LMFDB - Embedded newform 1502.2.a.g.1.14

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1502,2,Mod(1,1502)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1502, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([0]))

N = Newforms(chi, 2, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("1502.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1502 = 2 \cdot 751 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1502.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:	$11.9935303836$
Analytic rank:	$0$
Dimension:	$16$
Coefficient field:	$\mathbb{Q}[x]/(x^{16} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} - 3 x^{15} - 25 x^{14} + 59 x^{13} + 273 x^{12} - 443 x^{11} - 1620 x^{10} + 1595 x^{9} + \cdots + 864 $ x^16 - 3x^15 - 25x^14 + 59x^13 + 273x^12 - 443x^11 - 1620x^10 + 1595x^9 + 5490x^8 - 2787x^7 - 10540x^6 + 1919x^5 + 10822x^4 + 132x^3 - 5202x^2 - 408*x + 864
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.14
Root			$-1.78129$ of defining polynomial
Character	$\chi$	$=$	1502.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.00000 q^{2} +2.78129 q^{3} +1.00000 q^{4} +0.221151 q^{5} +2.78129 q^{6} +0.625043 q^{7} +1.00000 q^{8} +4.73559 q^{9} +O(q^{10})$	\(q+1.00000 q^{2} +2.78129 q^{3} +1.00000 q^{4} +0.221151 q^{5} +2.78129 q^{6} +0.625043 q^{7} +1.00000 q^{8} +4.73559 q^{9} +0.221151 q^{10} +3.00280 q^{11} +2.78129 q^{12} -1.42882 q^{13} +0.625043 q^{14} +0.615084 q^{15} +1.00000 q^{16} +4.60629 q^{17} +4.73559 q^{18} -6.76408 q^{19} +0.221151 q^{20} +1.73843 q^{21} +3.00280 q^{22} +1.59047 q^{23} +2.78129 q^{24} -4.95109 q^{25} -1.42882 q^{26} +4.82719 q^{27} +0.625043 q^{28} -7.25090 q^{29} +0.615084 q^{30} -6.25004 q^{31} +1.00000 q^{32} +8.35166 q^{33} +4.60629 q^{34} +0.138229 q^{35} +4.73559 q^{36} +2.62814 q^{37} -6.76408 q^{38} -3.97397 q^{39} +0.221151 q^{40} -6.82730 q^{41} +1.73843 q^{42} +2.62409 q^{43} +3.00280 q^{44} +1.04728 q^{45} +1.59047 q^{46} +8.53952 q^{47} +2.78129 q^{48} -6.60932 q^{49} -4.95109 q^{50} +12.8114 q^{51} -1.42882 q^{52} +4.50626 q^{53} +4.82719 q^{54} +0.664071 q^{55} +0.625043 q^{56} -18.8129 q^{57} -7.25090 q^{58} +1.39206 q^{59} +0.615084 q^{60} +9.06113 q^{61} -6.25004 q^{62} +2.95995 q^{63} +1.00000 q^{64} -0.315984 q^{65} +8.35166 q^{66} -15.7522 q^{67} +4.60629 q^{68} +4.42356 q^{69} +0.138229 q^{70} +15.1395 q^{71} +4.73559 q^{72} +11.2069 q^{73} +2.62814 q^{74} -13.7704 q^{75} -6.76408 q^{76} +1.87688 q^{77} -3.97397 q^{78} +6.05007 q^{79} +0.221151 q^{80} -0.780947 q^{81} -6.82730 q^{82} -14.4144 q^{83} +1.73843 q^{84} +1.01868 q^{85} +2.62409 q^{86} -20.1669 q^{87} +3.00280 q^{88} +16.7727 q^{89} +1.04728 q^{90} -0.893074 q^{91} +1.59047 q^{92} -17.3832 q^{93} +8.53952 q^{94} -1.49588 q^{95} +2.78129 q^{96} -16.7963 q^{97} -6.60932 q^{98} +14.2200 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q + 16 q^{2} + 13 q^{3} + 16 q^{4} + 4 q^{5} + 13 q^{6} + 7 q^{7} + 16 q^{8} + 21 q^{9}+O(q^{10}) $ 16 * q + 16 * q^2 + 13 * q^3 + 16 * q^4 + 4 * q^5 + 13 * q^6 + 7 * q^7 + 16 * q^8 + 21 * q^9	\( 16 q + 16 q^{2} + 13 q^{3} + 16 q^{4} + 4 q^{5} + 13 q^{6} + 7 q^{7} + 16 q^{8} + 21 q^{9} + 4 q^{10} + 4 q^{11} + 13 q^{12} + 17 q^{13} + 7 q^{14} + 8 q^{15} + 16 q^{16} - q^{17} + 21 q^{18} + 23 q^{19} + 4 q^{20} + 9 q^{21} + 4 q^{22} + 15 q^{23} + 13 q^{24} + 24 q^{25} + 17 q^{26} + 31 q^{27} + 7 q^{28} + 4 q^{29} + 8 q^{30} + 42 q^{31} + 16 q^{32} + 3 q^{33} - q^{34} - 13 q^{35} + 21 q^{36} + 31 q^{37} + 23 q^{38} - 2 q^{39} + 4 q^{40} - 9 q^{41} + 9 q^{42} + 13 q^{43} + 4 q^{44} - 2 q^{45} + 15 q^{46} + 18 q^{47} + 13 q^{48} - 9 q^{49} + 24 q^{50} - 2 q^{51} + 17 q^{52} - 14 q^{53} + 31 q^{54} - 2 q^{55} + 7 q^{56} - 18 q^{57} + 4 q^{58} + 4 q^{59} + 8 q^{60} + q^{61} + 42 q^{62} + 17 q^{63} + 16 q^{64} - 32 q^{65} + 3 q^{66} + 5 q^{67} - q^{68} + 6 q^{69} - 13 q^{70} + 9 q^{71} + 21 q^{72} + 28 q^{73} + 31 q^{74} + 16 q^{75} + 23 q^{76} - 30 q^{77} - 2 q^{78} + 10 q^{79} + 4 q^{80} + 12 q^{81} - 9 q^{82} + 3 q^{83} + 9 q^{84} - 7 q^{85} + 13 q^{86} - 22 q^{87} + 4 q^{88} - 17 q^{89} - 2 q^{90} + 12 q^{91} + 15 q^{92} - q^{93} + 18 q^{94} - 4 q^{95} + 13 q^{96} - 17 q^{97} - 9 q^{98} - 10 q^{99}+O(q^{100}) \) 16 * q + 16 * q^2 + 13 * q^3 + 16 * q^4 + 4 * q^5 + 13 * q^6 + 7 * q^7 + 16 * q^8 + 21 * q^9 + 4 * q^10 + 4 * q^11 + 13 * q^12 + 17 * q^13 + 7 * q^14 + 8 * q^15 + 16 * q^16 - q^17 + 21 * q^18 + 23 * q^19 + 4 * q^20 + 9 * q^21 + 4 * q^22 + 15 * q^23 + 13 * q^24 + 24 * q^25 + 17 * q^26 + 31 * q^27 + 7 * q^28 + 4 * q^29 + 8 * q^30 + 42 * q^31 + 16 * q^32 + 3 * q^33 - q^34 - 13 * q^35 + 21 * q^36 + 31 * q^37 + 23 * q^38 - 2 * q^39 + 4 * q^40 - 9 * q^41 + 9 * q^42 + 13 * q^43 + 4 * q^44 - 2 * q^45 + 15 * q^46 + 18 * q^47 + 13 * q^48 - 9 * q^49 + 24 * q^50 - 2 * q^51 + 17 * q^52 - 14 * q^53 + 31 * q^54 - 2 * q^55 + 7 * q^56 - 18 * q^57 + 4 * q^58 + 4 * q^59 + 8 * q^60 + q^61 + 42 * q^62 + 17 * q^63 + 16 * q^64 - 32 * q^65 + 3 * q^66 + 5 * q^67 - q^68 + 6 * q^69 - 13 * q^70 + 9 * q^71 + 21 * q^72 + 28 * q^73 + 31 * q^74 + 16 * q^75 + 23 * q^76 - 30 * q^77 - 2 * q^78 + 10 * q^79 + 4 * q^80 + 12 * q^81 - 9 * q^82 + 3 * q^83 + 9 * q^84 - 7 * q^85 + 13 * q^86 - 22 * q^87 + 4 * q^88 - 17 * q^89 - 2 * q^90 + 12 * q^91 + 15 * q^92 - q^93 + 18 * q^94 - 4 * q^95 + 13 * q^96 - 17 * q^97 - 9 * q^98 - 10 * 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 $

$2$	1.00000	0.707107
$2$	1.00000	0.707107
$3$	2.78129	1.60578	0.802890	−	0.596127i	$-0.203295\pi$
$3$	2.78129	1.60578	0.802890	+	0.596127i	$0.203295\pi$
$4$	1.00000	0.500000
$5$	0.221151	0.0989015	0.0494508	−	0.998777i	$-0.484253\pi$
$5$	0.221151	0.0989015	0.0494508	+	0.998777i	$0.484253\pi$
$6$	2.78129	1.13546
$7$	0.625043	0.236244	0.118122	−	0.992999i	$-0.462313\pi$
$7$	0.625043	0.236244	0.118122	+	0.992999i	$0.462313\pi$
$8$	1.00000	0.353553
$9$	4.73559	1.57853
$10$	0.221151	0.0699339
$11$	3.00280	0.905378	0.452689	−	0.891668i	$-0.350465\pi$
$11$	3.00280	0.905378	0.452689	+	0.891668i	$0.350465\pi$
$12$	2.78129	0.802890
$13$	−1.42882	−0.396283	−0.198142	−	0.980173i	$-0.563491\pi$
$13$	−1.42882	−0.396283	−0.198142	+	0.980173i	$0.563491\pi$
$14$	0.625043	0.167050
$15$	0.615084	0.158814
$16$	1.00000	0.250000
$17$	4.60629	1.11719	0.558595	−	0.829441i	$-0.311341\pi$
