LMFDB - Embedded newform 1027.2.a.c.1.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1027,2,Mod(1,1027)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1027, 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("1027.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1027 = 13 \cdot 79 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1027.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:	$8.20063628759$
Analytic rank:	$1$
Dimension:	$18$
Coefficient field:	$\mathbb{Q}[x]/(x^{18} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{18} - 6 x^{17} - 8 x^{16} + 106 x^{15} - 57 x^{14} - 715 x^{13} + 859 x^{12} + 2323 x^{11} - 3741 x^{10} + \cdots + 8 $ x^18 - 6x^17 - 8x^16 + 106x^15 - 57x^14 - 715x^13 + 859x^12 + 2323x^11 - 3741x^10 - 3768x^9 + 7603x^8 + 2785x^7 - 7585x^6 - 510x^5 + 3292x^4 - 241x^3 - 361x^2 + 32*x + 8
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Fricke sign:	$+1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.3
Root			$2.48580$ of defining polynomial
Character	$\chi$	$=$	1027.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-2.48580 q^{2} +0.872511 q^{3} +4.17920 q^{4} +2.96068 q^{5} -2.16889 q^{6} -5.12543 q^{7} -5.41705 q^{8} -2.23872 q^{9} +O(q^{10})$	\(q-2.48580 q^{2} +0.872511 q^{3} +4.17920 q^{4} +2.96068 q^{5} -2.16889 q^{6} -5.12543 q^{7} -5.41705 q^{8} -2.23872 q^{9} -7.35964 q^{10} +4.83917 q^{11} +3.64640 q^{12} -1.00000 q^{13} +12.7408 q^{14} +2.58322 q^{15} +5.10731 q^{16} -0.0483041 q^{17} +5.56502 q^{18} -3.04392 q^{19} +12.3733 q^{20} -4.47200 q^{21} -12.0292 q^{22} -7.27758 q^{23} -4.72644 q^{24} +3.76560 q^{25} +2.48580 q^{26} -4.57085 q^{27} -21.4202 q^{28} -6.81940 q^{29} -6.42137 q^{30} +8.46470 q^{31} -1.86164 q^{32} +4.22223 q^{33} +0.120074 q^{34} -15.1747 q^{35} -9.35607 q^{36} -9.27086 q^{37} +7.56657 q^{38} -0.872511 q^{39} -16.0381 q^{40} -5.01806 q^{41} +11.1165 q^{42} -3.85055 q^{43} +20.2238 q^{44} -6.62813 q^{45} +18.0906 q^{46} +10.3741 q^{47} +4.45618 q^{48} +19.2701 q^{49} -9.36052 q^{50} -0.0421459 q^{51} -4.17920 q^{52} -8.82632 q^{53} +11.3622 q^{54} +14.3272 q^{55} +27.7647 q^{56} -2.65585 q^{57} +16.9517 q^{58} -9.35495 q^{59} +10.7958 q^{60} -1.16921 q^{61} -21.0416 q^{62} +11.4744 q^{63} -5.58696 q^{64} -2.96068 q^{65} -10.4956 q^{66} +5.47836 q^{67} -0.201872 q^{68} -6.34978 q^{69} +37.7214 q^{70} +2.75247 q^{71} +12.1273 q^{72} -2.32708 q^{73} +23.0455 q^{74} +3.28553 q^{75} -12.7211 q^{76} -24.8028 q^{77} +2.16889 q^{78} -1.00000 q^{79} +15.1211 q^{80} +2.72806 q^{81} +12.4739 q^{82} +2.97741 q^{83} -18.6894 q^{84} -0.143013 q^{85} +9.57168 q^{86} -5.95001 q^{87} -26.2140 q^{88} -5.07050 q^{89} +16.4762 q^{90} +5.12543 q^{91} -30.4145 q^{92} +7.38555 q^{93} -25.7879 q^{94} -9.01205 q^{95} -1.62430 q^{96} -0.707128 q^{97} -47.9015 q^{98} -10.8336 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 18 q - 6 q^{2} - 8 q^{3} + 16 q^{4} - 7 q^{5} + 2 q^{6} - 6 q^{7} - 18 q^{8} + 10 q^{9}+O(q^{10}) $ 18 * q - 6 * q^2 - 8 * q^3 + 16 * q^4 - 7 * q^5 + 2 * q^6 - 6 * q^7 - 18 * q^8 + 10 * q^9	\( 18 q - 6 q^{2} - 8 q^{3} + 16 q^{4} - 7 q^{5} + 2 q^{6} - 6 q^{7} - 18 q^{8} + 10 q^{9} - 8 q^{10} - 2 q^{11} - 25 q^{12} - 18 q^{13} - 16 q^{14} - 8 q^{15} + 20 q^{16} - 25 q^{17} - 15 q^{18} - 3 q^{19} - 5 q^{20} - 14 q^{21} - 14 q^{22} - 21 q^{23} + 18 q^{24} + 9 q^{25} + 6 q^{26} - 35 q^{27} - q^{28} - 50 q^{29} - 8 q^{30} + 19 q^{31} - 37 q^{32} - 4 q^{33} + 26 q^{34} - 26 q^{35} + 14 q^{36} - 40 q^{37} - 3 q^{38} + 8 q^{39} - 36 q^{40} - q^{41} + 49 q^{42} - 17 q^{43} + 11 q^{44} - 12 q^{45} + 4 q^{46} - 15 q^{47} - 59 q^{48} + 24 q^{49} - 34 q^{50} + 10 q^{51} - 16 q^{52} - 79 q^{53} + 58 q^{54} + 12 q^{55} - 37 q^{56} - 3 q^{57} - 14 q^{58} + 7 q^{59} + 30 q^{60} - 30 q^{61} - 52 q^{62} - 3 q^{63} + 38 q^{64} + 7 q^{65} - 56 q^{66} + 8 q^{67} - 21 q^{68} - 22 q^{69} + 39 q^{70} - 20 q^{71} - 46 q^{72} - 9 q^{73} - 4 q^{74} + 10 q^{75} - 46 q^{76} - 75 q^{77} - 2 q^{78} - 18 q^{79} + 36 q^{80} - 18 q^{81} - 16 q^{82} - 13 q^{83} - 61 q^{84} - 21 q^{85} + 19 q^{86} - 8 q^{87} - 10 q^{88} + 18 q^{89} + 58 q^{90} + 6 q^{91} - 76 q^{92} - 41 q^{93} + 58 q^{94} - 25 q^{95} + 96 q^{96} + 24 q^{97} - 35 q^{98} + 26 q^{99}+O(q^{100}) \) 18 * q - 6 * q^2 - 8 * q^3 + 16 * q^4 - 7 * q^5 + 2 * q^6 - 6 * q^7 - 18 * q^8 + 10 * q^9 - 8 * q^10 - 2 * q^11 - 25 * q^12 - 18 * q^13 - 16 * q^14 - 8 * q^15 + 20 * q^16 - 25 * q^17 - 15 * q^18 - 3 * q^19 - 5 * q^20 - 14 * q^21 - 14 * q^22 - 21 * q^23 + 18 * q^24 + 9 * q^25 + 6 * q^26 - 35 * q^27 - q^28 - 50 * q^29 - 8 * q^30 + 19 * q^31 - 37 * q^32 - 4 * q^33 + 26 * q^34 - 26 * q^35 + 14 * q^36 - 40 * q^37 - 3 * q^38 + 8 * q^39 - 36 * q^40 - q^41 + 49 * q^42 - 17 * q^43 + 11 * q^44 - 12 * q^45 + 4 * q^46 - 15 * q^47 - 59 * q^48 + 24 * q^49 - 34 * q^50 + 10 * q^51 - 16 * q^52 - 79 * q^53 + 58 * q^54 + 12 * q^55 - 37 * q^56 - 3 * q^57 - 14 * q^58 + 7 * q^59 + 30 * q^60 - 30 * q^61 - 52 * q^62 - 3 * q^63 + 38 * q^64 + 7 * q^65 - 56 * q^66 + 8 * q^67 - 21 * q^68 - 22 * q^69 + 39 * q^70 - 20 * q^71 - 46 * q^72 - 9 * q^73 - 4 * q^74 + 10 * q^75 - 46 * q^76 - 75 * q^77 - 2 * q^78 - 18 * q^79 + 36 * q^80 - 18 * q^81 - 16 * q^82 - 13 * q^83 - 61 * q^84 - 21 * q^85 + 19 * q^86 - 8 * q^87 - 10 * q^88 + 18 * q^89 + 58 * q^90 + 6 * q^91 - 76 * q^92 - 41 * q^93 + 58 * q^94 - 25 * q^95 + 96 * q^96 + 24 * q^97 - 35 * q^98 + 26 * 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 $

$2$	−2.48580	−1.75773	−0.878863	−	0.477075i	$-0.841697\pi$
$2$	−2.48580	−1.75773	−0.878863	+	0.477075i	$0.841697\pi$
$3$	0.872511	0.503745	0.251872	−	0.967760i	$-0.418954\pi$
$3$	0.872511	0.503745	0.251872	+	0.967760i	$0.418954\pi$
$4$	4.17920	2.08960
$5$	2.96068	1.32405	0.662027	−	0.749480i	$-0.269696\pi$
$5$	2.96068	1.32405	0.662027	+	0.749480i	$0.269696\pi$
$6$	−2.16889	−0.885445
$7$	−5.12543	−1.93723	−0.968616	−	0.248562i	$-0.920042\pi$
$7$	−5.12543	−1.93723	−0.968616	+	0.248562i	$0.920042\pi$
$8$	−5.41705	−1.91522
$9$	−2.23872	−0.746241
$10$	−7.35964	−2.32732
$11$	4.83917	1.45906	0.729532	−	0.683947i	$-0.239738\pi$
$11$	4.83917	1.45906	0.729532	+	0.683947i	$0.239738\pi$
$12$	3.64640	1.05262
$13$	−1.00000	−0.277350
$13$	−1.00000	−0.277350
$14$	12.7408	3.40512
$15$	2.58322	0.666985
$16$	5.10731	1.27683
