LMFDB - Embedded newform 1003.2.a.i.1.3

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			1.3
Root			$-1.89397$ 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)

$f(q)$	$=$	$q-1.89397 q^{2} -0.0387693 q^{3} +1.58712 q^{4} +3.00387 q^{5} +0.0734279 q^{6} +0.643981 q^{7} +0.781977 q^{8} -2.99850 q^{9} +O(q^{10})$	\(q-1.89397 q^{2} -0.0387693 q^{3} +1.58712 q^{4} +3.00387 q^{5} +0.0734279 q^{6} +0.643981 q^{7} +0.781977 q^{8} -2.99850 q^{9} -5.68925 q^{10} +2.74182 q^{11} -0.0615316 q^{12} +5.33788 q^{13} -1.21968 q^{14} -0.116458 q^{15} -4.65529 q^{16} +1.00000 q^{17} +5.67906 q^{18} +4.06789 q^{19} +4.76752 q^{20} -0.0249667 q^{21} -5.19293 q^{22} -5.18141 q^{23} -0.0303167 q^{24} +4.02326 q^{25} -10.1098 q^{26} +0.232557 q^{27} +1.02208 q^{28} +3.49928 q^{29} +0.220568 q^{30} +6.36461 q^{31} +7.25302 q^{32} -0.106299 q^{33} -1.89397 q^{34} +1.93444 q^{35} -4.75898 q^{36} -4.12597 q^{37} -7.70446 q^{38} -0.206946 q^{39} +2.34896 q^{40} +0.691148 q^{41} +0.0472862 q^{42} -6.75318 q^{43} +4.35161 q^{44} -9.00711 q^{45} +9.81343 q^{46} -5.37976 q^{47} +0.180482 q^{48} -6.58529 q^{49} -7.61994 q^{50} -0.0387693 q^{51} +8.47187 q^{52} +9.68809 q^{53} -0.440457 q^{54} +8.23610 q^{55} +0.503578 q^{56} -0.157709 q^{57} -6.62754 q^{58} -1.00000 q^{59} -0.184833 q^{60} -7.56480 q^{61} -12.0544 q^{62} -1.93098 q^{63} -4.42643 q^{64} +16.0343 q^{65} +0.201326 q^{66} -8.43888 q^{67} +1.58712 q^{68} +0.200879 q^{69} -3.66377 q^{70} -1.57561 q^{71} -2.34475 q^{72} +10.0121 q^{73} +7.81447 q^{74} -0.155979 q^{75} +6.45624 q^{76} +1.76568 q^{77} +0.391949 q^{78} +3.93842 q^{79} -13.9839 q^{80} +8.98647 q^{81} -1.30901 q^{82} +14.3338 q^{83} -0.0396252 q^{84} +3.00387 q^{85} +12.7903 q^{86} -0.135665 q^{87} +2.14404 q^{88} -9.31442 q^{89} +17.0592 q^{90} +3.43749 q^{91} -8.22353 q^{92} -0.246751 q^{93} +10.1891 q^{94} +12.2194 q^{95} -0.281194 q^{96} +16.8361 q^{97} +12.4723 q^{98} -8.22135 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	−1.89397	−1.33924	−0.669620	−	0.742704i	$-0.733543\pi$
$2$	−1.89397	−1.33924	−0.669620	+	0.742704i	$0.733543\pi$
$3$	−0.0387693	−0.0223835	−0.0111917	−	0.999937i	$-0.503563\pi$
$3$	−0.0387693	−0.0223835	−0.0111917	+	0.999937i	$0.503563\pi$
$4$	1.58712	0.793561
$5$	3.00387	1.34337	0.671687	−	0.740835i	$-0.265570\pi$
$5$	3.00387	1.34337	0.671687	+	0.740835i	$0.265570\pi$
$6$	0.0734279	0.0299768
$7$	0.643981	0.243402	0.121701	−	0.992567i	$-0.461165\pi$
$7$	0.643981	0.243402	0.121701	+	0.992567i	$0.461165\pi$
$8$	0.781977	0.276471
$9$	−2.99850	−0.999499
$10$	−5.68925	−1.79910
$11$	2.74182	0.826691	0.413346	−	0.910574i	$-0.364360\pi$
$11$	2.74182	0.826691	0.413346	+	0.910574i	$0.364360\pi$
$12$	−0.0615316	−0.0177626
$13$	5.33788	1.48046	0.740230	−	0.672353i	$-0.234716\pi$
$13$	5.33788	1.48046	0.740230	+	0.672353i	$0.234716\pi$
$14$	−1.21968	−0.325974
$15$	−0.116458	−0.0300693
$16$	−4.65529	−1.16382
$17$	1.00000	0.242536
$17$	1.00000	0.242536
$18$	5.67906	1.33857
$19$	4.06789	0.933237	0.466619	−	0.884459i	$-0.345472\pi$
$19$	4.06789	0.933237	0.466619	+	0.884459i	$0.345472\pi$
$20$	4.76752	1.06605
$21$	−0.0249667	−0.00544818
$22$	−5.19293	−1.10714
$23$	−5.18141	−1.08040	−0.540199	−	0.841537i	$-0.681651\pi$
$23$	−5.18141	−1.08040	−0.540199	+	0.841537i	$0.681651\pi$
$24$	−0.0303167	−0.00618837
$25$	4.02326	0.804653
$26$	−10.1098	−1.98269
$27$	0.232557	0.0447557
$28$	1.02208	0.193155
$29$	3.49928	0.649801	0.324900	−	0.945748i	$-0.394669\pi$
$29$	3.49928	0.649801	0.324900	+	0.945748i	$0.394669\pi$
$30$	0.220568	0.0402700
$31$	6.36461	1.14312	0.571559	−	0.820561i	$-0.306339\pi$
$31$	6.36461	1.14312	0.571559	+	0.820561i	$0.306339\pi$
$32$	7.25302	1.28216
$33$	−0.106299	−0.0185042
$34$	−1.89397	−0.324813
$35$	1.93444	0.326980
$36$	−4.75898	−0.793164
$37$	−4.12597	−0.678306	−0.339153	−	0.940731i	$-0.610140\pi$
$37$	−4.12597	−0.678306	−0.339153	+	0.940731i	$0.610140\pi$
$38$	−7.70446	−1.24983
$39$	−0.206946	−0.0331378
$40$	2.34896	0.371403
$41$	0.691148	0.107939	0.0539696	−	0.998543i	$-0.482813\pi$
$41$	0.691148	0.107939	0.0539696	+	0.998543i	$0.482813\pi$
$42$	0.0472862	0.00729642
$43$	−6.75318	−1.02985	−0.514925	−	0.857235i	$-0.672180\pi$
$43$	−6.75318	−1.02985	−0.514925	+	0.857235i	$0.672180\pi$
$44$	4.35161	0.656030
$45$	−9.00711	−1.34270
$46$	9.81343	1.44691
$47$	−5.37976	−0.784719	−0.392360	−	0.919812i	$-0.628341\pi$
$47$	−5.37976	−0.784719	−0.392360	+	0.919812i	$0.628341\pi$
$48$	0.180482	0.0260503
$49$	−6.58529	−0.940755
$50$	−7.61994	−1.07762
$51$	−0.0387693	−0.00542879
$52$	8.47187	1.17484
$53$	9.68809	1.33076	0.665381	−	0.746504i	$-0.268269\pi$
$53$	9.68809	1.33076	0.665381	+	0.746504i	$0.268269\pi$
$54$	−0.440457	−0.0599386
$55$	8.23610	1.11056
$56$	0.503578	0.0672935
$57$	−0.157709	−0.0208891
$58$	−6.62754	−0.870239
$59$	−1.00000	−0.130189
$59$	−1.00000	−0.130189
$60$	−0.184833	−0.0238619
$61$	−7.56480	−0.968574	−0.484287	−	0.874909i	$-0.660921\pi$
$61$	−7.56480	−0.968574	−0.484287	+	0.874909i	$0.660921\pi$
$62$	−12.0544	−1.53091
$63$	−1.93098	−0.243280
$64$	−4.42643	−0.553304
$65$	16.0343	1.98881
$66$	0.201326	0.0247816
$67$	−8.43888	−1.03097	−0.515487	−	0.856897i	$-0.672389\pi$
$67$	−8.43888	−1.03097	−0.515487	+	0.856897i	$0.672389\pi$
$68$	1.58712	0.192467
$69$	0.200879	0.0241830
$70$	−3.66377	−0.437904
$71$	−1.57561	−0.186990	−0.0934952	−	0.995620i	$-0.529804\pi$
$71$	−1.57561	−0.186990	−0.0934952	+	0.995620i	$0.529804\pi$
$72$	−2.34475	−0.276332
$73$	10.0121	1.17183	0.585914	−	0.810373i	$-0.300736\pi$
$73$	10.0121	1.17183	0.585914	+	0.810373i	$0.300736\pi$
$74$	7.81447	0.908414
$75$	−0.155979	−0.0180109
$76$	6.45624	0.740581
