LMFDB - Embedded newform 1502.2.a.h.1.16

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:	$19$
Coefficient field:	$\mathbb{Q}[x]/(x^{19} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{19} - 6 x^{18} - 23 x^{17} + 190 x^{16} + 128 x^{15} - 2394 x^{14} + 749 x^{13} + 15539 x^{12} + \cdots + 4222 $ x^19 - 6x^18 - 23x^17 + 190x^16 + 128x^15 - 2394x^14 + 749x^13 + 15539x^12 - 11338x^11 - 56744x^10 + 50183x^9 + 120237x^8 - 102992x^7 - 148539x^6 + 99519x^5 + 104388x^4 - 41081x^3 - 35733x^2 + 5542x + 4222
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			1.16
Root			$2.66959$ 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)

$f(q)$	$=$	$q-1.00000 q^{2} +2.66959 q^{3} +1.00000 q^{4} +1.32740 q^{5} -2.66959 q^{6} -3.70251 q^{7} -1.00000 q^{8} +4.12668 q^{9} +O(q^{10})$	\(q-1.00000 q^{2} +2.66959 q^{3} +1.00000 q^{4} +1.32740 q^{5} -2.66959 q^{6} -3.70251 q^{7} -1.00000 q^{8} +4.12668 q^{9} -1.32740 q^{10} -3.81417 q^{11} +2.66959 q^{12} +6.69276 q^{13} +3.70251 q^{14} +3.54360 q^{15} +1.00000 q^{16} -0.918816 q^{17} -4.12668 q^{18} +5.96804 q^{19} +1.32740 q^{20} -9.88417 q^{21} +3.81417 q^{22} +5.79677 q^{23} -2.66959 q^{24} -3.23802 q^{25} -6.69276 q^{26} +3.00778 q^{27} -3.70251 q^{28} -4.03571 q^{29} -3.54360 q^{30} +8.04980 q^{31} -1.00000 q^{32} -10.1822 q^{33} +0.918816 q^{34} -4.91470 q^{35} +4.12668 q^{36} +7.96545 q^{37} -5.96804 q^{38} +17.8669 q^{39} -1.32740 q^{40} +7.52348 q^{41} +9.88417 q^{42} +11.3633 q^{43} -3.81417 q^{44} +5.47775 q^{45} -5.79677 q^{46} -7.16790 q^{47} +2.66959 q^{48} +6.70859 q^{49} +3.23802 q^{50} -2.45286 q^{51} +6.69276 q^{52} +7.48639 q^{53} -3.00778 q^{54} -5.06292 q^{55} +3.70251 q^{56} +15.9322 q^{57} +4.03571 q^{58} +9.13578 q^{59} +3.54360 q^{60} -7.79433 q^{61} -8.04980 q^{62} -15.2791 q^{63} +1.00000 q^{64} +8.88395 q^{65} +10.1822 q^{66} -11.9173 q^{67} -0.918816 q^{68} +15.4750 q^{69} +4.91470 q^{70} +0.656962 q^{71} -4.12668 q^{72} -6.67464 q^{73} -7.96545 q^{74} -8.64416 q^{75} +5.96804 q^{76} +14.1220 q^{77} -17.8669 q^{78} -10.8381 q^{79} +1.32740 q^{80} -4.35053 q^{81} -7.52348 q^{82} -3.43091 q^{83} -9.88417 q^{84} -1.21963 q^{85} -11.3633 q^{86} -10.7737 q^{87} +3.81417 q^{88} +16.5072 q^{89} -5.47775 q^{90} -24.7800 q^{91} +5.79677 q^{92} +21.4896 q^{93} +7.16790 q^{94} +7.92196 q^{95} -2.66959 q^{96} +12.2602 q^{97} -6.70859 q^{98} -15.7399 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 19 q - 19 q^{2} + 6 q^{3} + 19 q^{4} + 2 q^{5} - 6 q^{6} + 13 q^{7} - 19 q^{8} + 25 q^{9}+O(q^{10}) $ 19 * q - 19 * q^2 + 6 * q^3 + 19 * q^4 + 2 * q^5 - 6 * q^6 + 13 * q^7 - 19 * q^8 + 25 * q^9	\( 19 q - 19 q^{2} + 6 q^{3} + 19 q^{4} + 2 q^{5} - 6 q^{6} + 13 q^{7} - 19 q^{8} + 25 q^{9} - 2 q^{10} - 7 q^{11} + 6 q^{12} + 19 q^{13} - 13 q^{14} + 6 q^{15} + 19 q^{16} + 11 q^{17} - 25 q^{18} + 7 q^{19} + 2 q^{20} + 7 q^{21} + 7 q^{22} + 12 q^{23} - 6 q^{24} + 37 q^{25} - 19 q^{26} + 24 q^{27} + 13 q^{28} - 8 q^{29} - 6 q^{30} + 32 q^{31} - 19 q^{32} + 24 q^{33} - 11 q^{34} - 19 q^{35} + 25 q^{36} + 41 q^{37} - 7 q^{38} - 2 q^{39} - 2 q^{40} + 15 q^{41} - 7 q^{42} + 15 q^{43} - 7 q^{44} + 28 q^{45} - 12 q^{46} - 6 q^{47} + 6 q^{48} + 42 q^{49} - 37 q^{50} + 8 q^{51} + 19 q^{52} + 6 q^{53} - 24 q^{54} + 22 q^{55} - 13 q^{56} + 24 q^{57} + 8 q^{58} - 4 q^{59} + 6 q^{60} + 13 q^{61} - 32 q^{62} + 37 q^{63} + 19 q^{64} + 20 q^{65} - 24 q^{66} + 47 q^{67} + 11 q^{68} + 15 q^{69} + 19 q^{70} - 25 q^{72} + 64 q^{73} - 41 q^{74} - 3 q^{75} + 7 q^{76} - 4 q^{77} + 2 q^{78} + 34 q^{79} + 2 q^{80} + 27 q^{81} - 15 q^{82} + 4 q^{83} + 7 q^{84} + 21 q^{85} - 15 q^{86} + 7 q^{88} + 18 q^{89} - 28 q^{90} + 28 q^{91} + 12 q^{92} + 43 q^{93} + 6 q^{94} - 8 q^{95} - 6 q^{96} + 82 q^{97} - 42 q^{98} - 2 q^{99}+O(q^{100}) \) 19 * q - 19 * q^2 + 6 * q^3 + 19 * q^4 + 2 * q^5 - 6 * q^6 + 13 * q^7 - 19 * q^8 + 25 * q^9 - 2 * q^10 - 7 * q^11 + 6 * q^12 + 19 * q^13 - 13 * q^14 + 6 * q^15 + 19 * q^16 + 11 * q^17 - 25 * q^18 + 7 * q^19 + 2 * q^20 + 7 * q^21 + 7 * q^22 + 12 * q^23 - 6 * q^24 + 37 * q^25 - 19 * q^26 + 24 * q^27 + 13 * q^28 - 8 * q^29 - 6 * q^30 + 32 * q^31 - 19 * q^32 + 24 * q^33 - 11 * q^34 - 19 * q^35 + 25 * q^36 + 41 * q^37 - 7 * q^38 - 2 * q^39 - 2 * q^40 + 15 * q^41 - 7 * q^42 + 15 * q^43 - 7 * q^44 + 28 * q^45 - 12 * q^46 - 6 * q^47 + 6 * q^48 + 42 * q^49 - 37 * q^50 + 8 * q^51 + 19 * q^52 + 6 * q^53 - 24 * q^54 + 22 * q^55 - 13 * q^56 + 24 * q^57 + 8 * q^58 - 4 * q^59 + 6 * q^60 + 13 * q^61 - 32 * q^62 + 37 * q^63 + 19 * q^64 + 20 * q^65 - 24 * q^66 + 47 * q^67 + 11 * q^68 + 15 * q^69 + 19 * q^70 - 25 * q^72 + 64 * q^73 - 41 * q^74 - 3 * q^75 + 7 * q^76 - 4 * q^77 + 2 * q^78 + 34 * q^79 + 2 * q^80 + 27 * q^81 - 15 * q^82 + 4 * q^83 + 7 * q^84 + 21 * q^85 - 15 * q^86 + 7 * q^88 + 18 * q^89 - 28 * q^90 + 28 * q^91 + 12 * q^92 + 43 * q^93 + 6 * q^94 - 8 * q^95 - 6 * q^96 + 82 * q^97 - 42 * q^98 - 2 * 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
$3$	2.66959	1.54129	0.770643	−	0.637267i	$-0.219935\pi$
$3$	2.66959	1.54129	0.770643	+	0.637267i	$0.219935\pi$
$4$	1.00000	0.500000
$5$	1.32740	0.593630	0.296815	−	0.954935i	$-0.404076\pi$
$5$	1.32740	0.593630	0.296815	+	0.954935i	$0.404076\pi$
$6$	−2.66959	−1.08985
$7$	−3.70251	−1.39942	−0.699709	−	0.714428i	$-0.746687\pi$
$7$	−3.70251	−1.39942	−0.699709	+	0.714428i	$0.746687\pi$
$8$	−1.00000	−0.353553
$9$	4.12668	1.37556
$10$	−1.32740	−0.419760
$11$	−3.81417	−1.15002	−0.575008	−	0.818148i	$-0.695001\pi$
$11$	−3.81417	−1.15002	−0.575008	+	0.818148i	$0.695001\pi$
$12$	2.66959	0.770643
$13$	6.69276	1.85624	0.928119	−	0.372283i	$-0.121425\pi$
$13$	6.69276	1.85624	0.928119	+	0.372283i	$0.121425\pi$
$14$	3.70251	0.989538
$15$	3.54360	0.914953
$16$	1.00000	0.250000
$17$	−0.918816	−0.222846	−0.111423	−	0.993773i	$-0.535541\pi$
$17$	−0.918816	−0.222846	−0.111423	+	0.993773i	$0.535541\pi$
$18$	−4.12668	−0.972669
$19$	5.96804	1.36916	0.684581	−	0.728937i	$-0.259985\pi$
$19$	5.96804	1.36916	0.684581	+	0.728937i	$0.259985\pi$
$20$	1.32740	0.296815
$21$	−9.88417	−2.15690
$22$	3.81417	0.813184
$23$	5.79677	1.20871	0.604355	−	0.796715i	$-0.293431\pi$
$23$	5.79677	1.20871	0.604355	+	0.796715i	$0.293431\pi$
$24$	−2.66959	−0.544927
