LMFDB - Embedded newform 6031.2.a.d.1.15

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [6031,2,Mod(1,6031)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(6031, 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("6031.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 6031 = 37 \cdot 163 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	6031.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:	$48.1577774590$
Analytic rank:	$0$
Dimension:	$133$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.15
Character	$\chi$	$=$	6031.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-2.29540 q^{2} +2.78712 q^{3} +3.26888 q^{4} -0.0528483 q^{5} -6.39757 q^{6} +2.45561 q^{7} -2.91258 q^{8} +4.76805 q^{9} +O(q^{10})$	\(q-2.29540 q^{2} +2.78712 q^{3} +3.26888 q^{4} -0.0528483 q^{5} -6.39757 q^{6} +2.45561 q^{7} -2.91258 q^{8} +4.76805 q^{9} +0.121308 q^{10} -1.34715 q^{11} +9.11075 q^{12} +1.39523 q^{13} -5.63662 q^{14} -0.147295 q^{15} +0.147796 q^{16} -2.12489 q^{17} -10.9446 q^{18} -2.17110 q^{19} -0.172755 q^{20} +6.84409 q^{21} +3.09225 q^{22} +4.63607 q^{23} -8.11772 q^{24} -4.99721 q^{25} -3.20263 q^{26} +4.92776 q^{27} +8.02710 q^{28} +3.50777 q^{29} +0.338101 q^{30} -3.77922 q^{31} +5.48591 q^{32} -3.75467 q^{33} +4.87748 q^{34} -0.129775 q^{35} +15.5862 q^{36} -1.00000 q^{37} +4.98356 q^{38} +3.88869 q^{39} +0.153925 q^{40} -7.70582 q^{41} -15.7100 q^{42} +5.00767 q^{43} -4.40366 q^{44} -0.251983 q^{45} -10.6417 q^{46} +5.57890 q^{47} +0.411925 q^{48} -0.969960 q^{49} +11.4706 q^{50} -5.92233 q^{51} +4.56085 q^{52} +11.6307 q^{53} -11.3112 q^{54} +0.0711946 q^{55} -7.15217 q^{56} -6.05113 q^{57} -8.05175 q^{58} +4.94833 q^{59} -0.481488 q^{60} +8.49815 q^{61} +8.67483 q^{62} +11.7085 q^{63} -12.8880 q^{64} -0.0737358 q^{65} +8.61848 q^{66} +1.76106 q^{67} -6.94600 q^{68} +12.9213 q^{69} +0.297886 q^{70} +7.96584 q^{71} -13.8873 q^{72} -11.9306 q^{73} +2.29540 q^{74} -13.9278 q^{75} -7.09707 q^{76} -3.30808 q^{77} -8.92611 q^{78} +10.5916 q^{79} -0.00781076 q^{80} -0.569871 q^{81} +17.6880 q^{82} +12.8527 q^{83} +22.3725 q^{84} +0.112297 q^{85} -11.4946 q^{86} +9.77659 q^{87} +3.92368 q^{88} -3.24394 q^{89} +0.578403 q^{90} +3.42616 q^{91} +15.1547 q^{92} -10.5331 q^{93} -12.8058 q^{94} +0.114739 q^{95} +15.2899 q^{96} +7.46261 q^{97} +2.22645 q^{98} -6.42327 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 133 q + 14 q^{2} + 8 q^{3} + 142 q^{4} + 34 q^{5} + 20 q^{6} + 8 q^{7} + 42 q^{8} + 177 q^{9}+O(q^{10}) $ 133 * q + 14 * q^2 + 8 * q^3 + 142 * q^4 + 34 * q^5 + 20 * q^6 + 8 * q^7 + 42 * q^8 + 177 * q^9	\( 133 q + 14 q^{2} + 8 q^{3} + 142 q^{4} + 34 q^{5} + 20 q^{6} + 8 q^{7} + 42 q^{8} + 177 q^{9} + 9 q^{10} + 23 q^{11} + 24 q^{12} + 23 q^{13} + 31 q^{14} + 9 q^{15} + 168 q^{16} + 98 q^{17} + 38 q^{18} + 29 q^{19} + 83 q^{20} + 26 q^{21} + 2 q^{22} + 34 q^{23} + 75 q^{24} + 177 q^{25} + 67 q^{26} + 32 q^{27} + 32 q^{28} + 91 q^{29} + 12 q^{30} + 24 q^{31} + 88 q^{32} + 27 q^{33} + 23 q^{34} + 66 q^{35} + 232 q^{36} - 133 q^{37} + 26 q^{38} + 28 q^{39} + 41 q^{40} + 132 q^{41} + 13 q^{42} + 11 q^{43} + 65 q^{44} + 107 q^{45} + 20 q^{46} + 10 q^{47} + 27 q^{48} + 229 q^{49} + 78 q^{50} + 19 q^{51} + 71 q^{52} + 7 q^{53} + 43 q^{54} + 41 q^{55} + 67 q^{56} + 45 q^{57} + 25 q^{58} + 97 q^{59} - 42 q^{60} + 65 q^{61} + 24 q^{62} + 39 q^{63} + 200 q^{64} + 60 q^{65} + 35 q^{66} + 25 q^{67} + 227 q^{68} + 120 q^{69} + 37 q^{70} + 26 q^{71} + 93 q^{72} + 55 q^{73} - 14 q^{74} + 5 q^{75} + 34 q^{76} + 21 q^{77} - 2 q^{78} + 50 q^{79} + 162 q^{80} + 341 q^{81} + 66 q^{82} + 30 q^{83} - 89 q^{84} + 30 q^{85} - 12 q^{86} + 80 q^{87} - 85 q^{88} + 225 q^{89} - 86 q^{90} + q^{91} + 82 q^{92} + 42 q^{93} - 17 q^{94} + 70 q^{95} + 55 q^{96} + 12 q^{97} + 90 q^{98} + 17 q^{99}+O(q^{100}) \) 133 * q + 14 * q^2 + 8 * q^3 + 142 * q^4 + 34 * q^5 + 20 * q^6 + 8 * q^7 + 42 * q^8 + 177 * q^9 + 9 * q^10 + 23 * q^11 + 24 * q^12 + 23 * q^13 + 31 * q^14 + 9 * q^15 + 168 * q^16 + 98 * q^17 + 38 * q^18 + 29 * q^19 + 83 * q^20 + 26 * q^21 + 2 * q^22 + 34 * q^23 + 75 * q^24 + 177 * q^25 + 67 * q^26 + 32 * q^27 + 32 * q^28 + 91 * q^29 + 12 * q^30 + 24 * q^31 + 88 * q^32 + 27 * q^33 + 23 * q^34 + 66 * q^35 + 232 * q^36 - 133 * q^37 + 26 * q^38 + 28 * q^39 + 41 * q^40 + 132 * q^41 + 13 * q^42 + 11 * q^43 + 65 * q^44 + 107 * q^45 + 20 * q^46 + 10 * q^47 + 27 * q^48 + 229 * q^49 + 78 * q^50 + 19 * q^51 + 71 * q^52 + 7 * q^53 + 43 * q^54 + 41 * q^55 + 67 * q^56 + 45 * q^57 + 25 * q^58 + 97 * q^59 - 42 * q^60 + 65 * q^61 + 24 * q^62 + 39 * q^63 + 200 * q^64 + 60 * q^65 + 35 * q^66 + 25 * q^67 + 227 * q^68 + 120 * q^69 + 37 * q^70 + 26 * q^71 + 93 * q^72 + 55 * q^73 - 14 * q^74 + 5 * q^75 + 34 * q^76 + 21 * q^77 - 2 * q^78 + 50 * q^79 + 162 * q^80 + 341 * q^81 + 66 * q^82 + 30 * q^83 - 89 * q^84 + 30 * q^85 - 12 * q^86 + 80 * q^87 - 85 * q^88 + 225 * q^89 - 86 * q^90 + q^91 + 82 * q^92 + 42 * q^93 - 17 * q^94 + 70 * q^95 + 55 * q^96 + 12 * q^97 + 90 * q^98 + 17 * 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 $

$2$	−2.29540	−1.62310	−0.811548	−	0.584286i	$-0.801374\pi$
$2$	−2.29540	−1.62310	−0.811548	+	0.584286i	$0.801374\pi$
$3$	2.78712	1.60915	0.804573	−	0.593854i	$-0.202394\pi$
$3$	2.78712	1.60915	0.804573	+	0.593854i	$0.202394\pi$
$4$	3.26888	1.63444
$5$	−0.0528483	−0.0236345	−0.0118172	−	0.999930i	$-0.503762\pi$
$5$	−0.0528483	−0.0236345	−0.0118172	+	0.999930i	$0.503762\pi$
$6$	−6.39757	−2.61180
$7$	2.45561	0.928135	0.464067	−	0.885800i	$-0.346390\pi$
$7$	2.45561	0.928135	0.464067	+	0.885800i	$0.346390\pi$
$8$	−2.91258	−1.02975
$9$	4.76805	1.58935
$10$	0.121308	0.0383610
$11$	−1.34715	−0.406181	−0.203090	−	0.979160i	$-0.565099\pi$
$11$	−1.34715	−0.406181	−0.203090	+	0.979160i	$0.565099\pi$
$12$	9.11075	2.63005
$13$	1.39523	0.386968	0.193484	−	0.981103i	$-0.438021\pi$
$13$	1.39523	0.386968	0.193484	+	0.981103i	$0.438021\pi$
$14$	−5.63662	−1.50645
$15$	−0.147295	−0.0380313
$16$	0.147796	0.0369490
$17$	−2.12489	−0.515362	−0.257681	−	0.966230i	$-0.582958\pi$
$17$	−2.12489	−0.515362	−0.257681	+	0.966230i	$0.582958\pi$
$18$	−10.9446	−2.57966
$19$	−2.17110	−0.498085	−0.249043	−	0.968493i	$-0.580116\pi$
$19$	−2.17110	−0.498085	−0.249043	+	0.968493i	$0.580116\pi$
$20$	−0.172755	−0.0386291
