LMFDB - Embedded newform 6013.2.a.f.1.7

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [6013,2,Mod(1,6013)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(6013, 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("6013.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 6013 = 7 \cdot 859 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	6013.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:	$48.0140467354$
Analytic rank:	$0$
Dimension:	$110$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.7
Character	$\chi$	$=$	6013.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-2.55830 q^{2} -1.85077 q^{3} +4.54491 q^{4} +3.83295 q^{5} +4.73481 q^{6} -1.00000 q^{7} -6.51064 q^{8} +0.425331 q^{9} +O(q^{10})$	\(q-2.55830 q^{2} -1.85077 q^{3} +4.54491 q^{4} +3.83295 q^{5} +4.73481 q^{6} -1.00000 q^{7} -6.51064 q^{8} +0.425331 q^{9} -9.80585 q^{10} +3.01326 q^{11} -8.41155 q^{12} +2.53009 q^{13} +2.55830 q^{14} -7.09390 q^{15} +7.56636 q^{16} +0.588414 q^{17} -1.08813 q^{18} +0.607741 q^{19} +17.4204 q^{20} +1.85077 q^{21} -7.70883 q^{22} +6.48122 q^{23} +12.0497 q^{24} +9.69153 q^{25} -6.47274 q^{26} +4.76511 q^{27} -4.54491 q^{28} +2.43029 q^{29} +18.1483 q^{30} +1.55962 q^{31} -6.33575 q^{32} -5.57683 q^{33} -1.50534 q^{34} -3.83295 q^{35} +1.93309 q^{36} +7.58953 q^{37} -1.55478 q^{38} -4.68261 q^{39} -24.9550 q^{40} -7.23818 q^{41} -4.73481 q^{42} +7.92709 q^{43} +13.6950 q^{44} +1.63027 q^{45} -16.5809 q^{46} -4.57924 q^{47} -14.0036 q^{48} +1.00000 q^{49} -24.7939 q^{50} -1.08902 q^{51} +11.4990 q^{52} +4.74654 q^{53} -12.1906 q^{54} +11.5497 q^{55} +6.51064 q^{56} -1.12479 q^{57} -6.21742 q^{58} -2.37049 q^{59} -32.2411 q^{60} -8.64949 q^{61} -3.98999 q^{62} -0.425331 q^{63} +1.07605 q^{64} +9.69773 q^{65} +14.2672 q^{66} +7.62289 q^{67} +2.67429 q^{68} -11.9952 q^{69} +9.80585 q^{70} +8.52939 q^{71} -2.76918 q^{72} -9.65113 q^{73} -19.4163 q^{74} -17.9368 q^{75} +2.76213 q^{76} -3.01326 q^{77} +11.9795 q^{78} +13.0359 q^{79} +29.0015 q^{80} -10.0951 q^{81} +18.5174 q^{82} -5.55090 q^{83} +8.41155 q^{84} +2.25536 q^{85} -20.2799 q^{86} -4.49790 q^{87} -19.6182 q^{88} -4.67862 q^{89} -4.17073 q^{90} -2.53009 q^{91} +29.4565 q^{92} -2.88650 q^{93} +11.7151 q^{94} +2.32944 q^{95} +11.7260 q^{96} +11.3067 q^{97} -2.55830 q^{98} +1.28163 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 110 q + 16 q^{2} + 29 q^{3} + 118 q^{4} + 12 q^{6} - 110 q^{7} + 57 q^{8} + 127 q^{9}+O(q^{10}) $ 110 * q + 16 * q^2 + 29 * q^3 + 118 * q^4 + 12 * q^6 - 110 * q^7 + 57 * q^8 + 127 * q^9	\( 110 q + 16 q^{2} + 29 q^{3} + 118 q^{4} + 12 q^{6} - 110 q^{7} + 57 q^{8} + 127 q^{9} + 3 q^{10} + 52 q^{11} + 62 q^{12} - 9 q^{13} - 16 q^{14} + 39 q^{15} + 146 q^{16} + 11 q^{17} + 60 q^{18} + 14 q^{19} + 18 q^{20} - 29 q^{21} + 32 q^{22} + 73 q^{23} + 24 q^{24} + 132 q^{25} - 7 q^{26} + 116 q^{27} - 118 q^{28} + 35 q^{29} + 18 q^{30} + 36 q^{31} + 140 q^{32} + 42 q^{33} - 7 q^{34} + 180 q^{36} + 49 q^{37} + 45 q^{39} + 6 q^{40} - 14 q^{41} - 12 q^{42} + 58 q^{43} + 92 q^{44} + 17 q^{45} + 27 q^{46} + 87 q^{47} + 98 q^{48} + 110 q^{49} + 91 q^{50} + 42 q^{51} + 16 q^{52} + 95 q^{53} + 41 q^{54} + 8 q^{55} - 57 q^{56} + 61 q^{57} + 46 q^{58} + 114 q^{59} + 81 q^{60} - 47 q^{61} + 31 q^{62} - 127 q^{63} + 199 q^{64} + 62 q^{65} + 21 q^{66} + 95 q^{67} + 60 q^{68} - 39 q^{69} - 3 q^{70} + 131 q^{71} + 186 q^{72} + 31 q^{73} + 23 q^{74} + 121 q^{75} + 14 q^{76} - 52 q^{77} + 110 q^{78} + 9 q^{79} + 61 q^{80} + 194 q^{81} + 45 q^{82} + 73 q^{83} - 62 q^{84} + 59 q^{85} + 72 q^{86} + 64 q^{87} + 100 q^{88} - 17 q^{89} + 11 q^{90} + 9 q^{91} + 192 q^{92} + 85 q^{93} - 11 q^{94} + 108 q^{95} + 68 q^{96} + 32 q^{97} + 16 q^{98} + 160 q^{99}+O(q^{100}) \) 110 * q + 16 * q^2 + 29 * q^3 + 118 * q^4 + 12 * q^6 - 110 * q^7 + 57 * q^8 + 127 * q^9 + 3 * q^10 + 52 * q^11 + 62 * q^12 - 9 * q^13 - 16 * q^14 + 39 * q^15 + 146 * q^16 + 11 * q^17 + 60 * q^18 + 14 * q^19 + 18 * q^20 - 29 * q^21 + 32 * q^22 + 73 * q^23 + 24 * q^24 + 132 * q^25 - 7 * q^26 + 116 * q^27 - 118 * q^28 + 35 * q^29 + 18 * q^30 + 36 * q^31 + 140 * q^32 + 42 * q^33 - 7 * q^34 + 180 * q^36 + 49 * q^37 + 45 * q^39 + 6 * q^40 - 14 * q^41 - 12 * q^42 + 58 * q^43 + 92 * q^44 + 17 * q^45 + 27 * q^46 + 87 * q^47 + 98 * q^48 + 110 * q^49 + 91 * q^50 + 42 * q^51 + 16 * q^52 + 95 * q^53 + 41 * q^54 + 8 * q^55 - 57 * q^56 + 61 * q^57 + 46 * q^58 + 114 * q^59 + 81 * q^60 - 47 * q^61 + 31 * q^62 - 127 * q^63 + 199 * q^64 + 62 * q^65 + 21 * q^66 + 95 * q^67 + 60 * q^68 - 39 * q^69 - 3 * q^70 + 131 * q^71 + 186 * q^72 + 31 * q^73 + 23 * q^74 + 121 * q^75 + 14 * q^76 - 52 * q^77 + 110 * q^78 + 9 * q^79 + 61 * q^80 + 194 * q^81 + 45 * q^82 + 73 * q^83 - 62 * q^84 + 59 * q^85 + 72 * q^86 + 64 * q^87 + 100 * q^88 - 17 * q^89 + 11 * q^90 + 9 * q^91 + 192 * q^92 + 85 * q^93 - 11 * q^94 + 108 * q^95 + 68 * q^96 + 32 * q^97 + 16 * q^98 + 160 * 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 $

$2$	−2.55830	−1.80899	−0.904496	−	0.426482i	$-0.859753\pi$
$2$	−2.55830	−1.80899	−0.904496	+	0.426482i	$0.859753\pi$
$3$	−1.85077	−1.06854	−0.534270	−	0.845314i	$-0.679413\pi$
$3$	−1.85077	−1.06854	−0.534270	+	0.845314i	$0.679413\pi$
$4$	4.54491	2.27245
$5$	3.83295	1.71415	0.857074	−	0.515192i	$-0.172280\pi$
$5$	3.83295	1.71415	0.857074	+	0.515192i	$0.172280\pi$
$6$	4.73481	1.93298
$7$	−1.00000	−0.377964
$7$	−1.00000	−0.377964
$8$	−6.51064	−2.30186
$9$	0.425331	0.141777
$10$	−9.80585	−3.10088
$11$	3.01326	0.908532	0.454266	−	0.890866i	$-0.349902\pi$
$11$	3.01326	0.908532	0.454266	+	0.890866i	$0.349902\pi$
$12$	−8.41155	−2.42821
$13$	2.53009	0.701721	0.350861	−	0.936428i	$-0.385889\pi$
$13$	2.53009	0.701721	0.350861	+	0.936428i	$0.385889\pi$
$14$	2.55830	0.683735
$15$	−7.09390	−1.83164
$16$	7.56636	1.89159
$17$	0.588414	0.142711	0.0713557	−	0.997451i	$-0.477267\pi$
$17$	0.588414	0.142711	0.0713557	+	0.997451i	$0.477267\pi$
$18$	−1.08813	−0.256474
$19$	0.607741	0.139425	0.0697127	−	0.997567i	$-0.477792\pi$
$19$	0.607741	0.139425	0.0697127	+	0.997567i	$0.477792\pi$
$20$	17.4204	3.89532
$21$	1.85077	0.403870
$22$	−7.70883	−1.64353
$23$	6.48122	1.35143	0.675714	−	0.737164i	$-0.263835\pi$