$25$	−3.23802	−0.647603
$26$	−6.69276	−1.31256
$27$	3.00778	0.578847
$28$	−3.70251	−0.699709
$29$	−4.03571	−0.749413	−0.374706	−	0.927144i	$-0.622256\pi$
$29$	−4.03571	−0.749413	−0.374706	+	0.927144i	$0.622256\pi$
$30$	−3.54360	−0.646970
$31$	8.04980	1.44579	0.722893	−	0.690960i	$-0.242812\pi$
$31$	8.04980	1.44579	0.722893	+	0.690960i	$0.242812\pi$
$32$	−1.00000	−0.176777
$33$	−10.1822	−1.77250
$34$	0.918816	0.157576
$35$	−4.91470	−0.830736
$36$	4.12668	0.687781
$37$	7.96545	1.30951	0.654756	−	0.755840i	$-0.272771\pi$
$37$	7.96545	1.30951	0.654756	+	0.755840i	$0.272771\pi$
$38$	−5.96804	−0.968144
$39$	17.8669	2.86099
$40$	−1.32740	−0.209880
$41$	7.52348	1.17497	0.587485	−	0.809235i	$-0.300118\pi$
$41$	7.52348	1.17497	0.587485	+	0.809235i	$0.300118\pi$
$42$	9.88417	1.52516
$43$	11.3633	1.73288	0.866441	−	0.499280i	$-0.166402\pi$
$43$	11.3633	1.73288	0.866441	+	0.499280i	$0.166402\pi$
$44$	−3.81417	−0.575008
$45$	5.47775	0.816575
$46$	−5.79677	−0.854688
$47$	−7.16790	−1.04555	−0.522773	−	0.852472i	$-0.675102\pi$
$47$	−7.16790	−1.04555	−0.522773	+	0.852472i	$0.675102\pi$
$48$	2.66959	0.385321
$49$	6.70859	0.958369
$50$	3.23802	0.457925
$51$	−2.45286	−0.343469
$52$	6.69276	0.928119
$53$	7.48639	1.02833	0.514167	−	0.857690i	$-0.328101\pi$
$53$	7.48639	1.02833	0.514167	+	0.857690i	$0.328101\pi$
$54$	−3.00778	−0.409307
$55$	−5.06292	−0.682684
$56$	3.70251	0.494769
$57$	15.9322	2.11027
$58$	4.03571	0.529915
$59$	9.13578	1.18938	0.594689	−	0.803956i	$-0.297275\pi$
$59$	9.13578	1.18938	0.594689	+	0.803956i	$0.297275\pi$
$60$	3.54360	0.457477
$61$	−7.79433	−0.997962	−0.498981	−	0.866613i	$-0.666292\pi$
$61$	−7.79433	−0.997962	−0.498981	+	0.866613i	$0.666292\pi$
$62$	−8.04980	−1.02233
$63$	−15.2791	−1.92498
$64$	1.00000	0.125000
$65$	8.88395	1.10192
$66$	10.1822	1.25335
$67$	−11.9173	−1.45593	−0.727967	−	0.685612i	$-0.759535\pi$
$67$	−11.9173	−1.45593	−0.727967	+	0.685612i	$0.759535\pi$
$68$	−0.918816	−0.111423
$69$	15.4750	1.86297
$70$	4.91470	0.587419
$71$	0.656962	0.0779670	0.0389835	−	0.999240i	$-0.487588\pi$
$71$	0.656962	0.0779670	0.0389835	+	0.999240i	$0.487588\pi$
$72$	−4.12668	−0.486334
$73$	−6.67464	−0.781208	−0.390604	−	0.920559i	$-0.627734\pi$
$73$	−6.67464	−0.781208	−0.390604	+	0.920559i	$0.627734\pi$
$74$	−7.96545	−0.925965
$75$	−8.64416	−0.998142
$76$	5.96804	0.684581
$77$	14.1220	1.60935
$78$	−17.8669	−2.02303
$79$	−10.8381	−1.21938	−0.609692	−	0.792638i	$-0.708707\pi$
$79$	−10.8381	−1.21938	−0.609692	+	0.792638i	$0.708707\pi$
$80$	1.32740	0.148408
$81$	−4.35053	−0.483392
$82$	−7.52348	−0.830829
$83$	−3.43091	−0.376591	−0.188296	−	0.982112i	$-0.560296\pi$
$83$	−3.43091	−0.376591	−0.188296	+	0.982112i	$0.560296\pi$
$84$	−9.88417	−1.07845
$85$	−1.21963	−0.132288
$86$	−11.3633	−1.22533
$87$	−10.7737	−1.15506
$88$	3.81417	0.406592
$89$	16.5072	1.74976	0.874880	−	0.484339i	$-0.160940\pi$
$89$	16.5072	1.74976	0.874880	+	0.484339i	$0.160940\pi$
$90$	−5.47775	−0.577405
$91$	−24.7800	−2.59765
$92$	5.79677	0.604355
$93$	21.4896	2.22837
$94$	7.16790	0.739312
$95$	7.92196	0.812776
$96$	−2.66959	−0.272463
$97$	12.2602	1.24483	0.622415	−	0.782687i	$-0.286152\pi$
$97$	12.2602	1.24483	0.622415	+	0.782687i	$0.286152\pi$
$98$	−6.70859	−0.677669
$99$	−15.7399	−1.58192
$100$	−3.23802	−0.323802
$101$	−2.40660	−0.239466	−0.119733	−	0.992806i	$-0.538204\pi$
$101$	−2.40660	−0.239466	−0.119733	+	0.992806i	$0.538204\pi$
$102$	2.45286	0.242869
$103$	−10.3430	−1.01912	−0.509562	−	0.860434i	$-0.670193\pi$
$103$	−10.3430	−1.01912	−0.509562	+	0.860434i	$0.670193\pi$
$104$	−6.69276	−0.656279
$105$	−13.1202	−1.28040
$106$	−7.48639	−0.727143
$107$	−13.8920	−1.34299	−0.671494	−	0.741010i	$-0.734347\pi$
$107$	−13.8920	−1.34299	−0.671494	+	0.741010i	$0.734347\pi$
$108$	3.00778	0.289424
$109$	0.694912	0.0665605	0.0332802	−	0.999446i	$-0.489405\pi$
$109$	0.694912	0.0665605	0.0332802	+	0.999446i	$0.489405\pi$
$110$	5.06292	0.482730
$111$	21.2644	2.01833
$112$	−3.70251	−0.349854
$113$	−14.3092	−1.34609	−0.673046	−	0.739600i	$-0.735015\pi$
$113$	−14.3092	−1.34609	−0.673046	+	0.739600i	$0.735015\pi$
$114$	−15.9322	−1.49219
$115$	7.69462	0.717527
$116$	−4.03571	−0.374706
$117$	27.6189	2.55337
$118$	−9.13578	−0.841017
$119$	3.40193	0.311854
$120$	−3.54360	−0.323485
$121$	3.54788	0.322535
$122$	7.79433	0.705665
$123$	20.0846	1.81096
$124$	8.04980	0.722893
$125$	−10.9351	−0.978067
$126$	15.2791	1.36117
$127$	−13.3923	−1.18838	−0.594189	−	0.804325i	$-0.702527\pi$
$127$	−13.3923	−1.18838	−0.594189	+	0.804325i	$0.702527\pi$
$128$	−1.00000	−0.0883883
$129$	30.3352	2.67086
$130$	−8.88395	−0.779174
$131$	−8.47530	−0.740490	−0.370245	−	0.928934i	$-0.620726\pi$
$131$	−8.47530	−0.740490	−0.370245	+	0.928934i	$0.620726\pi$
$132$	−10.1822	−0.886251
$133$	−22.0967	−1.91603
$134$	11.9173	1.02950
$135$	3.99252	0.343621
$136$	0.918816	0.0787879
$137$	−2.81038	−0.240107	−0.120054	−	0.992767i	$-0.538307\pi$
$137$	−2.81038	−0.240107	−0.120054	+	0.992767i	$0.538307\pi$
$138$	−15.4750	−1.31732
$139$	10.1233	0.858651	0.429325	−	0.903150i	$-0.358751\pi$
$139$	10.1233	0.858651	0.429325	+	0.903150i	$0.358751\pi$
$140$	−4.91470	−0.415368
$141$	−19.1353	−1.61148
$142$	−0.656962	−0.0551310
$143$	−25.5273	−2.13470
$144$	4.12668	0.343890
$145$	−5.35699	−0.444874
$146$	6.67464	0.552397
$147$	17.9091	1.47712
$148$	7.96545	0.654756
$149$	−20.8855	−1.71101	−0.855503	−	0.517797i	$-0.826752\pi$
$149$	−20.8855	−1.71101	−0.855503	+	0.517797i	$0.826752\pi$
$150$	8.64416	0.705793
$151$	−10.4828	−0.853081	−0.426541	−	0.904468i	$-0.640268\pi$
$151$	−10.4828	−0.853081	−0.426541	+	0.904468i	$0.640268\pi$
$152$	−5.96804	−0.484072
$153$	−3.79167	−0.306538
$154$	−14.1220	−1.13798
$155$	10.6853	0.858262
$156$	17.8669	1.43050
$157$	18.0419	1.43990	0.719952	−	0.694024i	$-0.244164\pi$
$157$	18.0419	1.43990	0.719952	+	0.694024i	$0.244164\pi$
$158$	10.8381	0.862235
$159$	19.9856	1.58496
$160$	−1.32740	−0.104940
$161$	−21.4626	−1.69149
$162$	4.35053	0.341810
$163$	−0.125119	−0.00980009	−0.00490004	−	0.999988i	$-0.501560\pi$
$163$	−0.125119	−0.00980009	−0.00490004	+	0.999988i	$0.501560\pi$
$164$	7.52348	0.587485
$165$	−13.5159	−1.05221
$166$	3.43091	0.266290
$167$	1.73003	0.133874	0.0669369	−	0.997757i	$-0.478677\pi$
