LMFDB - Embedded newform 1003.2.a.i.1.13

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1003,2,Mod(1,1003)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1003, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("1003.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1003 = 17 \cdot 59 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1003.a (trivial)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	yes
Analytic conductor:	$8.00899532273$
Analytic rank:	$0$
Dimension:	$18$
Coefficient field:	$\mathbb{Q}[x]/(x^{18} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{18} - 5 x^{17} - 16 x^{16} + 112 x^{15} + 52 x^{14} - 984 x^{13} + 431 x^{12} + 4304 x^{11} + \cdots + 28 $ x^18 - 5x^17 - 16x^16 + 112x^15 + 52x^14 - 984x^13 + 431x^12 + 4304x^11 - 3825x^10 - 9826x^9 + 11533x^8 + 11182x^7 - 15697x^6 - 5604x^5 + 9201x^4 + 1189x^3 - 1952x^2 - 100*x + 28
Coefficient ring:	$\Z[a_1, \ldots, a_{11}]$
Coefficient ring index:	$ 2 $
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.13
Root			$1.64867$ of defining polynomial
Character	$\chi$	$=$	1003.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.64867 q^{2} +2.75148 q^{3} +0.718114 q^{4} +4.35847 q^{5} +4.53629 q^{6} -3.72637 q^{7} -2.11341 q^{8} +4.57066 q^{9} +O(q^{10})$	\(q+1.64867 q^{2} +2.75148 q^{3} +0.718114 q^{4} +4.35847 q^{5} +4.53629 q^{6} -3.72637 q^{7} -2.11341 q^{8} +4.57066 q^{9} +7.18568 q^{10} +2.79772 q^{11} +1.97588 q^{12} -4.88363 q^{13} -6.14356 q^{14} +11.9923 q^{15} -4.92054 q^{16} +1.00000 q^{17} +7.53551 q^{18} -2.51539 q^{19} +3.12988 q^{20} -10.2531 q^{21} +4.61252 q^{22} +4.96656 q^{23} -5.81501 q^{24} +13.9963 q^{25} -8.05150 q^{26} +4.32164 q^{27} -2.67596 q^{28} +0.482451 q^{29} +19.7713 q^{30} -0.697981 q^{31} -3.88553 q^{32} +7.69787 q^{33} +1.64867 q^{34} -16.2413 q^{35} +3.28225 q^{36} -4.31234 q^{37} -4.14706 q^{38} -13.4372 q^{39} -9.21122 q^{40} -8.72618 q^{41} -16.9039 q^{42} -7.93875 q^{43} +2.00908 q^{44} +19.9211 q^{45} +8.18823 q^{46} +11.6594 q^{47} -13.5388 q^{48} +6.88587 q^{49} +23.0752 q^{50} +2.75148 q^{51} -3.50701 q^{52} -4.64630 q^{53} +7.12496 q^{54} +12.1938 q^{55} +7.87535 q^{56} -6.92107 q^{57} +0.795403 q^{58} -1.00000 q^{59} +8.61181 q^{60} +0.565893 q^{61} -1.15074 q^{62} -17.0320 q^{63} +3.43512 q^{64} -21.2852 q^{65} +12.6913 q^{66} -5.91265 q^{67} +0.718114 q^{68} +13.6654 q^{69} -26.7765 q^{70} -11.1713 q^{71} -9.65967 q^{72} +2.94081 q^{73} -7.10963 q^{74} +38.5105 q^{75} -1.80634 q^{76} -10.4253 q^{77} -22.1536 q^{78} +6.38050 q^{79} -21.4460 q^{80} -1.82105 q^{81} -14.3866 q^{82} +1.06504 q^{83} -7.36286 q^{84} +4.35847 q^{85} -13.0884 q^{86} +1.32746 q^{87} -5.91272 q^{88} -9.12233 q^{89} +32.8433 q^{90} +18.1983 q^{91} +3.56656 q^{92} -1.92048 q^{93} +19.2225 q^{94} -10.9633 q^{95} -10.6910 q^{96} +1.32370 q^{97} +11.3525 q^{98} +12.7874 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 18 q + 5 q^{2} + q^{3} + 21 q^{4} + 21 q^{5} + 5 q^{6} - q^{7} + 9 q^{8} + 17 q^{9}+O(q^{10}) $ 18 * q + 5 * q^2 + q^3 + 21 * q^4 + 21 * q^5 + 5 * q^6 - q^7 + 9 * q^8 + 17 * q^9	\( 18 q + 5 q^{2} + q^{3} + 21 q^{4} + 21 q^{5} + 5 q^{6} - q^{7} + 9 q^{8} + 17 q^{9} + 10 q^{10} + 6 q^{11} + 20 q^{12} + 12 q^{13} + 9 q^{14} - q^{15} + 19 q^{16} + 18 q^{17} + 10 q^{18} - 14 q^{19} + 17 q^{20} - 14 q^{21} - 4 q^{22} + 7 q^{23} - 3 q^{24} + 35 q^{25} + 3 q^{26} + 13 q^{27} + q^{28} + 23 q^{29} + 17 q^{30} - q^{31} + 13 q^{32} + 7 q^{33} + 5 q^{34} + 5 q^{35} - 16 q^{36} + 36 q^{37} - 19 q^{38} + 8 q^{39} - 4 q^{40} + 37 q^{41} + 9 q^{42} - 15 q^{43} - 9 q^{44} + 17 q^{45} + q^{46} + 23 q^{47} + 17 q^{48} + 15 q^{49} + 32 q^{50} + q^{51} - 11 q^{52} + 35 q^{53} - 17 q^{54} - 6 q^{55} + 37 q^{56} - 16 q^{57} + 2 q^{58} - 18 q^{59} - 6 q^{60} + 39 q^{61} - q^{62} + 15 q^{63} + 5 q^{64} + 15 q^{65} - 36 q^{66} + 14 q^{67} + 21 q^{68} + 16 q^{69} - 45 q^{70} + 3 q^{71} - 71 q^{72} + 56 q^{73} - 27 q^{74} + 16 q^{75} - q^{76} + 39 q^{77} - 71 q^{78} - 22 q^{79} + 45 q^{80} - 18 q^{81} + 5 q^{82} + 12 q^{83} + 2 q^{84} + 21 q^{85} + 4 q^{86} + 8 q^{87} - 18 q^{88} + 34 q^{89} + 48 q^{90} + 3 q^{91} + 67 q^{92} - 19 q^{93} - 38 q^{94} - 72 q^{95} + 6 q^{96} + 31 q^{97} + 19 q^{98} + 44 q^{99}+O(q^{100}) \) 18 * q + 5 * q^2 + q^3 + 21 * q^4 + 21 * q^5 + 5 * q^6 - q^7 + 9 * q^8 + 17 * q^9 + 10 * q^10 + 6 * q^11 + 20 * q^12 + 12 * q^13 + 9 * q^14 - q^15 + 19 * q^16 + 18 * q^17 + 10 * q^18 - 14 * q^19 + 17 * q^20 - 14 * q^21 - 4 * q^22 + 7 * q^23 - 3 * q^24 + 35 * q^25 + 3 * q^26 + 13 * q^27 + q^28 + 23 * q^29 + 17 * q^30 - q^31 + 13 * q^32 + 7 * q^33 + 5 * q^34 + 5 * q^35 - 16 * q^36 + 36 * q^37 - 19 * q^38 + 8 * q^39 - 4 * q^40 + 37 * q^41 + 9 * q^42 - 15 * q^43 - 9 * q^44 + 17 * q^45 + q^46 + 23 * q^47 + 17 * q^48 + 15 * q^49 + 32 * q^50 + q^51 - 11 * q^52 + 35 * q^53 - 17 * q^54 - 6 * q^55 + 37 * q^56 - 16 * q^57 + 2 * q^58 - 18 * q^59 - 6 * q^60 + 39 * q^61 - q^62 + 15 * q^63 + 5 * q^64 + 15 * q^65 - 36 * q^66 + 14 * q^67 + 21 * q^68 + 16 * q^69 - 45 * q^70 + 3 * q^71 - 71 * q^72 + 56 * q^73 - 27 * q^74 + 16 * q^75 - q^76 + 39 * q^77 - 71 * q^78 - 22 * q^79 + 45 * q^80 - 18 * q^81 + 5 * q^82 + 12 * q^83 + 2 * q^84 + 21 * q^85 + 4 * q^86 + 8 * q^87 - 18 * q^88 + 34 * q^89 + 48 * q^90 + 3 * q^91 + 67 * q^92 - 19 * q^93 - 38 * q^94 - 72 * q^95 + 6 * q^96 + 31 * q^97 + 19 * q^98 + 44 * 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 $

$2$	1.64867	1.16579	0.582893	−	0.812549i	$-0.301921\pi$
$2$	1.64867	1.16579	0.582893	+	0.812549i	$0.301921\pi$
$3$	2.75148	1.58857	0.794285	−	0.607546i	$-0.207846\pi$
$3$	2.75148	1.58857	0.794285	+	0.607546i	$0.207846\pi$
$4$	0.718114	0.359057
$5$	4.35847	1.94917	0.974584	−	0.224024i	$-0.0719195\pi$
$5$	4.35847	1.94917	0.974584	+	0.224024i	$0.0719195\pi$
$6$	4.53629	1.85193
$7$	−3.72637	−1.40844	−0.704219	−	0.709983i	$-0.748702\pi$
$7$	−3.72637	−1.40844	−0.704219	+	0.709983i	$0.748702\pi$
$8$	−2.11341	−0.747202
$9$	4.57066	1.52355
$10$	7.18568	2.27231
$11$	2.79772	0.843544	0.421772	−	0.906702i	$-0.361408\pi$
$11$	2.79772	0.843544	0.421772	+	0.906702i	$0.361408\pi$
$12$	1.97588	0.570387
$13$	−4.88363	−1.35448	−0.677238	−	0.735764i	$-0.736823\pi$
$13$	−4.88363	−1.35448	−0.677238	+	0.735764i	$0.736823\pi$
$14$	−6.14356	−1.64194
