LMFDB - Embedded newform 6023.2.a.c.1.20

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [6023,2,Mod(1,6023)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(6023, 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("6023.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 6023 = 19 \cdot 317 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	6023.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:	$48.0938971374$
Analytic rank:	$0$
Dimension:	$138$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.20
Character	$\chi$	$=$	6023.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-2.14132 q^{2} +0.0864735 q^{3} +2.58523 q^{4} +2.84531 q^{5} -0.185167 q^{6} +1.71112 q^{7} -1.25317 q^{8} -2.99252 q^{9} +O(q^{10})$	\(q-2.14132 q^{2} +0.0864735 q^{3} +2.58523 q^{4} +2.84531 q^{5} -0.185167 q^{6} +1.71112 q^{7} -1.25317 q^{8} -2.99252 q^{9} -6.09271 q^{10} +5.95918 q^{11} +0.223554 q^{12} -1.24067 q^{13} -3.66404 q^{14} +0.246044 q^{15} -2.48704 q^{16} -2.99745 q^{17} +6.40794 q^{18} +1.00000 q^{19} +7.35579 q^{20} +0.147966 q^{21} -12.7605 q^{22} -1.71969 q^{23} -0.108366 q^{24} +3.09580 q^{25} +2.65667 q^{26} -0.518194 q^{27} +4.42364 q^{28} +5.51988 q^{29} -0.526858 q^{30} -5.02454 q^{31} +7.83187 q^{32} +0.515311 q^{33} +6.41849 q^{34} +4.86866 q^{35} -7.73637 q^{36} -5.96251 q^{37} -2.14132 q^{38} -0.107285 q^{39} -3.56566 q^{40} +3.75447 q^{41} -0.316842 q^{42} -9.47514 q^{43} +15.4059 q^{44} -8.51466 q^{45} +3.68241 q^{46} +2.62487 q^{47} -0.215063 q^{48} -4.07208 q^{49} -6.62908 q^{50} -0.259200 q^{51} -3.20743 q^{52} +8.56706 q^{53} +1.10962 q^{54} +16.9557 q^{55} -2.14432 q^{56} +0.0864735 q^{57} -11.8198 q^{58} -0.767009 q^{59} +0.636081 q^{60} -6.43011 q^{61} +10.7591 q^{62} -5.12056 q^{63} -11.7964 q^{64} -3.53010 q^{65} -1.10344 q^{66} +10.3051 q^{67} -7.74911 q^{68} -0.148708 q^{69} -10.4253 q^{70} -7.95730 q^{71} +3.75014 q^{72} +12.2031 q^{73} +12.7676 q^{74} +0.267704 q^{75} +2.58523 q^{76} +10.1969 q^{77} +0.229732 q^{78} +16.2344 q^{79} -7.07639 q^{80} +8.93276 q^{81} -8.03950 q^{82} +1.81871 q^{83} +0.382527 q^{84} -8.52868 q^{85} +20.2893 q^{86} +0.477324 q^{87} -7.46786 q^{88} +11.8057 q^{89} +18.2326 q^{90} -2.12294 q^{91} -4.44581 q^{92} -0.434489 q^{93} -5.62068 q^{94} +2.84531 q^{95} +0.677249 q^{96} +2.41720 q^{97} +8.71961 q^{98} -17.8330 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 138 q + 11 q^{2} + 29 q^{3} + 157 q^{4} + 12 q^{5} + 8 q^{6} + 18 q^{7} + 33 q^{8} + 171 q^{9}+O(q^{10}) $ 138 * q + 11 * q^2 + 29 * q^3 + 157 * q^4 + 12 * q^5 + 8 * q^6 + 18 * q^7 + 33 * q^8 + 171 * q^9	\( 138 q + 11 q^{2} + 29 q^{3} + 157 q^{4} + 12 q^{5} + 8 q^{6} + 18 q^{7} + 33 q^{8} + 171 q^{9} + 40 q^{10} + 4 q^{11} + 69 q^{12} + 72 q^{13} + 3 q^{14} + 30 q^{15} + 191 q^{16} + 31 q^{17} + 31 q^{18} + 138 q^{19} + 16 q^{20} + 16 q^{21} + 95 q^{22} + 34 q^{23} + 3 q^{24} + 244 q^{25} - 13 q^{26} + 107 q^{27} + 43 q^{28} + 30 q^{29} - 14 q^{30} + 60 q^{31} + 62 q^{32} + 77 q^{33} + 36 q^{34} + 2 q^{35} + 205 q^{36} + 142 q^{37} + 11 q^{38} + 20 q^{39} + 76 q^{40} + 46 q^{41} - 21 q^{42} + 69 q^{43} - 7 q^{44} + 30 q^{45} + 39 q^{46} + 8 q^{47} + 116 q^{48} + 236 q^{49} + 34 q^{51} + 165 q^{52} + 49 q^{53} + 6 q^{55} - 33 q^{56} + 29 q^{57} + 75 q^{58} + 8 q^{59} - 24 q^{60} + 38 q^{61} - 10 q^{62} + 2 q^{63} + 251 q^{64} + 72 q^{65} - 15 q^{66} + 158 q^{67} - 19 q^{68} + 33 q^{69} + 48 q^{70} + 23 q^{71} + 88 q^{72} + 134 q^{73} + 4 q^{74} + 118 q^{75} + 157 q^{76} + 13 q^{77} + 12 q^{78} + 78 q^{79} - 48 q^{80} + 254 q^{81} + 89 q^{82} - 27 q^{83} - 15 q^{84} + 37 q^{85} + 66 q^{86} + 43 q^{87} + 224 q^{88} + 26 q^{89} + 38 q^{90} + 108 q^{91} + 113 q^{92} + 83 q^{93} + 48 q^{94} + 12 q^{95} + 40 q^{96} + 254 q^{97} + 47 q^{98} + 11 q^{99}+O(q^{100}) \) 138 * q + 11 * q^2 + 29 * q^3 + 157 * q^4 + 12 * q^5 + 8 * q^6 + 18 * q^7 + 33 * q^8 + 171 * q^9 + 40 * q^10 + 4 * q^11 + 69 * q^12 + 72 * q^13 + 3 * q^14 + 30 * q^15 + 191 * q^16 + 31 * q^17 + 31 * q^18 + 138 * q^19 + 16 * q^20 + 16 * q^21 + 95 * q^22 + 34 * q^23 + 3 * q^24 + 244 * q^25 - 13 * q^26 + 107 * q^27 + 43 * q^28 + 30 * q^29 - 14 * q^30 + 60 * q^31 + 62 * q^32 + 77 * q^33 + 36 * q^34 + 2 * q^35 + 205 * q^36 + 142 * q^37 + 11 * q^38 + 20 * q^39 + 76 * q^40 + 46 * q^41 - 21 * q^42 + 69 * q^43 - 7 * q^44 + 30 * q^45 + 39 * q^46 + 8 * q^47 + 116 * q^48 + 236 * q^49 + 34 * q^51 + 165 * q^52 + 49 * q^53 + 6 * q^55 - 33 * q^56 + 29 * q^57 + 75 * q^58 + 8 * q^59 - 24 * q^60 + 38 * q^61 - 10 * q^62 + 2 * q^63 + 251 * q^64 + 72 * q^65 - 15 * q^66 + 158 * q^67 - 19 * q^68 + 33 * q^69 + 48 * q^70 + 23 * q^71 + 88 * q^72 + 134 * q^73 + 4 * q^74 + 118 * q^75 + 157 * q^76 + 13 * q^77 + 12 * q^78 + 78 * q^79 - 48 * q^80 + 254 * q^81 + 89 * q^82 - 27 * q^83 - 15 * q^84 + 37 * q^85 + 66 * q^86 + 43 * q^87 + 224 * q^88 + 26 * q^89 + 38 * q^90 + 108 * q^91 + 113 * q^92 + 83 * q^93 + 48 * q^94 + 12 * q^95 + 40 * q^96 + 254 * q^97 + 47 * q^98 + 11 * 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 $

$2$	−2.14132	−1.51414	−0.757069	−	0.653334i	$-0.773370\pi$
$2$	−2.14132	−1.51414	−0.757069	+	0.653334i	$0.773370\pi$
$3$	0.0864735	0.0499255	0.0249627	−	0.999688i	$-0.492053\pi$
$3$	0.0864735	0.0499255	0.0249627	+	0.999688i	$0.492053\pi$
$4$	2.58523	1.29262
$5$	2.84531	1.27246	0.636231	−	0.771499i	$-0.280493\pi$
$5$	2.84531	1.27246	0.636231	+	0.771499i	$0.280493\pi$
$6$	−0.185167	−0.0755941
$7$	1.71112	0.646741	0.323371	−	0.946272i	$-0.395184\pi$
$7$	1.71112	0.646741	0.323371	+	0.946272i	$0.395184\pi$
$8$	−1.25317	−0.443062
$9$	−2.99252	−0.997507
$10$	−6.09271	−1.92668
$11$	5.95918	1.79676	0.898380	−	0.439219i	$-0.144745\pi$
$11$	5.95918	1.79676	0.898380	+	0.439219i	$0.144745\pi$
$12$	0.223554	0.0645345
$13$	−1.24067	−0.344101	−0.172051	−	0.985088i	$-0.555039\pi$
$13$	−1.24067	−0.344101	−0.172051	+	0.985088i	$0.555039\pi$
$14$	−3.66404	−0.979256
$15$	0.246044	0.0635283
$16$	−2.48704	−0.621759
$17$	−2.99745	−0.726989	−0.363494	−	0.931596i	$-0.618416\pi$
$17$	−2.99745	−0.726989	−0.363494	+	0.931596i	$0.618416\pi$
$18$	6.40794	1.51036
$19$	1.00000	0.229416
$19$	1.00000	0.229416
$20$	7.35579	1.64481
$21$	0.147966	0.0322889
$22$	−12.7605	−2.72054
$23$	−1.71969	−0.358581	−0.179290	−	0.983796i	$-0.557380\pi$
