LMFDB - Embedded newform 889.2.a.d.1.10

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [889,2,Mod(1,889)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(889, 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("889.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 889 = 7 \cdot 127 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	889.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:	$7.09870073969$
Analytic rank:	$0$
Dimension:	$20$
Coefficient field:	$\mathbb{Q}[x]/(x^{20} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{20} - 8 x^{19} + 152 x^{17} - 274 x^{16} - 1061 x^{15} + 3125 x^{14} + 2977 x^{13} - 15474 x^{12} + \cdots + 31 $ x^20 - 8x^19 + 152x^17 - 274x^16 - 1061x^15 + 3125x^14 + 2977x^13 - 15474x^12 - 56x^11 + 39579x^10 - 17664x^9 - 52271x^8 + 35701x^7 + 32493x^6 - 25504x^5 - 8607x^4 + 6812x^3 + 609x^2 - 425x + 31
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 2 $
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.10
Root			$0.170762$ of defining polynomial
Character	$\chi$	$=$	889.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+0.170762 q^{2} -0.829007 q^{3} -1.97084 q^{4} +2.09248 q^{5} -0.141563 q^{6} +1.00000 q^{7} -0.678071 q^{8} -2.31275 q^{9} +O(q^{10})$	\(q+0.170762 q^{2} -0.829007 q^{3} -1.97084 q^{4} +2.09248 q^{5} -0.141563 q^{6} +1.00000 q^{7} -0.678071 q^{8} -2.31275 q^{9} +0.357317 q^{10} +0.105046 q^{11} +1.63384 q^{12} +0.808011 q^{13} +0.170762 q^{14} -1.73468 q^{15} +3.82589 q^{16} +2.11987 q^{17} -0.394931 q^{18} +0.0869343 q^{19} -4.12394 q^{20} -0.829007 q^{21} +0.0179379 q^{22} +5.49710 q^{23} +0.562125 q^{24} -0.621542 q^{25} +0.137978 q^{26} +4.40430 q^{27} -1.97084 q^{28} -6.62400 q^{29} -0.296218 q^{30} +5.84253 q^{31} +2.00946 q^{32} -0.0870840 q^{33} +0.361995 q^{34} +2.09248 q^{35} +4.55806 q^{36} +7.11832 q^{37} +0.0148451 q^{38} -0.669847 q^{39} -1.41885 q^{40} +12.0211 q^{41} -0.141563 q^{42} -7.06811 q^{43} -0.207029 q^{44} -4.83937 q^{45} +0.938699 q^{46} +2.31361 q^{47} -3.17169 q^{48} +1.00000 q^{49} -0.106136 q^{50} -1.75739 q^{51} -1.59246 q^{52} +6.77897 q^{53} +0.752090 q^{54} +0.219807 q^{55} -0.678071 q^{56} -0.0720691 q^{57} -1.13113 q^{58} +2.38189 q^{59} +3.41877 q^{60} +6.80820 q^{61} +0.997685 q^{62} -2.31275 q^{63} -7.30864 q^{64} +1.69074 q^{65} -0.0148707 q^{66} +10.7308 q^{67} -4.17793 q^{68} -4.55714 q^{69} +0.357317 q^{70} -9.05001 q^{71} +1.56821 q^{72} +11.3953 q^{73} +1.21554 q^{74} +0.515262 q^{75} -0.171334 q^{76} +0.105046 q^{77} -0.114385 q^{78} +10.2976 q^{79} +8.00559 q^{80} +3.28705 q^{81} +2.05275 q^{82} -0.600098 q^{83} +1.63384 q^{84} +4.43579 q^{85} -1.20697 q^{86} +5.49134 q^{87} -0.0712287 q^{88} -10.3716 q^{89} -0.826383 q^{90} +0.808011 q^{91} -10.8339 q^{92} -4.84350 q^{93} +0.395079 q^{94} +0.181908 q^{95} -1.66586 q^{96} -9.17979 q^{97} +0.170762 q^{98} -0.242945 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 20 q + 8 q^{2} + 24 q^{4} + 3 q^{5} + 6 q^{6} + 20 q^{7} + 24 q^{8} + 30 q^{9}+O(q^{10}) $ 20 * q + 8 * q^2 + 24 * q^4 + 3 * q^5 + 6 * q^6 + 20 * q^7 + 24 * q^8 + 30 * q^9	\( 20 q + 8 q^{2} + 24 q^{4} + 3 q^{5} + 6 q^{6} + 20 q^{7} + 24 q^{8} + 30 q^{9} - 8 q^{10} + 26 q^{11} - 4 q^{12} - 4 q^{13} + 8 q^{14} + 10 q^{15} + 24 q^{16} + 4 q^{17} + 5 q^{18} + q^{19} - 2 q^{20} + q^{22} + 31 q^{23} - 6 q^{24} + 27 q^{25} + 4 q^{26} - 18 q^{27} + 24 q^{28} + 16 q^{29} - 5 q^{30} + 6 q^{31} + 41 q^{32} - 18 q^{33} - 10 q^{34} + 3 q^{35} + 18 q^{36} + 2 q^{37} + 3 q^{38} + 43 q^{39} - 38 q^{40} + 25 q^{41} + 6 q^{42} + 13 q^{43} + 66 q^{44} - 2 q^{45} + 20 q^{46} + 19 q^{47} - 16 q^{48} + 20 q^{49} - 4 q^{50} + 4 q^{51} + 20 q^{52} + 24 q^{53} + 5 q^{54} - 3 q^{55} + 24 q^{56} - 4 q^{57} + 12 q^{58} + 23 q^{59} + 24 q^{60} - 27 q^{61} + 7 q^{62} + 30 q^{63} + 2 q^{64} + 26 q^{65} + 26 q^{66} + 9 q^{67} - 25 q^{68} - 3 q^{69} - 8 q^{70} + 63 q^{71} + 27 q^{72} - 21 q^{73} + 21 q^{74} - 52 q^{75} - 10 q^{76} + 26 q^{77} - 70 q^{78} + 18 q^{79} - 23 q^{80} + 40 q^{81} - 42 q^{82} - q^{83} - 4 q^{84} - 41 q^{85} - 12 q^{86} - 9 q^{87} + 57 q^{88} - 16 q^{89} + q^{90} - 4 q^{91} + 17 q^{92} - 41 q^{93} + 7 q^{94} + 75 q^{95} - 81 q^{96} - 32 q^{97} + 8 q^{98} + 15 q^{99}+O(q^{100}) \) 20 * q + 8 * q^2 + 24 * q^4 + 3 * q^5 + 6 * q^6 + 20 * q^7 + 24 * q^8 + 30 * q^9 - 8 * q^10 + 26 * q^11 - 4 * q^12 - 4 * q^13 + 8 * q^14 + 10 * q^15 + 24 * q^16 + 4 * q^17 + 5 * q^18 + q^19 - 2 * q^20 + q^22 + 31 * q^23 - 6 * q^24 + 27 * q^25 + 4 * q^26 - 18 * q^27 + 24 * q^28 + 16 * q^29 - 5 * q^30 + 6 * q^31 + 41 * q^32 - 18 * q^33 - 10 * q^34 + 3 * q^35 + 18 * q^36 + 2 * q^37 + 3 * q^38 + 43 * q^39 - 38 * q^40 + 25 * q^41 + 6 * q^42 + 13 * q^43 + 66 * q^44 - 2 * q^45 + 20 * q^46 + 19 * q^47 - 16 * q^48 + 20 * q^49 - 4 * q^50 + 4 * q^51 + 20 * q^52 + 24 * q^53 + 5 * q^54 - 3 * q^55 + 24 * q^56 - 4 * q^57 + 12 * q^58 + 23 * q^59 + 24 * q^60 - 27 * q^61 + 7 * q^62 + 30 * q^63 + 2 * q^64 + 26 * q^65 + 26 * q^66 + 9 * q^67 - 25 * q^68 - 3 * q^69 - 8 * q^70 + 63 * q^71 + 27 * q^72 - 21 * q^73 + 21 * q^74 - 52 * q^75 - 10 * q^76 + 26 * q^77 - 70 * q^78 + 18 * q^79 - 23 * q^80 + 40 * q^81 - 42 * q^82 - q^83 - 4 * q^84 - 41 * q^85 - 12 * q^86 - 9 * q^87 + 57 * q^88 - 16 * q^89 + q^90 - 4 * q^91 + 17 * q^92 - 41 * q^93 + 7 * q^94 + 75 * q^95 - 81 * q^96 - 32 * q^97 + 8 * q^98 + 15 * 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 $

$2$	0.170762	0.120747	0.0603737	−	0.998176i	$-0.480771\pi$
$2$	0.170762	0.120747	0.0603737	+	0.998176i	$0.480771\pi$
$3$	−0.829007	−0.478627	−0.239314	−	0.970942i	$-0.576922\pi$
$3$	−0.829007	−0.478627	−0.239314	+	0.970942i	$0.576922\pi$
$4$	−1.97084	−0.985420
$5$	2.09248	0.935784	0.467892	−	0.883786i	$-0.345014\pi$
$5$	2.09248	0.935784	0.467892	+	0.883786i	$0.345014\pi$
$6$	−0.141563	−0.0577930
$7$	1.00000	0.377964
$7$	1.00000	0.377964
$8$	−0.678071	−0.239734
$9$	−2.31275	−0.770916
$10$	0.357317	0.112993
$11$	0.105046	0.0316726	0.0158363	−	0.999875i	$-0.494959\pi$
$11$	0.105046	0.0316726	0.0158363	+	0.999875i	$0.494959\pi$
$12$	1.63384	0.471649
$13$	0.808011	0.224102	0.112051	−	0.993702i	$-0.464258\pi$
$13$	0.808011	0.224102	0.112051	+	0.993702i	$0.464258\pi$
$14$	0.170762	0.0456382
$15$	−1.73468	−0.447892
$16$	3.82589	0.956473
$17$	2.11987	0.514145	0.257072	−	0.966392i	$-0.417242\pi$
$17$	2.11987	0.514145	0.257072	+	0.966392i	$0.417242\pi$
