LMFDB - Embedded newform 4010.2.a.m.1.13

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:	$0$
Dimension:	$20$
Coefficient field:	$\mathbb{Q}[x]/(x^{20} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{20} - 4 x^{19} - 35 x^{18} + 154 x^{17} + 460 x^{16} - 2392 x^{15} - 2591 x^{14} + 19157 x^{13} + \cdots + 104 $ x^20 - 4x^19 - 35x^18 + 154x^17 + 460x^16 - 2392x^15 - 2591x^14 + 19157x^13 + 2776x^12 - 83577x^11 + 34362x^10 + 190617x^9 - 150697x^8 - 189098x^7 + 211360x^6 + 37365x^5 - 68876x^4 - 8984x^3 + 7920x^2 + 1972*x + 104
Coefficient ring:	$\Z[a_1, \ldots, a_{11}]$
Coefficient ring index:	$ 2^{2} $
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.13
Root			$1.03584$ 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)

$f(q)$	$=$	$q-1.00000 q^{2} +1.03584 q^{3} +1.00000 q^{4} +1.00000 q^{5} -1.03584 q^{6} -1.66553 q^{7} -1.00000 q^{8} -1.92705 q^{9} +O(q^{10})$	\(q-1.00000 q^{2} +1.03584 q^{3} +1.00000 q^{4} +1.00000 q^{5} -1.03584 q^{6} -1.66553 q^{7} -1.00000 q^{8} -1.92705 q^{9} -1.00000 q^{10} +4.72387 q^{11} +1.03584 q^{12} -5.82334 q^{13} +1.66553 q^{14} +1.03584 q^{15} +1.00000 q^{16} +1.61936 q^{17} +1.92705 q^{18} +5.62603 q^{19} +1.00000 q^{20} -1.72521 q^{21} -4.72387 q^{22} +9.52755 q^{23} -1.03584 q^{24} +1.00000 q^{25} +5.82334 q^{26} -5.10361 q^{27} -1.66553 q^{28} +7.93722 q^{29} -1.03584 q^{30} -10.7946 q^{31} -1.00000 q^{32} +4.89315 q^{33} -1.61936 q^{34} -1.66553 q^{35} -1.92705 q^{36} -4.80352 q^{37} -5.62603 q^{38} -6.03202 q^{39} -1.00000 q^{40} +11.2247 q^{41} +1.72521 q^{42} +2.21657 q^{43} +4.72387 q^{44} -1.92705 q^{45} -9.52755 q^{46} -9.24527 q^{47} +1.03584 q^{48} -4.22602 q^{49} -1.00000 q^{50} +1.67739 q^{51} -5.82334 q^{52} -2.66830 q^{53} +5.10361 q^{54} +4.72387 q^{55} +1.66553 q^{56} +5.82764 q^{57} -7.93722 q^{58} -1.55159 q^{59} +1.03584 q^{60} +7.05983 q^{61} +10.7946 q^{62} +3.20955 q^{63} +1.00000 q^{64} -5.82334 q^{65} -4.89315 q^{66} -0.573969 q^{67} +1.61936 q^{68} +9.86897 q^{69} +1.66553 q^{70} +4.75705 q^{71} +1.92705 q^{72} -7.51750 q^{73} +4.80352 q^{74} +1.03584 q^{75} +5.62603 q^{76} -7.86773 q^{77} +6.03202 q^{78} -10.3018 q^{79} +1.00000 q^{80} +0.494642 q^{81} -11.2247 q^{82} +5.68771 q^{83} -1.72521 q^{84} +1.61936 q^{85} -2.21657 q^{86} +8.22165 q^{87} -4.72387 q^{88} +16.3327 q^{89} +1.92705 q^{90} +9.69894 q^{91} +9.52755 q^{92} -11.1814 q^{93} +9.24527 q^{94} +5.62603 q^{95} -1.03584 q^{96} +8.23459 q^{97} +4.22602 q^{98} -9.10311 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 20 q - 20 q^{2} + 4 q^{3} + 20 q^{4} + 20 q^{5} - 4 q^{6} + 11 q^{7} - 20 q^{8} + 26 q^{9}+O(q^{10}) $ 20 * q - 20 * q^2 + 4 * q^3 + 20 * q^4 + 20 * q^5 - 4 * q^6 + 11 * q^7 - 20 * q^8 + 26 * q^9	\( 20 q - 20 q^{2} + 4 q^{3} + 20 q^{4} + 20 q^{5} - 4 q^{6} + 11 q^{7} - 20 q^{8} + 26 q^{9} - 20 q^{10} + 10 q^{11} + 4 q^{12} - 9 q^{13} - 11 q^{14} + 4 q^{15} + 20 q^{16} - 11 q^{17} - 26 q^{18} + 17 q^{19} + 20 q^{20} - 2 q^{21} - 10 q^{22} - 3 q^{23} - 4 q^{24} + 20 q^{25} + 9 q^{26} - 2 q^{27} + 11 q^{28} + 6 q^{29} - 4 q^{30} + 28 q^{31} - 20 q^{32} + 2 q^{33} + 11 q^{34} + 11 q^{35} + 26 q^{36} + 33 q^{37} - 17 q^{38} + 36 q^{39} - 20 q^{40} + 32 q^{41} + 2 q^{42} + 30 q^{43} + 10 q^{44} + 26 q^{45} + 3 q^{46} + 13 q^{47} + 4 q^{48} + 43 q^{49} - 20 q^{50} + 43 q^{51} - 9 q^{52} + 2 q^{54} + 10 q^{55} - 11 q^{56} + 19 q^{57} - 6 q^{58} + 52 q^{59} + 4 q^{60} + 25 q^{61} - 28 q^{62} + 16 q^{63} + 20 q^{64} - 9 q^{65} - 2 q^{66} + 40 q^{67} - 11 q^{68} + 39 q^{69} - 11 q^{70} + 25 q^{71} - 26 q^{72} - 5 q^{73} - 33 q^{74} + 4 q^{75} + 17 q^{76} - 9 q^{77} - 36 q^{78} + 40 q^{79} + 20 q^{80} + 48 q^{81} - 32 q^{82} + 10 q^{83} - 2 q^{84} - 11 q^{85} - 30 q^{86} + 10 q^{87} - 10 q^{88} + 17 q^{89} - 26 q^{90} + 88 q^{91} - 3 q^{92} - 4 q^{93} - 13 q^{94} + 17 q^{95} - 4 q^{96} - 2 q^{97} - 43 q^{98} + 50 q^{99}+O(q^{100}) \) 20 * q - 20 * q^2 + 4 * q^3 + 20 * q^4 + 20 * q^5 - 4 * q^6 + 11 * q^7 - 20 * q^8 + 26 * q^9 - 20 * q^10 + 10 * q^11 + 4 * q^12 - 9 * q^13 - 11 * q^14 + 4 * q^15 + 20 * q^16 - 11 * q^17 - 26 * q^18 + 17 * q^19 + 20 * q^20 - 2 * q^21 - 10 * q^22 - 3 * q^23 - 4 * q^24 + 20 * q^25 + 9 * q^26 - 2 * q^27 + 11 * q^28 + 6 * q^29 - 4 * q^30 + 28 * q^31 - 20 * q^32 + 2 * q^33 + 11 * q^34 + 11 * q^35 + 26 * q^36 + 33 * q^37 - 17 * q^38 + 36 * q^39 - 20 * q^40 + 32 * q^41 + 2 * q^42 + 30 * q^43 + 10 * q^44 + 26 * q^45 + 3 * q^46 + 13 * q^47 + 4 * q^48 + 43 * q^49 - 20 * q^50 + 43 * q^51 - 9 * q^52 + 2 * q^54 + 10 * q^55 - 11 * q^56 + 19 * q^57 - 6 * q^58 + 52 * q^59 + 4 * q^60 + 25 * q^61 - 28 * q^62 + 16 * q^63 + 20 * q^64 - 9 * q^65 - 2 * q^66 + 40 * q^67 - 11 * q^68 + 39 * q^69 - 11 * q^70 + 25 * q^71 - 26 * q^72 - 5 * q^73 - 33 * q^74 + 4 * q^75 + 17 * q^76 - 9 * q^77 - 36 * q^78 + 40 * q^79 + 20 * q^80 + 48 * q^81 - 32 * q^82 + 10 * q^83 - 2 * q^84 - 11 * q^85 - 30 * q^86 + 10 * q^87 - 10 * q^88 + 17 * q^89 - 26 * q^90 + 88 * q^91 - 3 * q^92 - 4 * q^93 - 13 * q^94 + 17 * q^95 - 4 * q^96 - 2 * q^97 - 43 * q^98 + 50 * 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
$3$	1.03584	0.598040	0.299020	−	0.954247i	$-0.403340\pi$
$3$	1.03584	0.598040	0.299020	+	0.954247i	$0.403340\pi$
$4$	1.00000	0.500000
$5$	1.00000	0.447214
$5$	1.00000	0.447214
$6$	−1.03584	−0.422878
$7$	−1.66553	−0.629510	−0.314755	−	0.949173i	$-0.601922\pi$
$7$	−1.66553	−0.629510	−0.314755	+	0.949173i	$0.601922\pi$
$8$	−1.00000	−0.353553
$9$	−1.92705	−0.642349
$10$	−1.00000	−0.316228
$11$	4.72387	1.42430	0.712150	−	0.702027i	$-0.247722\pi$
$11$	4.72387	1.42430	0.712150	+	0.702027i	$0.247722\pi$
$12$	1.03584	0.299020
$13$	−5.82334	−1.61511	−0.807553	−	0.589796i	$-0.799208\pi$
$13$	−5.82334	−1.61511	−0.807553	+	0.589796i	$0.799208\pi$
$14$	1.66553	0.445131
$15$	1.03584	0.267451
$16$	1.00000	0.250000
$17$	1.61936	0.392752	0.196376	−	0.980529i	$-0.437083\pi$
$17$	1.61936	0.392752	0.196376	+	0.980529i	$0.437083\pi$
$18$	1.92705	0.454209
$19$	5.62603	1.29070	0.645350	−	0.763887i	$-0.276712\pi$
$19$	5.62603	1.29070	0.645350	+	0.763887i	$0.276712\pi$
$20$	1.00000	0.223607
$21$	−1.72521	−0.376472
$22$	−4.72387	−1.00713
$23$	9.52755	1.98663	0.993316	−	0.115427i	$-0.0368236\pi$
$23$	9.52755	1.98663	0.993316	+	0.115427i	$0.0368236\pi$