$21$	6.84409	1.49350
$22$	3.09225	0.659270
$23$	4.63607	0.966688	0.483344	−	0.875431i	$-0.339422\pi$
$23$	4.63607	0.966688	0.483344	+	0.875431i	$0.339422\pi$
$24$	−8.11772	−1.65702
$25$	−4.99721	−0.999441
$26$	−3.20263	−0.628087
$27$	4.92776	0.948348
$28$	8.02710	1.51698
$29$	3.50777	0.651377	0.325689	−	0.945477i	$-0.394404\pi$
$29$	3.50777	0.651377	0.325689	+	0.945477i	$0.394404\pi$
$30$	0.338101	0.0617285
$31$	−3.77922	−0.678768	−0.339384	−	0.940648i	$-0.610219\pi$
$31$	−3.77922	−0.678768	−0.339384	+	0.940648i	$0.610219\pi$
$32$	5.48591	0.969781
$33$	−3.75467	−0.653604
$34$	4.87748	0.836481
$35$	−0.129775	−0.0219360
$36$	15.5862	2.59769
$37$	−1.00000	−0.164399
$37$	−1.00000	−0.164399
$38$	4.98356	0.808440
$39$	3.88869	0.622688
$40$	0.153925	0.0243377
$41$	−7.70582	−1.20345	−0.601723	−	0.798705i	$-0.705519\pi$
$41$	−7.70582	−1.20345	−0.601723	+	0.798705i	$0.705519\pi$
$42$	−15.7100	−2.42410
$43$	5.00767	0.763663	0.381831	−	0.924232i	$-0.375294\pi$
$43$	5.00767	0.763663	0.381831	+	0.924232i	$0.375294\pi$
$44$	−4.40366	−0.663877
$45$	−0.251983	−0.0375634
$46$	−10.6417	−1.56903
$47$	5.57890	0.813766	0.406883	−	0.913480i	$-0.366616\pi$
$47$	5.57890	0.813766	0.406883	+	0.913480i	$0.366616\pi$
$48$	0.411925	0.0594563
$49$	−0.969960	−0.138566
$50$	11.4706	1.62219
$51$	−5.92233	−0.829292
$52$	4.56085	0.632476
$53$	11.6307	1.59760	0.798800	−	0.601596i	$-0.205468\pi$
$53$	11.6307	1.59760	0.798800	+	0.601596i	$0.205468\pi$
$54$	−11.3112	−1.53926
$55$	0.0711946	0.00959987
$56$	−7.15217	−0.955749
$57$	−6.05113	−0.801492
$58$	−8.05175	−1.05725
$59$	4.94833	0.644218	0.322109	−	0.946703i	$-0.395608\pi$
$59$	4.94833	0.644218	0.322109	+	0.946703i	$0.395608\pi$
$60$	−0.481488	−0.0621598
$61$	8.49815	1.08808	0.544038	−	0.839061i	$-0.316895\pi$
$61$	8.49815	1.08808	0.544038	+	0.839061i	$0.316895\pi$
$62$	8.67483	1.10170
$63$	11.7085	1.47513
$64$	−12.8880	−1.61100
$65$	−0.0737358	−0.00914580
$66$	8.61848	1.06086
$67$	1.76106	0.215148	0.107574	−	0.994197i	$-0.465692\pi$
$67$	1.76106	0.215148	0.107574	+	0.994197i	$0.465692\pi$
$68$	−6.94600	−0.842326
$69$	12.9213	1.55554
$70$	0.297886	0.0356042
$71$	7.96584	0.945371	0.472686	−	0.881231i	$-0.343285\pi$
$71$	7.96584	0.945371	0.472686	+	0.881231i	$0.343285\pi$
$72$	−13.8873	−1.63664
$73$	−11.9306	−1.39637	−0.698184	−	0.715918i	$-0.746008\pi$
$73$	−11.9306	−1.39637	−0.698184	+	0.715918i	$0.746008\pi$
$74$	2.29540	0.266835
$75$	−13.9278	−1.60825
$76$	−7.09707	−0.814089
$77$	−3.30808	−0.376991
$78$	−8.92611	−1.01068
$79$	10.5916	1.19165	0.595823	−	0.803115i	$-0.296826\pi$
$79$	10.5916	1.19165	0.595823	+	0.803115i	$0.296826\pi$
$80$	−0.00781076	−0.000873270 0
$81$	−0.569871	−0.0633190
$82$	17.6880	1.95331
$83$	12.8527	1.41076	0.705381	−	0.708828i	$-0.250776\pi$
$83$	12.8527	1.41076	0.705381	+	0.708828i	$0.250776\pi$
$84$	22.3725	2.44104
$85$	0.112297	0.0121803
$86$	−11.4946	−1.23950
$87$	9.77659	1.04816
$88$	3.92368	0.418266
$89$	−3.24394	−0.343857	−0.171929	−	0.985109i	$-0.555000\pi$
$89$	−3.24394	−0.343857	−0.171929	+	0.985109i	$0.555000\pi$
$90$	0.578403	0.0609690
$91$	3.42616	0.359159
$92$	15.1547	1.57999
$93$	−10.5331	−1.09224
$94$	−12.8058	−1.32082
$95$	0.114739	0.0117720
$96$	15.2899	1.56052
$97$	7.46261	0.757714	0.378857	−	0.925455i	$-0.376317\pi$
$97$	7.46261	0.757714	0.378857	+	0.925455i	$0.376317\pi$
$98$	2.22645	0.224905
$99$	−6.42327	−0.645563
$100$	−16.3352	−1.63352
$101$	7.12379	0.708844	0.354422	−	0.935086i	$-0.384678\pi$
$101$	7.12379	0.708844	0.354422	+	0.935086i	$0.384678\pi$
$102$	13.5941	1.34602
$103$	18.3225	1.80537	0.902684	−	0.430305i	$-0.141594\pi$
$103$	18.3225	1.80537	0.902684	+	0.430305i	$0.141594\pi$
$104$	−4.06373	−0.398482
$105$	−0.361699	−0.0352982
$106$	−26.6972	−2.59306
$107$	16.0410	1.55074	0.775372	−	0.631505i	$-0.217563\pi$
$107$	16.0410	1.55074	0.775372	+	0.631505i	$0.217563\pi$
$108$	16.1082	1.55002
$109$	13.6184	1.30441	0.652204	−	0.758044i	$-0.273845\pi$
$109$	13.6184	1.30441	0.652204	+	0.758044i	$0.273845\pi$
$110$	−0.163420	−0.0155815
$111$	−2.78712	−0.264542
$112$	0.362930	0.0342936
$113$	14.1533	1.33143	0.665716	−	0.746206i	$-0.268126\pi$
$113$	14.1533	1.33143	0.665716	+	0.746206i	$0.268126\pi$
$114$	13.8898	1.30090
$115$	−0.245009	−0.0228472
$116$	11.4665	1.06464
$117$	6.65254	0.615028
$118$	−11.3584	−1.04563
$119$	−5.21791	−0.478325
$120$	0.429008	0.0391629
$121$	−9.18519	−0.835017
$122$	−19.5067	−1.76605
$123$	−21.4771	−1.93652
$124$	−12.3538	−1.10940
$125$	0.528336	0.0472558
$126$	−26.8757	−2.39428
$127$	7.94628	0.705118	0.352559	−	0.935790i	$-0.385312\pi$
$127$	7.94628	0.705118	0.352559	+	0.935790i	$0.385312\pi$
$128$	18.6113	1.64502
$129$	13.9570	1.22884
$130$	0.169253	0.0148445
$131$	−5.20059	−0.454377	−0.227189	−	0.973851i	$-0.572953\pi$
$131$	−5.20059	−0.454377	−0.227189	+	0.973851i	$0.572953\pi$
$132$	−12.2735	−1.06827
$133$	−5.33139	−0.462290
$134$	−4.04234	−0.349205
$135$	−0.260424	−0.0224137
$136$	6.18891	0.530695
$137$	−4.97420	−0.424974	−0.212487	−	0.977164i	$-0.568156\pi$
$137$	−4.97420	−0.424974	−0.212487	+	0.977164i	$0.568156\pi$
$138$	−29.6596	−2.52479
$139$	−10.6222	−0.900962	−0.450481	−	0.892786i	$-0.648747\pi$
$139$	−10.6222	−0.900962	−0.450481	+	0.892786i	$0.648747\pi$
$140$	−0.424219	−0.0358530
$141$	15.5491	1.30947
$142$	−18.2848	−1.53443
$143$	−1.87959	−0.157179
$144$	0.704698	0.0587248
$145$	−0.185380	−0.0153950
$146$	27.3855	2.26644
$147$	−2.70340	−0.222972
$148$	−3.26888	−0.268700
$149$	−3.28548	−0.269157	−0.134579	−	0.990903i	$-0.542968\pi$
$149$	−3.28548	−0.269157	−0.134579	+	0.990903i	$0.542968\pi$
$150$	31.9700	2.61034
$151$	−10.1524	−0.826188	−0.413094	−	0.910688i	$-0.635552\pi$
$151$	−10.1524	−0.826188	−0.413094	+	0.910688i	$0.635552\pi$
$152$	6.32351	0.512905
$153$	−10.1316	−0.819089
$154$	7.59337	0.611891
$155$	0.199725	0.0160423
$156$	12.7116	1.01775
$157$	−18.3879	−1.46752	−0.733759	−	0.679410i	$-0.762236\pi$
$157$	−18.3879	−1.46752	−0.733759	+	0.679410i	$0.762236\pi$
$158$	−24.3120	−1.93416
$159$	32.4162	2.57077
$160$	−0.289921	−0.0229203
$161$	11.3844	0.897217
$162$	1.30808	0.102773
$163$	1.00000	0.0783260
$163$	1.00000	0.0783260
$164$	−25.1894	−1.96696
$165$	0.198428	0.0154476
$166$	−29.5020	−2.28980
$167$	23.5270	1.82058	0.910288	−	0.413976i	$-0.135860\pi$