$18$	−0.394931	−0.0930860
$19$	0.0869343	0.0199441	0.00997205	−	0.999950i	$-0.496826\pi$
$19$	0.0869343	0.0199441	0.00997205	+	0.999950i	$0.496826\pi$
$20$	−4.12394	−0.922140
$21$	−0.829007	−0.180904
$22$	0.0179379	0.00382438
$23$	5.49710	1.14623	0.573113	−	0.819477i	$-0.305736\pi$
$23$	5.49710	1.14623	0.573113	+	0.819477i	$0.305736\pi$
$24$	0.562125	0.114743
$25$	−0.621542	−0.124308
$26$	0.137978	0.0270597
$27$	4.40430	0.847609
$28$	−1.97084	−0.372454
$29$	−6.62400	−1.23005	−0.615023	−	0.788509i	$-0.710853\pi$
$29$	−6.62400	−1.23005	−0.615023	+	0.788509i	$0.710853\pi$
$30$	−0.296218	−0.0540817
$31$	5.84253	1.04935	0.524675	−	0.851303i	$-0.324187\pi$
$31$	5.84253	1.04935	0.524675	+	0.851303i	$0.324187\pi$
$32$	2.00946	0.355226
$33$	−0.0870840	−0.0151594
$34$	0.361995	0.0620816
$35$	2.09248	0.353693
$36$	4.55806	0.759676
$37$	7.11832	1.17024	0.585122	−	0.810945i	$-0.301046\pi$
$37$	7.11832	1.17024	0.585122	+	0.810945i	$0.301046\pi$
$38$	0.0148451	0.00240820
$39$	−0.669847	−0.107261
$40$	−1.41885	−0.224339
$41$	12.0211	1.87737	0.938687	−	0.344770i	$-0.112043\pi$
$41$	12.0211	1.87737	0.938687	+	0.344770i	$0.112043\pi$
$42$	−0.141563	−0.0218437
$43$	−7.06811	−1.07788	−0.538939	−	0.842345i	$-0.681175\pi$
$43$	−7.06811	−1.07788	−0.538939	+	0.842345i	$0.681175\pi$
$44$	−0.207029	−0.0312108
$45$	−4.83937	−0.721411
$46$	0.938699	0.138404
$47$	2.31361	0.337475	0.168738	−	0.985661i	$-0.446031\pi$
$47$	2.31361	0.337475	0.168738	+	0.985661i	$0.446031\pi$
$48$	−3.17169	−0.457794
$49$	1.00000	0.142857
$50$	−0.106136	−0.0150099
$51$	−1.75739	−0.246084
$52$	−1.59246	−0.220835
$53$	6.77897	0.931164	0.465582	−	0.885005i	$-0.345845\pi$
$53$	6.77897	0.931164	0.465582	+	0.885005i	$0.345845\pi$
$54$	0.752090	0.102346
$55$	0.219807	0.0296387
$56$	−0.678071	−0.0906110
$57$	−0.0720691	−0.00954579
$58$	−1.13113	−0.148525
$59$	2.38189	0.310096	0.155048	−	0.987907i	$-0.450447\pi$
$59$	2.38189	0.310096	0.155048	+	0.987907i	$0.450447\pi$
$60$	3.41877	0.441361
$61$	6.80820	0.871701	0.435851	−	0.900019i	$-0.356448\pi$
$61$	6.80820	0.871701	0.435851	+	0.900019i	$0.356448\pi$
$62$	0.997685	0.126706
$63$	−2.31275	−0.291379
$64$	−7.30864	−0.913580
$65$	1.69074	0.209711
$66$	−0.0148707	−0.00183045
$67$	10.7308	1.31097	0.655487	−	0.755206i	$-0.272463\pi$
$67$	10.7308	1.31097	0.655487	+	0.755206i	$0.272463\pi$
$68$	−4.17793	−0.506649
$69$	−4.55714	−0.548615
$70$	0.357317	0.0427075
$71$	−9.05001	−1.07404	−0.537019	−	0.843570i	$-0.680450\pi$
$71$	−9.05001	−1.07404	−0.537019	+	0.843570i	$0.680450\pi$
$72$	1.56821	0.184815
$73$	11.3953	1.33372	0.666862	−	0.745181i	$-0.267637\pi$
$73$	11.3953	1.33372	0.666862	+	0.745181i	$0.267637\pi$
$74$	1.21554	0.141304
$75$	0.515262	0.0594974
$76$	−0.171334	−0.0196533
$77$	0.105046	0.0119711
$78$	−0.114385	−0.0129515
$79$	10.2976	1.15858	0.579288	−	0.815123i	$-0.303331\pi$
$79$	10.2976	1.15858	0.579288	+	0.815123i	$0.303331\pi$
$80$	8.00559	0.895052
$81$	3.28705	0.365227
$82$	2.05275	0.226688
$83$	−0.600098	−0.0658693	−0.0329347	−	0.999458i	$-0.510485\pi$
$83$	−0.600098	−0.0658693	−0.0329347	+	0.999458i	$0.510485\pi$
$84$	1.63384	0.178267
$85$	4.43579	0.481129
$86$	−1.20697	−0.130151
$87$	5.49134	0.588734
$88$	−0.0712287	−0.00759301
$89$	−10.3716	−1.09939	−0.549694	−	0.835366i	$-0.685256\pi$
$89$	−10.3716	−1.09939	−0.549694	+	0.835366i	$0.685256\pi$
$90$	−0.826383	−0.0871084
$91$	0.808011	0.0847026
$92$	−10.8339	−1.12951
$93$	−4.84350	−0.502247
$94$	0.395079	0.0407493
$95$	0.181908	0.0186634
$96$	−1.66586	−0.170021
$97$	−9.17979	−0.932066	−0.466033	−	0.884767i	$-0.654317\pi$
$97$	−9.17979	−0.932066	−0.466033	+	0.884767i	$0.654317\pi$
$98$	0.170762	0.0172496
$99$	−0.242945	−0.0244169
$100$	1.22496	0.122496
$101$	−10.1137	−1.00635	−0.503175	−	0.864184i	$-0.667835\pi$
$101$	−10.1137	−1.00635	−0.503175	+	0.864184i	$0.667835\pi$
$102$	−0.300096	−0.0297140
$103$	12.6686	1.24827	0.624137	−	0.781315i	$-0.285451\pi$
$103$	12.6686	1.24827	0.624137	+	0.781315i	$0.285451\pi$
$104$	−0.547889	−0.0537249
$105$	−1.73468	−0.169287
$106$	1.15759	0.112436
$107$	14.6879	1.41993	0.709965	−	0.704237i	$-0.248711\pi$
$107$	14.6879	1.41993	0.709965	+	0.704237i	$0.248711\pi$
$108$	−8.68018	−0.835251
$109$	−8.63491	−0.827074	−0.413537	−	0.910487i	$-0.635707\pi$
$109$	−8.63491	−0.827074	−0.413537	+	0.910487i	$0.635707\pi$
$110$	0.0375347	0.00357880
$111$	−5.90114	−0.560111
$112$	3.82589	0.361513
$113$	5.56432	0.523447	0.261724	−	0.965143i	$-0.415709\pi$
$113$	5.56432	0.523447	0.261724	+	0.965143i	$0.415709\pi$
$114$	−0.0123067	−0.00115263
$115$	11.5026	1.07262
$116$	13.0548	1.21211
$117$	−1.86873	−0.172764
$118$	0.406738	0.0374433
$119$	2.11987	0.194329
$120$	1.17623	0.107375
$121$	−10.9890	−0.998997
$122$	1.16259	0.105256
$123$	−9.96554	−0.898563
$124$	−11.5147	−1.03405
$125$	−11.7629	−1.05211
$126$	−0.394931	−0.0351832
$127$	−1.00000	−0.0887357
$127$	−1.00000	−0.0887357
$128$	−5.26696	−0.465538
$129$	5.85951	0.515901
$130$	0.288716	0.0253220
$131$	−17.9667	−1.56976	−0.784878	−	0.619650i	$-0.787274\pi$
$131$	−17.9667	−1.56976	−0.784878	+	0.619650i	$0.787274\pi$
$132$	0.171629	0.0149384
$133$	0.0869343	0.00753816
$134$	1.83242	0.158297
$135$	9.21590	0.793179
$136$	−1.43742	−0.123258
$137$	−22.1414	−1.89167	−0.945833	−	0.324654i	$-0.894752\pi$
$137$	−22.1414	−1.89167	−0.945833	+	0.324654i	$0.894752\pi$
$138$	−0.778188	−0.0662437
$139$	−12.1606	−1.03145	−0.515724	−	0.856755i	$-0.672477\pi$
$139$	−12.1606	−1.03145	−0.515724	+	0.856755i	$0.672477\pi$
$140$	−4.12394	−0.348536
$141$	−1.91800	−0.161525
$142$	−1.54540	−0.129687
$143$	0.0848785	0.00709790
$144$	−8.84832	−0.737360
$145$	−13.8606	−1.15106
$146$	1.94590	0.161044
$147$	−0.829007	−0.0683753
$148$	−14.0291	−1.15318
$149$	10.4825	0.858758	0.429379	−	0.903124i	$-0.358732\pi$
$149$	10.4825	0.858758	0.429379	+	0.903124i	$0.358732\pi$
$150$	0.0879875	0.00718415
$151$	3.13454	0.255085	0.127543	−	0.991833i	$-0.459291\pi$
$151$	3.13454	0.255085	0.127543	+	0.991833i	$0.459291\pi$
$152$	−0.0589476	−0.00478128
$153$	−4.90273	−0.396363
$154$	0.0179379	0.00144548
$155$	12.2254	0.981965
$156$	1.32016	0.105697
$157$	−17.7502	−1.41662	−0.708311	−	0.705900i	$-0.750543\pi$
$157$	−17.7502	−1.41662	−0.708311	+	0.705900i	$0.750543\pi$
$158$	1.75845	0.139895
$159$	−5.61982	−0.445680
$160$	4.20475	0.332414
$161$	5.49710	0.433232
$162$	0.561304	0.0441002
$163$	5.49492	0.430395	0.215198	−	0.976571i	$-0.430960\pi$
