LMFDB - Embedded newform 1339.2.a.d.1.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1339,2,Mod(1,1339)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1339, 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("1339.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1339 = 13 \cdot 103 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1339.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:	$10.6919688306$
Analytic rank:	$1$
Dimension:	$19$
Coefficient field:	$\mathbb{Q}[x]/(x^{19} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{19} - 9 x^{18} + 13 x^{17} + 106 x^{16} - 351 x^{15} - 279 x^{14} + 2337 x^{13} - 1079 x^{12} + \cdots - 63 $ x^19 - 9x^18 + 13x^17 + 106x^16 - 351x^15 - 279x^14 + 2337x^13 - 1079x^12 - 6826x^11 + 7199x^10 + 9364x^9 - 14841x^8 - 5183x^7 + 14037x^6 - 108x^5 - 6099x^4 + 855x^3 + 1062x^2 - 135x - 63
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 3 $
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.4
Root			$2.47938$ of defining polynomial
Character	$\chi$	$=$	1339.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-2.47938 q^{2} +2.80838 q^{3} +4.14734 q^{4} -2.79508 q^{5} -6.96305 q^{6} +0.439709 q^{7} -5.32409 q^{8} +4.88699 q^{9} +O(q^{10})$	\(q-2.47938 q^{2} +2.80838 q^{3} +4.14734 q^{4} -2.79508 q^{5} -6.96305 q^{6} +0.439709 q^{7} -5.32409 q^{8} +4.88699 q^{9} +6.93007 q^{10} -2.41454 q^{11} +11.6473 q^{12} +1.00000 q^{13} -1.09021 q^{14} -7.84964 q^{15} +4.90578 q^{16} -6.86756 q^{17} -12.1167 q^{18} +0.555302 q^{19} -11.5922 q^{20} +1.23487 q^{21} +5.98657 q^{22} +0.601422 q^{23} -14.9521 q^{24} +2.81246 q^{25} -2.47938 q^{26} +5.29939 q^{27} +1.82362 q^{28} +4.40222 q^{29} +19.4623 q^{30} -5.45317 q^{31} -1.51512 q^{32} -6.78095 q^{33} +17.0273 q^{34} -1.22902 q^{35} +20.2680 q^{36} +0.0596275 q^{37} -1.37681 q^{38} +2.80838 q^{39} +14.8813 q^{40} -7.29455 q^{41} -3.06171 q^{42} +0.473407 q^{43} -10.0139 q^{44} -13.6595 q^{45} -1.49116 q^{46} -10.0673 q^{47} +13.7773 q^{48} -6.80666 q^{49} -6.97317 q^{50} -19.2867 q^{51} +4.14734 q^{52} +0.817556 q^{53} -13.1392 q^{54} +6.74883 q^{55} -2.34105 q^{56} +1.55950 q^{57} -10.9148 q^{58} +6.00085 q^{59} -32.5552 q^{60} -9.74064 q^{61} +13.5205 q^{62} +2.14885 q^{63} -6.05498 q^{64} -2.79508 q^{65} +16.8126 q^{66} -0.957847 q^{67} -28.4822 q^{68} +1.68902 q^{69} +3.04721 q^{70} -10.3643 q^{71} -26.0188 q^{72} +8.97479 q^{73} -0.147840 q^{74} +7.89846 q^{75} +2.30303 q^{76} -1.06170 q^{77} -6.96305 q^{78} +6.96375 q^{79} -13.7120 q^{80} +0.221712 q^{81} +18.0860 q^{82} +7.32778 q^{83} +5.12143 q^{84} +19.1954 q^{85} -1.17376 q^{86} +12.3631 q^{87} +12.8552 q^{88} +4.92960 q^{89} +33.8672 q^{90} +0.439709 q^{91} +2.49430 q^{92} -15.3146 q^{93} +24.9608 q^{94} -1.55211 q^{95} -4.25504 q^{96} -9.17542 q^{97} +16.8763 q^{98} -11.7998 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 19 q - 9 q^{2} - 2 q^{3} + 17 q^{4} - 18 q^{5} - 8 q^{6} - 8 q^{7} - 24 q^{8} + 7 q^{9}+O(q^{10}) $ 19 * q - 9 * q^2 - 2 * q^3 + 17 * q^4 - 18 * q^5 - 8 * q^6 - 8 * q^7 - 24 * q^8 + 7 * q^9	\( 19 q - 9 q^{2} - 2 q^{3} + 17 q^{4} - 18 q^{5} - 8 q^{6} - 8 q^{7} - 24 q^{8} + 7 q^{9} - q^{11} + 18 q^{12} + 19 q^{13} - 8 q^{14} - 11 q^{15} + 21 q^{16} - 16 q^{17} - 10 q^{19} - 20 q^{20} - 33 q^{21} + 2 q^{22} - 14 q^{23} - 9 q^{24} + 23 q^{25} - 9 q^{26} + q^{27} + 10 q^{28} - 22 q^{29} + 28 q^{30} - 3 q^{31} - 47 q^{32} - 25 q^{33} - 35 q^{34} - 3 q^{35} - 33 q^{36} - 19 q^{37} - 15 q^{38} - 2 q^{39} + 8 q^{40} - 52 q^{41} - 3 q^{42} - 2 q^{43} - 54 q^{44} - 40 q^{45} + 33 q^{46} - 24 q^{47} - 8 q^{48} + 7 q^{49} - 10 q^{50} - 7 q^{51} + 17 q^{52} - 11 q^{53} - 23 q^{54} - 29 q^{55} - 17 q^{56} - 34 q^{57} + 18 q^{58} - 52 q^{59} - 71 q^{60} - 25 q^{61} - 22 q^{62} - 19 q^{63} + 48 q^{64} - 18 q^{65} + 9 q^{66} - 2 q^{67} + 18 q^{68} - 26 q^{69} - 12 q^{70} - 44 q^{71} - 6 q^{72} - 39 q^{73} - 4 q^{74} + 17 q^{75} - 10 q^{76} - 18 q^{77} - 8 q^{78} + q^{79} - 9 q^{80} - 13 q^{81} + 47 q^{82} - 27 q^{83} - 24 q^{84} - 26 q^{85} - q^{86} + 31 q^{87} + 19 q^{88} - 86 q^{89} + 48 q^{90} - 8 q^{91} - 19 q^{92} + 32 q^{93} + 45 q^{94} + 17 q^{95} - 25 q^{96} - 20 q^{97} + 39 q^{98} + 50 q^{99}+O(q^{100}) \) 19 * q - 9 * q^2 - 2 * q^3 + 17 * q^4 - 18 * q^5 - 8 * q^6 - 8 * q^7 - 24 * q^8 + 7 * q^9 - q^11 + 18 * q^12 + 19 * q^13 - 8 * q^14 - 11 * q^15 + 21 * q^16 - 16 * q^17 - 10 * q^19 - 20 * q^20 - 33 * q^21 + 2 * q^22 - 14 * q^23 - 9 * q^24 + 23 * q^25 - 9 * q^26 + q^27 + 10 * q^28 - 22 * q^29 + 28 * q^30 - 3 * q^31 - 47 * q^32 - 25 * q^33 - 35 * q^34 - 3 * q^35 - 33 * q^36 - 19 * q^37 - 15 * q^38 - 2 * q^39 + 8 * q^40 - 52 * q^41 - 3 * q^42 - 2 * q^43 - 54 * q^44 - 40 * q^45 + 33 * q^46 - 24 * q^47 - 8 * q^48 + 7 * q^49 - 10 * q^50 - 7 * q^51 + 17 * q^52 - 11 * q^53 - 23 * q^54 - 29 * q^55 - 17 * q^56 - 34 * q^57 + 18 * q^58 - 52 * q^59 - 71 * q^60 - 25 * q^61 - 22 * q^62 - 19 * q^63 + 48 * q^64 - 18 * q^65 + 9 * q^66 - 2 * q^67 + 18 * q^68 - 26 * q^69 - 12 * q^70 - 44 * q^71 - 6 * q^72 - 39 * q^73 - 4 * q^74 + 17 * q^75 - 10 * q^76 - 18 * q^77 - 8 * q^78 + q^79 - 9 * q^80 - 13 * q^81 + 47 * q^82 - 27 * q^83 - 24 * q^84 - 26 * q^85 - q^86 + 31 * q^87 + 19 * q^88 - 86 * q^89 + 48 * q^90 - 8 * q^91 - 19 * q^92 + 32 * q^93 + 45 * q^94 + 17 * q^95 - 25 * q^96 - 20 * q^97 + 39 * q^98 + 50 * 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 $

$2$	−2.47938	−1.75319	−0.876595	−	0.481230i	$-0.840190\pi$
$2$	−2.47938	−1.75319	−0.876595	+	0.481230i	$0.840190\pi$
$3$	2.80838	1.62142	0.810709	−	0.585449i	$-0.199082\pi$
$3$	2.80838	1.62142	0.810709	+	0.585449i	$0.199082\pi$
$4$	4.14734	2.07367
$5$	−2.79508	−1.25000	−0.624998	−	0.780626i	$-0.714900\pi$
$5$	−2.79508	−1.25000	−0.624998	+	0.780626i	$0.714900\pi$
$6$	−6.96305	−2.84265
$7$	0.439709	0.166194	0.0830972	−	0.996541i	$-0.473519\pi$
$7$	0.439709	0.166194	0.0830972	+	0.996541i	$0.473519\pi$
$8$	−5.32409	−1.88235
$9$	4.88699	1.62900
$10$	6.93007	2.19148
$11$	−2.41454	−0.728012	−0.364006	−	0.931397i	$-0.618591\pi$
$11$	−2.41454	−0.728012	−0.364006	+	0.931397i	$0.618591\pi$
$12$	11.6473	3.36229
$13$	1.00000	0.277350
$13$	1.00000	0.277350
$14$	−1.09021	−0.291370
$15$	−7.84964	−2.02677
$16$	4.90578	1.22644
$17$	−6.86756	−1.66563	−0.832814	−	0.553552i	$-0.813272\pi$