$167$	23.5270	1.82058	0.910288	+	0.413976i	$0.135860\pi$
$168$	−19.9340	−1.53794
$169$	−11.0533	−0.850255
$170$	−0.257767	−0.0197698
$171$	−10.3519	−0.791631
$172$	16.3695	1.24816
$173$	−5.24732	−0.398946	−0.199473	−	0.979903i	$-0.563923\pi$
$173$	−5.24732	−0.398946	−0.199473	+	0.979903i	$0.563923\pi$
$174$	−22.4412	−1.70126
$175$	−12.2712	−0.927616
$176$	−0.199103	−0.0150080
$177$	13.7916	1.03664
$178$	7.44616	0.558113
$179$	20.8047	1.55502	0.777509	−	0.628872i	$-0.216483\pi$
$179$	20.8047	1.55502	0.777509	+	0.628872i	$0.216483\pi$
$180$	−0.823702	−0.0613951
$181$	10.5068	0.780962	0.390481	−	0.920611i	$-0.372309\pi$
$181$	10.5068	0.780962	0.390481	+	0.920611i	$0.372309\pi$
$182$	−7.86441	−0.582949
$183$	23.6854	1.75087
$184$	−13.5029	−0.995449
$185$	0.0528483	0.00388549
$186$	24.1778	1.77280
$187$	2.86254	0.209330
$188$	18.2367	1.33005
$189$	12.1007	0.880195
$190$	−0.263373	−0.0191071
$191$	7.01383	0.507503	0.253752	−	0.967269i	$-0.418335\pi$
$191$	7.01383	0.507503	0.253752	+	0.967269i	$0.418335\pi$
$192$	−35.9203	−2.59233
$193$	11.5222	0.829383	0.414692	−	0.909962i	$-0.363889\pi$
$193$	11.5222	0.829383	0.414692	+	0.909962i	$0.363889\pi$
$194$	−17.1297	−1.22984
$195$	−0.205511	−0.0147169
$196$	−3.17068	−0.226477
$197$	−6.81689	−0.485683	−0.242842	−	0.970066i	$-0.578080\pi$
$197$	−6.81689	−0.485683	−0.242842	+	0.970066i	$0.578080\pi$
$198$	14.7440	1.04781
$199$	4.49616	0.318724	0.159362	−	0.987220i	$-0.449056\pi$
$199$	4.49616	0.318724	0.159362	+	0.987220i	$0.449056\pi$
$200$	14.5548	1.02918
$201$	4.90828	0.346204
$202$	−16.3520	−1.15052
$203$	8.61374	0.604566
$204$	−19.3594	−1.35543
$205$	0.407240	0.0284428
$206$	−42.0575	−2.93028
$207$	22.1050	1.53640
$208$	0.206210	0.0142981
$209$	2.92480	0.202313
$210$	0.830245	0.0572923
$211$	−9.87994	−0.680163	−0.340081	−	0.940396i	$-0.610455\pi$
$211$	−9.87994	−0.680163	−0.340081	+	0.940396i	$0.610455\pi$
$212$	38.0193	2.61118
$213$	22.2018	1.52124
$214$	−36.8206	−2.51700
$215$	−0.264647	−0.0180488
$216$	−14.3525	−0.976564
$217$	−9.28030	−0.629988
$218$	−31.2598	−2.11718
$219$	−33.2520	−2.24696
$220$	0.232726	0.0156904
$221$	−2.96472	−0.199429
$222$	6.39757	0.429377
$223$	14.7595	0.988372	0.494186	−	0.869356i	$-0.335466\pi$
$223$	14.7595	0.988372	0.494186	+	0.869356i	$0.335466\pi$
$224$	13.4713	0.900088
$225$	−23.8269	−1.58846
$226$	−32.4875	−2.16104
$227$	17.7433	1.17766	0.588831	−	0.808256i	$-0.299588\pi$
$227$	17.7433	1.17766	0.588831	+	0.808256i	$0.299588\pi$
$228$	−19.7804	−1.30999
$229$	21.9519	1.45063	0.725313	−	0.688420i	$-0.241695\pi$
$229$	21.9519	1.45063	0.725313	+	0.688420i	$0.241695\pi$
$230$	0.562393	0.0370831
$231$	−9.22002	−0.606633
$232$	−10.2167	−0.670757
$233$	24.1175	1.57999	0.789994	−	0.613115i	$-0.210084\pi$
$233$	24.1175	1.57999	0.789994	+	0.613115i	$0.210084\pi$
$234$	−15.2703	−0.998249
$235$	−0.294835	−0.0192329
$236$	16.1755	1.05293
$237$	29.5200	1.91753
$238$	11.9772	0.776367
$239$	−11.2141	−0.725380	−0.362690	−	0.931910i	$-0.618142\pi$
$239$	−11.2141	−0.725380	−0.362690	+	0.931910i	$0.618142\pi$
$240$	−0.0217695	−0.00140522
$241$	−16.9921	−1.09456	−0.547278	−	0.836951i	$-0.684336\pi$
$241$	−16.9921	−1.09456	−0.547278	+	0.836951i	$0.684336\pi$
$242$	21.0837	1.35531
$243$	−16.3716	−1.05024
$244$	27.7794	1.77839
$245$	0.0512607	0.00327493
$246$	49.2985	3.14316
$247$	−3.02920	−0.192743
$248$	11.0073	0.698963
$249$	35.8219	2.27012
$250$	−1.21274	−0.0767006
$251$	−24.3415	−1.53642	−0.768212	−	0.640195i	$-0.778853\pi$
$251$	−24.3415	−1.53642	−0.768212	+	0.640195i	$0.778853\pi$
$252$	38.2736	2.41101
$253$	−6.24548	−0.392650
$254$	−18.2399	−1.14447
$255$	0.312985	0.0195999
$256$	−16.9444	−1.05903
$257$	−15.4195	−0.961844	−0.480922	−	0.876763i	$-0.659698\pi$
$257$	−15.4195	−0.961844	−0.480922	+	0.876763i	$0.659698\pi$
$258$	−32.0369	−1.99453
$259$	−2.45561	−0.152584
$260$	−0.241033	−0.0149482
$261$	16.7252	1.03527
$262$	11.9374	0.737497
$263$	21.0502	1.29801	0.649006	−	0.760783i	$-0.275185\pi$
$263$	21.0502	1.29801	0.649006	+	0.760783i	$0.275185\pi$
$264$	10.9358	0.673050
$265$	−0.614663	−0.0377585
$266$	12.2377	0.750341
$267$	−9.04127	−0.553317
$268$	5.75668	0.351645
$269$	15.5612	0.948784	0.474392	−	0.880314i	$-0.342668\pi$
$269$	15.5612	0.948784	0.474392	+	0.880314i	$0.342668\pi$
$270$	0.597778	0.0363796
$271$	−15.3477	−0.932305	−0.466153	−	0.884704i	$-0.654360\pi$
$271$	−15.3477	−0.932305	−0.466153	+	0.884704i	$0.654360\pi$
$272$	−0.314050	−0.0190421
$273$	9.54912	0.577939
$274$	11.4178	0.689774
$275$	6.73198	0.405954
$276$	42.2381	2.54244
$277$	1.92004	0.115364	0.0576819	−	0.998335i	$-0.481629\pi$
$277$	1.92004	0.115364	0.0576819	+	0.998335i	$0.481629\pi$
$278$	24.3822	1.46235
$279$	−18.0195	−1.07880
$280$	0.377980	0.0225886
$281$	−25.7626	−1.53687	−0.768433	−	0.639930i	$-0.778963\pi$
$281$	−25.7626	−1.53687	−0.768433	+	0.639930i	$0.778963\pi$
$282$	−35.6914	−2.12539
$283$	−9.84154	−0.585019	−0.292509	−	0.956263i	$-0.594490\pi$
$283$	−9.84154	−0.585019	−0.292509	+	0.956263i	$0.594490\pi$
$284$	26.0393	1.54515
$285$	0.319792	0.0189428
$286$	4.31441	0.255117
$287$	−18.9225	−1.11696
$288$	26.1571	1.54132
$289$	−12.4848	−0.734402
$290$	0.425522	0.0249875
$291$	20.7992	1.21927
$292$	−38.9996	−2.28228
$293$	27.5407	1.60895	0.804473	−	0.593989i	$-0.202448\pi$
$293$	27.5407	1.60895	0.804473	+	0.593989i	$0.202448\pi$
$294$	6.20538	0.361905
$295$	−0.261511	−0.0152258
$296$	2.91258	0.169290
$297$	−6.63843	−0.385201
$298$	7.54151	0.436868
$299$	6.46841	0.374078
$300$	−45.5283	−2.62858
$301$	12.2969	0.708782
$302$	23.3038	1.34098
$303$	19.8549	1.14063
$304$	−0.320880	−0.0184037
$305$	−0.449113	−0.0257161
$306$	23.2561	1.32946
$307$	12.0241	0.686254	0.343127	−	0.939289i	$-0.388514\pi$
$307$	12.0241	0.686254	0.343127	+	0.939289i	$0.388514\pi$
$308$	−10.8137	−0.616168
$309$	51.0670	2.90510
$310$	−0.458450	−0.0260382
$311$	−19.7847	−1.12189	−0.560945	−	0.827853i	$-0.689562\pi$
$311$	−19.7847	−1.12189	−0.560945	+	0.827853i	$0.689562\pi$
$312$	−11.3261	−0.641215
$313$	−11.3950	−0.644085	−0.322042	−	0.946725i	$-0.604369\pi$
$313$	−11.3950	−0.644085	−0.322042	+	0.946725i	$0.604369\pi$
$314$	42.2077	2.38192
$315$	−0.618774	−0.0348639
$316$	34.6226	1.94767
$317$	−33.0222	−1.85471	−0.927354	−	0.374184i	$-0.877923\pi$