$163$	5.49492	0.430395	0.215198	+	0.976571i	$0.430960\pi$
$164$	−23.6916	−1.85000
$165$	−0.182221	−0.0141859
$166$	−0.102474	−0.00795354
$167$	4.21229	0.325957	0.162978	−	0.986630i	$-0.447890\pi$
$167$	4.21229	0.325957	0.162978	+	0.986630i	$0.447890\pi$
$168$	0.562125	0.0433689
$169$	−12.3471	−0.949778
$170$	0.757466	0.0580950
$171$	−0.201057	−0.0153752
$172$	13.9301	1.06216
$173$	−7.19299	−0.546873	−0.273437	−	0.961890i	$-0.588160\pi$
$173$	−7.19299	−0.546873	−0.273437	+	0.961890i	$0.588160\pi$
$174$	0.937715	0.0710880
$175$	−0.621542	−0.0469841
$176$	0.401895	0.0302940
$177$	−1.97461	−0.148421
$178$	−1.77108	−0.132748
$179$	22.8086	1.70479	0.852397	−	0.522895i	$-0.175148\pi$
$179$	22.8086	1.70479	0.852397	+	0.522895i	$0.175148\pi$
$180$	9.53763	0.710893
$181$	−23.6385	−1.75704	−0.878518	−	0.477709i	$-0.841467\pi$
$181$	−23.6385	−1.75704	−0.878518	+	0.477709i	$0.841467\pi$
$182$	0.137978	0.0102276
$183$	−5.64405	−0.417220
$184$	−3.72742	−0.274789
$185$	14.8949	1.09510
$186$	−0.827088	−0.0606450
$187$	0.222685	0.0162843
$188$	−4.55977	−0.332555
$189$	4.40430	0.320366
$190$	0.0310631	0.00225355
$191$	13.0130	0.941584	0.470792	−	0.882244i	$-0.343968\pi$
$191$	13.0130	0.941584	0.470792	+	0.882244i	$0.343968\pi$
$192$	6.05891	0.437264
$193$	8.54166	0.614842	0.307421	−	0.951574i	$-0.400534\pi$
$193$	8.54166	0.614842	0.307421	+	0.951574i	$0.400534\pi$
$194$	−1.56756	−0.112544
$195$	−1.40164	−0.100373
$196$	−1.97084	−0.140774
$197$	−7.31749	−0.521349	−0.260675	−	0.965427i	$-0.583945\pi$
$197$	−7.31749	−0.521349	−0.260675	+	0.965427i	$0.583945\pi$
$198$	−0.0414859	−0.00294828
$199$	−12.4704	−0.884006	−0.442003	−	0.897014i	$-0.645732\pi$
$199$	−12.4704	−0.884006	−0.442003	+	0.897014i	$0.645732\pi$
$200$	0.421449	0.0298010
$201$	−8.89590	−0.627468
$202$	−1.72704	−0.121514
$203$	−6.62400	−0.464914
$204$	3.46353	0.242496
$205$	25.1538	1.75682
$206$	2.16332	0.150726
$207$	−12.7134	−0.883643
$208$	3.09136	0.214347
$209$	0.00913211	0.000631682 0
$210$	−0.296218	−0.0204410
$211$	10.2642	0.706618	0.353309	−	0.935507i	$-0.385056\pi$
$211$	10.2642	0.706618	0.353309	+	0.935507i	$0.385056\pi$
$212$	−13.3603	−0.917587
$213$	7.50252	0.514064
$214$	2.50814	0.171453
$215$	−14.7899	−1.00866
$216$	−2.98643	−0.203201
$217$	5.84253	0.396617
$218$	−1.47452	−0.0998670
$219$	−9.44682	−0.638357
$220$	−0.433204	−0.0292066
$221$	1.71288	0.115221
$222$	−1.00769	−0.0676319
$223$	−10.7802	−0.721894	−0.360947	−	0.932586i	$-0.617546\pi$
$223$	−10.7802	−0.721894	−0.360947	+	0.932586i	$0.617546\pi$
$224$	2.00946	0.134263
$225$	1.43747	0.0958313
$226$	0.950178	0.0632049
$227$	16.1799	1.07390	0.536950	−	0.843614i	$-0.319577\pi$
$227$	16.1799	1.07390	0.536950	+	0.843614i	$0.319577\pi$
$228$	0.142037	0.00940661
$229$	−6.51569	−0.430569	−0.215284	−	0.976551i	$-0.569068\pi$
$229$	−6.51569	−0.430569	−0.215284	+	0.976551i	$0.569068\pi$
$230$	1.96421	0.129516
$231$	−0.0870840	−0.00572971
$232$	4.49154	0.294884
$233$	−5.54516	−0.363276	−0.181638	−	0.983365i	$-0.558140\pi$
$233$	−5.54516	−0.363276	−0.181638	+	0.983365i	$0.558140\pi$
$234$	−0.319108	−0.0208608
$235$	4.84119	0.315804
$236$	−4.69433	−0.305575
$237$	−8.53682	−0.554526
$238$	0.361995	0.0234646
$239$	20.4566	1.32323	0.661614	−	0.749844i	$-0.269872\pi$
$239$	20.4566	1.32323	0.661614	+	0.749844i	$0.269872\pi$
$240$	−6.63669	−0.428396
$241$	29.9718	1.93065	0.965325	−	0.261051i	$-0.0840690\pi$
$241$	29.9718	1.93065	0.965325	+	0.261051i	$0.0840690\pi$
$242$	−1.87650	−0.120626
$243$	−15.9379	−1.02242
$244$	−13.4179	−0.858992
$245$	2.09248	0.133683
$246$	−1.70174	−0.108499
$247$	0.0702439	0.00446951
$248$	−3.96165	−0.251565
$249$	0.497485	0.0315268
$250$	−2.00867	−0.127039
$251$	31.1102	1.96366	0.981828	−	0.189772i	$-0.0607748\pi$
$251$	31.1102	1.96366	0.981828	+	0.189772i	$0.0607748\pi$
$252$	4.55806	0.287131
$253$	0.577450	0.0363040
$254$	−0.170762	−0.0107146
$255$	−3.67730	−0.230281
$256$	13.7179	0.857368
$257$	12.6641	0.789964	0.394982	−	0.918689i	$-0.370751\pi$
$257$	12.6641	0.789964	0.394982	+	0.918689i	$0.370751\pi$
$258$	1.00059	0.0622937
$259$	7.11832	0.442311
$260$	−3.33219	−0.206653
$261$	15.3196	0.948262
$262$	−3.06804	−0.189544
$263$	−10.2863	−0.634281	−0.317141	−	0.948379i	$-0.602723\pi$
$263$	−10.2863	−0.634281	−0.317141	+	0.948379i	$0.602723\pi$
$264$	0.0590491	0.00363422
$265$	14.1848	0.871368
$266$	0.0148451	0.000910212 0
$267$	8.59813	0.526197
$268$	−21.1487	−1.29186
$269$	−20.6179	−1.25709	−0.628546	−	0.777772i	$-0.716350\pi$
$269$	−20.6179	−1.25709	−0.628546	+	0.777772i	$0.716350\pi$
$270$	1.57373	0.0957742
$271$	−5.78251	−0.351262	−0.175631	−	0.984456i	$-0.556197\pi$
$271$	−5.78251	−0.351262	−0.175631	+	0.984456i	$0.556197\pi$
$272$	8.11041	0.491766
$273$	−0.669847	−0.0405410
$274$	−3.78092	−0.228414
$275$	−0.0652906	−0.00393717
$276$	8.98139	0.540616
$277$	0.736630	0.0442598	0.0221299	−	0.999755i	$-0.492955\pi$
$277$	0.736630	0.0442598	0.0221299	+	0.999755i	$0.492955\pi$
$278$	−2.07657	−0.124545
$279$	−13.5123	−0.808960
$280$	−1.41885	−0.0847923
$281$	4.26864	0.254646	0.127323	−	0.991861i	$-0.459362\pi$
$281$	4.26864	0.254646	0.127323	+	0.991861i	$0.459362\pi$
$282$	−0.327523	−0.0195037
$283$	−10.8656	−0.645892	−0.322946	−	0.946417i	$-0.604673\pi$
$283$	−10.8656	−0.645892	−0.322946	+	0.946417i	$0.604673\pi$
$284$	17.8361	1.05838
$285$	−0.150803	−0.00893279
$286$	0.0144941	0.000857052 0
$287$	12.0211	0.709581
$288$	−4.64737	−0.273849
$289$	−12.5061	−0.735655
$290$	−2.36687	−0.138987
$291$	7.61011	0.446112
$292$	−22.4584	−1.31428
$293$	17.1990	1.00478	0.502388	−	0.864642i	$-0.332455\pi$
$293$	17.1990	1.00478	0.502388	+	0.864642i	$0.332455\pi$
$294$	−0.141563	−0.00825614
$295$	4.98406	0.290183
$296$	−4.82672	−0.280548
$297$	0.462655	0.0268460
$298$	1.79001	0.103693
$299$	4.44172	0.256871
$300$	−1.01550	−0.0586299
$301$	−7.06811	−0.407399
$302$	0.535262	0.0308008
$303$	8.38433	0.481667
$304$	0.332601	0.0190760
$305$	14.2460	0.815724
$306$	−0.837203	−0.0478597
$307$	−12.2262	−0.697787	−0.348893	−	0.937162i	$-0.613442\pi$
$307$	−12.2262	−0.697787	−0.348893	+	0.937162i	$0.613442\pi$
$308$	−0.207029	−0.0117966
$309$	−10.5023	−0.597458
$310$	2.08763	0.118570
$311$	6.40128	0.362983	0.181492	−	0.983392i	$-0.441907\pi$
$311$	6.40128	0.362983	0.181492	+	0.983392i	$0.441907\pi$
$312$	0.454203	0.0257142
$313$	0.142894	0.00807683	0.00403842	−	0.999992i	$-0.498715\pi$
