LMFDB - Embedded newform 671.2.a.a.1.5

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [671,2,Mod(1,671)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(671, 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("671.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 671 = 11 \cdot 61 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	671.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:	$5.35796197563$
Analytic rank:	$1$
Dimension:	$5$
Coefficient field:	5.5.24217.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{5} - 5x^{3} - x^{2} + 3x + 1 $ x^5 - 5x^3 - x^2 + 3x + 1
Coefficient ring:	$\Z[a_1, a_2]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.5
Root			$-0.369680$ of defining polynomial
Character	$\chi$	$=$	671.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.33536 q^{2} -0.586497 q^{3} -0.216816 q^{4} +1.70504 q^{5} -0.783184 q^{6} -3.82358 q^{7} -2.96025 q^{8} -2.65602 q^{9} +O(q^{10})$	\(q+1.33536 q^{2} -0.586497 q^{3} -0.216816 q^{4} +1.70504 q^{5} -0.783184 q^{6} -3.82358 q^{7} -2.96025 q^{8} -2.65602 q^{9} +2.27684 q^{10} +1.00000 q^{11} +0.127162 q^{12} -1.41350 q^{13} -5.10585 q^{14} -1.00000 q^{15} -3.51936 q^{16} -2.70504 q^{17} -3.54674 q^{18} -2.25521 q^{19} -0.369680 q^{20} +2.24252 q^{21} +1.33536 q^{22} +2.60270 q^{23} +1.73617 q^{24} -2.09284 q^{25} -1.88753 q^{26} +3.31724 q^{27} +0.829015 q^{28} -5.40314 q^{29} -1.33536 q^{30} +1.94062 q^{31} +1.22088 q^{32} -0.586497 q^{33} -3.61220 q^{34} -6.51936 q^{35} +0.575869 q^{36} +2.07879 q^{37} -3.01151 q^{38} +0.829015 q^{39} -5.04734 q^{40} -1.68627 q^{41} +2.99457 q^{42} +4.50699 q^{43} -0.216816 q^{44} -4.52862 q^{45} +3.47554 q^{46} -2.55218 q^{47} +2.06409 q^{48} +7.61978 q^{49} -2.79469 q^{50} +1.58650 q^{51} +0.306471 q^{52} -5.43865 q^{53} +4.42970 q^{54} +1.70504 q^{55} +11.3187 q^{56} +1.32267 q^{57} -7.21513 q^{58} +4.50124 q^{59} +0.216816 q^{60} +1.00000 q^{61} +2.59143 q^{62} +10.1555 q^{63} +8.66904 q^{64} -2.41008 q^{65} -0.783184 q^{66} +1.34599 q^{67} +0.586497 q^{68} -1.52647 q^{69} -8.70568 q^{70} -2.13067 q^{71} +7.86248 q^{72} -12.4393 q^{73} +2.77593 q^{74} +1.22744 q^{75} +0.488966 q^{76} -3.82358 q^{77} +1.10703 q^{78} -3.83244 q^{79} -6.00064 q^{80} +6.02252 q^{81} -2.25178 q^{82} -7.05810 q^{83} -0.486215 q^{84} -4.61220 q^{85} +6.01845 q^{86} +3.16892 q^{87} -2.96025 q^{88} -13.7435 q^{89} -6.04734 q^{90} +5.40465 q^{91} -0.564307 q^{92} -1.13817 q^{93} -3.40807 q^{94} -3.84522 q^{95} -0.716045 q^{96} +7.63215 q^{97} +10.1751 q^{98} -2.65602 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 5 q - 2 q^{2} - 2 q^{5} - 5 q^{6} - q^{7} - 6 q^{8} - 3 q^{9}+O(q^{10}) $ 5 * q - 2 * q^2 - 2 * q^5 - 5 * q^6 - q^7 - 6 * q^8 - 3 * q^9	$ 5 q - 2 q^{2} - 2 q^{5} - 5 q^{6} - q^{7} - 6 q^{8} - 3 q^{9} + 5 q^{10} + 5 q^{11} + 12 q^{12} - 10 q^{13} - 3 q^{14} - 5 q^{15} + 2 q^{16} - 3 q^{17} - 6 q^{18} - 13 q^{19} - 2 q^{21} - 2 q^{22} - 12 q^{24} - 15 q^{25} + 9 q^{26} - 9 q^{27} - 12 q^{28} - 7 q^{29} + 2 q^{30} - 13 q^{31} + q^{32} - 3 q^{34} - 13 q^{35} + 3 q^{36} - 6 q^{37} + 9 q^{38} - 12 q^{39} - 5 q^{40} - 9 q^{41} + 13 q^{42} + 2 q^{43} + 6 q^{45} - 7 q^{46} - 3 q^{47} + q^{48} - 6 q^{49} + 9 q^{50} + 5 q^{51} - 12 q^{52} + 3 q^{53} + 15 q^{54} - 2 q^{55} + 28 q^{56} - 17 q^{57} - 15 q^{58} - 14 q^{59} + 5 q^{61} + 31 q^{62} + 6 q^{64} + 9 q^{65} - 5 q^{66} - 5 q^{67} - 10 q^{69} - 5 q^{70} + 3 q^{71} + 5 q^{72} - 4 q^{73} + 2 q^{74} + 2 q^{75} - 19 q^{76} - q^{77} + 22 q^{78} - 27 q^{79} - 2 q^{80} + q^{81} + 11 q^{82} - 3 q^{83} - 15 q^{84} - 8 q^{85} + 5 q^{86} + 14 q^{87} - 6 q^{88} - 12 q^{89} - 10 q^{90} + 4 q^{91} + 13 q^{92} - 12 q^{93} - 18 q^{94} + 7 q^{95} + 12 q^{96} - 5 q^{97} + 14 q^{98} - 3 q^{99}+O(q^{100}) $ 5 * q - 2 * q^2 - 2 * q^5 - 5 * q^6 - q^7 - 6 * q^8 - 3 * q^9 + 5 * q^10 + 5 * q^11 + 12 * q^12 - 10 * q^13 - 3 * q^14 - 5 * q^15 + 2 * q^16 - 3 * q^17 - 6 * q^18 - 13 * q^19 - 2 * q^21 - 2 * q^22 - 12 * q^24 - 15 * q^25 + 9 * q^26 - 9 * q^27 - 12 * q^28 - 7 * q^29 + 2 * q^30 - 13 * q^31 + q^32 - 3 * q^34 - 13 * q^35 + 3 * q^36 - 6 * q^37 + 9 * q^38 - 12 * q^39 - 5 * q^40 - 9 * q^41 + 13 * q^42 + 2 * q^43 + 6 * q^45 - 7 * q^46 - 3 * q^47 + q^48 - 6 * q^49 + 9 * q^50 + 5 * q^51 - 12 * q^52 + 3 * q^53 + 15 * q^54 - 2 * q^55 + 28 * q^56 - 17 * q^57 - 15 * q^58 - 14 * q^59 + 5 * q^61 + 31 * q^62 + 6 * q^64 + 9 * q^65 - 5 * q^66 - 5 * q^67 - 10 * q^69 - 5 * q^70 + 3 * q^71 + 5 * q^72 - 4 * q^73 + 2 * q^74 + 2 * q^75 - 19 * q^76 - q^77 + 22 * q^78 - 27 * q^79 - 2 * q^80 + q^81 + 11 * q^82 - 3 * q^83 - 15 * q^84 - 8 * q^85 + 5 * q^86 + 14 * q^87 - 6 * q^88 - 12 * q^89 - 10 * q^90 + 4 * q^91 + 13 * q^92 - 12 * q^93 - 18 * q^94 + 7 * q^95 + 12 * q^96 - 5 * q^97 + 14 * q^98 - 3 * q^99

Display 100 coefficients 10 coefficients

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$	$a_n / n^{(k-1)/2}$	$ \alpha_n $			$ \theta_n $
$p$	$a_p$	$a_p / p^{(k-1)/2}$	$ \alpha_p$			$ \theta_p $

$2$	1.33536	0.944241	0.472121	−	0.881534i	$-0.343489\pi$
$2$	1.33536	0.944241	0.472121	+	0.881534i	$0.343489\pi$
$3$	−0.586497	−0.338614	−0.169307	−	0.985563i	$-0.554153\pi$
$3$	−0.586497	−0.338614	−0.169307	+	0.985563i	$0.554153\pi$
$4$	−0.216816	−0.108408
$5$	1.70504	0.762517	0.381258	−	0.924469i	$-0.375491\pi$
$5$	1.70504	0.762517	0.381258	+	0.924469i	$0.375491\pi$
$6$	−0.783184	−0.319733
$7$	−3.82358	−1.44518	−0.722589	−	0.691278i	$-0.757048\pi$
$7$	−3.82358	−1.44518	−0.722589	+	0.691278i	$0.757048\pi$
$8$	−2.96025	−1.04660
$9$	−2.65602	−0.885341
$10$	2.27684	0.720000
$11$	1.00000	0.301511
$11$	1.00000	0.301511
$12$	0.127162	0.0367085
$13$	−1.41350	−0.392035	−0.196018	−	0.980600i	$-0.562801\pi$
$13$	−1.41350	−0.392035	−0.196018	+	0.980600i	$0.562801\pi$
$14$	−5.10585	−1.36460
$15$	−1.00000	−0.258199
$16$	−3.51936	−0.879840
$17$	−2.70504	−0.656068	−0.328034	−	0.944666i	$-0.606386\pi$
$17$	−2.70504	−0.656068	−0.328034	+	0.944666i	$0.606386\pi$
$18$	−3.54674	−0.835975
$19$	−2.25521	−0.517380	−0.258690	−	0.965960i	$-0.583291\pi$
$19$	−2.25521	−0.517380	−0.258690	+	0.965960i	$0.583291\pi$
$20$	−0.369680	−0.0826630
$21$	2.24252	0.489358
$22$	1.33536	0.284699
$23$	2.60270	0.542700	0.271350	−	0.962481i	$-0.412530\pi$