$17$	−6.86756	−1.66563	−0.832814	+	0.553552i	$0.813272\pi$
$18$	−12.1167	−2.85594
$19$	0.555302	0.127395	0.0636975	−	0.997969i	$-0.479711\pi$
$19$	0.555302	0.127395	0.0636975	+	0.997969i	$0.479711\pi$
$20$	−11.5922	−2.59208
$21$	1.23487	0.269471
$22$	5.98657	1.27634
$23$	0.601422	0.125405	0.0627026	−	0.998032i	$-0.480028\pi$
$23$	0.601422	0.125405	0.0627026	+	0.998032i	$0.480028\pi$
$24$	−14.9521	−3.05208
$25$	2.81246	0.562492
$26$	−2.47938	−0.486247
$27$	5.29939	1.01987
$28$	1.82362	0.344633
$29$	4.40222	0.817472	0.408736	−	0.912653i	$-0.365970\pi$
$29$	4.40222	0.817472	0.408736	+	0.912653i	$0.365970\pi$
$30$	19.4623	3.55331
$31$	−5.45317	−0.979418	−0.489709	−	0.871886i	$-0.662897\pi$
$31$	−5.45317	−0.979418	−0.489709	+	0.871886i	$0.662897\pi$
$32$	−1.51512	−0.267838
$33$	−6.78095	−1.18041
$34$	17.0273	2.92016
$35$	−1.22902	−0.207742
$36$	20.2680	3.37801
$37$	0.0596275	0.00980270	0.00490135	−	0.999988i	$-0.498440\pi$
$37$	0.0596275	0.00980270	0.00490135	+	0.999988i	$0.498440\pi$
$38$	−1.37681	−0.223348
$39$	2.80838	0.449701
$40$	14.8813	2.35293
$41$	−7.29455	−1.13922	−0.569608	−	0.821916i	$-0.692905\pi$
$41$	−7.29455	−1.13922	−0.569608	+	0.821916i	$0.692905\pi$
$42$	−3.06171	−0.472433
$43$	0.473407	0.0721940	0.0360970	−	0.999348i	$-0.488507\pi$
$43$	0.473407	0.0721940	0.0360970	+	0.999348i	$0.488507\pi$
$44$	−10.0139	−1.50966
$45$	−13.6595	−2.03624
$46$	−1.49116	−0.219859
$47$	−10.0673	−1.46847	−0.734235	−	0.678895i	$-0.762459\pi$
$47$	−10.0673	−1.46847	−0.734235	+	0.678895i	$0.762459\pi$
$48$	13.7773	1.98858
$49$	−6.80666	−0.972379
$50$	−6.97317	−0.986156
$51$	−19.2867	−2.70068
$52$	4.14734	0.575133
$53$	0.817556	0.112300	0.0561500	−	0.998422i	$-0.482117\pi$
$53$	0.817556	0.112300	0.0561500	+	0.998422i	$0.482117\pi$
$54$	−13.1392	−1.78802
$55$	6.74883	0.910012
$56$	−2.34105	−0.312836
$57$	1.55950	0.206561
$58$	−10.9148	−1.43318
$59$	6.00085	0.781244	0.390622	−	0.920551i	$-0.372260\pi$
$59$	6.00085	0.781244	0.390622	+	0.920551i	$0.372260\pi$
$60$	−32.5552	−4.20285
$61$	−9.74064	−1.24716	−0.623581	−	0.781759i	$-0.714323\pi$
$61$	−9.74064	−1.24716	−0.623581	+	0.781759i	$0.714323\pi$
$62$	13.5205	1.71711
$63$	2.14885	0.270730
$64$	−6.05498	−0.756873
$65$	−2.79508	−0.346687
$66$	16.8126	2.06948
$67$	−0.957847	−0.117020	−0.0585098	−	0.998287i	$-0.518635\pi$
$67$	−0.957847	−0.117020	−0.0585098	+	0.998287i	$0.518635\pi$
$68$	−28.4822	−3.45397
$69$	1.68902	0.203334
$70$	3.04721	0.364212
$71$	−10.3643	−1.23001	−0.615005	−	0.788523i	$-0.710846\pi$
$71$	−10.3643	−1.23001	−0.615005	+	0.788523i	$0.710846\pi$
$72$	−26.0188	−3.06634
$73$	8.97479	1.05042	0.525210	−	0.850973i	$-0.323987\pi$
$73$	8.97479	1.05042	0.525210	+	0.850973i	$0.323987\pi$
$74$	−0.147840	−0.0171860
$75$	7.89846	0.912036
$76$	2.30303	0.264176
$77$	−1.06170	−0.120991
$78$	−6.96305	−0.788410
$79$	6.96375	0.783483	0.391741	−	0.920075i	$-0.371873\pi$
$79$	6.96375	0.783483	0.391741	+	0.920075i	$0.371873\pi$
$80$	−13.7120	−1.53305
$81$	0.221712	0.0246347
$82$	18.0860	1.99726
$83$	7.32778	0.804329	0.402164	−	0.915567i	$-0.368258\pi$
$83$	7.32778	0.804329	0.402164	+	0.915567i	$0.368258\pi$
$84$	5.12143	0.558794
$85$	19.1954	2.08203
$86$	−1.17376	−0.126570
$87$	12.3631	1.32546
$88$	12.8552	1.37037
$89$	4.92960	0.522536	0.261268	−	0.965266i	$-0.415859\pi$
$89$	4.92960	0.522536	0.261268	+	0.965266i	$0.415859\pi$
$90$	33.8672	3.56992
$91$	0.439709	0.0460940
$92$	2.49430	0.260049
$93$	−15.3146	−1.58805
$94$	24.9608	2.57451
$95$	−1.55211	−0.159243
$96$	−4.25504	−0.434278
$97$	−9.17542	−0.931623	−0.465811	−	0.884884i	$-0.654237\pi$
$97$	−9.17542	−0.931623	−0.465811	+	0.884884i	$0.654237\pi$
$98$	16.8763	1.70477
$99$	−11.7998	−1.18593
$100$	11.6642	1.16642
$101$	−11.2772	−1.12213	−0.561064	−	0.827772i	$-0.689608\pi$
$101$	−11.2772	−1.12213	−0.561064	+	0.827772i	$0.689608\pi$
$102$	47.8192	4.73480
$103$	1.00000	0.0985329
$103$	1.00000	0.0985329
$104$	−5.32409	−0.522070
$105$	−3.45156	−0.336837
$106$	−2.02704	−0.196883
$107$	−5.67870	−0.548980	−0.274490	−	0.961590i	$-0.588509\pi$
$107$	−5.67870	−0.548980	−0.274490	+	0.961590i	$0.588509\pi$
$108$	21.9784	2.11487
$109$	3.92018	0.375485	0.187742	−	0.982218i	$-0.439883\pi$
$109$	3.92018	0.375485	0.187742	+	0.982218i	$0.439883\pi$
$110$	−16.7329	−1.59542
$111$	0.167457	0.0158943
$112$	2.15711	0.203828
$113$	−14.0119	−1.31813	−0.659066	−	0.752085i	$-0.729048\pi$
$113$	−14.0119	−1.31813	−0.659066	+	0.752085i	$0.729048\pi$
$114$	−3.86660	−0.362140
$115$	−1.68102	−0.156756
$116$	18.2575	1.69517
$117$	4.88699	0.451803
$118$	−14.8784	−1.36967
$119$	−3.01973	−0.276818
$120$	41.7922	3.81509
$121$	−5.16999	−0.469999
$122$	24.1508	2.18651
$123$	−20.4858	−1.84715
$124$	−22.6162	−2.03099
$125$	6.11434	0.546883
$126$	−5.32783	−0.474641
$127$	−5.75030	−0.510257	−0.255128	−	0.966907i	$-0.582118\pi$
$127$	−5.75030	−0.510257	−0.255128	+	0.966907i	$0.582118\pi$
$128$	18.0429	1.59478
$129$	1.32951	0.117057
$130$	6.93007	0.607808
$131$	14.4067	1.25872	0.629359	−	0.777114i	$-0.283317\pi$
$131$	14.4067	1.25872	0.629359	+	0.777114i	$0.283317\pi$
$132$	−28.1229	−2.44779
$133$	0.244171	0.0211723
$134$	2.37487	0.205157
$135$	−14.8122	−1.27483
$136$	36.5635	3.13530
$137$	21.7872	1.86141	0.930705	−	0.365770i	$-0.119194\pi$
$137$	21.7872	1.86141	0.930705	+	0.365770i	$0.119194\pi$
$138$	−4.18773	−0.356483
$139$	1.20224	0.101973	0.0509865	−	0.998699i	$-0.483763\pi$
$139$	1.20224	0.101973	0.0509865	+	0.998699i	$0.483763\pi$
$140$	−5.09717	−0.430790
$141$	−28.2729	−2.38100
$142$	25.6970	2.15644
$143$	−2.41454	−0.201914
$144$	23.9745	1.99787
$145$	−12.3046	−1.02184
$146$	−22.2519	−1.84158
$147$	−19.1157	−1.57663
$148$	0.247296	0.0203276
$149$	2.47152	0.202475	0.101238	−	0.994862i	$-0.467720\pi$
$149$	2.47152	0.202475	0.101238	+	0.994862i	$0.467720\pi$
$150$	−19.5833	−1.59897
$151$	−11.8551	−0.964755	−0.482377	−	0.875963i	$-0.660227\pi$
$151$	−11.8551	−0.964755	−0.482377	+	0.875963i	$0.660227\pi$
$152$	−2.95648	−0.239802
$153$	−33.5617	−2.71330
$154$	2.63235	0.212121
$155$	15.2420	1.22427
$156$	11.6473	0.932531
$157$	−10.7470	−0.857703	−0.428852	−	0.903375i	$-0.641082\pi$
$157$	−10.7470	−0.857703	−0.428852	+	0.903375i	$0.641082\pi$
$158$	−17.2658	−1.37359
$159$	2.29601	0.182085
$160$	4.23489	0.334797