$313$	0.142894	0.00807683	0.00403842	+	0.999992i	$0.498715\pi$
$314$	−3.03107	−0.171053
$315$	−4.83937	−0.272668
$316$	−20.2950	−1.14168
$317$	−15.1694	−0.851997	−0.425999	−	0.904724i	$-0.640077\pi$
$317$	−15.1694	−0.851997	−0.425999	+	0.904724i	$0.640077\pi$
$318$	−0.959654	−0.0538147
$319$	−0.695826	−0.0389588
$320$	−15.2932	−0.854914
$321$	−12.1763	−0.679617
$322$	0.938699	0.0523117
$323$	0.184290	0.0102542
$324$	−6.47824	−0.359902
$325$	−0.502213	−0.0278577
$326$	0.938326	0.0519691
$327$	7.15840	0.395860
$328$	−8.15113	−0.450071
$329$	2.31361	0.127554
$330$	−0.0311165	−0.00171291
$331$	6.02629	0.331235	0.165617	−	0.986190i	$-0.447038\pi$
$331$	6.02629	0.331235	0.165617	+	0.986190i	$0.447038\pi$
$332$	1.18270	0.0649089
$333$	−16.4629	−0.902160
$334$	0.719301	0.0393584
$335$	22.4539	1.22679
$336$	−3.17169	−0.173030
$337$	−8.38437	−0.456726	−0.228363	−	0.973576i	$-0.573337\pi$
$337$	−8.38437	−0.456726	−0.228363	+	0.973576i	$0.573337\pi$
$338$	−2.10842	−0.114683
$339$	−4.61286	−0.250536
$340$	−8.74223	−0.474114
$341$	0.613736	0.0332356
$342$	−0.0343330	−0.00185652
$343$	1.00000	0.0539949
$344$	4.79268	0.258404
$345$	−9.53570	−0.513385
$346$	−1.22829	−0.0660335
$347$	14.7304	0.790772	0.395386	−	0.918515i	$-0.370611\pi$
$347$	14.7304	0.790772	0.395386	+	0.918515i	$0.370611\pi$
$348$	−10.8226	−0.580150
$349$	25.3999	1.35963	0.679813	−	0.733385i	$-0.262061\pi$
$349$	25.3999	1.35963	0.679813	+	0.733385i	$0.262061\pi$
$350$	−0.106136	−0.00567321
$351$	3.55873	0.189951
$352$	0.211086	0.0112509
$353$	−7.28959	−0.387986	−0.193993	−	0.981003i	$-0.562144\pi$
$353$	−7.28959	−0.387986	−0.193993	+	0.981003i	$0.562144\pi$
$354$	−0.337189	−0.0179214
$355$	−18.9369	−1.00507
$356$	20.4408	1.08336
$357$	−1.75739	−0.0930109
$358$	3.89485	0.205849
$359$	1.73147	0.0913834	0.0456917	−	0.998956i	$-0.485451\pi$
$359$	1.73147	0.0913834	0.0456917	+	0.998956i	$0.485451\pi$
$360$	3.28143	0.172947
$361$	−18.9924	−0.999602
$362$	−4.03657	−0.212157
$363$	9.10993	0.478147
$364$	−1.59246	−0.0834676
$365$	23.8445	1.24808
$366$	−0.963791	−0.0503782
$367$	11.3441	0.592156	0.296078	−	0.955164i	$-0.404321\pi$
$367$	11.3441	0.592156	0.296078	+	0.955164i	$0.404321\pi$
$368$	21.0313	1.09633
$369$	−27.8017	−1.44730
$370$	2.54349	0.132230
$371$	6.77897	0.351947
$372$	9.54576	0.494925
$373$	−21.2246	−1.09897	−0.549485	−	0.835504i	$-0.685176\pi$
$373$	−21.2246	−1.09897	−0.549485	+	0.835504i	$0.685176\pi$
$374$	0.0380262	0.00196629
$375$	9.75156	0.503568
$376$	−1.56879	−0.0809044
$377$	−5.35227	−0.275656
$378$	0.752090	0.0386833
$379$	−16.2256	−0.833455	−0.416728	−	0.909031i	$-0.636823\pi$
$379$	−16.2256	−0.833455	−0.416728	+	0.909031i	$0.636823\pi$
$380$	−0.358511	−0.0183913
$381$	0.829007	0.0424713
$382$	2.22212	0.113694
$383$	−35.8633	−1.83253	−0.916263	−	0.400576i	$-0.868810\pi$
$383$	−35.8633	−1.83253	−0.916263	+	0.400576i	$0.868810\pi$
$384$	4.36635	0.222819
$385$	0.219807	0.0112024
$386$	1.45860	0.0742405
$387$	16.3468	0.830953
$388$	18.0919	0.918477
$389$	33.5216	1.69961	0.849806	−	0.527096i	$-0.176719\pi$
$389$	33.5216	1.69961	0.849806	+	0.527096i	$0.176719\pi$
$390$	−0.239347	−0.0121198
$391$	11.6532	0.589326
$392$	−0.678071	−0.0342477
$393$	14.8945	0.751328
$394$	−1.24955	−0.0629515
$395$	21.5476	1.08418
$396$	0.478806	0.0240609
$397$	31.2291	1.56734	0.783672	−	0.621174i	$-0.213344\pi$
$397$	31.2291	1.56734	0.783672	+	0.621174i	$0.213344\pi$
$398$	−2.12948	−0.106741
$399$	−0.0720691	−0.00360797
$400$	−2.37795	−0.118898
$401$	15.4148	0.769779	0.384890	−	0.922963i	$-0.374240\pi$
$401$	15.4148	0.769779	0.384890	+	0.922963i	$0.374240\pi$
$402$	−1.51909	−0.0757651
$403$	4.72083	0.235161
$404$	19.9325	0.991678
$405$	6.87807	0.341774
$406$	−1.13113	−0.0561371
$407$	0.747752	0.0370647
$408$	1.19163	0.0589947
$409$	−35.5778	−1.75921	−0.879605	−	0.475704i	$-0.842193\pi$
$409$	−35.5778	−1.75921	−0.879605	+	0.475704i	$0.842193\pi$
$410$	4.29532	0.212131
$411$	18.3554	0.905403
$412$	−24.9678	−1.23007
$413$	2.38189	0.117205
$414$	−2.17097	−0.106698
$415$	−1.25569	−0.0616394
$416$	1.62367	0.0796068
$417$	10.0812	0.493679
$418$	0.00155942	7.62738e−5 0
$419$	−14.2947	−0.698342	−0.349171	−	0.937059i	$-0.613537\pi$
$419$	−14.2947	−0.698342	−0.349171	+	0.937059i	$0.613537\pi$
$420$	3.41877	0.166819
$421$	−16.8025	−0.818901	−0.409451	−	0.912332i	$-0.634280\pi$
$421$	−16.8025	−0.818901	−0.409451	+	0.912332i	$0.634280\pi$
$422$	1.75274	0.0853223
$423$	−5.35081	−0.260165
$424$	−4.59662	−0.223232
$425$	−1.31759	−0.0639125
$426$	1.28115	0.0620719
$427$	6.80820	0.329472
$428$	−28.9474	−1.39923
$429$	−0.0703648	−0.00339725
$430$	−2.52555	−0.121793
$431$	−9.43818	−0.454621	−0.227311	−	0.973822i	$-0.572993\pi$
$431$	−9.43818	−0.454621	−0.227311	+	0.973822i	$0.572993\pi$
$432$	16.8504	0.810715
$433$	−12.2811	−0.590192	−0.295096	−	0.955468i	$-0.595352\pi$
$433$	−12.2811	−0.590192	−0.295096	+	0.955468i	$0.595352\pi$
$434$	0.997685	0.0478904
$435$	11.4905	0.550928
$436$	17.0180	0.815016
$437$	0.477887	0.0228604
$438$	−1.61316	−0.0770799
$439$	−17.6112	−0.840537	−0.420268	−	0.907400i	$-0.638064\pi$
$439$	−17.6112	−0.840537	−0.420268	+	0.907400i	$0.638064\pi$
$440$	−0.149044	−0.00710541
$441$	−2.31275	−0.110131
$442$	0.292496	0.0139126
$443$	31.6272	1.50265	0.751326	−	0.659931i	$-0.229414\pi$
$443$	31.6272	1.50265	0.751326	+	0.659931i	$0.229414\pi$
$444$	11.6302	0.551945
$445$	−21.7024	−1.02879
$446$	−1.84085	−0.0871667
$447$	−8.69004	−0.411025
$448$	−7.30864	−0.345301
$449$	28.4968	1.34485	0.672424	−	0.740166i	$-0.265253\pi$
$449$	28.4968	1.34485	0.672424	+	0.740166i	$0.265253\pi$
$450$	0.245466	0.0115714
$451$	1.26277	0.0594614
$452$	−10.9664	−0.515816
$453$	−2.59855	−0.122091
$454$	2.76292	0.129670
$455$	1.69074	0.0792633
$456$	0.0488679	0.00228845
$457$	−3.02187	−0.141357	−0.0706786	−	0.997499i	$-0.522516\pi$
$457$	−3.02187	−0.141357	−0.0706786	+	0.997499i	$0.522516\pi$
$458$	−1.11264	−0.0519900
$459$	9.33657	0.435794
$460$	−22.6697	−1.05698
$461$	9.77331	0.455189	0.227594	−	0.973756i	$-0.426914\pi$
$461$	9.77331	0.455189	0.227594	+	0.973756i	$0.426914\pi$
$462$	−0.0148707	−0.000691847 0
$463$	13.4090	0.623170	0.311585	−	0.950218i	$-0.399140\pi$
$463$	13.4090	0.623170	0.311585	+	0.950218i	$0.399140\pi$
$464$	−25.3427	−1.17651
$465$	−10.1349	−0.469995
$466$	−0.946906	−0.0438646
$467$	2.76155	0.127789	0.0638946	−	0.997957i	$-0.479648\pi$
$467$	2.76155	0.127789	0.0638946	+	0.997957i	$0.479648\pi$