$23$	2.60270	0.542700	0.271350	+	0.962481i	$0.412530\pi$
$24$	1.73617	0.354395
$25$	−2.09284	−0.418568
$26$	−1.88753	−0.370176
$27$	3.31724	0.638403
$28$	0.829015	0.156669
$29$	−5.40314	−1.00334	−0.501669	−	0.865060i	$-0.667280\pi$
$29$	−5.40314	−1.00334	−0.501669	+	0.865060i	$0.667280\pi$
$30$	−1.33536	−0.243802
$31$	1.94062	0.348546	0.174273	−	0.984697i	$-0.444243\pi$
$31$	1.94062	0.348546	0.174273	+	0.984697i	$0.444243\pi$
$32$	1.22088	0.215824
$33$	−0.586497	−0.102096
$34$	−3.61220	−0.619487
$35$	−6.51936	−1.10197
$36$	0.575869	0.0959781
$37$	2.07879	0.341751	0.170875	−	0.985293i	$-0.445340\pi$
$37$	2.07879	0.341751	0.170875	+	0.985293i	$0.445340\pi$
$38$	−3.01151	−0.488531
$39$	0.829015	0.132749
$40$	−5.04734	−0.798054
$41$	−1.68627	−0.263352	−0.131676	−	0.991293i	$-0.542036\pi$
$41$	−1.68627	−0.263352	−0.131676	+	0.991293i	$0.542036\pi$
$42$	2.99457	0.462072
$43$	4.50699	0.687309	0.343655	−	0.939096i	$-0.388335\pi$
$43$	4.50699	0.687309	0.343655	+	0.939096i	$0.388335\pi$
$44$	−0.216816	−0.0326863
$45$	−4.52862	−0.675087
$46$	3.47554	0.512440
$47$	−2.55218	−0.372273	−0.186137	−	0.982524i	$-0.559597\pi$
$47$	−2.55218	−0.372273	−0.186137	+	0.982524i	$0.559597\pi$
$48$	2.06409	0.297926
$49$	7.61978	1.08854
$50$	−2.79469	−0.395229
$51$	1.58650	0.222154
$52$	0.306471	0.0424998
$53$	−5.43865	−0.747056	−0.373528	−	0.927619i	$-0.621852\pi$
$53$	−5.43865	−0.747056	−0.373528	+	0.927619i	$0.621852\pi$
$54$	4.42970	0.602806
$55$	1.70504	0.229907
$56$	11.3187	1.51253
$57$	1.32267	0.175192
$58$	−7.21513	−0.947394
$59$	4.50124	0.586011	0.293006	−	0.956111i	$-0.405345\pi$
$59$	4.50124	0.586011	0.293006	+	0.956111i	$0.405345\pi$
$60$	0.216816	0.0279909
$61$	1.00000	0.128037
$61$	1.00000	0.128037
$62$	2.59143	0.329111
$63$	10.1555	1.27947
$64$	8.66904	1.08363
$65$	−2.41008	−0.298933
$66$	−0.783184	−0.0964032
$67$	1.34599	0.164438	0.0822192	−	0.996614i	$-0.473799\pi$
$67$	1.34599	0.164438	0.0822192	+	0.996614i	$0.473799\pi$
$68$	0.586497	0.0711232
$69$	−1.52647	−0.183766
$70$	−8.70568	−1.04053
$71$	−2.13067	−0.252865	−0.126432	−	0.991975i	$-0.540353\pi$
$71$	−2.13067	−0.252865	−0.126432	+	0.991975i	$0.540353\pi$
$72$	7.86248	0.926602
$73$	−12.4393	−1.45591	−0.727955	−	0.685625i	$-0.759529\pi$
$73$	−12.4393	−1.45591	−0.727955	+	0.685625i	$0.759529\pi$
$74$	2.77593	0.322695
$75$	1.22744	0.141733
$76$	0.488966	0.0560882
$77$	−3.82358	−0.435738
$78$	1.10703	0.125347
$79$	−3.83244	−0.431183	−0.215592	−	0.976484i	$-0.569168\pi$
$79$	−3.83244	−0.431183	−0.215592	+	0.976484i	$0.569168\pi$
$80$	−6.00064	−0.670892
$81$	6.02252	0.669168
$82$	−2.25178	−0.248668
$83$	−7.05810	−0.774727	−0.387364	−	0.921927i	$-0.626614\pi$
$83$	−7.05810	−0.774727	−0.387364	+	0.921927i	$0.626614\pi$
$84$	−0.486215	−0.0530504
$85$	−4.61220	−0.500263
$86$	6.01845	0.648986
$87$	3.16892	0.339744
$88$	−2.96025	−0.315563
$89$	−13.7435	−1.45681	−0.728405	−	0.685147i	$-0.759738\pi$
$89$	−13.7435	−1.45681	−0.728405	+	0.685147i	$0.759738\pi$
$90$	−6.04734	−0.637445
$91$	5.40465	0.566561
$92$	−0.564307	−0.0588331
$93$	−1.13817	−0.118022
$94$	−3.40807	−0.351516
$95$	−3.84522	−0.394511
$96$	−0.716045	−0.0730810
$97$	7.63215	0.774927	0.387464	−	0.921885i	$-0.373351\pi$
$97$	7.63215	0.774927	0.387464	+	0.921885i	$0.373351\pi$
$98$	10.1751	1.02784
$99$	−2.65602	−0.266940
$100$	0.453762	0.0453762
$101$	0.540109	0.0537429	0.0268714	−	0.999639i	$-0.491446\pi$
$101$	0.540109	0.0537429	0.0268714	+	0.999639i	$0.491446\pi$
$102$	2.11854	0.209767
$103$	14.3630	1.41523	0.707613	−	0.706600i	$-0.249772\pi$
$103$	14.3630	1.41523	0.707613	+	0.706600i	$0.249772\pi$
$104$	4.18432	0.410306
$105$	3.82358	0.373143
$106$	−7.26255	−0.705401
$107$	−2.64826	−0.256017	−0.128009	−	0.991773i	$-0.540859\pi$
$107$	−2.64826	−0.256017	−0.128009	+	0.991773i	$0.540859\pi$
$108$	−0.719231	−0.0692081
$109$	−12.8191	−1.22785	−0.613923	−	0.789366i	$-0.710410\pi$
$109$	−12.8191	−1.22785	−0.613923	+	0.789366i	$0.710410\pi$
$110$	2.27684	0.217088
$111$	−1.21920	−0.115722
$112$	13.4566	1.27152
$113$	11.2624	1.05947	0.529737	−	0.848162i	$-0.322290\pi$
$113$	11.2624	1.05947	0.529737	+	0.848162i	$0.322290\pi$
$114$	1.76624	0.165424
$115$	4.43770	0.413818
$116$	1.17149	0.108770
$117$	3.75430	0.347085
$118$	6.01077	0.553336
$119$	10.3429	0.948136
$120$	2.96025	0.270232
$121$	1.00000	0.0909091
$122$	1.33536	0.120898
$123$	0.988994	0.0891746
$124$	−0.420758	−0.0377852
$125$	−12.0936	−1.08168
$126$	13.5613	1.20813
$127$	21.5844	1.91531	0.957654	−	0.287922i	$-0.0929645\pi$
$127$	21.5844	1.91531	0.957654	+	0.287922i	$0.0929645\pi$
$128$	9.13451	0.807384
$129$	−2.64333	−0.232733
$130$	−3.21832	−0.282265
$131$	−0.639961	−0.0559136	−0.0279568	−	0.999609i	$-0.508900\pi$
$131$	−0.639961	−0.0559136	−0.0279568	+	0.999609i	$0.508900\pi$
$132$	0.127162	0.0110680
$133$	8.62297	0.747706
$134$	1.79738	0.155270
$135$	5.65602	0.486793
$136$	8.00758	0.686644
$137$	12.9479	1.10621	0.553106	−	0.833111i	$-0.313442\pi$
$137$	12.9479	1.10621	0.553106	+	0.833111i	$0.313442\pi$
$138$	−2.03839	−0.173519
$139$	6.69742	0.568068	0.284034	−	0.958814i	$-0.408327\pi$
$139$	6.69742	0.568068	0.284034	+	0.958814i	$0.408327\pi$
$140$	1.41350	0.119463
$141$	1.49684	0.126057
$142$	−2.84522	−0.238765
$143$	−1.41350	−0.118203
$144$	9.34749	0.778958
$145$	−9.21257	−0.765062
$146$	−16.6109	−1.37473
$147$	−4.46898	−0.368595
$148$	−0.450715	−0.0370486
$149$	−9.11935	−0.747086	−0.373543	−	0.927613i	$-0.621857\pi$
$149$	−9.11935	−0.747086	−0.373543	+	0.927613i	$0.621857\pi$
$150$	1.63908	0.133830
$151$	1.89341	0.154084	0.0770418	−	0.997028i	$-0.475453\pi$
$151$	1.89341	0.154084	0.0770418	+	0.997028i	$0.475453\pi$
$152$	6.67596	0.541492
$153$	7.18464	0.580844
$154$	−5.10585	−0.411441
$155$	3.30883	0.265772
$156$	−0.179744	−0.0143910
$157$	−18.5119	−1.47741	−0.738705	−	0.674029i	$-0.764562\pi$
$157$	−18.5119	−1.47741	−0.738705	+	0.674029i	$0.764562\pi$
$158$	−5.11768	−0.407141
$159$	3.18975	0.252964
$160$	2.08166	0.164569
$161$	−9.95163	−0.784298
$162$	8.04222	0.631857
$163$	14.4961	1.13542	0.567712	−	0.823227i	$-0.307829\pi$
$163$	14.4961	1.13542	0.567712	+	0.823227i	$0.307829\pi$
$164$	0.365612	0.0285495
$165$	−1.00000	−0.0778499
$166$	−9.42510	−0.731530
$167$	−11.4744	−0.887919	−0.443959	−	0.896047i	$-0.646427\pi$
