LMFDB - Embedded newform 667.2.a.b.1.9

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [667,2,Mod(1,667)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(667, 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("667.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 667 = 23 \cdot 29 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	667.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:	$5.32602181482$
Analytic rank:	$1$
Dimension:	$12$
Coefficient field:	$\mathbb{Q}[x]/(x^{12} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{12} - 3 x^{11} - 13 x^{10} + 41 x^{9} + 54 x^{8} - 188 x^{7} - 77 x^{6} + 342 x^{5} + 13 x^{4} + \cdots - 5 $ x^12 - 3x^11 - 13x^10 + 41x^9 + 54x^8 - 188x^7 - 77x^6 + 342x^5 + 13x^4 - 215x^3 + 9x^2 + 37*x - 5
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 2^{2} $
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.9
Root			$-0.724122$ of defining polynomial
Character	$\chi$	$=$	667.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+0.724122 q^{2} +1.92599 q^{3} -1.47565 q^{4} -1.17886 q^{5} +1.39465 q^{6} -4.09140 q^{7} -2.51679 q^{8} +0.709431 q^{9} +O(q^{10})$	\(q+0.724122 q^{2} +1.92599 q^{3} -1.47565 q^{4} -1.17886 q^{5} +1.39465 q^{6} -4.09140 q^{7} -2.51679 q^{8} +0.709431 q^{9} -0.853636 q^{10} -3.08591 q^{11} -2.84208 q^{12} +2.42919 q^{13} -2.96267 q^{14} -2.27046 q^{15} +1.12883 q^{16} +0.237174 q^{17} +0.513714 q^{18} -2.02456 q^{19} +1.73958 q^{20} -7.87999 q^{21} -2.23457 q^{22} -1.00000 q^{23} -4.84731 q^{24} -3.61030 q^{25} +1.75903 q^{26} -4.41161 q^{27} +6.03746 q^{28} -1.00000 q^{29} -1.64409 q^{30} +0.00576952 q^{31} +5.85100 q^{32} -5.94343 q^{33} +0.171743 q^{34} +4.82317 q^{35} -1.04687 q^{36} +1.67676 q^{37} -1.46603 q^{38} +4.67860 q^{39} +2.96694 q^{40} -7.50127 q^{41} -5.70607 q^{42} +6.04004 q^{43} +4.55372 q^{44} -0.836317 q^{45} -0.724122 q^{46} +9.56040 q^{47} +2.17412 q^{48} +9.73954 q^{49} -2.61430 q^{50} +0.456794 q^{51} -3.58463 q^{52} -10.8627 q^{53} -3.19454 q^{54} +3.63784 q^{55} +10.2972 q^{56} -3.89928 q^{57} -0.724122 q^{58} +11.1467 q^{59} +3.35040 q^{60} -13.5738 q^{61} +0.00417784 q^{62} -2.90256 q^{63} +1.97917 q^{64} -2.86367 q^{65} -4.30376 q^{66} +0.167888 q^{67} -0.349985 q^{68} -1.92599 q^{69} +3.49256 q^{70} -6.07713 q^{71} -1.78549 q^{72} +14.9046 q^{73} +1.21418 q^{74} -6.95339 q^{75} +2.98754 q^{76} +12.6257 q^{77} +3.38787 q^{78} +5.39171 q^{79} -1.33073 q^{80} -10.6250 q^{81} -5.43183 q^{82} +4.61525 q^{83} +11.6281 q^{84} -0.279594 q^{85} +4.37373 q^{86} -1.92599 q^{87} +7.76659 q^{88} -2.09933 q^{89} -0.605595 q^{90} -9.93880 q^{91} +1.47565 q^{92} +0.0111120 q^{93} +6.92289 q^{94} +2.38667 q^{95} +11.2689 q^{96} -7.70879 q^{97} +7.05262 q^{98} -2.18924 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q - 3 q^{2} - 3 q^{3} + 11 q^{4} - 16 q^{5} - 2 q^{6} - 7 q^{7} - 9 q^{8} + 3 q^{9}+O(q^{10}) $ 12 * q - 3 * q^2 - 3 * q^3 + 11 * q^4 - 16 * q^5 - 2 * q^6 - 7 * q^7 - 9 * q^8 + 3 * q^9	\( 12 q - 3 q^{2} - 3 q^{3} + 11 q^{4} - 16 q^{5} - 2 q^{6} - 7 q^{7} - 9 q^{8} + 3 q^{9} - 6 q^{11} - 21 q^{12} - 15 q^{13} - 8 q^{14} + 6 q^{15} + 17 q^{16} - 18 q^{17} - 12 q^{18} - 6 q^{19} - 39 q^{20} - q^{21} - 5 q^{22} - 12 q^{23} + 4 q^{24} + 14 q^{25} - 3 q^{26} - 12 q^{27} - 19 q^{28} - 12 q^{29} - 11 q^{30} + 16 q^{31} - 21 q^{32} - 19 q^{33} - 7 q^{34} - 11 q^{35} - 13 q^{36} - q^{37} - 24 q^{38} + 6 q^{39} + 30 q^{40} + 3 q^{41} + 22 q^{42} - 23 q^{43} + 23 q^{44} - 22 q^{45} + 3 q^{46} - 35 q^{47} - 21 q^{48} + 3 q^{49} - 2 q^{50} - 34 q^{51} - 45 q^{53} + 55 q^{54} + 17 q^{55} - 17 q^{56} - 34 q^{57} + 3 q^{58} - 11 q^{59} + 93 q^{60} + 4 q^{61} - 7 q^{62} + q^{63} + 15 q^{64} + 5 q^{65} - 35 q^{66} - 19 q^{67} + q^{68} + 3 q^{69} + 14 q^{70} + 19 q^{71} + 4 q^{72} + 10 q^{73} - 15 q^{74} - 3 q^{75} - 4 q^{76} - 39 q^{77} + 16 q^{78} + 17 q^{79} - 90 q^{80} + 4 q^{81} - 3 q^{82} - 12 q^{83} + 42 q^{84} + 14 q^{85} + 17 q^{86} + 3 q^{87} - 2 q^{88} - 20 q^{89} + 65 q^{90} + 11 q^{91} - 11 q^{92} - 2 q^{93} + 13 q^{94} + 12 q^{95} + 14 q^{96} - 12 q^{97} + 75 q^{98} - 4 q^{99}+O(q^{100}) \) 12 * q - 3 * q^2 - 3 * q^3 + 11 * q^4 - 16 * q^5 - 2 * q^6 - 7 * q^7 - 9 * q^8 + 3 * q^9 - 6 * q^11 - 21 * q^12 - 15 * q^13 - 8 * q^14 + 6 * q^15 + 17 * q^16 - 18 * q^17 - 12 * q^18 - 6 * q^19 - 39 * q^20 - q^21 - 5 * q^22 - 12 * q^23 + 4 * q^24 + 14 * q^25 - 3 * q^26 - 12 * q^27 - 19 * q^28 - 12 * q^29 - 11 * q^30 + 16 * q^31 - 21 * q^32 - 19 * q^33 - 7 * q^34 - 11 * q^35 - 13 * q^36 - q^37 - 24 * q^38 + 6 * q^39 + 30 * q^40 + 3 * q^41 + 22 * q^42 - 23 * q^43 + 23 * q^44 - 22 * q^45 + 3 * q^46 - 35 * q^47 - 21 * q^48 + 3 * q^49 - 2 * q^50 - 34 * q^51 - 45 * q^53 + 55 * q^54 + 17 * q^55 - 17 * q^56 - 34 * q^57 + 3 * q^58 - 11 * q^59 + 93 * q^60 + 4 * q^61 - 7 * q^62 + q^63 + 15 * q^64 + 5 * q^65 - 35 * q^66 - 19 * q^67 + q^68 + 3 * q^69 + 14 * q^70 + 19 * q^71 + 4 * q^72 + 10 * q^73 - 15 * q^74 - 3 * q^75 - 4 * q^76 - 39 * q^77 + 16 * q^78 + 17 * q^79 - 90 * q^80 + 4 * q^81 - 3 * q^82 - 12 * q^83 + 42 * q^84 + 14 * q^85 + 17 * q^86 + 3 * q^87 - 2 * q^88 - 20 * q^89 + 65 * q^90 + 11 * q^91 - 11 * q^92 - 2 * q^93 + 13 * q^94 + 12 * q^95 + 14 * q^96 - 12 * q^97 + 75 * q^98 - 4 * 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 $

$2$	0.724122	0.512031	0.256016	−	0.966673i	$-0.417590\pi$
$2$	0.724122	0.512031	0.256016	+	0.966673i	$0.417590\pi$
$3$	1.92599	1.11197	0.555985	−	0.831192i	$-0.312341\pi$
$3$	1.92599	1.11197	0.555985	+	0.831192i	$0.312341\pi$
$4$	−1.47565	−0.737824
$5$	−1.17886	−0.527201	−0.263600	−	0.964632i	$-0.584910\pi$
$5$	−1.17886	−0.527201	−0.263600	+	0.964632i	$0.584910\pi$
$6$	1.39465	0.569364
$7$	−4.09140	−1.54640	−0.773202	−	0.634160i	$-0.781346\pi$
$7$	−4.09140	−1.54640	−0.773202	+	0.634160i	$0.781346\pi$
$8$	−2.51679	−0.889820
$9$	0.709431	0.236477
$10$	−0.853636	−0.269943
$11$	−3.08591	−0.930437	−0.465218	−	0.885196i	$-0.654024\pi$
$11$	−3.08591	−0.930437	−0.465218	+	0.885196i	$0.654024\pi$
$12$	−2.84208	−0.820438
$13$	2.42919	0.673737	0.336868	−	0.941552i	$-0.390632\pi$
$13$	2.42919	0.673737	0.336868	+	0.941552i	$0.390632\pi$
$14$	−2.96267	−0.791807
$15$	−2.27046	−0.586231
$16$	1.12883	0.282208
$17$	0.237174	0.0575230	0.0287615	−	0.999586i	$-0.490844\pi$
$17$	0.237174	0.0575230	0.0287615	+	0.999586i	$0.490844\pi$
