LMFDB - Embedded newform 1003.2.a.i.1.11

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			1.11
Root			$1.14480$ 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)

$f(q)$	$=$	$q+1.14480 q^{2} -1.66658 q^{3} -0.689428 q^{4} -2.63259 q^{5} -1.90791 q^{6} -1.31875 q^{7} -3.07886 q^{8} -0.222506 q^{9} +O(q^{10})$	\(q+1.14480 q^{2} -1.66658 q^{3} -0.689428 q^{4} -2.63259 q^{5} -1.90791 q^{6} -1.31875 q^{7} -3.07886 q^{8} -0.222506 q^{9} -3.01379 q^{10} +3.37072 q^{11} +1.14899 q^{12} -0.479455 q^{13} -1.50971 q^{14} +4.38742 q^{15} -2.14583 q^{16} +1.00000 q^{17} -0.254725 q^{18} +1.94900 q^{19} +1.81498 q^{20} +2.19781 q^{21} +3.85881 q^{22} +1.96311 q^{23} +5.13118 q^{24} +1.93052 q^{25} -0.548881 q^{26} +5.37057 q^{27} +0.909183 q^{28} -4.00179 q^{29} +5.02273 q^{30} +6.62041 q^{31} +3.70117 q^{32} -5.61758 q^{33} +1.14480 q^{34} +3.47173 q^{35} +0.153402 q^{36} +0.120607 q^{37} +2.23122 q^{38} +0.799050 q^{39} +8.10538 q^{40} +1.55179 q^{41} +2.51605 q^{42} -0.981400 q^{43} -2.32387 q^{44} +0.585766 q^{45} +2.24738 q^{46} +2.25003 q^{47} +3.57621 q^{48} -5.26090 q^{49} +2.21006 q^{50} -1.66658 q^{51} +0.330549 q^{52} +11.3325 q^{53} +6.14824 q^{54} -8.87372 q^{55} +4.06025 q^{56} -3.24817 q^{57} -4.58126 q^{58} -1.00000 q^{59} -3.02481 q^{60} +5.98639 q^{61} +7.57906 q^{62} +0.293430 q^{63} +8.52878 q^{64} +1.26221 q^{65} -6.43102 q^{66} -1.47335 q^{67} -0.689428 q^{68} -3.27169 q^{69} +3.97444 q^{70} -11.6281 q^{71} +0.685065 q^{72} -1.92154 q^{73} +0.138072 q^{74} -3.21736 q^{75} -1.34370 q^{76} -4.44514 q^{77} +0.914754 q^{78} +11.9763 q^{79} +5.64909 q^{80} -8.28297 q^{81} +1.77649 q^{82} -4.08687 q^{83} -1.51523 q^{84} -2.63259 q^{85} -1.12351 q^{86} +6.66932 q^{87} -10.3780 q^{88} -6.06041 q^{89} +0.670586 q^{90} +0.632281 q^{91} -1.35343 q^{92} -11.0335 q^{93} +2.57584 q^{94} -5.13092 q^{95} -6.16830 q^{96} +18.6904 q^{97} -6.02269 q^{98} -0.750005 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	1.14480	0.809497	0.404749	−	0.914428i	$-0.367359\pi$
$2$	1.14480	0.809497	0.404749	+	0.914428i	$0.367359\pi$
$3$	−1.66658	−0.962201	−0.481101	−	0.876665i	$-0.659763\pi$
$3$	−1.66658	−0.962201	−0.481101	+	0.876665i	$0.659763\pi$
$4$	−0.689428	−0.344714
$5$	−2.63259	−1.17733	−0.588664	−	0.808377i	$-0.700346\pi$
$5$	−2.63259	−1.17733	−0.588664	+	0.808377i	$0.700346\pi$
$6$	−1.90791	−0.778900
$7$	−1.31875	−0.498441	−0.249220	−	0.968447i	$-0.580174\pi$
$7$	−1.31875	−0.498441	−0.249220	+	0.968447i	$0.580174\pi$
$8$	−3.07886	−1.08854
$9$	−0.222506	−0.0741686
$10$	−3.01379	−0.953045
$11$	3.37072	1.01631	0.508155	−	0.861265i	$-0.330328\pi$
$11$	3.37072	1.01631	0.508155	+	0.861265i	$0.330328\pi$
$12$	1.14899	0.331684
$13$	−0.479455	−0.132977	−0.0664884	−	0.997787i	$-0.521180\pi$
$13$	−0.479455	−0.132977	−0.0664884	+	0.997787i	$0.521180\pi$
$14$	−1.50971	−0.403487
$15$	4.38742	1.13283
$16$	−2.14583	−0.536458
$17$	1.00000	0.242536
$17$	1.00000	0.242536
$18$	−0.254725	−0.0600393
$19$	1.94900	0.447132	0.223566	−	0.974689i	$-0.428230\pi$
$19$	1.94900	0.447132	0.223566	+	0.974689i	$0.428230\pi$
$20$	1.81498	0.405842
$21$	2.19781	0.479600
$22$	3.85881	0.822701
$23$	1.96311	0.409338	0.204669	−	0.978831i	$-0.434388\pi$
$23$	1.96311	0.409338	0.204669	+	0.978831i	$0.434388\pi$
$24$	5.13118	1.04740
$25$	1.93052	0.386103
$26$	−0.548881	−0.107644
$27$	5.37057	1.03357
$28$	0.909183	0.171820
$29$	−4.00179	−0.743114	−0.371557	−	0.928410i	$-0.621176\pi$
$29$	−4.00179	−0.743114	−0.371557	+	0.928410i	$0.621176\pi$
$30$	5.02273	0.917021
$31$	6.62041	1.18906	0.594531	−	0.804073i	$-0.297338\pi$
$31$	6.62041	1.18906	0.594531	+	0.804073i	$0.297338\pi$
$32$	3.70117	0.654281
$33$	−5.61758	−0.977896
$34$	1.14480	0.196332
$35$	3.47173	0.586829
$36$	0.153402	0.0255669
$37$	0.120607	0.0198277	0.00991387	−	0.999951i	$-0.496844\pi$
$37$	0.120607	0.0198277	0.00991387	+	0.999951i	$0.496844\pi$
$38$	2.23122	0.361952
$39$	0.799050	0.127950
$40$	8.10538	1.28157
$41$	1.55179	0.242349	0.121175	−	0.992631i	$-0.461334\pi$
$41$	1.55179	0.242349	0.121175	+	0.992631i	$0.461334\pi$
$42$	2.51605	0.388235
$43$	−0.981400	−0.149662	−0.0748311	−	0.997196i	$-0.523842\pi$
$43$	−0.981400	−0.149662	−0.0748311	+	0.997196i	$0.523842\pi$
$44$	−2.32387	−0.350337
$45$	0.585766	0.0873208
$46$	2.24738	0.331358
$47$	2.25003	0.328201	0.164100	−	0.986444i	$-0.447528\pi$
$47$	2.25003	0.328201	0.164100	+	0.986444i	$0.447528\pi$
$48$	3.57621	0.516181
$49$	−5.26090	−0.751557
$50$	2.21006	0.312550
$51$	−1.66658	−0.233368
$52$	0.330549	0.0458389
$53$	11.3325	1.55664	0.778318	−	0.627871i	$-0.216073\pi$
$53$	11.3325	1.55664	0.778318	+	0.627871i	$0.216073\pi$
$54$	6.14824	0.836669
$55$	−8.87372	−1.19653
$56$	4.06025	0.542574
$57$	−3.24817	−0.430231
$58$	−4.58126	−0.601549
$59$	−1.00000	−0.130189
$59$	−1.00000	−0.130189
$60$	−3.02481	−0.390501
$61$	5.98639	0.766478	0.383239	−	0.923649i	$-0.374809\pi$
$61$	5.98639	0.766478	0.383239	+	0.923649i	$0.374809\pi$
$62$	7.57906	0.962542
$63$	0.293430	0.0369687
$64$	8.52878	1.06610
$65$	1.26221	0.156557
$66$	−6.43102	−0.791604
$67$	−1.47335	−0.179998	−0.0899992	−	0.995942i	$-0.528686\pi$
$67$	−1.47335	−0.179998	−0.0899992	+	0.995942i	$0.528686\pi$
$68$	−0.689428	−0.0836054
$69$	−3.27169	−0.393865
$70$	3.97444	0.475036
$71$	−11.6281	−1.38001	−0.690003	−	0.723807i	$-0.742391\pi$
$71$	−11.6281	−1.38001	−0.690003	+	0.723807i	$0.742391\pi$
$72$	0.685065	0.0807357
$73$	−1.92154	−0.224899	−0.112449	−	0.993657i	$-0.535870\pi$
$73$	−1.92154	−0.224899	−0.112449	+	0.993657i	$0.535870\pi$
$74$	0.138072	0.0160505
$75$	−3.21736	−0.371509
$76$	−1.34370	−0.154132
