LMFDB - Embedded newform 6022.2.a.e.1.6

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [6022,2,Mod(1,6022)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(6022, 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("6022.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 6022 = 2 \cdot 3011 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	6022.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:	$48.0859120972$
Analytic rank:	$0$
Dimension:	$68$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.6
Character	$\chi$	$=$	6022.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.00000 q^{2} -2.61602 q^{3} +1.00000 q^{4} -0.861265 q^{5} -2.61602 q^{6} +0.881327 q^{7} +1.00000 q^{8} +3.84357 q^{9} +O(q^{10})$	\(q+1.00000 q^{2} -2.61602 q^{3} +1.00000 q^{4} -0.861265 q^{5} -2.61602 q^{6} +0.881327 q^{7} +1.00000 q^{8} +3.84357 q^{9} -0.861265 q^{10} -4.86252 q^{11} -2.61602 q^{12} +5.22408 q^{13} +0.881327 q^{14} +2.25309 q^{15} +1.00000 q^{16} -4.17494 q^{17} +3.84357 q^{18} +0.780461 q^{19} -0.861265 q^{20} -2.30557 q^{21} -4.86252 q^{22} +3.62641 q^{23} -2.61602 q^{24} -4.25822 q^{25} +5.22408 q^{26} -2.20681 q^{27} +0.881327 q^{28} +7.34471 q^{29} +2.25309 q^{30} -5.45376 q^{31} +1.00000 q^{32} +12.7205 q^{33} -4.17494 q^{34} -0.759056 q^{35} +3.84357 q^{36} -8.01513 q^{37} +0.780461 q^{38} -13.6663 q^{39} -0.861265 q^{40} +3.43448 q^{41} -2.30557 q^{42} +6.31118 q^{43} -4.86252 q^{44} -3.31034 q^{45} +3.62641 q^{46} +1.51961 q^{47} -2.61602 q^{48} -6.22326 q^{49} -4.25822 q^{50} +10.9217 q^{51} +5.22408 q^{52} -8.26101 q^{53} -2.20681 q^{54} +4.18792 q^{55} +0.881327 q^{56} -2.04170 q^{57} +7.34471 q^{58} +7.89642 q^{59} +2.25309 q^{60} -6.39714 q^{61} -5.45376 q^{62} +3.38744 q^{63} +1.00000 q^{64} -4.49932 q^{65} +12.7205 q^{66} +1.71851 q^{67} -4.17494 q^{68} -9.48676 q^{69} -0.759056 q^{70} +11.9689 q^{71} +3.84357 q^{72} +7.69878 q^{73} -8.01513 q^{74} +11.1396 q^{75} +0.780461 q^{76} -4.28547 q^{77} -13.6663 q^{78} +3.96834 q^{79} -0.861265 q^{80} -5.75767 q^{81} +3.43448 q^{82} -1.26947 q^{83} -2.30557 q^{84} +3.59573 q^{85} +6.31118 q^{86} -19.2139 q^{87} -4.86252 q^{88} -15.7365 q^{89} -3.31034 q^{90} +4.60412 q^{91} +3.62641 q^{92} +14.2672 q^{93} +1.51961 q^{94} -0.672184 q^{95} -2.61602 q^{96} -0.120244 q^{97} -6.22326 q^{98} -18.6894 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 68 q + 68 q^{2} + 25 q^{3} + 68 q^{4} + 20 q^{5} + 25 q^{6} + 29 q^{7} + 68 q^{8} + 87 q^{9}+O(q^{10}) $ 68 * q + 68 * q^2 + 25 * q^3 + 68 * q^4 + 20 * q^5 + 25 * q^6 + 29 * q^7 + 68 * q^8 + 87 * q^9	\( 68 q + 68 q^{2} + 25 q^{3} + 68 q^{4} + 20 q^{5} + 25 q^{6} + 29 q^{7} + 68 q^{8} + 87 q^{9} + 20 q^{10} + 46 q^{11} + 25 q^{12} + 30 q^{13} + 29 q^{14} + 13 q^{15} + 68 q^{16} + 73 q^{17} + 87 q^{18} + 56 q^{19} + 20 q^{20} - 5 q^{21} + 46 q^{22} + 63 q^{23} + 25 q^{24} + 88 q^{25} + 30 q^{26} + 67 q^{27} + 29 q^{28} + 43 q^{29} + 13 q^{30} + 68 q^{31} + 68 q^{32} + 26 q^{33} + 73 q^{34} + 50 q^{35} + 87 q^{36} + 8 q^{37} + 56 q^{38} + 6 q^{39} + 20 q^{40} + 64 q^{41} - 5 q^{42} + 52 q^{43} + 46 q^{44} + 7 q^{45} + 63 q^{46} + 94 q^{47} + 25 q^{48} + 91 q^{49} + 88 q^{50} + 20 q^{51} + 30 q^{52} + 38 q^{53} + 67 q^{54} + 37 q^{55} + 29 q^{56} + 4 q^{57} + 43 q^{58} + 84 q^{59} + 13 q^{60} + 26 q^{61} + 68 q^{62} + 22 q^{63} + 68 q^{64} - 20 q^{65} + 26 q^{66} + 54 q^{67} + 73 q^{68} - 11 q^{69} + 50 q^{70} + 46 q^{71} + 87 q^{72} + 62 q^{73} + 8 q^{74} + 54 q^{75} + 56 q^{76} + 67 q^{77} + 6 q^{78} + 67 q^{79} + 20 q^{80} + 120 q^{81} + 64 q^{82} + 130 q^{83} - 5 q^{84} - 24 q^{85} + 52 q^{86} + 72 q^{87} + 46 q^{88} + 61 q^{89} + 7 q^{90} + 43 q^{91} + 63 q^{92} + 40 q^{93} + 94 q^{94} + 55 q^{95} + 25 q^{96} + 41 q^{97} + 91 q^{98} + 106 q^{99}+O(q^{100}) \) 68 * q + 68 * q^2 + 25 * q^3 + 68 * q^4 + 20 * q^5 + 25 * q^6 + 29 * q^7 + 68 * q^8 + 87 * q^9 + 20 * q^10 + 46 * q^11 + 25 * q^12 + 30 * q^13 + 29 * q^14 + 13 * q^15 + 68 * q^16 + 73 * q^17 + 87 * q^18 + 56 * q^19 + 20 * q^20 - 5 * q^21 + 46 * q^22 + 63 * q^23 + 25 * q^24 + 88 * q^25 + 30 * q^26 + 67 * q^27 + 29 * q^28 + 43 * q^29 + 13 * q^30 + 68 * q^31 + 68 * q^32 + 26 * q^33 + 73 * q^34 + 50 * q^35 + 87 * q^36 + 8 * q^37 + 56 * q^38 + 6 * q^39 + 20 * q^40 + 64 * q^41 - 5 * q^42 + 52 * q^43 + 46 * q^44 + 7 * q^45 + 63 * q^46 + 94 * q^47 + 25 * q^48 + 91 * q^49 + 88 * q^50 + 20 * q^51 + 30 * q^52 + 38 * q^53 + 67 * q^54 + 37 * q^55 + 29 * q^56 + 4 * q^57 + 43 * q^58 + 84 * q^59 + 13 * q^60 + 26 * q^61 + 68 * q^62 + 22 * q^63 + 68 * q^64 - 20 * q^65 + 26 * q^66 + 54 * q^67 + 73 * q^68 - 11 * q^69 + 50 * q^70 + 46 * q^71 + 87 * q^72 + 62 * q^73 + 8 * q^74 + 54 * q^75 + 56 * q^76 + 67 * q^77 + 6 * q^78 + 67 * q^79 + 20 * q^80 + 120 * q^81 + 64 * q^82 + 130 * q^83 - 5 * q^84 - 24 * q^85 + 52 * q^86 + 72 * q^87 + 46 * q^88 + 61 * q^89 + 7 * q^90 + 43 * q^91 + 63 * q^92 + 40 * q^93 + 94 * q^94 + 55 * q^95 + 25 * q^96 + 41 * q^97 + 91 * q^98 + 106 * 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
$3$	−2.61602	−1.51036	−0.755181	−	0.655517i	$-0.772451\pi$
$3$	−2.61602	−1.51036	−0.755181	+	0.655517i	$0.772451\pi$
$4$	1.00000	0.500000
$5$	−0.861265	−0.385170	−0.192585	−	0.981280i	$-0.561687\pi$
$5$	−0.861265	−0.385170	−0.192585	+	0.981280i	$0.561687\pi$
$6$	−2.61602	−1.06799
$7$	0.881327	0.333110	0.166555	−	0.986032i	$-0.446736\pi$
$7$	0.881327	0.333110	0.166555	+	0.986032i	$0.446736\pi$
$8$	1.00000	0.353553
$9$	3.84357	1.28119
$10$	−0.861265	−0.272356
$11$	−4.86252	−1.46610	−0.733052	−	0.680172i	$-0.761905\pi$
$11$	−4.86252	−1.46610	−0.733052	+	0.680172i	$0.761905\pi$
$12$	−2.61602	−0.755181
$13$	5.22408	1.44890	0.724450	−	0.689327i	$-0.242094\pi$
$13$	5.22408	1.44890	0.724450	+	0.689327i	$0.242094\pi$
$14$	0.881327	0.235544
$15$	2.25309	0.581745
$16$	1.00000	0.250000
$17$	−4.17494	−1.01257	−0.506286	−	0.862366i	$-0.668982\pi$
$17$	−4.17494	−1.01257	−0.506286	+	0.862366i	$0.668982\pi$
$18$	3.84357	0.905939
$19$	0.780461	0.179050	0.0895251	−	0.995985i	$-0.471465\pi$
$19$	0.780461	0.179050	0.0895251	+	0.995985i	$0.471465\pi$
$20$	−0.861265	−0.192585
$21$	−2.30557	−0.503117
$22$	−4.86252	−1.03669
$23$	3.62641	0.756158	0.378079	−	0.925773i	$-0.376585\pi$
$23$	3.62641	0.756158	0.378079	+	0.925773i	$0.376585\pi$