$15$	11.9923	3.09639
$16$	−4.92054	−1.23014
$17$	1.00000	0.242536
$17$	1.00000	0.242536
$18$	7.53551	1.77614
$19$	−2.51539	−0.577071	−0.288536	−	0.957469i	$-0.593168\pi$
$19$	−2.51539	−0.577071	−0.288536	+	0.957469i	$0.593168\pi$
$20$	3.12988	0.699862
$21$	−10.2531	−2.23740
$22$	4.61252	0.983392
$23$	4.96656	1.03560	0.517800	−	0.855502i	$-0.326751\pi$
$23$	4.96656	1.03560	0.517800	+	0.855502i	$0.326751\pi$
$24$	−5.81501	−1.18698
$25$	13.9963	2.79925
$26$	−8.05150	−1.57903
$27$	4.32164	0.831700
$28$	−2.67596	−0.505709
$29$	0.482451	0.0895889	0.0447945	−	0.998996i	$-0.485737\pi$
$29$	0.482451	0.0895889	0.0447945	+	0.998996i	$0.485737\pi$
$30$	19.7713	3.60973
$31$	−0.697981	−0.125361	−0.0626805	−	0.998034i	$-0.519965\pi$
$31$	−0.697981	−0.125361	−0.0626805	+	0.998034i	$0.519965\pi$
$32$	−3.88553	−0.686872
$33$	7.69787	1.34003
$34$	1.64867	0.282745
$35$	−16.2413	−2.74528
$36$	3.28225	0.547042
$37$	−4.31234	−0.708945	−0.354472	−	0.935066i	$-0.615339\pi$
$37$	−4.31234	−0.708945	−0.354472	+	0.935066i	$0.615339\pi$
$38$	−4.14706	−0.672741
$39$	−13.4372	−2.15168
$40$	−9.21122	−1.45642
$41$	−8.72618	−1.36280	−0.681400	−	0.731911i	$-0.738629\pi$
$41$	−8.72618	−1.36280	−0.681400	+	0.731911i	$0.738629\pi$
$42$	−16.9039	−2.60833
$43$	−7.93875	−1.21065	−0.605324	−	0.795979i	$-0.706956\pi$
$43$	−7.93875	−1.21065	−0.605324	+	0.795979i	$0.706956\pi$
$44$	2.00908	0.302880
$45$	19.9211	2.96966
$46$	8.18823	1.20729
$47$	11.6594	1.70069	0.850347	−	0.526223i	$-0.176392\pi$
$47$	11.6594	1.70069	0.850347	+	0.526223i	$0.176392\pi$
$48$	−13.5388	−1.95416
$49$	6.88587	0.983695
$50$	23.0752	3.26333
$51$	2.75148	0.385285
$52$	−3.50701	−0.486334
$53$	−4.64630	−0.638218	−0.319109	−	0.947718i	$-0.603384\pi$
$53$	−4.64630	−0.638218	−0.319109	+	0.947718i	$0.603384\pi$
$54$	7.12496	0.969585
$55$	12.1938	1.64421
$56$	7.87535	1.05239
$57$	−6.92107	−0.916718
$58$	0.795403	0.104442
$59$	−1.00000	−0.130189
$59$	−1.00000	−0.130189
$60$	8.61181	1.11178
$61$	0.565893	0.0724552	0.0362276	−	0.999344i	$-0.488466\pi$
$61$	0.565893	0.0724552	0.0362276	+	0.999344i	$0.488466\pi$
$62$	−1.15074	−0.146144
$63$	−17.0320	−2.14583
$64$	3.43512	0.429390
$65$	−21.2852	−2.64010
$66$	12.6913	1.56219
$67$	−5.91265	−0.722346	−0.361173	−	0.932499i	$-0.617624\pi$
$67$	−5.91265	−0.722346	−0.361173	+	0.932499i	$0.617624\pi$
$68$	0.718114	0.0870841
$69$	13.6654	1.64512
$70$	−26.7765	−3.20041
$71$	−11.1713	−1.32579	−0.662895	−	0.748713i	$-0.730672\pi$
$71$	−11.1713	−1.32579	−0.662895	+	0.748713i	$0.730672\pi$
$72$	−9.65967	−1.13840
$73$	2.94081	0.344196	0.172098	−	0.985080i	$-0.444945\pi$
$73$	2.94081	0.344196	0.172098	+	0.985080i	$0.444945\pi$
$74$	−7.10963	−0.826478
$75$	38.5105	4.44681
$76$	−1.80634	−0.207201
$77$	−10.4253	−1.18808
$78$	−22.1536	−2.50840
$79$	6.38050	0.717862	0.358931	−	0.933364i	$-0.383141\pi$
$79$	6.38050	0.717862	0.358931	+	0.933364i	$0.383141\pi$
$80$	−21.4460	−2.39774
$81$	−1.82105	−0.202339
$82$	−14.3866	−1.58873
$83$	1.06504	0.116903	0.0584516	−	0.998290i	$-0.481384\pi$
$83$	1.06504	0.116903	0.0584516	+	0.998290i	$0.481384\pi$
$84$	−7.36286	−0.803354
$85$	4.35847	0.472742
$86$	−13.0884	−1.41136
$87$	1.32746	0.142318
$88$	−5.91272	−0.630298
$89$	−9.12233	−0.966965	−0.483482	−	0.875354i	$-0.660628\pi$
$89$	−9.12233	−0.966965	−0.483482	+	0.875354i	$0.660628\pi$
$90$	32.8433	3.46199
$91$	18.1983	1.90770
$92$	3.56656	0.371839
$93$	−1.92048	−0.199145
$94$	19.2225	1.98264
$95$	−10.9633	−1.12481
$96$	−10.6910	−1.09114
$97$	1.32370	0.134402	0.0672008	−	0.997739i	$-0.478593\pi$
$97$	1.32370	0.134402	0.0672008	+	0.997739i	$0.478593\pi$
$98$	11.3525	1.14678
$99$	12.7874	1.28518
$100$	10.0509	1.00509
$101$	18.4236	1.83322	0.916608	−	0.399788i	$-0.130916\pi$
$101$	18.4236	1.83322	0.916608	+	0.399788i	$0.130916\pi$
$102$	4.53629	0.449159
$103$	3.27820	0.323010	0.161505	−	0.986872i	$-0.448365\pi$
$103$	3.27820	0.323010	0.161505	+	0.986872i	$0.448365\pi$
$104$	10.3211	1.01207
$105$	−44.6876	−4.36107
$106$	−7.66022	−0.744026
$107$	−10.1306	−0.979358	−0.489679	−	0.871903i	$-0.662886\pi$
$107$	−10.1306	−0.979358	−0.489679	+	0.871903i	$0.662886\pi$
$108$	3.10343	0.298628
$109$	10.4044	0.996565	0.498282	−	0.867015i	$-0.333964\pi$
$109$	10.4044	0.996565	0.498282	+	0.867015i	$0.333964\pi$
$110$	20.1035	1.91679
$111$	−11.8653	−1.12621
$112$	18.3358	1.73257
$113$	2.25730	0.212349	0.106175	−	0.994347i	$-0.466140\pi$
$113$	2.25730	0.212349	0.106175	+	0.994347i	$0.466140\pi$
$114$	−11.4106	−1.06870
$115$	21.6466	2.01856
$116$	0.346455	0.0321675
$117$	−22.3214	−2.06362
$118$	−1.64867	−0.151772
$119$	−3.72637	−0.341596
$120$	−25.3445	−2.31363
$121$	−3.17277	−0.288434
$122$	0.932971	0.0844672
$123$	−24.0099	−2.16490
$124$	−0.501230	−0.0450118
$125$	39.2099	3.50704
$126$	−28.0801	−2.50158
$127$	6.38523	0.566597	0.283299	−	0.959032i	$-0.408571\pi$
$127$	6.38523	0.566597	0.283299	+	0.959032i	$0.408571\pi$
$128$	13.4344	1.18745
$129$	−21.8433	−1.92320
$130$	−35.0922	−3.07779
$131$	−16.2609	−1.42072	−0.710362	−	0.703837i	$-0.751469\pi$
$131$	−16.2609	−1.42072	−0.710362	+	0.703837i	$0.751469\pi$
$132$	5.52795	0.481146
$133$	9.37330	0.812768
$134$	−9.74802	−0.842100
$135$	18.8357	1.62112
$136$	−2.11341	−0.181223
$137$	10.9807	0.938144	0.469072	−	0.883160i	$-0.344588\pi$
$137$	10.9807	0.938144	0.469072	+	0.883160i	$0.344588\pi$
$138$	22.5298	1.91786
$139$	1.63325	0.138530	0.0692651	−	0.997598i	$-0.477935\pi$
$139$	1.63325	0.138530	0.0692651	+	0.997598i	$0.477935\pi$
$140$	−11.6631	−0.985712
$141$	32.0805	2.70167
$142$	−18.4178	−1.54559
$143$	−13.6630	−1.14256
$144$	−22.4901	−1.87418
$145$	2.10275	0.174624
$146$	4.84842	0.401259
$147$	18.9463	1.56267
$148$	−3.09675	−0.254552
$149$	20.4727	1.67719	0.838595	−	0.544755i	$-0.183377\pi$
$149$	20.4727	1.67719	0.838595	+	0.544755i	$0.183377\pi$
$150$	63.4911	5.18403
$151$	21.6806	1.76434	0.882172	−	0.470927i	$-0.156080\pi$
$151$	21.6806	1.76434	0.882172	+	0.470927i	$0.156080\pi$
$152$	5.31605	0.431189
$153$	4.57066	0.369516
$154$	−17.1880	−1.38505
$155$	−3.04213	−0.244350
$156$	−9.64947	−0.772576
$157$	22.6611	1.80855	0.904276	−	0.426949i	$-0.140412\pi$
$157$	22.6611	1.80855	0.904276	+	0.426949i	$0.140412\pi$
$158$	10.5193	0.836874
$159$	−12.7842	−1.01385
$160$	−16.9350	−1.33883