$77$	−4.44514	−0.506571
$78$	0.914754	0.103576
$79$	11.9763	1.34744	0.673722	−	0.738985i	$-0.264695\pi$
$79$	11.9763	1.34744	0.673722	+	0.738985i	$0.264695\pi$
$80$	5.64909	0.631588
$81$	−8.28297	−0.920330
$82$	1.77649	0.196181
$83$	−4.08687	−0.448593	−0.224296	−	0.974521i	$-0.572008\pi$
$83$	−4.08687	−0.448593	−0.224296	+	0.974521i	$0.572008\pi$
$84$	−1.51523	−0.165325
$85$	−2.63259	−0.285544
$86$	−1.12351	−0.121151
$87$	6.66932	0.715026
$88$	−10.3780	−1.10630
$89$	−6.06041	−0.642403	−0.321201	−	0.947011i	$-0.604087\pi$
$89$	−6.06041	−0.642403	−0.321201	+	0.947011i	$0.604087\pi$
$90$	0.670586	0.0706860
$91$	0.632281	0.0662811
$92$	−1.35343	−0.141104
$93$	−11.0335	−1.14412
$94$	2.57584	0.265678
$95$	−5.13092	−0.526421
$96$	−6.16830	−0.629550
$97$	18.6904	1.89772	0.948859	−	0.315701i	$-0.102240\pi$
$97$	18.6904	1.89772	0.948859	+	0.315701i	$0.102240\pi$
$98$	−6.02269	−0.608383
$99$	−0.750005	−0.0753783
$100$	−1.33095	−0.133095
$101$	−2.95276	−0.293810	−0.146905	−	0.989151i	$-0.546931\pi$
$101$	−2.95276	−0.293810	−0.146905	+	0.989151i	$0.546931\pi$
$102$	−1.90791	−0.188911
$103$	−8.17898	−0.805899	−0.402949	−	0.915222i	$-0.632015\pi$
$103$	−8.17898	−0.805899	−0.402949	+	0.915222i	$0.632015\pi$
$104$	1.47617	0.144751
$105$	−5.78592	−0.564647
$106$	12.9734	1.26009
$107$	−0.554026	−0.0535597	−0.0267799	−	0.999641i	$-0.508525\pi$
$107$	−0.554026	−0.0535597	−0.0267799	+	0.999641i	$0.508525\pi$
$108$	−3.70262	−0.356285
$109$	−4.63245	−0.443708	−0.221854	−	0.975080i	$-0.571211\pi$
$109$	−4.63245	−0.443708	−0.221854	+	0.975080i	$0.571211\pi$
$110$	−10.1587	−0.968590
$111$	−0.201002	−0.0190783
$112$	2.82982	0.267393
$113$	19.2541	1.81127	0.905636	−	0.424057i	$-0.139394\pi$
$113$	19.2541	1.81127	0.905636	+	0.424057i	$0.139394\pi$
$114$	−3.71851	−0.348271
$115$	−5.16807	−0.481925
$116$	2.75895	0.256162
$117$	0.106681	0.00986270
$118$	−1.14480	−0.105388
$119$	−1.31875	−0.120890
$120$	−13.5083	−1.23313
$121$	0.361768	0.0328880
$122$	6.85323	0.620462
$123$	−2.58619	−0.233189
$124$	−4.56430	−0.409886
$125$	8.08068	0.722758
$126$	0.335919	0.0299260
$127$	1.07393	0.0952963	0.0476481	−	0.998864i	$-0.484827\pi$
$127$	1.07393	0.0952963	0.0476481	+	0.998864i	$0.484827\pi$
$128$	2.36142	0.208722
$129$	1.63558	0.144005
$130$	1.44498	0.126733
$131$	20.3921	1.78167	0.890835	−	0.454327i	$-0.150120\pi$
$131$	20.3921	1.78167	0.890835	+	0.454327i	$0.150120\pi$
$132$	3.87292	0.337094
$133$	−2.57025	−0.222869
$134$	−1.68670	−0.145708
$135$	−14.1385	−1.21685
$136$	−3.07886	−0.264010
$137$	12.5872	1.07540	0.537699	−	0.843137i	$-0.319294\pi$
$137$	12.5872	1.07540	0.537699	+	0.843137i	$0.319294\pi$
$138$	−3.74544	−0.318833
$139$	−19.8301	−1.68197	−0.840986	−	0.541057i	$-0.818024\pi$
$139$	−19.8301	−1.68197	−0.840986	+	0.541057i	$0.818024\pi$
$140$	−2.39350	−0.202288
$141$	−3.74986	−0.315795
$142$	−13.3119	−1.11711
$143$	−1.61611	−0.135146
$144$	0.477460	0.0397884
$145$	10.5351	0.874890
$146$	−2.19978	−0.182055
$147$	8.76771	0.723149
$148$	−0.0831501	−0.00683490
$149$	10.4171	0.853401	0.426700	−	0.904393i	$-0.359676\pi$
$149$	10.4171	0.853401	0.426700	+	0.904393i	$0.359676\pi$
$150$	−3.68324	−0.300736
$151$	1.90867	0.155326	0.0776628	−	0.996980i	$-0.475254\pi$
$151$	1.90867	0.155326	0.0776628	+	0.996980i	$0.475254\pi$
$152$	−6.00071	−0.486722
$153$	−0.222506	−0.0179885
$154$	−5.08881	−0.410068
$155$	−17.4288	−1.39992
$156$	−0.550887	−0.0441063
$157$	−2.62382	−0.209404	−0.104702	−	0.994504i	$-0.533389\pi$
$157$	−2.62382	−0.209404	−0.104702	+	0.994504i	$0.533389\pi$
$158$	13.7105	1.09075
$159$	−18.8865	−1.49780
$160$	−9.74366	−0.770304
$161$	−2.58886	−0.204031
$162$	−9.48237	−0.745005
$163$	−1.36267	−0.106732	−0.0533661	−	0.998575i	$-0.516995\pi$
$163$	−1.36267	−0.106732	−0.0533661	+	0.998575i	$0.516995\pi$
$164$	−1.06985	−0.0835411
$165$	14.7888	1.15130
$166$	−4.67866	−0.363135
$167$	16.3700	1.26675	0.633375	−	0.773845i	$-0.281669\pi$
$167$	16.3700	1.26675	0.633375	+	0.773845i	$0.281669\pi$
$168$	−6.76674	−0.522065
$169$	−12.7701	−0.982317
$170$	−3.01379	−0.231147
$171$	−0.433664	−0.0331631
$172$	0.676605	0.0515906
$173$	18.6180	1.41550	0.707749	−	0.706464i	$-0.249711\pi$
$173$	18.6180	1.41550	0.707749	+	0.706464i	$0.249711\pi$
$174$	7.63505	0.578812
$175$	−2.54587	−0.192450
$176$	−7.23301	−0.545209
$177$	1.66658	0.125268
$178$	−6.93798	−0.520023
$179$	−15.9764	−1.19414	−0.597068	−	0.802191i	$-0.703668\pi$
$179$	−15.9764	−1.19414	−0.597068	+	0.802191i	$0.703668\pi$
$180$	−0.403843	−0.0301007
$181$	15.9332	1.18431	0.592153	−	0.805826i	$-0.298278\pi$
$181$	15.9332	1.18431	0.592153	+	0.805826i	$0.298278\pi$
$182$	0.723837	0.0536543
$183$	−9.97680	−0.737506
$184$	−6.04416	−0.445581
$185$	−0.317510	−0.0233438
$186$	−12.6311	−0.926159
$187$	3.37072	0.246492
$188$	−1.55123	−0.113135
$189$	−7.08244	−0.515172
$190$	−5.87388	−0.426136
$191$	−0.0192804	−0.00139508	−0.000697542	−	1.00000i	$-0.500222\pi$
$191$	−0.0192804	−0.00139508	−0.000697542		1.00000i	$0.500222\pi$
$192$	−14.2139	−1.02580
$193$	−10.4583	−0.752804	−0.376402	−	0.926456i	$-0.622839\pi$
$193$	−10.4583	−0.752804	−0.376402	+	0.926456i	$0.622839\pi$
$194$	21.3968	1.53620
$195$	−2.10357	−0.150640
$196$	3.62701	0.259072
$197$	1.78875	0.127443	0.0637216	−	0.997968i	$-0.479703\pi$
$197$	1.78875	0.127443	0.0637216	+	0.997968i	$0.479703\pi$
$198$	−0.858608	−0.0610186
$199$	6.87580	0.487412	0.243706	−	0.969849i	$-0.421637\pi$
$199$	6.87580	0.487412	0.243706	+	0.969849i	$0.421637\pi$
$200$	−5.94380	−0.420290
$201$	2.45546	0.173195
$202$	−3.38032	−0.237839
$203$	5.27737	0.370399
$204$	1.14899	0.0804452
$205$	−4.08523	−0.285325