$23$	6.48122	1.35143	0.675714	+	0.737164i	$0.263835\pi$
$24$	12.0497	2.45963
$25$	9.69153	1.93831
$26$	−6.47274	−1.26941
$27$	4.76511	0.917045
$28$	−4.54491	−0.858907
$29$	2.43029	0.451294	0.225647	−	0.974209i	$-0.427550\pi$
$29$	2.43029	0.451294	0.225647	+	0.974209i	$0.427550\pi$
$30$	18.1483	3.31342
$31$	1.55962	0.280117	0.140058	−	0.990143i	$-0.455271\pi$
$31$	1.55962	0.280117	0.140058	+	0.990143i	$0.455271\pi$
$32$	−6.33575	−1.12001
$33$	−5.57683	−0.970802
$34$	−1.50534	−0.258164
$35$	−3.83295	−0.647887
$36$	1.93309	0.322182
$37$	7.58953	1.24771	0.623855	−	0.781540i	$-0.285565\pi$
$37$	7.58953	1.24771	0.623855	+	0.781540i	$0.285565\pi$
$38$	−1.55478	−0.252219
$39$	−4.68261	−0.749817
$40$	−24.9550	−3.94573
$41$	−7.23818	−1.13041	−0.565207	−	0.824949i	$-0.691204\pi$
$41$	−7.23818	−1.13041	−0.565207	+	0.824949i	$0.691204\pi$
$42$	−4.73481	−0.730598
$43$	7.92709	1.20887	0.604435	−	0.796655i	$-0.293399\pi$
$43$	7.92709	1.20887	0.604435	+	0.796655i	$0.293399\pi$
$44$	13.6950	2.06460
$45$	1.63027	0.243027
$46$	−16.5809	−2.44472
$47$	−4.57924	−0.667950	−0.333975	−	0.942582i	$-0.608390\pi$
$47$	−4.57924	−0.667950	−0.333975	+	0.942582i	$0.608390\pi$
$48$	−14.0036	−2.02124
$49$	1.00000	0.142857
$50$	−24.7939	−3.50638
$51$	−1.08902	−0.152493
$52$	11.4990	1.59463
$53$	4.74654	0.651988	0.325994	−	0.945372i	$-0.394301\pi$
$53$	4.74654	0.651988	0.325994	+	0.945372i	$0.394301\pi$
$54$	−12.1906	−1.65893
$55$	11.5497	1.55736
$56$	6.51064	0.870020
$57$	−1.12479	−0.148982
$58$	−6.21742	−0.816387
$59$	−2.37049	−0.308611	−0.154306	−	0.988023i	$-0.549314\pi$
$59$	−2.37049	−0.308611	−0.154306	+	0.988023i	$0.549314\pi$
$60$	−32.2411	−4.16231
$61$	−8.64949	−1.10745	−0.553727	−	0.832698i	$-0.686795\pi$
$61$	−8.64949	−1.10745	−0.553727	+	0.832698i	$0.686795\pi$
$62$	−3.98999	−0.506729
$63$	−0.425331	−0.0535867
$64$	1.07605	0.134506
$65$	9.69773	1.20286
$66$	14.2672	1.75617
$67$	7.62289	0.931284	0.465642	−	0.884973i	$-0.345823\pi$
$67$	7.62289	0.931284	0.465642	+	0.884973i	$0.345823\pi$
$68$	2.67429	0.324305
$69$	−11.9952	−1.44405
$70$	9.80585	1.17202
$71$	8.52939	1.01225	0.506126	−	0.862460i	$-0.331077\pi$
$71$	8.52939	1.01225	0.506126	+	0.862460i	$0.331077\pi$
$72$	−2.76918	−0.326351
$73$	−9.65113	−1.12958	−0.564789	−	0.825235i	$-0.691043\pi$
$73$	−9.65113	−1.12958	−0.564789	+	0.825235i	$0.691043\pi$
$74$	−19.4163	−2.25710
$75$	−17.9368	−2.07116
$76$	2.76213	0.316838
$77$	−3.01326	−0.343393
$78$	11.9795	1.35641
$79$	13.0359	1.46665	0.733327	−	0.679876i	$-0.237966\pi$
$79$	13.0359	1.46665	0.733327	+	0.679876i	$0.237966\pi$
$80$	29.0015	3.24247
$81$	−10.0951	−1.12168
$82$	18.5174	2.04491
$83$	−5.55090	−0.609290	−0.304645	−	0.952466i	$-0.598538\pi$
$83$	−5.55090	−0.609290	−0.304645	+	0.952466i	$0.598538\pi$
$84$	8.41155	0.917776
$85$	2.25536	0.244628
$86$	−20.2799	−2.18684
$87$	−4.49790	−0.482225
$88$	−19.6182	−2.09131
$89$	−4.67862	−0.495933	−0.247966	−	0.968769i	$-0.579762\pi$
$89$	−4.67862	−0.495933	−0.247966	+	0.968769i	$0.579762\pi$
$90$	−4.17073	−0.439634
$91$	−2.53009	−0.265226
$92$	29.4565	3.07106
$93$	−2.88650	−0.299316
$94$	11.7151	1.20832
$95$	2.32944	0.238996
$96$	11.7260	1.19678
$97$	11.3067	1.14802	0.574012	−	0.818847i	$-0.305386\pi$
$97$	11.3067	1.14802	0.574012	+	0.818847i	$0.305386\pi$
$98$	−2.55830	−0.258427
$99$	1.28163	0.128809
$100$	44.0471	4.40471
$101$	6.39357	0.636184	0.318092	−	0.948060i	$-0.396958\pi$
$101$	6.39357	0.636184	0.318092	+	0.948060i	$0.396958\pi$
$102$	2.78603	0.275858
$103$	−0.822863	−0.0810791	−0.0405395	−	0.999178i	$-0.512908\pi$
$103$	−0.822863	−0.0810791	−0.0405395	+	0.999178i	$0.512908\pi$
$104$	−16.4725	−1.61526
$105$	7.09390	0.692293
$106$	−12.1431	−1.17944
$107$	10.7560	1.03982	0.519911	−	0.854221i	$-0.325965\pi$
$107$	10.7560	1.03982	0.519911	+	0.854221i	$0.325965\pi$
$108$	21.6570	2.08394
$109$	−1.02527	−0.0982027	−0.0491014	−	0.998794i	$-0.515636\pi$
$109$	−1.02527	−0.0982027	−0.0491014	+	0.998794i	$0.515636\pi$
$110$	−29.5476	−2.81725
$111$	−14.0464	−1.33323
$112$	−7.56636	−0.714954
$113$	−1.23970	−0.116621	−0.0583106	−	0.998298i	$-0.518571\pi$
$113$	−1.23970	−0.116621	−0.0583106	+	0.998298i	$0.518571\pi$
$114$	2.87754	0.269506
$115$	24.8422	2.31655
$116$	11.0454	1.02554
$117$	1.07613	0.0994880
$118$	6.06442	0.558275
$119$	−0.588414	−0.0539398
$120$	46.1858	4.21617
$121$	−1.92027	−0.174570
$122$	22.1280	2.00338
$123$	13.3962	1.20789
$124$	7.08835	0.636553
$125$	17.9824	1.60840
$126$	1.08813	0.0969379
$127$	6.62139	0.587554	0.293777	−	0.955874i	$-0.405088\pi$
$127$	6.62139	0.587554	0.293777	+	0.955874i	$0.405088\pi$
$128$	9.91865	0.876693
$129$	−14.6712	−1.29172
$130$	−24.8097	−2.17596
$131$	11.6986	1.02211	0.511056	−	0.859547i	$-0.329254\pi$
$131$	11.6986	1.02211	0.511056	+	0.859547i	$0.329254\pi$
$132$	−25.3462	−2.20610
$133$	−0.607741	−0.0526978
$134$	−19.5017	−1.68469
$135$	18.2644	1.57195
$136$	−3.83095	−0.328501
$137$	3.43535	0.293502	0.146751	−	0.989173i	$-0.453118\pi$
$137$	3.43535	0.293502	0.146751	+	0.989173i	$0.453118\pi$
$138$	30.6874	2.61228
$139$	−9.60680	−0.814838	−0.407419	−	0.913241i	$-0.633571\pi$
$139$	−9.60680	−0.814838	−0.407419	+	0.913241i	$0.633571\pi$
$140$	−17.4204	−1.47229
$141$	8.47509	0.713731
$142$	−21.8207	−1.83116
$143$	7.62383	0.637536
$144$	3.21821	0.268184
$145$	9.31519	0.773585
$146$	24.6905	2.04340
$147$	−1.85077	−0.152649
$148$	34.4937	2.83536
$149$	−1.23243	−0.100964	−0.0504822	−	0.998725i	$-0.516076\pi$
$149$	−1.23243	−0.100964	−0.0504822	+	0.998725i	$0.516076\pi$
$150$	45.8876	3.74671
$151$	1.90347	0.154903	0.0774513	−	0.996996i	$-0.475322\pi$
$151$	1.90347	0.154903	0.0774513	+	0.996996i	$0.475322\pi$
$152$	−3.95678	−0.320937
$153$	0.250271	0.0202332
$154$	7.70883	0.621195
$155$	5.97797	0.480162
$156$	−21.2820	−1.70392
$157$	4.96227	0.396032	0.198016	−	0.980199i	$-0.436550\pi$
$157$	4.96227	0.396032	0.198016	+	0.980199i	$0.436550\pi$
$158$	−33.3498	−2.65317
$159$	−8.78474	−0.696675
$160$	−24.2846	−1.91987
$161$	−6.48122	−0.510792
$162$	25.8263	2.02910
$163$	3.40621	0.266795	0.133397	−	0.991063i	$-0.457411\pi$
$163$	3.40621	0.266795	0.133397	+	0.991063i	$0.457411\pi$
$164$	−32.8968	−2.56881
$165$	−21.3757	−1.66410
$166$	14.2009	1.10220