$23$	−1.71969	−0.358581	−0.179290	+	0.983796i	$0.557380\pi$
$24$	−0.108366	−0.0221201
$25$	3.09580	0.619159
$26$	2.65667	0.521017
$27$	−0.518194	−0.0997265
$28$	4.42364	0.835989
$29$	5.51988	1.02502	0.512508	−	0.858682i	$-0.328716\pi$
$29$	5.51988	1.02502	0.512508	+	0.858682i	$0.328716\pi$
$30$	−0.526858	−0.0961907
$31$	−5.02454	−0.902434	−0.451217	−	0.892414i	$-0.649010\pi$
$31$	−5.02454	−0.902434	−0.451217	+	0.892414i	$0.649010\pi$
$32$	7.83187	1.38449
$33$	0.515311	0.0897041
$34$	6.41849	1.10076
$35$	4.86866	0.822954
$36$	−7.73637	−1.28939
$37$	−5.96251	−0.980231	−0.490116	−	0.871657i	$-0.663045\pi$
$37$	−5.96251	−0.980231	−0.490116	+	0.871657i	$0.663045\pi$
$38$	−2.14132	−0.347367
$39$	−0.107285	−0.0171794
$40$	−3.56566	−0.563780
$41$	3.75447	0.586350	0.293175	−	0.956059i	$-0.405288\pi$
$41$	3.75447	0.586350	0.293175	+	0.956059i	$0.405288\pi$
$42$	−0.316842	−0.0488898
$43$	−9.47514	−1.44495	−0.722473	−	0.691400i	$-0.756994\pi$
$43$	−9.47514	−1.44495	−0.722473	+	0.691400i	$0.756994\pi$
$44$	15.4059	2.32252
$45$	−8.51466	−1.26929
$46$	3.68241	0.542941
$47$	2.62487	0.382877	0.191439	−	0.981505i	$-0.438685\pi$
$47$	2.62487	0.382877	0.191439	+	0.981505i	$0.438685\pi$
$48$	−0.215063	−0.0310416
$49$	−4.07208	−0.581726
$50$	−6.62908	−0.937493
$51$	−0.259200	−0.0362953
$52$	−3.20743	−0.444791
$53$	8.56706	1.17678	0.588388	−	0.808579i	$-0.299763\pi$
$53$	8.56706	1.17678	0.588388	+	0.808579i	$0.299763\pi$
$54$	1.10962	0.151000
$55$	16.9557	2.28631
$56$	−2.14432	−0.286547
$57$	0.0864735	0.0114537
$58$	−11.8198	−1.55202
$59$	−0.767009	−0.0998561	−0.0499280	−	0.998753i	$-0.515899\pi$
$59$	−0.767009	−0.0998561	−0.0499280	+	0.998753i	$0.515899\pi$
$60$	0.636081	0.0821177
$61$	−6.43011	−0.823291	−0.411646	−	0.911344i	$-0.635046\pi$
$61$	−6.43011	−0.823291	−0.411646	+	0.911344i	$0.635046\pi$
$62$	10.7591	1.36641
$63$	−5.12056	−0.645129
$64$	−11.7964	−1.47455
$65$	−3.53010	−0.437856
$66$	−1.10344	−0.135825
$67$	10.3051	1.25897	0.629484	−	0.777014i	$-0.283266\pi$
$67$	10.3051	1.25897	0.629484	+	0.777014i	$0.283266\pi$
$68$	−7.74911	−0.939718
$69$	−0.148708	−0.0179023
$70$	−10.4253	−1.24607
$71$	−7.95730	−0.944357	−0.472179	−	0.881503i	$-0.656532\pi$
$71$	−7.95730	−0.944357	−0.472179	+	0.881503i	$0.656532\pi$
$72$	3.75014	0.441958
$73$	12.2031	1.42826	0.714131	−	0.700013i	$-0.246822\pi$
$73$	12.2031	1.42826	0.714131	+	0.700013i	$0.246822\pi$
$74$	12.7676	1.48421
$75$	0.267704	0.0309118
$76$	2.58523	0.296547
$77$	10.1969	1.16204
$78$	0.229732	0.0260120
$79$	16.2344	1.82652	0.913258	−	0.407382i	$-0.133558\pi$
$79$	16.2344	1.82652	0.913258	+	0.407382i	$0.133558\pi$
$80$	−7.07639	−0.791164
$81$	8.93276	0.992529
$82$	−8.03950	−0.887815
$83$	1.81871	0.199629	0.0998147	−	0.995006i	$-0.468175\pi$
$83$	1.81871	0.199629	0.0998147	+	0.995006i	$0.468175\pi$
$84$	0.382527	0.0417371
$85$	−8.52868	−0.925065
$86$	20.2893	2.18785
$87$	0.477324	0.0511745
$88$	−7.46786	−0.796077
$89$	11.8057	1.25140	0.625700	−	0.780064i	$-0.284813\pi$
$89$	11.8057	1.25140	0.625700	+	0.780064i	$0.284813\pi$
$90$	18.2326	1.92188
$91$	−2.12294	−0.222544
$92$	−4.44581	−0.463508
$93$	−0.434489	−0.0450544
$94$	−5.62068	−0.579729
$95$	2.84531	0.291923
$96$	0.677249	0.0691214
$97$	2.41720	0.245429	0.122715	−	0.992442i	$-0.460840\pi$
$97$	2.41720	0.245429	0.122715	+	0.992442i	$0.460840\pi$
$98$	8.71961	0.880813
$99$	−17.8330	−1.79228
$100$	8.00336	0.800336
$101$	−9.95906	−0.990963	−0.495482	−	0.868618i	$-0.665008\pi$
$101$	−9.95906	−0.990963	−0.495482	+	0.868618i	$0.665008\pi$
$102$	0.555029	0.0549561
$103$	16.0446	1.58092	0.790461	−	0.612513i	$-0.209841\pi$
$103$	16.0446	1.58092	0.790461	+	0.612513i	$0.209841\pi$
$104$	1.55477	0.152458
$105$	0.421010	0.0410864
$106$	−18.3448	−1.78180
$107$	16.5198	1.59703	0.798514	−	0.601976i	$-0.205620\pi$
$107$	16.5198	1.59703	0.798514	+	0.601976i	$0.205620\pi$
$108$	−1.33965	−0.128908
$109$	−14.2270	−1.36270	−0.681349	−	0.731959i	$-0.738606\pi$
$109$	−14.2270	−1.36270	−0.681349	+	0.731959i	$0.738606\pi$
$110$	−36.3076	−3.46179
$111$	−0.515599	−0.0489385
$112$	−4.25561	−0.402117
$113$	11.0878	1.04305	0.521527	−	0.853235i	$-0.325363\pi$
$113$	11.0878	1.04305	0.521527	+	0.853235i	$0.325363\pi$
$114$	−0.185167	−0.0173425
$115$	−4.89307	−0.456281
$116$	14.2702	1.32495
$117$	3.71274	0.343243
$118$	1.64241	0.151196
$119$	−5.12899	−0.470174
$120$	−0.308335	−0.0281470
$121$	24.5118	2.22835
$122$	13.7689	1.24658
$123$	0.324662	0.0292738
$124$	−12.9896	−1.16650
$125$	−5.41805	−0.484605
$126$	10.9647	0.976815
$127$	14.9962	1.33070	0.665348	−	0.746533i	$-0.268283\pi$
$127$	14.9962	1.33070	0.665348	+	0.746533i	$0.268283\pi$
$128$	9.59615	0.848188
$129$	−0.819348	−0.0721396
$130$	7.55907	0.662974
$131$	20.4390	1.78576	0.892882	−	0.450290i	$-0.148679\pi$
$131$	20.4390	1.78576	0.892882	+	0.450290i	$0.148679\pi$
$132$	1.33220	0.115953
$133$	1.71112	0.148373
$134$	−22.0665	−1.90625
$135$	−1.47442	−0.126898
$136$	3.75631	0.322101
$137$	15.9973	1.36674	0.683370	−	0.730073i	$-0.260514\pi$
$137$	15.9973	1.36674	0.683370	+	0.730073i	$0.260514\pi$
$138$	0.318431	0.0271066
$139$	−0.325507	−0.0276091	−0.0138046	−	0.999905i	$-0.504394\pi$
$139$	−0.325507	−0.0276091	−0.0138046	+	0.999905i	$0.504394\pi$
$140$	12.5866	1.06376
$141$	0.226982	0.0191153
$142$	17.0391	1.42989
$143$	−7.39340	−0.618267
$144$	7.44251	0.620209
$145$	15.7058	1.30429
$146$	−26.1306	−2.16259
$147$	−0.352127	−0.0290429
$148$	−15.4145	−1.26706
$149$	−4.21581	−0.345373	−0.172686	−	0.984977i	$-0.555245\pi$
$149$	−4.21581	−0.345373	−0.172686	+	0.984977i	$0.555245\pi$
$150$	−0.573240	−0.0468048
$151$	16.5227	1.34460	0.672301	−	0.740278i	$-0.265306\pi$
$151$	16.5227	1.34460	0.672301	+	0.740278i	$0.265306\pi$
$152$	−1.25317	−0.101645
$153$	8.96994	0.725177
$154$	−21.8347	−1.75949
$155$	−14.2964	−1.14831
$156$	−0.277358	−0.0222064
$157$	−10.7080	−0.854592	−0.427296	−	0.904112i	$-0.640534\pi$
$157$	−10.7080	−0.854592	−0.427296	+	0.904112i	$0.640534\pi$
$158$	−34.7630	−2.76560
$159$	0.740824	0.0587511
$160$	22.2841	1.76171
$161$	−2.94260	−0.231909
$162$	−19.1279	−1.50283
$163$	6.51847	0.510566	0.255283	−	0.966866i	$-0.417831\pi$
$163$	6.51847	0.510566	0.255283	+	0.966866i	$0.417831\pi$
$164$	9.70618	0.757925
$165$	1.46622	0.114145
$166$	−3.89443	−0.302267