$18$	0.513714	0.121084
$19$	−2.02456	−0.464466	−0.232233	−	0.972660i	$-0.574603\pi$
$19$	−2.02456	−0.464466	−0.232233	+	0.972660i	$0.574603\pi$
$20$	1.73958	0.388981
$21$	−7.87999	−1.71955
$22$	−2.23457	−0.476413
$23$	−1.00000	−0.208514
$23$	−1.00000	−0.208514
$24$	−4.84731	−0.989454
$25$	−3.61030	−0.722060
$26$	1.75903	0.344974
$27$	−4.41161	−0.849015
$28$	6.03746	1.14097
$29$	−1.00000	−0.185695
$29$	−1.00000	−0.185695
$30$	−1.64409	−0.300169
$31$	0.00576952	0.00103624	0.000518118	−	1.00000i	$-0.499835\pi$
$31$	0.00576952	0.00103624	0.000518118		1.00000i	$0.499835\pi$
$32$	5.85100	1.03432
$33$	−5.94343	−1.03462
$34$	0.171743	0.0294536
$35$	4.82317	0.815265
$36$	−1.04687	−0.174478
$37$	1.67676	0.275658	0.137829	−	0.990456i	$-0.455988\pi$
$37$	1.67676	0.275658	0.137829	+	0.990456i	$0.455988\pi$
$38$	−1.46603	−0.237821
$39$	4.67860	0.749175
$40$	2.96694	0.469114
$41$	−7.50127	−1.17150	−0.585751	−	0.810491i	$-0.699200\pi$
$41$	−7.50127	−1.17150	−0.585751	+	0.810491i	$0.699200\pi$
$42$	−5.70607	−0.880466
$43$	6.04004	0.921098	0.460549	−	0.887634i	$-0.347653\pi$
$43$	6.04004	0.921098	0.460549	+	0.887634i	$0.347653\pi$
$44$	4.55372	0.686498
$45$	−0.836317	−0.124671
$46$	−0.724122	−0.106766
$47$	9.56040	1.39453	0.697264	−	0.716815i	$-0.254401\pi$
$47$	9.56040	1.39453	0.697264	+	0.716815i	$0.254401\pi$
$48$	2.17412	0.313806
$49$	9.73954	1.39136
$50$	−2.61430	−0.369717
$51$	0.456794	0.0639639
$52$	−3.58463	−0.497099
$53$	−10.8627	−1.49210	−0.746051	−	0.665889i	$-0.768052\pi$
$53$	−10.8627	−1.49210	−0.746051	+	0.665889i	$0.768052\pi$
$54$	−3.19454	−0.434722
$55$	3.63784	0.490527
$56$	10.2972	1.37602
$57$	−3.89928	−0.516472
$58$	−0.724122	−0.0950819
$59$	11.1467	1.45117	0.725587	−	0.688130i	$-0.241568\pi$
$59$	11.1467	1.45117	0.725587	+	0.688130i	$0.241568\pi$
$60$	3.35040	0.432535
$61$	−13.5738	−1.73795	−0.868976	−	0.494854i	$-0.835221\pi$
$61$	−13.5738	−1.73795	−0.868976	+	0.494854i	$0.835221\pi$
$62$	0.00417784	0.000530586 0
$63$	−2.90256	−0.365689
$64$	1.97917	0.247397
$65$	−2.86367	−0.355194
$66$	−4.30376	−0.529757
$67$	0.167888	0.0205108	0.0102554	−	0.999947i	$-0.496736\pi$
$67$	0.167888	0.0205108	0.0102554	+	0.999947i	$0.496736\pi$
$68$	−0.349985	−0.0424419
$69$	−1.92599	−0.231862
$70$	3.49256	0.417441
$71$	−6.07713	−0.721222	−0.360611	−	0.932716i	$-0.617432\pi$
$71$	−6.07713	−0.721222	−0.360611	+	0.932716i	$0.617432\pi$
$72$	−1.78549	−0.210422
$73$	14.9046	1.74445	0.872227	−	0.489101i	$-0.162675\pi$
$73$	14.9046	1.74445	0.872227	+	0.489101i	$0.162675\pi$
$74$	1.21418	0.141145
$75$	−6.95339	−0.802908
$76$	2.98754	0.342694
$77$	12.6257	1.43883
$78$	3.38787	0.383601
$79$	5.39171	0.606615	0.303307	−	0.952893i	$-0.401909\pi$
$79$	5.39171	0.606615	0.303307	+	0.952893i	$0.401909\pi$
$80$	−1.33073	−0.148780
$81$	−10.6250	−1.18056
$82$	−5.43183	−0.599846
$83$	4.61525	0.506590	0.253295	−	0.967389i	$-0.418486\pi$
$83$	4.61525	0.506590	0.253295	+	0.967389i	$0.418486\pi$
$84$	11.6281	1.26873
$85$	−0.279594	−0.0303262
$86$	4.37373	0.471631
$87$	−1.92599	−0.206488
$88$	7.76659	0.827922
$89$	−2.09933	−0.222529	−0.111264	−	0.993791i	$-0.535490\pi$
$89$	−2.09933	−0.222529	−0.111264	+	0.993791i	$0.535490\pi$
$90$	−0.605595	−0.0638354
$91$	−9.93880	−1.04187
$92$	1.47565	0.153847
$93$	0.0111120	0.00115226
$94$	6.92289	0.714042
$95$	2.38667	0.244867
$96$	11.2689	1.15013
$97$	−7.70879	−0.782709	−0.391355	−	0.920240i	$-0.627993\pi$
$97$	−7.70879	−0.782709	−0.391355	+	0.920240i	$0.627993\pi$
$98$	7.05262	0.712422
$99$	−2.18924	−0.220027
$100$	5.32753	0.532753
$101$	−6.99073	−0.695603	−0.347802	−	0.937568i	$-0.613072\pi$
$101$	−6.99073	−0.695603	−0.347802	+	0.937568i	$0.613072\pi$
$102$	0.330774	0.0327515
$103$	−16.6495	−1.64052	−0.820262	−	0.571988i	$-0.806172\pi$
$103$	−16.6495	−1.64052	−0.820262	+	0.571988i	$0.806172\pi$
$104$	−6.11377	−0.599505
$105$	9.28937	0.906550
$106$	−7.86589	−0.764003
$107$	−4.79679	−0.463723	−0.231862	−	0.972749i	$-0.574482\pi$
$107$	−4.79679	−0.463723	−0.231862	+	0.972749i	$0.574482\pi$
$108$	6.50998	0.626423
$109$	−6.13707	−0.587825	−0.293912	−	0.955832i	$-0.594957\pi$
$109$	−6.13707	−0.587825	−0.293912	+	0.955832i	$0.594957\pi$
$110$	2.63424	0.251165
$111$	3.22942	0.306523
$112$	−4.61850	−0.436407
$113$	2.49867	0.235055	0.117527	−	0.993070i	$-0.462503\pi$
$113$	2.49867	0.235055	0.117527	+	0.993070i	$0.462503\pi$
$114$	−2.82355	−0.264450
$115$	1.17886	0.109929
$116$	1.47565	0.137010
$117$	1.72334	0.159323
$118$	8.07155	0.743047
$119$	−0.970372	−0.0889538
$120$	5.71428	0.521640
$121$	−1.47716	−0.134287
$122$	−9.82911	−0.889886
$123$	−14.4474	−1.30267
$124$	−0.00851378	−0.000764560 0
$125$	10.1503	0.907871
$126$	−2.10181	−0.187244
$127$	−10.8385	−0.961760	−0.480880	−	0.876786i	$-0.659683\pi$
$127$	−10.8385	−0.961760	−0.480880	+	0.876786i	$0.659683\pi$
$128$	−10.2688	−0.907645
$129$	11.6331	1.02423
$130$	−2.07365	−0.181871
$131$	7.42926	0.649097	0.324549	−	0.945869i	$-0.394788\pi$
$131$	7.42926	0.649097	0.324549	+	0.945869i	$0.394788\pi$
$132$	8.77040	0.763366
$133$	8.28329	0.718252
$134$	0.121571	0.0105022
$135$	5.20065	0.447601
$136$	−0.596917	−0.0511852
$137$	−7.37902	−0.630433	−0.315216	−	0.949020i	$-0.602077\pi$
$137$	−7.37902	−0.630433	−0.315216	+	0.949020i	$0.602077\pi$
$138$	−1.39465	−0.118721
$139$	12.8095	1.08649	0.543245	−	0.839574i	$-0.317195\pi$
$139$	12.8095	1.08649	0.543245	+	0.839574i	$0.317195\pi$
$140$	−7.11730	−0.601522
$141$	18.4132	1.55067
$142$	−4.40058	−0.369288
$143$	−7.49627	−0.626870
$144$	0.800827	0.0667356
$145$	1.17886	0.0978987
$146$	10.7928	0.893215
$147$	18.7582	1.54715
$148$	−2.47431	−0.203387
$149$	−9.58288	−0.785060	−0.392530	−	0.919739i	$-0.628400\pi$
$149$	−9.58288	−0.785060	−0.392530	+	0.919739i	$0.628400\pi$
$150$	−5.03510	−0.411114
$151$	−12.3299	−1.00339	−0.501695	−	0.865045i	$-0.667290\pi$
$151$	−12.3299	−1.00339	−0.501695	+	0.865045i	$0.667290\pi$
$152$	5.09540	0.413292
$153$	0.168258	0.0136029
$154$	9.14254	0.736727
$155$	−0.00680144	−0.000546305 0
$156$	−6.90396	−0.552759
$157$	−2.50048	−0.199560	−0.0997800	−	0.995010i	$-0.531814\pi$
$157$	−2.50048	−0.199560	−0.0997800	+	0.995010i	$0.531814\pi$
$158$	3.90426	0.310606
$159$	−20.9214	−1.65917
$160$	−6.89748	−0.545294
$161$	4.09140	0.322447
$162$	−7.69379	−0.604482
$163$	−2.50468	−0.196182	−0.0980909	−	0.995177i	$-0.531274\pi$