$317$	−33.0222	−1.85471	−0.927354	+	0.374184i	$0.877923\pi$
$318$	−74.4082	−4.17261
$319$	−4.72549	−0.264577
$320$	0.681107	0.0380751
$321$	44.7083	2.49537
$322$	−26.1318	−1.45627
$323$	4.61336	0.256694
$324$	−1.86284	−0.103491
$325$	−6.97228	−0.386752
$326$	−2.29540	−0.127131
$327$	37.9562	2.09898
$328$	22.4438	1.23925
$329$	13.6996	0.755284
$330$	−0.455472	−0.0250729
$331$	15.5905	0.856933	0.428467	−	0.903558i	$-0.359054\pi$
$331$	15.5905	0.856933	0.428467	+	0.903558i	$0.359054\pi$
$332$	42.0137	2.30580
$333$	−4.76805	−0.261287
$334$	−54.0040	−2.95497
$335$	−0.0930690	−0.00508490
$336$	1.01153	0.0551834
$337$	8.22709	0.448158	0.224079	−	0.974571i	$-0.428063\pi$
$337$	8.22709	0.448158	0.224079	+	0.974571i	$0.428063\pi$
$338$	25.3718	1.38005
$339$	39.4470	2.14247
$340$	0.367085	0.0199080
$341$	5.09117	0.275702
$342$	23.7618	1.28489
$343$	−19.5711	−1.05674
$344$	−14.5852	−0.786384
$345$	−0.682869	−0.0367644
$346$	12.0447	0.647528
$347$	−10.2147	−0.548353	−0.274176	−	0.961679i	$-0.588405\pi$
$347$	−10.2147	−0.548353	−0.274176	+	0.961679i	$0.588405\pi$
$348$	31.9585	1.71315
$349$	−20.4492	−1.09462	−0.547311	−	0.836929i	$-0.684349\pi$
$349$	−20.4492	−1.09462	−0.547311	+	0.836929i	$0.684349\pi$
$350$	28.1674	1.50561
$351$	6.87538	0.366981
$352$	−7.39034	−0.393906
$353$	−19.4908	−1.03739	−0.518695	−	0.854960i	$-0.673582\pi$
$353$	−19.4908	−1.03739	−0.518695	+	0.854960i	$0.673582\pi$
$354$	−31.6573	−1.68257
$355$	−0.420981	−0.0223434
$356$	−10.6041	−0.562014
$357$	−14.5430	−0.769695
$358$	−47.7552	−2.52394
$359$	−10.8558	−0.572947	−0.286474	−	0.958088i	$-0.592483\pi$
$359$	−10.8558	−0.572947	−0.286474	+	0.958088i	$0.592483\pi$
$360$	0.733922	0.0386811
$361$	−14.2863	−0.751911
$362$	−24.1173	−1.26758
$363$	−25.6002	−1.34366
$364$	11.1997	0.587023
$365$	0.630511	0.0330024
$366$	−54.3675	−2.84183
$367$	24.4221	1.27482	0.637411	−	0.770524i	$-0.280005\pi$
$367$	24.4221	1.27482	0.637411	+	0.770524i	$0.280005\pi$
$368$	0.685192	0.0357181
$369$	−36.7417	−1.91270
$370$	−0.121308	−0.00630651
$371$	28.5605	1.48279
$372$	−34.4315	−1.78519
$373$	−6.96568	−0.360669	−0.180335	−	0.983605i	$-0.557718\pi$
$373$	−6.96568	−0.360669	−0.180335	+	0.983605i	$0.557718\pi$
$374$	−6.57069	−0.339762
$375$	1.47254	0.0760414
$376$	−16.2490	−0.837977
$377$	4.89417	0.252062
$378$	−27.7759	−1.42864
$379$	1.31337	0.0674632	0.0337316	−	0.999431i	$-0.489261\pi$
$379$	1.31337	0.0674632	0.0337316	+	0.999431i	$0.489261\pi$
$380$	0.375068	0.0192406
$381$	22.1472	1.13464
$382$	−16.0996	−0.823726
$383$	−19.4780	−0.995282	−0.497641	−	0.867383i	$-0.665800\pi$
$383$	−19.4780	−0.995282	−0.497641	+	0.867383i	$0.665800\pi$
$384$	51.8718	2.64707
$385$	0.174826	0.00890998
$386$	−26.4480	−1.34617
$387$	23.8768	1.21373
$388$	24.3944	1.23844
$389$	28.6777	1.45401	0.727007	−	0.686630i	$-0.240911\pi$
$389$	28.6777	1.45401	0.727007	+	0.686630i	$0.240911\pi$
$390$	0.471730	0.0238870
$391$	−9.85114	−0.498194
$392$	2.82509	0.142688
$393$	−14.4947	−0.731159
$394$	15.6475	0.788310
$395$	−0.559748	−0.0281640
$396$	−20.9969	−1.05513
$397$	−32.3920	−1.62571	−0.812853	−	0.582469i	$-0.802087\pi$
$397$	−32.3920	−1.62571	−0.812853	+	0.582469i	$0.802087\pi$
$398$	−10.3205	−0.517320
$399$	−14.8592	−0.743892
$400$	−0.738567	−0.0369283
$401$	1.64740	0.0822670	0.0411335	−	0.999154i	$-0.486903\pi$
$401$	1.64740	0.0822670	0.0411335	+	0.999154i	$0.486903\pi$
$402$	−11.2665	−0.561921
$403$	−5.27289	−0.262662
$404$	23.2868	1.15856
$405$	0.0301167	0.00149651
$406$	−19.7720	−0.981268
$407$	1.34715	0.0667757
$408$	17.2493	0.853965
$409$	−15.2615	−0.754630	−0.377315	−	0.926085i	$-0.623153\pi$
$409$	−15.2615	−0.754630	−0.377315	+	0.926085i	$0.623153\pi$
$410$	−0.934779	−0.0461654
$411$	−13.8637	−0.683845
$412$	59.8939	2.95076
$413$	12.1512	0.597921
$414$	−50.7399	−2.49373
$415$	−0.679241	−0.0333426
$416$	7.65413	0.375275
$417$	−29.6053	−1.44978
$418$	−6.71360	−0.328373
$419$	−30.9689	−1.51293	−0.756465	−	0.654034i	$-0.773075\pi$
$419$	−30.9689	−1.51293	−0.756465	+	0.654034i	$0.773075\pi$
$420$	−1.18235	−0.0576927
$421$	−23.3509	−1.13806	−0.569028	−	0.822318i	$-0.692680\pi$
$421$	−23.3509	−1.13806	−0.569028	+	0.822318i	$0.692680\pi$
$422$	22.6784	1.10397
$423$	26.6004	1.29336
$424$	−33.8754	−1.64513
$425$	10.6185	0.515074
$426$	−50.9620	−2.46912
$427$	20.8682	1.00988
$428$	52.4361	2.53459
$429$	−5.23864	−0.252924
$430$	0.607471	0.0292949
$431$	−9.74545	−0.469422	−0.234711	−	0.972065i	$-0.575414\pi$
$431$	−9.74545	−0.469422	−0.234711	+	0.972065i	$0.575414\pi$
$432$	0.728303	0.0350405
$433$	−4.50231	−0.216367	−0.108184	−	0.994131i	$-0.534503\pi$
$433$	−4.50231	−0.216367	−0.108184	+	0.994131i	$0.534503\pi$
$434$	21.3020	1.02253
$435$	−0.516676	−0.0247727
$436$	44.5169	2.13197
$437$	−10.0654	−0.481493
$438$	76.3266	3.64703
$439$	−17.8709	−0.852931	−0.426466	−	0.904504i	$-0.640241\pi$
$439$	−17.8709	−0.852931	−0.426466	+	0.904504i	$0.640241\pi$
$440$	−0.207360	−0.00988550
$441$	−4.62481	−0.220229
$442$	6.80523	0.323692
$443$	−18.7189	−0.889363	−0.444682	−	0.895689i	$-0.646683\pi$
$443$	−18.7189	−0.889363	−0.444682	+	0.895689i	$0.646683\pi$
$444$	−9.11075	−0.432377
$445$	0.171437	0.00812689
$446$	−33.8791	−1.60422
$447$	−9.15704	−0.433113
$448$	−31.6479	−1.49522
$449$	20.8752	0.985163	0.492581	−	0.870266i	$-0.336053\pi$
$449$	20.8752	0.985163	0.492581	+	0.870266i	$0.336053\pi$
$450$	54.6924	2.57822
$451$	10.3809	0.488817
$452$	46.2654	2.17614
$453$	−28.2959	−1.32946
$454$	−40.7280	−1.91146
$455$	−0.181067	−0.00848854
$456$	17.6244	0.825338
$457$	0.337540	0.0157895	0.00789474	−	0.999969i	$-0.497487\pi$
$457$	0.337540	0.0157895	0.00789474	+	0.999969i	$0.497487\pi$
$458$	−50.3886	−2.35450
$459$	−10.4710	−0.488742
$460$	−0.800903	−0.0373423
$461$	−39.6920	−1.84864	−0.924320	−	0.381619i	$-0.875367\pi$
$461$	−39.6920	−1.84864	−0.924320	+	0.381619i	$0.875367\pi$
$462$	21.1637	0.984622
$463$	−6.55212	−0.304503	−0.152252	−	0.988342i	$-0.548652\pi$
$463$	−6.55212	−0.304503	−0.152252	+	0.988342i	$0.548652\pi$
$464$	0.518435	0.0240677
$465$	0.556659	0.0258144
$466$	−55.3593	−2.56447
$467$	−19.7913	−0.915834	−0.457917	−	0.888995i	$-0.651404\pi$
$467$	−19.7913	−0.915834	−0.457917	+	0.888995i	$0.651404\pi$
$468$	21.7463	1.00522
$469$	4.32448	0.199686
$470$	0.676766	0.0312169
$471$	−51.2494	−2.36145