$161$	−18.5073	−1.45858
$162$	−3.00232	−0.235884
$163$	−10.7185	−0.839535	−0.419768	−	0.907632i	$-0.637888\pi$
$163$	−10.7185	−0.839535	−0.419768	+	0.907632i	$0.637888\pi$
$164$	−6.26639	−0.489323
$165$	33.5510	2.61194
$166$	1.75590	0.136284
$167$	−16.5443	−1.28024	−0.640120	−	0.768275i	$-0.721115\pi$
$167$	−16.5443	−1.28024	−0.640120	+	0.768275i	$0.721115\pi$
$168$	21.6689	1.67179
$169$	10.8499	0.834607
$170$	7.18568	0.551117
$171$	−11.4970	−0.879199
$172$	−5.70093	−0.434692
$173$	16.3119	1.24017	0.620085	−	0.784535i	$-0.287098\pi$
$173$	16.3119	1.24017	0.620085	+	0.784535i	$0.287098\pi$
$174$	2.18854	0.165913
$175$	−52.1553	−3.94257
$176$	−13.7663	−1.03767
$177$	−2.75148	−0.206814
$178$	−15.0397	−1.12727
$179$	−0.821853	−0.0614282	−0.0307141	−	0.999528i	$-0.509778\pi$
$179$	−0.821853	−0.0614282	−0.0307141	+	0.999528i	$0.509778\pi$
$180$	14.3056	1.06628
$181$	−20.8408	−1.54908	−0.774542	−	0.632522i	$-0.782020\pi$
$181$	−20.8408	−1.54908	−0.774542	+	0.632522i	$0.782020\pi$
$182$	30.0029	2.22396
$183$	1.55705	0.115100
$184$	−10.4964	−0.773803
$185$	−18.7952	−1.38185
$186$	−3.16624	−0.232160
$187$	2.79772	0.204589
$188$	8.37275	0.610646
$189$	−16.1041	−1.17140
$190$	−18.0748	−1.31129
$191$	−17.9787	−1.30089	−0.650446	−	0.759552i	$-0.725418\pi$
$191$	−17.9787	−1.30089	−0.650446	+	0.759552i	$0.725418\pi$
$192$	9.45167	0.682115
$193$	24.8111	1.78594	0.892970	−	0.450117i	$-0.148618\pi$
$193$	24.8111	1.78594	0.892970	+	0.450117i	$0.148618\pi$
$194$	2.18235	0.156683
$195$	−58.5658	−4.19398
$196$	4.94484	0.353203
$197$	25.3012	1.80263	0.901316	−	0.433162i	$-0.142602\pi$
$197$	25.3012	1.80263	0.901316	+	0.433162i	$0.142602\pi$
$198$	21.0822	1.49825
$199$	8.46142	0.599814	0.299907	−	0.953968i	$-0.403044\pi$
$199$	8.46142	0.599814	0.299907	+	0.953968i	$0.403044\pi$
$200$	−29.5798	−2.09161
$201$	−16.2686	−1.14750
$202$	30.3744	2.13714
$203$	−1.79779	−0.126180
$204$	1.97588	0.138339
$205$	−38.0328	−2.65632
$206$	5.40467	0.376561
$207$	22.7005	1.57779
$208$	24.0301	1.66619
$209$	−7.03737	−0.486785
$210$	−73.6752	−5.08407
$211$	−3.32801	−0.229109	−0.114555	−	0.993417i	$-0.536544\pi$
$211$	−3.32801	−0.229109	−0.114555	+	0.993417i	$0.536544\pi$
$212$	−3.33657	−0.229157
$213$	−30.7376	−2.10611
$214$	−16.7020	−1.14172
$215$	−34.6008	−2.35976
$216$	−9.13339	−0.621449
$217$	2.60094	0.176563
$218$	17.1535	1.16178
$219$	8.09159	0.546779
$220$	8.75652	0.590364
$221$	−4.88363	−0.328509
$222$	−19.5620	−1.31292
$223$	−7.00733	−0.469246	−0.234623	−	0.972086i	$-0.575385\pi$
$223$	−7.00733	−0.469246	−0.234623	+	0.972086i	$0.575385\pi$
$224$	14.4790	0.967416
$225$	63.9721	4.26481
$226$	3.72155	0.247554
$227$	0.653987	0.0434066	0.0217033	−	0.999764i	$-0.493091\pi$
$227$	0.653987	0.0434066	0.0217033	+	0.999764i	$0.493091\pi$
$228$	−4.97011	−0.329154
$229$	10.8369	0.716123	0.358062	−	0.933698i	$-0.383438\pi$
$229$	10.8369	0.716123	0.358062	+	0.933698i	$0.383438\pi$
$230$	35.6881	2.35321
$231$	−28.6852	−1.88735
$232$	−1.01962	−0.0669411
$233$	−18.0118	−1.17999	−0.589997	−	0.807406i	$-0.700871\pi$
$233$	−18.0118	−1.17999	−0.589997	+	0.807406i	$0.700871\pi$
$234$	−36.8007	−2.40574
$235$	50.8170	3.31494
$236$	−0.718114	−0.0467452
$237$	17.5558	1.14037
$238$	−6.14356	−0.398228
$239$	15.7073	1.01602	0.508012	−	0.861350i	$-0.330381\pi$
$239$	15.7073	1.01602	0.508012	+	0.861350i	$0.330381\pi$
$240$	−59.0084	−3.80897
$241$	13.6058	0.876424	0.438212	−	0.898872i	$-0.355612\pi$
$241$	13.6058	0.876424	0.438212	+	0.898872i	$0.355612\pi$
$242$	−5.23085	−0.336252
$243$	−17.9755	−1.15313
$244$	0.406376	0.0260155
$245$	30.0118	1.91739
$246$	−39.5845	−2.52381
$247$	12.2843	0.781629
$248$	1.47512	0.0936701
$249$	2.93044	0.185709
$250$	64.6443	4.08846
$251$	−29.8503	−1.88413	−0.942067	−	0.335426i	$-0.891120\pi$
$251$	−29.8503	−1.88413	−0.942067	+	0.335426i	$0.891120\pi$
$252$	−12.2309	−0.770475
$253$	13.8950	0.873574
$254$	10.5271	0.660531
$255$	11.9923	0.750984
$256$	15.2787	0.954921
$257$	12.8649	0.802491	0.401246	−	0.915971i	$-0.368577\pi$
$257$	12.8649	0.802491	0.401246	+	0.915971i	$0.368577\pi$
$258$	−36.0125	−2.24204
$259$	16.0694	0.998504
$260$	−15.2852	−0.947947
$261$	2.20512	0.136494
$262$	−26.8089	−1.65626
$263$	−8.42465	−0.519486	−0.259743	−	0.965678i	$-0.583638\pi$
$263$	−8.42465	−0.519486	−0.259743	+	0.965678i	$0.583638\pi$
$264$	−16.2687	−1.00127
$265$	−20.2508	−1.24399
$266$	15.4535	0.947514
$267$	−25.0999	−1.53609
$268$	−4.24596	−0.259363
$269$	−12.4173	−0.757093	−0.378547	−	0.925582i	$-0.623576\pi$
$269$	−12.4173	−0.757093	−0.378547	+	0.925582i	$0.623576\pi$
$270$	31.0539	1.88988
$271$	−27.4544	−1.66774	−0.833868	−	0.551964i	$-0.813878\pi$
$271$	−27.4544	−1.66774	−0.833868	+	0.551964i	$0.813878\pi$
$272$	−4.92054	−0.298352
$273$	50.0722	3.03051
$274$	18.1035	1.09367
$275$	39.1576	2.36129
$276$	9.81333	0.590693
$277$	−17.3356	−1.04159	−0.520797	−	0.853680i	$-0.674365\pi$
$277$	−17.3356	−1.04159	−0.520797	+	0.853680i	$0.674365\pi$
$278$	2.69268	0.161496
$279$	−3.19023	−0.190994
$280$	34.3245	2.05128
$281$	−26.2640	−1.56678	−0.783389	−	0.621531i	$-0.786511\pi$
$281$	−26.2640	−1.56678	−0.783389	+	0.621531i	$0.786511\pi$
$282$	52.8903	3.14957
$283$	−3.94085	−0.234259	−0.117130	−	0.993117i	$-0.537369\pi$
$283$	−3.94085	−0.234259	−0.117130	+	0.993117i	$0.537369\pi$
$284$	−8.02226	−0.476034
$285$	−30.1653	−1.78684
$286$	−22.5258	−1.33198
$287$	32.5170	1.91942
$288$	−17.7594	−1.04649
$289$	1.00000	0.0588235
$290$	3.46674	0.203574
$291$	3.64214	0.213506
$292$	2.11184	0.123586
$293$	25.9151	1.51398	0.756988	−	0.653428i	$-0.226670\pi$
$293$	25.9151	1.51398	0.756988	+	0.653428i	$0.226670\pi$
$294$	31.2363	1.82174
$295$	−4.35847	−0.253760
$296$	9.11374	0.529725
$297$	12.0907	0.701576
$298$	33.7528	1.95525
$299$	−24.2549	−1.40270
$300$	27.6549	1.59666
$301$	29.5828	1.70512
$302$	35.7442	2.05685
$303$	50.6922	2.91219
$304$	12.3771	0.709875
$305$	2.46643	0.141227
$306$	7.53551	0.430776
$307$	15.7061	0.896395	0.448198	−	0.893934i	$-0.352066\pi$
$307$	15.7061	0.896395	0.448198	+	0.893934i	$0.352066\pi$
$308$	−7.48659	−0.426588
$309$	9.01990	0.513124
$310$	−5.01547	−0.284859
$311$	−6.59474	−0.373953	−0.186977	−	0.982364i	$-0.559869\pi$
$311$	−6.59474	−0.373953	−0.186977	+	0.982364i	$0.559869\pi$
$312$	28.3984	1.60774
