LMFDB - Embedded newform 4029.2.a.e.1.8

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [4029,2,Mod(1,4029)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(4029, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([0, 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("4029.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 4029 = 3 \cdot 17 \cdot 79 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	4029.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:	$32.1717269744$
Analytic rank:	$1$
Dimension:	$18$
Coefficient field:	$\mathbb{Q}[x]/(x^{18} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{18} - 6 x^{17} - 10 x^{16} + 120 x^{15} - 56 x^{14} - 921 x^{13} + 1181 x^{12} + 3316 x^{11} + \cdots + 138 $ x^18 - 6x^17 - 10x^16 + 120x^15 - 56x^14 - 921x^13 + 1181x^12 + 3316x^11 - 6280x^10 - 5249x^9 + 15005x^8 + 1809x^7 - 16711x^6 + 2434x^5 + 8758x^4 - 1858x^3 - 1942x^2 + 318*x + 138
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			1.8
Root			$1.44853$ of defining polynomial
Character	$\chi$	$=$	4029.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.44853 q^{2} +1.00000 q^{3} +0.0982249 q^{4} +1.34868 q^{5} -1.44853 q^{6} -1.91511 q^{7} +2.75477 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q-1.44853 q^{2} +1.00000 q^{3} +0.0982249 q^{4} +1.34868 q^{5} -1.44853 q^{6} -1.91511 q^{7} +2.75477 q^{8} +1.00000 q^{9} -1.95360 q^{10} +0.405704 q^{11} +0.0982249 q^{12} -2.52652 q^{13} +2.77408 q^{14} +1.34868 q^{15} -4.18680 q^{16} +1.00000 q^{17} -1.44853 q^{18} -2.25891 q^{19} +0.132474 q^{20} -1.91511 q^{21} -0.587672 q^{22} -0.136278 q^{23} +2.75477 q^{24} -3.18106 q^{25} +3.65973 q^{26} +1.00000 q^{27} -0.188111 q^{28} +9.63258 q^{29} -1.95360 q^{30} -0.651619 q^{31} +0.555149 q^{32} +0.405704 q^{33} -1.44853 q^{34} -2.58287 q^{35} +0.0982249 q^{36} -0.831880 q^{37} +3.27208 q^{38} -2.52652 q^{39} +3.71531 q^{40} -1.26330 q^{41} +2.77408 q^{42} -5.63796 q^{43} +0.0398502 q^{44} +1.34868 q^{45} +0.197402 q^{46} +0.751697 q^{47} -4.18680 q^{48} -3.33236 q^{49} +4.60784 q^{50} +1.00000 q^{51} -0.248167 q^{52} -3.44340 q^{53} -1.44853 q^{54} +0.547166 q^{55} -5.27568 q^{56} -2.25891 q^{57} -13.9530 q^{58} +0.782394 q^{59} +0.132474 q^{60} -2.58361 q^{61} +0.943886 q^{62} -1.91511 q^{63} +7.56946 q^{64} -3.40747 q^{65} -0.587672 q^{66} +4.16645 q^{67} +0.0982249 q^{68} -0.136278 q^{69} +3.74136 q^{70} -7.82487 