LMFDB - Embedded newform 4010.2.a.l.1.1

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:	$17$
Coefficient field:	$\mathbb{Q}[x]/(x^{17} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{17} - 3 x^{16} - 24 x^{15} + 70 x^{14} + 228 x^{13} - 638 x^{12} - 1075 x^{11} + 2854 x^{10} + \cdots - 2 $ x^17 - 3x^16 - 24x^15 + 70x^14 + 228x^13 - 638x^12 - 1075x^11 + 2854x^10 + 2544x^9 - 6415x^8 - 2573x^7 + 6456x^6 + 485x^5 - 1839x^4 + 67x^3 + 136x^2 - 8x - 2
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.1
Root			$-2.56168$ 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)

$f(q)$	$=$	$q-1.00000 q^{2} -2.56168 q^{3} +1.00000 q^{4} -1.00000 q^{5} +2.56168 q^{6} +0.101571 q^{7} -1.00000 q^{8} +3.56218 q^{9} +O(q^{10})$	\(q-1.00000 q^{2} -2.56168 q^{3} +1.00000 q^{4} -1.00000 q^{5} +2.56168 q^{6} +0.101571 q^{7} -1.00000 q^{8} +3.56218 q^{9} +1.00000 q^{10} -2.35567 q^{11} -2.56168 q^{12} +0.933399 q^{13} -0.101571 q^{14} +2.56168 q^{15} +1.00000 q^{16} +6.89027 q^{17} -3.56218 q^{18} +5.91382 q^{19} -1.00000 q^{20} -0.260191 q^{21} +2.35567 q^{22} -0.299804 q^{23} +2.56168 q^{24} +1.00000 q^{25} -0.933399 q^{26} -1.44013 q^{27} +0.101571 q^{28} -5.80564 q^{29} -2.56168 q^{30} +0.226557 q^{31} -1.00000 q^{32} +6.03447 q^{33} -6.89027 q^{34} -0.101571 q^{35} +3.56218 q^{36} -0.370002 q^{37} -5.91382 q^{38} -2.39107 q^{39} +1.00000 q^{40} -10.2787 q^{41} +0.260191 q^{42} +9.53194 q^{43} -2.35567 q^{44} -3.56218 q^{45} +0.299804 q^{46} -0.370569 q^{47} -2.56168 q^{48} -6.98968 q^{49} -1.00000 q^{50} -17.6507 q^{51} +0.933399 q^{52} +10.9008 q^{53} +1.44013 q^{54} +2.35567 q^{55} -0.101571 q^{56} -15.1493 q^{57} +5.80564 q^{58} -3.49221 q^{59} +2.56168 q^{60} -2.72375 q^{61} -0.226557 q^{62} +0.361813 q^{63} +1.00000 q^{64} -0.933399 q^{65} -6.03447 q^{66} +0.815547 q^{67} +6.89027 q^{68} +0.768000 q^{69} +0.101571 q^{70} +3.03374 q^{71} -3.56218 q^{72} -4.76547 q^{73} +0.370002 q^{74} -2.56168 q^{75} +5.91382 q^{76} -0.239267 q^{77} +2.39107 q^{78} +4.89926 q^{79} -1.00000 q^{80} -6.99740 q^{81} +10.2787 q^{82} +9.57485 q^{83} -0.260191 q^{84} -6.89027 q^{85} -9.53194 q^{86} +14.8722 q^{87} +2.35567 q^{88} -3.20708 q^{89} +3.56218 q^{90} +0.0948058 q^{91} -0.299804 q^{92} -0.580366 q^{93} +0.370569 q^{94} -5.91382 q^{95} +2.56168 q^{96} -1.88379 q^{97} +6.98968 q^{98} -8.39134 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 17 q - 17 q^{2} + 3 q^{3} + 17 q^{4} - 17 q^{5} - 3 q^{6} + 4 q^{7} - 17 q^{8} + 6 q^{9}+O(q^{10}) $ 17 * q - 17 * q^2 + 3 * q^3 + 17 * q^4 - 17 * q^5 - 3 * q^6 + 4 * q^7 - 17 * q^8 + 6 * q^9	\( 17 q - 17 q^{2} + 3 q^{3} + 17 q^{4} - 17 q^{5} - 3 q^{6} + 4 q^{7} - 17 q^{8} + 6 q^{9} + 17 q^{10} - 8 q^{11} + 3 q^{12} + 14 q^{13} - 4 q^{14} - 3 q^{15} + 17 q^{16} - 8 q^{17} - 6 q^{18} + 7 q^{19} - 17 q^{20} - 11 q^{21} + 8 q^{22} + q^{23} - 3 q^{24} + 17 q^{25} - 14 q^{26} + 15 q^{27} + 4 q^{28} - 18 q^{29} + 3 q^{30} + 8 q^{31} - 17 q^{32} + 3 q^{33} + 8 q^{34} - 4 q^{35} + 6 q^{36} + 49 q^{37} - 7 q^{38} - 12 q^{39} + 17 q^{40} - 23 q^{41} + 11 q^{42} + 35 q^{43} - 8 q^{44} - 6 q^{45} - q^{46} + 11 q^{47} + 3 q^{48} + 27 q^{49} - 17 q^{50} - 16 q^{51} + 14 q^{52} - 3 q^{53} - 15 q^{54} + 8 q^{55} - 4 q^{56} + 9 q^{57} + 18 q^{58} - 6 q^{59} - 3 q^{60} + 6 q^{61} - 8 q^{62} + 10 q^{63} + 17 q^{64} - 14 q^{65} - 3 q^{66} + 55 q^{67} - 8 q^{68} - q^{69} + 4 q^{70} + 5 q^{71} - 6 q^{72} + 62 q^{73} - 49 q^{74} + 3 q^{75} + 7 q^{76} + 2 q^{77} + 12 q^{78} - 3 q^{79} - 17 q^{80} - 15 q^{81} + 23 q^{82} + 7 q^{83} - 11 q^{84} + 8 q^{85} - 35 q^{86} + 10 q^{87} + 8 q^{88} - 18 q^{89} + 6 q^{90} + 18 q^{91} + q^{92} + 33 q^{93} - 11 q^{94} - 7 q^{95} - 3 q^{96} + 63 q^{97} - 27 q^{98} - 11 q^{99}+O(q^{100}) \) 17 * q - 17 * q^2 + 3 * q^3 + 17 * q^4 - 17 * q^5 - 3 * q^6 + 4 * q^7 - 17 * q^8 + 6 * q^9 + 17 * q^10 - 8 * q^11 + 3 * q^12 + 14 * q^13 - 4 * q^14 - 3 * q^15 + 17 * q^16 - 8 * q^17 - 6 * q^18 + 7 * q^19 - 17 * q^20 - 11 * q^21 + 8 * q^22 + q^23 - 3 * q^24 + 17 * q^25 - 14 * q^26 + 15 * q^27 + 4 * q^28 - 18 * q^29 + 3 * q^30 + 8 * q^31 - 17 * q^32 + 3 * q^33 + 8 * q^34 - 4 * q^35 + 6 * q^36 + 49 * q^37 - 7 * q^38 - 12 * q^39 + 17 * q^40 - 23 * q^41 + 11 * q^42 + 35 * q^43 - 8 * q^44 - 6 * q^45 - q^46 + 11 * q^47 + 3 * q^48 + 27 * q^49 - 17 * q^50 - 16 * q^51 + 14 * q^52 - 3 * q^53 - 15 * q^54 + 8 * q^55 - 4 * q^56 + 9 * q^57 + 18 * q^58 - 6 * q^59 - 3 * q^60 + 6 * q^61 - 8 * q^62 + 10 * q^63 + 17 * q^64 - 14 * q^65 - 3 * q^66 + 55 * q^67 - 8 * q^68 - q^69 + 4 * q^70 + 5 * q^71 - 6 * q^72 + 62 * q^73 - 49 * q^74 + 3 * q^75 + 7 * q^76 + 2 * q^77 + 12 * q^78 - 3 * q^79 - 17 * q^80 - 15 * q^81 + 23 * q^82 + 7 * q^83 - 11 * q^84 + 8 * q^85 - 35 * q^86 + 10 * q^87 + 8 * q^88 - 18 * q^89 + 6 * q^90 + 18 * q^91 + q^92 + 33 * q^93 - 11 * q^94 - 7 * q^95 - 3 * q^96 + 63 * q^97 - 27 * q^98 - 11 * 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
$3$	−2.56168	−1.47898	−0.739492	−	0.673165i	$-0.764934\pi$
$3$	−2.56168	−1.47898	−0.739492	+	0.673165i	$0.764934\pi$
$4$	1.00000	0.500000
$5$	−1.00000	−0.447214
$5$	−1.00000	−0.447214
$6$	2.56168	1.04580
$7$	0.101571	0.0383900	0.0191950	−	0.999816i	$-0.493890\pi$
$7$	0.101571	0.0383900	0.0191950	+	0.999816i	$0.493890\pi$
$8$	−1.00000	−0.353553
$9$	3.56218	1.18739
$10$	1.00000	0.316228
$11$	−2.35567	−0.710262	−0.355131	−	0.934817i	$-0.615564\pi$
$11$	−2.35567	−0.710262	−0.355131	+	0.934817i	$0.615564\pi$
$12$	−2.56168	−0.739492
$13$	0.933399	0.258878	0.129439	−	0.991587i	$-0.458682\pi$
$13$	0.933399	0.258878	0.129439	+	0.991587i	$0.458682\pi$
$14$	−0.101571	−0.0271459
$15$	2.56168	0.661422
$16$	1.00000	0.250000
$17$	6.89027	1.67114	0.835569	−	0.549386i	$-0.185138\pi$
$17$	6.89027	1.67114	0.835569	+	0.549386i	$0.185138\pi$
$18$	−3.56218	−0.839615
$19$	5.91382	1.35672	0.678362	−	0.734728i	$-0.262690\pi$
$19$	5.91382	1.35672	0.678362	+	0.734728i	$0.262690\pi$
$20$	−1.00000	−0.223607
$21$	−0.260191	−0.0567783
$22$	2.35567	0.502231
$23$	−0.299804	−0.0625134	−0.0312567	−	0.999511i	$-0.509951\pi$
$23$	−0.299804	−0.0625134	−0.0312567	+	0.999511i	$0.509951\pi$
$24$	2.56168	0.522900
$25$	1.00000	0.200000
$26$	−0.933399	−0.183055
$27$	−1.44013	−0.277154
$28$	0.101571	0.0191950
$29$	−5.80564	−1.07808	−0.539040	−	0.842280i	$-0.681213\pi$