$468$	3.68296	0.170245
$469$	10.7308	0.495502
$470$	0.826693	0.0381325
$471$	14.7151	0.678034
$472$	−1.61509	−0.0743407
$473$	−0.742478	−0.0341392
$474$	−1.45777	−0.0669575
$475$	−0.0540333	−0.00247922
$476$	−4.17793	−0.191495
$477$	−15.6781	−0.717849
$478$	3.49322	0.159776
$479$	8.67556	0.396396	0.198198	−	0.980162i	$-0.436491\pi$
$479$	8.67556	0.396396	0.198198	+	0.980162i	$0.436491\pi$
$480$	−3.48576	−0.159103
$481$	5.75168	0.262254
$482$	5.11805	0.233121
$483$	−4.55714	−0.207357
$484$	21.6575	0.984432
$485$	−19.2085	−0.872213
$486$	−2.72159	−0.123454
$487$	6.71387	0.304235	0.152117	−	0.988362i	$-0.451391\pi$
$487$	6.71387	0.304235	0.152117	+	0.988362i	$0.451391\pi$
$488$	−4.61644	−0.208977
$489$	−4.55533	−0.205999
$490$	0.357317	0.0161419
$491$	−4.78940	−0.216143	−0.108071	−	0.994143i	$-0.534467\pi$
$491$	−4.78940	−0.216143	−0.108071	+	0.994143i	$0.534467\pi$
$492$	19.6405	0.885462
$493$	−14.0420	−0.632422
$494$	0.0119950	0.000539681 0
$495$	−0.508357	−0.0228490
$496$	22.3529	1.00367
$497$	−9.05001	−0.405948
$498$	0.0849518	0.00380678
$499$	25.3569	1.13513	0.567565	−	0.823329i	$-0.307886\pi$
$499$	25.3569	1.13513	0.567565	+	0.823329i	$0.307886\pi$
$500$	23.1829	1.03677
$501$	−3.49202	−0.156012
$502$	5.31245	0.237106
$503$	4.99236	0.222599	0.111299	−	0.993787i	$-0.464499\pi$
$503$	4.99236	0.222599	0.111299	+	0.993787i	$0.464499\pi$
$504$	1.56821	0.0698535
$505$	−21.1627	−0.941727
$506$	0.0986067	0.00438360
$507$	10.2358	0.454590
$508$	1.97084	0.0874419
$509$	−10.3690	−0.459597	−0.229798	−	0.973238i	$-0.573807\pi$
$509$	−10.3690	−0.459597	−0.229798	+	0.973238i	$0.573807\pi$
$510$	−0.627944	−0.0278058
$511$	11.3953	0.504100
$512$	12.8764	0.569063
$513$	0.382885	0.0169048
$514$	2.16255	0.0953861
$515$	26.5087	1.16811
$516$	−11.5482	−0.508380
$517$	0.243036	0.0106887
$518$	1.21554	0.0534079
$519$	5.96304	0.261748
$520$	−1.14644	−0.0502749
$521$	−2.16505	−0.0948526	−0.0474263	−	0.998875i	$-0.515102\pi$
$521$	−2.16505	−0.0948526	−0.0474263	+	0.998875i	$0.515102\pi$
$522$	2.61602	0.114500
$523$	9.70712	0.424463	0.212231	−	0.977219i	$-0.431927\pi$
$523$	9.70712	0.424463	0.212231	+	0.977219i	$0.431927\pi$
$524$	35.4095	1.54687
$525$	0.515262	0.0224879
$526$	−1.75652	−0.0765878
$527$	12.3854	0.539518
$528$	−0.333174	−0.0144995
$529$	7.21815	0.313832
$530$	2.42224	0.105215
$531$	−5.50872	−0.239058
$532$	−0.171334	−0.00742825
$533$	9.71315	0.420723
$534$	1.46824	0.0635369
$535$	30.7340	1.32875
$536$	−7.27623	−0.314285
$537$	−18.9085	−0.815961
$538$	−3.52076	−0.151791
$539$	0.105046	0.00452466
$540$	−18.1631	−0.781614
$541$	−42.9242	−1.84545	−0.922727	−	0.385453i	$-0.874045\pi$
$541$	−42.9242	−1.84545	−0.922727	+	0.385453i	$0.874045\pi$
$542$	−0.987435	−0.0424140
$543$	19.5965	0.840965
$544$	4.25980	0.182637
$545$	−18.0683	−0.773963
$546$	−0.114385	−0.00489521
$547$	27.2813	1.16646	0.583232	−	0.812306i	$-0.301788\pi$
$547$	27.2813	1.16646	0.583232	+	0.812306i	$0.301788\pi$
$548$	43.6371	1.86409
$549$	−15.7457	−0.672008
$550$	−0.0111492	−0.000475403 0
$551$	−0.575853	−0.0245322
$552$	3.09006	0.131522
$553$	10.2976	0.437900
$554$	0.125789	0.00534425
$555$	−12.3480	−0.524143
$556$	23.9666	1.01641
$557$	−26.2213	−1.11103	−0.555517	−	0.831505i	$-0.687480\pi$
$557$	−26.2213	−1.11103	−0.555517	+	0.831505i	$0.687480\pi$
$558$	−2.30739	−0.0976798
$559$	−5.71111	−0.241554
$560$	8.00559	0.338298
$561$	−0.184607	−0.00779412
$562$	0.728924	0.0307478
$563$	0.982962	0.0414269	0.0207134	−	0.999785i	$-0.493406\pi$
$563$	0.982962	0.0414269	0.0207134	+	0.999785i	$0.493406\pi$
$564$	3.78008	0.159170
$565$	11.6432	0.489834
$566$	−1.85543	−0.0779897
$567$	3.28705	0.138043
$568$	6.13655	0.257484
$569$	35.5211	1.48912	0.744560	−	0.667555i	$-0.232659\pi$
$569$	35.5211	1.48912	0.744560	+	0.667555i	$0.232659\pi$
$570$	−0.0257515	−0.00107861
$571$	−33.2896	−1.39313	−0.696563	−	0.717495i	$-0.745288\pi$
$571$	−33.2896	−1.39313	−0.696563	+	0.717495i	$0.745288\pi$
$572$	−0.167282	−0.00699441
$573$	−10.7878	−0.450668
$574$	2.05275	0.0856800
$575$	−3.41668	−0.142485
$576$	16.9030	0.704294
$577$	−2.58118	−0.107456	−0.0537280	−	0.998556i	$-0.517110\pi$
$577$	−2.58118	−0.107456	−0.0537280	+	0.998556i	$0.517110\pi$
$578$	−2.13558	−0.0888284
$579$	−7.08109	−0.294280
$580$	27.3170	1.13428
$581$	−0.600098	−0.0248963
$582$	1.29952	0.0538669
$583$	0.712105	0.0294924
$584$	−7.72685	−0.319739
$585$	−3.91027	−0.161670
$586$	2.93694	0.121324
$587$	13.9735	0.576748	0.288374	−	0.957518i	$-0.406885\pi$
$587$	13.9735	0.576748	0.288374	+	0.957518i	$0.406885\pi$
$588$	1.63384	0.0673784
$589$	0.507916	0.0209283
$590$	0.851090	0.0350388
$591$	6.06625	0.249532
$592$	27.2339	1.11931
$593$	22.4345	0.921273	0.460636	−	0.887589i	$-0.347621\pi$
$593$	22.4345	0.921273	0.460636	+	0.887589i	$0.347621\pi$
$594$	0.0790042	0.00324158
$595$	4.43579	0.181850
$596$	−20.6593	−0.846237
$597$	10.3381	0.423109
$598$	0.758479	0.0310165
$599$	−14.2568	−0.582518	−0.291259	−	0.956644i	$-0.594074\pi$
$599$	−14.2568	−0.582518	−0.291259	+	0.956644i	$0.594074\pi$
$600$	−0.349384	−0.0142635
$601$	23.0253	0.939222	0.469611	−	0.882873i	$-0.344394\pi$
$601$	23.0253	0.939222	0.469611	+	0.882873i	$0.344394\pi$
$602$	−1.20697	−0.0491924
$603$	−24.8176	−1.01065
$604$	−6.17767	−0.251366
$605$	−22.9942	−0.934845
$606$	1.43173	0.0581600
$607$	−36.8434	−1.49543	−0.747715	−	0.664020i	$-0.768849\pi$
$607$	−36.8434	−1.49543	−0.747715	+	0.664020i	$0.768849\pi$
$608$	0.174691	0.00708465
$609$	5.49134	0.222520
$610$	2.43268	0.0984965
$611$	1.86943	0.0756289
$612$	9.66250	0.390584
$613$	−45.1182	−1.82231	−0.911154	−	0.412066i	$-0.864807\pi$
$613$	−45.1182	−1.82231	−0.911154	+	0.412066i	$0.864807\pi$
$614$	−2.08778	−0.0842559
$615$	−20.8527	−0.840861
$616$	−0.0712287	−0.00286989
$617$	2.17969	0.0877511	0.0438755	−	0.999037i	$-0.486029\pi$
$617$	2.17969	0.0877511	0.0438755	+	0.999037i	$0.486029\pi$
$618$	−1.79341	−0.0721414
$619$	−4.55502	−0.183082	−0.0915408	−	0.995801i	$-0.529179\pi$
$619$	−4.55502	−0.183082	−0.0915408	+	0.995801i	$0.529179\pi$
$620$	−24.0942	−0.967648
$621$	24.2109	0.971550
$622$	1.09310	0.0438293
$623$	−10.3716	−0.415530
$624$	−2.56276	−0.102593
$625$	−21.5060	−0.860239
$626$	0.0244009	0.000975256 0
$627$	−0.00757058	−0.000302340 0
$628$	34.9829	1.39597
$629$	15.0899	0.601675
$630$	−0.826383	−0.0329239
$631$	4.01294	0.159753	0.0798763	−	0.996805i	$-0.474547\pi$
