LMFDB - Embedded newform 4010.2.a.i.1.10

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			1.10
Root			$2.54891$ 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)

$f(q)$	$=$	$q-1.00000 q^{2} +2.40579 q^{3} +1.00000 q^{4} +1.00000 q^{5} -2.40579 q^{6} -1.75221 q^{7} -1.00000 q^{8} +2.78781 q^{9} +O(q^{10})$	\(q-1.00000 q^{2} +2.40579 q^{3} +1.00000 q^{4} +1.00000 q^{5} -2.40579 q^{6} -1.75221 q^{7} -1.00000 q^{8} +2.78781 q^{9} -1.00000 q^{10} -5.60615 q^{11} +2.40579 q^{12} -0.293332 q^{13} +1.75221 q^{14} +2.40579 q^{15} +1.00000 q^{16} -4.41428 q^{17} -2.78781 q^{18} +5.95884 q^{19} +1.00000 q^{20} -4.21545 q^{21} +5.60615 q^{22} +0.532230 q^{23} -2.40579 q^{24} +1.00000 q^{25} +0.293332 q^{26} -0.510485 q^{27} -1.75221 q^{28} +3.48505 q^{29} -2.40579 q^{30} -8.31509 q^{31} -1.00000 q^{32} -13.4872 q^{33} +4.41428 q^{34} -1.75221 q^{35} +2.78781 q^{36} -6.82337 q^{37} -5.95884 q^{38} -0.705695 q^{39} -1.00000 q^{40} -3.49734 q^{41} +4.21545 q^{42} +9.84698 q^{43} -5.60615 q^{44} +2.78781 q^{45} -0.532230 q^{46} +6.31687 q^{47} +2.40579 q^{48} -3.92975 q^{49} -1.00000 q^{50} -10.6198 q^{51} -0.293332 q^{52} +11.0638 q^{53} +0.510485 q^{54} -5.60615 q^{55} +1.75221 q^{56} +14.3357 q^{57} -3.48505 q^{58} +7.19256 q^{59} +2.40579 q^{60} -13.8248 q^{61} +8.31509 q^{62} -4.88484 q^{63} +1.00000 q^{64} -0.293332 q^{65} +13.4872 q^{66} -13.3508 q^{67} -4.41428 q^{68} +1.28043 q^{69} +1.75221 q^{70} -1.33532 q^{71} -2.78781 q^{72} -10.1801 q^{73} +6.82337 q^{74} +2.40579 q^{75} +5.95884 q^{76} +9.82317 q^{77} +0.705695 q^{78} -2.23194 q^{79} +1.00000 q^{80} -9.59155 q^{81} +3.49734 q^{82} -4.18417 q^{83} -4.21545 q^{84} -4.41428 q^{85} -9.84698 q^{86} +8.38428 q^{87} +5.60615 q^{88} -13.2291 q^{89} -2.78781 q^{90} +0.513981 q^{91} +0.532230 q^{92} -20.0043 q^{93} -6.31687 q^{94} +5.95884 q^{95} -2.40579 q^{96} -10.0926 q^{97} +3.92975 q^{98} -15.6289 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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
$3$	2.40579	1.38898	0.694491	−	0.719502i	$-0.255630\pi$
$3$	2.40579	1.38898	0.694491	+	0.719502i	$0.255630\pi$
$4$	1.00000	0.500000
$5$	1.00000	0.447214
$5$	1.00000	0.447214
$6$	−2.40579	−0.982158
$7$	−1.75221	−0.662274	−0.331137	−	0.943583i	$-0.607432\pi$
$7$	−1.75221	−0.662274	−0.331137	+	0.943583i	$0.607432\pi$
$8$	−1.00000	−0.353553
$9$	2.78781	0.929270
$10$	−1.00000	−0.316228
$11$	−5.60615	−1.69032	−0.845159	−	0.534515i	$-0.820494\pi$
$11$	−5.60615	−1.69032	−0.845159	+	0.534515i	$0.820494\pi$
$12$	2.40579	0.694491
$13$	−0.293332	−0.0813558	−0.0406779	−	0.999172i	$-0.512952\pi$
$13$	−0.293332	−0.0813558	−0.0406779	+	0.999172i	$0.512952\pi$
$14$	1.75221	0.468299
$15$	2.40579	0.621171
$16$	1.00000	0.250000
$17$	−4.41428	−1.07062	−0.535310	−	0.844656i	$-0.679805\pi$
$17$	−4.41428	−1.07062	−0.535310	+	0.844656i	$0.679805\pi$
$18$	−2.78781	−0.657093
$19$	5.95884	1.36705	0.683525	−	0.729927i	$-0.260446\pi$
$19$	5.95884	1.36705	0.683525	+	0.729927i	$0.260446\pi$
$20$	1.00000	0.223607
$21$	−4.21545	−0.919887
$22$	5.60615	1.19523
$23$	0.532230	0.110978	0.0554888	−	0.998459i	$-0.482328\pi$
$23$	0.532230	0.110978	0.0554888	+	0.998459i	$0.482328\pi$
$24$	−2.40579	−0.491079
$25$	1.00000	0.200000
$26$	0.293332	0.0575272
$27$	−0.510485	−0.0982428
$28$	−1.75221	−0.331137
$29$	3.48505	0.647157	0.323578	−	0.946201i	$-0.395114\pi$
$29$	3.48505	0.647157	0.323578	+	0.946201i	$0.395114\pi$
$30$	−2.40579	−0.439235
$31$	−8.31509	−1.49343	−0.746717	−	0.665142i	$-0.768371\pi$
$31$	−8.31509	−1.49343	−0.746717	+	0.665142i	$0.768371\pi$
$32$	−1.00000	−0.176777
$33$	−13.4872	−2.34782
$34$	4.41428	0.757042
$35$	−1.75221	−0.296178
$36$	2.78781	0.464635
$37$	−6.82337	−1.12176	−0.560878	−	0.827899i	$-0.689536\pi$
$37$	−6.82337	−1.12176	−0.560878	+	0.827899i	$0.689536\pi$
$38$	−5.95884	−0.966651
$39$	−0.705695	−0.113002
$40$	−1.00000	−0.158114
$41$	−3.49734	−0.546192	−0.273096	−	0.961987i	$-0.588048\pi$
$41$	−3.49734	−0.546192	−0.273096	+	0.961987i	$0.588048\pi$
$42$	4.21545	0.650458
$43$	9.84698	1.50165	0.750825	−	0.660501i	$-0.229656\pi$
$43$	9.84698	1.50165	0.750825	+	0.660501i	$0.229656\pi$
$44$	−5.60615	−0.845159
$45$	2.78781	0.415582
$46$	−0.532230	−0.0784730
$47$	6.31687	0.921410	0.460705	−	0.887553i	$-0.347597\pi$
$47$	6.31687	0.921410	0.460705	+	0.887553i	$0.347597\pi$
$48$	2.40579	0.347245
$49$	−3.92975	−0.561393
$50$	−1.00000	−0.141421
$51$	−10.6198	−1.48707
$52$	−0.293332	−0.0406779
$53$	11.0638	1.51973	0.759864	−	0.650083i	$-0.225266\pi$
$53$	11.0638	1.51973	0.759864	+	0.650083i	$0.225266\pi$
$54$	0.510485	0.0694682
$55$	−5.60615	−0.755933
$56$	1.75221	0.234149
$57$	14.3357	1.89881
$58$	−3.48505	−0.457609
$59$	7.19256	0.936392	0.468196	−	0.883625i	$-0.344904\pi$
$59$	7.19256	0.936392	0.468196	+	0.883625i	$0.344904\pi$
$60$	2.40579	0.310586
$61$	−13.8248	−1.77008	−0.885040	−	0.465515i	$-0.845869\pi$
$61$	−13.8248	−1.77008	−0.885040	+	0.465515i	$0.845869\pi$
$62$	8.31509	1.05602
$63$	−4.88484	−0.615431
$64$	1.00000	0.125000
$65$	−0.293332	−0.0363834
$66$	13.4872	1.66016
$67$	−13.3508	−1.63106	−0.815529	−	0.578717i	$-0.803554\pi$
$67$	−13.3508	−1.63106	−0.815529	+	0.578717i	$0.803554\pi$
$68$	−4.41428	−0.535310
$69$	1.28043	0.154146
$70$	1.75221	0.209429
$71$	−1.33532	−0.158473	−0.0792367	−	0.996856i	$-0.525248\pi$
$71$	−1.33532	−0.158473	−0.0792367	+	0.996856i	$0.525248\pi$
$72$	−2.78781	−0.328547
$73$	−10.1801	−1.19148	−0.595742	−	0.803176i	$-0.703142\pi$
$73$	−10.1801	−1.19148	−0.595742	+	0.803176i	$0.703142\pi$
$74$	6.82337	0.793201
$75$	2.40579	0.277796