$161$	0.264451	0.0208416
$162$	−0.549709	−0.0431892
$163$	−13.4541	−1.05381	−0.526903	−	0.849925i	$-0.676647\pi$
$163$	−13.4541	−1.05381	−0.526903	+	0.849925i	$0.676647\pi$
$164$	−30.2530	−2.36236
$165$	18.9533	1.47551
$166$	−18.1684	−1.41014
$167$	−17.4833	−1.35290	−0.676450	−	0.736489i	$-0.736482\pi$
$167$	−17.4833	−1.35290	−0.676450	+	0.736489i	$0.736482\pi$
$168$	−6.57456	−0.507238
$169$	1.00000	0.0769231
$170$	−47.5927	−3.65019
$171$	2.71376	0.207526
$172$	1.96338	0.149707
$173$	15.2062	1.15610	0.578052	−	0.816000i	$-0.303813\pi$
$173$	15.2062	1.15610	0.578052	+	0.816000i	$0.303813\pi$
$174$	−30.6529	−2.32379
$175$	1.23666	0.0934831
$176$	−11.8452	−0.892866
$177$	16.8527	1.26672
$178$	−12.2224	−0.916105
$179$	16.2365	1.21357	0.606785	−	0.794866i	$-0.292459\pi$
$179$	16.2365	1.21357	0.606785	+	0.794866i	$0.292459\pi$
$180$	−56.6508	−4.22250
$181$	−10.9093	−0.810881	−0.405440	−	0.914122i	$-0.632882\pi$
$181$	−10.9093	−0.810881	−0.405440	+	0.914122i	$0.632882\pi$
$182$	−1.09021	−0.0808115
$183$	−27.3554	−2.02217
$184$	−3.20202	−0.236056
$185$	−0.166664	−0.0122534
$186$	37.9707	2.78415
$187$	16.5820	1.21260
$188$	−41.7527	−3.04513
$189$	2.33019	0.169496
$190$	3.84828	0.279184
$191$	−7.08492	−0.512647	−0.256324	−	0.966591i	$-0.582511\pi$
$191$	−7.08492	−0.512647	−0.256324	+	0.966591i	$0.582511\pi$
$192$	−17.0047	−1.22721
$193$	22.8401	1.64406	0.822032	−	0.569442i	$-0.192841\pi$
$193$	22.8401	1.64406	0.822032	+	0.569442i	$0.192841\pi$
$194$	22.7494	1.63331
$195$	−7.84964	−0.562124
$196$	−28.2295	−2.01640
$197$	−21.3300	−1.51970	−0.759851	−	0.650098i	$-0.774728\pi$
$197$	−21.3300	−1.51970	−0.759851	+	0.650098i	$0.774728\pi$
$198$	29.2563	2.07916
$199$	−15.3787	−1.09016	−0.545082	−	0.838382i	$-0.683502\pi$
$199$	−15.3787	−1.09016	−0.545082	+	0.838382i	$0.683502\pi$
$200$	−14.9738	−1.05881
$201$	−2.69000	−0.189738
$202$	27.9606	1.96730
$203$	1.93570	0.135859
$204$	−79.9887	−5.60033
$205$	20.3888	1.42402
$206$	−2.47938	−0.172747
$207$	2.93914	0.204285
$208$	4.90578	0.340154
$209$	−1.34080	−0.0927451
$210$	8.55773	0.590540
$211$	12.5782	0.865921	0.432960	−	0.901413i	$-0.357469\pi$
$211$	12.5782	0.865921	0.432960	+	0.901413i	$0.357469\pi$
$212$	3.39069	0.232873
$213$	−29.1068	−1.99436
$214$	14.0797	0.962466
$215$	−1.32321	−0.0902422
$216$	−28.2144	−1.91975
$217$	−2.39781	−0.162774
$218$	−9.71963	−0.658296
$219$	25.2046	1.70317
$220$	27.9897	1.88707
$221$	−6.86756	−0.461962
$222$	−0.415189	−0.0278657
$223$	−22.8871	−1.53264	−0.766318	−	0.642461i	$-0.777913\pi$
$223$	−22.8871	−1.53264	−0.766318	+	0.642461i	$0.777913\pi$
$224$	−0.666213	−0.0445132
$225$	13.7445	0.916299
$226$	34.7410	2.31094
$227$	−6.22856	−0.413404	−0.206702	−	0.978404i	$-0.566273\pi$
$227$	−6.22856	−0.413404	−0.206702	+	0.978404i	$0.566273\pi$
$228$	6.46778	0.428339
$229$	−9.93019	−0.656206	−0.328103	−	0.944642i	$-0.606409\pi$
$229$	−9.93019	−0.656206	−0.328103	+	0.944642i	$0.606409\pi$
$230$	4.16790	0.274823
$231$	−2.98164	−0.196178
$232$	−23.4378	−1.53877
$233$	−19.8434	−1.29998	−0.649992	−	0.759941i	$-0.725228\pi$
$233$	−19.8434	−1.29998	−0.649992	+	0.759941i	$0.725228\pi$
$234$	−12.1167	−0.792095
$235$	28.1390	1.83558
$236$	24.8876	1.62004
$237$	19.5568	1.27035
$238$	7.48707	0.485315
$239$	−11.3794	−0.736072	−0.368036	−	0.929812i	$-0.619970\pi$
$239$	−11.3794	−0.736072	−0.368036	+	0.929812i	$0.619970\pi$
$240$	−38.5086	−2.48572
$241$	26.7115	1.72064	0.860321	−	0.509753i	$-0.170263\pi$
$241$	26.7115	1.72064	0.860321	+	0.509753i	$0.170263\pi$
$242$	12.8184	0.823998
$243$	−15.2755	−0.979924
$244$	−40.3978	−2.58620
$245$	19.0251	1.21547
$246$	50.7923	3.23840
$247$	0.555302	0.0353330
$248$	29.0332	1.84361
$249$	20.5792	1.30415
$250$	−15.1598	−0.958790
$251$	−6.20530	−0.391675	−0.195837	−	0.980636i	$-0.562743\pi$
$251$	−6.20530	−0.391675	−0.195837	+	0.980636i	$0.562743\pi$
$252$	8.91204	0.561406
$253$	−1.45216	−0.0912964
$254$	14.2572	0.894577
$255$	53.9079	3.37584
$256$	−32.6252	−2.03908
$257$	13.3913	0.835325	0.417663	−	0.908602i	$-0.362849\pi$
$257$	13.3913	0.835325	0.417663	+	0.908602i	$0.362849\pi$
$258$	−3.29636	−0.205222
$259$	0.0262188	0.00162915
$260$	−11.5922	−0.718915
$261$	21.5136	1.33166
$262$	−35.7197	−2.20677
$263$	19.9560	1.23054	0.615270	−	0.788317i	$-0.289047\pi$
$263$	19.9560	1.23054	0.615270	+	0.788317i	$0.289047\pi$
$264$	36.1024	2.22195
$265$	−2.28513	−0.140375
$266$	−0.605394	−0.0371191
$267$	13.8442	0.847250
$268$	−3.97252	−0.242660
$269$	−26.4809	−1.61457	−0.807285	−	0.590162i	$-0.799064\pi$
$269$	−26.4809	−1.61457	−0.807285	+	0.590162i	$0.799064\pi$
$270$	36.7251	2.23502
$271$	−11.9888	−0.728267	−0.364134	−	0.931347i	$-0.618635\pi$
$271$	−11.9888	−0.728267	−0.364134	+	0.931347i	$0.618635\pi$
$272$	−33.6907	−2.04280
$273$	1.23487	0.0747377
$274$	−54.0190	−3.26340
$275$	−6.79081	−0.409501
$276$	7.00495	0.421648
$277$	31.0318	1.86452	0.932260	−	0.361788i	$-0.117834\pi$
$277$	31.0318	1.86452	0.932260	+	0.361788i	$0.117834\pi$
$278$	−2.98083	−0.178778
$279$	−26.6496	−1.59547
$280$	6.54342	0.391044
$281$	10.2089	0.609010	0.304505	−	0.952511i	$-0.401509\pi$
$281$	10.2089	0.609010	0.304505	+	0.952511i	$0.401509\pi$
$282$	70.0993	4.17435
$283$	25.5508	1.51884	0.759419	−	0.650602i	$-0.225484\pi$
$283$	25.5508	1.51884	0.759419	+	0.650602i	$0.225484\pi$
$284$	−42.9841	−2.55064
$285$	−4.35892	−0.258200
$286$	5.98657	0.353994
$287$	−3.20748	−0.189331
$288$	−7.40439	−0.436308
$289$	30.1634	1.77432
$290$	30.5077	1.79147
$291$	−25.7681	−1.51055
$292$	37.2215	2.17823
$293$	13.5036	0.788888	0.394444	−	0.918920i	$-0.370937\pi$
$293$	13.5036	0.788888	0.394444	+	0.918920i	$0.370937\pi$
$294$	47.3951	2.76414
$295$	−16.7728	−0.976553
$296$	−0.317462	−0.0184521
$297$	−12.7956	−0.742475
$298$	−6.12786	−0.354977
$299$	0.601422	0.0347811
$300$	32.7576	1.89126
$301$	0.208161	0.0119982
$302$	29.3934	1.69140
$303$	−31.6708	−1.81944
$304$	2.72419	0.156243
$305$	27.2259	1.55895
$306$	83.2124	4.75694
$307$	−3.37652	−0.192708	−0.0963542	−	0.995347i	$-0.530718\pi$
$307$	−3.37652	−0.192708	−0.0963542	+	0.995347i	$0.530718\pi$
$308$	−4.40322	−0.250897
$309$	2.80838	0.159763
$310$	−37.7909	−2.14638
$311$	−0.439450	−0.0249189	−0.0124595	−	0.999922i	$-0.503966\pi$
$311$	−0.439450	−0.0249189	−0.0124595	+	0.999922i	$0.503966\pi$