$167$	−17.0296	−1.31779	−0.658897	−	0.752233i	$-0.728977\pi$
$167$	−17.0296	−1.31779	−0.658897	+	0.752233i	$0.728977\pi$
$168$	−12.0497	−0.929651
$169$	−6.59863	−0.507587
$170$	−5.76990	−0.442531
$171$	0.258491	0.0197673
$172$	36.0279	2.74710
$173$	−1.80965	−0.137585	−0.0687925	−	0.997631i	$-0.521915\pi$
$173$	−1.80965	−0.137585	−0.0687925	+	0.997631i	$0.521915\pi$
$174$	11.5070	0.872342
$175$	−9.69153	−0.732611
$176$	22.7994	1.71857
$177$	4.38722	0.329763
$178$	11.9693	0.897139
$179$	12.5438	0.937570	0.468785	−	0.883312i	$-0.344692\pi$
$179$	12.5438	0.937570	0.468785	+	0.883312i	$0.344692\pi$
$180$	7.40945	0.552268
$181$	−17.2011	−1.27855	−0.639273	−	0.768980i	$-0.720764\pi$
$181$	−17.2011	−1.27855	−0.639273	+	0.768980i	$0.720764\pi$
$182$	6.47274	0.479791
$183$	16.0082	1.18336
$184$	−42.1969	−3.11080
$185$	29.0903	2.13876
$186$	7.38454	0.541460
$187$	1.77304	0.129658
$188$	−20.8122	−1.51789
$189$	−4.76511	−0.346611
$190$	−5.95942	−0.432342
$191$	1.44289	0.104404	0.0522020	−	0.998637i	$-0.483376\pi$
$191$	1.44289	0.104404	0.0522020	+	0.998637i	$0.483376\pi$
$192$	−1.99151	−0.143725
$193$	−8.66495	−0.623717	−0.311858	−	0.950129i	$-0.600951\pi$
$193$	−8.66495	−0.623717	−0.311858	+	0.950129i	$0.600951\pi$
$194$	−28.9260	−2.07676
$195$	−17.9482	−1.28530
$196$	4.54491	0.324636
$197$	1.41847	0.101062	0.0505309	−	0.998722i	$-0.483909\pi$
$197$	1.41847	0.101062	0.0505309	+	0.998722i	$0.483909\pi$
$198$	−3.27880	−0.233014
$199$	−6.43989	−0.456511	−0.228256	−	0.973601i	$-0.573302\pi$
$199$	−6.43989	−0.456511	−0.228256	+	0.973601i	$0.573302\pi$
$200$	−63.0981	−4.46171
$201$	−14.1082	−0.995114
$202$	−16.3567	−1.15085
$203$	−2.43029	−0.170573
$204$	−4.94947	−0.346533
$205$	−27.7436	−1.93770
$206$	2.10513	0.146671
$207$	2.75667	0.191602
$208$	19.1436	1.32737
$209$	1.83128	0.126672
$210$	−18.1483	−1.25235
$211$	−25.6402	−1.76514	−0.882571	−	0.470180i	$-0.844189\pi$
$211$	−25.6402	−1.76514	−0.882571	+	0.470180i	$0.844189\pi$
$212$	21.5726	1.48161
$213$	−15.7859	−1.08163
$214$	−27.5171	−1.88103
$215$	30.3842	2.07218
$216$	−31.0239	−2.11091
$217$	−1.55962	−0.105874
$218$	2.62294	0.177648
$219$	17.8620	1.20700
$220$	52.4922	3.53902
$221$	1.48874	0.100144
$222$	35.9350	2.41180
$223$	28.9900	1.94131	0.970657	−	0.240469i	$-0.0773013\pi$
$223$	28.9900	1.94131	0.970657	+	0.240469i	$0.0773013\pi$
$224$	6.33575	0.423325
$225$	4.12211	0.274807
$226$	3.17153	0.210967
$227$	−2.58993	−0.171900	−0.0859500	−	0.996299i	$-0.527393\pi$
$227$	−2.58993	−0.171900	−0.0859500	+	0.996299i	$0.527393\pi$
$228$	−5.11205	−0.338554
$229$	−15.1296	−0.999789	−0.499895	−	0.866086i	$-0.666628\pi$
$229$	−15.1296	−0.999789	−0.499895	+	0.866086i	$0.666628\pi$
$230$	−63.5539	−4.19062
$231$	5.57683	0.366929
$232$	−15.8227	−1.03881
$233$	−9.67737	−0.633986	−0.316993	−	0.948428i	$-0.602673\pi$
$233$	−9.67737	−0.633986	−0.316993	+	0.948428i	$0.602673\pi$
$234$	−2.75306	−0.179973
$235$	−17.5520	−1.14497
$236$	−10.7736	−0.701305
$237$	−24.1264	−1.56718
$238$	1.50534	0.0975767
$239$	−18.9515	−1.22587	−0.612936	−	0.790133i	$-0.710012\pi$
$239$	−18.9515	−1.22587	−0.612936	+	0.790133i	$0.710012\pi$
$240$	−53.6750	−3.46470
$241$	12.2145	0.786802	0.393401	−	0.919367i	$-0.371298\pi$
$241$	12.2145	0.786802	0.393401	+	0.919367i	$0.371298\pi$
$242$	4.91263	0.315796
$243$	4.38831	0.281510
$244$	−39.3111	−2.51664
$245$	3.83295	0.244878
$246$	−34.2714	−2.18507
$247$	1.53764	0.0978378
$248$	−10.1542	−0.644789
$249$	10.2734	0.651051
$250$	−46.0045	−2.90958
$251$	−5.06686	−0.319817	−0.159909	−	0.987132i	$-0.551120\pi$
$251$	−5.06686	−0.319817	−0.159909	+	0.987132i	$0.551120\pi$
$252$	−1.93309	−0.121773
$253$	19.5296	1.22782
$254$	−16.9395	−1.06288
$255$	−4.17415	−0.261395
$256$	−27.5270	−1.72044
$257$	−16.4911	−1.02869	−0.514344	−	0.857584i	$-0.671964\pi$
$257$	−16.4911	−1.02869	−0.514344	+	0.857584i	$0.671964\pi$
$258$	37.5333	2.33672
$259$	−7.58953	−0.471590
$260$	44.0753	2.73343
$261$	1.03368	0.0639831
$262$	−29.9286	−1.84899
$263$	17.2961	1.06652	0.533262	−	0.845950i	$-0.320966\pi$
$263$	17.2961	1.06652	0.533262	+	0.845950i	$0.320966\pi$
$264$	36.3087	2.23465
$265$	18.1933	1.11760
$266$	1.55478	0.0953300
$267$	8.65903	0.529924
$268$	34.6453	2.11630
$269$	11.9981	0.731539	0.365770	−	0.930705i	$-0.380806\pi$
$269$	11.9981	0.731539	0.365770	+	0.930705i	$0.380806\pi$
$270$	−46.7259	−2.84365
$271$	25.1684	1.52887	0.764437	−	0.644699i	$-0.223017\pi$
$271$	25.1684	1.52887	0.764437	+	0.644699i	$0.223017\pi$
$272$	4.45215	0.269951
$273$	4.68261	0.283404
$274$	−8.78867	−0.530943
$275$	29.2031	1.76101
$276$	−54.5171	−3.28155
$277$	−26.2855	−1.57934	−0.789670	−	0.613532i	$-0.789748\pi$
$277$	−26.2855	−1.57934	−0.789670	+	0.613532i	$0.789748\pi$
$278$	24.5771	1.47404
$279$	0.663357	0.0397142
$280$	24.9550	1.49134
$281$	−10.6651	−0.636226	−0.318113	−	0.948053i	$-0.603049\pi$
$281$	−10.6651	−0.636226	−0.318113	+	0.948053i	$0.603049\pi$
$282$	−21.6818	−1.29113
$283$	−26.0535	−1.54872	−0.774359	−	0.632746i	$-0.781928\pi$
$283$	−26.0535	−1.54872	−0.774359	+	0.632746i	$0.781928\pi$
$284$	38.7653	2.30030
$285$	−4.31125	−0.255377
$286$	−19.5040	−1.15330
$287$	7.23818	0.427256
$288$	−2.69479	−0.158792
$289$	−16.6538	−0.979633
$290$	−23.8311	−1.39941
$291$	−20.9261	−1.22671
$292$	−43.8635	−2.56692
$293$	29.5087	1.72392	0.861959	−	0.506979i	$-0.169238\pi$
$293$	29.5087	1.72392	0.861959	+	0.506979i	$0.169238\pi$
$294$	4.73481	0.276140
$295$	−9.08597	−0.529006
$296$	−49.4127	−2.87205
$297$	14.3585	0.833165
$298$	3.15292	0.182644
$299$	16.3981	0.948326
$300$	−81.5209	−4.70661
$301$	−7.92709	−0.456910
$302$	−4.86966	−0.280218
$303$	−11.8330	−0.679788
$304$	4.59839	0.263736
$305$	−33.1531	−1.89834
$306$	−0.640268	−0.0366017
$307$	−3.39435	−0.193726	−0.0968629	−	0.995298i	$-0.530881\pi$
$307$	−3.39435	−0.193726	−0.0968629	+	0.995298i	$0.530881\pi$
$308$	−13.6950	−0.780344
$309$	1.52293	0.0866362
$310$	−15.2934	−0.868610
$311$	10.5514	0.598313	0.299156	−	0.954204i	$-0.403295\pi$
$311$	10.5514	0.598313	0.299156	+	0.954204i	$0.403295\pi$
$312$	30.4868	1.72597
$313$	2.56305	0.144872	0.0724362	−	0.997373i	$-0.476923\pi$
$313$	2.56305	0.144872	0.0724362	+	0.997373i	$0.476923\pi$
$314$	−12.6950	−0.716420
$315$	−1.63027	−0.0918556