$29$	−5.80564	−1.07808	−0.539040	+	0.842280i	$0.681213\pi$
$30$	−2.56168	−0.467696
$31$	0.226557	0.0406908	0.0203454	−	0.999793i	$-0.493523\pi$
$31$	0.226557	0.0406908	0.0203454	+	0.999793i	$0.493523\pi$
$32$	−1.00000	−0.176777
$33$	6.03447	1.05047
$34$	−6.89027	−1.18167
$35$	−0.101571	−0.0171685
$36$	3.56218	0.593697
$37$	−0.370002	−0.0608280	−0.0304140	−	0.999537i	$-0.509683\pi$
$37$	−0.370002	−0.0608280	−0.0304140	+	0.999537i	$0.509683\pi$
$38$	−5.91382	−0.959349
$39$	−2.39107	−0.382877
$40$	1.00000	0.158114
$41$	−10.2787	−1.60526	−0.802632	−	0.596474i	$-0.796568\pi$
$41$	−10.2787	−1.60526	−0.802632	+	0.596474i	$0.796568\pi$
$42$	0.260191	0.0401483
$43$	9.53194	1.45361	0.726804	−	0.686845i	$-0.241005\pi$
$43$	9.53194	1.45361	0.726804	+	0.686845i	$0.241005\pi$
$44$	−2.35567	−0.355131
$45$	−3.56218	−0.531019
$46$	0.299804	0.0442037
$47$	−0.370569	−0.0540530	−0.0270265	−	0.999635i	$-0.508604\pi$
$47$	−0.370569	−0.0540530	−0.0270265	+	0.999635i	$0.508604\pi$
$48$	−2.56168	−0.369746
$49$	−6.98968	−0.998526
$50$	−1.00000	−0.141421
$51$	−17.6507	−2.47159
$52$	0.933399	0.129439
$53$	10.9008	1.49735	0.748673	−	0.662940i	$-0.230691\pi$
$53$	10.9008	1.49735	0.748673	+	0.662940i	$0.230691\pi$
$54$	1.44013	0.195977
$55$	2.35567	0.317639
$56$	−0.101571	−0.0135729
$57$	−15.1493	−2.00657
$58$	5.80564	0.762317
$59$	−3.49221	−0.454647	−0.227323	−	0.973819i	$-0.572997\pi$
$59$	−3.49221	−0.454647	−0.227323	+	0.973819i	$0.572997\pi$
$60$	2.56168	0.330711
$61$	−2.72375	−0.348740	−0.174370	−	0.984680i	$-0.555789\pi$
$61$	−2.72375	−0.348740	−0.174370	+	0.984680i	$0.555789\pi$
$62$	−0.226557	−0.0287728
$63$	0.361813	0.0455841
$64$	1.00000	0.125000
$65$	−0.933399	−0.115774
$66$	−6.03447	−0.742792
$67$	0.815547	0.0996349	0.0498175	−	0.998758i	$-0.484136\pi$
$67$	0.815547	0.0996349	0.0498175	+	0.998758i	$0.484136\pi$
$68$	6.89027	0.835569
$69$	0.768000	0.0924564
$70$	0.101571	0.0121400
$71$	3.03374	0.360038	0.180019	−	0.983663i	$-0.442384\pi$
$71$	3.03374	0.360038	0.180019	+	0.983663i	$0.442384\pi$
$72$	−3.56218	−0.419807
$73$	−4.76547	−0.557756	−0.278878	−	0.960327i	$-0.589962\pi$
$73$	−4.76547	−0.557756	−0.278878	+	0.960327i	$0.589962\pi$
$74$	0.370002	0.0430119
$75$	−2.56168	−0.295797
$76$	5.91382	0.678362
$77$	−0.239267	−0.0272670
$78$	2.39107	0.270735
$79$	4.89926	0.551210	0.275605	−	0.961271i	$-0.411122\pi$
$79$	4.89926	0.551210	0.275605	+	0.961271i	$0.411122\pi$
$80$	−1.00000	−0.111803
$81$	−6.99740	−0.777489
$82$	10.2787	1.13509
$83$	9.57485	1.05098	0.525488	−	0.850801i	$-0.323883\pi$
$83$	9.57485	1.05098	0.525488	+	0.850801i	$0.323883\pi$
$84$	−0.260191	−0.0283891
$85$	−6.89027	−0.747355
$86$	−9.53194	−1.02786
$87$	14.8722	1.59446
$88$	2.35567	0.251116
$89$	−3.20708	−0.339950	−0.169975	−	0.985448i	$-0.554369\pi$
$89$	−3.20708	−0.339950	−0.169975	+	0.985448i	$0.554369\pi$
$90$	3.56218	0.375487
$91$	0.0948058	0.00993835
$92$	−0.299804	−0.0312567
$93$	−0.580366	−0.0601811
$94$	0.370569	0.0382213
$95$	−5.91382	−0.606745
$96$	2.56168	0.261450
$97$	−1.88379	−0.191270	−0.0956350	−	0.995416i	$-0.530488\pi$
$97$	−1.88379	−0.191270	−0.0956350	+	0.995416i	$0.530488\pi$
$98$	6.98968	0.706065
$99$	−8.39134	−0.843361
$100$	1.00000	0.100000
$101$	−7.62439	−0.758655	−0.379328	−	0.925262i	$-0.623845\pi$
$101$	−7.62439	−0.758655	−0.379328	+	0.925262i	$0.623845\pi$
$102$	17.6507	1.74767
$103$	11.6391	1.14684	0.573418	−	0.819263i	$-0.305617\pi$
$103$	11.6391	1.14684	0.573418	+	0.819263i	$0.305617\pi$
$104$	−0.933399	−0.0915273
$105$	0.260191	0.0253920
$106$	−10.9008	−1.05878
$107$	−17.9115	−1.73157	−0.865785	−	0.500416i	$-0.833180\pi$
$107$	−17.9115	−1.73157	−0.865785	+	0.500416i	$0.833180\pi$
$108$	−1.44013	−0.138577
$109$	4.64180	0.444604	0.222302	−	0.974978i	$-0.428643\pi$
$109$	4.64180	0.444604	0.222302	+	0.974978i	$0.428643\pi$
$110$	−2.35567	−0.224605
$111$	0.947826	0.0899637
$112$	0.101571	0.00959751
$113$	−14.2711	−1.34251	−0.671256	−	0.741225i	$-0.734245\pi$
$113$	−14.2711	−1.34251	−0.671256	+	0.741225i	$0.734245\pi$
$114$	15.1493	1.41886
$115$	0.299804	0.0279569
$116$	−5.80564	−0.539040
$117$	3.32494	0.307391
$118$	3.49221	0.321484
$119$	0.699849	0.0641550
$120$	−2.56168	−0.233848
$121$	−5.45081	−0.495528
$122$	2.72375	0.246597
$123$	26.3307	2.37416
$124$	0.226557	0.0203454
$125$	−1.00000	−0.0894427
$126$	−0.361813	−0.0322328
$127$	4.00424	0.355319	0.177659	−	0.984092i	$-0.443147\pi$
$127$	4.00424	0.355319	0.177659	+	0.984092i	$0.443147\pi$
$128$	−1.00000	−0.0883883
$129$	−24.4178	−2.14986
$130$	0.933399	0.0818645
$131$	3.68456	0.321921	0.160961	−	0.986961i	$-0.448541\pi$
$131$	3.68456	0.321921	0.160961	+	0.986961i	$0.448541\pi$
$132$	6.03447	0.525233
$133$	0.600670	0.0520847
$134$	−0.815547	−0.0704525
$135$	1.44013	0.123947
$136$	−6.89027	−0.590836
$137$	−2.56701	−0.219314	−0.109657	−	0.993969i	$-0.534975\pi$
$137$	−2.56701	−0.219314	−0.109657	+	0.993969i	$0.534975\pi$
$138$	−0.768000	−0.0653765
$139$	3.49022	0.296037	0.148018	−	0.988985i	$-0.452710\pi$
$139$	3.49022	0.296037	0.148018	+	0.988985i	$0.452710\pi$
$140$	−0.101571	−0.00858427
$141$	0.949277	0.0799436
$142$	−3.03374	−0.254586
$143$	−2.19878	−0.183871
$144$	3.56218	0.296849
$145$	5.80564	0.482132
$146$	4.76547	0.394393
$147$	17.9053	1.47680
$148$	−0.370002	−0.0304140
$149$	15.9946	1.31033	0.655163	−	0.755487i	$-0.272600\pi$
$149$	15.9946	1.31033	0.655163	+	0.755487i	$0.272600\pi$
$150$	2.56168	0.209160
$151$	−9.19779	−0.748506	−0.374253	−	0.927327i	$-0.622101\pi$
$151$	−9.19779	−0.748506	−0.374253	+	0.927327i	$0.622101\pi$
$152$	−5.91382	−0.479674
$153$	24.5444	1.98430
$154$	0.239267	0.0192807
$155$	−0.226557	−0.0181975
$156$	−2.39107	−0.191438
$157$	3.09596	0.247085	0.123542	−	0.992339i	$-0.460575\pi$
$157$	3.09596	0.247085	0.123542	+	0.992339i	$0.460575\pi$
$158$	−4.89926	−0.389765
$159$	−27.9244	−2.21455
$160$	1.00000	0.0790569
$161$	−0.0304512	−0.00239989
$162$	6.99740	0.549767
$163$	−7.18846	−0.563044	−0.281522	−	0.959555i	$-0.590839\pi$
$163$	−7.18846	−0.563044	−0.281522	+	0.959555i	$0.590839\pi$
$164$	−10.2787	−0.802632
$165$	−6.03447	−0.469783
$166$	−9.57485	−0.743152
$167$	2.56708	0.198647	0.0993234	−	0.995055i	$-0.468332\pi$
$167$	2.56708	0.198647	0.0993234	+	0.995055i	$0.468332\pi$
$168$	0.260191	0.0200742