$77$	1.76568	0.201218
$78$	0.391949	0.0443795
$79$	3.93842	0.443107	0.221554	−	0.975148i	$-0.428887\pi$
$79$	3.93842	0.443107	0.221554	+	0.975148i	$0.428887\pi$
$80$	−13.9839	−1.56345
$81$	8.98647	0.998497
$82$	−1.30901	−0.144556
$83$	14.3338	1.57334	0.786668	−	0.617377i	$-0.211805\pi$
$83$	14.3338	1.57334	0.786668	+	0.617377i	$0.211805\pi$
$84$	−0.0396252	−0.00432347
$85$	3.00387	0.325816
$86$	12.7903	1.37922
$87$	−0.135665	−0.0145448
$88$	2.14404	0.228556
$89$	−9.31442	−0.987327	−0.493663	−	0.869653i	$-0.664342\pi$
$89$	−9.31442	−0.987327	−0.493663	+	0.869653i	$0.664342\pi$
$90$	17.0592	1.79820
$91$	3.43749	0.360347
$92$	−8.22353	−0.857362
$93$	−0.246751	−0.0255869
$94$	10.1891	1.05093
$95$	12.2194	1.25369
$96$	−0.281194	−0.0286993
$97$	16.8361	1.70945	0.854724	−	0.519083i	$-0.173726\pi$
$97$	16.8361	1.70945	0.854724	+	0.519083i	$0.173726\pi$
$98$	12.4723	1.25990
$99$	−8.22135	−0.826277
$100$	6.38541	0.638541
$101$	18.0674	1.79778	0.898888	−	0.438179i	$-0.144376\pi$
$101$	18.0674	1.79778	0.898888	+	0.438179i	$0.144376\pi$
$102$	0.0734279	0.00727044
$103$	11.1875	1.10234	0.551170	−	0.834393i	$-0.314181\pi$
$103$	11.1875	1.10234	0.551170	+	0.834393i	$0.314181\pi$
$104$	4.17409	0.409304
$105$	−0.0749968	−0.00731894
$106$	−18.3489	−1.78221
$107$	14.1915	1.37194	0.685970	−	0.727630i	$-0.259378\pi$
$107$	14.1915	1.37194	0.685970	+	0.727630i	$0.259378\pi$
$108$	0.369097	0.0355164
$109$	12.8342	1.22929	0.614646	−	0.788803i	$-0.289299\pi$
$109$	12.8342	1.22929	0.614646	+	0.788803i	$0.289299\pi$
$110$	−15.5989	−1.48730
$111$	0.159961	0.0151828
$112$	−2.99792	−0.283277
$113$	−7.62884	−0.717661	−0.358831	−	0.933403i	$-0.616824\pi$
$113$	−7.62884	−0.717661	−0.358831	+	0.933403i	$0.616824\pi$
$114$	0.298696	0.0279755
$115$	−15.5643	−1.45138
$116$	5.55380	0.515657
$117$	−16.0056	−1.47972
$118$	1.89397	0.174354
$119$	0.643981	0.0590337
$120$	−0.0910675	−0.00831329
$121$	−3.48240	−0.316582
$122$	14.3275	1.29715
$123$	−0.0267953	−0.00241605
$124$	10.1014	0.907134
$125$	−2.93399	−0.262424
$126$	3.65721	0.325810
$127$	−10.4627	−0.928415	−0.464207	−	0.885727i	$-0.653661\pi$
$127$	−10.4627	−0.928415	−0.464207	+	0.885727i	$0.653661\pi$
$128$	−6.12251	−0.541159
$129$	0.261816	0.0230516
$130$	−30.3685	−2.66349
$131$	0.0322114	0.00281433	0.00140716	−	0.999999i	$-0.499552\pi$
$131$	0.0322114	0.00281433	0.00140716	+	0.999999i	$0.499552\pi$
$132$	−0.168709	−0.0146842
$133$	2.61964	0.227152
$134$	15.9830	1.38072
$135$	0.698573	0.0601236
$136$	0.781977	0.0670540
$137$	12.6791	1.08325	0.541623	−	0.840622i	$-0.317810\pi$
$137$	12.6791	1.08325	0.541623	+	0.840622i	$0.317810\pi$
$138$	−0.380460	−0.0323869
$139$	−14.3882	−1.22039	−0.610194	−	0.792252i	$-0.708908\pi$
$139$	−14.3882	−1.22039	−0.610194	+	0.792252i	$0.708908\pi$
$140$	3.07019	0.259479
$141$	0.208570	0.0175647
$142$	2.98416	0.250425
$143$	14.6355	1.22388
$144$	13.9589	1.16324
$145$	10.5114	0.872925
$146$	−18.9626	−1.56936
$147$	0.255307	0.0210574
$148$	−6.54843	−0.538278
$149$	14.1568	1.15977	0.579885	−	0.814699i	$-0.303098\pi$
$149$	14.1568	1.15977	0.579885	+	0.814699i	$0.303098\pi$
$150$	0.295420	0.0241209
$151$	−17.7862	−1.44742	−0.723709	−	0.690105i	$-0.757564\pi$
$151$	−17.7862	−1.44742	−0.723709	+	0.690105i	$0.757564\pi$
$152$	3.18099	0.258013
$153$	−2.99850	−0.242414
$154$	−3.34415	−0.269480
$155$	19.1185	1.53563
$156$	−0.328448	−0.0262969
$157$	−12.5068	−0.998152	−0.499076	−	0.866558i	$-0.666327\pi$
$157$	−12.5068	−0.998152	−0.499076	+	0.866558i	$0.666327\pi$
$158$	−7.45925	−0.593426
$159$	−0.375600	−0.0297870
$160$	21.7872	1.72243
$161$	−3.33673	−0.262971
$162$	−17.0201	−1.33723
$163$	−13.2223	−1.03565	−0.517825	−	0.855487i	$-0.673258\pi$
$163$	−13.2223	−1.03565	−0.517825	+	0.855487i	$0.673258\pi$
$164$	1.09694	0.0856563
$165$	−0.319308	−0.0248581
$166$	−27.1477	−2.10707
$167$	−2.27175	−0.175793	−0.0878967	−	0.996130i	$-0.528015\pi$
$167$	−2.27175	−0.175793	−0.0878967	+	0.996130i	$0.528015\pi$
$168$	−0.0195234	−0.00150626
$169$	15.4929	1.19176
$170$	−5.68925	−0.436345
$171$	−12.1975	−0.932770
$172$	−10.7181	−0.817249
$173$	11.3043	0.859452	0.429726	−	0.902959i	$-0.358610\pi$
$173$	11.3043	0.859452	0.429726	+	0.902959i	$0.358610\pi$
$174$	0.256945	0.0194789
$175$	2.59091	0.195854
$176$	−12.7640	−0.962121
$177$	0.0387693	0.00291408
$178$	17.6412	1.32227
$179$	14.9031	1.11391	0.556955	−	0.830543i	$-0.311970\pi$
$179$	14.9031	1.11391	0.556955	+	0.830543i	$0.311970\pi$
$180$	−14.2954	−1.06552
$181$	−17.5625	−1.30541	−0.652704	−	0.757613i	$-0.726365\pi$
$181$	−17.5625	−1.30541	−0.652704	+	0.757613i	$0.726365\pi$
$182$	−6.51051	−0.482591
$183$	0.293282	0.0216800
$184$	−4.05174	−0.298698
$185$	−12.3939	−0.911219
$186$	0.467339	0.0342670
$187$	2.74182	0.200502
$188$	−8.53834	−0.622723
$189$	0.149763	0.0108936
$190$	−23.1432	−1.67899
$191$	18.0705	1.30754	0.653769	−	0.756694i	$-0.273187\pi$
$191$	18.0705	1.30754	0.653769	+	0.756694i	$0.273187\pi$
$192$	0.171610	0.0123849
$193$	6.47836	0.466323	0.233161	−	0.972438i	$-0.425093\pi$
$193$	6.47836	0.466323	0.233161	+	0.972438i	$0.425093\pi$
$194$	−31.8871	−2.28936
$195$	−0.621639	−0.0445165
$196$	−10.4517	−0.746547
$197$	−12.8699	−0.916940	−0.458470	−	0.888710i	$-0.651602\pi$
$197$	−12.8699	−0.916940	−0.458470	+	0.888710i	$0.651602\pi$
$198$	15.5710	1.10658
$199$	−12.1539	−0.861571	−0.430785	−	0.902454i	$-0.641763\pi$
$199$	−12.1539	−0.861571	−0.430785	+	0.902454i	$0.641763\pi$
$200$	3.14610	0.222463
$201$	0.327169	0.0230768
$202$	−34.2191	−2.40765
$203$	2.25347	0.158163
$204$	−0.0615316	−0.00430807
$205$	2.07612	0.145003
$206$	−21.1889	−1.47630
$207$	15.5364	1.07986
$208$	−24.8493	−1.72299