$206$	−9.36331	−0.652373
$207$	−0.436804	−0.0303600
$208$	1.02883	0.0713365
$209$	6.56954	0.454425
$210$	−6.62373	−0.457081
$211$	−3.75384	−0.258425	−0.129212	−	0.991617i	$-0.541245\pi$
$211$	−3.75384	−0.258425	−0.129212	+	0.991617i	$0.541245\pi$
$212$	−7.81293	−0.536594
$213$	19.3792	1.32784
$214$	−0.634250	−0.0433565
$215$	2.58362	0.176202
$216$	−16.5352	−1.12508
$217$	−8.73067	−0.592677
$218$	−5.30324	−0.359181
$219$	3.20240	0.216398
$220$	6.11779	0.412461
$221$	−0.479455	−0.0322516
$222$	−0.230108	−0.0154438
$223$	14.9145	0.998750	0.499375	−	0.866386i	$-0.333563\pi$
$223$	14.9145	0.998750	0.499375	+	0.866386i	$0.333563\pi$
$224$	−4.88092	−0.326120
$225$	−0.429551	−0.0286367
$226$	22.0421	1.46622
$227$	18.9723	1.25924	0.629619	−	0.776904i	$-0.283211\pi$
$227$	18.9723	1.25924	0.629619	+	0.776904i	$0.283211\pi$
$228$	2.23938	0.148306
$229$	17.7950	1.17592	0.587962	−	0.808889i	$-0.299931\pi$
$229$	17.7950	1.17592	0.587962	+	0.808889i	$0.299931\pi$
$230$	−5.91642	−0.390117
$231$	7.40819	0.487423
$232$	12.3210	0.808912
$233$	−14.7713	−0.967700	−0.483850	−	0.875151i	$-0.660762\pi$
$233$	−14.7713	−0.967700	−0.483850	+	0.875151i	$0.660762\pi$
$234$	0.122129	0.00798383
$235$	−5.92340	−0.386400
$236$	0.689428	0.0448779
$237$	−19.9596	−1.29651
$238$	−1.50971	−0.0978599
$239$	−25.8608	−1.67279	−0.836397	−	0.548125i	$-0.815342\pi$
$239$	−25.8608	−1.67279	−0.836397	+	0.548125i	$0.815342\pi$
$240$	−9.41468	−0.607715
$241$	5.01678	0.323159	0.161580	−	0.986860i	$-0.448341\pi$
$241$	5.01678	0.323159	0.161580	+	0.986860i	$0.448341\pi$
$242$	0.414152	0.0266227
$243$	−2.30745	−0.148023
$244$	−4.12718	−0.264216
$245$	13.8498	0.884829
$246$	−2.96067	−0.188766
$247$	−0.934457	−0.0594581
$248$	−20.3833	−1.29434
$249$	6.81111	0.431637
$250$	9.25078	0.585071
$251$	6.34142	0.400267	0.200134	−	0.979769i	$-0.435862\pi$
$251$	6.34142	0.400267	0.200134	+	0.979769i	$0.435862\pi$
$252$	−0.202299	−0.0127436
$253$	6.61711	0.416014
$254$	1.22944	0.0771421
$255$	4.38742	0.274751
$256$	−14.3542	−0.897137
$257$	5.27323	0.328935	0.164467	−	0.986383i	$-0.447409\pi$
$257$	5.27323	0.328935	0.164467	+	0.986383i	$0.447409\pi$
$258$	1.87242	0.116572
$259$	−0.159051	−0.00988296
$260$	−0.870200	−0.0539675
$261$	0.890422	0.0551158
$262$	23.3450	1.44226
$263$	16.1789	0.997635	0.498818	−	0.866707i	$-0.333768\pi$
$263$	16.1789	0.997635	0.498818	+	0.866707i	$0.333768\pi$
$264$	17.2958	1.06448
$265$	−29.8337	−1.83267
$266$	−2.94242	−0.180412
$267$	10.1002	0.618121
$268$	1.01577	0.0620480
$269$	23.5880	1.43819	0.719093	−	0.694914i	$-0.244557\pi$
$269$	23.5880	1.43819	0.719093	+	0.694914i	$0.244557\pi$
$270$	−16.1858	−0.985035
$271$	4.62564	0.280988	0.140494	−	0.990082i	$-0.455131\pi$
$271$	4.62564	0.280988	0.140494	+	0.990082i	$0.455131\pi$
$272$	−2.14583	−0.130110
$273$	−1.05375	−0.0637757
$274$	14.4099	0.870532
$275$	6.50724	0.392401
$276$	2.25559	0.135771
$277$	−13.1117	−0.787807	−0.393903	−	0.919152i	$-0.628876\pi$
$277$	−13.1117	−0.787807	−0.393903	+	0.919152i	$0.628876\pi$
$278$	−22.7016	−1.36155
$279$	−1.47308	−0.0881910
$280$	−10.6890	−0.638788
$281$	−15.2897	−0.912105	−0.456052	−	0.889953i	$-0.650737\pi$
$281$	−15.2897	−0.912105	−0.456052	+	0.889953i	$0.650737\pi$
$282$	−4.29285	−0.255635
$283$	14.5370	0.864135	0.432067	−	0.901841i	$-0.357784\pi$
$283$	14.5370	0.864135	0.432067	+	0.901841i	$0.357784\pi$
$284$	8.01676	0.475707
$285$	8.55109	0.506523
$286$	−1.85012	−0.109400
$287$	−2.04643	−0.120797
$288$	−0.823532	−0.0485271
$289$	1.00000	0.0588235
$290$	12.0606	0.708221
$291$	−31.1490	−1.82599
$292$	1.32476	0.0775258
$293$	1.04482	0.0610388	0.0305194	−	0.999534i	$-0.490284\pi$
$293$	1.04482	0.0610388	0.0305194	+	0.999534i	$0.490284\pi$
$294$	10.0373	0.585387
$295$	2.63259	0.153275
$296$	−0.371334	−0.0215833
$297$	18.1027	1.05042
$298$	11.9255	0.690826
$299$	−0.941224	−0.0544324
$300$	2.21814	0.128064
$301$	1.29422	0.0745977
$302$	2.18505	0.125736
$303$	4.92101	0.282705
$304$	−4.18223	−0.239867
$305$	−15.7597	−0.902397
$306$	−0.254725	−0.0145617
$307$	6.40419	0.365507	0.182753	−	0.983159i	$-0.441499\pi$
$307$	6.40419	0.365507	0.182753	+	0.983159i	$0.441499\pi$
$308$	3.06460	0.174622
$309$	13.6309	0.775437
$310$	−19.9525	−1.13323
$311$	−7.75287	−0.439625	−0.219812	−	0.975542i	$-0.570545\pi$
$311$	−7.75287	−0.439625	−0.219812	+	0.975542i	$0.570545\pi$
$312$	−2.46017	−0.139279
$313$	−7.60552	−0.429890	−0.214945	−	0.976626i	$-0.568957\pi$
$313$	−7.60552	−0.429890	−0.214945	+	0.976626i	$0.568957\pi$
$314$	−3.00376	−0.169512
$315$	−0.772479	−0.0435243
$316$	−8.25683	−0.464483
$317$	16.4898	0.926160	0.463080	−	0.886316i	$-0.346744\pi$
$317$	16.4898	0.926160	0.463080	+	0.886316i	$0.346744\pi$
$318$	−21.6213	−1.21246
$319$	−13.4889	−0.755235
$320$	−22.4527	−1.25515
$321$	0.923330	0.0515353
$322$	−2.96373	−0.165162
$323$	1.94900	0.108445
$324$	5.71051	0.317251
$325$	−0.925595	−0.0513428
$326$	−1.55998	−0.0863995
$327$	7.72035	0.426937
$328$	−4.77776	−0.263807
$329$	−2.96723	−0.163589
$330$	16.9302	0.931978
$331$	10.5748	0.581244	0.290622	−	0.956838i	$-0.406138\pi$
$331$	10.5748	0.581244	0.290622	+	0.956838i	$0.406138\pi$
$332$	2.81761	0.154636
$333$	−0.0268359	−0.00147060
$334$	18.7404	1.02543
$335$	3.87872	0.211917
$336$	−4.71612	−0.257286
$337$	7.17531	0.390864	0.195432	−	0.980717i	$-0.437389\pi$
$337$	7.17531	0.390864	0.195432	+	0.980717i	$0.437389\pi$
$338$	−14.6193	−0.795183
$339$	−32.0885	−1.74281
$340$	1.81498	0.0984311
$341$	22.3156	1.20846
$342$	−0.496460	−0.0268455
$343$	16.1691	0.873047
$344$	3.02160	0.162914
$345$	8.61301	0.463709
$346$	21.3139	1.14584