$472$	−14.4124	−0.663385
$473$	−6.74608	−0.310185
$474$	−67.7604	−3.11234
$475$	10.8495	0.497807
$476$	−17.0567	−0.781793
$477$	55.4558	2.53914
$478$	25.7409	1.17736
$479$	−7.07093	−0.323079	−0.161540	−	0.986866i	$-0.551646\pi$
$479$	−7.07093	−0.323079	−0.161540	+	0.986866i	$0.551646\pi$
$480$	−0.808045	−0.0368821
$481$	−1.39523	−0.0636172
$482$	39.0037	1.77657
$483$	31.7297	1.44375
$484$	−30.0252	−1.36478
$485$	−0.394387	−0.0179082
$486$	37.5794	1.70464
$487$	−22.6901	−1.02819	−0.514094	−	0.857734i	$-0.671872\pi$
$487$	−22.6901	−1.02819	−0.514094	+	0.857734i	$0.671872\pi$
$488$	−24.7515	−1.12045
$489$	2.78712	0.126038
$490$	−0.117664	−0.00531552
$491$	−22.1287	−0.998655	−0.499328	−	0.866413i	$-0.666420\pi$
$491$	−22.1287	−0.998655	−0.499328	+	0.866413i	$0.666420\pi$
$492$	−70.2058	−3.16512
$493$	−7.45363	−0.335695
$494$	6.95323	0.312841
$495$	0.339459	0.0152575
$496$	−0.558553	−0.0250798
$497$	19.5610	0.877432
$498$	−82.2257	−3.68462
$499$	−10.6606	−0.477232	−0.238616	−	0.971114i	$-0.576694\pi$
$499$	−10.6606	−0.477232	−0.238616	+	0.971114i	$0.576694\pi$
$500$	1.72706	0.0772366
$501$	65.5727	2.92957
$502$	55.8737	2.49376
$503$	31.3889	1.39956	0.699782	−	0.714357i	$-0.253281\pi$
$503$	31.3889	1.39956	0.699782	+	0.714357i	$0.253281\pi$
$504$	−34.1019	−1.51902
$505$	−0.376480	−0.0167532
$506$	14.3359	0.637308
$507$	−30.8069	−1.36818
$508$	25.9754	1.15247
$509$	22.7335	1.00764	0.503822	−	0.863808i	$-0.331927\pi$
$509$	22.7335	1.00764	0.503822	+	0.863808i	$0.331927\pi$
$510$	−0.718427	−0.0318125
$511$	−29.2969	−1.29602
$512$	1.67173	0.0738807
$513$	−10.6987	−0.472358
$514$	35.3940	1.56116
$515$	−0.968312	−0.0426689
$516$	45.6236	2.00847
$517$	−7.51560	−0.330536
$518$	5.63662	0.247659
$519$	−14.6249	−0.641963
$520$	0.214761	0.00941791
$521$	−34.6606	−1.51851	−0.759254	−	0.650795i	$-0.774436\pi$
$521$	−34.6606	−1.51851	−0.759254	+	0.650795i	$0.774436\pi$
$522$	−38.3911	−1.68033
$523$	0.577680	0.0252602	0.0126301	−	0.999920i	$-0.495980\pi$
$523$	0.577680	0.0252602	0.0126301	+	0.999920i	$0.495980\pi$
$524$	−17.0001	−0.742651
$525$	−34.2014	−1.49267
$526$	−48.3187	−2.10680
$527$	8.03042	0.349811
$528$	−0.554925	−0.0241500
$529$	−1.50684	−0.0655147
$530$	1.41090	0.0612856
$531$	23.5939	1.02389
$532$	−17.4277	−0.755585
$533$	−10.7514	−0.465696
$534$	20.7534	0.898086
$535$	−0.847741	−0.0366510
$536$	−5.12922	−0.221549
$537$	57.9853	2.50225
$538$	−35.7193	−1.53997
$539$	1.30668	0.0562827
$540$	−0.851293	−0.0366338
$541$	35.3251	1.51875	0.759373	−	0.650655i	$-0.225506\pi$
$541$	35.3251	1.51875	0.759373	+	0.650655i	$0.225506\pi$
$542$	35.2291	1.51322
$543$	29.2836	1.25668
$544$	−11.6570	−0.499788
$545$	−0.719710	−0.0308290
$546$	−21.9191	−0.938050
$547$	6.08628	0.260231	0.130115	−	0.991499i	$-0.458465\pi$
$547$	6.08628	0.260231	0.130115	+	0.991499i	$0.458465\pi$
$548$	−16.2600	−0.694594
$549$	40.5196	1.72933
$550$	−15.4526	−0.658902
$551$	−7.61574	−0.324441
$552$	−37.6343	−1.60182
$553$	26.0089	1.10601
$554$	−4.40726	−0.187247
$555$	0.147295	0.00625231
$556$	−34.7226	−1.47257
$557$	11.5597	0.489802	0.244901	−	0.969548i	$-0.421245\pi$
$557$	11.5597	0.489802	0.244901	+	0.969548i	$0.421245\pi$
$558$	41.3620	1.75099
$559$	6.98687	0.295513
$560$	−0.0191802	−0.000810512 0
$561$	7.97826	0.336842
$562$	59.1355	2.49448
$563$	26.7995	1.12947	0.564733	−	0.825274i	$-0.308979\pi$
$563$	26.7995	1.12947	0.564733	+	0.825274i	$0.308979\pi$
$564$	50.8279	2.14024
$565$	−0.747979	−0.0314677
$566$	22.5903	0.949541
$567$	−1.39938	−0.0587686
$568$	−23.2012	−0.973499
$569$	−26.4603	−1.10927	−0.554637	−	0.832092i	$-0.687143\pi$
$569$	−26.4603	−1.10927	−0.554637	+	0.832092i	$0.687143\pi$
$570$	−0.734052	−0.0307460
$571$	9.51223	0.398074	0.199037	−	0.979992i	$-0.436219\pi$
$571$	9.51223	0.398074	0.199037	+	0.979992i	$0.436219\pi$
$572$	−6.14414	−0.256899
$573$	19.5484	0.816646
$574$	43.4348	1.81293
$575$	−23.1674	−0.966148
$576$	−61.4504	−2.56043
$577$	39.6088	1.64894	0.824468	−	0.565908i	$-0.191474\pi$
$577$	39.6088	1.64894	0.824468	+	0.565908i	$0.191474\pi$
$578$	28.6577	1.19200
$579$	32.1137	1.33460
$580$	−0.605984	−0.0251621
$581$	31.5612	1.30938
$582$	−47.7426	−1.97899
$583$	−15.6683	−0.648915
$584$	34.7488	1.43791
$585$	−0.351576	−0.0145359
$586$	−63.2171	−2.61147
$587$	−41.6226	−1.71795	−0.858974	−	0.512019i	$-0.828898\pi$
$587$	−41.6226	−1.71795	−0.858974	+	0.512019i	$0.828898\pi$
$588$	−8.83706	−0.364434
$589$	8.20507	0.338084
$590$	0.600273	0.0247128
$591$	−18.9995	−0.781535
$592$	−0.147796	−0.00607437
$593$	−0.570622	−0.0234326	−0.0117163	−	0.999931i	$-0.503730\pi$
$593$	−0.570622	−0.0234326	−0.0117163	+	0.999931i	$0.503730\pi$
$594$	15.2379	0.625217
$595$	0.275758	0.0113050
$596$	−10.7398	−0.439921
$597$	12.5313	0.512874
$598$	−14.8476	−0.607164
$599$	30.6984	1.25430	0.627151	−	0.778898i	$-0.284221\pi$
$599$	30.6984	1.25430	0.627151	+	0.778898i	$0.284221\pi$
$600$	40.5659	1.65610
$601$	−2.28502	−0.0932078	−0.0466039	−	0.998913i	$-0.514840\pi$
$601$	−2.28502	−0.0932078	−0.0466039	+	0.998913i	$0.514840\pi$
$602$	−28.2264	−1.15042
$603$	8.39681	0.341944
$604$	−33.1868	−1.35035
$605$	0.485422	0.0197352
$606$	−45.5749	−1.85136
$607$	25.0871	1.01826	0.509128	−	0.860691i	$-0.329968\pi$
$607$	25.0871	1.01826	0.509128	+	0.860691i	$0.329968\pi$
$608$	−11.9105	−0.483034
$609$	24.0075	0.972834
$610$	1.03089	0.0417397
$611$	7.78387	0.314902
$612$	−33.1189	−1.33875
$613$	−34.2215	−1.38219	−0.691096	−	0.722763i	$-0.742872\pi$
$613$	−34.2215	−1.38219	−0.691096	+	0.722763i	$0.742872\pi$
$614$	−27.6002	−1.11385
$615$	1.13503	0.0457687
$616$	9.63504	0.388207
$617$	1.18511	0.0477107	0.0238553	−	0.999715i	$-0.492406\pi$
$617$	1.18511	0.0477107	0.0238553	+	0.999715i	$0.492406\pi$
$618$	−117.219	−4.71525
$619$	−8.55625	−0.343905	−0.171952	−	0.985105i	$-0.555008\pi$
$619$	−8.55625	−0.343905	−0.171952	+	0.985105i	$0.555008\pi$
$620$	0.652877	0.0262202
$621$	22.8455	0.916756
$622$	45.4139	1.82093
$623$	−7.96588	−0.319146
$624$	0.574732	0.0230077
$625$	24.9581	0.998325
$626$	26.1562	1.04541
$627$	8.15177	0.325550
$628$	−60.1079	−2.39857
$629$	2.12489	0.0847249
$630$	1.42033	0.0565875
$631$	−27.9874	−1.11416	−0.557081	−	0.830458i	$-0.688079\pi$
$631$	−27.9874	−1.11416	−0.557081	+	0.830458i	$0.688079\pi$
$632$	−30.8489	−1.22710
