + 23 q^{95} + 105 q^{96} + 43 q^{97} + 67 q^{98} + 140 q^{99}+O(q^{100}) \) 123 * q + 10 * q^2 + q^3 + 136 * q^4 + 46 * q^5 + 16 * q^6 + 12 * q^7 + 30 * q^8 + 154 * q^9 + 5 * q^10 + 53 * q^11 - 6 * q^12 - 123 * q^13 + 21 * q^14 + 29 * q^15 + 166 * q^16 - 35 * q^17 + 28 * q^18 + 23 * q^19 + 93 * q^20 + 72 * q^21 + 8 * q^22 + 42 * q^23 + 55 * q^24 + 153 * q^25 - 10 * q^26 + 7 * q^27 + 39 * q^28 + 86 * q^29 + 44 * q^30 + 16 * q^31 + 70 * q^32 + 40 * q^33 + 10 * q^34 + 6 * q^35 + 222 * q^36 + 52 * q^37 + 12 * q^38 - q^39 + 14 * q^40 + 80 * q^41 + 29 * q^42 + 2 * q^43 + 143 * q^44 + 137 * q^45 + 39 * q^46 + 45 * q^47 - 27 * q^48 + 163 * q^49 + 102 * q^50 + 48 * q^51 - 136 * q^52 + 117 * q^53 + 75 * q^54 + 20 * q^55 + 88 * q^56 + 67 * q^57 + 56 * q^58 + 88 * q^59 + 96 * q^60 + 57 * q^61 - 13 * q^62 + 48 * q^63 + 228 * q^64 - 46 * q^65 + 28 * q^66 + 43 * q^67 - 56 * q^68 + 92 * q^69 + 14 * q^70 + 90 * q^71 + 98 * q^72 + 25 * q^73 + 80 * q^74 + 21 * q^75 + 75 * q^76 + 112 * q^77 - 16 * q^78 + 36 * q^79 + 208 * q^80 + 231 * q^81 - 27 * q^82 + 93 * q^83 + 175 * q^84 + 77 * q^85 + 199 * q^86 + 15 * q^87 + 43 * q^88 + 140 * q^89 + 11 * q^90 - 12 * q^91 + 93 * q^92 + 140 * q^93 + 4 * q^94 + 23 * q^95 + 105 * q^96 + 43 * q^97 + 67 * q^98 + 140 * q^99

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