$17$	−0.0483041	−0.0117155	−0.00585773	−	0.999983i	$-0.501865\pi$
$17$	−0.0483041	−0.0117155	−0.00585773	+	0.999983i	$0.501865\pi$
$18$	5.56502	1.31169
$19$	−3.04392	−0.698323	−0.349161	−	0.937063i	$-0.613533\pi$
$19$	−3.04392	−0.698323	−0.349161	+	0.937063i	$0.613533\pi$
$20$	12.3733	2.76674
$21$	−4.47200	−0.975870
$22$	−12.0292	−2.56463
$23$	−7.27758	−1.51748	−0.758741	−	0.651393i	$-0.774185\pi$
$23$	−7.27758	−1.51748	−0.758741	+	0.651393i	$0.774185\pi$
$24$	−4.72644	−0.964781
$25$	3.76560	0.753119
$26$	2.48580	0.487505
$27$	−4.57085	−0.879660
$28$	−21.4202	−4.04804
$29$	−6.81940	−1.26633	−0.633165	−	0.774016i	$-0.718245\pi$
$29$	−6.81940	−1.26633	−0.633165	+	0.774016i	$0.718245\pi$
$30$	−6.42137	−1.17238
$31$	8.46470	1.52031	0.760153	−	0.649744i	$-0.225124\pi$
$31$	8.46470	1.52031	0.760153	+	0.649744i	$0.225124\pi$
$32$	−1.86164	−0.329094
$33$	4.22223	0.734996
$34$	0.120074	0.0205926
$35$	−15.1747	−2.56500
$36$	−9.35607	−1.55935
$37$	−9.27086	−1.52412	−0.762060	−	0.647506i	$-0.775812\pi$
$37$	−9.27086	−1.52412	−0.762060	+	0.647506i	$0.775812\pi$
$38$	7.56657	1.22746
$39$	−0.872511	−0.139714
$40$	−16.0381	−2.53585
$41$	−5.01806	−0.783689	−0.391844	−	0.920031i	$-0.628163\pi$
$41$	−5.01806	−0.783689	−0.391844	+	0.920031i	$0.628163\pi$
$42$	11.1165	1.71531
$43$	−3.85055	−0.587203	−0.293601	−	0.955928i	$-0.594854\pi$
$43$	−3.85055	−0.587203	−0.293601	+	0.955928i	$0.594854\pi$
$44$	20.2238	3.04886
$45$	−6.62813	−0.988064
$46$	18.0906	2.66732
$47$	10.3741	1.51322	0.756609	−	0.653867i	$-0.226855\pi$
$47$	10.3741	1.51322	0.756609	+	0.653867i	$0.226855\pi$
$48$	4.45618	0.643195
$49$	19.2701	2.75287
$50$	−9.36052	−1.32378
$51$	−0.0421459	−0.00590160
$52$	−4.17920	−0.579551
$53$	−8.82632	−1.21239	−0.606194	−	0.795317i	$-0.707305\pi$
$53$	−8.82632	−1.21239	−0.606194	+	0.795317i	$0.707305\pi$
$54$	11.3622	1.54620
$55$	14.3272	1.93188
$56$	27.7647	3.71022
$57$	−2.65585	−0.351776
$58$	16.9517	2.22586
$59$	−9.35495	−1.21791	−0.608955	−	0.793205i	$-0.708411\pi$
$59$	−9.35495	−1.21791	−0.608955	+	0.793205i	$0.708411\pi$
$60$	10.7958	1.39373
$61$	−1.16921	−0.149702	−0.0748509	−	0.997195i	$-0.523848\pi$
$61$	−1.16921	−0.149702	−0.0748509	+	0.997195i	$0.523848\pi$
$62$	−21.0416	−2.67228
$63$	11.4744	1.44564
$64$	−5.58696	−0.698369
$65$	−2.96068	−0.367227
$66$	−10.4956	−1.29192
$67$	5.47836	0.669288	0.334644	−	0.942345i	$-0.391384\pi$
$67$	5.47836	0.669288	0.334644	+	0.942345i	$0.391384\pi$
$68$	−0.201872	−0.0244806
$69$	−6.34978	−0.764423
$70$	37.7214	4.50857
$71$	2.75247	0.326658	0.163329	−	0.986572i	$-0.447777\pi$
$71$	2.75247	0.326658	0.163329	+	0.986572i	$0.447777\pi$
$72$	12.1273	1.42921
$73$	−2.32708	−0.272364	−0.136182	−	0.990684i	$-0.543483\pi$
$73$	−2.32708	−0.272364	−0.136182	+	0.990684i	$0.543483\pi$
$74$	23.0455	2.67899
$75$	3.28553	0.379380
$76$	−12.7211	−1.45921
$77$	−24.8028	−2.82655
$78$	2.16889	0.245578
$79$	−1.00000	−0.112509
$79$	−1.00000	−0.112509
$80$	15.1211	1.69059
$81$	2.72806	0.303117
$82$	12.4739	1.37751
$83$	2.97741	0.326813	0.163407	−	0.986559i	$-0.447752\pi$
$83$	2.97741	0.326813	0.163407	+	0.986559i	$0.447752\pi$
$84$	−18.6894	−2.03918
$85$	−0.143013	−0.0155119
$86$	9.57168	1.03214
$87$	−5.95001	−0.637908
$88$	−26.2140	−2.79442
$89$	−5.07050	−0.537472	−0.268736	−	0.963214i	$-0.586606\pi$
$89$	−5.07050	−0.537472	−0.268736	+	0.963214i	$0.586606\pi$
$90$	16.4762	1.73675
$91$	5.12543	0.537291
$92$	−30.4145	−3.17093
$93$	7.38555	0.765846
$94$	−25.7879	−2.65982
$95$	−9.01205	−0.924617
$96$	−1.62430	−0.165780
$97$	−0.707128	−0.0717980	−0.0358990	−	0.999355i	$-0.511429\pi$
$97$	−0.707128	−0.0717980	−0.0358990	+	0.999355i	$0.511429\pi$
$98$	−47.9015	−4.83879
$99$	−10.8336	−1.08881
$100$	15.7372	1.57372
$101$	0.387756	0.0385832	0.0192916	−	0.999814i	$-0.493859\pi$
$101$	0.387756	0.0385832	0.0192916	+	0.999814i	$0.493859\pi$
$102$	0.104766	0.0103734
$103$	−6.48519	−0.639005	−0.319503	−	0.947585i	$-0.603516\pi$
$103$	−6.48519	−0.639005	−0.319503	+	0.947585i	$0.603516\pi$
$104$	5.41705	0.531186
$105$	−13.2401	−1.29211
$106$	21.9405	2.13105
$107$	−6.77766	−0.655221	−0.327610	−	0.944813i	$-0.606243\pi$
$107$	−6.77766	−0.655221	−0.327610	+	0.944813i	$0.606243\pi$
$108$	−19.1025	−1.83814
$109$	0.141581	0.0135610	0.00678050	−	0.999977i	$-0.497842\pi$
$109$	0.141581	0.0135610	0.00678050	+	0.999977i	$0.497842\pi$
$110$	−35.6146	−3.39571
$111$	−8.08893	−0.767768
$112$	−26.1772	−2.47351
$113$	−10.0963	−0.949783	−0.474892	−	0.880044i	$-0.657513\pi$
$113$	−10.0963	−0.949783	−0.474892	+	0.880044i	$0.657513\pi$
$114$	6.60192	0.618326
$115$	−21.5466	−2.00923
$116$	−28.4996	−2.64612
$117$	2.23872	0.206970
$118$	23.2545	2.14075
$119$	0.247579	0.0226956
$120$	−13.9935	−1.27742
$121$	12.4175	1.12887
$122$	2.90642	0.263135
$123$	−4.37831	−0.394779
$124$	35.3757	3.17683
$125$	−3.65467	−0.326883
$126$	−28.5231	−2.54104
$127$	6.62269	0.587669	0.293834	−	0.955856i	$-0.405069\pi$
$127$	6.62269	0.587669	0.293834	+	0.955856i	$0.405069\pi$
$128$	17.6113	1.55664
$129$	−3.35965	−0.295800
$130$	7.35964	0.645484
$131$	0.653783	0.0571213	0.0285606	−	0.999592i	$-0.490908\pi$
$131$	0.653783	0.0571213	0.0285606	+	0.999592i	$0.490908\pi$
$132$	17.6455	1.53585
$133$	15.6014	1.35281
$134$	−13.6181	−1.17642
$135$	−13.5328	−1.16472
$136$	0.261666	0.0224377
$137$	12.8766	1.10012	0.550059	−	0.835126i	$-0.314605\pi$
$137$	12.8766	1.10012	0.550059	+	0.835126i	$0.314605\pi$
$138$	15.7843	1.34365
$139$	−9.62501	−0.816383	−0.408191	−	0.912896i	$-0.633840\pi$
$139$	−9.62501	−0.816383	−0.408191	+	0.912896i	$0.633840\pi$
$140$	−63.4183	−5.35982
$141$	9.05152	0.762276
$142$	−6.84210	−0.574176
$143$	−4.83917	−0.404672
$144$	−11.4339	−0.952821
$145$	−20.1900	−1.67669
$146$	5.78465	0.478741
$147$	16.8134	1.38674
$148$	−38.7448	−3.18480
$149$	−14.8832	−1.21928	−0.609639	−	0.792679i	$-0.708685\pi$
$149$	−14.8832	−1.21928	−0.609639	+	0.792679i	$0.708685\pi$
$150$	−8.16716	−0.666846
$151$	2.70104	0.219807	0.109904	−	0.993942i	$-0.464946\pi$
$151$	2.70104	0.219807	0.109904	+	0.993942i	$0.464946\pi$
$152$	16.4891	1.33744
$153$	0.108140	0.00874256
$154$	61.6549	4.96829
$155$	25.0612	2.01297
$156$	−3.64640	−0.291946
$157$	−1.29990	−0.103743	−0.0518716	−	0.998654i	$-0.516519\pi$
$157$	−1.29990	−0.103743	−0.0518716	+	0.998654i	$0.516519\pi$
$158$	2.48580	0.197760