$76$	5.95884	0.683525
$77$	9.82317	1.11945
$78$	0.705695	0.0799042
$79$	−2.23194	−0.251112	−0.125556	−	0.992087i	$-0.540072\pi$
$79$	−2.23194	−0.251112	−0.125556	+	0.992087i	$0.540072\pi$
$80$	1.00000	0.111803
$81$	−9.59155	−1.06573
$82$	3.49734	0.386216
$83$	−4.18417	−0.459272	−0.229636	−	0.973277i	$-0.573754\pi$
$83$	−4.18417	−0.459272	−0.229636	+	0.973277i	$0.573754\pi$
$84$	−4.21545	−0.459943
$85$	−4.41428	−0.478796
$86$	−9.84698	−1.06183
$87$	8.38428	0.898889
$88$	5.60615	0.597617
$89$	−13.2291	−1.40228	−0.701139	−	0.713025i	$-0.747325\pi$
$89$	−13.2291	−1.40228	−0.701139	+	0.713025i	$0.747325\pi$
$90$	−2.78781	−0.293861
$91$	0.513981	0.0538798
$92$	0.532230	0.0554888
$93$	−20.0043	−2.07435
$94$	−6.31687	−0.651536
$95$	5.95884	0.611364
$96$	−2.40579	−0.245540
$97$	−10.0926	−1.02474	−0.512372	−	0.858763i	$-0.671233\pi$
$97$	−10.0926	−1.02474	−0.512372	+	0.858763i	$0.671233\pi$
$98$	3.92975	0.396965
$99$	−15.6289	−1.57076
$100$	1.00000	0.100000
$101$	−9.78984	−0.974125	−0.487063	−	0.873367i	$-0.661932\pi$
$101$	−9.78984	−0.974125	−0.487063	+	0.873367i	$0.661932\pi$
$102$	10.6198	1.05152
$103$	−13.3534	−1.31575	−0.657874	−	0.753128i	$-0.728544\pi$
$103$	−13.3534	−1.31575	−0.657874	+	0.753128i	$0.728544\pi$
$104$	0.293332	0.0287636
$105$	−4.21545	−0.411386
$106$	−11.0638	−1.07461
$107$	−1.99022	−0.192402	−0.0962009	−	0.995362i	$-0.530669\pi$
$107$	−1.99022	−0.192402	−0.0962009	+	0.995362i	$0.530669\pi$
$108$	−0.510485	−0.0491214
$109$	−2.34125	−0.224251	−0.112126	−	0.993694i	$-0.535766\pi$
$109$	−2.34125	−0.224251	−0.112126	+	0.993694i	$0.535766\pi$
$110$	5.60615	0.534525
$111$	−16.4156	−1.55810
$112$	−1.75221	−0.165569
$113$	15.4709	1.45538	0.727690	−	0.685906i	$-0.240594\pi$
$113$	15.4709	1.45538	0.727690	+	0.685906i	$0.240594\pi$
$114$	−14.3357	−1.34266
$115$	0.532230	0.0496307
$116$	3.48505	0.323578
$117$	−0.817755	−0.0756015
$118$	−7.19256	−0.662129
$119$	7.73475	0.709043
$120$	−2.40579	−0.219617
$121$	20.4289	1.85717
$122$	13.8248	1.25164
$123$	−8.41385	−0.758651
$124$	−8.31509	−0.746717
$125$	1.00000	0.0894427
$126$	4.88484	0.435176
$127$	−18.6217	−1.65241	−0.826203	−	0.563372i	$-0.809504\pi$
$127$	−18.6217	−1.65241	−0.826203	+	0.563372i	$0.809504\pi$
$128$	−1.00000	−0.0883883
$129$	23.6897	2.08576
$130$	0.293332	0.0257270
$131$	−5.69531	−0.497602	−0.248801	−	0.968555i	$-0.580036\pi$
$131$	−5.69531	−0.497602	−0.248801	+	0.968555i	$0.580036\pi$
$132$	−13.4872	−1.17391
$133$	−10.4411	−0.905362
$134$	13.3508	1.15333
$135$	−0.510485	−0.0439355
$136$	4.41428	0.378521
$137$	−10.5675	−0.902844	−0.451422	−	0.892311i	$-0.649083\pi$
$137$	−10.5675	−0.902844	−0.451422	+	0.892311i	$0.649083\pi$
$138$	−1.28043	−0.108998
$139$	9.57211	0.811896	0.405948	−	0.913896i	$-0.366941\pi$
$139$	9.57211	0.811896	0.405948	+	0.913896i	$0.366941\pi$
$140$	−1.75221	−0.148089
$141$	15.1970	1.27982
$142$	1.33532	0.112058
$143$	1.64446	0.137517
$144$	2.78781	0.232317
$145$	3.48505	0.289417
$146$	10.1801	0.842507
$147$	−9.45414	−0.779764
$148$	−6.82337	−0.560878
$149$	−11.9011	−0.974979	−0.487489	−	0.873129i	$-0.662087\pi$
$149$	−11.9011	−0.974979	−0.487489	+	0.873129i	$0.662087\pi$
$150$	−2.40579	−0.196432
$151$	−4.48113	−0.364669	−0.182335	−	0.983237i	$-0.558365\pi$
$151$	−4.48113	−0.364669	−0.182335	+	0.983237i	$0.558365\pi$
$152$	−5.95884	−0.483325
$153$	−12.3062	−0.994894
$154$	−9.82317	−0.791573
$155$	−8.31509	−0.667884
$156$	−0.705695	−0.0565008
$157$	2.69235	0.214873	0.107436	−	0.994212i	$-0.465736\pi$
$157$	2.69235	0.214873	0.107436	+	0.994212i	$0.465736\pi$
$158$	2.23194	0.177563
$159$	26.6171	2.11087
$160$	−1.00000	−0.0790569
$161$	−0.932580	−0.0734976
$162$	9.59155	0.753583
$163$	−23.1986	−1.81706	−0.908529	−	0.417822i	$-0.862794\pi$
$163$	−23.1986	−1.81706	−0.908529	+	0.417822i	$0.862794\pi$
$164$	−3.49734	−0.273096
$165$	−13.4872	−1.04998
$166$	4.18417	0.324755
$167$	−10.5614	−0.817268	−0.408634	−	0.912698i	$-0.633995\pi$
$167$	−10.5614	−0.817268	−0.408634	+	0.912698i	$0.633995\pi$
$168$	4.21545	0.325229
$169$	−12.9140	−0.993381
$170$	4.41428	0.338560
$171$	16.6121	1.27036
$172$	9.84698	0.750825
$173$	19.0268	1.44658	0.723291	−	0.690543i	$-0.242628\pi$
$173$	19.0268	1.44658	0.723291	+	0.690543i	$0.242628\pi$
$174$	−8.38428	−0.635610
$175$	−1.75221	−0.132455
$176$	−5.60615	−0.422579
$177$	17.3038	1.30063
$178$	13.2291	0.991560
$179$	17.9349	1.34052	0.670260	−	0.742126i	$-0.266183\pi$
$179$	17.9349	1.34052	0.670260	+	0.742126i	$0.266183\pi$
$180$	2.78781	0.207791
$181$	15.9037	1.18211	0.591055	−	0.806631i	$-0.298711\pi$
$181$	15.9037	1.18211	0.591055	+	0.806631i	$0.298711\pi$
$182$	−0.513981	−0.0380988
$183$	−33.2594	−2.45861
$184$	−0.532230	−0.0392365
$185$	−6.82337	−0.501664
$186$	20.0043	1.46679
$187$	24.7471	1.80969
$188$	6.31687	0.460705
$189$	0.894478	0.0650637
$190$	−5.95884	−0.432299
$191$	−17.0814	−1.23596	−0.617982	−	0.786192i	$-0.712050\pi$
$191$	−17.0814	−1.23596	−0.617982	+	0.786192i	$0.712050\pi$
$192$	2.40579	0.173623
$193$	23.0755	1.66101	0.830505	−	0.557011i	$-0.188052\pi$
$193$	23.0755	1.66101	0.830505	+	0.557011i	$0.188052\pi$
$194$	10.0926	0.724604
$195$	−0.705695	−0.0505359
$196$	−3.92975	−0.280696
$197$	19.5317	1.39158	0.695789	−	0.718246i	$-0.255055\pi$
$197$	19.5317	1.39158	0.695789	+	0.718246i	$0.255055\pi$
$198$	15.6289	1.11070
$199$	7.42826	0.526576	0.263288	−	0.964717i	$-0.415193\pi$
$199$	7.42826	0.526576	0.263288	+	0.964717i	$0.415193\pi$
$200$	−1.00000	−0.0707107
$201$	−32.1191	−2.26551
$202$	9.78984	0.688811
$203$	−6.10654	−0.428595
$204$	−10.6198	−0.743535