$209$	11.1534	0.771499
$210$	0.142042	0.00980181
$211$	−17.6448	−1.21472	−0.607358	−	0.794428i	$-0.707771\pi$
$211$	−17.6448	−1.21472	−0.607358	+	0.794428i	$0.707771\pi$
$212$	15.3762	1.05604
$213$	0.0610852	0.00418549
$214$	−26.8782	−1.83736
$215$	−20.2857	−1.38347
$216$	0.181854	0.0123736
$217$	4.09869	0.278237
$218$	−24.3076	−1.64632
$219$	−0.388162	−0.0262296
$220$	13.0717	0.881294
$221$	5.33788	0.359064
$222$	−0.302962	−0.0203334
$223$	11.9997	0.803562	0.401781	−	0.915736i	$-0.368391\pi$
$223$	11.9997	0.803562	0.401781	+	0.915736i	$0.368391\pi$
$224$	4.67081	0.312082
$225$	−12.0637	−0.804249
$226$	14.4488	0.961120
$227$	−6.64579	−0.441096	−0.220548	−	0.975376i	$-0.570785\pi$
$227$	−6.64579	−0.441096	−0.220548	+	0.975376i	$0.570785\pi$
$228$	−0.250304	−0.0165768
$229$	−12.2424	−0.809002	−0.404501	−	0.914538i	$-0.632555\pi$
$229$	−12.2424	−0.809002	−0.404501	+	0.914538i	$0.632555\pi$
$230$	29.4783	1.94374
$231$	−0.0684543	−0.00450396
$232$	2.73636	0.179651
$233$	19.2825	1.26324	0.631620	−	0.775278i	$-0.282390\pi$
$233$	19.2825	1.26324	0.631620	+	0.775278i	$0.282390\pi$
$234$	30.3141	1.98170
$235$	−16.1601	−1.05417
$236$	−1.58712	−0.103313
$237$	−0.152690	−0.00991827
$238$	−1.21968	−0.0790602
$239$	−9.73662	−0.629809	−0.314905	−	0.949123i	$-0.601973\pi$
$239$	−9.73662	−0.629809	−0.314905	+	0.949123i	$0.601973\pi$
$240$	0.542146	0.0349954
$241$	−1.19064	−0.0766959	−0.0383480	−	0.999264i	$-0.512210\pi$
$241$	−1.19064	−0.0766959	−0.0383480	+	0.999264i	$0.512210\pi$
$242$	6.59556	0.423978
$243$	−1.04607	−0.0671055
$244$	−12.0063	−0.768623
$245$	−19.7814	−1.26379
$246$	0.0507495	0.00323567
$247$	21.7139	1.38162
$248$	4.97697	0.316038
$249$	−0.555710	−0.0352167
$250$	5.55690	0.351449
$251$	−9.84990	−0.621720	−0.310860	−	0.950456i	$-0.600617\pi$
$251$	−9.84990	−0.621720	−0.310860	+	0.950456i	$0.600617\pi$
$252$	−3.06470	−0.193058
$253$	−14.2065	−0.893156
$254$	19.8160	1.24337
$255$	−0.116458	−0.00729289
$256$	20.4487	1.27804
$257$	21.0379	1.31231	0.656153	−	0.754628i	$-0.272183\pi$
$257$	21.0379	1.31231	0.656153	+	0.754628i	$0.272183\pi$
$258$	−0.495871	−0.0308716
$259$	−2.65705	−0.165101
$260$	25.4484	1.57824
$261$	−10.4926	−0.649475
$262$	−0.0610075	−0.00376906
$263$	30.7100	1.89366	0.946828	−	0.321739i	$-0.104267\pi$
$263$	30.7100	1.89366	0.946828	+	0.321739i	$0.104267\pi$
$264$	−0.0831230	−0.00511587
$265$	29.1018	1.78771
$266$	−4.96153	−0.304211
$267$	0.361113	0.0220998
$268$	−13.3935	−0.818141
$269$	−20.6048	−1.25629	−0.628147	−	0.778095i	$-0.716186\pi$
$269$	−20.6048	−1.25629	−0.628147	+	0.778095i	$0.716186\pi$
$270$	−1.32308	−0.0805199
$271$	−23.5242	−1.42899	−0.714495	−	0.699640i	$-0.753344\pi$
$271$	−23.5242	−1.42899	−0.714495	+	0.699640i	$0.753344\pi$
$272$	−4.65529	−0.282268
$273$	−0.133269	−0.00806581
$274$	−24.0138	−1.45072
$275$	11.0311	0.665199
$276$	0.318820	0.0191907
$277$	−14.9914	−0.900746	−0.450373	−	0.892840i	$-0.648709\pi$
$277$	−14.9914	−0.900746	−0.450373	+	0.892840i	$0.648709\pi$
$278$	27.2507	1.63439
$279$	−19.0843	−1.14254
$280$	1.51269	0.0904003
$281$	−1.67752	−0.100073	−0.0500363	−	0.998747i	$-0.515934\pi$
$281$	−1.67752	−0.100073	−0.0500363	+	0.998747i	$0.515934\pi$
$282$	−0.395024	−0.0235234
$283$	−20.5335	−1.22059	−0.610296	−	0.792173i	$-0.708950\pi$
$283$	−20.5335	−1.22059	−0.610296	+	0.792173i	$0.708950\pi$
$284$	−2.50068	−0.148388
$285$	−0.473738	−0.0280618
$286$	−27.7192	−1.63907
$287$	0.445086	0.0262726
$288$	−21.7482	−1.28152
$289$	1.00000	0.0588235
$290$	−19.9083	−1.16906
$291$	−0.652724	−0.0382633
$292$	15.8904	0.929918
$293$	−7.75978	−0.453331	−0.226666	−	0.973973i	$-0.572782\pi$
$293$	−7.75978	−0.453331	−0.226666	+	0.973973i	$0.572782\pi$
$294$	−0.483544	−0.0282008
$295$	−3.00387	−0.174892
$296$	−3.22642	−0.187532
$297$	0.637632	0.0369991
$298$	−26.8125	−1.55321
$299$	−27.6577	−1.59949
$300$	−0.247558	−0.0142928
$301$	−4.34892	−0.250668
$302$	33.6865	1.93844
$303$	−0.700461	−0.0402404
$304$	−18.9372	−1.08612
$305$	−22.7237	−1.30116
$306$	5.67906	0.324650
$307$	−15.8882	−0.906790	−0.453395	−	0.891310i	$-0.649787\pi$
$307$	−15.8882	−0.906790	−0.453395	+	0.891310i	$0.649787\pi$
$308$	2.80236	0.159679
$309$	−0.433733	−0.0246742
$310$	−36.2098	−2.05658
$311$	−23.2351	−1.31754	−0.658770	−	0.752344i	$-0.728923\pi$
$311$	−23.2351	−1.31754	−0.658770	+	0.752344i	$0.728923\pi$
$312$	−0.161827	−0.00916163
$313$	28.6593	1.61992	0.809959	−	0.586486i	$-0.199489\pi$
$313$	28.6593	1.61992	0.809959	+	0.586486i	$0.199489\pi$
$314$	23.6875	1.33676
$315$	−5.80041	−0.326816
$316$	6.25076	0.351633
$317$	−19.7267	−1.10796	−0.553982	−	0.832529i	$-0.686892\pi$
$317$	−19.7267	−1.10796	−0.553982	+	0.832529i	$0.686892\pi$
$318$	0.711375	0.0398920
$319$	9.59442	0.537185
$320$	−13.2964	−0.743294
$321$	−0.550193	−0.0307088
$322$	6.31967	0.352181
$323$	4.06789	0.226343
$324$	14.2626	0.792369
$325$	21.4757	1.19126
$326$	25.0426	1.38698
$327$	−0.497572	−0.0275158
$328$	0.540461	0.0298420
$329$	−3.46447	−0.191002
$330$	0.604759	0.0332909
$331$	−7.30798	−0.401683	−0.200841	−	0.979624i	$-0.564368\pi$
$331$	−7.30798	−0.401683	−0.200841	+	0.979624i	$0.564368\pi$
$332$	22.7495	1.24854
$333$	12.3717	0.677966
$334$	4.30263	0.235429
$335$	−25.3494	−1.38498
$336$	0.116227	0.00634071
$337$	22.0959	1.20364	0.601820	−	0.798632i	$-0.294443\pi$
$337$	22.0959	1.20364	0.601820	+	0.798632i	$0.294443\pi$
$338$	−29.3431	−1.59606
$339$	0.295765	0.0160637
$340$	4.76752	0.258555
$341$	17.4506	0.945005
$342$	23.1018	1.24920
$343$	−8.74867	−0.472384
$344$	−5.28083	−0.284723
$345$	0.603417	0.0324869
$346$	−21.4100	−1.15101
$347$	4.79025	0.257154	0.128577	−	0.991700i	$-0.458959\pi$