$167$	−11.4744	−0.887919	−0.443959	+	0.896047i	$0.646427\pi$
$168$	−6.63841	−0.512164
$169$	−11.0020	−0.846308
$170$	−6.15894	−0.472369
$171$	5.98988	0.458057
$172$	−0.977189	−0.0745099
$173$	21.0366	1.59938	0.799690	−	0.600413i	$-0.204997\pi$
$173$	21.0366	1.59938	0.799690	+	0.600413i	$0.204997\pi$
$174$	4.23165	0.320801
$175$	8.00215	0.604906
$176$	−3.51936	−0.265282
$177$	−2.63996	−0.198432
$178$	−18.3525	−1.37558
$179$	−15.9191	−1.18985	−0.594924	−	0.803782i	$-0.702818\pi$
$179$	−15.9191	−1.18985	−0.594924	+	0.803782i	$0.702818\pi$
$180$	0.981879	0.0731849
$181$	−0.154850	−0.0115099	−0.00575497	−	0.999983i	$-0.501832\pi$
$181$	−0.154850	−0.0115099	−0.00575497	+	0.999983i	$0.501832\pi$
$182$	7.21714	0.534970
$183$	−0.586497	−0.0433551
$184$	−7.70462	−0.567992
$185$	3.54442	0.260591
$186$	−1.51986	−0.111442
$187$	−2.70504	−0.197812
$188$	0.553353	0.0403574
$189$	−12.6837	−0.922606
$190$	−5.13474	−0.372513
$191$	−12.4405	−0.900165	−0.450083	−	0.892987i	$-0.648605\pi$
$191$	−12.4405	−0.900165	−0.450083	+	0.892987i	$0.648605\pi$
$192$	−5.08436	−0.366932
$193$	−10.9260	−0.786470	−0.393235	−	0.919438i	$-0.628644\pi$
$193$	−10.9260	−0.786470	−0.393235	+	0.919438i	$0.628644\pi$
$194$	10.1917	0.731719
$195$	1.41350	0.101223
$196$	−1.65209	−0.118007
$197$	−13.4945	−0.961441	−0.480720	−	0.876874i	$-0.659625\pi$
$197$	−13.4945	−0.961441	−0.480720	+	0.876874i	$0.659625\pi$
$198$	−3.54674	−0.252056
$199$	−10.3413	−0.733074	−0.366537	−	0.930403i	$-0.619457\pi$
$199$	−10.3413	−0.733074	−0.366537	+	0.930403i	$0.619457\pi$
$200$	6.19532	0.438075
$201$	−0.789417	−0.0556812
$202$	0.721240	0.0507463
$203$	20.6594	1.45000
$204$	−0.343978	−0.0240833
$205$	−2.87516	−0.200810
$206$	19.1797	1.33631
$207$	−6.91282	−0.480474
$208$	4.97462	0.344928
$209$	−2.25521	−0.155996
$210$	5.10585	0.352337
$211$	−19.4268	−1.33739	−0.668697	−	0.743535i	$-0.733148\pi$
$211$	−19.4268	−1.33739	−0.668697	+	0.743535i	$0.733148\pi$
$212$	1.17919	0.0809870
$213$	1.24963	0.0856235
$214$	−3.53638	−0.241742
$215$	7.68459	0.524085
$216$	−9.81984	−0.668155
$217$	−7.42012	−0.503711
$218$	−17.1181	−1.15938
$219$	7.29560	0.492991
$220$	−0.369680	−0.0249238
$221$	3.82358	0.257202
$222$	−1.62807	−0.109269
$223$	−18.3560	−1.22921	−0.614603	−	0.788837i	$-0.710684\pi$
$223$	−18.3560	−1.22921	−0.614603	+	0.788837i	$0.710684\pi$
$224$	−4.66815	−0.311904
$225$	5.55863	0.370575
$226$	15.0393	1.00040
$227$	−7.69300	−0.510602	−0.255301	−	0.966862i	$-0.582175\pi$
$227$	−7.69300	−0.510602	−0.255301	+	0.966862i	$0.582175\pi$
$228$	−0.286777	−0.0189923
$229$	−23.2490	−1.53634	−0.768169	−	0.640247i	$-0.778832\pi$
$229$	−23.2490	−1.53634	−0.768169	+	0.640247i	$0.778832\pi$
$230$	5.92592	0.390744
$231$	2.24252	0.147547
$232$	15.9946	1.05010
$233$	−14.1638	−0.927898	−0.463949	−	0.885862i	$-0.653568\pi$
$233$	−14.1638	−0.927898	−0.463949	+	0.885862i	$0.653568\pi$
$234$	5.01333	0.327732
$235$	−4.35156	−0.283864
$236$	−0.975942	−0.0635284
$237$	2.24771	0.146005
$238$	13.8115	0.895269
$239$	18.0080	1.16484	0.582422	−	0.812887i	$-0.302105\pi$
$239$	18.0080	1.16484	0.582422	+	0.812887i	$0.302105\pi$
$240$	3.51936	0.227174
$241$	18.1562	1.16955	0.584773	−	0.811197i	$-0.301183\pi$
$241$	18.1562	1.16955	0.584773	+	0.811197i	$0.301183\pi$
$242$	1.33536	0.0858401
$243$	−13.4839	−0.864993
$244$	−0.216816	−0.0138802
$245$	12.9920	0.830030
$246$	1.32066	0.0842024
$247$	3.18774	0.202831
$248$	−5.74471	−0.364790
$249$	4.13955	0.262334
$250$	−16.1493	−1.02137
$251$	2.13114	0.134517	0.0672583	−	0.997736i	$-0.478575\pi$
$251$	2.13114	0.134517	0.0672583	+	0.997736i	$0.478575\pi$
$252$	−2.20188	−0.138706
$253$	2.60270	0.163630
$254$	28.8229	1.80851
$255$	2.70504	0.169396
$256$	−5.14023	−0.321264
$257$	5.50360	0.343305	0.171653	−	0.985158i	$-0.445089\pi$
$257$	5.50360	0.343305	0.171653	+	0.985158i	$0.445089\pi$
$258$	−3.52980	−0.219756
$259$	−7.94842	−0.493891
$260$	0.522544	0.0324068
$261$	14.3509	0.888296
$262$	−0.854577	−0.0527960
$263$	−8.52076	−0.525413	−0.262706	−	0.964876i	$-0.584615\pi$
$263$	−8.52076	−0.525413	−0.262706	+	0.964876i	$0.584615\pi$
$264$	1.73617	0.106854
$265$	−9.27311	−0.569643
$266$	11.5148	0.706015
$267$	8.06053	0.493296
$268$	−0.291832	−0.0178265
$269$	−6.75644	−0.411948	−0.205974	−	0.978558i	$-0.566036\pi$
$269$	−6.75644	−0.411948	−0.205974	+	0.978558i	$0.566036\pi$
$270$	7.55282	0.459650
$271$	17.8835	1.08635	0.543174	−	0.839620i	$-0.317223\pi$
$271$	17.8835	1.08635	0.543174	+	0.839620i	$0.317223\pi$
$272$	9.52000	0.577235
$273$	−3.16981	−0.191845
$274$	17.2901	1.04453
$275$	−2.09284	−0.126203
$276$	0.330964	0.0199217
$277$	−19.4528	−1.16881	−0.584403	−	0.811464i	$-0.698671\pi$
$277$	−19.4528	−1.16881	−0.584403	+	0.811464i	$0.698671\pi$
$278$	8.94346	0.536393
$279$	−5.15433	−0.308582
$280$	19.2989	1.15333
$281$	4.87363	0.290736	0.145368	−	0.989378i	$-0.453563\pi$
$281$	4.87363	0.290736	0.145368	+	0.989378i	$0.453563\pi$
$282$	1.99882	0.119028
$283$	−11.7696	−0.699631	−0.349815	−	0.936819i	$-0.613756\pi$
$283$	−11.7696	−0.699631	−0.349815	+	0.936819i	$0.613756\pi$
$284$	0.461965	0.0274126
$285$	2.25521	0.133587
$286$	−1.88753	−0.111612
$287$	6.44761	0.380590
$288$	−3.24270	−0.191078
$289$	−9.68276	−0.569574
$290$	−12.3021	−0.722403
$291$	−4.47623	−0.262401
$292$	2.69704	0.157832
$293$	6.94596	0.405787	0.202894	−	0.979201i	$-0.434965\pi$
$293$	6.94596	0.405787	0.202894	+	0.979201i	$0.434965\pi$
$294$	−5.96769	−0.348043
$295$	7.67479	0.446843
$296$	−6.15372	−0.357678
$297$	3.31724	0.192486
$298$	−12.1776	−0.705430
$299$	−3.67892	−0.212757
$300$	−0.266130	−0.0153650
$301$	−17.2328	−0.993284
$302$	2.52838	0.145492
$303$	−0.316772	−0.0181981
$304$	7.93688	0.455211
$305$	1.70504	0.0976303
$306$	9.59408	0.548457
$307$	−11.6737	−0.666256	−0.333128	−	0.942882i	$-0.608104\pi$
$307$	−11.6737	−0.666256	−0.333128	+	0.942882i	$0.608104\pi$
$308$	0.829015	0.0472375
$309$	−8.42384	−0.479215
$310$	4.41848	0.250953
$311$	−1.00838	−0.0571797	−0.0285899	−	0.999591i	$-0.509102\pi$
$311$	−1.00838	−0.0571797	−0.0285899	+	0.999591i	$0.509102\pi$
$312$	−2.45409	−0.138935
$313$	2.72938	0.154274	0.0771369	−	0.997021i	$-0.475422\pi$
$313$	2.72938	0.154274	0.0771369	+	0.997021i	$0.475422\pi$
$314$	−24.7200	−1.39503
$315$	17.3156	0.975621