$169$	−12.1288	−0.932982
$170$	6.89027	0.528460
$171$	21.0661	1.61097
$172$	9.53194	0.726804
$173$	−10.6975	−0.813317	−0.406658	−	0.913580i	$-0.633306\pi$
$173$	−10.6975	−0.813317	−0.406658	+	0.913580i	$0.633306\pi$
$174$	−14.8722	−1.12746
$175$	0.101571	0.00767801
$176$	−2.35567	−0.177566
$177$	8.94591	0.672416
$178$	3.20708	0.240381
$179$	16.3976	1.22561	0.612807	−	0.790233i	$-0.290040\pi$
$179$	16.3976	1.22561	0.612807	+	0.790233i	$0.290040\pi$
$180$	−3.56218	−0.265510
$181$	13.3931	0.995504	0.497752	−	0.867320i	$-0.334159\pi$
$181$	13.3931	0.995504	0.497752	+	0.867320i	$0.334159\pi$
$182$	−0.0948058	−0.00702747
$183$	6.97736	0.515782
$184$	0.299804	0.0221018
$185$	0.370002	0.0272031
$186$	0.580366	0.0425545
$187$	−16.2312	−1.18695
$188$	−0.370569	−0.0270265
$189$	−0.146275	−0.0106399
$190$	5.91382	0.429034
$191$	−12.7794	−0.924684	−0.462342	−	0.886702i	$-0.652991\pi$
$191$	−12.7794	−0.924684	−0.462342	+	0.886702i	$0.652991\pi$
$192$	−2.56168	−0.184873
$193$	−5.40703	−0.389206	−0.194603	−	0.980882i	$-0.562342\pi$
$193$	−5.40703	−0.389206	−0.194603	+	0.980882i	$0.562342\pi$
$194$	1.88379	0.135248
$195$	2.39107	0.171228
$196$	−6.98968	−0.499263
$197$	−0.0341803	−0.00243525	−0.00121762	−	0.999999i	$-0.500388\pi$
$197$	−0.0341803	−0.00243525	−0.00121762	+	0.999999i	$0.500388\pi$
$198$	8.39134	0.596347
$199$	−3.51663	−0.249287	−0.124644	−	0.992202i	$-0.539779\pi$
$199$	−3.51663	−0.249287	−0.124644	+	0.992202i	$0.539779\pi$
$200$	−1.00000	−0.0707107
$201$	−2.08917	−0.147358
$202$	7.62439	0.536450
$203$	−0.589681	−0.0413875
$204$	−17.6507	−1.23579
$205$	10.2787	0.717896
$206$	−11.6391	−0.810935
$207$	−1.06796	−0.0742281
$208$	0.933399	0.0647196
$209$	−13.9310	−0.963630
$210$	−0.260191	−0.0179549
$211$	25.4249	1.75032	0.875161	−	0.483832i	$-0.160756\pi$
$211$	25.4249	1.75032	0.875161	+	0.483832i	$0.160756\pi$
$212$	10.9008	0.748673
$213$	−7.77145	−0.532491
$214$	17.9115	1.22440
$215$	−9.53194	−0.650073
$216$	1.44013	0.0979886
$217$	0.0230115	0.00156212
$218$	−4.64180	−0.314382
$219$	12.2076	0.824912
$220$	2.35567	0.158819
$221$	6.43137	0.432621
$222$	−0.947826	−0.0636139
$223$	4.79249	0.320929	0.160464	−	0.987042i	$-0.448701\pi$
$223$	4.79249	0.320929	0.160464	+	0.987042i	$0.448701\pi$
$224$	−0.101571	−0.00678647
$225$	3.56218	0.237479
$226$	14.2711	0.949300
$227$	12.5386	0.832217	0.416109	−	0.909315i	$-0.363394\pi$
$227$	12.5386	0.832217	0.416109	+	0.909315i	$0.363394\pi$
$228$	−15.1493	−1.00329
$229$	5.03580	0.332775	0.166388	−	0.986060i	$-0.446790\pi$
$229$	5.03580	0.332775	0.166388	+	0.986060i	$0.446790\pi$
$230$	−0.299804	−0.0197685
$231$	0.612924	0.0403275
$232$	5.80564	0.381159
$233$	−4.34105	−0.284391	−0.142196	−	0.989839i	$-0.545416\pi$
$233$	−4.34105	−0.284391	−0.142196	+	0.989839i	$0.545416\pi$
$234$	−3.32494	−0.217358
$235$	0.370569	0.0241732
$236$	−3.49221	−0.227323
$237$	−12.5503	−0.815231
$238$	−0.699849	−0.0453645
$239$	−18.5322	−1.19875	−0.599375	−	0.800469i	$-0.704584\pi$
$239$	−18.5322	−1.19875	−0.599375	+	0.800469i	$0.704584\pi$
$240$	2.56168	0.165355
$241$	20.1212	1.29612	0.648059	−	0.761590i	$-0.275581\pi$
$241$	20.1212	1.29612	0.648059	+	0.761590i	$0.275581\pi$
$242$	5.45081	0.350391
$243$	22.2455	1.42705
$244$	−2.72375	−0.174370
$245$	6.98968	0.446554
$246$	−26.3307	−1.67879
$247$	5.51995	0.351226
$248$	−0.226557	−0.0143864
$249$	−24.5277	−1.55438
$250$	1.00000	0.0632456
$251$	16.2819	1.02771	0.513853	−	0.857878i	$-0.328218\pi$
$251$	16.2819	1.02771	0.513853	+	0.857878i	$0.328218\pi$
$252$	0.361813	0.0227921
$253$	0.706240	0.0444009
$254$	−4.00424	−0.251248
$255$	17.6507	1.10533
$256$	1.00000	0.0625000
$257$	12.9399	0.807169	0.403585	−	0.914942i	$-0.367764\pi$
$257$	12.9399	0.807169	0.403585	+	0.914942i	$0.367764\pi$
$258$	24.4178	1.52018
$259$	−0.0375813	−0.00233519
$260$	−0.933399	−0.0578869
$261$	−20.6807	−1.28011
$262$	−3.68456	−0.227633
$263$	15.4674	0.953760	0.476880	−	0.878968i	$-0.341768\pi$
$263$	15.4674	0.953760	0.476880	+	0.878968i	$0.341768\pi$
$264$	−6.03447	−0.371396
$265$	−10.9008	−0.669633
$266$	−0.600670	−0.0368294
$267$	8.21551	0.502781
$268$	0.815547	0.0498175
$269$	22.3699	1.36392	0.681960	−	0.731390i	$-0.261128\pi$
$269$	22.3699	1.36392	0.681960	+	0.731390i	$0.261128\pi$
$270$	−1.44013	−0.0876437
$271$	31.1521	1.89235	0.946176	−	0.323652i	$-0.104911\pi$
$271$	31.1521	1.89235	0.946176	+	0.323652i	$0.104911\pi$
$272$	6.89027	0.417784
$273$	−0.242862	−0.0146987
$274$	2.56701	0.155079
$275$	−2.35567	−0.142052
$276$	0.768000	0.0462282
$277$	−16.1441	−0.970008	−0.485004	−	0.874512i	$-0.661182\pi$
$277$	−16.1441	−0.970008	−0.485004	+	0.874512i	$0.661182\pi$
$278$	−3.49022	−0.209330
$279$	0.807038	0.0483161
$280$	0.101571	0.00607000
$281$	23.0568	1.37545	0.687726	−	0.725971i	$-0.258609\pi$
$281$	23.0568	1.37545	0.687726	+	0.725971i	$0.258609\pi$
$282$	−0.949277	−0.0565286
$283$	9.00828	0.535487	0.267743	−	0.963490i	$-0.413722\pi$
$283$	9.00828	0.535487	0.267743	+	0.963490i	$0.413722\pi$
$284$	3.03374	0.180019
$285$	15.1493	0.897367
$286$	2.19878	0.130017
$287$	−1.04401	−0.0616262
$288$	−3.56218	−0.209904
$289$	30.4759	1.79270
$290$	−5.80564	−0.340919
$291$	4.82566	0.282885
$292$	−4.76547	−0.278878
$293$	13.0515	0.762477	0.381239	−	0.924477i	$-0.375498\pi$
$293$	13.0515	0.762477	0.381239	+	0.924477i	$0.375498\pi$
$294$	−17.9053	−1.04426
$295$	3.49221	0.203324
$296$	0.370002	0.0215060
$297$	3.39248	0.196852
$298$	−15.9946	−0.926541
$299$	−0.279837	−0.0161834
$300$	−2.56168	−0.147898
$301$	0.968164	0.0558041
$302$	9.19779	0.529273
$303$	19.5312	1.12204
$304$	5.91382	0.339181
$305$	2.72375	0.155961
$306$	−24.5444	−1.40311
$307$	24.1569	1.37871	0.689354	−	0.724425i	$-0.257895\pi$
$307$	24.1569	1.37871	0.689354	+	0.724425i	$0.257895\pi$
$308$	−0.239267	−0.0136335
$309$	−29.8156	−1.69615
$310$	0.226557	0.0128676
$311$	−16.8836	−0.957382	−0.478691	−	0.877983i	$-0.658889\pi$
$311$	−16.8836	−0.957382	−0.478691	+	0.877983i	$0.658889\pi$
$312$	2.39107	0.135367
$313$	−10.9344	−0.618051	−0.309026	−	0.951054i	$-0.600003\pi$
$313$	−10.9344	−0.618051	−0.309026	+	0.951054i	$0.600003\pi$
$314$	−3.09596	−0.174715
$315$	−0.361813	−0.0203858
$316$	4.89926	0.275605
$317$	8.07009	0.453262	0.226631	−	0.973981i	$-0.427229\pi$
$317$	8.07009	0.453262	0.226631	+	0.973981i	$0.427229\pi$