$312$	−14.9521	−0.846494
$313$	−2.33990	−0.132259	−0.0661296	−	0.997811i	$-0.521065\pi$
$313$	−2.33990	−0.132259	−0.0661296	+	0.997811i	$0.521065\pi$
$314$	26.6459	1.50372
$315$	−6.00621	−0.338412
$316$	28.8811	1.62469
$317$	11.1198	0.624548	0.312274	−	0.949992i	$-0.398909\pi$
$317$	11.1198	0.624548	0.312274	+	0.949992i	$0.398909\pi$
$318$	−5.69269	−0.319230
$319$	−10.6293	−0.595129
$320$	16.9242	0.946089
$321$	−15.9479	−0.890127
$322$	−0.655674	−0.0365393
$323$	−3.81357	−0.212193
$324$	0.919516	0.0510842
$325$	2.81246	0.156007
$326$	33.3579	1.84752
$327$	11.0093	0.608818
$328$	38.8368	2.14441
$329$	−4.42669	−0.244051
$330$	−46.9924	−2.58685
$331$	15.3551	0.843994	0.421997	−	0.906597i	$-0.361329\pi$
$331$	15.3551	0.843994	0.421997	+	0.906597i	$0.361329\pi$
$332$	30.3908	1.66791
$333$	0.291399	0.0159686
$334$	43.3478	2.37189
$335$	2.67726	0.146274
$336$	6.05799	0.330491
$337$	−10.2480	−0.558242	−0.279121	−	0.960256i	$-0.590043\pi$
$337$	−10.2480	−0.558242	−0.279121	+	0.960256i	$0.590043\pi$
$338$	−2.47938	−0.134861
$339$	−39.3508	−2.13724
$340$	79.6098	4.31745
$341$	13.1669	0.713028
$342$	−6.72844	−0.363833
$343$	−6.07091	−0.327798
$344$	−2.52046	−0.135894
$345$	−4.72094	−0.254167
$346$	−37.7019	−2.02687
$347$	−9.12589	−0.489903	−0.244952	−	0.969535i	$-0.578772\pi$
$347$	−9.12589	−0.489903	−0.244952	+	0.969535i	$0.578772\pi$
$348$	51.2741	2.74858
$349$	−34.3261	−1.83744	−0.918718	−	0.394915i	$-0.870774\pi$
$349$	−34.3261	−1.83744	−0.918718	+	0.394915i	$0.870774\pi$
$350$	−3.06617	−0.163893
$351$	5.29939	0.282860
$352$	3.65833	0.194989
$353$	7.65636	0.407507	0.203754	−	0.979022i	$-0.434686\pi$
$353$	7.65636	0.407507	0.203754	+	0.979022i	$0.434686\pi$
$354$	−41.7842	−2.22081
$355$	28.9689	1.53751
$356$	20.4447	1.08357
$357$	−8.48054	−0.448838
$358$	−40.2564	−2.12762
$359$	−20.3182	−1.07235	−0.536176	−	0.844106i	$-0.680132\pi$
$359$	−20.3182	−1.07235	−0.536176	+	0.844106i	$0.680132\pi$
$360$	72.7246	3.83292
$361$	−18.6916	−0.983771
$362$	27.0483	1.42163
$363$	−14.5193	−0.762065
$364$	1.82362	0.0955839
$365$	−25.0852	−1.31302
$366$	67.8246	3.54525
$367$	−0.678596	−0.0354224	−0.0177112	−	0.999843i	$-0.505638\pi$
$367$	−0.678596	−0.0354224	−0.0177112	+	0.999843i	$0.505638\pi$
$368$	2.95044	0.153802
$369$	−35.6484	−1.85578
$370$	0.413223	0.0214824
$371$	0.359487	0.0186636
$372$	−63.5148	−3.29309
$373$	35.0797	1.81636	0.908179	−	0.418583i	$-0.137473\pi$
$373$	35.0797	1.81636	0.908179	+	0.418583i	$0.137473\pi$
$374$	−41.1132	−2.12591
$375$	17.1714	0.886726
$376$	53.5994	2.76418
$377$	4.40222	0.226726
$378$	−5.77743	−0.297159
$379$	8.58968	0.441222	0.220611	−	0.975362i	$-0.429195\pi$
$379$	8.58968	0.441222	0.220611	+	0.975362i	$0.429195\pi$
$380$	−6.43715	−0.330219
$381$	−16.1490	−0.827340
$382$	17.5662	0.898767
$383$	31.6341	1.61643	0.808213	−	0.588890i	$-0.200435\pi$
$383$	31.6341	1.61643	0.808213	+	0.588890i	$0.200435\pi$
$384$	50.6712	2.58581
$385$	2.96752	0.151239
$386$	−56.6293	−2.88235
$387$	2.31354	0.117604
$388$	−38.0536	−1.93188
$389$	3.75212	0.190240	0.0951200	−	0.995466i	$-0.469677\pi$
$389$	3.75212	0.190240	0.0951200	+	0.995466i	$0.469677\pi$
$390$	19.4623	0.985510
$391$	−4.13030	−0.208878
$392$	36.2393	1.83036
$393$	40.4595	2.04091
$394$	52.8853	2.66432
$395$	−19.4642	−0.979351
$396$	−48.9380	−2.45923
$397$	26.9327	1.35171	0.675856	−	0.737033i	$-0.263774\pi$
$397$	26.9327	1.35171	0.675856	+	0.737033i	$0.263774\pi$
$398$	38.1296	1.91127
$399$	0.685725	0.0343292
$400$	13.7973	0.689866
$401$	7.74785	0.386909	0.193455	−	0.981109i	$-0.438031\pi$
$401$	7.74785	0.386909	0.193455	+	0.981109i	$0.438031\pi$
$402$	6.66953	0.332646
$403$	−5.45317	−0.271642
$404$	−46.7706	−2.32693
$405$	−0.619703	−0.0307933
$406$	−4.79933	−0.238187
$407$	−0.143973	−0.00713648
$408$	102.684	5.08363
$409$	21.8892	1.08235	0.541176	−	0.840909i	$-0.317979\pi$
$409$	21.8892	1.08235	0.541176	+	0.840909i	$0.317979\pi$
$410$	−50.5517	−2.49657
$411$	61.1868	3.01812
$412$	4.14734	0.204325
$413$	2.63863	0.129838
$414$	−7.28726	−0.358150
$415$	−20.4817	−1.00541
$416$	−1.51512	−0.0742850
$417$	3.37636	0.165341
$418$	3.32436	0.162600
$419$	−19.1802	−0.937012	−0.468506	−	0.883460i	$-0.655208\pi$
$419$	−19.1802	−0.937012	−0.468506	+	0.883460i	$0.655208\pi$
$420$	−14.3148	−0.698490
$421$	22.5640	1.09970	0.549850	−	0.835263i	$-0.314685\pi$
$421$	22.5640	1.09970	0.549850	+	0.835263i	$0.314685\pi$
$422$	−31.1863	−1.51812
$423$	−49.1989	−2.39213
$424$	−4.35274	−0.211388
$425$	−19.3148	−0.936904
$426$	72.1668	3.49649
$427$	−4.28305	−0.207271
$428$	−23.5515	−1.13841
$429$	−6.78095	−0.327387
$430$	3.28075	0.158212
$431$	35.0208	1.68689	0.843447	−	0.537212i	$-0.180523\pi$
$431$	35.0208	1.68689	0.843447	+	0.537212i	$0.180523\pi$
$432$	25.9976	1.25081
$433$	30.4959	1.46554	0.732770	−	0.680476i	$-0.238227\pi$
$433$	30.4959	1.46554	0.732770	+	0.680476i	$0.238227\pi$
$434$	5.94509	0.285373
$435$	−34.5559	−1.65683
$436$	16.2583	0.778633
$437$	0.333971	0.0159760
$438$	−62.4919	−2.98598
$439$	−32.5904	−1.55546	−0.777729	−	0.628600i	$-0.783628\pi$
$439$	−32.5904	−1.55546	−0.777729	+	0.628600i	$0.783628\pi$
$440$	−35.9314	−1.71296
$441$	−33.2641	−1.58400
$442$	17.0273	0.809907
$443$	8.48647	0.403204	0.201602	−	0.979467i	$-0.435385\pi$
$443$	8.48647	0.403204	0.201602	+	0.979467i	$0.435385\pi$
$444$	0.694501	0.0329595
$445$	−13.7786	−0.653169
$446$	56.7460	2.68700
$447$	6.94097	0.328297
$448$	−2.66243	−0.125788
$449$	35.3026	1.66603	0.833017	−	0.553247i	$-0.186612\pi$
$449$	35.3026	1.66603	0.833017	+	0.553247i	$0.186612\pi$
$450$	−34.0778	−1.60644
$451$	17.6130	0.829363
$452$	−58.1123	−2.73337
$453$	−33.2936	−1.56427
$454$	15.4430	0.724775
$455$	−1.22902	−0.0576174
$456$	−8.30291	−0.388820
$457$	2.92392	0.136775	0.0683877	−	0.997659i	$-0.478215\pi$
$457$	2.92392	0.136775	0.0683877	+	0.997659i	$0.478215\pi$
$458$	24.6208	1.15045
$459$	−36.3939	−1.69872
$460$	−6.97177	−0.325061
$461$	−15.0333	−0.700169	−0.350085	−	0.936718i	$-0.613847\pi$
$461$	−15.0333	−0.700169	−0.350085	+	0.936718i	$0.613847\pi$
$462$	7.39264	0.343937
$463$	−11.3037	−0.525326	−0.262663	−	0.964888i	$-0.584601\pi$
$463$	−11.3037	−0.525326	−0.262663	+	0.964888i	$0.584601\pi$
$464$	21.5963	1.00258
$465$	42.8054	1.98505
$466$	49.1994	2.27912