$316$	0.830935	0.0467438
$317$	−16.6058	−0.932676	−0.466338	−	0.884607i	$-0.654427\pi$
$317$	−16.6058	−0.932676	−0.466338	+	0.884607i	$0.654427\pi$
$318$	4.25946	0.238859
$319$	−5.40314	−0.302518
$320$	14.7810	0.826286
$321$	1.55320	0.0866910
$322$	−13.2890	−0.740567
$323$	6.10042	0.339437
$324$	−1.30578	−0.0725433
$325$	2.95824	0.164093
$326$	19.3575	1.07211
$327$	7.51836	0.415766
$328$	4.99179	0.275625
$329$	9.75845	0.538001
$330$	−1.33536	−0.0735091
$331$	−20.5759	−1.13095	−0.565476	−	0.824765i	$-0.691307\pi$
$331$	−20.5759	−1.13095	−0.565476	+	0.824765i	$0.691307\pi$
$332$	1.53031	0.0839868
$333$	−5.52131	−0.302566
$334$	−15.3225	−0.838410
$335$	2.29496	0.125387
$336$	−7.89222	−0.430556
$337$	−18.6890	−1.01806	−0.509028	−	0.860750i	$-0.669995\pi$
$337$	−18.6890	−1.01806	−0.509028	+	0.860750i	$0.669995\pi$
$338$	−14.6916	−0.799119
$339$	−6.60534	−0.358753
$340$	1.00000	0.0542326
$341$	1.94062	0.105091
$342$	7.99864	0.432517
$343$	−2.36978	−0.127956
$344$	−13.3418	−0.719341
$345$	−2.60270	−0.140125
$346$	28.0914	1.51020
$347$	−2.11153	−0.113353	−0.0566765	−	0.998393i	$-0.518050\pi$
$347$	−2.11153	−0.113353	−0.0566765	+	0.998393i	$0.518050\pi$
$348$	−0.687075	−0.0368311
$349$	−21.3375	−1.14217	−0.571084	−	0.820891i	$-0.693477\pi$
$349$	−21.3375	−1.14217	−0.571084	+	0.820891i	$0.693477\pi$
$350$	10.6857	0.571177
$351$	−4.68893	−0.250276
$352$	1.22088	0.0650734
$353$	23.1273	1.23094	0.615471	−	0.788159i	$-0.288966\pi$
$353$	23.1273	1.23094	0.615471	+	0.788159i	$0.288966\pi$
$354$	−3.52530	−0.187367
$355$	−3.63288	−0.192813
$356$	2.97982	0.157930
$357$	−6.06610	−0.321052
$358$	−21.2577	−1.12350
$359$	5.99727	0.316524	0.158262	−	0.987397i	$-0.449411\pi$
$359$	5.99727	0.316524	0.158262	+	0.987397i	$0.449411\pi$
$360$	13.4058	0.706549
$361$	−13.9140	−0.732318
$362$	−0.206781	−0.0108682
$363$	−0.586497	−0.0307831
$364$	−1.17182	−0.0614198
$365$	−21.2095	−1.11016
$366$	−0.783184	−0.0409377
$367$	15.5421	0.811292	0.405646	−	0.914030i	$-0.367047\pi$
$367$	15.5421	0.811292	0.405646	+	0.914030i	$0.367047\pi$
$368$	−9.15982	−0.477489
$369$	4.47878	0.233156
$370$	4.73307	0.246060
$371$	20.7951	1.07963
$372$	0.246773	0.0127946
$373$	32.9020	1.70360	0.851800	−	0.523868i	$-0.175511\pi$
$373$	32.9020	1.70360	0.851800	+	0.523868i	$0.175511\pi$
$374$	−3.61220	−0.186782
$375$	7.09284	0.366273
$376$	7.55507	0.389623
$377$	7.63736	0.393344
$378$	−16.9373	−0.871163
$379$	−16.2472	−0.834561	−0.417281	−	0.908778i	$-0.637017\pi$
$379$	−16.2472	−0.834561	−0.417281	+	0.908778i	$0.637017\pi$
$380$	0.833706	0.0427682
$381$	−12.6592	−0.648550
$382$	−16.6126	−0.849973
$383$	31.4959	1.60936	0.804682	−	0.593706i	$-0.202336\pi$
$383$	31.4959	1.60936	0.804682	+	0.593706i	$0.202336\pi$
$384$	−5.35736	−0.273391
$385$	−6.51936	−0.332257
$386$	−14.5901	−0.742618
$387$	−11.9707	−0.608503
$388$	−1.65477	−0.0840085
$389$	39.1814	1.98658	0.993289	−	0.115662i	$-0.0368990\pi$
$389$	39.1814	1.98658	0.993289	+	0.115662i	$0.0368990\pi$
$390$	1.88753	0.0955790
$391$	−7.04040	−0.356048
$392$	−22.5564	−1.13927
$393$	0.375335	0.0189331
$394$	−18.0200	−0.907832
$395$	−6.53446	−0.328784
$396$	0.575869	0.0289385
$397$	22.2329	1.11584	0.557920	−	0.829895i	$-0.311600\pi$
$397$	22.2329	1.11584	0.557920	+	0.829895i	$0.311600\pi$
$398$	−13.8093	−0.692199
$399$	−5.05734	−0.253184
$400$	7.36546	0.368273
$401$	−21.6821	−1.08275	−0.541377	−	0.840780i	$-0.682097\pi$
$401$	−21.6821	−1.08275	−0.541377	+	0.840780i	$0.682097\pi$
$402$	−1.05415	−0.0525765
$403$	−2.74307	−0.136642
$404$	−0.117105	−0.00582617
$405$	10.2686	0.510252
$406$	27.5877	1.36915
$407$	2.07879	0.103042
$408$	−4.69642	−0.232507
$409$	−31.4770	−1.55644	−0.778218	−	0.627994i	$-0.783876\pi$
$409$	−31.4770	−1.55644	−0.778218	+	0.627994i	$0.783876\pi$
$410$	−3.83938	−0.189613
$411$	−7.59389	−0.374579
$412$	−3.11413	−0.153422
$413$	−17.2108	−0.846891
$414$	−9.23110	−0.453684
$415$	−12.0343	−0.590743
$416$	−1.72572	−0.0846106
$417$	−3.92801	−0.192356
$418$	−3.01151	−0.147298
$419$	10.2586	0.501167	0.250583	−	0.968095i	$-0.419378\pi$
$419$	10.2586	0.501167	0.250583	+	0.968095i	$0.419378\pi$
$420$	−0.829015	−0.0404518
$421$	15.1615	0.738928	0.369464	−	0.929245i	$-0.379541\pi$
$421$	15.1615	0.738928	0.369464	+	0.929245i	$0.379541\pi$
$422$	−25.9417	−1.26282
$423$	6.77863	0.329588
$424$	16.0997	0.781872
$425$	5.66122	0.274609
$426$	1.66871	0.0808492
$427$	−3.82358	−0.185036
$428$	0.574187	0.0277544
$429$	0.829015	0.0400252
$430$	10.2617	0.494863
$431$	11.3162	0.545081	0.272541	−	0.962144i	$-0.412136\pi$
$431$	11.3162	0.545081	0.272541	+	0.962144i	$0.412136\pi$
$432$	−11.6745	−0.561692
$433$	23.5749	1.13294	0.566469	−	0.824083i	$-0.308309\pi$
$433$	23.5749	1.13294	0.566469	+	0.824083i	$0.308309\pi$
$434$	−9.90853	−0.475625
$435$	5.40314	0.259061
$436$	2.77939	0.133109
$437$	−5.86962	−0.280782
$438$	9.74225	0.465503
$439$	11.4939	0.548572	0.274286	−	0.961648i	$-0.411559\pi$
$439$	11.4939	0.548572	0.274286	+	0.961648i	$0.411559\pi$
$440$	−5.04734	−0.240622
$441$	−20.2383	−0.963729
$442$	5.10585	0.242861
$443$	−3.89812	−0.185205	−0.0926027	−	0.995703i	$-0.529519\pi$
$443$	−3.89812	−0.185205	−0.0926027	+	0.995703i	$0.529519\pi$
$444$	0.264343	0.0125452
$445$	−23.4332	−1.11084
$446$	−24.5118	−1.16067
$447$	5.34847	0.252974
$448$	−33.1468	−1.56604
$449$	9.64992	0.455408	0.227704	−	0.973730i	$-0.426878\pi$
$449$	9.64992	0.455408	0.227704	+	0.973730i	$0.426878\pi$
$450$	7.42277	0.349913
$451$	−1.68627	−0.0794036
$452$	−2.44187	−0.114856
$453$	−1.11048	−0.0521749
$454$	−10.2729	−0.482132
$455$	9.21513	0.432012
$456$	−3.91543	−0.183357
$457$	6.14484	0.287443	0.143722	−	0.989618i	$-0.454093\pi$
$457$	6.14484	0.287443	0.143722	+	0.989618i	$0.454093\pi$
$458$	−31.0458	−1.45067
$459$	−8.97326	−0.418836
$460$	−0.962166	−0.0448612
$461$	29.4655	1.37235	0.686173	−	0.727438i	$-0.259289\pi$
$461$	29.4655	1.37235	0.686173	+	0.727438i	$0.259289\pi$
$462$	2.99457	0.139320
$463$	−20.0053	−0.929727	−0.464864	−	0.885382i	$-0.653897\pi$
$463$	−20.0053	−0.929727	−0.464864	+	0.885382i	$0.653897\pi$
$464$	19.0156	0.882777
$465$	−1.94062	−0.0899941
$466$	−18.9137	−0.876160
$467$	9.14972	0.423399	0.211699	−	0.977335i	$-0.432100\pi$
$467$	9.14972	0.423399	0.211699	+	0.977335i	$0.432100\pi$