q^{71} +2.75477 q^{72} -1.82703 q^{73} +1.20500 q^{74} -3.18106 q^{75} -0.221881 q^{76} -0.776967 q^{77} +3.65973 q^{78} -1.00000 q^{79} -5.64667 q^{80} +1.00000 q^{81} +1.82992 q^{82} -10.0307 q^{83} -0.188111 q^{84} +1.34868 q^{85} +8.16673 q^{86} +9.63258 q^{87} +1.11762 q^{88} -17.9451 q^{89} -1.95360 q^{90} +4.83856 q^{91} -0.0133859 q^{92} -0.651619 q^{93} -1.08885 q^{94} -3.04655 q^{95} +0.555149 q^{96} +0.769383 q^{97} +4.82701 q^{98} +0.405704 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 18 q - 6 q^{2} + 18 q^{3} + 20 q^{4} - 5 q^{5} - 6 q^{6} - 13 q^{7} - 12 q^{8} + 18 q^{9}+O(q^{10}) $ 18 * q - 6 * q^2 + 18 * q^3 + 20 * q^4 - 5 * q^5 - 6 * q^6 - 13 * q^7 - 12 * q^8 + 18 * q^9	\( 18 q - 6 q^{2} + 18 q^{3} + 20 q^{4} - 5 q^{5} - 6 q^{6} - 13 q^{7} - 12 q^{8} + 18 q^{9} - 15 q^{10} - 27 q^{11} + 20 q^{12} - 4 q^{13} - 5 q^{14} - 5 q^{15} + 16 q^{16} + 18 q^{17} - 6 q^{18} - 30 q^{19} - 16 q^{20} - 13 q^{21} + 13 q^{22} - 21 q^{23} - 12 q^{24} + 13 q^{25} - 20 q^{26} + 18 q^{27} - 33 q^{28} - 47 q^{29} - 15 q^{30} - 18 q^{31} - 45 q^{32} - 27 q^{33} - 6 q^{34} - 17 q^{35} + 20 q^{36} + q^{37} + 5 q^{38} - 4 q^{39} - 12 q^{40} - 18 q^{41} - 5 q^{42} - 39 q^{43} - 34 q^{44} - 5 q^{45} - 7 q^{46} + 16 q^{48} + 15 q^{49} - 23 q^{50} + 18 q^{51} + 5 q^{52} - 9 q^{53} - 6 q^{54} + q^{55} - 24 q^{56} - 30 q^{57} + 41 q^{58} - 42 q^{59} - 16 q^{60} - 43 q^{61} - 54 q^{62} - 13 q^{63} + 22 q^{64} - 25 q^{65} + 13 q^{66} + 20 q^{68} - 21 q^{69} + 17 q^{70} + 9 q^{71} - 12 q^{72} + 19 q^{73} - 30 q^{74} + 13 q^{75} - 17 q^{76} - 14 q^{77} - 20 q^{78} - 18 q^{79} + 36 q^{80} + 18 q^{81} - 3 q^{82} - 61 q^{83} - 33 q^{84} - 5 q^{85} - 24 q^{86} - 47 q^{87} - 25 q^{88} + 10 q^{89} - 15 q^{90} - 52 q^{91} - 74 q^{92} - 18 q^{93} + 31 q^{94} - 37 q^{95} - 45 q^{96} - 9 q^{97} + 27 q^{98} - 27 q^{99}+O(q^{100}) \) 18 * q - 6 * q^2 + 18 * q^3 + 20 * q^4 - 5 * q^5 - 6 * q^6 - 13 * q^7 - 12 * q^8 + 18 * q^9 - 15 * q^10 - 27 * q^11 + 20 * q^12 - 4 * q^13 - 5 * q^14 - 5 * q^15 + 16 * q^16 + 18 * q^17 - 6 * q^18 - 30 * q^19 - 16 * q^20 - 13 * q^21 + 13 * q^22 - 21 * q^23 - 12 * q^24 + 13 * q^25 - 20 * q^26 + 18 * q^27 - 33 * q^28 - 47 * q^29 - 15 * q^30 - 18 * q^31 - 45 * q^32 - 27 * q^33 - 6 * q^34 - 17 * q^35 + 20 * q^36 + q^37 + 5 * q^38 - 4 * q^39 - 12 * q^40 - 18 * q^41 - 5 * q^42 - 39 * q^43 - 34 * q^44 - 5 * q^45 - 7 * q^46 + 16 * q^48 + 15 * q^49 - 23 * q^50 + 18 * q^51 + 5 * q^52 - 9 * q^53 - 6 * q^54 + q^55 - 24 * q^56 - 30 * q^57 + 41 * q^58 - 42 * q^59 - 16 * q^60 - 43 * q^61 - 54 * q^62 - 13 * q^63 + 22 * q^64 - 25 * q^65 + 13 * q^66 + 20 * q^68 - 21 * q^69 + 17 * q^70 + 9 * q^71 - 12 * q^72 + 19 * q^73 - 30 * q^74 + 13 * q^75 - 17 * q^76 - 14 * q^77 - 20 * q^78 - 18 * q^79 + 36 * q^80 + 18 * q^81 - 3 * q^82 - 61 * q^83 - 33 * q^84 - 5 * q^85 - 24 * q^86 - 47 * q^87 - 25 * q^88 + 10 * q^89 - 15 * q^90 - 52 * q^91 - 74 * q^92 - 18 * q^93 + 31 * q^94 - 37 * q^95 - 45 * q^96 - 9 * q^97 + 27 * q^98 - 27 * 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 $

$2$	−1.44853	−1.02426	−0.512131	−	0.858907i	$-0.671144\pi$
$2$	−1.44853	−1.02426	−0.512131	+	0.858907i	$0.671144\pi$
$3$	1.00000	0.577350
$3$	1.00000	0.577350
$4$	0.0982249	0.0491124
$5$	1.34868	0.603149	0.301575	−	0.953443i	$-0.402488\pi$
$5$	1.34868	0.603149	0.301575	+	0.953443i	$0.402488\pi$
$6$	−1.44853	−0.591358
$7$	−1.91511	−0.723843	−0.361921	−	0.932209i	$-0.617879\pi$
$7$	−1.91511	−0.723843	−0.361921	+	0.932209i	$0.617879\pi$
$8$	2.75477	0.973958
$9$	1.00000	0.333333
$10$	−1.95360	−0.617783
$11$	0.405704	0.122324	0.0611622	−	0.998128i	$-0.480519\pi$
$11$	0.405704	0.122324	0.0611622	+	0.998128i	$0.480519\pi$
$12$	0.0982249	0.0283551
$13$	−2.52652	−0.700731	−0.350365	−	0.936613i	$-0.613943\pi$
$13$	−2.52652	−0.700731	−0.350365	+	0.936613i	$0.613943\pi$
$14$	2.77408	0.741405
$15$	1.34868	0.348228
$16$	−4.18680	−1.04670
$17$	1.00000	0.242536
$17$	1.00000	0.242536
$18$	−1.44853	−0.341421
$19$	−2.25891	−0.518228	−0.259114	−	0.965847i	$-0.583431\pi$
$19$	−2.25891	−0.518228	−0.259114	+	0.965847i	$0.583431\pi$
$20$	0.132474	0.0296221
$21$	−1.91511	−0.417911
$22$	−0.587672	−0.125292
$23$	−0.136278	−0.0284160	−0.0142080	−	0.999899i	$-0.504523\pi$
$23$	−0.136278	−0.0284160	−0.0142080	+	0.999899i	$0.504523\pi$
$24$	2.75477	0.562315
$25$	−3.18106	−0.636211
$26$	3.65973	0.717732
$27$	1.00000	0.192450
$28$	−0.188111	−0.0355497
$29$	9.63258	1.78873	0.894363	−	0.447343i	$-0.147630\pi$
$29$	9.63258	1.78873	0.894363	+	0.447343i	$0.147630\pi$
$30$	−1.95360	−0.356677
$31$	−0.651619	−0.117034	−0.0585171	−	0.998286i	$-0.518637\pi$
$31$	−0.651619	−0.117034	−0.0585171	+	0.998286i	$0.518637\pi$
$32$	0.555149	0.0981375
$33$	0.405704	0.0706240
$34$	−1.44853	−0.248420
$35$	−2.58287	−0.436585
$36$	0.0982249	0.0163708
$37$	−0.831880	−0.136760	−0.0683802	−	0.997659i	$-0.521783\pi$