$167$	1.73003	0.133874	0.0669369	+	0.997757i	$0.478677\pi$
$168$	9.88417	0.762580
$169$	31.7931	2.44562
$170$	1.21963	0.0935417
$171$	24.6282	1.88337
$172$	11.3633	0.866441
$173$	−16.1390	−1.22703	−0.613514	−	0.789684i	$-0.710245\pi$
$173$	−16.1390	−1.22703	−0.613514	+	0.789684i	$0.710245\pi$
$174$	10.7737	0.816750
$175$	11.9888	0.906267
$176$	−3.81417	−0.287504
$177$	24.3887	1.83317
$178$	−16.5072	−1.23727
$179$	2.17701	0.162717	0.0813586	−	0.996685i	$-0.474074\pi$
$179$	2.17701	0.162717	0.0813586	+	0.996685i	$0.474074\pi$
$180$	5.47775	0.408287
$181$	9.08772	0.675485	0.337743	−	0.941239i	$-0.390337\pi$
$181$	9.08772	0.675485	0.337743	+	0.941239i	$0.390337\pi$
$182$	24.7800	1.83682
$183$	−20.8076	−1.53814
$184$	−5.79677	−0.427344
$185$	10.5733	0.777366
$186$	−21.4896	−1.57570
$187$	3.50452	0.256276
$188$	−7.16790	−0.522773
$189$	−11.1363	−0.810049
$190$	−7.92196	−0.574719
$191$	−15.5578	−1.12572	−0.562860	−	0.826552i	$-0.690299\pi$
$191$	−15.5578	−1.12572	−0.562860	+	0.826552i	$0.690299\pi$
$192$	2.66959	0.192661
$193$	24.2512	1.74564	0.872821	−	0.488040i	$-0.162288\pi$
$193$	24.2512	1.74564	0.872821	+	0.488040i	$0.162288\pi$
$194$	−12.2602	−0.880228
$195$	23.7165	1.69837
$196$	6.70859	0.479185
$197$	−1.46725	−0.104538	−0.0522688	−	0.998633i	$-0.516645\pi$
$197$	−1.46725	−0.104538	−0.0522688	+	0.998633i	$0.516645\pi$
$198$	15.7399	1.11858
$199$	−9.94494	−0.704978	−0.352489	−	0.935816i	$-0.614665\pi$
$199$	−9.94494	−0.704978	−0.352489	+	0.935816i	$0.614665\pi$
$200$	3.23802	0.228962
$201$	−31.8143	−2.24401
$202$	2.40660	0.169328
$203$	14.9423	1.04874
$204$	−2.45286	−0.171734
$205$	9.98665	0.697498
$206$	10.3430	0.720629
$207$	23.9215	1.66266
$208$	6.69276	0.464060
$209$	−22.7631	−1.57456
$210$	13.1202	0.905381
$211$	11.9251	0.820957	0.410478	−	0.911870i	$-0.365362\pi$
$211$	11.9251	0.820957	0.410478	+	0.911870i	$0.365362\pi$
$212$	7.48639	0.514167
$213$	1.75382	0.120169
$214$	13.8920	0.949636
$215$	15.0836	1.02869
$216$	−3.00778	−0.204653
$217$	−29.8045	−2.02326
$218$	−0.694912	−0.0470654
$219$	−17.8185	−1.20406
$220$	−5.06292	−0.341342
$221$	−6.14942	−0.413655
$222$	−21.2644	−1.42718
$223$	6.63000	0.443978	0.221989	−	0.975049i	$-0.428745\pi$
$223$	6.63000	0.443978	0.221989	+	0.975049i	$0.428745\pi$
$224$	3.70251	0.247384
$225$	−13.3623	−0.890818
$226$	14.3092	0.951831
$227$	4.62077	0.306691	0.153346	−	0.988173i	$-0.450995\pi$
$227$	4.62077	0.306691	0.153346	+	0.988173i	$0.450995\pi$
$228$	15.9322	1.05513
$229$	8.37870	0.553680	0.276840	−	0.960916i	$-0.410713\pi$
$229$	8.37870	0.553680	0.276840	+	0.960916i	$0.410713\pi$
$230$	−7.69462	−0.507368
$231$	37.6999	2.48047
$232$	4.03571	0.264957
$233$	4.79915	0.314403	0.157201	−	0.987567i	$-0.449753\pi$
$233$	4.79915	0.314403	0.157201	+	0.987567i	$0.449753\pi$
$234$	−27.6189	−1.80551
$235$	−9.51465	−0.620667
$236$	9.13578	0.594689
$237$	−28.9333	−1.87942
$238$	−3.40193	−0.220514
$239$	−20.5152	−1.32702	−0.663510	−	0.748168i	$-0.730934\pi$
$239$	−20.5152	−1.32702	−0.663510	+	0.748168i	$0.730934\pi$
$240$	3.54360	0.228738
$241$	3.17547	0.204550	0.102275	−	0.994756i	$-0.467388\pi$
$241$	3.17547	0.204550	0.102275	+	0.994756i	$0.467388\pi$
$242$	−3.54788	−0.228067
$243$	−20.6374	−1.32389
$244$	−7.79433	−0.498981
$245$	8.90496	0.568917
$246$	−20.0846	−1.28055
$247$	39.9427	2.54149
$248$	−8.04980	−0.511163
$249$	−9.15911	−0.580435
$250$	10.9351	0.691598
$251$	−6.84023	−0.431751	−0.215876	−	0.976421i	$-0.569261\pi$
$251$	−6.84023	−0.431751	−0.215876	+	0.976421i	$0.569261\pi$
$252$	−15.2791	−0.962492
$253$	−22.1099	−1.39004
$254$	13.3923	0.840311
$255$	−3.25592	−0.203893
$256$	1.00000	0.0625000
$257$	−3.52809	−0.220076	−0.110038	−	0.993927i	$-0.535097\pi$
$257$	−3.52809	−0.220076	−0.110038	+	0.993927i	$0.535097\pi$
$258$	−30.3352	−1.88859
$259$	−29.4922	−1.83255
$260$	8.88395	0.550959
$261$	−16.6541	−1.03086
$262$	8.47530	0.523606
$263$	−24.8221	−1.53059	−0.765297	−	0.643677i	$-0.777408\pi$
$263$	−24.8221	−1.53059	−0.765297	+	0.643677i	$0.777408\pi$
$264$	10.1822	0.626674
$265$	9.93741	0.610451
$266$	22.0967	1.35484
$267$	44.0674	2.69688
$268$	−11.9173	−0.727967
$269$	17.8486	1.08825	0.544125	−	0.839004i	$-0.316862\pi$
$269$	17.8486	1.08825	0.544125	+	0.839004i	$0.316862\pi$
$270$	−3.99252	−0.242977
$271$	18.8958	1.14784	0.573920	−	0.818911i	$-0.305422\pi$
$271$	18.8958	1.14784	0.573920	+	0.818911i	$0.305422\pi$
$272$	−0.918816	−0.0557114
$273$	−66.1524	−4.00372
$274$	2.81038	0.169782
$275$	12.3503	0.744754
$276$	15.4750	0.931484
$277$	28.1743	1.69283	0.846414	−	0.532525i	$-0.178757\pi$
$277$	28.1743	1.69283	0.846414	+	0.532525i	$0.178757\pi$
$278$	−10.1233	−0.607158
$279$	33.2190	1.98877
$280$	4.91470	0.293710
$281$	0.984698	0.0587421	0.0293711	−	0.999569i	$-0.490650\pi$
$281$	0.984698	0.0587421	0.0293711	+	0.999569i	$0.490650\pi$
$282$	19.1353	1.13949
$283$	−6.06451	−0.360498	−0.180249	−	0.983621i	$-0.557690\pi$
$283$	−6.06451	−0.360498	−0.180249	+	0.983621i	$0.557690\pi$
$284$	0.656962	0.0389835
$285$	21.1483	1.25272
$286$	25.5273	1.50946
$287$	−27.8558	−1.64427
$288$	−4.12668	−0.243167
$289$	−16.1558	−0.950340
$290$	5.35699	0.314573
$291$	32.7295	1.91864
$292$	−6.67464	−0.390604
$293$	8.71152	0.508932	0.254466	−	0.967082i	$-0.418100\pi$
$293$	8.71152	0.508932	0.254466	+	0.967082i	$0.418100\pi$
$294$	−17.9091	−1.04448
$295$	12.1268	0.706050
$296$	−7.96545	−0.462982
$297$	−11.4722	−0.665683
$298$	20.8855	1.20986
$299$	38.7964	2.24366
$300$	−8.64416	−0.499071
$301$	−42.0726	−2.42502
$302$	10.4828	0.603220
$303$	−6.42462	−0.369085
$304$	5.96804	0.342290
$305$	−10.3462	−0.592420
$306$	3.79167	0.216755
$307$	−19.9752	−1.14004	−0.570021	−	0.821630i	$-0.693065\pi$
$307$	−19.9752	−1.14004	−0.570021	+	0.821630i	$0.693065\pi$
$308$	14.1220	0.804676
$309$	−27.6115	−1.57076
$310$	−10.6853	−0.606883
$311$	−31.0882	−1.76285	−0.881424	−	0.472325i	$-0.843415\pi$
$311$	−31.0882	−1.76285	−0.881424	+	0.472325i	$0.843415\pi$
$312$	−17.8669	−1.01151
$313$	−6.18576	−0.349640	−0.174820	−	0.984600i	$-0.555934\pi$
$313$	−6.18576	−0.349640	−0.174820	+	0.984600i	$0.555934\pi$
$314$	−18.0419	−1.01817
$315$	−20.2814	−1.14273
$316$	−10.8381	−0.609692
$317$	32.7718	1.84065	0.920323	−	0.391159i	$-0.127926\pi$