$167$	−1.56337	−0.120977	−0.0604886	−	0.998169i	$-0.519266\pi$
$167$	−1.56337	−0.120977	−0.0604886	+	0.998169i	$0.519266\pi$
$168$	−0.185427	−0.0143060
$169$	−11.4607	−0.881594
$170$	18.2626	1.40068
$171$	−2.99252	−0.228844
$172$	−24.4954	−1.86776
$173$	−6.65463	−0.505942	−0.252971	−	0.967474i	$-0.581408\pi$
$173$	−6.65463	−0.505942	−0.252971	+	0.967474i	$0.581408\pi$
$174$	−1.02210	−0.0774852
$175$	5.29727	0.400436
$176$	−14.8207	−1.11715
$177$	−0.0663259	−0.00498536
$178$	−25.2797	−1.89479
$179$	6.09154	0.455303	0.227652	−	0.973743i	$-0.426895\pi$
$179$	6.09154	0.455303	0.227652	+	0.973743i	$0.426895\pi$
$180$	−22.0124	−1.64071
$181$	5.20557	0.386927	0.193464	−	0.981107i	$-0.438028\pi$
$181$	5.20557	0.386927	0.193464	+	0.981107i	$0.438028\pi$
$182$	4.54588	0.336963
$183$	−0.556034	−0.0411032
$184$	2.15507	0.158874
$185$	−16.9652	−1.24731
$186$	0.930379	0.0682187
$187$	−17.8623	−1.30622
$188$	6.78591	0.494913
$189$	−0.886691	−0.0644973
$190$	−6.09271	−0.442012
$191$	−9.61155	−0.695467	−0.347734	−	0.937593i	$-0.613049\pi$
$191$	−9.61155	−0.695467	−0.347734	+	0.937593i	$0.613049\pi$
$192$	−1.02008	−0.0736178
$193$	−0.327136	−0.0235478	−0.0117739	−	0.999931i	$-0.503748\pi$
$193$	−0.327136	−0.0235478	−0.0117739	+	0.999931i	$0.503748\pi$
$194$	−5.17599	−0.371614
$195$	−0.305260	−0.0218602
$196$	−10.5273	−0.751948
$197$	5.79085	0.412581	0.206290	−	0.978491i	$-0.433861\pi$
$197$	5.79085	0.412581	0.206290	+	0.978491i	$0.433861\pi$
$198$	38.1860	2.71376
$199$	9.45331	0.670127	0.335064	−	0.942196i	$-0.391242\pi$
$199$	9.45331	0.670127	0.335064	+	0.942196i	$0.391242\pi$
$200$	−3.87956	−0.274326
$201$	0.891117	0.0628546
$202$	21.3255	1.50046
$203$	9.44517	0.662921
$204$	−0.670093	−0.0469159
$205$	10.6826	0.746108
$206$	−34.3566	−2.39373
$207$	5.14622	0.357687
$208$	3.08560	0.213948
$209$	5.95918	0.412205
$210$	−0.901515	−0.0622105
$211$	20.8414	1.43478	0.717391	−	0.696670i	$-0.245336\pi$
$211$	20.8414	1.43478	0.717391	+	0.696670i	$0.245336\pi$
$212$	22.1479	1.52112
$213$	−0.688095	−0.0471475
$214$	−35.3741	−2.41812
$215$	−26.9597	−1.83864
$216$	0.649385	0.0441851
$217$	−8.59757	−0.583641
$218$	30.4645	2.06331
$219$	1.05524	0.0713066
$220$	43.8345	2.95532
$221$	3.71886	0.250158
$222$	1.10406	0.0740997
$223$	21.8351	1.46219	0.731094	−	0.682277i	$-0.239010\pi$
$223$	21.8351	1.46219	0.731094	+	0.682277i	$0.239010\pi$
$224$	13.4012	0.895408
$225$	−9.26424	−0.617616
$226$	−23.7425	−1.57933
$227$	9.02240	0.598837	0.299419	−	0.954122i	$-0.403207\pi$
$227$	9.02240	0.598837	0.299419	+	0.954122i	$0.403207\pi$
$228$	0.223554	0.0148052
$229$	12.2148	0.807174	0.403587	−	0.914941i	$-0.367763\pi$
$229$	12.2148	0.807174	0.403587	+	0.914941i	$0.367763\pi$
$230$	10.4776	0.690872
$231$	0.881757	0.0580154
$232$	−6.91735	−0.454146
$233$	4.98121	0.326330	0.163165	−	0.986599i	$-0.447830\pi$
$233$	4.98121	0.326330	0.163165	+	0.986599i	$0.447830\pi$
$234$	−7.95016	−0.519718
$235$	7.46858	0.487197
$236$	−1.98290	−0.129076
$237$	1.40385	0.0911897
$238$	10.9828	0.711908
$239$	15.0585	0.974055	0.487027	−	0.873387i	$-0.338081\pi$
$239$	15.0585	0.974055	0.487027	+	0.873387i	$0.338081\pi$
$240$	−0.611920	−0.0394993
$241$	−18.6859	−1.20367	−0.601833	−	0.798622i	$-0.705563\pi$
$241$	−18.6859	−1.20367	−0.601833	+	0.798622i	$0.705563\pi$
$242$	−52.4875	−3.37403
$243$	2.32703	0.149279
$244$	−16.6233	−1.06420
$245$	−11.5863	−0.740224
$246$	−0.695204	−0.0443246
$247$	−1.24067	−0.0789422
$248$	6.29660	0.399834
$249$	0.157270	0.00996660
$250$	11.6018	0.733759
$251$	−19.2290	−1.21372	−0.606862	−	0.794807i	$-0.707572\pi$
$251$	−19.2290	−1.21372	−0.606862	+	0.794807i	$0.707572\pi$
$252$	−13.2378	−0.833905
$253$	−10.2480	−0.644284
$254$	−32.1116	−2.01486
$255$	−0.737505	−0.0461843
$256$	3.04448	0.190280
$257$	−16.1571	−1.00786	−0.503928	−	0.863746i	$-0.668112\pi$
$257$	−16.1571	−1.00786	−0.503928	+	0.863746i	$0.668112\pi$
$258$	1.75448	0.109229
$259$	−10.2026	−0.633956
$260$	−9.12614	−0.565979
$261$	−16.5184	−1.02246
$262$	−43.7664	−2.70390
$263$	4.36746	0.269309	0.134654	−	0.990893i	$-0.457008\pi$
$263$	4.36746	0.269309	0.134654	+	0.990893i	$0.457008\pi$
$264$	−0.645772	−0.0397445
$265$	24.3760	1.49740
$266$	−3.66404	−0.224657
$267$	1.02088	0.0624768
$268$	26.6411	1.62736
$269$	−8.94080	−0.545130	−0.272565	−	0.962137i	$-0.587872\pi$
$269$	−8.94080	−0.545130	−0.272565	+	0.962137i	$0.587872\pi$
$270$	3.15721	0.192142
$271$	−0.899088	−0.0546157	−0.0273079	−	0.999627i	$-0.508693\pi$
$271$	−0.899088	−0.0546157	−0.0273079	+	0.999627i	$0.508693\pi$
$272$	7.45477	0.452012
$273$	−0.183578	−0.0111106
$274$	−34.2552	−2.06943
$275$	18.4484	1.11248
$276$	−0.384445	−0.0231409
$277$	−19.3278	−1.16130	−0.580648	−	0.814155i	$-0.697201\pi$
$277$	−19.3278	−1.16130	−0.580648	+	0.814155i	$0.697201\pi$
$278$	0.697013	0.0418041
$279$	15.0360	0.900184
$280$	−6.10126	−0.364620
$281$	26.1224	1.55833	0.779166	−	0.626818i	$-0.215643\pi$
$281$	26.1224	1.55833	0.779166	+	0.626818i	$0.215643\pi$
$282$	−0.486040	−0.0289433
$283$	14.0333	0.834196	0.417098	−	0.908862i	$-0.363047\pi$
$283$	14.0333	0.834196	0.417098	+	0.908862i	$0.363047\pi$
$284$	−20.5715	−1.22069
$285$	0.246044	0.0145744
$286$	15.8316	0.936142
$287$	6.42434	0.379217
$288$	−23.4370	−1.38104
$289$	−8.01529	−0.471488
$290$	−33.6311	−1.97488
$291$	0.209024	0.0122532
$292$	31.5478	1.84619
$293$	12.7002	0.741951	0.370975	−	0.928643i	$-0.379023\pi$
$293$	12.7002	0.741951	0.370975	+	0.928643i	$0.379023\pi$
$294$	0.754015	0.0439750
$295$	−2.18238	−0.127063
$296$	7.47204	0.434304
$297$	−3.08801	−0.179185
$298$	9.02739	0.522942
$299$	2.13358	0.123388
$300$	0.692078	0.0399572
$301$	−16.2131	−0.934506
$302$	−35.3804	−2.03591
$303$	−0.861194	−0.0494743
$304$	−2.48704	−0.142641
$305$	−18.2957	−1.04761
$306$	−19.2075	−1.09802
$307$	−22.6666	−1.29365	−0.646827	−	0.762637i	$-0.723904\pi$
$307$	−22.6666	−1.29365	−0.646827	+	0.762637i	$0.723904\pi$
$308$	26.3612	1.50207
$309$	1.38743	0.0789283
$310$	30.6131	1.73870
$311$	−24.5900	−1.39437	−0.697185	−	0.716892i	$-0.745564\pi$
$311$	−24.5900	−1.39437	−0.697185	+	0.716892i	$0.745564\pi$
$312$	0.134447	0.00761155
$313$	11.6508	0.658540	0.329270	−	0.944236i	$-0.393197\pi$
$313$	11.6508	0.658540	0.329270	+	0.944236i	$0.393197\pi$
$314$	22.9292	1.29397
$315$	−14.5696	−0.820903
$316$	41.9698	2.36098