$205$	−3.49734	−0.244265
$206$	13.3534	0.930375
$207$	1.48376	0.103128
$208$	−0.293332	−0.0203389
$209$	−33.4061	−2.31075
$210$	4.21545	0.290894
$211$	7.26922	0.500434	0.250217	−	0.968190i	$-0.419498\pi$
$211$	7.26922	0.500434	0.250217	+	0.968190i	$0.419498\pi$
$212$	11.0638	0.759864
$213$	−3.21250	−0.220117
$214$	1.99022	0.136049
$215$	9.84698	0.671558
$216$	0.510485	0.0347341
$217$	14.5698	0.989063
$218$	2.34125	0.158570
$219$	−24.4910	−1.65495
$220$	−5.60615	−0.377966
$221$	1.29485	0.0871011
$222$	16.4156	1.10174
$223$	−20.1554	−1.34971	−0.674853	−	0.737952i	$-0.735793\pi$
$223$	−20.1554	−1.34971	−0.674853	+	0.737952i	$0.735793\pi$
$224$	1.75221	0.117075
$225$	2.78781	0.185854
$226$	−15.4709	−1.02911
$227$	25.1632	1.67014	0.835071	−	0.550142i	$-0.185427\pi$
$227$	25.1632	1.67014	0.835071	+	0.550142i	$0.185427\pi$
$228$	14.3357	0.949404
$229$	−7.80188	−0.515563	−0.257781	−	0.966203i	$-0.582991\pi$
$229$	−7.80188	−0.515563	−0.257781	+	0.966203i	$0.582991\pi$
$230$	−0.532230	−0.0350942
$231$	23.6324	1.55490
$232$	−3.48505	−0.228804
$233$	−8.21279	−0.538038	−0.269019	−	0.963135i	$-0.586699\pi$
$233$	−8.21279	−0.538038	−0.269019	+	0.963135i	$0.586699\pi$
$234$	0.817755	0.0534583
$235$	6.31687	0.412067
$236$	7.19256	0.468196
$237$	−5.36956	−0.348791
$238$	−7.73475	−0.501369
$239$	−17.3544	−1.12256	−0.561280	−	0.827626i	$-0.689691\pi$
$239$	−17.3544	−1.12256	−0.561280	+	0.827626i	$0.689691\pi$
$240$	2.40579	0.155293
$241$	−0.0952985	−0.00613871	−0.00306936	−	0.999995i	$-0.500977\pi$
$241$	−0.0952985	−0.00613871	−0.00306936	+	0.999995i	$0.500977\pi$
$242$	−20.4289	−1.31322
$243$	−21.5438	−1.38203
$244$	−13.8248	−0.885040
$245$	−3.92975	−0.251063
$246$	8.41385	0.536447
$247$	−1.74792	−0.111217
$248$	8.31509	0.528009
$249$	−10.0662	−0.637921
$250$	−1.00000	−0.0632456
$251$	2.70106	0.170489	0.0852447	−	0.996360i	$-0.472833\pi$
$251$	2.70106	0.170489	0.0852447	+	0.996360i	$0.472833\pi$
$252$	−4.88484	−0.307716
$253$	−2.98376	−0.187587
$254$	18.6217	1.16843
$255$	−10.6198	−0.665038
$256$	1.00000	0.0625000
$257$	−23.6741	−1.47675	−0.738376	−	0.674389i	$-0.764407\pi$
$257$	−23.6741	−1.47675	−0.738376	+	0.674389i	$0.764407\pi$
$258$	−23.6897	−1.47486
$259$	11.9560	0.742910
$260$	−0.293332	−0.0181917
$261$	9.71564	0.601383
$262$	5.69531	0.351858
$263$	4.31583	0.266126	0.133063	−	0.991108i	$-0.457519\pi$
$263$	4.31583	0.266126	0.133063	+	0.991108i	$0.457519\pi$
$264$	13.4872	0.830080
$265$	11.0638	0.679643
$266$	10.4411	0.640188
$267$	−31.8263	−1.94774
$268$	−13.3508	−0.815529
$269$	14.2846	0.870948	0.435474	−	0.900201i	$-0.356581\pi$
$269$	14.2846	0.870948	0.435474	+	0.900201i	$0.356581\pi$
$270$	0.510485	0.0310671
$271$	4.17693	0.253730	0.126865	−	0.991920i	$-0.459508\pi$
$271$	4.17693	0.253730	0.126865	+	0.991920i	$0.459508\pi$
$272$	−4.41428	−0.267655
$273$	1.23653	0.0748381
$274$	10.5675	0.638407
$275$	−5.60615	−0.338063
$276$	1.28043	0.0770729
$277$	31.1285	1.87033	0.935165	−	0.354212i	$-0.115251\pi$
$277$	31.1285	1.87033	0.935165	+	0.354212i	$0.115251\pi$
$278$	−9.57211	−0.574097
$279$	−23.1809	−1.38780
$280$	1.75221	0.104715
$281$	31.5560	1.88247	0.941236	−	0.337751i	$-0.109666\pi$
$281$	31.5560	1.88247	0.941236	+	0.337751i	$0.109666\pi$
$282$	−15.1970	−0.904971
$283$	28.7658	1.70995	0.854973	−	0.518672i	$-0.173573\pi$
$283$	28.7658	1.70995	0.854973	+	0.518672i	$0.173573\pi$
$284$	−1.33532	−0.0792367
$285$	14.3357	0.849173
$286$	−1.64446	−0.0972392
$287$	6.12808	0.361729
$288$	−2.78781	−0.164273
$289$	2.48584	0.146226
$290$	−3.48505	−0.204649
$291$	−24.2806	−1.42335
$292$	−10.1801	−0.595742
$293$	17.5541	1.02552	0.512760	−	0.858532i	$-0.328623\pi$
$293$	17.5541	1.02552	0.512760	+	0.858532i	$0.328623\pi$
$294$	9.45414	0.551377
$295$	7.19256	0.418767
$296$	6.82337	0.396600
$297$	2.86185	0.166062
$298$	11.9011	0.689414
$299$	−0.156120	−0.00902867
$300$	2.40579	0.138898
$301$	−17.2540	−0.994504
$302$	4.48113	0.257860
$303$	−23.5523	−1.35304
$304$	5.95884	0.341763
$305$	−13.8248	−0.791604
$306$	12.3062	0.703497
$307$	0.103139	0.00588646	0.00294323	−	0.999996i	$-0.499063\pi$
$307$	0.103139	0.00588646	0.00294323	+	0.999996i	$0.499063\pi$
$308$	9.82317	0.559727
$309$	−32.1254	−1.82755
$310$	8.31509	0.472265
$311$	25.3389	1.43684	0.718419	−	0.695611i	$-0.244866\pi$
$311$	25.3389	1.43684	0.718419	+	0.695611i	$0.244866\pi$
$312$	0.705695	0.0399521
$313$	17.7254	1.00190	0.500950	−	0.865476i	$-0.332984\pi$
$313$	17.7254	1.00190	0.500950	+	0.865476i	$0.332984\pi$
$314$	−2.69235	−0.151938
$315$	−4.88484	−0.275229
$316$	−2.23194	−0.125556
$317$	11.4292	0.641927	0.320964	−	0.947092i	$-0.395993\pi$
$317$	11.4292	0.641927	0.320964	+	0.947092i	$0.395993\pi$
$318$	−26.6171	−1.49261
$319$	−19.5377	−1.09390
$320$	1.00000	0.0559017
$321$	−4.78804	−0.267242
$322$	0.932580	0.0519707
$323$	−26.3039	−1.46359
$324$	−9.59155	−0.532864
$325$	−0.293332	−0.0162712
$326$	23.1986	1.28485
$327$	−5.63256	−0.311481
$328$	3.49734	0.193108
$329$	−11.0685	−0.610226
$330$	13.4872	0.742446
$331$	−2.57374	−0.141465	−0.0707326	−	0.997495i	$-0.522534\pi$
$331$	−2.57374	−0.141465	−0.0707326	+	0.997495i	$0.522534\pi$
$332$	−4.18417	−0.229636
$333$	−19.0223	−1.04241
$334$	10.5614	0.577896
$335$	−13.3508	−0.729431
$336$	−4.21545	−0.229972
$337$	23.1351	1.26025	0.630124	−	0.776494i	$-0.283004\pi$
$337$	23.1351	1.26025	0.630124	+	0.776494i	$0.283004\pi$
$338$	12.9140	0.702427
$339$	37.2197	2.02150
$340$	−4.41428	−0.239398
$341$	46.6156	2.52438
$342$	−16.6121	−0.898279
$343$	19.1512	1.03407
$344$	−9.84698	−0.530913
$345$	1.28043	0.0689361