$317$	32.7718	1.84065	0.920323	+	0.391159i	$0.127926\pi$
$318$	−19.9856	−1.12073
$319$	15.3929	0.861836
$320$	1.32740	0.0742038
$321$	−37.0858	−2.06993
$322$	21.4626	1.19606
$323$	−5.48353	−0.305112
$324$	−4.35053	−0.241696
$325$	−21.6713	−1.20211
$326$	0.125119	0.00692971
$327$	1.85513	0.102589
$328$	−7.52348	−0.415415
$329$	26.5392	1.46315
$330$	13.5159	0.744025
$331$	−0.172461	−0.00947934	−0.00473967	−	0.999989i	$-0.501509\pi$
$331$	−0.172461	−0.00947934	−0.00473967	+	0.999989i	$0.501509\pi$
$332$	−3.43091	−0.188296
$333$	32.8709	1.80131
$334$	−1.73003	−0.0946630
$335$	−15.8190	−0.864286
$336$	−9.88417	−0.539226
$337$	−1.35990	−0.0740782	−0.0370391	−	0.999314i	$-0.511793\pi$
$337$	−1.35990	−0.0740782	−0.0370391	+	0.999314i	$0.511793\pi$
$338$	−31.7931	−1.72931
$339$	−38.1995	−2.07471
$340$	−1.21963	−0.0661440
$341$	−30.7033	−1.66268
$342$	−24.6282	−1.33174
$343$	1.07896	0.0582586
$344$	−11.3633	−0.612666
$345$	20.5414	1.10591
$346$	16.1390	0.867640
$347$	17.8604	0.958798	0.479399	−	0.877597i	$-0.340855\pi$
$347$	17.8604	0.958798	0.479399	+	0.877597i	$0.340855\pi$
$348$	−10.7737	−0.577529
$349$	−5.87763	−0.314622	−0.157311	−	0.987549i	$-0.550283\pi$
$349$	−5.87763	−0.314622	−0.157311	+	0.987549i	$0.550283\pi$
$350$	−11.9888	−0.640828
$351$	20.1304	1.07448
$352$	3.81417	0.203296
$353$	28.1700	1.49934	0.749669	−	0.661813i	$-0.230213\pi$
$353$	28.1700	1.49934	0.749669	+	0.661813i	$0.230213\pi$
$354$	−24.3887	−1.29625
$355$	0.872049	0.0462836
$356$	16.5072	0.874880
$357$	9.08173	0.480656
$358$	−2.17701	−0.115058
$359$	−28.3107	−1.49418	−0.747091	−	0.664722i	$-0.768550\pi$
$359$	−28.3107	−1.49418	−0.747091	+	0.664722i	$0.768550\pi$
$360$	−5.47775	−0.288703
$361$	16.6175	0.874604
$362$	−9.08772	−0.477640
$363$	9.47138	0.497118
$364$	−24.7800	−1.29883
$365$	−8.85990	−0.463748
$366$	20.8076	1.08763
$367$	−37.0823	−1.93568	−0.967841	−	0.251564i	$-0.919055\pi$
$367$	−37.0823	−1.93568	−0.967841	+	0.251564i	$0.919055\pi$
$368$	5.79677	0.302178
$369$	31.0470	1.61624
$370$	−10.5733	−0.549680
$371$	−27.7184	−1.43907
$372$	21.4896	1.11419
$373$	4.46576	0.231228	0.115614	−	0.993294i	$-0.463116\pi$
$373$	4.46576	0.231228	0.115614	+	0.993294i	$0.463116\pi$
$374$	−3.50452	−0.181214
$375$	−29.1922	−1.50748
$376$	7.16790	0.369656
$377$	−27.0100	−1.39109
$378$	11.1363	0.572791
$379$	31.3692	1.61133	0.805664	−	0.592372i	$-0.201809\pi$
$379$	31.3692	1.61133	0.805664	+	0.592372i	$0.201809\pi$
$380$	7.92196	0.406388
$381$	−35.7520	−1.83163
$382$	15.5578	0.796004
$383$	3.72287	0.190230	0.0951150	−	0.995466i	$-0.469678\pi$
$383$	3.72287	0.190230	0.0951150	+	0.995466i	$0.469678\pi$
$384$	−2.66959	−0.136232
$385$	18.7455	0.955359
$386$	−24.2512	−1.23436
$387$	46.8926	2.38368
$388$	12.2602	0.622415
$389$	19.3152	0.979321	0.489660	−	0.871913i	$-0.337121\pi$
$389$	19.3152	0.979321	0.489660	+	0.871913i	$0.337121\pi$
$390$	−23.7165	−1.20093
$391$	−5.32617	−0.269356
$392$	−6.70859	−0.338835
$393$	−22.6255	−1.14131
$394$	1.46725	0.0739192
$395$	−14.3865	−0.723863
$396$	−15.7399	−0.790958
$397$	−7.55951	−0.379401	−0.189700	−	0.981842i	$-0.560752\pi$
$397$	−7.55951	−0.379401	−0.189700	+	0.981842i	$0.560752\pi$
$398$	9.94494	0.498495
$399$	−58.9891	−2.95315
$400$	−3.23802	−0.161901
$401$	−2.86639	−0.143141	−0.0715704	−	0.997436i	$-0.522801\pi$
$401$	−2.86639	−0.143141	−0.0715704	+	0.997436i	$0.522801\pi$
$402$	31.8143	1.58675
$403$	53.8754	2.68372
$404$	−2.40660	−0.119733
$405$	−5.77488	−0.286956
$406$	−14.9423	−0.741572
$407$	−30.3816	−1.50596
$408$	2.45286	0.121435
$409$	−29.0448	−1.43617	−0.718087	−	0.695954i	$-0.754982\pi$
$409$	−29.0448	−1.43617	−0.718087	+	0.695954i	$0.754982\pi$
$410$	−9.98665	−0.493205
$411$	−7.50256	−0.370074
$412$	−10.3430	−0.509562
$413$	−33.8253	−1.66444
$414$	−23.9215	−1.17568
$415$	−4.55418	−0.223556
$416$	−6.69276	−0.328140
$417$	27.0251	1.32343
$418$	22.7631	1.11338
$419$	−16.1726	−0.790082	−0.395041	−	0.918664i	$-0.629270\pi$
$419$	−16.1726	−0.790082	−0.395041	+	0.918664i	$0.629270\pi$
$420$	−13.1202	−0.640201
$421$	−36.0400	−1.75648	−0.878241	−	0.478218i	$-0.841283\pi$
$421$	−36.0400	−1.75648	−0.878241	+	0.478218i	$0.841283\pi$
$422$	−11.9251	−0.580504
$423$	−29.5796	−1.43821
$424$	−7.48639	−0.363571
$425$	2.97514	0.144316
$426$	−1.75382	−0.0849726
$427$	28.8586	1.39657
$428$	−13.8920	−0.671494
$429$	−68.1474	−3.29019
$430$	−15.0836	−0.727394
$431$	−1.77671	−0.0855812	−0.0427906	−	0.999084i	$-0.513625\pi$
$431$	−1.77671	−0.0855812	−0.0427906	+	0.999084i	$0.513625\pi$
$432$	3.00778	0.144712
$433$	13.2361	0.636088	0.318044	−	0.948076i	$-0.396974\pi$
$433$	13.2361	0.636088	0.318044	+	0.948076i	$0.396974\pi$
$434$	29.8045	1.43066
$435$	−14.3009	−0.685678
$436$	0.694912	0.0332802
$437$	34.5954	1.65492
$438$	17.8185	0.851402
$439$	−8.50884	−0.406105	−0.203052	−	0.979168i	$-0.565086\pi$
$439$	−8.50884	−0.406105	−0.203052	+	0.979168i	$0.565086\pi$
$440$	5.06292	0.241365
$441$	27.6842	1.31830
$442$	6.14942	0.292498
$443$	33.4395	1.58876	0.794379	−	0.607423i	$-0.207797\pi$
$443$	33.4395	1.58876	0.794379	+	0.607423i	$0.207797\pi$
$444$	21.2644	1.00917
$445$	21.9116	1.03871
$446$	−6.63000	−0.313940
$447$	−55.7556	−2.63715
$448$	−3.70251	−0.174927
$449$	3.00981	0.142042	0.0710208	−	0.997475i	$-0.477374\pi$
$449$	3.00981	0.142042	0.0710208	+	0.997475i	$0.477374\pi$
$450$	13.3623	0.629904
$451$	−28.6958	−1.35123
$452$	−14.3092	−0.673046
$453$	−27.9848	−1.31484
$454$	−4.62077	−0.216864
$455$	−32.8929	−1.54204
$456$	−15.9322	−0.746093
$457$	−13.9639	−0.653205	−0.326603	−	0.945162i	$-0.605904\pi$
$457$	−13.9639	−0.653205	−0.326603	+	0.945162i	$0.605904\pi$
$458$	−8.37870	−0.391511
$459$	−2.76360	−0.128994
$460$	7.69462	0.358764
$461$	−9.58609	−0.446469	−0.223234	−	0.974765i	$-0.571662\pi$
$461$	−9.58609	−0.446469	−0.223234	+	0.974765i	$0.571662\pi$
$462$	−37.6999	−1.75396
$463$	2.81915	0.131017	0.0655086	−	0.997852i	$-0.479133\pi$
$463$	2.81915	0.131017	0.0655086	+	0.997852i	$0.479133\pi$
$464$	−4.03571	−0.187353
$465$	28.5253	1.32283
$466$	−4.79915	−0.222316
$467$	−2.46815	−0.114213	−0.0571063	−	0.998368i	$-0.518187\pi$
$467$	−2.46815	−0.114213	−0.0571063	+	0.998368i	$0.518187\pi$
$468$	27.6189	1.27668