$316$	59.2470	3.33290
$317$	−3.57584	−0.200839	−0.100420	−	0.994945i	$-0.532019\pi$
$317$	−3.57584	−0.200839	−0.100420	+	0.994945i	$0.532019\pi$
$318$	22.4740	1.26028
$319$	7.32310	0.410015
$320$	4.12444	0.230563
$321$	−19.9068	−1.11109
$322$	16.5809	0.924019
$323$	0.357603	0.0198976
$324$	−45.8812	−2.54896
$325$	24.5205	1.36015
$326$	−8.71411	−0.482630
$327$	1.89753	0.104934
$328$	47.1252	2.60205
$329$	4.57924	0.252461
$330$	54.6856	3.01034
$331$	−5.84170	−0.321089	−0.160544	−	0.987029i	$-0.551325\pi$
$331$	−5.84170	−0.321089	−0.160544	+	0.987029i	$0.551325\pi$
$332$	−25.2283	−1.38458
$333$	3.22806	0.176897
$334$	43.5670	2.38388
$335$	29.2182	1.59636
$336$	14.0036	0.763956
$337$	−16.8025	−0.915292	−0.457646	−	0.889134i	$-0.651307\pi$
$337$	−16.8025	−0.915292	−0.457646	+	0.889134i	$0.651307\pi$
$338$	16.8813	0.918221
$339$	2.29439	0.124614
$340$	10.2504	0.555907
$341$	4.69955	0.254495
$342$	−0.661299	−0.0357589
$343$	−1.00000	−0.0539949
$344$	−51.6104	−2.78264
$345$	−45.9771	−2.47533
$346$	4.62963	0.248890
$347$	23.1847	1.24462	0.622309	−	0.782772i	$-0.286195\pi$
$347$	23.1847	1.24462	0.622309	+	0.782772i	$0.286195\pi$
$348$	−20.4425	−1.09583
$349$	−24.0418	−1.28693	−0.643465	−	0.765475i	$-0.722504\pi$
$349$	−24.0418	−1.28693	−0.643465	+	0.765475i	$0.722504\pi$
$350$	24.7939	1.32529
$351$	12.0562	0.643510
$352$	−19.0913	−1.01757
$353$	5.48505	0.291940	0.145970	−	0.989289i	$-0.453370\pi$
$353$	5.48505	0.291940	0.145970	+	0.989289i	$0.453370\pi$
$354$	−11.2238	−0.596539
$355$	32.6927	1.73515
$356$	−21.2639	−1.12698
$357$	1.08902	0.0576368
$358$	−32.0909	−1.69606
$359$	−17.7830	−0.938550	−0.469275	−	0.883052i	$-0.655485\pi$
$359$	−17.7830	−0.938550	−0.469275	+	0.883052i	$0.655485\pi$
$360$	−10.6141	−0.559414
$361$	−18.6307	−0.980561
$362$	44.0055	2.31288
$363$	3.55397	0.186535
$364$	−11.4990	−0.602713
$365$	−36.9923	−1.93627
$366$	−40.9537	−2.14069
$367$	13.3238	0.695499	0.347750	−	0.937587i	$-0.386946\pi$
$367$	13.3238	0.695499	0.347750	+	0.937587i	$0.386946\pi$
$368$	49.0393	2.55635
$369$	−3.07862	−0.160267
$370$	−74.4218	−3.86900
$371$	−4.74654	−0.246428
$372$	−13.1189	−0.680182
$373$	4.06440	0.210447	0.105223	−	0.994449i	$-0.466444\pi$
$373$	4.06440	0.210447	0.105223	+	0.994449i	$0.466444\pi$
$374$	−4.53598	−0.234550
$375$	−33.2813	−1.71864
$376$	29.8137	1.53753
$377$	6.14886	0.316682
$378$	12.1906	0.627016
$379$	−3.64075	−0.187013	−0.0935064	−	0.995619i	$-0.529808\pi$
$379$	−3.64075	−0.187013	−0.0935064	+	0.995619i	$0.529808\pi$
$380$	10.5871	0.543107
$381$	−12.2546	−0.627824
$382$	−3.69136	−0.188866
$383$	−29.2045	−1.49228	−0.746140	−	0.665789i	$-0.768095\pi$
$383$	−29.2045	−1.49228	−0.746140	+	0.665789i	$0.768095\pi$
$384$	−18.3571	−0.936782
$385$	−11.5497	−0.588626
$386$	22.1676	1.12830
$387$	3.37164	0.171390
$388$	51.3880	2.60883
$389$	22.0212	1.11652	0.558259	−	0.829667i	$-0.311470\pi$
$389$	22.0212	1.11652	0.558259	+	0.829667i	$0.311470\pi$
$390$	45.9169	2.32509
$391$	3.81364	0.192864
$392$	−6.51064	−0.328837
$393$	−21.6514	−1.09217
$394$	−3.62888	−0.182820
$395$	49.9661	2.51406
$396$	5.82490	0.292712
$397$	−0.118644	−0.00595457	−0.00297728	−	0.999996i	$-0.500948\pi$
$397$	−0.118644	−0.00595457	−0.00297728	+	0.999996i	$0.500948\pi$
$398$	16.4752	0.825826
$399$	1.12479	0.0563097
$400$	73.3296	3.66648
$401$	26.4976	1.32323	0.661613	−	0.749845i	$-0.269872\pi$
$401$	26.4976	1.32323	0.661613	+	0.749845i	$0.269872\pi$
$402$	36.0930	1.80015
$403$	3.94600	0.196564
$404$	29.0582	1.44570
$405$	−38.6940	−1.92272
$406$	6.21742	0.308565
$407$	22.8692	1.13358
$408$	7.09019	0.351017
$409$	−6.69220	−0.330908	−0.165454	−	0.986218i	$-0.552909\pi$
$409$	−6.69220	−0.330908	−0.165454	+	0.986218i	$0.552909\pi$
$410$	70.9765	3.50528
$411$	−6.35803	−0.313619
$412$	−3.73983	−0.184248
$413$	2.37049	0.116644
$414$	−7.05238	−0.346606
$415$	−21.2763	−1.04441
$416$	−16.0300	−0.785937
$417$	17.7799	0.870687
$418$	−4.68497	−0.229149
$419$	−25.8202	−1.26140	−0.630700	−	0.776027i	$-0.717232\pi$
$419$	−25.8202	−1.26140	−0.630700	+	0.776027i	$0.717232\pi$
$420$	32.2411	1.57320
$421$	−26.6015	−1.29648	−0.648239	−	0.761437i	$-0.724494\pi$
$421$	−26.6015	−1.29648	−0.648239	+	0.761437i	$0.724494\pi$
$422$	65.5952	3.19313
$423$	−1.94769	−0.0947000
$424$	−30.9030	−1.50078
$425$	5.70263	0.276618
$426$	40.3851	1.95666
$427$	8.64949	0.418578
$428$	48.8850	2.36294
$429$	−14.1099	−0.681233
$430$	−77.7318	−3.74856
$431$	22.7380	1.09525	0.547625	−	0.836724i	$-0.315532\pi$
$431$	22.7380	1.09525	0.547625	+	0.836724i	$0.315532\pi$
$432$	36.0545	1.73467
$433$	18.9072	0.908623	0.454312	−	0.890843i	$-0.349885\pi$
$433$	18.9072	0.908623	0.454312	+	0.890843i	$0.349885\pi$
$434$	3.98999	0.191526
$435$	−17.2402	−0.826606
$436$	−4.65974	−0.223161
$437$	3.93890	0.188423
$438$	−45.6963	−2.18345
$439$	−41.4772	−1.97960	−0.989799	−	0.142473i	$-0.954495\pi$
$439$	−41.4772	−1.97960	−0.989799	+	0.142473i	$0.954495\pi$
$440$	−75.1958	−3.58482
$441$	0.425331	0.0202539
$442$	−3.80865	−0.181159
$443$	−22.2612	−1.05766	−0.528831	−	0.848727i	$-0.677370\pi$
$443$	−22.2612	−1.05766	−0.528831	+	0.848727i	$0.677370\pi$
$444$	−63.8397	−3.02970
$445$	−17.9329	−0.850103
$446$	−74.1651	−3.51182
$447$	2.28093	0.107884
$448$	−1.07605	−0.0508385
$449$	26.6003	1.25534	0.627672	−	0.778478i	$-0.284008\pi$
$449$	26.6003	1.25534	0.627672	+	0.778478i	$0.284008\pi$
$450$	−10.5456	−0.497125
$451$	−21.8105	−1.02702
$452$	−5.63432	−0.265016
$453$	−3.52288	−0.165520
$454$	6.62583	0.310966
$455$	−9.69773	−0.454637
$456$	7.32307	0.342934
$457$	−19.8068	−0.926521	−0.463261	−	0.886222i	$-0.653321\pi$
$457$	−19.8068	−0.926521	−0.463261	+	0.886222i	$0.653321\pi$
$458$	38.7060	1.80861
$459$	2.80386	0.130873
$460$	112.906	5.26425
$461$	−3.50274	−0.163139	−0.0815695	−	0.996668i	$-0.525993\pi$
$461$	−3.50274	−0.163139	−0.0815695	+	0.996668i	$0.525993\pi$
$462$	−14.2672	−0.663771
$463$	27.0011	1.25485	0.627423	−	0.778679i	$-0.284110\pi$
$463$	27.0011	1.25485	0.627423	+	0.778679i	$0.284110\pi$
$464$	18.3885	0.853662
$465$	−11.0638	−0.513072
$466$	24.7576	1.14687
$467$	−26.8543	−1.24267	−0.621334	−	0.783546i	$-0.713409\pi$
$467$	−26.8543	−1.24267	−0.621334	+	0.783546i	$0.713409\pi$
$468$	4.89090	0.226082