$346$	−19.0268	−1.02289
$347$	−5.29245	−0.284114	−0.142057	−	0.989859i	$-0.545372\pi$
$347$	−5.29245	−0.284114	−0.142057	+	0.989859i	$0.545372\pi$
$348$	8.38428	0.449444
$349$	31.2995	1.67543	0.837713	−	0.546111i	$-0.183892\pi$
$349$	31.2995	1.67543	0.837713	+	0.546111i	$0.183892\pi$
$350$	1.75221	0.0936597
$351$	0.149742	0.00799262
$352$	5.60615	0.298809
$353$	24.8184	1.32095	0.660475	−	0.750848i	$-0.270355\pi$
$353$	24.8184	1.32095	0.660475	+	0.750848i	$0.270355\pi$
$354$	−17.3038	−0.919685
$355$	−1.33532	−0.0708715
$356$	−13.2291	−0.701139
$357$	18.6082	0.984848
$358$	−17.9349	−0.947891
$359$	6.33468	0.334332	0.167166	−	0.985929i	$-0.446538\pi$
$359$	6.33468	0.334332	0.167166	+	0.985929i	$0.446538\pi$
$360$	−2.78781	−0.146930
$361$	16.5077	0.868827
$362$	−15.9037	−0.835878
$363$	49.1476	2.57958
$364$	0.513981	0.0269399
$365$	−10.1801	−0.532848
$366$	33.2594	1.73850
$367$	−31.1149	−1.62418	−0.812092	−	0.583529i	$-0.801671\pi$
$367$	−31.1149	−1.62418	−0.812092	+	0.583529i	$0.801671\pi$
$368$	0.532230	0.0277444
$369$	−9.74991	−0.507560
$370$	6.82337	0.354730
$371$	−19.3861	−1.00648
$372$	−20.0043	−1.03718
$373$	20.0301	1.03712	0.518559	−	0.855042i	$-0.326469\pi$
$373$	20.0301	1.03712	0.518559	+	0.855042i	$0.326469\pi$
$374$	−24.7471	−1.27964
$375$	2.40579	0.124234
$376$	−6.31687	−0.325768
$377$	−1.02228	−0.0526499
$378$	−0.894478	−0.0460070
$379$	−32.5737	−1.67320	−0.836600	−	0.547814i	$-0.815460\pi$
$379$	−32.5737	−1.67320	−0.836600	+	0.547814i	$0.815460\pi$
$380$	5.95884	0.305682
$381$	−44.7998	−2.29516
$382$	17.0814	0.873958
$383$	10.7995	0.551830	0.275915	−	0.961182i	$-0.411019\pi$
$383$	10.7995	0.551830	0.275915	+	0.961182i	$0.411019\pi$
$384$	−2.40579	−0.122770
$385$	9.82317	0.500635
$386$	−23.0755	−1.17451
$387$	27.4515	1.39544
$388$	−10.0926	−0.512372
$389$	−3.29764	−0.167197	−0.0835985	−	0.996500i	$-0.526641\pi$
$389$	−3.29764	−0.167197	−0.0835985	+	0.996500i	$0.526641\pi$
$390$	0.705695	0.0357343
$391$	−2.34941	−0.118815
$392$	3.92975	0.198482
$393$	−13.7017	−0.691160
$394$	−19.5317	−0.983994
$395$	−2.23194	−0.112301
$396$	−15.6289	−0.785381
$397$	30.4380	1.52764	0.763819	−	0.645431i	$-0.223322\pi$
$397$	30.4380	1.52764	0.763819	+	0.645431i	$0.223322\pi$
$398$	−7.42826	−0.372345
$399$	−25.1192	−1.25753
$400$	1.00000	0.0500000
$401$	1.00000	0.0499376
$401$	1.00000	0.0499376
$402$	32.1191	1.60196
$403$	2.43909	0.121500
$404$	−9.78984	−0.487063
$405$	−9.59155	−0.476608
$406$	6.10654	0.303063
$407$	38.2528	1.89612
$408$	10.6198	0.525759
$409$	−2.25032	−0.111271	−0.0556355	−	0.998451i	$-0.517718\pi$
$409$	−2.25032	−0.111271	−0.0556355	+	0.998451i	$0.517718\pi$
$410$	3.49734	0.172721
$411$	−25.4232	−1.25403
$412$	−13.3534	−0.657874
$413$	−12.6029	−0.620148
$414$	−1.48376	−0.0729226
$415$	−4.18417	−0.205393
$416$	0.293332	0.0143818
$417$	23.0284	1.12771
$418$	33.4061	1.63395
$419$	−20.2395	−0.988763	−0.494381	−	0.869245i	$-0.664605\pi$
$419$	−20.2395	−0.988763	−0.494381	+	0.869245i	$0.664605\pi$
$420$	−4.21545	−0.205693
$421$	−6.12535	−0.298531	−0.149266	−	0.988797i	$-0.547691\pi$
$421$	−6.12535	−0.298531	−0.149266	+	0.988797i	$0.547691\pi$
$422$	−7.26922	−0.353860
$423$	17.6102	0.856239
$424$	−11.0638	−0.537305
$425$	−4.41428	−0.214124
$426$	3.21250	0.155646
$427$	24.2239	1.17228
$428$	−1.99022	−0.0962009
$429$	3.95623	0.191009
$430$	−9.84698	−0.474863
$431$	16.8163	0.810011	0.405005	−	0.914314i	$-0.367270\pi$
$431$	16.8163	0.810011	0.405005	+	0.914314i	$0.367270\pi$
$432$	−0.510485	−0.0245607
$433$	−1.18090	−0.0567503	−0.0283752	−	0.999597i	$-0.509033\pi$
$433$	−1.18090	−0.0567503	−0.0283752	+	0.999597i	$0.509033\pi$
$434$	−14.5698	−0.699373
$435$	8.38428	0.401995
$436$	−2.34125	−0.112126
$437$	3.17147	0.151712
$438$	24.4910	1.17023
$439$	−25.4663	−1.21544	−0.607720	−	0.794151i	$-0.707916\pi$
$439$	−25.4663	−1.21544	−0.607720	+	0.794151i	$0.707916\pi$
$440$	5.60615	0.267263
$441$	−10.9554	−0.521686
$442$	−1.29485	−0.0615897
$443$	−16.4471	−0.781426	−0.390713	−	0.920513i	$-0.627772\pi$
$443$	−16.4471	−0.781426	−0.390713	+	0.920513i	$0.627772\pi$
$444$	−16.4156	−0.779049
$445$	−13.2291	−0.627118
$446$	20.1554	0.954387
$447$	−28.6316	−1.35423
$448$	−1.75221	−0.0827843
$449$	9.13398	0.431059	0.215530	−	0.976497i	$-0.430852\pi$
$449$	9.13398	0.431059	0.215530	+	0.976497i	$0.430852\pi$
$450$	−2.78781	−0.131419
$451$	19.6066	0.923238
$452$	15.4709	0.727690
$453$	−10.7806	−0.506519
$454$	−25.1632	−1.18097
$455$	0.513981	0.0240958
$456$	−14.3357	−0.671330
$457$	−27.2144	−1.27304	−0.636518	−	0.771262i	$-0.719626\pi$
$457$	−27.2144	−1.27304	−0.636518	+	0.771262i	$0.719626\pi$
$458$	7.80188	0.364558
$459$	2.25342	0.105181
$460$	0.532230	0.0248154
$461$	−7.78685	−0.362670	−0.181335	−	0.983421i	$-0.558042\pi$
$461$	−7.78685	−0.362670	−0.181335	+	0.983421i	$0.558042\pi$
$462$	−23.6324	−1.09948
$463$	24.6432	1.14527	0.572633	−	0.819812i	$-0.305922\pi$
$463$	24.6432	1.14527	0.572633	+	0.819812i	$0.305922\pi$
$464$	3.48505	0.161789
$465$	−20.0043	−0.927679
$466$	8.21279	0.380450
$467$	−4.37222	−0.202322	−0.101161	−	0.994870i	$-0.532256\pi$
$467$	−4.37222	−0.202322	−0.101161	+	0.994870i	$0.532256\pi$
$468$	−0.817755	−0.0378007
$469$	23.3934	1.08021
$470$	−6.31687	−0.291376
$471$	6.47722	0.298454
$472$	−7.19256	−0.331064
$473$	−55.2036	−2.53827
$474$	5.36956	0.246632
$475$	5.95884	0.273410
$476$	7.73475	0.354522
$477$	30.8437	1.41224
$478$	17.3544	0.793770
$479$	12.8369	0.586531	0.293266	−	0.956031i	$-0.405258\pi$
$479$	12.8369	0.586531	0.293266	+	0.956031i	$0.405258\pi$
$480$	−2.40579	−0.109809
$481$	2.00152	0.0912613