$313$	9.94850	0.562323	0.281161	−	0.959661i	$-0.409280\pi$
$313$	9.94850	0.562323	0.281161	+	0.959661i	$0.409280\pi$
$314$	37.3607	2.10838
$315$	−74.2334	−4.18258
$316$	4.58192	0.257753
$317$	−2.21597	−0.124461	−0.0622307	−	0.998062i	$-0.519821\pi$
$317$	−2.21597	−0.124461	−0.0622307	+	0.998062i	$0.519821\pi$
$318$	−21.0770	−1.18194
$319$	1.34976	0.0755722
$320$	14.9719	0.836952
$321$	−27.8741	−1.55578
$322$	−30.5124	−1.70039
$323$	−2.51539	−0.139960
$324$	−1.30772	−0.0726513
$325$	−68.3526	−3.79152
$326$	−17.6712	−0.978719
$327$	28.6276	1.58311
$328$	18.4420	1.01829
$329$	−43.4472	−2.39532
$330$	55.3145	3.04496
$331$	−22.0754	−1.21337	−0.606687	−	0.794941i	$-0.707502\pi$
$331$	−22.0754	−1.21337	−0.606687	+	0.794941i	$0.707502\pi$
$332$	0.764819	0.0419749
$333$	−19.7102	−1.08011
$334$	−27.2762	−1.49249
$335$	−25.7701	−1.40797
$336$	50.4506	2.75230
$337$	−1.10527	−0.0602077	−0.0301038	−	0.999547i	$-0.509584\pi$
$337$	−1.10527	−0.0602077	−0.0301038	+	0.999547i	$0.509584\pi$
$338$	17.8879	0.972973
$339$	6.21093	0.337332
$340$	3.12988	0.169741
$341$	−1.95275	−0.105748
$342$	−18.9548	−1.02496
$343$	0.425306	0.0229644
$344$	16.7778	0.904599
$345$	59.5603	3.20662
$346$	26.8929	1.44577
$347$	−7.21288	−0.387208	−0.193604	−	0.981080i	$-0.562018\pi$
$347$	−7.21288	−0.387208	−0.193604	+	0.981080i	$0.562018\pi$
$348$	0.953265	0.0511004
$349$	−7.21140	−0.386018	−0.193009	−	0.981197i	$-0.561825\pi$
$349$	−7.21140	−0.386018	−0.193009	+	0.981197i	$0.561825\pi$
$350$	−85.9869	−4.59619
$351$	−21.1053	−1.12652
$352$	−10.8706	−0.579406
$353$	25.2214	1.34240	0.671199	−	0.741277i	$-0.265780\pi$
$353$	25.2214	1.34240	0.671199	+	0.741277i	$0.265780\pi$
$354$	−4.53629	−0.241101
$355$	−48.6898	−2.58418
$356$	−6.55087	−0.347195
$357$	−10.2531	−0.542649
$358$	−1.35497	−0.0716121
$359$	−2.58257	−0.136303	−0.0681514	−	0.997675i	$-0.521710\pi$
$359$	−2.58257	−0.136303	−0.0681514	+	0.997675i	$0.521710\pi$
$360$	−42.1014	−2.21894
$361$	−12.6728	−0.666989
$362$	−34.3596	−1.80590
$363$	−8.72983	−0.458197
$364$	13.0684	0.684971
$365$	12.8174	0.670895
$366$	2.56705	0.134182
$367$	18.8865	0.985870	0.492935	−	0.870066i	$-0.335924\pi$
$367$	18.8865	0.985870	0.492935	+	0.870066i	$0.335924\pi$
$368$	−24.4382	−1.27393
$369$	−39.8844	−2.07630
$370$	−30.9871	−1.61094
$371$	17.3139	0.898890
$372$	−1.37913	−0.0715043
$373$	−26.8759	−1.39158	−0.695791	−	0.718244i	$-0.744946\pi$
$373$	−26.8759	−1.39158	−0.695791	+	0.718244i	$0.744946\pi$
$374$	4.61252	0.238507
$375$	107.886	5.57118
$376$	−24.6410	−1.27076
$377$	−2.35612	−0.121346
$378$	−26.5503	−1.36560
$379$	19.5234	1.00285	0.501424	−	0.865202i	$-0.332810\pi$
$379$	19.5234	1.00285	0.501424	+	0.865202i	$0.332810\pi$
$380$	−7.87288	−0.403870
$381$	17.5688	0.900079
$382$	−29.6409	−1.51656
$383$	−10.1572	−0.519009	−0.259505	−	0.965742i	$-0.583559\pi$
$383$	−10.1572	−0.519009	−0.259505	+	0.965742i	$0.583559\pi$
$384$	36.9646	1.88634
$385$	−45.4386	−2.31576
$386$	40.9053	2.08202
$387$	−36.2853	−1.84449
$388$	0.950568	0.0482578
$389$	16.5866	0.840976	0.420488	−	0.907298i	$-0.361859\pi$
$389$	16.5866	0.840976	0.420488	+	0.907298i	$0.361859\pi$
$390$	−96.5557	−4.88929
$391$	4.96656	0.251170
$392$	−14.5526	−0.735019
$393$	−44.7417	−2.25692
$394$	41.7133	2.10148
$395$	27.8092	1.39923
$396$	9.18282	0.461454
$397$	4.10213	0.205880	0.102940	−	0.994688i	$-0.467175\pi$
$397$	4.10213	0.205880	0.102940	+	0.994688i	$0.467175\pi$
$398$	13.9501	0.699255
$399$	25.7905	1.29114
$400$	−68.8692	−3.44346
$401$	0.461417	0.0230421	0.0115210	−	0.999934i	$-0.496333\pi$
$401$	0.461417	0.0230421	0.0115210	+	0.999934i	$0.496333\pi$
$402$	−26.8215	−1.33773
$403$	3.40868	0.169799
$404$	13.2302	0.658229
$405$	−7.93700	−0.394393
$406$	−2.96397	−0.147099
$407$	−12.0647	−0.598026
$408$	−5.81501	−0.287886
$409$	−35.6609	−1.76332	−0.881659	−	0.471888i	$-0.843573\pi$
$409$	−35.6609	−1.76332	−0.881659	+	0.471888i	$0.843573\pi$
$410$	−62.7035	−3.09671
$411$	30.2132	1.49031
$412$	2.35412	0.115979
$413$	3.72637	0.183363
$414$	37.4256	1.83937
$415$	4.64194	0.227864
$416$	18.9755	0.930352
$417$	4.49385	0.220065
$418$	−11.6023	−0.567487
$419$	23.3682	1.14161	0.570805	−	0.821086i	$-0.306631\pi$
$419$	23.3682	1.14161	0.570805	+	0.821086i	$0.306631\pi$
$420$	−32.0908	−1.56587
$421$	29.8201	1.45334	0.726670	−	0.686986i	$-0.241067\pi$
$421$	29.8201	1.45334	0.726670	+	0.686986i	$0.241067\pi$
$422$	−5.48678	−0.267092
$423$	53.2910	2.59110
$424$	9.81952	0.476878
$425$	13.9963	0.678919
$426$	−50.6762	−2.45527
$427$	−2.10873	−0.102049
$428$	−7.27490	−0.351645
$429$	−37.5936	−1.81504
$430$	−57.0453	−2.75097
$431$	4.13945	0.199390	0.0996951	−	0.995018i	$-0.468213\pi$
$431$	4.13945	0.199390	0.0996951	+	0.995018i	$0.468213\pi$
$432$	−21.2648	−1.02310
$433$	32.6781	1.57041	0.785205	−	0.619236i	$-0.212557\pi$
$433$	32.6781	1.57041	0.785205	+	0.619236i	$0.212557\pi$
$434$	4.28809	0.205835
$435$	5.78568	0.277402
$436$	7.47157	0.357823
$437$	−12.4929	−0.597615
$438$	13.3404	0.637427
$439$	−25.9240	−1.23728	−0.618642	−	0.785673i	$-0.712317\pi$
$439$	−25.9240	−1.23728	−0.618642	+	0.785673i	$0.712317\pi$
$440$	−25.7704	−1.22856
$441$	31.4729	1.49871
$442$	−8.05150	−0.382971
$443$	−15.8958	−0.755234	−0.377617	−	0.925962i	$-0.623256\pi$
$443$	−15.8958	−0.755234	−0.377617	+	0.925962i	$0.623256\pi$
$444$	−8.52066	−0.404373
$445$	−39.7594	−1.88478
$446$	−11.5528	−0.547040
$447$	56.3304	2.66433
$448$	−12.8005	−0.604768
$449$	27.9962	1.32122	0.660611	−	0.750728i	$-0.270297\pi$
$449$	27.9962	1.32122	0.660611	+	0.750728i	$0.270297\pi$
$450$	105.469	4.97186
$451$	−24.4134	−1.14958
$452$	1.62100	0.0762455
$453$	59.6539	2.80278
$454$	1.07821	0.0506028
$455$	79.3165	3.71842
$456$	14.6270	0.684974
$457$	−23.0381	−1.07768	−0.538839	−	0.842409i	$-0.681137\pi$
$457$	−23.0381	−1.07768	−0.538839	+	0.842409i	$0.681137\pi$
$458$	17.8665	0.834847
$459$	4.32164	0.201717
$460$	15.5447	0.724777
$461$	−0.618810	−0.0288209	−0.0144104	−	0.999896i	$-0.504587\pi$
$461$	−0.618810	−0.0288209	−0.0144104	+	0.999896i	$0.504587\pi$
$462$	−47.2924	−2.20024
$463$	−5.88395	−0.273451	−0.136725	−	0.990609i	$-0.543658\pi$
$463$	−5.88395	−0.273451	−0.136725	+	0.990609i	$0.543658\pi$
$464$	−2.37392	−0.110207
$465$	−8.37037	−0.388166
$466$	−29.6955	−1.37562