$347$	4.79025	0.257154	0.128577	+	0.991700i	$0.458959\pi$
$348$	−0.215317	−0.0115422
$349$	11.2478	0.602083	0.301042	−	0.953611i	$-0.402666\pi$
$349$	11.2478	0.602083	0.301042	+	0.953611i	$0.402666\pi$
$350$	−4.90710	−0.262296
$351$	1.24136	0.0662590
$352$	19.8865	1.05995
$353$	−12.1650	−0.647479	−0.323740	−	0.946146i	$-0.604940\pi$
$353$	−12.1650	−0.647479	−0.323740	+	0.946146i	$0.604940\pi$
$354$	−0.0734279	−0.00390265
$355$	−4.73293	−0.251198
$356$	−14.7831	−0.783504
$357$	−0.0249667	−0.00132138
$358$	−28.2260	−1.49179
$359$	−32.7647	−1.72925	−0.864627	−	0.502414i	$-0.832445\pi$
$359$	−32.7647	−1.72925	−0.864627	+	0.502414i	$0.832445\pi$
$360$	−7.04335	−0.371217
$361$	−2.45229	−0.129068
$362$	33.2628	1.74825
$363$	0.135010	0.00708619
$364$	5.45572	0.285958
$365$	30.0751	1.57420
$366$	−0.555467	−0.0290347
$367$	11.5542	0.603125	0.301562	−	0.953446i	$-0.402492\pi$
$367$	11.5542	0.603125	0.301562	+	0.953446i	$0.402492\pi$
$368$	24.1209	1.25739
$369$	−2.07240	−0.107885
$370$	23.4737	1.22034
$371$	6.23895	0.323910
$372$	−0.391625	−0.0203048
$373$	15.4373	0.799313	0.399657	−	0.916665i	$-0.369129\pi$
$373$	15.4373	0.799313	0.399657	+	0.916665i	$0.369129\pi$
$374$	−5.19293	−0.268520
$375$	0.113749	0.00587397
$376$	−4.20685	−0.216952
$377$	18.6787	0.962004
$378$	−0.283646	−0.0145892
$379$	−0.820156	−0.0421286	−0.0210643	−	0.999778i	$-0.506705\pi$
$379$	−0.820156	−0.0421286	−0.0210643	+	0.999778i	$0.506705\pi$
$380$	19.3937	0.994877
$381$	0.405631	0.0207811
$382$	−34.2251	−1.75111
$383$	3.46491	0.177049	0.0885243	−	0.996074i	$-0.471785\pi$
$383$	3.46491	0.177049	0.0885243	+	0.996074i	$0.471785\pi$
$384$	0.237365	0.0121130
$385$	5.30389	0.270311
$386$	−12.2698	−0.624518
$387$	20.2494	1.02933
$388$	26.7210	1.35655
$389$	10.9586	0.555625	0.277813	−	0.960635i	$-0.410391\pi$
$389$	10.9586	0.555625	0.277813	+	0.960635i	$0.410391\pi$
$390$	1.17737	0.0596182
$391$	−5.18141	−0.262035
$392$	−5.14954	−0.260091
$393$	−0.00124881	−6.29944e−5 0
$394$	24.3751	1.22800
$395$	11.8305	0.595258
$396$	−13.0483	−0.655702
$397$	−5.61622	−0.281870	−0.140935	−	0.990019i	$-0.545011\pi$
$397$	−5.61622	−0.281870	−0.140935	+	0.990019i	$0.545011\pi$
$398$	23.0192	1.15385
$399$	−0.101562	−0.00508444
$400$	−18.7294	−0.936472
$401$	8.64082	0.431502	0.215751	−	0.976448i	$-0.430780\pi$
$401$	8.64082	0.431502	0.215751	+	0.976448i	$0.430780\pi$
$402$	−0.619649	−0.0309053
$403$	33.9735	1.69234
$404$	28.6752	1.42665
$405$	26.9942	1.34135
$406$	−4.26801	−0.211818
$407$	−11.3127	−0.560750
$408$	−0.0303167	−0.00150090
$409$	1.49392	0.0738697	0.0369349	−	0.999318i	$-0.488241\pi$
$409$	1.49392	0.0738697	0.0369349	+	0.999318i	$0.488241\pi$
$410$	−3.93211	−0.194193
$411$	−0.491558	−0.0242468
$412$	17.7560	0.874775
$413$	−0.643981	−0.0316883
$414$	−29.4255	−1.44619
$415$	43.0568	2.11358
$416$	38.7157	1.89819
$417$	0.557819	0.0273165
$418$	−21.1243	−1.03322
$419$	−35.3583	−1.72737	−0.863683	−	0.504035i	$-0.831848\pi$
$419$	−35.3583	−1.72737	−0.863683	+	0.504035i	$0.831848\pi$
$420$	−0.119029	−0.00580803
$421$	22.8888	1.11553	0.557765	−	0.829999i	$-0.311659\pi$
$421$	22.8888	1.11553	0.557765	+	0.829999i	$0.311659\pi$
$422$	33.4187	1.62679
$423$	16.1312	0.784326
$424$	7.57586	0.367916
$425$	4.02326	0.195157
$426$	−0.115694	−0.00560537
$427$	−4.87159	−0.235753
$428$	22.5236	1.08872
$429$	−0.567409	−0.0273947
$430$	38.4205	1.85280
$431$	−37.3809	−1.80057	−0.900287	−	0.435296i	$-0.856644\pi$
$431$	−37.3809	−1.80057	−0.900287	+	0.435296i	$0.856644\pi$
$432$	−1.08262	−0.0520876
$433$	26.8692	1.29125	0.645626	−	0.763654i	$-0.276597\pi$
$433$	26.8692	1.29125	0.645626	+	0.763654i	$0.276597\pi$
$434$	−7.76279	−0.372626
$435$	−0.407520	−0.0195391
$436$	20.3694	0.975519
$437$	−21.0774	−1.00827
$438$	0.735168	0.0351277
$439$	5.89477	0.281342	0.140671	−	0.990056i	$-0.455074\pi$
$439$	5.89477	0.281342	0.140671	+	0.990056i	$0.455074\pi$
$440$	6.44044	0.307036
$441$	19.7460	0.940284
$442$	−10.1098	−0.480873
$443$	12.9098	0.613363	0.306682	−	0.951812i	$-0.400781\pi$
$443$	12.9098	0.613363	0.306682	+	0.951812i	$0.400781\pi$
$444$	0.253878	0.0120485
$445$	−27.9794	−1.32635
$446$	−22.7272	−1.07616
$447$	−0.548849	−0.0259596
$448$	−2.85054	−0.134675
$449$	−7.15681	−0.337751	−0.168875	−	0.985637i	$-0.554014\pi$
$449$	−7.15681	−0.337751	−0.168875	+	0.985637i	$0.554014\pi$
$450$	22.8484	1.07708
$451$	1.89501	0.0892323
$452$	−12.1079	−0.569508
$453$	0.689557	0.0323982
$454$	12.5869	0.590733
$455$	10.3258	0.484081
$456$	−0.123325	−0.00577521
$457$	−29.1704	−1.36453	−0.682266	−	0.731104i	$-0.739006\pi$
$457$	−29.1704	−1.36453	−0.682266	+	0.731104i	$0.739006\pi$
$458$	23.1868	1.08345
$459$	0.232557	0.0108549
$460$	−24.7025	−1.15176
$461$	−19.4388	−0.905356	−0.452678	−	0.891674i	$-0.649531\pi$
$461$	−19.4388	−0.905356	−0.452678	+	0.891674i	$0.649531\pi$
$462$	0.129650	0.00603188
$463$	−23.3068	−1.08316	−0.541579	−	0.840650i	$-0.682173\pi$
$463$	−23.3068	−1.08316	−0.541579	+	0.840650i	$0.682173\pi$
$464$	−16.2902	−0.756252
$465$	−0.741210	−0.0343728
$466$	−36.5205	−1.69178
$467$	−17.2184	−0.796771	−0.398386	−	0.917218i	$-0.630429\pi$
$467$	−17.2184	−0.796771	−0.398386	+	0.917218i	$0.630429\pi$
$468$	−25.4029	−1.17425
$469$	−5.43448	−0.250941
$470$	30.6068	1.41179
$471$	0.484880	0.0223421
$472$	−0.781977	−0.0359934
$473$	−18.5160	−0.851368
$474$	0.289190	0.0132829
$475$	16.3662	0.750932
$476$	1.02208	0.0468469
$477$	−29.0497	−1.33009
$478$	18.4409	0.843465
$479$	−1.15059	−0.0525719	−0.0262859	−	0.999654i	$-0.508368\pi$
$479$	−1.15059	−0.0525719	−0.0262859	+	0.999654i	$0.508368\pi$
$480$	−0.844673	−0.0385539
$481$	−22.0239	−1.00421