$482$	0.0952985	0.00434073
$483$	−2.24359	−0.102087
$484$	20.4289	0.928587
$485$	−10.0926	−0.458280
$486$	21.5438	0.977245
$487$	−17.4018	−0.788552	−0.394276	−	0.918992i	$-0.629005\pi$
$487$	−17.4018	−0.788552	−0.394276	+	0.918992i	$0.629005\pi$
$488$	13.8248	0.625818
$489$	−55.8110	−2.52386
$490$	3.92975	0.177528
$491$	−38.1358	−1.72104	−0.860522	−	0.509413i	$-0.829863\pi$
$491$	−38.1358	−1.72104	−0.860522	+	0.509413i	$0.829863\pi$
$492$	−8.41385	−0.379325
$493$	−15.3840	−0.692858
$494$	1.74792	0.0786426
$495$	−15.6289	−0.702466
$496$	−8.31509	−0.373359
$497$	2.33977	0.104953
$498$	10.0662	0.451078
$499$	−33.3663	−1.49368	−0.746841	−	0.665003i	$-0.768430\pi$
$499$	−33.3663	−1.49368	−0.746841	+	0.665003i	$0.768430\pi$
$500$	1.00000	0.0447214
$501$	−25.4086	−1.13517
$502$	−2.70106	−0.120554
$503$	−5.78208	−0.257810	−0.128905	−	0.991657i	$-0.541146\pi$
$503$	−5.78208	−0.257810	−0.128905	+	0.991657i	$0.541146\pi$
$504$	4.88484	0.217588
$505$	−9.78984	−0.435642
$506$	2.98376	0.132644
$507$	−31.0682	−1.37979
$508$	−18.6217	−0.826203
$509$	2.32636	0.103114	0.0515571	−	0.998670i	$-0.483582\pi$
$509$	2.32636	0.103114	0.0515571	+	0.998670i	$0.483582\pi$
$510$	10.6198	0.470253
$511$	17.8376	0.789090
$512$	−1.00000	−0.0441942
$513$	−3.04189	−0.134303
$514$	23.6741	1.04422
$515$	−13.3534	−0.588421
$516$	23.6897	1.04288
$517$	−35.4133	−1.55748
$518$	−11.9560	−0.525316
$519$	45.7745	2.00928
$520$	0.293332	0.0128635
$521$	−7.39413	−0.323943	−0.161971	−	0.986795i	$-0.551785\pi$
$521$	−7.39413	−0.323943	−0.161971	+	0.986795i	$0.551785\pi$
$522$	−9.71564	−0.425242
$523$	−41.3423	−1.80777	−0.903886	−	0.427774i	$-0.859298\pi$
$523$	−41.3423	−1.80777	−0.903886	+	0.427774i	$0.859298\pi$
$524$	−5.69531	−0.248801
$525$	−4.21545	−0.183977
$526$	−4.31583	−0.188179
$527$	36.7051	1.59890
$528$	−13.4872	−0.586955
$529$	−22.7167	−0.987684
$530$	−11.0638	−0.480580
$531$	20.0515	0.870161
$532$	−10.4411	−0.452681
$533$	1.02588	0.0444359
$534$	31.8263	1.37726
$535$	−1.99022	−0.0860447
$536$	13.3508	0.576666
$537$	43.1476	1.86196
$538$	−14.2846	−0.615853
$539$	22.0308	0.948932
$540$	−0.510485	−0.0219678
$541$	−4.07929	−0.175382	−0.0876912	−	0.996148i	$-0.527949\pi$
$541$	−4.07929	−0.175382	−0.0876912	+	0.996148i	$0.527949\pi$
$542$	−4.17693	−0.179414
$543$	38.2608	1.64193
$544$	4.41428	0.189261
$545$	−2.34125	−0.100288
$546$	−1.23653	−0.0529185
$547$	−9.99288	−0.427265	−0.213632	−	0.976914i	$-0.568529\pi$
$547$	−9.99288	−0.427265	−0.213632	+	0.976914i	$0.568529\pi$
$548$	−10.5675	−0.451422
$549$	−38.5408	−1.64488
$550$	5.60615	0.239047
$551$	20.7668	0.884696
$552$	−1.28043	−0.0544988
$553$	3.91083	0.166305
$554$	−31.1285	−1.32252
$555$	−16.4156	−0.696802
$556$	9.57211	0.405948
$557$	0.828239	0.0350936	0.0175468	−	0.999846i	$-0.494414\pi$
$557$	0.828239	0.0350936	0.0175468	+	0.999846i	$0.494414\pi$
$558$	23.1809	0.981325
$559$	−2.88844	−0.122168
$560$	−1.75221	−0.0740445
$561$	59.5362	2.51362
$562$	−31.5560	−1.33111
$563$	0.532790	0.0224544	0.0112272	−	0.999937i	$-0.496426\pi$
$563$	0.532790	0.0224544	0.0112272	+	0.999937i	$0.496426\pi$
$564$	15.1970	0.639911
$565$	15.4709	0.650866
$566$	−28.7658	−1.20911
$567$	16.8064	0.705804
$568$	1.33532	0.0560288
$569$	−17.8871	−0.749865	−0.374932	−	0.927052i	$-0.622334\pi$
$569$	−17.8871	−0.749865	−0.374932	+	0.927052i	$0.622334\pi$
$570$	−14.3357	−0.600456
$571$	13.6191	0.569943	0.284971	−	0.958536i	$-0.408016\pi$
$571$	13.6191	0.569943	0.284971	+	0.958536i	$0.408016\pi$
$572$	1.64446	0.0687585
$573$	−41.0941	−1.71673
$574$	−6.12808	−0.255781
$575$	0.532230	0.0221955
$576$	2.78781	0.116159
$577$	−21.2418	−0.884310	−0.442155	−	0.896939i	$-0.645786\pi$
$577$	−21.2418	−0.884310	−0.442155	+	0.896939i	$0.645786\pi$
$578$	−2.48584	−0.103397
$579$	55.5147	2.30711
$580$	3.48505	0.144709
$581$	7.33156	0.304164
$582$	24.2806	1.00646
$583$	−62.0252	−2.56882
$584$	10.1801	0.421253
$585$	−0.817755	−0.0338100
$586$	−17.5541	−0.725153
$587$	26.6077	1.09822	0.549109	−	0.835750i	$-0.314967\pi$
$587$	26.6077	1.09822	0.549109	+	0.835750i	$0.314967\pi$
$588$	−9.45414	−0.389882
$589$	−49.5483	−2.04160
$590$	−7.19256	−0.296113
$591$	46.9892	1.93288
$592$	−6.82337	−0.280439
$593$	31.0830	1.27643	0.638213	−	0.769860i	$-0.279674\pi$
$593$	31.0830	1.27643	0.638213	+	0.769860i	$0.279674\pi$
$594$	−2.86185	−0.117423
$595$	7.73475	0.317094
$596$	−11.9011	−0.487489
$597$	17.8708	0.731404
$598$	0.156120	0.00638423
$599$	−13.0196	−0.531965	−0.265983	−	0.963978i	$-0.585696\pi$
$599$	−13.0196	−0.531965	−0.265983	+	0.963978i	$0.585696\pi$
$600$	−2.40579	−0.0982158
$601$	−11.9314	−0.486691	−0.243345	−	0.969940i	$-0.578245\pi$
$601$	−11.9314	−0.486691	−0.243345	+	0.969940i	$0.578245\pi$
$602$	17.2540	0.703221
$603$	−37.2194	−1.51569
$604$	−4.48113	−0.182335
$605$	20.4289	0.830553
$606$	23.5523	0.956745
$607$	28.3130	1.14919	0.574595	−	0.818438i	$-0.305160\pi$
$607$	28.3130	1.14919	0.574595	+	0.818438i	$0.305160\pi$
$608$	−5.95884	−0.241663
$609$	−14.6910	−0.595311
$610$	13.8248	0.559748
$611$	−1.85294	−0.0749621
$612$	−12.3062	−0.497447
$613$	27.8312	1.12409	0.562046	−	0.827106i	$-0.310014\pi$
$613$	27.8312	1.12409	0.562046	+	0.827106i	$0.310014\pi$
$614$	−0.103139	−0.00416235
$615$	−8.41385	−0.339279
$616$	−9.82317	−0.395787
$617$	15.7270	0.633146	0.316573	−	0.948568i	$-0.397468\pi$
$617$	15.7270	0.633146	0.316573	+	0.948568i	$0.397468\pi$
$618$	32.1254	1.29227
$619$	−5.82742	−0.234224	−0.117112	−	0.993119i	$-0.537364\pi$
$619$	−5.82742	−0.234224	−0.117112	+	0.993119i	$0.537364\pi$
$620$	−8.31509	−0.333942