$37$	−0.831880	−0.136760	−0.0683802	+	0.997659i	$0.521783\pi$
$38$	3.27208	0.530802
$39$	−2.52652	−0.404567
$40$	3.71531	0.587442
$41$	−1.26330	−0.197295	−0.0986473	−	0.995122i	$-0.531452\pi$
$41$	−1.26330	−0.197295	−0.0986473	+	0.995122i	$0.531452\pi$
$42$	2.77408	0.428050
$43$	−5.63796	−0.859781	−0.429890	−	0.902881i	$-0.641448\pi$
$43$	−5.63796	−0.859781	−0.429890	+	0.902881i	$0.641448\pi$
$44$	0.0398502	0.00600765
$45$	1.34868	0.201050
$46$	0.197402	0.0291054
$47$	0.751697	0.109646	0.0548232	−	0.998496i	$-0.482540\pi$
$47$	0.751697	0.109646	0.0548232	+	0.998496i	$0.482540\pi$
$48$	−4.18680	−0.604313
$49$	−3.33236	−0.476052
$50$	4.60784	0.651647
$51$	1.00000	0.140028
$52$	−0.248167	−0.0344146
$53$	−3.44340	−0.472987	−0.236493	−	0.971633i	$-0.575998\pi$
$53$	−3.44340	−0.472987	−0.236493	+	0.971633i	$0.575998\pi$
$54$	−1.44853	−0.197119
$55$	0.547166	0.0737798
$56$	−5.27568	−0.704992
$57$	−2.25891	−0.299199
$58$	−13.9530	−1.83212
$59$	0.782394	0.101859	0.0509295	−	0.998702i	$-0.483782\pi$
$59$	0.782394	0.101859	0.0509295	+	0.998702i	$0.483782\pi$
$60$	0.132474	0.0171023
$61$	−2.58361	−0.330798	−0.165399	−	0.986227i	$-0.552891\pi$
$61$	−2.58361	−0.330798	−0.165399	+	0.986227i	$0.552891\pi$
$62$	0.943886	0.119874
$63$	−1.91511	−0.241281
$64$	7.56946	0.946182
$65$	−3.40747	−0.422645
$66$	−0.587672	−0.0723375
$67$	4.16645	0.509013	0.254506	−	0.967071i	$-0.418087\pi$
$67$	4.16645	0.509013	0.254506	+	0.967071i	$0.418087\pi$
$68$	0.0982249	0.0119115
$69$	−0.136278	−0.0164060
$70$	3.74136	0.447177
$71$	−7.82487	−0.928641	−0.464321	−	0.885667i	$-0.653701\pi$
$71$	−7.82487	−0.928641	−0.464321	+	0.885667i	$0.653701\pi$
$72$	2.75477	0.324653
$73$	−1.82703	−0.213838	−0.106919	−	0.994268i	$-0.534099\pi$
$73$	−1.82703	−0.213838	−0.106919	+	0.994268i	$0.534099\pi$
$74$	1.20500	0.140078
$75$	−3.18106	−0.367317
$76$	−0.221881	−0.0254515
$77$	−0.776967	−0.0885436
$78$	3.65973	0.414383
$79$	−1.00000	−0.112509
$79$	−1.00000	−0.112509
$80$	−5.64667	−0.631316
$81$	1.00000	0.111111
$82$	1.82992	0.202081
$83$	−10.0307	−1.10101	−0.550504	−	0.834832i	$-0.685565\pi$
$83$	−10.0307	−1.10101	−0.550504	+	0.834832i	$0.685565\pi$
$84$	−0.188111	−0.0205246
$85$	1.34868	0.146285
$86$	8.16673	0.880641
$87$	9.63258	1.03272
$88$	1.11762	0.119139
$89$	−17.9451	−1.90217	−0.951087	−	0.308923i	$-0.900032\pi$
$89$	−17.9451	−1.90217	−0.951087	+	0.308923i	$0.900032\pi$
$90$	−1.95360	−0.205928