$159$	−7.70107	−0.610734
$160$	−5.51171	−0.435739
$161$	37.3008	2.93971
$162$	−6.78140	−0.532797
$163$	9.49337	0.743578	0.371789	−	0.928317i	$-0.378745\pi$
$163$	9.49337	0.743578	0.371789	+	0.928317i	$0.378745\pi$
$164$	−20.9715	−1.63760
$165$	12.5006	0.973174
$166$	−7.40124	−0.574448
$167$	−3.25219	−0.251662	−0.125831	−	0.992052i	$-0.540160\pi$
$167$	−3.25219	−0.251662	−0.125831	+	0.992052i	$0.540160\pi$
$168$	24.2251	1.86900
$169$	1.00000	0.0769231
$170$	0.355501	0.0272657
$171$	6.81449	0.521117
$172$	−16.0922	−1.22702
$173$	−21.0995	−1.60417	−0.802083	−	0.597213i	$-0.796275\pi$
$173$	−21.0995	−1.60417	−0.802083	+	0.597213i	$0.796275\pi$
$174$	14.7905	1.12127
$175$	−19.3003	−1.45897
$176$	24.7151	1.86297
$177$	−8.16230	−0.613516
$178$	12.6042	0.944728
$179$	21.0428	1.57281	0.786406	−	0.617709i	$-0.211939\pi$
$179$	21.0428	1.57281	0.786406	+	0.617709i	$0.211939\pi$
$180$	−27.7003	−2.06466
$181$	−22.8214	−1.69630	−0.848152	−	0.529752i	$-0.822285\pi$
$181$	−22.8214	−1.69630	−0.848152	+	0.529752i	$0.822285\pi$
$182$	−12.7408	−0.944411
$183$	−1.02015	−0.0754115
$184$	39.4231	2.90631
$185$	−27.4480	−2.01802
$186$	−18.3590	−1.34615
$187$	−0.233752	−0.0170936
$188$	43.3554	3.16202
$189$	23.4276	1.70411
$190$	22.4022	1.62522
$191$	4.78616	0.346314	0.173157	−	0.984894i	$-0.444603\pi$
$191$	4.78616	0.346314	0.173157	+	0.984894i	$0.444603\pi$
$192$	−4.87468	−0.351800
$193$	17.3496	1.24885	0.624426	−	0.781084i	$-0.285333\pi$
$193$	17.3496	1.24885	0.624426	+	0.781084i	$0.285333\pi$
$194$	1.75778	0.126201
$195$	−2.58322	−0.184988
$196$	80.5335	5.75239
$197$	−26.8921	−1.91598	−0.957991	−	0.286798i	$-0.907409\pi$
$197$	−26.8921	−1.91598	−0.957991	+	0.286798i	$0.907409\pi$
$198$	26.9301	1.91384
$199$	18.6582	1.32265	0.661324	−	0.750101i	$-0.269995\pi$
$199$	18.6582	1.32265	0.661324	+	0.750101i	$0.269995\pi$
$200$	−20.3984	−1.44239
$201$	4.77993	0.337150
$202$	−0.963885	−0.0678187
$203$	34.9524	2.45318
$204$	−0.176136	−0.0123320
$205$	−14.8568	−1.03765
$206$	16.1209	1.12320
$207$	16.2925	1.13241
$208$	−5.10731	−0.354128
$209$	−14.7300	−1.01890
$210$	32.9123	2.27117
$211$	−9.81830	−0.675920	−0.337960	−	0.941160i	$-0.609737\pi$
$211$	−9.81830	−0.675920	−0.337960	+	0.941160i	$0.609737\pi$
$212$	−36.8870	−2.53341
$213$	2.40156	0.164552
$214$	16.8479	1.15170
$215$	−11.4002	−0.777488
$216$	24.7605	1.68474
$217$	−43.3853	−2.94518
$218$	−0.351942	−0.0238365
$219$	−2.03040	−0.137202
$220$	59.8762	4.03686
$221$	0.0483041	0.00324929
$222$	20.1075	1.34952
$223$	−4.98773	−0.334003	−0.167002	−	0.985957i	$-0.553408\pi$
$223$	−4.98773	−0.334003	−0.167002	+	0.985957i	$0.553408\pi$
$224$	9.54171	0.637532
$225$	−8.43013	−0.562009
$226$	25.0975	1.66946
$227$	−25.9016	−1.71915	−0.859574	−	0.511012i	$-0.829271\pi$
$227$	−25.9016	−1.71915	−0.859574	+	0.511012i	$0.829271\pi$
$228$	−11.0993	−0.735072
$229$	−12.0720	−0.797738	−0.398869	−	0.917008i	$-0.630597\pi$
$229$	−12.0720	−0.797738	−0.398869	+	0.917008i	$0.630597\pi$
$230$	53.5604	3.53167
$231$	−21.6408	−1.42386
$232$	36.9411	2.42530
$233$	−9.11049	−0.596848	−0.298424	−	0.954433i	$-0.596461\pi$
$233$	−9.11049	−0.596848	−0.298424	+	0.954433i	$0.596461\pi$
$234$	−5.56502	−0.363797
$235$	30.7143	2.00358
$236$	−39.0962	−2.54495
$237$	−0.872511	−0.0566757
$238$	−0.615433	−0.0398926
$239$	−17.1316	−1.10815	−0.554077	−	0.832466i	$-0.686929\pi$
$239$	−17.1316	−1.10815	−0.554077	+	0.832466i	$0.686929\pi$
$240$	13.1933	0.851625
$241$	−2.57086	−0.165603	−0.0828017	−	0.996566i	$-0.526387\pi$
$241$	−2.57086	−0.165603	−0.0828017	+	0.996566i	$0.526387\pi$
$242$	−30.8675	−1.98424
$243$	16.0928	1.03235
$244$	−4.88635	−0.312817
$245$	57.0524	3.64495
$246$	10.8836	0.693913
$247$	3.04392	0.193680
$248$	−45.8537	−2.91172
$249$	2.59782	0.164630
$250$	9.08477	0.574571
$251$	−3.38329	−0.213551	−0.106776	−	0.994283i	$-0.534053\pi$
$251$	−3.38329	−0.213551	−0.106776	+	0.994283i	$0.534053\pi$
$252$	47.9539	3.02081
$253$	−35.2174	−2.21410
$254$	−16.4627	−1.03296
$255$	−0.124780	−0.00781404
$256$	−32.6043	−2.03777
$257$	1.90503	0.118832	0.0594162	−	0.998233i	$-0.481076\pi$
$257$	1.90503	0.118832	0.0594162	+	0.998233i	$0.481076\pi$
$258$	8.35140	0.519936
$259$	47.5172	2.95257
$260$	−12.3733	−0.767356
$261$	15.2668	0.944988
$262$	−1.62517	−0.100404
$263$	16.8638	1.03987	0.519933	−	0.854207i	$-0.325957\pi$
$263$	16.8638	1.03987	0.519933	+	0.854207i	$0.325957\pi$
$264$	−22.8720	−1.40768
$265$	−26.1319	−1.60527
$266$	−38.7820	−2.37787
$267$	−4.42407	−0.270749
$268$	22.8951	1.39854
$269$	15.6548	0.954492	0.477246	−	0.878770i	$-0.341635\pi$
$269$	15.6548	0.954492	0.477246	+	0.878770i	$0.341635\pi$
$270$	33.6398	2.04725
$271$	−3.15889	−0.191889	−0.0959445	−	0.995387i	$-0.530587\pi$
$271$	−3.15889	−0.191889	−0.0959445	+	0.995387i	$0.530587\pi$
$272$	−0.246704	−0.0149586
$273$	4.47200	0.270658
$274$	−32.0085	−1.93371
$275$	18.2224	1.09885
$276$	−26.5370	−1.59734
$277$	13.1516	0.790200	0.395100	−	0.918638i	$-0.370710\pi$
$277$	13.1516	0.790200	0.395100	+	0.918638i	$0.370710\pi$
$278$	23.9258	1.43498
$279$	−18.9501	−1.13451
$280$	82.2024	4.91253
$281$	20.3760	1.21553	0.607766	−	0.794116i	$-0.292066\pi$
$281$	20.3760	1.21553	0.607766	+	0.794116i	$0.292066\pi$
$282$	−22.5003	−1.33987
$283$	16.2101	0.963589	0.481795	−	0.876284i	$-0.339985\pi$
$283$	16.2101	0.963589	0.481795	+	0.876284i	$0.339985\pi$
$284$	11.5031	0.682585
$285$	−7.86312	−0.465771
$286$	12.0292	0.711302
$287$	25.7197	1.51819
$288$	4.16769	0.245584
$289$	−16.9977	−0.999863
$290$	50.1884	2.94716
$291$	−0.616977	−0.0361679
$292$	−9.72533	−0.569132
$293$	28.2075	1.64790	0.823949	−	0.566665i	$-0.191766\pi$
$293$	28.2075	1.64790	0.823949	+	0.566665i	$0.191766\pi$
$294$	−41.7946	−2.43751
$295$	−27.6970	−1.61258
$296$	50.2207	2.91902
$297$	−22.1191	−1.28348
$298$	36.9966	2.14316
$299$	7.27758	0.420874
$300$	13.7309	0.792752
$301$	19.7357	1.13755
$302$	−6.71423	−0.386361
$303$	0.338322	0.0194361
$304$	−15.5462	−0.891637
$305$	−3.46164	−0.198213
$306$	−0.268813	−0.0153670
$307$	9.46558	0.540229	0.270115	−	0.962828i	$-0.412938\pi$
$307$	9.46558	0.540229	0.270115	+	0.962828i	$0.412938\pi$
$308$	−103.656	−5.90635
$309$	−5.65841	−0.321896
$310$	−62.2972	−3.53824
$311$	15.3356	0.869602	0.434801	−	0.900527i	$-0.356819\pi$
$311$	15.3356	0.869602	0.434801	+	0.900527i	$0.356819\pi$