$467$	14.1437	0.654494	0.327247	−	0.944939i	$-0.393879\pi$
$467$	14.1437	0.654494	0.327247	+	0.944939i	$0.393879\pi$
$468$	−16.0293	−0.740956
$469$	22.0328	1.01738
$470$	83.7805	3.86451
$471$	62.3516	2.87301
$472$	2.11341	0.0972775
$473$	−22.2104	−1.02123
$474$	28.9438	1.32943
$475$	−35.2061	−1.61537
$476$	−2.67596	−0.122652
$477$	−21.2366	−0.972359
$478$	25.8962	1.18447
$479$	0.610007	0.0278719	0.0139360	−	0.999903i	$-0.495564\pi$
$479$	0.610007	0.0278719	0.0139360	+	0.999903i	$0.495564\pi$
$480$	−46.5963	−2.12682
$481$	21.0599	0.960249
$482$	22.4314	1.02172
$483$	−50.9225	−2.31705
$484$	−2.27841	−0.103564
$485$	5.76931	0.261971
$486$	−29.6357	−1.34430
$487$	10.0370	0.454819	0.227410	−	0.973799i	$-0.426974\pi$
$487$	10.0370	0.454819	0.227410	+	0.973799i	$0.426974\pi$
$488$	−1.19596	−0.0541387
$489$	−29.4917	−1.33366
$490$	49.4796	2.23526
$491$	9.49823	0.428649	0.214325	−	0.976762i	$-0.431245\pi$
$491$	9.49823	0.428649	0.214325	+	0.976762i	$0.431245\pi$
$492$	−17.2419	−0.777323
$493$	0.482451	0.0217285
$494$	20.2527	0.911213
$495$	55.7336	2.50504
$496$	3.43444	0.154211
$497$	41.6284	1.86729
$498$	4.83132	0.216497
$499$	−4.77656	−0.213828	−0.106914	−	0.994268i	$-0.534097\pi$
$499$	−4.77656	−0.213828	−0.106914	+	0.994268i	$0.534097\pi$
$500$	28.1572	1.25923
$501$	−45.5215	−2.03375
$502$	−49.2133	−2.19650
$503$	0.0523954	0.00233619	0.00116810	−	0.999999i	$-0.499628\pi$
$503$	0.0523954	0.00233619	0.00116810	+	0.999999i	$0.499628\pi$
$504$	35.9955	1.60337
$505$	80.2987	3.57324
$506$	22.9084	1.01840
$507$	29.8533	1.32583
$508$	4.58532	0.203441
$509$	−9.36114	−0.414925	−0.207463	−	0.978243i	$-0.566521\pi$
$509$	−9.36114	−0.414925	−0.207463	+	0.978243i	$0.566521\pi$
$510$	19.7713	0.875487
$511$	−10.9586	−0.484778
$512$	−1.67929	−0.0742149
$513$	−10.8706	−0.479950
$514$	21.2100	0.935533
$515$	14.2879	0.629601
$516$	−15.6860	−0.690538
$517$	32.6196	1.43461
$518$	26.4931	1.16404
$519$	44.8819	1.97010
$520$	44.9843	1.97269
$521$	5.68405	0.249023	0.124511	−	0.992218i	$-0.460264\pi$
$521$	5.68405	0.249023	0.124511	+	0.992218i	$0.460264\pi$
$522$	3.63552	0.159122
$523$	25.1380	1.09921	0.549604	−	0.835425i	$-0.314779\pi$
$523$	25.1380	1.09921	0.549604	+	0.835425i	$0.314779\pi$
$524$	−11.6772	−0.510121
$525$	−143.504	−6.26305
$526$	−13.8895	−0.605609
$527$	−0.697981	−0.0304045
$528$	−37.8777	−1.64842
$529$	1.66676	0.0724678
$530$	−33.3868	−1.45023
$531$	−4.57066	−0.198350
$532$	6.73110	0.291830
$533$	42.6155	1.84588
$534$	−41.3815	−1.79075
$535$	−44.1537	−1.90893
$536$	12.4958	0.539738
$537$	−2.26132	−0.0975830
$538$	−20.4720	−0.882609
$539$	19.2647	0.829790
$540$	13.5262	0.582075
$541$	15.3248	0.658863	0.329432	−	0.944179i	$-0.393143\pi$
$541$	15.3248	0.658863	0.329432	+	0.944179i	$0.393143\pi$
$542$	−45.2632	−1.94422
$543$	−57.3431	−2.46083
$544$	−3.88553	−0.166591
$545$	45.3474	1.94247
$546$	82.5525	3.53292
$547$	17.4657	0.746778	0.373389	−	0.927675i	$-0.378196\pi$
$547$	17.4657	0.746778	0.373389	+	0.927675i	$0.378196\pi$
$548$	7.88539	0.336847
$549$	2.58650	0.110389
$550$	64.5580	2.75276
$551$	−1.21356	−0.0516992
$552$	−28.8806	−1.22924
$553$	−23.7761	−1.01106
$554$	−28.5807	−1.21428
$555$	−51.7147	−2.19517
$556$	1.17286	0.0497402
$557$	−23.6047	−1.00016	−0.500082	−	0.865978i	$-0.666697\pi$
$557$	−23.6047	−1.00016	−0.500082	+	0.865978i	$0.666697\pi$
$558$	−5.25964	−0.222658
$559$	38.7700	1.63979
$560$	79.9159	3.37706
$561$	7.69787	0.325005
$562$	−43.3007	−1.82653
$563$	−5.83973	−0.246115	−0.123058	−	0.992400i	$-0.539270\pi$
$563$	−5.83973	−0.246115	−0.123058	+	0.992400i	$0.539270\pi$
$564$	23.0375	0.970053
$565$	9.83839	0.413904
$566$	−6.49716	−0.273096
$567$	6.78592	0.284982
$568$	23.6095	0.990633
$569$	−14.8582	−0.622888	−0.311444	−	0.950265i	$-0.600813\pi$
$569$	−14.8582	−0.622888	−0.311444	+	0.950265i	$0.600813\pi$
$570$	−49.7326	−2.08307
$571$	9.49710	0.397441	0.198721	−	0.980056i	$-0.436321\pi$
$571$	9.49710	0.397441	0.198721	+	0.980056i	$0.436321\pi$
$572$	−9.81161	−0.410244
$573$	−49.4681	−2.06656
$574$	53.6098	2.23763
$575$	69.5133	2.89891
$576$	15.7007	0.654198
$577$	−19.0488	−0.793012	−0.396506	−	0.918032i	$-0.629777\pi$
$577$	−19.0488	−0.793012	−0.396506	+	0.918032i	$0.629777\pi$
$578$	1.64867	0.0685756
$579$	68.2672	2.83709
$580$	1.51001	0.0626999
$581$	−3.96873	−0.164651
$582$	6.00469	0.248902
$583$	−12.9990	−0.538365
$584$	−6.21513	−0.257184
$585$	−97.2873	−4.02233
$586$	42.7255	1.76497
$587$	22.3927	0.924246	0.462123	−	0.886816i	$-0.347088\pi$
$587$	22.3927	0.924246	0.462123	+	0.886816i	$0.347088\pi$
$588$	13.6056	0.561087
$589$	1.75570	0.0723423
$590$	−7.18568	−0.295830
$591$	69.6157	2.86361
$592$	21.2191	0.872098
$593$	16.2607	0.667749	0.333874	−	0.942618i	$-0.391644\pi$
$593$	16.2607	0.667749	0.333874	+	0.942618i	$0.391644\pi$
$594$	19.9336	0.817887
$595$	−16.2413	−0.665828
$596$	14.7017	0.602207
$597$	23.2814	0.952846
$598$	−39.9883	−1.63524
$599$	12.1333	0.495752	0.247876	−	0.968792i	$-0.420267\pi$
$599$	12.1333	0.495752	0.247876	+	0.968792i	$0.420267\pi$
$600$	−81.3883	−3.32267
$601$	−3.01801	−0.123107	−0.0615536	−	0.998104i	$-0.519606\pi$
$601$	−3.01801	−0.123107	−0.0615536	+	0.998104i	$0.519606\pi$
$602$	48.7722	1.98781
$603$	−27.0247	−1.10053
$604$	15.5692	0.633500
$605$	−13.8284	−0.562206
$606$	83.5747	3.39499
$607$	−24.1914	−0.981899	−0.490950	−	0.871188i	$-0.663350\pi$
$607$	−24.1914	−0.981899	−0.490950	+	0.871188i	$0.663350\pi$
$608$	9.77365	0.396374
$609$	−4.94660	−0.200446
$610$	4.06633	0.164641
$611$	−56.9401	−2.30355
$612$	3.28225	0.132677
$613$	−5.44529	−0.219933	−0.109967	−	0.993935i	$-0.535074\pi$
$613$	−5.44529	−0.219933	−0.109967	+	0.993935i	$0.535074\pi$
$614$	25.8942	1.04501
$615$	−104.647	−4.21976
$616$	22.0330	0.887735
$617$	14.6097	0.588163	0.294082	−	0.955780i	$-0.404986\pi$
$617$	14.6097	0.588163	0.294082	+	0.955780i	$0.404986\pi$
$618$	14.8708	0.598193
$619$	2.19349	0.0881637	0.0440819	−	0.999028i	$-0.485964\pi$
$619$	2.19349	0.0881637	0.0440819	+	0.999028i	$0.485964\pi$
$620$	−2.18459	−0.0877354
$621$	21.4637	0.861309
$622$	−10.8725	−0.435949
$623$	33.9932	1.36191
$624$	66.1185	2.64686
$625$	100.914	4.03656
$626$	16.4018	0.655548
$627$	−19.3632	−0.773292
$628$	16.2732	0.649373
$629$	−4.31234	−0.171944
$630$	−122.386	−4.87599