$347$	21.9473	1.17819	0.589096	−	0.808063i	$-0.299484\pi$
$347$	21.9473	1.17819	0.589096	+	0.808063i	$0.299484\pi$
$348$	−4.59801	−0.246479
$349$	27.3529	1.46417	0.732083	−	0.681215i	$-0.238548\pi$
$349$	27.3529	1.46417	0.732083	+	0.681215i	$0.238548\pi$
$350$	−2.91452	−0.155788
$351$	−2.57494	−0.137440
$352$	12.4756	0.664953
$353$	−11.7462	−0.625185	−0.312593	−	0.949887i	$-0.601197\pi$
$353$	−11.7462	−0.625185	−0.312593	+	0.949887i	$0.601197\pi$
$354$	1.90791	0.101404
$355$	30.6121	1.62472
$356$	4.17822	0.221445
$357$	2.19781	0.116320
$358$	−18.2899	−0.966650
$359$	−12.4619	−0.657713	−0.328856	−	0.944380i	$-0.606663\pi$
$359$	−12.4619	−0.657713	−0.328856	+	0.944380i	$0.606663\pi$
$360$	−1.80349	−0.0950524
$361$	−15.2014	−0.800073
$362$	18.2404	0.958693
$363$	−0.602915	−0.0316449
$364$	−0.435912	−0.0228480
$365$	5.05862	0.264780
$366$	−11.4215	−0.597009
$367$	−30.9905	−1.61769	−0.808846	−	0.588021i	$-0.799907\pi$
$367$	−30.9905	−1.61769	−0.808846	+	0.588021i	$0.799907\pi$
$368$	−4.21252	−0.219593
$369$	−0.345283	−0.0179747
$370$	−0.363486	−0.0188967
$371$	−14.9447	−0.775891
$372$	7.60677	0.394393
$373$	6.02966	0.312204	0.156102	−	0.987741i	$-0.450107\pi$
$373$	6.02966	0.312204	0.156102	+	0.987741i	$0.450107\pi$
$374$	3.85881	0.199534
$375$	−13.4671	−0.695439
$376$	−6.92754	−0.357260
$377$	1.91868	0.0988170
$378$	−8.10799	−0.417030
$379$	−22.4992	−1.15571	−0.577853	−	0.816141i	$-0.696109\pi$
$379$	−22.4992	−1.15571	−0.577853	+	0.816141i	$0.696109\pi$
$380$	3.53740	0.181465
$381$	−1.78980	−0.0916942
$382$	−0.0220723	−0.00112932
$383$	11.9414	0.610176	0.305088	−	0.952324i	$-0.401314\pi$
$383$	11.9414	0.610176	0.305088	+	0.952324i	$0.401314\pi$
$384$	−3.93550	−0.200833
$385$	11.7022	0.596401
$386$	−11.9727	−0.609393
$387$	0.218367	0.0111002
$388$	−12.8856	−0.654170
$389$	5.26548	0.266970	0.133485	−	0.991051i	$-0.457383\pi$
$389$	5.26548	0.266970	0.133485	+	0.991051i	$0.457383\pi$
$390$	−2.40817	−0.121942
$391$	1.96311	0.0992790
$392$	16.1976	0.818101
$393$	−33.9852	−1.71433
$394$	2.04777	0.103165
$395$	−31.5288	−1.58638
$396$	0.517074	0.0259840
$397$	12.8846	0.646660	0.323330	−	0.946286i	$-0.395198\pi$
$397$	12.8846	0.646660	0.323330	+	0.946286i	$0.395198\pi$
$398$	7.87143	0.394559
$399$	4.28353	0.214445
$400$	−4.14257	−0.207128
$401$	33.2134	1.65860	0.829299	−	0.558806i	$-0.188740\pi$
$401$	33.2134	1.65860	0.829299	+	0.558806i	$0.188740\pi$
$402$	2.81102	0.140201
$403$	−3.17419	−0.158118
$404$	2.03571	0.101281
$405$	21.8057	1.08353
$406$	6.04154	0.299837
$407$	0.406534	0.0201512
$408$	5.13118	0.254031
$409$	−27.5665	−1.36307	−0.681537	−	0.731784i	$-0.738688\pi$
$409$	−27.5665	−1.36307	−0.681537	+	0.731784i	$0.738688\pi$
$410$	−4.67678	−0.230970
$411$	−20.9776	−1.03475
$412$	5.63882	0.277805
$413$	1.31875	0.0648915
$414$	−0.500054	−0.0245763
$415$	10.7591	0.528141
$416$	−1.77454	−0.0870041
$417$	33.0486	1.61839
$418$	7.52083	0.367856
$419$	19.4824	0.951775	0.475888	−	0.879506i	$-0.342127\pi$
$419$	19.4824	0.951775	0.475888	+	0.879506i	$0.342127\pi$
$420$	3.98897	0.194642
$421$	14.2218	0.693127	0.346563	−	0.938027i	$-0.387349\pi$
$421$	14.2218	0.693127	0.346563	+	0.938027i	$0.387349\pi$
$422$	−4.29740	−0.209194
$423$	−0.500645	−0.0243422
$424$	−34.8911	−1.69446
$425$	1.93052	0.0936438
$426$	22.1854	1.07489
$427$	−7.89455	−0.382044
$428$	0.381961	0.0184628
$429$	2.69338	0.130037
$430$	2.95774	0.142635
$431$	−3.06729	−0.147746	−0.0738731	−	0.997268i	$-0.523536\pi$
$431$	−3.06729	−0.147746	−0.0738731	+	0.997268i	$0.523536\pi$
$432$	−11.5243	−0.554465
$433$	17.2899	0.830899	0.415450	−	0.909616i	$-0.363624\pi$
$433$	17.2899	0.830899	0.415450	+	0.909616i	$0.363624\pi$
$434$	−9.99489	−0.479770
$435$	−17.5576	−0.841820
$436$	3.19374	0.152952
$437$	3.82611	0.183028
$438$	3.66611	0.175174
$439$	−1.97503	−0.0942632	−0.0471316	−	0.998889i	$-0.515008\pi$
$439$	−1.97503	−0.0942632	−0.0471316	+	0.998889i	$0.515008\pi$
$440$	27.3210	1.30248
$441$	1.17058	0.0557419
$442$	−0.548881	−0.0261076
$443$	−22.4198	−1.06520	−0.532598	−	0.846368i	$-0.678784\pi$
$443$	−22.4198	−1.06520	−0.532598	+	0.846368i	$0.678784\pi$
$444$	0.138576	0.00657655
$445$	15.9546	0.756319
$446$	17.0742	0.808486
$447$	−17.3609	−0.821143
$448$	−11.2473	−0.531386
$449$	−0.633708	−0.0299065	−0.0149533	−	0.999888i	$-0.504760\pi$
$449$	−0.633708	−0.0299065	−0.0149533	+	0.999888i	$0.504760\pi$
$450$	−0.491751	−0.0231814
$451$	5.23066	0.246302
$452$	−13.2743	−0.624370
$453$	−3.18096	−0.149455
$454$	21.7196	1.01935
$455$	−1.66453	−0.0780346
$456$	10.0007	0.468324
$457$	−1.87131	−0.0875361	−0.0437681	−	0.999042i	$-0.513936\pi$
$457$	−1.87131	−0.0875361	−0.0437681	+	0.999042i	$0.513936\pi$
$458$	20.3717	0.951907
$459$	5.37057	0.250677
$460$	3.56301	0.166126
$461$	16.7137	0.778434	0.389217	−	0.921146i	$-0.372746\pi$
$461$	16.7137	0.778434	0.389217	+	0.921146i	$0.372746\pi$
$462$	8.48091	0.394568
$463$	5.47353	0.254377	0.127188	−	0.991879i	$-0.459405\pi$
$463$	5.47353	0.254377	0.127188	+	0.991879i	$0.459405\pi$
$464$	8.58718	0.398650
$465$	29.0465	1.34700
$466$	−16.9102	−0.783351
$467$	8.66136	0.400800	0.200400	−	0.979714i	$-0.435776\pi$
$467$	8.66136	0.400800	0.200400	+	0.979714i	$0.435776\pi$
$468$	−0.0735491	−0.00339981
$469$	1.94298	0.0897186
$470$	−6.78112	−0.312790
$471$	4.37281	0.201488
$472$	3.07886	0.141716
$473$	−3.30803	−0.152103
$474$	−22.8497	−1.04952
$475$	3.76258	0.172639
$476$	0.909183	0.0416724
$477$	−2.52154	−0.115453
$478$	−29.6055	−1.35412
$479$	−35.0965	−1.60360	−0.801800	−	0.597592i	$-0.796124\pi$
$479$	−35.0965	−1.60360	−0.801800	+	0.597592i	$0.796124\pi$
$480$	16.2386	0.741187
