LMFDB - Embedded newform 4010.2.a.i.1.7

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [4010,2,Mod(1,4010)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(4010, 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("4010.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 4010 = 2 \cdot 5 \cdot 401 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	4010.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:	$32.0200112105$
Analytic rank:	$1$
Dimension:	$10$
Coefficient field:	$\mathbb{Q}[x]/(x^{10} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{10} - 3x^{9} - 12x^{8} + 34x^{7} + 46x^{6} - 104x^{5} - 90x^{4} + 89x^{3} + 82x^{2} + 12x - 1 $ x^10 - 3x^9 - 12x^8 + 34x^7 + 46x^6 - 104x^5 - 90x^4 + 89x^3 + 82x^2 + 12*x - 1
Coefficient ring:	$\Z[a_1, \ldots, a_{13}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.7
Root			$-2.65028$ of defining polynomial
Character	$\chi$	$=$	4010.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.00000 q^{2} +0.675556 q^{3} +1.00000 q^{4} +1.00000 q^{5} -0.675556 q^{6} -1.96617 q^{7} -1.00000 q^{8} -2.54362 q^{9} +O(q^{10})$	\(q-1.00000 q^{2} +0.675556 q^{3} +1.00000 q^{4} +1.00000 q^{5} -0.675556 q^{6} -1.96617 q^{7} -1.00000 q^{8} -2.54362 q^{9} -1.00000 q^{10} -0.702842 q^{11} +0.675556 q^{12} +3.63999 q^{13} +1.96617 q^{14} +0.675556 q^{15} +1.00000 q^{16} -0.463370 q^{17} +2.54362 q^{18} +1.64115 q^{19} +1.00000 q^{20} -1.32826 q^{21} +0.702842 q^{22} -3.53333 q^{23} -0.675556 q^{24} +1.00000 q^{25} -3.63999 q^{26} -3.74503 q^{27} -1.96617 q^{28} +2.53753 q^{29} -0.675556 q^{30} -6.10965 q^{31} -1.00000 q^{32} -0.474809 q^{33} +0.463370 q^{34} -1.96617 q^{35} -2.54362 q^{36} +5.76322 q^{37} -1.64115 q^{38} +2.45902 q^{39} -1.00000 q^{40} +7.14911 q^{41} +1.32826 q^{42} -6.31705 q^{43} -0.702842 q^{44} -2.54362 q^{45} +3.53333 q^{46} +5.97612 q^{47} +0.675556 q^{48} -3.13418 q^{49} -1.00000 q^{50} -0.313032 q^{51} +3.63999 q^{52} -4.57721 q^{53} +3.74503 q^{54} -0.702842 q^{55} +1.96617 q^{56} +1.10869 q^{57} -2.53753 q^{58} -2.56548 q^{59} +0.675556 q^{60} -9.20668 q^{61} +6.10965 q^{62} +5.00120 q^{63} +1.00000 q^{64} +3.63999 q^{65} +0.474809 q^{66} +2.71402 q^{67} -0.463370 q^{68} -2.38696 q^{69} +1.96617 q^{70} -3.57818 q^{71} +2.54362 q^{72} -1.05604 q^{73} -5.76322 q^{74} +0.675556 q^{75} +1.64115 q^{76} +1.38191 q^{77} -2.45902 q^{78} -7.77888 q^{79} +1.00000 q^{80} +5.10089 q^{81} -7.14911 q^{82} -5.64286 q^{83} -1.32826 q^{84} -0.463370 q^{85} +6.31705 q^{86} +1.71424 q^{87} +0.702842 q^{88} +2.42510 q^{89} +2.54362 q^{90} -7.15683 q^{91} -3.53333 q^{92} -4.12741 q^{93} -5.97612 q^{94} +1.64115 q^{95} -0.675556 q^{96} +14.3124 q^{97} +3.13418 q^{98} +1.78776 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 10 q - 10 q^{2} - 4 q^{3} + 10 q^{4} + 10 q^{5} + 4 q^{6} - 3 q^{7} - 10 q^{8} + 6 q^{9}+O(q^{10}) $ 10 * q - 10 * q^2 - 4 * q^3 + 10 * q^4 + 10 * q^5 + 4 * q^6 - 3 * q^7 - 10 * q^8 + 6 * q^9	\( 10 q - 10 q^{2} - 4 q^{3} + 10 q^{4} + 10 q^{5} + 4 q^{6} - 3 q^{7} - 10 q^{8} + 6 q^{9} - 10 q^{10} - 11 q^{11} - 4 q^{12} + 6 q^{13} + 3 q^{14} - 4 q^{15} + 10 q^{16} + 9 q^{17} - 6 q^{18} - 13 q^{19} + 10 q^{20} - 24 q^{21} + 11 q^{22} - 3 q^{23} + 4 q^{24} + 10 q^{25} - 6 q^{26} - 10 q^{27} - 3 q^{28} - 4 q^{29} + 4 q^{30} - 17 q^{31} - 10 q^{32} - 2 q^{33} - 9 q^{34} - 3 q^{35} + 6 q^{36} - 15 q^{37} + 13 q^{38} - 6 q^{39} - 10 q^{40} - 11 q^{41} + 24 q^{42} - 11 q^{43} - 11 q^{44} + 6 q^{45} + 3 q^{46} + 3 q^{47} - 4 q^{48} - 5 q^{49} - 10 q^{50} - 21 q^{51} + 6 q^{52} + 25 q^{53} + 10 q^{54} - 11 q^{55} + 3 q^{56} + 31 q^{57} + 4 q^{58} - 46 q^{59} - 4 q^{60} - 54 q^{61} + 17 q^{62} - 6 q^{63} + 10 q^{64} + 6 q^{65} + 2 q^{66} - 26 q^{67} + 9 q^{68} - 9 q^{69} + 3 q^{70} - 16 q^{71} - 6 q^{72} + 4 q^{73} + 15 q^{74} - 4 q^{75} - 13 q^{76} + 11 q^{77} + 6 q^{78} - 19 q^{79} + 10 q^{80} - 6 q^{81} + 11 q^{82} + 19 q^{83} - 24 q^{84} + 9 q^{85} + 11 q^{86} + 28 q^{87} + 11 q^{88} - 30 q^{89} - 6 q^{90} - 38 q^{91} - 3 q^{92} - 18 q^{93} - 3 q^{94} - 13 q^{95} + 4 q^{96} - 16 q^{97} + 5 q^{98} - 59 q^{99}+O(q^{100}) \) 10 * q - 10 * q^2 - 4 * q^3 + 10 * q^4 + 10 * q^5 + 4 * q^6 - 3 * q^7 - 10 * q^8 + 6 * q^9 - 10 * q^10 - 11 * q^11 - 4 * q^12 + 6 * q^13 + 3 * q^14 - 4 * q^15 + 10 * q^16 + 9 * q^17 - 6 * q^18 - 13 * q^19 + 10 * q^20 - 24 * q^21 + 11 * q^22 - 3 * q^23 + 4 * q^24 + 10 * q^25 - 6 * q^26 - 10 * q^27 - 3 * q^28 - 4 * q^29 + 4 * q^30 - 17 * q^31 - 10 * q^32 - 2 * q^33 - 9 * q^34 - 3 * q^35 + 6 * q^36 - 15 * q^37 + 13 * q^38 - 6 * q^39 - 10 * q^40 - 11 * q^41 + 24 * q^42 - 11 * q^43 - 11 * q^44 + 6 * q^45 + 3 * q^46 + 3 * q^47 - 4 * q^48 - 5 * q^49 - 10 * q^50 - 21 * q^51 + 6 * q^52 + 25 * q^53 + 10 * q^54 - 11 * q^55 + 3 * q^56 + 31 * q^57 + 4 * q^58 - 46 * q^59 - 4 * q^60 - 54 * q^61 + 17 * q^62 - 6 * q^63 + 10 * q^64 + 6 * q^65 + 2 * q^66 - 26 * q^67 + 9 * q^68 - 9 * q^69 + 3 * q^70 - 16 * q^71 - 6 * q^72 + 4 * q^73 + 15 * q^74 - 4 * q^75 - 13 * q^76 + 11 * q^77 + 6 * q^78 - 19 * q^79 + 10 * q^80 - 6 * q^81 + 11 * q^82 + 19 * q^83 - 24 * q^84 + 9 * q^85 + 11 * q^86 + 28 * q^87 + 11 * q^88 - 30 * q^89 - 6 * q^90 - 38 * q^91 - 3 * q^92 - 18 * q^93 - 3 * q^94 - 13 * q^95 + 4 * q^96 - 16 * q^97 + 5 * q^98 - 59 * 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 $

$2$	−1.00000	−0.707107
$2$	−1.00000	−0.707107
$3$	0.675556	0.390033	0.195016	−	0.980800i	$-0.437524\pi$
$3$	0.675556	0.390033	0.195016	+	0.980800i	$0.437524\pi$
$4$	1.00000	0.500000
$5$	1.00000	0.447214
$5$	1.00000	0.447214
$6$	−0.675556	−0.275795
$7$	−1.96617	−0.743142	−0.371571	−	0.928404i	$-0.621181\pi$
$7$	−1.96617	−0.743142	−0.371571	+	0.928404i	$0.621181\pi$
$8$	−1.00000	−0.353553
$9$	−2.54362	−0.847875
$10$	−1.00000	−0.316228
$11$	−0.702842	−0.211915	−0.105957	−	0.994371i	$-0.533791\pi$
$11$	−0.702842	−0.211915	−0.105957	+	0.994371i	$0.533791\pi$
$12$	0.675556	0.195016
$13$	3.63999	1.00955	0.504775	−	0.863251i	$-0.331575\pi$
$13$	3.63999	1.00955	0.504775	+	0.863251i	$0.331575\pi$
$14$	1.96617	0.525481
$15$	0.675556	0.174428
$16$	1.00000	0.250000
$17$	−0.463370	−0.112384	−0.0561919	−	0.998420i	$-0.517896\pi$
$17$	−0.463370	−0.112384	−0.0561919	+	0.998420i	$0.517896\pi$
$18$	2.54362	0.599538
$19$	1.64115	0.376505	0.188252	−	0.982121i	$-0.439718\pi$