$24$	−1.03584	−0.211439
$25$	1.00000	0.200000
$26$	5.82334	1.14205
$27$	−5.10361	−0.982190
$28$	−1.66553	−0.314755
$29$	7.93722	1.47390	0.736952	−	0.675945i	$-0.236264\pi$
$29$	7.93722	1.47390	0.736952	+	0.675945i	$0.236264\pi$
$30$	−1.03584	−0.189117
$31$	−10.7946	−1.93877	−0.969384	−	0.245549i	$-0.921032\pi$
$31$	−10.7946	−1.93877	−0.969384	+	0.245549i	$0.921032\pi$
$32$	−1.00000	−0.176777
$33$	4.89315	0.851788
$34$	−1.61936	−0.277718
$35$	−1.66553	−0.281525
$36$	−1.92705	−0.321174
$37$	−4.80352	−0.789694	−0.394847	−	0.918747i	$-0.629202\pi$
$37$	−4.80352	−0.789694	−0.394847	+	0.918747i	$0.629202\pi$
$38$	−5.62603	−0.912663
$39$	−6.03202	−0.965897
$40$	−1.00000	−0.158114
$41$	11.2247	1.75300	0.876500	−	0.481401i	$-0.159872\pi$
$41$	11.2247	1.75300	0.876500	+	0.481401i	$0.159872\pi$
$42$	1.72521	0.266206
$43$	2.21657	0.338023	0.169012	−	0.985614i	$-0.445942\pi$
$43$	2.21657	0.338023	0.169012	+	0.985614i	$0.445942\pi$
$44$	4.72387	0.712150
$45$	−1.92705	−0.287267
$46$	−9.52755	−1.40476
$47$	−9.24527	−1.34856	−0.674281	−	0.738475i	$-0.735546\pi$
$47$	−9.24527	−1.34856	−0.674281	+	0.738475i	$0.735546\pi$
$48$	1.03584	0.149510
$49$	−4.22602	−0.603717
$50$	−1.00000	−0.141421
$51$	1.67739	0.234881
$52$	−5.82334	−0.807553
$53$	−2.66830	−0.366519	−0.183260	−	0.983065i	$-0.558665\pi$
$53$	−2.66830	−0.366519	−0.183260	+	0.983065i	$0.558665\pi$
$54$	5.10361	0.694513
$55$	4.72387	0.636966
$56$	1.66553	0.222565
$57$	5.82764	0.771890
$58$	−7.93722	−1.04221
$59$	−1.55159	−0.202000	−0.101000	−	0.994886i	$-0.532204\pi$
$59$	−1.55159	−0.202000	−0.101000	+	0.994886i	$0.532204\pi$
$60$	1.03584	0.133726
$61$	7.05983	0.903919	0.451959	−	0.892038i	$-0.350725\pi$
$61$	7.05983	0.903919	0.451959	+	0.892038i	$0.350725\pi$
$62$	10.7946	1.37092
$63$	3.20955	0.404365
$64$	1.00000	0.125000
$65$	−5.82334	−0.722297
$66$	−4.89315	−0.602305
$67$	−0.573969	−0.0701214	−0.0350607	−	0.999385i	$-0.511162\pi$
$67$	−0.573969	−0.0701214	−0.0350607	+	0.999385i	$0.511162\pi$
$68$	1.61936	0.196376
$69$	9.86897	1.18808
$70$	1.66553	0.199069
$71$	4.75705	0.564558	0.282279	−	0.959332i	$-0.408910\pi$
$71$	4.75705	0.564558	0.282279	+	0.959332i	$0.408910\pi$
$72$	1.92705	0.227105
$73$	−7.51750	−0.879857	−0.439929	−	0.898033i	$-0.644996\pi$
$73$	−7.51750	−0.879857	−0.439929	+	0.898033i	$0.644996\pi$
$74$	4.80352	0.558398
$75$	1.03584	0.119608
$76$	5.62603	0.645350
$77$	−7.86773	−0.896611
$78$	6.03202	0.682992
$79$	−10.3018	−1.15904	−0.579519	−	0.814959i	$-0.696759\pi$
$79$	−10.3018	−1.15904	−0.579519	+	0.814959i	$0.696759\pi$
$80$	1.00000	0.111803
$81$	0.494642	0.0549603
$82$	−11.2247	−1.23956
$83$	5.68771	0.624308	0.312154	−	0.950032i	$-0.398950\pi$
$83$	5.68771	0.624308	0.312154	+	0.950032i	$0.398950\pi$
$84$	−1.72521	−0.188236
$85$	1.61936	0.175644
$86$	−2.21657	−0.239019
$87$	8.22165	0.881453
$88$	−4.72387	−0.503566
$89$	16.3327	1.73126	0.865631	−	0.500682i	$-0.166917\pi$
$89$	16.3327	1.73126	0.865631	+	0.500682i	$0.166917\pi$
$90$	1.92705	0.203128
$91$	9.69894	1.01672
$92$	9.52755	0.993316
$93$	−11.1814	−1.15946
$94$	9.24527	0.953577
$95$	5.62603	0.577219
$96$	−1.03584	−0.105719
$97$	8.23459	0.836096	0.418048	−	0.908425i	$-0.362714\pi$
$97$	8.23459	0.836096	0.418048	+	0.908425i	$0.362714\pi$
$98$	4.22602	0.426893
$99$	−9.10311	−0.914897
$100$	1.00000	0.100000
$101$	−7.39797	−0.736126	−0.368063	−	0.929801i	$-0.619979\pi$
$101$	−7.39797	−0.736126	−0.368063	+	0.929801i	$0.619979\pi$
$102$	−1.67739	−0.166086
$103$	8.14686	0.802734	0.401367	−	0.915917i	$-0.368535\pi$
$103$	8.14686	0.802734	0.401367	+	0.915917i	$0.368535\pi$
$104$	5.82334	0.571026
$105$	−1.72521	−0.168363
$106$	2.66830	0.259168
$107$	12.7670	1.23424	0.617118	−	0.786871i	$-0.288300\pi$
$107$	12.7670	1.23424	0.617118	+	0.786871i	$0.288300\pi$
$108$	−5.10361	−0.491095
$109$	18.3958	1.76200	0.880999	−	0.473118i	$-0.156872\pi$
$109$	18.3958	1.76200	0.880999	+	0.473118i	$0.156872\pi$
$110$	−4.72387	−0.450403
$111$	−4.97566	−0.472268
$112$	−1.66553	−0.157377
$113$	20.3301	1.91249	0.956246	−	0.292564i	$-0.0945085\pi$
$113$	20.3301	1.91249	0.956246	+	0.292564i	$0.0945085\pi$
$114$	−5.82764	−0.545808
$115$	9.52755	0.888449
$116$	7.93722	0.736952
$117$	11.2219	1.03746
$118$	1.55159	0.142835
$119$	−2.69708	−0.247241
$120$	−1.03584	−0.0945584
$121$	11.3149	1.02863
$122$	−7.05983	−0.639167
$123$	11.6269	1.04836
$124$	−10.7946	−0.969384
$125$	1.00000	0.0894427
$126$	−3.20955	−0.285929
$127$	−13.2705	−1.17756	−0.588781	−	0.808292i	$-0.700392\pi$
$127$	−13.2705	−1.17756	−0.588781	+	0.808292i	$0.700392\pi$
$128$	−1.00000	−0.0883883
$129$	2.29600	0.202151
$130$	5.82334	0.510741
$131$	−1.39809	−0.122151	−0.0610757	−	0.998133i	$-0.519453\pi$
$131$	−1.39809	−0.122151	−0.0610757	+	0.998133i	$0.519453\pi$
$132$	4.89315	0.425894
$133$	−9.37030	−0.812508
$134$	0.573969	0.0495833
$135$	−5.10361	−0.439249
$136$	−1.61936	−0.138859
$137$	5.78456	0.494208	0.247104	−	0.968989i	$-0.420521\pi$
$137$	5.78456	0.494208	0.247104	+	0.968989i	$0.420521\pi$
$138$	−9.86897	−0.840103
$139$	−2.66652	−0.226172	−0.113086	−	0.993585i	$-0.536073\pi$
$139$	−2.66652	−0.226172	−0.113086	+	0.993585i	$0.536073\pi$
$140$	−1.66553	−0.140763
$141$	−9.57657	−0.806493
$142$	−4.75705	−0.399203
$143$	−27.5087	−2.30039
$144$	−1.92705	−0.160587
$145$	7.93722	0.659150
$146$	7.51750	0.622153
$147$	−4.37746	−0.361047
$148$	−4.80352	−0.394847
$149$	11.0691	0.906813	0.453406	−	0.891304i	$-0.350209\pi$
$149$	11.0691	0.906813	0.453406	+	0.891304i	$0.350209\pi$
$150$	−1.03584	−0.0845756
$151$	7.53958	0.613562	0.306781	−	0.951780i	$-0.400748\pi$
$151$	7.53958	0.613562	0.306781	+	0.951780i	$0.400748\pi$
$152$	−5.62603	−0.456331
$153$	−3.12058	−0.252284
$154$	7.86773	0.634000
$155$	−10.7946	−0.867044
$156$	−6.03202	−0.482948
$157$	12.9614	1.03443	0.517215	−	0.855855i	$-0.326969\pi$
$157$	12.9614	1.03443	0.517215	+	0.855855i	$0.326969\pi$
$158$	10.3018	0.819563
$159$	−2.76392	−0.219193
$160$	−1.00000	−0.0790569
$161$	−15.8684	−1.25060
$162$	−0.494642	−0.0388628
$163$	0.679433	0.0532173	0.0266086	−	0.999646i	$-0.491529\pi$
$163$	0.679433	0.0532173	0.0266086	+	0.999646i	$0.491529\pi$
$164$	11.2247	0.876500
$165$	4.89315	0.380931
$166$	−5.68771	−0.441452
$167$	8.12728	0.628908	0.314454	−	0.949273i	$-0.398179\pi$