$24$	−2.61602	−0.533993
$25$	−4.25822	−0.851644
$26$	5.22408	1.02453
$27$	−2.20681	−0.424700
$28$	0.881327	0.166555
$29$	7.34471	1.36388	0.681939	−	0.731409i	$-0.261137\pi$
$29$	7.34471	1.36388	0.681939	+	0.731409i	$0.261137\pi$
$30$	2.25309	0.411356
$31$	−5.45376	−0.979524	−0.489762	−	0.871856i	$-0.662916\pi$
$31$	−5.45376	−0.979524	−0.489762	+	0.871856i	$0.662916\pi$
$32$	1.00000	0.176777
$33$	12.7205	2.21435
$34$	−4.17494	−0.715997
$35$	−0.759056	−0.128304
$36$	3.84357	0.640596
$37$	−8.01513	−1.31768	−0.658840	−	0.752283i	$-0.728952\pi$
$37$	−8.01513	−1.31768	−0.658840	+	0.752283i	$0.728952\pi$
$38$	0.780461	0.126608
$39$	−13.6663	−2.18836
$40$	−0.861265	−0.136178
$41$	3.43448	0.536376	0.268188	−	0.963367i	$-0.413575\pi$
$41$	3.43448	0.536376	0.268188	+	0.963367i	$0.413575\pi$
$42$	−2.30557	−0.355757
$43$	6.31118	0.962446	0.481223	−	0.876598i	$-0.340193\pi$
$43$	6.31118	0.962446	0.481223	+	0.876598i	$0.340193\pi$
$44$	−4.86252	−0.733052
$45$	−3.31034	−0.493476
$46$	3.62641	0.534685
$47$	1.51961	0.221658	0.110829	−	0.993839i	$-0.464649\pi$
$47$	1.51961	0.221658	0.110829	+	0.993839i	$0.464649\pi$
$48$	−2.61602	−0.377590
$49$	−6.22326	−0.889038
$50$	−4.25822	−0.602204
$51$	10.9217	1.52935
$52$	5.22408	0.724450
$53$	−8.26101	−1.13474	−0.567369	−	0.823464i	$-0.692039\pi$
$53$	−8.26101	−1.13474	−0.567369	+	0.823464i	$0.692039\pi$
$54$	−2.20681	−0.300308
$55$	4.18792	0.564699
$56$	0.881327	0.117772
$57$	−2.04170	−0.270430
$58$	7.34471	0.964407
$59$	7.89642	1.02803	0.514013	−	0.857782i	$-0.328158\pi$
$59$	7.89642	1.02803	0.514013	+	0.857782i	$0.328158\pi$
$60$	2.25309	0.290873
$61$	−6.39714	−0.819070	−0.409535	−	0.912294i	$-0.634309\pi$
$61$	−6.39714	−0.819070	−0.409535	+	0.912294i	$0.634309\pi$
$62$	−5.45376	−0.692628
$63$	3.38744	0.426778
$64$	1.00000	0.125000
$65$	−4.49932	−0.558072
$66$	12.7205	1.56578
$67$	1.71851	0.209949	0.104975	−	0.994475i	$-0.466524\pi$
$67$	1.71851	0.209949	0.104975	+	0.994475i	$0.466524\pi$
$68$	−4.17494	−0.506286
$69$	−9.48676	−1.14207
$70$	−0.759056	−0.0907246
$71$	11.9689	1.42045	0.710223	−	0.703977i	$-0.248594\pi$
$71$	11.9689	1.42045	0.710223	+	0.703977i	$0.248594\pi$
$72$	3.84357	0.452969
$73$	7.69878	0.901075	0.450537	−	0.892758i	$-0.351232\pi$
$73$	7.69878	0.901075	0.450537	+	0.892758i	$0.351232\pi$
$74$	−8.01513	−0.931740
$75$	11.1396	1.28629
$76$	0.780461	0.0895251
$77$	−4.28547	−0.488374
$78$	−13.6663	−1.54741
$79$	3.96834	0.446473	0.223237	−	0.974764i	$-0.428338\pi$
$79$	3.96834	0.446473	0.223237	+	0.974764i	$0.428338\pi$
$80$	−0.861265	−0.0962924
$81$	−5.75767	−0.639741
$82$	3.43448	0.379275
$83$	−1.26947	−0.139342	−0.0696711	−	0.997570i	$-0.522195\pi$
$83$	−1.26947	−0.139342	−0.0696711	+	0.997570i	$0.522195\pi$
$84$	−2.30557	−0.251558
$85$	3.59573	0.390012
$86$	6.31118	0.680552
$87$	−19.2139	−2.05995
$88$	−4.86252	−0.518346
$89$	−15.7365	−1.66807	−0.834035	−	0.551711i	$-0.813975\pi$
$89$	−15.7365	−1.66807	−0.834035	+	0.551711i	$0.813975\pi$
$90$	−3.31034	−0.348940
$91$	4.60412	0.482643
$92$	3.62641	0.378079
$93$	14.2672	1.47943
$94$	1.51961	0.156736
$95$	−0.672184	−0.0689647
$96$	−2.61602	−0.266997
$97$	−0.120244	−0.0122090	−0.00610449	−	0.999981i	$-0.501943\pi$
$97$	−0.120244	−0.0122090	−0.00610449	+	0.999981i	$0.501943\pi$
$98$	−6.22326	−0.628645
$99$	−18.6894	−1.87836
$100$	−4.25822	−0.425822
$101$	13.6008	1.35333	0.676664	−	0.736292i	$-0.263425\pi$
$101$	13.6008	1.35333	0.676664	+	0.736292i	$0.263425\pi$
$102$	10.9217	1.08141
$103$	−7.55445	−0.744362	−0.372181	−	0.928160i	$-0.621390\pi$
$103$	−7.55445	−0.744362	−0.372181	+	0.928160i	$0.621390\pi$
$104$	5.22408	0.512264
$105$	1.98571	0.193785
$106$	−8.26101	−0.802381
$107$	−5.27798	−0.510242	−0.255121	−	0.966909i	$-0.582115\pi$
$107$	−5.27798	−0.510242	−0.255121	+	0.966909i	$0.582115\pi$
$108$	−2.20681	−0.212350
$109$	−12.5429	−1.20139	−0.600694	−	0.799479i	$-0.705109\pi$
$109$	−12.5429	−1.20139	−0.600694	+	0.799479i	$0.705109\pi$
$110$	4.18792	0.399302
$111$	20.9678	1.99017
$112$	0.881327	0.0832775
$113$	0.0667373	0.00627812	0.00313906	−	0.999995i	$-0.499001\pi$
$113$	0.0667373	0.00627812	0.00313906	+	0.999995i	$0.499001\pi$
$114$	−2.04170	−0.191223
$115$	−3.12330	−0.291249
$116$	7.34471	0.681939
$117$	20.0791	1.85632
$118$	7.89642	0.726924
$119$	−3.67949	−0.337298
$120$	2.25309	0.205678
$121$	12.6441	1.14946
$122$	−6.39714	−0.579170
$123$	−8.98468	−0.810121
$124$	−5.45376	−0.489762
$125$	7.97379	0.713197
$126$	3.38744	0.301777
$127$	7.42560	0.658915	0.329458	−	0.944170i	$-0.393134\pi$
$127$	7.42560	0.658915	0.329458	+	0.944170i	$0.393134\pi$
$128$	1.00000	0.0883883
$129$	−16.5102	−1.45364
$130$	−4.49932	−0.394617
$131$	19.2056	1.67800	0.838999	−	0.544132i	$-0.183141\pi$
$131$	19.2056	1.67800	0.838999	+	0.544132i	$0.183141\pi$
$132$	12.7205	1.10717
$133$	0.687841	0.0596434
$134$	1.71851	0.148456
$135$	1.90065	0.163582
$136$	−4.17494	−0.357998
$137$	0.0337742	0.00288553	0.00144276	−	0.999999i	$-0.499541\pi$
$137$	0.0337742	0.00288553	0.00144276	+	0.999999i	$0.499541\pi$
$138$	−9.48676	−0.807567
$139$	−10.2569	−0.869975	−0.434988	−	0.900436i	$-0.643247\pi$
$139$	−10.2569	−0.869975	−0.434988	+	0.900436i	$0.643247\pi$
$140$	−0.759056	−0.0641520
$141$	−3.97534	−0.334784
$142$	11.9689	1.00441
$143$	−25.4022	−2.12424
$144$	3.84357	0.320298
$145$	−6.32574	−0.525324
$146$	7.69878	0.637156
$147$	16.2802	1.34277
$148$	−8.01513	−0.658840
$149$	20.6139	1.68876	0.844379	−	0.535746i	$-0.179969\pi$
$149$	20.6139	1.68876	0.844379	+	0.535746i	$0.179969\pi$
$150$	11.1396	0.909545
$151$	17.2779	1.40605	0.703026	−	0.711164i	$-0.251832\pi$
$151$	17.2779	1.40605	0.703026	+	0.711164i	$0.251832\pi$
$152$	0.780461	0.0633038
$153$	−16.0467	−1.29730
$154$	−4.28547	−0.345333
$155$	4.69713	0.377283
$156$	−13.6663	−1.09418
$157$	12.0525	0.961895	0.480947	−	0.876749i	$-0.340293\pi$
$157$	12.0525	0.961895	0.480947	+	0.876749i	$0.340293\pi$
$158$	3.96834	0.315704
$159$	21.6110	1.71386
$160$	−0.861265	−0.0680890
$161$	3.19605	0.251884
$162$	−5.75767	−0.452365
$163$	2.46926	0.193407	0.0967036	−	0.995313i	$-0.469170\pi$
$163$	2.46926	0.193407	0.0967036	+	0.995313i	$0.469170\pi$
$164$	3.43448	0.268188
$165$	−10.9557	−0.852899
$166$	−1.26947	−0.0985298
$167$	25.1009	1.94236	0.971181	−	0.238342i	$-0.0766039\pi$