$163$	−2.50468	−0.196182	−0.0980909	+	0.995177i	$0.531274\pi$
$164$	11.0692	0.864362
$165$	7.00645	0.545451
$166$	3.34200	0.259390
$167$	12.7653	0.987809	0.493905	−	0.869516i	$-0.335569\pi$
$167$	12.7653	0.987809	0.493905	+	0.869516i	$0.335569\pi$
$168$	19.8323	1.53009
$169$	−7.09902	−0.546079
$170$	−0.202460	−0.0155280
$171$	−1.43629	−0.109836
$172$	−8.91298	−0.679608
$173$	−18.4750	−1.40462	−0.702312	−	0.711869i	$-0.747849\pi$
$173$	−18.4750	−1.40462	−0.702312	+	0.711869i	$0.747849\pi$
$174$	−1.39465	−0.105728
$175$	14.7712	1.11660
$176$	−3.48347	−0.262576
$177$	21.4684	1.61366
$178$	−1.52017	−0.113942
$179$	7.18991	0.537399	0.268700	−	0.963224i	$-0.413406\pi$
$179$	7.18991	0.537399	0.268700	+	0.963224i	$0.413406\pi$
$180$	1.23411	0.0919851
$181$	13.9824	1.03930	0.519651	−	0.854379i	$-0.326062\pi$
$181$	13.9824	1.03930	0.519651	+	0.854379i	$0.326062\pi$
$182$	−7.19690	−0.533470
$183$	−26.1431	−1.93255
$184$	2.51679	0.185540
$185$	−1.97666	−0.145327
$186$	0.00804646	0.000589995 0
$187$	−0.731896	−0.0535216
$188$	−14.1078	−1.02892
$189$	18.0497	1.31292
$190$	1.72824	0.125380
$191$	−12.2623	−0.887270	−0.443635	−	0.896208i	$-0.646311\pi$
$191$	−12.2623	−0.887270	−0.443635	+	0.896208i	$0.646311\pi$
$192$	3.81186	0.275097
$193$	−0.989143	−0.0712001	−0.0356001	−	0.999366i	$-0.511334\pi$
$193$	−0.989143	−0.0712001	−0.0356001	+	0.999366i	$0.511334\pi$
$194$	−5.58210	−0.400772
$195$	−5.51539	−0.394966
$196$	−14.3721	−1.02658
$197$	−20.0897	−1.43133	−0.715664	−	0.698444i	$-0.753876\pi$
$197$	−20.0897	−1.43133	−0.715664	+	0.698444i	$0.753876\pi$
$198$	−1.58528	−0.112661
$199$	13.1054	0.929015	0.464508	−	0.885569i	$-0.346231\pi$
$199$	13.1054	0.929015	0.464508	+	0.885569i	$0.346231\pi$
$200$	9.08637	0.642503
$201$	0.323350	0.0228074
$202$	−5.06214	−0.356171
$203$	4.09140	0.287160
$204$	−0.674066	−0.0471941
$205$	8.84292	0.617616
$206$	−12.0563	−0.840000
$207$	−0.709431	−0.0493089
$208$	2.74215	0.190134
$209$	6.24761	0.432156
$210$	6.72664	0.464182
$211$	15.3424	1.05621	0.528106	−	0.849179i	$-0.322902\pi$
$211$	15.3424	1.05621	0.528106	+	0.849179i	$0.322902\pi$
$212$	16.0295	1.10091
$213$	−11.7045	−0.801977
$214$	−3.47346	−0.237441
$215$	−7.12034	−0.485603
$216$	11.1031	0.755471
$217$	−0.0236054	−0.00160244
$218$	−4.44399	−0.300985
$219$	28.7061	1.93978
$220$	−5.36818	−0.361922
$221$	0.576140	0.0387554
$222$	2.33849	0.156949
$223$	23.9433	1.60336	0.801679	−	0.597754i	$-0.203940\pi$
$223$	23.9433	1.60336	0.801679	+	0.597754i	$0.203940\pi$
$224$	−23.9388	−1.59948
$225$	−2.56126	−0.170750
$226$	1.80934	0.120355
$227$	−8.81659	−0.585178	−0.292589	−	0.956238i	$-0.594517\pi$
$227$	−8.81659	−0.585178	−0.292589	+	0.956238i	$0.594517\pi$
$228$	5.75397	0.381066
$229$	14.8752	0.982981	0.491491	−	0.870883i	$-0.336452\pi$
$229$	14.8752	0.982981	0.491491	+	0.870883i	$0.336452\pi$
$230$	0.853636	0.0562871
$231$	24.3169	1.59994
$232$	2.51679	0.165236
$233$	12.7248	0.833630	0.416815	−	0.908991i	$-0.363146\pi$
$233$	12.7248	0.833630	0.416815	+	0.908991i	$0.363146\pi$
$234$	1.24791	0.0815785
$235$	−11.2703	−0.735196
$236$	−16.4486	−1.07071
$237$	10.3844	0.674537
$238$	−0.702667	−0.0455472
$239$	−8.33010	−0.538829	−0.269415	−	0.963024i	$-0.586830\pi$
$239$	−8.33010	−0.538829	−0.269415	+	0.963024i	$0.586830\pi$
$240$	−2.56297	−0.165439
$241$	11.1245	0.716594	0.358297	−	0.933608i	$-0.383357\pi$
$241$	11.1245	0.716594	0.358297	+	0.933608i	$0.383357\pi$
$242$	−1.06964	−0.0687594
$243$	−7.22880	−0.463728
$244$	20.0302	1.28230
$245$	−11.4815	−0.733528
$246$	−10.4616	−0.667010
$247$	−4.91805	−0.312928
$248$	−0.0145207	−0.000922064 0
$249$	8.88892	0.563312
$250$	7.35006	0.464858
$251$	−20.0438	−1.26516	−0.632578	−	0.774497i	$-0.718003\pi$
$251$	−20.0438	−1.26516	−0.632578	+	0.774497i	$0.718003\pi$
$252$	4.28316	0.269814
$253$	3.08591	0.194009
$254$	−7.84838	−0.492451
$255$	−0.538494	−0.0337218
$256$	−11.3942	−0.712139
$257$	−6.94240	−0.433055	−0.216527	−	0.976277i	$-0.569473\pi$
$257$	−6.94240	−0.433055	−0.216527	+	0.976277i	$0.569473\pi$
$258$	8.42375	0.524440
$259$	−6.86029	−0.426278
$260$	4.22577	0.262071
$261$	−0.709431	−0.0439127
$262$	5.37969	0.332358
$263$	−13.1040	−0.808028	−0.404014	−	0.914753i	$-0.632385\pi$
$263$	−13.1040	−0.808028	−0.404014	+	0.914753i	$0.632385\pi$
$264$	14.9584	0.920624
$265$	12.8055	0.786637
$266$	5.99811	0.367768
$267$	−4.04329	−0.247445
$268$	−0.247743	−0.0151333
$269$	−26.4529	−1.61286	−0.806430	−	0.591329i	$-0.798603\pi$
$269$	−26.4529	−1.61286	−0.806430	+	0.591329i	$0.798603\pi$
$270$	3.76591	0.229186
$271$	−13.9142	−0.845229	−0.422614	−	0.906310i	$-0.638888\pi$
$271$	−13.9142	−0.845229	−0.422614	+	0.906310i	$0.638888\pi$
$272$	0.267729	0.0162334
$273$	−19.1420	−1.15853
$274$	−5.34331	−0.322801
$275$	11.1411	0.671831
$276$	2.84208	0.171073
$277$	20.4584	1.22923	0.614614	−	0.788828i	$-0.289312\pi$
$277$	20.4584	1.22923	0.614614	+	0.788828i	$0.289312\pi$
$278$	9.27566	0.556317
$279$	0.00409308	0.000245046 0
$280$	−12.1389	−0.725439
$281$	18.0185	1.07489	0.537446	−	0.843298i	$-0.319389\pi$
$281$	18.0185	1.07489	0.537446	+	0.843298i	$0.319389\pi$
$282$	13.3334	0.793993
$283$	30.6847	1.82402	0.912009	−	0.410169i	$-0.134530\pi$
$283$	30.6847	1.82402	0.912009	+	0.410169i	$0.134530\pi$
$284$	8.96770	0.532135
$285$	4.59669	0.272285
$286$	−5.42821	−0.320977
$287$	30.6907	1.81161
$288$	4.15088	0.244593
$289$	−16.9437	−0.996691
$290$	0.853636	0.0501272
$291$	−14.8470	−0.870349
$292$	−21.9940	−1.28710
$293$	−6.47983	−0.378556	−0.189278	−	0.981924i	$-0.560615\pi$
$293$	−6.47983	−0.378556	−0.189278	+	0.981924i	$0.560615\pi$
$294$	13.5833	0.792192
$295$	−13.1403	−0.765060
$296$	−4.22005	−0.245286
$297$	13.6138	0.789954
$298$	−6.93917	−0.401976
$299$	−2.42919	−0.140484
$300$	10.2608	0.592405
$301$	−24.7122	−1.42439
$302$	−8.92832	−0.513767
$303$	−13.4641	−0.773490
$304$	−2.28539	−0.131076
$305$	16.0016	0.916249
$306$	0.121839	0.00696510
$307$	12.7332	0.726724	0.363362	−	0.931648i	$-0.381629\pi$
$307$	12.7332	0.726724	0.363362	+	0.931648i	$0.381629\pi$
$308$	−18.6311	−1.06160
$309$	−32.0667	−1.82421
$310$	−0.00492507	−0.000279725 0
$311$	−30.2599	−1.71588	−0.857941	−	0.513748i	$-0.828257\pi$
$311$	−30.2599	−1.71588	−0.857941	+	0.513748i	$0.828257\pi$
$312$	−11.7751	−0.666631
$313$	13.0447	0.737332	0.368666	−	0.929562i	$-0.379815\pi$