$633$	−27.5366	−1.09448
$634$	75.7991	3.01037
$635$	−0.419947	−0.0166651
$636$	105.965	4.20177
$637$	−1.35332	−0.0536205
$638$	10.8469	0.429433
$639$	37.9815	1.50252
$640$	−0.983574	−0.0388792
$641$	−31.8356	−1.25743	−0.628715	−	0.777636i	$-0.716419\pi$
$641$	−31.8356	−1.25743	−0.628715	+	0.777636i	$0.716419\pi$
$642$	−102.623	−4.05023
$643$	20.4747	0.807443	0.403721	−	0.914882i	$-0.367717\pi$
$643$	20.4747	0.807443	0.403721	+	0.914882i	$0.367717\pi$
$644$	37.2142	1.46644
$645$	−0.737603	−0.0290431
$646$	−10.5895	−0.416639
$647$	−27.4791	−1.08031	−0.540157	−	0.841565i	$-0.681635\pi$
$647$	−27.4791	−1.08031	−0.540157	+	0.841565i	$0.681635\pi$
$648$	1.65980	0.0652029
$649$	−6.66614	−0.261669
$650$	16.0042	0.627736
$651$	−25.8653	−1.01374
$652$	3.26888	0.128019
$653$	−30.5596	−1.19589	−0.597945	−	0.801537i	$-0.704016\pi$
$653$	−30.5596	−1.19589	−0.597945	+	0.801537i	$0.704016\pi$
$654$	−87.1247	−3.40685
$655$	0.274842	0.0107390
$656$	−1.13889	−0.0444661
$657$	−56.8855	−2.21932
$658$	−31.4461	−1.22590
$659$	38.5951	1.50345	0.751727	−	0.659475i	$-0.229221\pi$
$659$	38.5951	1.50345	0.751727	+	0.659475i	$0.229221\pi$
$660$	0.648636	0.0252481
$661$	19.4069	0.754839	0.377420	−	0.926042i	$-0.376811\pi$
$661$	19.4069	0.754839	0.377420	+	0.926042i	$0.376811\pi$
$662$	−35.7866	−1.39088
$663$	−8.26303	−0.320910
$664$	−37.4344	−1.45274
$665$	0.281755	0.0109260
$666$	10.9446	0.424094
$667$	16.2623	0.629678
$668$	76.9069	2.97562
$669$	41.1366	1.59043
$670$	0.213631	0.00825328
$671$	−11.4483	−0.441956
$672$	37.5461	1.44837
$673$	−12.8354	−0.494768	−0.247384	−	0.968917i	$-0.579571\pi$
$673$	−12.8354	−0.494768	−0.247384	+	0.968917i	$0.579571\pi$
$674$	−18.8845	−0.727403
$675$	−24.6250	−0.947818
$676$	−36.1319	−1.38969
$677$	38.4433	1.47750	0.738749	−	0.673981i	$-0.235417\pi$
$677$	38.4433	1.47750	0.738749	+	0.673981i	$0.235417\pi$
$678$	−90.5467	−3.47743
$679$	18.3253	0.703260
$680$	−0.327074	−0.0125427
$681$	49.4527	1.89503
$682$	−11.6863	−0.447491
$683$	40.5546	1.55178	0.775889	−	0.630870i	$-0.217302\pi$
$683$	40.5546	1.55178	0.775889	+	0.630870i	$0.217302\pi$
$684$	−33.8391	−1.29387
$685$	0.262878	0.0100440
$686$	44.9237	1.71519
$687$	61.1827	2.33427
$688$	0.740113	0.0282165
$689$	16.2276	0.618221
$690$	1.56746	0.0596721
$691$	33.6569	1.28037	0.640185	−	0.768221i	$-0.278858\pi$
$691$	33.6569	1.28037	0.640185	+	0.768221i	$0.278858\pi$
$692$	−17.1528	−0.652053
$693$	−15.7731	−0.599169
$694$	23.4468	0.890029
$695$	0.561365	0.0212938
$696$	−28.4751	−1.07935
$697$	16.3740	0.620210
$698$	46.9392	1.77668
$699$	67.2183	2.54243
$700$	−40.1131	−1.51613
$701$	−4.23754	−0.160050	−0.0800248	−	0.996793i	$-0.525500\pi$
$701$	−4.23754	−0.160050	−0.0800248	+	0.996793i	$0.525500\pi$
$702$	−15.7818	−0.595645
$703$	2.17110	0.0818847
$704$	17.3620	0.654356
$705$	−0.821742	−0.0309486
$706$	44.7392	1.68378
$707$	17.4933	0.657903
$708$	45.0830	1.69432
$709$	−27.3116	−1.02571	−0.512854	−	0.858476i	$-0.671412\pi$
$709$	−27.3116	−1.02571	−0.512854	+	0.858476i	$0.671412\pi$
$710$	0.966322	0.0362654
$711$	50.5012	1.89394
$712$	9.44825	0.354088
$713$	−17.5207	−0.656156
$714$	33.3819	1.24929
$715$	0.0993331	0.00371485
$716$	68.0080	2.54158
$717$	−31.2551	−1.16724
$718$	24.9184	0.929948
$719$	0.364327	0.0135871	0.00679355	−	0.999977i	$-0.497838\pi$
$719$	0.364327	0.0135871	0.00679355	+	0.999977i	$0.497838\pi$
$720$	−0.0372421	−0.00138793
$721$	44.9929	1.67562
$722$	32.7928	1.22042
$723$	−47.3590	−1.76130
$724$	34.3453	1.27643
$725$	−17.5291	−0.651013
$726$	58.7629	2.18089
$727$	35.9189	1.33216	0.666080	−	0.745880i	$-0.267971\pi$
$727$	35.9189	1.33216	0.666080	+	0.745880i	$0.267971\pi$
$728$	−9.97896	−0.369845
$729$	−43.9200	−1.62667
$730$	−1.44728	−0.0535661
$731$	−10.6407	−0.393562
$732$	77.4245	2.86169
$733$	45.6887	1.68755	0.843775	−	0.536697i	$-0.180328\pi$
$733$	45.6887	1.68755	0.843775	+	0.536697i	$0.180328\pi$
$734$	−56.0585	−2.06916
$735$	0.142870	0.00526984
$736$	25.4331	0.937476
$737$	−2.37241	−0.0873888
$738$	84.3370	3.10449
$739$	−9.57959	−0.352391	−0.176195	−	0.984355i	$-0.556379\pi$
$739$	−9.57959	−0.352391	−0.176195	+	0.984355i	$0.556379\pi$
$740$	0.172755	0.00635058
$741$	−8.44274	−0.310152
$742$	−65.5579	−2.40671
$743$	−43.7415	−1.60472	−0.802360	−	0.596840i	$-0.796423\pi$
$743$	−43.7415	−1.60472	−0.802360	+	0.596840i	$0.796423\pi$
$744$	30.6786	1.12473
$745$	0.173632	0.00636140
$746$	15.9891	0.585401
$747$	61.2821	2.24219
$748$	9.35730	0.342137
$749$	39.3905	1.43930
$750$	−3.38006	−0.123422
$751$	4.32744	0.157910	0.0789552	−	0.996878i	$-0.474842\pi$
$751$	4.32744	0.157910	0.0789552	+	0.996878i	$0.474842\pi$
$752$	0.824538	0.0300678
$753$	−67.8428	−2.47233
$754$	−11.2341	−0.409121
$755$	0.536536	0.0195265
$756$	39.5556	1.43862
$757$	−9.80858	−0.356499	−0.178249	−	0.983985i	$-0.557043\pi$
$757$	−9.80858	−0.356499	−0.178249	+	0.983985i	$0.557043\pi$
$758$	−3.01471	−0.109499
$759$	−17.4069	−0.631831
$760$	−0.334187	−0.0121222
$761$	39.4964	1.43174	0.715872	−	0.698232i	$-0.246030\pi$
$761$	39.4964	1.43174	0.715872	+	0.698232i	$0.246030\pi$
$762$	−50.8368	−1.84162
$763$	33.4416	1.21067
$764$	22.9273	0.829482
$765$	0.535437	0.0193588
$766$	44.7100	1.61544
$767$	6.90408	0.249292
$768$	−47.2261	−1.70413
$769$	−39.2469	−1.41528	−0.707639	−	0.706574i	$-0.750240\pi$
$769$	−39.2469	−1.41528	−0.707639	+	0.706574i	$0.750240\pi$
$770$	−0.401297	−0.0144617
$771$	−42.9761	−1.54775
$772$	37.6645	1.35558
$773$	−41.8724	−1.50605	−0.753023	−	0.657994i	$-0.771405\pi$
$773$	−41.8724	−1.50605	−0.753023	+	0.657994i	$0.771405\pi$
$774$	−54.8069	−1.96999
$775$	18.8855	0.678388
$776$	−21.7355	−0.780258
$777$	−6.84409	−0.245531
$778$	−65.8268	−2.36000
$779$	16.7301	0.599419
$780$	−0.671789	−0.0240539
$781$	−10.7312	−0.383992
$782$	22.6123	0.808616
$783$	17.2855	0.617732
$784$	−0.143356	−0.00511986
$785$	0.971772	0.0346840
$786$	33.2711	1.18674
$787$	44.3472	1.58081	0.790403	−	0.612587i	$-0.209871\pi$
$787$	44.3472	1.58081	0.790403	+	0.612587i	$0.209871\pi$
$788$	−22.2836	−0.793819
$789$	58.6695	2.08869
$790$	1.28485	0.0457128
$791$	34.7551	1.23575
$792$	18.7083	0.664770
$793$	11.8569	0.421051
$794$	74.3526	2.63868
$795$	−1.71314	−0.0607589
$796$	14.6974	0.520935
$797$	48.0077	1.70052	0.850260	−	0.526363i	$-0.176445\pi$