$481$	−0.0578258	−0.00263663
$482$	5.74322	0.261597
$483$	4.31454	0.196319
$484$	−0.249413	−0.0113369
$485$	−49.2040	−2.23424
$486$	−2.64158	−0.119824
$487$	−18.7408	−0.849225	−0.424613	−	0.905375i	$-0.639590\pi$
$487$	−18.7408	−0.849225	−0.424613	+	0.905375i	$0.639590\pi$
$488$	−18.4313	−0.834344
$489$	2.27099	0.102698
$490$	15.8552	0.716267
$491$	11.8747	0.535898	0.267949	−	0.963433i	$-0.413654\pi$
$491$	11.8747	0.535898	0.267949	+	0.963433i	$0.413654\pi$
$492$	1.78299	0.0803834
$493$	−4.00179	−0.180232
$494$	−1.06977	−0.0481312
$495$	1.97445	0.0887451
$496$	−14.2063	−0.637882
$497$	15.3346	0.687851
$498$	7.79737	0.349409
$499$	18.0016	0.805864	0.402932	−	0.915230i	$-0.367991\pi$
$499$	18.0016	0.805864	0.402932	+	0.915230i	$0.367991\pi$
$500$	−5.57105	−0.249145
$501$	−27.2820	−1.21887
$502$	7.25968	0.324015
$503$	−38.1503	−1.70104	−0.850519	−	0.525944i	$-0.823712\pi$
$503$	−38.1503	−1.70104	−0.850519	+	0.525944i	$0.823712\pi$
$504$	−0.903430	−0.0402420
$505$	7.77339	0.345912
$506$	7.57529	0.336763
$507$	21.2825	0.945187
$508$	−0.740400	−0.0328500
$509$	32.1501	1.42503	0.712514	−	0.701658i	$-0.247557\pi$
$509$	32.1501	1.42503	0.712514	+	0.701658i	$0.247557\pi$
$510$	5.02273	0.222410
$511$	2.53403	0.112099
$512$	−21.1556	−0.934952
$513$	10.4672	0.462140
$514$	6.03680	0.266272
$515$	21.5319	0.948808
$516$	−1.12762	−0.0496406
$517$	7.58423	0.333554
$518$	−0.182082	−0.00800023
$519$	−31.0284	−1.36199
$520$	−3.88616	−0.170419
$521$	9.77393	0.428204	0.214102	−	0.976811i	$-0.431318\pi$
$521$	9.77393	0.428204	0.214102	+	0.976811i	$0.431318\pi$
$522$	1.01936	0.0446161
$523$	−14.9400	−0.653279	−0.326640	−	0.945149i	$-0.605916\pi$
$523$	−14.9400	−0.653279	−0.326640	+	0.945149i	$0.605916\pi$
$524$	−14.0589	−0.614167
$525$	4.24290	0.185175
$526$	18.5217	0.807583
$527$	6.62041	0.288390
$528$	12.0544	0.524600
$529$	−19.1462	−0.832443
$530$	−34.1537	−1.48354
$531$	0.222506	0.00965593
$532$	1.77200	0.0768259
$533$	−0.744014	−0.0322268
$534$	11.5627	0.500367
$535$	1.45852	0.0630574
$536$	4.53624	0.195936
$537$	26.6261	1.14900
$538$	27.0036	1.16421
$539$	−17.7330	−0.763815
$540$	9.74747	0.419464
$541$	−40.3477	−1.73468	−0.867341	−	0.497714i	$-0.834173\pi$
$541$	−40.3477	−1.73468	−0.867341	+	0.497714i	$0.834173\pi$
$542$	5.29545	0.227459
$543$	−26.5540	−1.13954
$544$	3.70117	0.158686
$545$	12.1953	0.522390
$546$	−1.20633	−0.0516263
$547$	−32.1751	−1.37571	−0.687854	−	0.725849i	$-0.741447\pi$
$547$	−32.1751	−1.37571	−0.687854	+	0.725849i	$0.741447\pi$
$548$	−8.67797	−0.370705
$549$	−1.33201	−0.0568486
$550$	7.44950	0.317648
$551$	−7.79950	−0.332270
$552$	10.0731	0.428739
$553$	−15.7938	−0.671621
$554$	−15.0103	−0.637728
$555$	0.529156	0.0224614
$556$	13.6715	0.579799
$557$	13.4404	0.569490	0.284745	−	0.958603i	$-0.408091\pi$
$557$	13.4404	0.569490	0.284745	+	0.958603i	$0.408091\pi$
$558$	−1.68639	−0.0713904
$559$	0.470537	0.0199016
$560$	−7.44975	−0.314809
$561$	−5.61758	−0.237175
$562$	−17.5036	−0.738347
$563$	9.03758	0.380889	0.190444	−	0.981698i	$-0.439007\pi$
$563$	9.03758	0.380889	0.190444	+	0.981698i	$0.439007\pi$
$564$	2.58526	0.108859
$565$	−50.6880	−2.13246
$566$	16.6420	0.699515
$567$	10.9232	0.458730
$568$	35.8014	1.50219
$569$	9.46825	0.396930	0.198465	−	0.980108i	$-0.436404\pi$
$569$	9.46825	0.396930	0.198465	+	0.980108i	$0.436404\pi$
$570$	9.78931	0.410029
$571$	−14.6052	−0.611208	−0.305604	−	0.952159i	$-0.598858\pi$
$571$	−14.6052	−0.611208	−0.305604	+	0.952159i	$0.598858\pi$
$572$	1.11419	0.0465866
$573$	0.0321324	0.00134235
$574$	−2.34275	−0.0977847
$575$	3.78982	0.158047
$576$	−1.89770	−0.0790709
$577$	−22.6172	−0.941567	−0.470784	−	0.882249i	$-0.656029\pi$
$577$	−22.6172	−0.941567	−0.470784	+	0.882249i	$0.656029\pi$
$578$	1.14480	0.0476175
$579$	17.4296	0.724349
$580$	−7.26317	−0.301587
$581$	5.38957	0.223597
$582$	−35.6594	−1.47813
$583$	38.1986	1.58203
$584$	5.91615	0.244812
$585$	−0.280848	−0.0116116
$586$	1.19611	0.0494108
$587$	0.624776	0.0257873	0.0128936	−	0.999917i	$-0.495896\pi$
$587$	0.624776	0.0257873	0.0128936	+	0.999917i	$0.495896\pi$
$588$	−6.04471	−0.249279
$589$	12.9032	0.531667
$590$	3.01379	0.124076
$591$	−2.98110	−0.122626
$592$	−0.258804	−0.0106368
$593$	0.463357	0.0190278	0.00951389	−	0.999955i	$-0.496972\pi$
$593$	0.463357	0.0190278	0.00951389	+	0.999955i	$0.496972\pi$
$594$	20.7240	0.850316
$595$	3.47173	0.142327
$596$	−7.18183	−0.294179
$597$	−11.4591	−0.468989
$598$	−1.07752	−0.0440629
$599$	28.0530	1.14621	0.573107	−	0.819481i	$-0.305738\pi$
$599$	28.0530	1.14621	0.573107	+	0.819481i	$0.305738\pi$
$600$	9.90582	0.404403
$601$	−30.5820	−1.24747	−0.623734	−	0.781637i	$-0.714385\pi$
$601$	−30.5820	−1.24747	−0.623734	+	0.781637i	$0.714385\pi$
$602$	1.48163	0.0603867
$603$	0.327829	0.0133502
$604$	−1.31589	−0.0535429
$605$	−0.952385	−0.0387200
$606$	5.63359	0.228849
$607$	29.3320	1.19055	0.595274	−	0.803523i	$-0.297044\pi$
$607$	29.3320	1.19055	0.595274	+	0.803523i	$0.297044\pi$
$608$	7.21359	0.292550
$609$	−8.79516	−0.356398
$610$	−18.0417	−0.730488
$611$	−1.07879	−0.0436431
$612$	0.153402	0.00620089
$613$	−16.8215	−0.679412	−0.339706	−	0.940532i	$-0.610328\pi$
$613$	−16.8215	−0.679412	−0.339706	+	0.940532i	$0.610328\pi$
$614$	7.33154	0.295877
$615$	6.80837	0.274540
$616$	13.6860	0.551424
$617$	39.1733	1.57706	0.788529	−	0.614997i	$-0.210843\pi$
$617$	39.1733	1.57706	0.788529	+	0.614997i	$0.210843\pi$
$618$	15.6047	0.627714
$619$	−18.2188	−0.732274	−0.366137	−	0.930561i	$-0.619320\pi$
$619$	−18.2188	−0.732274	−0.366137	+	0.930561i	$0.619320\pi$
$620$	12.0159	0.482571
$621$	10.5430	0.423078
$622$	−8.87550	−0.355875