$631$	−15.5718	−0.619904	−0.309952	−	0.950752i	$-0.600313\pi$
$631$	−15.5718	−0.619904	−0.309952	+	0.950752i	$0.600313\pi$
$632$	−13.4846	−0.536388
$633$	−9.15695	−0.363956
$634$	−3.65341	−0.145095
$635$	27.8298	1.10439
$636$	−9.18052	−0.364031
$637$	−33.6281	−1.33239
$638$	2.22531	0.0881010
$639$	−51.0602	−2.01991
$640$	58.5536	2.31453
$641$	−11.2097	−0.442757	−0.221379	−	0.975188i	$-0.571056\pi$
$641$	−11.2097	−0.442757	−0.221379	+	0.975188i	$0.571056\pi$
$642$	−45.9551	−1.81370
$643$	−22.2175	−0.876172	−0.438086	−	0.898933i	$-0.644344\pi$
$643$	−22.2175	−0.876172	−0.438086	+	0.898933i	$0.644344\pi$
$644$	−13.2903	−0.523712
$645$	−95.2035	−3.74864
$646$	−4.14706	−0.163164
$647$	−8.39581	−0.330073	−0.165037	−	0.986287i	$-0.552774\pi$
$647$	−8.39581	−0.330073	−0.165037	+	0.986287i	$0.552774\pi$
$648$	3.84863	0.151188
$649$	−2.79772	−0.109820
$650$	−112.691	−4.42010
$651$	7.15644	0.280483
$652$	−7.69708	−0.301441
$653$	−38.8725	−1.52120	−0.760599	−	0.649222i	$-0.775094\pi$
$653$	−38.8725	−1.52120	−0.760599	+	0.649222i	$0.775094\pi$
$654$	47.1975	1.84557
$655$	−70.8728	−2.76923
$656$	42.9375	1.67643
$657$	13.4414	0.524400
$658$	−71.6301	−2.79243
$659$	−49.8899	−1.94344	−0.971718	−	0.236145i	$-0.924116\pi$
$659$	−49.8899	−1.94344	−0.971718	+	0.236145i	$0.924116\pi$
$660$	24.0934	0.937835
$661$	3.99656	0.155448	0.0777240	−	0.996975i	$-0.475235\pi$
$661$	3.99656	0.155448	0.0777240	+	0.996975i	$0.475235\pi$
$662$	−36.3950	−1.41453
$663$	−13.4372	−0.521859
$664$	−2.25086	−0.0873503
$665$	40.8533	1.58422
$666$	−32.4957	−1.25918
$667$	2.39612	0.0927783
$668$	−11.8807	−0.459679
$669$	−19.2806	−0.745429
$670$	−42.4864	−1.64139
$671$	1.58321	0.0611191
$672$	39.8386	1.53681
$673$	30.3162	1.16860	0.584301	−	0.811537i	$-0.301369\pi$
$673$	30.3162	1.16860	0.584301	+	0.811537i	$0.301369\pi$
$674$	−1.82222	−0.0701892
$675$	60.4868	2.32814
$676$	7.79145	0.299671
$677$	12.8168	0.492591	0.246295	−	0.969195i	$-0.420787\pi$
$677$	12.8168	0.492591	0.246295	+	0.969195i	$0.420787\pi$
$678$	10.2398	0.393256
$679$	−4.93261	−0.189296
$680$	−9.21122	−0.353234
$681$	1.79943	0.0689544
$682$	−3.21945	−0.123279
$683$	16.8445	0.644536	0.322268	−	0.946649i	$-0.395555\pi$
$683$	16.8445	0.644536	0.322268	+	0.946649i	$0.395555\pi$
$684$	−8.25616	−0.315682
$685$	47.8590	1.82860
$686$	0.701189	0.0267715
$687$	29.8176	1.13761
$688$	39.0629	1.48926
$689$	22.6908	0.864452
$690$	98.1953	3.73823
$691$	28.1696	1.07162	0.535811	−	0.844338i	$-0.320006\pi$
$691$	28.1696	1.07162	0.535811	+	0.844338i	$0.320006\pi$
$692$	11.7138	0.445292
$693$	−47.6507	−1.81010
$694$	−11.8917	−0.451402
$695$	7.11845	0.270018
$696$	−2.80546	−0.106341
$697$	−8.72618	−0.330527
$698$	−11.8892	−0.450014
$699$	−49.5592	−1.87450
$700$	−37.4535	−1.41561
$701$	14.3889	0.543462	0.271731	−	0.962373i	$-0.412404\pi$
$701$	14.3889	0.543462	0.271731	+	0.962373i	$0.412404\pi$
$702$	−34.7957	−1.31328
$703$	10.8472	0.409112
$704$	9.61049	0.362209
$705$	139.822	5.26601
$706$	41.5817	1.56495
$707$	−68.6532	−2.58197
$708$	−1.97588	−0.0742580
$709$	−36.2467	−1.36127	−0.680637	−	0.732621i	$-0.738297\pi$
$709$	−36.2467	−1.36127	−0.680637	+	0.732621i	$0.738297\pi$
$710$	−80.2734	−3.01261
$711$	29.1631	1.09370
$712$	19.2792	0.722518
$713$	−3.46657	−0.129824
$714$	−16.9039	−0.632613
$715$	−59.5499	−2.22704
$716$	−0.590184	−0.0220562
$717$	43.2185	1.61402
$718$	−4.25780	−0.158900
$719$	16.5927	0.618802	0.309401	−	0.950932i	$-0.399872\pi$
$719$	16.5927	0.618802	0.309401	+	0.950932i	$0.399872\pi$
$720$	−98.0225	−3.65308
$721$	−12.2158	−0.454940
$722$	−20.8933	−0.777566
$723$	37.4360	1.39226
$724$	−14.9661	−0.556210
$725$	6.75251	0.250782
$726$	−14.3926	−0.534160
$727$	−39.5218	−1.46578	−0.732892	−	0.680345i	$-0.761830\pi$
$727$	−39.5218	−1.46578	−0.732892	+	0.680345i	$0.761830\pi$
$728$	−38.4603	−1.42543
$729$	−43.9962	−1.62949
$730$	21.1317	0.782120
$731$	−7.93875	−0.293625
$732$	1.11814	0.0413275
$733$	15.0634	0.556378	0.278189	−	0.960526i	$-0.410266\pi$
$733$	15.0634	0.556378	0.278189	+	0.960526i	$0.410266\pi$
$734$	31.1377	1.14931
$735$	82.5771	3.04590
$736$	−19.2978	−0.711325
$737$	−16.5419	−0.609330
$738$	−65.7562	−2.42052
$739$	32.2005	1.18451	0.592257	−	0.805749i	$-0.298237\pi$
$739$	32.2005	1.18451	0.592257	+	0.805749i	$0.298237\pi$
$740$	−13.4971	−0.496163
$741$	33.8000	1.24167
$742$	28.5448	1.04791
$743$	−27.1302	−0.995310	−0.497655	−	0.867375i	$-0.665805\pi$
$743$	−27.1302	−0.995310	−0.497655	+	0.867375i	$0.665805\pi$
$744$	4.05876	0.148801
$745$	89.2298	3.26913
$746$	−44.3095	−1.62229
$747$	4.86793	0.178108
$748$	2.00908	0.0734593
$749$	37.7503	1.37936
$750$	177.868	6.49481
$751$	−28.6391	−1.04505	−0.522527	−	0.852623i	$-0.675011\pi$
$751$	−28.6391	−1.04505	−0.522527	+	0.852623i	$0.675011\pi$
$752$	−57.3704	−2.09208
$753$	−82.1326	−2.99308
$754$	−3.88446	−0.141464
$755$	94.4944	3.43900
$756$	−11.5645	−0.420598
$757$	33.7173	1.22548	0.612738	−	0.790286i	$-0.290068\pi$
$757$	33.7173	1.22548	0.612738	+	0.790286i	$0.290068\pi$
$758$	32.1876	1.16911
$759$	38.2320	1.38773
$760$	23.1699	0.840459
$761$	25.3801	0.920028	0.460014	−	0.887912i	$-0.347844\pi$
$761$	25.3801	0.920028	0.460014	+	0.887912i	$0.347844\pi$
$762$	28.9652	1.04930
$763$	−38.7708	−1.40360
$764$	−12.9107	−0.467094
$765$	19.9211	0.720248
$766$	−16.7459	−0.605054
$767$	4.88363	0.176338
$768$	42.0392	1.51696
$769$	−40.1373	−1.44739	−0.723695	−	0.690120i	$-0.757558\pi$
$769$	−40.1373	−1.44739	−0.723695	+	0.690120i	$0.757558\pi$
$770$	−74.9132	−2.69968
$771$	35.3976	1.27481
$772$	17.8172	0.641254
$773$	−24.1369	−0.868144	−0.434072	−	0.900878i	$-0.642924\pi$
$773$	−24.1369	−0.868144	−0.434072	+	0.900878i	$0.642924\pi$
$774$	−59.8225	−2.15028
$775$	−9.76912	−0.350917
$776$	−2.79752	−0.100425
$777$	44.2147	1.58619
$778$	27.3459	0.980398
$779$	21.9498	0.786432
$780$	−42.0569	−1.50588
$781$	−31.2541	−1.11836
$782$	8.18823	0.292810
$783$	2.08498	0.0745112
$784$	−33.8822	−1.21008
$785$	98.7677	3.52517
$786$	−73.7643	−2.63108
$787$	−3.79339	−0.135220	−0.0676099	−	0.997712i	$-0.521537\pi$
$787$	−3.79339	−0.135220	−0.0676099	+	0.997712i	$0.521537\pi$
$788$	18.1691	0.647248
$789$	−23.1803	−0.825239
$790$	45.8482	1.63121
$791$	−8.41156	−0.299081
$792$	−27.0250	−0.960292
$793$	−2.76361	−0.0981388
$794$	6.76306	0.240012
$795$	−55.7196	−1.97617