$467$	−14.1840	−0.656356	−0.328178	−	0.944616i	$-0.606435\pi$
$467$	−14.1840	−0.656356	−0.328178	+	0.944616i	$0.606435\pi$
$468$	20.2680	0.936890
$469$	−0.421174	−0.0194480
$470$	−69.7673	−3.21813
$471$	−30.1816	−1.39070
$472$	−31.9491	−1.47058
$473$	−1.14306	−0.0525580
$474$	−48.4889	−2.22717
$475$	1.56177	0.0716587
$476$	−12.5239	−0.574030
$477$	3.99539	0.182936
$478$	28.2139	1.29047
$479$	8.22273	0.375706	0.187853	−	0.982197i	$-0.439847\pi$
$479$	8.22273	0.375706	0.187853	+	0.982197i	$0.439847\pi$
$480$	11.8932	0.542846
$481$	0.0596275	0.00271878
$482$	−66.2281	−3.01661
$483$	0.742677	0.0337930
$484$	−21.4417	−0.974624
$485$	25.6460	1.16453
$486$	37.8739	1.71799
$487$	31.3701	1.42152	0.710759	−	0.703436i	$-0.248352\pi$
$487$	31.3701	1.42152	0.710759	+	0.703436i	$0.248352\pi$
$488$	51.8601	2.34760
$489$	−37.7842	−1.70866
$490$	−47.1706	−2.13095
$491$	9.78706	0.441684	0.220842	−	0.975310i	$-0.429120\pi$
$491$	9.78706	0.441684	0.220842	+	0.975310i	$0.429120\pi$
$492$	−84.9619	−3.83038
$493$	−30.2325	−1.36161
$494$	−1.37681	−0.0619455
$495$	32.9815	1.48241
$496$	−26.7520	−1.20120
$497$	−4.55726	−0.204421
$498$	−51.0237	−2.28643
$499$	−29.4882	−1.32007	−0.660036	−	0.751234i	$-0.729459\pi$
$499$	−29.4882	−1.32007	−0.660036	+	0.751234i	$0.729459\pi$
$500$	25.3583	1.13406
$501$	−49.0998	−2.19362
$502$	15.3853	0.686680
$503$	14.4401	0.643852	0.321926	−	0.946765i	$-0.395670\pi$
$503$	14.4401	0.643852	0.321926	+	0.946765i	$0.395670\pi$
$504$	−11.4407	−0.509609
$505$	31.5208	1.40266
$506$	3.60046	0.160060
$507$	2.80838	0.124724
$508$	−23.8485	−1.05811
$509$	−23.9894	−1.06331	−0.531657	−	0.846960i	$-0.678430\pi$
$509$	−23.9894	−1.06331	−0.531657	+	0.846960i	$0.678430\pi$
$510$	−133.658	−5.91849
$511$	3.94629	0.174574
$512$	44.8048	1.98011
$513$	2.94276	0.129926
$514$	−33.2021	−1.46448
$515$	−2.79508	−0.123166
$516$	5.51393	0.242737
$517$	24.3080	1.06906
$518$	−0.0650064	−0.00285622
$519$	42.7047	1.87453
$520$	14.8813	0.652586
$521$	23.1204	1.01292	0.506461	−	0.862263i	$-0.330953\pi$
$521$	23.1204	1.01292	0.506461	+	0.862263i	$0.330953\pi$
$522$	−53.3405	−2.33465
$523$	−19.6643	−0.859860	−0.429930	−	0.902862i	$-0.641462\pi$
$523$	−19.6643	−0.859860	−0.429930	+	0.902862i	$0.641462\pi$
$524$	59.7495	2.61017
$525$	3.47302	0.151575
$526$	−49.4786	−2.15737
$527$	37.4500	1.63135
$528$	−33.2658	−1.44771
$529$	−22.6383	−0.984274
$530$	5.66572	0.246103
$531$	29.3261	1.27264
$532$	1.01266	0.0439045
$533$	−7.29455	−0.315962
$534$	−34.3250	−1.48539
$535$	15.8724	0.686224
$536$	5.09966	0.220272
$537$	45.5982	1.96771
$538$	65.6564	2.83065
$539$	16.4350	0.707903
$540$	−61.4313	−2.64358
$541$	−2.19588	−0.0944081	−0.0472040	−	0.998885i	$-0.515031\pi$
$541$	−2.19588	−0.0944081	−0.0472040	+	0.998885i	$0.515031\pi$
$542$	29.7248	1.27679
$543$	−30.6374	−1.31478
$544$	10.4052	0.446119
$545$	−10.9572	−0.469355
$546$	−3.06171	−0.131029
$547$	−13.7748	−0.588968	−0.294484	−	0.955656i	$-0.595148\pi$
$547$	−13.7748	−0.588968	−0.294484	+	0.955656i	$0.595148\pi$
$548$	90.3592	3.85995
$549$	−47.6024	−2.03162
$550$	16.8370	0.717933
$551$	2.44456	0.104142
$552$	−8.99250	−0.382746
$553$	3.06202	0.130210
$554$	−76.9398	−3.26886
$555$	−0.468055	−0.0198678
$556$	4.98612	0.211459
$557$	3.19166	0.135235	0.0676175	−	0.997711i	$-0.478460\pi$
$557$	3.19166	0.135235	0.0676175	+	0.997711i	$0.478460\pi$
$558$	66.0746	2.79716
$559$	0.473407	0.0200230
$560$	−6.02930	−0.254785
$561$	46.5686	1.96613
$562$	−25.3117	−1.06771
$563$	5.51160	0.232286	0.116143	−	0.993232i	$-0.462947\pi$
$563$	5.51160	0.232286	0.116143	+	0.993232i	$0.462947\pi$
$564$	−117.257	−4.93742
$565$	39.1645	1.64766
$566$	−63.3502	−2.66281
$567$	0.0974888	0.00409414
$568$	55.1802	2.31531
$569$	14.4501	0.605780	0.302890	−	0.953025i	$-0.402048\pi$
$569$	14.4501	0.605780	0.302890	+	0.953025i	$0.402048\pi$
$570$	10.8074	0.452674
$571$	−9.76682	−0.408729	−0.204364	−	0.978895i	$-0.565513\pi$
$571$	−9.76682	−0.408729	−0.204364	+	0.978895i	$0.565513\pi$
$572$	−10.0139	−0.418704
$573$	−19.8971	−0.831215
$574$	7.95257	0.331934
$575$	1.69148	0.0705394
$576$	−29.5907	−1.23294
$577$	−0.977206	−0.0406816	−0.0203408	−	0.999793i	$-0.506475\pi$
$577$	−0.977206	−0.0406816	−0.0203408	+	0.999793i	$0.506475\pi$
$578$	−74.7867	−3.11072
$579$	64.1435	2.66571
$580$	−51.0312	−2.11896
$581$	3.22209	0.133675
$582$	63.8889	2.64828
$583$	−1.97402	−0.0817557
$584$	−47.7826	−1.97726
$585$	−13.6595	−0.564752
$586$	−33.4806	−1.38307
$587$	37.7969	1.56005	0.780023	−	0.625750i	$-0.215207\pi$
$587$	37.7969	1.56005	0.780023	+	0.625750i	$0.215207\pi$
$588$	−79.2793	−3.26942
$589$	−3.02816	−0.124773
$590$	41.5863	1.71208
$591$	−59.9028	−2.46407
$592$	0.292519	0.0120225
$593$	−21.2939	−0.874434	−0.437217	−	0.899356i	$-0.644036\pi$
$593$	−21.2939	−0.874434	−0.437217	+	0.899356i	$0.644036\pi$
$594$	31.7252	1.30170
$595$	8.44038	0.346022
$596$	10.2503	0.419867
$597$	−43.1891	−1.76761
$598$	−1.49116	−0.0609779
$599$	−27.4678	−1.12231	−0.561153	−	0.827712i	$-0.689642\pi$
$599$	−27.4678	−1.12231	−0.561153	+	0.827712i	$0.689642\pi$
$600$	−42.0521	−1.71677
$601$	19.6234	0.800457	0.400229	−	0.916415i	$-0.368931\pi$
$601$	19.6234	0.800457	0.400229	+	0.916415i	$0.368931\pi$
$602$	−0.516112	−0.0210352
$603$	−4.68099	−0.190625
$604$	−49.1672	−2.00059
$605$	14.4505	0.587498
$606$	78.5240	3.18982
$607$	43.0611	1.74779	0.873897	−	0.486110i	$-0.161585\pi$
$607$	43.0611	1.74779	0.873897	+	0.486110i	$0.161585\pi$
$608$	−0.841351	−0.0341213
$609$	5.43617	0.220285
$610$	−67.5034	−2.73313
$611$	−10.0673	−0.407280
$612$	−139.192	−5.62650
$613$	35.3880	1.42931	0.714654	−	0.699478i	$-0.246584\pi$
$613$	35.3880	1.42931	0.714654	+	0.699478i	$0.246584\pi$
$614$	8.37170	0.337854
$615$	57.2595	2.30893
$616$	5.65256	0.227748
$617$	10.1626	0.409130	0.204565	−	0.978853i	$-0.434422\pi$
$617$	10.1626	0.409130	0.204565	+	0.978853i	$0.434422\pi$
$618$	−6.96305	−0.280095
$619$	35.1429	1.41251	0.706255	−	0.707957i	$-0.250383\pi$
$619$	35.1429	1.41251	0.706255	+	0.707957i	$0.250383\pi$
$620$	63.2140	2.53873
$621$	3.18717	0.127897
$622$	1.08956	0.0436876
$623$	2.16759	0.0868426
$624$	13.7773	0.551533
$625$	−31.1524	−1.24609
$626$	5.80152	0.231875
$627$	−3.76547	−0.150379
$628$	−44.5715	−1.77860
$629$	−0.409496	−0.0163277
$630$	14.8917	0.593300