$469$	−7.62289	−0.351992
$470$	44.9033	2.07123
$471$	−9.18400	−0.423176
$472$	15.4334	0.710379
$473$	23.8864	1.09830
$474$	61.7226	2.83501
$475$	5.88994	0.270249
$476$	−2.67429	−0.122576
$477$	2.01885	0.0924369
$478$	48.4837	2.21759
$479$	28.8894	1.31999	0.659995	−	0.751270i	$-0.270558\pi$
$479$	28.8894	1.31999	0.659995	+	0.751270i	$0.270558\pi$
$480$	44.9452	2.05146
$481$	19.2022	0.875545
$482$	−31.2483	−1.42332
$483$	11.9952	0.545801
$484$	−8.72744	−0.396702
$485$	43.3381	1.96788
$486$	−11.2266	−0.509250
$487$	12.7904	0.579589	0.289794	−	0.957089i	$-0.406413\pi$
$487$	12.7904	0.579589	0.289794	+	0.957089i	$0.406413\pi$
$488$	56.3137	2.54920
$489$	−6.30409	−0.285081
$490$	−9.80585	−0.442983
$491$	−0.546492	−0.0246628	−0.0123314	−	0.999924i	$-0.503925\pi$
$491$	−0.546492	−0.0246628	−0.0123314	+	0.999924i	$0.503925\pi$
$492$	60.8843	2.74488
$493$	1.43002	0.0644047
$494$	−3.93375	−0.176988
$495$	4.91244	0.220798
$496$	11.8007	0.529866
$497$	−8.52939	−0.382595
$498$	−26.2825	−1.17775
$499$	25.2296	1.12943	0.564716	−	0.825285i	$-0.308986\pi$
$499$	25.2296	1.12943	0.564716	+	0.825285i	$0.308986\pi$
$500$	81.7285	3.65501
$501$	31.5179	1.40811
$502$	12.9625	0.578547
$503$	13.8465	0.617386	0.308693	−	0.951162i	$-0.400108\pi$
$503$	13.8465	0.617386	0.308693	+	0.951162i	$0.400108\pi$
$504$	2.76918	0.123349
$505$	24.5062	1.09051
$506$	−49.9626	−2.22111
$507$	12.2125	0.542377
$508$	30.0936	1.33519
$509$	−23.3875	−1.03663	−0.518316	−	0.855189i	$-0.673441\pi$
$509$	−23.3875	−1.03663	−0.518316	+	0.855189i	$0.673441\pi$
$510$	10.6787	0.472862
$511$	9.65113	0.426941
$512$	50.5850	2.23556
$513$	2.89595	0.127859
$514$	42.1893	1.86089
$515$	−3.15399	−0.138982
$516$	−66.6791	−2.93538
$517$	−13.7984	−0.606854
$518$	19.4163	0.853103
$519$	3.34924	0.147015
$520$	−63.1384	−2.76880
$521$	−23.3759	−1.02412	−0.512059	−	0.858950i	$-0.671117\pi$
$521$	−23.3759	−1.02412	−0.512059	+	0.858950i	$0.671117\pi$
$522$	−2.64446	−0.115745
$523$	−3.25169	−0.142186	−0.0710932	−	0.997470i	$-0.522649\pi$
$523$	−3.25169	−0.142186	−0.0710932	+	0.997470i	$0.522649\pi$
$524$	53.1691	2.32270
$525$	17.9368	0.782824
$526$	−44.2487	−1.92933
$527$	0.917705	0.0399759
$528$	−42.1963	−1.83636
$529$	19.0062	0.826359
$530$	−46.5439	−2.02174
$531$	−1.00824	−0.0437540
$532$	−2.76213	−0.119753
$533$	−18.3133	−0.793236
$534$	−22.1524	−0.958629
$535$	41.2272	1.78241
$536$	−49.6299	−2.14368
$537$	−23.2157	−1.00183
$538$	−30.6948	−1.32335
$539$	3.01326	0.129790
$540$	83.0101	3.57219
$541$	19.9560	0.857976	0.428988	−	0.903310i	$-0.358870\pi$
$541$	19.9560	0.857976	0.428988	+	0.903310i	$0.358870\pi$
$542$	−64.3884	−2.76572
$543$	31.8351	1.36618
$544$	−3.72804	−0.159839
$545$	−3.92980	−0.168334
$546$	−11.9795	−0.512676
$547$	−40.5135	−1.73223	−0.866116	−	0.499842i	$-0.833391\pi$
$547$	−40.5135	−1.73223	−0.866116	+	0.499842i	$0.833391\pi$
$548$	15.6134	0.666970
$549$	−3.67890	−0.157012
$550$	−74.7103	−3.18566
$551$	1.47699	0.0629218
$552$	78.0965	3.32401
$553$	−13.0359	−0.554343
$554$	67.2461	2.85701
$555$	−53.8393	−2.28535
$556$	−43.6620	−1.85168
$557$	8.75113	0.370797	0.185399	−	0.982663i	$-0.440642\pi$
$557$	8.75113	0.370797	0.185399	+	0.982663i	$0.440642\pi$
$558$	−1.69707	−0.0718426
$559$	20.0563	0.848289
$560$	−29.0015	−1.22554
$561$	−3.28149	−0.138544
$562$	27.2845	1.15093
$563$	9.42636	0.397274	0.198637	−	0.980073i	$-0.436349\pi$
$563$	9.42636	0.397274	0.198637	+	0.980073i	$0.436349\pi$
$564$	38.5185	1.62192
$565$	−4.75171	−0.199906
$566$	66.6526	2.80162
$567$	10.0951	0.423954
$568$	−55.5317	−2.33006
$569$	34.0319	1.42669	0.713345	−	0.700813i	$-0.247179\pi$
$569$	34.0319	1.42669	0.713345	+	0.700813i	$0.247179\pi$
$570$	11.0295	0.461974
$571$	11.4667	0.479867	0.239933	−	0.970789i	$-0.422874\pi$
$571$	11.4667	0.479867	0.239933	+	0.970789i	$0.422874\pi$
$572$	34.6496	1.44877
$573$	−2.67046	−0.111560
$574$	−18.5174	−0.772903
$575$	62.8130	2.61948
$576$	0.457677	0.0190699
$577$	−23.3162	−0.970667	−0.485334	−	0.874329i	$-0.661302\pi$
$577$	−23.3162	−0.970667	−0.485334	+	0.874329i	$0.661302\pi$
$578$	42.6054	1.77215
$579$	16.0368	0.666466
$580$	42.3367	1.75793
$581$	5.55090	0.230290
$582$	53.5352	2.21911
$583$	14.3026	0.592352
$584$	62.8350	2.60013
$585$	4.12475	0.170537
$586$	−75.4922	−3.11855
$587$	30.3804	1.25393	0.626967	−	0.779046i	$-0.284296\pi$
$587$	30.3804	1.25393	0.626967	+	0.779046i	$0.284296\pi$
$588$	−8.41155	−0.346887
$589$	0.947848	0.0390554
$590$	23.2447	0.956967
$591$	−2.62526	−0.107989
$592$	57.4251	2.36016
$593$	−11.7729	−0.483453	−0.241727	−	0.970344i	$-0.577714\pi$
$593$	−11.7729	−0.483453	−0.241727	+	0.970344i	$0.577714\pi$
$594$	−36.7334	−1.50719
$595$	−2.25536	−0.0924609
$596$	−5.60127	−0.229437
$597$	11.9187	0.487801
$598$	−41.9513	−1.71551
$599$	20.2918	0.829102	0.414551	−	0.910026i	$-0.363939\pi$
$599$	20.2918	0.829102	0.414551	+	0.910026i	$0.363939\pi$
$600$	116.780	4.76751
$601$	−32.5012	−1.32575	−0.662876	−	0.748729i	$-0.730664\pi$
$601$	−32.5012	−1.32575	−0.662876	+	0.748729i	$0.730664\pi$
$602$	20.2799	0.826546
$603$	3.24225	0.132035
$604$	8.65111	0.352009
$605$	−7.36030	−0.299239
$606$	30.2724	1.22973
$607$	15.6391	0.634771	0.317385	−	0.948297i	$-0.397195\pi$
$607$	15.6391	0.634771	0.317385	+	0.948297i	$0.397195\pi$
$608$	−3.85050	−0.156158
$609$	4.49790	0.182264
$610$	84.8156	3.43408
$611$	−11.5859	−0.468715
$612$	1.13746	0.0459790
$613$	1.48390	0.0599341	0.0299670	−	0.999551i	$-0.490460\pi$
$613$	1.48390	0.0599341	0.0299670	+	0.999551i	$0.490460\pi$
$614$	8.68377	0.350448
$615$	51.3469	2.07051
$616$	19.6182	0.790441
$617$	13.5220	0.544375	0.272188	−	0.962244i	$-0.412253\pi$
$617$	13.5220	0.544375	0.272188	+	0.962244i	$0.412253\pi$
$618$	−3.89610	−0.156724
$619$	26.9685	1.08396	0.541979	−	0.840392i	$-0.317675\pi$
$619$	26.9685	1.08396	0.541979	+	0.840392i	$0.317675\pi$
$620$	27.1693	1.09115
$621$	30.8837	1.23932
$622$	−26.9936	−1.08234
$623$	4.67862	0.187445
$624$	−35.4303	−1.41835
$625$	20.4682	0.818726
$626$	−6.55706	−0.262073
$627$	−3.38927	−0.135354
$628$	22.5531	0.899965
$629$	4.46578	0.178062
$630$	4.17073	0.166166
$631$	−22.6779	−0.902795	−0.451397	−	0.892323i	$-0.649074\pi$
$631$	−22.6779	−0.902795	−0.451397	+	0.892323i	$0.649074\pi$