$19$	1.64115	0.376505	0.188252	+	0.982121i	$0.439718\pi$
$20$	1.00000	0.223607
$21$	−1.32826	−0.289850
$22$	0.702842	0.149846
$23$	−3.53333	−0.736750	−0.368375	−	0.929677i	$-0.620086\pi$
$23$	−3.53333	−0.736750	−0.368375	+	0.929677i	$0.620086\pi$
$24$	−0.675556	−0.137897
$25$	1.00000	0.200000
$26$	−3.63999	−0.713860
$27$	−3.74503	−0.720731
$28$	−1.96617	−0.371571
$29$	2.53753	0.471208	0.235604	−	0.971849i	$-0.424293\pi$
$29$	2.53753	0.471208	0.235604	+	0.971849i	$0.424293\pi$
$30$	−0.675556	−0.123339
$31$	−6.10965	−1.09733	−0.548663	−	0.836044i	$-0.684863\pi$
$31$	−6.10965	−1.09733	−0.548663	+	0.836044i	$0.684863\pi$
$32$	−1.00000	−0.176777
$33$	−0.474809	−0.0826537
$34$	0.463370	0.0794673
$35$	−1.96617	−0.332343
$36$	−2.54362	−0.423937
$37$	5.76322	0.947468	0.473734	−	0.880668i	$-0.342906\pi$
$37$	5.76322	0.947468	0.473734	+	0.880668i	$0.342906\pi$
$38$	−1.64115	−0.266229
$39$	2.45902	0.393758
$40$	−1.00000	−0.158114
$41$	7.14911	1.11650	0.558251	−	0.829672i	$-0.311472\pi$
$41$	7.14911	1.11650	0.558251	+	0.829672i	$0.311472\pi$
$42$	1.32826	0.204955
$43$	−6.31705	−0.963342	−0.481671	−	0.876352i	$-0.659970\pi$
$43$	−6.31705	−0.963342	−0.481671	+	0.876352i	$0.659970\pi$
$44$	−0.702842	−0.105957
$45$	−2.54362	−0.379181
$46$	3.53333	0.520961
$47$	5.97612	0.871707	0.435854	−	0.900018i	$-0.356447\pi$
$47$	5.97612	0.871707	0.435854	+	0.900018i	$0.356447\pi$
$48$	0.675556	0.0975082
$49$	−3.13418	−0.447739
$50$	−1.00000	−0.141421
$51$	−0.313032	−0.0438333
$52$	3.63999	0.504775
$53$	−4.57721	−0.628729	−0.314364	−	0.949302i	$-0.601791\pi$
$53$	−4.57721	−0.628729	−0.314364	+	0.949302i	$0.601791\pi$
$54$	3.74503	0.509634
$55$	−0.702842	−0.0947711
$56$	1.96617	0.262741
$57$	1.10869	0.146849
$58$	−2.53753	−0.333194
$59$	−2.56548	−0.333997	−0.166998	−	0.985957i	$-0.553407\pi$
$59$	−2.56548	−0.333997	−0.166998	+	0.985957i	$0.553407\pi$
$60$	0.675556	0.0872139
$61$	−9.20668	−1.17879	−0.589397	−	0.807843i	$-0.700635\pi$
$61$	−9.20668	−1.17879	−0.589397	+	0.807843i	$0.700635\pi$
$62$	6.10965	0.775926
$63$	5.00120	0.630092
$64$	1.00000	0.125000
$65$	3.63999	0.451485
$66$	0.474809	0.0584450
$67$	2.71402	0.331570	0.165785	−	0.986162i	$-0.446984\pi$
$67$	2.71402	0.331570	0.165785	+	0.986162i	$0.446984\pi$
$68$	−0.463370	−0.0561919
$69$	−2.38696	−0.287357
$70$	1.96617	0.235002
$71$	−3.57818	−0.424651	−0.212326	−	0.977199i	$-0.568104\pi$
$71$	−3.57818	−0.424651	−0.212326	+	0.977199i	$0.568104\pi$
$72$	2.54362	0.299769
$73$	−1.05604	−0.123600	−0.0617999	−	0.998089i	$-0.519684\pi$
$73$	−1.05604	−0.123600	−0.0617999	+	0.998089i	$0.519684\pi$
$74$	−5.76322	−0.669961
$75$	0.675556	0.0780065
$76$	1.64115	0.188252
$77$	1.38191	0.157483
$78$	−2.45902	−0.278429
$79$	−7.77888	−0.875192	−0.437596	−	0.899172i	$-0.644170\pi$
$79$	−7.77888	−0.875192	−0.437596	+	0.899172i	$0.644170\pi$
$80$	1.00000	0.111803
$81$	5.10089	0.566766
$82$	−7.14911	−0.789487
$83$	−5.64286	−0.619384	−0.309692	−	0.950837i	$-0.600226\pi$
$83$	−5.64286	−0.619384	−0.309692	+	0.950837i	$0.600226\pi$
$84$	−1.32826	−0.144925
$85$	−0.463370	−0.0502595
$86$	6.31705	0.681186
$87$	1.71424	0.183786
$88$	0.702842	0.0749232
$89$	2.42510	0.257060	0.128530	−	0.991706i	$-0.458974\pi$
$89$	2.42510	0.257060	0.128530	+	0.991706i	$0.458974\pi$
$90$	2.54362	0.268121
$91$	−7.15683	−0.750240
$92$	−3.53333	−0.368375
$93$	−4.12741	−0.427993
$94$	−5.97612	−0.616390
$95$	1.64115	0.168378
$96$	−0.675556	−0.0689487
$97$	14.3124	1.45321	0.726604	−	0.687057i	$-0.241098\pi$
$97$	14.3124	1.45321	0.726604	+	0.687057i	$0.241098\pi$
$98$	3.13418	0.316599
$99$	1.78776	0.179677
$100$	1.00000	0.100000
$101$	11.1101	1.10549	0.552747	−	0.833349i	$-0.313580\pi$
$101$	11.1101	1.10549	0.552747	+	0.833349i	$0.313580\pi$
$102$	0.313032	0.0309948
$103$	−13.5007	−1.33026	−0.665130	−	0.746727i	$-0.731624\pi$
$103$	−13.5007	−1.33026	−0.665130	+	0.746727i	$0.731624\pi$
$104$	−3.63999	−0.356930
$105$	−1.32826	−0.129625
$106$	4.57721	0.444578
$107$	−9.98140	−0.964939	−0.482469	−	0.875913i	$-0.660260\pi$
$107$	−9.98140	−0.964939	−0.482469	+	0.875913i	$0.660260\pi$
$108$	−3.74503	−0.360366
$109$	−17.3033	−1.65736	−0.828678	−	0.559725i	$-0.810907\pi$
$109$	−17.3033	−1.65736	−0.828678	+	0.559725i	$0.810907\pi$
$110$	0.702842	0.0670133
$111$	3.89338	0.369543
$112$	−1.96617	−0.185786
$113$	−15.8435	−1.49043	−0.745215	−	0.666824i	$-0.767653\pi$
$113$	−15.8435	−1.49043	−0.745215	+	0.666824i	$0.767653\pi$
$114$	−1.10869	−0.103838
$115$	−3.53333	−0.329485
$116$	2.53753	0.235604
$117$	−9.25876	−0.855972
$118$	2.56548	0.236171
$119$	0.911064	0.0835171
$120$	−0.675556	−0.0616696
$121$	−10.5060	−0.955092
$122$	9.20668	0.833534
$123$	4.82962	0.435472
$124$	−6.10965	−0.548663
$125$	1.00000	0.0894427
$126$	−5.00120	−0.445542
$127$	−2.46196	−0.218463	−0.109232	−	0.994016i	$-0.534839\pi$
$127$	−2.46196	−0.218463	−0.109232	+	0.994016i	$0.534839\pi$
$128$	−1.00000	−0.0883883
$129$	−4.26753	−0.375735
$130$	−3.63999	−0.319248
$131$	−12.1540	−1.06190	−0.530950	−	0.847403i	$-0.678165\pi$
$131$	−12.1540	−1.06190	−0.530950	+	0.847403i	$0.678165\pi$
$132$	−0.474809	−0.0413268
$133$	−3.22677	−0.279797
$134$	−2.71402	−0.234456
$135$	−3.74503	−0.322321
$136$	0.463370	0.0397336
$137$	−14.9534	−1.27755	−0.638777	−	0.769392i	$-0.720559\pi$
$137$	−14.9534	−1.27755	−0.638777	+	0.769392i	$0.720559\pi$
$138$	2.38696	0.203192
$139$	−21.8514	−1.85341	−0.926704	−	0.375792i	$-0.877371\pi$
$139$	−21.8514	−1.85341	−0.926704	+	0.375792i	$0.877371\pi$
$140$	−1.96617	−0.166172
$141$	4.03721	0.339994
$142$	3.57818	0.300274
$143$	−2.55833	−0.213939
$144$	−2.54362	−0.211969
$145$	2.53753	0.210730
$146$	1.05604	0.0873982
$147$	−2.11731	−0.174633
$148$	5.76322	0.473734
$149$	3.79711	0.311071	0.155536	−	0.987830i	$-0.450290\pi$
$149$	3.79711	0.311071	0.155536	+	0.987830i	$0.450290\pi$
$150$	−0.675556	−0.0551589
$151$	−5.98467	−0.487026	−0.243513	−	0.969898i	$-0.578300\pi$
$151$	−5.98467	−0.487026	−0.243513	+	0.969898i	$0.578300\pi$
$152$	−1.64115	−0.133114
$153$	1.17864	0.0952873
$154$	−1.38191	−0.111357
$155$	−6.10965	−0.490739
$156$	2.45902	0.196879
$157$	18.7300	1.49482	0.747409	−	0.664364i	$-0.231297\pi$
$157$	18.7300	1.49482	0.747409	+	0.664364i	$0.231297\pi$
$158$	7.77888	0.618854
$159$	−3.09217	−0.245225
$160$	−1.00000	−0.0790569
$161$	6.94712	0.547510
$162$	−5.10089	−0.400764