$312$	4.72644	0.267582
$313$	7.62818	0.431170	0.215585	−	0.976485i	$-0.430834\pi$
$313$	7.62818	0.431170	0.215585	+	0.976485i	$0.430834\pi$
$314$	3.23129	0.182352
$315$	33.9721	1.91411
$316$	−4.17920	−0.235098
$317$	−16.5286	−0.928340	−0.464170	−	0.885746i	$-0.653647\pi$
$317$	−16.5286	−0.928340	−0.464170	+	0.885746i	$0.653647\pi$
$318$	19.1433	1.07350
$319$	−33.0002	−1.84766
$320$	−16.5412	−0.924679
$321$	−5.91358	−0.330064
$322$	−92.7223	−5.16721
$323$	0.147034	0.00818117
$324$	11.4011	0.633394
$325$	−3.76560	−0.208878
$326$	−23.5986	−1.30701
$327$	0.123531	0.00683128
$328$	27.1831	1.50093
$329$	−53.1718	−2.93145
$330$	−31.0741	−1.71057
$331$	23.9278	1.31519	0.657595	−	0.753372i	$-0.271574\pi$
$331$	23.9278	1.31519	0.657595	+	0.753372i	$0.271574\pi$
$332$	12.4432	0.682909
$333$	20.7549	1.13736
$334$	8.08429	0.442353
$335$	16.2196	0.886173
$336$	−22.8399	−1.24602
$337$	25.0357	1.36378	0.681890	−	0.731455i	$-0.261158\pi$
$337$	25.0357	1.36378	0.681890	+	0.731455i	$0.261158\pi$
$338$	−2.48580	−0.135210
$339$	−8.80917	−0.478448
$340$	−0.597679	−0.0324137
$341$	40.9621	2.21822
$342$	−16.9395	−0.915981
$343$	−62.8895	−3.39571
$344$	20.8586	1.12462
$345$	−18.7996	−1.01214
$346$	52.4491	2.81968
$347$	−22.6926	−1.21820	−0.609100	−	0.793093i	$-0.708469\pi$
$347$	−22.6926	−1.21820	−0.609100	+	0.793093i	$0.708469\pi$
$348$	−24.8663	−1.33297
$349$	11.3847	0.609407	0.304703	−	0.952447i	$-0.401443\pi$
$349$	11.3847	0.609407	0.304703	+	0.952447i	$0.401443\pi$
$350$	47.9767	2.56446
$351$	4.57085	0.243974
$352$	−9.00878	−0.480170
$353$	32.2640	1.71724	0.858621	−	0.512611i	$-0.171322\pi$
$353$	32.2640	1.71724	0.858621	+	0.512611i	$0.171322\pi$
$354$	20.2898	1.07839
$355$	8.14918	0.432513
$356$	−21.1906	−1.12310
$357$	0.216016	0.0114328
$358$	−52.3082	−2.76457
$359$	18.4641	0.974495	0.487248	−	0.873264i	$-0.338001\pi$
$359$	18.4641	0.974495	0.487248	+	0.873264i	$0.338001\pi$
$360$	35.9049	1.89236
$361$	−9.73456	−0.512345
$362$	56.7295	2.98164
$363$	10.8345	0.568661
$364$	21.4202	1.12272
$365$	−6.88972	−0.360625
$366$	2.53588	0.132553
$367$	−8.33572	−0.435121	−0.217560	−	0.976047i	$-0.569810\pi$
$367$	−8.33572	−0.435121	−0.217560	+	0.976047i	$0.569810\pi$
$368$	−37.1689	−1.93756
$369$	11.2340	0.584821
$370$	68.2303	3.54712
$371$	45.2387	2.34868
$372$	30.8657	1.60031
$373$	24.4684	1.26693	0.633463	−	0.773773i	$-0.281633\pi$
$373$	24.4684	1.26693	0.633463	+	0.773773i	$0.281633\pi$
$374$	0.581060	0.0300459
$375$	−3.18874	−0.164666
$376$	−56.1971	−2.89814
$377$	6.81940	0.351217
$378$	−58.2362	−2.99535
$379$	25.5781	1.31386	0.656929	−	0.753953i	$-0.271855\pi$
$379$	25.5781	1.31386	0.656929	+	0.753953i	$0.271855\pi$
$380$	−37.6632	−1.93208
$381$	5.77838	0.296035
$382$	−11.8974	−0.608726
$383$	8.58389	0.438616	0.219308	−	0.975656i	$-0.429620\pi$
$383$	8.58389	0.438616	0.219308	+	0.975656i	$0.429620\pi$
$384$	15.3661	0.784147
$385$	−73.4331	−3.74250
$386$	−43.1276	−2.19514
$387$	8.62031	0.438195
$388$	−2.95523	−0.150029
$389$	−36.9016	−1.87098	−0.935492	−	0.353349i	$-0.885043\pi$
$389$	−36.9016	−1.87098	−0.935492	+	0.353349i	$0.885043\pi$
$390$	6.42137	0.325159
$391$	0.351537	0.0177780
$392$	−104.387	−5.27234
$393$	0.570433	0.0287745
$394$	66.8484	3.36777
$395$	−2.96068	−0.148968
$396$	−45.2756	−2.27518
$397$	−24.5765	−1.23346	−0.616730	−	0.787175i	$-0.711543\pi$
$397$	−24.5765	−1.23346	−0.616730	+	0.787175i	$0.711543\pi$
$398$	−46.3806	−2.32485
$399$	13.6124	0.681472
$400$	19.2321	0.961603
$401$	27.0713	1.35187	0.675937	−	0.736960i	$-0.263739\pi$
$401$	27.0713	1.35187	0.675937	+	0.736960i	$0.263739\pi$
$402$	−11.8819	−0.592618
$403$	−8.46470	−0.421657
$404$	1.62051	0.0806235
$405$	8.07688	0.401344
$406$	−86.8846	−4.31201
$407$	−44.8633	−2.22379
$408$	0.228306	0.0113029
$409$	−12.5787	−0.621979	−0.310990	−	0.950413i	$-0.600660\pi$
$409$	−12.5787	−0.621979	−0.310990	+	0.950413i	$0.600660\pi$
$410$	36.9311	1.82390
$411$	11.2349	0.554179
$412$	−27.1029	−1.33527
$413$	47.9482	2.35938
$414$	−40.4999	−1.99046
$415$	8.81514	0.432718
$416$	1.86164	0.0912743
$417$	−8.39793	−0.411248
$418$	36.6159	1.79094
$419$	−24.4250	−1.19324	−0.596620	−	0.802524i	$-0.703490\pi$
$419$	−24.4250	−1.19324	−0.596620	+	0.802524i	$0.703490\pi$
$420$	−55.3332	−2.69998
$421$	14.2818	0.696051	0.348026	−	0.937485i	$-0.386852\pi$
$421$	14.2818	0.696051	0.348026	+	0.937485i	$0.386852\pi$
$422$	24.4063	1.18808
$423$	−23.2247	−1.12923
$424$	47.8126	2.32199
$425$	−0.181894	−0.00882314
$426$	−5.96981	−0.289238
$427$	5.99270	0.290007
$428$	−28.3252	−1.36915
$429$	−4.22223	−0.203851
$430$	28.3386	1.36661
$431$	9.33184	0.449499	0.224750	−	0.974417i	$-0.427844\pi$
$431$	9.33184	0.449499	0.224750	+	0.974417i	$0.427844\pi$
$432$	−23.3447	−1.12317
$433$	31.6434	1.52069	0.760343	−	0.649521i	$-0.225031\pi$
$433$	31.6434	1.52069	0.760343	+	0.649521i	$0.225031\pi$
$434$	107.847	5.17683
$435$	−17.6160	−0.844624
$436$	0.591695	0.0283370
$437$	22.1524	1.05969
$438$	5.04718	0.241163
$439$	−14.3352	−0.684180	−0.342090	−	0.939667i	$-0.611135\pi$
$439$	−14.3352	−0.684180	−0.342090	+	0.939667i	$0.611135\pi$
$440$	−77.6112	−3.69997
$441$	−43.1404	−2.05430
$442$	−0.120074	−0.00571135
$443$	−9.07177	−0.431013	−0.215506	−	0.976502i	$-0.569140\pi$
$443$	−9.07177	−0.431013	−0.215506	+	0.976502i	$0.569140\pi$
$444$	−33.8053	−1.60433
$445$	−15.0121	−0.711642
$446$	12.3985	0.587086
$447$	−12.9857	−0.614205
$448$	28.6356	1.35290
$449$	−4.49117	−0.211951	−0.105976	−	0.994369i	$-0.533797\pi$
$449$	−4.49117	−0.211951	−0.105976	+	0.994369i	$0.533797\pi$
$450$	20.9556	0.987857
$451$	−24.2832	−1.14345
$452$	−42.1946	−1.98467
$453$	2.35668	0.110727
$454$	64.3861	3.02179
$455$	15.1747	0.711403
$456$	14.3869	0.673728
$457$	−13.1440	−0.614852	−0.307426	−	0.951572i	$-0.599468\pi$
$457$	−13.1440	−0.614852	−0.307426	+	0.951572i	$0.599468\pi$
$458$	30.0085	1.40221
$459$	0.220791	0.0103056
$460$	−90.0474	−4.19848
$461$	−0.641825	−0.0298928	−0.0149464	−	0.999888i	$-0.504758\pi$
$461$	−0.641825	−0.0298928	−0.0149464	+	0.999888i	$0.504758\pi$
$462$	53.7946	2.50275
$463$	−6.57622	−0.305623	−0.152811	−	0.988255i	$-0.548833\pi$
$463$	−6.57622	−0.305623	−0.152811	+	0.988255i	$0.548833\pi$
$464$	−34.8288	−1.61689
$465$	21.8662	1.01402
$466$	22.6469	1.04910