$17$	4.60629	1.11719	0.558595	+	0.829441i	$0.311341\pi$
$18$	4.73559	1.11619
$19$	−6.76408	−1.55179	−0.775893	−	0.630864i	$-0.782701\pi$
$19$	−6.76408	−1.55179	−0.775893	+	0.630864i	$0.782701\pi$
$20$	0.221151	0.0494508
$21$	1.73843	0.379356
$22$	3.00280	0.640199
$23$	1.59047	0.331635	0.165818	−	0.986156i	$-0.446974\pi$
$23$	1.59047	0.331635	0.165818	+	0.986156i	$0.446974\pi$
$24$	2.78129	0.567729
$25$	−4.95109	−0.990218
$26$	−1.42882	−0.280215
$27$	4.82719	0.928993
$28$	0.625043	0.118122
$29$	−7.25090	−1.34646	−0.673229	−	0.739434i	$-0.735093\pi$
$29$	−7.25090	−1.34646	−0.673229	+	0.739434i	$0.735093\pi$
$30$	0.615084	0.112299
$31$	−6.25004	−1.12254	−0.561270	−	0.827633i	$-0.689687\pi$
$31$	−6.25004	−1.12254	−0.561270	+	0.827633i	$0.689687\pi$
$32$	1.00000	0.176777
$33$	8.35166	1.45384
$34$	4.60629	0.789972
$35$	0.138229	0.0233649
$36$	4.73559	0.789265
$37$	2.62814	0.432063	0.216031	−	0.976386i	$-0.430689\pi$
$37$	2.62814	0.432063	0.216031	+	0.976386i	$0.430689\pi$
$38$	−6.76408	−1.09728
$39$	−3.97397	−0.636344
$40$	0.221151	0.0349670
$41$	−6.82730	−1.06625	−0.533123	−	0.846038i	$-0.678982\pi$
$41$	−6.82730	−1.06625	−0.533123	+	0.846038i	$0.678982\pi$
$42$	1.73843	0.268245
$43$	2.62409	0.400170	0.200085	−	0.979779i	$-0.435878\pi$
$43$	2.62409	0.400170	0.200085	+	0.979779i	$0.435878\pi$
$44$	3.00280	0.452689
$45$	1.04728	0.156119
$46$	1.59047	0.234502
$47$	8.53952	1.24562	0.622809	−	0.782374i	$-0.285991\pi$
$47$	8.53952	1.24562	0.622809	+	0.782374i	$0.285991\pi$
$48$	2.78129	0.401445
$49$	−6.60932	−0.944189
$50$	−4.95109	−0.700190
$51$	12.8114	1.79396
$52$	−1.42882	−0.198142
$53$	4.50626	0.618983	0.309491	−	0.950902i	$-0.399841\pi$
$53$	4.50626	0.618983	0.309491	+	0.950902i	$0.399841\pi$
$54$	4.82719	0.656897
$55$	0.664071	0.0895433
$56$	0.625043	0.0835249
$57$	−18.8129	−2.49183
$58$	−7.25090	−0.952090
$59$	1.39206	0.181231	0.0906157	−	0.995886i	$-0.471117\pi$
$59$	1.39206	0.181231	0.0906157	+	0.995886i	$0.471117\pi$
$60$	0.615084	0.0794071
$61$	9.06113	1.16016	0.580079	−	0.814560i	$-0.303022\pi$
$61$	9.06113	1.16016	0.580079	+	0.814560i	$0.303022\pi$
$62$	−6.25004	−0.793755
$63$	2.95995	0.372919
$64$	1.00000	0.125000
$65$	−0.315984	−0.0391930
$66$	8.35166	1.02802
$67$	−15.7522	−1.92444	−0.962218	−	0.272280i	$-0.912222\pi$
$67$	−15.7522	−1.92444	−0.962218	+	0.272280i	$0.912222\pi$
$68$	4.60629	0.558595
$69$	4.42356	0.532534
$70$	0.138229	0.0165215
$71$	15.1395	1.79673	0.898363	−	0.439254i	$-0.144757\pi$
$71$	15.1395	1.79673	0.898363	+	0.439254i	$0.144757\pi$
$72$	4.73559	0.558095
$73$	11.2069	1.31167	0.655836	−	0.754903i	$-0.272316\pi$
$73$	11.2069	1.31167	0.655836	+	0.754903i	$0.272316\pi$
$74$	2.62814	0.305515
$75$	−13.7704	−1.59007
$76$	−6.76408	−0.775893
$77$	1.87688	0.213890
$78$	−3.97397	−0.449963
$79$	6.05007	0.680686	0.340343	−	0.940301i	$-0.389457\pi$
$79$	6.05007	0.680686	0.340343	+	0.940301i	$0.389457\pi$
$80$	0.221151	0.0247254
$81$	−0.780947	−0.0867718
$82$	−6.82730	−0.753950
$83$	−14.4144	−1.58218	−0.791092	−	0.611697i	$-0.790487\pi$
$83$	−14.4144	−1.58218	−0.791092	+	0.611697i	$0.790487\pi$
$84$	1.73843	0.189678
$85$	1.01868	0.110492
$86$	2.62409	0.282963
$87$	−20.1669	−2.16212
$88$	3.00280	0.320099
$89$	16.7727	1.77791	0.888953	−	0.457998i	$-0.151433\pi$
$89$	16.7727	1.77791	0.888953	+	0.457998i	$0.151433\pi$
$90$	1.04728	0.110393
$91$	−0.893074	−0.0936196
$92$	1.59047	0.165818
$93$	−17.3832	−1.80255
$94$	8.53952	0.880785
$95$	−1.49588	−0.153474
$96$	2.78129	0.283865
$97$	−16.7963	−1.70540	−0.852701	−	0.522400i	$-0.825037\pi$
$97$	−16.7963	−1.70540	−0.852701	+	0.522400i	$0.825037\pi$
$98$	−6.60932	−0.667642
$99$	14.2200	1.42917
$100$	−4.95109	−0.495109
$101$	3.22097	0.320498	0.160249	−	0.987077i	$-0.448770\pi$
$101$	3.22097	0.320498	0.160249	+	0.987077i	$0.448770\pi$
$102$	12.8114	1.26852
$103$	9.49678	0.935745	0.467873	−	0.883796i	$-0.345021\pi$
$103$	9.49678	0.935745	0.467873	+	0.883796i	$0.345021\pi$
$104$	−1.42882	−0.140107
$105$	0.384455	0.0375189
$106$	4.50626	0.437687
$107$	12.6330	1.22128	0.610640	−	0.791908i	$-0.290912\pi$
$107$	12.6330	1.22128	0.610640	+	0.791908i	$0.290912\pi$
$108$	4.82719	0.464497
$109$	15.4966	1.48431	0.742153	−	0.670231i	$-0.233805\pi$
$109$	15.4966	1.48431	0.742153	+	0.670231i	$0.233805\pi$
$110$	0.664071	0.0633166
$111$	7.30961	0.693798
$112$	0.625043	0.0590611
$113$	−18.6567	−1.75508	−0.877538	−	0.479507i	$-0.840815\pi$
$113$	−18.6567	−1.75508	−0.877538	+	0.479507i	$0.840815\pi$
$114$	−18.8129	−1.76199
$115$	0.351733	0.0327992
$116$	−7.25090	−0.673229
$117$	−6.76631	−0.625545
$118$	1.39206	0.128150
$119$	2.87913	0.263929
$120$	0.615084	0.0561493
$121$	−1.98320	−0.180291
$122$	9.06113	0.820356
$123$	−18.9887	−1.71216
$124$	−6.25004	−0.561270
$125$	−2.20069	−0.196836
$126$	2.95995	0.263693
$127$	−21.0189	−1.86513	−0.932564	−	0.361004i	$-0.882434\pi$
$127$	−21.0189	−1.86513	−0.932564	+	0.361004i	$0.882434\pi$
$128$	1.00000	0.0883883
$129$	7.29836	0.642585
$130$	−0.315984	−0.0277137
$131$	−11.7300	−1.02485	−0.512427	−	0.858731i	$-0.671253\pi$
$131$	−11.7300	−1.02485	−0.512427	+	0.858731i	$0.671253\pi$
$132$	8.35166	0.726919
$133$	−4.22785	−0.366601
$134$	−15.7522	−1.36078
$135$	1.06754	0.0918788
$136$	4.60629	0.394986
$137$	−9.39711	−0.802849	−0.401424	−	0.915892i	$-0.631485\pi$
$137$	−9.39711	−0.802849	−0.401424	+	0.915892i	$0.631485\pi$
$138$	4.42356	0.376558
$139$	−7.56198	−0.641399	−0.320699	−	0.947181i	$-0.603918\pi$
$139$	−7.56198	−0.641399	−0.320699	+	0.947181i	$0.603918\pi$
$140$	0.138229	0.0116825
$141$	23.7509	2.00019
$142$	15.1395	1.27048
$143$	−4.29046	−0.358786
$144$	4.73559	0.394633
$145$	−1.60354	−0.133167
$146$	11.2069	0.927492
$147$	−18.3825	−1.51616
$148$	2.62814	0.216031
$149$	−3.11458	−0.255157	−0.127578	−	0.991829i	$-0.540720\pi$
$149$	−3.11458	−0.255157	−0.127578	+	0.991829i	$0.540720\pi$
$150$	−13.7704	−1.12435
$151$	−0.763004	−0.0620924	−0.0310462	−	0.999518i	$-0.509884\pi$
$151$	−0.763004	−0.0620924	−0.0310462	+	0.999518i	$0.509884\pi$
$152$	−6.76408	−0.548640
$153$	21.8135	1.76352
$154$	1.87688	0.151243
$155$	−1.38220	−0.111021
$156$	−3.97397	−0.318172
$157$	16.0307	1.27939	0.639694	−	0.768630i	$-0.279061\pi$
$157$	16.0307	1.27939	0.639694	+	0.768630i	$0.279061\pi$
$158$	6.05007	0.481317
$159$	12.5332	0.993951