$468$	−0.813993	−0.0376268
$469$	−5.14649	−0.237643
$470$	−5.81089	−0.268037
$471$	10.8572	0.500272
$472$	−13.3248	−0.613322
$473$	4.50699	0.207232
$474$	3.00150	0.137864
$475$	4.71979	0.216559
$476$	−2.24252	−0.102786
$477$	14.4452	0.661399
$478$	24.0472	1.09989
$479$	−32.8073	−1.49900	−0.749501	−	0.662003i	$-0.769707\pi$
$479$	−32.8073	−1.49900	−0.749501	+	0.662003i	$0.769707\pi$
$480$	−1.22088	−0.0557255
$481$	−2.93837	−0.133978
$482$	24.2451	1.10433
$483$	5.83660	0.265574
$484$	−0.216816	−0.00985529
$485$	13.0131	0.590895
$486$	−18.0058	−0.816762
$487$	−23.6056	−1.06967	−0.534835	−	0.844956i	$-0.679626\pi$
$487$	−23.6056	−1.06967	−0.534835	+	0.844956i	$0.679626\pi$
$488$	−2.96025	−0.134004
$489$	−8.50193	−0.384471
$490$	17.3490	0.783749
$491$	−12.5762	−0.567556	−0.283778	−	0.958890i	$-0.591588\pi$
$491$	−12.5762	−0.567556	−0.283778	+	0.958890i	$0.591588\pi$
$492$	−0.214430	−0.00966726
$493$	14.6157	0.658259
$494$	4.25678	0.191522
$495$	−4.52862	−0.203546
$496$	−6.82974	−0.306664
$497$	8.14681	0.365434
$498$	5.52779	0.247706
$499$	25.9798	1.16301	0.581507	−	0.813542i	$-0.302463\pi$
$499$	25.9798	1.16301	0.581507	+	0.813542i	$0.302463\pi$
$500$	2.62208	0.117263
$501$	6.72972	0.300662
$502$	2.84584	0.127016
$503$	−22.2224	−0.990846	−0.495423	−	0.868652i	$-0.664987\pi$
$503$	−22.2224	−0.990846	−0.495423	+	0.868652i	$0.664987\pi$
$504$	−30.0628	−1.33910
$505$	0.920908	0.0409799
$506$	3.47554	0.154506
$507$	6.45264	0.286572
$508$	−4.67985	−0.207635
$509$	13.1445	0.582620	0.291310	−	0.956629i	$-0.405909\pi$
$509$	13.1445	0.582620	0.291310	+	0.956629i	$0.405909\pi$
$510$	3.61220	0.159951
$511$	47.5627	2.10405
$512$	−25.1331	−1.11073
$513$	−7.48106	−0.330297
$514$	7.34928	0.324163
$515$	24.4894	1.07913
$516$	0.573118	0.0252301
$517$	−2.55218	−0.112245
$518$	−10.6140	−0.466352
$519$	−12.3379	−0.541572
$520$	7.13443	0.312865
$521$	28.1051	1.23131	0.615653	−	0.788017i	$-0.288892\pi$
$521$	28.1051	1.23131	0.615653	+	0.788017i	$0.288892\pi$
$522$	19.1636	0.838766
$523$	29.7361	1.30027	0.650134	−	0.759820i	$-0.274713\pi$
$523$	29.7361	1.30027	0.650134	+	0.759820i	$0.274713\pi$
$524$	0.138754	0.00606149
$525$	−4.69323	−0.204830
$526$	−11.3783	−0.496117
$527$	−5.24946	−0.228670
$528$	2.06409	0.0898281
$529$	−16.2260	−0.705477
$530$	−12.3829	−0.537880
$531$	−11.9554	−0.518819
$532$	−1.86960	−0.0810574
$533$	2.38355	0.103243
$534$	10.7637	0.465791
$535$	−4.51539	−0.195217
$536$	−3.98445	−0.172102
$537$	9.33649	0.402899
$538$	−9.02228	−0.388978
$539$	7.61978	0.328207
$540$	−1.22632	−0.0527723
$541$	3.77397	0.162256	0.0811278	−	0.996704i	$-0.474148\pi$
$541$	3.77397	0.162256	0.0811278	+	0.996704i	$0.474148\pi$
$542$	23.8809	1.02577
$543$	0.0908193	0.00389743
$544$	−3.30254	−0.141595
$545$	−21.8571	−0.936254
$546$	−4.23283	−0.181148
$547$	−24.3850	−1.04263	−0.521315	−	0.853365i	$-0.674558\pi$
$547$	−24.3850	−1.04263	−0.521315	+	0.853365i	$0.674558\pi$
$548$	−2.80731	−0.119922
$549$	−2.65602	−0.113356
$550$	−2.79469	−0.119166
$551$	12.1852	0.519107
$552$	4.51874	0.192330
$553$	14.6536	0.623136
$554$	−25.9765	−1.10363
$555$	−2.07879	−0.0882396
$556$	−1.45211	−0.0615832
$557$	40.2900	1.70714	0.853571	−	0.520977i	$-0.174432\pi$
$557$	40.2900	1.70714	0.853571	+	0.520977i	$0.174432\pi$
$558$	−6.88288	−0.291376
$559$	−6.37064	−0.269449
$560$	22.9440	0.969559
$561$	1.58650	0.0669819
$562$	6.50804	0.274525
$563$	−18.6626	−0.786534	−0.393267	−	0.919424i	$-0.628655\pi$
$563$	−18.6626	−0.786534	−0.393267	+	0.919424i	$0.628655\pi$
$564$	−0.324540	−0.0136656
$565$	19.2028	0.807867
$566$	−15.7167	−0.660620
$567$	−23.0276	−0.967068
$568$	6.30732	0.264649
$569$	−24.0420	−1.00789	−0.503946	−	0.863735i	$-0.668119\pi$
$569$	−24.0420	−1.00789	−0.503946	+	0.863735i	$0.668119\pi$
$570$	3.01151	0.126138
$571$	−2.78884	−0.116710	−0.0583548	−	0.998296i	$-0.518585\pi$
$571$	−2.78884	−0.116710	−0.0583548	+	0.998296i	$0.518585\pi$
$572$	0.306471	0.0128142
$573$	7.29633	0.304809
$574$	8.60987	0.359369
$575$	−5.44703	−0.227157
$576$	−23.0251	−0.959381
$577$	20.3226	0.846040	0.423020	−	0.906120i	$-0.360970\pi$
$577$	20.3226	0.846040	0.423020	+	0.906120i	$0.360970\pi$
$578$	−12.9300	−0.537816
$579$	6.40806	0.266310
$580$	1.99744	0.0829390
$581$	26.9872	1.11962
$582$	−5.97738	−0.247770
$583$	−5.43865	−0.225246
$584$	36.8234	1.52376
$585$	6.40122	0.264658
$586$	9.27534	0.383161
$587$	45.0937	1.86122	0.930608	−	0.366017i	$-0.119279\pi$
$587$	45.0937	1.86122	0.930608	+	0.366017i	$0.119279\pi$
$588$	0.968947	0.0399587
$589$	−4.37650	−0.180331
$590$	10.2486	0.421928
$591$	7.91446	0.325557
$592$	−7.31600	−0.300686
$593$	−15.7514	−0.646833	−0.323417	−	0.946257i	$-0.604832\pi$
$593$	−15.7514	−0.646833	−0.323417	+	0.946257i	$0.604832\pi$
$594$	4.42970	0.181753
$595$	17.6351	0.722969
$596$	1.97722	0.0809903
$597$	6.06513	0.248229
$598$	−4.91268	−0.200894
$599$	−6.67520	−0.272741	−0.136371	−	0.990658i	$-0.543544\pi$
$599$	−6.67520	−0.272741	−0.136371	+	0.990658i	$0.543544\pi$
$600$	−3.63354	−0.148338
$601$	−5.63719	−0.229946	−0.114973	−	0.993369i	$-0.536678\pi$
$601$	−5.63719	−0.229946	−0.114973	+	0.993369i	$0.536678\pi$
$602$	−23.0120	−0.937900
$603$	−3.57497	−0.145584
$604$	−0.410522	−0.0167039
$605$	1.70504	0.0693197
$606$	−0.423005	−0.0171834
$607$	24.1058	0.978423	0.489212	−	0.872165i	$-0.337285\pi$
$607$	24.1058	0.978423	0.489212	+	0.872165i	$0.337285\pi$
$608$	−2.75335	−0.111663
$609$	−12.1166	−0.490991
$610$	2.27684	0.0921865
$611$	3.60751	0.145944
$612$	−1.55775	−0.0629682
$613$	−32.8312	−1.32604	−0.663019	−	0.748603i	$-0.730725\pi$
$613$	−32.8312	−1.32604	−0.663019	+	0.748603i	$0.730725\pi$
$614$	−15.5886	−0.629107
$615$	1.68627	0.0679971
$616$	11.3187	0.456045
$617$	−25.0263	−1.00752	−0.503760	−	0.863844i	$-0.668050\pi$
$617$	−25.0263	−1.00752	−0.503760	+	0.863844i	$0.668050\pi$
$618$	−11.2488	−0.452495
$619$	−18.4385	−0.741106	−0.370553	−	0.928811i	$-0.620832\pi$
$619$	−18.4385	−0.741106	−0.370553	+	0.928811i	$0.620832\pi$
$620$	−0.717409	−0.0288119
$621$	8.63377	0.346461
$622$	−1.34654	−0.0539915
$623$	52.5495	2.10535
$624$	−2.91760	−0.116798
$625$	−10.1558	−0.406233
$626$	3.64471	0.145672
$627$	1.32267	0.0528224
$628$	4.01368	0.160163
$629$	−5.62320	−0.224212
$630$	23.1225	0.921222