$318$	27.9244	1.56592
$319$	13.6762	0.765719
$320$	−1.00000	−0.0559017
$321$	45.8835	2.56096
$322$	0.0304512	0.00169698
$323$	40.7479	2.26727
$324$	−6.99740	−0.388744
$325$	0.933399	0.0517756
$326$	7.18846	0.398132
$327$	−11.8908	−0.657562
$328$	10.2787	0.567547
$329$	−0.0376389	−0.00207510
$330$	6.03447	0.332187
$331$	14.5155	0.797846	0.398923	−	0.916984i	$-0.369384\pi$
$331$	14.5155	0.797846	0.398923	+	0.916984i	$0.369384\pi$
$332$	9.57485	0.525488
$333$	−1.31802	−0.0722269
$334$	−2.56708	−0.140465
$335$	−0.815547	−0.0445581
$336$	−0.260191	−0.0141946
$337$	−3.23261	−0.176091	−0.0880457	−	0.996116i	$-0.528062\pi$
$337$	−3.23261	−0.176091	−0.0880457	+	0.996116i	$0.528062\pi$
$338$	12.1288	0.659718
$339$	36.5580	1.98556
$340$	−6.89027	−0.373678
$341$	−0.533694	−0.0289012
$342$	−21.0661	−1.13913
$343$	−1.42094	−0.0767235
$344$	−9.53194	−0.513928
$345$	−0.768000	−0.0413477
$346$	10.6975	0.575102
$347$	−9.01791	−0.484107	−0.242053	−	0.970263i	$-0.577821\pi$
$347$	−9.01791	−0.484107	−0.242053	+	0.970263i	$0.577821\pi$
$348$	14.8722	0.797231
$349$	−6.65934	−0.356466	−0.178233	−	0.983988i	$-0.557038\pi$
$349$	−6.65934	−0.356466	−0.178233	+	0.983988i	$0.557038\pi$
$350$	−0.101571	−0.00542917
$351$	−1.34422	−0.0717491
$352$	2.35567	0.125558
$353$	25.5128	1.35791	0.678954	−	0.734181i	$-0.262434\pi$
$353$	25.5128	1.35791	0.678954	+	0.734181i	$0.262434\pi$
$354$	−8.94591	−0.475470
$355$	−3.03374	−0.161014
$356$	−3.20708	−0.169975
$357$	−1.79279	−0.0948843
$358$	−16.3976	−0.866640
$359$	−17.6711	−0.932646	−0.466323	−	0.884615i	$-0.654422\pi$
$359$	−17.6711	−0.932646	−0.466323	+	0.884615i	$0.654422\pi$
$360$	3.56218	0.187744
$361$	15.9733	0.840700
$362$	−13.3931	−0.703927
$363$	13.9632	0.732878
$364$	0.0948058	0.00496917
$365$	4.76547	0.249436
$366$	−6.97736	−0.364713
$367$	−4.88854	−0.255180	−0.127590	−	0.991827i	$-0.540724\pi$
$367$	−4.88854	−0.255180	−0.127590	+	0.991827i	$0.540724\pi$
$368$	−0.299804	−0.0156284
$369$	−36.6147	−1.90608
$370$	−0.370002	−0.0192355
$371$	1.10720	0.0574832
$372$	−0.580366	−0.0300906
$373$	2.90307	0.150315	0.0751575	−	0.997172i	$-0.476054\pi$
$373$	2.90307	0.150315	0.0751575	+	0.997172i	$0.476054\pi$
$374$	16.2312	0.839297
$375$	2.56168	0.132284
$376$	0.370569	0.0191106
$377$	−5.41897	−0.279091
$378$	0.146275	0.00752358
$379$	5.83593	0.299772	0.149886	−	0.988703i	$-0.452109\pi$
$379$	5.83593	0.299772	0.149886	+	0.988703i	$0.452109\pi$
$380$	−5.91382	−0.303373
$381$	−10.2576	−0.525511
$382$	12.7794	0.653851
$383$	32.2264	1.64669	0.823347	−	0.567538i	$-0.192104\pi$
$383$	32.2264	1.64669	0.823347	+	0.567538i	$0.192104\pi$
$384$	2.56168	0.130725
$385$	0.239267	0.0121942
$386$	5.40703	0.275211
$387$	33.9545	1.72601
$388$	−1.88379	−0.0956350
$389$	13.2910	0.673880	0.336940	−	0.941526i	$-0.390608\pi$
$389$	13.2910	0.673880	0.336940	+	0.941526i	$0.390608\pi$
$390$	−2.39107	−0.121076
$391$	−2.06573	−0.104468
$392$	6.98968	0.353032
$393$	−9.43864	−0.476116
$394$	0.0341803	0.00172198
$395$	−4.89926	−0.246509
$396$	−8.39134	−0.421681
$397$	−6.58628	−0.330556	−0.165278	−	0.986247i	$-0.552852\pi$
$397$	−6.58628	−0.330556	−0.165278	+	0.986247i	$0.552852\pi$
$398$	3.51663	0.176273
$399$	−1.53872	−0.0770324
$400$	1.00000	0.0500000
$401$	1.00000	0.0499376
$401$	1.00000	0.0499376
$402$	2.08917	0.104198
$403$	0.211468	0.0105340
$404$	−7.62439	−0.379328
$405$	6.99740	0.347703
$406$	0.589681	0.0292654
$407$	0.871605	0.0432038
$408$	17.6507	0.873837
$409$	14.9046	0.736987	0.368493	−	0.929630i	$-0.379874\pi$
$409$	14.9046	0.736987	0.368493	+	0.929630i	$0.379874\pi$
$410$	−10.2787	−0.507629
$411$	6.57584	0.324362
$412$	11.6391	0.573418
$413$	−0.354705	−0.0174539
$414$	1.06796	0.0524872
$415$	−9.57485	−0.470011
$416$	−0.933399	−0.0457636
$417$	−8.94082	−0.437834
$418$	13.9310	0.681389
$419$	−34.1831	−1.66995	−0.834977	−	0.550284i	$-0.814519\pi$
$419$	−34.1831	−1.66995	−0.834977	+	0.550284i	$0.814519\pi$
$420$	0.260191	0.0126960
$421$	−8.36065	−0.407473	−0.203737	−	0.979026i	$-0.565309\pi$
$421$	−8.36065	−0.407473	−0.203737	+	0.979026i	$0.565309\pi$
$422$	−25.4249	−1.23766
$423$	−1.32003	−0.0641823
$424$	−10.9008	−0.529392
$425$	6.89027	0.334227
$426$	7.77145	0.376528
$427$	−0.276653	−0.0133882
$428$	−17.9115	−0.865785
$429$	5.63257	0.271943
$430$	9.53194	0.459671
$431$	−13.6820	−0.659038	−0.329519	−	0.944149i	$-0.606887\pi$
$431$	−13.6820	−0.659038	−0.329519	+	0.944149i	$0.606887\pi$
$432$	−1.44013	−0.0692884
$433$	11.6875	0.561664	0.280832	−	0.959757i	$-0.409390\pi$
$433$	11.6875	0.561664	0.280832	+	0.959757i	$0.409390\pi$
$434$	−0.0230115	−0.00110459
$435$	−14.8722	−0.713065
$436$	4.64180	0.222302
$437$	−1.77299	−0.0848134
$438$	−12.2076	−0.583301
$439$	−32.6392	−1.55778	−0.778892	−	0.627158i	$-0.784218\pi$
$439$	−32.6392	−1.55778	−0.778892	+	0.627158i	$0.784218\pi$
$440$	−2.35567	−0.112302
$441$	−24.8985	−1.18564
$442$	−6.43137	−0.305909
$443$	1.72669	0.0820373	0.0410187	−	0.999158i	$-0.486940\pi$
$443$	1.72669	0.0820373	0.0410187	+	0.999158i	$0.486940\pi$
$444$	0.947826	0.0449819
$445$	3.20708	0.152030
$446$	−4.79249	−0.226931
$447$	−40.9729	−1.93795
$448$	0.101571	0.00479876
$449$	9.68294	0.456966	0.228483	−	0.973548i	$-0.426623\pi$
$449$	9.68294	0.456966	0.228483	+	0.973548i	$0.426623\pi$
$450$	−3.56218	−0.167923
$451$	24.2133	1.14016
$452$	−14.2711	−0.671256
$453$	23.5618	1.10703
$454$	−12.5386	−0.588467
$455$	−0.0948058	−0.00444456
$456$	15.1493	0.709431
$457$	34.8306	1.62930	0.814652	−	0.579949i	$-0.196928\pi$
$457$	34.8306	1.62930	0.814652	+	0.579949i	$0.196928\pi$
$458$	−5.03580	−0.235308
$459$	−9.92291	−0.463162
$460$	0.299804	0.0139784
$461$	−19.6070	−0.913187	−0.456594	−	0.889675i	$-0.650931\pi$
$461$	−19.6070	−0.913187	−0.456594	+	0.889675i	$0.650931\pi$
$462$	−0.612924	−0.0285158
$463$	17.0494	0.792353	0.396176	−	0.918174i	$-0.370337\pi$
$463$	17.0494	0.792353	0.396176	+	0.918174i	$0.370337\pi$
$464$	−5.80564	−0.269520
$465$	0.580366	0.0269138
$466$	4.34105	0.201095
$467$	11.1783	0.517271	0.258636	−	0.965975i	$-0.416727\pi$
$467$	11.1783	0.517271	0.258636	+	0.965975i	$0.416727\pi$
$468$	3.32494	0.153695
$469$	0.0828355	0.00382499
$470$	−0.370569	−0.0170931
$471$	−7.93085	−0.365434
$472$	3.49221	0.160742
$473$	−22.4541	−1.03244
$474$	12.5503	0.576456