$467$	30.6356	1.41765	0.708824	−	0.705385i	$-0.249226\pi$
$467$	30.6356	1.41765	0.708824	+	0.705385i	$0.249226\pi$
$468$	9.35607	0.432485
$469$	−28.0790	−1.29657
$470$	−76.3497	−3.52175
$471$	−1.13418	−0.0522601
$472$	50.6762	2.33256
$473$	−18.6334	−0.856766
$474$	2.16889	0.0996204
$475$	−11.4622	−0.525920
$476$	1.03468	0.0474247
$477$	19.7597	0.904734
$478$	42.5858	1.94783
$479$	27.2017	1.24288	0.621439	−	0.783462i	$-0.286548\pi$
$479$	27.2017	1.24288	0.621439	+	0.783462i	$0.286548\pi$
$480$	−4.80903	−0.219501
$481$	9.27086	0.422715
$482$	6.39063	0.291085
$483$	32.5454	1.48086
$484$	51.8954	2.35888
$485$	−2.09358	−0.0950644
$486$	−40.0035	−1.81459
$487$	23.0285	1.04352	0.521760	−	0.853092i	$-0.325276\pi$
$487$	23.0285	1.04352	0.521760	+	0.853092i	$0.325276\pi$
$488$	6.33366	0.286711
$489$	8.28307	0.374573
$490$	−141.821	−6.40682
$491$	24.4780	1.10468	0.552338	−	0.833620i	$-0.313736\pi$
$491$	24.4780	1.10468	0.552338	+	0.833620i	$0.313736\pi$
$492$	−18.2978	−0.824930
$493$	0.329405	0.0148357
$494$	−7.56657	−0.340436
$495$	−32.0747	−1.44165
$496$	43.2318	1.94117
$497$	−14.1076	−0.632813
$498$	−6.45767	−0.289375
$499$	−13.0116	−0.582479	−0.291239	−	0.956650i	$-0.594068\pi$
$499$	−13.0116	−0.582479	−0.291239	+	0.956650i	$0.594068\pi$
$500$	−15.2736	−0.683055
$501$	−2.83757	−0.126773
$502$	8.41018	0.375365
$503$	6.89066	0.307240	0.153620	−	0.988130i	$-0.450907\pi$
$503$	6.89066	0.307240	0.153620	+	0.988130i	$0.450907\pi$
$504$	−62.1576	−2.76872
$505$	1.14802	0.0510863
$506$	87.5435	3.89178
$507$	0.872511	0.0387496
$508$	27.6776	1.22799
$509$	−37.2533	−1.65122	−0.825612	−	0.564238i	$-0.809170\pi$
$509$	−37.2533	−1.65122	−0.825612	+	0.564238i	$0.809170\pi$
$510$	0.310179	0.0137349
$511$	11.9273	0.527632
$512$	45.8251	2.02520
$513$	13.9133	0.614286
$514$	−4.73552	−0.208875
$515$	−19.2006	−0.846077
$516$	−14.0406	−0.618104
$517$	50.2020	2.20788
$518$	−118.118	−5.18982
$519$	−18.4096	−0.808090
$520$	16.0381	0.703319
$521$	−17.1815	−0.752737	−0.376368	−	0.926470i	$-0.622827\pi$
$521$	−17.1815	−0.752737	−0.376368	+	0.926470i	$0.622827\pi$
$522$	−37.9501	−1.66103
$523$	−8.67270	−0.379231	−0.189615	−	0.981858i	$-0.560724\pi$
$523$	−8.67270	−0.379231	−0.189615	+	0.981858i	$0.560724\pi$
$524$	2.73229	0.119361
$525$	−16.8397	−0.734947
$526$	−41.9200	−1.82780
$527$	−0.408880	−0.0178111
$528$	21.5642	0.938462
$529$	29.9632	1.30275
$530$	64.9586	2.82162
$531$	20.9431	0.908855
$532$	65.2014	2.82684
$533$	5.01806	0.217356
$534$	10.9973	0.475902
$535$	−20.0664	−0.867548
$536$	−29.6765	−1.28183
$537$	18.3601	0.792296
$538$	−38.9148	−1.67773
$539$	93.2511	4.01661
$540$	−56.5562	−2.43379
$541$	10.1739	0.437412	0.218706	−	0.975791i	$-0.429816\pi$
$541$	10.1739	0.437412	0.218706	+	0.975791i	$0.429816\pi$
$542$	7.85237	0.337288
$543$	−19.9120	−0.854505
$544$	0.0899248	0.00385549
$545$	0.419175	0.0179555
$546$	−11.1165	−0.475742
$547$	5.12276	0.219034	0.109517	−	0.993985i	$-0.465070\pi$
$547$	5.12276	0.219034	0.109517	+	0.993985i	$0.465070\pi$
$548$	53.8137	2.29881
$549$	2.61753	0.111714
$550$	−45.2971	−1.93148
$551$	20.7577	0.884308
$552$	34.3971	1.46404
$553$	5.12543	0.217956
$554$	−32.6921	−1.38896
$555$	−23.9487	−1.01657
$556$	−40.2248	−1.70591
$557$	−37.7380	−1.59901	−0.799506	−	0.600658i	$-0.794905\pi$
$557$	−37.7380	−1.59901	−0.799506	+	0.600658i	$0.794905\pi$
$558$	47.1062	1.99417
$559$	3.85055	0.162861
$560$	−77.5021	−3.27506
$561$	−0.203951	−0.00861082
$562$	−50.6507	−2.13657
$563$	−13.4090	−0.565120	−0.282560	−	0.959250i	$-0.591184\pi$
$563$	−13.4090	−0.565120	−0.282560	+	0.959250i	$0.591184\pi$
$564$	37.8281	1.59285
$565$	−29.8920	−1.25756
$566$	−40.2950	−1.69373
$567$	−13.9825	−0.587208
$568$	−14.9103	−0.625622
$569$	−1.39220	−0.0583642	−0.0291821	−	0.999574i	$-0.509290\pi$
$569$	−1.39220	−0.0583642	−0.0291821	+	0.999574i	$0.509290\pi$
$570$	19.5461	0.818698
$571$	−33.4529	−1.39996	−0.699981	−	0.714162i	$-0.746808\pi$
$571$	−33.4529	−1.39996	−0.699981	+	0.714162i	$0.746808\pi$
$572$	−20.2238	−0.845602
$573$	4.17598	0.174454
$574$	−63.9341	−2.66856
$575$	−27.4044	−1.14284
$576$	12.5076	0.521152
$577$	7.43176	0.309388	0.154694	−	0.987962i	$-0.450561\pi$
$577$	7.43176	0.309388	0.154694	+	0.987962i	$0.450561\pi$
$578$	42.2528	1.75748
$579$	15.1377	0.629102
$580$	−84.3782	−3.50361
$581$	−15.2605	−0.633113
$582$	1.53368	0.0635732
$583$	−42.7120	−1.76895
$584$	12.6059	0.521636
$585$	6.62813	0.274040
$586$	−70.1181	−2.89655
$587$	−34.4948	−1.42375	−0.711876	−	0.702305i	$-0.752154\pi$
$587$	−34.4948	−1.42375	−0.711876	+	0.702305i	$0.752154\pi$
$588$	70.2664	2.89774
$589$	−25.7659	−1.06166
$590$	68.8491	2.83447
$591$	−23.4637	−0.965166
$592$	−47.3491	−1.94604
$593$	37.4490	1.53784	0.768922	−	0.639342i	$-0.220793\pi$
$593$	37.4490	1.53784	0.768922	+	0.639342i	$0.220793\pi$
$594$	54.9836	2.25601
$595$	0.733002	0.0300502
$596$	−62.1998	−2.54780
$597$	16.2795	0.666277
$598$	−18.0906	−0.739780
$599$	−10.1019	−0.412753	−0.206376	−	0.978473i	$-0.566167\pi$
$599$	−10.1019	−0.412753	−0.206376	+	0.978473i	$0.566167\pi$
$600$	−17.7979	−0.726595
$601$	29.9146	1.22024	0.610122	−	0.792308i	$-0.291121\pi$
$601$	29.9146	1.22024	0.610122	+	0.792308i	$0.291121\pi$
$602$	−49.0590	−1.99950
$603$	−12.2645	−0.499450
$604$	11.2882	0.459309
$605$	36.7643	1.49468
$606$	−0.841000	−0.0341633
$607$	−18.5737	−0.753884	−0.376942	−	0.926237i	$-0.623024\pi$
$607$	−18.5737	−0.753884	−0.376942	+	0.926237i	$0.623024\pi$
$608$	5.66668	0.229814
$609$	30.4964	1.23577
$610$	8.60496	0.348404
$611$	−10.3741	−0.419691
$612$	0.451937	0.0182685
$613$	43.2139	1.74539	0.872697	−	0.488263i	$-0.162369\pi$
$613$	43.2139	1.74539	0.872697	+	0.488263i	$0.162369\pi$
$614$	−23.5295	−0.949575
$615$	−12.9628	−0.522709
$616$	134.358	5.41345
$617$	22.7595	0.916262	0.458131	−	0.888885i	$-0.348519\pi$
$617$	22.7595	0.916262	0.458131	+	0.888885i	$0.348519\pi$
$618$	14.0657	0.565804
$619$	9.52240	0.382738	0.191369	−	0.981518i	$-0.438707\pi$
$619$	9.52240	0.382738	0.191369	+	0.981518i	$0.438707\pi$
$620$	104.736	4.20630
$621$	33.2647	1.33487
$622$	−38.1212	−1.52852
$623$	25.9885	1.04121
$624$	−4.45618	−0.178390
$625$	−29.6483	−1.18593
$626$	−18.9621	−0.757879
$627$	−12.8521	−0.513264
$628$	−5.43254	−0.216782
$629$	0.447821	0.0178558
$630$	−84.4477	−3.36448
$631$	41.7230	1.66097	0.830483	−	0.557043i	$-0.188064\pi$