$631$	−37.3227	−1.48579	−0.742897	−	0.669406i	$-0.766549\pi$
$631$	−37.3227	−1.48579	−0.742897	+	0.669406i	$0.766549\pi$
$632$	−37.0756	−1.47479
$633$	35.3244	1.40402
$634$	−27.5702	−1.09495
$635$	16.0725	0.637820
$636$	9.52234	0.377585
$637$	−6.80666	−0.269690
$638$	26.3542	1.04337
$639$	−50.6500	−2.00368
$640$	−50.4312	−1.99347
$641$	10.0977	0.398835	0.199417	−	0.979915i	$-0.436095\pi$
$641$	10.0977	0.398835	0.199417	+	0.979915i	$0.436095\pi$
$642$	39.5410	1.56056
$643$	−35.4818	−1.39926	−0.699632	−	0.714503i	$-0.746653\pi$
$643$	−35.4818	−1.39926	−0.699632	+	0.714503i	$0.746653\pi$
$644$	1.09677	0.0432187
$645$	−3.71608	−0.146320
$646$	9.45531	0.372014
$647$	−6.66219	−0.261918	−0.130959	−	0.991388i	$-0.541806\pi$
$647$	−6.66219	−0.261918	−0.130959	+	0.991388i	$0.541806\pi$
$648$	−1.18042	−0.0463711
$649$	−14.4893	−0.568755
$650$	−6.97317	−0.273510
$651$	−6.73395	−0.263924
$652$	−55.7988	−2.18525
$653$	−8.25836	−0.323175	−0.161587	−	0.986858i	$-0.551661\pi$
$653$	−8.25836	−0.323175	−0.161587	+	0.986858i	$0.551661\pi$
$654$	−27.2964	−1.06737
$655$	−40.2678	−1.57339
$656$	−35.7854	−1.39719
$657$	43.8597	1.71113
$658$	10.9755	0.427868
$659$	1.69876	0.0661742	0.0330871	−	0.999452i	$-0.489466\pi$
$659$	1.69876	0.0661742	0.0330871	+	0.999452i	$0.489466\pi$
$660$	78.6058	3.05972
$661$	−28.2481	−1.09872	−0.549362	−	0.835584i	$-0.685129\pi$
$661$	−28.2481	−1.09872	−0.549362	+	0.835584i	$0.685129\pi$
$662$	−38.0712	−1.47968
$663$	−19.2867	−0.749034
$664$	−39.0138	−1.51403
$665$	−0.682478	−0.0264654
$666$	−0.722491	−0.0279959
$667$	2.64759	0.102515
$668$	−72.5093	−2.80547
$669$	−64.2758	−2.48505
$670$	−6.63795	−0.256446
$671$	23.5192	0.907948
$672$	−1.87098	−0.0721745
$673$	38.8072	1.49591	0.747954	−	0.663751i	$-0.231036\pi$
$673$	38.8072	1.49591	0.747954	+	0.663751i	$0.231036\pi$
$674$	25.4086	0.978704
$675$	14.9043	0.573668
$676$	4.14734	0.159513
$677$	1.05550	0.0405663	0.0202831	−	0.999794i	$-0.493543\pi$
$677$	1.05550	0.0405663	0.0202831	+	0.999794i	$0.493543\pi$
$678$	97.5658	3.74699
$679$	−4.03451	−0.154830
$680$	−102.198	−3.91911
$681$	−17.4921	−0.670301
$682$	−32.6458	−1.25007
$683$	−1.13361	−0.0433765	−0.0216883	−	0.999765i	$-0.506904\pi$
$683$	−1.13361	−0.0433765	−0.0216883	+	0.999765i	$0.506904\pi$
$684$	11.2549	0.430341
$685$	−60.8971	−2.32676
$686$	15.0521	0.574692
$687$	−27.8877	−1.06398
$688$	2.32243	0.0885419
$689$	0.817556	0.0311464
$690$	11.7050	0.445603
$691$	11.6659	0.443790	0.221895	−	0.975071i	$-0.428776\pi$
$691$	11.6659	0.443790	0.221895	+	0.975071i	$0.428776\pi$
$692$	63.0652	2.39738
$693$	−5.18850	−0.197095
$694$	22.6266	0.858893
$695$	−3.36037	−0.127466
$696$	−65.8223	−2.49499
$697$	50.0958	1.89751
$698$	85.1077	3.22137
$699$	−55.7277	−2.10782
$700$	5.12887	0.193853
$701$	−11.0507	−0.417377	−0.208689	−	0.977982i	$-0.566920\pi$
$701$	−11.0507	−0.417377	−0.208689	+	0.977982i	$0.566920\pi$
$702$	−13.1392	−0.495908
$703$	0.0331113	0.00124882
$704$	14.6200	0.551012
$705$	79.0249	2.97625
$706$	−18.9831	−0.714437
$707$	−4.95871	−0.186491
$708$	69.8938	2.62677
$709$	−39.0311	−1.46584	−0.732922	−	0.680313i	$-0.761844\pi$
$709$	−39.0311	−1.46584	−0.732922	+	0.680313i	$0.761844\pi$
$710$	−71.8250	−2.69555
$711$	34.0318	1.27629
$712$	−26.2456	−0.983597
$713$	−3.27966	−0.122824
$714$	21.0265	0.786898
$715$	6.74883	0.252392
$716$	67.3382	2.51655
$717$	−31.9576	−1.19348
$718$	50.3766	1.88004
$719$	30.7955	1.14848	0.574239	−	0.818688i	$-0.305298\pi$
$719$	30.7955	1.14848	0.574239	+	0.818688i	$0.305298\pi$
$720$	−67.0106	−2.49734
$721$	0.439709	0.0163756
$722$	46.3437	1.72474
$723$	75.0161	2.78988
$724$	−45.2445	−1.68150
$725$	12.3811	0.459822
$726$	35.9989	1.33604
$727$	−9.39997	−0.348625	−0.174313	−	0.984690i	$-0.555770\pi$
$727$	−9.39997	−0.348625	−0.174313	+	0.984690i	$0.555770\pi$
$728$	−2.34105	−0.0867651
$729$	−43.5646	−1.61350
$730$	62.1959	2.30197
$731$	−3.25116	−0.120248
$732$	−113.452	−4.19332
$733$	45.5285	1.68164	0.840818	−	0.541318i	$-0.182075\pi$
$733$	45.5285	1.68164	0.840818	+	0.541318i	$0.182075\pi$
$734$	1.68250	0.0621022
$735$	53.4298	1.97079
$736$	−0.911228	−0.0335883
$737$	2.31276	0.0851916
$738$	88.3860	3.25353
$739$	53.4247	1.96526	0.982629	−	0.185580i	$-0.0594163\pi$
$739$	53.4247	1.96526	0.982629	+	0.185580i	$0.0594163\pi$
$740$	−0.691211	−0.0254094
$741$	1.55950	0.0572896
$742$	−0.891306	−0.0327209
$743$	35.9016	1.31710	0.658550	−	0.752537i	$-0.271170\pi$
$743$	35.9016	1.31710	0.658550	+	0.752537i	$0.271170\pi$
$744$	81.5362	2.98926
$745$	−6.90810	−0.253093
$746$	−86.9760	−3.18442
$747$	35.8108	1.31025
$748$	68.7713	2.51453
$749$	−2.49697	−0.0912374
$750$	−42.5744	−1.55460
$751$	−34.0959	−1.24418	−0.622088	−	0.782947i	$-0.713715\pi$
$751$	−34.0959	−1.24418	−0.622088	+	0.782947i	$0.713715\pi$
$752$	−49.3881	−1.80100
$753$	−17.4268	−0.635069
$754$	−10.9148	−0.397494
$755$	33.1360	1.20594
$756$	9.66409	0.351480
$757$	41.9465	1.52457	0.762285	−	0.647241i	$-0.224077\pi$
$757$	41.9465	1.52457	0.762285	+	0.647241i	$0.224077\pi$
$758$	−21.2971	−0.773546
$759$	−4.07821	−0.148030
$760$	8.26359	0.299752
$761$	−29.9169	−1.08449	−0.542244	−	0.840221i	$-0.682425\pi$
$761$	−29.9169	−1.08449	−0.542244	+	0.840221i	$0.682425\pi$
$762$	40.0396	1.45048
$763$	1.72374	0.0624035
$764$	−29.3836	−1.06306
$765$	93.8077	3.39162
$766$	−78.4330	−2.83390
$767$	6.00085	0.216678
$768$	−91.6240	−3.30620
$769$	−26.8605	−0.968615	−0.484307	−	0.874898i	$-0.660928\pi$
$769$	−26.8605	−0.968615	−0.484307	+	0.874898i	$0.660928\pi$
$770$	−7.35762	−0.265150
$771$	37.6078	1.35441
$772$	94.7256	3.40925
$773$	18.4397	0.663231	0.331616	−	0.943415i	$-0.392406\pi$
$773$	18.4397	0.663231	0.331616	+	0.943415i	$0.392406\pi$
$774$	−5.73615	−0.206182
$775$	−15.3368	−0.550915
$776$	48.8508	1.75364
$777$	0.0736322	0.00264154
$778$	−9.30294	−0.333527
$779$	−4.05068	−0.145131
$780$	−32.5552	−1.16566
$781$	25.0249	0.895462
$782$	10.2406	0.366203
$783$	23.3291	0.833713
$784$	−33.3919	−1.19257
$785$	30.0387	1.07213
$786$	−100.315	−3.57810
$787$	−21.8102	−0.777448	−0.388724	−	0.921354i	$-0.627084\pi$
$787$	−21.8102	−0.777448	−0.388724	+	0.921354i	$0.627084\pi$
$788$	−88.4630	−3.15136
$789$	56.0440	1.99522
$790$	48.2593	1.71699
$791$	−6.16117	−0.219066
$792$	62.8234	2.23233
$793$	−9.74064	−0.345900