$469$	44.1240	2.03746
$470$	9.51465	0.438878
$471$	48.1645	2.21930
$472$	−9.13578	−0.420508
$473$	−43.3414	−1.99284
$474$	28.9333	1.32895
$475$	−19.3246	−0.886674
$476$	3.40193	0.155927
$477$	30.8940	1.41454
$478$	20.5152	0.938344
$479$	−30.5986	−1.39809	−0.699043	−	0.715080i	$-0.746390\pi$
$479$	−30.5986	−1.39809	−0.699043	+	0.715080i	$0.746390\pi$
$480$	−3.54360	−0.161742
$481$	53.3109	2.43077
$482$	−3.17547	−0.144639
$483$	−57.2963	−2.60707
$484$	3.54788	0.161267
$485$	16.2741	0.738969
$486$	20.6374	0.936134
$487$	−12.3920	−0.561536	−0.280768	−	0.959776i	$-0.590589\pi$
$487$	−12.3920	−0.561536	−0.280768	+	0.959776i	$0.590589\pi$
$488$	7.79433	0.352833
$489$	−0.334016	−0.0151047
$490$	−8.90496	−0.402285
$491$	24.3308	1.09804	0.549018	−	0.835811i	$-0.315002\pi$
$491$	24.3308	1.09804	0.549018	+	0.835811i	$0.315002\pi$
$492$	20.0846	0.905482
$493$	3.70808	0.167003
$494$	−39.9427	−1.79711
$495$	−20.8931	−0.939073
$496$	8.04980	0.361447
$497$	−2.43241	−0.109108
$498$	9.15911	0.410429
$499$	36.2112	1.62104	0.810518	−	0.585714i	$-0.199186\pi$
$499$	36.2112	1.62104	0.810518	+	0.585714i	$0.199186\pi$
$500$	−10.9351	−0.489033
$501$	4.61846	0.206338
$502$	6.84023	0.305294
$503$	14.3210	0.638540	0.319270	−	0.947664i	$-0.396562\pi$
$503$	14.3210	0.638540	0.319270	+	0.947664i	$0.396562\pi$
$504$	15.2791	0.680585
$505$	−3.19451	−0.142154
$506$	22.1099	0.982904
$507$	84.8743	3.76940
$508$	−13.3923	−0.594189
$509$	−30.2668	−1.34155	−0.670776	−	0.741660i	$-0.734039\pi$
$509$	−30.2668	−1.34155	−0.670776	+	0.741660i	$0.734039\pi$
$510$	3.25592	0.144174
$511$	24.7129	1.09324
$512$	−1.00000	−0.0441942
$513$	17.9505	0.792536
$514$	3.52809	0.155618
$515$	−13.7292	−0.604983
$516$	30.3352	1.33543
$517$	27.3396	1.20239
$518$	29.4922	1.29581
$519$	−43.0845	−1.89120
$520$	−8.88395	−0.389587
$521$	31.0299	1.35945	0.679723	−	0.733469i	$-0.262100\pi$
$521$	31.0299	1.35945	0.679723	+	0.733469i	$0.262100\pi$
$522$	16.6541	0.728930
$523$	−20.3038	−0.887824	−0.443912	−	0.896070i	$-0.646410\pi$
$523$	−20.3038	−0.887824	−0.443912	+	0.896070i	$0.646410\pi$
$524$	−8.47530	−0.370245
$525$	32.0051	1.39682
$526$	24.8221	1.08229
$527$	−7.39629	−0.322187
$528$	−10.1822	−0.443125
$529$	10.6026	0.460982
$530$	−9.93741	−0.431654
$531$	37.7005	1.63606
$532$	−22.0967	−0.958015
$533$	50.3529	2.18102
$534$	−44.0674	−1.90698
$535$	−18.4402	−0.797238
$536$	11.9173	0.514750
$537$	5.81171	0.250794
$538$	−17.8486	−0.769509
$539$	−25.5877	−1.10214
$540$	3.99252	0.171811
$541$	10.6672	0.458617	0.229308	−	0.973354i	$-0.426354\pi$
$541$	10.6672	0.458617	0.229308	+	0.973354i	$0.426354\pi$
$542$	−18.8958	−0.811646
$543$	24.2605	1.04112
$544$	0.918816	0.0393939
$545$	0.922424	0.0395123
$546$	66.1524	2.83106
$547$	−0.691320	−0.0295587	−0.0147794	−	0.999891i	$-0.504705\pi$
$547$	−0.691320	−0.0295587	−0.0147794	+	0.999891i	$0.504705\pi$
$548$	−2.81038	−0.120054
$549$	−32.1647	−1.37276
$550$	−12.3503	−0.526620
$551$	−24.0853	−1.02607
$552$	−15.4750	−0.658659
$553$	40.1283	1.70643
$554$	−28.1743	−1.19701
$555$	28.2264	1.19814
$556$	10.1233	0.429325
$557$	1.47367	0.0624414	0.0312207	−	0.999513i	$-0.490061\pi$
$557$	1.47367	0.0624414	0.0312207	+	0.999513i	$0.490061\pi$
$558$	−33.2190	−1.40627
$559$	76.0516	3.21664
$560$	−4.91470	−0.207684
$561$	9.35562	0.394994
$562$	−0.984698	−0.0415370
$563$	0.883029	0.0372153	0.0186076	−	0.999827i	$-0.494077\pi$
$563$	0.883029	0.0372153	0.0186076	+	0.999827i	$0.494077\pi$
$564$	−19.1353	−0.805742
$565$	−18.9939	−0.799081
$566$	6.06451	0.254911
$567$	16.1079	0.676468
$568$	−0.656962	−0.0275655
$569$	−39.8125	−1.66903	−0.834514	−	0.550986i	$-0.814252\pi$
$569$	−39.8125	−1.66903	−0.834514	+	0.550986i	$0.814252\pi$
$570$	−21.1483	−0.885806
$571$	−22.5505	−0.943709	−0.471855	−	0.881676i	$-0.656415\pi$
$571$	−22.5505	−0.943709	−0.471855	+	0.881676i	$0.656415\pi$
$572$	−25.5273	−1.06735
$573$	−41.5328	−1.73506
$574$	27.8558	1.16268
$575$	−18.7700	−0.782765
$576$	4.12668	0.171945
$577$	1.49576	0.0622692	0.0311346	−	0.999515i	$-0.490088\pi$
$577$	1.49576	0.0622692	0.0311346	+	0.999515i	$0.490088\pi$
$578$	16.1558	0.671992
$579$	64.7407	2.69053
$580$	−5.35699	−0.222437
$581$	12.7030	0.527009
$582$	−32.7295	−1.35668
$583$	−28.5544	−1.18260
$584$	6.67464	0.276199
$585$	36.6613	1.51576
$586$	−8.71152	−0.359869
$587$	11.6933	0.482636	0.241318	−	0.970446i	$-0.422420\pi$
$587$	11.6933	0.482636	0.241318	+	0.970446i	$0.422420\pi$
$588$	17.9091	0.738560
$589$	48.0415	1.97952
$590$	−12.1268	−0.499253
$591$	−3.91696	−0.161122
$592$	7.96545	0.327378
$593$	20.4905	0.841446	0.420723	−	0.907189i	$-0.361776\pi$
$593$	20.4905	0.841446	0.420723	+	0.907189i	$0.361776\pi$
$594$	11.4722	0.470709
$595$	4.51571	0.185126
$596$	−20.8855	−0.855503
$597$	−26.5489	−1.08657
$598$	−38.7964	−1.58650
$599$	0.333788	0.0136382	0.00681911	−	0.999977i	$-0.497829\pi$
$599$	0.333788	0.0136382	0.00681911	+	0.999977i	$0.497829\pi$
$600$	8.64416	0.352896
$601$	−3.07719	−0.125521	−0.0627606	−	0.998029i	$-0.519990\pi$
$601$	−3.07719	−0.125521	−0.0627606	+	0.998029i	$0.519990\pi$
$602$	42.0726	1.71475
$603$	−49.1791	−2.00273
$604$	−10.4828	−0.426541
$605$	4.70945	0.191466
$606$	6.42462	0.260983
$607$	−13.4597	−0.546313	−0.273157	−	0.961970i	$-0.588068\pi$
$607$	−13.4597	−0.546313	−0.273157	+	0.961970i	$0.588068\pi$
$608$	−5.96804	−0.242036
$609$	39.8896	1.61641
$610$	10.3462	0.418904
$611$	−47.9730	−1.94078
$612$	−3.79167	−0.153269
$613$	−2.14033	−0.0864470	−0.0432235	−	0.999065i	$-0.513763\pi$
$613$	−2.14033	−0.0864470	−0.0432235	+	0.999065i	$0.513763\pi$
$614$	19.9752	0.806132
$615$	26.6602	1.07504
$616$	−14.1220	−0.568992
$617$	−39.3033	−1.58229	−0.791147	−	0.611627i	$-0.790516\pi$
$617$	−39.3033	−1.58229	−0.791147	+	0.611627i	$0.790516\pi$
$618$	27.6115	1.11070
$619$	−13.7186	−0.551396	−0.275698	−	0.961244i	$-0.588909\pi$
$619$	−13.7186	−0.551396	−0.275698	+	0.961244i	$0.588909\pi$
$620$	10.6853	0.429131
$621$	17.4354	0.699659
$622$	31.0882	1.24652
$623$	−61.1181	−2.44865
$624$	17.8669	0.715248
$625$	1.67484	0.0669934
$626$	6.18576	0.247233
$627$	−60.7680	−2.42684
$628$	18.0419	0.719952
$629$	−7.31879	−0.291819
$630$	20.2814	0.808031
$631$	11.0031	0.438027	0.219013	−	0.975722i	$-0.429716\pi$