$797$	48.0077	1.70052	0.850260	+	0.526363i	$0.176445\pi$
$798$	34.1079	1.20741
$799$	−11.8545	−0.419384
$800$	−27.4142	−0.969239
$801$	−15.4673	−0.546510
$802$	−3.78144	−0.133527
$803$	16.0723	0.567178
$804$	16.0446	0.565848
$805$	−0.601647	−0.0212053
$806$	12.1034	0.426325
$807$	43.3710	1.52673
$808$	−20.7486	−0.729934
$809$	−35.0264	−1.23146	−0.615731	−	0.787957i	$-0.711139\pi$
$809$	−35.0264	−1.23146	−0.615731	+	0.787957i	$0.711139\pi$
$810$	−0.0691301	−0.00242898
$811$	28.5946	1.00409	0.502045	−	0.864841i	$-0.332581\pi$
$811$	28.5946	1.00409	0.502045	+	0.864841i	$0.332581\pi$
$812$	28.1572	0.988125
$813$	−42.7758	−1.50021
$814$	−3.09225	−0.108383
$815$	−0.0528483	−0.00185120
$816$	−0.875296	−0.0306415
$817$	−10.8722	−0.380369
$818$	35.0312	1.22484
$819$	16.3361	0.570829
$820$	1.33122	0.0464881
$821$	52.7986	1.84268	0.921342	−	0.388753i	$-0.127094\pi$
$821$	52.7986	1.84268	0.921342	+	0.388753i	$0.127094\pi$
$822$	31.8228	1.10995
$823$	−46.7397	−1.62924	−0.814622	−	0.579993i	$-0.803055\pi$
$823$	−46.7397	−1.62924	−0.814622	+	0.579993i	$0.803055\pi$
$824$	−53.3657	−1.85908
$825$	18.7629	0.653239
$826$	−27.8919	−0.970482
$827$	10.4660	0.363938	0.181969	−	0.983304i	$-0.441753\pi$
$827$	10.4660	0.363938	0.181969	+	0.983304i	$0.441753\pi$
$828$	72.2585	2.51116
$829$	21.0636	0.731568	0.365784	−	0.930700i	$-0.380801\pi$
$829$	21.0636	0.731568	0.365784	+	0.930700i	$0.380801\pi$
$830$	1.55913	0.0541183
$831$	5.35138	0.185637
$832$	−17.9817	−0.623404
$833$	2.06106	0.0714114
$834$	67.9561	2.35313
$835$	−1.24336	−0.0430284
$836$	9.56081	0.330667
$837$	−18.6231	−0.643708
$838$	71.0861	2.45563
$839$	32.5229	1.12281	0.561407	−	0.827540i	$-0.310260\pi$
$839$	32.5229	1.12281	0.561407	+	0.827540i	$0.310260\pi$
$840$	1.05348	0.0363484
$841$	−16.6955	−0.575708
$842$	53.5998	1.84717
$843$	−71.8034	−2.47304
$844$	−32.2963	−1.11168
$845$	0.584149	0.0200954
$846$	−61.0587	−2.09924
$847$	−22.5553	−0.775009
$848$	1.71897	0.0590297
$849$	−27.4296	−0.941381
$850$	−24.3738	−0.836014
$851$	−4.63607	−0.158922
$852$	72.5748	2.48637
$853$	21.8689	0.748777	0.374388	−	0.927272i	$-0.377853\pi$
$853$	21.8689	0.748777	0.374388	+	0.927272i	$0.377853\pi$
$854$	−47.9009	−1.63913
$855$	0.547082	0.0187098
$856$	−46.7207	−1.59688
$857$	22.9383	0.783558	0.391779	−	0.920059i	$-0.371860\pi$
$857$	22.9383	0.783558	0.391779	+	0.920059i	$0.371860\pi$
$858$	12.0248	0.410520
$859$	2.27293	0.0775513	0.0387756	−	0.999248i	$-0.487654\pi$
$859$	2.27293	0.0775513	0.0387756	+	0.999248i	$0.487654\pi$
$860$	−0.865098	−0.0294996
$861$	−52.7394	−1.79735
$862$	22.3697	0.761916
$863$	20.0548	0.682674	0.341337	−	0.939941i	$-0.389120\pi$
$863$	20.0548	0.682674	0.341337	+	0.939941i	$0.389120\pi$
$864$	27.0333	0.919690
$865$	0.277312	0.00942889
$866$	10.3346	0.351184
$867$	−34.7968	−1.18176
$868$	−30.3361	−1.02968
$869$	−14.2684	−0.484024
$870$	1.18598	0.0402085
$871$	2.45709	0.0832553
$872$	−39.6647	−1.34322
$873$	35.5821	1.20427
$874$	23.1041	0.781509
$875$	1.29739	0.0438597
$876$	−108.697	−3.67251
$877$	48.2112	1.62798	0.813988	−	0.580882i	$-0.197292\pi$
$877$	48.2112	1.62798	0.813988	+	0.580882i	$0.197292\pi$
$878$	41.0209	1.38439
$879$	76.7593	2.58903
$880$	0.0105223	0.000354705 0
$881$	−50.4384	−1.69931	−0.849657	−	0.527336i	$-0.823191\pi$
$881$	−50.4384	−1.69931	−0.849657	+	0.527336i	$0.823191\pi$
$882$	10.6158	0.357453
$883$	−47.0901	−1.58471	−0.792355	−	0.610061i	$-0.791145\pi$
$883$	−47.0901	−1.58471	−0.792355	+	0.610061i	$0.791145\pi$
$884$	−9.69130	−0.325954
$885$	−0.728863	−0.0245004
$886$	42.9675	1.44352
$887$	5.82647	0.195634	0.0978168	−	0.995204i	$-0.468814\pi$
$887$	5.82647	0.195634	0.0978168	+	0.995204i	$0.468814\pi$
$888$	8.11772	0.272413
$889$	19.5130	0.654445
$890$	−0.393517	−0.0131907
$891$	0.767702	0.0257190
$892$	48.2471	1.61543
$893$	−12.1124	−0.405325
$894$	21.0191	0.702984
$895$	−1.09949	−0.0367520
$896$	45.7021	1.52680
$897$	18.0282	0.601945
$898$	−47.9171	−1.59901
$899$	−13.2566	−0.442134
$900$	−77.8872	−2.59624
$901$	−24.7140	−0.823342
$902$	−23.8283	−0.793396
$903$	34.2730	1.14053
$904$	−41.2227	−1.37105
$905$	−0.555265	−0.0184576
$906$	64.9505	2.15783
$907$	15.1510	0.503082	0.251541	−	0.967847i	$-0.419063\pi$
$907$	15.1510	0.503082	0.251541	+	0.967847i	$0.419063\pi$
$908$	58.0006	1.92482
$909$	33.9666	1.12660
$910$	0.415621	0.0137777
$911$	−19.4366	−0.643963	−0.321982	−	0.946746i	$-0.604349\pi$
$911$	−19.4366	−0.643963	−0.321982	+	0.946746i	$0.604349\pi$
$912$	−0.894332	−0.0296143
$913$	−17.3144	−0.573024
$914$	−0.774791	−0.0256278
$915$	−1.25173	−0.0413810
$916$	71.7582	2.37096
$917$	−12.7706	−0.421723
$918$	24.0351	0.793275
$919$	7.37542	0.243293	0.121646	−	0.992574i	$-0.461183\pi$
$919$	7.37542	0.243293	0.121646	+	0.992574i	$0.461183\pi$
$920$	0.713607	0.0235269
$921$	33.5127	1.10428
$922$	91.1091	3.00052
$923$	11.1142	0.365829
$924$	−30.1391	−0.991503
$925$	4.99721	0.164307
$926$	15.0398	0.494237
$927$	87.3624	2.86936
$928$	19.2433	0.631693
$929$	13.2323	0.434138	0.217069	−	0.976156i	$-0.430350\pi$
$929$	13.2323	0.434138	0.217069	+	0.976156i	$0.430350\pi$
$930$	−1.27776	−0.0418993
$931$	2.10588	0.0690175
$932$	78.8370	2.58239
$933$	−55.1425	−1.80528
$934$	45.4291	1.48649
$935$	−0.151281	−0.00494741
$936$	−19.3761	−0.633327
$937$	11.7624	0.384261	0.192131	−	0.981369i	$-0.438460\pi$
$937$	11.7624	0.384261	0.192131	+	0.981369i	$0.438460\pi$
$938$	−9.92642	−0.324109
$939$	−31.7593	−1.03643
$940$	−0.963780	−0.0314350
$941$	43.4138	1.41525	0.707624	−	0.706589i	$-0.249767\pi$
$941$	43.4138	1.41525	0.707624	+	0.706589i	$0.249767\pi$
$942$	117.638	3.83286
$943$	−35.7247	−1.16336
$944$	0.731343	0.0238032
$945$	−0.639501	−0.0208030
$946$	15.4850	0.503460
$947$	38.4921	1.25082	0.625412	−	0.780295i	$-0.284931\pi$
$947$	38.4921	1.25082	0.625412	+	0.780295i	$0.284931\pi$
$948$	96.4973	3.13409
$949$	−16.6459	−0.540350
$950$	−24.9039	−0.807988
$951$	−92.0368	−2.98450
$952$	15.1976	0.492557
$953$	1.01804	0.0329775	0.0164888	−	0.999864i	$-0.494751\pi$
$953$	1.01804	0.0329775	0.0164888	+	0.999864i	$0.494751\pi$
$954$	−127.293	−4.12127
$955$	−0.370669	−0.0119946
$956$	−36.6575	−1.18559
$957$	−13.1705	−0.425743
$958$	16.2306	0.524388
$959$	−12.2147	−0.394433
$960$	1.89833	0.0612683
$961$	−16.7175	−0.539275
$962$	3.20263	0.103257
$963$	76.4843	2.46467