$163$	24.0979	1.88750	0.943748	−	0.330666i	$-0.107273\pi$
$163$	24.0979	1.88750	0.943748	+	0.330666i	$0.107273\pi$
$164$	7.14911	0.558251
$165$	−0.474809	−0.0369638
$166$	5.64286	0.437971
$167$	−6.60551	−0.511150	−0.255575	−	0.966789i	$-0.582265\pi$
$167$	−6.60551	−0.511150	−0.255575	+	0.966789i	$0.582265\pi$
$168$	1.32826	0.102477
$169$	0.249501	0.0191924
$170$	0.463370	0.0355389
$171$	−4.17446	−0.319229
$172$	−6.31705	−0.481671
$173$	−15.0557	−1.14466	−0.572332	−	0.820022i	$-0.693961\pi$
$173$	−15.0557	−1.14466	−0.572332	+	0.820022i	$0.693961\pi$
$174$	−1.71424	−0.129957
$175$	−1.96617	−0.148628
$176$	−0.702842	−0.0529787
$177$	−1.73312	−0.130270
$178$	−2.42510	−0.181769
$179$	12.5215	0.935904	0.467952	−	0.883754i	$-0.344992\pi$
$179$	12.5215	0.935904	0.467952	+	0.883754i	$0.344992\pi$
$180$	−2.54362	−0.189591
$181$	−23.0329	−1.71202	−0.856012	−	0.516956i	$-0.827065\pi$
$181$	−23.0329	−1.71202	−0.856012	+	0.516956i	$0.827065\pi$
$182$	7.15683	0.530500
$183$	−6.21963	−0.459768
$184$	3.53333	0.260480
$185$	5.76322	0.423721
$186$	4.12741	0.302637
$187$	0.325676	0.0238158
$188$	5.97612	0.435854
$189$	7.36337	0.535606
$190$	−1.64115	−0.119061
$191$	15.0467	1.08874	0.544371	−	0.838844i	$-0.316768\pi$
$191$	15.0467	1.08874	0.544371	+	0.838844i	$0.316768\pi$
$192$	0.675556	0.0487541
$193$	−19.7068	−1.41852	−0.709262	−	0.704945i	$-0.750972\pi$
$193$	−19.7068	−1.41852	−0.709262	+	0.704945i	$0.750972\pi$
$194$	−14.3124	−1.02757
$195$	2.45902	0.176094
$196$	−3.13418	−0.223870
$197$	15.6305	1.11363	0.556813	−	0.830638i	$-0.312024\pi$
$197$	15.6305	1.11363	0.556813	+	0.830638i	$0.312024\pi$
$198$	−1.78776	−0.127051
$199$	−6.63045	−0.470020	−0.235010	−	0.971993i	$-0.575512\pi$
$199$	−6.63045	−0.470020	−0.235010	+	0.971993i	$0.575512\pi$
$200$	−1.00000	−0.0707107
$201$	1.83347	0.129323
$202$	−11.1101	−0.781703
$203$	−4.98922	−0.350174
$204$	−0.313032	−0.0219167
$205$	7.14911	0.499315
$206$	13.5007	0.940636
$207$	8.98746	0.624671
$208$	3.63999	0.252388
$209$	−1.15347	−0.0797869
$210$	1.32826	0.0916586
$211$	18.7194	1.28870	0.644350	−	0.764731i	$-0.277128\pi$
$211$	18.7194	1.28870	0.644350	+	0.764731i	$0.277128\pi$
$212$	−4.57721	−0.314364
$213$	−2.41726	−0.165628
$214$	9.98140	0.682315
$215$	−6.31705	−0.430820
$216$	3.74503	0.254817
$217$	12.0126	0.815469
$218$	17.3033	1.17193
$219$	−0.713412	−0.0482079
$220$	−0.702842	−0.0473856
$221$	−1.68666	−0.113457
$222$	−3.89338	−0.261307
$223$	−7.21360	−0.483059	−0.241529	−	0.970394i	$-0.577649\pi$
$223$	−7.21360	−0.483059	−0.241529	+	0.970394i	$0.577649\pi$
$224$	1.96617	0.131370
$225$	−2.54362	−0.169575
$226$	15.8435	1.05389
$227$	19.4540	1.29120	0.645602	−	0.763674i	$-0.276606\pi$
$227$	19.4540	1.29120	0.645602	+	0.763674i	$0.276606\pi$
$228$	1.10869	0.0734245
$229$	11.2055	0.740479	0.370239	−	0.928936i	$-0.379276\pi$
$229$	11.2055	0.740479	0.370239	+	0.928936i	$0.379276\pi$
$230$	3.53333	0.232981
$231$	0.933555	0.0614234
$232$	−2.53753	−0.166597
$233$	17.7284	1.16143	0.580714	−	0.814108i	$-0.302773\pi$
$233$	17.7284	1.16143	0.580714	+	0.814108i	$0.302773\pi$
$234$	9.25876	0.605264
$235$	5.97612	0.389839
$236$	−2.56548	−0.166998
$237$	−5.25507	−0.341353
$238$	−0.911064	−0.0590555
$239$	−13.2487	−0.856990	−0.428495	−	0.903544i	$-0.640956\pi$
$239$	−13.2487	−0.856990	−0.428495	+	0.903544i	$0.640956\pi$
$240$	0.675556	0.0436070
$241$	6.61312	0.425989	0.212994	−	0.977053i	$-0.431678\pi$
$241$	6.61312	0.425989	0.212994	+	0.977053i	$0.431678\pi$
$242$	10.5060	0.675352
$243$	14.6810	0.941789
$244$	−9.20668	−0.589397
$245$	−3.13418	−0.200235
$246$	−4.82962	−0.307926
$247$	5.97375	0.380100
$248$	6.10965	0.387963
$249$	−3.81207	−0.241580
$250$	−1.00000	−0.0632456
$251$	−26.0274	−1.64283	−0.821417	−	0.570329i	$-0.806816\pi$
$251$	−26.0274	−1.64283	−0.821417	+	0.570329i	$0.806816\pi$
$252$	5.00120	0.315046
$253$	2.48337	0.156128
$254$	2.46196	0.154477
$255$	−0.313032	−0.0196029
$256$	1.00000	0.0625000
$257$	−8.14027	−0.507776	−0.253888	−	0.967234i	$-0.581710\pi$
$257$	−8.14027	−0.507776	−0.253888	+	0.967234i	$0.581710\pi$
$258$	4.26753	0.265685
$259$	−11.3315	−0.704104
$260$	3.63999	0.225742
$261$	−6.45452	−0.399525
$262$	12.1540	0.750877
$263$	2.11090	0.130164	0.0650820	−	0.997880i	$-0.479269\pi$
$263$	2.11090	0.130164	0.0650820	+	0.997880i	$0.479269\pi$
$264$	0.474809	0.0292225
$265$	−4.57721	−0.281176
$266$	3.22677	0.197846
$267$	1.63829	0.100262
$268$	2.71402	0.165785
$269$	−19.0580	−1.16199	−0.580993	−	0.813909i	$-0.697336\pi$
$269$	−19.0580	−1.16199	−0.580993	+	0.813909i	$0.697336\pi$
$270$	3.74503	0.227915
$271$	−5.04991	−0.306760	−0.153380	−	0.988167i	$-0.549016\pi$
$271$	−5.04991	−0.306760	−0.153380	+	0.988167i	$0.549016\pi$
$272$	−0.463370	−0.0280959
$273$	−4.83484	−0.292618
$274$	14.9534	0.903367
$275$	−0.702842	−0.0423829
$276$	−2.38696	−0.143678
$277$	−9.21670	−0.553778	−0.276889	−	0.960902i	$-0.589303\pi$
$277$	−9.21670	−0.553778	−0.276889	+	0.960902i	$0.589303\pi$
$278$	21.8514	1.31056
$279$	15.5407	0.930394
$280$	1.96617	0.117501
$281$	−6.57568	−0.392272	−0.196136	−	0.980577i	$-0.562839\pi$
$281$	−6.57568	−0.392272	−0.196136	+	0.980577i	$0.562839\pi$
$282$	−4.03721	−0.240412
$283$	18.7413	1.11406	0.557028	−	0.830494i	$-0.311942\pi$
$283$	18.7413	1.11406	0.557028	+	0.830494i	$0.311942\pi$
$284$	−3.57818	−0.212326
$285$	1.10869	0.0656729
$286$	2.55833	0.151277
$287$	−14.0564	−0.829721
$288$	2.54362	0.149884
$289$	−16.7853	−0.987370
$290$	−2.53753	−0.149009
$291$	9.66886	0.566798
$292$	−1.05604	−0.0617999
$293$	20.3420	1.18839	0.594195	−	0.804321i	$-0.297471\pi$
$293$	20.3420	1.18839	0.594195	+	0.804321i	$0.297471\pi$
$294$	2.11731	0.123484
$295$	−2.56548	−0.149368
$296$	−5.76322	−0.334981
$297$	2.63216	0.152734
$298$	−3.79711	−0.219961
$299$	−12.8613	−0.743786
$300$	0.675556	0.0390033
$301$	12.4204	0.715900
$302$	5.98467	0.344379
$303$	7.50548	0.431179
$304$	1.64115	0.0941261
$305$	−9.20668	−0.527173
$306$	−1.17864	−0.0673783
$307$	−9.26421	−0.528737	−0.264368	−	0.964422i	$-0.585163\pi$
$307$	−9.26421	−0.528737	−0.264368	+	0.964422i	$0.585163\pi$
$308$	1.38191	0.0787414
$309$	−9.12046	−0.518845
$310$	6.10965	0.347005
$311$	−10.3280	−0.585650	−0.292825	−	0.956166i	$-0.594595\pi$
$311$	−10.3280	−0.585650	−0.292825	+	0.956166i	$0.594595\pi$
$312$	−2.45902	−0.139214