$794$	−66.7765	−2.36981
$795$	−6.41752	−0.227606
$796$	−63.7806	−2.26064
$797$	−40.6396	−1.43953	−0.719763	−	0.694219i	$-0.755750\pi$
$797$	−40.6396	−1.43953	−0.719763	+	0.694219i	$0.755750\pi$
$798$	−1.70018	−0.0601856
$799$	69.1380	2.44593
$800$	−4.26122	−0.150657
$801$	24.0909	0.851210
$802$	−19.2099	−0.678325
$803$	−21.6700	−0.764717
$804$	−11.1563	−0.393454
$805$	−0.739160	−0.0260520
$806$	13.5205	0.476239
$807$	−74.3684	−2.61789
$808$	60.0411	2.11224
$809$	27.9843	0.983877	0.491938	−	0.870630i	$-0.336289\pi$
$809$	27.9843	0.983877	0.491938	+	0.870630i	$0.336289\pi$
$810$	1.53648	0.0539864
$811$	−39.4054	−1.38371	−0.691855	−	0.722037i	$-0.743206\pi$
$811$	−39.4054	−1.38371	−0.691855	+	0.722037i	$0.743206\pi$
$812$	8.02800	0.281728
$813$	−33.6691	−1.18083
$814$	0.356965	0.0125116
$815$	37.6052	1.31725
$816$	−94.6164	−3.31223
$817$	0.262884	0.00919715
$818$	−54.2718	−1.89757
$819$	2.14885	0.0750870
$820$	84.5595	2.95295
$821$	−45.3985	−1.58442	−0.792209	−	0.610250i	$-0.791069\pi$
$821$	−45.3985	−1.58442	−0.792209	+	0.610250i	$0.791069\pi$
$822$	−151.706	−5.29134
$823$	31.7519	1.10680	0.553401	−	0.832915i	$-0.313330\pi$
$823$	31.7519	1.10680	0.553401	+	0.832915i	$0.313330\pi$
$824$	−5.32409	−0.185474
$825$	−19.0712	−0.663972
$826$	−6.54217	−0.227631
$827$	−46.1585	−1.60509	−0.802545	−	0.596592i	$-0.796521\pi$
$827$	−46.1585	−1.60509	−0.802545	+	0.596592i	$0.796521\pi$
$828$	12.1896	0.423619
$829$	−43.8156	−1.52178	−0.760889	−	0.648883i	$-0.775237\pi$
$829$	−43.8156	−1.52178	−0.760889	+	0.648883i	$0.775237\pi$
$830$	50.7821	1.76267
$831$	87.1491	3.02317
$832$	−6.05498	−0.209919
$833$	46.7451	1.61962
$834$	−8.37129	−0.289874
$835$	48.8672	1.69112
$836$	−5.56076	−0.192323
$837$	−28.8985	−0.998877
$838$	47.5550	1.64276
$839$	6.70835	0.231598	0.115799	−	0.993273i	$-0.463057\pi$
$839$	6.70835	0.231598	0.115799	+	0.993273i	$0.463057\pi$
$840$	18.3764	0.634046
$841$	−9.62044	−0.331739
$842$	−55.9447	−1.92798
$843$	28.6704	0.987460
$844$	52.1662	1.79564
$845$	−2.79508	−0.0961536
$846$	121.983	4.19386
$847$	−2.27329	−0.0781112
$848$	4.01075	0.137730
$849$	71.7563	2.46267
$850$	47.8887	1.64257
$851$	0.0358613	0.00122931
$852$	−120.716	−4.13565
$853$	−9.21683	−0.315578	−0.157789	−	0.987473i	$-0.550437\pi$
$853$	−9.21683	−0.315578	−0.157789	+	0.987473i	$0.550437\pi$
$854$	10.6193	0.363386
$855$	−7.58516	−0.259407
$856$	30.2339	1.03337
$857$	−31.7301	−1.08388	−0.541940	−	0.840417i	$-0.682310\pi$
$857$	−31.7301	−1.08388	−0.541940	+	0.840417i	$0.682310\pi$
$858$	16.8126	0.573972
$859$	−21.5705	−0.735976	−0.367988	−	0.929831i	$-0.619953\pi$
$859$	−21.5705	−0.735976	−0.367988	+	0.929831i	$0.619953\pi$
$860$	−5.48781	−0.187133
$861$	−9.00781	−0.306985
$862$	−86.8301	−2.95744
$863$	−27.9728	−0.952205	−0.476103	−	0.879390i	$-0.657951\pi$
$863$	−27.9728	−0.952205	−0.476103	+	0.879390i	$0.657951\pi$
$864$	−8.02922	−0.273160
$865$	−42.5024	−1.44513
$866$	−75.6111	−2.56937
$867$	84.7103	2.87691
$868$	−9.94453	−0.337539
$869$	−16.8142	−0.570384
$870$	85.6772	2.90473
$871$	−0.957847	−0.0324554
$872$	−20.8714	−0.706794
$873$	−44.8402	−1.51761
$874$	−0.828042	−0.0280089
$875$	2.68853	0.0908889
$876$	104.532	3.53181
$877$	−26.5814	−0.897589	−0.448795	−	0.893635i	$-0.648147\pi$
$877$	−26.5814	−0.897589	−0.448795	+	0.893635i	$0.648147\pi$
$878$	80.8042	2.72701
$879$	37.9232	1.27912
$880$	33.1083	1.11608
$881$	−45.5085	−1.53322	−0.766610	−	0.642113i	$-0.778058\pi$
$881$	−45.5085	−1.53322	−0.766610	+	0.642113i	$0.778058\pi$
$882$	82.4744	2.77706
$883$	−49.1014	−1.65240	−0.826198	−	0.563380i	$-0.809501\pi$
$883$	−49.1014	−1.65240	−0.826198	+	0.563380i	$0.809501\pi$
$884$	−28.4822	−0.957958
$885$	−47.1045	−1.58340
$886$	−21.0412	−0.706893
$887$	19.5357	0.655944	0.327972	−	0.944688i	$-0.393635\pi$
$887$	19.5357	0.655944	0.327972	+	0.944688i	$0.393635\pi$
$888$	−0.891555	−0.0299186
$889$	−2.52846	−0.0848018
$890$	34.1625	1.14513
$891$	−0.535333	−0.0179343
$892$	−94.9209	−3.17819
$893$	−5.59041	−0.187076
$894$	−17.2093	−0.575566
$895$	−45.3822	−1.51696
$896$	7.93361	0.265043
$897$	1.68902	0.0563947
$898$	−87.5288	−2.92087
$899$	−24.0061	−0.800647
$900$	57.0031	1.90010
$901$	−5.61462	−0.187050
$902$	−43.6693	−1.45403
$903$	0.584596	0.0194541
$904$	74.6008	2.48119
$905$	30.4923	1.01360
$906$	82.5477	2.74246
$907$	11.6779	0.387759	0.193880	−	0.981025i	$-0.437893\pi$
$907$	11.6779	0.387759	0.193880	+	0.981025i	$0.437893\pi$
$908$	−25.8320	−0.857264
$909$	−55.1118	−1.82794
$910$	3.04721	0.101014
$911$	59.2423	1.96279	0.981393	−	0.192010i	$-0.0615007\pi$
$911$	59.2423	1.96279	0.981393	+	0.192010i	$0.0615007\pi$
$912$	7.65055	0.253335
$913$	−17.6932	−0.585561
$914$	−7.24953	−0.239793
$915$	76.4605	2.52771
$916$	−41.1839	−1.36076
$917$	6.33475	0.209192
$918$	90.2344	2.97818
$919$	19.7994	0.653123	0.326562	−	0.945176i	$-0.394110\pi$
$919$	19.7994	0.653123	0.326562	+	0.945176i	$0.394110\pi$
$920$	8.94991	0.295070
$921$	−9.48256	−0.312461
$922$	37.2732	1.22753
$923$	−10.3643	−0.341144
$924$	−12.3659	−0.406808
$925$	0.167700	0.00551395
$926$	28.0262	0.920997
$927$	4.88699	0.160510
$928$	−6.66991	−0.218950
$929$	26.1306	0.857317	0.428659	−	0.903467i	$-0.358986\pi$
$929$	26.1306	0.857317	0.428659	+	0.903467i	$0.358986\pi$
$930$	−106.131	−3.48017
$931$	−3.77975	−0.123876
$932$	−82.2973	−2.69574
$933$	−1.23414	−0.0404040
$934$	35.1675	1.15072
$935$	−46.3480	−1.51574
$936$	−26.0188	−0.850451
$937$	−15.8026	−0.516248	−0.258124	−	0.966112i	$-0.583104\pi$
$937$	−15.8026	−0.516248	−0.258124	+	0.966112i	$0.583104\pi$
$938$	1.04425	0.0340960
$939$	−6.57133	−0.214447
$940$	116.702	3.80640
$941$	−34.8582	−1.13634	−0.568172	−	0.822910i	$-0.692349\pi$
$941$	−34.8582	−1.13634	−0.568172	+	0.822910i	$0.692349\pi$
$942$	74.8318	2.43815
$943$	−4.38710	−0.142864
$944$	29.4388	0.958152
$945$	−6.51306	−0.211870
$946$	2.83409	0.0921442
$947$	3.00080	0.0975130	0.0487565	−	0.998811i	$-0.484474\pi$
$947$	3.00080	0.0975130	0.0487565	+	0.998811i	$0.484474\pi$
$948$	81.1089	2.63430
$949$	8.97479	0.291334
$950$	−3.87222	−0.125631
$951$	31.2285	1.01265
$952$	16.0773	0.521069
$953$	40.4963	1.31181	0.655903	−	0.754846i	$-0.272288\pi$
$953$	40.4963	1.31181	0.655903	+	0.754846i	$0.272288\pi$
$954$	−9.90611	−0.320722
$955$	19.8029	0.640807