$167$	8.12728	0.628908	0.314454	+	0.949273i	$0.398179\pi$
$168$	1.72521	0.133103
$169$	20.9113	1.60856
$170$	−1.61936	−0.124199
$171$	−10.8416	−0.829079
$172$	2.21657	0.169012
$173$	−16.8927	−1.28433	−0.642164	−	0.766567i	$-0.721963\pi$
$173$	−16.8927	−1.28433	−0.642164	+	0.766567i	$0.721963\pi$
$174$	−8.22165	−0.623282
$175$	−1.66553	−0.125902
$176$	4.72387	0.356075
$177$	−1.60719	−0.120804
$178$	−16.3327	−1.22419
$179$	6.12619	0.457893	0.228947	−	0.973439i	$-0.426472\pi$
$179$	6.12619	0.457893	0.228947	+	0.973439i	$0.426472\pi$
$180$	−1.92705	−0.143634
$181$	23.5370	1.74949	0.874746	−	0.484581i	$-0.161028\pi$
$181$	23.5370	1.74949	0.874746	+	0.484581i	$0.161028\pi$
$182$	−9.69894	−0.718933
$183$	7.31282	0.540579
$184$	−9.52755	−0.702380
$185$	−4.80352	−0.353162
$186$	11.1814	0.819862
$187$	7.64963	0.559397
$188$	−9.24527	−0.674281
$189$	8.50019	0.618298
$190$	−5.62603	−0.408155
$191$	26.9385	1.94920	0.974601	−	0.223947i	$-0.0718943\pi$
$191$	26.9385	1.94920	0.974601	+	0.223947i	$0.0718943\pi$
$192$	1.03584	0.0747550
$193$	−0.532847	−0.0383552	−0.0191776	−	0.999816i	$-0.506105\pi$
$193$	−0.532847	−0.0383552	−0.0191776	+	0.999816i	$0.506105\pi$
$194$	−8.23459	−0.591209
$195$	−6.03202	−0.431962
$196$	−4.22602	−0.301859
$197$	−11.8930	−0.847340	−0.423670	−	0.905817i	$-0.639258\pi$
$197$	−11.8930	−0.847340	−0.423670	+	0.905817i	$0.639258\pi$
$198$	9.10311	0.646930
$199$	−6.33307	−0.448940	−0.224470	−	0.974481i	$-0.572065\pi$
$199$	−6.33307	−0.448940	−0.224470	+	0.974481i	$0.572065\pi$
$200$	−1.00000	−0.0707107
$201$	−0.594537	−0.0419354
$202$	7.39797	0.520520
$203$	−13.2196	−0.927838
$204$	1.67739	0.117441
$205$	11.2247	0.783966
$206$	−8.14686	−0.567619
$207$	−18.3600	−1.27611
$208$	−5.82334	−0.403776
$209$	26.5766	1.83834
$210$	1.72521	0.119051
$211$	−8.39422	−0.577882	−0.288941	−	0.957347i	$-0.593303\pi$
$211$	−8.39422	−0.577882	−0.288941	+	0.957347i	$0.593303\pi$
$212$	−2.66830	−0.183260
$213$	4.92752	0.337628
$214$	−12.7670	−0.872736
$215$	2.21657	0.151169
$216$	5.10361	0.347256
$217$	17.9787	1.22047
$218$	−18.3958	−1.24592
$219$	−7.78689	−0.526189
$220$	4.72387	0.318483
$221$	−9.43008	−0.634336
$222$	4.97566	0.333944
$223$	12.8422	0.859980	0.429990	−	0.902834i	$-0.358517\pi$
$223$	12.8422	0.859980	0.429990	+	0.902834i	$0.358517\pi$
$224$	1.66553	0.111283
$225$	−1.92705	−0.128470
$226$	−20.3301	−1.35234
$227$	21.7757	1.44531	0.722654	−	0.691210i	$-0.242922\pi$
$227$	21.7757	1.44531	0.722654	+	0.691210i	$0.242922\pi$
$228$	5.82764	0.385945
$229$	−11.3427	−0.749549	−0.374775	−	0.927116i	$-0.622280\pi$
$229$	−11.3427	−0.749549	−0.374775	+	0.927116i	$0.622280\pi$
$230$	−9.52755	−0.628228
$231$	−8.14967	−0.536209
$232$	−7.93722	−0.521104
$233$	18.4497	1.20868	0.604341	−	0.796725i	$-0.293436\pi$
$233$	18.4497	1.20868	0.604341	+	0.796725i	$0.293436\pi$
$234$	−11.2219	−0.733595
$235$	−9.24527	−0.603095
$236$	−1.55159	−0.101000
$237$	−10.6709	−0.693150
$238$	2.69708	0.174826
$239$	2.83782	0.183564	0.0917818	−	0.995779i	$-0.470744\pi$
$239$	2.83782	0.183564	0.0917818	+	0.995779i	$0.470744\pi$
$240$	1.03584	0.0668629
$241$	−8.93858	−0.575784	−0.287892	−	0.957663i	$-0.592954\pi$
$241$	−8.93858	−0.575784	−0.287892	+	0.957663i	$0.592954\pi$
$242$	−11.3149	−0.727351
$243$	15.8232	1.01506
$244$	7.05983	0.451959
$245$	−4.22602	−0.269991
$246$	−11.6269	−0.741305
$247$	−32.7623	−2.08462
$248$	10.7946	0.685458
$249$	5.89153	0.373361
$250$	−1.00000	−0.0632456
$251$	−17.8421	−1.12619	−0.563093	−	0.826394i	$-0.690389\pi$
$251$	−17.8421	−1.12619	−0.563093	+	0.826394i	$0.690389\pi$
$252$	3.20955	0.202182
$253$	45.0069	2.82956
$254$	13.2705	0.832663
$255$	1.67739	0.105042
$256$	1.00000	0.0625000
$257$	−9.64819	−0.601838	−0.300919	−	0.953650i	$-0.597293\pi$
$257$	−9.64819	−0.601838	−0.300919	+	0.953650i	$0.597293\pi$
$258$	−2.29600	−0.142943
$259$	8.00039	0.497120
$260$	−5.82334	−0.361149
$261$	−15.2954	−0.946761
$262$	1.39809	0.0863741
$263$	−11.2982	−0.696679	−0.348339	−	0.937369i	$-0.613254\pi$
$263$	−11.2982	−0.696679	−0.348339	+	0.937369i	$0.613254\pi$
$264$	−4.89315	−0.301152
$265$	−2.66830	−0.163912
$266$	9.37030	0.574530
$267$	16.9180	1.03536
$268$	−0.573969	−0.0350607
$269$	13.9397	0.849920	0.424960	−	0.905212i	$-0.360288\pi$
$269$	13.9397	0.849920	0.424960	+	0.905212i	$0.360288\pi$
$270$	5.10361	0.310596
$271$	18.8091	1.14257	0.571285	−	0.820752i	$-0.306445\pi$
$271$	18.8091	1.14257	0.571285	+	0.820752i	$0.306445\pi$
$272$	1.61936	0.0981880
$273$	10.0465	0.608042
$274$	−5.78456	−0.349458
$275$	4.72387	0.284860
$276$	9.86897	0.594042
$277$	−23.5195	−1.41315	−0.706575	−	0.707638i	$-0.749761\pi$
$277$	−23.5195	−1.41315	−0.706575	+	0.707638i	$0.749761\pi$
$278$	2.66652	0.159927
$279$	20.8017	1.24537
$280$	1.66553	0.0995343
$281$	−30.6947	−1.83109	−0.915546	−	0.402212i	$-0.868241\pi$
$281$	−30.6947	−1.83109	−0.915546	+	0.402212i	$0.868241\pi$
$282$	9.57657	0.570277
$283$	3.77440	0.224365	0.112182	−	0.993688i	$-0.464216\pi$
$283$	3.77440	0.224365	0.112182	+	0.993688i	$0.464216\pi$
$284$	4.75705	0.282279
$285$	5.82764	0.345200
$286$	27.5087	1.62662
$287$	−18.6950	−1.10353
$288$	1.92705	0.113552
$289$	−14.3777	−0.845746
$290$	−7.93722	−0.466090
$291$	8.52968	0.500019
$292$	−7.51750	−0.439929
$293$	11.5981	0.677566	0.338783	−	0.940864i	$-0.389985\pi$
$293$	11.5981	0.677566	0.338783	+	0.940864i	$0.389985\pi$
$294$	4.37746	0.255299
$295$	−1.55159	−0.0903370
$296$	4.80352	0.279199
$297$	−24.1088	−1.39893
$298$	−11.0691	−0.641214
$299$	−55.4822	−3.20862
$300$	1.03584	0.0598040
$301$	−3.69175	−0.212789
$302$	−7.53958	−0.433854
$303$	−7.66308	−0.440232
$304$	5.62603	0.322675
$305$	7.05983	0.404245
$306$	3.12058	0.178391
$307$	33.5923	1.91721	0.958606	−	0.284735i	$-0.0919057\pi$
$307$	33.5923	1.91721	0.958606	+	0.284735i	$0.0919057\pi$
$308$	−7.86773	−0.448305
$309$	8.43880	0.480067
$310$	10.7946	0.613092
$311$	−19.9419	−1.13080	−0.565401	−	0.824816i	$-0.691278\pi$
$311$	−19.9419	−1.13080	−0.565401	+	0.824816i	$0.691278\pi$
$312$	6.03202	0.341496
$313$	7.41064	0.418874	0.209437	−	0.977822i	$-0.432837\pi$
$313$	7.41064	0.418874	0.209437	+	0.977822i	$0.432837\pi$
$314$	−12.9614	−0.731453
$315$	3.20955	0.180837
$316$	−10.3018	−0.579519