$631$	11.0031	0.438027	0.219013	+	0.975722i	$0.429716\pi$
$632$	10.8381	0.431118
$633$	31.8350	1.26533
$634$	−32.7718	−1.30153
$635$	−17.7770	−0.705457
$636$	19.9856	0.792479
$637$	44.8990	1.77896
$638$	−15.3929	−0.609410
$639$	2.71107	0.107248
$640$	−1.32740	−0.0524700
$641$	8.21460	0.324457	0.162229	−	0.986753i	$-0.448132\pi$
$641$	8.21460	0.324457	0.162229	+	0.986753i	$0.448132\pi$
$642$	37.0858	1.46366
$643$	47.0720	1.85634	0.928169	−	0.372159i	$-0.121383\pi$
$643$	47.0720	1.85634	0.928169	+	0.372159i	$0.121383\pi$
$644$	−21.4626	−0.845746
$645$	40.2668	1.58551
$646$	5.48353	0.215747
$647$	−36.9848	−1.45402	−0.727011	−	0.686626i	$-0.759091\pi$
$647$	−36.9848	−1.45402	−0.727011	+	0.686626i	$0.759091\pi$
$648$	4.35053	0.170905
$649$	−34.8454	−1.36780
$650$	21.6713	0.850017
$651$	−79.5656	−3.11842
$652$	−0.125119	−0.00490004
$653$	25.2600	0.988499	0.494250	−	0.869320i	$-0.335443\pi$
$653$	25.2600	0.988499	0.494250	+	0.869320i	$0.335443\pi$
$654$	−1.85513	−0.0725412
$655$	−11.2501	−0.439577
$656$	7.52348	0.293743
$657$	−27.5441	−1.07460
$658$	−26.5392	−1.03461
$659$	−22.1100	−0.861284	−0.430642	−	0.902523i	$-0.641713\pi$
$659$	−22.1100	−0.861284	−0.430642	+	0.902523i	$0.641713\pi$
$660$	−13.5159	−0.526105
$661$	−42.9342	−1.66995	−0.834974	−	0.550290i	$-0.814517\pi$
$661$	−42.9342	−1.66995	−0.834974	+	0.550290i	$0.814517\pi$
$662$	0.172461	0.00670290
$663$	−16.4164	−0.637560
$664$	3.43091	0.133145
$665$	−29.3311	−1.13741
$666$	−32.8709	−1.27372
$667$	−23.3941	−0.905823
$668$	1.73003	0.0669369
$669$	17.6993	0.684296
$670$	15.8190	0.611142
$671$	29.7289	1.14767
$672$	9.88417	0.381290
$673$	18.5463	0.714906	0.357453	−	0.933931i	$-0.383645\pi$
$673$	18.5463	0.714906	0.357453	+	0.933931i	$0.383645\pi$
$674$	1.35990	0.0523812
$675$	−9.73924	−0.374864
$676$	31.7931	1.22281
$677$	−42.4792	−1.63261	−0.816304	−	0.577622i	$-0.803981\pi$
$677$	−42.4792	−1.63261	−0.816304	+	0.577622i	$0.803981\pi$
$678$	38.1995	1.46704
$679$	−45.3934	−1.74204
$680$	1.21963	0.0467708
$681$	12.3355	0.472699
$682$	30.7033	1.17569
$683$	−9.14222	−0.349817	−0.174909	−	0.984585i	$-0.555963\pi$
$683$	−9.14222	−0.349817	−0.174909	+	0.984585i	$0.555963\pi$
$684$	24.6282	0.941683
$685$	−3.73050	−0.142535
$686$	−1.07896	−0.0411951
$687$	22.3676	0.853379
$688$	11.3633	0.433220
$689$	50.1046	1.90883
$690$	−20.5414	−0.781999
$691$	−40.8956	−1.55574	−0.777871	−	0.628424i	$-0.783700\pi$
$691$	−40.8956	−1.55574	−0.777871	+	0.628424i	$0.783700\pi$
$692$	−16.1390	−0.613514
$693$	58.2770	2.21376
$694$	−17.8604	−0.677972
$695$	13.4377	0.509721
$696$	10.7737	0.408375
$697$	−6.91270	−0.261837
$698$	5.87763	0.222472
$699$	12.8117	0.484584
$700$	11.9888	0.453134
$701$	46.7920	1.76731	0.883655	−	0.468139i	$-0.155075\pi$
$701$	46.7920	1.76731	0.883655	+	0.468139i	$0.155075\pi$
$702$	−20.1304	−0.759771
$703$	47.5381	1.79293
$704$	−3.81417	−0.143752
$705$	−25.4002	−0.956625
$706$	−28.1700	−1.06019
$707$	8.91046	0.335112
$708$	24.3887	0.916585
$709$	−12.2980	−0.461862	−0.230931	−	0.972970i	$-0.574177\pi$
$709$	−12.2980	−0.461862	−0.230931	+	0.972970i	$0.574177\pi$
$710$	−0.872049	−0.0327274
$711$	−44.7255	−1.67734
$712$	−16.5072	−0.618634
$713$	46.6629	1.74754
$714$	−9.08173	−0.339875
$715$	−33.8849	−1.26722
$716$	2.17701	0.0813586
$717$	−54.7671	−2.04532
$718$	28.3107	1.05655
$719$	−27.2733	−1.01712	−0.508561	−	0.861026i	$-0.669822\pi$
$719$	−27.2733	−1.01712	−0.508561	+	0.861026i	$0.669822\pi$
$720$	5.47775	0.204144
$721$	38.2950	1.42618
$722$	−16.6175	−0.618439
$723$	8.47719	0.315270
$724$	9.08772	0.337743
$725$	13.0677	0.485322
$726$	−9.47138	−0.351516
$727$	32.6457	1.21076	0.605382	−	0.795935i	$-0.293020\pi$
$727$	32.6457	1.21076	0.605382	+	0.795935i	$0.293020\pi$
$728$	24.7800	0.918409
$729$	−42.0418	−1.55710
$730$	8.85990	0.327920
$731$	−10.4408	−0.386165
$732$	−20.8076	−0.769072
$733$	−5.01610	−0.185274	−0.0926369	−	0.995700i	$-0.529530\pi$
$733$	−5.01610	−0.185274	−0.0926369	+	0.995700i	$0.529530\pi$
$734$	37.0823	1.36873
$735$	23.7725	0.876863
$736$	−5.79677	−0.213672
$737$	45.4547	1.67435
$738$	−31.0470	−1.14286
$739$	25.3073	0.930944	0.465472	−	0.885063i	$-0.345885\pi$
$739$	25.3073	0.930944	0.465472	+	0.885063i	$0.345885\pi$
$740$	10.5733	0.388683
$741$	106.630	3.91716
$742$	27.7184	1.01758
$743$	22.7564	0.834852	0.417426	−	0.908711i	$-0.362932\pi$
$743$	22.7564	0.834852	0.417426	+	0.908711i	$0.362932\pi$
$744$	−21.4896	−0.787848
$745$	−27.7233	−1.01570
$746$	−4.46576	−0.163503
$747$	−14.1583	−0.518025
$748$	3.50452	0.128138
$749$	51.4352	1.87940
$750$	29.1922	1.06595
$751$	1.00000	0.0364905
$751$	1.00000	0.0364905
$752$	−7.16790	−0.261386
$753$	−18.2606	−0.665452
$754$	27.0100	0.983648
$755$	−13.9149	−0.506415
$756$	−11.1363	−0.405025
$757$	−6.37126	−0.231567	−0.115784	−	0.993274i	$-0.536938\pi$
$757$	−6.37126	−0.231567	−0.115784	+	0.993274i	$0.536938\pi$
$758$	−31.3692	−1.13938
$759$	−59.0242	−2.14244
$760$	−7.92196	−0.287360
$761$	−25.8663	−0.937652	−0.468826	−	0.883291i	$-0.655323\pi$
$761$	−25.8663	−0.937652	−0.468826	+	0.883291i	$0.655323\pi$
$762$	35.7520	1.29516
$763$	−2.57292	−0.0931459
$764$	−15.5578	−0.562860
$765$	−5.03305	−0.181970
$766$	−3.72287	−0.134513
$767$	61.1436	2.20777
$768$	2.66959	0.0963304
$769$	−10.6823	−0.385215	−0.192607	−	0.981276i	$-0.561694\pi$
$769$	−10.6823	−0.385215	−0.192607	+	0.981276i	$0.561694\pi$
$770$	−18.7455	−0.675541
$771$	−9.41854	−0.339201
$772$	24.2512	0.872821
$773$	−30.4430	−1.09496	−0.547480	−	0.836819i	$-0.684413\pi$
$773$	−30.4430	−1.09496	−0.547480	+	0.836819i	$0.684413\pi$
$774$	−46.8926	−1.68552
$775$	−26.0654	−0.936296
$776$	−12.2602	−0.440114
$777$	−78.7318	−2.82449
$778$	−19.3152	−0.692484
$779$	44.9004	1.60872
$780$	23.7165	0.849186
$781$	−2.50576	−0.0896633
$782$	5.32617	0.190463
$783$	−12.1385	−0.433796
$784$	6.70859	0.239592
$785$	23.9488	0.854770
$786$	22.6255	0.807026
$787$	18.1781	0.647979	0.323989	−	0.946061i	$-0.394976\pi$
$787$	18.1781	0.647979	0.323989	+	0.946061i	$0.394976\pi$
$788$	−1.46725	−0.0522688
$789$	−66.2646	−2.35908
$790$	14.3865	0.511849
$791$	52.9798	1.88375
$792$	15.7399	0.559292
$793$	−52.1656	−1.85245
$794$	7.55951	0.268277
$795$	26.5288	0.940879
$796$	−9.94494	−0.352489