$631$	4.01294	0.159753	0.0798763	+	0.996805i	$0.474547\pi$
$632$	−6.98253	−0.277750
$633$	−8.50911	−0.338207
$634$	−2.59036	−0.102876
$635$	−2.09248	−0.0830374
$636$	11.0758	0.439182
$637$	0.808011	0.0320146
$638$	−0.118821	−0.00470417
$639$	20.9304	0.827994
$640$	−11.0210	−0.435643
$641$	15.3614	0.606739	0.303369	−	0.952873i	$-0.401888\pi$
$641$	15.3614	0.606739	0.303369	+	0.952873i	$0.401888\pi$
$642$	−2.07926	−0.0820619
$643$	−16.6240	−0.655585	−0.327792	−	0.944750i	$-0.606305\pi$
$643$	−16.6240	−0.655585	−0.327792	+	0.944750i	$0.606305\pi$
$644$	−10.8339	−0.426916
$645$	12.2609	0.482772
$646$	0.0314698	0.00123816
$647$	3.33572	0.131141	0.0655704	−	0.997848i	$-0.479113\pi$
$647$	3.33572	0.131141	0.0655704	+	0.997848i	$0.479113\pi$
$648$	−2.22885	−0.0875575
$649$	0.250209	0.00982156
$650$	−0.0857591	−0.00336375
$651$	−4.84350	−0.189832
$652$	−10.8296	−0.424120
$653$	−2.02411	−0.0792094	−0.0396047	−	0.999215i	$-0.512610\pi$
$653$	−2.02411	−0.0792094	−0.0396047	+	0.999215i	$0.512610\pi$
$654$	1.22239	0.0477991
$655$	−37.5949	−1.46895
$656$	45.9913	1.79566
$657$	−26.3546	−1.02819
$658$	0.395079	0.0154018
$659$	−7.73013	−0.301123	−0.150562	−	0.988601i	$-0.548108\pi$
$659$	−7.73013	−0.301123	−0.150562	+	0.988601i	$0.548108\pi$
$660$	0.359129	0.0139791
$661$	4.41299	0.171646	0.0858228	−	0.996310i	$-0.472648\pi$
$661$	4.41299	0.171646	0.0858228	+	0.996310i	$0.472648\pi$
$662$	1.02906	0.0399957
$663$	−1.41999	−0.0551479
$664$	0.406909	0.0157911
$665$	0.181908	0.00705409
$666$	−2.81124	−0.108933
$667$	−36.4128	−1.40991
$668$	−8.30175	−0.321205
$669$	8.93684	0.345518
$670$	3.83429	0.148132
$671$	0.715176	0.0276091
$672$	−1.66586	−0.0642618
$673$	−45.8987	−1.76927	−0.884633	−	0.466289i	$-0.845591\pi$
$673$	−45.8987	−1.76927	−0.884633	+	0.466289i	$0.845591\pi$
$674$	−1.43174	−0.0551484
$675$	−2.73746	−0.105365
$676$	24.3342	0.935931
$677$	14.7478	0.566804	0.283402	−	0.959001i	$-0.408537\pi$
$677$	14.7478	0.566804	0.283402	+	0.959001i	$0.408537\pi$
$678$	−0.787704	−0.0302516
$679$	−9.17979	−0.352288
$680$	−3.00778	−0.115343
$681$	−13.4133	−0.513997
$682$	0.104803	0.00401312
$683$	−0.702351	−0.0268747	−0.0134373	−	0.999910i	$-0.504277\pi$
$683$	−0.702351	−0.0268747	−0.0134373	+	0.999910i	$0.504277\pi$
$684$	0.396251	0.0151510
$685$	−46.3303	−1.77019
$686$	0.170762	0.00651974
$687$	5.40155	0.206082
$688$	−27.0418	−1.03096
$689$	5.47749	0.208676
$690$	−1.62834	−0.0619898
$691$	9.88041	0.375868	0.187934	−	0.982182i	$-0.439821\pi$
$691$	9.88041	0.375868	0.187934	+	0.982182i	$0.439821\pi$
$692$	14.1762	0.538900
$693$	−0.242945	−0.00922873
$694$	2.51541	0.0954835
$695$	−25.4457	−0.965212
$696$	−3.72352	−0.141140
$697$	25.4831	0.965243
$698$	4.33735	0.164171
$699$	4.59698	0.173874
$700$	1.22496	0.0462991
$701$	−8.29961	−0.313472	−0.156736	−	0.987641i	$-0.550097\pi$
$701$	−8.29961	−0.313472	−0.156736	+	0.987641i	$0.550097\pi$
$702$	0.607697	0.0229360
$703$	0.618826	0.0233395
$704$	−0.767745	−0.0289355
$705$	−4.01337	−0.151152
$706$	−1.24479	−0.0468482
$707$	−10.1137	−0.380365
$708$	3.89163	0.146257
$709$	40.1970	1.50963	0.754815	−	0.655938i	$-0.227727\pi$
$709$	40.1970	1.50963	0.754815	+	0.655938i	$0.227727\pi$
$710$	−3.23372	−0.121359
$711$	−23.8159	−0.893165
$712$	7.03268	0.263561
$713$	32.1170	1.20279
$714$	−0.300096	−0.0112308
$715$	0.177606	0.00664210
$716$	−44.9521	−1.67994
$717$	−16.9587	−0.633333
$718$	0.295670	0.0110343
$719$	15.5900	0.581408	0.290704	−	0.956813i	$-0.406111\pi$
$719$	15.5900	0.581408	0.290704	+	0.956813i	$0.406111\pi$
$720$	−18.5149	−0.690010
$721$	12.6686	0.471803
$722$	−3.24320	−0.120699
$723$	−24.8468	−0.924062
$724$	46.5877	1.73142
$725$	4.11709	0.152905
$726$	1.55563	0.0577350
$727$	−31.1166	−1.15405	−0.577025	−	0.816727i	$-0.695786\pi$
$727$	−31.1166	−1.15405	−0.577025	+	0.816727i	$0.695786\pi$
$728$	−0.547889	−0.0203061
$729$	3.35148	0.124129
$730$	4.07174	0.150702
$731$	−14.9835	−0.554185
$732$	11.1235	0.411137
$733$	1.46591	0.0541446	0.0270723	−	0.999633i	$-0.491382\pi$
$733$	1.46591	0.0541446	0.0270723	+	0.999633i	$0.491382\pi$
$734$	1.93714	0.0715012
$735$	−1.73468	−0.0639845
$736$	11.0462	0.407169
$737$	1.12723	0.0415220
$738$	−4.74749	−0.174757
$739$	−31.4380	−1.15647	−0.578234	−	0.815871i	$-0.696258\pi$
$739$	−31.4380	−1.15647	−0.578234	+	0.815871i	$0.696258\pi$
$740$	−29.3555	−1.07913
$741$	−0.0582326	−0.00213923
$742$	1.15759	0.0424966
$743$	−22.3714	−0.820728	−0.410364	−	0.911922i	$-0.634598\pi$
$743$	−22.3714	−0.820728	−0.410364	+	0.911922i	$0.634598\pi$
$744$	3.28423	0.120406
$745$	21.9343	0.803612
$746$	−3.62437	−0.132698
$747$	1.38788	0.0507797
$748$	−0.438876	−0.0160469
$749$	14.6879	0.536683
$750$	1.66520	0.0608045
$751$	41.1115	1.50018	0.750090	−	0.661335i	$-0.230010\pi$
$751$	41.1115	1.50018	0.750090	+	0.661335i	$0.230010\pi$
$752$	8.85164	0.322786
$753$	−25.7905	−0.939860
$754$	−0.913966	−0.0332847
$755$	6.55895	0.238705
$756$	−8.68018	−0.315695
$757$	−9.51476	−0.345820	−0.172910	−	0.984938i	$-0.555317\pi$
$757$	−9.51476	−0.345820	−0.172910	+	0.984938i	$0.555317\pi$
$758$	−2.77073	−0.100638
$759$	−0.478710	−0.0173761
$760$	−0.123346	−0.00447425
$761$	35.3516	1.28150	0.640748	−	0.767752i	$-0.278625\pi$
$761$	35.3516	1.28150	0.640748	+	0.767752i	$0.278625\pi$
$762$	0.141563	0.00512830
$763$	−8.63491	−0.312605
$764$	−25.6465	−0.927856
$765$	−10.2589	−0.370910
$766$	−6.12410	−0.221273
$767$	1.92460	0.0694932
$768$	−11.3722	−0.410360
$769$	7.40477	0.267023	0.133511	−	0.991047i	$-0.457375\pi$
$769$	7.40477	0.267023	0.133511	+	0.991047i	$0.457375\pi$
$770$	0.0375347	0.00135266
$771$	−10.4986	−0.378098
$772$	−16.8342	−0.605878
$773$	−38.4610	−1.38335	−0.691673	−	0.722210i	$-0.743126\pi$
$773$	−38.4610	−1.38335	−0.691673	+	0.722210i	$0.743126\pi$
$774$	2.79141	0.100335
$775$	−3.63138	−0.130443
$776$	6.22454	0.223448
$777$	−5.90114	−0.211702
$778$	5.72423	0.205224
$779$	1.04504	0.0374425
$780$	2.76241	0.0989100
$781$	−0.950669	−0.0340176
$782$	1.98992	0.0711595
$783$	−29.1741	−1.04260
$784$	3.82589	0.136639
$785$	−37.1419	−1.32565
$786$	2.54342	0.0907209
$787$	−0.555186	−0.0197902	−0.00989512	−	0.999951i	$-0.503150\pi$
$787$	−0.555186	−0.0197902	−0.00989512	+	0.999951i	$0.503150\pi$
$788$	14.4216	0.513748
$789$	8.52742	0.303584
$790$	3.67952	0.130911
$791$	5.56432	0.197845
$792$	0.164734	0.00585357
$793$	5.50110	0.195350
$794$	5.33276	0.189253
$795$	−11.7593	−0.417061