$623$	7.99217	0.320200
$624$	−1.71463	−0.0686401
$625$	−30.9257	−1.23703
$626$	−8.70682	−0.347994
$627$	−10.9487	−0.437248
$628$	1.80893	0.0721844
$629$	0.120607	0.00480893
$630$	−0.884336	−0.0352328
$631$	9.18406	0.365612	0.182806	−	0.983149i	$-0.441482\pi$
$631$	9.18406	0.365612	0.182806	+	0.983149i	$0.441482\pi$
$632$	−36.8735	−1.46675
$633$	6.25608	0.248657
$634$	18.8776	0.749724
$635$	−2.82723	−0.112195
$636$	13.0209	0.516311
$637$	2.52236	0.0999396
$638$	−15.4422	−0.611361
$639$	2.58733	0.102353
$640$	−6.21664	−0.245734
$641$	9.30239	0.367422	0.183711	−	0.982980i	$-0.441189\pi$
$641$	9.30239	0.367422	0.183711	+	0.982980i	$0.441189\pi$
$642$	1.05703	0.0417177
$643$	−3.78773	−0.149374	−0.0746868	−	0.997207i	$-0.523796\pi$
$643$	−3.78773	−0.149374	−0.0746868	+	0.997207i	$0.523796\pi$
$644$	1.78483	0.0703322
$645$	−4.30582	−0.169541
$646$	2.23122	0.0877862
$647$	19.5637	0.769130	0.384565	−	0.923098i	$-0.374352\pi$
$647$	19.5637	0.769130	0.384565	+	0.923098i	$0.374352\pi$
$648$	25.5021	1.00182
$649$	−3.37072	−0.132312
$650$	−1.05962	−0.0415618
$651$	14.5504	0.570274
$652$	0.939460	0.0367921
$653$	45.6084	1.78479	0.892396	−	0.451252i	$-0.149023\pi$
$653$	45.6084	1.78479	0.892396	+	0.451252i	$0.149023\pi$
$654$	8.83828	0.345604
$655$	−53.6841	−2.09761
$656$	−3.32989	−0.130010
$657$	0.427553	0.0166804
$658$	−3.39689	−0.132425
$659$	11.7731	0.458615	0.229308	−	0.973354i	$-0.426354\pi$
$659$	11.7731	0.458615	0.229308	+	0.973354i	$0.426354\pi$
$660$	−10.1958	−0.396871
$661$	17.1478	0.666974	0.333487	−	0.942755i	$-0.391775\pi$
$661$	17.1478	0.666974	0.333487	+	0.942755i	$0.391775\pi$
$662$	12.1061	0.470516
$663$	0.799050	0.0310325
$664$	12.5829	0.488312
$665$	6.76640	0.262390
$666$	−0.0307217	−0.00119044
$667$	−7.85598	−0.304185
$668$	−11.2860	−0.436667
$669$	−24.8563	−0.960999
$670$	4.44037	0.171547
$671$	20.1784	0.778980
$672$	8.13445	0.313793
$673$	1.17439	0.0452693	0.0226346	−	0.999744i	$-0.492795\pi$
$673$	1.17439	0.0452693	0.0226346	+	0.999744i	$0.492795\pi$
$674$	8.21431	0.316403
$675$	10.3680	0.399063
$676$	8.80408	0.338618
$677$	43.2025	1.66041	0.830203	−	0.557461i	$-0.188225\pi$
$677$	43.2025	1.66041	0.830203	+	0.557461i	$0.188225\pi$
$678$	−36.7350	−1.41080
$679$	−24.6479	−0.945900
$680$	8.10538	0.310827
$681$	−31.6189	−1.21164
$682$	25.5469	0.978242
$683$	−29.6170	−1.13326	−0.566631	−	0.823971i	$-0.691754\pi$
$683$	−29.6170	−1.13326	−0.566631	+	0.823971i	$0.691754\pi$
$684$	0.298980	0.0114318
$685$	−33.1369	−1.26610
$686$	18.5104	0.706730
$687$	−29.6567	−1.13148
$688$	2.10592	0.0802875
$689$	−5.43341	−0.206996
$690$	9.86019	0.375371
$691$	3.53144	0.134342	0.0671711	−	0.997741i	$-0.478603\pi$
$691$	3.53144	0.134342	0.0671711	+	0.997741i	$0.478603\pi$
$692$	−12.8357	−0.487942
$693$	0.989070	0.0375716
$694$	25.1253	0.953743
$695$	52.2046	1.98023
$696$	−20.5339	−0.778336
$697$	1.55179	0.0587783
$698$	31.3136	1.18524
$699$	24.6176	0.931123
$700$	1.75519	0.0663401
$701$	−2.10150	−0.0793726	−0.0396863	−	0.999212i	$-0.512636\pi$
$701$	−2.10150	−0.0793726	−0.0396863	+	0.999212i	$0.512636\pi$
$702$	−2.94780	−0.111258
$703$	0.235064	0.00886561
$704$	28.7481	1.08349
$705$	9.87183	0.371795
$706$	−13.4470	−0.506086
$707$	3.89395	0.146447
$708$	−1.14899	−0.0431816
$709$	0.0598502	0.00224772	0.00112386	−	0.999999i	$-0.499642\pi$
$709$	0.0598502	0.00224772	0.00112386	+	0.999999i	$0.499642\pi$
$710$	35.0448	1.31521
$711$	−2.66481	−0.0999380
$712$	18.6592	0.699282
$713$	12.9966	0.486727
$714$	2.51605	0.0941609
$715$	4.25455	0.159111
$716$	11.0146	0.411635
$717$	43.0991	1.60956
$718$	−14.2664	−0.532417
$719$	22.8710	0.852944	0.426472	−	0.904501i	$-0.359756\pi$
$719$	22.8710	0.852944	0.426472	+	0.904501i	$0.359756\pi$
$720$	−1.25696	−0.0468440
$721$	10.7860	0.401693
$722$	−17.4026	−0.647657
$723$	−8.36087	−0.310944
$724$	−10.9848	−0.408247
$725$	−7.72553	−0.286919
$726$	−0.690219	−0.0256164
$727$	−9.90640	−0.367408	−0.183704	−	0.982982i	$-0.558809\pi$
$727$	−9.90640	−0.367408	−0.183704	+	0.982982i	$0.558809\pi$
$728$	−1.94671	−0.0721497
$729$	28.6945	1.06276
$730$	5.79111	0.214339
$731$	−0.981400	−0.0362984
$732$	6.87828	0.254229
$733$	18.4516	0.681526	0.340763	−	0.940149i	$-0.389315\pi$
$733$	18.4516	0.681526	0.340763	+	0.940149i	$0.389315\pi$
$734$	−35.4780	−1.30952
$735$	−23.0818	−0.851384
$736$	7.26582	0.267822
$737$	−4.96626	−0.182934
$738$	−0.395280	−0.0145505
$739$	7.14001	0.262649	0.131325	−	0.991339i	$-0.458077\pi$
$739$	7.14001	0.262649	0.131325	+	0.991339i	$0.458077\pi$
$740$	0.218900	0.00804692
$741$	1.55735	0.0572107
$742$	−17.1087	−0.628082
$743$	−0.966150	−0.0354446	−0.0177223	−	0.999843i	$-0.505641\pi$
$743$	−0.966150	−0.0354446	−0.0177223	+	0.999843i	$0.505641\pi$
$744$	33.9705	1.24542
$745$	−27.4239	−1.00473
$746$	6.90277	0.252728
$747$	0.909353	0.0332715
$748$	−2.32387	−0.0849691
$749$	0.730622	0.0266964
$750$	−15.4172	−0.562956
$751$	7.03929	0.256867	0.128434	−	0.991718i	$-0.459005\pi$
$751$	7.03929	0.256867	0.128434	+	0.991718i	$0.459005\pi$
$752$	−4.82819	−0.176066
$753$	−10.5685	−0.385138
$754$	2.19651	0.0799921
$755$	−5.02475	−0.182869
$756$	4.88283	0.177587
$757$	39.9230	1.45102	0.725512	−	0.688209i	$-0.241603\pi$
$757$	39.9230	1.45102	0.725512	+	0.688209i	$0.241603\pi$
$758$	−25.7571	−0.935542
$759$	−11.0280	−0.400290
$760$	15.7974	0.573032
$761$	5.01902	0.181939	0.0909696	−	0.995854i	$-0.471003\pi$
$761$	5.01902	0.181939	0.0909696	+	0.995854i	$0.471003\pi$
$762$	−2.04897	−0.0742262
$763$	6.10905	0.221162
$764$	0.0132925	0.000480905 0
$765$	0.585766	0.0211784
$766$	13.6705	0.493936
$767$	0.479455	0.0173121