$317$	−1.00000	−0.0561656
$317$	−1.00000	−0.0561656
$318$	−1.58634	−0.0889574
$319$	32.8940	1.84171
$320$	−33.5645	−1.87631
$321$	1.42852	0.0797324
$322$	6.30103	0.351143
$323$	−2.99745	−0.166783
$324$	23.0933	1.28296
$325$	−3.84088	−0.213053
$326$	−13.9581	−0.773068
$327$	−1.23026	−0.0680333
$328$	−4.70499	−0.259789
$329$	4.49146	0.247622
$330$	−3.13964	−0.172832
$331$	−12.6651	−0.696136	−0.348068	−	0.937469i	$-0.613162\pi$
$331$	−12.6651	−0.696136	−0.348068	+	0.937469i	$0.613162\pi$
$332$	4.70179	0.258044
$333$	17.8430	0.977788
$334$	3.34767	0.183176
$335$	29.3212	1.60199
$336$	−0.367997	−0.0200759
$337$	−34.2139	−1.86375	−0.931874	−	0.362782i	$-0.881827\pi$
$337$	−34.2139	−1.86375	−0.931874	+	0.362782i	$0.881827\pi$
$338$	24.5410	1.33486
$339$	0.958801	0.0520749
$340$	−22.0486	−1.19575
$341$	−29.9421	−1.62146
$342$	6.40794	0.346501
$343$	−18.9456	−1.02297
$344$	11.8740	0.640201
$345$	−0.423120	−0.0227800
$346$	14.2497	0.766067
$347$	−31.3904	−1.68512	−0.842561	−	0.538601i	$-0.818953\pi$
$347$	−31.3904	−1.68512	−0.842561	+	0.538601i	$0.818953\pi$
$348$	1.23399	0.0661490
$349$	19.3835	1.03758	0.518788	−	0.854903i	$-0.326383\pi$
$349$	19.3835	1.03758	0.518788	+	0.854903i	$0.326383\pi$
$350$	−11.3431	−0.606316
$351$	0.642910	0.0343160
$352$	46.6715	2.48760
$353$	31.2602	1.66381	0.831907	−	0.554914i	$-0.187249\pi$
$353$	31.2602	1.66381	0.831907	+	0.554914i	$0.187249\pi$
$354$	0.142025	0.00754853
$355$	−22.6410	−1.20166
$356$	30.5204	1.61758
$357$	−0.443522	−0.0234736
$358$	−13.0439	−0.689393
$359$	−10.0254	−0.529121	−0.264561	−	0.964369i	$-0.585227\pi$
$359$	−10.0254	−0.529121	−0.264561	+	0.964369i	$0.585227\pi$
$360$	10.6703	0.562375
$361$	1.00000	0.0526316
$362$	−11.1468	−0.585862
$363$	2.11962	0.111251
$364$	−5.48829	−0.287665
$365$	34.7215	1.81741
$366$	1.19064	0.0622360
$367$	−31.5620	−1.64752	−0.823761	−	0.566937i	$-0.808128\pi$
$367$	−31.5620	−1.64752	−0.823761	+	0.566937i	$0.808128\pi$
$368$	4.27694	0.222951
$369$	−11.2353	−0.584888
$370$	36.3279	1.88860
$371$	14.6592	0.761070
$372$	−1.12326	−0.0582381
$373$	−3.96566	−0.205334	−0.102667	−	0.994716i	$-0.532738\pi$
$373$	−3.96566	−0.205334	−0.102667	+	0.994716i	$0.532738\pi$
$374$	38.2489	1.97780
$375$	−0.468518	−0.0241941
$376$	−3.28941	−0.169638
$377$	−6.84838	−0.352709
$378$	1.89869	0.0976578
$379$	−5.65098	−0.290271	−0.145136	−	0.989412i	$-0.546362\pi$
$379$	−5.65098	−0.290271	−0.145136	+	0.989412i	$0.546362\pi$
$380$	7.35579	0.377344
$381$	1.29677	0.0664357
$382$	20.5814	1.05303
$383$	−34.3137	−1.75335	−0.876675	−	0.481083i	$-0.840244\pi$
$383$	−34.3137	−1.75335	−0.876675	+	0.481083i	$0.840244\pi$
$384$	0.829812	0.0423462
$385$	29.0132	1.47865
$386$	0.700502	0.0356546
$387$	28.3546	1.44134
$388$	6.24902	0.317246
$389$	−17.8159	−0.903300	−0.451650	−	0.892195i	$-0.649164\pi$
$389$	−17.8159	−0.903300	−0.451650	+	0.892195i	$0.649164\pi$
$390$	0.653659	0.0330993
$391$	5.15470	0.260684
$392$	5.10301	0.257741
$393$	1.76743	0.0891552
$394$	−12.4000	−0.624705
$395$	46.1920	2.32417
$396$	−46.1024	−2.31673
$397$	−6.07738	−0.305015	−0.152508	−	0.988302i	$-0.548735\pi$
$397$	−6.07738	−0.305015	−0.152508	+	0.988302i	$0.548735\pi$
$398$	−20.2425	−1.01467
$399$	0.147966	0.00740758
$400$	−7.69936	−0.384968
$401$	−0.431948	−0.0215704	−0.0107852	−	0.999942i	$-0.503433\pi$
$401$	−0.431948	−0.0215704	−0.0107852	+	0.999942i	$0.503433\pi$
$402$	−1.90816	−0.0951705
$403$	6.23381	0.310528
$404$	−25.7465	−1.28094
$405$	25.4165	1.26295
$406$	−20.2251	−1.00375
$407$	−35.5317	−1.76124
$408$	0.324822	0.0160811
$409$	−20.2128	−0.999460	−0.499730	−	0.866181i	$-0.666567\pi$
$409$	−20.2128	−0.999460	−0.499730	+	0.866181i	$0.666567\pi$
$410$	−22.8749	−1.12971
$411$	1.38334	0.0682351
$412$	41.4790	2.04353
$413$	−1.31244	−0.0645811
$414$	−11.0197	−0.541588
$415$	5.17480	0.254021
$416$	−9.71679	−0.476405
$417$	−0.0281477	−0.00137840
$418$	−12.7605	−0.624136
$419$	−23.2107	−1.13392	−0.566959	−	0.823746i	$-0.691880\pi$
$419$	−23.2107	−1.13392	−0.566959	+	0.823746i	$0.691880\pi$
$420$	1.08841	0.0531089
$421$	−11.0949	−0.540732	−0.270366	−	0.962758i	$-0.587145\pi$
$421$	−11.0949	−0.540732	−0.270366	+	0.962758i	$0.587145\pi$
$422$	−44.6281	−2.17246
$423$	−7.85499	−0.381923
$424$	−10.7360	−0.521385
$425$	−9.27950	−0.450122
$426$	1.47343	0.0713879
$427$	−11.0027	−0.532457
$428$	42.7075	2.06434
$429$	−0.639333	−0.0308673
$430$	57.7293	2.78395
$431$	−26.5558	−1.27915	−0.639573	−	0.768730i	$-0.720889\pi$
$431$	−26.5558	−1.27915	−0.639573	+	0.768730i	$0.720889\pi$
$432$	1.28877	0.0620059
$433$	5.18687	0.249265	0.124633	−	0.992203i	$-0.460225\pi$
$433$	5.18687	0.249265	0.124633	+	0.992203i	$0.460225\pi$
$434$	18.4101	0.883714
$435$	1.35813	0.0651176
$436$	−36.7801	−1.76145
$437$	−1.71969	−0.0822641
$438$	−2.25961	−0.107968
$439$	−12.5693	−0.599900	−0.299950	−	0.953955i	$-0.596970\pi$
$439$	−12.5693	−0.599900	−0.299950	+	0.953955i	$0.596970\pi$
$440$	−21.2484	−1.01298
$441$	12.1858	0.580276
$442$	−7.96325	−0.378773
$443$	10.8162	0.513891	0.256946	−	0.966426i	$-0.417284\pi$
$443$	10.8162	0.513891	0.256946	+	0.966426i	$0.417284\pi$
$444$	−1.33294	−0.0632588
$445$	33.5908	1.59236
$446$	−46.7559	−2.21396
$447$	−0.364556	−0.0172429
$448$	−20.1851	−0.953655
$449$	34.5655	1.63125	0.815623	−	0.578584i	$-0.196395\pi$
$449$	34.5655	1.63125	0.815623	+	0.578584i	$0.196395\pi$
$450$	19.8377	0.935157
$451$	22.3736	1.05353
$452$	28.6646	1.34827
$453$	1.42878	0.0671299
$454$	−19.3198	−0.906723
$455$	−6.04042	−0.283179
$456$	−0.108366	−0.00507470
$457$	18.0536	0.844510	0.422255	−	0.906477i	$-0.361239\pi$
$457$	18.0536	0.844510	0.422255	+	0.906477i	$0.361239\pi$
$458$	−26.1557	−1.22217
$459$	1.55326	0.0725001
$460$	−12.6497	−0.589796
$461$	17.8394	0.830862	0.415431	−	0.909625i	$-0.363631\pi$
$461$	17.8394	0.830862	0.415431	+	0.909625i	$0.363631\pi$
$462$	−1.88812	−0.0878433
$463$	15.1848	0.705696	0.352848	−	0.935681i	$-0.385213\pi$
$463$	15.1848	0.705696	0.352848	+	0.935681i	$0.385213\pi$
$464$	−13.7281	−0.637313
$465$	−1.23626	−0.0573301
$466$	−10.6664	−0.494109
$467$	35.1455	1.62634	0.813170	−	0.582026i	$-0.197740\pi$
$467$	35.1455	1.62634	0.813170	+	0.582026i	$0.197740\pi$
$468$	9.59831	0.443682
$469$	17.6332	0.814226
$470$	−15.9926	−0.737683
$471$	−0.925959	−0.0426659
$472$	0.961192	0.0442425