$796$	6.07626	0.215367
$797$	−42.5651	−1.50773	−0.753866	−	0.657028i	$-0.771813\pi$
$797$	−42.5651	−1.50773	−0.753866	+	0.657028i	$0.771813\pi$
$798$	42.5200	1.50519
$799$	11.6594	0.412479
$800$	−54.3829	−1.92273
$801$	−41.6950	−1.47322
$802$	0.760725	0.0268621
$803$	8.22756	0.290344
$804$	−11.6827	−0.412016
$805$	−80.6634	−2.84301
$806$	5.61980	0.197949
$807$	−34.1659	−1.20270
$808$	−38.9366	−1.36978
$809$	7.15064	0.251403	0.125702	−	0.992068i	$-0.459882\pi$
$809$	7.15064	0.251403	0.125702	+	0.992068i	$0.459882\pi$
$810$	−13.0855	−0.459778
$811$	−45.2404	−1.58860	−0.794302	−	0.607523i	$-0.792163\pi$
$811$	−45.2404	−1.58860	−0.794302	+	0.607523i	$0.792163\pi$
$812$	−1.29102	−0.0453059
$813$	−75.5403	−2.64931
$814$	−19.8907	−0.697170
$815$	−46.7161	−1.63639
$816$	−13.5388	−0.473952
$817$	19.9691	0.698630
$818$	−58.7930	−2.05565
$819$	83.1780	2.90647
$820$	−27.3119	−0.953772
$821$	−2.80680	−0.0979580	−0.0489790	−	0.998800i	$-0.515597\pi$
$821$	−2.80680	−0.0979580	−0.0489790	+	0.998800i	$0.515597\pi$
$822$	49.8116	1.73738
$823$	27.6653	0.964351	0.482176	−	0.876075i	$-0.339847\pi$
$823$	27.6653	0.964351	0.482176	+	0.876075i	$0.339847\pi$
$824$	−6.92817	−0.241354
$825$	107.741	3.75108
$826$	6.14356	0.213762
$827$	44.4411	1.54537	0.772684	−	0.634791i	$-0.218914\pi$
$827$	44.4411	1.54537	0.772684	+	0.634791i	$0.218914\pi$
$828$	16.3015	0.566517
$829$	−0.170810	−0.00593247	−0.00296624	−	0.999996i	$-0.500944\pi$
$829$	−0.170810	−0.00593247	−0.00296624	+	0.999996i	$0.500944\pi$
$830$	7.65303	0.265640
$831$	−47.6986	−1.65465
$832$	−16.7759	−0.581598
$833$	6.88587	0.238581
$834$	7.40887	0.256548
$835$	−72.1080	−2.49540
$836$	−5.05363	−0.174783
$837$	−3.01642	−0.104263
$838$	38.5264	1.33087
$839$	42.0387	1.45134	0.725669	−	0.688044i	$-0.241530\pi$
$839$	42.0387	1.45134	0.725669	+	0.688044i	$0.241530\pi$
$840$	94.4432	3.25860
$841$	−28.7672	−0.991974
$842$	49.1634	1.69428
$843$	−72.2649	−2.48894
$844$	−2.38989	−0.0822633
$845$	47.2889	1.62679
$846$	87.8593	3.02066
$847$	11.8229	0.406241
$848$	22.8623	0.785095
$849$	−10.8432	−0.372137
$850$	23.0752	0.791474
$851$	−21.4175	−0.734183
$852$	−22.0731	−0.756213
$853$	−30.5732	−1.04681	−0.523403	−	0.852085i	$-0.675338\pi$
$853$	−30.5732	−1.04681	−0.523403	+	0.852085i	$0.675338\pi$
$854$	−3.47660	−0.118967
$855$	−50.1094	−1.71370
$856$	21.4100	0.731779
$857$	−32.3088	−1.10365	−0.551824	−	0.833960i	$-0.686068\pi$
$857$	−32.3088	−1.10365	−0.551824	+	0.833960i	$0.686068\pi$
$858$	−61.9795	−2.11594
$859$	−2.95193	−0.100718	−0.0503592	−	0.998731i	$-0.516037\pi$
$859$	−2.95193	−0.100718	−0.0503592	+	0.998731i	$0.516037\pi$
$860$	−24.8473	−0.847287
$861$	89.4700	3.04913
$862$	6.82458	0.232446
$863$	−33.0830	−1.12616	−0.563079	−	0.826403i	$-0.690383\pi$
$863$	−33.0830	−1.12616	−0.563079	+	0.826403i	$0.690383\pi$
$864$	−16.7919	−0.571271
$865$	71.0949	2.41730
$866$	53.8755	1.83076
$867$	2.75148	0.0934453
$868$	1.86777	0.0633962
$869$	17.8508	0.605548
$870$	9.53868	0.323391
$871$	28.8752	0.978400
$872$	−21.9888	−0.744636
$873$	6.05019	0.204768
$874$	−20.5966	−0.696691
$875$	−146.111	−4.93945
$876$	5.81068	0.196325
$877$	42.5191	1.43577	0.717884	−	0.696163i	$-0.245111\pi$
$877$	42.5191	1.43577	0.717884	+	0.696163i	$0.245111\pi$
$878$	−42.7401	−1.44241
$879$	71.3050	2.40506
$880$	−59.9999	−2.02260
$881$	−23.8658	−0.804058	−0.402029	−	0.915627i	$-0.631695\pi$
$881$	−23.8658	−0.804058	−0.402029	+	0.915627i	$0.631695\pi$
$882$	51.8885	1.74718
$883$	−23.0560	−0.775897	−0.387948	−	0.921681i	$-0.626816\pi$
$883$	−23.0560	−0.775897	−0.387948	+	0.921681i	$0.626816\pi$
$884$	−3.50701	−0.117953
$885$	−11.9923	−0.403115
$886$	−26.2070	−0.880442
$887$	23.2752	0.781505	0.390752	−	0.920496i	$-0.372215\pi$
$887$	23.2752	0.781505	0.390752	+	0.920496i	$0.372215\pi$
$888$	25.0763	0.841505
$889$	−23.7937	−0.798017
$890$	−65.5501	−2.19725
$891$	−5.09479	−0.170682
$892$	−5.03206	−0.168486
$893$	−29.3279	−0.981421
$894$	92.8702	3.10604
$895$	−3.58202	−0.119734
$896$	−50.0618	−1.67245
$897$	−66.7369	−2.22828
$898$	46.1565	1.54026
$899$	−0.336742	−0.0112310
$900$	45.9393	1.53131
$901$	−4.64630	−0.154791
$902$	−40.2496	−1.34017
$903$	81.3964	2.70870
$904$	−4.77060	−0.158668
$905$	−90.8340	−3.01942
$906$	98.3496	3.26745
$907$	40.8951	1.35790	0.678950	−	0.734184i	$-0.262435\pi$
$907$	40.8951	1.35790	0.678950	+	0.734184i	$0.262435\pi$
$908$	0.469637	0.0155854
$909$	84.2079	2.79300
$910$	130.767	4.33488
$911$	−47.1206	−1.56117	−0.780587	−	0.625047i	$-0.785080\pi$
$911$	−47.1206	−1.56117	−0.780587	+	0.625047i	$0.785080\pi$
$912$	34.0554	1.12769
$913$	2.97968	0.0986129
$914$	−37.9823	−1.25634
$915$	6.78634	0.224349
$916$	7.78214	0.257129
$917$	60.5943	2.00100
$918$	7.12496	0.235159
$919$	22.3847	0.738403	0.369201	−	0.929349i	$-0.379631\pi$
$919$	22.3847	0.738403	0.369201	+	0.929349i	$0.379631\pi$
$920$	−45.7481	−1.50827
$921$	43.2151	1.42399
$922$	−1.02021	−0.0335990
$923$	54.5565	1.79575
$924$	−20.5992	−0.677664
$925$	−60.3567	−1.98452
$926$	−9.70070	−0.318785
$927$	14.9835	0.492123
$928$	−1.87458	−0.0615361
$929$	−41.8371	−1.37263	−0.686315	−	0.727304i	$-0.740773\pi$
$929$	−41.8371	−1.37263	−0.686315	+	0.727304i	$0.740773\pi$
$930$	−13.8000	−0.452519
$931$	−17.3207	−0.567662
$932$	−12.9345	−0.423685
$933$	−18.1453	−0.594051
$934$	23.3184	0.763000
$935$	12.1938	0.398779
$936$	47.1743	1.54194
$937$	−26.4597	−0.864400	−0.432200	−	0.901778i	$-0.642263\pi$
$937$	−26.4597	−0.864400	−0.432200	+	0.901778i	$0.642263\pi$
$938$	36.3248	1.18605
$939$	27.3731	0.893288
$940$	36.4924	1.19025
$941$	−19.7437	−0.643626	−0.321813	−	0.946803i	$-0.604292\pi$
$941$	−19.7437	−0.643626	−0.321813	+	0.946803i	$0.604292\pi$
$942$	102.797	3.34931
$943$	−43.3391	−1.41132
$944$	4.92054	0.160150
$945$	−70.1890	−2.28325
$946$	−36.6176	−1.19054
$947$	−9.54171	−0.310064	−0.155032	−	0.987909i	$-0.549548\pi$
$947$	−9.54171	−0.310064	−0.155032	+	0.987909i	$0.549548\pi$
$948$	12.6071	0.409459
$949$	−14.3618	−0.466205
$950$	−58.0433	−1.88317
$951$	−6.09721	−0.197716
$952$	7.87535	0.255241
$953$	18.5147	0.599750	0.299875	−	0.953978i	$-0.403055\pi$
$953$	18.5147	0.599750	0.299875	+	0.953978i	$0.403055\pi$
$954$	−35.0122	−1.13356
$955$	−78.3596	−2.53566
$956$	11.2797	0.364810
$957$	3.71385	0.120052