$796$	24.5772	0.871117
$797$	−42.6739	−1.51159	−0.755794	−	0.654809i	$-0.772749\pi$
$797$	−42.6739	−1.51159	−0.755794	+	0.654809i	$0.772749\pi$
$798$	−0.0123067	−0.000435652 0
$799$	4.90457	0.173511
$800$	−1.24896	−0.0441575
$801$	23.9869	0.847536
$802$	2.63227	0.0929488
$803$	1.19704	0.0422425
$804$	17.5324	0.618320
$805$	11.5026	0.405412
$806$	0.806141	0.0283951
$807$	17.0923	0.601679
$808$	6.85780	0.241257
$809$	37.6590	1.32402	0.662011	−	0.749494i	$-0.269703\pi$
$809$	37.6590	1.32402	0.662011	+	0.749494i	$0.269703\pi$
$810$	1.17452	0.0412683
$811$	−53.5990	−1.88211	−0.941057	−	0.338248i	$-0.890166\pi$
$811$	−53.5990	−1.88211	−0.941057	+	0.338248i	$0.890166\pi$
$812$	13.0548	0.458135
$813$	4.79374	0.168124
$814$	0.127688	0.00447546
$815$	11.4980	0.402757
$816$	−6.72358	−0.235372
$817$	−0.614461	−0.0214973
$818$	−6.07536	−0.212420
$819$	−1.86873	−0.0652986
$820$	−49.5741	−1.73120
$821$	12.7495	0.444962	0.222481	−	0.974937i	$-0.428585\pi$
$821$	12.7495	0.444962	0.222481	+	0.974937i	$0.428585\pi$
$822$	3.13441	0.109325
$823$	−54.0883	−1.88540	−0.942700	−	0.333642i	$-0.891722\pi$
$823$	−54.0883	−1.88540	−0.942700	+	0.333642i	$0.891722\pi$
$824$	−8.59020	−0.299254
$825$	0.0541263	0.00188444
$826$	0.406738	0.0141522
$827$	−42.6925	−1.48456	−0.742281	−	0.670089i	$-0.766256\pi$
$827$	−42.6925	−1.48456	−0.742281	+	0.670089i	$0.766256\pi$
$828$	25.0561	0.870760
$829$	−10.9337	−0.379744	−0.189872	−	0.981809i	$-0.560807\pi$
$829$	−10.9337	−0.379744	−0.189872	+	0.981809i	$0.560807\pi$
$830$	−0.214425	−0.00744280
$831$	−0.610671	−0.0211840
$832$	−5.90546	−0.204735
$833$	2.11987	0.0734493
$834$	1.72149	0.0596104
$835$	8.81412	0.305025
$836$	−0.0179979	−0.000622472 0
$837$	25.7323	0.889438
$838$	−2.44100	−0.0843230
$839$	−34.6305	−1.19558	−0.597788	−	0.801654i	$-0.703954\pi$
$839$	−34.6305	−1.19558	−0.597788	+	0.801654i	$0.703954\pi$
$840$	1.17623	0.0405839
$841$	14.8774	0.513014
$842$	−2.86923	−0.0988802
$843$	−3.53873	−0.121880
$844$	−20.2291	−0.696316
$845$	−25.8361	−0.888787
$846$	−0.913717	−0.0314142
$847$	−10.9890	−0.377585
$848$	25.9356	0.890633
$849$	9.00764	0.309141
$850$	−0.224995	−0.00771726
$851$	39.1301	1.34136
$852$	−14.7863	−0.506569
$853$	−31.8641	−1.09101	−0.545503	−	0.838109i	$-0.683661\pi$
$853$	−31.8641	−1.09101	−0.545503	+	0.838109i	$0.683661\pi$
$854$	1.16259	0.0397829
$855$	−0.420707	−0.0143879
$856$	−9.95941	−0.340406
$857$	−15.1325	−0.516918	−0.258459	−	0.966022i	$-0.583215\pi$
$857$	−15.1325	−0.516918	−0.258459	+	0.966022i	$0.583215\pi$
$858$	−0.0120157	−0.000410208 0
$859$	−5.42054	−0.184946	−0.0924731	−	0.995715i	$-0.529477\pi$
$859$	−5.42054	−0.184946	−0.0924731	+	0.995715i	$0.529477\pi$
$860$	29.1485	0.993954
$861$	−9.96554	−0.339625
$862$	−1.61169	−0.0548943
$863$	34.1292	1.16177	0.580886	−	0.813985i	$-0.302706\pi$
$863$	34.1292	1.16177	0.580886	+	0.813985i	$0.302706\pi$
$864$	8.85027	0.301092
$865$	−15.0512	−0.511755
$866$	−2.09715	−0.0712642
$867$	10.3677	0.352105
$868$	−11.5147	−0.390834
$869$	1.08173	0.0366951
$870$	1.96215	0.0665230
$871$	8.67060	0.293792
$872$	5.85508	0.198278
$873$	21.2305	0.718545
$874$	0.0816051	0.00276033
$875$	−11.7629	−0.397660
$876$	18.6182	0.629050
$877$	35.6664	1.20437	0.602184	−	0.798357i	$-0.294297\pi$
$877$	35.6664	1.20437	0.602184	+	0.798357i	$0.294297\pi$
$878$	−3.00733	−0.101493
$879$	−14.2581	−0.480913
$880$	0.840956	0.0283486
$881$	46.1962	1.55639	0.778195	−	0.628023i	$-0.216136\pi$
$881$	46.1962	1.55639	0.778195	+	0.628023i	$0.216136\pi$
$882$	−0.394931	−0.0132980
$883$	5.83935	0.196510	0.0982549	−	0.995161i	$-0.468674\pi$
$883$	5.83935	0.196510	0.0982549	+	0.995161i	$0.468674\pi$
$884$	−3.37582	−0.113541
$885$	−4.13182	−0.138890
$886$	5.40074	0.181441
$887$	−30.1007	−1.01068	−0.505341	−	0.862920i	$-0.668633\pi$
$887$	−30.1007	−1.01068	−0.505341	+	0.862920i	$0.668633\pi$
$888$	4.00139	0.134278
$889$	−1.00000	−0.0335389
$890$	−3.70595	−0.124224
$891$	0.345292	0.0115677
$892$	21.2460	0.711369
$893$	0.201132	0.00673064
$894$	−1.48393	−0.0496302
$895$	47.7264	1.59532
$896$	−5.26696	−0.175957
$897$	−3.68222	−0.122946
$898$	4.86619	0.162387
$899$	−38.7009	−1.29075
$900$	−2.83302	−0.0944341
$901$	14.3706	0.478753
$902$	0.215633	0.00717980
$903$	5.85951	0.194992
$904$	−3.77300	−0.125488
$905$	−49.4630	−1.64421
$906$	−0.443735	−0.0147421
$907$	25.6126	0.850454	0.425227	−	0.905087i	$-0.360194\pi$
$907$	25.6126	0.850454	0.425227	+	0.905087i	$0.360194\pi$
$908$	−31.8880	−1.05824
$909$	23.3904	0.775812
$910$	0.288716	0.00957083
$911$	25.1999	0.834908	0.417454	−	0.908698i	$-0.362922\pi$
$911$	25.1999	0.834908	0.417454	+	0.908698i	$0.362922\pi$
$912$	−0.275729	−0.00913028
$913$	−0.0630380	−0.00208625
$914$	−0.516023	−0.0170685
$915$	−11.8100	−0.390428
$916$	12.8414	0.424291
$917$	−17.9667	−0.593312
$918$	1.59434	0.0526209
$919$	36.1759	1.19333	0.596667	−	0.802489i	$-0.296492\pi$
$919$	36.1759	1.19333	0.596667	+	0.802489i	$0.296492\pi$
$920$	−7.79955	−0.257143
$921$	10.1356	0.333980
$922$	1.66892	0.0549628
$923$	−7.31251	−0.240694
$924$	0.171629	0.00564617
$925$	−4.42433	−0.145471
$926$	2.28976	0.0752461
$927$	−29.2993	−0.962314
$928$	−13.3107	−0.436944
$929$	−29.7844	−0.977195	−0.488597	−	0.872509i	$-0.662491\pi$
$929$	−29.7844	−0.977195	−0.488597	+	0.872509i	$0.662491\pi$
$930$	−1.73066	−0.0567506
$931$	0.0869343	0.00284916
$932$	10.9286	0.357979
$933$	−5.30671	−0.173734
$934$	0.471569	0.0154302
$935$	0.465962	0.0152386
$936$	1.26713	0.0414174
$937$	19.6196	0.640945	0.320472	−	0.947258i	$-0.396158\pi$
$937$	19.6196	0.640945	0.320472	+	0.947258i	$0.396158\pi$
$938$	1.83242	0.0598305
$939$	−0.118460	−0.00386579
$940$	−9.54120	−0.311200
$941$	−7.55777	−0.246376	−0.123188	−	0.992383i	$-0.539312\pi$
$941$	−7.55777	−0.246376	−0.123188	+	0.992383i	$0.539312\pi$
$942$	2.51278	0.0818708
$943$	66.0810	2.15189
$944$	9.11287	0.296599
$945$	9.21590	0.299793
$946$	−0.126787	−0.00412222
$947$	−45.6186	−1.48241	−0.741203	−	0.671281i	$-0.765744\pi$
$947$	−45.6186	−1.48241	−0.741203	+	0.671281i	$0.765744\pi$
$948$	16.8247	0.546441
$949$	9.20756	0.298890
$950$	−0.00922686	−0.000299359 0
$951$	12.5755	0.407789
$952$	−1.43742	−0.0465872
$953$	−0.279229	−0.00904511	−0.00452255	−	0.999990i	$-0.501440\pi$
$953$	−0.279229	−0.00904511	−0.00452255	+	0.999990i	$0.501440\pi$
$954$	−2.67722	−0.0866783
$955$	27.2293	0.881120
$956$	−40.3167	−1.30394
$957$	0.576844	0.0186467