$631$	12.0576	0.480004	0.240002	−	0.970772i	$-0.422852\pi$
$631$	12.0576	0.480004	0.240002	+	0.970772i	$0.422852\pi$
$632$	11.3450	0.451278
$633$	11.3937	0.452861
$634$	−22.1747	−0.880671
$635$	36.8023	1.46045
$636$	−0.691590	−0.0274233
$637$	−10.7706	−0.426746
$638$	−7.21513	−0.285650
$639$	5.65912	0.223871
$640$	15.5747	0.615644
$641$	32.4028	1.27983	0.639917	−	0.768444i	$-0.278969\pi$
$641$	32.4028	1.27983	0.639917	+	0.768444i	$0.278969\pi$
$642$	2.07408	0.0818572
$643$	1.25921	0.0496584	0.0248292	−	0.999692i	$-0.492096\pi$
$643$	1.25921	0.0496584	0.0248292	+	0.999692i	$0.492096\pi$
$644$	2.15768	0.0850243
$645$	−4.50699	−0.177462
$646$	8.14625	0.320510
$647$	−9.53579	−0.374890	−0.187445	−	0.982275i	$-0.560021\pi$
$647$	−9.53579	−0.374890	−0.187445	+	0.982275i	$0.560021\pi$
$648$	−17.8281	−0.700355
$649$	4.50124	0.176689
$650$	3.95031	0.154944
$651$	4.35188	0.170564
$652$	−3.14300	−0.123089
$653$	23.6093	0.923904	0.461952	−	0.886905i	$-0.347149\pi$
$653$	23.6093	0.923904	0.461952	+	0.886905i	$0.347149\pi$
$654$	10.0397	0.392584
$655$	−1.09116	−0.0426351
$656$	5.93460	0.231707
$657$	33.0390	1.28898
$658$	13.0310	0.508003
$659$	−32.2394	−1.25587	−0.627934	−	0.778267i	$-0.716099\pi$
$659$	−32.2394	−1.25587	−0.627934	+	0.778267i	$0.716099\pi$
$660$	0.216816	0.00843956
$661$	30.2262	1.17566	0.587831	−	0.808984i	$-0.299982\pi$
$661$	30.2262	1.17566	0.587831	+	0.808984i	$0.299982\pi$
$662$	−27.4762	−1.06789
$663$	−2.24252	−0.0870922
$664$	20.8937	0.810834
$665$	14.7025	0.570138
$666$	−7.37293	−0.285695
$667$	−14.0627	−0.544512
$668$	2.48785	0.0962576
$669$	10.7657	0.416226
$670$	3.06460	0.118396
$671$	1.00000	0.0386046
$672$	2.73786	0.105615
$673$	−41.0579	−1.58267	−0.791333	−	0.611385i	$-0.790613\pi$
$673$	−41.0579	−1.58267	−0.791333	+	0.611385i	$0.790613\pi$
$674$	−24.9566	−0.961291
$675$	−6.94245	−0.267215
$676$	2.38542	0.0917467
$677$	23.1892	0.891232	0.445616	−	0.895224i	$-0.352985\pi$
$677$	23.1892	0.891232	0.445616	+	0.895224i	$0.352985\pi$
$678$	−8.82051	−0.338749
$679$	−29.1822	−1.11991
$680$	13.6532	0.523578
$681$	4.51192	0.172897
$682$	2.59143	0.0992308
$683$	33.4783	1.28101	0.640506	−	0.767953i	$-0.278724\pi$
$683$	33.4783	1.28101	0.640506	+	0.767953i	$0.278724\pi$
$684$	−1.29870	−0.0496572
$685$	22.0767	0.843506
$686$	−3.16451	−0.120821
$687$	13.6355	0.520226
$688$	−15.8617	−0.604722
$689$	7.68755	0.292872
$690$	−3.47554	−0.132311
$691$	10.4751	0.398493	0.199247	−	0.979949i	$-0.436150\pi$
$691$	10.4751	0.398493	0.199247	+	0.979949i	$0.436150\pi$
$692$	−4.56107	−0.173386
$693$	10.1555	0.385776
$694$	−2.81965	−0.107033
$695$	11.4194	0.433161
$696$	−9.38080	−0.355578
$697$	4.56144	0.172777
$698$	−28.4932	−1.07848
$699$	8.30699	0.314199
$700$	−1.73500	−0.0655767
$701$	−6.90150	−0.260666	−0.130333	−	0.991470i	$-0.541605\pi$
$701$	−6.90150	−0.260666	−0.130333	+	0.991470i	$0.541605\pi$
$702$	−6.26140	−0.236321
$703$	−4.68810	−0.176815
$704$	8.66904	0.326727
$705$	2.55218	0.0961205
$706$	30.8833	1.16231
$707$	−2.06515	−0.0776680
$708$	0.572387	0.0215116
$709$	−25.7827	−0.968290	−0.484145	−	0.874988i	$-0.660869\pi$
$709$	−25.7827	−0.968290	−0.484145	+	0.874988i	$0.660869\pi$
$710$	−4.85120	−0.182062
$711$	10.1790	0.381744
$712$	40.6842	1.52470
$713$	5.05085	0.189156
$714$	−8.10042	−0.303151
$715$	−2.41008	−0.0901318
$716$	3.45152	0.128989
$717$	−10.5617	−0.394432
$718$	8.00851	0.298875
$719$	22.4484	0.837182	0.418591	−	0.908175i	$-0.362524\pi$
$719$	22.4484	0.837182	0.418591	+	0.908175i	$0.362524\pi$
$720$	15.9378	0.593968
$721$	−54.9180	−2.04525
$722$	−18.5802	−0.691485
$723$	−10.6486	−0.396025
$724$	0.0335741	0.00124777
$725$	11.3079	0.419965
$726$	−0.783184	−0.0290667
$727$	17.2835	0.641011	0.320505	−	0.947247i	$-0.396147\pi$
$727$	17.2835	0.641011	0.320505	+	0.947247i	$0.396147\pi$
$728$	−15.9991	−0.592965
$729$	−10.1593	−0.376270
$730$	−28.3223	−1.04825
$731$	−12.1916	−0.450922
$732$	0.127162	0.00470005
$733$	−14.8357	−0.547969	−0.273984	−	0.961734i	$-0.588342\pi$
$733$	−14.8357	−0.547969	−0.273984	+	0.961734i	$0.588342\pi$
$734$	20.7543	0.766055
$735$	−7.61978	−0.281060
$736$	3.17759	0.117128
$737$	1.34599	0.0495801
$738$	5.98078	0.220156
$739$	44.5903	1.64028	0.820141	−	0.572162i	$-0.193895\pi$
$739$	44.5903	1.64028	0.820141	+	0.572162i	$0.193895\pi$
$740$	−0.768487	−0.0282502
$741$	−1.86960	−0.0686815
$742$	27.7690	1.01943
$743$	−7.79582	−0.286001	−0.143000	−	0.989723i	$-0.545675\pi$
$743$	−7.79582	−0.286001	−0.143000	+	0.989723i	$0.545675\pi$
$744$	3.36926	0.123523
$745$	−15.5489	−0.569666
$746$	43.9359	1.60861
$747$	18.7465	0.685898
$748$	0.586497	0.0214444
$749$	10.1258	0.369990
$750$	9.47149	0.345850
$751$	27.4136	1.00034	0.500169	−	0.865928i	$-0.333271\pi$
$751$	27.4136	1.00034	0.500169	+	0.865928i	$0.333271\pi$
$752$	8.98202	0.327541
$753$	−1.24991	−0.0455492
$754$	10.1986	0.371412
$755$	3.22834	0.117491
$756$	2.75004	0.100018
$757$	−17.2330	−0.626345	−0.313172	−	0.949696i	$-0.601392\pi$
$757$	−17.2330	−0.626345	−0.313172	+	0.949696i	$0.601392\pi$
$758$	−21.6958	−0.788028
$759$	−1.52647	−0.0554075
$760$	11.3828	0.412897
$761$	48.2896	1.75050	0.875248	−	0.483674i	$-0.160698\pi$
$761$	48.2896	1.75050	0.875248	+	0.483674i	$0.160698\pi$
$762$	−16.9046	−0.612388
$763$	49.0149	1.77446
$764$	2.69731	0.0975853
$765$	12.2501	0.442903
$766$	42.0583	1.51963
$767$	−6.36251	−0.229737
$768$	3.01473	0.108785
$769$	−4.13048	−0.148949	−0.0744745	−	0.997223i	$-0.523728\pi$
$769$	−4.13048	−0.148949	−0.0744745	+	0.997223i	$0.523728\pi$
$770$	−8.70568	−0.313731
$771$	−3.22784	−0.116248
$772$	2.36893	0.0852598
$773$	−2.03774	−0.0732926	−0.0366463	−	0.999328i	$-0.511667\pi$
$773$	−2.03774	−0.0732926	−0.0366463	+	0.999328i	$0.511667\pi$
$774$	−15.9851	−0.574573
$775$	−4.06141	−0.145890
$776$	−22.5930	−0.811043
$777$	4.66172	0.167238
$778$	52.3213	1.87581
$779$	3.80290	0.136253
$780$	−0.306471	−0.0109734
$781$	−2.13067	−0.0762415
$782$	−9.40146	−0.336196
$783$	−17.9235	−0.640534
$784$	−26.8167	−0.957740
$785$	−31.5635	−1.12655
$786$	0.501207	0.0178775
$787$	31.5037	1.12299	0.561494	−	0.827481i	$-0.310227\pi$
$787$	31.5037	1.12299	0.561494	+	0.827481i	$0.310227\pi$
$788$	2.92582	0.104228
$789$	4.99740	0.177912
$790$	−8.72585	−0.310452
$791$	−43.0626	−1.53113
$792$	7.86248	0.279381