$91$	4.83856	0.507219
$92$	−0.0133859	−0.00139558
$93$	−0.651619	−0.0675697
$94$	−1.08885	−0.112307
$95$	−3.04655	−0.312569
$96$	0.555149	0.0566597
$97$	0.769383	0.0781190	0.0390595	−	0.999237i	$-0.487564\pi$
$97$	0.769383	0.0781190	0.0390595	+	0.999237i	$0.487564\pi$
$98$	4.82701	0.487602
$99$	0.405704	0.0407748
$100$	−0.312459	−0.0312459
$101$	−6.66083	−0.662777	−0.331389	−	0.943494i	$-0.607517\pi$
$101$	−6.66083	−0.662777	−0.331389	+	0.943494i	$0.607517\pi$
$102$	−1.44853	−0.143425
$103$	2.36257	0.232791	0.116395	−	0.993203i	$-0.462866\pi$
$103$	2.36257	0.232791	0.116395	+	0.993203i	$0.462866\pi$
$104$	−6.95998	−0.682482
$105$	−2.58287	−0.252063
$106$	4.98784	0.484462
$107$	14.0176	1.35513	0.677565	−	0.735463i	$-0.263035\pi$
$107$	14.0176	1.35513	0.677565	+	0.735463i	$0.263035\pi$
$108$	0.0982249	0.00945169
$109$	12.6333	1.21005	0.605026	−	0.796206i	$-0.293163\pi$
$109$	12.6333	1.21005	0.605026	+	0.796206i	$0.293163\pi$
$110$	−0.792583	−0.0755699
$111$	−0.831880	−0.0789586
$112$	8.01818	0.757647
$113$	13.5991	1.27929	0.639646	−	0.768669i	$-0.279081\pi$
$113$	13.5991	1.27929	0.639646	+	0.768669i	$0.279081\pi$
$114$	3.27208	0.306458
$115$	−0.183796	−0.0171391
$116$	0.946159	0.0878487
$117$	−2.52652	−0.233577
$118$	−1.13332	−0.104330
$119$	−1.91511	−0.175558
$120$	3.71531	0.339160
$121$	−10.8354	−0.985037
$122$	3.74243	0.338824
$123$	−1.26330	−0.113908
$124$	−0.0640052	−0.00574783
$125$	−11.0336	−0.986879
$126$	2.77408	0.247135
$127$	−12.4223	−1.10230	−0.551151	−	0.834405i	$-0.685811\pi$
$127$	−12.4223	−1.10230	−0.551151	+	0.834405i	$0.685811\pi$
$128$	−12.0748	−1.06728
$129$	−5.63796	−0.496395
$130$	4.93581	0.432899
$131$	−2.85917	−0.249807	−0.124903	−	0.992169i	$-0.539862\pi$
$131$	−2.85917	−0.249807	−0.124903	+	0.992169i	$0.539862\pi$
$132$	0.0398502	0.00346852
$133$	4.32605	0.375116
$134$	−6.03521	−0.521363
$135$	1.34868	0.116076
$136$	2.75477	0.236219
$137$	16.2463	1.38801	0.694006	−	0.719969i	$-0.255844\pi$
$137$	16.2463	1.38801	0.694006	+	0.719969i	$0.255844\pi$
$138$	0.197402	0.0168040
$139$	−7.17092	−0.608230	−0.304115	−	0.952635i	$-0.598361\pi$
$139$	−7.17092	−0.608230	−0.304115	+	0.952635i	$0.598361\pi$
$140$	−0.253702	−0.0214418
$141$	0.751697	0.0633043
$142$	11.3345	0.951172
$143$	−1.02502	−0.0857164
$144$	−4.18680	−0.348900
$145$	12.9913	1.07887
$146$	2.64650	0.219026
$147$	−3.33236	−0.274849
$148$	−0.0817114	−0.00671663