$317$	2.42278	0.136077	0.0680385	−	0.997683i	$-0.478326\pi$
$317$	2.42278	0.136077	0.0680385	+	0.997683i	$0.478326\pi$
$318$	2.76392	0.154993
$319$	37.4944	2.09928
$320$	1.00000	0.0559017
$321$	13.2245	0.738122
$322$	15.8684	0.884311
$323$	9.11056	0.506925
$324$	0.494642	0.0274801
$325$	−5.82334	−0.323021
$326$	−0.679433	−0.0376303
$327$	19.0550	1.05374
$328$	−11.2247	−0.619779
$329$	15.3982	0.848932
$330$	−4.89315	−0.269359
$331$	−7.47034	−0.410607	−0.205303	−	0.978698i	$-0.565818\pi$
$331$	−7.47034	−0.410607	−0.205303	+	0.978698i	$0.565818\pi$
$332$	5.68771	0.312154
$333$	9.25661	0.507259
$334$	−8.12728	−0.444705
$335$	−0.573969	−0.0313593
$336$	−1.72521	−0.0941180
$337$	−17.8009	−0.969675	−0.484837	−	0.874604i	$-0.661121\pi$
$337$	−17.8009	−0.969675	−0.484837	+	0.874604i	$0.661121\pi$
$338$	−20.9113	−1.13743
$339$	21.0586	1.14375
$340$	1.61936	0.0878220
$341$	−50.9923	−2.76139
$342$	10.8416	0.586248
$343$	18.6972	1.00956
$344$	−2.21657	−0.119509
$345$	9.86897	0.531328
$346$	16.8927	0.908158
$347$	−8.86060	−0.475662	−0.237831	−	0.971307i	$-0.576436\pi$
$347$	−8.86060	−0.475662	−0.237831	+	0.971307i	$0.576436\pi$
$348$	8.22165	0.440727
$349$	−30.6916	−1.64289	−0.821443	−	0.570290i	$-0.806831\pi$
$349$	−30.6916	−1.64289	−0.821443	+	0.570290i	$0.806831\pi$
$350$	1.66553	0.0890261
$351$	29.7201	1.58634
$352$	−4.72387	−0.251783
$353$	19.8945	1.05888	0.529439	−	0.848348i	$-0.322402\pi$
$353$	19.8945	1.05888	0.529439	+	0.848348i	$0.322402\pi$
$354$	1.60719	0.0854212
$355$	4.75705	0.252478
$356$	16.3327	0.865631
$357$	−2.79373	−0.147860
$358$	−6.12619	−0.323779
$359$	16.9154	0.892762	0.446381	−	0.894843i	$-0.352713\pi$
$359$	16.9154	0.892762	0.446381	+	0.894843i	$0.352713\pi$
$360$	1.92705	0.101564
$361$	12.6522	0.665906
$362$	−23.5370	−1.23708
$363$	11.7204	0.615162
$364$	9.69894	0.508362
$365$	−7.51750	−0.393484
$366$	−7.31282	−0.382247
$367$	−28.3977	−1.48235	−0.741175	−	0.671312i	$-0.765731\pi$
$367$	−28.3977	−1.48235	−0.741175	+	0.671312i	$0.765731\pi$
$368$	9.52755	0.496658
$369$	−21.6305	−1.12604
$370$	4.80352	0.249723
$371$	4.44413	0.230728
$372$	−11.1814	−0.579730
$373$	−3.60069	−0.186436	−0.0932182	−	0.995646i	$-0.529715\pi$
$373$	−3.60069	−0.186436	−0.0932182	+	0.995646i	$0.529715\pi$
$374$	−7.64963	−0.395553
$375$	1.03584	0.0534903
$376$	9.24527	0.476788
$377$	−46.2212	−2.38051
$378$	−8.50019	−0.437203
$379$	28.4064	1.45914	0.729570	−	0.683906i	$-0.239720\pi$
$379$	28.4064	1.45914	0.729570	+	0.683906i	$0.239720\pi$
$380$	5.62603	0.288609
$381$	−13.7460	−0.704229
$382$	−26.9385	−1.37829
$383$	−3.14885	−0.160899	−0.0804493	−	0.996759i	$-0.525636\pi$
$383$	−3.14885	−0.160899	−0.0804493	+	0.996759i	$0.525636\pi$
$384$	−1.03584	−0.0528597
$385$	−7.86773	−0.400977
$386$	0.532847	0.0271212
$387$	−4.27143	−0.217129
$388$	8.23459	0.418048
$389$	0.723500	0.0366829	0.0183415	−	0.999832i	$-0.494161\pi$
$389$	0.723500	0.0366829	0.0183415	+	0.999832i	$0.494161\pi$
$390$	6.03202	0.305443
$391$	15.4285	0.780254
$392$	4.22602	0.213446
$393$	−1.44819	−0.0730514
$394$	11.8930	0.599160
$395$	−10.3018	−0.518337
$396$	−9.10311	−0.457449
$397$	−15.1418	−0.759948	−0.379974	−	0.924997i	$-0.624067\pi$
$397$	−15.1418	−0.759948	−0.379974	+	0.924997i	$0.624067\pi$
$398$	6.33307	0.317448
$399$	−9.70609	−0.485912
$400$	1.00000	0.0500000
$401$	−1.00000	−0.0499376
$401$	−1.00000	−0.0499376
$402$	0.594537	0.0296528
$403$	62.8607	3.13131
$404$	−7.39797	−0.368063
$405$	0.494642	0.0245790
$406$	13.2196	0.656080
$407$	−22.6912	−1.12476
$408$	−1.67739	−0.0830431
$409$	2.14977	0.106299	0.0531496	−	0.998587i	$-0.483074\pi$
$409$	2.14977	0.106299	0.0531496	+	0.998587i	$0.483074\pi$
$410$	−11.2247	−0.554348
$411$	5.99185	0.295556
$412$	8.14686	0.401367
$413$	2.58421	0.127161
$414$	18.3600	0.902346
$415$	5.68771	0.279199
$416$	5.82334	0.285513
$417$	−2.76208	−0.135260
$418$	−26.5766	−1.29991
$419$	−2.81607	−0.137574	−0.0687869	−	0.997631i	$-0.521913\pi$
$419$	−2.81607	−0.137574	−0.0687869	+	0.997631i	$0.521913\pi$
$420$	−1.72521	−0.0841817
$421$	−29.1441	−1.42040	−0.710198	−	0.704002i	$-0.751394\pi$
$421$	−29.1441	−1.42040	−0.710198	+	0.704002i	$0.751394\pi$
$422$	8.39422	0.408624
$423$	17.8161	0.866246
$424$	2.66830	0.129584
$425$	1.61936	0.0785504
$426$	−4.92752	−0.238739
$427$	−11.7583	−0.569026
$428$	12.7670	0.617118
$429$	−28.4945	−1.37573
$430$	−2.21657	−0.106892
$431$	−33.2506	−1.60163	−0.800814	−	0.598914i	$-0.795599\pi$
$431$	−33.2506	−1.60163	−0.800814	+	0.598914i	$0.795599\pi$
$432$	−5.10361	−0.245547
$433$	−31.5996	−1.51858	−0.759291	−	0.650751i	$-0.774454\pi$
$433$	−31.5996	−1.51858	−0.759291	+	0.650751i	$0.774454\pi$
$434$	−17.9787	−0.863005
$435$	8.22165	0.394198
$436$	18.3958	0.880999
$437$	53.6023	2.56415
$438$	7.78689	0.372072
$439$	18.1972	0.868503	0.434252	−	0.900792i	$-0.357013\pi$
$439$	18.1972	0.868503	0.434252	+	0.900792i	$0.357013\pi$
$440$	−4.72387	−0.225202
$441$	8.14374	0.387797
$442$	9.43008	0.448543
$443$	3.50414	0.166487	0.0832434	−	0.996529i	$-0.473472\pi$
$443$	3.50414	0.166487	0.0832434	+	0.996529i	$0.473472\pi$
$444$	−4.97566	−0.236134
$445$	16.3327	0.774244
$446$	−12.8422	−0.608098
$447$	11.4657	0.542310
$448$	−1.66553	−0.0786887
$449$	31.8501	1.50310	0.751550	−	0.659676i	$-0.229307\pi$
$449$	31.8501	1.50310	0.751550	+	0.659676i	$0.229307\pi$
$450$	1.92705	0.0908418
$451$	53.0239	2.49680
$452$	20.3301	0.956246
$453$	7.80976	0.366935
$454$	−21.7757	−1.02199
$455$	9.69894	0.454693
$456$	−5.82764	−0.272904
$457$	−26.1813	−1.22471	−0.612355	−	0.790583i	$-0.709778\pi$
$457$	−26.1813	−1.22471	−0.612355	+	0.790583i	$0.709778\pi$
$458$	11.3427	0.530011
$459$	−8.26456	−0.385757
$460$	9.52755	0.444224
$461$	−21.4655	−0.999749	−0.499875	−	0.866098i	$-0.666621\pi$
$461$	−21.4655	−0.999749	−0.499875	+	0.866098i	$0.666621\pi$
$462$	8.14967	0.379157
$463$	18.0650	0.839552	0.419776	−	0.907628i	$-0.362109\pi$
$463$	18.0650	0.839552	0.419776	+	0.907628i	$0.362109\pi$
$464$	7.93722	0.368476
$465$	−11.1814	−0.518526
$466$	−18.4497	−0.854668
$467$	−6.42131	−0.297143	−0.148571	−	0.988902i	$-0.547467\pi$
$467$	−6.42131	−0.297143	−0.148571	+	0.988902i	$0.547467\pi$
$468$	11.2219	0.518730
$469$	0.955960	0.0441421
$470$	9.24527	0.426452
$471$	13.4259	0.618631
$472$	1.55159	0.0714176