$482$	2.25504	0.102714
$483$	0.129363	0.00588620
$484$	−5.52699	−0.251227
$485$	50.5736	2.29643
$486$	1.98123	0.0898703
$487$	1.93888	0.0878589	0.0439295	−	0.999035i	$-0.486012\pi$
$487$	1.93888	0.0878589	0.0439295	+	0.999035i	$0.486012\pi$
$488$	−5.91550	−0.267782
$489$	0.512619	0.0231814
$490$	37.4653	1.69251
$491$	7.82622	0.353192	0.176596	−	0.984283i	$-0.443491\pi$
$491$	7.82622	0.353192	0.176596	+	0.984283i	$0.443491\pi$
$492$	−0.0425274	−0.00191728
$493$	3.49928	0.157600
$494$	−41.1254	−1.85032
$495$	−24.6959	−1.11000
$496$	−29.6291	−1.33038
$497$	−1.01466	−0.0455138
$498$	1.05250	0.0471636
$499$	−40.1158	−1.79583	−0.897916	−	0.440167i	$-0.854919\pi$
$499$	−40.1158	−1.79583	−0.897916	+	0.440167i	$0.854919\pi$
$500$	−4.65661	−0.208250
$501$	0.0880742	0.00393486
$502$	18.6554	0.832632
$503$	22.1132	0.985979	0.492989	−	0.870035i	$-0.335904\pi$
$503$	22.1132	0.985979	0.492989	+	0.870035i	$0.335904\pi$
$504$	−1.50998	−0.0672598
$505$	54.2723	2.41508
$506$	26.9067	1.19615
$507$	−0.600649	−0.0266758
$508$	−16.6056	−0.736754
$509$	3.82052	0.169342	0.0846708	−	0.996409i	$-0.473016\pi$
$509$	3.82052	0.169342	0.0846708	+	0.996409i	$0.473016\pi$
$510$	0.220568	0.00976692
$511$	6.44761	0.285226
$512$	−26.4842	−1.17045
$513$	0.946017	0.0417677
$514$	−39.8451	−1.75749
$515$	33.6060	1.48086
$516$	0.415534	0.0182929
$517$	−14.7504	−0.648720
$518$	5.03238	0.221110
$519$	−0.438260	−0.0192375
$520$	12.5385	0.549848
$521$	35.0454	1.53537	0.767684	−	0.640828i	$-0.221409\pi$
$521$	35.0454	1.53537	0.767684	+	0.640828i	$0.221409\pi$
$522$	19.8727	0.869803
$523$	−4.18967	−0.183201	−0.0916007	−	0.995796i	$-0.529198\pi$
$523$	−4.18967	−0.183201	−0.0916007	+	0.995796i	$0.529198\pi$
$524$	0.0511235	0.00223334
$525$	−0.100448	−0.00438389
$526$	−58.1637	−2.53606
$527$	6.36461	0.277247
$528$	0.494850	0.0215356
$529$	3.84698	0.167260
$530$	−55.1179	−2.39417
$531$	2.99850	0.130124
$532$	4.15770	0.180259
$533$	3.68926	0.159800
$534$	−0.683938	−0.0295969
$535$	42.6294	1.84303
$536$	−6.59901	−0.285034
$537$	−0.577782	−0.0249331
$538$	39.0248	1.68248
$539$	−18.0557	−0.777714
$540$	1.10872	0.0477118
$541$	11.6140	0.499326	0.249663	−	0.968333i	$-0.419680\pi$
$541$	11.6140	0.499326	0.249663	+	0.968333i	$0.419680\pi$
$542$	44.5540	1.91376
$543$	0.680884	0.0292195
$544$	7.25302	0.310971
$545$	38.5523	1.65140
$546$	0.252408	0.0108021
$547$	18.2717	0.781244	0.390622	−	0.920551i	$-0.372260\pi$
$547$	18.2717	0.781244	0.390622	+	0.920551i	$0.372260\pi$
$548$	20.1232	0.859622
$549$	22.6830	0.968089
$550$	−20.8925	−0.890861
$551$	14.2347	0.606418
$552$	0.157083	0.00668590
$553$	2.53627	0.107853
$554$	28.3933	1.20631
$555$	0.480503	0.0203962
$556$	−22.8358	−0.968453
$557$	−39.0033	−1.65262	−0.826312	−	0.563212i	$-0.809565\pi$
$557$	−39.0033	−1.65262	−0.826312	+	0.563212i	$0.809565\pi$
$558$	36.1450	1.53014
$559$	−36.0476	−1.52465
$560$	−9.00537	−0.380546
$561$	−0.106299	−0.00448793
$562$	3.17718	0.134021
$563$	−30.3672	−1.27982	−0.639912	−	0.768448i	$-0.721029\pi$
$563$	−30.3672	−1.27982	−0.639912	+	0.768448i	$0.721029\pi$
$564$	0.331025	0.0139387
$565$	−22.9161	−0.964087
$566$	38.8899	1.63466
$567$	5.78712	0.243036
$568$	−1.23209	−0.0516973
$569$	−3.37209	−0.141365	−0.0706827	−	0.997499i	$-0.522518\pi$
$569$	−3.37209	−0.141365	−0.0706827	+	0.997499i	$0.522518\pi$
$570$	0.897246	0.0375815
$571$	19.6110	0.820695	0.410347	−	0.911929i	$-0.365407\pi$
$571$	19.6110	0.820695	0.410347	+	0.911929i	$0.365407\pi$
$572$	23.2284	0.971227
$573$	−0.700582	−0.0292672
$574$	−0.842980	−0.0351853
$575$	−20.8462	−0.869345
$576$	13.2726	0.553027
$577$	−10.3503	−0.430887	−0.215444	−	0.976516i	$-0.569120\pi$
$577$	−10.3503	−0.430887	−0.215444	+	0.976516i	$0.569120\pi$
$578$	−1.89397	−0.0787788
$579$	−0.251161	−0.0104379
$580$	16.6829	0.692720
$581$	9.23068	0.382953
$582$	1.23624	0.0512438
$583$	26.5630	1.10013
$584$	7.82923	0.323976
$585$	−48.0788	−1.98782
$586$	14.6968	0.607119
$587$	6.31623	0.260699	0.130349	−	0.991468i	$-0.458390\pi$
$587$	6.31623	0.260699	0.130349	+	0.991468i	$0.458390\pi$
$588$	0.405203	0.0167103
$589$	25.8905	1.06680
$590$	5.68925	0.234223
$591$	0.498955	0.0205243
$592$	19.2076	0.789427
$593$	18.3415	0.753197	0.376598	−	0.926377i	$-0.377094\pi$
$593$	18.3415	0.753197	0.376598	+	0.926377i	$0.377094\pi$
$594$	−1.20766	−0.0495507
$595$	1.93444	0.0793043
$596$	22.4686	0.920348
$597$	0.471200	0.0192849
$598$	52.3829	2.14210
$599$	−27.7010	−1.13183	−0.565916	−	0.824463i	$-0.691477\pi$
$599$	−27.7010	−1.13183	−0.565916	+	0.824463i	$0.691477\pi$
$600$	−0.121972	−0.00497948
$601$	−44.0700	−1.79765	−0.898826	−	0.438305i	$-0.855579\pi$
$601$	−44.0700	−1.79765	−0.898826	+	0.438305i	$0.855579\pi$
$602$	8.23672	0.335704
$603$	25.3040	1.03046
$604$	−28.2288	−1.14862
$605$	−10.4607	−0.425287
$606$	1.32665	0.0538915
$607$	−32.8030	−1.33143	−0.665717	−	0.746205i	$-0.731874\pi$
$607$	−32.8030	−1.33143	−0.665717	+	0.746205i	$0.731874\pi$
$608$	29.5045	1.19656
$609$	−0.0873656	−0.00354023
$610$	43.0381	1.74256
$611$	−28.7165	−1.16175
$612$	−4.75898	−0.192371
$613$	13.5729	0.548203	0.274102	−	0.961701i	$-0.411620\pi$
$613$	13.5729	0.548203	0.274102	+	0.961701i	$0.411620\pi$
$614$	30.0919	1.21441
$615$	−0.0804897	−0.00324566
$616$	1.38072	0.0556310
$617$	13.4672	0.542171	0.271085	−	0.962555i	$-0.412617\pi$
$617$	13.4672	0.542171	0.271085	+	0.962555i	$0.412617\pi$
$618$	0.821477	0.0330447
$619$	32.0507	1.28823	0.644113	−	0.764930i	$-0.277226\pi$
$619$	32.0507	1.28823	0.644113	+	0.764930i	$0.277226\pi$
$620$	30.3434	1.21862
$621$	−1.20497	−0.0483540
$622$	44.0065	1.76450
$623$	−5.99831	−0.240317
$624$	0.963391	0.0385665