$149$	20.0766	1.64474	0.822368	−	0.568956i	$-0.192653\pi$
$149$	20.0766	1.64474	0.822368	+	0.568956i	$0.192653\pi$
$150$	4.60784	0.376229
$151$	−15.1473	−1.23267	−0.616334	−	0.787485i	$-0.711383\pi$
$151$	−15.1473	−1.23267	−0.616334	+	0.787485i	$0.711383\pi$
$152$	−6.22276	−0.504733
$153$	1.00000	0.0808452
$154$	1.12546	0.0906918
$155$	−0.878827	−0.0705891
$156$	−0.248167	−0.0198693
$157$	−4.38337	−0.349831	−0.174915	−	0.984583i	$-0.555965\pi$
$157$	−4.38337	−0.349831	−0.174915	+	0.984583i	$0.555965\pi$
$158$	1.44853	0.115238
$159$	−3.44340	−0.273079
$160$	0.748720	0.0591915
$161$	0.260987	0.0205687
$162$	−1.44853	−0.113807
$163$	8.33338	0.652721	0.326360	−	0.945245i	$-0.394178\pi$
$163$	8.33338	0.652721	0.326360	+	0.945245i	$0.394178\pi$
$164$	−0.124088	−0.00968962
$165$	0.547166	0.0425968
$166$	14.5297	1.12772
$167$	−20.3974	−1.57840	−0.789199	−	0.614138i	$-0.789504\pi$
$167$	−20.3974	−1.57840	−0.789199	+	0.614138i	$0.789504\pi$
$168$	−5.27568	−0.407028
$169$	−6.61670	−0.508977
$170$	−1.95360	−0.149834
$171$	−2.25891	−0.172743
$172$	−0.553788	−0.0422259
$173$	−15.3119	−1.16414	−0.582070	−	0.813138i	$-0.697757\pi$
$173$	−15.3119	−1.16414	−0.582070	+	0.813138i	$0.697757\pi$
$174$	−13.9530	−1.05778
$175$	6.09207	0.460517
$176$	−1.69860	−0.128037
$177$	0.782394	0.0588083
$178$	25.9939	1.94832
$179$	−22.1804	−1.65784	−0.828919	−	0.559368i	$-0.811044\pi$
$179$	−22.1804	−1.65784	−0.828919	+	0.559368i	$0.811044\pi$
$180$	0.132474	0.00987404
$181$	−17.3732	−1.29134	−0.645670	−	0.763617i	$-0.723422\pi$
$181$	−17.3732	−1.29134	−0.645670	+	0.763617i	$0.723422\pi$
$182$	−7.00877	−0.519525
$183$	−2.58361	−0.190986
$184$	−0.375415	−0.0276760
$185$	−1.12194	−0.0824868
$186$	0.943886	0.0692091
$187$	0.405704	0.0296680
$188$	0.0738354	0.00538500
$189$	−1.91511	−0.139304
$190$	4.41300	0.320153
$191$	8.82296	0.638407	0.319203	−	0.947686i	$-0.396585\pi$
$191$	8.82296	0.638407	0.319203	+	0.947686i	$0.396585\pi$
$192$	7.56946	0.546278
$193$	3.52116	0.253458	0.126729	−	0.991937i	$-0.459552\pi$
$193$	3.52116	0.253458	0.126729	+	0.991937i	$0.459552\pi$
$194$	−1.11447	−0.0800144
$195$	−3.40747	−0.244014
$196$	−0.327321	−0.0233801
$197$	11.6980	0.833449	0.416725	−	0.909033i	$-0.363178\pi$
$197$	11.6980	0.833449	0.416725	+	0.909033i	$0.363178\pi$
$198$	−0.587672	−0.0417641
$199$	−7.72016	−0.547268	−0.273634	−	0.961834i	$-0.588226\pi$
$199$	−7.72016	−0.547268	−0.273634	+	0.961834i	$0.588226\pi$