$768$	23.9224	0.863226
$769$	−7.55632	−0.272488	−0.136244	−	0.990675i	$-0.543503\pi$
$769$	−7.55632	−0.272488	−0.136244	+	0.990675i	$0.543503\pi$
$770$	13.3967	0.482785
$771$	−8.78826	−0.316502
$772$	7.21023	0.259502
$773$	−24.6698	−0.887313	−0.443656	−	0.896197i	$-0.646319\pi$
$773$	−24.6698	−0.887313	−0.443656	+	0.896197i	$0.646319\pi$
$774$	0.249987	0.00898561
$775$	12.7808	0.459101
$776$	−57.5450	−2.06575
$777$	0.265072	0.00950940
$778$	6.02793	0.216112
$779$	3.02444	0.108362
$780$	1.45026	0.0519276
$781$	−39.1952	−1.40251
$782$	2.24738	0.0803661
$783$	−21.4919	−0.768058
$784$	11.2890	0.403179
$785$	6.90744	0.246537
$786$	−38.9063	−1.38774
$787$	6.70603	0.239044	0.119522	−	0.992832i	$-0.461864\pi$
$787$	6.70603	0.239044	0.119522	+	0.992832i	$0.461864\pi$
$788$	−1.23321	−0.0439315
$789$	−26.9635	−0.959926
$790$	−36.0942	−1.28417
$791$	−25.3913	−0.902812
$792$	2.30916	0.0820525
$793$	−2.87020	−0.101924
$794$	14.7503	0.523469
$795$	49.7204	1.76340
$796$	−4.74037	−0.168018
$797$	−13.1189	−0.464694	−0.232347	−	0.972633i	$-0.574641\pi$
$797$	−13.1189	−0.464694	−0.232347	+	0.972633i	$0.574641\pi$
$798$	4.90379	0.173592
$799$	2.25003	0.0796004
$800$	7.14517	0.252620
$801$	1.34848	0.0476461
$802$	38.0228	1.34263
$803$	−6.47697	−0.228567
$804$	−1.69286	−0.0597026
$805$	6.81540	0.240211
$806$	−3.63382	−0.127996
$807$	−39.3113	−1.38383
$808$	9.09114	0.319825
$809$	−14.7742	−0.519432	−0.259716	−	0.965685i	$-0.583629\pi$
$809$	−14.7742	−0.519432	−0.259716	+	0.965685i	$0.583629\pi$
$810$	24.9632	0.877116
$811$	−36.5080	−1.28197	−0.640985	−	0.767553i	$-0.721474\pi$
$811$	−36.5080	−1.28197	−0.640985	+	0.767553i	$0.721474\pi$
$812$	−3.63836	−0.127682
$813$	−7.70901	−0.270367
$814$	0.465401	0.0163123
$815$	3.58734	0.125659
$816$	3.57621	0.125192
$817$	−1.91275	−0.0669187
$818$	−31.5581	−1.10340
$819$	−0.140686	−0.00491597
$820$	2.81647	0.0983554
$821$	34.0806	1.18942	0.594710	−	0.803940i	$-0.297267\pi$
$821$	34.0806	1.18942	0.594710	+	0.803940i	$0.297267\pi$
$822$	−24.0152	−0.837627
$823$	−28.4223	−0.990737	−0.495369	−	0.868683i	$-0.664967\pi$
$823$	−28.4223	−0.990737	−0.495369	+	0.868683i	$0.664967\pi$
$824$	25.1820	0.877255
$825$	−10.8448	−0.377569
$826$	1.50971	0.0525295
$827$	9.51380	0.330827	0.165414	−	0.986224i	$-0.447104\pi$
$827$	9.51380	0.330827	0.165414	+	0.986224i	$0.447104\pi$
$828$	0.301145	0.0104655
$829$	4.31998	0.150039	0.0750195	−	0.997182i	$-0.476098\pi$
$829$	4.31998	0.150039	0.0750195	+	0.997182i	$0.476098\pi$
$830$	12.3170	0.427529
$831$	21.8517	0.758029
$832$	−4.08916	−0.141766
$833$	−5.26090	−0.182279
$834$	37.8341	1.31009
$835$	−43.0955	−1.49138
$836$	−4.52923	−0.156647
$837$	35.5554	1.22897
$838$	22.3034	0.770460
$839$	−19.0757	−0.658566	−0.329283	−	0.944231i	$-0.606807\pi$
$839$	−19.0757	−0.658566	−0.329283	+	0.944231i	$0.606807\pi$
$840$	17.8140	0.614643
$841$	−12.9856	−0.447781
$842$	16.2811	0.561084
$843$	25.4815	0.877629
$844$	2.58800	0.0890826
$845$	33.6185	1.15651
$846$	−0.573139	−0.0197049
$847$	−0.477081	−0.0163927
$848$	−24.3176	−0.835070
$849$	−24.2271	−0.831472
$850$	2.21006	0.0758044
$851$	0.236766	0.00811624
$852$	−13.3606	−0.457726
$853$	−11.5968	−0.397068	−0.198534	−	0.980094i	$-0.563618\pi$
$853$	−11.5968	−0.397068	−0.198534	+	0.980094i	$0.563618\pi$
$854$	−9.03770	−0.309264
$855$	1.14166	0.0390439
$856$	1.70577	0.0583021
$857$	−20.4622	−0.698977	−0.349488	−	0.936941i	$-0.613645\pi$
$857$	−20.4622	−0.698977	−0.349488	+	0.936941i	$0.613645\pi$
$858$	3.08338	0.105265
$859$	14.1897	0.484147	0.242073	−	0.970258i	$-0.422173\pi$
$859$	14.1897	0.484147	0.242073	+	0.970258i	$0.422173\pi$
$860$	−1.78122	−0.0607391
$861$	3.41054	0.116231
$862$	−3.51144	−0.119600
$863$	−12.5593	−0.427524	−0.213762	−	0.976886i	$-0.568572\pi$
$863$	−12.5593	−0.427524	−0.213762	+	0.976886i	$0.568572\pi$
$864$	19.8774	0.676243
$865$	−49.0134	−1.66651
$866$	19.7935	0.672611
$867$	−1.66658	−0.0566001
$868$	6.01917	0.204304
$869$	40.3689	1.36942
$870$	−20.0999	−0.681452
$871$	0.706405	0.0239356
$872$	14.2627	0.482995
$873$	−4.15871	−0.140751
$874$	4.38014	0.148161
$875$	−10.6564	−0.360252
$876$	−2.20782	−0.0745954
$877$	−31.4555	−1.06218	−0.531089	−	0.847316i	$-0.678217\pi$
$877$	−31.4555	−1.06218	−0.531089	+	0.847316i	$0.678217\pi$
$878$	−2.26102	−0.0763058
$879$	−1.74127	−0.0587316
$880$	19.0415	0.641890
$881$	30.8837	1.04050	0.520249	−	0.854015i	$-0.325839\pi$
$881$	30.8837	1.04050	0.520249	+	0.854015i	$0.325839\pi$
$882$	1.34008	0.0451229
$883$	−13.2891	−0.447215	−0.223607	−	0.974679i	$-0.571783\pi$
$883$	−13.2891	−0.447215	−0.223607	+	0.974679i	$0.571783\pi$
$884$	0.330549	0.0111176
$885$	−4.38742	−0.147482
$886$	−25.6662	−0.862274
$887$	14.9740	0.502779	0.251389	−	0.967886i	$-0.419113\pi$
$887$	14.9740	0.502779	0.251389	+	0.967886i	$0.419113\pi$
$888$	0.618858	0.0207675
$889$	−1.41625	−0.0474996
$890$	18.2648	0.612238
$891$	−27.9196	−0.935342
$892$	−10.2825	−0.344283
$893$	4.38531	0.146749
$894$	−19.8748	−0.664713
$895$	42.0594	1.40589
$896$	−3.11412	−0.104036
$897$	1.56863	0.0523749
$898$	−0.725470	−0.0242092
$899$	−26.4935	−0.883609
$900$	0.296144	0.00987148
$901$	11.3325	0.377540
$902$	5.98807	0.199381
$903$	−2.15693	−0.0717780
$904$	−59.2807	−1.97165
$905$	−41.9456	−1.39432
$906$	−3.64157	−0.120983
$907$	−15.7194	−0.521954	−0.260977	−	0.965345i	$-0.584045\pi$
$907$	−15.7194	−0.521954	−0.260977	+	0.965345i	$0.584045\pi$
$908$	−13.0800	−0.434077
$909$	0.657006	0.0217915
$910$	−1.90556	−0.0631688
$911$	5.22426	0.173088	0.0865438	−	0.996248i	$-0.472418\pi$
$911$	5.22426	0.173088	0.0865438	+	0.996248i	$0.472418\pi$
$912$	6.97003	0.230801