$625$	−28.9297	−1.15719
$626$	−54.2798	−2.16946
$627$	−0.432411	−0.0172688
$628$	−19.8499	−0.792095
$629$	−4.12597	−0.164513
$630$	10.9858	0.437685
$631$	30.9299	1.23130	0.615649	−	0.788021i	$-0.288894\pi$
$631$	30.9299	1.23130	0.615649	+	0.788021i	$0.288894\pi$
$632$	3.07975	0.122506
$633$	0.684075	0.0271895
$634$	37.3618	1.48383
$635$	−31.4287	−1.24721
$636$	−0.596124	−0.0236378
$637$	−35.1515	−1.39275
$638$	−18.1716	−0.719419
$639$	4.72446	0.186897
$640$	−18.3913	−0.726978
$641$	−21.2009	−0.837386	−0.418693	−	0.908128i	$-0.637512\pi$
$641$	−21.2009	−0.837386	−0.418693	+	0.908128i	$0.637512\pi$
$642$	1.04205	0.0411264
$643$	−19.8756	−0.783817	−0.391908	−	0.920004i	$-0.628185\pi$
$643$	−19.8756	−0.783817	−0.391908	+	0.920004i	$0.628185\pi$
$644$	−5.29580	−0.208684
$645$	0.786462	0.0309669
$646$	−7.70446	−0.303128
$647$	−29.8936	−1.17524	−0.587620	−	0.809137i	$-0.699935\pi$
$647$	−29.8936	−1.17524	−0.587620	+	0.809137i	$0.699935\pi$
$648$	7.02721	0.276055
$649$	−2.74182	−0.107626
$650$	−40.6743	−1.59538
$651$	−0.158903	−0.00622791
$652$	−20.9854	−0.821852
$653$	1.61170	0.0630707	0.0315354	−	0.999503i	$-0.489960\pi$
$653$	1.61170	0.0630707	0.0315354	+	0.999503i	$0.489960\pi$
$654$	0.942387	0.0368502
$655$	0.0967592	0.00378069
$656$	−3.21749	−0.125622
$657$	−30.0213	−1.17124
$658$	6.56160	0.255798
$659$	8.37509	0.326247	0.163124	−	0.986606i	$-0.447843\pi$
$659$	8.37509	0.326247	0.163124	+	0.986606i	$0.447843\pi$
$660$	−0.506780	−0.0197264
$661$	−10.5849	−0.411706	−0.205853	−	0.978583i	$-0.565997\pi$
$661$	−10.5849	−0.411706	−0.205853	+	0.978583i	$0.565997\pi$
$662$	13.8411	0.537950
$663$	−0.206946	−0.00803710
$664$	11.2087	0.434981
$665$	7.86908	0.305150
$666$	−23.4317	−0.907959
$667$	−18.1312	−0.702044
$668$	−3.60555	−0.139503
$669$	−0.465221	−0.0179865
$670$	48.0109	1.85482
$671$	−20.7414	−0.800712
$672$	−0.181084	−0.00698547
$673$	−25.8710	−0.997253	−0.498626	−	0.866817i	$-0.666162\pi$
$673$	−25.8710	−0.997253	−0.498626	+	0.866817i	$0.666162\pi$
$674$	−41.8490	−1.61196
$675$	0.935640	0.0360128
$676$	24.5892	0.945737
$677$	−22.7692	−0.875090	−0.437545	−	0.899196i	$-0.644152\pi$
$677$	−22.7692	−0.875090	−0.437545	+	0.899196i	$0.644152\pi$
$678$	−0.560170	−0.0215132
$679$	10.8421	0.416083
$680$	2.34896	0.0900785
$681$	0.257652	0.00987326
$682$	−33.0510	−1.26559
$683$	28.5690	1.09316	0.546581	−	0.837406i	$-0.315929\pi$
$683$	28.5690	1.09316	0.546581	+	0.837406i	$0.315929\pi$
$684$	−19.3590	−0.740210
$685$	38.0863	1.45520
$686$	16.5697	0.632635
$687$	0.474630	0.0181083
$688$	31.4380	1.19856
$689$	51.7138	1.97014
$690$	−1.14285	−0.0435077
$691$	14.0285	0.533670	0.266835	−	0.963742i	$-0.414022\pi$
$691$	14.0285	0.533670	0.266835	+	0.963742i	$0.414022\pi$
$692$	17.9413	0.682028
$693$	−5.29440	−0.201118
$694$	−9.07259	−0.344391
$695$	−43.2202	−1.63944
$696$	−0.106087	−0.00402121
$697$	0.691148	0.0261791
$698$	−21.3031	−0.806334
$699$	−0.747569	−0.0282757
$700$	4.11209	0.155422
$701$	11.7481	0.443721	0.221861	−	0.975078i	$-0.428787\pi$
$701$	11.7481	0.443721	0.221861	+	0.975078i	$0.428787\pi$
$702$	−2.35110	−0.0887367
$703$	−16.7840	−0.633021
$704$	−12.1365	−0.457411
$705$	0.626517	0.0235960
$706$	23.0402	0.867129
$707$	11.6351	0.437582
$708$	0.0615316	0.00231250
$709$	−9.27350	−0.348274	−0.174137	−	0.984721i	$-0.555714\pi$
$709$	−9.27350	−0.348274	−0.174137	+	0.984721i	$0.555714\pi$
$710$	8.96403	0.336414
$711$	−11.8093	−0.442885
$712$	−7.28366	−0.272967
$713$	−32.9776	−1.23502
$714$	0.0472862	0.00176964
$715$	43.9633	1.64413
$716$	23.6530	0.883956
$717$	0.377482	0.0140973
$718$	62.0554	2.31589
$719$	10.7547	0.401084	0.200542	−	0.979685i	$-0.435730\pi$
$719$	10.7547	0.401084	0.200542	+	0.979685i	$0.435730\pi$
$720$	41.9307	1.56266
$721$	7.20457	0.268312
$722$	4.64457	0.172853
$723$	0.0461603	0.00171672
$724$	−27.8738	−1.03592
$725$	14.0785	0.522864
$726$	−0.255705	−0.00949010
$727$	0.628818	0.0233216	0.0116608	−	0.999932i	$-0.496288\pi$
$727$	0.628818	0.0233216	0.0116608	+	0.999932i	$0.496288\pi$
$728$	2.68804	0.0996254
$729$	−26.9189	−0.996995
$730$	−56.9614	−2.10823
$731$	−6.75318	−0.249775
$732$	0.465475	0.0172044
$733$	38.6524	1.42766	0.713830	−	0.700319i	$-0.246959\pi$
$733$	38.6524	1.42766	0.713830	+	0.700319i	$0.246959\pi$
$734$	−21.8833	−0.807728
$735$	0.766910	0.0282879
$736$	−37.5809	−1.38525
$737$	−23.1379	−0.852297
$738$	3.92507	0.144484
$739$	−11.4350	−0.420642	−0.210321	−	0.977632i	$-0.567451\pi$
$739$	−11.4350	−0.420642	−0.210321	+	0.977632i	$0.567451\pi$
$740$	−19.6707	−0.723108
$741$	−0.841831	−0.0309254
$742$	−11.8164	−0.433793
$743$	−49.5870	−1.81917	−0.909586	−	0.415516i	$-0.863601\pi$
$743$	−49.5870	−1.81917	−0.909586	+	0.415516i	$0.863601\pi$
$744$	−0.192954	−0.00707403
$745$	42.5252	1.55800
$746$	−29.2378	−1.07047
$747$	−42.9798	−1.57255
$748$	4.35161	0.159111
$749$	9.13903	0.333933
$750$	−0.215437	−0.00786665
$751$	−3.49032	−0.127364	−0.0636818	−	0.997970i	$-0.520284\pi$
$751$	−3.49032	−0.127364	−0.0636818	+	0.997970i	$0.520284\pi$
$752$	25.0443	0.913273
$753$	0.381873	0.0139162
$754$	−35.3770	−1.28835
$755$	−53.4274	−1.94442
$756$	0.237692	0.00864476
$757$	−30.8662	−1.12185	−0.560925	−	0.827866i	$-0.689555\pi$
$757$	−30.8662	−1.12185	−0.560925	+	0.827866i	$0.689555\pi$
$758$	1.55335	0.0564203
$759$	0.550776	0.0199919
$760$	9.55531	0.346607
$761$	−49.0749	−1.77896	−0.889481	−	0.456972i	$-0.848934\pi$
$761$	−49.0749	−1.77896	−0.889481	+	0.456972i	$0.848934\pi$
$762$	−0.768254	−0.0278309
$763$	8.26498	0.299212
$764$	28.6802	1.03761
$765$	−9.00711	−0.325653
$766$	−6.56243	−0.237110
$767$	−5.33788	−0.192740
$768$	−0.792782	−0.0286071