$167$	25.1009	1.94236	0.971181	+	0.238342i	$0.0766039\pi$
$168$	−2.30557	−0.177879
$169$	14.2911	1.09931
$170$	3.59573	0.275780
$171$	2.99976	0.229397
$172$	6.31118	0.481223
$173$	−12.3524	−0.939133	−0.469567	−	0.882897i	$-0.655590\pi$
$173$	−12.3524	−0.939133	−0.469567	+	0.882897i	$0.655590\pi$
$174$	−19.2139	−1.45660
$175$	−3.75288	−0.283691
$176$	−4.86252	−0.366526
$177$	−20.6572	−1.55269
$178$	−15.7365	−1.17950
$179$	0.537483	0.0401733	0.0200867	−	0.999798i	$-0.493606\pi$
$179$	0.537483	0.0401733	0.0200867	+	0.999798i	$0.493606\pi$
$180$	−3.31034	−0.246738
$181$	−20.6441	−1.53447	−0.767233	−	0.641368i	$-0.778367\pi$
$181$	−20.6441	−1.53447	−0.767233	+	0.641368i	$0.778367\pi$
$182$	4.60412	0.341280
$183$	16.7351	1.23709
$184$	3.62641	0.267342
$185$	6.90316	0.507530
$186$	14.2672	1.04612
$187$	20.3007	1.48454
$188$	1.51961	0.110829
$189$	−1.94492	−0.141472
$190$	−0.672184	−0.0487654
$191$	−9.13081	−0.660683	−0.330341	−	0.943862i	$-0.607164\pi$
$191$	−9.13081	−0.660683	−0.330341	+	0.943862i	$0.607164\pi$
$192$	−2.61602	−0.188795
$193$	1.84610	0.132885	0.0664425	−	0.997790i	$-0.478835\pi$
$193$	1.84610	0.132885	0.0664425	+	0.997790i	$0.478835\pi$
$194$	−0.120244	−0.00863305
$195$	11.7703	0.842891
$196$	−6.22326	−0.444519
$197$	−5.88435	−0.419243	−0.209621	−	0.977783i	$-0.567223\pi$
$197$	−5.88435	−0.419243	−0.209621	+	0.977783i	$0.567223\pi$
$198$	−18.6894	−1.32820
$199$	12.5058	0.886515	0.443258	−	0.896394i	$-0.353823\pi$
$199$	12.5058	0.886515	0.443258	+	0.896394i	$0.353823\pi$
$200$	−4.25822	−0.301102
$201$	−4.49565	−0.317099
$202$	13.6008	0.956948
$203$	6.47309	0.454322
$204$	10.9217	0.764675
$205$	−2.95800	−0.206596
$206$	−7.55445	−0.526343
$207$	13.9384	0.968783
$208$	5.22408	0.362225
$209$	−3.79501	−0.262506
$210$	1.98571	0.137027
$211$	26.7066	1.83856	0.919279	−	0.393607i	$-0.128773\pi$
$211$	26.7066	1.83856	0.919279	+	0.393607i	$0.128773\pi$
$212$	−8.26101	−0.567369
$213$	−31.3109	−2.14539
$214$	−5.27798	−0.360795
$215$	−5.43560	−0.370705
$216$	−2.20681	−0.150154
$217$	−4.80654	−0.326289
$218$	−12.5429	−0.849509
$219$	−20.1402	−1.36095
$220$	4.18792	0.282349
$221$	−21.8102	−1.46712
$222$	20.9678	1.40726
$223$	−6.64379	−0.444901	−0.222450	−	0.974944i	$-0.571406\pi$
$223$	−6.64379	−0.444901	−0.222450	+	0.974944i	$0.571406\pi$
$224$	0.881327	0.0588861
$225$	−16.3668	−1.09112
$226$	0.0667373	0.00443930
$227$	−4.44691	−0.295152	−0.147576	−	0.989051i	$-0.547147\pi$
$227$	−4.44691	−0.295152	−0.147576	+	0.989051i	$0.547147\pi$
$228$	−2.04170	−0.135215
$229$	−3.26327	−0.215643	−0.107822	−	0.994170i	$-0.534388\pi$
$229$	−3.26327	−0.215643	−0.107822	+	0.994170i	$0.534388\pi$
$230$	−3.12330	−0.205944
$231$	11.2109	0.737622
$232$	7.34471	0.482204
$233$	6.09787	0.399485	0.199742	−	0.979848i	$-0.435989\pi$
$233$	6.09787	0.399485	0.199742	+	0.979848i	$0.435989\pi$
$234$	20.0791	1.31262
$235$	−1.30879	−0.0853760
$236$	7.89642	0.514013
$237$	−10.3813	−0.674336
$238$	−3.67949	−0.238506
$239$	26.3417	1.70390	0.851952	−	0.523620i	$-0.175419\pi$
$239$	26.3417	1.70390	0.851952	+	0.523620i	$0.175419\pi$
$240$	2.25309	0.145436
$241$	24.9020	1.60408	0.802038	−	0.597273i	$-0.203749\pi$
$241$	24.9020	1.60408	0.802038	+	0.597273i	$0.203749\pi$
$242$	12.6441	0.812793
$243$	21.6826	1.39094
$244$	−6.39714	−0.409535
$245$	5.35988	0.342430
$246$	−8.98468	−0.572842
$247$	4.07720	0.259426
$248$	−5.45376	−0.346314
$249$	3.32096	0.210457
$250$	7.97379	0.504307
$251$	13.4491	0.848902	0.424451	−	0.905451i	$-0.360467\pi$
$251$	13.4491	0.848902	0.424451	+	0.905451i	$0.360467\pi$
$252$	3.38744	0.213389
$253$	−17.6335	−1.10861
$254$	7.42560	0.465923
$255$	−9.40652	−0.589059
$256$	1.00000	0.0625000
$257$	24.7111	1.54144	0.770718	−	0.637176i	$-0.219898\pi$
$257$	24.7111	1.54144	0.770718	+	0.637176i	$0.219898\pi$
$258$	−16.5102	−1.02788
$259$	−7.06395	−0.438932
$260$	−4.49932	−0.279036
$261$	28.2299	1.74739
$262$	19.2056	1.18652
$263$	17.4200	1.07416	0.537082	−	0.843530i	$-0.319526\pi$
$263$	17.4200	1.07416	0.537082	+	0.843530i	$0.319526\pi$
$264$	12.7205	0.782890
$265$	7.11493	0.437066
$266$	0.687841	0.0421743
$267$	41.1671	2.51939
$268$	1.71851	0.104975
$269$	13.4765	0.821675	0.410838	−	0.911709i	$-0.365236\pi$
$269$	13.4765	0.821675	0.410838	+	0.911709i	$0.365236\pi$
$270$	1.90065	0.115670
$271$	12.6559	0.768793	0.384396	−	0.923168i	$-0.374410\pi$
$271$	12.6559	0.768793	0.384396	+	0.923168i	$0.374410\pi$
$272$	−4.17494	−0.253143
$273$	−12.0445	−0.728966
$274$	0.0337742	0.00204038
$275$	20.7057	1.24860
$276$	−9.48676	−0.571036
$277$	−24.4508	−1.46910	−0.734552	−	0.678552i	$-0.762608\pi$
$277$	−24.4508	−1.46910	−0.734552	+	0.678552i	$0.762608\pi$
$278$	−10.2569	−0.615165
$279$	−20.9619	−1.25496
$280$	−0.759056	−0.0453623
$281$	−20.1334	−1.20106	−0.600529	−	0.799603i	$-0.705043\pi$
$281$	−20.1334	−1.20106	−0.600529	+	0.799603i	$0.705043\pi$
$282$	−3.97534	−0.236728
$283$	−14.6877	−0.873094	−0.436547	−	0.899682i	$-0.643799\pi$
$283$	−14.6877	−0.873094	−0.436547	+	0.899682i	$0.643799\pi$
$284$	11.9689	0.710223
$285$	1.75845	0.104162
$286$	−25.4022	−1.50206
$287$	3.02690	0.178672
$288$	3.84357	0.226485
$289$	0.430134	0.0253020
$290$	−6.32574	−0.371460
$291$	0.314562	0.0184400
$292$	7.69878	0.450537
$293$	23.8066	1.39080	0.695399	−	0.718624i	$-0.255228\pi$
$293$	23.8066	1.39080	0.695399	+	0.718624i	$0.255228\pi$
$294$	16.2802	0.949480
$295$	−6.80091	−0.395964
$296$	−8.01513	−0.465870
$297$	10.7306	0.622655
$298$	20.6139	1.19413
$299$	18.9447	1.09560
$300$	11.1396	0.643145
$301$	5.56221	0.320600
$302$	17.2779	0.994229
$303$	−35.5800	−2.04402
$304$	0.780461	0.0447625
$305$	5.50964	0.315481
$306$	−16.0467	−0.917328
$307$	−8.59496	−0.490540	−0.245270	−	0.969455i	$-0.578877\pi$
$307$	−8.59496	−0.490540	−0.245270	+	0.969455i	$0.578877\pi$
$308$	−4.28547	−0.244187
$309$	19.7626	1.12426
$310$	4.69713	0.266779
$311$	31.3724	1.77896	0.889482	−	0.456971i	$-0.151066\pi$
$311$	31.3724	1.77896	0.889482	+	0.456971i	$0.151066\pi$
$312$	−13.6663	−0.773703
$313$	33.6776	1.90357	0.951784	−	0.306768i	$-0.0992475\pi$
$313$	33.6776	1.90357	0.951784	+	0.306768i	$0.0992475\pi$
$314$	12.0525	0.680162
$315$	−2.91749	−0.164382
$316$	3.96834	0.223237
$317$	−17.3469	−0.974298	−0.487149	−	0.873319i	$-0.661963\pi$
$317$	−17.3469	−0.974298	−0.487149	+	0.873319i	$0.661963\pi$