$631$	41.7230	1.66097	0.830483	+	0.557043i	$0.188064\pi$
$632$	5.41705	0.215479
$633$	−8.56658	−0.340491
$634$	41.0868	1.63177
$635$	19.6076	0.778106
$636$	−32.1843	−1.27619
$637$	−19.2701	−0.763508
$638$	82.0319	3.24768
$639$	−6.16203	−0.243766
$640$	52.1414	2.06107
$641$	−30.1579	−1.19117	−0.595583	−	0.803294i	$-0.703079\pi$
$641$	−30.1579	−1.19117	−0.595583	+	0.803294i	$0.703079\pi$
$642$	14.7000	0.580162
$643$	−11.8674	−0.468003	−0.234001	−	0.972236i	$-0.575182\pi$
$643$	−11.8674	−0.468003	−0.234001	+	0.972236i	$0.575182\pi$
$644$	155.887	6.14282
$645$	−9.94682	−0.391656
$646$	−0.365496	−0.0143803
$647$	−21.7368	−0.854562	−0.427281	−	0.904119i	$-0.640528\pi$
$647$	−21.7368	−0.854562	−0.427281	+	0.904119i	$0.640528\pi$
$648$	−14.7780	−0.580535
$649$	−45.2702	−1.77701
$650$	9.36052	0.367150
$651$	−37.8542	−1.48362
$652$	39.6747	1.55378
$653$	−47.7476	−1.86851	−0.934254	−	0.356608i	$-0.883933\pi$
$653$	−47.7476	−1.86851	−0.934254	+	0.356608i	$0.883933\pi$
$654$	−0.307073	−0.0120075
$655$	1.93564	0.0756317
$656$	−25.6288	−1.00064
$657$	5.20969	0.203249
$658$	132.174	5.15269
$659$	47.7403	1.85970	0.929849	−	0.367943i	$-0.119938\pi$
$659$	47.7403	1.85970	0.929849	+	0.367943i	$0.119938\pi$
$660$	52.2427	2.03354
$661$	−9.74264	−0.378945	−0.189472	−	0.981886i	$-0.560678\pi$
$661$	−9.74264	−0.378945	−0.189472	+	0.981886i	$0.560678\pi$
$662$	−59.4797	−2.31174
$663$	0.0421459	0.00163681
$664$	−16.1288	−0.625918
$665$	46.1907	1.79120
$666$	−51.5925	−1.99917
$667$	49.6288	1.92163
$668$	−13.5915	−0.525873
$669$	−4.35185	−0.168252
$670$	−40.3188	−1.55765
$671$	−5.65799	−0.218424
$672$	8.32525	0.321153
$673$	27.1916	1.04816	0.524079	−	0.851670i	$-0.324410\pi$
$673$	27.1916	1.04816	0.524079	+	0.851670i	$0.324410\pi$
$674$	−62.2336	−2.39715
$675$	−17.2120	−0.662489
$676$	4.17920	0.160738
$677$	−49.8929	−1.91754	−0.958770	−	0.284182i	$-0.908278\pi$
$677$	−49.8929	−1.91754	−0.958770	+	0.284182i	$0.908278\pi$
$678$	21.8978	0.840981
$679$	3.62434	0.139089
$680$	0.774707	0.0297087
$681$	−22.5994	−0.866011
$682$	−101.824	−3.89903
$683$	−41.2066	−1.57673	−0.788363	−	0.615210i	$-0.789071\pi$
$683$	−41.2066	−1.57673	−0.788363	+	0.615210i	$0.789071\pi$
$684$	28.4791	1.08893
$685$	38.1233	1.45662
$686$	156.331	5.96873
$687$	−10.5329	−0.401856
$688$	−19.6659	−0.749756
$689$	8.82632	0.336256
$690$	46.7321	1.77906
$691$	−43.6791	−1.66163	−0.830816	−	0.556548i	$-0.812126\pi$
$691$	−43.6791	−1.66163	−0.830816	+	0.556548i	$0.812126\pi$
$692$	−88.1790	−3.35206
$693$	55.5267	2.10928
$694$	56.4092	2.14126
$695$	−28.4965	−1.08093
$696$	32.2315	1.22173
$697$	0.242393	0.00918128
$698$	−28.3000	−1.07117
$699$	−7.94901	−0.300659
$700$	−80.6599	−3.04866
$701$	35.2162	1.33010	0.665049	−	0.746800i	$-0.268411\pi$
$701$	35.2162	1.33010	0.665049	+	0.746800i	$0.268411\pi$
$702$	−11.3622	−0.428839
$703$	28.2197	1.06433
$704$	−27.0362	−1.01897
$705$	26.7986	1.00929
$706$	−80.2019	−3.01844
$707$	−1.98742	−0.0747446
$708$	−34.1119	−1.28200
$709$	7.00200	0.262966	0.131483	−	0.991318i	$-0.458026\pi$
$709$	7.00200	0.262966	0.131483	+	0.991318i	$0.458026\pi$
$710$	−20.2572	−0.760240
$711$	2.23872	0.0839587
$712$	27.4672	1.02938
$713$	−61.6026	−2.30704
$714$	−0.536972	−0.0200957
$715$	−14.3272	−0.535807
$716$	87.9421	3.28655
$717$	−14.9475	−0.558226
$718$	−45.8979	−1.71290
$719$	22.6912	0.846238	0.423119	−	0.906074i	$-0.360935\pi$
$719$	22.6912	0.846238	0.423119	+	0.906074i	$0.360935\pi$
$720$	−33.8519	−1.26159
$721$	33.2394	1.23790
$722$	24.1982	0.900563
$723$	−2.24310	−0.0834218
$724$	−95.3754	−3.54460
$725$	−25.6791	−0.953698
$726$	−26.9323	−0.999550
$727$	42.9196	1.59180	0.795900	−	0.605428i	$-0.206998\pi$
$727$	42.9196	1.59180	0.795900	+	0.605428i	$0.206998\pi$
$728$	−27.7647	−1.02903
$729$	5.85699	0.216925
$730$	17.1265	0.633879
$731$	0.185997	0.00687935
$732$	−4.26340	−0.157580
$733$	33.3677	1.23246	0.616231	−	0.787565i	$-0.288659\pi$
$733$	33.3677	1.23246	0.616231	+	0.787565i	$0.288659\pi$
$734$	20.7209	0.764823
$735$	49.7789	1.83612
$736$	13.5482	0.499394
$737$	26.5107	0.976534
$738$	−27.9256	−1.02795
$739$	−1.94271	−0.0714638	−0.0357319	−	0.999361i	$-0.511376\pi$
$739$	−1.94271	−0.0714638	−0.0357319	+	0.999361i	$0.511376\pi$
$740$	−114.711	−4.21685
$741$	2.65585	0.0975652
$742$	−112.454	−4.12833
$743$	0.768920	0.0282089	0.0141045	−	0.999901i	$-0.495510\pi$
$743$	0.768920	0.0282089	0.0141045	+	0.999901i	$0.495510\pi$
$744$	−40.0079	−1.46676
$745$	−44.0643	−1.61439
$746$	−60.8235	−2.22691
$747$	−6.66560	−0.243881
$748$	−0.976895	−0.0357188
$749$	34.7384	1.26931
$750$	7.92656	0.289437
$751$	−37.3122	−1.36154	−0.680770	−	0.732497i	$-0.738355\pi$
$751$	−37.3122	−1.36154	−0.680770	+	0.732497i	$0.738355\pi$
$752$	52.9837	1.93212
$753$	−2.95196	−0.107575
$754$	−16.9517	−0.617343
$755$	7.99689	0.291037
$756$	97.9085	3.56090
$757$	25.1976	0.915823	0.457912	−	0.888998i	$-0.348598\pi$
$757$	25.1976	0.915823	0.457912	+	0.888998i	$0.348598\pi$
$758$	−63.5820	−2.30940
$759$	−30.7276	−1.11534
$760$	48.8188	1.77084
$761$	26.2913	0.953061	0.476530	−	0.879158i	$-0.341894\pi$
$761$	26.2913	0.953061	0.476530	+	0.879158i	$0.341894\pi$
$762$	−14.3639	−0.520349
$763$	−0.725664	−0.0262708
$764$	20.0023	0.723658
$765$	0.320166	0.0115756
$766$	−21.3378	−0.770967
$767$	9.35495	0.337788
$768$	−28.4476	−1.02652
$769$	−21.7736	−0.785175	−0.392588	−	0.919715i	$-0.628420\pi$
$769$	−21.7736	−0.785175	−0.392588	+	0.919715i	$0.628420\pi$
$770$	182.540	6.57829
$771$	1.66216	0.0598612
$772$	72.5074	2.60960
$773$	−45.1806	−1.62503	−0.812517	−	0.582938i	$-0.801903\pi$
$773$	−45.1806	−1.62503	−0.812517	+	0.582938i	$0.801903\pi$
$774$	−21.4284	−0.770226
$775$	31.8747	1.14497
$776$	3.83055	0.137509
$777$	41.4593	1.48734
$778$	91.7299	3.28868
$779$	15.2746	0.547268
$780$	−10.7958	−0.386552
$781$	13.3197	0.476616
$782$	−0.873851	−0.0312488
$783$	31.1704	1.11394
$784$	98.4182	3.51494
$785$	−3.84858	−0.137362
$786$	−1.41798	−0.0505777
$787$	21.7388	0.774903	0.387452	−	0.921890i	$-0.373355\pi$
$787$	21.7388	0.774903	0.387452	+	0.921890i	$0.373355\pi$
$788$	−112.387	−4.00364
$789$	14.7138	0.523827
$790$	7.35964	0.261844
$791$	51.7481	1.83995
$792$	58.6860	2.08531
$793$	1.16921	0.0415198
$794$	61.0923	2.16808
$795$	−22.8004	−0.808645
$796$	77.9765	2.76380