$313$	13.0447	0.737332	0.368666	+	0.929562i	$0.379815\pi$
$314$	−1.81065	−0.102181
$315$	3.42171	0.192791
$316$	−7.95627	−0.447575
$317$	8.93249	0.501699	0.250849	−	0.968026i	$-0.419290\pi$
$317$	8.93249	0.501699	0.250849	+	0.968026i	$0.419290\pi$
$318$	−15.1496	−0.849548
$319$	3.08591	0.172778
$320$	−2.33316	−0.130428
$321$	−9.23857	−0.515646
$322$	2.96267	0.165103
$323$	−0.480172	−0.0267175
$324$	15.6788	0.871042
$325$	−8.77011	−0.486478
$326$	−1.81370	−0.100451
$327$	−11.8199	−0.653643
$328$	18.8791	1.04243
$329$	−39.1154	−2.15650
$330$	5.07352	0.279288
$331$	−19.6340	−1.07918	−0.539590	−	0.841928i	$-0.681421\pi$
$331$	−19.6340	−1.07918	−0.539590	+	0.841928i	$0.681421\pi$
$332$	−6.81048	−0.373774
$333$	1.18954	0.0651866
$334$	9.24364	0.505789
$335$	−0.197916	−0.0108133
$336$	−8.89517	−0.485271
$337$	23.2024	1.26392	0.631958	−	0.775003i	$-0.282252\pi$
$337$	23.2024	1.26392	0.631958	+	0.775003i	$0.282252\pi$
$338$	−5.14056	−0.279609
$339$	4.81240	0.261374
$340$	0.412582	0.0223754
$341$	−0.0178042	−0.000964153 0
$342$	−1.04005	−0.0562393
$343$	−11.2086	−0.605206
$344$	−15.2015	−0.819612
$345$	2.27046	0.122238
$346$	−13.3781	−0.719212
$347$	−29.0651	−1.56030	−0.780148	−	0.625595i	$-0.784856\pi$
$347$	−29.0651	−1.56030	−0.780148	+	0.625595i	$0.784856\pi$
$348$	2.84208	0.152351
$349$	−0.112702	−0.00603280	−0.00301640	−	0.999995i	$-0.500960\pi$
$349$	−0.112702	−0.00603280	−0.00301640	+	0.999995i	$0.500960\pi$
$350$	10.6961	0.571732
$351$	−10.7166	−0.572012
$352$	−18.0556	−0.962369
$353$	−1.37872	−0.0733820	−0.0366910	−	0.999327i	$-0.511682\pi$
$353$	−1.37872	−0.0733820	−0.0366910	+	0.999327i	$0.511682\pi$
$354$	15.5457	0.826246
$355$	7.16406	0.380229
$356$	3.09788	0.164187
$357$	−1.86892	−0.0989140
$358$	5.20637	0.275165
$359$	−9.37848	−0.494977	−0.247489	−	0.968891i	$-0.579605\pi$
$359$	−9.37848	−0.494977	−0.247489	+	0.968891i	$0.579605\pi$
$360$	2.10484	0.110935
$361$	−14.9012	−0.784271
$362$	10.1249	0.532155
$363$	−2.84500	−0.149324
$364$	14.6662	0.768716
$365$	−17.5704	−0.919677
$366$	−18.9308	−0.989526
$367$	−29.5188	−1.54087	−0.770435	−	0.637519i	$-0.779961\pi$
$367$	−29.5188	−1.54087	−0.770435	+	0.637519i	$0.779961\pi$
$368$	−1.12883	−0.0588444
$369$	−5.32163	−0.277033
$370$	−1.43134	−0.0744119
$371$	44.4435	2.30739
$372$	−0.0163974	−0.000850168 0
$373$	−29.4937	−1.52712	−0.763562	−	0.645735i	$-0.776551\pi$
$373$	−29.4937	−1.52712	−0.763562	+	0.645735i	$0.776551\pi$
$374$	−0.529982	−0.0274047
$375$	19.5494	1.00952
$376$	−24.0615	−1.24088
$377$	−2.42919	−0.125110
$378$	13.0701	0.672256
$379$	7.25592	0.372711	0.186356	−	0.982482i	$-0.440332\pi$
$379$	7.25592	0.372711	0.186356	+	0.982482i	$0.440332\pi$
$380$	−3.52188	−0.180669
$381$	−20.8748	−1.06945
$382$	−8.87941	−0.454310
$383$	−32.0799	−1.63920	−0.819602	−	0.572933i	$-0.805805\pi$
$383$	−32.0799	−1.63920	−0.819602	+	0.572933i	$0.805805\pi$
$384$	−19.7776	−1.00927
$385$	−14.8839	−0.758552
$386$	−0.716260	−0.0364567
$387$	4.28499	0.217818
$388$	11.3755	0.577501
$389$	−8.07054	−0.409193	−0.204596	−	0.978846i	$-0.565588\pi$
$389$	−8.07054	−0.409193	−0.204596	+	0.978846i	$0.565588\pi$
$390$	−3.99382	−0.202235
$391$	−0.237174	−0.0119944
$392$	−24.5124	−1.23806
$393$	14.3087	0.721777
$394$	−14.5474	−0.732885
$395$	−6.35605	−0.319808
$396$	3.23055	0.162341
$397$	34.8476	1.74895	0.874476	−	0.485069i	$-0.161206\pi$
$397$	34.8476	1.74895	0.874476	+	0.485069i	$0.161206\pi$
$398$	9.48989	0.475685
$399$	15.9535	0.798675
$400$	−4.07542	−0.203771
$401$	−9.55698	−0.477253	−0.238626	−	0.971111i	$-0.576697\pi$
$401$	−9.55698	−0.477253	−0.238626	+	0.971111i	$0.576697\pi$
$402$	0.234145	0.0116781
$403$	0.0140153	0.000698151 0
$404$	10.3158	0.513233
$405$	12.5253	0.622390
$406$	2.96267	0.147035
$407$	−5.17433	−0.256482
$408$	−1.14965	−0.0569164
$409$	−6.77875	−0.335188	−0.167594	−	0.985856i	$-0.553600\pi$
$409$	−6.77875	−0.335188	−0.167594	+	0.985856i	$0.553600\pi$
$410$	6.40335	0.316239
$411$	−14.2119	−0.701022
$412$	24.5688	1.21042
$413$	−45.6055	−2.24410
$414$	−0.513714	−0.0252477
$415$	−5.44072	−0.267074
$416$	14.2132	0.696859
$417$	24.6710	1.20814
$418$	4.52403	0.221278
$419$	24.9543	1.21910	0.609549	−	0.792748i	$-0.291350\pi$
$419$	24.9543	1.21910	0.609549	+	0.792748i	$0.291350\pi$
$420$	−13.7078	−0.668874
$421$	−8.34962	−0.406935	−0.203468	−	0.979082i	$-0.565221\pi$
$421$	−8.34962	−0.406935	−0.203468	+	0.979082i	$0.565221\pi$
$422$	11.1097	0.540814
$423$	6.78244	0.329774
$424$	27.3391	1.32770
$425$	−0.856267	−0.0415351
$426$	−8.47546	−0.410638
$427$	55.5360	2.68757
$428$	7.07838	0.342146
$429$	−14.4377	−0.697060
$430$	−5.15600	−0.248644
$431$	16.1008	0.775550	0.387775	−	0.921754i	$-0.373244\pi$
$431$	16.1008	0.775550	0.387775	+	0.921754i	$0.373244\pi$
$432$	−4.97996	−0.239598
$433$	−19.7843	−0.950771	−0.475385	−	0.879778i	$-0.657691\pi$
$433$	−19.7843	−0.950771	−0.475385	+	0.879778i	$0.657691\pi$
$434$	−0.0170932	−0.000820500 0
$435$	2.27046	0.108860
$436$	9.05615	0.433711
$437$	2.02456	0.0968479
$438$	20.7867	0.993229
$439$	6.78432	0.323798	0.161899	−	0.986807i	$-0.448238\pi$
$439$	6.78432	0.323798	0.161899	+	0.986807i	$0.448238\pi$
$440$	−9.15570	−0.436481
$441$	6.90953	0.329025
$442$	0.417196	0.0198440
$443$	39.0520	1.85541	0.927707	−	0.373308i	$-0.121777\pi$
$443$	39.0520	1.85541	0.927707	+	0.373308i	$0.121777\pi$
$444$	−4.76548	−0.226160
$445$	2.47481	0.117317
$446$	17.3378	0.820970
$447$	−18.4565	−0.872963
$448$	−8.09758	−0.382575
$449$	13.1416	0.620188	0.310094	−	0.950706i	$-0.399639\pi$
$449$	13.1416	0.620188	0.310094	+	0.950706i	$0.399639\pi$
$450$	−1.85466	−0.0874296
$451$	23.1482	1.09001
$452$	−3.68715	−0.173429
$453$	−23.7472	−1.11574
$454$	−6.38429	−0.299629
$455$	11.7164	0.549274
$456$	9.81368	0.459568
$457$	−11.4555	−0.535866	−0.267933	−	0.963438i	$-0.586341\pi$
$457$	−11.4555	−0.535866	−0.267933	+	0.963438i	$0.586341\pi$
$458$	10.7715	0.503317
$459$	−1.04632	−0.0488379
$460$	−1.73958	−0.0811082
$461$	−13.0768	−0.609047	−0.304523	−	0.952505i	$-0.598497\pi$
$461$	−13.0768	−0.609047	−0.304523	+	0.952505i	$0.598497\pi$
$462$	17.6084	0.819218
$463$	26.8054	1.24575	0.622876	−	0.782320i	$-0.285964\pi$
$463$	26.8054	1.24575	0.622876	+	0.782320i	$0.285964\pi$
$464$	−1.12883	−0.0524047
$465$	−0.0130995	−0.000607474 0
$466$	9.21431	0.426845
$467$	7.09497	0.328316	0.164158	−	0.986434i	$-0.447509\pi$