$473$	10.4708	0.481447
$474$	10.6709	0.490131
$475$	5.62603	0.258140
$476$	−2.69708	−0.123621
$477$	5.14194	0.235433
$478$	−2.83782	−0.129799
$479$	9.27551	0.423809	0.211904	−	0.977290i	$-0.432033\pi$
$479$	9.27551	0.423809	0.211904	+	0.977290i	$0.432033\pi$
$480$	−1.03584	−0.0472792
$481$	27.9726	1.27544
$482$	8.93858	0.407141
$483$	−16.4370	−0.747911
$484$	11.3149	0.514315
$485$	8.23459	0.373914
$486$	−15.8232	−0.717754
$487$	−5.53604	−0.250862	−0.125431	−	0.992102i	$-0.540031\pi$
$487$	−5.53604	−0.250862	−0.125431	+	0.992102i	$0.540031\pi$
$488$	−7.05983	−0.319584
$489$	0.703780	0.0318260
$490$	4.22602	0.190912
$491$	26.0940	1.17760	0.588802	−	0.808277i	$-0.299600\pi$
$491$	26.0940	1.17760	0.588802	+	0.808277i	$0.299600\pi$
$492$	11.6269	0.524182
$493$	12.8532	0.578879
$494$	32.7623	1.47405
$495$	−9.10311	−0.409154
$496$	−10.7946	−0.484692
$497$	−7.92299	−0.355395
$498$	−5.89153	−0.264006
$499$	13.2711	0.594095	0.297048	−	0.954863i	$-0.403998\pi$
$499$	13.2711	0.594095	0.297048	+	0.954863i	$0.403998\pi$
$500$	1.00000	0.0447214
$501$	8.41853	0.376112
$502$	17.8421	0.796333
$503$	39.6478	1.76781	0.883904	−	0.467668i	$-0.154906\pi$
$503$	39.6478	1.76781	0.883904	+	0.467668i	$0.154906\pi$
$504$	−3.20955	−0.142965
$505$	−7.39797	−0.329205
$506$	−45.0069	−2.00080
$507$	21.6607	0.961986
$508$	−13.2705	−0.588781
$509$	14.9701	0.663538	0.331769	−	0.943361i	$-0.392355\pi$
$509$	14.9701	0.663538	0.331769	+	0.943361i	$0.392355\pi$
$510$	−1.67739	−0.0742760
$511$	12.5206	0.553879
$512$	−1.00000	−0.0441942
$513$	−28.7130	−1.26771
$514$	9.64819	0.425563
$515$	8.14686	0.358993
$516$	2.29600	0.101076
$517$	−43.6734	−1.92076
$518$	−8.00039	−0.351517
$519$	−17.4981	−0.768080
$520$	5.82334	0.255371
$521$	−36.4944	−1.59885	−0.799425	−	0.600766i	$-0.794862\pi$
$521$	−36.4944	−1.59885	−0.799425	+	0.600766i	$0.794862\pi$
$522$	15.2954	0.669461
$523$	−3.28161	−0.143495	−0.0717473	−	0.997423i	$-0.522858\pi$
$523$	−3.28161	−0.143495	−0.0717473	+	0.997423i	$0.522858\pi$
$524$	−1.39809	−0.0610757
$525$	−1.72521	−0.0752944
$526$	11.2982	0.492626
$527$	−17.4803	−0.761455
$528$	4.89315	0.212947
$529$	67.7743	2.94671
$530$	2.66830	0.115904
$531$	2.98998	0.129754
$532$	−9.37030	−0.406254
$533$	−65.3652	−2.83128
$534$	−16.9180	−0.732113
$535$	12.7670	0.551967
$536$	0.573969	0.0247917
$537$	6.34573	0.273838
$538$	−13.9397	−0.600984
$539$	−19.9632	−0.859875
$540$	−5.10361	−0.219624
$541$	−19.7662	−0.849817	−0.424908	−	0.905236i	$-0.639694\pi$
$541$	−19.7662	−0.849817	−0.424908	+	0.905236i	$0.639694\pi$
$542$	−18.8091	−0.807919
$543$	24.3805	1.04627
$544$	−1.61936	−0.0694294
$545$	18.3958	0.787990
$546$	−10.0465	−0.429950
$547$	−9.71002	−0.415170	−0.207585	−	0.978217i	$-0.566560\pi$
$547$	−9.71002	−0.415170	−0.207585	+	0.978217i	$0.566560\pi$
$548$	5.78456	0.247104
$549$	−13.6046	−0.580631
$550$	−4.72387	−0.201426
$551$	44.6550	1.90237
$552$	−9.86897	−0.420051
$553$	17.1578	0.729626
$554$	23.5195	0.999248
$555$	−4.97566	−0.211205
$556$	−2.66652	−0.113086
$557$	−9.54033	−0.404237	−0.202118	−	0.979361i	$-0.564783\pi$
$557$	−9.54033	−0.404237	−0.202118	+	0.979361i	$0.564783\pi$
$558$	−20.8017	−0.880606
$559$	−12.9078	−0.545943
$560$	−1.66553	−0.0703813
$561$	7.92376	0.334541
$562$	30.6947	1.29478
$563$	−17.3192	−0.729918	−0.364959	−	0.931024i	$-0.618917\pi$
$563$	−17.3192	−0.729918	−0.364959	+	0.931024i	$0.618917\pi$
$564$	−9.57657	−0.403246
$565$	20.3301	0.855292
$566$	−3.77440	−0.158650
$567$	−0.823840	−0.0345980
$568$	−4.75705	−0.199601
$569$	16.0921	0.674618	0.337309	−	0.941394i	$-0.390483\pi$
$569$	16.0921	0.674618	0.337309	+	0.941394i	$0.390483\pi$
$570$	−5.82764	−0.244093
$571$	9.98286	0.417770	0.208885	−	0.977940i	$-0.433017\pi$
$571$	9.98286	0.417770	0.208885	+	0.977940i	$0.433017\pi$
$572$	−27.5087	−1.15020
$573$	27.9039	1.16570
$574$	18.6950	0.780314
$575$	9.52755	0.397326
$576$	−1.92705	−0.0802936
$577$	−0.433415	−0.0180433	−0.00902164	−	0.999959i	$-0.502872\pi$
$577$	−0.433415	−0.0180433	−0.00902164	+	0.999959i	$0.502872\pi$
$578$	14.3777	0.598033
$579$	−0.551942	−0.0229379
$580$	7.93722	0.329575
$581$	−9.47304	−0.393008
$582$	−8.52968	−0.353567
$583$	−12.6047	−0.522034
$584$	7.51750	0.311076
$585$	11.2219	0.463966
$586$	−11.5981	−0.479112
$587$	−18.6725	−0.770698	−0.385349	−	0.922771i	$-0.625919\pi$
$587$	−18.6725	−0.770698	−0.385349	+	0.922771i	$0.625919\pi$
$588$	−4.37746	−0.180523
$589$	−60.7308	−2.50237
$590$	1.55159	0.0638779
$591$	−12.3192	−0.506743
$592$	−4.80352	−0.197424
$593$	−14.8569	−0.610102	−0.305051	−	0.952336i	$-0.598673\pi$
$593$	−14.8569	−0.610102	−0.305051	+	0.952336i	$0.598673\pi$
$594$	24.1088	0.989195
$595$	−2.69708	−0.110570
$596$	11.0691	0.453406
$597$	−6.56002	−0.268484
$598$	55.4822	2.26884
$599$	36.9734	1.51069	0.755346	−	0.655326i	$-0.227469\pi$
$599$	36.9734	1.51069	0.755346	+	0.655326i	$0.227469\pi$
$600$	−1.03584	−0.0422878
$601$	−0.118550	−0.00483574	−0.00241787	−	0.999997i	$-0.500770\pi$
$601$	−0.118550	−0.00483574	−0.00241787	+	0.999997i	$0.500770\pi$
$602$	3.69175	0.150465
$603$	1.10606	0.0450424
$604$	7.53958	0.306781
$605$	11.3149	0.460017
$606$	7.66308	0.311291
$607$	−14.3435	−0.582187	−0.291093	−	0.956695i	$-0.594019\pi$
$607$	−14.3435	−0.582187	−0.291093	+	0.956695i	$0.594019\pi$
$608$	−5.62603	−0.228166
$609$	−13.6934	−0.554884
$610$	−7.05983	−0.285844
$611$	53.8384	2.17807
$612$	−3.12058	−0.126142
$613$	28.3870	1.14654	0.573270	−	0.819367i	$-0.305675\pi$
$613$	28.3870	1.14654	0.573270	+	0.819367i	$0.305675\pi$
$614$	−33.5923	−1.35567
$615$	11.6269	0.468843
$616$	7.86773	0.317000
$617$	20.7414	0.835017	0.417508	−	0.908673i	$-0.362903\pi$
$617$	20.7414	0.835017	0.417508	+	0.908673i	$0.362903\pi$
$618$	−8.43880	−0.339458
$619$	−8.41434	−0.338201	−0.169100	−	0.985599i	$-0.554086\pi$
$619$	−8.41434	−0.338201	−0.169100	+	0.985599i	$0.554086\pi$
$620$	−10.7946	−0.433522
$621$	−48.6249	−1.95125
$622$	19.9419	0.799597
$623$	−27.2025	−1.08985
$624$	−6.03202	−0.241474
$625$	1.00000	0.0400000
$626$	−7.41064	−0.296189
$627$	27.5290	1.09940
$628$	12.9614	0.517215
$629$	−7.77862	−0.310154
$630$	−3.20955	−0.127871
$631$	−26.2886	−1.04653	−0.523267	−	0.852169i	$-0.675287\pi$
$631$	−26.2886	−1.04653	−0.523267	+	0.852169i	$0.675287\pi$
$632$	10.3018	0.409782