$475$	5.91382	0.271345
$476$	0.699849	0.0320775
$477$	38.8308	1.77794
$478$	18.5322	0.847644
$479$	−18.9330	−0.865071	−0.432536	−	0.901617i	$-0.642381\pi$
$479$	−18.9330	−0.865071	−0.432536	+	0.901617i	$0.642381\pi$
$480$	−2.56168	−0.116924
$481$	−0.345360	−0.0157471
$482$	−20.1212	−0.916493
$483$	0.0780062	0.00354940
$484$	−5.45081	−0.247764
$485$	1.88379	0.0855385
$486$	−22.2455	−1.00907
$487$	25.6376	1.16175	0.580875	−	0.813993i	$-0.302711\pi$
$487$	25.6376	1.16175	0.580875	+	0.813993i	$0.302711\pi$
$488$	2.72375	0.123298
$489$	18.4145	0.832733
$490$	−6.98968	−0.315762
$491$	−13.0144	−0.587331	−0.293665	−	0.955908i	$-0.594875\pi$
$491$	−13.0144	−0.587331	−0.293665	+	0.955908i	$0.594875\pi$
$492$	26.3307	1.18708
$493$	−40.0024	−1.80162
$494$	−5.51995	−0.248354
$495$	8.39134	0.377163
$496$	0.226557	0.0101727
$497$	0.308138	0.0138219
$498$	24.5277	1.09911
$499$	4.49939	0.201420	0.100710	−	0.994916i	$-0.467889\pi$
$499$	4.49939	0.201420	0.100710	+	0.994916i	$0.467889\pi$
$500$	−1.00000	−0.0447214
$501$	−6.57603	−0.293796
$502$	−16.2819	−0.726698
$503$	0.924358	0.0412151	0.0206075	−	0.999788i	$-0.493440\pi$
$503$	0.924358	0.0412151	0.0206075	+	0.999788i	$0.493440\pi$
$504$	−0.361813	−0.0161164
$505$	7.62439	0.339281
$506$	−0.706240	−0.0313962
$507$	31.0700	1.37987
$508$	4.00424	0.177659
$509$	−26.5062	−1.17487	−0.587434	−	0.809272i	$-0.699862\pi$
$509$	−26.5062	−1.17487	−0.587434	+	0.809272i	$0.699862\pi$
$510$	−17.6507	−0.781584
$511$	−0.484031	−0.0214123
$512$	−1.00000	−0.0441942
$513$	−8.51669	−0.376021
$514$	−12.9399	−0.570755
$515$	−11.6391	−0.512880
$516$	−24.4178	−1.07493
$517$	0.872939	0.0383918
$518$	0.0375813	0.00165123
$519$	27.4036	1.20288
$520$	0.933399	0.0409322
$521$	−33.3132	−1.45948	−0.729738	−	0.683727i	$-0.760358\pi$
$521$	−33.3132	−1.45948	−0.729738	+	0.683727i	$0.760358\pi$
$522$	20.6807	0.905171
$523$	16.8161	0.735317	0.367659	−	0.929961i	$-0.380160\pi$
$523$	16.8161	0.735317	0.367659	+	0.929961i	$0.380160\pi$
$524$	3.68456	0.160961
$525$	−0.260191	−0.0113557
$526$	−15.4674	−0.674410
$527$	1.56104	0.0680000
$528$	6.03447	0.262617
$529$	−22.9101	−0.996092
$530$	10.9008	0.473502
$531$	−12.4399	−0.539845
$532$	0.600670	0.0260423
$533$	−9.59414	−0.415568
$534$	−8.21551	−0.355520
$535$	17.9115	0.774382
$536$	−0.815547	−0.0352263
$537$	−42.0053	−1.81266
$538$	−22.3699	−0.964437
$539$	16.4654	0.709215
$540$	1.44013	0.0619735
$541$	15.4906	0.665995	0.332997	−	0.942928i	$-0.391940\pi$
$541$	15.4906	0.665995	0.332997	+	0.942928i	$0.391940\pi$
$542$	−31.1521	−1.33810
$543$	−34.3089	−1.47233
$544$	−6.89027	−0.295418
$545$	−4.64180	−0.198833
$546$	0.242862	0.0103935
$547$	39.6019	1.69325	0.846627	−	0.532187i	$-0.178630\pi$
$547$	39.6019	1.69325	0.846627	+	0.532187i	$0.178630\pi$
$548$	−2.56701	−0.109657
$549$	−9.70250	−0.414092
$550$	2.35567	0.100446
$551$	−34.3335	−1.46266
$552$	−0.768000	−0.0326883
$553$	0.497621	0.0211610
$554$	16.1441	0.685899
$555$	−0.947826	−0.0402330
$556$	3.49022	0.148018
$557$	−36.9741	−1.56664	−0.783321	−	0.621618i	$-0.786476\pi$
$557$	−36.9741	−1.56664	−0.783321	+	0.621618i	$0.786476\pi$
$558$	−0.807038	−0.0341646
$559$	8.89710	0.376307
$560$	−0.101571	−0.00429214
$561$	41.5792	1.75547
$562$	−23.0568	−0.972591
$563$	−8.98448	−0.378651	−0.189325	−	0.981914i	$-0.560630\pi$
$563$	−8.98448	−0.378651	−0.189325	+	0.981914i	$0.560630\pi$
$564$	0.949277	0.0399718
$565$	14.2711	0.600390
$566$	−9.00828	−0.378646
$567$	−0.710729	−0.0298478
$568$	−3.03374	−0.127293
$569$	−5.31057	−0.222631	−0.111315	−	0.993785i	$-0.535506\pi$
$569$	−5.31057	−0.222631	−0.111315	+	0.993785i	$0.535506\pi$
$570$	−15.1493	−0.634534
$571$	11.6332	0.486835	0.243417	−	0.969922i	$-0.421732\pi$
$571$	11.6332	0.486835	0.243417	+	0.969922i	$0.421732\pi$
$572$	−2.19878	−0.0919357
$573$	32.7367	1.36759
$574$	1.04401	0.0435763
$575$	−0.299804	−0.0125027
$576$	3.56218	0.148424
$577$	−23.3037	−0.970146	−0.485073	−	0.874474i	$-0.661207\pi$
$577$	−23.3037	−0.970146	−0.485073	+	0.874474i	$0.661207\pi$
$578$	−30.4759	−1.26763
$579$	13.8511	0.575630
$580$	5.80564	0.241066
$581$	0.972522	0.0403470
$582$	−4.82566	−0.200030
$583$	−25.6788	−1.06351
$584$	4.76547	0.197196
$585$	−3.32494	−0.137469
$586$	−13.0515	−0.539153
$587$	−9.99199	−0.412413	−0.206207	−	0.978508i	$-0.566112\pi$
$587$	−9.99199	−0.412413	−0.206207	+	0.978508i	$0.566112\pi$
$588$	17.9053	0.738402
$589$	1.33982	0.0552062
$590$	−3.49221	−0.143772
$591$	0.0875589	0.00360169
$592$	−0.370002	−0.0152070
$593$	−3.88435	−0.159511	−0.0797555	−	0.996814i	$-0.525414\pi$
$593$	−3.88435	−0.159511	−0.0797555	+	0.996814i	$0.525414\pi$
$594$	−3.39248	−0.139195
$595$	−0.699849	−0.0286910
$596$	15.9946	0.655163
$597$	9.00847	0.368692
$598$	0.279837	0.0114434
$599$	22.6292	0.924604	0.462302	−	0.886722i	$-0.347024\pi$
$599$	22.6292	0.924604	0.462302	+	0.886722i	$0.347024\pi$
$600$	2.56168	0.104580
$601$	36.4015	1.48485	0.742424	−	0.669931i	$-0.233676\pi$
$601$	36.4015	1.48485	0.742424	+	0.669931i	$0.233676\pi$
$602$	−0.968164	−0.0394594
$603$	2.90513	0.118306
$604$	−9.19779	−0.374253
$605$	5.45081	0.221607
$606$	−19.5312	−0.793402
$607$	−9.75722	−0.396033	−0.198017	−	0.980199i	$-0.563450\pi$
$607$	−9.75722	−0.396033	−0.198017	+	0.980199i	$0.563450\pi$
$608$	−5.91382	−0.239837
$609$	1.51057	0.0612115
$610$	−2.72375	−0.110281
$611$	−0.345889	−0.0139932
$612$	24.5444	0.992150
$613$	4.46305	0.180261	0.0901304	−	0.995930i	$-0.471272\pi$
$613$	4.46305	0.180261	0.0901304	+	0.995930i	$0.471272\pi$
$614$	−24.1569	−0.974893
$615$	−26.3307	−1.06176
$616$	0.239267	0.00964034
$617$	12.9316	0.520608	0.260304	−	0.965527i	$-0.416177\pi$
$617$	12.9316	0.520608	0.260304	+	0.965527i	$0.416177\pi$
$618$	29.8156	1.19936
$619$	−25.1894	−1.01245	−0.506225	−	0.862402i	$-0.668959\pi$
$619$	−25.1894	−1.01245	−0.506225	+	0.862402i	$0.668959\pi$
$620$	−0.226557	−0.00909875
$621$	0.431757	0.0173258
$622$	16.8836	0.676972
$623$	−0.325745	−0.0130507
$624$	−2.39107	−0.0957192
$625$	1.00000	0.0400000
$626$	10.9344	0.437028
$627$	35.6868	1.42519
$628$	3.09596	0.123542
$629$	−2.54942	−0.101652
$630$	0.361813	0.0144150
$631$	19.3100	0.768720	0.384360	−	0.923183i	$-0.374422\pi$
$631$	19.3100	0.768720	0.384360	+	0.923183i	$0.374422\pi$
$632$	−4.89926	−0.194882
$633$	−65.1303	−2.58870