$313$	−24.1184	−1.36325	−0.681626	−	0.731701i	$-0.738727\pi$
$313$	−24.1184	−1.36325	−0.681626	+	0.731701i	$0.738727\pi$
$314$	−18.7300	−1.05700
$315$	5.00120	0.281786
$316$	−7.77888	−0.437596
$317$	19.8911	1.11720	0.558598	−	0.829438i	$-0.311339\pi$
$317$	19.8911	1.11720	0.558598	+	0.829438i	$0.311339\pi$
$318$	3.09217	0.173400
$319$	−1.78348	−0.0998558
$320$	1.00000	0.0559017
$321$	−6.74300	−0.376358
$322$	−6.94712	−0.387148
$323$	−0.760457	−0.0423130
$324$	5.10089	0.283383
$325$	3.63999	0.201910
$326$	−24.0979	−1.33466
$327$	−11.6894	−0.646423
$328$	−7.14911	−0.394743
$329$	−11.7501	−0.647803
$330$	0.474809	0.0261374
$331$	−25.8891	−1.42299	−0.711496	−	0.702691i	$-0.751982\pi$
$331$	−25.8891	−1.42299	−0.711496	+	0.702691i	$0.751982\pi$
$332$	−5.64286	−0.309692
$333$	−14.6595	−0.803334
$334$	6.60551	0.361437
$335$	2.71402	0.148283
$336$	−1.32826	−0.0724625
$337$	14.9572	0.814770	0.407385	−	0.913257i	$-0.366441\pi$
$337$	14.9572	0.814770	0.407385	+	0.913257i	$0.366441\pi$
$338$	−0.249501	−0.0135711
$339$	−10.7032	−0.581317
$340$	−0.463370	−0.0251298
$341$	4.29412	0.232539
$342$	4.17446	0.225729
$343$	19.9255	1.07588
$344$	6.31705	0.340593
$345$	−2.38696	−0.128510
$346$	15.0557	0.809400
$347$	27.7319	1.48873	0.744363	−	0.667776i	$-0.232753\pi$
$347$	27.7319	1.48873	0.744363	+	0.667776i	$0.232753\pi$
$348$	1.71424	0.0918932
$349$	2.15312	0.115254	0.0576270	−	0.998338i	$-0.481647\pi$
$349$	2.15312	0.115254	0.0576270	+	0.998338i	$0.481647\pi$
$350$	1.96617	0.105096
$351$	−13.6319	−0.727615
$352$	0.702842	0.0374616
$353$	6.05838	0.322455	0.161228	−	0.986917i	$-0.448455\pi$
$353$	6.05838	0.322455	0.161228	+	0.986917i	$0.448455\pi$
$354$	1.73312	0.0921145
$355$	−3.57818	−0.189910
$356$	2.42510	0.128530
$357$	0.615475	0.0325744
$358$	−12.5215	−0.661784
$359$	−26.0891	−1.37693	−0.688465	−	0.725270i	$-0.741715\pi$
$359$	−26.0891	−1.37693	−0.688465	+	0.725270i	$0.741715\pi$
$360$	2.54362	0.134061
$361$	−16.3066	−0.858244
$362$	23.0329	1.21058
$363$	−7.09740	−0.372517
$364$	−7.15683	−0.375120
$365$	−1.05604	−0.0552755
$366$	6.21963	0.325105
$367$	2.08709	0.108945	0.0544725	−	0.998515i	$-0.482652\pi$
$367$	2.08709	0.108945	0.0544725	+	0.998515i	$0.482652\pi$
$368$	−3.53333	−0.184187
$369$	−18.1846	−0.946654
$370$	−5.76322	−0.299616
$371$	8.99958	0.467235
$372$	−4.12741	−0.213996
$373$	−28.8649	−1.49457	−0.747284	−	0.664504i	$-0.768643\pi$
$373$	−28.8649	−1.49457	−0.747284	+	0.664504i	$0.768643\pi$
$374$	−0.325676	−0.0168403
$375$	0.675556	0.0348856
$376$	−5.97612	−0.308195
$377$	9.23658	0.475708
$378$	−7.36337	−0.378731
$379$	7.44485	0.382416	0.191208	−	0.981550i	$-0.438759\pi$
$379$	7.44485	0.382416	0.191208	+	0.981550i	$0.438759\pi$
$380$	1.64115	0.0841890
$381$	−1.66319	−0.0852079
$382$	−15.0467	−0.769858
$383$	−18.3001	−0.935092	−0.467546	−	0.883969i	$-0.654862\pi$
$383$	−18.3001	−0.935092	−0.467546	+	0.883969i	$0.654862\pi$
$384$	−0.675556	−0.0344743
$385$	1.38191	0.0704285
$386$	19.7068	1.00305
$387$	16.0682	0.816793
$388$	14.3124	0.726604
$389$	22.2317	1.12719	0.563597	−	0.826050i	$-0.309417\pi$
$389$	22.2317	1.12719	0.563597	+	0.826050i	$0.309417\pi$
$390$	−2.45902	−0.124517
$391$	1.63724	0.0827987
$392$	3.13418	0.158300
$393$	−8.21071	−0.414176
$394$	−15.6305	−0.787452
$395$	−7.77888	−0.391398
$396$	1.78776	0.0898385
$397$	3.83234	0.192340	0.0961699	−	0.995365i	$-0.469341\pi$
$397$	3.83234	0.192340	0.0961699	+	0.995365i	$0.469341\pi$
$398$	6.63045	0.332354
$399$	−2.17987	−0.109130
$400$	1.00000	0.0500000
$401$	1.00000	0.0499376
$401$	1.00000	0.0499376
$402$	−1.83347	−0.0914453
$403$	−22.2390	−1.10781
$404$	11.1101	0.552747
$405$	5.10089	0.253465
$406$	4.98922	0.247611
$407$	−4.05063	−0.200782
$408$	0.313032	0.0154974
$409$	20.3572	1.00660	0.503300	−	0.864112i	$-0.332119\pi$
$409$	20.3572	1.00660	0.503300	+	0.864112i	$0.332119\pi$
$410$	−7.14911	−0.353069
$411$	−10.1019	−0.498288
$412$	−13.5007	−0.665130
$413$	5.04416	0.248207
$414$	−8.98746	−0.441709
$415$	−5.64286	−0.276997
$416$	−3.63999	−0.178465
$417$	−14.7618	−0.722890
$418$	1.15347	0.0564178
$419$	20.8407	1.01814	0.509068	−	0.860726i	$-0.329990\pi$
$419$	20.8407	1.01814	0.509068	+	0.860726i	$0.329990\pi$
$420$	−1.32826	−0.0648124
$421$	23.1118	1.12640	0.563200	−	0.826321i	$-0.309570\pi$
$421$	23.1118	1.12640	0.563200	+	0.826321i	$0.309570\pi$
$422$	−18.7194	−0.911248
$423$	−15.2010	−0.739098
$424$	4.57721	0.222289
$425$	−0.463370	−0.0224767
$426$	2.41726	0.117117
$427$	18.1019	0.876012
$428$	−9.98140	−0.482469
$429$	−1.72830	−0.0834430
$430$	6.31705	0.304635
$431$	−26.9560	−1.29842	−0.649212	−	0.760608i	$-0.724901\pi$
$431$	−26.9560	−1.29842	−0.649212	+	0.760608i	$0.724901\pi$
$432$	−3.74503	−0.180183
$433$	1.05846	0.0508662	0.0254331	−	0.999677i	$-0.491904\pi$
$433$	1.05846	0.0508662	0.0254331	+	0.999677i	$0.491904\pi$
$434$	−12.0126	−0.576624
$435$	1.71424	0.0821917
$436$	−17.3033	−0.828678
$437$	−5.79871	−0.277390
$438$	0.713412	0.0340882
$439$	−26.9332	−1.28545	−0.642725	−	0.766097i	$-0.722196\pi$
$439$	−26.9332	−1.28545	−0.642725	+	0.766097i	$0.722196\pi$
$440$	0.702842	0.0335067
$441$	7.97216	0.379627
$442$	1.68666	0.0802262
$443$	3.79606	0.180356	0.0901782	−	0.995926i	$-0.471256\pi$
$443$	3.79606	0.180356	0.0901782	+	0.995926i	$0.471256\pi$
$444$	3.89338	0.184772
$445$	2.42510	0.114961
$446$	7.21360	0.341574
$447$	2.56516	0.121328
$448$	−1.96617	−0.0928928
$449$	−19.9784	−0.942841	−0.471420	−	0.881909i	$-0.656258\pi$
$449$	−19.9784	−0.942841	−0.471420	+	0.881909i	$0.656258\pi$
$450$	2.54362	0.119908
$451$	−5.02469	−0.236603
$452$	−15.8435	−0.745215
$453$	−4.04298	−0.189956
$454$	−19.4540	−0.913020
$455$	−7.15683	−0.335517
$456$	−1.10869	−0.0519190
$457$	−12.0619	−0.564231	−0.282115	−	0.959380i	$-0.591036\pi$
$457$	−12.0619	−0.564231	−0.282115	+	0.959380i	$0.591036\pi$
$458$	−11.2055	−0.523598
$459$	1.73533	0.0809985
$460$	−3.53333	−0.164742
$461$	−23.7685	−1.10701	−0.553504	−	0.832847i	$-0.686710\pi$
$461$	−23.7685	−1.10701	−0.553504	+	0.832847i	$0.686710\pi$
$462$	−0.933555	−0.0434329
$463$	−25.5650	−1.18810	−0.594052	−	0.804426i	$-0.702473\pi$
$463$	−25.5650	−1.18810	−0.594052	+	0.804426i	$0.702473\pi$
$464$	2.53753	0.117802
$465$	−4.12741	−0.191404
$466$	−17.7284	−0.821254
$467$	1.38486	0.0640835	0.0320418	−	0.999487i	$-0.489799\pi$