$467$	7.09497	0.328316	0.164158	+	0.986434i	$0.447509\pi$
$468$	−2.54305	−0.117552
$469$	−0.686896	−0.0317179
$470$	−8.16110	−0.376443
$471$	−4.81589	−0.221905
$472$	−28.0539	−1.29128
$473$	−18.6390	−0.857024
$474$	7.51955	0.345384
$475$	7.30927	0.335372
$476$	1.43193	0.0656322
$477$	−7.70631	−0.352848
$478$	−6.03200	−0.275897
$479$	34.1103	1.55854	0.779270	−	0.626688i	$-0.215590\pi$
$479$	34.1103	1.55854	0.779270	+	0.626688i	$0.215590\pi$
$480$	−13.2845	−0.606350
$481$	4.07317	0.185721
$482$	8.05552	0.366919
$483$	7.87999	0.358552
$484$	2.17977	0.0990804
$485$	9.08756	0.412645
$486$	−5.23453	−0.237443
$487$	42.1047	1.90795	0.953973	−	0.299894i	$-0.0969513\pi$
$487$	42.1047	1.90795	0.953973	+	0.299894i	$0.0969513\pi$
$488$	34.1625	1.54647
$489$	−4.82399	−0.218148
$490$	−8.31402	−0.375589
$491$	−2.34913	−0.106015	−0.0530073	−	0.998594i	$-0.516881\pi$
$491$	−2.34913	−0.106015	−0.0530073	+	0.998594i	$0.516881\pi$
$492$	21.3192	0.961144
$493$	−0.237174	−0.0106818
$494$	−3.56127	−0.160229
$495$	2.58080	0.115998
$496$	0.00651281	0.000292434 0
$497$	24.8639	1.11530
$498$	6.43666	0.288434
$499$	7.43721	0.332935	0.166468	−	0.986047i	$-0.446764\pi$
$499$	7.43721	0.332935	0.166468	+	0.986047i	$0.446764\pi$
$500$	−14.9783	−0.669849
$501$	24.5858	1.09841
$502$	−14.5142	−0.647799
$503$	−28.8324	−1.28557	−0.642786	−	0.766046i	$-0.722221\pi$
$503$	−28.8324	−1.28557	−0.642786	+	0.766046i	$0.722221\pi$
$504$	7.30515	0.325397
$505$	8.24106	0.366722
$506$	2.23457	0.0993390
$507$	−13.6726	−0.607223
$508$	15.9938	0.709610
$509$	23.9116	1.05986	0.529932	−	0.848040i	$-0.322217\pi$
$509$	23.9116	1.05986	0.529932	+	0.848040i	$0.322217\pi$
$510$	−0.389935	−0.0172666
$511$	−60.9808	−2.69763
$512$	12.2869	0.543007
$513$	8.93157	0.394339
$514$	−5.02714	−0.221738
$515$	19.6274	0.864885
$516$	−17.1663	−0.755704
$517$	−29.5025	−1.29752
$518$	−4.96769	−0.218268
$519$	−35.5825	−1.56190
$520$	7.20726	0.316059
$521$	−29.8605	−1.30821	−0.654106	−	0.756403i	$-0.726955\pi$
$521$	−29.8605	−1.30821	−0.654106	+	0.756403i	$0.726955\pi$
$522$	−0.513714	−0.0224847
$523$	−26.7914	−1.17151	−0.585753	−	0.810489i	$-0.699201\pi$
$523$	−26.7914	−1.17151	−0.585753	+	0.810489i	$0.699201\pi$
$524$	−10.9630	−0.478920
$525$	28.4491	1.24162
$526$	−9.48890	−0.413736
$527$	0.00136838	5.96075e−5 0
$528$	−6.70912	−0.291977
$529$	1.00000	0.0434783
$530$	9.27275	0.402783
$531$	7.90780	0.343169
$532$	−12.2232	−0.529944
$533$	−18.2220	−0.789284
$534$	−2.92784	−0.126700
$535$	5.65473	0.244475
$536$	−0.422539	−0.0182509
$537$	13.8477	0.597572
$538$	−19.1551	−0.825835
$539$	−30.0554	−1.29458
$540$	−7.67433	−0.330251
$541$	17.5034	0.752531	0.376266	−	0.926512i	$-0.377208\pi$
$541$	17.5034	0.752531	0.376266	+	0.926512i	$0.377208\pi$
$542$	−10.0756	−0.432784
$543$	26.9299	1.15567
$544$	1.38770	0.0594972
$545$	7.23472	0.309901
$546$	−13.8611	−0.593202
$547$	−21.8166	−0.932812	−0.466406	−	0.884571i	$-0.654451\pi$
$547$	−21.8166	−0.932812	−0.466406	+	0.884571i	$0.654451\pi$
$548$	10.8888	0.465148
$549$	−9.62970	−0.410986
$550$	8.06748	0.343998
$551$	2.02456	0.0862492
$552$	4.84731	0.206315
$553$	−22.0596	−0.938071
$554$	14.8144	0.629404
$555$	−3.80702	−0.161599
$556$	−18.9024	−0.801639
$557$	−25.5295	−1.08172	−0.540860	−	0.841113i	$-0.681901\pi$
$557$	−25.5295	−1.08172	−0.540860	+	0.841113i	$0.681901\pi$
$558$	0.00296389	0.000125471 0
$559$	14.6724	0.620578
$560$	5.44454	0.230074
$561$	−1.40962	−0.0595144
$562$	13.0476	0.550379
$563$	40.7060	1.71555	0.857777	−	0.514022i	$-0.171845\pi$
$563$	40.7060	1.71555	0.857777	+	0.514022i	$0.171845\pi$
$564$	−27.1714	−1.14412
$565$	−2.94557	−0.123921
$566$	22.2195	0.933955
$567$	43.4711	1.82562
$568$	15.2949	0.641758
$569$	−23.8159	−0.998413	−0.499206	−	0.866483i	$-0.666375\pi$
$569$	−23.8159	−0.998413	−0.499206	+	0.866483i	$0.666375\pi$
$570$	3.32857	0.139418
$571$	43.1369	1.80522	0.902612	−	0.430455i	$-0.141647\pi$
$571$	43.1369	1.80522	0.902612	+	0.430455i	$0.141647\pi$
$572$	11.0619	0.462519
$573$	−23.6171	−0.986618
$574$	22.2238	0.927603
$575$	3.61030	0.150560
$576$	1.40409	0.0585036
$577$	−23.6828	−0.985929	−0.492964	−	0.870050i	$-0.664087\pi$
$577$	−23.6828	−0.985929	−0.492964	+	0.870050i	$0.664087\pi$
$578$	−12.2693	−0.510337
$579$	−1.90508	−0.0791724
$580$	−1.73958	−0.0722320
$581$	−18.8828	−0.783392
$582$	−10.7511	−0.445646
$583$	33.5212	1.38831
$584$	−37.5118	−1.55225
$585$	−2.03158	−0.0839953
$586$	−4.69219	−0.193833
$587$	−16.4654	−0.679599	−0.339799	−	0.940498i	$-0.610359\pi$
$587$	−16.4654	−0.679599	−0.339799	+	0.940498i	$0.610359\pi$
$588$	−27.6806	−1.14153
$589$	−0.0116807	−0.000481297 0
$590$	−9.51520	−0.391735
$591$	−38.6924	−1.59159
$592$	1.89278	0.0777927
$593$	−3.09974	−0.127291	−0.0636456	−	0.997973i	$-0.520273\pi$
$593$	−3.09974	−0.127291	−0.0636456	+	0.997973i	$0.520273\pi$
$594$	9.85807	0.404482
$595$	1.14393	0.0468965
$596$	14.1410	0.579236
$597$	25.2408	1.03304
$598$	−1.75903	−0.0719321
$599$	−19.8538	−0.811204	−0.405602	−	0.914050i	$-0.632938\pi$
$599$	−19.8538	−0.811204	−0.405602	+	0.914050i	$0.632938\pi$
$600$	17.5002	0.714444
$601$	32.3423	1.31927	0.659634	−	0.751587i	$-0.270711\pi$
$601$	32.3423	1.31927	0.659634	+	0.751587i	$0.270711\pi$
$602$	−17.8947	−0.729332
$603$	0.119105	0.00485033
$604$	18.1945	0.740325
$605$	1.74136	0.0707964
$606$	−9.74962	−0.396051
$607$	41.1837	1.67159	0.835796	−	0.549039i	$-0.185006\pi$
$607$	41.1837	1.67159	0.835796	+	0.549039i	$0.185006\pi$
$608$	−11.8457	−0.480407
$609$	7.87999	0.319313
$610$	11.5871	0.469148
$611$	23.2240	0.939544
$612$	−0.248290	−0.0100365
$613$	−4.93002	−0.199122	−0.0995608	−	0.995031i	$-0.531744\pi$
$613$	−4.93002	−0.199122	−0.0995608	+	0.995031i	$0.531744\pi$
$614$	9.22041	0.372106
$615$	17.0314	0.686771
$616$	−31.7762	−1.28030
$617$	−3.79379	−0.152732	−0.0763660	−	0.997080i	$-0.524332\pi$
$617$	−3.79379	−0.152732	−0.0763660	+	0.997080i	$0.524332\pi$
$618$	−23.2202	−0.934054
$619$	−5.02514	−0.201977	−0.100989	−	0.994888i	$-0.532201\pi$
$619$	−5.02514	−0.201977	−0.100989	+	0.994888i	$0.532201\pi$
$620$	0.0100365	0.000403076 0
$621$	4.41161	0.177032
$622$	−21.9119	−0.878586
$623$	8.58921	0.344120
$624$	5.28134	0.211423
$625$	6.08574	0.243430
$626$	9.44597	0.377537
$627$	12.0328	0.480545
$628$	3.68983	0.147240
$629$	0.397683	0.0158567
$630$	2.47773	0.0987152