$160$	0.221151	0.0174835
$161$	0.994111	0.0783469
$162$	−0.780947	−0.0613570
$163$	5.20235	0.407480	0.203740	−	0.979025i	$-0.434690\pi$
$163$	5.20235	0.407480	0.203740	+	0.979025i	$0.434690\pi$
$164$	−6.82730	−0.533123
$165$	1.84698	0.143787
$166$	−14.4144	−1.11877
$167$	−23.3254	−1.80497	−0.902487	−	0.430717i	$-0.858261\pi$
$167$	−23.3254	−1.80497	−0.902487	+	0.430717i	$0.858261\pi$
$168$	1.73843	0.134123
$169$	−10.9585	−0.842960
$170$	1.01868	0.0781294
$171$	−32.0319	−2.44954
$172$	2.62409	0.200085
$173$	−16.9882	−1.29159	−0.645794	−	0.763512i	$-0.723473\pi$
$173$	−16.9882	−1.29159	−0.645794	+	0.763512i	$0.723473\pi$
$174$	−20.1669	−1.52885
$175$	−3.09465	−0.233933
$176$	3.00280	0.226344
$177$	3.87174	0.291018
$178$	16.7727	1.25717
$179$	−8.14151	−0.608525	−0.304262	−	0.952588i	$-0.598410\pi$
$179$	−8.14151	−0.608525	−0.304262	+	0.952588i	$0.598410\pi$
$180$	1.04728	0.0780595
$181$	11.9688	0.889638	0.444819	−	0.895621i	$-0.353268\pi$
$181$	11.9688	0.889638	0.444819	+	0.895621i	$0.353268\pi$
$182$	−0.893074	−0.0661991
$183$	25.2017	1.86296
$184$	1.59047	0.117251
$185$	0.581214	0.0427317
$186$	−17.3832	−1.27460
$187$	13.8318	1.01148
$188$	8.53952	0.622809
$189$	3.01720	0.219469
$190$	−1.49588	−0.108523
$191$	−7.86991	−0.569447	−0.284723	−	0.958610i	$-0.591902\pi$
$191$	−7.86991	−0.569447	−0.284723	+	0.958610i	$0.591902\pi$
$192$	2.78129	0.200723
$193$	−0.820086	−0.0590311	−0.0295155	−	0.999564i	$-0.509396\pi$
$193$	−0.820086	−0.0590311	−0.0295155	+	0.999564i	$0.509396\pi$
$194$	−16.7963	−1.20590
$195$	−0.878845	−0.0629354
$196$	−6.60932	−0.472094
$197$	2.69274	0.191850	0.0959250	−	0.995389i	$-0.469419\pi$
$197$	2.69274	0.191850	0.0959250	+	0.995389i	$0.469419\pi$
$198$	14.2200	1.01057
$199$	−13.0340	−0.923958	−0.461979	−	0.886891i	$-0.652860\pi$
$199$	−13.0340	−0.923958	−0.461979	+	0.886891i	$0.652860\pi$
$200$	−4.95109	−0.350095
$201$	−43.8115	−3.09022
$202$	3.22097	0.226626
$203$	−4.53213	−0.318093
$204$	12.8114	0.896980
$205$	−1.50986	−0.105453
$206$	9.49678	0.661672
$207$	7.53180	0.523497
$208$	−1.42882	−0.0990708
$209$	−20.3112	−1.40495
$210$	0.384455	0.0265299
$211$	9.46429	0.651549	0.325774	−	0.945448i	$-0.394375\pi$
$211$	9.46429	0.651549	0.325774	+	0.945448i	$0.394375\pi$
$212$	4.50626	0.309491
$213$	42.1073	2.88515
$214$	12.6330	0.863576
$215$	0.580319	0.0395774
$216$	4.82719	0.328449
$217$	−3.90654	−0.265193
$218$	15.4966	1.04956
$219$	31.1698	2.10626
$220$	0.664071	0.0447716
$221$	−6.58156	−0.442723
$222$	7.30961	0.490589
$223$	12.2620	0.821127	0.410563	−	0.911832i	$-0.365332\pi$
$223$	12.2620	0.821127	0.410563	+	0.911832i	$0.365332\pi$
$224$	0.625043	0.0417625
$225$	−23.4464	−1.56309
$226$	−18.6567	−1.24103
$227$	19.8681	1.31869	0.659347	−	0.751839i	$-0.270833\pi$
$227$	19.8681	1.31869	0.659347	+	0.751839i	$0.270833\pi$
$228$	−18.8129	−1.24591
$229$	20.5794	1.35992	0.679961	−	0.733248i	$-0.261997\pi$
$229$	20.5794	1.35992	0.679961	+	0.733248i	$0.261997\pi$
$230$	0.351733	0.0231926
$231$	5.22015	0.343461
$232$	−7.25090	−0.476045
$233$	−18.7148	−1.22604	−0.613022	−	0.790066i	$-0.710046\pi$
$233$	−18.7148	−1.22604	−0.613022	+	0.790066i	$0.710046\pi$
$234$	−6.76631	−0.442327
$235$	1.88852	0.123193
$236$	1.39206	0.0906157
$237$	16.8270	1.09303
$238$	2.87913	0.186626
$239$	5.97285	0.386351	0.193176	−	0.981164i	$-0.438121\pi$
$239$	5.97285	0.386351	0.193176	+	0.981164i	$0.438121\pi$
$240$	0.615084	0.0397035
$241$	27.1973	1.75193	0.875965	−	0.482375i	$-0.160226\pi$
$241$	27.1973	1.75193	0.875965	+	0.482375i	$0.160226\pi$
$242$	−1.98320	−0.127485
$243$	−16.6536	−1.06833
$244$	9.06113	0.580079
$245$	−1.46165	−0.0933817
$246$	−18.9887	−1.21068
$247$	9.66465	0.614947
$248$	−6.25004	−0.396878
$249$	−40.0906	−2.54064
$250$	−2.20069	−0.139184
$251$	21.0955	1.33153	0.665767	−	0.746159i	$-0.268104\pi$
$251$	21.0955	1.33153	0.665767	+	0.746159i	$0.268104\pi$
$252$	2.95995	0.186459
$253$	4.77585	0.300255
$254$	−21.0189	−1.31885
$255$	2.83326	0.177425
$256$	1.00000	0.0625000
$257$	17.9409	1.11912	0.559560	−	0.828790i	$-0.310970\pi$
$257$	17.9409	1.11912	0.559560	+	0.828790i	$0.310970\pi$
$258$	7.29836	0.454376
$259$	1.64270	0.102072
$260$	−0.315984	−0.0195965
$261$	−34.3373	−2.12543
$262$	−11.7300	−0.724681
$263$	−13.3591	−0.823756	−0.411878	−	0.911239i	$-0.635127\pi$
$263$	−13.3591	−0.823756	−0.411878	+	0.911239i	$0.635127\pi$
$264$	8.35166	0.514009
$265$	0.996563	0.0612184
$266$	−4.22785	−0.259226
$267$	46.6499	2.85493
$268$	−15.7522	−0.962218
$269$	3.15080	0.192108	0.0960538	−	0.995376i	$-0.469378\pi$
$269$	3.15080	0.192108	0.0960538	+	0.995376i	$0.469378\pi$
$270$	1.06754	0.0649681
$271$	18.1597	1.10312	0.551560	−	0.834135i	$-0.314033\pi$
$271$	18.1597	1.10312	0.551560	+	0.834135i	$0.314033\pi$
$272$	4.60629	0.279297
$273$	−2.48390	−0.150333
$274$	−9.39711	−0.567700
$275$	−14.8671	−0.896522
$276$	4.42356	0.266267
$277$	−15.9402	−0.957757	−0.478878	−	0.877881i	$-0.658956\pi$
$277$	−15.9402	−0.957757	−0.478878	+	0.877881i	$0.658956\pi$
$278$	−7.56198	−0.453537
$279$	−29.5976	−1.77196
$280$	0.138229	0.00826074
$281$	0.784228	0.0467831	0.0233916	−	0.999726i	$-0.492554\pi$
$281$	0.784228	0.0467831	0.0233916	+	0.999726i	$0.492554\pi$
$282$	23.7509	1.41435
$283$	−21.1158	−1.25521	−0.627603	−	0.778533i	$-0.715964\pi$
$283$	−21.1158	−1.25521	−0.627603	+	0.778533i	$0.715964\pi$
$284$	15.1395	0.898363
$285$	−4.16048	−0.246446
$286$	−4.29046	−0.253700
$287$	−4.26736	−0.251894
$288$	4.73559	0.279047
$289$	4.21790	0.248112
$290$	−1.60354	−0.0941631
$291$	−46.7153	−2.73850
$292$	11.2069	0.655836
$293$	14.8386	0.866878	0.433439	−	0.901183i	$-0.357300\pi$
$293$	14.8386	0.866878	0.433439	+	0.901183i	$0.357300\pi$
$294$	−18.3825	−1.07209
$295$	0.307856	0.0179241
$296$	2.62814	0.152757
$297$	14.4951	0.841090
$298$	−3.11458	−0.180423
$299$	−2.27249	−0.131422
$300$	−13.7704	−0.795037
$301$	1.64017	0.0945378
$302$	−0.763004	−0.0439059
$303$	8.95845	0.514649
$304$	−6.76408	−0.387947
$305$	2.00387	0.114741
$306$	21.8135	1.24699
$307$	17.1973	0.981504	0.490752	−	0.871299i	$-0.336722\pi$
$307$	17.1973	0.981504	0.490752	+	0.871299i	$0.336722\pi$
$308$	1.87688	0.106945
$309$	26.4133	1.50260
$310$	−1.38220	−0.0785036
$311$	30.5495	1.73230	0.866151	−	0.499782i	$-0.166586\pi$
$311$	30.5495	1.73230	0.866151	+	0.499782i	$0.166586\pi$