$621$	−0.271695	−0.0109028
$622$	−25.3389	−1.01600
$623$	23.1801	0.928692
$624$	−0.705695	−0.0282504
$625$	1.00000	0.0400000
$626$	−17.7254	−0.708450
$627$	−80.3680	−3.20959
$628$	2.69235	0.107436
$629$	30.1202	1.20097
$630$	4.88484	0.194617
$631$	1.93094	0.0768693	0.0384347	−	0.999261i	$-0.487763\pi$
$631$	1.93094	0.0768693	0.0384347	+	0.999261i	$0.487763\pi$
$632$	2.23194	0.0887817
$633$	17.4882	0.695094
$634$	−11.4292	−0.453911
$635$	−18.6217	−0.738979
$636$	26.6171	1.05544
$637$	1.15272	0.0456726
$638$	19.5377	0.773504
$639$	−3.72262	−0.147265
$640$	−1.00000	−0.0395285
$641$	−18.6773	−0.737710	−0.368855	−	0.929487i	$-0.620250\pi$
$641$	−18.6773	−0.737710	−0.368855	+	0.929487i	$0.620250\pi$
$642$	4.78804	0.188969
$643$	43.3949	1.71133	0.855665	−	0.517531i	$-0.173149\pi$
$643$	43.3949	1.71133	0.855665	+	0.517531i	$0.173149\pi$
$644$	−0.932580	−0.0367488
$645$	23.6897	0.932782
$646$	26.3039	1.03491
$647$	11.3229	0.445150	0.222575	−	0.974916i	$-0.428554\pi$
$647$	11.3229	0.445150	0.222575	+	0.974916i	$0.428554\pi$
$648$	9.59155	0.376792
$649$	−40.3226	−1.58280
$650$	0.293332	0.0115054
$651$	35.0519	1.37379
$652$	−23.1986	−0.908529
$653$	−30.3222	−1.18660	−0.593300	−	0.804982i	$-0.702175\pi$
$653$	−30.3222	−1.18660	−0.593300	+	0.804982i	$0.702175\pi$
$654$	5.63256	0.220250
$655$	−5.69531	−0.222534
$656$	−3.49734	−0.136548
$657$	−28.3800	−1.10721
$658$	11.0685	0.431495
$659$	10.2859	0.400681	0.200340	−	0.979726i	$-0.435795\pi$
$659$	10.2859	0.400681	0.200340	+	0.979726i	$0.435795\pi$
$660$	−13.4872	−0.524988
$661$	−14.2306	−0.553505	−0.276753	−	0.960941i	$-0.589258\pi$
$661$	−14.2306	−0.553505	−0.276753	+	0.960941i	$0.589258\pi$
$662$	2.57374	0.100031
$663$	3.11513	0.120982
$664$	4.18417	0.162377
$665$	−10.4411	−0.404890
$666$	19.0223	0.737098
$667$	1.85485	0.0718199
$668$	−10.5614	−0.408634
$669$	−48.4896	−1.87472
$670$	13.3508	0.515786
$671$	77.5037	2.99200
$672$	4.21545	0.162615
$673$	−22.9868	−0.886076	−0.443038	−	0.896503i	$-0.646099\pi$
$673$	−22.9868	−0.886076	−0.443038	+	0.896503i	$0.646099\pi$
$674$	−23.1351	−0.891130
$675$	−0.510485	−0.0196486
$676$	−12.9140	−0.496691
$677$	−13.3790	−0.514199	−0.257099	−	0.966385i	$-0.582767\pi$
$677$	−13.3790	−0.514199	−0.257099	+	0.966385i	$0.582767\pi$
$678$	−37.2197	−1.42941
$679$	17.6843	0.678662
$680$	4.41428	0.169280
$681$	60.5374	2.31980
$682$	−46.6156	−1.78501
$683$	20.1226	0.769970	0.384985	−	0.922923i	$-0.374207\pi$
$683$	20.1226	0.769970	0.384985	+	0.922923i	$0.374207\pi$
$684$	16.6121	0.635179
$685$	−10.5675	−0.403764
$686$	−19.1512	−0.731198
$687$	−18.7697	−0.716107
$688$	9.84698	0.375413
$689$	−3.24536	−0.123639
$690$	−1.28043	−0.0487452
$691$	−8.07108	−0.307038	−0.153519	−	0.988146i	$-0.549061\pi$
$691$	−8.07108	−0.307038	−0.153519	+	0.988146i	$0.549061\pi$
$692$	19.0268	0.723291
$693$	27.3851	1.04027
$694$	5.29245	0.200899
$695$	9.57211	0.363091
$696$	−8.38428	−0.317805
$697$	15.4382	0.584764
$698$	−31.2995	−1.18471
$699$	−19.7582	−0.747325
$700$	−1.75221	−0.0662274
$701$	−4.74431	−0.179190	−0.0895951	−	0.995978i	$-0.528557\pi$
$701$	−4.74431	−0.179190	−0.0895951	+	0.995978i	$0.528557\pi$
$702$	−0.149742	−0.00565163
$703$	−40.6593	−1.53350
$704$	−5.60615	−0.211290
$705$	15.1970	0.572354
$706$	−24.8184	−0.934052
$707$	17.1539	0.645138
$708$	17.3038	0.650315
$709$	−4.01101	−0.150636	−0.0753182	−	0.997160i	$-0.523997\pi$
$709$	−4.01101	−0.150636	−0.0753182	+	0.997160i	$0.523997\pi$
$710$	1.33532	0.0501137
$711$	−6.22221	−0.233351
$712$	13.2291	0.495780
$713$	−4.42554	−0.165738
$714$	−18.6082	−0.696393
$715$	1.64446	0.0614995
$716$	17.9349	0.670260
$717$	−41.7509	−1.55922
$718$	−6.33468	−0.236408
$719$	31.3475	1.16906	0.584532	−	0.811371i	$-0.301278\pi$
$719$	31.3475	1.16906	0.584532	+	0.811371i	$0.301278\pi$
$720$	2.78781	0.103896
$721$	23.3980	0.871386
$722$	−16.5077	−0.614354
$723$	−0.229268	−0.00852656
$724$	15.9037	0.591055
$725$	3.48505	0.129431
$726$	−49.1476	−1.82404
$727$	−7.19320	−0.266781	−0.133390	−	0.991064i	$-0.542586\pi$
$727$	−7.19320	−0.266781	−0.133390	+	0.991064i	$0.542586\pi$
$728$	−0.513981	−0.0190494
$729$	−23.0551	−0.853891
$730$	10.1801	0.376781
$731$	−43.4673	−1.60770
$732$	−33.2594	−1.22930
$733$	20.0145	0.739254	0.369627	−	0.929180i	$-0.379486\pi$
$733$	20.0145	0.739254	0.369627	+	0.929180i	$0.379486\pi$
$734$	31.1149	1.14847
$735$	−9.45414	−0.348721
$736$	−0.532230	−0.0196183
$737$	74.8465	2.75700
$738$	9.74991	0.358899
$739$	−11.0093	−0.404984	−0.202492	−	0.979284i	$-0.564904\pi$
$739$	−11.0093	−0.404984	−0.202492	+	0.979284i	$0.564904\pi$
$740$	−6.82337	−0.250832
$741$	−4.20512	−0.154479
$742$	19.3861	0.711686
$743$	−38.7143	−1.42029	−0.710144	−	0.704056i	$-0.751370\pi$
$743$	−38.7143	−1.42029	−0.710144	+	0.704056i	$0.751370\pi$
$744$	20.0043	0.733395
$745$	−11.9011	−0.436024
$746$	−20.0301	−0.733353
$747$	−11.6647	−0.426788
$748$	24.7471	0.904843
$749$	3.48729	0.127423
$750$	−2.40579	−0.0878469
$751$	20.5252	0.748974	0.374487	−	0.927232i	$-0.377819\pi$
$751$	20.5252	0.748974	0.374487	+	0.927232i	$0.377819\pi$
$752$	6.31687	0.230353
$753$	6.49817	0.236807
$754$	1.02228	0.0372291
$755$	−4.48113	−0.163085
$756$	0.894478	0.0325318
$757$	17.1690	0.624019	0.312009	−	0.950079i	$-0.398998\pi$
$757$	17.1690	0.624019	0.312009	+	0.950079i	$0.398998\pi$
$758$	32.5737	1.18313
$759$	−7.17829	−0.260555
$760$	−5.95884	−0.216150
$761$	21.7443	0.788231	0.394115	−	0.919061i	$-0.371051\pi$
$761$	21.7443	0.788231	0.394115	+	0.919061i	$0.371051\pi$
$762$	44.7998	1.62292
$763$	4.10238	0.148516
$764$	−17.0814	−0.617982