$631$	28.4900	1.13417	0.567084	−	0.823660i	$-0.308071\pi$
$631$	28.4900	1.13417	0.567084	+	0.823660i	$0.308071\pi$
$632$	−13.5698	−0.539778
$633$	29.5492	1.17448
$634$	6.46821	0.256886
$635$	12.7770	0.507041
$636$	30.8726	1.22418
$637$	23.6592	0.937413
$638$	2.23457	0.0884677
$639$	−4.31130	−0.170552
$640$	12.1055	0.478511
$641$	−8.48927	−0.335306	−0.167653	−	0.985846i	$-0.553619\pi$
$641$	−8.48927	−0.335306	−0.167653	+	0.985846i	$0.553619\pi$
$642$	−6.68985	−0.264027
$643$	21.3205	0.840798	0.420399	−	0.907339i	$-0.361890\pi$
$643$	21.3205	0.840798	0.420399	+	0.907339i	$0.361890\pi$
$644$	−6.03746	−0.237909
$645$	−13.7137	−0.539976
$646$	−0.347703	−0.0136802
$647$	−19.1958	−0.754666	−0.377333	−	0.926078i	$-0.623159\pi$
$647$	−19.1958	−0.754666	−0.377333	+	0.926078i	$0.623159\pi$
$648$	26.7409	1.05048
$649$	−34.3976	−1.35023
$650$	−6.35063	−0.249092
$651$	−0.0454637	−0.00178186
$652$	3.69603	0.144748
$653$	−6.25556	−0.244799	−0.122399	−	0.992481i	$-0.539059\pi$
$653$	−6.25556	−0.244799	−0.122399	+	0.992481i	$0.539059\pi$
$654$	−8.55906	−0.334686
$655$	−8.75803	−0.342205
$656$	−8.46767	−0.330607
$657$	10.5738	0.412523
$658$	−28.3243	−1.10420
$659$	37.2600	1.45144	0.725722	−	0.687988i	$-0.241506\pi$
$659$	37.2600	1.45144	0.725722	+	0.687988i	$0.241506\pi$
$660$	−10.3390	−0.402447
$661$	11.4199	0.444183	0.222091	−	0.975026i	$-0.428712\pi$
$661$	11.4199	0.444183	0.222091	+	0.975026i	$0.428712\pi$
$662$	−14.2174	−0.552574
$663$	1.10964	0.0430948
$664$	−11.6156	−0.450774
$665$	−9.76481	−0.378663
$666$	0.861375	0.0333776
$667$	1.00000	0.0387202
$668$	−18.8371	−0.728829
$669$	46.1144	1.78289
$670$	−0.143315	−0.00553675
$671$	41.8876	1.61705
$672$	−46.1058	−1.77857
$673$	33.3489	1.28550	0.642752	−	0.766074i	$-0.277793\pi$
$673$	33.3489	1.28550	0.642752	+	0.766074i	$0.277793\pi$
$674$	16.8014	0.647165
$675$	15.9272	0.613039
$676$	10.4757	0.402910
$677$	12.7153	0.488687	0.244343	−	0.969689i	$-0.421428\pi$
$677$	12.7153	0.488687	0.244343	+	0.969689i	$0.421428\pi$
$678$	3.48476	0.133832
$679$	31.5397	1.21038
$680$	0.703679	0.0269849
$681$	−16.9807	−0.650700
$682$	−0.0128924	−0.000493676 0
$683$	−23.8362	−0.912068	−0.456034	−	0.889962i	$-0.650730\pi$
$683$	−23.8362	−0.912068	−0.456034	+	0.889962i	$0.650730\pi$
$684$	2.11945	0.0810393
$685$	8.69881	0.332364
$686$	−8.11637	−0.309884
$687$	28.6495	1.09305
$688$	6.81819	0.259941
$689$	−26.3875	−1.00528
$690$	1.64409	0.0625895
$691$	−3.45761	−0.131534	−0.0657668	−	0.997835i	$-0.520949\pi$
$691$	−3.45761	−0.131534	−0.0657668	+	0.997835i	$0.520949\pi$
$692$	27.2625	1.03637
$693$	8.95705	0.340250
$694$	−21.0467	−0.798921
$695$	−15.1006	−0.572798
$696$	4.84731	0.183737
$697$	−1.77910	−0.0673883
$698$	−0.0816100	−0.00308898
$699$	24.5078	0.926971
$700$	−21.7970	−0.823851
$701$	−15.2400	−0.575606	−0.287803	−	0.957690i	$-0.592925\pi$
$701$	−15.2400	−0.575606	−0.287803	+	0.957690i	$0.592925\pi$
$702$	−7.76016	−0.292888
$703$	−3.39470	−0.128034
$704$	−6.10755	−0.230187
$705$	−21.7065	−0.817515
$706$	−0.998363	−0.0375739
$707$	28.6019	1.07568
$708$	−31.6798	−1.19060
$709$	−37.0045	−1.38973	−0.694866	−	0.719139i	$-0.744536\pi$
$709$	−37.0045	−1.38973	−0.694866	+	0.719139i	$0.744536\pi$
$710$	5.18765	0.194689
$711$	3.82505	0.143450
$712$	5.28359	0.198011
$713$	−0.00576952	−0.000216070 0
$714$	−1.35333	−0.0506471
$715$	8.83702	0.330486
$716$	−10.6098	−0.396506
$717$	−16.0437	−0.599162
$718$	−6.79116	−0.253444
$719$	−5.03681	−0.187841	−0.0939206	−	0.995580i	$-0.529940\pi$
$719$	−5.03681	−0.187841	−0.0939206	+	0.995580i	$0.529940\pi$
$720$	−0.944060	−0.0351831
$721$	68.1197	2.53691
$722$	−10.7902	−0.401571
$723$	21.4257	0.796831
$724$	−20.6331	−0.766822
$725$	3.61030	0.134083
$726$	−2.06012	−0.0764584
$727$	8.96392	0.332453	0.166227	−	0.986088i	$-0.446842\pi$
$727$	8.96392	0.332453	0.166227	+	0.986088i	$0.446842\pi$
$728$	25.0139	0.927076
$729$	17.9524	0.664904
$730$	−12.7231	−0.470904
$731$	1.43254	0.0529844
$732$	38.5779	1.42588
$733$	20.2174	0.746746	0.373373	−	0.927681i	$-0.378201\pi$
$733$	20.2174	0.746746	0.373373	+	0.927681i	$0.378201\pi$
$734$	−21.3752	−0.788974
$735$	−22.1133	−0.815661
$736$	−5.85100	−0.215671
$737$	−0.518087	−0.0190840
$738$	−3.85351	−0.141850
$739$	−24.6664	−0.907368	−0.453684	−	0.891163i	$-0.649890\pi$
$739$	−24.6664	−0.907368	−0.453684	+	0.891163i	$0.649890\pi$
$740$	2.91685	0.107226
$741$	−9.47211	−0.347967
$742$	32.1825	1.18146
$743$	4.68390	0.171836	0.0859179	−	0.996302i	$-0.472618\pi$
$743$	4.68390	0.171836	0.0859179	+	0.996302i	$0.472618\pi$
$744$	−0.0279667	−0.00102531
$745$	11.2968	0.413884
$746$	−21.3570	−0.781935
$747$	3.27420	0.119797
$748$	1.08002	0.0394895
$749$	19.6256	0.717103
$750$	14.1561	0.516909
$751$	1.17784	0.0429799	0.0214899	−	0.999769i	$-0.493159\pi$
$751$	1.17784	0.0429799	0.0214899	+	0.999769i	$0.493159\pi$
$752$	10.7921	0.393546
$753$	−38.6042	−1.40681
$754$	−1.75903	−0.0640601
$755$	14.5351	0.528988
$756$	−26.6349	−0.968703
$757$	−33.9047	−1.23229	−0.616144	−	0.787634i	$-0.711306\pi$
$757$	−33.9047	−1.23229	−0.616144	+	0.787634i	$0.711306\pi$
$758$	5.25417	0.190840
$759$	5.94343	0.215733
$760$	−6.00675	−0.217888
$761$	1.56648	0.0567849	0.0283924	−	0.999597i	$-0.490961\pi$
$761$	1.56648	0.0567849	0.0283924	+	0.999597i	$0.490961\pi$
$762$	−15.1159	−0.547591
$763$	25.1092	0.909014
$764$	18.0949	0.654649
$765$	−0.198352	−0.00717144
$766$	−23.2297	−0.839324
$767$	27.0774	0.977709
$768$	−21.9451	−0.791877
$769$	39.5943	1.42781	0.713904	−	0.700244i	$-0.246925\pi$
$769$	39.5943	1.42781	0.713904	+	0.700244i	$0.246925\pi$
$770$	−10.7777	−0.388403
$771$	−13.3710	−0.481544
$772$	1.45963	0.0525331
$773$	−40.8881	−1.47064	−0.735320	−	0.677720i	$-0.762968\pi$
$773$	−40.8881	−1.47064	−0.735320	+	0.677720i	$0.762968\pi$
$774$	3.10286	0.111530
$775$	−0.0208297	−0.000748225 0
$776$	19.4014	0.696471
$777$	−13.2128	−0.474008
$778$	−5.84405	−0.209519
$779$	15.1868	0.544123
$780$	8.13878	0.291415
$781$	18.7535	0.671052
$782$	−0.171743	−0.00614150
$783$	4.41161	0.157658
$784$	10.9943	0.392653
$785$	2.94771	0.105208
$786$	10.3612	0.369572
$787$	16.9993	0.605958	0.302979	−	0.952997i	$-0.402019\pi$
$787$	16.9993	0.605958	0.302979	+	0.952997i	$0.402019\pi$
$788$	29.6452	1.05607
$789$	−25.2382	−0.898503
$790$	−4.60256	−0.163752
$791$	−10.2230	−0.363489
$792$	5.50986	0.195784
$793$	−32.9735	−1.17092
$794$	25.2339	0.895518