$312$	−3.97397	−0.224982
$313$	0.196432	0.0111030	0.00555149	−	0.999985i	$-0.498233\pi$
$313$	0.196432	0.0111030	0.00555149	+	0.999985i	$0.498233\pi$
$314$	16.0307	0.904664
$315$	0.654595	0.0368822
$316$	6.05007	0.340343
$317$	−6.49637	−0.364873	−0.182436	−	0.983218i	$-0.558398\pi$
$317$	−6.49637	−0.364873	−0.182436	+	0.983218i	$0.558398\pi$
$318$	12.5332	0.702829
$319$	−21.7730	−1.21905
$320$	0.221151	0.0123627
$321$	35.1361	1.96111
$322$	0.994111	0.0553997
$323$	−31.1573	−1.73364
$324$	−0.780947	−0.0433859
$325$	7.07422	0.392407
$326$	5.20235	0.288132
$327$	43.1006	2.38347
$328$	−6.82730	−0.376975
$329$	5.33757	0.294270
$330$	1.84698	0.101673
$331$	11.2337	0.617460	0.308730	−	0.951150i	$-0.400096\pi$
$331$	11.2337	0.617460	0.308730	+	0.951150i	$0.400096\pi$
$332$	−14.4144	−0.791092
$333$	12.4458	0.682024
$334$	−23.3254	−1.27631
$335$	−3.48361	−0.190330
$336$	1.73843	0.0948391
$337$	−9.29957	−0.506580	−0.253290	−	0.967390i	$-0.581513\pi$
$337$	−9.29957	−0.506580	−0.253290	+	0.967390i	$0.581513\pi$
$338$	−10.9585	−0.596062
$339$	−51.8898	−2.81827
$340$	1.01868	0.0552459
$341$	−18.7676	−1.01632
$342$	−32.0319	−1.73209
$343$	−8.50642	−0.459303
$344$	2.62409	0.141481
$345$	0.978272	0.0526684
$346$	−16.9882	−0.913291
$347$	18.3134	0.983113	0.491556	−	0.870846i	$-0.336428\pi$
$347$	18.3134	0.983113	0.491556	+	0.870846i	$0.336428\pi$
$348$	−20.1669	−1.08106
$349$	−26.7072	−1.42960	−0.714801	−	0.699328i	$-0.753483\pi$
$349$	−26.7072	−1.42960	−0.714801	+	0.699328i	$0.753483\pi$
$350$	−3.09465	−0.165416
$351$	−6.89718	−0.368144
$352$	3.00280	0.160050
$353$	28.5286	1.51842	0.759212	−	0.650844i	$-0.225585\pi$
$353$	28.5286	1.51842	0.759212	+	0.650844i	$0.225585\pi$
$354$	3.87174	0.205781
$355$	3.34810	0.177699
$356$	16.7727	0.888953
$357$	8.00771	0.423813
$358$	−8.14151	−0.430292
$359$	−26.8279	−1.41592	−0.707961	−	0.706252i	$-0.750385\pi$
$359$	−26.8279	−1.41592	−0.707961	+	0.706252i	$0.750385\pi$
$360$	1.04728	0.0551964
$361$	26.7528	1.40804
$362$	11.9688	0.629069
$363$	−5.51586	−0.289507
$364$	−0.893074	−0.0468098
$365$	2.47842	0.129726
$366$	25.2017	1.31731
$367$	−22.2116	−1.15944	−0.579719	−	0.814816i	$-0.696838\pi$
$367$	−22.2116	−1.15944	−0.579719	+	0.814816i	$0.696838\pi$
$368$	1.59047	0.0829088
$369$	−32.3313	−1.68310
$370$	0.581214	0.0302159
$371$	2.81661	0.146231
$372$	−17.3832	−0.901276
$373$	31.9530	1.65446	0.827232	−	0.561860i	$-0.189914\pi$
$373$	31.9530	1.65446	0.827232	+	0.561860i	$0.189914\pi$
$374$	13.8318	0.715223
$375$	−6.12076	−0.316075
$376$	8.53952	0.440392
$377$	10.3602	0.533579
$378$	3.01720	0.155188
$379$	26.3174	1.35183	0.675917	−	0.736977i	$-0.263748\pi$
$379$	26.3174	1.35183	0.675917	+	0.736977i	$0.263748\pi$
$380$	−1.49588	−0.0767371
$381$	−58.4598	−2.99499
$382$	−7.86991	−0.402660
$383$	−15.2755	−0.780543	−0.390272	−	0.920700i	$-0.627619\pi$
$383$	−15.2755	−0.780543	−0.390272	+	0.920700i	$0.627619\pi$
$384$	2.78129	0.141932
$385$	0.415073	0.0211541
$386$	−0.820086	−0.0417413
$387$	12.4266	0.631680
$388$	−16.7963	−0.852701
$389$	−18.8031	−0.953354	−0.476677	−	0.879079i	$-0.658159\pi$
$389$	−18.8031	−0.953354	−0.476677	+	0.879079i	$0.658159\pi$
$390$	−0.878845	−0.0445020
$391$	7.32615	0.370499
$392$	−6.60932	−0.333821
$393$	−32.6245	−1.64569
$394$	2.69274	0.135658
$395$	1.33798	0.0673208
$396$	14.2200	0.714583
$397$	9.08989	0.456208	0.228104	−	0.973637i	$-0.426747\pi$
$397$	9.08989	0.456208	0.228104	+	0.973637i	$0.426747\pi$
$398$	−13.0340	−0.653337
$399$	−11.7589	−0.588680
$400$	−4.95109	−0.247555
$401$	5.94395	0.296827	0.148413	−	0.988925i	$-0.452583\pi$
$401$	5.94395	0.296827	0.148413	+	0.988925i	$0.452583\pi$
$402$	−43.8115	−2.18512
$403$	8.93018	0.444844
$404$	3.22097	0.160249
$405$	−0.172707	−0.00858187
$406$	−4.53213	−0.224926
$407$	7.89176	0.391180
$408$	12.8114	0.634261
$409$	−2.25225	−0.111367	−0.0556834	−	0.998448i	$-0.517734\pi$
$409$	−2.25225	−0.111367	−0.0556834	+	0.998448i	$0.517734\pi$
$410$	−1.50986	−0.0745668
$411$	−26.1361	−1.28920
$412$	9.49678	0.467873
$413$	0.870101	0.0428149
$414$	7.53180	0.370168
$415$	−3.18775	−0.156480
$416$	−1.42882	−0.0700537
$417$	−21.0321	−1.02995
$418$	−20.3112	−0.993452
$419$	25.6083	1.25105	0.625525	−	0.780204i	$-0.284885\pi$
$419$	25.6083	1.25105	0.625525	+	0.780204i	$0.284885\pi$
$420$	0.384455	0.0187595
$421$	−3.30259	−0.160958	−0.0804791	−	0.996756i	$-0.525645\pi$
$421$	−3.30259	−0.160958	−0.0804791	+	0.996756i	$0.525645\pi$
$422$	9.46429	0.460714
$423$	40.4397	1.96625
$424$	4.50626	0.218843
$425$	−22.8062	−1.10626
$426$	42.1073	2.04011
$427$	5.66360	0.274081
$428$	12.6330	0.610640
$429$	−11.9330	−0.576132
$430$	0.580319	0.0279854
$431$	6.08762	0.293231	0.146615	−	0.989194i	$-0.453162\pi$
$431$	6.08762	0.293231	0.146615	+	0.989194i	$0.453162\pi$
$432$	4.82719	0.232248
$433$	−15.5156	−0.745632	−0.372816	−	0.927905i	$-0.621608\pi$
$433$	−15.5156	−0.745632	−0.372816	+	0.927905i	$0.621608\pi$
$434$	−3.90654	−0.187520
$435$	−4.45992	−0.213837
$436$	15.4966	0.742153
$437$	−10.7581	−0.514627
$438$	31.1698	1.48935
$439$	−5.87942	−0.280609	−0.140305	−	0.990108i	$-0.544808\pi$
$439$	−5.87942	−0.280609	−0.140305	+	0.990108i	$0.544808\pi$
$440$	0.664071	0.0316583
$441$	−31.2990	−1.49043
$442$	−6.58156	−0.313053
$443$	17.5074	0.831800	0.415900	−	0.909410i	$-0.363467\pi$
$443$	17.5074	0.831800	0.415900	+	0.909410i	$0.363467\pi$
$444$	7.30961	0.346899
$445$	3.70930	0.175838
$446$	12.2620	0.580624
$447$	−8.66257	−0.409725
$448$	0.625043	0.0295305
$449$	1.24584	0.0587950	0.0293975	−	0.999568i	$-0.490641\pi$
$449$	1.24584	0.0587950	0.0293975	+	0.999568i	$0.490641\pi$
$450$	−23.4464	−1.10527
$451$	−20.5010	−0.965355
$452$	−18.6567	−0.877538
$453$	−2.12214	−0.0997067
$454$	19.8681	0.932457
$455$	−0.197504	−0.00925913
$456$	−18.8129	−0.880995
$457$	−3.43136	−0.160512	−0.0802561	−	0.996774i	$-0.525574\pi$
$457$	−3.43136	−0.160512	−0.0802561	+	0.996774i	$0.525574\pi$
$458$	20.5794	0.961610
$459$	22.2354	1.03786
$460$	0.351733	0.0163996
$461$	3.90957	0.182087	0.0910433	−	0.995847i	$-0.470980\pi$
$461$	3.90957	0.182087	0.0910433	+	0.995847i	$0.470980\pi$
$462$	5.22015	0.242863
$463$	34.2091	1.58983	0.794915	−	0.606721i	$-0.207515\pi$
$463$	34.2091	1.58983	0.794915	+	0.606721i	$0.207515\pi$
$464$	−7.25090	−0.336615
$465$	−3.84430	−0.178275