$473$	−56.4641	−2.59622
$474$	−3.00608	−0.138074
$475$	3.09580	0.142045
$476$	−13.2596	−0.607754
$477$	−25.6371	−1.17384
$478$	−32.2451	−1.47485
$479$	39.0759	1.78542	0.892712	−	0.450628i	$-0.148800\pi$
$479$	39.0759	1.78542	0.892712	+	0.450628i	$0.148800\pi$
$480$	1.92698	0.0879544
$481$	7.39754	0.337299
$482$	40.0124	1.82252
$483$	−0.254457	−0.0115782
$484$	63.3688	2.88040
$485$	6.87768	0.312299
$486$	−4.98290	−0.226029
$487$	35.3329	1.60109	0.800543	−	0.599276i	$-0.204545\pi$
$487$	35.3329	1.60109	0.800543	+	0.599276i	$0.204545\pi$
$488$	8.05802	0.364769
$489$	0.563675	0.0254902
$490$	24.8100	1.12080
$491$	35.5375	1.60379	0.801893	−	0.597468i	$-0.203826\pi$
$491$	35.5375	1.60379	0.801893	+	0.597468i	$0.203826\pi$
$492$	0.839327	0.0378398
$493$	−16.5456	−0.745176
$494$	2.65667	0.119529
$495$	−50.7404	−2.28061
$496$	12.4962	0.561096
$497$	−13.6159	−0.610755
$498$	−0.336765	−0.0150908
$499$	−35.1585	−1.57391	−0.786955	−	0.617010i	$-0.788344\pi$
$499$	−35.1585	−1.57391	−0.786955	+	0.617010i	$0.788344\pi$
$500$	−14.0069	−0.626409
$501$	−0.135190	−0.00603984
$502$	41.1754	1.83775
$503$	−23.1326	−1.03143	−0.515717	−	0.856759i	$-0.672474\pi$
$503$	−23.1326	−1.03143	−0.515717	+	0.856759i	$0.672474\pi$
$504$	6.41692	0.285832
$505$	−28.3366	−1.26096
$506$	21.9441	0.975535
$507$	−0.991049	−0.0440140
$508$	38.7687	1.72008
$509$	18.4922	0.819653	0.409826	−	0.912164i	$-0.365589\pi$
$509$	18.4922	0.819653	0.409826	+	0.912164i	$0.365589\pi$
$510$	1.57923	0.0699295
$511$	20.8809	0.923716
$512$	−25.7115	−1.13630
$513$	−0.518194	−0.0228788
$514$	34.5976	1.52603
$515$	45.6519	2.01166
$516$	−2.11821	−0.0932488
$517$	15.6421	0.687938
$518$	21.8469	0.959898
$519$	−0.575449	−0.0252594
$520$	4.42382	0.193997
$521$	−13.0894	−0.573458	−0.286729	−	0.958012i	$-0.592568\pi$
$521$	−13.0894	−0.573458	−0.286729	+	0.958012i	$0.592568\pi$
$522$	35.3711	1.54815
$523$	33.4938	1.46458	0.732290	−	0.680993i	$-0.238451\pi$
$523$	33.4938	1.46458	0.732290	+	0.680993i	$0.238451\pi$
$524$	52.8396	2.30831
$525$	0.458073	0.0199920
$526$	−9.35210	−0.407771
$527$	15.0608	0.656059
$528$	−1.28160	−0.0557743
$529$	−20.0427	−0.871420
$530$	−52.1966	−2.26728
$531$	2.29529	0.0996072
$532$	4.42364	0.191789
$533$	−4.65807	−0.201764
$534$	−2.18602	−0.0945985
$535$	47.0039	2.03216
$536$	−12.9140	−0.557801
$537$	0.526757	0.0227312
$538$	19.1451	0.825403
$539$	−24.2662	−1.04522
$540$	−3.81173	−0.164031
$541$	7.04582	0.302924	0.151462	−	0.988463i	$-0.451602\pi$
$541$	7.04582	0.302924	0.151462	+	0.988463i	$0.451602\pi$
$542$	1.92523	0.0826958
$543$	0.450144	0.0193175
$544$	−23.4756	−1.00651
$545$	−40.4802	−1.73398
$546$	0.393098	0.0168230
$547$	25.5253	1.09138	0.545691	−	0.837986i	$-0.316267\pi$
$547$	25.5253	1.09138	0.545691	+	0.837986i	$0.316267\pi$
$548$	41.3567	1.76667
$549$	19.2422	0.821239
$550$	−39.5039	−1.68445
$551$	5.51988	0.235155
$552$	0.186356	0.00793185
$553$	27.7790	1.18128
$554$	41.3869	1.75836
$555$	−1.46704	−0.0622724
$556$	−0.841511	−0.0356880
$557$	−19.6101	−0.830908	−0.415454	−	0.909614i	$-0.636377\pi$
$557$	−19.6101	−0.830908	−0.415454	+	0.909614i	$0.636377\pi$
$558$	−32.1969	−1.36300
$559$	11.7556	0.497207
$560$	−12.1085	−0.511679
$561$	−1.54462	−0.0652139
$562$	−55.9363	−2.35953
$563$	−3.01103	−0.126900	−0.0634499	−	0.997985i	$-0.520210\pi$
$563$	−3.01103	−0.126900	−0.0634499	+	0.997985i	$0.520210\pi$
$564$	0.586801	0.0247088
$565$	31.5483	1.32725
$566$	−30.0498	−1.26309
$567$	15.2850	0.641909
$568$	9.97184	0.418409
$569$	42.1399	1.76660	0.883298	−	0.468812i	$-0.155318\pi$
$569$	42.1399	1.76660	0.883298	+	0.468812i	$0.155318\pi$
$570$	−0.526858	−0.0220676
$571$	37.4875	1.56880	0.784402	−	0.620253i	$-0.212970\pi$
$571$	37.4875	1.56880	0.784402	+	0.620253i	$0.212970\pi$
$572$	−19.1137	−0.799182
$573$	−0.831144	−0.0347216
$574$	−13.7565	−0.574187
$575$	−5.32382	−0.222019
$576$	35.3011	1.47088
$577$	7.85013	0.326805	0.163403	−	0.986559i	$-0.447753\pi$
$577$	7.85013	0.326805	0.163403	+	0.986559i	$0.447753\pi$
$578$	17.1633	0.713898
$579$	−0.0282886	−0.00117563
$580$	40.6031	1.68595
$581$	3.11203	0.129109
$582$	−0.447585	−0.0185530
$583$	51.0527	2.11439
$584$	−15.2925	−0.632809
$585$	10.5639	0.436764
$586$	−27.1950	−1.12342
$587$	−7.71527	−0.318443	−0.159222	−	0.987243i	$-0.550898\pi$
$587$	−7.71527	−0.318443	−0.159222	+	0.987243i	$0.550898\pi$
$588$	−0.910330	−0.0375414
$589$	−5.02454	−0.207032
$590$	4.67316	0.192391
$591$	0.500755	0.0205983
$592$	14.8290	0.609467
$593$	9.14412	0.375504	0.187752	−	0.982216i	$-0.439880\pi$
$593$	9.14412	0.375504	0.187752	+	0.982216i	$0.439880\pi$
$594$	6.61241	0.271310
$595$	−14.5936	−0.598278
$596$	−10.8989	−0.446435
$597$	0.817460	0.0334564
$598$	−4.56867	−0.186827
$599$	−34.0705	−1.39208	−0.696042	−	0.718001i	$-0.745057\pi$
$599$	−34.0705	−1.39208	−0.696042	+	0.718001i	$0.745057\pi$
$600$	−0.335479	−0.0136959
$601$	−15.7137	−0.640974	−0.320487	−	0.947253i	$-0.603847\pi$
$601$	−15.7137	−0.640974	−0.320487	+	0.947253i	$0.603847\pi$
$602$	34.7173	1.41497
$603$	−30.8382	−1.25583
$604$	42.7151	1.73805
$605$	69.7437	2.83549
$606$	1.84409	0.0749110
$607$	44.0977	1.78987	0.894936	−	0.446195i	$-0.147221\pi$
$607$	44.0977	1.78987	0.894936	+	0.446195i	$0.147221\pi$
$608$	7.83187	0.317624
$609$	0.816756	0.0330966
$610$	39.1768	1.58622
$611$	−3.25661	−0.131748
$612$	23.1894	0.937375
$613$	−17.7598	−0.717310	−0.358655	−	0.933470i	$-0.616764\pi$
$613$	−17.7598	−0.717310	−0.358655	+	0.933470i	$0.616764\pi$
$614$	48.5364	1.95877
$615$	0.923765	0.0372498
$616$	−12.7784	−0.514856
$617$	21.8248	0.878634	0.439317	−	0.898332i	$-0.355221\pi$
$617$	21.8248	0.878634	0.439317	+	0.898332i	$0.355221\pi$
$618$	−2.97093	−0.119508
$619$	32.5816	1.30956	0.654782	−	0.755818i	$-0.272760\pi$
$619$	32.5816	1.30956	0.654782	+	0.755818i	$0.272760\pi$
$620$	−36.9595	−1.48433
$621$	0.891136	0.0357600
$622$	52.6549	2.11127
$623$	20.2009	0.809332
$624$	0.266823	0.0106815
$625$	−30.8950	−1.23580
$626$	−24.9479	−0.997121
$627$	0.515311	0.0205795
$628$	−27.6827	−1.10466
$629$	17.8723	0.712617
$630$	31.1981	1.24296
$631$	3.40831	0.135683	0.0678413	−	0.997696i	$-0.478389\pi$
$631$	3.40831	0.135683	0.0678413	+	0.997696i	$0.478389\pi$
$632$	−20.3445	−0.809260
$633$	1.80223	0.0716322
$634$	2.14132	0.0850425
$635$	42.6688	1.69326