$769$	30.8746	1.11337	0.556683	−	0.830725i	$-0.312074\pi$
$769$	30.8746	1.11337	0.556683	+	0.830725i	$0.312074\pi$
$770$	−10.0454	−0.362012
$771$	−0.815623	−0.0293739
$772$	10.2820	0.370056
$773$	−18.9927	−0.683121	−0.341561	−	0.939860i	$-0.610956\pi$
$773$	−18.9927	−0.683121	−0.341561	+	0.939860i	$0.610956\pi$
$774$	−38.3517	−1.37852
$775$	25.6065	0.919812
$776$	13.1654	0.472612
$777$	0.103012	0.00369553
$778$	−20.7553	−0.744115
$779$	2.81151	0.100733
$780$	−0.986617	−0.0353266
$781$	−4.32004	−0.154583
$782$	9.81343	0.350928
$783$	0.813785	0.0290823
$784$	30.6564	1.09487
$785$	−37.5689	−1.34089
$786$	0.00236522	8.43645e−5 0
$787$	39.0053	1.39039	0.695195	−	0.718821i	$-0.255318\pi$
$787$	39.0053	1.39039	0.695195	+	0.718821i	$0.255318\pi$
$788$	−20.4261	−0.727648
$789$	−1.19060	−0.0423866
$790$	−22.4067	−0.797193
$791$	−4.91283	−0.174680
$792$	−6.42891	−0.228441
$793$	−40.3800	−1.43394
$794$	10.6370	0.377492
$795$	−1.12826	−0.0400151
$796$	−19.2898	−0.683709
$797$	13.1994	0.467547	0.233774	−	0.972291i	$-0.424893\pi$
$797$	13.1994	0.467547	0.233774	+	0.972291i	$0.424893\pi$
$798$	0.192355	0.00680929
$799$	−5.37976	−0.190322
$800$	29.1808	1.03170
$801$	27.9293	0.986832
$802$	−16.3654	−0.577884
$803$	27.4514	0.968740
$804$	0.519258	0.0183128
$805$	−10.0231	−0.353269
$806$	−64.3448	−2.26645
$807$	0.798831	0.0281202
$808$	14.1283	0.497032
$809$	48.6767	1.71138	0.855691	−	0.517486i	$-0.173132\pi$
$809$	48.6767	1.71138	0.855691	+	0.517486i	$0.173132\pi$
$810$	−51.1263	−1.79639
$811$	−42.7578	−1.50143	−0.750714	−	0.660627i	$-0.770290\pi$
$811$	−42.7578	−1.50143	−0.750714	+	0.660627i	$0.770290\pi$
$812$	3.57654	0.125512
$813$	0.912015	0.0319857
$814$	21.4259	0.750978
$815$	−39.7181	−1.39127
$816$	0.180482	0.00631814
$817$	−27.4712	−0.961094
$818$	−2.82944	−0.0989292
$819$	−10.3073	−0.360167
$820$	3.29506	0.115068
$821$	−5.11787	−0.178615	−0.0893075	−	0.996004i	$-0.528465\pi$
$821$	−5.11787	−0.178615	−0.0893075	+	0.996004i	$0.528465\pi$
$822$	0.930997	0.0324722
$823$	−17.5644	−0.612257	−0.306129	−	0.951990i	$-0.599034\pi$
$823$	−17.5644	−0.612257	−0.306129	+	0.951990i	$0.599034\pi$
$824$	8.74840	0.304765
$825$	−0.427667	−0.0148895
$826$	1.21968	0.0424381
$827$	48.8803	1.69973	0.849867	−	0.526997i	$-0.176682\pi$
$827$	48.8803	1.69973	0.849867	+	0.526997i	$0.176682\pi$
$828$	24.6582	0.856933
$829$	−29.5141	−1.02507	−0.512534	−	0.858667i	$-0.671293\pi$
$829$	−29.5141	−1.02507	−0.512534	+	0.858667i	$0.671293\pi$
$830$	−81.5484	−2.83059
$831$	0.581206	0.0201618
$832$	−23.6277	−0.819145
$833$	−6.58529	−0.228167
$834$	−1.05649	−0.0365833
$835$	−6.82406	−0.236156
$836$	17.7019	0.612232
$837$	1.48014	0.0511610
$838$	66.9676	2.31336
$839$	−12.9082	−0.445641	−0.222820	−	0.974860i	$-0.571526\pi$
$839$	−12.9082	−0.445641	−0.222820	+	0.974860i	$0.571526\pi$
$840$	−0.0586458	−0.00202347
$841$	−16.7550	−0.577759
$842$	−43.3506	−1.49396
$843$	0.0650364	0.00223997
$844$	−28.0044	−0.963951
$845$	46.5388	1.60098
$846$	−30.5520	−1.05040
$847$	−2.24260	−0.0770566
$848$	−45.1008	−1.54877
$849$	0.796070	0.0273211
$850$	−7.61994	−0.261362
$851$	21.3784	0.732841
$852$	0.0969497	0.00332144
$853$	−12.1669	−0.416585	−0.208293	−	0.978067i	$-0.566791\pi$
$853$	−12.1669	−0.416585	−0.208293	+	0.978067i	$0.566791\pi$
$854$	9.22665	0.315730
$855$	−36.6399	−1.25306
$856$	11.0974	0.379301
$857$	48.6664	1.66241	0.831206	−	0.555965i	$-0.187651\pi$
$857$	48.6664	1.66241	0.831206	+	0.555965i	$0.187651\pi$
$858$	1.07465	0.0366881
$859$	−11.8252	−0.403471	−0.201735	−	0.979440i	$-0.564658\pi$
$859$	−11.8252	−0.403471	−0.201735	+	0.979440i	$0.564658\pi$
$860$	−32.1959	−1.09787
$861$	−0.0172557	−0.000588072 0
$862$	70.7983	2.41140
$863$	50.7392	1.72718	0.863592	−	0.504192i	$-0.168209\pi$
$863$	50.7392	1.72718	0.863592	+	0.504192i	$0.168209\pi$
$864$	1.68674	0.0573842
$865$	33.9568	1.15456
$866$	−50.8895	−1.72929
$867$	−0.0387693	−0.00131667
$868$	6.50512	0.220798
$869$	10.7985	0.366313
$870$	0.771831	0.0261675
$871$	−45.0457	−1.52632
$872$	10.0360	0.339863
$873$	−50.4830	−1.70859
$874$	39.9199	1.35031
$875$	−1.88944	−0.0638747
$876$	−0.616061	−0.0208148
$877$	−54.8858	−1.85336	−0.926681	−	0.375849i	$-0.877351\pi$
$877$	−54.8858	−1.85336	−0.926681	+	0.375849i	$0.877351\pi$
$878$	−11.1645	−0.376784
$879$	0.300841	0.0101471
$880$	−38.3414	−1.29249
$881$	13.7120	0.461970	0.230985	−	0.972957i	$-0.425805\pi$
$881$	13.7120	0.461970	0.230985	+	0.972957i	$0.425805\pi$
$882$	−37.3983	−1.25927
$883$	−2.91968	−0.0982551	−0.0491276	−	0.998793i	$-0.515644\pi$
$883$	−2.91968	−0.0982551	−0.0491276	+	0.998793i	$0.515644\pi$
$884$	8.47187	0.284940
$885$	0.116458	0.00391469
$886$	−24.4508	−0.821440
$887$	14.0526	0.471839	0.235920	−	0.971773i	$-0.424190\pi$
$887$	14.0526	0.471839	0.235920	+	0.971773i	$0.424190\pi$
$888$	0.125086	0.00419761
$889$	−6.73779	−0.225978
$890$	52.9921	1.77630
$891$	24.6393	0.825449
$892$	19.0451	0.637676
$893$	−21.8843	−0.732329
$894$	1.03950	0.0347662
$895$	44.7670	1.49640
$896$	−3.94278	−0.131719
$897$	1.07227	0.0358020
$898$	13.5548	0.452329
$899$	22.2716	0.742798
$900$	−19.1466	−0.638221
$901$	9.68809	0.322757
$902$	−3.58908	−0.119503
$903$	0.168605	0.00561081
$904$	−5.96558	−0.198412
$905$	−52.7554	−1.75365
$906$	−1.30600	−0.0433890
$907$	10.1896	0.338339	0.169170	−	0.985587i	$-0.445891\pi$
$907$	10.1896	0.338339	0.169170	+	0.985587i	$0.445891\pi$
$908$	−10.5477	−0.350037
$909$	−54.1751	−1.79687
$910$	−19.5568	−0.648300
$911$	−8.36558	−0.277164	−0.138582	−	0.990351i	$-0.544254\pi$
$911$	−8.36558	−0.277164	−0.138582	+	0.990351i	$0.544254\pi$
$912$	0.734181	0.0243112
$913$	39.3007	1.30066
$914$	55.2478	1.82744