$318$	21.6110	1.21188
$319$	−35.7138	−1.99959
$320$	−0.861265	−0.0481462
$321$	13.8073	0.770649
$322$	3.19605	0.178109
$323$	−3.25838	−0.181301
$324$	−5.75767	−0.319870
$325$	−22.2453	−1.23395
$326$	2.46926	0.136760
$327$	32.8124	1.81453
$328$	3.43448	0.189637
$329$	1.33927	0.0738366
$330$	−10.9557	−0.603091
$331$	−15.4995	−0.851929	−0.425965	−	0.904740i	$-0.640065\pi$
$331$	−15.4995	−0.851929	−0.425965	+	0.904740i	$0.640065\pi$
$332$	−1.26947	−0.0696711
$333$	−30.8067	−1.68820
$334$	25.1009	1.37346
$335$	−1.48009	−0.0808660
$336$	−2.30557	−0.125779
$337$	19.0316	1.03672	0.518359	−	0.855163i	$-0.326543\pi$
$337$	19.0316	1.03672	0.518359	+	0.855163i	$0.326543\pi$
$338$	14.2911	0.777331
$339$	−0.174586	−0.00948222
$340$	3.59573	0.195006
$341$	26.5190	1.43608
$342$	2.99976	0.162208
$343$	−11.6540	−0.629258
$344$	6.31118	0.340276
$345$	8.17062	0.439891
$346$	−12.3524	−0.664068
$347$	−4.57120	−0.245395	−0.122697	−	0.992444i	$-0.539154\pi$
$347$	−4.57120	−0.245395	−0.122697	+	0.992444i	$0.539154\pi$
$348$	−19.2139	−1.02997
$349$	15.9000	0.851109	0.425554	−	0.904933i	$-0.360079\pi$
$349$	15.9000	0.851109	0.425554	+	0.904933i	$0.360079\pi$
$350$	−3.75288	−0.200600
$351$	−11.5285	−0.615348
$352$	−4.86252	−0.259173
$353$	24.1864	1.28731	0.643656	−	0.765315i	$-0.277417\pi$
$353$	24.1864	1.28731	0.643656	+	0.765315i	$0.277417\pi$
$354$	−20.6572	−1.09792
$355$	−10.3084	−0.547113
$356$	−15.7365	−0.834035
$357$	9.62562	0.509442
$358$	0.537483	0.0284068
$359$	27.7860	1.46649	0.733245	−	0.679965i	$-0.238005\pi$
$359$	27.7860	1.46649	0.733245	+	0.679965i	$0.238005\pi$
$360$	−3.31034	−0.174470
$361$	−18.3909	−0.967941
$362$	−20.6441	−1.08503
$363$	−33.0772	−1.73610
$364$	4.60412	0.241322
$365$	−6.63070	−0.347066
$366$	16.7351	0.874756
$367$	12.8361	0.670038	0.335019	−	0.942211i	$-0.391257\pi$
$367$	12.8361	0.670038	0.335019	+	0.942211i	$0.391257\pi$
$368$	3.62641	0.189040
$369$	13.2007	0.687200
$370$	6.90316	0.358878
$371$	−7.28065	−0.377993
$372$	14.2672	0.739717
$373$	−11.4451	−0.592606	−0.296303	−	0.955094i	$-0.595754\pi$
$373$	−11.4451	−0.592606	−0.296303	+	0.955094i	$0.595754\pi$
$374$	20.3007	1.04973
$375$	−20.8596	−1.07719
$376$	1.51961	0.0783680
$377$	38.3694	1.97612
$378$	−1.94492	−0.100036
$379$	−12.6864	−0.651657	−0.325828	−	0.945429i	$-0.605643\pi$
$379$	−12.6864	−0.651657	−0.325828	+	0.945429i	$0.605643\pi$
$380$	−0.672184	−0.0344823
$381$	−19.4255	−0.995200
$382$	−9.13081	−0.467173
$383$	22.9578	1.17309	0.586545	−	0.809917i	$-0.300488\pi$
$383$	22.9578	1.17309	0.586545	+	0.809917i	$0.300488\pi$
$384$	−2.61602	−0.133498
$385$	3.69092	0.188107
$386$	1.84610	0.0939639
$387$	24.2575	1.23308
$388$	−0.120244	−0.00610449
$389$	7.64905	0.387822	0.193911	−	0.981019i	$-0.437883\pi$
$389$	7.64905	0.387822	0.193911	+	0.981019i	$0.437883\pi$
$390$	11.7703	0.596014
$391$	−15.1400	−0.765664
$392$	−6.22326	−0.314322
$393$	−50.2422	−2.53438
$394$	−5.88435	−0.296449
$395$	−3.41780	−0.171968
$396$	−18.6894	−0.939180
$397$	−24.7428	−1.24181	−0.620904	−	0.783887i	$-0.713234\pi$
$397$	−24.7428	−1.24181	−0.620904	+	0.783887i	$0.713234\pi$
$398$	12.5058	0.626861
$399$	−1.79941	−0.0900831
$400$	−4.25822	−0.212911
$401$	8.31187	0.415075	0.207538	−	0.978227i	$-0.433455\pi$
$401$	8.31187	0.415075	0.207538	+	0.978227i	$0.433455\pi$
$402$	−4.49565	−0.224223
$403$	−28.4909	−1.41923
$404$	13.6008	0.676664
$405$	4.95888	0.246409
$406$	6.47309	0.321254
$407$	38.9737	1.93186
$408$	10.9217	0.540707
$409$	−12.5233	−0.619238	−0.309619	−	0.950861i	$-0.600202\pi$
$409$	−12.5233	−0.619238	−0.309619	+	0.950861i	$0.600202\pi$
$410$	−2.95800	−0.146085
$411$	−0.0883541	−0.00435819
$412$	−7.55445	−0.372181
$413$	6.95932	0.342446
$414$	13.9384	0.685033
$415$	1.09335	0.0536704
$416$	5.22408	0.256132
$417$	26.8322	1.31398
$418$	−3.79501	−0.185620
$419$	−29.3849	−1.43554	−0.717772	−	0.696278i	$-0.754838\pi$
$419$	−29.3849	−1.43554	−0.717772	+	0.696278i	$0.754838\pi$
$420$	1.98571	0.0968926
$421$	18.0824	0.881282	0.440641	−	0.897683i	$-0.354751\pi$
$421$	18.0824	0.881282	0.440641	+	0.897683i	$0.354751\pi$
$422$	26.7066	1.30006
$423$	5.84074	0.283986
$424$	−8.26101	−0.401190
$425$	17.7778	0.862351
$426$	−31.3109	−1.51702
$427$	−5.63797	−0.272841
$428$	−5.27798	−0.255121
$429$	66.4527	3.20837
$430$	−5.43560	−0.262128
$431$	−5.31401	−0.255967	−0.127983	−	0.991776i	$-0.540850\pi$
$431$	−5.31401	−0.255967	−0.127983	+	0.991776i	$0.540850\pi$
$432$	−2.20681	−0.106175
$433$	20.2601	0.973640	0.486820	−	0.873502i	$-0.338157\pi$
$433$	20.2601	0.973640	0.486820	+	0.873502i	$0.338157\pi$
$434$	−4.80654	−0.230721
$435$	16.5483	0.793429
$436$	−12.5429	−0.600694
$437$	2.83027	0.135390
$438$	−20.1402	−0.962336
$439$	−2.27076	−0.108377	−0.0541886	−	0.998531i	$-0.517257\pi$
$439$	−2.27076	−0.108377	−0.0541886	+	0.998531i	$0.517257\pi$
$440$	4.18792	0.199651
$441$	−23.9196	−1.13903
$442$	−21.8102	−1.03741
$443$	23.1739	1.10102	0.550512	−	0.834827i	$-0.314432\pi$
$443$	23.1739	1.10102	0.550512	+	0.834827i	$0.314432\pi$
$444$	20.9678	0.995086
$445$	13.5533	0.642490
$446$	−6.64379	−0.314592
$447$	−53.9265	−2.55064
$448$	0.881327	0.0416388
$449$	7.39191	0.348846	0.174423	−	0.984671i	$-0.444194\pi$
$449$	7.39191	0.348846	0.174423	+	0.984671i	$0.444194\pi$
$450$	−16.3668	−0.771538
$451$	−16.7002	−0.786383
$452$	0.0667373	0.00313906
$453$	−45.1993	−2.12365
$454$	−4.44691	−0.208704
$455$	−3.96537	−0.185900
$456$	−2.04170	−0.0956116
$457$	29.4057	1.37554	0.687771	−	0.725928i	$-0.258589\pi$
$457$	29.4057	1.37554	0.687771	+	0.725928i	$0.258589\pi$
$458$	−3.26327	−0.152483
$459$	9.21328	0.430039
$460$	−3.12330	−0.145625
$461$	15.8245	0.737019	0.368510	−	0.929624i	$-0.379868\pi$
$461$	15.8245	0.737019	0.368510	+	0.929624i	$0.379868\pi$
$462$	11.2109	0.521577
$463$	10.4458	0.485459	0.242729	−	0.970094i	$-0.421957\pi$
$463$	10.4458	0.485459	0.242729	+	0.970094i	$0.421957\pi$
$464$	7.34471	0.340969
$465$	−12.2878	−0.569833
$466$	6.09787	0.282478
$467$	−5.28523	−0.244571	−0.122286	−	0.992495i	$-0.539022\pi$
$467$	−5.28523	−0.244571	−0.122286	+	0.992495i	$0.539022\pi$
$468$	20.0791	0.928159
$469$	1.51457	0.0699362
$470$	−1.30879	−0.0603699
$471$	−31.5296	−1.45281
$472$	7.89642	0.363462
$473$	−30.6882	−1.41105
$474$	−10.3813	−0.476828