$633$	−8.69502	−0.345596
$634$	−2.42278	−0.0962210
$635$	−13.2705	−0.526622
$636$	−2.76392	−0.109597
$637$	24.6096	0.975067
$638$	−37.4944	−1.48442
$639$	−9.16705	−0.362643
$640$	−1.00000	−0.0395285
$641$	31.8808	1.25922	0.629608	−	0.776913i	$-0.283215\pi$
$641$	31.8808	1.25922	0.629608	+	0.776913i	$0.283215\pi$
$642$	−13.2245	−0.521931
$643$	−20.7974	−0.820170	−0.410085	−	0.912047i	$-0.634501\pi$
$643$	−20.7974	−0.820170	−0.410085	+	0.912047i	$0.634501\pi$
$644$	−15.8684	−0.625302
$645$	2.29600	0.0904048
$646$	−9.11056	−0.358450
$647$	−28.3136	−1.11312	−0.556562	−	0.830806i	$-0.687880\pi$
$647$	−28.3136	−1.11312	−0.556562	+	0.830806i	$0.687880\pi$
$648$	−0.494642	−0.0194314
$649$	−7.32950	−0.287708
$650$	5.82334	0.228410
$651$	18.6230	0.729892
$652$	0.679433	0.0266086
$653$	−10.9981	−0.430390	−0.215195	−	0.976571i	$-0.569039\pi$
$653$	−10.9981	−0.430390	−0.215195	+	0.976571i	$0.569039\pi$
$654$	−19.0550	−0.745110
$655$	−1.39809	−0.0546278
$656$	11.2247	0.438250
$657$	14.4866	0.565175
$658$	−15.3982	−0.600286
$659$	4.19594	0.163451	0.0817253	−	0.996655i	$-0.473957\pi$
$659$	4.19594	0.163451	0.0817253	+	0.996655i	$0.473957\pi$
$660$	4.89315	0.190466
$661$	19.4414	0.756182	0.378091	−	0.925768i	$-0.376581\pi$
$661$	19.4414	0.756182	0.378091	+	0.925768i	$0.376581\pi$
$662$	7.47034	0.290343
$663$	−9.76800	−0.379358
$664$	−5.68771	−0.220726
$665$	−9.37030	−0.363365
$666$	−9.25661	−0.358686
$667$	75.6223	2.92811
$668$	8.12728	0.314454
$669$	13.3024	0.514302
$670$	0.573969	0.0221743
$671$	33.3497	1.28745
$672$	1.72521	0.0665515
$673$	−28.5381	−1.10006	−0.550032	−	0.835144i	$-0.685385\pi$
$673$	−28.5381	−1.10006	−0.550032	+	0.835144i	$0.685385\pi$
$674$	17.8009	0.685664
$675$	−5.10361	−0.196438
$676$	20.9113	0.804282
$677$	−37.3112	−1.43398	−0.716992	−	0.697081i	$-0.754482\pi$
$677$	−37.3112	−1.43398	−0.716992	+	0.697081i	$0.754482\pi$
$678$	−21.0586	−0.808751
$679$	−13.7149	−0.526331
$680$	−1.61936	−0.0620995
$681$	22.5561	0.864351
$682$	50.9923	1.95260
$683$	20.3579	0.778973	0.389486	−	0.921032i	$-0.372653\pi$
$683$	20.3579	0.778973	0.389486	+	0.921032i	$0.372653\pi$
$684$	−10.8416	−0.414540
$685$	5.78456	0.221017
$686$	−18.6972	−0.713864
$687$	−11.7492	−0.448260
$688$	2.21657	0.0845058
$689$	15.5384	0.591968
$690$	−9.86897	−0.375705
$691$	−25.8238	−0.982383	−0.491192	−	0.871052i	$-0.663438\pi$
$691$	−25.8238	−0.982383	−0.491192	+	0.871052i	$0.663438\pi$
$692$	−16.8927	−0.642164
$693$	15.1615	0.575937
$694$	8.86060	0.336344
$695$	−2.66652	−0.101147
$696$	−8.22165	−0.311641
$697$	18.1768	0.688494
$698$	30.6916	1.16170
$699$	19.1109	0.722840
$700$	−1.66553	−0.0629510
$701$	−33.8126	−1.27708	−0.638541	−	0.769588i	$-0.720462\pi$
$701$	−33.8126	−1.27708	−0.638541	+	0.769588i	$0.720462\pi$
$702$	−29.7201	−1.12171
$703$	−27.0248	−1.01926
$704$	4.72387	0.178037
$705$	−9.57657	−0.360675
$706$	−19.8945	−0.748740
$707$	12.3215	0.463398
$708$	−1.60719	−0.0604019
$709$	45.8254	1.72101	0.860504	−	0.509444i	$-0.170149\pi$
$709$	45.8254	1.72101	0.860504	+	0.509444i	$0.170149\pi$
$710$	−4.75705	−0.178529
$711$	19.8519	0.744506
$712$	−16.3327	−0.612094
$713$	−102.846	−3.85162
$714$	2.79373	0.104553
$715$	−27.5087	−1.02877
$716$	6.12619	0.228947
$717$	2.93952	0.109778
$718$	−16.9154	−0.631278
$719$	19.8325	0.739629	0.369814	−	0.929106i	$-0.379421\pi$
$719$	19.8325	0.739629	0.369814	+	0.929106i	$0.379421\pi$
$720$	−1.92705	−0.0718168
$721$	−13.5688	−0.505329
$722$	−12.6522	−0.470867
$723$	−9.25889	−0.344342
$724$	23.5370	0.874746
$725$	7.93722	0.294781
$726$	−11.7204	−0.434985
$727$	−19.6801	−0.729895	−0.364947	−	0.931028i	$-0.618913\pi$
$727$	−19.6801	−0.729895	−0.364947	+	0.931028i	$0.618913\pi$
$728$	−9.69894	−0.359466
$729$	14.9063	0.552085
$730$	7.51750	0.278235
$731$	3.58941	0.132759
$732$	7.31282	0.270290
$733$	−10.4700	−0.386716	−0.193358	−	0.981128i	$-0.561938\pi$
$733$	−10.4700	−0.386716	−0.193358	+	0.981128i	$0.561938\pi$
$734$	28.3977	1.04818
$735$	−4.37746	−0.161465
$736$	−9.52755	−0.351190
$737$	−2.71135	−0.0998740
$738$	21.6305	0.796229
$739$	2.60887	0.0959688	0.0479844	−	0.998848i	$-0.484720\pi$
$739$	2.60887	0.0959688	0.0479844	+	0.998848i	$0.484720\pi$
$740$	−4.80352	−0.176581
$741$	−33.9364	−1.24668
$742$	−4.44413	−0.163149
$743$	5.29172	0.194134	0.0970672	−	0.995278i	$-0.469054\pi$
$743$	5.29172	0.194134	0.0970672	+	0.995278i	$0.469054\pi$
$744$	11.1814	0.409931
$745$	11.0691	0.405539
$746$	3.60069	0.131830
$747$	−10.9605	−0.401023
$748$	7.64963	0.279698
$749$	−21.2638	−0.776964
$750$	−1.03584	−0.0378233
$751$	13.6352	0.497556	0.248778	−	0.968561i	$-0.419971\pi$
$751$	13.6352	0.497556	0.248778	+	0.968561i	$0.419971\pi$
$752$	−9.24527	−0.337140
$753$	−18.4815	−0.673503
$754$	46.2212	1.68328
$755$	7.53958	0.274393
$756$	8.50019	0.309149
$757$	12.3372	0.448402	0.224201	−	0.974543i	$-0.428023\pi$
$757$	12.3372	0.448402	0.224201	+	0.974543i	$0.428023\pi$
$758$	−28.4064	−1.03177
$759$	46.6197	1.69219
$760$	−5.62603	−0.204078
$761$	28.9852	1.05071	0.525356	−	0.850882i	$-0.323932\pi$
$761$	28.9852	1.05071	0.525356	+	0.850882i	$0.323932\pi$
$762$	13.7460	0.497965
$763$	−30.6387	−1.10920
$764$	26.9385	0.974601
$765$	−3.12058	−0.112825
$766$	3.14885	0.113773
$767$	9.03543	0.326251
$768$	1.03584	0.0373775
$769$	−45.7395	−1.64941	−0.824705	−	0.565563i	$-0.808659\pi$
$769$	−45.7395	−1.64941	−0.824705	+	0.565563i	$0.808659\pi$
$770$	7.86773	0.283533
$771$	−9.99393	−0.359923
$772$	−0.532847	−0.0191776
$773$	12.0965	0.435080	0.217540	−	0.976051i	$-0.430197\pi$
$773$	12.0965	0.435080	0.217540	+	0.976051i	$0.430197\pi$
$774$	4.27143	0.153533
$775$	−10.7946	−0.387754
$776$	−8.23459	−0.295605
$777$	8.28709	0.297298
$778$	−0.723500	−0.0259387
$779$	63.1504	2.26260
$780$	−6.03202	−0.215981
$781$	22.4717	0.804099
$782$	−15.4285	−0.551723
$783$	−40.5084	−1.44765
$784$	−4.22602	−0.150929
$785$	12.9614	0.462612
$786$	1.44819	0.0516551
$787$	−45.9358	−1.63743	−0.818717	−	0.574197i	$-0.805314\pi$
$787$	−45.9358	−1.63743	−0.818717	+	0.574197i	$0.805314\pi$
$788$	−11.8930	−0.423670
$789$	−11.7031	−0.416641
$790$	10.3018	0.366520
$791$	−33.8603	−1.20393
$792$	9.10311	0.323465
$793$	−41.1118	−1.45992
$794$	15.1418	0.537364
$795$	−2.76392	−0.0980262
$796$	−6.33307	−0.224470