$915$	0.880982	0.0291244
$916$	−19.4302	−0.641993
$917$	0.0207436	0.000685013 0
$918$	−0.440457	−0.0145372
$919$	24.7013	0.814821	0.407411	−	0.913245i	$-0.366432\pi$
$919$	24.7013	0.814821	0.407411	+	0.913245i	$0.366432\pi$
$920$	−12.1709	−0.401263
$921$	0.615976	0.0202971
$922$	36.8165	1.21249
$923$	−8.41040	−0.276832
$924$	−0.108645	−0.00357417
$925$	−16.5999	−0.545801
$926$	44.1424	1.45061
$927$	−33.5458	−1.10179
$928$	25.3804	0.833152
$929$	45.6211	1.49678	0.748390	−	0.663259i	$-0.230827\pi$
$929$	45.6211	1.49678	0.748390	+	0.663259i	$0.230827\pi$
$930$	1.40383	0.0460334
$931$	−26.7882	−0.877948
$932$	30.6037	1.00246
$933$	0.900807	0.0294911
$934$	32.6111	1.06707
$935$	8.23610	0.269349
$936$	−12.5160	−0.409099
$937$	−55.5632	−1.81517	−0.907585	−	0.419869i	$-0.862076\pi$
$937$	−55.5632	−1.81517	−0.907585	+	0.419869i	$0.862076\pi$
$938$	10.2928	0.336070
$939$	−1.11110	−0.0362594
$940$	−25.6481	−0.836549
$941$	−46.1992	−1.50605	−0.753025	−	0.657991i	$-0.771406\pi$
$941$	−46.1992	−1.50605	−0.753025	+	0.657991i	$0.771406\pi$
$942$	−0.918349	−0.0299214
$943$	−3.58112	−0.116617
$944$	4.65529	0.151517
$945$	0.449868	0.0146342
$946$	35.0688	1.14019
$947$	45.7712	1.48737	0.743683	−	0.668533i	$-0.233077\pi$
$947$	45.7712	1.48737	0.743683	+	0.668533i	$0.233077\pi$
$948$	−0.242337	−0.00787075
$949$	53.4434	1.73485
$950$	−30.9971	−1.00568
$951$	0.764791	0.0248000
$952$	0.503578	0.0163211
$953$	12.5026	0.404999	0.202499	−	0.979282i	$-0.435094\pi$
$953$	12.5026	0.404999	0.202499	+	0.979282i	$0.435094\pi$
$954$	55.0193	1.78131
$955$	54.2817	1.75651
$956$	−15.4532	−0.499793
$957$	−0.371969	−0.0120240
$958$	2.17919	0.0704063
$959$	8.16508	0.263664
$960$	0.515494	0.0166375
$961$	9.50822	0.306717
$962$	41.7127	1.34487
$963$	−42.5530	−1.37125
$964$	−1.88969	−0.0608629
$965$	19.4602	0.626446
$966$	−0.245009	−0.00788303
$967$	26.9218	0.865747	0.432873	−	0.901455i	$-0.357500\pi$
$967$	26.9218	0.865747	0.432873	+	0.901455i	$0.357500\pi$
$968$	−2.72315	−0.0875255
$969$	−0.157709	−0.00506634
$970$	−95.7848	−3.07546
$971$	−14.0038	−0.449404	−0.224702	−	0.974427i	$-0.572141\pi$
$971$	−14.0038	−0.449404	−0.224702	+	0.974427i	$0.572141\pi$
$972$	−1.66024	−0.0532523
$973$	−9.26571	−0.297045
$974$	−3.67218	−0.117664
$975$	−0.832597	−0.0266644
$976$	35.2163	1.12725
$977$	−23.6570	−0.756855	−0.378428	−	0.925631i	$-0.623535\pi$
$977$	−23.6570	−0.756855	−0.378428	+	0.925631i	$0.623535\pi$
$978$	−0.970885	−0.0310455
$979$	−25.5385	−0.816214
$980$	−31.3955	−1.00289
$981$	−38.4833	−1.22868
$982$	−14.8226	−0.473009
$983$	−31.5757	−1.00711	−0.503554	−	0.863964i	$-0.667974\pi$
$983$	−31.5757	−1.00711	−0.503554	+	0.863964i	$0.667974\pi$
$984$	−0.0209533	−0.000667967 0
$985$	−38.6595	−1.23179
$986$	−6.62754	−0.211064
$987$	0.134315	0.00427529
$988$	34.4626	1.09640
$989$	34.9910	1.11265
$990$	46.7733	1.48655
$991$	20.0408	0.636617	0.318309	−	0.947987i	$-0.396885\pi$
$991$	20.0408	0.636617	0.318309	+	0.947987i	$0.396885\pi$
$992$	46.1626	1.46566
$993$	0.283325	0.00899105
$994$	1.92174	0.0609539
$995$	−36.5089	−1.15741
$996$	−0.881980	−0.0279466
$997$	28.0003	0.886779	0.443390	−	0.896329i	$-0.353776\pi$
$997$	28.0003	0.886779	0.443390	+	0.896329i	$0.353776\pi$
$998$	75.9782	2.40505
$999$	−0.959526	−0.0303581

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1003.2.a.i.1.3	✓	18
3.2	odd	2		9027.2.a.q.1.16		18

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1003.2.a.i.1.3	✓	18	1.1	even	1	trivial
9027.2.a.q.1.16		18	3.2	odd	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

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

\(f(q)\)	\(=\)	\(q-1.89397 q^{2} -0.0387693 q^{3} +1.58712 q^{4} +3.00387 q^{5} +0.0734279 q^{6} +0.643981 q^{7} +0.781977 q^{8} -2.99850 q^{9} +O(q^{10})\)	\(q-1.89397 q^{2} -0.0387693 q^{3} +1.58712 q^{4} +3.00387 q^{5} +0.0734279 q^{6} +0.643981 q^{7} +0.781977 q^{8} -2.99850 q^{9} -5.68925 q^{10} +2.74182 q^{11} -0.0615316 q^{12} +5.33788 q^{13} -1.21968 q^{14} -0.116458 q^{15} -4.65529 q^{16} +1.00000 q^{17} +5.67906 q^{18} +4.06789 q^{19} +4.76752 q^{20} -0.0249667 q^{21} -5.19293 q^{22} -5.18141 q^{23} -0.0303167 q^{24} +4.02326 q^{25} -10.1098 q^{26} +0.232557 q^{27} +1.02208 q^{28} +3.49928 q^{29} +0.220568 q^{30} +6.36461 q^{31} +7.25302 q^{32} -0.106299 q^{33} -1.89397 q^{34} +1.93444 q^{35} -4.75898 q^{36} -4.12597 q^{37} -7.70446 q^{38} -0.206946 q^{39} +2.34896 q^{40} +0.691148 q^{41} +0.0472862 q^{42} -6.75318 q^{43} +4.35161 q^{44} -9.00711 q^{45} +9.81343 q^{46} -5.37976 q^{47} +0.180482 q^{48} -6.58529 q^{49} -7.61994 q^{50} -0.0387693 q^{51} +8.47187 q^{52} +9.68809 q^{53} -0.440457 q^{54} +8.23610 q^{55} +0.503578 q^{56} -0.157709 q^{57} -6.62754 q^{58} -1.00000 q^{59} -0.184833 q^{60} -7.56480 q^{61} -12.0544 q^{62} -1.93098 q^{63} -4.42643 q^{64} +16.0343 q^{65} +0.201326 q^{66} -8.43888 q^{67} +1.58712 q^{68} +0.200879 q^{69} -3.66377 q^{70} -1.57561 q^{71} -2.34475 q^{72} +10.0121 q^{73} +7.81447 q^{74} -0.155979 q^{75} +6.45624 q^{76} +1.76568 q^{77} +0.391949 q^{78} +3.93842 q^{79} -13.9839 q^{80} +8.98647 q^{81} -1.30901 q^{82} +14.3338 q^{83} -0.0396252 q^{84} +3.00387 q^{85} +12.7903 q^{86} -0.135665 q^{87} +2.14404 q^{88} -9.31442 q^{89} +17.0592 q^{90} +3.43749 q^{91} -8.22353 q^{92} -0.246751 q^{93} +10.1891 q^{94} +12.2194 q^{95} -0.281194 q^{96} +16.8361 q^{97} +12.4723 q^{98} -8.22135 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 18 q + 5 q^{2} + q^{3} + 21 q^{4} + 21 q^{5} + 5 q^{6} - q^{7} + 9 q^{8} + 17 q^{9}+O(q^{10}) \) 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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