$475$	−3.32338	−0.152487
$476$	−3.67949	−0.168649
$477$	−31.7518	−1.45382
$478$	26.3417	1.20484
$479$	−25.0287	−1.14359	−0.571795	−	0.820397i	$-0.693753\pi$
$479$	−25.0287	−1.14359	−0.571795	+	0.820397i	$0.693753\pi$
$480$	2.25309	0.102839
$481$	−41.8717	−1.90919
$482$	24.9020	1.13425
$483$	−8.36094	−0.380436
$484$	12.6441	0.574731
$485$	0.103562	0.00470253
$486$	21.6826	0.983543
$487$	−3.34302	−0.151487	−0.0757433	−	0.997127i	$-0.524133\pi$
$487$	−3.34302	−0.151487	−0.0757433	+	0.997127i	$0.524133\pi$
$488$	−6.39714	−0.289585
$489$	−6.45963	−0.292115
$490$	5.35988	0.242135
$491$	33.4815	1.51100	0.755500	−	0.655149i	$-0.227394\pi$
$491$	33.4815	1.51100	0.755500	+	0.655149i	$0.227394\pi$
$492$	−8.98468	−0.405061
$493$	−30.6637	−1.38102
$494$	4.07720	0.183442
$495$	16.0966	0.723487
$496$	−5.45376	−0.244881
$497$	10.5485	0.473165
$498$	3.32096	0.148816
$499$	−24.5110	−1.09726	−0.548631	−	0.836065i	$-0.684851\pi$
$499$	−24.5110	−1.09726	−0.548631	+	0.836065i	$0.684851\pi$
$500$	7.97379	0.356599
$501$	−65.6644	−2.93367
$502$	13.4491	0.600264
$503$	−1.84455	−0.0822443	−0.0411221	−	0.999154i	$-0.513093\pi$
$503$	−1.84455	−0.0822443	−0.0411221	+	0.999154i	$0.513093\pi$
$504$	3.38744	0.150889
$505$	−11.7139	−0.521261
$506$	−17.6335	−0.783903
$507$	−37.3857	−1.66036
$508$	7.42560	0.329458
$509$	21.6020	0.957491	0.478746	−	0.877954i	$-0.341092\pi$
$509$	21.6020	0.957491	0.478746	+	0.877954i	$0.341092\pi$
$510$	−9.40652	−0.416528
$511$	6.78514	0.300157
$512$	1.00000	0.0441942
$513$	−1.72233	−0.0760426
$514$	24.7111	1.08996
$515$	6.50639	0.286706
$516$	−16.5102	−0.726820
$517$	−7.38914	−0.324974
$518$	−7.06395	−0.310372
$519$	32.3141	1.41843
$520$	−4.49932	−0.197308
$521$	39.5642	1.73334	0.866670	−	0.498882i	$-0.166256\pi$
$521$	39.5642	1.73334	0.866670	+	0.498882i	$0.166256\pi$
$522$	28.2299	1.23559
$523$	−9.17105	−0.401022	−0.200511	−	0.979691i	$-0.564260\pi$
$523$	−9.17105	−0.401022	−0.200511	+	0.979691i	$0.564260\pi$
$524$	19.2056	0.838999
$525$	9.81763	0.428477
$526$	17.4200	0.759549
$527$	22.7691	0.991838
$528$	12.7205	0.553587
$529$	−9.84917	−0.428225
$530$	7.11493	0.309053
$531$	30.3505	1.31710
$532$	0.687841	0.0298217
$533$	17.9420	0.777155
$534$	41.1671	1.78148
$535$	4.54574	0.196530
$536$	1.71851	0.0742282
$537$	−1.40607	−0.0606762
$538$	13.4765	0.581012
$539$	30.2607	1.30342
$540$	1.90065	0.0817908
$541$	0.710989	0.0305678	0.0152839	−	0.999883i	$-0.495135\pi$
$541$	0.710989	0.0305678	0.0152839	+	0.999883i	$0.495135\pi$
$542$	12.6559	0.543619
$543$	54.0055	2.31760
$544$	−4.17494	−0.178999
$545$	10.8027	0.462738
$546$	−12.0445	−0.515457
$547$	19.0290	0.813620	0.406810	−	0.913513i	$-0.366641\pi$
$547$	19.0290	0.813620	0.406810	+	0.913513i	$0.366641\pi$
$548$	0.0337742	0.00144276
$549$	−24.5879	−1.04939
$550$	20.7057	0.882893
$551$	5.73226	0.244202
$552$	−9.48676	−0.403783
$553$	3.49741	0.148725
$554$	−24.4508	−1.03881
$555$	−18.0588	−0.766554
$556$	−10.2569	−0.434988
$557$	−12.6002	−0.533888	−0.266944	−	0.963712i	$-0.586014\pi$
$557$	−12.6002	−0.533888	−0.266944	+	0.963712i	$0.586014\pi$
$558$	−20.9619	−0.887389
$559$	32.9701	1.39449
$560$	−0.759056	−0.0320760
$561$	−53.1072	−2.24219
$562$	−20.1334	−0.849276
$563$	−33.7191	−1.42109	−0.710546	−	0.703650i	$-0.751552\pi$
$563$	−33.7191	−1.42109	−0.710546	+	0.703650i	$0.751552\pi$
$564$	−3.97534	−0.167392
$565$	−0.0574785	−0.00241814
$566$	−14.6877	−0.617370
$567$	−5.07438	−0.213104
$568$	11.9689	0.502203
$569$	27.3683	1.14734	0.573669	−	0.819087i	$-0.305520\pi$
$569$	27.3683	1.14734	0.573669	+	0.819087i	$0.305520\pi$
$570$	1.75845	0.0736533
$571$	−1.65330	−0.0691886	−0.0345943	−	0.999401i	$-0.511014\pi$
$571$	−1.65330	−0.0691886	−0.0345943	+	0.999401i	$0.511014\pi$
$572$	−25.4022	−1.06212
$573$	23.8864	0.997869
$574$	3.02690	0.126340
$575$	−15.4420	−0.643978
$576$	3.84357	0.160149
$577$	31.8929	1.32772	0.663860	−	0.747857i	$-0.268917\pi$
$577$	31.8929	1.32772	0.663860	+	0.747857i	$0.268917\pi$
$578$	0.430134	0.0178912
$579$	−4.82943	−0.200704
$580$	−6.32574	−0.262662
$581$	−1.11882	−0.0464163
$582$	0.314562	0.0130390
$583$	40.1693	1.66364
$584$	7.69878	0.318578
$585$	−17.2935	−0.714997
$586$	23.8066	0.983442
$587$	−39.0496	−1.61175	−0.805874	−	0.592087i	$-0.798304\pi$
$587$	−39.0496	−1.61175	−0.805874	+	0.592087i	$0.798304\pi$
$588$	16.2802	0.671384
$589$	−4.25645	−0.175384
$590$	−6.80091	−0.279989
$591$	15.3936	0.633208
$592$	−8.01513	−0.329420
$593$	−1.94184	−0.0797419	−0.0398709	−	0.999205i	$-0.512695\pi$
$593$	−1.94184	−0.0797419	−0.0398709	+	0.999205i	$0.512695\pi$
$594$	10.7306	0.440283
$595$	3.16901	0.129917
$596$	20.6139	0.844379
$597$	−32.7156	−1.33896
$598$	18.9447	0.774705
$599$	−16.2010	−0.661956	−0.330978	−	0.943639i	$-0.607379\pi$
$599$	−16.2010	−0.661956	−0.330978	+	0.943639i	$0.607379\pi$
$600$	11.1396	0.454772
$601$	−24.7040	−1.00770	−0.503848	−	0.863792i	$-0.668083\pi$
$601$	−24.7040	−1.00770	−0.503848	+	0.863792i	$0.668083\pi$
$602$	5.56221	0.226699
$603$	6.60521	0.268985
$604$	17.2779	0.703026
$605$	−10.8899	−0.442738
$606$	−35.5800	−1.44534
$607$	−1.37848	−0.0559508	−0.0279754	−	0.999609i	$-0.508906\pi$
$607$	−1.37848	−0.0559508	−0.0279754	+	0.999609i	$0.508906\pi$
$608$	0.780461	0.0316519
$609$	−16.9337	−0.686190
$610$	5.50964	0.223079
$611$	7.93858	0.321161
$612$	−16.0467	−0.648649
$613$	−0.0232910	−0.000940716 0	−0.000470358	−	1.00000i	$-0.500150\pi$
$613$	−0.0232910	−0.000940716 0	−0.000470358		1.00000i	$0.500150\pi$
$614$	−8.59496	−0.346864
$615$	7.73819	0.312034
$616$	−4.28547	−0.172666
$617$	−48.0894	−1.93601	−0.968003	−	0.250940i	$-0.919260\pi$
$617$	−48.0894	−1.93601	−0.968003	+	0.250940i	$0.919260\pi$
$618$	19.7626	0.794969
$619$	16.3158	0.655786	0.327893	−	0.944715i	$-0.393662\pi$
$619$	16.3158	0.655786	0.327893	+	0.944715i	$0.393662\pi$
$620$	4.69713	0.188641
$621$	−8.00278	−0.321140
$622$	31.3724	1.25792
$623$	−13.8690	−0.555651
$624$	−13.6663	−0.547091
$625$	14.4236	0.576943
$626$	33.6776	1.34603
$627$	9.92783	0.396479
$628$	12.0525	0.480947
$629$	33.4627	1.33425
$630$	−2.91749	−0.116235
$631$	−32.5707	−1.29662	−0.648310	−	0.761376i	$-0.724524\pi$
$631$	−32.5707	−1.29662	−0.648310	+	0.761376i	$0.724524\pi$
$632$	3.96834	0.157852
$633$	−69.8650	−2.77689
$634$	−17.3469	−0.688932
$635$	−6.39541	−0.253794