$466$	−18.7148	−0.866944
$467$	−23.7349	−1.09832	−0.549160	−	0.835718i	$-0.685052\pi$
$467$	−23.7349	−1.09832	−0.549160	+	0.835718i	$0.685052\pi$
$468$	−6.76631	−0.312773
$469$	−9.84580	−0.454637
$470$	1.88852	0.0871109
$471$	44.5861	2.05442
$472$	1.39206	0.0640750
$473$	7.87961	0.362305
$474$	16.8270	0.772890
$475$	33.4896	1.53661
$476$	2.87913	0.131965
$477$	21.3398	0.977083
$478$	5.97285	0.273192
$479$	0.126165	0.00576464	0.00288232	−	0.999996i	$-0.499083\pi$
$479$	0.126165	0.00576464	0.00288232	+	0.999996i	$0.499083\pi$
$480$	0.615084	0.0280746
$481$	−3.75513	−0.171219
$482$	27.1973	1.23880
$483$	2.76491	0.125808
$484$	−1.98320	−0.0901454
$485$	−3.71450	−0.168667
$486$	−16.6536	−0.755423
$487$	29.0131	1.31471	0.657354	−	0.753582i	$-0.271676\pi$
$487$	29.0131	1.31471	0.657354	+	0.753582i	$0.271676\pi$
$488$	9.06113	0.410178
$489$	14.4693	0.654323
$490$	−1.46165	−0.0660308
$491$	15.9849	0.721388	0.360694	−	0.932684i	$-0.382540\pi$
$491$	15.9849	0.721388	0.360694	+	0.932684i	$0.382540\pi$
$492$	−18.9887	−0.856078
$493$	−33.3997	−1.50425
$494$	9.66465	0.434833
$495$	3.14477	0.141347
$496$	−6.25004	−0.280635
$497$	9.46283	0.424466
$498$	−40.0906	−1.79650
$499$	−14.9042	−0.667203	−0.333602	−	0.942714i	$-0.608264\pi$
$499$	−14.9042	−0.667203	−0.333602	+	0.942714i	$0.608264\pi$
$500$	−2.20069	−0.0984178
$501$	−64.8748	−2.89839
$502$	21.0955	0.941537
$503$	−32.7997	−1.46247	−0.731233	−	0.682128i	$-0.761055\pi$
$503$	−32.7997	−1.46247	−0.731233	+	0.682128i	$0.761055\pi$
$504$	2.95995	0.131847
$505$	0.712318	0.0316977
$506$	4.77585	0.212313
$507$	−30.4787	−1.35361
$508$	−21.0189	−0.932564
$509$	−20.9708	−0.929515	−0.464757	−	0.885438i	$-0.653858\pi$
$509$	−20.9708	−0.929515	−0.464757	+	0.885438i	$0.653858\pi$
$510$	2.83326	0.125459
$511$	7.00482	0.309875
$512$	1.00000	0.0441942
$513$	−32.6515	−1.44160
$514$	17.9409	0.791338
$515$	2.10022	0.0925466
$516$	7.29836	0.321292
$517$	25.6425	1.12775
$518$	1.64270	0.0721760
$519$	−47.2491	−2.07401
$520$	−0.315984	−0.0138568
$521$	−4.03540	−0.176794	−0.0883971	−	0.996085i	$-0.528174\pi$
$521$	−4.03540	−0.176794	−0.0883971	+	0.996085i	$0.528174\pi$
$522$	−34.3373	−1.50290
$523$	7.06380	0.308878	0.154439	−	0.988002i	$-0.450643\pi$
$523$	7.06380	0.308878	0.154439	+	0.988002i	$0.450643\pi$
$524$	−11.7300	−0.512427
$525$	−8.60712	−0.375646
$526$	−13.3591	−0.582484
$527$	−28.7895	−1.25409
$528$	8.35166	0.363460
$529$	−20.4704	−0.890018
$530$	0.996563	0.0432879
$531$	6.59225	0.286079
$532$	−4.22785	−0.183300
$533$	9.75499	0.422535
$534$	46.6499	2.01874
$535$	2.79380	0.120786
$536$	−15.7522	−0.680391
$537$	−22.6439	−0.977157
$538$	3.15080	0.135841
$539$	−19.8465	−0.854848
$540$	1.06754	0.0459394
$541$	−3.29240	−0.141551	−0.0707756	−	0.997492i	$-0.522547\pi$
$541$	−3.29240	−0.141551	−0.0707756	+	0.997492i	$0.522547\pi$
$542$	18.1597	0.780024
$543$	33.2889	1.42856
$544$	4.60629	0.197493
$545$	3.42708	0.146800
$546$	−2.48390	−0.106301
$547$	−21.4258	−0.916100	−0.458050	−	0.888926i	$-0.651452\pi$
$547$	−21.4258	−0.916100	−0.458050	+	0.888926i	$0.651452\pi$
$548$	−9.39711	−0.401424
$549$	42.9098	1.83135
$550$	−14.8671	−0.633937
$551$	49.0457	2.08942
$552$	4.42356	0.188279
$553$	3.78155	0.160808
$554$	−15.9402	−0.677236
$555$	1.61653	0.0686177
$556$	−7.56198	−0.320699
$557$	−31.8393	−1.34908	−0.674538	−	0.738240i	$-0.735657\pi$
$557$	−31.8393	−1.34908	−0.674538	+	0.738240i	$0.735657\pi$
$558$	−29.5976	−1.25297
$559$	−3.74935	−0.158581
$560$	0.138229	0.00584123
$561$	38.4702	1.62421
$562$	0.784228	0.0330807
$563$	6.35033	0.267634	0.133817	−	0.991006i	$-0.457277\pi$
$563$	6.35033	0.267634	0.133817	+	0.991006i	$0.457277\pi$
$564$	23.7509	1.00009
$565$	−4.12594	−0.173580
$566$	−21.1158	−0.887565
$567$	−0.488126	−0.0204993
$568$	15.1395	0.635238
$569$	26.2881	1.10206	0.551028	−	0.834487i	$-0.314236\pi$
$569$	26.2881	1.10206	0.551028	+	0.834487i	$0.314236\pi$
$570$	−4.16048	−0.174263
$571$	−3.93616	−0.164723	−0.0823615	−	0.996603i	$-0.526246\pi$
$571$	−3.93616	−0.164723	−0.0823615	+	0.996603i	$0.526246\pi$
$572$	−4.29046	−0.179393
$573$	−21.8885	−0.914407
$574$	−4.26736	−0.178116
$575$	−7.87455	−0.328392
$576$	4.73559	0.197316
$577$	10.9456	0.455671	0.227835	−	0.973700i	$-0.426835\pi$
$577$	10.9456	0.455671	0.227835	+	0.973700i	$0.426835\pi$
$578$	4.21790	0.175441
$579$	−2.28090	−0.0947909
$580$	−1.60354	−0.0665834
$581$	−9.00962	−0.373782
$582$	−46.7153	−1.93641
$583$	13.5314	0.560413
$584$	11.2069	0.463746
$585$	−1.49637	−0.0618674
$586$	14.8386	0.612976
$587$	−10.4314	−0.430551	−0.215275	−	0.976553i	$-0.569065\pi$
$587$	−10.4314	−0.430551	−0.215275	+	0.976553i	$0.569065\pi$
$588$	−18.3825	−0.758080
$589$	42.2758	1.74194
$590$	0.307856	0.0126742
$591$	7.48930	0.308069
$592$	2.62814	0.108016
$593$	−15.1081	−0.620415	−0.310207	−	0.950669i	$-0.600398\pi$
$593$	−15.1081	−0.620415	−0.310207	+	0.950669i	$0.600398\pi$
$594$	14.4951	0.594740
$595$	0.636721	0.0261030
$596$	−3.11458	−0.127578
$597$	−36.2515	−1.48367
$598$	−2.27249	−0.0929291
$599$	6.20232	0.253420	0.126710	−	0.991940i	$-0.459558\pi$
$599$	6.20232	0.253420	0.126710	+	0.991940i	$0.459558\pi$
$600$	−13.7704	−0.562176
$601$	−3.13407	−0.127841	−0.0639206	−	0.997955i	$-0.520360\pi$
$601$	−3.13407	−0.127841	−0.0639206	+	0.997955i	$0.520360\pi$
$602$	1.64017	0.0668483
$603$	−74.5959	−3.03778
$604$	−0.763004	−0.0310462
$605$	−0.438586	−0.0178310
$606$	8.95845	0.363912
$607$	41.5053	1.68465	0.842324	−	0.538971i	$-0.181187\pi$
$607$	41.5053	1.68465	0.842324	+	0.538971i	$0.181187\pi$
$608$	−6.76408	−0.274320
$609$	−12.6052	−0.510787
$610$	2.00387	0.0811345
$611$	−12.2014	−0.493617
$612$	21.8135	0.881759
$613$	−15.8080	−0.638479	−0.319239	−	0.947674i	$-0.603427\pi$
$613$	−15.8080	−0.638479	−0.319239	+	0.947674i	$0.603427\pi$
$614$	17.1973	0.694028
$615$	−4.19937	−0.169335
$616$	1.87688	0.0756216
$617$	7.89516	0.317847	0.158924	−	0.987291i	$-0.449198\pi$
$617$	7.89516	0.317847	0.158924	+	0.987291i	$0.449198\pi$
$618$	26.4133	1.06250
$619$	23.4650	0.943138	0.471569	−	0.881829i	$-0.343688\pi$
$619$	23.4650	0.943138	0.471569	+	0.881829i	$0.343688\pi$
$620$	−1.38220	−0.0555104
$621$	7.67749	0.308087
$622$	30.5495	1.22492
$623$	10.4837	0.420020
$624$	−3.97397	−0.159086
$625$	24.2688	0.970751
$626$	0.196432	0.00785100
$627$	−56.4913	−2.25605