$797$	−37.9312	−1.34359	−0.671796	−	0.740736i	$-0.734477\pi$
$797$	−37.9312	−1.34359	−0.671796	+	0.740736i	$0.734477\pi$
$798$	9.70609	0.343592
$799$	−14.9714	−0.529650
$800$	−1.00000	−0.0353553
$801$	−31.4739	−1.11207
$802$	1.00000	0.0353112
$803$	−35.5117	−1.25318
$804$	−0.594537	−0.0209677
$805$	−15.8684	−0.559287
$806$	−62.8607	−2.21417
$807$	14.4393	0.508286
$808$	7.39797	0.260260
$809$	−0.592632	−0.0208358	−0.0104179	−	0.999946i	$-0.503316\pi$
$809$	−0.592632	−0.0208358	−0.0104179	+	0.999946i	$0.503316\pi$
$810$	−0.494642	−0.0173800
$811$	−37.5892	−1.31993	−0.659967	−	0.751295i	$-0.729430\pi$
$811$	−37.5892	−1.31993	−0.659967	+	0.751295i	$0.729430\pi$
$812$	−13.2196	−0.463919
$813$	19.4831	0.683302
$814$	22.6912	0.795326
$815$	0.679433	0.0237995
$816$	1.67739	0.0587203
$817$	12.4705	0.436287
$818$	−2.14977	−0.0751649
$819$	−18.6903	−0.653092
$820$	11.2247	0.391983
$821$	0.00135271	4.72099e−5 0	2.36049e−5	−	1.00000i	$-0.499992\pi$
$821$	0.00135271	4.72099e−5 0	2.36049e−5		1.00000i	$0.499992\pi$
$822$	−5.99185	−0.208990
$823$	35.9012	1.25144	0.625719	−	0.780049i	$-0.284806\pi$
$823$	35.9012	1.25144	0.625719	+	0.780049i	$0.284806\pi$
$824$	−8.14686	−0.283809
$825$	4.89315	0.170358
$826$	−2.58421	−0.0899162
$827$	−14.9768	−0.520793	−0.260396	−	0.965502i	$-0.583853\pi$
$827$	−14.9768	−0.520793	−0.260396	+	0.965502i	$0.583853\pi$
$828$	−18.3600	−0.638055
$829$	−35.6081	−1.23672	−0.618359	−	0.785895i	$-0.712202\pi$
$829$	−35.6081	−1.23672	−0.618359	+	0.785895i	$0.712202\pi$
$830$	−5.68771	−0.197423
$831$	−24.3623	−0.845120
$832$	−5.82334	−0.201888
$833$	−6.84344	−0.237111
$834$	2.76208	0.0956429
$835$	8.12728	0.281256
$836$	26.5766	0.919172
$837$	55.0914	1.90424
$838$	2.81607	0.0972794
$839$	−9.45233	−0.326331	−0.163165	−	0.986599i	$-0.552170\pi$
$839$	−9.45233	−0.326331	−0.163165	+	0.986599i	$0.552170\pi$
$840$	1.72521	0.0595254
$841$	33.9994	1.17239
$842$	29.1441	1.00437
$843$	−31.7947	−1.09507
$844$	−8.39422	−0.288941
$845$	20.9113	0.719372
$846$	−17.8161	−0.612529
$847$	−18.8453	−0.647533
$848$	−2.66830	−0.0916299
$849$	3.90965	0.134179
$850$	−1.61936	−0.0555435
$851$	−45.7658	−1.56883
$852$	4.92752	0.168814
$853$	−37.9011	−1.29771	−0.648854	−	0.760913i	$-0.724751\pi$
$853$	−37.9011	−1.29771	−0.648854	+	0.760913i	$0.724751\pi$
$854$	11.7583	0.402362
$855$	−10.8416	−0.370776
$856$	−12.7670	−0.436368
$857$	−2.01594	−0.0688632	−0.0344316	−	0.999407i	$-0.510962\pi$
$857$	−2.01594	−0.0688632	−0.0344316	+	0.999407i	$0.510962\pi$
$858$	28.4945	0.972786
$859$	−24.9813	−0.852352	−0.426176	−	0.904640i	$-0.640140\pi$
$859$	−24.9813	−0.852352	−0.426176	+	0.904640i	$0.640140\pi$
$860$	2.21657	0.0755843
$861$	−19.3649	−0.659955
$862$	33.2506	1.13252
$863$	−36.9721	−1.25855	−0.629273	−	0.777185i	$-0.716647\pi$
$863$	−36.9721	−1.25855	−0.629273	+	0.777185i	$0.716647\pi$
$864$	5.10361	0.173628
$865$	−16.8927	−0.574369
$866$	31.5996	1.07380
$867$	−14.8929	−0.505790
$868$	17.9787	0.610237
$869$	−48.6641	−1.65082
$870$	−8.22165	−0.278740
$871$	3.34242	0.113253
$872$	−18.3958	−0.622960
$873$	−15.8684	−0.537065
$874$	−53.6023	−1.81312
$875$	−1.66553	−0.0563051
$876$	−7.78689	−0.263095
$877$	11.7451	0.396603	0.198301	−	0.980141i	$-0.436458\pi$
$877$	11.7451	0.396603	0.198301	+	0.980141i	$0.436458\pi$
$878$	−18.1972	−0.614125
$879$	12.0137	0.405212
$880$	4.72387	0.159242
$881$	−19.9965	−0.673699	−0.336849	−	0.941559i	$-0.609361\pi$
$881$	−19.9965	−0.673699	−0.336849	+	0.941559i	$0.609361\pi$
$882$	−8.14374	−0.274214
$883$	−44.2854	−1.49032	−0.745162	−	0.666884i	$-0.767628\pi$
$883$	−44.2854	−1.49032	−0.745162	+	0.666884i	$0.767628\pi$
$884$	−9.43008	−0.317168
$885$	−1.60719	−0.0540251
$886$	−3.50414	−0.117724
$887$	−1.56633	−0.0525922	−0.0262961	−	0.999654i	$-0.508371\pi$
$887$	−1.56633	−0.0525922	−0.0262961	+	0.999654i	$0.508371\pi$
$888$	4.97566	0.166972
$889$	22.1023	0.741287
$890$	−16.3327	−0.547473
$891$	2.33663	0.0782799
$892$	12.8422	0.429990
$893$	−52.0142	−1.74059
$894$	−11.4657	−0.383471
$895$	6.12619	0.204776
$896$	1.66553	0.0556413
$897$	−57.4704	−1.91888
$898$	−31.8501	−1.06285
$899$	−85.6791	−2.85756
$900$	−1.92705	−0.0642349
$901$	−4.32094	−0.143951
$902$	−53.0239	−1.76550
$903$	−3.82405	−0.127256
$904$	−20.3301	−0.676168
$905$	23.5370	0.782397
$906$	−7.80976	−0.259462
$907$	21.2410	0.705296	0.352648	−	0.935756i	$-0.385281\pi$
$907$	21.2410	0.705296	0.352648	+	0.935756i	$0.385281\pi$
$908$	21.7757	0.722654
$909$	14.2562	0.472849
$910$	−9.69894	−0.321517
$911$	−30.0830	−0.996694	−0.498347	−	0.866978i	$-0.666059\pi$
$911$	−30.0830	−0.996694	−0.498347	+	0.866978i	$0.666059\pi$
$912$	5.82764	0.192972
$913$	26.8680	0.889201
$914$	26.1813	0.866001
$915$	7.31282	0.241754
$916$	−11.3427	−0.374775
$917$	2.32855	0.0768955
$918$	8.26456	0.272771
$919$	−32.8407	−1.08331	−0.541657	−	0.840599i	$-0.682203\pi$
$919$	−32.8407	−1.08331	−0.541657	+	0.840599i	$0.682203\pi$
$920$	−9.52755	−0.314114
$921$	34.7961	1.14657
$922$	21.4655	0.706930
$923$	−27.7019	−0.911820
$924$	−8.14967	−0.268104
$925$	−4.80352	−0.157939
$926$	−18.0650	−0.593653
$927$	−15.6994	−0.515635
$928$	−7.93722	−0.260552
$929$	−18.1305	−0.594843	−0.297422	−	0.954746i	$-0.596127\pi$
$929$	−18.1305	−0.594843	−0.297422	+	0.954746i	$0.596127\pi$
$930$	11.1814	0.366654
$931$	−23.7757	−0.779218
$932$	18.4497	0.604341
$933$	−20.6565	−0.676264
$934$	6.42131	0.210112
$935$	7.64963	0.250170
$936$	−11.2219	−0.366798
$937$	33.3154	1.08837	0.544184	−	0.838966i	$-0.316839\pi$
$937$	33.3154	1.08837	0.544184	+	0.838966i	$0.316839\pi$
$938$	−0.955960	−0.0312132
$939$	7.67620	0.250503
$940$	−9.24527	−0.301547
$941$	−8.60501	−0.280515	−0.140258	−	0.990115i	$-0.544793\pi$
$941$	−8.60501	−0.280515	−0.140258	+	0.990115i	$0.544793\pi$
$942$	−13.4259	−0.437438
$943$	106.944	3.48257
$944$	−1.55159	−0.0504999
$945$	8.50019	0.276511
$946$	−10.4708	−0.340434
$947$	−23.8554	−0.775197	−0.387599	−	0.921828i	$-0.626695\pi$
$947$	−23.8554	−0.775197	−0.387599	+	0.921828i	$0.626695\pi$
$948$	−10.6709	−0.346575
$949$	43.7770	1.42106
$950$	−5.62603	−0.182533
$951$	2.50960	0.0813794
$952$	2.69708	0.0874130
$953$	6.92560	0.224342	0.112171	−	0.993689i	$-0.464220\pi$
$953$	6.92560	0.224342	0.112171	+	0.993689i	$0.464220\pi$
$954$	−5.14194	−0.166476