$467$	1.38486	0.0640835	0.0320418	+	0.999487i	$0.489799\pi$
$468$	−9.25876	−0.427986
$469$	−5.33623	−0.246404
$470$	−5.97612	−0.275658
$471$	12.6532	0.583028
$472$	2.56548	0.118086
$473$	4.43989	0.204146
$474$	5.25507	0.241373
$475$	1.64115	0.0753009
$476$	0.911064	0.0417586
$477$	11.6427	0.533083
$478$	13.2487	0.605983
$479$	−9.15088	−0.418114	−0.209057	−	0.977903i	$-0.567039\pi$
$479$	−9.15088	−0.418114	−0.209057	+	0.977903i	$0.567039\pi$
$480$	−0.675556	−0.0308348
$481$	20.9781	0.956517
$482$	−6.61312	−0.301219
$483$	4.69317	0.213547
$484$	−10.5060	−0.477546
$485$	14.3124	0.649894
$486$	−14.6810	−0.665945
$487$	9.41697	0.426724	0.213362	−	0.976973i	$-0.431559\pi$
$487$	9.41697	0.426724	0.213362	+	0.976973i	$0.431559\pi$
$488$	9.20668	0.416767
$489$	16.2795	0.736185
$490$	3.13418	0.141588
$491$	21.6913	0.978917	0.489458	−	0.872027i	$-0.337195\pi$
$491$	21.6913	0.978917	0.489458	+	0.872027i	$0.337195\pi$
$492$	4.82962	0.217736
$493$	−1.17582	−0.0529561
$494$	−5.97375	−0.268772
$495$	1.78776	0.0803540
$496$	−6.10965	−0.274331
$497$	7.03530	0.315577
$498$	3.81207	0.170823
$499$	−38.4965	−1.72334	−0.861670	−	0.507468i	$-0.830581\pi$
$499$	−38.4965	−1.72334	−0.861670	+	0.507468i	$0.830581\pi$
$500$	1.00000	0.0447214
$501$	−4.46239	−0.199365
$502$	26.0274	1.16166
$503$	−18.5035	−0.825029	−0.412515	−	0.910951i	$-0.635349\pi$
$503$	−18.5035	−0.825029	−0.412515	+	0.910951i	$0.635349\pi$
$504$	−5.00120	−0.222771
$505$	11.1101	0.494392
$506$	−2.48337	−0.110399
$507$	0.168552	0.00748566
$508$	−2.46196	−0.109232
$509$	29.3133	1.29929	0.649644	−	0.760239i	$-0.274918\pi$
$509$	29.3133	1.29929	0.649644	+	0.760239i	$0.274918\pi$
$510$	0.313032	0.0138613
$511$	2.07635	0.0918522
$512$	−1.00000	−0.0441942
$513$	−6.14614	−0.271359
$514$	8.14027	0.359052
$515$	−13.5007	−0.594910
$516$	−4.26753	−0.187867
$517$	−4.20027	−0.184728
$518$	11.3315	0.497877
$519$	−10.1710	−0.446456
$520$	−3.63999	−0.159624
$521$	−28.6667	−1.25591	−0.627956	−	0.778249i	$-0.716108\pi$
$521$	−28.6667	−1.25591	−0.627956	+	0.778249i	$0.716108\pi$
$522$	6.45452	0.282507
$523$	35.7366	1.56265	0.781326	−	0.624123i	$-0.214543\pi$
$523$	35.7366	1.56265	0.781326	+	0.624123i	$0.214543\pi$
$524$	−12.1540	−0.530950
$525$	−1.32826	−0.0579700
$526$	−2.11090	−0.0920398
$527$	2.83103	0.123322
$528$	−0.474809	−0.0206634
$529$	−10.5156	−0.457200
$530$	4.57721	0.198821
$531$	6.52561	0.283187
$532$	−3.22677	−0.139898
$533$	26.0226	1.12717
$534$	−1.63829	−0.0708959
$535$	−9.98140	−0.431534
$536$	−2.71402	−0.117228
$537$	8.45900	0.365033
$538$	19.0580	0.821648
$539$	2.20283	0.0948826
$540$	−3.74503	−0.161160
$541$	34.4528	1.48124	0.740620	−	0.671924i	$-0.234532\pi$
$541$	34.4528	1.48124	0.740620	+	0.671924i	$0.234532\pi$
$542$	5.04991	0.216912
$543$	−15.5600	−0.667745
$544$	0.463370	0.0198668
$545$	−17.3033	−0.741192
$546$	4.83484	0.206912
$547$	−23.5201	−1.00565	−0.502824	−	0.864389i	$-0.667705\pi$
$547$	−23.5201	−1.00565	−0.502824	+	0.864389i	$0.667705\pi$
$548$	−14.9534	−0.638777
$549$	23.4183	0.999470
$550$	0.702842	0.0299693
$551$	4.16446	0.177412
$552$	2.38696	0.101596
$553$	15.2946	0.650392
$554$	9.21670	0.391580
$555$	3.89338	0.165265
$556$	−21.8514	−0.926704
$557$	7.16891	0.303757	0.151878	−	0.988399i	$-0.451468\pi$
$557$	7.16891	0.303757	0.151878	+	0.988399i	$0.451468\pi$
$558$	−15.5407	−0.657888
$559$	−22.9940	−0.972542
$560$	−1.96617	−0.0830859
$561$	0.220012	0.00928893
$562$	6.57568	0.277378
$563$	−6.13281	−0.258467	−0.129234	−	0.991614i	$-0.541252\pi$
$563$	−6.13281	−0.258467	−0.129234	+	0.991614i	$0.541252\pi$
$564$	4.03721	0.169997
$565$	−15.8435	−0.666541
$566$	−18.7413	−0.787757
$567$	−10.0292	−0.421188
$568$	3.57818	0.150137
$569$	−36.2932	−1.52149	−0.760745	−	0.649050i	$-0.775166\pi$
$569$	−36.2932	−1.52149	−0.760745	+	0.649050i	$0.775166\pi$
$570$	−1.10869	−0.0464378
$571$	−4.27540	−0.178920	−0.0894600	−	0.995990i	$-0.528514\pi$
$571$	−4.27540	−0.178920	−0.0894600	+	0.995990i	$0.528514\pi$
$572$	−2.55833	−0.106969
$573$	10.1649	0.424645
$574$	14.0564	0.586701
$575$	−3.53333	−0.147350
$576$	−2.54362	−0.105984
$577$	13.9229	0.579616	0.289808	−	0.957085i	$-0.406408\pi$
$577$	13.9229	0.579616	0.289808	+	0.957085i	$0.406408\pi$
$578$	16.7853	0.698176
$579$	−13.3130	−0.553271
$580$	2.53753	0.105365
$581$	11.0948	0.460291
$582$	−9.66886	−0.400787
$583$	3.21706	0.133237
$584$	1.05604	0.0436991
$585$	−9.25876	−0.382802
$586$	−20.3420	−0.840319
$587$	−30.9970	−1.27938	−0.639692	−	0.768631i	$-0.720938\pi$
$587$	−30.9970	−1.27938	−0.639692	+	0.768631i	$0.720938\pi$
$588$	−2.11731	−0.0873165
$589$	−10.0268	−0.413148
$590$	2.56548	0.105619
$591$	10.5593	0.434350
$592$	5.76322	0.236867
$593$	29.1063	1.19525	0.597625	−	0.801775i	$-0.296111\pi$
$593$	29.1063	1.19525	0.597625	+	0.801775i	$0.296111\pi$
$594$	−2.63216	−0.107999
$595$	0.911064	0.0373500
$596$	3.79711	0.155536
$597$	−4.47924	−0.183323
$598$	12.8613	0.525936
$599$	34.1254	1.39433	0.697163	−	0.716912i	$-0.254445\pi$
$599$	34.1254	1.39433	0.697163	+	0.716912i	$0.254445\pi$
$600$	−0.675556	−0.0275795
$601$	34.7085	1.41579	0.707895	−	0.706318i	$-0.249645\pi$
$601$	34.7085	1.41579	0.707895	+	0.706318i	$0.249645\pi$
$602$	−12.4204	−0.506218
$603$	−6.90345	−0.281130
$604$	−5.98467	−0.243513
$605$	−10.5060	−0.427130
$606$	−7.50548	−0.304889
$607$	3.38718	0.137481	0.0687407	−	0.997635i	$-0.478102\pi$
$607$	3.38718	0.137481	0.0687407	+	0.997635i	$0.478102\pi$
$608$	−1.64115	−0.0665572
$609$	−3.37050	−0.136579
$610$	9.20668	0.372768
$611$	21.7530	0.880032
$612$	1.17864	0.0476436
$613$	−44.1473	−1.78309	−0.891547	−	0.452928i	$-0.850379\pi$
$613$	−44.1473	−1.78309	−0.891547	+	0.452928i	$0.850379\pi$
$614$	9.26421	0.373873
$615$	4.82962	0.194749
$616$	−1.38191	−0.0556786
$617$	24.2323	0.975555	0.487777	−	0.872968i	$-0.337808\pi$
$617$	24.2323	0.975555	0.487777	+	0.872968i	$0.337808\pi$
$618$	9.12046	0.366879
$619$	−32.1593	−1.29259	−0.646295	−	0.763088i	$-0.723682\pi$
$619$	−32.1593	−1.29259	−0.646295	+	0.763088i	$0.723682\pi$
$620$	−6.10965	−0.245369
$621$	13.2324	0.530999
$622$	10.3280	0.414117
$623$	−4.76816	−0.191032
$624$	2.45902	0.0984394
$625$	1.00000	0.0400000
$626$	24.1184	0.963965
$627$	−0.779231	−0.0311195
$628$	18.7300	0.747409
$629$	−2.67050	−0.106480
$630$	−5.00120	−0.199252
$631$	−39.2786	−1.56366	−0.781829	−	0.623493i	$-0.785713\pi$