$632$	−84.8721	−3.37603
$633$	47.4539	1.88612
$634$	9.14809	0.363317
$635$	25.3795	1.00715
$636$	−39.9258	−1.58316
$637$	2.53009	0.100246
$638$	−18.7347	−0.741713
$639$	3.62781	0.143514
$640$	38.0177	1.50278
$641$	6.13553	0.242339	0.121169	−	0.992632i	$-0.461336\pi$
$641$	6.13553	0.242339	0.121169	+	0.992632i	$0.461336\pi$
$642$	50.9276	2.00995
$643$	40.7041	1.60521	0.802606	−	0.596509i	$-0.203446\pi$
$643$	40.7041	1.60521	0.802606	+	0.596509i	$0.203446\pi$
$644$	−29.4565	−1.16075
$645$	−56.2339	−2.21421
$646$	−0.914857	−0.0359946
$647$	−3.90482	−0.153514	−0.0767571	−	0.997050i	$-0.524457\pi$
$647$	−3.90482	−0.153514	−0.0767571	+	0.997050i	$0.524457\pi$
$648$	65.7254	2.58194
$649$	−7.14289	−0.280383
$650$	−62.7308	−2.46050
$651$	2.88650	0.113131
$652$	15.4809	0.606279
$653$	17.8347	0.697926	0.348963	−	0.937136i	$-0.386534\pi$
$653$	17.8347	0.697926	0.348963	+	0.937136i	$0.386534\pi$
$654$	−4.85445	−0.189824
$655$	44.8402	1.75205
$656$	−54.7667	−2.13828
$657$	−4.10493	−0.160148
$658$	−11.7151	−0.456701
$659$	11.5763	0.450950	0.225475	−	0.974249i	$-0.427607\pi$
$659$	11.5763	0.450950	0.225475	+	0.974249i	$0.427607\pi$
$660$	−97.1508	−3.78159
$661$	46.9192	1.82495	0.912473	−	0.409138i	$-0.134170\pi$
$661$	46.9192	1.82495	0.912473	+	0.409138i	$0.134170\pi$
$662$	14.9448	0.580847
$663$	−2.75531	−0.107007
$664$	36.1399	1.40250
$665$	−2.32944	−0.0903319
$666$	−8.25836	−0.320005
$667$	15.7513	0.609891
$668$	−77.3981	−2.99462
$669$	−53.6537	−2.07437
$670$	−74.7489	−2.88780
$671$	−26.0632	−1.00616
$672$	−11.7260	−0.452340
$673$	20.7132	0.798436	0.399218	−	0.916856i	$-0.369282\pi$
$673$	20.7132	0.798436	0.399218	+	0.916856i	$0.369282\pi$
$674$	42.9859	1.65576
$675$	46.1812	1.77752
$676$	−29.9902	−1.15347
$677$	−9.43630	−0.362666	−0.181333	−	0.983422i	$-0.558041\pi$
$677$	−9.43630	−0.362666	−0.181333	+	0.983422i	$0.558041\pi$
$678$	−5.86975	−0.225426
$679$	−11.3067	−0.433912
$680$	−14.6839	−0.563100
$681$	4.79336	0.183682
$682$	−12.0229	−0.460380
$683$	18.5390	0.709376	0.354688	−	0.934985i	$-0.384587\pi$
$683$	18.5390	0.709376	0.354688	+	0.934985i	$0.384587\pi$
$684$	1.17482	0.0449203
$685$	13.1676	0.503106
$686$	2.55830	0.0976764
$687$	28.0013	1.06831
$688$	59.9792	2.28668
$689$	12.0092	0.457514
$690$	117.623	4.47784
$691$	−35.7212	−1.35890	−0.679449	−	0.733723i	$-0.737781\pi$
$691$	−35.7212	−1.35890	−0.679449	+	0.733723i	$0.737781\pi$
$692$	−8.22468	−0.312656
$693$	−1.28163	−0.0486852
$694$	−59.3134	−2.25150
$695$	−36.8224	−1.39675
$696$	29.2842	1.11001
$697$	−4.25905	−0.161323
$698$	61.5063	2.32805
$699$	17.9105	0.677439
$700$	−44.0471	−1.66482
$701$	2.00593	0.0757628	0.0378814	−	0.999282i	$-0.487939\pi$
$701$	2.00593	0.0757628	0.0378814	+	0.999282i	$0.487939\pi$
$702$	−30.8433	−1.16411
$703$	4.61247	0.173963
$704$	3.24241	0.122203
$705$	32.4846	1.22344
$706$	−14.0324	−0.528117
$707$	−6.39357	−0.240455
$708$	19.9395	0.749372
$709$	−50.5425	−1.89816	−0.949081	−	0.315032i	$-0.897985\pi$
$709$	−50.5425	−1.89816	−0.949081	+	0.315032i	$0.897985\pi$
$710$	−83.6379	−3.13887
$711$	5.54458	0.207938
$712$	30.4608	1.14157
$713$	10.1083	0.378558
$714$	−2.78603	−0.104265
$715$	29.2218	1.09283
$716$	57.0106	2.13058
$717$	35.0748	1.30989
$718$	45.4943	1.69783
$719$	28.5287	1.06394	0.531970	−	0.846763i	$-0.321452\pi$
$719$	28.5287	1.06394	0.531970	+	0.846763i	$0.321452\pi$
$720$	12.3352	0.459707
$721$	0.822863	0.0306450
$722$	47.6628	1.77383
$723$	−22.6061	−0.840729
$724$	−78.1772	−2.90543
$725$	23.5532	0.874746
$726$	−9.09212	−0.337440
$727$	−25.4645	−0.944427	−0.472213	−	0.881484i	$-0.656545\pi$
$727$	−25.4645	−0.944427	−0.472213	+	0.881484i	$0.656545\pi$
$728$	16.4725	0.610512
$729$	22.1635	0.820871
$730$	94.6375	3.50269
$731$	4.66441	0.172519
$732$	72.7557	2.68913
$733$	34.0604	1.25805	0.629025	−	0.777385i	$-0.283454\pi$
$733$	34.0604	1.25805	0.629025	+	0.777385i	$0.283454\pi$
$734$	−34.0864	−1.25815
$735$	−7.09390	−0.261662
$736$	−41.0634	−1.51362
$737$	22.9697	0.846102
$738$	7.87605	0.289921
$739$	−24.7602	−0.910819	−0.455409	−	0.890282i	$-0.650507\pi$
$739$	−24.7602	−0.910819	−0.455409	+	0.890282i	$0.650507\pi$
$740$	132.213	4.86024
$741$	−2.84581	−0.104544
$742$	12.1431	0.445787
$743$	−41.4839	−1.52190	−0.760948	−	0.648813i	$-0.775266\pi$
$743$	−41.4839	−1.52190	−0.760948	+	0.648813i	$0.775266\pi$
$744$	18.7929	0.688983
$745$	−4.72384	−0.173068
$746$	−10.3980	−0.380697
$747$	−2.36097	−0.0863834
$748$	8.05832	0.294641
$749$	−10.7560	−0.393015
$750$	85.1435	3.10900
$751$	−3.35334	−0.122365	−0.0611826	−	0.998127i	$-0.519487\pi$
$751$	−3.35334	−0.122365	−0.0611826	+	0.998127i	$0.519487\pi$
$752$	−34.6481	−1.26349
$753$	9.37756	0.341737
$754$	−15.7306	−0.572876
$755$	7.29593	0.265526
$756$	−21.6570	−0.787656
$757$	−26.9951	−0.981154	−0.490577	−	0.871398i	$-0.663214\pi$
$757$	−26.9951	−0.981154	−0.490577	+	0.871398i	$0.663214\pi$
$758$	9.31413	0.338305
$759$	−36.1447	−1.31197
$760$	−15.1662	−0.550134
$761$	−2.45226	−0.0888943	−0.0444472	−	0.999012i	$-0.514153\pi$
$761$	−2.45226	−0.0888943	−0.0444472	+	0.999012i	$0.514153\pi$
$762$	31.3511	1.13573
$763$	1.02527	0.0371171
$764$	6.55781	0.237253
$765$	0.959276	0.0346827
$766$	74.7139	2.69952
$767$	−5.99755	−0.216559
$768$	50.9460	1.83836
$769$	−44.3677	−1.59994	−0.799971	−	0.600039i	$-0.795152\pi$
$769$	−44.3677	−1.59994	−0.799971	+	0.600039i	$0.795152\pi$
$770$	29.5476	1.06482
$771$	30.5212	1.09919
$772$	−39.3814	−1.41737
$773$	31.4987	1.13293	0.566465	−	0.824086i	$-0.308311\pi$
$773$	31.4987	1.13293	0.566465	+	0.824086i	$0.308311\pi$
$774$	−8.62566	−0.310043
$775$	15.1152	0.542953
$776$	−73.6139	−2.64259
$777$	14.0464	0.503913
$778$	−56.3368	−2.01977
$779$	−4.39894	−0.157608
$780$	−81.5730	−2.92078
$781$	25.7013	0.919663
$782$	−9.75644	−0.348890
$783$	11.5806	0.413857
$784$	7.56636	0.270227
$785$	19.0202	0.678859
$786$	55.3907	1.97572
$787$	0.621994	0.0221717	0.0110859	−	0.999939i	$-0.496471\pi$
$787$	0.621994	0.0221717	0.0110859	+	0.999939i	$0.496471\pi$
$788$	6.44682	0.229658
$789$	−32.0110	−1.13962
$790$	−127.828	−4.54792
$791$	1.23970	0.0440787
$792$	−8.34425	−0.296500
$793$	−21.8840	−0.777124
$794$	0.303527	0.0107718
$795$	−33.6715	−1.19420
$796$	−29.2687	−1.03740