$795$	24.6633	0.874716
$796$	−19.3389	−0.685450
$797$	13.6227	0.482539	0.241270	−	0.970458i	$-0.422436\pi$
$797$	13.6227	0.482539	0.241270	+	0.970458i	$0.422436\pi$
$798$	11.5523	0.408947
$799$	2.26747	0.0802174
$800$	−21.1238	−0.746840
$801$	−1.48933	−0.0526230
$802$	−6.92042	−0.244369
$803$	−45.9943	−1.62310
$804$	−0.477151	−0.0168278
$805$	−4.82317	−0.169994
$806$	0.0101488	0.000357475 0
$807$	−50.9479	−1.79345
$808$	17.5942	0.618962
$809$	−25.5001	−0.896537	−0.448268	−	0.893899i	$-0.647959\pi$
$809$	−25.5001	−0.896537	−0.448268	+	0.893899i	$0.647959\pi$
$810$	9.06988	0.318683
$811$	−26.6838	−0.936994	−0.468497	−	0.883465i	$-0.655204\pi$
$811$	−26.6838	−0.936994	−0.468497	+	0.883465i	$0.655204\pi$
$812$	−6.03746	−0.211873
$813$	−26.7986	−0.939869
$814$	−3.74684	−0.131327
$815$	2.95266	0.103427
$816$	0.515643	0.0180511
$817$	−12.2284	−0.427819
$818$	−4.90864	−0.171627
$819$	−7.05089	−0.246378
$820$	−13.0490	−0.455692
$821$	53.8480	1.87931	0.939653	−	0.342128i	$-0.111148\pi$
$821$	53.8480	1.87931	0.939653	+	0.342128i	$0.111148\pi$
$822$	−10.2912	−0.358945
$823$	−14.9934	−0.522637	−0.261319	−	0.965253i	$-0.584157\pi$
$823$	−14.9934	−0.522637	−0.261319	+	0.965253i	$0.584157\pi$
$824$	41.9033	1.45977
$825$	21.4575	0.747056
$826$	−33.0239	−1.14905
$827$	33.6879	1.17144	0.585722	−	0.810512i	$-0.300811\pi$
$827$	33.6879	1.17144	0.585722	+	0.810512i	$0.300811\pi$
$828$	1.04687	0.0363812
$829$	38.3682	1.33258	0.666292	−	0.745691i	$-0.267880\pi$
$829$	38.3682	1.33258	0.666292	+	0.745691i	$0.267880\pi$
$830$	−3.93974	−0.136750
$831$	39.4027	1.36687
$832$	4.80779	0.166680
$833$	2.30996	0.0800354
$834$	17.8648	0.618608
$835$	−15.0485	−0.520774
$836$	−9.21928	−0.318855
$837$	−0.0254529	−0.000879780 0
$838$	18.0700	0.624217
$839$	4.94162	0.170604	0.0853019	−	0.996355i	$-0.472815\pi$
$839$	4.94162	0.170604	0.0853019	+	0.996355i	$0.472815\pi$
$840$	−23.3794	−0.806667
$841$	1.00000	0.0344828
$842$	−6.04614	−0.208364
$843$	34.7034	1.19525
$844$	−22.6399	−0.779298
$845$	8.36873	0.287893
$846$	4.91131	0.168854
$847$	6.04366	0.207662
$848$	−12.2621	−0.421083
$849$	59.0985	2.02825
$850$	−0.620042	−0.0212673
$851$	−1.67676	−0.0574786
$852$	17.2717	0.591718
$853$	−28.5213	−0.976551	−0.488276	−	0.872689i	$-0.662374\pi$
$853$	−28.5213	−0.976551	−0.488276	+	0.872689i	$0.662374\pi$
$854$	40.2148	1.37612
$855$	1.69318	0.0579054
$856$	12.0725	0.412631
$857$	−51.9724	−1.77534	−0.887671	−	0.460478i	$-0.847678\pi$
$857$	−51.9724	−1.77534	−0.887671	+	0.460478i	$0.847678\pi$
$858$	−10.4547	−0.356917
$859$	17.7424	0.605363	0.302681	−	0.953092i	$-0.402118\pi$
$859$	17.7424	0.605363	0.302681	+	0.953092i	$0.402118\pi$
$860$	10.5071	0.358290
$861$	59.1099	2.01446
$862$	11.6590	0.397106
$863$	−16.2492	−0.553129	−0.276564	−	0.960995i	$-0.589196\pi$
$863$	−16.2492	−0.553129	−0.276564	+	0.960995i	$0.589196\pi$
$864$	−25.8123	−0.878153
$865$	21.7793	0.740519
$866$	−14.3262	−0.486824
$867$	−32.6335	−1.10829
$868$	0.0348333	0.00118232
$869$	−16.6383	−0.564417
$870$	1.64409	0.0557399
$871$	0.407832	0.0138189
$872$	15.4457	0.523058
$873$	−5.46885	−0.185093
$874$	1.46603	0.0495892
$875$	−41.5289	−1.40393
$876$	−42.3601	−1.43122
$877$	33.8094	1.14166	0.570831	−	0.821068i	$-0.306621\pi$
$877$	33.8094	1.14166	0.570831	+	0.821068i	$0.306621\pi$
$878$	4.91268	0.165795
$879$	−12.4801	−0.420943
$880$	4.10651	0.138430
$881$	5.56211	0.187392	0.0936962	−	0.995601i	$-0.470132\pi$
$881$	5.56211	0.187392	0.0936962	+	0.995601i	$0.470132\pi$
$882$	5.00334	0.168471
$883$	−39.1935	−1.31897	−0.659484	−	0.751719i	$-0.729225\pi$
$883$	−39.1935	−1.31897	−0.659484	+	0.751719i	$0.729225\pi$
$884$	−0.850180	−0.0285946
$885$	−25.3081	−0.850723
$886$	28.2784	0.950031
$887$	−21.3202	−0.715861	−0.357931	−	0.933748i	$-0.616518\pi$
$887$	−21.3202	−0.715861	−0.357931	+	0.933748i	$0.616518\pi$
$888$	−8.12778	−0.272750
$889$	44.3446	1.48727
$890$	1.79207	0.0600702
$891$	32.7878	1.09843
$892$	−35.3318	−1.18300
$893$	−19.3556	−0.647711
$894$	−13.3648	−0.446985
$895$	−8.47587	−0.283317
$896$	42.0139	1.40359
$897$	−4.67860	−0.156214
$898$	9.51609	0.317556
$899$	−0.00576952	−0.000192424 0
$900$	3.77951	0.125984
$901$	−2.57634	−0.0858302
$902$	16.7621	0.558119
$903$	−47.5955	−1.58388
$904$	−6.28862	−0.209156
$905$	−16.4832	−0.547921
$906$	−17.1958	−0.571294
$907$	−12.2435	−0.406537	−0.203269	−	0.979123i	$-0.565156\pi$
$907$	−12.2435	−0.406537	−0.203269	+	0.979123i	$0.565156\pi$
$908$	13.0102	0.431758
$909$	−4.95944	−0.164494
$910$	8.48411	0.281246
$911$	52.8702	1.75167	0.875835	−	0.482611i	$-0.160312\pi$
$911$	52.8702	1.75167	0.875835	+	0.482611i	$0.160312\pi$
$912$	−4.40163	−0.145753
$913$	−14.2422	−0.471350
$914$	−8.29519	−0.274380
$915$	30.8189	1.01884
$916$	−21.9506	−0.725267
$917$	−30.3961	−1.00377
$918$	−0.757661	−0.0250065
$919$	−49.6021	−1.63622	−0.818112	−	0.575059i	$-0.804979\pi$
$919$	−49.6021	−1.63622	−0.818112	+	0.575059i	$0.804979\pi$
$920$	−2.96694	−0.0978170
$921$	24.5241	0.808095
$922$	−9.46919	−0.311851
$923$	−14.7625	−0.485914
$924$	−35.8832	−1.18047
$925$	−6.05360	−0.199041
$926$	19.4104	0.637864
$927$	−11.8117	−0.387946
$928$	−5.85100	−0.192068
$929$	−24.9510	−0.818617	−0.409309	−	0.912396i	$-0.634230\pi$
$929$	−24.9510	−0.818617	−0.409309	+	0.912396i	$0.634230\pi$
$930$	−0.00948562	−0.000311046 0
$931$	−19.7183	−0.646241
$932$	−18.7773	−0.615072
$933$	−58.2802	−1.90801
$934$	5.13763	0.168108
$935$	0.862800	0.0282166
$936$	−4.33730	−0.141769
$937$	27.8390	0.909460	0.454730	−	0.890629i	$-0.349736\pi$
$937$	27.8390	0.909460	0.454730	+	0.890629i	$0.349736\pi$
$938$	−0.497397	−0.0162406
$939$	25.1240	0.819891
$940$	16.6310	0.542445
$941$	23.5204	0.766742	0.383371	−	0.923595i	$-0.374763\pi$
$941$	23.5204	0.766742	0.383371	+	0.923595i	$0.374763\pi$
$942$	−3.48729	−0.113622
$943$	7.50127	0.244275
$944$	12.5827	0.409533
$945$	−21.2779	−0.692172
$946$	−13.4969	−0.438823
$947$	−24.8678	−0.808096	−0.404048	−	0.914738i	$-0.632397\pi$
$947$	−24.8678	−0.808096	−0.404048	+	0.914738i	$0.632397\pi$
$948$	−15.3237	−0.497690
$949$	36.2062	1.17530
$950$	5.29280	0.171721
$951$	17.2039	0.557874
$952$	2.44222	0.0791529
$953$	10.0494	0.325531	0.162766	−	0.986665i	$-0.447959\pi$
$953$	10.0494	0.325531	0.162766	+	0.986665i	$0.447959\pi$
$954$	−5.58031	−0.180669
$955$	14.4555	0.467769
$956$	12.2923	0.397561