$631$	−39.2786	−1.56366	−0.781829	+	0.623493i	$0.785713\pi$
$632$	7.77888	0.309427
$633$	12.6460	0.502635
$634$	−19.8911	−0.789977
$635$	−2.46196	−0.0976998
$636$	−3.09217	−0.122612
$637$	−11.4084	−0.452015
$638$	1.78348	0.0706087
$639$	9.10154	0.360051
$640$	−1.00000	−0.0395285
$641$	31.9114	1.26042	0.630212	−	0.776423i	$-0.282968\pi$
$641$	31.9114	1.26042	0.630212	+	0.776423i	$0.282968\pi$
$642$	6.74300	0.266125
$643$	28.2686	1.11480	0.557402	−	0.830243i	$-0.311798\pi$
$643$	28.2686	1.11480	0.557402	+	0.830243i	$0.311798\pi$
$644$	6.94712	0.273755
$645$	−4.26753	−0.168034
$646$	0.760457	0.0299198
$647$	5.22465	0.205402	0.102701	−	0.994712i	$-0.467251\pi$
$647$	5.22465	0.205402	0.102701	+	0.994712i	$0.467251\pi$
$648$	−5.10089	−0.200382
$649$	1.80312	0.0707788
$650$	−3.63999	−0.142772
$651$	8.11520	0.318060
$652$	24.0979	0.943748
$653$	9.99605	0.391176	0.195588	−	0.980686i	$-0.437339\pi$
$653$	9.99605	0.391176	0.195588	+	0.980686i	$0.437339\pi$
$654$	11.6894	0.457090
$655$	−12.1540	−0.474896
$656$	7.14911	0.279126
$657$	2.68616	0.104797
$658$	11.7501	0.458066
$659$	31.5145	1.22763	0.613816	−	0.789449i	$-0.289634\pi$
$659$	31.5145	1.22763	0.613816	+	0.789449i	$0.289634\pi$
$660$	−0.474809	−0.0184819
$661$	43.0557	1.67467	0.837336	−	0.546688i	$-0.184112\pi$
$661$	43.0557	1.67467	0.837336	+	0.546688i	$0.184112\pi$
$662$	25.8891	1.00621
$663$	−1.13943	−0.0442520
$664$	5.64286	0.218985
$665$	−3.22677	−0.125129
$666$	14.6595	0.568043
$667$	−8.96593	−0.347162
$668$	−6.60551	−0.255575
$669$	−4.87320	−0.188409
$670$	−2.71402	−0.104852
$671$	6.47084	0.249804
$672$	1.32826	0.0512387
$673$	19.2058	0.740331	0.370165	−	0.928966i	$-0.379301\pi$
$673$	19.2058	0.740331	0.370165	+	0.928966i	$0.379301\pi$
$674$	−14.9572	−0.576129
$675$	−3.74503	−0.144146
$676$	0.249501	0.00959619
$677$	29.2520	1.12425	0.562123	−	0.827054i	$-0.309985\pi$
$677$	29.2520	1.12425	0.562123	+	0.827054i	$0.309985\pi$
$678$	10.7032	0.411053
$679$	−28.1407	−1.07994
$680$	0.463370	0.0177694
$681$	13.1422	0.503612
$682$	−4.29412	−0.164430
$683$	19.8552	0.759737	0.379869	−	0.925040i	$-0.375969\pi$
$683$	19.8552	0.759737	0.379869	+	0.925040i	$0.375969\pi$
$684$	−4.17446	−0.159614
$685$	−14.9534	−0.571339
$686$	−19.9255	−0.760760
$687$	7.56993	0.288811
$688$	−6.31705	−0.240835
$689$	−16.6610	−0.634733
$690$	2.38696	0.0908701
$691$	−31.8422	−1.21133	−0.605667	−	0.795718i	$-0.707094\pi$
$691$	−31.8422	−1.21133	−0.605667	+	0.795718i	$0.707094\pi$
$692$	−15.0557	−0.572332
$693$	−3.51505	−0.133526
$694$	−27.7319	−1.05269
$695$	−21.8514	−0.828869
$696$	−1.71424	−0.0649783
$697$	−3.31268	−0.125477
$698$	−2.15312	−0.0814969
$699$	11.9766	0.452995
$700$	−1.96617	−0.0743142
$701$	31.8457	1.20280	0.601398	−	0.798950i	$-0.294611\pi$
$701$	31.8457	1.20280	0.601398	+	0.798950i	$0.294611\pi$
$702$	13.6319	0.514501
$703$	9.45829	0.356726
$704$	−0.702842	−0.0264893
$705$	4.03721	0.152050
$706$	−6.05838	−0.228010
$707$	−21.8443	−0.821540
$708$	−1.73312	−0.0651348
$709$	−39.1770	−1.47132	−0.735661	−	0.677350i	$-0.763128\pi$
$709$	−39.1770	−1.47132	−0.735661	+	0.677350i	$0.763128\pi$
$710$	3.57818	0.134287
$711$	19.7865	0.742053
$712$	−2.42510	−0.0908845
$713$	21.5874	0.808454
$714$	−0.615475	−0.0230336
$715$	−2.55833	−0.0956763
$716$	12.5215	0.467952
$717$	−8.95027	−0.334254
$718$	26.0891	0.973636
$719$	−10.4263	−0.388836	−0.194418	−	0.980919i	$-0.562282\pi$
$719$	−10.4263	−0.388836	−0.194418	+	0.980919i	$0.562282\pi$
$720$	−2.54362	−0.0947953
$721$	26.5446	0.988573
$722$	16.3066	0.606870
$723$	4.46754	0.166149
$724$	−23.0329	−0.856012
$725$	2.53753	0.0942415
$726$	7.09740	0.263409
$727$	18.9553	0.703014	0.351507	−	0.936185i	$-0.385669\pi$
$727$	18.9553	0.703014	0.351507	+	0.936185i	$0.385669\pi$
$728$	7.15683	0.265250
$729$	−5.38481	−0.199438
$730$	1.05604	0.0390857
$731$	2.92713	0.108264
$732$	−6.21963	−0.229884
$733$	−31.9555	−1.18030	−0.590151	−	0.807293i	$-0.700932\pi$
$733$	−31.9555	−1.18030	−0.590151	+	0.807293i	$0.700932\pi$
$734$	−2.08709	−0.0770358
$735$	−2.11731	−0.0780982
$736$	3.53333	0.130240
$737$	−1.90753	−0.0702646
$738$	18.1846	0.669386
$739$	52.0858	1.91601	0.958004	−	0.286755i	$-0.0925766\pi$
$739$	52.0858	1.91601	0.958004	+	0.286755i	$0.0925766\pi$
$740$	5.76322	0.211860
$741$	4.03560	0.148252
$742$	−8.99958	−0.330385
$743$	38.5288	1.41349	0.706743	−	0.707470i	$-0.250164\pi$
$743$	38.5288	1.41349	0.706743	+	0.707470i	$0.250164\pi$
$744$	4.12741	0.151318
$745$	3.79711	0.139115
$746$	28.8649	1.05682
$747$	14.3533	0.525160
$748$	0.325676	0.0119079
$749$	19.6251	0.717087
$750$	−0.675556	−0.0246678
$751$	11.6188	0.423977	0.211988	−	0.977272i	$-0.432006\pi$
$751$	11.6188	0.423977	0.211988	+	0.977272i	$0.432006\pi$
$752$	5.97612	0.217927
$753$	−17.5830	−0.640759
$754$	−9.23658	−0.336376
$755$	−5.98467	−0.217805
$756$	7.36337	0.267803
$757$	−1.94600	−0.0707286	−0.0353643	−	0.999374i	$-0.511259\pi$
$757$	−1.94600	−0.0707286	−0.0353643	+	0.999374i	$0.511259\pi$
$758$	−7.44485	−0.270409
$759$	1.67766	0.0608951
$760$	−1.64115	−0.0595306
$761$	−41.4858	−1.50386	−0.751930	−	0.659243i	$-0.770877\pi$
$761$	−41.4858	−1.50386	−0.751930	+	0.659243i	$0.770877\pi$
$762$	1.66319	0.0602511
$763$	34.0212	1.23165
$764$	15.0467	0.544371
$765$	1.17864	0.0426138
$766$	18.3001	0.661210
$767$	−9.33830	−0.337186
$768$	0.675556	0.0243770
$769$	−29.7575	−1.07308	−0.536541	−	0.843874i	$-0.680269\pi$
$769$	−29.7575	−1.07308	−0.536541	+	0.843874i	$0.680269\pi$
$770$	−1.38191	−0.0498004
$771$	−5.49921	−0.198049
$772$	−19.7068	−0.709262
$773$	19.3525	0.696061	0.348030	−	0.937483i	$-0.386851\pi$
$773$	19.3525	0.696061	0.348030	+	0.937483i	$0.386851\pi$
$774$	−16.0682	−0.577560
$775$	−6.10965	−0.219465
$776$	−14.3124	−0.513786
$777$	−7.65505	−0.274623
$778$	−22.2317	−0.797046
$779$	11.7327	0.420368
$780$	2.45902	0.0880469
$781$	2.51489	0.0899899
$782$	−1.63724	−0.0585475
$783$	−9.50313	−0.339614
$784$	−3.13418	−0.111935
$785$	18.7300	0.668503
$786$	8.21071	0.292866
$787$	20.6864	0.737390	0.368695	−	0.929550i	$-0.379805\pi$
$787$	20.6864	0.737390	0.368695	+	0.929550i	$0.379805\pi$
$788$	15.6305	0.556813
$789$	1.42604	0.0507682
$790$	7.77888	0.276760
$791$	31.1510	1.10760
$792$	−1.78776	−0.0635254
$793$	−33.5122	−1.19005
$794$	−3.83234	−0.136005
$795$	−3.09217	−0.109668
$796$	−6.63045	−0.235010