$797$	−6.58566	−0.233276	−0.116638	−	0.993174i	$-0.537212\pi$
$797$	−6.58566	−0.233276	−0.116638	+	0.993174i	$0.537212\pi$
$798$	−2.87754	−0.101864
$799$	−2.69449	−0.0953241
$800$	−61.4032	−2.17093
$801$	−1.98996	−0.0703119
$802$	−67.7888	−2.39371
$803$	−29.0813	−1.02626
$804$	−64.1204	−2.26135
$805$	−24.8422	−0.875573
$806$	−10.0950	−0.355583
$807$	−22.2057	−0.781679
$808$	−41.6262	−1.46440
$809$	33.7002	1.18483	0.592417	−	0.805631i	$-0.298174\pi$
$809$	33.7002	1.18483	0.592417	+	0.805631i	$0.298174\pi$
$810$	98.9909	3.47819
$811$	12.4840	0.438374	0.219187	−	0.975683i	$-0.429659\pi$
$811$	12.4840	0.438374	0.219187	+	0.975683i	$0.429659\pi$
$812$	−11.0454	−0.387619
$813$	−46.5808	−1.63366
$814$	−58.5063	−2.05065
$815$	13.0558	0.457326
$816$	−8.23988	−0.288454
$817$	4.81761	0.168547
$818$	17.1207	0.598610
$819$	−1.07613	−0.0376029
$820$	−126.092	−4.40333
$821$	15.8237	0.552251	0.276125	−	0.961122i	$-0.410949\pi$
$821$	15.8237	0.552251	0.276125	+	0.961122i	$0.410949\pi$
$822$	16.2658	0.567334
$823$	40.2189	1.40194	0.700971	−	0.713189i	$-0.252750\pi$
$823$	40.2189	1.40194	0.700971	+	0.713189i	$0.252750\pi$
$824$	5.35736	0.186632
$825$	−54.0481	−1.88171
$826$	−6.06442	−0.211008
$827$	−6.76248	−0.235154	−0.117577	−	0.993064i	$-0.537513\pi$
$827$	−6.76248	−0.235154	−0.117577	+	0.993064i	$0.537513\pi$
$828$	12.5288	0.435406
$829$	39.9123	1.38621	0.693105	−	0.720837i	$-0.256242\pi$
$829$	39.9123	1.38621	0.693105	+	0.720837i	$0.256242\pi$
$830$	54.4313	1.88934
$831$	48.6482	1.68759
$832$	2.72250	0.0943857
$833$	0.588414	0.0203873
$834$	−45.4864	−1.57507
$835$	−65.2738	−2.25889
$836$	8.32300	0.287857
$837$	7.43178	0.256880
$838$	66.0559	2.28186
$839$	−10.9686	−0.378678	−0.189339	−	0.981912i	$-0.560635\pi$
$839$	−10.9686	−0.378678	−0.189339	+	0.981912i	$0.560635\pi$
$840$	−46.1858	−1.59356
$841$	−23.0937	−0.796334
$842$	68.0547	2.34532
$843$	19.7386	0.679833
$844$	−116.532	−4.01120
$845$	−25.2922	−0.870080
$846$	4.98278	0.171312
$847$	1.92027	0.0659812
$848$	35.9140	1.23329
$849$	48.2189	1.65487
$850$	−14.5891	−0.500400
$851$	49.1894	1.68619
$852$	−71.7454	−2.45796
$853$	45.7276	1.56568	0.782841	−	0.622222i	$-0.213770\pi$
$853$	45.7276	1.56568	0.782841	+	0.622222i	$0.213770\pi$
$854$	−22.1280	−0.757205
$855$	0.990785	0.0338841
$856$	−70.0284	−2.39352
$857$	30.5859	1.04479	0.522397	−	0.852702i	$-0.325038\pi$
$857$	30.5859	1.04479	0.522397	+	0.852702i	$0.325038\pi$
$858$	36.0974	1.23234
$859$	1.00000	0.0341196
$859$	1.00000	0.0341196
$860$	138.093	4.70894
$861$	−13.3962	−0.456540
$862$	−58.1706	−1.98130
$863$	−33.5198	−1.14103	−0.570514	−	0.821288i	$-0.693256\pi$
$863$	−33.5198	−1.14103	−0.570514	+	0.821288i	$0.693256\pi$
$864$	−30.1905	−1.02710
$865$	−6.93630	−0.235841
$866$	−48.3704	−1.64369
$867$	30.8222	1.04678
$868$	−7.08835	−0.240594
$869$	39.2806	1.33250
$870$	44.1057	1.49532
$871$	19.2866	0.653502
$872$	6.67514	0.226049
$873$	4.80910	0.162763
$874$	−10.0769	−0.340856
$875$	−17.9824	−0.607917
$876$	81.1810	2.74285
$877$	−20.9869	−0.708676	−0.354338	−	0.935117i	$-0.615294\pi$
$877$	−20.9869	−0.708676	−0.354338	+	0.935117i	$0.615294\pi$
$878$	106.111	3.58108
$879$	−54.6137	−1.84207
$880$	87.3890	2.94588
$881$	−42.9643	−1.44750	−0.723752	−	0.690060i	$-0.757584\pi$
$881$	−42.9643	−1.44750	−0.723752	+	0.690060i	$0.757584\pi$
$882$	−1.08813	−0.0366391
$883$	−28.0293	−0.943262	−0.471631	−	0.881796i	$-0.656335\pi$
$883$	−28.0293	−0.943262	−0.471631	+	0.881796i	$0.656335\pi$
$884$	6.76619	0.227572
$885$	16.8160	0.565264
$886$	56.9509	1.91330
$887$	−27.0923	−0.909670	−0.454835	−	0.890576i	$-0.650302\pi$
$887$	−27.0923	−0.909670	−0.454835	+	0.890576i	$0.650302\pi$
$888$	91.4512	3.06890
$889$	−6.62139	−0.222074
$890$	45.8779	1.53783
$891$	−30.4191	−1.01908
$892$	131.757	4.41154
$893$	−2.78299	−0.0931292
$894$	−5.83531	−0.195162
$895$	48.0799	1.60714
$896$	−9.91865	−0.331359
$897$	−30.3490	−1.01332
$898$	−68.0515	−2.27091
$899$	3.79034	0.126415
$900$	18.7346	0.624487
$901$	2.79293	0.0930461
$902$	55.7979	1.85787
$903$	14.6712	0.488226
$904$	8.07124	0.268445
$905$	−65.9309	−2.19162
$906$	9.01260	0.299424
$907$	−7.90802	−0.262582	−0.131291	−	0.991344i	$-0.541912\pi$
$907$	−7.90802	−0.262582	−0.131291	+	0.991344i	$0.541912\pi$
$908$	−11.7710	−0.390635
$909$	2.71938	0.0901963
$910$	24.8097	0.822434
$911$	49.3470	1.63494	0.817470	−	0.575971i	$-0.195376\pi$
$911$	49.3470	1.63494	0.817470	+	0.575971i	$0.195376\pi$
$912$	−8.51053	−0.281812
$913$	−16.7263	−0.553559
$914$	50.6717	1.67607
$915$	61.3586	2.02845
$916$	−68.7624	−2.27197
$917$	−11.6986	−0.386322
$918$	−7.17311	−0.236748
$919$	−0.871430	−0.0287458	−0.0143729	−	0.999897i	$-0.504575\pi$
$919$	−0.871430	−0.0287458	−0.0143729	+	0.999897i	$0.504575\pi$
$920$	−161.739	−5.33237
$921$	6.28214	0.207004
$922$	8.96108	0.295117
$923$	21.5801	0.710319
$924$	25.3462	0.833828
$925$	73.5542	2.41845
$926$	−69.0769	−2.27001
$927$	−0.349989	−0.0114952
$928$	−15.3977	−0.505455
$929$	28.0615	0.920667	0.460333	−	0.887746i	$-0.347730\pi$
$929$	28.0615	0.920667	0.460333	+	0.887746i	$0.347730\pi$
$930$	28.3046	0.928144
$931$	0.607741	0.0199179
$932$	−43.9827	−1.44070
$933$	−19.5281	−0.639321
$934$	68.7013	2.24798
$935$	6.79599	0.222253
$936$	−7.00628	−0.229007
$937$	30.8453	1.00767	0.503835	−	0.863800i	$-0.331922\pi$
$937$	30.8453	1.00767	0.503835	+	0.863800i	$0.331922\pi$
$938$	19.5017	0.636752
$939$	−4.74361	−0.154802
$940$	−79.7722	−2.60188
$941$	9.87376	0.321875	0.160938	−	0.986965i	$-0.448548\pi$
$941$	9.87376	0.321875	0.160938	+	0.986965i	$0.448548\pi$
$942$	23.4954	0.765523
$943$	−46.9123	−1.52767
$944$	−17.9360	−0.583766
$945$	−18.2644	−0.594142
$946$	−61.1085	−1.98681
$947$	−9.10722	−0.295945	−0.147972	−	0.988991i	$-0.547275\pi$
$947$	−9.10722	−0.295945	−0.147972	+	0.988991i	$0.547275\pi$
$948$	−109.652	−3.56134
$949$	−24.4182	−0.792650
$950$	−15.0682	−0.488879
$951$	6.61805	0.214605
$952$	3.83095	0.124162
$953$	4.15647	0.134641	0.0673207	−	0.997731i	$-0.478555\pi$
$953$	4.15647	0.134641	0.0673207	+	0.997731i	$0.478555\pi$
$954$	−5.16483	−0.167218
$955$	5.53054	0.178964
$956$	−86.1329	−2.78574
$957$	−13.5533	−0.438117
$958$	−73.9078	−2.38785
$959$	−3.43535	−0.110933
$960$	−7.63337	−0.246366
$961$	−28.5676	−0.921535