$628$	16.0307	0.639694
$629$	12.1060	0.482696
$630$	0.654595	0.0260797
$631$	26.7997	1.06688	0.533440	−	0.845838i	$-0.320899\pi$
$631$	26.7997	1.06688	0.533440	+	0.845838i	$0.320899\pi$
$632$	6.05007	0.240659
$633$	26.3230	1.04624
$634$	−6.49637	−0.258004
$635$	−4.64835	−0.184464
$636$	12.5332	0.496975
$637$	9.44353	0.374166
$638$	−21.7730	−0.862001
$639$	71.6944	2.83619
$640$	0.221151	0.00874174
$641$	−3.03428	−0.119847	−0.0599235	−	0.998203i	$-0.519086\pi$
$641$	−3.03428	−0.119847	−0.0599235	+	0.998203i	$0.519086\pi$
$642$	35.1361	1.38671
$643$	−10.2714	−0.405064	−0.202532	−	0.979276i	$-0.564917\pi$
$643$	−10.2714	−0.405064	−0.202532	+	0.979276i	$0.564917\pi$
$644$	0.994111	0.0391735
$645$	1.61404	0.0635526
$646$	−31.1573	−1.22587
$647$	43.2824	1.70161	0.850804	−	0.525484i	$-0.176116\pi$
$647$	43.2824	1.70161	0.850804	+	0.525484i	$0.176116\pi$
$648$	−0.780947	−0.0306785
$649$	4.18009	0.164083
$650$	7.07422	0.277474
$651$	−10.8652	−0.425842
$652$	5.20235	0.203740
$653$	24.6993	0.966558	0.483279	−	0.875466i	$-0.339446\pi$
$653$	24.6993	0.966558	0.483279	+	0.875466i	$0.339446\pi$
$654$	43.1006	1.68537
$655$	−2.59409	−0.101360
$656$	−6.82730	−0.266561
$657$	53.0714	2.07051
$658$	5.33757	0.208080
$659$	−37.0909	−1.44486	−0.722428	−	0.691446i	$-0.756974\pi$
$659$	−37.0909	−1.44486	−0.722428	+	0.691446i	$0.756974\pi$
$660$	1.84698	0.0718934
$661$	−34.7335	−1.35098	−0.675488	−	0.737371i	$-0.736067\pi$
$661$	−34.7335	−1.35098	−0.675488	+	0.737371i	$0.736067\pi$
$662$	11.2337	0.436610
$663$	−18.3052	−0.710917
$664$	−14.4144	−0.559387
$665$	−0.934990	−0.0362574
$666$	12.4458	0.482264
$667$	−11.5323	−0.446533
$668$	−23.3254	−0.902487
$669$	34.1043	1.31855
$670$	−3.48361	−0.134583
$671$	27.2087	1.05038
$672$	1.73843	0.0670614
$673$	−3.70311	−0.142745	−0.0713723	−	0.997450i	$-0.522738\pi$
$673$	−3.70311	−0.142745	−0.0713723	+	0.997450i	$0.522738\pi$
$674$	−9.29957	−0.358206
$675$	−23.8999	−0.919906
$676$	−10.9585	−0.421480
$677$	−23.7618	−0.913239	−0.456620	−	0.889662i	$-0.650940\pi$
$677$	−23.7618	−0.913239	−0.456620	+	0.889662i	$0.650940\pi$
$678$	−51.8898	−1.99282
$679$	−10.4984	−0.402891
$680$	1.01868	0.0390647
$681$	55.2591	2.11753
$682$	−18.7676	−0.718649
$683$	42.0989	1.61087	0.805435	−	0.592684i	$-0.201932\pi$
$683$	42.0989	1.61087	0.805435	+	0.592684i	$0.201932\pi$
$684$	−32.0319	−1.22477
$685$	−2.07818	−0.0794030
$686$	−8.50642	−0.324776
$687$	57.2372	2.18374
$688$	2.62409	0.100042
$689$	−6.43864	−0.245293
$690$	0.978272	0.0372422
$691$	39.1121	1.48789	0.743947	−	0.668238i	$-0.232951\pi$
$691$	39.1121	1.48789	0.743947	+	0.668238i	$0.232951\pi$
$692$	−16.9882	−0.645794
$693$	8.88814	0.337632
$694$	18.3134	0.695166
$695$	−1.67234	−0.0634353
$696$	−20.1669	−0.764423
$697$	−31.4485	−1.19120
$698$	−26.7072	−1.01088
$699$	−52.0512	−1.96876
$700$	−3.09465	−0.116967
$701$	−5.48511	−0.207170	−0.103585	−	0.994621i	$-0.533031\pi$
$701$	−5.48511	−0.207170	−0.103585	+	0.994621i	$0.533031\pi$
$702$	−6.89718	−0.260317
$703$	−17.7769	−0.670469
$704$	3.00280	0.113172
$705$	5.25253	0.197822
$706$	28.5286	1.07369
$707$	2.01324	0.0757158
$708$	3.87174	0.145509
$709$	−33.6406	−1.26340	−0.631699	−	0.775214i	$-0.717642\pi$
$709$	−33.6406	−1.26340	−0.631699	+	0.775214i	$0.717642\pi$
$710$	3.34810	0.125652
$711$	28.6506	1.07448
$712$	16.7727	0.628585
$713$	−9.94048	−0.372274
$714$	8.00771	0.299681
$715$	−0.948837	−0.0354845
$716$	−8.14151	−0.304262
$717$	16.6122	0.620396
$718$	−26.8279	−1.00121
$719$	51.9949	1.93908	0.969542	−	0.244924i	$-0.0787632\pi$
$719$	51.9949	1.93908	0.969542	+	0.244924i	$0.0787632\pi$
$720$	1.04728	0.0390298
$721$	5.93590	0.221064
$722$	26.7528	0.995637
$723$	75.6436	2.81321
$724$	11.9688	0.444819
$725$	35.8999	1.33329
$726$	−5.51586	−0.204713
$727$	40.9747	1.51967	0.759834	−	0.650117i	$-0.225280\pi$
$727$	40.9747	1.51967	0.759834	+	0.650117i	$0.225280\pi$
$728$	−0.893074	−0.0330995
$729$	−43.9757	−1.62873
$730$	2.47842	0.0917304
$731$	12.0873	0.447065
$732$	25.2017	0.931480
$733$	47.4101	1.75113	0.875566	−	0.483099i	$-0.160489\pi$
$733$	47.4101	1.75113	0.875566	+	0.483099i	$0.160489\pi$
$734$	−22.2116	−0.819847
$735$	−4.06529	−0.149951
$736$	1.59047	0.0586254
$737$	−47.3007	−1.74234
$738$	−32.3313	−1.19013
$739$	25.6307	0.942840	0.471420	−	0.881909i	$-0.343742\pi$
$739$	25.6307	0.942840	0.471420	+	0.881909i	$0.343742\pi$
$740$	0.581214	0.0213658
$741$	26.8802	0.987470
$742$	2.81661	0.103401
$743$	−32.2421	−1.18285	−0.591424	−	0.806361i	$-0.701434\pi$
$743$	−32.2421	−1.18285	−0.591424	+	0.806361i	$0.701434\pi$
$744$	−17.3832	−0.637298
$745$	−0.688792	−0.0252354
$746$	31.9530	1.16988
$747$	−68.2607	−2.49753
$748$	13.8318	0.505739
$749$	7.89619	0.288520
$750$	−6.12076	−0.223499
$751$	−1.00000	−0.0364905
$751$	−1.00000	−0.0364905
$752$	8.53952	0.311404
$753$	58.6727	2.13815
$754$	10.3602	0.377297
$755$	−0.168739	−0.00614103
$756$	3.01720	0.109735
$757$	−3.84648	−0.139803	−0.0699013	−	0.997554i	$-0.522268\pi$
$757$	−3.84648	−0.139803	−0.0699013	+	0.997554i	$0.522268\pi$
$758$	26.3174	0.955892
$759$	13.2830	0.482144
$760$	−1.49588	−0.0542613
$761$	−13.9352	−0.505152	−0.252576	−	0.967577i	$-0.581278\pi$
$761$	−13.9352	−0.505152	−0.252576	+	0.967577i	$0.581278\pi$
$762$	−58.4598	−2.11778
$763$	9.68605	0.350659
$764$	−7.86991	−0.284723
$765$	4.82407	0.174415
$766$	−15.2755	−0.551927
$767$	−1.98901	−0.0718190
$768$	2.78129	0.100361
$769$	−32.8364	−1.18411	−0.592056	−	0.805897i	$-0.701683\pi$
$769$	−32.8364	−1.18411	−0.592056	+	0.805897i	$0.701683\pi$
$770$	0.415073	0.0149582
$771$	49.8988	1.79706
$772$	−0.820086	−0.0295155
$773$	14.5246	0.522412	0.261206	−	0.965283i	$-0.415880\pi$
$773$	14.5246	0.522412	0.261206	+	0.965283i	$0.415880\pi$
$774$	12.4266	0.446665
$775$	30.9445	1.11156
$776$	−16.7963	−0.602950
$777$	4.56883	0.163906
$778$	−18.8031	−0.674123
$779$	46.1804	1.65459
$780$	−0.878845	−0.0314677
$781$	45.4608	1.62672
$782$	7.32615	0.261983
$783$	−35.0015	−1.25085
$784$	−6.60932	−0.236047
$785$	3.54520	0.126533
$786$	−32.6245	−1.16368
$787$	42.0762	1.49985	0.749927	−	0.661521i	$-0.230089\pi$
$787$	42.0762	1.49985	0.749927	+	0.661521i	$0.230089\pi$
$788$	2.69274	0.0959250
$789$	−37.1555	−1.32277
$790$	1.33798	0.0476030
$791$	−11.6613	−0.414627
$792$	14.2200	0.505287
$793$	−12.9467	−0.459751