$765$	−12.3062	−0.444930
$766$	−10.7995	−0.390202
$767$	−2.10981	−0.0761809
$768$	2.40579	0.0868114
$769$	−24.0187	−0.866136	−0.433068	−	0.901361i	$-0.642569\pi$
$769$	−24.0187	−0.866136	−0.433068	+	0.901361i	$0.642569\pi$
$770$	−9.82317	−0.354002
$771$	−56.9549	−2.05118
$772$	23.0755	0.830505
$773$	−46.2409	−1.66317	−0.831585	−	0.555397i	$-0.812566\pi$
$773$	−46.2409	−1.66317	−0.831585	+	0.555397i	$0.812566\pi$
$774$	−27.4515	−0.986724
$775$	−8.31509	−0.298687
$776$	10.0926	0.362302
$777$	28.7636	1.03189
$778$	3.29764	0.118226
$779$	−20.8401	−0.746672
$780$	−0.705695	−0.0252679
$781$	7.48601	0.267870
$782$	2.34941	0.0840148
$783$	−1.77906	−0.0635785
$784$	−3.92975	−0.140348
$785$	2.69235	0.0960940
$786$	13.7017	0.488724
$787$	10.0082	0.356754	0.178377	−	0.983962i	$-0.442915\pi$
$787$	10.0082	0.356754	0.178377	+	0.983962i	$0.442915\pi$
$788$	19.5317	0.695789
$789$	10.3830	0.369644
$790$	2.23194	0.0794087
$791$	−27.1083	−0.963861
$792$	15.6289	0.555348
$793$	4.05525	0.144006
$794$	−30.4380	−1.08020
$795$	26.6171	0.944011
$796$	7.42826	0.263288
$797$	13.5133	0.478667	0.239333	−	0.970937i	$-0.423071\pi$
$797$	13.5133	0.478667	0.239333	+	0.970937i	$0.423071\pi$
$798$	25.1192	0.889209
$799$	−27.8844	−0.986480
$800$	−1.00000	−0.0353553
$801$	−36.8801	−1.30309
$802$	−1.00000	−0.0353112
$803$	57.0709	2.01399
$804$	−32.1191	−1.13275
$805$	−0.932580	−0.0328691
$806$	−2.43909	−0.0859131
$807$	34.3657	1.20973
$808$	9.78984	0.344405
$809$	−28.2194	−0.992141	−0.496071	−	0.868282i	$-0.665224\pi$
$809$	−28.2194	−0.992141	−0.496071	+	0.868282i	$0.665224\pi$
$810$	9.59155	0.337013
$811$	−36.6501	−1.28696	−0.643480	−	0.765463i	$-0.722510\pi$
$811$	−36.6501	−1.28696	−0.643480	+	0.765463i	$0.722510\pi$
$812$	−6.10654	−0.214298
$813$	10.0488	0.352427
$814$	−38.2528	−1.34076
$815$	−23.1986	−0.812613
$816$	−10.6198	−0.371768
$817$	58.6765	2.05283
$818$	2.25032	0.0786804
$819$	1.43288	0.0500689
$820$	−3.49734	−0.122132
$821$	49.5635	1.72978	0.864889	−	0.501963i	$-0.167389\pi$
$821$	49.5635	1.72978	0.864889	+	0.501963i	$0.167389\pi$
$822$	25.4232	0.886736
$823$	37.7484	1.31583	0.657913	−	0.753094i	$-0.271439\pi$
$823$	37.7484	1.31583	0.657913	+	0.753094i	$0.271439\pi$
$824$	13.3534	0.465187
$825$	−13.4872	−0.469564
$826$	12.6029	0.438511
$827$	31.1848	1.08440	0.542201	−	0.840249i	$-0.317591\pi$
$827$	31.1848	1.08440	0.542201	+	0.840249i	$0.317591\pi$
$828$	1.48376	0.0515641
$829$	37.5310	1.30350	0.651752	−	0.758432i	$-0.274034\pi$
$829$	37.5310	1.30350	0.651752	+	0.758432i	$0.274034\pi$
$830$	4.18417	0.145235
$831$	74.8885	2.59785
$832$	−0.293332	−0.0101695
$833$	17.3470	0.601038
$834$	−23.0284	−0.797410
$835$	−10.5614	−0.365493
$836$	−33.4061	−1.15537
$837$	4.24473	0.146719
$838$	20.2395	0.699161
$839$	−25.7680	−0.889611	−0.444806	−	0.895627i	$-0.646727\pi$
$839$	−25.7680	−0.889611	−0.444806	+	0.895627i	$0.646727\pi$
$840$	4.21545	0.145447
$841$	−16.8545	−0.581188
$842$	6.12535	0.211094
$843$	75.9169	2.61472
$844$	7.26922	0.250217
$845$	−12.9140	−0.444254
$846$	−17.6102	−0.605452
$847$	−35.7958	−1.22996
$848$	11.0638	0.379932
$849$	69.2043	2.37508
$850$	4.41428	0.151408
$851$	−3.63160	−0.124490
$852$	−3.21250	−0.110058
$853$	52.8961	1.81113	0.905564	−	0.424209i	$-0.139448\pi$
$853$	52.8961	1.81113	0.905564	+	0.424209i	$0.139448\pi$
$854$	−24.2239	−0.828926
$855$	16.6121	0.568122
$856$	1.99022	0.0680243
$857$	−8.61059	−0.294132	−0.147066	−	0.989127i	$-0.546983\pi$
$857$	−8.61059	−0.294132	−0.147066	+	0.989127i	$0.546983\pi$
$858$	−3.95623	−0.135064
$859$	−7.84399	−0.267633	−0.133817	−	0.991006i	$-0.542723\pi$
$859$	−7.84399	−0.267633	−0.133817	+	0.991006i	$0.542723\pi$
$860$	9.84698	0.335779
$861$	14.7428	0.502435
$862$	−16.8163	−0.572764
$863$	−21.3242	−0.725885	−0.362943	−	0.931811i	$-0.618228\pi$
$863$	−21.3242	−0.725885	−0.362943	+	0.931811i	$0.618228\pi$
$864$	0.510485	0.0173670
$865$	19.0268	0.646931
$866$	1.18090	0.0401285
$867$	5.98039	0.203105
$868$	14.5698	0.494532
$869$	12.5126	0.424460
$870$	−8.38428	−0.284254
$871$	3.91622	0.132696
$872$	2.34125	0.0792849
$873$	−28.1361	−0.952264
$874$	−3.17147	−0.107277
$875$	−1.75221	−0.0592356
$876$	−24.4910	−0.827475
$877$	−52.8173	−1.78351	−0.891757	−	0.452515i	$-0.850527\pi$
$877$	−52.8173	−1.78351	−0.891757	+	0.452515i	$0.850527\pi$
$878$	25.4663	0.859446
$879$	42.2314	1.42443
$880$	−5.60615	−0.188983
$881$	−36.3310	−1.22402	−0.612011	−	0.790849i	$-0.709639\pi$
$881$	−36.3310	−1.22402	−0.612011	+	0.790849i	$0.709639\pi$
$882$	10.9554	0.368887
$883$	−22.7038	−0.764044	−0.382022	−	0.924153i	$-0.624772\pi$
$883$	−22.7038	−0.764044	−0.382022	+	0.924153i	$0.624772\pi$
$884$	1.29485	0.0435505
$885$	17.3038	0.581660
$886$	16.4471	0.552552
$887$	−24.5134	−0.823081	−0.411540	−	0.911392i	$-0.635009\pi$
$887$	−24.5134	−0.823081	−0.411540	+	0.911392i	$0.635009\pi$
$888$	16.4156	0.550871
$889$	32.6291	1.09435
$890$	13.2291	0.443439
$891$	53.7716	1.80142
$892$	−20.1554	−0.674853
$893$	37.6412	1.25961
$894$	28.6316	0.957584
$895$	17.9349	0.599499
$896$	1.75221	0.0585373
$897$	−0.375592	−0.0125407
$898$	−9.13398	−0.304805
$899$	−28.9785	−0.966486
$900$	2.78781	0.0929270
$901$	−48.8386	−1.62705
$902$	−19.6066	−0.652828
$903$	−41.5094	−1.38135
$904$	−15.4709	−0.514555
$905$	15.9037	0.528656
$906$	10.7806	0.358163
$907$	45.0931	1.49729	0.748646	−	0.662971i	$-0.230705\pi$
$907$	45.0931	1.49729	0.748646	+	0.662971i	$0.230705\pi$
$908$	25.1632	0.835071
$909$	−27.2922	−0.905225
$910$	−0.513981	−0.0170383
$911$	−50.8279	−1.68400	−0.842002	−	0.539474i	$-0.818623\pi$