$913$	−13.7757	−0.455910
$914$	−2.14228	−0.0708602
$915$	26.2648	0.868287
$916$	−12.2683	−0.405357
$917$	−26.8922	−0.888057
$918$	6.14824	0.202922
$919$	−28.8184	−0.950632	−0.475316	−	0.879815i	$-0.657666\pi$
$919$	−28.8184	−0.950632	−0.475316	+	0.879815i	$0.657666\pi$
$920$	15.9118	0.524596
$921$	−10.6731	−0.351691
$922$	19.1339	0.630140
$923$	5.57516	0.183509
$924$	−5.10741	−0.168022
$925$	0.232835	0.00765556
$926$	6.26611	0.205917
$927$	1.81987	0.0597724
$928$	−14.8113	−0.486206
$929$	−52.3120	−1.71630	−0.858151	−	0.513397i	$-0.828387\pi$
$929$	−52.3120	−1.71630	−0.858151	+	0.513397i	$0.828387\pi$
$930$	33.2525	1.09039
$931$	−10.2535	−0.336045
$932$	10.1837	0.333580
$933$	12.9208	0.423008
$934$	9.91554	0.324446
$935$	−8.87372	−0.290202
$936$	−0.328457	−0.0107360
$937$	−43.7187	−1.42823	−0.714114	−	0.700030i	$-0.753170\pi$
$937$	−43.7187	−1.42823	−0.714114	+	0.700030i	$0.753170\pi$
$938$	2.22433	0.0726270
$939$	12.6752	0.413640
$940$	4.08376	0.133198
$941$	−35.3939	−1.15381	−0.576904	−	0.816812i	$-0.695739\pi$
$941$	−35.3939	−1.15381	−0.576904	+	0.816812i	$0.695739\pi$
$942$	5.00600	0.163104
$943$	3.04634	0.0992026
$944$	2.14583	0.0698409
$945$	18.6451	0.606527
$946$	−3.78704	−0.123127
$947$	−52.3395	−1.70081	−0.850403	−	0.526132i	$-0.823642\pi$
$947$	−52.3395	−1.70081	−0.850403	+	0.526132i	$0.823642\pi$
$948$	13.7607	0.446926
$949$	0.921290	0.0299063
$950$	4.30741	0.139751
$951$	−27.4816	−0.891153
$952$	4.06025	0.131594
$953$	56.7754	1.83914	0.919568	−	0.392931i	$-0.128539\pi$
$953$	56.7754	1.83914	0.919568	+	0.392931i	$0.128539\pi$
$954$	−2.88667	−0.0934593
$955$	0.0507574	0.00164247
$956$	17.8291	0.576635
$957$	22.4804	0.726689
$958$	−40.1786	−1.29811
$959$	−16.5994	−0.536022
$960$	37.4193	1.20770
$961$	12.8299	0.413867
$962$	−0.0661991	−0.00213434
$963$	0.123274	0.00397245
$964$	−3.45871	−0.111397
$965$	27.5324	0.886298
$966$	4.93930	0.158919
$967$	35.5715	1.14390	0.571951	−	0.820288i	$-0.306187\pi$
$967$	35.5715	1.14390	0.571951	+	0.820288i	$0.306187\pi$
$968$	−1.11383	−0.0358000
$969$	−3.24817	−0.104346
$970$	−56.3288	−1.80861
$971$	−21.2208	−0.681008	−0.340504	−	0.940243i	$-0.610598\pi$
$971$	−21.2208	−0.681008	−0.340504	+	0.940243i	$0.610598\pi$
$972$	1.59082	0.0510257
$973$	26.1510	0.838363
$974$	−21.4545	−0.687446
$975$	1.54258	0.0494021
$976$	−12.8458	−0.411184
$977$	−19.0594	−0.609764	−0.304882	−	0.952390i	$-0.598617\pi$
$977$	−19.0594	−0.609764	−0.304882	+	0.952390i	$0.598617\pi$
$978$	2.59984	0.0831337
$979$	−20.4280	−0.652881
$980$	−9.54842	−0.305013
$981$	1.03075	0.0329092
$982$	13.5942	0.433808
$983$	−46.7839	−1.49217	−0.746087	−	0.665849i	$-0.768070\pi$
$983$	−46.7839	−1.49217	−0.746087	+	0.665849i	$0.768070\pi$
$984$	7.96252	0.253836
$985$	−4.70904	−0.150043
$986$	−4.58126	−0.145897
$987$	4.94513	0.157405
$988$	0.644241	0.0204960
$989$	−1.92660	−0.0612623
$990$	2.26036	0.0718389
$991$	−37.3467	−1.18636	−0.593179	−	0.805071i	$-0.702127\pi$
$991$	−37.3467	−1.18636	−0.593179	+	0.805071i	$0.702127\pi$
$992$	24.5033	0.777980
$993$	−17.6238	−0.559274
$994$	17.5551	0.556814
$995$	−18.1011	−0.573845
$996$	−4.69577	−0.148791
$997$	−21.0567	−0.666872	−0.333436	−	0.942773i	$-0.608208\pi$
$997$	−21.0567	−0.666872	−0.333436	+	0.942773i	$0.608208\pi$
$998$	20.6083	0.652345
$999$	0.647731	0.0204933

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1003.2.a.i.1.11	✓	18
3.2	odd	2		9027.2.a.q.1.8		18

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1003.2.a.i.1.11	✓	18	1.1	even	1	trivial
9027.2.a.q.1.8		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)

\(f(q)\)	\(=\)	\(q+1.14480 q^{2} -1.66658 q^{3} -0.689428 q^{4} -2.63259 q^{5} -1.90791 q^{6} -1.31875 q^{7} -3.07886 q^{8} -0.222506 q^{9} +O(q^{10})\)	\(q+1.14480 q^{2} -1.66658 q^{3} -0.689428 q^{4} -2.63259 q^{5} -1.90791 q^{6} -1.31875 q^{7} -3.07886 q^{8} -0.222506 q^{9} -3.01379 q^{10} +3.37072 q^{11} +1.14899 q^{12} -0.479455 q^{13} -1.50971 q^{14} +4.38742 q^{15} -2.14583 q^{16} +1.00000 q^{17} -0.254725 q^{18} +1.94900 q^{19} +1.81498 q^{20} +2.19781 q^{21} +3.85881 q^{22} +1.96311 q^{23} +5.13118 q^{24} +1.93052 q^{25} -0.548881 q^{26} +5.37057 q^{27} +0.909183 q^{28} -4.00179 q^{29} +5.02273 q^{30} +6.62041 q^{31} +3.70117 q^{32} -5.61758 q^{33} +1.14480 q^{34} +3.47173 q^{35} +0.153402 q^{36} +0.120607 q^{37} +2.23122 q^{38} +0.799050 q^{39} +8.10538 q^{40} +1.55179 q^{41} +2.51605 q^{42} -0.981400 q^{43} -2.32387 q^{44} +0.585766 q^{45} +2.24738 q^{46} +2.25003 q^{47} +3.57621 q^{48} -5.26090 q^{49} +2.21006 q^{50} -1.66658 q^{51} +0.330549 q^{52} +11.3325 q^{53} +6.14824 q^{54} -8.87372 q^{55} +4.06025 q^{56} -3.24817 q^{57} -4.58126 q^{58} -1.00000 q^{59} -3.02481 q^{60} +5.98639 q^{61} +7.57906 q^{62} +0.293430 q^{63} +8.52878 q^{64} +1.26221 q^{65} -6.43102 q^{66} -1.47335 q^{67} -0.689428 q^{68} -3.27169 q^{69} +3.97444 q^{70} -11.6281 q^{71} +0.685065 q^{72} -1.92154 q^{73} +0.138072 q^{74} -3.21736 q^{75} -1.34370 q^{76} -4.44514 q^{77} +0.914754 q^{78} +11.9763 q^{79} +5.64909 q^{80} -8.28297 q^{81} +1.77649 q^{82} -4.08687 q^{83} -1.51523 q^{84} -2.63259 q^{85} -1.12351 q^{86} +6.66932 q^{87} -10.3780 q^{88} -6.06041 q^{89} +0.670586 q^{90} +0.632281 q^{91} -1.35343 q^{92} -11.0335 q^{93} +2.57584 q^{94} -5.13092 q^{95} -6.16830 q^{96} +18.6904 q^{97} -6.02269 q^{98} -0.750005 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 18 q + 5 q^{2} + q^{3} + 21 q^{4} + 21 q^{5} + 5 q^{6} - q^{7} + 9 q^{8} + 17 q^{9}+O(q^{10}) \) 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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