$955$	26.9385	0.871710
$956$	2.83782	0.0917818
$957$	38.8380	1.25545
$958$	−9.27551	−0.299678
$959$	−9.63434	−0.311109
$960$	1.03584	0.0334314
$961$	85.5235	2.75882
$962$	−27.9726	−0.901872
$963$	−24.6027	−0.792810
$964$	−8.93858	−0.287892
$965$	−0.532847	−0.0171529
$966$	16.4370	0.528853
$967$	6.44442	0.207239	0.103619	−	0.994617i	$-0.466958\pi$
$967$	6.44442	0.207239	0.103619	+	0.994617i	$0.466958\pi$
$968$	−11.3149	−0.363676
$969$	9.43703	0.303161
$970$	−8.23459	−0.264397
$971$	44.8587	1.43958	0.719792	−	0.694190i	$-0.244237\pi$
$971$	44.8587	1.43958	0.719792	+	0.694190i	$0.244237\pi$
$972$	15.8232	0.507529
$973$	4.44117	0.142377
$974$	5.53604	0.177386
$975$	−6.03202	−0.193179
$976$	7.05983	0.225980
$977$	49.7368	1.59122	0.795611	−	0.605808i	$-0.207150\pi$
$977$	49.7368	1.59122	0.795611	+	0.605808i	$0.207150\pi$
$978$	−0.703780	−0.0225044
$979$	77.1535	2.46584
$980$	−4.22602	−0.134995
$981$	−35.4496	−1.13182
$982$	−26.0940	−0.832692
$983$	−24.9152	−0.794670	−0.397335	−	0.917674i	$-0.630065\pi$
$983$	−24.9152	−0.794670	−0.397335	+	0.917674i	$0.630065\pi$
$984$	−11.6269	−0.370653
$985$	−11.8930	−0.378942
$986$	−12.8532	−0.409329
$987$	15.9500	0.507695
$988$	−32.7623	−1.04231
$989$	21.1185	0.671528
$990$	9.10311	0.289316
$991$	−26.3691	−0.837643	−0.418822	−	0.908069i	$-0.637557\pi$
$991$	−26.3691	−0.837643	−0.418822	+	0.908069i	$0.637557\pi$
$992$	10.7946	0.342729
$993$	−7.73803	−0.245559
$994$	7.92299	0.251302
$995$	−6.33307	−0.200772
$996$	5.89153	0.186680
$997$	36.3152	1.15011	0.575057	−	0.818113i	$-0.304980\pi$
$997$	36.3152	1.15011	0.575057	+	0.818113i	$0.304980\pi$
$998$	−13.2711	−0.420089
$999$	24.5153	0.775629

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	4010.2.a.m.1.13	✓	20

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
4010.2.a.m.1.13	✓	20	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)

\(f(q)\)	\(=\)	\(q-1.00000 q^{2} +1.03584 q^{3} +1.00000 q^{4} +1.00000 q^{5} -1.03584 q^{6} -1.66553 q^{7} -1.00000 q^{8} -1.92705 q^{9} +O(q^{10})\)	\(q-1.00000 q^{2} +1.03584 q^{3} +1.00000 q^{4} +1.00000 q^{5} -1.03584 q^{6} -1.66553 q^{7} -1.00000 q^{8} -1.92705 q^{9} -1.00000 q^{10} +4.72387 q^{11} +1.03584 q^{12} -5.82334 q^{13} +1.66553 q^{14} +1.03584 q^{15} +1.00000 q^{16} +1.61936 q^{17} +1.92705 q^{18} +5.62603 q^{19} +1.00000 q^{20} -1.72521 q^{21} -4.72387 q^{22} +9.52755 q^{23} -1.03584 q^{24} +1.00000 q^{25} +5.82334 q^{26} -5.10361 q^{27} -1.66553 q^{28} +7.93722 q^{29} -1.03584 q^{30} -10.7946 q^{31} -1.00000 q^{32} +4.89315 q^{33} -1.61936 q^{34} -1.66553 q^{35} -1.92705 q^{36} -4.80352 q^{37} -5.62603 q^{38} -6.03202 q^{39} -1.00000 q^{40} +11.2247 q^{41} +1.72521 q^{42} +2.21657 q^{43} +4.72387 q^{44} -1.92705 q^{45} -9.52755 q^{46} -9.24527 q^{47} +1.03584 q^{48} -4.22602 q^{49} -1.00000 q^{50} +1.67739 q^{51} -5.82334 q^{52} -2.66830 q^{53} +5.10361 q^{54} +4.72387 q^{55} +1.66553 q^{56} +5.82764 q^{57} -7.93722 q^{58} -1.55159 q^{59} +1.03584 q^{60} +7.05983 q^{61} +10.7946 q^{62} +3.20955 q^{63} +1.00000 q^{64} -5.82334 q^{65} -4.89315 q^{66} -0.573969 q^{67} +1.61936 q^{68} +9.86897 q^{69} +1.66553 q^{70} +4.75705 q^{71} +1.92705 q^{72} -7.51750 q^{73} +4.80352 q^{74} +1.03584 q^{75} +5.62603 q^{76} -7.86773 q^{77} +6.03202 q^{78} -10.3018 q^{79} +1.00000 q^{80} +0.494642 q^{81} -11.2247 q^{82} +5.68771 q^{83} -1.72521 q^{84} +1.61936 q^{85} -2.21657 q^{86} +8.22165 q^{87} -4.72387 q^{88} +16.3327 q^{89} +1.92705 q^{90} +9.69894 q^{91} +9.52755 q^{92} -11.1814 q^{93} +9.24527 q^{94} +5.62603 q^{95} -1.03584 q^{96} +8.23459 q^{97} +4.22602 q^{98} -9.10311 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 20 q - 20 q^{2} + 4 q^{3} + 20 q^{4} + 20 q^{5} - 4 q^{6} + 11 q^{7} - 20 q^{8} + 26 q^{9}+O(q^{10}) \) 20 * q - 20 * q^2 + 4 * q^3 + 20 * q^4 + 20 * q^5 - 4 * q^6 + 11 * q^7 - 20 * q^8 + 26 * q^9	\( 20 q - 20 q^{2} + 4 q^{3} + 20 q^{4} + 20 q^{5} - 4 q^{6} + 11 q^{7} - 20 q^{8} + 26 q^{9} - 20 q^{10} + 10 q^{11} + 4 q^{12} - 9 q^{13} - 11 q^{14} + 4 q^{15} + 20 q^{16} - 11 q^{17} - 26 q^{18} + 17 q^{19} + 20 q^{20} - 2 q^{21} - 10 q^{22} - 3 q^{23} - 4 q^{24} + 20 q^{25} + 9 q^{26} - 2 q^{27} + 11 q^{28} + 6 q^{29} - 4 q^{30} + 28 q^{31} - 20 q^{32} + 2 q^{33} + 11 q^{34} + 11 q^{35} + 26 q^{36} + 33 q^{37} - 17 q^{38} + 36 q^{39} - 20 q^{40} + 32 q^{41} + 2 q^{42} + 30 q^{43} + 10 q^{44} + 26 q^{45} + 3 q^{46} + 13 q^{47} + 4 q^{48} + 43 q^{49} - 20 q^{50} + 43 q^{51} - 9 q^{52} + 2 q^{54} + 10 q^{55} - 11 q^{56} + 19 q^{57} - 6 q^{58} + 52 q^{59} + 4 q^{60} + 25 q^{61} - 28 q^{62} + 16 q^{63} + 20 q^{64} - 9 q^{65} - 2 q^{66} + 40 q^{67} - 11 q^{68} + 39 q^{69} - 11 q^{70} + 25 q^{71} - 26 q^{72} - 5 q^{73} - 33 q^{74} + 4 q^{75} + 17 q^{76} - 9 q^{77} - 36 q^{78} + 40 q^{79} + 20 q^{80} + 48 q^{81} - 32 q^{82} + 10 q^{83} - 2 q^{84} - 11 q^{85} - 30 q^{86} + 10 q^{87} - 10 q^{88} + 17 q^{89} - 26 q^{90} + 88 q^{91} - 3 q^{92} - 4 q^{93} - 13 q^{94} + 17 q^{95} - 4 q^{96} - 2 q^{97} - 43 q^{98} + 50 q^{99}+O(q^{100}) \) 20 * q - 20 * q^2 + 4 * q^3 + 20 * q^4 + 20 * q^5 - 4 * q^6 + 11 * q^7 - 20 * q^8 + 26 * q^9 - 20 * q^10 + 10 * q^11 + 4 * q^12 - 9 * q^13 - 11 * q^14 + 4 * q^15 + 20 * q^16 - 11 * q^17 - 26 * q^18 + 17 * q^19 + 20 * q^20 - 2 * q^21 - 10 * q^22 - 3 * q^23 - 4 * q^24 + 20 * q^25 + 9 * q^26 - 2 * q^27 + 11 * q^28 + 6 * q^29 - 4 * q^30 + 28 * q^31 - 20 * q^32 + 2 * q^33 + 11 * q^34 + 11 * q^35 + 26 * q^36 + 33 * q^37 - 17 * q^38 + 36 * q^39 - 20 * q^40 + 32 * q^41 + 2 * q^42 + 30 * q^43 + 10 * q^44 + 26 * q^45 + 3 * q^46 + 13 * q^47 + 4 * q^48 + 43 * q^49 - 20 * q^50 + 43 * q^51 - 9 * q^52 + 2 * q^54 + 10 * q^55 - 11 * q^56 + 19 * q^57 - 6 * q^58 + 52 * q^59 + 4 * q^60 + 25 * q^61 - 28 * q^62 + 16 * q^63 + 20 * q^64 - 9 * q^65 - 2 * q^66 + 40 * q^67 - 11 * q^68 + 39 * q^69 - 11 * q^70 + 25 * q^71 - 26 * q^72 - 5 * q^73 - 33 * q^74 + 4 * q^75 + 17 * q^76 - 9 * q^77 - 36 * q^78 + 40 * q^79 + 20 * q^80 + 48 * q^81 - 32 * q^82 + 10 * q^83 - 2 * q^84 - 11 * q^85 - 30 * q^86 + 10 * q^87 - 10 * q^88 + 17 * q^89 - 26 * q^90 + 88 * q^91 - 3 * q^92 - 4 * q^93 - 13 * q^94 + 17 * q^95 - 4 * q^96 - 2 * q^97 - 43 * q^98 + 50 * q^99

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