$636$	1.91520	0.0759427
$637$	5.05212	0.200172
$638$	−70.4364	−2.78860
$639$	23.8124	0.942004
$640$	27.3040	1.07929
$641$	14.8625	0.587035	0.293518	−	0.955954i	$-0.405174\pi$
$641$	14.8625	0.587035	0.293518	+	0.955954i	$0.405174\pi$
$642$	−3.05892	−0.120726
$643$	5.16933	0.203858	0.101929	−	0.994792i	$-0.467498\pi$
$643$	5.16933	0.203858	0.101929	+	0.994792i	$0.467498\pi$
$644$	−7.60730	−0.299770
$645$	−2.33130	−0.0917949
$646$	6.41849	0.252532
$647$	−44.3143	−1.74218	−0.871088	−	0.491128i	$-0.836585\pi$
$647$	−44.3143	−1.74218	−0.871088	+	0.491128i	$0.836585\pi$
$648$	−11.1943	−0.439752
$649$	−4.57074	−0.179417
$650$	8.22453	0.322592
$651$	−0.743462	−0.0291386
$652$	16.8518	0.659966
$653$	−15.4734	−0.605519	−0.302760	−	0.953067i	$-0.597908\pi$
$653$	−15.4734	−0.605519	−0.302760	+	0.953067i	$0.597908\pi$
$654$	2.63437	0.103012
$655$	58.1553	2.27232
$656$	−9.33750	−0.364568
$657$	−36.5180	−1.42470
$658$	−9.61764	−0.374935
$659$	−23.4548	−0.913669	−0.456835	−	0.889552i	$-0.651017\pi$
$659$	−23.4548	−0.913669	−0.456835	+	0.889552i	$0.651017\pi$
$660$	3.79052	0.147546
$661$	−20.9375	−0.814373	−0.407186	−	0.913345i	$-0.633490\pi$
$661$	−20.9375	−0.814373	−0.407186	+	0.913345i	$0.633490\pi$
$662$	27.1200	1.05405
$663$	0.321583	0.0124892
$664$	−2.27915	−0.0884483
$665$	4.86866	0.188799
$666$	−38.2074	−1.48051
$667$	−9.49251	−0.367552
$668$	−4.04167	−0.156377
$669$	1.88816	0.0730004
$670$	−62.7859	−2.42563
$671$	−38.3182	−1.47926
$672$	1.15885	0.0447037
$673$	19.3423	0.745591	0.372795	−	0.927914i	$-0.378399\pi$
$673$	19.3423	0.745591	0.372795	+	0.927914i	$0.378399\pi$
$674$	73.2627	2.82197
$675$	−1.60422	−0.0617466
$676$	−29.6287	−1.13956
$677$	−16.9484	−0.651379	−0.325690	−	0.945477i	$-0.605596\pi$
$677$	−16.9484	−0.651379	−0.325690	+	0.945477i	$0.605596\pi$
$678$	−2.05310	−0.0788487
$679$	4.13611	0.158729
$680$	10.6879	0.409862
$681$	0.780198	0.0298973
$682$	64.1155	2.45511
$683$	12.1822	0.466139	0.233069	−	0.972460i	$-0.425123\pi$
$683$	12.1822	0.466139	0.233069	+	0.972460i	$0.425123\pi$
$684$	−7.73637	−0.295807
$685$	45.5172	1.73912
$686$	40.5686	1.54891
$687$	1.05625	0.0402986
$688$	23.5650	0.898407
$689$	−10.6289	−0.404930
$690$	0.906034	0.0344921
$691$	45.4323	1.72833	0.864163	−	0.503212i	$-0.167848\pi$
$691$	45.4323	1.72833	0.864163	+	0.503212i	$0.167848\pi$
$692$	−17.2038	−0.653989
$693$	−30.5143	−1.15914
$694$	67.2167	2.55151
$695$	−0.926168	−0.0351316
$696$	−0.598167	−0.0226735
$697$	−11.2538	−0.426269
$698$	−41.5062	−1.57103
$699$	0.430743	0.0162922
$700$	13.6947	0.517610
$701$	13.6710	0.516348	0.258174	−	0.966098i	$-0.416879\pi$
$701$	13.6710	0.516348	0.258174	+	0.966098i	$0.416879\pi$
$702$	−1.37667	−0.0519592
$703$	−5.96251	−0.224880
$704$	−70.2970	−2.64942
$705$	0.645834	0.0243235
$706$	−66.9381	−2.51925
$707$	−17.0411	−0.640897
$708$	−0.171468	−0.00644416
$709$	10.1854	0.382520	0.191260	−	0.981539i	$-0.438743\pi$
$709$	10.1854	0.382520	0.191260	+	0.981539i	$0.438743\pi$
$710$	48.4815	1.81948
$711$	−48.5819	−1.82196
$712$	−14.7945	−0.554448
$713$	8.64067	0.323596
$714$	0.949720	0.0355424
$715$	−21.0365	−0.786721
$716$	15.7481	0.588533
$717$	1.30216	0.0486302
$718$	21.4676	0.801163
$719$	−16.7230	−0.623665	−0.311832	−	0.950137i	$-0.600943\pi$
$719$	−16.7230	−0.623665	−0.311832	+	0.950137i	$0.600943\pi$
$720$	21.1763	0.789192
$721$	27.4542	1.02245
$722$	−2.14132	−0.0796915
$723$	−1.61584	−0.0600936
$724$	13.4576	0.500149
$725$	17.0884	0.634649
$726$	−4.53878	−0.168450
$727$	−0.528715	−0.0196090	−0.00980449	−	0.999952i	$-0.503121\pi$
$727$	−0.528715	−0.0196090	−0.00980449	+	0.999952i	$0.503121\pi$
$728$	2.66040	0.0986010
$729$	−26.5970	−0.985076
$730$	−74.3498	−2.75181
$731$	28.4013	1.05046
$732$	−1.43748	−0.0531307
$733$	32.2537	1.19132	0.595659	−	0.803238i	$-0.296891\pi$
$733$	32.2537	1.19132	0.595659	+	0.803238i	$0.296891\pi$
$734$	67.5842	2.49458
$735$	−1.00191	−0.0369560
$736$	−13.4684	−0.496452
$737$	61.4099	2.26206
$738$	24.0584	0.885602
$739$	−45.9161	−1.68905	−0.844525	−	0.535516i	$-0.820117\pi$
$739$	−45.9161	−1.68905	−0.844525	+	0.535516i	$0.820117\pi$
$740$	−43.8590	−1.61229
$741$	−0.107285	−0.00394123
$742$	−31.3901	−1.15237
$743$	3.27720	0.120229	0.0601144	−	0.998191i	$-0.480853\pi$
$743$	3.27720	0.120229	0.0601144	+	0.998191i	$0.480853\pi$
$744$	0.544489	0.0199619
$745$	−11.9953	−0.439474
$746$	8.49172	0.310904
$747$	−5.44253	−0.199132
$748$	−46.1783	−1.68845
$749$	28.2673	1.03286
$750$	1.00324	0.0366333
$751$	−41.4708	−1.51329	−0.756645	−	0.653826i	$-0.773163\pi$
$751$	−41.4708	−1.51329	−0.756645	+	0.653826i	$0.773163\pi$
$752$	−6.52815	−0.238057
$753$	−1.66280	−0.0605958
$754$	14.6645	0.534051
$755$	47.0124	1.71095
$756$	−2.29230	−0.0833703
$757$	11.5725	0.420608	0.210304	−	0.977636i	$-0.432555\pi$
$757$	11.5725	0.420608	0.210304	+	0.977636i	$0.432555\pi$
$758$	12.1005	0.439511
$759$	−0.886177	−0.0321662
$760$	−3.56566	−0.129340
$761$	−49.0866	−1.77939	−0.889694	−	0.456558i	$-0.849082\pi$
$761$	−49.0866	−1.77939	−0.889694	+	0.456558i	$0.849082\pi$
$762$	−2.77680	−0.100593
$763$	−24.3440	−0.881313
$764$	−24.8481	−0.898973
$765$	25.5223	0.922760
$766$	73.4766	2.65482
$767$	0.951608	0.0343606
$768$	0.263267	0.00949981
$769$	19.9555	0.719615	0.359808	−	0.933027i	$-0.382842\pi$
$769$	19.9555	0.719615	0.359808	+	0.933027i	$0.382842\pi$
$770$	−62.1265	−2.23888
$771$	−1.39716	−0.0503177
$772$	−0.845723	−0.0304382
$773$	3.72006	0.133801	0.0669006	−	0.997760i	$-0.478689\pi$
$773$	3.72006	0.133801	0.0669006	+	0.997760i	$0.478689\pi$
$774$	−60.7161	−2.18239
$775$	−15.5549	−0.558750
$776$	−3.02916	−0.108740
$777$	−0.882251	−0.0316506
$778$	38.1494	1.36772
$779$	3.75447	0.134518
$780$	−0.789169	−0.0282568
$781$	−47.4190	−1.69678
$782$	−11.0378	−0.394712
$783$	−2.86037	−0.102221
$784$	10.1274	0.361693
$785$	−30.4676	−1.08744
$786$	−3.78463	−0.134993
$787$	3.47897	0.124012	0.0620060	−	0.998076i	$-0.480250\pi$
$787$	3.47897	0.124012	0.0620060	+	0.998076i	$0.480250\pi$
$788$	14.9707	0.533309
$789$	0.377669	0.0134454
$790$	−98.9116	−3.51912
$791$	18.9725	0.674586
$792$	22.3477	0.794092
$793$	7.97767	0.283295
$794$	13.0136	0.461835
$795$	2.10787	0.0747586
$796$	24.4390	0.866217
$797$	18.5455	0.656916	0.328458	−	0.944519i	$-0.393471\pi$
$797$	18.5455	0.656916	0.328458	+	0.944519i	$0.393471\pi$