$958$	1.48146	0.0478638
$959$	−22.1414	−0.714982
$960$	12.6781	0.409185
$961$	3.13518	0.101135
$962$	0.982172	0.0316665
$963$	−33.9693	−1.09465
$964$	−59.0695	−1.90250
$965$	17.8732	0.575359
$966$	−0.778188	−0.0250378
$967$	54.5935	1.75561	0.877804	−	0.479021i	$-0.159008\pi$
$967$	54.5935	1.75561	0.877804	+	0.479021i	$0.159008\pi$
$968$	7.45129	0.239494
$969$	−0.152777	−0.00490792
$970$	−3.28009	−0.105317
$971$	13.5864	0.436007	0.218004	−	0.975948i	$-0.430046\pi$
$971$	13.5864	0.436007	0.218004	+	0.975948i	$0.430046\pi$
$972$	31.4110	1.00751
$973$	−12.1606	−0.389850
$974$	1.14648	0.0367355
$975$	0.416338	0.0133335
$976$	26.0474	0.833758
$977$	−19.3476	−0.618984	−0.309492	−	0.950902i	$-0.600159\pi$
$977$	−19.3476	−0.618984	−0.309492	+	0.950902i	$0.600159\pi$
$978$	−0.777879	−0.0248738
$979$	−1.08950	−0.0348205
$980$	−4.12394	−0.131734
$981$	19.9704	0.637605
$982$	−0.817850	−0.0260986
$983$	−52.9492	−1.68882	−0.844409	−	0.535699i	$-0.820048\pi$
$983$	−52.9492	−1.68882	−0.844409	+	0.535699i	$0.820048\pi$
$984$	6.75734	0.215416
$985$	−15.3117	−0.487870
$986$	−2.39785	−0.0763633
$987$	−1.91800	−0.0610507
$988$	−0.138439	−0.00440435
$989$	−38.8542	−1.23549
$990$	−0.0868084	−0.00275895
$991$	39.0942	1.24187	0.620934	−	0.783863i	$-0.286754\pi$
$991$	39.0942	1.24187	0.620934	+	0.783863i	$0.286754\pi$
$992$	11.7403	0.372756
$993$	−4.99583	−0.158538
$994$	−1.54540	−0.0490172
$995$	−26.0941	−0.827239
$996$	−0.980464	−0.0310672
$997$	25.4016	0.804476	0.402238	−	0.915535i	$-0.368232\pi$
$997$	25.4016	0.804476	0.402238	+	0.915535i	$0.368232\pi$
$998$	4.33000	0.137064
$999$	31.3512	0.991909

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	889.2.a.d.1.10	✓	20
3.2	odd	2		8001.2.a.w.1.11		20
7.6	odd	2		6223.2.a.l.1.10		20

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
889.2.a.d.1.10	✓	20	1.1	even	1	trivial
6223.2.a.l.1.10		20	7.6	odd	2
8001.2.a.w.1.11		20	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:	\( N \)	\(=\)	\( 889 = 7 \cdot 127 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	889.a (trivial)

\(f(q)\)	\(=\)	\(q+0.170762 q^{2} -0.829007 q^{3} -1.97084 q^{4} +2.09248 q^{5} -0.141563 q^{6} +1.00000 q^{7} -0.678071 q^{8} -2.31275 q^{9} +O(q^{10})\)	\(q+0.170762 q^{2} -0.829007 q^{3} -1.97084 q^{4} +2.09248 q^{5} -0.141563 q^{6} +1.00000 q^{7} -0.678071 q^{8} -2.31275 q^{9} +0.357317 q^{10} +0.105046 q^{11} +1.63384 q^{12} +0.808011 q^{13} +0.170762 q^{14} -1.73468 q^{15} +3.82589 q^{16} +2.11987 q^{17} -0.394931 q^{18} +0.0869343 q^{19} -4.12394 q^{20} -0.829007 q^{21} +0.0179379 q^{22} +5.49710 q^{23} +0.562125 q^{24} -0.621542 q^{25} +0.137978 q^{26} +4.40430 q^{27} -1.97084 q^{28} -6.62400 q^{29} -0.296218 q^{30} +5.84253 q^{31} +2.00946 q^{32} -0.0870840 q^{33} +0.361995 q^{34} +2.09248 q^{35} +4.55806 q^{36} +7.11832 q^{37} +0.0148451 q^{38} -0.669847 q^{39} -1.41885 q^{40} +12.0211 q^{41} -0.141563 q^{42} -7.06811 q^{43} -0.207029 q^{44} -4.83937 q^{45} +0.938699 q^{46} +2.31361 q^{47} -3.17169 q^{48} +1.00000 q^{49} -0.106136 q^{50} -1.75739 q^{51} -1.59246 q^{52} +6.77897 q^{53} +0.752090 q^{54} +0.219807 q^{55} -0.678071 q^{56} -0.0720691 q^{57} -1.13113 q^{58} +2.38189 q^{59} +3.41877 q^{60} +6.80820 q^{61} +0.997685 q^{62} -2.31275 q^{63} -7.30864 q^{64} +1.69074 q^{65} -0.0148707 q^{66} +10.7308 q^{67} -4.17793 q^{68} -4.55714 q^{69} +0.357317 q^{70} -9.05001 q^{71} +1.56821 q^{72} +11.3953 q^{73} +1.21554 q^{74} +0.515262 q^{75} -0.171334 q^{76} +0.105046 q^{77} -0.114385 q^{78} +10.2976 q^{79} +8.00559 q^{80} +3.28705 q^{81} +2.05275 q^{82} -0.600098 q^{83} +1.63384 q^{84} +4.43579 q^{85} -1.20697 q^{86} +5.49134 q^{87} -0.0712287 q^{88} -10.3716 q^{89} -0.826383 q^{90} +0.808011 q^{91} -10.8339 q^{92} -4.84350 q^{93} +0.395079 q^{94} +0.181908 q^{95} -1.66586 q^{96} -9.17979 q^{97} +0.170762 q^{98} -0.242945 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 20 q + 8 q^{2} + 24 q^{4} + 3 q^{5} + 6 q^{6} + 20 q^{7} + 24 q^{8} + 30 q^{9}+O(q^{10}) \) 20 * q + 8 * q^2 + 24 * q^4 + 3 * q^5 + 6 * q^6 + 20 * q^7 + 24 * q^8 + 30 * q^9	\( 20 q + 8 q^{2} + 24 q^{4} + 3 q^{5} + 6 q^{6} + 20 q^{7} + 24 q^{8} + 30 q^{9} - 8 q^{10} + 26 q^{11} - 4 q^{12} - 4 q^{13} + 8 q^{14} + 10 q^{15} + 24 q^{16} + 4 q^{17} + 5 q^{18} + q^{19} - 2 q^{20} + q^{22} + 31 q^{23} - 6 q^{24} + 27 q^{25} + 4 q^{26} - 18 q^{27} + 24 q^{28} + 16 q^{29} - 5 q^{30} + 6 q^{31} + 41 q^{32} - 18 q^{33} - 10 q^{34} + 3 q^{35} + 18 q^{36} + 2 q^{37} + 3 q^{38} + 43 q^{39} - 38 q^{40} + 25 q^{41} + 6 q^{42} + 13 q^{43} + 66 q^{44} - 2 q^{45} + 20 q^{46} + 19 q^{47} - 16 q^{48} + 20 q^{49} - 4 q^{50} + 4 q^{51} + 20 q^{52} + 24 q^{53} + 5 q^{54} - 3 q^{55} + 24 q^{56} - 4 q^{57} + 12 q^{58} + 23 q^{59} + 24 q^{60} - 27 q^{61} + 7 q^{62} + 30 q^{63} + 2 q^{64} + 26 q^{65} + 26 q^{66} + 9 q^{67} - 25 q^{68} - 3 q^{69} - 8 q^{70} + 63 q^{71} + 27 q^{72} - 21 q^{73} + 21 q^{74} - 52 q^{75} - 10 q^{76} + 26 q^{77} - 70 q^{78} + 18 q^{79} - 23 q^{80} + 40 q^{81} - 42 q^{82} - q^{83} - 4 q^{84} - 41 q^{85} - 12 q^{86} - 9 q^{87} + 57 q^{88} - 16 q^{89} + q^{90} - 4 q^{91} + 17 q^{92} - 41 q^{93} + 7 q^{94} + 75 q^{95} - 81 q^{96} - 32 q^{97} + 8 q^{98} + 15 q^{99}+O(q^{100}) \) 20 * q + 8 * q^2 + 24 * q^4 + 3 * q^5 + 6 * q^6 + 20 * q^7 + 24 * q^8 + 30 * q^9 - 8 * q^10 + 26 * q^11 - 4 * q^12 - 4 * q^13 + 8 * q^14 + 10 * q^15 + 24 * q^16 + 4 * q^17 + 5 * q^18 + q^19 - 2 * q^20 + q^22 + 31 * q^23 - 6 * q^24 + 27 * q^25 + 4 * q^26 - 18 * q^27 + 24 * q^28 + 16 * q^29 - 5 * q^30 + 6 * q^31 + 41 * q^32 - 18 * q^33 - 10 * q^34 + 3 * q^35 + 18 * q^36 + 2 * q^37 + 3 * q^38 + 43 * q^39 - 38 * q^40 + 25 * q^41 + 6 * q^42 + 13 * q^43 + 66 * q^44 - 2 * q^45 + 20 * q^46 + 19 * q^47 - 16 * q^48 + 20 * q^49 - 4 * q^50 + 4 * q^51 + 20 * q^52 + 24 * q^53 + 5 * q^54 - 3 * q^55 + 24 * q^56 - 4 * q^57 + 12 * q^58 + 23 * q^59 + 24 * q^60 - 27 * q^61 + 7 * q^62 + 30 * q^63 + 2 * q^64 + 26 * q^65 + 26 * q^66 + 9 * q^67 - 25 * q^68 - 3 * q^69 - 8 * q^70 + 63 * q^71 + 27 * q^72 - 21 * q^73 + 21 * q^74 - 52 * q^75 - 10 * q^76 + 26 * q^77 - 70 * q^78 + 18 * q^79 - 23 * q^80 + 40 * q^81 - 42 * q^82 - q^83 - 4 * q^84 - 41 * q^85 - 12 * q^86 - 9 * q^87 + 57 * q^88 - 16 * q^89 + q^90 - 4 * q^91 + 17 * q^92 - 41 * q^93 + 7 * q^94 + 75 * q^95 - 81 * q^96 - 32 * q^97 + 8 * q^98 + 15 * q^99

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