$636$	21.6110	0.856932
$637$	−32.5109	−1.28813
$638$	−35.7138	−1.41392
$639$	46.0033	1.81986
$640$	−0.861265	−0.0340445
$641$	−21.2319	−0.838611	−0.419305	−	0.907845i	$-0.637726\pi$
$641$	−21.2319	−0.838611	−0.419305	+	0.907845i	$0.637726\pi$
$642$	13.8073	0.544931
$643$	−7.69312	−0.303387	−0.151694	−	0.988428i	$-0.548473\pi$
$643$	−7.69312	−0.303387	−0.151694	+	0.988428i	$0.548473\pi$
$644$	3.19605	0.125942
$645$	14.2196	0.559898
$646$	−3.25838	−0.128199
$647$	11.8164	0.464550	0.232275	−	0.972650i	$-0.425383\pi$
$647$	11.8164	0.464550	0.232275	+	0.972650i	$0.425383\pi$
$648$	−5.75767	−0.226182
$649$	−38.3965	−1.50719
$650$	−22.2453	−0.872533
$651$	12.5740	0.492815
$652$	2.46926	0.0967036
$653$	−24.5309	−0.959970	−0.479985	−	0.877277i	$-0.659358\pi$
$653$	−24.5309	−0.959970	−0.479985	+	0.877277i	$0.659358\pi$
$654$	32.8124	1.28307
$655$	−16.5411	−0.646314
$656$	3.43448	0.134094
$657$	29.5908	1.15445
$658$	1.33927	0.0522104
$659$	−18.8399	−0.733899	−0.366950	−	0.930241i	$-0.619598\pi$
$659$	−18.8399	−0.733899	−0.366950	+	0.930241i	$0.619598\pi$
$660$	−10.9557	−0.426450
$661$	29.5104	1.14782	0.573911	−	0.818918i	$-0.305426\pi$
$661$	29.5104	1.14782	0.573911	+	0.818918i	$0.305426\pi$
$662$	−15.4995	−0.602405
$663$	57.0561	2.21587
$664$	−1.26947	−0.0492649
$665$	−0.592414	−0.0229728
$666$	−30.8067	−1.19374
$667$	26.6349	1.03131
$668$	25.1009	0.971181
$669$	17.3803	0.671961
$670$	−1.48009	−0.0571809
$671$	31.1062	1.20084
$672$	−2.30557	−0.0889393
$673$	−4.52521	−0.174434	−0.0872169	−	0.996189i	$-0.527797\pi$
$673$	−4.52521	−0.174434	−0.0872169	+	0.996189i	$0.527797\pi$
$674$	19.0316	0.733071
$675$	9.39707	0.361693
$676$	14.2911	0.549656
$677$	26.9548	1.03596	0.517978	−	0.855394i	$-0.326685\pi$
$677$	26.9548	1.03596	0.517978	+	0.855394i	$0.326685\pi$
$678$	−0.174586	−0.00670495
$679$	−0.105975	−0.00406693
$680$	3.59573	0.137890
$681$	11.6332	0.445785
$682$	26.5190	1.01547
$683$	−7.77297	−0.297425	−0.148712	−	0.988881i	$-0.547513\pi$
$683$	−7.77297	−0.297425	−0.148712	+	0.988881i	$0.547513\pi$
$684$	2.99976	0.114699
$685$	−0.0290886	−0.00111142
$686$	−11.6540	−0.444952
$687$	8.53679	0.325699
$688$	6.31118	0.240611
$689$	−43.1562	−1.64412
$690$	8.17062	0.311050
$691$	−46.0033	−1.75005	−0.875024	−	0.484079i	$-0.839155\pi$
$691$	−46.0033	−1.75005	−0.875024	+	0.484079i	$0.839155\pi$
$692$	−12.3524	−0.469567
$693$	−16.4715	−0.625701
$694$	−4.57120	−0.173520
$695$	8.83387	0.335088
$696$	−19.2139	−0.728302
$697$	−14.3388	−0.543119
$698$	15.9000	0.601825
$699$	−15.9522	−0.603366
$700$	−3.75288	−0.141846
$701$	14.9480	0.564579	0.282289	−	0.959329i	$-0.408906\pi$
$701$	14.9480	0.564579	0.282289	+	0.959329i	$0.408906\pi$
$702$	−11.5285	−0.435117
$703$	−6.25550	−0.235931
$704$	−4.86252	−0.183263
$705$	3.42382	0.128949
$706$	24.1864	0.910267
$707$	11.9867	0.450808
$708$	−20.6572	−0.776345
$709$	−21.1004	−0.792444	−0.396222	−	0.918155i	$-0.629679\pi$
$709$	−21.1004	−0.792444	−0.396222	+	0.918155i	$0.629679\pi$
$710$	−10.3084	−0.386867
$711$	15.2526	0.572018
$712$	−15.7365	−0.589752
$713$	−19.7775	−0.740675
$714$	9.62562	0.360230
$715$	21.8780	0.818192
$716$	0.537483	0.0200867
$717$	−68.9105	−2.57351
$718$	27.7860	1.03696
$719$	−34.9676	−1.30407	−0.652036	−	0.758188i	$-0.726085\pi$
$719$	−34.9676	−1.30407	−0.652036	+	0.758188i	$0.726085\pi$
$720$	−3.31034	−0.123369
$721$	−6.65794	−0.247955
$722$	−18.3909	−0.684438
$723$	−65.1441	−2.42273
$724$	−20.6441	−0.767233
$725$	−31.2754	−1.16154
$726$	−33.0772	−1.22761
$727$	33.4679	1.24125	0.620627	−	0.784106i	$-0.286878\pi$
$727$	33.4679	1.24125	0.620627	+	0.784106i	$0.286878\pi$
$728$	4.60412	0.170640
$729$	−39.4492	−1.46108
$730$	−6.63070	−0.245413
$731$	−26.3488	−0.974546
$732$	16.7351	0.618546
$733$	4.91794	0.181648	0.0908242	−	0.995867i	$-0.471050\pi$
$733$	4.91794	0.181648	0.0908242	+	0.995867i	$0.471050\pi$
$734$	12.8361	0.473788
$735$	−14.0216	−0.517193
$736$	3.62641	0.133671
$737$	−8.35628	−0.307807
$738$	13.2007	0.485924
$739$	−5.39554	−0.198478	−0.0992390	−	0.995064i	$-0.531641\pi$
$739$	−5.39554	−0.198478	−0.0992390	+	0.995064i	$0.531641\pi$
$740$	6.90316	0.253765
$741$	−10.6660	−0.391827
$742$	−7.28065	−0.267281
$743$	26.3831	0.967901	0.483950	−	0.875095i	$-0.339202\pi$
$743$	26.3831	0.967901	0.483950	+	0.875095i	$0.339202\pi$
$744$	14.2672	0.523059
$745$	−17.7541	−0.650458
$746$	−11.4451	−0.419036
$747$	−4.87929	−0.178524
$748$	20.3007	0.742268
$749$	−4.65163	−0.169967
$750$	−20.8596	−0.761685
$751$	−30.5969	−1.11650	−0.558248	−	0.829674i	$-0.688526\pi$
$751$	−30.5969	−1.11650	−0.558248	+	0.829674i	$0.688526\pi$
$752$	1.51961	0.0554145
$753$	−35.1832	−1.28215
$754$	38.3694	1.39733
$755$	−14.8808	−0.541568
$756$	−1.94492	−0.0707359
$757$	5.51911	0.200596	0.100298	−	0.994957i	$-0.468020\pi$
$757$	5.51911	0.200596	0.100298	+	0.994957i	$0.468020\pi$
$758$	−12.6864	−0.460791
$759$	46.1296	1.67440
$760$	−0.672184	−0.0243827
$761$	2.54275	0.0921744	0.0460872	−	0.998937i	$-0.485325\pi$
$761$	2.54275	0.0921744	0.0460872	+	0.998937i	$0.485325\pi$
$762$	−19.4255	−0.703713
$763$	−11.0544	−0.400195
$764$	−9.13081	−0.330341
$765$	13.8205	0.499680
$766$	22.9578	0.829500
$767$	41.2516	1.48951
$768$	−2.61602	−0.0943976
$769$	−34.3245	−1.23777	−0.618887	−	0.785480i	$-0.712416\pi$
$769$	−34.3245	−1.23777	−0.618887	+	0.785480i	$0.712416\pi$
$770$	3.69092	0.133012
$771$	−64.6448	−2.32813
$772$	1.84610	0.0664425
$773$	49.6978	1.78751	0.893753	−	0.448560i	$-0.148063\pi$
$773$	49.6978	1.78751	0.893753	+	0.448560i	$0.148063\pi$
$774$	24.2575	0.871917
$775$	23.2233	0.834206
$776$	−0.120244	−0.00431653
$777$	18.4794	0.662947
$778$	7.64905	0.274232
$779$	2.68048	0.0960381
$780$	11.7703	0.421445
$781$	−58.1990	−2.08252
$782$	−15.1400	−0.541407
$783$	−16.2083	−0.579239
$784$	−6.22326	−0.222259
$785$	−10.3804	−0.370493
$786$	−50.2422	−1.79208
$787$	21.9657	0.782992	0.391496	−	0.920180i	$-0.371958\pi$
$787$	21.9657	0.782992	0.391496	+	0.920180i	$0.371958\pi$
$788$	−5.88435	−0.209621
$789$	−45.5712	−1.62238
$790$	−3.41780	−0.121600
$791$	0.0588174	0.00209130
$792$	−18.6894	−0.664101
$793$	−33.4192	−1.18675
$794$	−24.7428	−0.878090
$795$	−18.6128	−0.660128
$796$	12.5058	0.443258
$797$	−28.6650	−1.01537	−0.507683	−	0.861544i	$-0.669498\pi$