$798$	−0.316842	−0.0112161
$799$	−7.86793	−0.278347
$800$	24.2459	0.857221
$801$	−35.3288	−1.24828
$802$	0.924937	0.0326607
$803$	72.7203	2.56624
$804$	2.30375	0.0812469
$805$	−8.37261	−0.295096
$806$	−13.3486	−0.470183
$807$	−0.773142	−0.0272159
$808$	12.4804	0.439058
$809$	−6.84483	−0.240651	−0.120326	−	0.992734i	$-0.538394\pi$
$809$	−6.84483	−0.240651	−0.120326	+	0.992734i	$0.538394\pi$
$810$	−54.4247	−1.91229
$811$	−42.0522	−1.47665	−0.738326	−	0.674444i	$-0.764384\pi$
$811$	−42.0522	−1.47665	−0.738326	+	0.674444i	$0.764384\pi$
$812$	24.4180	0.856902
$813$	−0.0777473	−0.00272672
$814$	76.0846	2.66676
$815$	18.5471	0.649676
$816$	0.644640	0.0225669
$817$	−9.47514	−0.331493
$818$	43.2820	1.51332
$819$	6.35294	0.221990
$820$	27.6171	0.964431
$821$	−37.3917	−1.30498	−0.652489	−	0.757798i	$-0.726275\pi$
$821$	−37.3917	−1.30498	−0.652489	+	0.757798i	$0.726275\pi$
$822$	−2.96217	−0.103317
$823$	0.675869	0.0235593	0.0117797	−	0.999931i	$-0.496250\pi$
$823$	0.675869	0.0235593	0.0117797	+	0.999931i	$0.496250\pi$
$824$	−20.1066	−0.700447
$825$	1.59530	0.0555412
$826$	2.81035	0.0977847
$827$	−13.4550	−0.467876	−0.233938	−	0.972252i	$-0.575161\pi$
$827$	−13.4550	−0.467876	−0.233938	+	0.972252i	$0.575161\pi$
$828$	13.3042	0.462352
$829$	38.9239	1.35188	0.675941	−	0.736956i	$-0.263737\pi$
$829$	38.9239	1.35188	0.675941	+	0.736956i	$0.263737\pi$
$830$	−11.0809	−0.384623
$831$	−1.67134	−0.0579782
$832$	14.6355	0.507395
$833$	12.2059	0.422908
$834$	0.0602731	0.00208709
$835$	−4.44827	−0.153939
$836$	15.4059	0.532823
$837$	2.60369	0.0899966
$838$	49.7014	1.71691
$839$	−10.7508	−0.371159	−0.185580	−	0.982629i	$-0.559416\pi$
$839$	−10.7508	−0.371159	−0.185580	+	0.982629i	$0.559416\pi$
$840$	−0.527597	−0.0182038
$841$	1.46912	0.0506594
$842$	23.7577	0.818744
$843$	2.25889	0.0778004
$844$	53.8799	1.85462
$845$	−32.6093	−1.12180
$846$	16.8200	0.578284
$847$	41.9426	1.44116
$848$	−21.3066	−0.731671
$849$	1.21351	0.0416476
$850$	19.8703	0.681547
$851$	10.2537	0.351492
$852$	−1.77889	−0.0609437
$853$	24.7350	0.846909	0.423454	−	0.905917i	$-0.360817\pi$
$853$	24.7350	0.846909	0.423454	+	0.905917i	$0.360817\pi$
$854$	23.5602	0.806213
$855$	−8.51466	−0.291195
$856$	−20.7021	−0.707583
$857$	−49.4612	−1.68956	−0.844782	−	0.535111i	$-0.820270\pi$
$857$	−49.4612	−1.68956	−0.844782	+	0.535111i	$0.820270\pi$
$858$	1.36901	0.0467374
$859$	6.35326	0.216770	0.108385	−	0.994109i	$-0.465432\pi$
$859$	6.35326	0.216770	0.108385	+	0.994109i	$0.465432\pi$
$860$	−69.6972	−2.37665
$861$	0.555535	0.0189326
$862$	56.8643	1.93680
$863$	−7.62833	−0.259671	−0.129836	−	0.991536i	$-0.541445\pi$
$863$	−7.62833	−0.259671	−0.129836	+	0.991536i	$0.541445\pi$
$864$	−4.05843	−0.138071
$865$	−18.9345	−0.643792
$866$	−11.1067	−0.377422
$867$	−0.693110	−0.0235392
$868$	−22.2267	−0.754424
$869$	96.7438	3.28181
$870$	−2.90819	−0.0985970
$871$	−12.7853	−0.433212
$872$	17.8288	0.603760
$873$	−7.23352	−0.244818
$874$	3.68241	0.124559
$875$	−9.27092	−0.313414
$876$	2.72805	0.0921721
$877$	4.47552	0.151127	0.0755637	−	0.997141i	$-0.475924\pi$
$877$	4.47552	0.151127	0.0755637	+	0.997141i	$0.475924\pi$
$878$	26.9148	0.908332
$879$	1.09823	0.0370423
$880$	−42.1695	−1.42153
$881$	−25.4393	−0.857071	−0.428536	−	0.903525i	$-0.640970\pi$
$881$	−25.4393	−0.857071	−0.428536	+	0.903525i	$0.640970\pi$
$882$	−26.0936	−0.878618
$883$	−3.69416	−0.124319	−0.0621593	−	0.998066i	$-0.519799\pi$
$883$	−3.69416	−0.124319	−0.0621593	+	0.998066i	$0.519799\pi$
$884$	9.61412	0.323358
$885$	−0.188718	−0.00634369
$886$	−23.1608	−0.778103
$887$	−44.2832	−1.48688	−0.743442	−	0.668801i	$-0.766808\pi$
$887$	−44.2832	−1.48688	−0.743442	+	0.668801i	$0.766808\pi$
$888$	0.646133	0.0216828
$889$	25.6602	0.860617
$890$	−71.9286	−2.41105
$891$	53.2319	1.78334
$892$	56.4489	1.89005
$893$	2.62487	0.0878380
$894$	0.780630	0.0261082
$895$	17.3323	0.579356
$896$	16.4201	0.548558
$897$	0.184498	0.00616021
$898$	−74.0156	−2.46993
$899$	−27.7349	−0.925010
$900$	−23.9502	−0.798341
$901$	−25.6793	−0.855503
$902$	−47.9088	−1.59519
$903$	−1.40200	−0.0466557
$904$	−13.8949	−0.462138
$905$	14.8115	0.492350
$906$	−3.05947	−0.101644
$907$	3.82325	0.126949	0.0634744	−	0.997983i	$-0.479782\pi$
$907$	3.82325	0.126949	0.0634744	+	0.997983i	$0.479782\pi$
$908$	23.3250	0.774067
$909$	29.8027	0.988493
$910$	12.9344	0.428773
$911$	26.7355	0.885787	0.442893	−	0.896574i	$-0.353952\pi$
$911$	26.7355	0.885787	0.442893	+	0.896574i	$0.353952\pi$
$912$	−0.215063	−0.00712143
$913$	10.8380	0.358686
$914$	−38.6584	−1.27871
$915$	−1.58209	−0.0523023
$916$	31.5780	1.04337
$917$	34.9735	1.15493
$918$	−3.32602	−0.109775
$919$	41.6453	1.37375	0.686876	−	0.726775i	$-0.258982\pi$
$919$	41.6453	1.37375	0.686876	+	0.726775i	$0.258982\pi$
$920$	6.13184	0.202161
$921$	−1.96006	−0.0645863
$922$	−38.1997	−1.25804
$923$	9.87241	0.324954
$924$	2.27955	0.0749916
$925$	−18.4587	−0.606919
$926$	−32.5154	−1.06852
$927$	−48.0138	−1.57698
$928$	43.2310	1.41913
$929$	20.8723	0.684797	0.342398	−	0.939555i	$-0.388761\pi$
$929$	20.8723	0.684797	0.342398	+	0.939555i	$0.388761\pi$
$930$	2.64722	0.0868057
$931$	−4.07208	−0.133457
$932$	12.8776	0.421820
$933$	−2.12638	−0.0696146
$934$	−75.2576	−2.46251
$935$	−50.8239	−1.66212
$936$	−4.65270	−0.152078
$937$	−38.1022	−1.24475	−0.622373	−	0.782721i	$-0.713831\pi$
$937$	−38.1022	−1.24475	−0.622373	+	0.782721i	$0.713831\pi$
$938$	−37.7583	−1.23285
$939$	1.00748	0.0328779
$940$	19.3080	0.629758
$941$	−20.9477	−0.682875	−0.341438	−	0.939904i	$-0.610914\pi$
$941$	−20.9477	−0.682875	−0.341438	+	0.939904i	$0.610914\pi$
$942$	1.98277	0.0646022
$943$	−6.45654	−0.210254
$944$	1.90758	0.0620864
$945$	−2.52291	−0.0820703
$946$	120.907	3.93104
$947$	−0.478072	−0.0155353	−0.00776763	−	0.999970i	$-0.502473\pi$
$947$	−0.478072	−0.0155353	−0.00776763	+	0.999970i	$0.502473\pi$
$948$	3.62927	0.117873
$949$	−15.1400	−0.491466
$950$	−6.62908	−0.215076
$951$	−0.0864735	−0.00280409
$952$	6.42749	0.208316
$953$	−19.8647	−0.643480	−0.321740	−	0.946828i	$-0.604268\pi$
$953$	−19.8647	−0.643480	−0.321740	+	0.946828i	$0.604268\pi$
$954$	54.8972	1.77736
$955$	−27.3479	−0.884956
$956$	38.9298	1.25908
$957$	2.84446	0.0919482
$958$	−83.6738	−2.70338
$959$	27.3732	0.883927
$960$	−2.90244	−0.0936759
$961$	−5.75402	−0.185614