$956$	−47.1943	−1.52637
$957$	−29.8512	−0.964953
$958$	−20.3873	−0.658684
$959$	9.58005	0.309356
$960$	47.5294	1.53401
$961$	−1.26294	−0.0407399
$962$	−0.147840	−0.00476654
$963$	−27.7517	−0.894288
$964$	110.782	3.56805
$965$	−63.8398	−2.05507
$966$	−1.84138	−0.0592455
$967$	−55.5867	−1.78755	−0.893775	−	0.448517i	$-0.851953\pi$
$967$	−55.5867	−1.78755	−0.893775	+	0.448517i	$0.851953\pi$
$968$	27.5255	0.884703
$969$	−10.7100	−0.344053
$970$	−63.5863	−2.04163
$971$	15.7663	0.505964	0.252982	−	0.967471i	$-0.418589\pi$
$971$	15.7663	0.505964	0.252982	+	0.967471i	$0.418589\pi$
$972$	−63.3528	−2.03204
$973$	0.528638	0.0169473
$974$	−77.7786	−2.49219
$975$	7.89846	0.252953
$976$	−47.7854	−1.52957
$977$	−48.1357	−1.54000	−0.769999	−	0.638045i	$-0.779743\pi$
$977$	−48.1357	−1.54000	−0.769999	+	0.638045i	$0.779743\pi$
$978$	93.6815	2.99560
$979$	−11.9027	−0.380413
$980$	78.9038	2.52049
$981$	19.1579	0.611664
$982$	−24.2659	−0.774355
$983$	11.1158	0.354540	0.177270	−	0.984162i	$-0.443273\pi$
$983$	11.1158	0.354540	0.177270	+	0.984162i	$0.443273\pi$
$984$	109.069	3.47698
$985$	59.6191	1.89962
$986$	74.9581	2.38715
$987$	−12.4318	−0.395710
$988$	2.30303	0.0732691
$989$	0.284718	0.00905349
$990$	−81.7738	−2.59894
$991$	39.6884	1.26074	0.630372	−	0.776293i	$-0.282903\pi$
$991$	39.6884	1.26074	0.630372	+	0.776293i	$0.282903\pi$
$992$	8.26222	0.262326
$993$	43.1230	1.36847
$994$	11.2992	0.358388
$995$	42.9846	1.36270
$996$	85.3490	2.70439
$997$	4.49786	0.142449	0.0712243	−	0.997460i	$-0.477309\pi$
$997$	4.49786	0.142449	0.0712243	+	0.997460i	$0.477309\pi$
$998$	73.1125	2.31434
$999$	0.315989	0.00999746

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1339.2.a.d.1.4	✓	19

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1339.2.a.d.1.4	✓	19	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:	\( N \)	\(=\)	\( 1339 = 13 \cdot 103 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1339.a (trivial)

\(f(q)\)	\(=\)	\(q-2.47938 q^{2} +2.80838 q^{3} +4.14734 q^{4} -2.79508 q^{5} -6.96305 q^{6} +0.439709 q^{7} -5.32409 q^{8} +4.88699 q^{9} +O(q^{10})\)	\(q-2.47938 q^{2} +2.80838 q^{3} +4.14734 q^{4} -2.79508 q^{5} -6.96305 q^{6} +0.439709 q^{7} -5.32409 q^{8} +4.88699 q^{9} +6.93007 q^{10} -2.41454 q^{11} +11.6473 q^{12} +1.00000 q^{13} -1.09021 q^{14} -7.84964 q^{15} +4.90578 q^{16} -6.86756 q^{17} -12.1167 q^{18} +0.555302 q^{19} -11.5922 q^{20} +1.23487 q^{21} +5.98657 q^{22} +0.601422 q^{23} -14.9521 q^{24} +2.81246 q^{25} -2.47938 q^{26} +5.29939 q^{27} +1.82362 q^{28} +4.40222 q^{29} +19.4623 q^{30} -5.45317 q^{31} -1.51512 q^{32} -6.78095 q^{33} +17.0273 q^{34} -1.22902 q^{35} +20.2680 q^{36} +0.0596275 q^{37} -1.37681 q^{38} +2.80838 q^{39} +14.8813 q^{40} -7.29455 q^{41} -3.06171 q^{42} +0.473407 q^{43} -10.0139 q^{44} -13.6595 q^{45} -1.49116 q^{46} -10.0673 q^{47} +13.7773 q^{48} -6.80666 q^{49} -6.97317 q^{50} -19.2867 q^{51} +4.14734 q^{52} +0.817556 q^{53} -13.1392 q^{54} +6.74883 q^{55} -2.34105 q^{56} +1.55950 q^{57} -10.9148 q^{58} +6.00085 q^{59} -32.5552 q^{60} -9.74064 q^{61} +13.5205 q^{62} +2.14885 q^{63} -6.05498 q^{64} -2.79508 q^{65} +16.8126 q^{66} -0.957847 q^{67} -28.4822 q^{68} +1.68902 q^{69} +3.04721 q^{70} -10.3643 q^{71} -26.0188 q^{72} +8.97479 q^{73} -0.147840 q^{74} +7.89846 q^{75} +2.30303 q^{76} -1.06170 q^{77} -6.96305 q^{78} +6.96375 q^{79} -13.7120 q^{80} +0.221712 q^{81} +18.0860 q^{82} +7.32778 q^{83} +5.12143 q^{84} +19.1954 q^{85} -1.17376 q^{86} +12.3631 q^{87} +12.8552 q^{88} +4.92960 q^{89} +33.8672 q^{90} +0.439709 q^{91} +2.49430 q^{92} -15.3146 q^{93} +24.9608 q^{94} -1.55211 q^{95} -4.25504 q^{96} -9.17542 q^{97} +16.8763 q^{98} -11.7998 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 19 q - 9 q^{2} - 2 q^{3} + 17 q^{4} - 18 q^{5} - 8 q^{6} - 8 q^{7} - 24 q^{8} + 7 q^{9}+O(q^{10}) \) 19 * q - 9 * q^2 - 2 * q^3 + 17 * q^4 - 18 * q^5 - 8 * q^6 - 8 * q^7 - 24 * q^8 + 7 * q^9	\( 19 q - 9 q^{2} - 2 q^{3} + 17 q^{4} - 18 q^{5} - 8 q^{6} - 8 q^{7} - 24 q^{8} + 7 q^{9} - q^{11} + 18 q^{12} + 19 q^{13} - 8 q^{14} - 11 q^{15} + 21 q^{16} - 16 q^{17} - 10 q^{19} - 20 q^{20} - 33 q^{21} + 2 q^{22} - 14 q^{23} - 9 q^{24} + 23 q^{25} - 9 q^{26} + q^{27} + 10 q^{28} - 22 q^{29} + 28 q^{30} - 3 q^{31} - 47 q^{32} - 25 q^{33} - 35 q^{34} - 3 q^{35} - 33 q^{36} - 19 q^{37} - 15 q^{38} - 2 q^{39} + 8 q^{40} - 52 q^{41} - 3 q^{42} - 2 q^{43} - 54 q^{44} - 40 q^{45} + 33 q^{46} - 24 q^{47} - 8 q^{48} + 7 q^{49} - 10 q^{50} - 7 q^{51} + 17 q^{52} - 11 q^{53} - 23 q^{54} - 29 q^{55} - 17 q^{56} - 34 q^{57} + 18 q^{58} - 52 q^{59} - 71 q^{60} - 25 q^{61} - 22 q^{62} - 19 q^{63} + 48 q^{64} - 18 q^{65} + 9 q^{66} - 2 q^{67} + 18 q^{68} - 26 q^{69} - 12 q^{70} - 44 q^{71} - 6 q^{72} - 39 q^{73} - 4 q^{74} + 17 q^{75} - 10 q^{76} - 18 q^{77} - 8 q^{78} + q^{79} - 9 q^{80} - 13 q^{81} + 47 q^{82} - 27 q^{83} - 24 q^{84} - 26 q^{85} - q^{86} + 31 q^{87} + 19 q^{88} - 86 q^{89} + 48 q^{90} - 8 q^{91} - 19 q^{92} + 32 q^{93} + 45 q^{94} + 17 q^{95} - 25 q^{96} - 20 q^{97} + 39 q^{98} + 50 q^{99}+O(q^{100}) \) 19 * q - 9 * q^2 - 2 * q^3 + 17 * q^4 - 18 * q^5 - 8 * q^6 - 8 * q^7 - 24 * q^8 + 7 * q^9 - q^11 + 18 * q^12 + 19 * q^13 - 8 * q^14 - 11 * q^15 + 21 * q^16 - 16 * q^17 - 10 * q^19 - 20 * q^20 - 33 * q^21 + 2 * q^22 - 14 * q^23 - 9 * q^24 + 23 * q^25 - 9 * q^26 + q^27 + 10 * q^28 - 22 * q^29 + 28 * q^30 - 3 * q^31 - 47 * q^32 - 25 * q^33 - 35 * q^34 - 3 * q^35 - 33 * q^36 - 19 * q^37 - 15 * q^38 - 2 * q^39 + 8 * q^40 - 52 * q^41 - 3 * q^42 - 2 * q^43 - 54 * q^44 - 40 * q^45 + 33 * q^46 - 24 * q^47 - 8 * q^48 + 7 * q^49 - 10 * q^50 - 7 * q^51 + 17 * q^52 - 11 * q^53 - 23 * q^54 - 29 * q^55 - 17 * q^56 - 34 * q^57 + 18 * q^58 - 52 * q^59 - 71 * q^60 - 25 * q^61 - 22 * q^62 - 19 * q^63 + 48 * q^64 - 18 * q^65 + 9 * q^66 - 2 * q^67 + 18 * q^68 - 26 * q^69 - 12 * q^70 - 44 * q^71 - 6 * q^72 - 39 * q^73 - 4 * q^74 + 17 * q^75 - 10 * q^76 - 18 * q^77 - 8 * q^78 + q^79 - 9 * q^80 - 13 * q^81 + 47 * q^82 - 27 * q^83 - 24 * q^84 - 26 * q^85 - q^86 + 31 * q^87 + 19 * q^88 - 86 * q^89 + 48 * q^90 - 8 * q^91 - 19 * q^92 + 32 * q^93 + 45 * q^94 + 17 * q^95 - 25 * q^96 - 20 * q^97 + 39 * q^98 + 50 * q^99

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