$797$	8.55911	0.303179	0.151590	−	0.988444i	$-0.451561\pi$
$797$	8.55911	0.303179	0.151590	+	0.988444i	$0.451561\pi$
$798$	−33.8377	−1.19784
$799$	−0.501112	−0.0177281
$800$	−7.01018	−0.247847
$801$	11.3514	0.401084
$802$	−67.2937	−2.37622
$803$	−11.2611	−0.397396
$804$	19.9763	0.704509
$805$	110.435	3.89234
$806$	21.0416	0.741157
$807$	13.6590	0.480820
$808$	−2.10050	−0.0738952
$809$	32.9700	1.15916	0.579581	−	0.814915i	$-0.303216\pi$
$809$	32.9700	1.15916	0.579581	+	0.814915i	$0.303216\pi$
$810$	−20.0775	−0.705452
$811$	0.590487	0.0207348	0.0103674	−	0.999946i	$-0.496700\pi$
$811$	0.590487	0.0207348	0.0103674	+	0.999946i	$0.496700\pi$
$812$	146.073	5.12616
$813$	−2.75617	−0.0966631
$814$	111.521	3.90881
$815$	28.1068	0.984537
$816$	−0.215252	−0.00753533
$817$	11.7207	0.410057
$818$	31.2682	1.09327
$819$	−11.4744	−0.400949
$820$	−62.0897	−2.16827
$821$	−22.6423	−0.790222	−0.395111	−	0.918633i	$-0.629294\pi$
$821$	−22.6423	−0.790222	−0.395111	+	0.918633i	$0.629294\pi$
$822$	−27.9278	−0.974094
$823$	8.56440	0.298536	0.149268	−	0.988797i	$-0.452308\pi$
$823$	8.56440	0.298536	0.149268	+	0.988797i	$0.452308\pi$
$824$	35.1306	1.22383
$825$	15.8992	0.553540
$826$	−119.190	−4.14713
$827$	−34.5731	−1.20222	−0.601112	−	0.799165i	$-0.705276\pi$
$827$	−34.5731	−1.20222	−0.601112	+	0.799165i	$0.705276\pi$
$828$	68.0896	2.36628
$829$	−1.49980	−0.0520901	−0.0260451	−	0.999661i	$-0.508291\pi$
$829$	−1.49980	−0.0520901	−0.0260451	+	0.999661i	$0.508291\pi$
$830$	−21.9127	−0.760600
$831$	11.4749	0.398059
$832$	5.58696	0.193693
$833$	−0.930824	−0.0322511
$834$	20.8756	0.722862
$835$	−9.62868	−0.333214
$836$	−61.5597	−2.12909
$837$	−38.6909	−1.33735
$838$	60.7156	2.09739
$839$	−39.8096	−1.37438	−0.687190	−	0.726477i	$-0.741156\pi$
$839$	−39.8096	−1.37438	−0.687190	+	0.726477i	$0.741156\pi$
$840$	71.7225	2.47466
$841$	17.5042	0.603594
$842$	−35.5016	−1.22347
$843$	17.7783	0.612318
$844$	−41.0326	−1.41240
$845$	2.96068	0.101850
$846$	57.7321	1.98487
$847$	−63.6453	−2.18688
$848$	−45.0787	−1.54801
$849$	14.1435	0.485403
$850$	0.452151	0.0155087
$851$	67.4695	2.31282
$852$	10.0366	0.343849
$853$	−24.8182	−0.849761	−0.424880	−	0.905250i	$-0.639684\pi$
$853$	−24.8182	−0.849761	−0.424880	+	0.905250i	$0.639684\pi$
$854$	−14.8966	−0.509753
$855$	20.1755	0.689987
$856$	36.7149	1.25489
$857$	−5.68445	−0.194177	−0.0970886	−	0.995276i	$-0.530953\pi$
$857$	−5.68445	−0.194177	−0.0970886	+	0.995276i	$0.530953\pi$
$858$	10.4956	0.358314
$859$	14.9117	0.508782	0.254391	−	0.967102i	$-0.418125\pi$
$859$	14.9117	0.508782	0.254391	+	0.967102i	$0.418125\pi$
$860$	−47.6438	−1.62464
$861$	22.4408	0.764779
$862$	−23.1971	−0.790096
$863$	−3.30556	−0.112523	−0.0562613	−	0.998416i	$-0.517918\pi$
$863$	−3.30556	−0.112523	−0.0562613	+	0.998416i	$0.517918\pi$
$864$	8.50926	0.289491
$865$	−62.4688	−2.12400
$866$	−78.6592	−2.67295
$867$	−14.8307	−0.503676
$868$	−181.316	−6.15426
$869$	−4.83917	−0.164158
$870$	43.7899	1.48462
$871$	−5.47836	−0.185627
$872$	−0.766951	−0.0259722
$873$	1.58306	0.0535786
$874$	−55.0663	−1.86265
$875$	18.7318	0.633249
$876$	−8.48546	−0.286697
$877$	17.8726	0.603513	0.301757	−	0.953385i	$-0.402427\pi$
$877$	17.8726	0.603513	0.301757	+	0.953385i	$0.402427\pi$
$878$	35.6344	1.20260
$879$	24.6113	0.830120
$880$	73.1734	2.46668
$881$	−25.6140	−0.862959	−0.431480	−	0.902123i	$-0.642008\pi$
$881$	−25.6140	−0.862959	−0.431480	+	0.902123i	$0.642008\pi$
$882$	107.238	3.61090
$883$	7.32573	0.246530	0.123265	−	0.992374i	$-0.460663\pi$
$883$	7.32573	0.246530	0.123265	+	0.992374i	$0.460663\pi$
$884$	0.201872	0.00678970
$885$	−24.1659	−0.812328
$886$	22.5506	0.757602
$887$	1.29658	0.0435349	0.0217675	−	0.999763i	$-0.493071\pi$
$887$	1.29658	0.0435349	0.0217675	+	0.999763i	$0.493071\pi$
$888$	43.8182	1.47044
$889$	−33.9442	−1.13845
$890$	37.3171	1.25087
$891$	13.2015	0.442267
$892$	−20.8447	−0.697933
$893$	−31.5779	−1.05671
$894$	32.2800	1.07960
$895$	62.3009	2.08249
$896$	−90.2657	−3.01557
$897$	6.34978	0.212013
$898$	11.1641	0.372552
$899$	−57.7242	−1.92521
$900$	−35.2312	−1.17437
$901$	0.426347	0.0142037
$902$	60.3632	2.00988
$903$	17.2196	0.573034
$904$	54.6924	1.81904
$905$	−67.5669	−2.24600
$906$	−5.85825	−0.194627
$907$	−13.5917	−0.451305	−0.225652	−	0.974208i	$-0.572451\pi$
$907$	−13.5917	−0.451305	−0.225652	+	0.974208i	$0.572451\pi$
$908$	−108.248	−3.59233
$909$	−0.868080	−0.0287924
$910$	−37.7214	−1.25045
$911$	−27.2579	−0.903093	−0.451546	−	0.892248i	$-0.649127\pi$
$911$	−27.2579	−0.903093	−0.451546	+	0.892248i	$0.649127\pi$
$912$	−13.5643	−0.449158
$913$	14.4082	0.476841
$914$	32.6734	1.08074
$915$	−3.02032	−0.0998489
$916$	−50.4512	−1.66695
$917$	−3.35092	−0.110657
$918$	−0.548841	−0.0181145
$919$	57.2506	1.88852	0.944262	−	0.329194i	$-0.106777\pi$
$919$	57.2506	1.88852	0.944262	+	0.329194i	$0.106777\pi$
$920$	116.719	3.84811
$921$	8.25883	0.272138
$922$	1.59545	0.0525433
$923$	−2.75247	−0.0905988
$924$	−90.4410	−2.97529
$925$	−34.9103	−1.14784
$926$	16.3472	0.537201
$927$	14.5186	0.476852
$928$	12.6953	0.416742
$929$	21.1527	0.693998	0.346999	−	0.937866i	$-0.387201\pi$
$929$	21.1527	0.693998	0.346999	+	0.937866i	$0.387201\pi$
$930$	−54.3550	−1.78237
$931$	−58.6565	−1.92239
$932$	−38.0746	−1.24717
$933$	13.3805	0.438058
$934$	−76.1541	−2.49184
$935$	−0.692063	−0.0226329
$936$	−12.1273	−0.396393
$937$	1.74295	0.0569397	0.0284699	−	0.999595i	$-0.490937\pi$
$937$	1.74295	0.0569397	0.0284699	+	0.999595i	$0.490937\pi$
$938$	69.7987	2.27901
$939$	6.65568	0.217200
$940$	128.361	4.18669
$941$	−45.3351	−1.47788	−0.738941	−	0.673770i	$-0.764674\pi$
$941$	−45.3351	−1.47788	−0.738941	+	0.673770i	$0.764674\pi$
$942$	2.81934	0.0918589
$943$	36.5193	1.18923
$944$	−47.7786	−1.55506
$945$	69.3614	2.25633
$946$	46.3190	1.50596
$947$	8.91824	0.289804	0.144902	−	0.989446i	$-0.453713\pi$
$947$	8.91824	0.289804	0.144902	+	0.989446i	$0.453713\pi$
$948$	−3.64640	−0.118430
$949$	2.32708	0.0755402
$950$	28.4927	0.924424
$951$	−14.4214	−0.467646
$952$	−1.34115	−0.0434669
$953$	−37.2444	−1.20647	−0.603233	−	0.797565i	$-0.706121\pi$
$953$	−37.2444	−1.20647	−0.603233	+	0.797565i	$0.706121\pi$
$954$	−49.1186	−1.59027
$955$	14.1703	0.458539
$956$	−71.5965	−2.31560
$957$	−28.7931	−0.930748
$958$	−67.6180	−2.18464
$959$	−65.9979	−2.13118
$960$	−14.4324	−0.465802