$964$	−55.5450	−1.78898
$965$	−0.608927	−0.0196020
$966$	−72.8325	−2.34335
$967$	−42.1431	−1.35523	−0.677616	−	0.735416i	$-0.736987\pi$
$967$	−42.1431	−1.35523	−0.677616	+	0.735416i	$0.736987\pi$
$968$	26.7526	0.859861
$969$	12.8580	0.413058
$970$	0.905276	0.0290667
$971$	1.24953	0.0400993	0.0200496	−	0.999799i	$-0.493618\pi$
$971$	1.24953	0.0400993	0.0200496	+	0.999799i	$0.493618\pi$
$972$	−53.5167	−1.71655
$973$	−26.0840	−0.836214
$974$	52.0830	1.66885
$975$	−19.4326	−0.622341
$976$	1.25599	0.0402033
$977$	10.6515	0.340770	0.170385	−	0.985378i	$-0.445499\pi$
$977$	10.6515	0.340770	0.170385	+	0.985378i	$0.445499\pi$
$978$	−6.39757	−0.204572
$979$	4.37008	0.139668
$980$	0.167565	0.00535267
$981$	64.9332	2.07316
$982$	50.7943	1.62091
$983$	−15.2863	−0.487558	−0.243779	−	0.969831i	$-0.578387\pi$
$983$	−15.2863	−0.487558	−0.243779	+	0.969831i	$0.578387\pi$
$984$	62.5537	1.99414
$985$	0.360261	0.0114789
$986$	17.1091	0.544865
$987$	38.1825	1.21536
$988$	−9.90207	−0.315027
$989$	23.2159	0.738223
$990$	−0.779195	−0.0247645
$991$	0.854743	0.0271518	0.0135759	−	0.999908i	$-0.495679\pi$
$991$	0.854743	0.0271518	0.0135759	+	0.999908i	$0.495679\pi$
$992$	−20.7325	−0.658256
$993$	43.4527	1.37893
$994$	−44.9005	−1.42416
$995$	−0.237614	−0.00753288
$996$	117.097	3.71037
$997$	−53.5354	−1.69548	−0.847742	−	0.530409i	$-0.822038\pi$
$997$	−53.5354	−1.69548	−0.847742	+	0.530409i	$0.822038\pi$
$998$	24.4703	0.774593
$999$	−4.92776	−0.155907

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	6031.2.a.d.1.15	✓	133

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
6031.2.a.d.1.15	✓	133	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:	\( N \)	\(=\)	\( 6031 = 37 \cdot 163 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	6031.a (trivial)

\(f(q)\)	\(=\)	\(q-2.29540 q^{2} +2.78712 q^{3} +3.26888 q^{4} -0.0528483 q^{5} -6.39757 q^{6} +2.45561 q^{7} -2.91258 q^{8} +4.76805 q^{9} +O(q^{10})\)	\(q-2.29540 q^{2} +2.78712 q^{3} +3.26888 q^{4} -0.0528483 q^{5} -6.39757 q^{6} +2.45561 q^{7} -2.91258 q^{8} +4.76805 q^{9} +0.121308 q^{10} -1.34715 q^{11} +9.11075 q^{12} +1.39523 q^{13} -5.63662 q^{14} -0.147295 q^{15} +0.147796 q^{16} -2.12489 q^{17} -10.9446 q^{18} -2.17110 q^{19} -0.172755 q^{20} +6.84409 q^{21} +3.09225 q^{22} +4.63607 q^{23} -8.11772 q^{24} -4.99721 q^{25} -3.20263 q^{26} +4.92776 q^{27} +8.02710 q^{28} +3.50777 q^{29} +0.338101 q^{30} -3.77922 q^{31} +5.48591 q^{32} -3.75467 q^{33} +4.87748 q^{34} -0.129775 q^{35} +15.5862 q^{36} -1.00000 q^{37} +4.98356 q^{38} +3.88869 q^{39} +0.153925 q^{40} -7.70582 q^{41} -15.7100 q^{42} +5.00767 q^{43} -4.40366 q^{44} -0.251983 q^{45} -10.6417 q^{46} +5.57890 q^{47} +0.411925 q^{48} -0.969960 q^{49} +11.4706 q^{50} -5.92233 q^{51} +4.56085 q^{52} +11.6307 q^{53} -11.3112 q^{54} +0.0711946 q^{55} -7.15217 q^{56} -6.05113 q^{57} -8.05175 q^{58} +4.94833 q^{59} -0.481488 q^{60} +8.49815 q^{61} +8.67483 q^{62} +11.7085 q^{63} -12.8880 q^{64} -0.0737358 q^{65} +8.61848 q^{66} +1.76106 q^{67} -6.94600 q^{68} +12.9213 q^{69} +0.297886 q^{70} +7.96584 q^{71} -13.8873 q^{72} -11.9306 q^{73} +2.29540 q^{74} -13.9278 q^{75} -7.09707 q^{76} -3.30808 q^{77} -8.92611 q^{78} +10.5916 q^{79} -0.00781076 q^{80} -0.569871 q^{81} +17.6880 q^{82} +12.8527 q^{83} +22.3725 q^{84} +0.112297 q^{85} -11.4946 q^{86} +9.77659 q^{87} +3.92368 q^{88} -3.24394 q^{89} +0.578403 q^{90} +3.42616 q^{91} +15.1547 q^{92} -10.5331 q^{93} -12.8058 q^{94} +0.114739 q^{95} +15.2899 q^{96} +7.46261 q^{97} +2.22645 q^{98} -6.42327 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 133 q + 14 q^{2} + 8 q^{3} + 142 q^{4} + 34 q^{5} + 20 q^{6} + 8 q^{7} + 42 q^{8} + 177 q^{9}+O(q^{10}) \) 133 * q + 14 * q^2 + 8 * q^3 + 142 * q^4 + 34 * q^5 + 20 * q^6 + 8 * q^7 + 42 * q^8 + 177 * q^9	\( 133 q + 14 q^{2} + 8 q^{3} + 142 q^{4} + 34 q^{5} + 20 q^{6} + 8 q^{7} + 42 q^{8} + 177 q^{9} + 9 q^{10} + 23 q^{11} + 24 q^{12} + 23 q^{13} + 31 q^{14} + 9 q^{15} + 168 q^{16} + 98 q^{17} + 38 q^{18} + 29 q^{19} + 83 q^{20} + 26 q^{21} + 2 q^{22} + 34 q^{23} + 75 q^{24} + 177 q^{25} + 67 q^{26} + 32 q^{27} + 32 q^{28} + 91 q^{29} + 12 q^{30} + 24 q^{31} + 88 q^{32} + 27 q^{33} + 23 q^{34} + 66 q^{35} + 232 q^{36} - 133 q^{37} + 26 q^{38} + 28 q^{39} + 41 q^{40} + 132 q^{41} + 13 q^{42} + 11 q^{43} + 65 q^{44} + 107 q^{45} + 20 q^{46} + 10 q^{47} + 27 q^{48} + 229 q^{49} + 78 q^{50} + 19 q^{51} + 71 q^{52} + 7 q^{53} + 43 q^{54} + 41 q^{55} + 67 q^{56} + 45 q^{57} + 25 q^{58} + 97 q^{59} - 42 q^{60} + 65 q^{61} + 24 q^{62} + 39 q^{63} + 200 q^{64} + 60 q^{65} + 35 q^{66} + 25 q^{67} + 227 q^{68} + 120 q^{69} + 37 q^{70} + 26 q^{71} + 93 q^{72} + 55 q^{73} - 14 q^{74} + 5 q^{75} + 34 q^{76} + 21 q^{77} - 2 q^{78} + 50 q^{79} + 162 q^{80} + 341 q^{81} + 66 q^{82} + 30 q^{83} - 89 q^{84} + 30 q^{85} - 12 q^{86} + 80 q^{87} - 85 q^{88} + 225 q^{89} - 86 q^{90} + q^{91} + 82 q^{92} + 42 q^{93} - 17 q^{94} + 70 q^{95} + 55 q^{96} + 12 q^{97} + 90 q^{98} + 17 q^{99}+O(q^{100}) \) 133 * q + 14 * q^2 + 8 * q^3 + 142 * q^4 + 34 * q^5 + 20 * q^6 + 8 * q^7 + 42 * q^8 + 177 * q^9 + 9 * q^10 + 23 * q^11 + 24 * q^12 + 23 * q^13 + 31 * q^14 + 9 * q^15 + 168 * q^16 + 98 * q^17 + 38 * q^18 + 29 * q^19 + 83 * q^20 + 26 * q^21 + 2 * q^22 + 34 * q^23 + 75 * q^24 + 177 * q^25 + 67 * q^26 + 32 * q^27 + 32 * q^28 + 91 * q^29 + 12 * q^30 + 24 * q^31 + 88 * q^32 + 27 * q^33 + 23 * q^34 + 66 * q^35 + 232 * q^36 - 133 * q^37 + 26 * q^38 + 28 * q^39 + 41 * q^40 + 132 * q^41 + 13 * q^42 + 11 * q^43 + 65 * q^44 + 107 * q^45 + 20 * q^46 + 10 * q^47 + 27 * q^48 + 229 * q^49 + 78 * q^50 + 19 * q^51 + 71 * q^52 + 7 * q^53 + 43 * q^54 + 41 * q^55 + 67 * q^56 + 45 * q^57 + 25 * q^58 + 97 * q^59 - 42 * q^60 + 65 * q^61 + 24 * q^62 + 39 * q^63 + 200 * q^64 + 60 * q^65 + 35 * q^66 + 25 * q^67 + 227 * q^68 + 120 * q^69 + 37 * q^70 + 26 * q^71 + 93 * q^72 + 55 * q^73 - 14 * q^74 + 5 * q^75 + 34 * q^76 + 21 * q^77 - 2 * q^78 + 50 * q^79 + 162 * q^80 + 341 * q^81 + 66 * q^82 + 30 * q^83 - 89 * q^84 + 30 * q^85 - 12 * q^86 + 80 * q^87 - 85 * q^88 + 225 * q^89 - 86 * q^90 + q^91 + 82 * q^92 + 42 * q^93 - 17 * q^94 + 70 * q^95 + 55 * q^96 + 12 * q^97 + 90 * q^98 + 17 * q^99

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