$958$	1.00570	0.0324927
$959$	−40.9182	−1.32132
$960$	41.1948	1.32956
$961$	−30.5128	−0.984285
$962$	34.7208	1.11944
$963$	−46.3033	−1.49210
$964$	9.77049	0.314686
$965$	108.138	3.48109
$966$	−83.9543	−2.70119
$967$	14.5623	0.468291	0.234146	−	0.972202i	$-0.424771\pi$
$967$	14.5623	0.468291	0.234146	+	0.972202i	$0.424771\pi$
$968$	6.70536	0.215518
$969$	−6.92107	−0.222337
$970$	9.51170	0.305402
$971$	−17.8860	−0.573989	−0.286994	−	0.957932i	$-0.592656\pi$
$971$	−17.8860	−0.573989	−0.286994	+	0.957932i	$0.592656\pi$
$972$	−12.9085	−0.414039
$973$	−6.08609	−0.195111
$974$	16.5477	0.530222
$975$	−188.071	−6.02310
$976$	−2.78450	−0.0891297
$977$	38.4361	1.22968	0.614840	−	0.788652i	$-0.289221\pi$
$977$	38.4361	1.22968	0.614840	+	0.788652i	$0.289221\pi$
$978$	−48.6221	−1.55476
$979$	−25.5217	−0.815677
$980$	21.5519	0.688451
$981$	47.5552	1.51832
$982$	15.6595	0.499713
$983$	−43.2399	−1.37914	−0.689569	−	0.724220i	$-0.742200\pi$
$983$	−43.2399	−1.37914	−0.689569	+	0.724220i	$0.742200\pi$
$984$	50.7428	1.61762
$985$	110.274	3.51363
$986$	0.795403	0.0253308
$987$	−119.544	−3.80513
$988$	8.82150	0.280649
$989$	−39.4283	−1.25375
$990$	91.8863	2.92034
$991$	−16.3550	−0.519534	−0.259767	−	0.965671i	$-0.583646\pi$
$991$	−16.3550	−0.519534	−0.259767	+	0.965671i	$0.583646\pi$
$992$	2.71203	0.0861070
$993$	−60.7401	−1.92753
$994$	68.6316	2.17686
$995$	36.8788	1.16914
$996$	2.10439	0.0666800
$997$	−17.0792	−0.540904	−0.270452	−	0.962734i	$-0.587173\pi$
$997$	−17.0792	−0.540904	−0.270452	+	0.962734i	$0.587173\pi$
$998$	−7.87497	−0.249278
$999$	−18.6364	−0.589630

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1003.2.a.i.1.13	✓	18
3.2	odd	2		9027.2.a.q.1.6		18

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1003.2.a.i.1.13	✓	18	1.1	even	1	trivial
9027.2.a.q.1.6		18	3.2	odd	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 1003 = 17 \cdot 59 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1003.a (trivial)

\(f(q)\)	\(=\)	\(q+1.64867 q^{2} +2.75148 q^{3} +0.718114 q^{4} +4.35847 q^{5} +4.53629 q^{6} -3.72637 q^{7} -2.11341 q^{8} +4.57066 q^{9} +O(q^{10})\)	\(q+1.64867 q^{2} +2.75148 q^{3} +0.718114 q^{4} +4.35847 q^{5} +4.53629 q^{6} -3.72637 q^{7} -2.11341 q^{8} +4.57066 q^{9} +7.18568 q^{10} +2.79772 q^{11} +1.97588 q^{12} -4.88363 q^{13} -6.14356 q^{14} +11.9923 q^{15} -4.92054 q^{16} +1.00000 q^{17} +7.53551 q^{18} -2.51539 q^{19} +3.12988 q^{20} -10.2531 q^{21} +4.61252 q^{22} +4.96656 q^{23} -5.81501 q^{24} +13.9963 q^{25} -8.05150 q^{26} +4.32164 q^{27} -2.67596 q^{28} +0.482451 q^{29} +19.7713 q^{30} -0.697981 q^{31} -3.88553 q^{32} +7.69787 q^{33} +1.64867 q^{34} -16.2413 q^{35} +3.28225 q^{36} -4.31234 q^{37} -4.14706 q^{38} -13.4372 q^{39} -9.21122 q^{40} -8.72618 q^{41} -16.9039 q^{42} -7.93875 q^{43} +2.00908 q^{44} +19.9211 q^{45} +8.18823 q^{46} +11.6594 q^{47} -13.5388 q^{48} +6.88587 q^{49} +23.0752 q^{50} +2.75148 q^{51} -3.50701 q^{52} -4.64630 q^{53} +7.12496 q^{54} +12.1938 q^{55} +7.87535 q^{56} -6.92107 q^{57} +0.795403 q^{58} -1.00000 q^{59} +8.61181 q^{60} +0.565893 q^{61} -1.15074 q^{62} -17.0320 q^{63} +3.43512 q^{64} -21.2852 q^{65} +12.6913 q^{66} -5.91265 q^{67} +0.718114 q^{68} +13.6654 q^{69} -26.7765 q^{70} -11.1713 q^{71} -9.65967 q^{72} +2.94081 q^{73} -7.10963 q^{74} +38.5105 q^{75} -1.80634 q^{76} -10.4253 q^{77} -22.1536 q^{78} +6.38050 q^{79} -21.4460 q^{80} -1.82105 q^{81} -14.3866 q^{82} +1.06504 q^{83} -7.36286 q^{84} +4.35847 q^{85} -13.0884 q^{86} +1.32746 q^{87} -5.91272 q^{88} -9.12233 q^{89} +32.8433 q^{90} +18.1983 q^{91} +3.56656 q^{92} -1.92048 q^{93} +19.2225 q^{94} -10.9633 q^{95} -10.6910 q^{96} +1.32370 q^{97} +11.3525 q^{98} +12.7874 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 18 q + 5 q^{2} + q^{3} + 21 q^{4} + 21 q^{5} + 5 q^{6} - q^{7} + 9 q^{8} + 17 q^{9}+O(q^{10}) \) 18 * q + 5 * q^2 + q^3 + 21 * q^4 + 21 * q^5 + 5 * q^6 - q^7 + 9 * q^8 + 17 * q^9	\( 18 q + 5 q^{2} + q^{3} + 21 q^{4} + 21 q^{5} + 5 q^{6} - q^{7} + 9 q^{8} + 17 q^{9} + 10 q^{10} + 6 q^{11} + 20 q^{12} + 12 q^{13} + 9 q^{14} - q^{15} + 19 q^{16} + 18 q^{17} + 10 q^{18} - 14 q^{19} + 17 q^{20} - 14 q^{21} - 4 q^{22} + 7 q^{23} - 3 q^{24} + 35 q^{25} + 3 q^{26} + 13 q^{27} + q^{28} + 23 q^{29} + 17 q^{30} - q^{31} + 13 q^{32} + 7 q^{33} + 5 q^{34} + 5 q^{35} - 16 q^{36} + 36 q^{37} - 19 q^{38} + 8 q^{39} - 4 q^{40} + 37 q^{41} + 9 q^{42} - 15 q^{43} - 9 q^{44} + 17 q^{45} + q^{46} + 23 q^{47} + 17 q^{48} + 15 q^{49} + 32 q^{50} + q^{51} - 11 q^{52} + 35 q^{53} - 17 q^{54} - 6 q^{55} + 37 q^{56} - 16 q^{57} + 2 q^{58} - 18 q^{59} - 6 q^{60} + 39 q^{61} - q^{62} + 15 q^{63} + 5 q^{64} + 15 q^{65} - 36 q^{66} + 14 q^{67} + 21 q^{68} + 16 q^{69} - 45 q^{70} + 3 q^{71} - 71 q^{72} + 56 q^{73} - 27 q^{74} + 16 q^{75} - q^{76} + 39 q^{77} - 71 q^{78} - 22 q^{79} + 45 q^{80} - 18 q^{81} + 5 q^{82} + 12 q^{83} + 2 q^{84} + 21 q^{85} + 4 q^{86} + 8 q^{87} - 18 q^{88} + 34 q^{89} + 48 q^{90} + 3 q^{91} + 67 q^{92} - 19 q^{93} - 38 q^{94} - 72 q^{95} + 6 q^{96} + 31 q^{97} + 19 q^{98} + 44 q^{99}+O(q^{100}) \) 18 * q + 5 * q^2 + q^3 + 21 * q^4 + 21 * q^5 + 5 * q^6 - q^7 + 9 * q^8 + 17 * q^9 + 10 * q^10 + 6 * q^11 + 20 * q^12 + 12 * q^13 + 9 * q^14 - q^15 + 19 * q^16 + 18 * q^17 + 10 * q^18 - 14 * q^19 + 17 * q^20 - 14 * q^21 - 4 * q^22 + 7 * q^23 - 3 * q^24 + 35 * q^25 + 3 * q^26 + 13 * q^27 + q^28 + 23 * q^29 + 17 * q^30 - q^31 + 13 * q^32 + 7 * q^33 + 5 * q^34 + 5 * q^35 - 16 * q^36 + 36 * q^37 - 19 * q^38 + 8 * q^39 - 4 * q^40 + 37 * q^41 + 9 * q^42 - 15 * q^43 - 9 * q^44 + 17 * q^45 + q^46 + 23 * q^47 + 17 * q^48 + 15 * q^49 + 32 * q^50 + q^51 - 11 * q^52 + 35 * q^53 - 17 * q^54 - 6 * q^55 + 37 * q^56 - 16 * q^57 + 2 * q^58 - 18 * q^59 - 6 * q^60 + 39 * q^61 - q^62 + 15 * q^63 + 5 * q^64 + 15 * q^65 - 36 * q^66 + 14 * q^67 + 21 * q^68 + 16 * q^69 - 45 * q^70 + 3 * q^71 - 71 * q^72 + 56 * q^73 - 27 * q^74 + 16 * q^75 - q^76 + 39 * q^77 - 71 * q^78 - 22 * q^79 + 45 * q^80 - 18 * q^81 + 5 * q^82 + 12 * q^83 + 2 * q^84 + 21 * q^85 + 4 * q^86 + 8 * q^87 - 18 * q^88 + 34 * q^89 + 48 * q^90 + 3 * q^91 + 67 * q^92 - 19 * q^93 - 38 * q^94 - 72 * q^95 + 6 * q^96 + 31 * q^97 + 19 * q^98 + 44 * q^99

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