$794$	9.08989	0.322588
$795$	2.77173	0.0983032
$796$	−13.0340	−0.461979
$797$	32.2036	1.14071	0.570355	−	0.821399i	$-0.306806\pi$
$797$	32.2036	1.14071	0.570355	+	0.821399i	$0.306806\pi$
$798$	−11.7589	−0.416260
$799$	39.3355	1.39159
$800$	−4.95109	−0.175048
$801$	79.4288	2.80648
$802$	5.94395	0.209888
$803$	33.6522	1.18756
$804$	−43.8115	−1.54511
$805$	0.219848	0.00774863
$806$	8.93018	0.314552
$807$	8.76330	0.308483
$808$	3.22097	0.113313
$809$	−14.1893	−0.498870	−0.249435	−	0.968391i	$-0.580245\pi$
$809$	−14.1893	−0.498870	−0.249435	+	0.968391i	$0.580245\pi$
$810$	−0.172707	−0.00606830
$811$	0.992431	0.0348490	0.0174245	−	0.999848i	$-0.494453\pi$
$811$	0.992431	0.0348490	0.0174245	+	0.999848i	$0.494453\pi$
$812$	−4.53213	−0.159046
$813$	50.5073	1.77137
$814$	7.89176	0.276606
$815$	1.15050	0.0403004
$816$	12.8114	0.448490
$817$	−17.7495	−0.620978
$818$	−2.25225	−0.0787482
$819$	−4.22924	−0.147781
$820$	−1.50986	−0.0527267
$821$	19.6527	0.685883	0.342941	−	0.939357i	$-0.388577\pi$
$821$	19.6527	0.685883	0.342941	+	0.939357i	$0.388577\pi$
$822$	−26.1361	−0.911601
$823$	−34.0261	−1.18607	−0.593037	−	0.805175i	$-0.702071\pi$
$823$	−34.0261	−1.18607	−0.593037	+	0.805175i	$0.702071\pi$
$824$	9.49678	0.330836
$825$	−41.3499	−1.43962
$826$	0.870101	0.0302747
$827$	−17.5321	−0.609652	−0.304826	−	0.952408i	$-0.598598\pi$
$827$	−17.5321	−0.609652	−0.304826	+	0.952408i	$0.598598\pi$
$828$	7.53180	0.261748
$829$	−10.8983	−0.378514	−0.189257	−	0.981928i	$-0.560608\pi$
$829$	−10.8983	−0.378514	−0.189257	+	0.981928i	$0.560608\pi$
$830$	−3.18775	−0.110648
$831$	−44.3345	−1.53795
$832$	−1.42882	−0.0495354
$833$	−30.4444	−1.05484
$834$	−21.0321	−0.728281
$835$	−5.15843	−0.178515
$836$	−20.3112	−0.702477
$837$	−30.1701	−1.04283
$838$	25.6083	0.884625
$839$	−17.3953	−0.600552	−0.300276	−	0.953852i	$-0.597079\pi$
$839$	−17.3953	−0.600552	−0.300276	+	0.953852i	$0.597079\pi$
$840$	0.384455	0.0132649
$841$	23.5755	0.812950
$842$	−3.30259	−0.113815
$843$	2.18117	0.0751234
$844$	9.46429	0.325774
$845$	−2.42347	−0.0833700
$846$	40.4397	1.39035
$847$	−1.23959	−0.0425927
$848$	4.50626	0.154746
$849$	−58.7294	−2.01559
$850$	−22.8062	−0.782245
$851$	4.17996	0.143287
$852$	42.1073	1.44257
$853$	13.0107	0.445476	0.222738	−	0.974878i	$-0.428501\pi$
$853$	13.0107	0.445476	0.222738	+	0.974878i	$0.428501\pi$
$854$	5.66360	0.193804
$855$	−7.08388	−0.242264
$856$	12.6330	0.431788
$857$	11.7890	0.402704	0.201352	−	0.979519i	$-0.435467\pi$
$857$	11.7890	0.402704	0.201352	+	0.979519i	$0.435467\pi$
$858$	−11.9330	−0.407387
$859$	−52.8841	−1.80438	−0.902191	−	0.431336i	$-0.858042\pi$
$859$	−52.8841	−1.80438	−0.902191	+	0.431336i	$0.858042\pi$
$860$	0.580319	0.0197887
$861$	−11.8688	−0.404487
$862$	6.08762	0.207345
$863$	38.3464	1.30533	0.652663	−	0.757648i	$-0.273652\pi$
$863$	38.3464	1.30533	0.652663	+	0.757648i	$0.273652\pi$
$864$	4.82719	0.164224
$865$	−3.75695	−0.127740
$866$	−15.5156	−0.527242
$867$	11.7312	0.398413
$868$	−3.90654	−0.132597
$869$	18.1671	0.616278
$870$	−4.45992	−0.151205
$871$	22.5070	0.762622
$872$	15.4966	0.524781
$873$	−79.5402	−2.69203
$874$	−10.7581	−0.363897
$875$	−1.37553	−0.0465013
$876$	31.1698	1.05313
$877$	0.934834	0.0315671	0.0157836	−	0.999875i	$-0.494976\pi$
$877$	0.934834	0.0315671	0.0157836	+	0.999875i	$0.494976\pi$
$878$	−5.87942	−0.198421
$879$	41.2704	1.39202
$880$	0.664071	0.0223858
$881$	−29.8128	−1.00442	−0.502210	−	0.864746i	$-0.667480\pi$
$881$	−29.8128	−1.00442	−0.502210	+	0.864746i	$0.667480\pi$
$882$	−31.2990	−1.05389
$883$	−24.2015	−0.814447	−0.407223	−	0.913329i	$-0.633503\pi$
$883$	−24.2015	−0.814447	−0.407223	+	0.913329i	$0.633503\pi$
$884$	−6.58156	−0.221362
$885$	0.856238	0.0287821
$886$	17.5074	0.588171
$887$	37.3231	1.25319	0.626593	−	0.779347i	$-0.284449\pi$
$887$	37.3231	1.25319	0.626593	+	0.779347i	$0.284449\pi$
$888$	7.30961	0.245295
$889$	−13.1377	−0.440626
$890$	3.70930	0.124336
$891$	−2.34503	−0.0785613
$892$	12.2620	0.410563
$893$	−57.7620	−1.93293
$894$	−8.66257	−0.289720
$895$	−1.80050	−0.0601840
$896$	0.625043	0.0208812
$897$	−6.32046	−0.211034
$898$	1.24584	0.0415743
$899$	45.3184	1.51145
$900$	−23.4464	−0.781545
$901$	20.7572	0.691521
$902$	−20.5010	−0.682609
$903$	4.56179	0.151807
$904$	−18.6567	−0.620513
$905$	2.64692	0.0879865
$906$	−2.12214	−0.0705033
$907$	23.2961	0.773533	0.386767	−	0.922178i	$-0.373592\pi$
$907$	23.2961	0.773533	0.386767	+	0.922178i	$0.373592\pi$
$908$	19.8681	0.659347
$909$	15.2532	0.505916
$910$	−0.197504	−0.00654719
$911$	30.4392	1.00850	0.504248	−	0.863559i	$-0.331770\pi$
$911$	30.4392	1.00850	0.504248	+	0.863559i	$0.331770\pi$
$912$	−18.8129	−0.622957
$913$	−43.2835	−1.43247
$914$	−3.43136	−0.113499
$915$	5.57336	0.184250
$916$	20.5794	0.679961
$917$	−7.33175	−0.242116
$918$	22.2354	0.733878
$919$	26.1192	0.861594	0.430797	−	0.902449i	$-0.358232\pi$
$919$	26.1192	0.861594	0.430797	+	0.902449i	$0.358232\pi$
$920$	0.351733	0.0115963
$921$	47.8308	1.57608
$922$	3.90957	0.128755
$923$	−21.6316	−0.712012
$924$	5.22015	0.171730
$925$	−13.0121	−0.427837
$926$	34.2091	1.12418
$927$	44.9729	1.47710
$928$	−7.25090	−0.238022
$929$	−43.0081	−1.41105	−0.705525	−	0.708685i	$-0.749289\pi$
$929$	−43.0081	−1.41105	−0.705525	+	0.708685i	$0.749289\pi$
$930$	−3.84430	−0.126060
$931$	44.7060	1.46518
$932$	−18.7148	−0.613022
$933$	84.9671	2.78170
$934$	−23.7349	−0.776629
$935$	3.05890	0.100037
$936$	−6.76631	−0.221164
$937$	21.7229	0.709656	0.354828	−	0.934932i	$-0.384539\pi$
$937$	21.7229	0.709656	0.354828	+	0.934932i	$0.384539\pi$
$938$	−9.84580	−0.321477
$939$	0.546335	0.0178290
$940$	1.88852	0.0615967
$941$	−43.1656	−1.40716	−0.703579	−	0.710617i	$-0.748416\pi$
$941$	−43.1656	−1.40716	−0.703579	+	0.710617i	$0.748416\pi$
$942$	44.5861	1.45269
$943$	−10.8586	−0.353605
$944$	1.39206	0.0453079
$945$	0.667256	0.0217058
$946$	7.87961	0.256188
$947$	−2.22030	−0.0721499	−0.0360750	−	0.999349i	$-0.511486\pi$
$947$	−2.22030	−0.0721499	−0.0360750	+	0.999349i	$0.511486\pi$
$948$	16.8270	0.546516
$949$	−16.0127	−0.519794
$950$	33.4896	1.08655
$951$	−18.0683	−0.585905
$952$	2.87913	0.0933132
$953$	12.5684	0.407131	0.203566	−	0.979061i	$-0.434747\pi$
$953$	12.5684	0.407131	0.203566	+	0.979061i	$0.434747\pi$
$954$	21.3398	0.690902
$955$	−1.74044	−0.0563192