$634$	−8.07009	−0.320504
$635$	−4.00424	−0.158903
$636$	−27.9244	−1.10728
$637$	−6.52416	−0.258497
$638$	−13.6762	−0.541445
$639$	10.8067	0.427508
$640$	1.00000	0.0395285
$641$	30.1877	1.19234	0.596171	−	0.802857i	$-0.296688\pi$
$641$	30.1877	1.19234	0.596171	+	0.802857i	$0.296688\pi$
$642$	−45.8835	−1.81088
$643$	27.1861	1.07212	0.536058	−	0.844181i	$-0.319913\pi$
$643$	27.1861	1.07212	0.536058	+	0.844181i	$0.319913\pi$
$644$	−0.0304512	−0.00119995
$645$	24.4178	0.961448
$646$	−40.7479	−1.60320
$647$	−20.1467	−0.792048	−0.396024	−	0.918240i	$-0.629610\pi$
$647$	−20.1467	−0.792048	−0.396024	+	0.918240i	$0.629610\pi$
$648$	6.99740	0.274884
$649$	8.22650	0.322918
$650$	−0.933399	−0.0366109
$651$	−0.0589480	−0.00231036
$652$	−7.18846	−0.281522
$653$	27.5042	1.07632	0.538162	−	0.842841i	$-0.319119\pi$
$653$	27.5042	1.07632	0.538162	+	0.842841i	$0.319119\pi$
$654$	11.8908	0.464966
$655$	−3.68456	−0.143968
$656$	−10.2787	−0.401316
$657$	−16.9755	−0.662276
$658$	0.0376389	0.00146732
$659$	−31.5429	−1.22874	−0.614368	−	0.789020i	$-0.710589\pi$
$659$	−31.5429	−1.22874	−0.614368	+	0.789020i	$0.710589\pi$
$660$	−6.03447	−0.234891
$661$	−2.33768	−0.0909251	−0.0454625	−	0.998966i	$-0.514476\pi$
$661$	−2.33768	−0.0909251	−0.0454625	+	0.998966i	$0.514476\pi$
$662$	−14.5155	−0.564162
$663$	−16.4751	−0.639840
$664$	−9.57485	−0.371576
$665$	−0.600670	−0.0232930
$666$	1.31802	0.0510721
$667$	1.74055	0.0673944
$668$	2.56708	0.0993234
$669$	−12.2768	−0.474649
$670$	0.815547	0.0315073
$671$	6.41626	0.247697
$672$	0.260191	0.0100371
$673$	−10.6996	−0.412439	−0.206219	−	0.978506i	$-0.566116\pi$
$673$	−10.6996	−0.412439	−0.206219	+	0.978506i	$0.566116\pi$
$674$	3.23261	0.124515
$675$	−1.44013	−0.0554307
$676$	−12.1288	−0.466491
$677$	−2.31189	−0.0888531	−0.0444266	−	0.999013i	$-0.514146\pi$
$677$	−2.31189	−0.0888531	−0.0444266	+	0.999013i	$0.514146\pi$
$678$	−36.5580	−1.40400
$679$	−0.191338	−0.00734286
$680$	6.89027	0.264230
$681$	−32.1199	−1.23084
$682$	0.533694	0.0204362
$683$	8.98833	0.343929	0.171964	−	0.985103i	$-0.444989\pi$
$683$	8.98833	0.343929	0.171964	+	0.985103i	$0.444989\pi$
$684$	21.0661	0.805483
$685$	2.56701	0.0980803
$686$	1.42094	0.0542517
$687$	−12.9001	−0.492169
$688$	9.53194	0.363402
$689$	10.1748	0.387630
$690$	0.768000	0.0292373
$691$	−9.91468	−0.377172	−0.188586	−	0.982057i	$-0.560390\pi$
$691$	−9.91468	−0.377172	−0.188586	+	0.982057i	$0.560390\pi$
$692$	−10.6975	−0.406658
$693$	−0.852313	−0.0323767
$694$	9.01791	0.342315
$695$	−3.49022	−0.132392
$696$	−14.8722	−0.563728
$697$	−70.8231	−2.68262
$698$	6.65934	0.252060
$699$	11.1204	0.420610
$700$	0.101571	0.00383900
$701$	33.0538	1.24842	0.624212	−	0.781255i	$-0.285420\pi$
$701$	33.0538	1.24842	0.624212	+	0.781255i	$0.285420\pi$
$702$	1.34422	0.0507343
$703$	−2.18813	−0.0825268
$704$	−2.35567	−0.0887828
$705$	−0.949277	−0.0357519
$706$	−25.5128	−0.960186
$707$	−0.774413	−0.0291248
$708$	8.94591	0.336208
$709$	42.9136	1.61165	0.805826	−	0.592152i	$-0.201722\pi$
$709$	42.9136	1.61165	0.805826	+	0.592152i	$0.201722\pi$
$710$	3.03374	0.113854
$711$	17.4521	0.654504
$712$	3.20708	0.120191
$713$	−0.0679227	−0.00254372
$714$	1.79279	0.0670933
$715$	2.19878	0.0822298
$716$	16.3976	0.612807
$717$	47.4735	1.77293
$718$	17.6711	0.659480
$719$	12.8246	0.478275	0.239138	−	0.970986i	$-0.423135\pi$
$719$	12.8246	0.478275	0.239138	+	0.970986i	$0.423135\pi$
$720$	−3.56218	−0.132755
$721$	1.18219	0.0440271
$722$	−15.9733	−0.594465
$723$	−51.5439	−1.91694
$724$	13.3931	0.497752
$725$	−5.80564	−0.215616
$726$	−13.9632	−0.518223
$727$	−41.3346	−1.53301	−0.766507	−	0.642236i	$-0.778007\pi$
$727$	−41.3346	−1.53301	−0.766507	+	0.642236i	$0.778007\pi$
$728$	−0.0948058	−0.00351374
$729$	−35.9935	−1.33309
$730$	−4.76547	−0.176378
$731$	65.6777	2.42918
$732$	6.97736	0.257891
$733$	45.8780	1.69454	0.847272	−	0.531160i	$-0.178244\pi$
$733$	45.8780	1.69454	0.847272	+	0.531160i	$0.178244\pi$
$734$	4.88854	0.180439
$735$	−17.9053	−0.660447
$736$	0.299804	0.0110509
$737$	−1.92116	−0.0707669
$738$	36.6147	1.34780
$739$	39.2245	1.44290	0.721448	−	0.692469i	$-0.243477\pi$
$739$	39.2245	1.44290	0.721448	+	0.692469i	$0.243477\pi$
$740$	0.370002	0.0136016
$741$	−14.1403	−0.519458
$742$	−1.10720	−0.0406467
$743$	17.0131	0.624149	0.312074	−	0.950058i	$-0.398976\pi$
$743$	17.0131	0.624149	0.312074	+	0.950058i	$0.398976\pi$
$744$	0.580366	0.0212772
$745$	−15.9946	−0.585996
$746$	−2.90307	−0.106289
$747$	34.1074	1.24792
$748$	−16.2312	−0.593473
$749$	−1.81928	−0.0664750
$750$	−2.56168	−0.0935392
$751$	11.8950	0.434056	0.217028	−	0.976165i	$-0.430364\pi$
$751$	11.8950	0.434056	0.217028	+	0.976165i	$0.430364\pi$
$752$	−0.370569	−0.0135133
$753$	−41.7090	−1.51996
$754$	5.41897	0.197347
$755$	9.19779	0.334742
$756$	−0.146275	−0.00531997
$757$	39.7750	1.44565	0.722824	−	0.691033i	$-0.242844\pi$
$757$	39.7750	1.44565	0.722824	+	0.691033i	$0.242844\pi$
$758$	−5.83593	−0.211971
$759$	−1.80916	−0.0656682
$760$	5.91382	0.214517
$761$	10.7875	0.391046	0.195523	−	0.980699i	$-0.437360\pi$
$761$	10.7875	0.391046	0.195523	+	0.980699i	$0.437360\pi$
$762$	10.2576	0.371592
$763$	0.471470	0.0170684
$764$	−12.7794	−0.462342
$765$	−24.5444	−0.887406
$766$	−32.2264	−1.16439
$767$	−3.25962	−0.117698
$768$	−2.56168	−0.0924365
$769$	−32.1030	−1.15766	−0.578831	−	0.815447i	$-0.696491\pi$
$769$	−32.1030	−1.15766	−0.578831	+	0.815447i	$0.696491\pi$
$770$	−0.239267	−0.00862258
$771$	−33.1479	−1.19379
$772$	−5.40703	−0.194603
$773$	26.3044	0.946104	0.473052	−	0.881035i	$-0.343152\pi$
$773$	26.3044	0.946104	0.473052	+	0.881035i	$0.343152\pi$
$774$	−33.9545	−1.22047
$775$	0.226557	0.00813817
$776$	1.88379	0.0676241
$777$	0.0962712	0.00345371
$778$	−13.2910	−0.476505
$779$	−60.7865	−2.17790
$780$	2.39107	0.0856139
$781$	−7.14649	−0.255722
$782$	2.06573	0.0738704
$783$	8.36089	0.298794
$784$	−6.98968	−0.249632
$785$	−3.09596	−0.110500
$786$	9.43864	0.336665
$787$	−1.36663	−0.0487152	−0.0243576	−	0.999703i	$-0.507754\pi$
$787$	−1.36663	−0.0487152	−0.0243576	+	0.999703i	$0.507754\pi$
$788$	−0.0341803	−0.00121762
$789$	−39.6224	−1.41060
$790$	4.89926	0.174308
$791$	−1.44952	−0.0515391
$792$	8.39134	0.298173
$793$	−2.54234	−0.0902813
$794$	6.58628	0.233738
$795$	27.9244	0.990377
$796$	−3.51663	−0.124644