$793$	−1.41350	−0.0501950
$794$	29.6890	1.05362
$795$	5.43865	0.192889
$796$	2.24216	0.0794712
$797$	−40.5246	−1.43545	−0.717727	−	0.696325i	$-0.754817\pi$
$797$	−40.5246	−1.43545	−0.717727	+	0.696325i	$0.754817\pi$
$798$	−6.75337	−0.239067
$799$	6.90373	0.244237
$800$	−2.55512	−0.0903370
$801$	36.5031	1.28977
$802$	−28.9534	−1.02238
$803$	−12.4393	−0.438973
$804$	0.171158	0.00603629
$805$	−16.9679	−0.598040
$806$	−3.66299	−0.129023
$807$	3.96263	0.139491
$808$	−1.59886	−0.0562476
$809$	45.9846	1.61673	0.808367	−	0.588679i	$-0.200352\pi$
$809$	45.9846	1.61673	0.808367	+	0.588679i	$0.200352\pi$
$810$	13.7123	0.481801
$811$	−21.5553	−0.756909	−0.378454	−	0.925620i	$-0.623544\pi$
$811$	−21.5553	−0.756909	−0.378454	+	0.925620i	$0.623544\pi$
$812$	−4.47929	−0.157192
$813$	−10.4886	−0.367852
$814$	2.77593	0.0972963
$815$	24.7165	0.865780
$816$	−5.58345	−0.195460
$817$	−10.1642	−0.355600
$818$	−42.0331	−1.46965
$819$	−14.3549	−0.501599
$820$	0.623383	0.0217695
$821$	−31.9758	−1.11596	−0.557982	−	0.829853i	$-0.688424\pi$
$821$	−31.9758	−1.11596	−0.557982	+	0.829853i	$0.688424\pi$
$822$	−10.1406	−0.353693
$823$	4.65642	0.162313	0.0811563	−	0.996701i	$-0.474139\pi$
$823$	4.65642	0.162313	0.0811563	+	0.996701i	$0.474139\pi$
$824$	−42.5179	−1.48118
$825$	1.22744	0.0427341
$826$	−22.9827	−0.799669
$827$	48.3361	1.68081	0.840405	−	0.541959i	$-0.182317\pi$
$827$	48.3361	1.68081	0.840405	+	0.541959i	$0.182317\pi$
$828$	1.49881	0.0520873
$829$	−22.7090	−0.788717	−0.394358	−	0.918957i	$-0.629033\pi$
$829$	−22.7090	−0.788717	−0.394358	+	0.918957i	$0.629033\pi$
$830$	−16.0702	−0.557804
$831$	11.4090	0.395774
$832$	−12.2537	−0.424821
$833$	−20.6118	−0.714157
$834$	−5.24531	−0.181630
$835$	−19.5644	−0.677053
$836$	0.488966	0.0169112
$837$	6.43750	0.222513
$838$	13.6990	0.473222
$839$	7.55301	0.260759	0.130379	−	0.991464i	$-0.458380\pi$
$839$	7.55301	0.260759	0.130379	+	0.991464i	$0.458380\pi$
$840$	−11.3187	−0.390534
$841$	0.193941	0.00668761
$842$	20.2461	0.697727
$843$	−2.85837	−0.0984474
$844$	4.21204	0.144985
$845$	−18.7589	−0.645324
$846$	9.05191	0.311211
$847$	−3.82358	−0.131380
$848$	19.1406	0.657289
$849$	6.90284	0.236905
$850$	7.55976	0.259298
$851$	5.41046	0.185468
$852$	−0.270941	−0.00928229
$853$	−29.3846	−1.00611	−0.503054	−	0.864255i	$-0.667790\pi$
$853$	−29.3846	−1.00611	−0.503054	+	0.864255i	$0.667790\pi$
$854$	−5.10585	−0.174719
$855$	10.2130	0.349276
$856$	7.83951	0.267949
$857$	−7.21276	−0.246383	−0.123192	−	0.992383i	$-0.539313\pi$
$857$	−7.21276	−0.246383	−0.123192	+	0.992383i	$0.539313\pi$
$858$	1.10703	0.0377935
$859$	26.9437	0.919308	0.459654	−	0.888098i	$-0.347973\pi$
$859$	26.9437	0.919308	0.459654	+	0.888098i	$0.347973\pi$
$860$	−1.66615	−0.0568151
$861$	−3.78150	−0.128873
$862$	15.1112	0.514689
$863$	0.507609	0.0172792	0.00863961	−	0.999963i	$-0.497250\pi$
$863$	0.507609	0.0172792	0.00863961	+	0.999963i	$0.497250\pi$
$864$	4.04997	0.137783
$865$	35.8682	1.21955
$866$	31.4810	1.06977
$867$	5.67891	0.192866
$868$	1.60880	0.0546064
$869$	−3.83244	−0.130007
$870$	7.21513	0.244616
$871$	−1.90256	−0.0644657
$872$	37.9477	1.28507
$873$	−20.2712	−0.686075
$874$	−7.83805	−0.265126
$875$	46.2408	1.56322
$876$	−1.58181	−0.0534443
$877$	43.3897	1.46517	0.732583	−	0.680677i	$-0.238314\pi$
$877$	43.3897	1.46517	0.732583	+	0.680677i	$0.238314\pi$
$878$	15.3484	0.517984
$879$	−4.07378	−0.137405
$880$	−6.00064	−0.202282
$881$	−28.8083	−0.970575	−0.485288	−	0.874355i	$-0.661285\pi$
$881$	−28.8083	−0.970575	−0.485288	+	0.874355i	$0.661285\pi$
$882$	−27.0254	−0.909992
$883$	−33.4794	−1.12667	−0.563336	−	0.826228i	$-0.690482\pi$
$883$	−33.4794	−1.12667	−0.563336	+	0.826228i	$0.690482\pi$
$884$	−0.829015	−0.0278828
$885$	−4.50124	−0.151307
$886$	−5.20539	−0.174879
$887$	40.9969	1.37654	0.688271	−	0.725453i	$-0.258370\pi$
$887$	40.9969	1.37654	0.688271	+	0.725453i	$0.258370\pi$
$888$	3.60914	0.121115
$889$	−82.5298	−2.76796
$890$	−31.2918	−1.04890
$891$	6.02252	0.201762
$892$	3.97987	0.133256
$893$	5.75568	0.192607
$894$	7.14213	0.238868
$895$	−27.1427	−0.907279
$896$	−34.9265	−1.16681
$897$	2.15768	0.0720427
$898$	12.8861	0.430015
$899$	−10.4854	−0.349709
$900$	−1.20520	−0.0401734
$901$	14.7118	0.490120
$902$	−2.25178	−0.0749761
$903$	10.1070	0.336340
$904$	−33.3394	−1.10885
$905$	−0.264026	−0.00877652
$906$	−1.48289	−0.0492657
$907$	−9.25129	−0.307184	−0.153592	−	0.988134i	$-0.549084\pi$
$907$	−9.25129	−0.307184	−0.153592	+	0.988134i	$0.549084\pi$
$908$	1.66797	0.0553534
$909$	−1.43454	−0.0475808
$910$	12.3055	0.407924
$911$	−45.2640	−1.49966	−0.749831	−	0.661629i	$-0.769865\pi$
$911$	−45.2640	−1.49966	−0.749831	+	0.661629i	$0.769865\pi$
$912$	−4.65495	−0.154141
$913$	−7.05810	−0.233589
$914$	8.20556	0.271416
$915$	−1.00000	−0.0330590
$916$	5.04077	0.166552
$917$	2.44694	0.0808052
$918$	−11.9825	−0.395482
$919$	−55.4379	−1.82873	−0.914364	−	0.404892i	$-0.867309\pi$
$919$	−55.4379	−1.82873	−0.914364	+	0.404892i	$0.867309\pi$
$920$	−13.1367	−0.433104
$921$	6.84661	0.225604
$922$	39.3470	1.29583
$923$	3.01172	0.0991318
$924$	−0.486215	−0.0159953
$925$	−4.35057	−0.143046
$926$	−26.7143	−0.877887
$927$	−38.1484	−1.25296
$928$	−6.59661	−0.216544
$929$	−18.7740	−0.615955	−0.307977	−	0.951394i	$-0.599652\pi$
$929$	−18.7740	−0.615955	−0.307977	+	0.951394i	$0.599652\pi$
$930$	−2.59143	−0.0849762
$931$	−17.1842	−0.563189
$932$	3.07093	0.100592
$933$	0.591409	0.0193619
$934$	12.2182	0.399791
$935$	−4.61220	−0.150835
$936$	−11.1136	−0.363261
$937$	−18.9016	−0.617488	−0.308744	−	0.951145i	$-0.599909\pi$
$937$	−18.9016	−0.617488	−0.308744	+	0.951145i	$0.599909\pi$
$938$	−6.87241	−0.224392
$939$	−1.60077	−0.0522393
$940$	0.943489	0.0307732
$941$	−40.7528	−1.32850	−0.664252	−	0.747509i	$-0.731250\pi$
$941$	−40.7528	−1.32850	−0.664252	+	0.747509i	$0.731250\pi$
$942$	14.4982	0.472377
$943$	−4.38886	−0.142921
$944$	−15.8415	−0.515596
$945$	−21.6263	−0.703502
$946$	6.01845	0.195677
$947$	45.2880	1.47166	0.735831	−	0.677166i	$-0.236792\pi$
$947$	45.2880	1.47166	0.735831	+	0.677166i	$0.236792\pi$
$948$	−0.487341	−0.0158281
$949$	17.5830	0.570768
$950$	6.30261	0.204484
$951$	9.73926	0.315817
$952$	−30.6176	−0.992324
$953$	−28.1077	−0.910498	−0.455249	−	0.890364i	$-0.650450\pi$