$797$	−28.6650	−1.01537	−0.507683	+	0.861544i	$0.669498\pi$
$798$	−1.79941	−0.0636984
$799$	−6.34429	−0.224445
$800$	−4.25822	−0.150551
$801$	−60.4846	−2.13712
$802$	8.31187	0.293502
$803$	−37.4355	−1.32107
$804$	−4.49565	−0.158550
$805$	−2.75265	−0.0970180
$806$	−28.4909	−1.00355
$807$	−35.2548	−1.24103
$808$	13.6008	0.478474
$809$	−48.3929	−1.70140	−0.850701	−	0.525650i	$-0.823822\pi$
$809$	−48.3929	−1.70140	−0.850701	+	0.525650i	$0.823822\pi$
$810$	4.95888	0.174237
$811$	15.4182	0.541406	0.270703	−	0.962663i	$-0.412744\pi$
$811$	15.4182	0.541406	0.270703	+	0.962663i	$0.412744\pi$
$812$	6.47309	0.227161
$813$	−33.1082	−1.16115
$814$	38.9737	1.36603
$815$	−2.12669	−0.0744946
$816$	10.9217	0.382337
$817$	4.92563	0.172326
$818$	−12.5233	−0.437867
$819$	17.6963	0.618358
$820$	−2.95800	−0.103298
$821$	49.5824	1.73044	0.865220	−	0.501393i	$-0.167179\pi$
$821$	49.5824	1.73044	0.865220	+	0.501393i	$0.167179\pi$
$822$	−0.0883541	−0.00308170
$823$	22.0298	0.767910	0.383955	−	0.923352i	$-0.374562\pi$
$823$	22.0298	0.767910	0.383955	+	0.923352i	$0.374562\pi$
$824$	−7.55445	−0.263172
$825$	−54.1665	−1.88584
$826$	6.95932	0.242146
$827$	−34.2943	−1.19253	−0.596265	−	0.802787i	$-0.703349\pi$
$827$	−34.2943	−1.19253	−0.596265	+	0.802787i	$0.703349\pi$
$828$	13.9384	0.484391
$829$	−28.9304	−1.00479	−0.502397	−	0.864637i	$-0.667548\pi$
$829$	−28.9304	−1.00479	−0.502397	+	0.864637i	$0.667548\pi$
$830$	1.09335	0.0379507
$831$	63.9638	2.21888
$832$	5.22408	0.181113
$833$	25.9818	0.900215
$834$	26.8322	0.929122
$835$	−21.6185	−0.748139
$836$	−3.79501	−0.131253
$837$	12.0354	0.416004
$838$	−29.3849	−1.01508
$839$	18.1442	0.626409	0.313205	−	0.949686i	$-0.398597\pi$
$839$	18.1442	0.626409	0.313205	+	0.949686i	$0.398597\pi$
$840$	1.98571	0.0685134
$841$	24.9447	0.860162
$842$	18.0824	0.623160
$843$	52.6694	1.81403
$844$	26.7066	0.919279
$845$	−12.3084	−0.423422
$846$	5.84074	0.200809
$847$	11.1436	0.382898
$848$	−8.26101	−0.283684
$849$	38.4234	1.31869
$850$	17.7778	0.609774
$851$	−29.0661	−0.996374
$852$	−31.3109	−1.07269
$853$	0.581957	0.0199258	0.00996292	−	0.999950i	$-0.496829\pi$
$853$	0.581957	0.0199258	0.00996292	+	0.999950i	$0.496829\pi$
$854$	−5.63797	−0.192928
$855$	−2.58359	−0.0883569
$856$	−5.27798	−0.180398
$857$	−3.89283	−0.132976	−0.0664882	−	0.997787i	$-0.521179\pi$
$857$	−3.89283	−0.132976	−0.0664882	+	0.997787i	$0.521179\pi$
$858$	66.4527	2.26866
$859$	−20.2732	−0.691713	−0.345856	−	0.938287i	$-0.612412\pi$
$859$	−20.2732	−0.691713	−0.345856	+	0.938287i	$0.612412\pi$
$860$	−5.43560	−0.185352
$861$	−7.91844	−0.269860
$862$	−5.31401	−0.180996
$863$	−9.42563	−0.320852	−0.160426	−	0.987048i	$-0.551287\pi$
$863$	−9.42563	−0.320852	−0.160426	+	0.987048i	$0.551287\pi$
$864$	−2.20681	−0.0750771
$865$	10.6387	0.361726
$866$	20.2601	0.688468
$867$	−1.12524	−0.0382151
$868$	−4.80654	−0.163145
$869$	−19.2961	−0.654577
$870$	16.5483	0.561039
$871$	8.97763	0.304195
$872$	−12.5429	−0.424755
$873$	−0.462168	−0.0156420
$874$	2.83027	0.0957353
$875$	7.02751	0.237573
$876$	−20.1402	−0.680474
$877$	26.0140	0.878429	0.439215	−	0.898382i	$-0.355257\pi$
$877$	26.0140	0.878429	0.439215	+	0.898382i	$0.355257\pi$
$878$	−2.27076	−0.0766343
$879$	−62.2786	−2.10061
$880$	4.18792	0.141175
$881$	−25.0543	−0.844100	−0.422050	−	0.906572i	$-0.638689\pi$
$881$	−25.0543	−0.844100	−0.422050	+	0.906572i	$0.638689\pi$
$882$	−23.9196	−0.805414
$883$	−25.4596	−0.856782	−0.428391	−	0.903593i	$-0.640919\pi$
$883$	−25.4596	−0.856782	−0.428391	+	0.903593i	$0.640919\pi$
$884$	−21.8102	−0.733558
$885$	17.7913	0.598049
$886$	23.1739	0.778542
$887$	51.3347	1.72365	0.861825	−	0.507206i	$-0.169322\pi$
$887$	51.3347	1.72365	0.861825	+	0.507206i	$0.169322\pi$
$888$	20.9678	0.703632
$889$	6.54438	0.219491
$890$	13.5533	0.454309
$891$	27.9968	0.937927
$892$	−6.64379	−0.222450
$893$	1.18600	0.0396879
$894$	−53.9265	−1.80357
$895$	−0.462915	−0.0154735
$896$	0.881327	0.0294431
$897$	−49.5596	−1.65475
$898$	7.39191	0.246671
$899$	−40.0563	−1.33595
$900$	−16.3668	−0.545560
$901$	34.4893	1.14900
$902$	−16.7002	−0.556057
$903$	−14.5509	−0.484222
$904$	0.0667373	0.00221965
$905$	17.7801	0.591030
$906$	−45.1993	−1.50164
$907$	−8.32860	−0.276547	−0.138273	−	0.990394i	$-0.544155\pi$
$907$	−8.32860	−0.276547	−0.138273	+	0.990394i	$0.544155\pi$
$908$	−4.44691	−0.147576
$909$	52.2756	1.73387
$910$	−3.96537	−0.131451
$911$	−0.605185	−0.0200507	−0.0100253	−	0.999950i	$-0.503191\pi$
$911$	−0.605185	−0.0200507	−0.0100253	+	0.999950i	$0.503191\pi$
$912$	−2.04170	−0.0676076
$913$	6.17281	0.204290
$914$	29.4057	0.972655
$915$	−14.4133	−0.476490
$916$	−3.26327	−0.107822
$917$	16.9264	0.558959
$918$	9.21328	0.304084
$919$	−35.0931	−1.15761	−0.578807	−	0.815465i	$-0.696481\pi$
$919$	−35.0931	−1.15761	−0.578807	+	0.815465i	$0.696481\pi$
$920$	−3.12330	−0.102972
$921$	22.4846	0.740893
$922$	15.8245	0.521151
$923$	62.5265	2.05808
$924$	11.2109	0.368811
$925$	34.1302	1.12219
$926$	10.4458	0.343271
$927$	−29.0361	−0.953670
$928$	7.34471	0.241102
$929$	38.7901	1.27266	0.636332	−	0.771416i	$-0.280451\pi$
$929$	38.7901	1.27266	0.636332	+	0.771416i	$0.280451\pi$
$930$	−12.2878	−0.402933
$931$	−4.85702	−0.159182
$932$	6.09787	0.199742
$933$	−82.0708	−2.68688
$934$	−5.28523	−0.172938
$935$	−17.4843	−0.571798
$936$	20.0791	0.656308
$937$	−29.8684	−0.975756	−0.487878	−	0.872912i	$-0.662229\pi$
$937$	−29.8684	−0.975756	−0.487878	+	0.872912i	$0.662229\pi$
$938$	1.51457	0.0494524
$939$	−88.1013	−2.87508
$940$	−1.30879	−0.0426880
$941$	−58.4360	−1.90496	−0.952480	−	0.304600i	$-0.901477\pi$
$941$	−58.4360	−1.90496	−0.952480	+	0.304600i	$0.901477\pi$
$942$	−31.5296	−1.02729
$943$	12.4548	0.405585
$944$	7.89642	0.257007
$945$	1.67509	0.0544907
$946$	−30.6882	−0.997760
$947$	−26.4751	−0.860324	−0.430162	−	0.902752i	$-0.641544\pi$
$947$	−26.4751	−0.860324	−0.430162	+	0.902752i	$0.641544\pi$
$948$	−10.3813	−0.337168
$949$	40.2191	1.30557
$950$	−3.32338	−0.107825
$951$	45.3798	1.47154
$952$	−3.67949	−0.119253
$953$	−59.2463	−1.91918	−0.959588	−	0.281410i	$-0.909198\pi$
$953$	−59.2463	−1.91918	−0.959588	+	0.281410i	$0.909198\pi$
$954$	−31.7518	−1.02800
$955$	7.86405	0.254475
$956$	26.3417	0.851952
$957$	93.4280	3.02010
$958$	−25.0287	−0.808640
$959$	0.0297661	0.000961198 0
$960$	2.25309	0.0727182