$797$	−22.9217	−0.811928	−0.405964	−	0.913889i	$-0.633064\pi$
$797$	−22.9217	−0.811928	−0.405964	+	0.913889i	$0.633064\pi$
$798$	1.53872	0.0544702
$799$	−2.55332	−0.0903300
$800$	−1.00000	−0.0353553
$801$	−11.4242	−0.403655
$802$	−1.00000	−0.0353112
$803$	11.2259	0.396153
$804$	−2.08917	−0.0736792
$805$	0.0304512	0.00107326
$806$	−0.211468	−0.00744864
$807$	−57.3045	−2.01722
$808$	7.62439	0.268225
$809$	−47.4325	−1.66764	−0.833818	−	0.552039i	$-0.813850\pi$
$809$	−47.4325	−1.66764	−0.833818	+	0.552039i	$0.813850\pi$
$810$	−6.99740	−0.245863
$811$	50.3750	1.76891	0.884453	−	0.466630i	$-0.154532\pi$
$811$	50.3750	1.76891	0.884453	+	0.466630i	$0.154532\pi$
$812$	−0.589681	−0.0206938
$813$	−79.8015	−2.79876
$814$	−0.871605	−0.0305497
$815$	7.18846	0.251801
$816$	−17.6507	−0.617896
$817$	56.3702	1.97214
$818$	−14.9046	−0.521128
$819$	0.337716	0.0118007
$820$	10.2787	0.358948
$821$	−14.4903	−0.505715	−0.252857	−	0.967504i	$-0.581370\pi$
$821$	−14.4903	−0.505715	−0.252857	+	0.967504i	$0.581370\pi$
$822$	−6.57584	−0.229359
$823$	−19.3738	−0.675329	−0.337665	−	0.941267i	$-0.609637\pi$
$823$	−19.3738	−0.675329	−0.337665	+	0.941267i	$0.609637\pi$
$824$	−11.6391	−0.405468
$825$	6.03447	0.210093
$826$	0.354705	0.0123418
$827$	38.1601	1.32696	0.663478	−	0.748195i	$-0.269079\pi$
$827$	38.1601	1.32696	0.663478	+	0.748195i	$0.269079\pi$
$828$	−1.06796	−0.0371140
$829$	−9.72346	−0.337710	−0.168855	−	0.985641i	$-0.554007\pi$
$829$	−9.72346	−0.337710	−0.168855	+	0.985641i	$0.554007\pi$
$830$	9.57485	0.332348
$831$	41.3561	1.43463
$832$	0.933399	0.0323598
$833$	−48.1608	−1.66867
$834$	8.94082	0.309595
$835$	−2.56708	−0.0888376
$836$	−13.9310	−0.481815
$837$	−0.326272	−0.0112776
$838$	34.1831	1.18084
$839$	−0.778332	−0.0268710	−0.0134355	−	0.999910i	$-0.504277\pi$
$839$	−0.778332	−0.0268710	−0.0134355	+	0.999910i	$0.504277\pi$
$840$	−0.260191	−0.00897743
$841$	4.70540	0.162255
$842$	8.36065	0.288127
$843$	−59.0640	−2.03427
$844$	25.4249	0.875161
$845$	12.1288	0.417242
$846$	1.32003	0.0453837
$847$	−0.553641	−0.0190233
$848$	10.9008	0.374336
$849$	−23.0763	−0.791976
$850$	−6.89027	−0.236334
$851$	0.110928	0.00380257
$852$	−7.77145	−0.266246
$853$	26.2538	0.898912	0.449456	−	0.893303i	$-0.351618\pi$
$853$	26.2538	0.898912	0.449456	+	0.893303i	$0.351618\pi$
$854$	0.276653	0.00946686
$855$	−21.0661	−0.720446
$856$	17.9115	0.612202
$857$	17.9724	0.613927	0.306963	−	0.951721i	$-0.400687\pi$
$857$	17.9724	0.613927	0.306963	+	0.951721i	$0.400687\pi$
$858$	−5.63257	−0.192293
$859$	−41.2933	−1.40891	−0.704455	−	0.709748i	$-0.748809\pi$
$859$	−41.2933	−1.40891	−0.704455	+	0.709748i	$0.748809\pi$
$860$	−9.53194	−0.325037
$861$	2.67443	0.0911442
$862$	13.6820	0.466011
$863$	38.1059	1.29714	0.648570	−	0.761155i	$-0.275367\pi$
$863$	38.1059	1.29714	0.648570	+	0.761155i	$0.275367\pi$
$864$	1.44013	0.0489943
$865$	10.6975	0.363726
$866$	−11.6875	−0.397157
$867$	−78.0693	−2.65137
$868$	0.0230115	0.000781062 0
$869$	−11.5411	−0.391504
$870$	14.8722	0.504213
$871$	0.761231	0.0257933
$872$	−4.64180	−0.157191
$873$	−6.71041	−0.227113
$874$	1.77299	0.0599722
$875$	−0.101571	−0.00343371
$876$	12.2076	0.412456
$877$	−17.3888	−0.587177	−0.293588	−	0.955932i	$-0.594849\pi$
$877$	−17.3888	−0.587177	−0.293588	+	0.955932i	$0.594849\pi$
$878$	32.6392	1.10152
$879$	−33.4337	−1.12769
$880$	2.35567	0.0794097
$881$	32.8597	1.10707	0.553536	−	0.832825i	$-0.313278\pi$
$881$	32.8597	1.10707	0.553536	+	0.832825i	$0.313278\pi$
$882$	24.8985	0.838377
$883$	−26.0349	−0.876145	−0.438072	−	0.898940i	$-0.644339\pi$
$883$	−26.0349	−0.876145	−0.438072	+	0.898940i	$0.644339\pi$
$884$	6.43137	0.216311
$885$	−8.94591	−0.300713
$886$	−1.72669	−0.0580091
$887$	−0.778712	−0.0261466	−0.0130733	−	0.999915i	$-0.504161\pi$
$887$	−0.778712	−0.0261466	−0.0130733	+	0.999915i	$0.504161\pi$
$888$	−0.947826	−0.0318070
$889$	0.406712	0.0136407
$890$	−3.20708	−0.107502
$891$	16.4836	0.552221
$892$	4.79249	0.160464
$893$	−2.19148	−0.0733350
$894$	40.9729	1.37034
$895$	−16.3976	−0.548111
$896$	−0.101571	−0.00339323
$897$	0.716850	0.0239349
$898$	−9.68294	−0.323124
$899$	−1.31531	−0.0438680
$900$	3.56218	0.118739
$901$	75.1098	2.50227
$902$	−24.2133	−0.806214
$903$	−2.48012	−0.0825333
$904$	14.2711	0.474650
$905$	−13.3931	−0.445203
$906$	−23.5618	−0.782787
$907$	−4.61877	−0.153364	−0.0766819	−	0.997056i	$-0.524433\pi$
$907$	−4.61877	−0.153364	−0.0766819	+	0.997056i	$0.524433\pi$
$908$	12.5386	0.416109
$909$	−27.1595	−0.900823
$910$	0.0948058	0.00314278
$911$	18.3892	0.609262	0.304631	−	0.952470i	$-0.401467\pi$
$911$	18.3892	0.609262	0.304631	+	0.952470i	$0.401467\pi$
$912$	−15.1493	−0.501643
$913$	−22.5552	−0.746468
$914$	−34.8306	−1.15209
$915$	−6.97736	−0.230665
$916$	5.03580	0.166388
$917$	0.374242	0.0123586
$918$	9.92291	0.327505
$919$	−2.63671	−0.0869770	−0.0434885	−	0.999054i	$-0.513847\pi$
$919$	−2.63671	−0.0869770	−0.0434885	+	0.999054i	$0.513847\pi$
$920$	−0.299804	−0.00988424
$921$	−61.8822	−2.03909
$922$	19.6070	0.645721
$923$	2.83169	0.0932061
$924$	0.612924	0.0201637
$925$	−0.370002	−0.0121656
$926$	−17.0494	−0.560278
$927$	41.4606	1.36175
$928$	5.80564	0.190579
$929$	4.36578	0.143236	0.0716182	−	0.997432i	$-0.477184\pi$
$929$	4.36578	0.143236	0.0716182	+	0.997432i	$0.477184\pi$
$930$	−0.580366	−0.0190309
$931$	−41.3357	−1.35472
$932$	−4.34105	−0.142196
$933$	43.2504	1.41595
$934$	−11.1783	−0.365766
$935$	16.2312	0.530818
$936$	−3.32494	−0.108679
$937$	−39.2884	−1.28350	−0.641748	−	0.766915i	$-0.721791\pi$
$937$	−39.2884	−1.28350	−0.641748	+	0.766915i	$0.721791\pi$
$938$	−0.0828355	−0.00270468
$939$	28.0105	0.914088
$940$	0.370569	0.0120866
$941$	−24.1500	−0.787269	−0.393634	−	0.919267i	$-0.628782\pi$
$941$	−24.1500	−0.787269	−0.393634	+	0.919267i	$0.628782\pi$
$942$	7.93085	0.258401
$943$	3.08160	0.100351
$944$	−3.49221	−0.113662
$945$	0.146275	0.00475833
$946$	22.4541	0.730047
$947$	32.5117	1.05649	0.528245	−	0.849092i	$-0.322850\pi$
$947$	32.5117	1.05649	0.528245	+	0.849092i	$0.322850\pi$
$948$	−12.5503	−0.407616
$949$	−4.44808	−0.144391
$950$	−5.91382	−0.191870
$951$	−20.6730	−0.670367
$952$	−0.699849	−0.0226822
$953$	−20.3053	−0.657753	−0.328877	−	0.944373i	$-0.606670\pi$
$953$	−20.3053	−0.657753	−0.328877	+	0.944373i	$0.606670\pi$