$911$	−50.8279	−1.68400	−0.842002	+	0.539474i	$0.818623\pi$
$912$	14.3357	0.474702
$913$	23.4571	0.776316
$914$	27.2144	0.900173
$915$	−33.2594	−1.09952
$916$	−7.80188	−0.257781
$917$	9.97940	0.329549
$918$	−2.25342	−0.0743739
$919$	−20.8817	−0.688823	−0.344412	−	0.938819i	$-0.611922\pi$
$919$	−20.8817	−0.688823	−0.344412	+	0.938819i	$0.611922\pi$
$920$	−0.532230	−0.0175471
$921$	0.248131	0.00817618
$922$	7.78685	0.256446
$923$	0.391693	0.0128927
$924$	23.6324	0.777450
$925$	−6.82337	−0.224351
$926$	−24.6432	−0.809826
$927$	−37.2267	−1.22269
$928$	−3.48505	−0.114402
$929$	−43.9574	−1.44220	−0.721098	−	0.692833i	$-0.756362\pi$
$929$	−43.9574	−1.44220	−0.721098	+	0.692833i	$0.756362\pi$
$930$	20.0043	0.655968
$931$	−23.4167	−0.767453
$932$	−8.21279	−0.269019
$933$	60.9600	1.99574
$934$	4.37222	0.143063
$935$	24.7471	0.809316
$936$	0.817755	0.0267292
$937$	−54.3703	−1.77620	−0.888099	−	0.459652i	$-0.847974\pi$
$937$	−54.3703	−1.77620	−0.888099	+	0.459652i	$0.847974\pi$
$938$	−23.3934	−0.763822
$939$	42.6435	1.39162
$940$	6.31687	0.206034
$941$	16.6596	0.543086	0.271543	−	0.962426i	$-0.412466\pi$
$941$	16.6596	0.543086	0.271543	+	0.962426i	$0.412466\pi$
$942$	−6.47722	−0.211039
$943$	−1.86139	−0.0606151
$944$	7.19256	0.234098
$945$	0.894478	0.0290974
$946$	55.2036	1.79482
$947$	38.2608	1.24331	0.621654	−	0.783292i	$-0.286461\pi$
$947$	38.2608	1.24331	0.621654	+	0.783292i	$0.286461\pi$
$948$	−5.36956	−0.174395
$949$	2.98614	0.0969342
$950$	−5.95884	−0.193330
$951$	27.4962	0.891625
$952$	−7.73475	−0.250685
$953$	29.5278	0.956498	0.478249	−	0.878224i	$-0.341272\pi$
$953$	29.5278	0.956498	0.478249	+	0.878224i	$0.341272\pi$
$954$	−30.8437	−0.998602
$955$	−17.0814	−0.552740
$956$	−17.3544	−0.561280
$957$	−47.0035	−1.51941
$958$	−12.8369	−0.414740
$959$	18.5165	0.597930
$960$	2.40579	0.0776464
$961$	38.1407	1.23035
$962$	−2.00152	−0.0645315
$963$	−5.54835	−0.178793
$964$	−0.0952985	−0.00306936
$965$	23.0755	0.742826
$966$	2.24359	0.0721863
$967$	22.1456	0.712155	0.356078	−	0.934456i	$-0.384114\pi$
$967$	22.1456	0.712155	0.356078	+	0.934456i	$0.384114\pi$
$968$	−20.4289	−0.656610
$969$	−63.2817	−2.03290
$970$	10.0926	0.324053
$971$	−14.7008	−0.471770	−0.235885	−	0.971781i	$-0.575799\pi$
$971$	−14.7008	−0.471770	−0.235885	+	0.971781i	$0.575799\pi$
$972$	−21.5438	−0.691016
$973$	−16.7724	−0.537697
$974$	17.4018	0.557591
$975$	−0.705695	−0.0226003
$976$	−13.8248	−0.442520
$977$	−8.97781	−0.287225	−0.143613	−	0.989634i	$-0.545872\pi$
$977$	−8.97781	−0.287225	−0.143613	+	0.989634i	$0.545872\pi$
$978$	55.8110	1.78464
$979$	74.1641	2.37029
$980$	−3.92975	−0.125531
$981$	−6.52697	−0.208390
$982$	38.1358	1.21696
$983$	−17.1411	−0.546715	−0.273358	−	0.961913i	$-0.588134\pi$
$983$	−17.1411	−0.546715	−0.273358	+	0.961913i	$0.588134\pi$
$984$	8.41385	0.268224
$985$	19.5317	0.622332
$986$	15.3840	0.489925
$987$	−26.6285	−0.847593
$988$	−1.74792	−0.0556087
$989$	5.24086	0.166650
$990$	15.6289	0.496718
$991$	34.1073	1.08345	0.541727	−	0.840554i	$-0.317771\pi$
$991$	34.1073	1.08345	0.541727	+	0.840554i	$0.317771\pi$
$992$	8.31509	0.264004
$993$	−6.19186	−0.196493
$994$	−2.33977	−0.0742129
$995$	7.42826	0.235492
$996$	−10.0662	−0.318961
$997$	−36.2444	−1.14787	−0.573936	−	0.818900i	$-0.694584\pi$
$997$	−36.2444	−1.14787	−0.573936	+	0.818900i	$0.694584\pi$
$998$	33.3663	1.05619
$999$	3.48323	0.110204

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	4010.2.a.i.1.10	✓	10

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
4010.2.a.i.1.10	✓	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)

\(f(q)\)	\(=\)	\(q-1.00000 q^{2} +2.40579 q^{3} +1.00000 q^{4} +1.00000 q^{5} -2.40579 q^{6} -1.75221 q^{7} -1.00000 q^{8} +2.78781 q^{9} +O(q^{10})\)	\(q-1.00000 q^{2} +2.40579 q^{3} +1.00000 q^{4} +1.00000 q^{5} -2.40579 q^{6} -1.75221 q^{7} -1.00000 q^{8} +2.78781 q^{9} -1.00000 q^{10} -5.60615 q^{11} +2.40579 q^{12} -0.293332 q^{13} +1.75221 q^{14} +2.40579 q^{15} +1.00000 q^{16} -4.41428 q^{17} -2.78781 q^{18} +5.95884 q^{19} +1.00000 q^{20} -4.21545 q^{21} +5.60615 q^{22} +0.532230 q^{23} -2.40579 q^{24} +1.00000 q^{25} +0.293332 q^{26} -0.510485 q^{27} -1.75221 q^{28} +3.48505 q^{29} -2.40579 q^{30} -8.31509 q^{31} -1.00000 q^{32} -13.4872 q^{33} +4.41428 q^{34} -1.75221 q^{35} +2.78781 q^{36} -6.82337 q^{37} -5.95884 q^{38} -0.705695 q^{39} -1.00000 q^{40} -3.49734 q^{41} +4.21545 q^{42} +9.84698 q^{43} -5.60615 q^{44} +2.78781 q^{45} -0.532230 q^{46} +6.31687 q^{47} +2.40579 q^{48} -3.92975 q^{49} -1.00000 q^{50} -10.6198 q^{51} -0.293332 q^{52} +11.0638 q^{53} +0.510485 q^{54} -5.60615 q^{55} +1.75221 q^{56} +14.3357 q^{57} -3.48505 q^{58} +7.19256 q^{59} +2.40579 q^{60} -13.8248 q^{61} +8.31509 q^{62} -4.88484 q^{63} +1.00000 q^{64} -0.293332 q^{65} +13.4872 q^{66} -13.3508 q^{67} -4.41428 q^{68} +1.28043 q^{69} +1.75221 q^{70} -1.33532 q^{71} -2.78781 q^{72} -10.1801 q^{73} +6.82337 q^{74} +2.40579 q^{75} +5.95884 q^{76} +9.82317 q^{77} +0.705695 q^{78} -2.23194 q^{79} +1.00000 q^{80} -9.59155 q^{81} +3.49734 q^{82} -4.18417 q^{83} -4.21545 q^{84} -4.41428 q^{85} -9.84698 q^{86} +8.38428 q^{87} +5.60615 q^{88} -13.2291 q^{89} -2.78781 q^{90} +0.513981 q^{91} +0.532230 q^{92} -20.0043 q^{93} -6.31687 q^{94} +5.95884 q^{95} -2.40579 q^{96} -10.0926 q^{97} +3.92975 q^{98} -15.6289 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 10 q - 10 q^{2} - 4 q^{3} + 10 q^{4} + 10 q^{5} + 4 q^{6} - 3 q^{7} - 10 q^{8} + 6 q^{9}+O(q^{10}) \) 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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