$957$	5.94343	0.192124
$958$	24.7000	0.798022
$959$	30.1905	0.974903
$960$	−4.49364	−0.145032
$961$	−31.0000	−0.999999
$962$	2.94947	0.0950948
$963$	−3.40299	−0.109660
$964$	−16.4159	−0.528720
$965$	1.16606	0.0375367
$966$	5.70607	0.183590
$967$	−35.2339	−1.13305	−0.566524	−	0.824046i	$-0.691712\pi$
$967$	−35.2339	−1.13305	−0.566524	+	0.824046i	$0.691712\pi$
$968$	3.71771	0.119492
$969$	−0.924807	−0.0297091
$970$	6.58050	0.211287
$971$	4.97818	0.159758	0.0798788	−	0.996805i	$-0.474547\pi$
$971$	4.97818	0.159758	0.0798788	+	0.996805i	$0.474547\pi$
$972$	10.6672	0.342149
$973$	−52.4089	−1.68015
$974$	30.4889	0.976928
$975$	−16.8911	−0.540949
$976$	−15.3226	−0.490463
$977$	−10.8940	−0.348529	−0.174264	−	0.984699i	$-0.555755\pi$
$977$	−10.8940	−0.348529	−0.174264	+	0.984699i	$0.555755\pi$
$978$	−3.49316	−0.111699
$979$	6.47835	0.207049
$980$	16.9427	0.541214
$981$	−4.35383	−0.139007
$982$	−1.70105	−0.0542828
$983$	0.224404	0.00715737	0.00357868	−	0.999994i	$-0.498861\pi$
$983$	0.224404	0.00715737	0.00357868	+	0.999994i	$0.498861\pi$
$984$	36.3610	1.15915
$985$	23.6828	0.754597
$986$	−0.171743	−0.00546940
$987$	−75.3358	−2.39796
$988$	7.25731	0.230886
$989$	−6.04004	−0.192062
$990$	1.86881	0.0593948
$991$	−9.77464	−0.310502	−0.155251	−	0.987875i	$-0.549619\pi$
$991$	−9.77464	−0.310502	−0.155251	+	0.987875i	$0.549619\pi$
$992$	0.0337574	0.00107180
$993$	−37.8148	−1.20002
$994$	18.0045	0.571069
$995$	−15.4494	−0.489777
$996$	−13.1169	−0.415625
$997$	−58.5358	−1.85385	−0.926923	−	0.375252i	$-0.877556\pi$
$997$	−58.5358	−1.85385	−0.926923	+	0.375252i	$0.877556\pi$
$998$	5.38544	0.170473
$999$	−7.39721	−0.234037

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	667.2.a.b.1.9	✓	12
3.2	odd	2		6003.2.a.n.1.4		12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
667.2.a.b.1.9	✓	12	1.1	even	1	trivial
6003.2.a.n.1.4		12	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:	\( N \)	\(=\)	\( 667 = 23 \cdot 29 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	667.a (trivial)

\(f(q)\)	\(=\)	\(q+0.724122 q^{2} +1.92599 q^{3} -1.47565 q^{4} -1.17886 q^{5} +1.39465 q^{6} -4.09140 q^{7} -2.51679 q^{8} +0.709431 q^{9} +O(q^{10})\)	\(q+0.724122 q^{2} +1.92599 q^{3} -1.47565 q^{4} -1.17886 q^{5} +1.39465 q^{6} -4.09140 q^{7} -2.51679 q^{8} +0.709431 q^{9} -0.853636 q^{10} -3.08591 q^{11} -2.84208 q^{12} +2.42919 q^{13} -2.96267 q^{14} -2.27046 q^{15} +1.12883 q^{16} +0.237174 q^{17} +0.513714 q^{18} -2.02456 q^{19} +1.73958 q^{20} -7.87999 q^{21} -2.23457 q^{22} -1.00000 q^{23} -4.84731 q^{24} -3.61030 q^{25} +1.75903 q^{26} -4.41161 q^{27} +6.03746 q^{28} -1.00000 q^{29} -1.64409 q^{30} +0.00576952 q^{31} +5.85100 q^{32} -5.94343 q^{33} +0.171743 q^{34} +4.82317 q^{35} -1.04687 q^{36} +1.67676 q^{37} -1.46603 q^{38} +4.67860 q^{39} +2.96694 q^{40} -7.50127 q^{41} -5.70607 q^{42} +6.04004 q^{43} +4.55372 q^{44} -0.836317 q^{45} -0.724122 q^{46} +9.56040 q^{47} +2.17412 q^{48} +9.73954 q^{49} -2.61430 q^{50} +0.456794 q^{51} -3.58463 q^{52} -10.8627 q^{53} -3.19454 q^{54} +3.63784 q^{55} +10.2972 q^{56} -3.89928 q^{57} -0.724122 q^{58} +11.1467 q^{59} +3.35040 q^{60} -13.5738 q^{61} +0.00417784 q^{62} -2.90256 q^{63} +1.97917 q^{64} -2.86367 q^{65} -4.30376 q^{66} +0.167888 q^{67} -0.349985 q^{68} -1.92599 q^{69} +3.49256 q^{70} -6.07713 q^{71} -1.78549 q^{72} +14.9046 q^{73} +1.21418 q^{74} -6.95339 q^{75} +2.98754 q^{76} +12.6257 q^{77} +3.38787 q^{78} +5.39171 q^{79} -1.33073 q^{80} -10.6250 q^{81} -5.43183 q^{82} +4.61525 q^{83} +11.6281 q^{84} -0.279594 q^{85} +4.37373 q^{86} -1.92599 q^{87} +7.76659 q^{88} -2.09933 q^{89} -0.605595 q^{90} -9.93880 q^{91} +1.47565 q^{92} +0.0111120 q^{93} +6.92289 q^{94} +2.38667 q^{95} +11.2689 q^{96} -7.70879 q^{97} +7.05262 q^{98} -2.18924 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q - 3 q^{2} - 3 q^{3} + 11 q^{4} - 16 q^{5} - 2 q^{6} - 7 q^{7} - 9 q^{8} + 3 q^{9}+O(q^{10}) \) 12 * q - 3 * q^2 - 3 * q^3 + 11 * q^4 - 16 * q^5 - 2 * q^6 - 7 * q^7 - 9 * q^8 + 3 * q^9	\( 12 q - 3 q^{2} - 3 q^{3} + 11 q^{4} - 16 q^{5} - 2 q^{6} - 7 q^{7} - 9 q^{8} + 3 q^{9} - 6 q^{11} - 21 q^{12} - 15 q^{13} - 8 q^{14} + 6 q^{15} + 17 q^{16} - 18 q^{17} - 12 q^{18} - 6 q^{19} - 39 q^{20} - q^{21} - 5 q^{22} - 12 q^{23} + 4 q^{24} + 14 q^{25} - 3 q^{26} - 12 q^{27} - 19 q^{28} - 12 q^{29} - 11 q^{30} + 16 q^{31} - 21 q^{32} - 19 q^{33} - 7 q^{34} - 11 q^{35} - 13 q^{36} - q^{37} - 24 q^{38} + 6 q^{39} + 30 q^{40} + 3 q^{41} + 22 q^{42} - 23 q^{43} + 23 q^{44} - 22 q^{45} + 3 q^{46} - 35 q^{47} - 21 q^{48} + 3 q^{49} - 2 q^{50} - 34 q^{51} - 45 q^{53} + 55 q^{54} + 17 q^{55} - 17 q^{56} - 34 q^{57} + 3 q^{58} - 11 q^{59} + 93 q^{60} + 4 q^{61} - 7 q^{62} + q^{63} + 15 q^{64} + 5 q^{65} - 35 q^{66} - 19 q^{67} + q^{68} + 3 q^{69} + 14 q^{70} + 19 q^{71} + 4 q^{72} + 10 q^{73} - 15 q^{74} - 3 q^{75} - 4 q^{76} - 39 q^{77} + 16 q^{78} + 17 q^{79} - 90 q^{80} + 4 q^{81} - 3 q^{82} - 12 q^{83} + 42 q^{84} + 14 q^{85} + 17 q^{86} + 3 q^{87} - 2 q^{88} - 20 q^{89} + 65 q^{90} + 11 q^{91} - 11 q^{92} - 2 q^{93} + 13 q^{94} + 12 q^{95} + 14 q^{96} - 12 q^{97} + 75 q^{98} - 4 q^{99}+O(q^{100}) \) 12 * q - 3 * q^2 - 3 * q^3 + 11 * q^4 - 16 * q^5 - 2 * q^6 - 7 * q^7 - 9 * q^8 + 3 * q^9 - 6 * q^11 - 21 * q^12 - 15 * q^13 - 8 * q^14 + 6 * q^15 + 17 * q^16 - 18 * q^17 - 12 * q^18 - 6 * q^19 - 39 * q^20 - q^21 - 5 * q^22 - 12 * q^23 + 4 * q^24 + 14 * q^25 - 3 * q^26 - 12 * q^27 - 19 * q^28 - 12 * q^29 - 11 * q^30 + 16 * q^31 - 21 * q^32 - 19 * q^33 - 7 * q^34 - 11 * q^35 - 13 * q^36 - q^37 - 24 * q^38 + 6 * q^39 + 30 * q^40 + 3 * q^41 + 22 * q^42 - 23 * q^43 + 23 * q^44 - 22 * q^45 + 3 * q^46 - 35 * q^47 - 21 * q^48 + 3 * q^49 - 2 * q^50 - 34 * q^51 - 45 * q^53 + 55 * q^54 + 17 * q^55 - 17 * q^56 - 34 * q^57 + 3 * q^58 - 11 * q^59 + 93 * q^60 + 4 * q^61 - 7 * q^62 + q^63 + 15 * q^64 + 5 * q^65 - 35 * q^66 - 19 * q^67 + q^68 + 3 * q^69 + 14 * q^70 + 19 * q^71 + 4 * q^72 + 10 * q^73 - 15 * q^74 - 3 * q^75 - 4 * q^76 - 39 * q^77 + 16 * q^78 + 17 * q^79 - 90 * q^80 + 4 * q^81 - 3 * q^82 - 12 * q^83 + 42 * q^84 + 14 * q^85 + 17 * q^86 + 3 * q^87 - 2 * q^88 - 20 * q^89 + 65 * q^90 + 11 * q^91 - 11 * q^92 - 2 * q^93 + 13 * q^94 + 12 * q^95 + 14 * q^96 - 12 * q^97 + 75 * q^98 - 4 * q^99

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