$956$	5.97285	0.193176
$957$	−60.5571	−1.95753
$958$	0.126165	0.00407621
$959$	−5.87360	−0.189668
$960$	0.615084	0.0198518
$961$	8.06295	0.260095
$962$	−3.75513	−0.121070
$963$	59.8248	1.92783
$964$	27.1973	0.875965
$965$	−0.181362	−0.00583826
$966$	2.76491	0.0889597
$967$	25.6781	0.825752	0.412876	−	0.910787i	$-0.364524\pi$
$967$	25.6781	0.825752	0.412876	+	0.910787i	$0.364524\pi$
$968$	−1.98320	−0.0637424
$969$	−86.6576	−2.78384
$970$	−3.71450	−0.119265
$971$	47.0586	1.51018	0.755091	−	0.655620i	$-0.227593\pi$
$971$	47.0586	1.51018	0.755091	+	0.655620i	$0.227593\pi$
$972$	−16.6536	−0.534165
$973$	−4.72656	−0.151527
$974$	29.0131	0.929639
$975$	19.6755	0.630120
$976$	9.06113	0.290040
$977$	−48.1499	−1.54045	−0.770225	−	0.637772i	$-0.779856\pi$
$977$	−48.1499	−1.54045	−0.770225	+	0.637772i	$0.779856\pi$
$978$	14.4693	0.462676
$979$	50.3651	1.60968
$980$	−1.46165	−0.0466909
$981$	73.3856	2.34302
$982$	15.9849	0.510098
$983$	−26.4097	−0.842337	−0.421169	−	0.906982i	$-0.638380\pi$
$983$	−26.4097	−0.842337	−0.421169	+	0.906982i	$0.638380\pi$
$984$	−18.9887	−0.605339
$985$	0.595501	0.0189742
$986$	−33.3997	−1.06366
$987$	14.8454	0.472533
$988$	9.66465	0.307474
$989$	4.17353	0.132710
$990$	3.14477	0.0999473
$991$	31.8517	1.01180	0.505901	−	0.862592i	$-0.331160\pi$
$991$	31.8517	1.01180	0.505901	+	0.862592i	$0.331160\pi$
$992$	−6.25004	−0.198439
$993$	31.2442	0.991505
$994$	9.46283	0.300143
$995$	−2.88248	−0.0913809
$996$	−40.0906	−1.27032
$997$	−18.8092	−0.595692	−0.297846	−	0.954614i	$-0.596268\pi$
$997$	−18.8092	−0.595692	−0.297846	+	0.954614i	$0.596268\pi$
$998$	−14.9042	−0.471784
$999$	12.6865	0.401383

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1502.2.a.g.1.14	✓	16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1502.2.a.g.1.14	✓	16	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:	\( N \)	\(=\)	\( 1502 = 2 \cdot 751 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1502.a (trivial)

\(f(q)\)	\(=\)	\(q+1.00000 q^{2} +2.78129 q^{3} +1.00000 q^{4} +0.221151 q^{5} +2.78129 q^{6} +0.625043 q^{7} +1.00000 q^{8} +4.73559 q^{9} +O(q^{10})\)	\(q+1.00000 q^{2} +2.78129 q^{3} +1.00000 q^{4} +0.221151 q^{5} +2.78129 q^{6} +0.625043 q^{7} +1.00000 q^{8} +4.73559 q^{9} +0.221151 q^{10} +3.00280 q^{11} +2.78129 q^{12} -1.42882 q^{13} +0.625043 q^{14} +0.615084 q^{15} +1.00000 q^{16} +4.60629 q^{17} +4.73559 q^{18} -6.76408 q^{19} +0.221151 q^{20} +1.73843 q^{21} +3.00280 q^{22} +1.59047 q^{23} +2.78129 q^{24} -4.95109 q^{25} -1.42882 q^{26} +4.82719 q^{27} +0.625043 q^{28} -7.25090 q^{29} +0.615084 q^{30} -6.25004 q^{31} +1.00000 q^{32} +8.35166 q^{33} +4.60629 q^{34} +0.138229 q^{35} +4.73559 q^{36} +2.62814 q^{37} -6.76408 q^{38} -3.97397 q^{39} +0.221151 q^{40} -6.82730 q^{41} +1.73843 q^{42} +2.62409 q^{43} +3.00280 q^{44} +1.04728 q^{45} +1.59047 q^{46} +8.53952 q^{47} +2.78129 q^{48} -6.60932 q^{49} -4.95109 q^{50} +12.8114 q^{51} -1.42882 q^{52} +4.50626 q^{53} +4.82719 q^{54} +0.664071 q^{55} +0.625043 q^{56} -18.8129 q^{57} -7.25090 q^{58} +1.39206 q^{59} +0.615084 q^{60} +9.06113 q^{61} -6.25004 q^{62} +2.95995 q^{63} +1.00000 q^{64} -0.315984 q^{65} +8.35166 q^{66} -15.7522 q^{67} +4.60629 q^{68} +4.42356 q^{69} +0.138229 q^{70} +15.1395 q^{71} +4.73559 q^{72} +11.2069 q^{73} +2.62814 q^{74} -13.7704 q^{75} -6.76408 q^{76} +1.87688 q^{77} -3.97397 q^{78} +6.05007 q^{79} +0.221151 q^{80} -0.780947 q^{81} -6.82730 q^{82} -14.4144 q^{83} +1.73843 q^{84} +1.01868 q^{85} +2.62409 q^{86} -20.1669 q^{87} +3.00280 q^{88} +16.7727 q^{89} +1.04728 q^{90} -0.893074 q^{91} +1.59047 q^{92} -17.3832 q^{93} +8.53952 q^{94} -1.49588 q^{95} +2.78129 q^{96} -16.7963 q^{97} -6.60932 q^{98} +14.2200 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q + 16 q^{2} + 13 q^{3} + 16 q^{4} + 4 q^{5} + 13 q^{6} + 7 q^{7} + 16 q^{8} + 21 q^{9}+O(q^{10}) \) 16 * q + 16 * q^2 + 13 * q^3 + 16 * q^4 + 4 * q^5 + 13 * q^6 + 7 * q^7 + 16 * q^8 + 21 * q^9	\( 16 q + 16 q^{2} + 13 q^{3} + 16 q^{4} + 4 q^{5} + 13 q^{6} + 7 q^{7} + 16 q^{8} + 21 q^{9} + 4 q^{10} + 4 q^{11} + 13 q^{12} + 17 q^{13} + 7 q^{14} + 8 q^{15} + 16 q^{16} - q^{17} + 21 q^{18} + 23 q^{19} + 4 q^{20} + 9 q^{21} + 4 q^{22} + 15 q^{23} + 13 q^{24} + 24 q^{25} + 17 q^{26} + 31 q^{27} + 7 q^{28} + 4 q^{29} + 8 q^{30} + 42 q^{31} + 16 q^{32} + 3 q^{33} - q^{34} - 13 q^{35} + 21 q^{36} + 31 q^{37} + 23 q^{38} - 2 q^{39} + 4 q^{40} - 9 q^{41} + 9 q^{42} + 13 q^{43} + 4 q^{44} - 2 q^{45} + 15 q^{46} + 18 q^{47} + 13 q^{48} - 9 q^{49} + 24 q^{50} - 2 q^{51} + 17 q^{52} - 14 q^{53} + 31 q^{54} - 2 q^{55} + 7 q^{56} - 18 q^{57} + 4 q^{58} + 4 q^{59} + 8 q^{60} + q^{61} + 42 q^{62} + 17 q^{63} + 16 q^{64} - 32 q^{65} + 3 q^{66} + 5 q^{67} - q^{68} + 6 q^{69} - 13 q^{70} + 9 q^{71} + 21 q^{72} + 28 q^{73} + 31 q^{74} + 16 q^{75} + 23 q^{76} - 30 q^{77} - 2 q^{78} + 10 q^{79} + 4 q^{80} + 12 q^{81} - 9 q^{82} + 3 q^{83} + 9 q^{84} - 7 q^{85} + 13 q^{86} - 22 q^{87} + 4 q^{88} - 17 q^{89} - 2 q^{90} + 12 q^{91} + 15 q^{92} - q^{93} + 18 q^{94} - 4 q^{95} + 13 q^{96} - 17 q^{97} - 9 q^{98} - 10 q^{99}+O(q^{100}) \) 16 * q + 16 * q^2 + 13 * q^3 + 16 * q^4 + 4 * q^5 + 13 * q^6 + 7 * q^7 + 16 * q^8 + 21 * q^9 + 4 * q^10 + 4 * q^11 + 13 * q^12 + 17 * q^13 + 7 * q^14 + 8 * q^15 + 16 * q^16 - q^17 + 21 * q^18 + 23 * q^19 + 4 * q^20 + 9 * q^21 + 4 * q^22 + 15 * q^23 + 13 * q^24 + 24 * q^25 + 17 * q^26 + 31 * q^27 + 7 * q^28 + 4 * q^29 + 8 * q^30 + 42 * q^31 + 16 * q^32 + 3 * q^33 - q^34 - 13 * q^35 + 21 * q^36 + 31 * q^37 + 23 * q^38 - 2 * q^39 + 4 * q^40 - 9 * q^41 + 9 * q^42 + 13 * q^43 + 4 * q^44 - 2 * q^45 + 15 * q^46 + 18 * q^47 + 13 * q^48 - 9 * q^49 + 24 * q^50 - 2 * q^51 + 17 * q^52 - 14 * q^53 + 31 * q^54 - 2 * q^55 + 7 * q^56 - 18 * q^57 + 4 * q^58 + 4 * q^59 + 8 * q^60 + q^61 + 42 * q^62 + 17 * q^63 + 16 * q^64 - 32 * q^65 + 3 * q^66 + 5 * q^67 - q^68 + 6 * q^69 - 13 * q^70 + 9 * q^71 + 21 * q^72 + 28 * q^73 + 31 * q^74 + 16 * q^75 + 23 * q^76 - 30 * q^77 - 2 * q^78 + 10 * q^79 + 4 * q^80 + 12 * q^81 - 9 * q^82 + 3 * q^83 + 9 * q^84 - 7 * q^85 + 13 * q^86 - 22 * q^87 + 4 * q^88 - 17 * q^89 - 2 * q^90 + 12 * q^91 + 15 * q^92 - q^93 + 18 * q^94 - 4 * q^95 + 13 * q^96 - 17 * q^97 - 9 * q^98 - 10 * q^99

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