$962$	−49.1250	−1.58385
$963$	4.57486	0.147423
$964$	55.5135	1.78797
$965$	−33.2124	−1.06914
$966$	−30.6874	−0.987351
$967$	−34.7051	−1.11604	−0.558020	−	0.829827i	$-0.688439\pi$
$967$	−34.7051	−1.11604	−0.558020	+	0.829827i	$0.688439\pi$
$968$	12.5022	0.401835
$969$	−0.661840	−0.0212614
$970$	−110.872	−3.55988
$971$	17.3111	0.555539	0.277769	−	0.960648i	$-0.410405\pi$
$971$	17.3111	0.555539	0.277769	+	0.960648i	$0.410405\pi$
$972$	19.9445	0.639719
$973$	9.60680	0.307980
$974$	−32.7217	−1.04847
$975$	−45.3816	−1.45338
$976$	−65.4452	−2.09485
$977$	9.67847	0.309642	0.154821	−	0.987943i	$-0.450520\pi$
$977$	9.67847	0.309642	0.154821	+	0.987943i	$0.450520\pi$
$978$	16.1278	0.515709
$979$	−14.0979	−0.450571
$980$	17.4204	0.556475
$981$	−0.436078	−0.0139229
$982$	1.39809	0.0446149
$983$	20.3636	0.649497	0.324749	−	0.945800i	$-0.394720\pi$
$983$	20.3636	0.649497	0.324749	+	0.945800i	$0.394720\pi$
$984$	−87.2176	−2.78040
$985$	5.43693	0.173235
$986$	−3.65841	−0.116508
$987$	−8.47509	−0.269765
$988$	6.98843	0.222332
$989$	51.3772	1.63370
$990$	−12.5675	−0.399422
$991$	61.7469	1.96145	0.980727	−	0.195382i	$-0.0625947\pi$
$991$	61.7469	1.96145	0.980727	+	0.195382i	$0.0625947\pi$
$992$	−9.88140	−0.313735
$993$	10.8116	0.343096
$994$	21.8207	0.692112
$995$	−24.6838	−0.782529
$996$	46.6917	1.47948
$997$	−51.8110	−1.64087	−0.820436	−	0.571739i	$-0.806269\pi$
$997$	−51.8110	−1.64087	−0.820436	+	0.571739i	$0.806269\pi$
$998$	−64.5449	−2.04313
$999$	36.1649	1.14421

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	6013.2.a.f.1.7	✓	110

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
6013.2.a.f.1.7	✓	110	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:	\( N \)	\(=\)	\( 6013 = 7 \cdot 859 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	6013.a (trivial)

\(f(q)\)	\(=\)	\(q-2.55830 q^{2} -1.85077 q^{3} +4.54491 q^{4} +3.83295 q^{5} +4.73481 q^{6} -1.00000 q^{7} -6.51064 q^{8} +0.425331 q^{9} +O(q^{10})\)	\(q-2.55830 q^{2} -1.85077 q^{3} +4.54491 q^{4} +3.83295 q^{5} +4.73481 q^{6} -1.00000 q^{7} -6.51064 q^{8} +0.425331 q^{9} -9.80585 q^{10} +3.01326 q^{11} -8.41155 q^{12} +2.53009 q^{13} +2.55830 q^{14} -7.09390 q^{15} +7.56636 q^{16} +0.588414 q^{17} -1.08813 q^{18} +0.607741 q^{19} +17.4204 q^{20} +1.85077 q^{21} -7.70883 q^{22} +6.48122 q^{23} +12.0497 q^{24} +9.69153 q^{25} -6.47274 q^{26} +4.76511 q^{27} -4.54491 q^{28} +2.43029 q^{29} +18.1483 q^{30} +1.55962 q^{31} -6.33575 q^{32} -5.57683 q^{33} -1.50534 q^{34} -3.83295 q^{35} +1.93309 q^{36} +7.58953 q^{37} -1.55478 q^{38} -4.68261 q^{39} -24.9550 q^{40} -7.23818 q^{41} -4.73481 q^{42} +7.92709 q^{43} +13.6950 q^{44} +1.63027 q^{45} -16.5809 q^{46} -4.57924 q^{47} -14.0036 q^{48} +1.00000 q^{49} -24.7939 q^{50} -1.08902 q^{51} +11.4990 q^{52} +4.74654 q^{53} -12.1906 q^{54} +11.5497 q^{55} +6.51064 q^{56} -1.12479 q^{57} -6.21742 q^{58} -2.37049 q^{59} -32.2411 q^{60} -8.64949 q^{61} -3.98999 q^{62} -0.425331 q^{63} +1.07605 q^{64} +9.69773 q^{65} +14.2672 q^{66} +7.62289 q^{67} +2.67429 q^{68} -11.9952 q^{69} +9.80585 q^{70} +8.52939 q^{71} -2.76918 q^{72} -9.65113 q^{73} -19.4163 q^{74} -17.9368 q^{75} +2.76213 q^{76} -3.01326 q^{77} +11.9795 q^{78} +13.0359 q^{79} +29.0015 q^{80} -10.0951 q^{81} +18.5174 q^{82} -5.55090 q^{83} +8.41155 q^{84} +2.25536 q^{85} -20.2799 q^{86} -4.49790 q^{87} -19.6182 q^{88} -4.67862 q^{89} -4.17073 q^{90} -2.53009 q^{91} +29.4565 q^{92} -2.88650 q^{93} +11.7151 q^{94} +2.32944 q^{95} +11.7260 q^{96} +11.3067 q^{97} -2.55830 q^{98} +1.28163 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 110 q + 16 q^{2} + 29 q^{3} + 118 q^{4} + 12 q^{6} - 110 q^{7} + 57 q^{8} + 127 q^{9}+O(q^{10}) \) 110 * q + 16 * q^2 + 29 * q^3 + 118 * q^4 + 12 * q^6 - 110 * q^7 + 57 * q^8 + 127 * q^9	\( 110 q + 16 q^{2} + 29 q^{3} + 118 q^{4} + 12 q^{6} - 110 q^{7} + 57 q^{8} + 127 q^{9} + 3 q^{10} + 52 q^{11} + 62 q^{12} - 9 q^{13} - 16 q^{14} + 39 q^{15} + 146 q^{16} + 11 q^{17} + 60 q^{18} + 14 q^{19} + 18 q^{20} - 29 q^{21} + 32 q^{22} + 73 q^{23} + 24 q^{24} + 132 q^{25} - 7 q^{26} + 116 q^{27} - 118 q^{28} + 35 q^{29} + 18 q^{30} + 36 q^{31} + 140 q^{32} + 42 q^{33} - 7 q^{34} + 180 q^{36} + 49 q^{37} + 45 q^{39} + 6 q^{40} - 14 q^{41} - 12 q^{42} + 58 q^{43} + 92 q^{44} + 17 q^{45} + 27 q^{46} + 87 q^{47} + 98 q^{48} + 110 q^{49} + 91 q^{50} + 42 q^{51} + 16 q^{52} + 95 q^{53} + 41 q^{54} + 8 q^{55} - 57 q^{56} + 61 q^{57} + 46 q^{58} + 114 q^{59} + 81 q^{60} - 47 q^{61} + 31 q^{62} - 127 q^{63} + 199 q^{64} + 62 q^{65} + 21 q^{66} + 95 q^{67} + 60 q^{68} - 39 q^{69} - 3 q^{70} + 131 q^{71} + 186 q^{72} + 31 q^{73} + 23 q^{74} + 121 q^{75} + 14 q^{76} - 52 q^{77} + 110 q^{78} + 9 q^{79} + 61 q^{80} + 194 q^{81} + 45 q^{82} + 73 q^{83} - 62 q^{84} + 59 q^{85} + 72 q^{86} + 64 q^{87} + 100 q^{88} - 17 q^{89} + 11 q^{90} + 9 q^{91} + 192 q^{92} + 85 q^{93} - 11 q^{94} + 108 q^{95} + 68 q^{96} + 32 q^{97} + 16 q^{98} + 160 q^{99}+O(q^{100}) \) 110 * q + 16 * q^2 + 29 * q^3 + 118 * q^4 + 12 * q^6 - 110 * q^7 + 57 * q^8 + 127 * q^9 + 3 * q^10 + 52 * q^11 + 62 * q^12 - 9 * q^13 - 16 * q^14 + 39 * q^15 + 146 * q^16 + 11 * q^17 + 60 * q^18 + 14 * q^19 + 18 * q^20 - 29 * q^21 + 32 * q^22 + 73 * q^23 + 24 * q^24 + 132 * q^25 - 7 * q^26 + 116 * q^27 - 118 * q^28 + 35 * q^29 + 18 * q^30 + 36 * q^31 + 140 * q^32 + 42 * q^33 - 7 * q^34 + 180 * q^36 + 49 * q^37 + 45 * q^39 + 6 * q^40 - 14 * q^41 - 12 * q^42 + 58 * q^43 + 92 * q^44 + 17 * q^45 + 27 * q^46 + 87 * q^47 + 98 * q^48 + 110 * q^49 + 91 * q^50 + 42 * q^51 + 16 * q^52 + 95 * q^53 + 41 * q^54 + 8 * q^55 - 57 * q^56 + 61 * q^57 + 46 * q^58 + 114 * q^59 + 81 * q^60 - 47 * q^61 + 31 * q^62 - 127 * q^63 + 199 * q^64 + 62 * q^65 + 21 * q^66 + 95 * q^67 + 60 * q^68 - 39 * q^69 - 3 * q^70 + 131 * q^71 + 186 * q^72 + 31 * q^73 + 23 * q^74 + 121 * q^75 + 14 * q^76 - 52 * q^77 + 110 * q^78 + 9 * q^79 + 61 * q^80 + 194 * q^81 + 45 * q^82 + 73 * q^83 - 62 * q^84 + 59 * q^85 + 72 * q^86 + 64 * q^87 + 100 * q^88 - 17 * q^89 + 11 * q^90 + 9 * q^91 + 192 * q^92 + 85 * q^93 - 11 * q^94 + 108 * q^95 + 68 * q^96 + 32 * q^97 + 16 * q^98 + 160 * q^99

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