$797$	35.4361	1.25521	0.627606	−	0.778531i	$-0.284035\pi$
$797$	35.4361	1.25521	0.627606	+	0.778531i	$0.284035\pi$
$798$	2.17987	0.0771664
$799$	−2.76916	−0.0979657
$800$	−1.00000	−0.0353553
$801$	−6.16855	−0.217955
$802$	−1.00000	−0.0353112
$803$	0.742227	0.0261926
$804$	1.83347	0.0646616
$805$	6.94712	0.244854
$806$	22.2390	0.783337
$807$	−12.8747	−0.453213
$808$	−11.1101	−0.390851
$809$	27.9959	0.984283	0.492142	−	0.870515i	$-0.336214\pi$
$809$	27.9959	0.984283	0.492142	+	0.870515i	$0.336214\pi$
$810$	−5.10089	−0.179227
$811$	22.3971	0.786469	0.393234	−	0.919438i	$-0.371356\pi$
$811$	22.3971	0.786469	0.393234	+	0.919438i	$0.371356\pi$
$812$	−4.98922	−0.175087
$813$	−3.41150	−0.119647
$814$	4.05063	0.141975
$815$	24.0979	0.844114
$816$	−0.313032	−0.0109583
$817$	−10.3672	−0.362703
$818$	−20.3572	−0.711774
$819$	18.2043	0.636109
$820$	7.14911	0.249658
$821$	20.9374	0.730722	0.365361	−	0.930866i	$-0.380946\pi$
$821$	20.9374	0.730722	0.365361	+	0.930866i	$0.380946\pi$
$822$	10.1019	0.352343
$823$	47.8076	1.66647	0.833234	−	0.552921i	$-0.186487\pi$
$823$	47.8076	1.66647	0.833234	+	0.552921i	$0.186487\pi$
$824$	13.5007	0.470318
$825$	−0.474809	−0.0165307
$826$	−5.04416	−0.175509
$827$	−14.9690	−0.520522	−0.260261	−	0.965538i	$-0.583809\pi$
$827$	−14.9690	−0.520522	−0.260261	+	0.965538i	$0.583809\pi$
$828$	8.98746	0.312336
$829$	−21.5059	−0.746929	−0.373465	−	0.927644i	$-0.621830\pi$
$829$	−21.5059	−0.746929	−0.373465	+	0.927644i	$0.621830\pi$
$830$	5.64286	0.195866
$831$	−6.22640	−0.215991
$832$	3.63999	0.126194
$833$	1.45228	0.0503186
$834$	14.7618	0.511160
$835$	−6.60551	−0.228593
$836$	−1.15347	−0.0398934
$837$	22.8808	0.790877
$838$	−20.8407	−0.719931
$839$	13.8121	0.476846	0.238423	−	0.971161i	$-0.423370\pi$
$839$	13.8121	0.476846	0.238423	+	0.971161i	$0.423370\pi$
$840$	1.32826	0.0458293
$841$	−22.5609	−0.777963
$842$	−23.1118	−0.796485
$843$	−4.44224	−0.152999
$844$	18.7194	0.644350
$845$	0.249501	0.00858310
$846$	15.2010	0.522621
$847$	20.6566	0.709770
$848$	−4.57721	−0.157182
$849$	12.6608	0.434518
$850$	0.463370	0.0158935
$851$	−20.3634	−0.698047
$852$	−2.41726	−0.0828140
$853$	−9.04546	−0.309711	−0.154855	−	0.987937i	$-0.549491\pi$
$853$	−9.04546	−0.309711	−0.154855	+	0.987937i	$0.549491\pi$
$854$	−18.1019	−0.619434
$855$	−4.17446	−0.142763
$856$	9.98140	0.341157
$857$	−1.35948	−0.0464389	−0.0232194	−	0.999730i	$-0.507392\pi$
$857$	−1.35948	−0.0464389	−0.0232194	+	0.999730i	$0.507392\pi$
$858$	1.72830	0.0590031
$859$	−6.15779	−0.210101	−0.105051	−	0.994467i	$-0.533500\pi$
$859$	−6.15779	−0.210101	−0.105051	+	0.994467i	$0.533500\pi$
$860$	−6.31705	−0.215410
$861$	−9.49586	−0.323618
$862$	26.9560	0.918124
$863$	6.62312	0.225454	0.112727	−	0.993626i	$-0.464041\pi$
$863$	6.62312	0.225454	0.112727	+	0.993626i	$0.464041\pi$
$864$	3.74503	0.127409
$865$	−15.0557	−0.511909
$866$	−1.05846	−0.0359678
$867$	−11.3394	−0.385106
$868$	12.0126	0.407735
$869$	5.46732	0.185466
$870$	−1.71424	−0.0581183
$871$	9.87900	0.334737
$872$	17.3033	0.585964
$873$	−36.4054	−1.23214
$874$	5.79871	0.196144
$875$	−1.96617	−0.0664687
$876$	−0.713412	−0.0241040
$877$	−25.9471	−0.876170	−0.438085	−	0.898934i	$-0.644343\pi$
$877$	−25.9471	−0.876170	−0.438085	+	0.898934i	$0.644343\pi$
$878$	26.9332	0.908950
$879$	13.7421	0.463511
$880$	−0.702842	−0.0236928
$881$	−32.5527	−1.09673	−0.548365	−	0.836239i	$-0.684749\pi$
$881$	−32.5527	−1.09673	−0.548365	+	0.836239i	$0.684749\pi$
$882$	−7.97216	−0.268437
$883$	−17.9716	−0.604793	−0.302396	−	0.953182i	$-0.597787\pi$
$883$	−17.9716	−0.604793	−0.302396	+	0.953182i	$0.597787\pi$
$884$	−1.68666	−0.0567285
$885$	−1.73312	−0.0582583
$886$	−3.79606	−0.127531
$887$	22.3570	0.750674	0.375337	−	0.926889i	$-0.377527\pi$
$887$	22.3570	0.750674	0.375337	+	0.926889i	$0.377527\pi$
$888$	−3.89338	−0.130653
$889$	4.84063	0.162349
$890$	−2.42510	−0.0812896
$891$	−3.58512	−0.120106
$892$	−7.21360	−0.241529
$893$	9.80769	0.328202
$894$	−2.56516	−0.0857919
$895$	12.5215	0.418549
$896$	1.96617	0.0656851
$897$	−8.68851	−0.290101
$898$	19.9784	0.666689
$899$	−15.5034	−0.517068
$900$	−2.54362	−0.0847875
$901$	2.12094	0.0706589
$902$	5.02469	0.167304
$903$	8.39068	0.279224
$904$	15.8435	0.526947
$905$	−23.0329	−0.765641
$906$	4.04298	0.134319
$907$	1.71251	0.0568629	0.0284315	−	0.999596i	$-0.490949\pi$
$907$	1.71251	0.0568629	0.0284315	+	0.999596i	$0.490949\pi$
$908$	19.4540	0.645602
$909$	−28.2599	−0.937320
$910$	7.15683	0.237247
$911$	48.8985	1.62008	0.810040	−	0.586374i	$-0.199445\pi$
$911$	48.8985	1.62008	0.810040	+	0.586374i	$0.199445\pi$
$912$	1.10869	0.0367123
$913$	3.96603	0.131257
$914$	12.0619	0.398971
$915$	−6.21963	−0.205615
$916$	11.2055	0.370239
$917$	23.8968	0.789143
$918$	−1.73533	−0.0572746
$919$	−22.4082	−0.739177	−0.369589	−	0.929195i	$-0.620501\pi$
$919$	−22.4082	−0.739177	−0.369589	+	0.929195i	$0.620501\pi$
$920$	3.53333	0.116490
$921$	−6.25850	−0.206225
$922$	23.7685	0.782773
$923$	−13.0245	−0.428707
$924$	0.933555	0.0307117
$925$	5.76322	0.189494
$926$	25.5650	0.840117
$927$	34.3406	1.12789
$928$	−2.53753	−0.0832985
$929$	−8.82972	−0.289694	−0.144847	−	0.989454i	$-0.546269\pi$
$929$	−8.82972	−0.289694	−0.144847	+	0.989454i	$0.546269\pi$
$930$	4.12741	0.135343
$931$	−5.14364	−0.168576
$932$	17.7284	0.580714
$933$	−6.97718	−0.228423
$934$	−1.38486	−0.0453139
$935$	0.325676	0.0106507
$936$	9.25876	0.302632
$937$	−39.4540	−1.28891	−0.644453	−	0.764644i	$-0.722915\pi$
$937$	−39.4540	−1.28891	−0.644453	+	0.764644i	$0.722915\pi$
$938$	5.33623	0.174234
$939$	−16.2933	−0.531713
$940$	5.97612	0.194920
$941$	36.8693	1.20190	0.600952	−	0.799285i	$-0.294788\pi$
$941$	36.8693	1.20190	0.600952	+	0.799285i	$0.294788\pi$
$942$	−12.6532	−0.412263
$943$	−25.2601	−0.822583
$944$	−2.56548	−0.0834991
$945$	7.36337	0.239530
$946$	−4.43989	−0.144353
$947$	33.8844	1.10110	0.550548	−	0.834804i	$-0.314419\pi$
$947$	33.8844	1.10110	0.550548	+	0.834804i	$0.314419\pi$
$948$	−5.25507	−0.170677
$949$	−3.84396	−0.124780
$950$	−1.64115	−0.0532458
$951$	13.4376	0.435743
$952$	−0.911064	−0.0295278
$953$	12.8001	0.414635	0.207317	−	0.978274i	$-0.433527\pi$
$953$	12.8001	0.414635	0.207317	+	0.978274i	$0.433527\pi$
$954$	−11.6427	−0.376947
$955$	15.0467	0.486901
$956$	−13.2487	−0.428495
$957$	−1.20484	−0.0389470
$958$	9.15088	0.295651