$797$	−3.26969	−0.115818	−0.0579091	−	0.998322i	$-0.518443\pi$
$797$	−3.26969	−0.115818	−0.0579091	+	0.998322i	$0.518443\pi$
$798$	58.9891	2.08819
$799$	6.58598	0.232995
$800$	3.23802	0.114481
$801$	68.1200	2.40690
$802$	2.86639	0.101216
$803$	25.4582	0.898401
$804$	−31.8143	−1.12200
$805$	−28.4894	−1.00412
$806$	−53.8754	−1.89768
$807$	47.6484	1.67730
$808$	2.40660	0.0846639
$809$	−1.39619	−0.0490875	−0.0245437	−	0.999699i	$-0.507813\pi$
$809$	−1.39619	−0.0490875	−0.0245437	+	0.999699i	$0.507813\pi$
$810$	5.77488	0.202909
$811$	54.8033	1.92440	0.962202	−	0.272338i	$-0.0877969\pi$
$811$	54.8033	1.92440	0.962202	+	0.272338i	$0.0877969\pi$
$812$	14.9423	0.524371
$813$	50.4440	1.76915
$814$	30.3816	1.06487
$815$	−0.166083	−0.00581763
$816$	−2.45286	−0.0858672
$817$	67.8164	2.37259
$818$	29.0448	1.01553
$819$	−102.259	−3.57323
$820$	9.98665	0.348749
$821$	36.7787	1.28359	0.641793	−	0.766878i	$-0.278191\pi$
$821$	36.7787	1.28359	0.641793	+	0.766878i	$0.278191\pi$
$822$	7.50256	0.261682
$823$	−27.3701	−0.954062	−0.477031	−	0.878887i	$-0.658287\pi$
$823$	−27.3701	−0.954062	−0.477031	+	0.878887i	$0.658287\pi$
$824$	10.3430	0.360315
$825$	32.9703	1.14788
$826$	33.8253	1.17693
$827$	15.6443	0.544006	0.272003	−	0.962296i	$-0.412314\pi$
$827$	15.6443	0.544006	0.272003	+	0.962296i	$0.412314\pi$
$828$	23.9215	0.831328
$829$	−18.8674	−0.655291	−0.327646	−	0.944801i	$-0.606255\pi$
$829$	−18.8674	−0.655291	−0.327646	+	0.944801i	$0.606255\pi$
$830$	4.55418	0.158078
$831$	75.2136	2.60913
$832$	6.69276	0.232030
$833$	−6.16396	−0.213568
$834$	−27.0251	−0.935804
$835$	2.29644	0.0794715
$836$	−22.7631	−0.787279
$837$	24.2120	0.836890
$838$	16.1726	0.558672
$839$	30.3277	1.04703	0.523514	−	0.852017i	$-0.324621\pi$
$839$	30.3277	1.04703	0.523514	+	0.852017i	$0.324621\pi$
$840$	13.1202	0.452690
$841$	−12.7130	−0.438381
$842$	36.0400	1.24202
$843$	2.62873	0.0905384
$844$	11.9251	0.410478
$845$	42.2020	1.45179
$846$	29.5796	1.01697
$847$	−13.1361	−0.451361
$848$	7.48639	0.257084
$849$	−16.1897	−0.555630
$850$	−2.97514	−0.102047
$851$	46.1739	1.58282
$852$	1.75382	0.0600847
$853$	30.3615	1.03956	0.519780	−	0.854300i	$-0.326014\pi$
$853$	30.3615	1.03956	0.519780	+	0.854300i	$0.326014\pi$
$854$	−28.8586	−0.987521
$855$	32.6914	1.11802
$856$	13.8920	0.474818
$857$	−49.6858	−1.69723	−0.848617	−	0.529008i	$-0.822564\pi$
$857$	−49.6858	−1.69723	−0.848617	+	0.529008i	$0.822564\pi$
$858$	68.1474	2.32651
$859$	53.4827	1.82481	0.912403	−	0.409294i	$-0.134225\pi$
$859$	53.4827	1.82481	0.912403	+	0.409294i	$0.134225\pi$
$860$	15.0836	0.514345
$861$	−74.3633	−2.53430
$862$	1.77671	0.0605150
$863$	−25.8335	−0.879383	−0.439692	−	0.898149i	$-0.644912\pi$
$863$	−25.8335	−0.879383	−0.439692	+	0.898149i	$0.644912\pi$
$864$	−3.00778	−0.102327
$865$	−21.4229	−0.728401
$866$	−13.2361	−0.449782
$867$	−43.1292	−1.46475
$868$	−29.8045	−1.01163
$869$	41.3384	1.40231
$870$	14.3009	0.484847
$871$	−79.7599	−2.70256
$872$	−0.694912	−0.0235327
$873$	50.5938	1.71234
$874$	−34.5954	−1.17021
$875$	40.4874	1.36872
$876$	−17.8185	−0.602032
$877$	25.8205	0.871895	0.435947	−	0.899972i	$-0.356413\pi$
$877$	25.8205	0.871895	0.435947	+	0.899972i	$0.356413\pi$
$878$	8.50884	0.287160
$879$	23.2561	0.784410
$880$	−5.06292	−0.170671
$881$	36.3913	1.22605	0.613027	−	0.790062i	$-0.289952\pi$
$881$	36.3913	1.22605	0.613027	+	0.790062i	$0.289952\pi$
$882$	−27.6842	−0.932176
$883$	10.8185	0.364070	0.182035	−	0.983292i	$-0.441732\pi$
$883$	10.8185	0.364070	0.182035	+	0.983292i	$0.441732\pi$
$884$	−6.14942	−0.206827
$885$	32.3735	1.08822
$886$	−33.4395	−1.12342
$887$	−37.1084	−1.24598	−0.622988	−	0.782231i	$-0.714082\pi$
$887$	−37.1084	−1.24598	−0.622988	+	0.782231i	$0.714082\pi$
$888$	−21.2644	−0.713588
$889$	49.5853	1.66304
$890$	−21.9116	−0.734479
$891$	16.5937	0.555908
$892$	6.63000	0.221989
$893$	−42.7783	−1.43152
$894$	55.7556	1.86475
$895$	2.88976	0.0965939
$896$	3.70251	0.123692
$897$	103.570	3.45811
$898$	−3.00981	−0.100439
$899$	−32.4867	−1.08349
$900$	−13.3623	−0.445409
$901$	−6.87862	−0.229160
$902$	28.6958	0.955466
$903$	−112.316	−3.73765
$904$	14.3092	0.475916
$905$	12.0630	0.400988
$906$	27.9848	0.929734
$907$	28.6115	0.950029	0.475014	−	0.879978i	$-0.342443\pi$
$907$	28.6115	0.950029	0.475014	+	0.879978i	$0.342443\pi$
$908$	4.62077	0.153346
$909$	−9.93128	−0.329400
$910$	32.8929	1.09039
$911$	−24.7752	−0.820840	−0.410420	−	0.911897i	$-0.634618\pi$
$911$	−24.7752	−0.820840	−0.410420	+	0.911897i	$0.634618\pi$
$912$	15.9322	0.527567
$913$	13.0861	0.433086
$914$	13.9639	0.461886
$915$	−27.6200	−0.913088
$916$	8.37870	0.276840
$917$	31.3799	1.03625
$918$	2.76360	0.0912123
$919$	−11.8093	−0.389551	−0.194776	−	0.980848i	$-0.562398\pi$
$919$	−11.8093	−0.389551	−0.194776	+	0.980848i	$0.562398\pi$
$920$	−7.69462	−0.253684
$921$	−53.3254	−1.75713
$922$	9.58609	0.315701
$923$	4.39689	0.144725
$924$	37.6999	1.24024
$925$	−25.7923	−0.848044
$926$	−2.81915	−0.0926432
$927$	−42.6822	−1.40187
$928$	4.03571	0.132479
$929$	5.76799	0.189242	0.0946208	−	0.995513i	$-0.469836\pi$
$929$	5.76799	0.189242	0.0946208	+	0.995513i	$0.469836\pi$
$930$	−28.5253	−0.935380
$931$	40.0371	1.31216
$932$	4.79915	0.157201
$933$	−82.9925	−2.71705
$934$	2.46815	0.0807605
$935$	4.65189	0.152133
$936$	−27.6189	−0.902753
$937$	−46.1167	−1.50657	−0.753284	−	0.657696i	$-0.771531\pi$
$937$	−46.1167	−1.50657	−0.753284	+	0.657696i	$0.771531\pi$
$938$	−44.1240	−1.44070
$939$	−16.5134	−0.538894
$940$	−9.51465	−0.310334
$941$	−36.2820	−1.18276	−0.591380	−	0.806393i	$-0.701417\pi$
$941$	−36.2820	−1.18276	−0.591380	+	0.806393i	$0.701417\pi$
$942$	−48.1645	−1.56928
$943$	43.6119	1.42020
$944$	9.13578	0.297344
$945$	−14.7823	−0.480870
$946$	43.3414	1.40915
$947$	−1.95190	−0.0634282	−0.0317141	−	0.999497i	$-0.510097\pi$
$947$	−1.95190	−0.0634282	−0.0317141	+	0.999497i	$0.510097\pi$
$948$	−28.9333	−0.939710
$949$	−44.6718	−1.45011
$950$	19.3246	0.626973
$951$	87.4870	2.83696
$952$	−3.40193	−0.110257
$953$	5.80093	0.187911	0.0939553	−	0.995576i	$-0.470049\pi$
$953$	5.80093	0.187911	0.0939553	+	0.995576i	$0.470049\pi$
$954$	−30.8940	−1.00023
$955$	−20.6513	−0.668261
$956$	−20.5152	−0.663510
$957$	41.0926	1.32834
$958$	30.5986	0.988596
$959$	10.4055	0.336010