$961$	−1.25652	−0.0405329
$962$	−41.8717	−1.35000
$963$	−20.2863	−0.653717
$964$	24.9020	0.802038
$965$	−1.58998	−0.0511833
$966$	−8.36094	−0.269009
$967$	54.4349	1.75051	0.875254	−	0.483663i	$-0.160694\pi$
$967$	54.4349	1.75051	0.875254	+	0.483663i	$0.160694\pi$
$968$	12.6441	0.406396
$969$	8.52400	0.273830
$970$	0.103562	0.00332519
$971$	28.8454	0.925694	0.462847	−	0.886438i	$-0.346828\pi$
$971$	28.8454	0.925694	0.462847	+	0.886438i	$0.346828\pi$
$972$	21.6826	0.695470
$973$	−9.03964	−0.289798
$974$	−3.34302	−0.107117
$975$	58.1942	1.86371
$976$	−6.39714	−0.204768
$977$	−25.6546	−0.820763	−0.410382	−	0.911914i	$-0.634604\pi$
$977$	−25.6546	−0.820763	−0.410382	+	0.911914i	$0.634604\pi$
$978$	−6.45963	−0.206556
$979$	76.5192	2.44557
$980$	5.35988	0.171215
$981$	−48.2094	−1.53921
$982$	33.4815	1.06844
$983$	43.8523	1.39867	0.699336	−	0.714793i	$-0.253479\pi$
$983$	43.8523	1.39867	0.699336	+	0.714793i	$0.253479\pi$
$984$	−8.98468	−0.286421
$985$	5.06799	0.161480
$986$	−30.6637	−0.976532
$987$	−3.50357	−0.111520
$988$	4.07720	0.129713
$989$	22.8869	0.727761
$990$	16.0966	0.511583
$991$	−34.1335	−1.08429	−0.542143	−	0.840286i	$-0.682387\pi$
$991$	−34.1335	−1.08429	−0.542143	+	0.840286i	$0.682387\pi$
$992$	−5.45376	−0.173157
$993$	40.5470	1.28672
$994$	10.5485	0.334578
$995$	−10.7708	−0.341459
$996$	3.32096	0.105229
$997$	20.8711	0.660995	0.330497	−	0.943807i	$-0.392783\pi$
$997$	20.8711	0.660995	0.330497	+	0.943807i	$0.392783\pi$
$998$	−24.5110	−0.775881
$999$	17.6878	0.559619

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	6022.2.a.e.1.6	✓	68

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
6022.2.a.e.1.6	✓	68	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:	\( N \)	\(=\)	\( 6022 = 2 \cdot 3011 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	6022.a (trivial)

\(f(q)\)	\(=\)	\(q+1.00000 q^{2} -2.61602 q^{3} +1.00000 q^{4} -0.861265 q^{5} -2.61602 q^{6} +0.881327 q^{7} +1.00000 q^{8} +3.84357 q^{9} +O(q^{10})\)	\(q+1.00000 q^{2} -2.61602 q^{3} +1.00000 q^{4} -0.861265 q^{5} -2.61602 q^{6} +0.881327 q^{7} +1.00000 q^{8} +3.84357 q^{9} -0.861265 q^{10} -4.86252 q^{11} -2.61602 q^{12} +5.22408 q^{13} +0.881327 q^{14} +2.25309 q^{15} +1.00000 q^{16} -4.17494 q^{17} +3.84357 q^{18} +0.780461 q^{19} -0.861265 q^{20} -2.30557 q^{21} -4.86252 q^{22} +3.62641 q^{23} -2.61602 q^{24} -4.25822 q^{25} +5.22408 q^{26} -2.20681 q^{27} +0.881327 q^{28} +7.34471 q^{29} +2.25309 q^{30} -5.45376 q^{31} +1.00000 q^{32} +12.7205 q^{33} -4.17494 q^{34} -0.759056 q^{35} +3.84357 q^{36} -8.01513 q^{37} +0.780461 q^{38} -13.6663 q^{39} -0.861265 q^{40} +3.43448 q^{41} -2.30557 q^{42} +6.31118 q^{43} -4.86252 q^{44} -3.31034 q^{45} +3.62641 q^{46} +1.51961 q^{47} -2.61602 q^{48} -6.22326 q^{49} -4.25822 q^{50} +10.9217 q^{51} +5.22408 q^{52} -8.26101 q^{53} -2.20681 q^{54} +4.18792 q^{55} +0.881327 q^{56} -2.04170 q^{57} +7.34471 q^{58} +7.89642 q^{59} +2.25309 q^{60} -6.39714 q^{61} -5.45376 q^{62} +3.38744 q^{63} +1.00000 q^{64} -4.49932 q^{65} +12.7205 q^{66} +1.71851 q^{67} -4.17494 q^{68} -9.48676 q^{69} -0.759056 q^{70} +11.9689 q^{71} +3.84357 q^{72} +7.69878 q^{73} -8.01513 q^{74} +11.1396 q^{75} +0.780461 q^{76} -4.28547 q^{77} -13.6663 q^{78} +3.96834 q^{79} -0.861265 q^{80} -5.75767 q^{81} +3.43448 q^{82} -1.26947 q^{83} -2.30557 q^{84} +3.59573 q^{85} +6.31118 q^{86} -19.2139 q^{87} -4.86252 q^{88} -15.7365 q^{89} -3.31034 q^{90} +4.60412 q^{91} +3.62641 q^{92} +14.2672 q^{93} +1.51961 q^{94} -0.672184 q^{95} -2.61602 q^{96} -0.120244 q^{97} -6.22326 q^{98} -18.6894 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 68 q + 68 q^{2} + 25 q^{3} + 68 q^{4} + 20 q^{5} + 25 q^{6} + 29 q^{7} + 68 q^{8} + 87 q^{9}+O(q^{10}) \) 68 * q + 68 * q^2 + 25 * q^3 + 68 * q^4 + 20 * q^5 + 25 * q^6 + 29 * q^7 + 68 * q^8 + 87 * q^9	\( 68 q + 68 q^{2} + 25 q^{3} + 68 q^{4} + 20 q^{5} + 25 q^{6} + 29 q^{7} + 68 q^{8} + 87 q^{9} + 20 q^{10} + 46 q^{11} + 25 q^{12} + 30 q^{13} + 29 q^{14} + 13 q^{15} + 68 q^{16} + 73 q^{17} + 87 q^{18} + 56 q^{19} + 20 q^{20} - 5 q^{21} + 46 q^{22} + 63 q^{23} + 25 q^{24} + 88 q^{25} + 30 q^{26} + 67 q^{27} + 29 q^{28} + 43 q^{29} + 13 q^{30} + 68 q^{31} + 68 q^{32} + 26 q^{33} + 73 q^{34} + 50 q^{35} + 87 q^{36} + 8 q^{37} + 56 q^{38} + 6 q^{39} + 20 q^{40} + 64 q^{41} - 5 q^{42} + 52 q^{43} + 46 q^{44} + 7 q^{45} + 63 q^{46} + 94 q^{47} + 25 q^{48} + 91 q^{49} + 88 q^{50} + 20 q^{51} + 30 q^{52} + 38 q^{53} + 67 q^{54} + 37 q^{55} + 29 q^{56} + 4 q^{57} + 43 q^{58} + 84 q^{59} + 13 q^{60} + 26 q^{61} + 68 q^{62} + 22 q^{63} + 68 q^{64} - 20 q^{65} + 26 q^{66} + 54 q^{67} + 73 q^{68} - 11 q^{69} + 50 q^{70} + 46 q^{71} + 87 q^{72} + 62 q^{73} + 8 q^{74} + 54 q^{75} + 56 q^{76} + 67 q^{77} + 6 q^{78} + 67 q^{79} + 20 q^{80} + 120 q^{81} + 64 q^{82} + 130 q^{83} - 5 q^{84} - 24 q^{85} + 52 q^{86} + 72 q^{87} + 46 q^{88} + 61 q^{89} + 7 q^{90} + 43 q^{91} + 63 q^{92} + 40 q^{93} + 94 q^{94} + 55 q^{95} + 25 q^{96} + 41 q^{97} + 91 q^{98} + 106 q^{99}+O(q^{100}) \) 68 * q + 68 * q^2 + 25 * q^3 + 68 * q^4 + 20 * q^5 + 25 * q^6 + 29 * q^7 + 68 * q^8 + 87 * q^9 + 20 * q^10 + 46 * q^11 + 25 * q^12 + 30 * q^13 + 29 * q^14 + 13 * q^15 + 68 * q^16 + 73 * q^17 + 87 * q^18 + 56 * q^19 + 20 * q^20 - 5 * q^21 + 46 * q^22 + 63 * q^23 + 25 * q^24 + 88 * q^25 + 30 * q^26 + 67 * q^27 + 29 * q^28 + 43 * q^29 + 13 * q^30 + 68 * q^31 + 68 * q^32 + 26 * q^33 + 73 * q^34 + 50 * q^35 + 87 * q^36 + 8 * q^37 + 56 * q^38 + 6 * q^39 + 20 * q^40 + 64 * q^41 - 5 * q^42 + 52 * q^43 + 46 * q^44 + 7 * q^45 + 63 * q^46 + 94 * q^47 + 25 * q^48 + 91 * q^49 + 88 * q^50 + 20 * q^51 + 30 * q^52 + 38 * q^53 + 67 * q^54 + 37 * q^55 + 29 * q^56 + 4 * q^57 + 43 * q^58 + 84 * q^59 + 13 * q^60 + 26 * q^61 + 68 * q^62 + 22 * q^63 + 68 * q^64 - 20 * q^65 + 26 * q^66 + 54 * q^67 + 73 * q^68 - 11 * q^69 + 50 * q^70 + 46 * q^71 + 87 * q^72 + 62 * q^73 + 8 * q^74 + 54 * q^75 + 56 * q^76 + 67 * q^77 + 6 * q^78 + 67 * q^79 + 20 * q^80 + 120 * q^81 + 64 * q^82 + 130 * q^83 - 5 * q^84 - 24 * q^85 + 52 * q^86 + 72 * q^87 + 46 * q^88 + 61 * q^89 + 7 * q^90 + 43 * q^91 + 63 * q^92 + 40 * q^93 + 94 * q^94 + 55 * q^95 + 25 * q^96 + 41 * q^97 + 91 * q^98 + 106 * q^99

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