$954$	−38.8308	−1.25719
$955$	12.7794	0.413531
$956$	−18.5322	−0.599375
$957$	−35.0339	−1.13249
$958$	18.9330	0.611698
$959$	−0.260732	−0.00841948
$960$	2.56168	0.0826777
$961$	−30.9487	−0.998344
$962$	0.345360	0.0111348
$963$	−63.8041	−2.05606
$964$	20.1212	0.648059
$965$	5.40703	0.174058
$966$	−0.0780062	−0.00250981
$967$	6.43159	0.206826	0.103413	−	0.994639i	$-0.467024\pi$
$967$	6.43159	0.206826	0.103413	+	0.994639i	$0.467024\pi$
$968$	5.45081	0.175196
$969$	−104.383	−3.35326
$970$	−1.88379	−0.0604849
$971$	−10.1722	−0.326442	−0.163221	−	0.986590i	$-0.552188\pi$
$971$	−10.1722	−0.326442	−0.163221	+	0.986590i	$0.552188\pi$
$972$	22.2455	0.713524
$973$	0.354504	0.0113649
$974$	−25.6376	−0.821481
$975$	−2.39107	−0.0765754
$976$	−2.72375	−0.0871851
$977$	38.5221	1.23243	0.616215	−	0.787578i	$-0.288665\pi$
$977$	38.5221	1.23243	0.616215	+	0.787578i	$0.288665\pi$
$978$	−18.4145	−0.588831
$979$	7.55484	0.241454
$980$	6.98968	0.223277
$981$	16.5349	0.527920
$982$	13.0144	0.415306
$983$	−39.5553	−1.26162	−0.630809	−	0.775938i	$-0.717277\pi$
$983$	−39.5553	−1.26162	−0.630809	+	0.775938i	$0.717277\pi$
$984$	−26.3307	−0.839393
$985$	0.0341803	0.00108908
$986$	40.0024	1.27394
$987$	0.0964186	0.00306904
$988$	5.51995	0.175613
$989$	−2.85771	−0.0908700
$990$	−8.39134	−0.266694
$991$	59.2462	1.88202	0.941008	−	0.338384i	$-0.109880\pi$
$991$	59.2462	1.88202	0.941008	+	0.338384i	$0.109880\pi$
$992$	−0.226557	−0.00719319
$993$	−37.1841	−1.18000
$994$	−0.308138	−0.00977355
$995$	3.51663	0.111485
$996$	−24.5277	−0.777189
$997$	−48.4841	−1.53551	−0.767754	−	0.640745i	$-0.778626\pi$
$997$	−48.4841	−1.53551	−0.767754	+	0.640745i	$0.778626\pi$
$998$	−4.49939	−0.142426
$999$	0.532853	0.0168587

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	4010.2.a.l.1.1	✓	17

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
4010.2.a.l.1.1	✓	17	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)

\(f(q)\)	\(=\)	\(q-1.00000 q^{2} -2.56168 q^{3} +1.00000 q^{4} -1.00000 q^{5} +2.56168 q^{6} +0.101571 q^{7} -1.00000 q^{8} +3.56218 q^{9} +O(q^{10})\)	\(q-1.00000 q^{2} -2.56168 q^{3} +1.00000 q^{4} -1.00000 q^{5} +2.56168 q^{6} +0.101571 q^{7} -1.00000 q^{8} +3.56218 q^{9} +1.00000 q^{10} -2.35567 q^{11} -2.56168 q^{12} +0.933399 q^{13} -0.101571 q^{14} +2.56168 q^{15} +1.00000 q^{16} +6.89027 q^{17} -3.56218 q^{18} +5.91382 q^{19} -1.00000 q^{20} -0.260191 q^{21} +2.35567 q^{22} -0.299804 q^{23} +2.56168 q^{24} +1.00000 q^{25} -0.933399 q^{26} -1.44013 q^{27} +0.101571 q^{28} -5.80564 q^{29} -2.56168 q^{30} +0.226557 q^{31} -1.00000 q^{32} +6.03447 q^{33} -6.89027 q^{34} -0.101571 q^{35} +3.56218 q^{36} -0.370002 q^{37} -5.91382 q^{38} -2.39107 q^{39} +1.00000 q^{40} -10.2787 q^{41} +0.260191 q^{42} +9.53194 q^{43} -2.35567 q^{44} -3.56218 q^{45} +0.299804 q^{46} -0.370569 q^{47} -2.56168 q^{48} -6.98968 q^{49} -1.00000 q^{50} -17.6507 q^{51} +0.933399 q^{52} +10.9008 q^{53} +1.44013 q^{54} +2.35567 q^{55} -0.101571 q^{56} -15.1493 q^{57} +5.80564 q^{58} -3.49221 q^{59} +2.56168 q^{60} -2.72375 q^{61} -0.226557 q^{62} +0.361813 q^{63} +1.00000 q^{64} -0.933399 q^{65} -6.03447 q^{66} +0.815547 q^{67} +6.89027 q^{68} +0.768000 q^{69} +0.101571 q^{70} +3.03374 q^{71} -3.56218 q^{72} -4.76547 q^{73} +0.370002 q^{74} -2.56168 q^{75} +5.91382 q^{76} -0.239267 q^{77} +2.39107 q^{78} +4.89926 q^{79} -1.00000 q^{80} -6.99740 q^{81} +10.2787 q^{82} +9.57485 q^{83} -0.260191 q^{84} -6.89027 q^{85} -9.53194 q^{86} +14.8722 q^{87} +2.35567 q^{88} -3.20708 q^{89} +3.56218 q^{90} +0.0948058 q^{91} -0.299804 q^{92} -0.580366 q^{93} +0.370569 q^{94} -5.91382 q^{95} +2.56168 q^{96} -1.88379 q^{97} +6.98968 q^{98} -8.39134 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 17 q - 17 q^{2} + 3 q^{3} + 17 q^{4} - 17 q^{5} - 3 q^{6} + 4 q^{7} - 17 q^{8} + 6 q^{9}+O(q^{10}) \) 17 * q - 17 * q^2 + 3 * q^3 + 17 * q^4 - 17 * q^5 - 3 * q^6 + 4 * q^7 - 17 * q^8 + 6 * q^9	\( 17 q - 17 q^{2} + 3 q^{3} + 17 q^{4} - 17 q^{5} - 3 q^{6} + 4 q^{7} - 17 q^{8} + 6 q^{9} + 17 q^{10} - 8 q^{11} + 3 q^{12} + 14 q^{13} - 4 q^{14} - 3 q^{15} + 17 q^{16} - 8 q^{17} - 6 q^{18} + 7 q^{19} - 17 q^{20} - 11 q^{21} + 8 q^{22} + q^{23} - 3 q^{24} + 17 q^{25} - 14 q^{26} + 15 q^{27} + 4 q^{28} - 18 q^{29} + 3 q^{30} + 8 q^{31} - 17 q^{32} + 3 q^{33} + 8 q^{34} - 4 q^{35} + 6 q^{36} + 49 q^{37} - 7 q^{38} - 12 q^{39} + 17 q^{40} - 23 q^{41} + 11 q^{42} + 35 q^{43} - 8 q^{44} - 6 q^{45} - q^{46} + 11 q^{47} + 3 q^{48} + 27 q^{49} - 17 q^{50} - 16 q^{51} + 14 q^{52} - 3 q^{53} - 15 q^{54} + 8 q^{55} - 4 q^{56} + 9 q^{57} + 18 q^{58} - 6 q^{59} - 3 q^{60} + 6 q^{61} - 8 q^{62} + 10 q^{63} + 17 q^{64} - 14 q^{65} - 3 q^{66} + 55 q^{67} - 8 q^{68} - q^{69} + 4 q^{70} + 5 q^{71} - 6 q^{72} + 62 q^{73} - 49 q^{74} + 3 q^{75} + 7 q^{76} + 2 q^{77} + 12 q^{78} - 3 q^{79} - 17 q^{80} - 15 q^{81} + 23 q^{82} + 7 q^{83} - 11 q^{84} + 8 q^{85} - 35 q^{86} + 10 q^{87} + 8 q^{88} - 18 q^{89} + 6 q^{90} + 18 q^{91} + q^{92} + 33 q^{93} - 11 q^{94} - 7 q^{95} - 3 q^{96} + 63 q^{97} - 27 q^{98} - 11 q^{99}+O(q^{100}) \) 17 * q - 17 * q^2 + 3 * q^3 + 17 * q^4 - 17 * q^5 - 3 * q^6 + 4 * q^7 - 17 * q^8 + 6 * q^9 + 17 * q^10 - 8 * q^11 + 3 * q^12 + 14 * q^13 - 4 * q^14 - 3 * q^15 + 17 * q^16 - 8 * q^17 - 6 * q^18 + 7 * q^19 - 17 * q^20 - 11 * q^21 + 8 * q^22 + q^23 - 3 * q^24 + 17 * q^25 - 14 * q^26 + 15 * q^27 + 4 * q^28 - 18 * q^29 + 3 * q^30 + 8 * q^31 - 17 * q^32 + 3 * q^33 + 8 * q^34 - 4 * q^35 + 6 * q^36 + 49 * q^37 - 7 * q^38 - 12 * q^39 + 17 * q^40 - 23 * q^41 + 11 * q^42 + 35 * q^43 - 8 * q^44 - 6 * q^45 - q^46 + 11 * q^47 + 3 * q^48 + 27 * q^49 - 17 * q^50 - 16 * q^51 + 14 * q^52 - 3 * q^53 - 15 * q^54 + 8 * q^55 - 4 * q^56 + 9 * q^57 + 18 * q^58 - 6 * q^59 - 3 * q^60 + 6 * q^61 - 8 * q^62 + 10 * q^63 + 17 * q^64 - 14 * q^65 - 3 * q^66 + 55 * q^67 - 8 * q^68 - q^69 + 4 * q^70 + 5 * q^71 - 6 * q^72 + 62 * q^73 - 49 * q^74 + 3 * q^75 + 7 * q^76 + 2 * q^77 + 12 * q^78 - 3 * q^79 - 17 * q^80 - 15 * q^81 + 23 * q^82 + 7 * q^83 - 11 * q^84 + 8 * q^85 - 35 * q^86 + 10 * q^87 + 8 * q^88 - 18 * q^89 + 6 * q^90 + 18 * q^91 + q^92 + 33 * q^93 - 11 * q^94 - 7 * q^95 - 3 * q^96 + 63 * q^97 - 27 * q^98 - 11 * q^99

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