$962$	−15.8405	−0.510717
$963$	−49.4358	−1.59305
$964$	−48.3074	−1.55588
$965$	−0.930804	−0.0299636
$966$	0.544872	0.0175310
$967$	43.7547	1.40706	0.703528	−	0.710668i	$-0.251607\pi$
$967$	43.7547	1.40706	0.703528	+	0.710668i	$0.251607\pi$
$968$	−30.7175	−0.987296
$969$	−0.259200	−0.00832670
$970$	−14.7273	−0.472865
$971$	34.3621	1.10273	0.551366	−	0.834263i	$-0.314107\pi$
$971$	34.3621	1.10273	0.551366	+	0.834263i	$0.314107\pi$
$972$	6.01591	0.192961
$973$	−0.556980	−0.0178560
$974$	−75.6588	−2.42427
$975$	−0.332134	−0.0106368
$976$	15.9919	0.511889
$977$	16.1975	0.518205	0.259103	−	0.965850i	$-0.416573\pi$
$977$	16.1975	0.518205	0.259103	+	0.965850i	$0.416573\pi$
$978$	−1.20701	−0.0385958
$979$	70.3522	2.24847
$980$	−29.9534	−0.956826
$981$	42.5746	1.35930
$982$	−76.0971	−2.42836
$983$	−45.6456	−1.45587	−0.727935	−	0.685646i	$-0.759520\pi$
$983$	−45.6456	−1.45587	−0.727935	+	0.685646i	$0.759520\pi$
$984$	−0.406857	−0.0129701
$985$	16.4768	0.524993
$986$	35.4293	1.12830
$987$	0.388393	0.0123627
$988$	−3.20743	−0.102042
$989$	16.2943	0.518130
$990$	108.651	3.45316
$991$	−36.9644	−1.17421	−0.587107	−	0.809509i	$-0.699733\pi$
$991$	−36.9644	−1.17421	−0.587107	+	0.809509i	$0.699733\pi$
$992$	−39.3515	−1.24941
$993$	−1.09519	−0.0347549
$994$	29.1559	0.924768
$995$	26.8976	0.852711
$996$	0.406580	0.0128830
$997$	−24.0945	−0.763079	−0.381540	−	0.924352i	$-0.624606\pi$
$997$	−24.0945	−0.763079	−0.381540	+	0.924352i	$0.624606\pi$
$998$	75.2854	2.38312
$999$	3.08974	0.0977551

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	6023.2.a.c.1.20	✓	138

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
6023.2.a.c.1.20	✓	138	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:	\( N \)	\(=\)	\( 6023 = 19 \cdot 317 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	6023.a (trivial)

\(f(q)\)	\(=\)	\(q-2.14132 q^{2} +0.0864735 q^{3} +2.58523 q^{4} +2.84531 q^{5} -0.185167 q^{6} +1.71112 q^{7} -1.25317 q^{8} -2.99252 q^{9} +O(q^{10})\)	\(q-2.14132 q^{2} +0.0864735 q^{3} +2.58523 q^{4} +2.84531 q^{5} -0.185167 q^{6} +1.71112 q^{7} -1.25317 q^{8} -2.99252 q^{9} -6.09271 q^{10} +5.95918 q^{11} +0.223554 q^{12} -1.24067 q^{13} -3.66404 q^{14} +0.246044 q^{15} -2.48704 q^{16} -2.99745 q^{17} +6.40794 q^{18} +1.00000 q^{19} +7.35579 q^{20} +0.147966 q^{21} -12.7605 q^{22} -1.71969 q^{23} -0.108366 q^{24} +3.09580 q^{25} +2.65667 q^{26} -0.518194 q^{27} +4.42364 q^{28} +5.51988 q^{29} -0.526858 q^{30} -5.02454 q^{31} +7.83187 q^{32} +0.515311 q^{33} +6.41849 q^{34} +4.86866 q^{35} -7.73637 q^{36} -5.96251 q^{37} -2.14132 q^{38} -0.107285 q^{39} -3.56566 q^{40} +3.75447 q^{41} -0.316842 q^{42} -9.47514 q^{43} +15.4059 q^{44} -8.51466 q^{45} +3.68241 q^{46} +2.62487 q^{47} -0.215063 q^{48} -4.07208 q^{49} -6.62908 q^{50} -0.259200 q^{51} -3.20743 q^{52} +8.56706 q^{53} +1.10962 q^{54} +16.9557 q^{55} -2.14432 q^{56} +0.0864735 q^{57} -11.8198 q^{58} -0.767009 q^{59} +0.636081 q^{60} -6.43011 q^{61} +10.7591 q^{62} -5.12056 q^{63} -11.7964 q^{64} -3.53010 q^{65} -1.10344 q^{66} +10.3051 q^{67} -7.74911 q^{68} -0.148708 q^{69} -10.4253 q^{70} -7.95730 q^{71} +3.75014 q^{72} +12.2031 q^{73} +12.7676 q^{74} +0.267704 q^{75} +2.58523 q^{76} +10.1969 q^{77} +0.229732 q^{78} +16.2344 q^{79} -7.07639 q^{80} +8.93276 q^{81} -8.03950 q^{82} +1.81871 q^{83} +0.382527 q^{84} -8.52868 q^{85} +20.2893 q^{86} +0.477324 q^{87} -7.46786 q^{88} +11.8057 q^{89} +18.2326 q^{90} -2.12294 q^{91} -4.44581 q^{92} -0.434489 q^{93} -5.62068 q^{94} +2.84531 q^{95} +0.677249 q^{96} +2.41720 q^{97} +8.71961 q^{98} -17.8330 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 138 q + 11 q^{2} + 29 q^{3} + 157 q^{4} + 12 q^{5} + 8 q^{6} + 18 q^{7} + 33 q^{8} + 171 q^{9}+O(q^{10}) \) 138 * q + 11 * q^2 + 29 * q^3 + 157 * q^4 + 12 * q^5 + 8 * q^6 + 18 * q^7 + 33 * q^8 + 171 * q^9	\( 138 q + 11 q^{2} + 29 q^{3} + 157 q^{4} + 12 q^{5} + 8 q^{6} + 18 q^{7} + 33 q^{8} + 171 q^{9} + 40 q^{10} + 4 q^{11} + 69 q^{12} + 72 q^{13} + 3 q^{14} + 30 q^{15} + 191 q^{16} + 31 q^{17} + 31 q^{18} + 138 q^{19} + 16 q^{20} + 16 q^{21} + 95 q^{22} + 34 q^{23} + 3 q^{24} + 244 q^{25} - 13 q^{26} + 107 q^{27} + 43 q^{28} + 30 q^{29} - 14 q^{30} + 60 q^{31} + 62 q^{32} + 77 q^{33} + 36 q^{34} + 2 q^{35} + 205 q^{36} + 142 q^{37} + 11 q^{38} + 20 q^{39} + 76 q^{40} + 46 q^{41} - 21 q^{42} + 69 q^{43} - 7 q^{44} + 30 q^{45} + 39 q^{46} + 8 q^{47} + 116 q^{48} + 236 q^{49} + 34 q^{51} + 165 q^{52} + 49 q^{53} + 6 q^{55} - 33 q^{56} + 29 q^{57} + 75 q^{58} + 8 q^{59} - 24 q^{60} + 38 q^{61} - 10 q^{62} + 2 q^{63} + 251 q^{64} + 72 q^{65} - 15 q^{66} + 158 q^{67} - 19 q^{68} + 33 q^{69} + 48 q^{70} + 23 q^{71} + 88 q^{72} + 134 q^{73} + 4 q^{74} + 118 q^{75} + 157 q^{76} + 13 q^{77} + 12 q^{78} + 78 q^{79} - 48 q^{80} + 254 q^{81} + 89 q^{82} - 27 q^{83} - 15 q^{84} + 37 q^{85} + 66 q^{86} + 43 q^{87} + 224 q^{88} + 26 q^{89} + 38 q^{90} + 108 q^{91} + 113 q^{92} + 83 q^{93} + 48 q^{94} + 12 q^{95} + 40 q^{96} + 254 q^{97} + 47 q^{98} + 11 q^{99}+O(q^{100}) \) 138 * q + 11 * q^2 + 29 * q^3 + 157 * q^4 + 12 * q^5 + 8 * q^6 + 18 * q^7 + 33 * q^8 + 171 * q^9 + 40 * q^10 + 4 * q^11 + 69 * q^12 + 72 * q^13 + 3 * q^14 + 30 * q^15 + 191 * q^16 + 31 * q^17 + 31 * q^18 + 138 * q^19 + 16 * q^20 + 16 * q^21 + 95 * q^22 + 34 * q^23 + 3 * q^24 + 244 * q^25 - 13 * q^26 + 107 * q^27 + 43 * q^28 + 30 * q^29 - 14 * q^30 + 60 * q^31 + 62 * q^32 + 77 * q^33 + 36 * q^34 + 2 * q^35 + 205 * q^36 + 142 * q^37 + 11 * q^38 + 20 * q^39 + 76 * q^40 + 46 * q^41 - 21 * q^42 + 69 * q^43 - 7 * q^44 + 30 * q^45 + 39 * q^46 + 8 * q^47 + 116 * q^48 + 236 * q^49 + 34 * q^51 + 165 * q^52 + 49 * q^53 + 6 * q^55 - 33 * q^56 + 29 * q^57 + 75 * q^58 + 8 * q^59 - 24 * q^60 + 38 * q^61 - 10 * q^62 + 2 * q^63 + 251 * q^64 + 72 * q^65 - 15 * q^66 + 158 * q^67 - 19 * q^68 + 33 * q^69 + 48 * q^70 + 23 * q^71 + 88 * q^72 + 134 * q^73 + 4 * q^74 + 118 * q^75 + 157 * q^76 + 13 * q^77 + 12 * q^78 + 78 * q^79 - 48 * q^80 + 254 * q^81 + 89 * q^82 - 27 * q^83 - 15 * q^84 + 37 * q^85 + 66 * q^86 + 43 * q^87 + 224 * q^88 + 26 * q^89 + 38 * q^90 + 108 * q^91 + 113 * q^92 + 83 * q^93 + 48 * q^94 + 12 * q^95 + 40 * q^96 + 254 * q^97 + 47 * q^98 + 11 * q^99

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