$961$	40.6512	1.31133
$962$	−23.0455	−0.743017
$963$	15.1733	0.488953
$964$	−10.7441	−0.346045
$965$	51.3665	1.65355
$966$	−80.9012	−2.60295
$967$	−25.9524	−0.834573	−0.417287	−	0.908775i	$-0.637019\pi$
$967$	−25.9524	−0.834573	−0.417287	+	0.908775i	$0.637019\pi$
$968$	−67.2665	−2.16203
$969$	0.128289	0.00412122
$970$	5.20421	0.167097
$971$	8.41160	0.269941	0.134971	−	0.990850i	$-0.456906\pi$
$971$	8.41160	0.269941	0.134971	+	0.990850i	$0.456906\pi$
$972$	67.2550	2.15721
$973$	49.3323	1.58152
$974$	−57.2442	−1.83422
$975$	−3.28553	−0.105221
$976$	−5.97150	−0.191143
$977$	19.6795	0.629603	0.314802	−	0.949157i	$-0.398062\pi$
$977$	19.6795	0.629603	0.314802	+	0.949157i	$0.398062\pi$
$978$	−20.5901	−0.658397
$979$	−24.5370	−0.784206
$980$	238.433	7.61648
$981$	−0.316961	−0.0101198
$982$	−60.8473	−1.94172
$983$	4.48329	0.142995	0.0714974	−	0.997441i	$-0.477222\pi$
$983$	4.48329	0.142995	0.0714974	+	0.997441i	$0.477222\pi$
$984$	23.7175	0.756088
$985$	−79.6188	−2.53686
$986$	−0.818835	−0.0260770
$987$	−46.3930	−1.47670
$988$	12.7211	0.404713
$989$	28.0227	0.891069
$990$	79.7312	2.53402
$991$	−20.0487	−0.636867	−0.318434	−	0.947945i	$-0.603157\pi$
$991$	−20.0487	−0.636867	−0.318434	+	0.947945i	$0.603157\pi$
$992$	−15.7582	−0.500324
$993$	20.8773	0.662520
$994$	35.0687	1.11231
$995$	55.2410	1.75126
$996$	10.8568	0.344012
$997$	−20.1722	−0.638861	−0.319430	−	0.947610i	$-0.603492\pi$
$997$	−20.1722	−0.638861	−0.319430	+	0.947610i	$0.603492\pi$
$998$	32.3442	1.02384
$999$	42.3757	1.34071

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1027.2.a.c.1.3	✓	18
3.2	odd	2		9243.2.a.m.1.16		18

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1027.2.a.c.1.3	✓	18	1.1	even	1	trivial
9243.2.a.m.1.16		18	3.2	odd	2

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:	\( N \)	\(=\)	\( 1027 = 13 \cdot 79 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1027.a (trivial)

\(f(q)\)	\(=\)	\(q-2.48580 q^{2} +0.872511 q^{3} +4.17920 q^{4} +2.96068 q^{5} -2.16889 q^{6} -5.12543 q^{7} -5.41705 q^{8} -2.23872 q^{9} +O(q^{10})\)	\(q-2.48580 q^{2} +0.872511 q^{3} +4.17920 q^{4} +2.96068 q^{5} -2.16889 q^{6} -5.12543 q^{7} -5.41705 q^{8} -2.23872 q^{9} -7.35964 q^{10} +4.83917 q^{11} +3.64640 q^{12} -1.00000 q^{13} +12.7408 q^{14} +2.58322 q^{15} +5.10731 q^{16} -0.0483041 q^{17} +5.56502 q^{18} -3.04392 q^{19} +12.3733 q^{20} -4.47200 q^{21} -12.0292 q^{22} -7.27758 q^{23} -4.72644 q^{24} +3.76560 q^{25} +2.48580 q^{26} -4.57085 q^{27} -21.4202 q^{28} -6.81940 q^{29} -6.42137 q^{30} +8.46470 q^{31} -1.86164 q^{32} +4.22223 q^{33} +0.120074 q^{34} -15.1747 q^{35} -9.35607 q^{36} -9.27086 q^{37} +7.56657 q^{38} -0.872511 q^{39} -16.0381 q^{40} -5.01806 q^{41} +11.1165 q^{42} -3.85055 q^{43} +20.2238 q^{44} -6.62813 q^{45} +18.0906 q^{46} +10.3741 q^{47} +4.45618 q^{48} +19.2701 q^{49} -9.36052 q^{50} -0.0421459 q^{51} -4.17920 q^{52} -8.82632 q^{53} +11.3622 q^{54} +14.3272 q^{55} +27.7647 q^{56} -2.65585 q^{57} +16.9517 q^{58} -9.35495 q^{59} +10.7958 q^{60} -1.16921 q^{61} -21.0416 q^{62} +11.4744 q^{63} -5.58696 q^{64} -2.96068 q^{65} -10.4956 q^{66} +5.47836 q^{67} -0.201872 q^{68} -6.34978 q^{69} +37.7214 q^{70} +2.75247 q^{71} +12.1273 q^{72} -2.32708 q^{73} +23.0455 q^{74} +3.28553 q^{75} -12.7211 q^{76} -24.8028 q^{77} +2.16889 q^{78} -1.00000 q^{79} +15.1211 q^{80} +2.72806 q^{81} +12.4739 q^{82} +2.97741 q^{83} -18.6894 q^{84} -0.143013 q^{85} +9.57168 q^{86} -5.95001 q^{87} -26.2140 q^{88} -5.07050 q^{89} +16.4762 q^{90} +5.12543 q^{91} -30.4145 q^{92} +7.38555 q^{93} -25.7879 q^{94} -9.01205 q^{95} -1.62430 q^{96} -0.707128 q^{97} -47.9015 q^{98} -10.8336 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 18 q - 6 q^{2} - 8 q^{3} + 16 q^{4} - 7 q^{5} + 2 q^{6} - 6 q^{7} - 18 q^{8} + 10 q^{9}+O(q^{10}) \) 18 * q - 6 * q^2 - 8 * q^3 + 16 * q^4 - 7 * q^5 + 2 * q^6 - 6 * q^7 - 18 * q^8 + 10 * q^9	\( 18 q - 6 q^{2} - 8 q^{3} + 16 q^{4} - 7 q^{5} + 2 q^{6} - 6 q^{7} - 18 q^{8} + 10 q^{9} - 8 q^{10} - 2 q^{11} - 25 q^{12} - 18 q^{13} - 16 q^{14} - 8 q^{15} + 20 q^{16} - 25 q^{17} - 15 q^{18} - 3 q^{19} - 5 q^{20} - 14 q^{21} - 14 q^{22} - 21 q^{23} + 18 q^{24} + 9 q^{25} + 6 q^{26} - 35 q^{27} - q^{28} - 50 q^{29} - 8 q^{30} + 19 q^{31} - 37 q^{32} - 4 q^{33} + 26 q^{34} - 26 q^{35} + 14 q^{36} - 40 q^{37} - 3 q^{38} + 8 q^{39} - 36 q^{40} - q^{41} + 49 q^{42} - 17 q^{43} + 11 q^{44} - 12 q^{45} + 4 q^{46} - 15 q^{47} - 59 q^{48} + 24 q^{49} - 34 q^{50} + 10 q^{51} - 16 q^{52} - 79 q^{53} + 58 q^{54} + 12 q^{55} - 37 q^{56} - 3 q^{57} - 14 q^{58} + 7 q^{59} + 30 q^{60} - 30 q^{61} - 52 q^{62} - 3 q^{63} + 38 q^{64} + 7 q^{65} - 56 q^{66} + 8 q^{67} - 21 q^{68} - 22 q^{69} + 39 q^{70} - 20 q^{71} - 46 q^{72} - 9 q^{73} - 4 q^{74} + 10 q^{75} - 46 q^{76} - 75 q^{77} - 2 q^{78} - 18 q^{79} + 36 q^{80} - 18 q^{81} - 16 q^{82} - 13 q^{83} - 61 q^{84} - 21 q^{85} + 19 q^{86} - 8 q^{87} - 10 q^{88} + 18 q^{89} + 58 q^{90} + 6 q^{91} - 76 q^{92} - 41 q^{93} + 58 q^{94} - 25 q^{95} + 96 q^{96} + 24 q^{97} - 35 q^{98} + 26 q^{99}+O(q^{100}) \) 18 * q - 6 * q^2 - 8 * q^3 + 16 * q^4 - 7 * q^5 + 2 * q^6 - 6 * q^7 - 18 * q^8 + 10 * q^9 - 8 * q^10 - 2 * q^11 - 25 * q^12 - 18 * q^13 - 16 * q^14 - 8 * q^15 + 20 * q^16 - 25 * q^17 - 15 * q^18 - 3 * q^19 - 5 * q^20 - 14 * q^21 - 14 * q^22 - 21 * q^23 + 18 * q^24 + 9 * q^25 + 6 * q^26 - 35 * q^27 - q^28 - 50 * q^29 - 8 * q^30 + 19 * q^31 - 37 * q^32 - 4 * q^33 + 26 * q^34 - 26 * q^35 + 14 * q^36 - 40 * q^37 - 3 * q^38 + 8 * q^39 - 36 * q^40 - q^41 + 49 * q^42 - 17 * q^43 + 11 * q^44 - 12 * q^45 + 4 * q^46 - 15 * q^47 - 59 * q^48 + 24 * q^49 - 34 * q^50 + 10 * q^51 - 16 * q^52 - 79 * q^53 + 58 * q^54 + 12 * q^55 - 37 * q^56 - 3 * q^57 - 14 * q^58 + 7 * q^59 + 30 * q^60 - 30 * q^61 - 52 * q^62 - 3 * q^63 + 38 * q^64 + 7 * q^65 - 56 * q^66 + 8 * q^67 - 21 * q^68 - 22 * q^69 + 39 * q^70 - 20 * q^71 - 46 * q^72 - 9 * q^73 - 4 * q^74 + 10 * q^75 - 46 * q^76 - 75 * q^77 - 2 * q^78 - 18 * q^79 + 36 * q^80 - 18 * q^81 - 16 * q^82 - 13 * q^83 - 61 * q^84 - 21 * q^85 + 19 * q^86 - 8 * q^87 - 10 * q^88 + 18 * q^89 + 58 * q^90 + 6 * q^91 - 76 * q^92 - 41 * q^93 + 58 * q^94 - 25 * q^95 + 96 * q^96 + 24 * q^97 - 35 * q^98 + 26 * q^99

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