$953$	−28.1077	−0.910498	−0.455249	+	0.890364i	$0.650450\pi$
$954$	19.2895	0.624520
$955$	−21.2116	−0.686391
$956$	−3.90444	−0.126279
$957$	3.16892	0.102437
$958$	−43.8095	−1.41542
$959$	−49.5073	−1.59867
$960$	−8.66904	−0.279792
$961$	−27.2340	−0.878516
$962$	−3.92378	−0.126508
$963$	7.03384	0.226662
$964$	−3.93657	−0.126788
$965$	−18.6292	−0.599697
$966$	7.79395	0.250766
$967$	−29.7895	−0.957966	−0.478983	−	0.877824i	$-0.658994\pi$
$967$	−29.7895	−0.957966	−0.478983	+	0.877824i	$0.658994\pi$
$968$	−2.96025	−0.0951459
$969$	−3.57788	−0.114938
$970$	17.3772	0.557948
$971$	28.0668	0.900706	0.450353	−	0.892851i	$-0.351298\pi$
$971$	28.0668	0.900706	0.450353	+	0.892851i	$0.351298\pi$
$972$	2.92353	0.0937723
$973$	−25.6081	−0.820959
$974$	−31.5219	−1.01003
$975$	−1.73500	−0.0555644
$976$	−3.51936	−0.112652
$977$	−21.3268	−0.682306	−0.341153	−	0.940008i	$-0.610817\pi$
$977$	−21.3268	−0.682306	−0.341153	+	0.940008i	$0.610817\pi$
$978$	−11.3531	−0.363033
$979$	−13.7435	−0.439245
$980$	−2.81688	−0.0899820
$981$	34.0478	1.08706
$982$	−16.7938	−0.535910
$983$	53.8387	1.71719	0.858594	−	0.512657i	$-0.171339\pi$
$983$	53.8387	1.71719	0.858594	+	0.512657i	$0.171339\pi$
$984$	−2.92767	−0.0933306
$985$	−23.0086	−0.733115
$986$	19.5172	0.621555
$987$	−5.72330	−0.182175
$988$	−0.691154	−0.0219886
$989$	11.7303	0.373003
$990$	−6.04734	−0.192197
$991$	24.4123	0.775484	0.387742	−	0.921768i	$-0.373255\pi$
$991$	24.4123	0.775484	0.387742	+	0.921768i	$0.373255\pi$
$992$	2.36927	0.0752245
$993$	12.0677	0.382956
$994$	10.8789	0.345058
$995$	−17.6323	−0.558981
$996$	−0.897523	−0.0284391
$997$	44.4541	1.40788	0.703938	−	0.710262i	$-0.251423\pi$
$997$	44.4541	1.40788	0.703938	+	0.710262i	$0.251423\pi$
$998$	34.6923	1.09817
$999$	6.89584	0.218175

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	671.2.a.a.1.5	✓	5
3.2	odd	2		6039.2.a.a.1.1		5
11.10	odd	2		7381.2.a.g.1.1		5

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
671.2.a.a.1.5	✓	5	1.1	even	1	trivial
6039.2.a.a.1.1		5	3.2	odd	2
7381.2.a.g.1.1		5	11.10	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:	\( N \)	\(=\)	\( 671 = 11 \cdot 61 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	671.a (trivial)

\(f(q)\)	\(=\)	\(q+1.33536 q^{2} -0.586497 q^{3} -0.216816 q^{4} +1.70504 q^{5} -0.783184 q^{6} -3.82358 q^{7} -2.96025 q^{8} -2.65602 q^{9} +O(q^{10})\)	\(q+1.33536 q^{2} -0.586497 q^{3} -0.216816 q^{4} +1.70504 q^{5} -0.783184 q^{6} -3.82358 q^{7} -2.96025 q^{8} -2.65602 q^{9} +2.27684 q^{10} +1.00000 q^{11} +0.127162 q^{12} -1.41350 q^{13} -5.10585 q^{14} -1.00000 q^{15} -3.51936 q^{16} -2.70504 q^{17} -3.54674 q^{18} -2.25521 q^{19} -0.369680 q^{20} +2.24252 q^{21} +1.33536 q^{22} +2.60270 q^{23} +1.73617 q^{24} -2.09284 q^{25} -1.88753 q^{26} +3.31724 q^{27} +0.829015 q^{28} -5.40314 q^{29} -1.33536 q^{30} +1.94062 q^{31} +1.22088 q^{32} -0.586497 q^{33} -3.61220 q^{34} -6.51936 q^{35} +0.575869 q^{36} +2.07879 q^{37} -3.01151 q^{38} +0.829015 q^{39} -5.04734 q^{40} -1.68627 q^{41} +2.99457 q^{42} +4.50699 q^{43} -0.216816 q^{44} -4.52862 q^{45} +3.47554 q^{46} -2.55218 q^{47} +2.06409 q^{48} +7.61978 q^{49} -2.79469 q^{50} +1.58650 q^{51} +0.306471 q^{52} -5.43865 q^{53} +4.42970 q^{54} +1.70504 q^{55} +11.3187 q^{56} +1.32267 q^{57} -7.21513 q^{58} +4.50124 q^{59} +0.216816 q^{60} +1.00000 q^{61} +2.59143 q^{62} +10.1555 q^{63} +8.66904 q^{64} -2.41008 q^{65} -0.783184 q^{66} +1.34599 q^{67} +0.586497 q^{68} -1.52647 q^{69} -8.70568 q^{70} -2.13067 q^{71} +7.86248 q^{72} -12.4393 q^{73} +2.77593 q^{74} +1.22744 q^{75} +0.488966 q^{76} -3.82358 q^{77} +1.10703 q^{78} -3.83244 q^{79} -6.00064 q^{80} +6.02252 q^{81} -2.25178 q^{82} -7.05810 q^{83} -0.486215 q^{84} -4.61220 q^{85} +6.01845 q^{86} +3.16892 q^{87} -2.96025 q^{88} -13.7435 q^{89} -6.04734 q^{90} +5.40465 q^{91} -0.564307 q^{92} -1.13817 q^{93} -3.40807 q^{94} -3.84522 q^{95} -0.716045 q^{96} +7.63215 q^{97} +10.1751 q^{98} -2.65602 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 5 q - 2 q^{2} - 2 q^{5} - 5 q^{6} - q^{7} - 6 q^{8} - 3 q^{9}+O(q^{10}) \) 5 * q - 2 * q^2 - 2 * q^5 - 5 * q^6 - q^7 - 6 * q^8 - 3 * q^9	\( 5 q - 2 q^{2} - 2 q^{5} - 5 q^{6} - q^{7} - 6 q^{8} - 3 q^{9} + 5 q^{10} + 5 q^{11} + 12 q^{12} - 10 q^{13} - 3 q^{14} - 5 q^{15} + 2 q^{16} - 3 q^{17} - 6 q^{18} - 13 q^{19} - 2 q^{21} - 2 q^{22} - 12 q^{24} - 15 q^{25} + 9 q^{26} - 9 q^{27} - 12 q^{28} - 7 q^{29} + 2 q^{30} - 13 q^{31} + q^{32} - 3 q^{34} - 13 q^{35} + 3 q^{36} - 6 q^{37} + 9 q^{38} - 12 q^{39} - 5 q^{40} - 9 q^{41} + 13 q^{42} + 2 q^{43} + 6 q^{45} - 7 q^{46} - 3 q^{47} + q^{48} - 6 q^{49} + 9 q^{50} + 5 q^{51} - 12 q^{52} + 3 q^{53} + 15 q^{54} - 2 q^{55} + 28 q^{56} - 17 q^{57} - 15 q^{58} - 14 q^{59} + 5 q^{61} + 31 q^{62} + 6 q^{64} + 9 q^{65} - 5 q^{66} - 5 q^{67} - 10 q^{69} - 5 q^{70} + 3 q^{71} + 5 q^{72} - 4 q^{73} + 2 q^{74} + 2 q^{75} - 19 q^{76} - q^{77} + 22 q^{78} - 27 q^{79} - 2 q^{80} + q^{81} + 11 q^{82} - 3 q^{83} - 15 q^{84} - 8 q^{85} + 5 q^{86} + 14 q^{87} - 6 q^{88} - 12 q^{89} - 10 q^{90} + 4 q^{91} + 13 q^{92} - 12 q^{93} - 18 q^{94} + 7 q^{95} + 12 q^{96} - 5 q^{97} + 14 q^{98} - 3 q^{99}+O(q^{100}) \) 5 * q - 2 * q^2 - 2 * q^5 - 5 * q^6 - q^7 - 6 * q^8 - 3 * q^9 + 5 * q^10 + 5 * q^11 + 12 * q^12 - 10 * q^13 - 3 * q^14 - 5 * q^15 + 2 * q^16 - 3 * q^17 - 6 * q^18 - 13 * q^19 - 2 * q^21 - 2 * q^22 - 12 * q^24 - 15 * q^25 + 9 * q^26 - 9 * q^27 - 12 * q^28 - 7 * q^29 + 2 * q^30 - 13 * q^31 + q^32 - 3 * q^34 - 13 * q^35 + 3 * q^36 - 6 * q^37 + 9 * q^38 - 12 * q^39 - 5 * q^40 - 9 * q^41 + 13 * q^42 + 2 * q^43 + 6 * q^45 - 7 * q^46 - 3 * q^47 + q^48 - 6 * q^49 + 9 * q^50 + 5 * q^51 - 12 * q^52 + 3 * q^53 + 15 * q^54 - 2 * q^55 + 28 * q^56 - 17 * q^57 - 15 * q^58 - 14 * q^59 + 5 * q^61 + 31 * q^62 + 6 * q^64 + 9 * q^65 - 5 * q^66 - 5 * q^67 - 10 * q^69 - 5 * q^70 + 3 * q^71 + 5 * q^72 - 4 * q^73 + 2 * q^74 + 2 * q^75 - 19 * q^76 - q^77 + 22 * q^78 - 27 * q^79 - 2 * q^80 + q^81 + 11 * q^82 - 3 * q^83 - 15 * q^84 - 8 * q^85 + 5 * q^86 + 14 * q^87 - 6 * q^88 - 12 * q^89 - 10 * q^90 + 4 * q^91 + 13 * q^92 - 12 * q^93 - 18 * q^94 + 7 * q^95 + 12 * q^96 - 5 * q^97 + 14 * q^98 - 3 * q^99

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