$960$	3.54360	0.114369
$961$	33.7993	1.09030
$962$	−53.3109	−1.71881
$963$	−57.3278	−1.84736
$964$	3.17547	0.102275
$965$	32.1910	1.03627
$966$	57.2963	1.84348
$967$	−9.28922	−0.298721	−0.149361	−	0.988783i	$-0.547722\pi$
$967$	−9.28922	−0.298721	−0.149361	+	0.988783i	$0.547722\pi$
$968$	−3.54788	−0.114033
$969$	−14.6388	−0.470265
$970$	−16.2741	−0.522530
$971$	0.830037	0.0266372	0.0133186	−	0.999911i	$-0.495760\pi$
$971$	0.830037	0.0266372	0.0133186	+	0.999911i	$0.495760\pi$
$972$	−20.6374	−0.661946
$973$	−37.4818	−1.20161
$974$	12.3920	0.397066
$975$	−57.8533	−1.85279
$976$	−7.79433	−0.249490
$977$	1.73325	0.0554515	0.0277258	−	0.999616i	$-0.491173\pi$
$977$	1.73325	0.0554515	0.0277258	+	0.999616i	$0.491173\pi$
$978$	0.334016	0.0106807
$979$	−62.9613	−2.01225
$980$	8.90496	0.284458
$981$	2.86768	0.0915581
$982$	−24.3308	−0.776428
$983$	−10.8105	−0.344801	−0.172400	−	0.985027i	$-0.555152\pi$
$983$	−10.8105	−0.344801	−0.172400	+	0.985027i	$0.555152\pi$
$984$	−20.0846	−0.640273
$985$	−1.94763	−0.0620566
$986$	−3.70808	−0.118089
$987$	70.8487	2.25514
$988$	39.9427	1.27075
$989$	65.8703	2.09455
$990$	20.8931	0.664025
$991$	−8.62133	−0.273866	−0.136933	−	0.990580i	$-0.543724\pi$
$991$	−8.62133	−0.273866	−0.136933	+	0.990580i	$0.543724\pi$
$992$	−8.04980	−0.255581
$993$	−0.460401	−0.0146104
$994$	2.43241	0.0771513
$995$	−13.2009	−0.418496
$996$	−9.15911	−0.290217
$997$	5.25981	0.166580	0.0832899	−	0.996525i	$-0.473457\pi$
$997$	5.25981	0.166580	0.0832899	+	0.996525i	$0.473457\pi$
$998$	−36.2112	−1.14625
$999$	23.9583	0.758008

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1502.2.a.h.1.16	✓	19

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1502.2.a.h.1.16	✓	19	1.1	even	1	trivial

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 1502 = 2 \cdot 751 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1502.a (trivial)

\(f(q)\)	\(=\)	\(q-1.00000 q^{2} +2.66959 q^{3} +1.00000 q^{4} +1.32740 q^{5} -2.66959 q^{6} -3.70251 q^{7} -1.00000 q^{8} +4.12668 q^{9} +O(q^{10})\)	\(q-1.00000 q^{2} +2.66959 q^{3} +1.00000 q^{4} +1.32740 q^{5} -2.66959 q^{6} -3.70251 q^{7} -1.00000 q^{8} +4.12668 q^{9} -1.32740 q^{10} -3.81417 q^{11} +2.66959 q^{12} +6.69276 q^{13} +3.70251 q^{14} +3.54360 q^{15} +1.00000 q^{16} -0.918816 q^{17} -4.12668 q^{18} +5.96804 q^{19} +1.32740 q^{20} -9.88417 q^{21} +3.81417 q^{22} +5.79677 q^{23} -2.66959 q^{24} -3.23802 q^{25} -6.69276 q^{26} +3.00778 q^{27} -3.70251 q^{28} -4.03571 q^{29} -3.54360 q^{30} +8.04980 q^{31} -1.00000 q^{32} -10.1822 q^{33} +0.918816 q^{34} -4.91470 q^{35} +4.12668 q^{36} +7.96545 q^{37} -5.96804 q^{38} +17.8669 q^{39} -1.32740 q^{40} +7.52348 q^{41} +9.88417 q^{42} +11.3633 q^{43} -3.81417 q^{44} +5.47775 q^{45} -5.79677 q^{46} -7.16790 q^{47} +2.66959 q^{48} +6.70859 q^{49} +3.23802 q^{50} -2.45286 q^{51} +6.69276 q^{52} +7.48639 q^{53} -3.00778 q^{54} -5.06292 q^{55} +3.70251 q^{56} +15.9322 q^{57} +4.03571 q^{58} +9.13578 q^{59} +3.54360 q^{60} -7.79433 q^{61} -8.04980 q^{62} -15.2791 q^{63} +1.00000 q^{64} +8.88395 q^{65} +10.1822 q^{66} -11.9173 q^{67} -0.918816 q^{68} +15.4750 q^{69} +4.91470 q^{70} +0.656962 q^{71} -4.12668 q^{72} -6.67464 q^{73} -7.96545 q^{74} -8.64416 q^{75} +5.96804 q^{76} +14.1220 q^{77} -17.8669 q^{78} -10.8381 q^{79} +1.32740 q^{80} -4.35053 q^{81} -7.52348 q^{82} -3.43091 q^{83} -9.88417 q^{84} -1.21963 q^{85} -11.3633 q^{86} -10.7737 q^{87} +3.81417 q^{88} +16.5072 q^{89} -5.47775 q^{90} -24.7800 q^{91} +5.79677 q^{92} +21.4896 q^{93} +7.16790 q^{94} +7.92196 q^{95} -2.66959 q^{96} +12.2602 q^{97} -6.70859 q^{98} -15.7399 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 19 q - 19 q^{2} + 6 q^{3} + 19 q^{4} + 2 q^{5} - 6 q^{6} + 13 q^{7} - 19 q^{8} + 25 q^{9}+O(q^{10}) \) 19 * q - 19 * q^2 + 6 * q^3 + 19 * q^4 + 2 * q^5 - 6 * q^6 + 13 * q^7 - 19 * q^8 + 25 * q^9	\( 19 q - 19 q^{2} + 6 q^{3} + 19 q^{4} + 2 q^{5} - 6 q^{6} + 13 q^{7} - 19 q^{8} + 25 q^{9} - 2 q^{10} - 7 q^{11} + 6 q^{12} + 19 q^{13} - 13 q^{14} + 6 q^{15} + 19 q^{16} + 11 q^{17} - 25 q^{18} + 7 q^{19} + 2 q^{20} + 7 q^{21} + 7 q^{22} + 12 q^{23} - 6 q^{24} + 37 q^{25} - 19 q^{26} + 24 q^{27} + 13 q^{28} - 8 q^{29} - 6 q^{30} + 32 q^{31} - 19 q^{32} + 24 q^{33} - 11 q^{34} - 19 q^{35} + 25 q^{36} + 41 q^{37} - 7 q^{38} - 2 q^{39} - 2 q^{40} + 15 q^{41} - 7 q^{42} + 15 q^{43} - 7 q^{44} + 28 q^{45} - 12 q^{46} - 6 q^{47} + 6 q^{48} + 42 q^{49} - 37 q^{50} + 8 q^{51} + 19 q^{52} + 6 q^{53} - 24 q^{54} + 22 q^{55} - 13 q^{56} + 24 q^{57} + 8 q^{58} - 4 q^{59} + 6 q^{60} + 13 q^{61} - 32 q^{62} + 37 q^{63} + 19 q^{64} + 20 q^{65} - 24 q^{66} + 47 q^{67} + 11 q^{68} + 15 q^{69} + 19 q^{70} - 25 q^{72} + 64 q^{73} - 41 q^{74} - 3 q^{75} + 7 q^{76} - 4 q^{77} + 2 q^{78} + 34 q^{79} + 2 q^{80} + 27 q^{81} - 15 q^{82} + 4 q^{83} + 7 q^{84} + 21 q^{85} - 15 q^{86} + 7 q^{88} + 18 q^{89} - 28 q^{90} + 28 q^{91} + 12 q^{92} + 43 q^{93} + 6 q^{94} - 8 q^{95} - 6 q^{96} + 82 q^{97} - 42 q^{98} - 2 q^{99}+O(q^{100}) \) 19 * q - 19 * q^2 + 6 * q^3 + 19 * q^4 + 2 * q^5 - 6 * q^6 + 13 * q^7 - 19 * q^8 + 25 * q^9 - 2 * q^10 - 7 * q^11 + 6 * q^12 + 19 * q^13 - 13 * q^14 + 6 * q^15 + 19 * q^16 + 11 * q^17 - 25 * q^18 + 7 * q^19 + 2 * q^20 + 7 * q^21 + 7 * q^22 + 12 * q^23 - 6 * q^24 + 37 * q^25 - 19 * q^26 + 24 * q^27 + 13 * q^28 - 8 * q^29 - 6 * q^30 + 32 * q^31 - 19 * q^32 + 24 * q^33 - 11 * q^34 - 19 * q^35 + 25 * q^36 + 41 * q^37 - 7 * q^38 - 2 * q^39 - 2 * q^40 + 15 * q^41 - 7 * q^42 + 15 * q^43 - 7 * q^44 + 28 * q^45 - 12 * q^46 - 6 * q^47 + 6 * q^48 + 42 * q^49 - 37 * q^50 + 8 * q^51 + 19 * q^52 + 6 * q^53 - 24 * q^54 + 22 * q^55 - 13 * q^56 + 24 * q^57 + 8 * q^58 - 4 * q^59 + 6 * q^60 + 13 * q^61 - 32 * q^62 + 37 * q^63 + 19 * q^64 + 20 * q^65 - 24 * q^66 + 47 * q^67 + 11 * q^68 + 15 * q^69 + 19 * q^70 - 25 * q^72 + 64 * q^73 - 41 * q^74 - 3 * q^75 + 7 * q^76 - 4 * q^77 + 2 * q^78 + 34 * q^79 + 2 * q^80 + 27 * q^81 - 15 * q^82 + 4 * q^83 + 7 * q^84 + 21 * q^85 - 15 * q^86 + 7 * q^88 + 18 * q^89 - 28 * q^90 + 28 * q^91 + 12 * q^92 + 43 * q^93 + 6 * q^94 - 8 * q^95 - 6 * q^96 + 82 * q^97 - 42 * q^98 - 2 * q^99

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