$959$	29.4009	0.949405
$960$	0.675556	0.0218035
$961$	6.32782	0.204123
$962$	−20.9781	−0.676360
$963$	25.3889	0.818147
$964$	6.61312	0.212994
$965$	−19.7068	−0.634383
$966$	−4.69317	−0.151000
$967$	−16.6147	−0.534293	−0.267147	−	0.963656i	$-0.586081\pi$
$967$	−16.6147	−0.534293	−0.267147	+	0.963656i	$0.586081\pi$
$968$	10.5060	0.337676
$969$	−0.513732	−0.0165034
$970$	−14.3124	−0.459545
$971$	−38.9312	−1.24936	−0.624681	−	0.780880i	$-0.714771\pi$
$971$	−38.9312	−1.24936	−0.624681	+	0.780880i	$0.714771\pi$
$972$	14.6810	0.470894
$973$	42.9635	1.37735
$974$	−9.41697	−0.301739
$975$	2.45902	0.0787515
$976$	−9.20668	−0.294699
$977$	−11.9325	−0.381755	−0.190878	−	0.981614i	$-0.561133\pi$
$977$	−11.9325	−0.381755	−0.190878	+	0.981614i	$0.561133\pi$
$978$	−16.2795	−0.520561
$979$	−1.70446	−0.0544749
$980$	−3.13418	−0.100118
$981$	44.0131	1.40523
$982$	−21.6913	−0.692199
$983$	13.2389	0.422254	0.211127	−	0.977459i	$-0.432287\pi$
$983$	13.2389	0.422254	0.211127	+	0.977459i	$0.432287\pi$
$984$	−4.82962	−0.153963
$985$	15.6305	0.498029
$986$	1.17582	0.0374456
$987$	−7.93784	−0.252664
$988$	5.97375	0.190050
$989$	22.3202	0.709742
$990$	−1.78776	−0.0568189
$991$	25.3896	0.806526	0.403263	−	0.915084i	$-0.367876\pi$
$991$	25.3896	0.806526	0.403263	+	0.915084i	$0.367876\pi$
$992$	6.10965	0.193982
$993$	−17.4895	−0.555013
$994$	−7.03530	−0.223146
$995$	−6.63045	−0.210199
$996$	−3.81207	−0.120790
$997$	−13.2384	−0.419263	−0.209632	−	0.977780i	$-0.567226\pi$
$997$	−13.2384	−0.419263	−0.209632	+	0.977780i	$0.567226\pi$
$998$	38.4965	1.21859
$999$	−21.5834	−0.682870

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	4010.2.a.i.1.7	✓	10

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
4010.2.a.i.1.7	✓	10	1.1	even	1	trivial

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:	\( N \)	\(=\)	\( 4010 = 2 \cdot 5 \cdot 401 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	4010.a (trivial)

\(f(q)\)	\(=\)	\(q-1.00000 q^{2} +0.675556 q^{3} +1.00000 q^{4} +1.00000 q^{5} -0.675556 q^{6} -1.96617 q^{7} -1.00000 q^{8} -2.54362 q^{9} +O(q^{10})\)	\(q-1.00000 q^{2} +0.675556 q^{3} +1.00000 q^{4} +1.00000 q^{5} -0.675556 q^{6} -1.96617 q^{7} -1.00000 q^{8} -2.54362 q^{9} -1.00000 q^{10} -0.702842 q^{11} +0.675556 q^{12} +3.63999 q^{13} +1.96617 q^{14} +0.675556 q^{15} +1.00000 q^{16} -0.463370 q^{17} +2.54362 q^{18} +1.64115 q^{19} +1.00000 q^{20} -1.32826 q^{21} +0.702842 q^{22} -3.53333 q^{23} -0.675556 q^{24} +1.00000 q^{25} -3.63999 q^{26} -3.74503 q^{27} -1.96617 q^{28} +2.53753 q^{29} -0.675556 q^{30} -6.10965 q^{31} -1.00000 q^{32} -0.474809 q^{33} +0.463370 q^{34} -1.96617 q^{35} -2.54362 q^{36} +5.76322 q^{37} -1.64115 q^{38} +2.45902 q^{39} -1.00000 q^{40} +7.14911 q^{41} +1.32826 q^{42} -6.31705 q^{43} -0.702842 q^{44} -2.54362 q^{45} +3.53333 q^{46} +5.97612 q^{47} +0.675556 q^{48} -3.13418 q^{49} -1.00000 q^{50} -0.313032 q^{51} +3.63999 q^{52} -4.57721 q^{53} +3.74503 q^{54} -0.702842 q^{55} +1.96617 q^{56} +1.10869 q^{57} -2.53753 q^{58} -2.56548 q^{59} +0.675556 q^{60} -9.20668 q^{61} +6.10965 q^{62} +5.00120 q^{63} +1.00000 q^{64} +3.63999 q^{65} +0.474809 q^{66} +2.71402 q^{67} -0.463370 q^{68} -2.38696 q^{69} +1.96617 q^{70} -3.57818 q^{71} +2.54362 q^{72} -1.05604 q^{73} -5.76322 q^{74} +0.675556 q^{75} +1.64115 q^{76} +1.38191 q^{77} -2.45902 q^{78} -7.77888 q^{79} +1.00000 q^{80} +5.10089 q^{81} -7.14911 q^{82} -5.64286 q^{83} -1.32826 q^{84} -0.463370 q^{85} +6.31705 q^{86} +1.71424 q^{87} +0.702842 q^{88} +2.42510 q^{89} +2.54362 q^{90} -7.15683 q^{91} -3.53333 q^{92} -4.12741 q^{93} -5.97612 q^{94} +1.64115 q^{95} -0.675556 q^{96} +14.3124 q^{97} +3.13418 q^{98} +1.78776 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 10 q - 10 q^{2} - 4 q^{3} + 10 q^{4} + 10 q^{5} + 4 q^{6} - 3 q^{7} - 10 q^{8} + 6 q^{9}+O(q^{10}) \) 10 * q - 10 * q^2 - 4 * q^3 + 10 * q^4 + 10 * q^5 + 4 * q^6 - 3 * q^7 - 10 * q^8 + 6 * q^9	\( 10 q - 10 q^{2} - 4 q^{3} + 10 q^{4} + 10 q^{5} + 4 q^{6} - 3 q^{7} - 10 q^{8} + 6 q^{9} - 10 q^{10} - 11 q^{11} - 4 q^{12} + 6 q^{13} + 3 q^{14} - 4 q^{15} + 10 q^{16} + 9 q^{17} - 6 q^{18} - 13 q^{19} + 10 q^{20} - 24 q^{21} + 11 q^{22} - 3 q^{23} + 4 q^{24} + 10 q^{25} - 6 q^{26} - 10 q^{27} - 3 q^{28} - 4 q^{29} + 4 q^{30} - 17 q^{31} - 10 q^{32} - 2 q^{33} - 9 q^{34} - 3 q^{35} + 6 q^{36} - 15 q^{37} + 13 q^{38} - 6 q^{39} - 10 q^{40} - 11 q^{41} + 24 q^{42} - 11 q^{43} - 11 q^{44} + 6 q^{45} + 3 q^{46} + 3 q^{47} - 4 q^{48} - 5 q^{49} - 10 q^{50} - 21 q^{51} + 6 q^{52} + 25 q^{53} + 10 q^{54} - 11 q^{55} + 3 q^{56} + 31 q^{57} + 4 q^{58} - 46 q^{59} - 4 q^{60} - 54 q^{61} + 17 q^{62} - 6 q^{63} + 10 q^{64} + 6 q^{65} + 2 q^{66} - 26 q^{67} + 9 q^{68} - 9 q^{69} + 3 q^{70} - 16 q^{71} - 6 q^{72} + 4 q^{73} + 15 q^{74} - 4 q^{75} - 13 q^{76} + 11 q^{77} + 6 q^{78} - 19 q^{79} + 10 q^{80} - 6 q^{81} + 11 q^{82} + 19 q^{83} - 24 q^{84} + 9 q^{85} + 11 q^{86} + 28 q^{87} + 11 q^{88} - 30 q^{89} - 6 q^{90} - 38 q^{91} - 3 q^{92} - 18 q^{93} - 3 q^{94} - 13 q^{95} + 4 q^{96} - 16 q^{97} + 5 q^{98} - 59 q^{99}+O(q^{100}) \) 10 * q - 10 * q^2 - 4 * q^3 + 10 * q^4 + 10 * q^5 + 4 * q^6 - 3 * q^7 - 10 * q^8 + 6 * q^9 - 10 * q^10 - 11 * q^11 - 4 * q^12 + 6 * q^13 + 3 * q^14 - 4 * q^15 + 10 * q^16 + 9 * q^17 - 6 * q^18 - 13 * q^19 + 10 * q^20 - 24 * q^21 + 11 * q^22 - 3 * q^23 + 4 * q^24 + 10 * q^25 - 6 * q^26 - 10 * q^27 - 3 * q^28 - 4 * q^29 + 4 * q^30 - 17 * q^31 - 10 * q^32 - 2 * q^33 - 9 * q^34 - 3 * q^35 + 6 * q^36 - 15 * q^37 + 13 * q^38 - 6 * q^39 - 10 * q^40 - 11 * q^41 + 24 * q^42 - 11 * q^43 - 11 * q^44 + 6 * q^45 + 3 * q^46 + 3 * q^47 - 4 * q^48 - 5 * q^49 - 10 * q^50 - 21 * q^51 + 6 * q^52 + 25 * q^53 + 10 * q^54 - 11 * q^55 + 3 * q^56 + 31 * q^57 + 4 * q^58 - 46 * q^59 - 4 * q^60 - 54 * q^61 + 17 * q^62 - 6 * q^63 + 10 * q^64 + 6 * q^65 + 2 * q^66 - 26 * q^67 + 9 * q^68 - 9 * q^69 + 3 * q^70 - 16 * q^71 - 6 * q^72 + 4 * q^73 + 15 * q^74 - 4 * q^75 - 13 * q^76 + 11 * q^77 + 6 * q^78 - 19 * q^79 + 10 * q^80 - 6 * q^81 + 11 * q^82 + 19 * q^83 - 24 * q^84 + 9 * q^85 + 11 * q^86 + 28 * q^87 + 11 * q^88 - 30 * q^89 - 6 * q^90 - 38 * q^91 - 3 * q^92 - 18 * q^93 - 3 * q^94 - 13 * q^95 + 4 * q^96 - 16 * q^97 + 5 * q^98 - 59 * q^99

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