$200$	−8.76307	−0.619643
$201$	4.16645	0.293879
$202$	9.64837	0.678857
$203$	−18.4474	−1.29476
$204$	0.0982249	0.00687712
$205$	−1.70379	−0.118998
$206$	−3.42224	−0.238439
$207$	−0.136278	−0.00947199
$208$	10.5780	0.733455
$209$	−0.916447	−0.0633920
$210$	3.74136	0.258178
$211$	18.8135	1.29518	0.647588	−	0.761991i	$-0.275778\pi$
$211$	18.8135	1.29518	0.647588	+	0.761991i	$0.275778\pi$
$212$	−0.338227	−0.0232295
$213$	−7.82487	−0.536151
$214$	−20.3048	−1.38801
$215$	−7.60382	−0.518576
$216$	2.75477	0.187438
$217$	1.24792	0.0847143
$218$	−18.2997	−1.23941
$219$	−1.82703	−0.123459
$220$	0.0537453	0.00362351
$221$	−2.52652	−0.169952
$222$	1.20500	0.0808743
$223$	−10.5494	−0.706437	−0.353218	−	0.935541i	$-0.614913\pi$
$223$	−10.5494	−0.706437	−0.353218	+	0.935541i	$0.614913\pi$
$224$	−1.06317	−0.0710361
$225$	−3.18106	−0.212070
$226$	−19.6986	−1.31033
$227$	−2.90062	−0.192521	−0.0962604	−	0.995356i	$-0.530688\pi$
$227$	−2.90062	−0.192521	−0.0962604	+	0.995356i	$0.530688\pi$
$228$	−0.221881	−0.0146944
$229$	10.9191	0.721552	0.360776	−	0.932653i	$-0.382512\pi$
$229$	10.9191	0.721552	0.360776	+	0.932653i	$0.382512\pi$
$230$	0.266233	0.0175549
$231$	−0.776967	−0.0511207
$232$	26.5355	1.74214
$233$	7.99164	0.523550	0.261775	−	0.965129i	$-0.415692\pi$
$233$	7.99164	0.523550	0.261775	+	0.965129i	$0.415692\pi$
$234$	3.65973	0.239244
$235$	1.01380	0.0661331
$236$	0.0768506	0.00500255
$237$	−1.00000	−0.0649570
$238$	2.77408	0.179817
$239$	−17.2202	−1.11388	−0.556940	−	0.830553i	$-0.688024\pi$
$239$	−17.2202	−1.11388	−0.556940	+	0.830553i	$0.688024\pi$
$240$	−5.64667	−0.364491
$241$	18.0128	1.16030	0.580152	−	0.814508i	$-0.302993\pi$
$241$	18.0128	1.16030	0.580152	+	0.814508i	$0.302993\pi$
$242$	15.6954	1.00894
$243$	1.00000	0.0641500
$244$	−0.253775	−0.0162463
$245$	−4.49430	−0.287130
$246$	1.82992	0.116672
$247$	5.70717	0.363139
$248$	−1.79506	−0.113986
$249$	−10.0307	−0.635668
$250$	15.9825	1.01082
$251$	7.28210	0.459642	0.229821	−	0.973233i	$-0.426186\pi$
$251$	7.28210	0.459642	0.229821	+	0.973233i	$0.426186\pi$
$252$	−0.188111	−0.0118499
$253$	−0.0552886	−0.00347597
$254$	17.9940	1.12905
$255$	1.34868	0.0844578
$256$	2.35180	0.146988
$257$	−26.4171	−1.64785	−0.823927	−	0.566695i	$-0.808222\pi$
$257$	−26.4171	−1.64785	−0.823927	+	0.566695i	$0.808222\pi$
$258$	8.16673	0.508438
$259$	1.59314	0.0989930
$260$	−0.334699	−0.0207571
$261$	9.63258	0.596242
$262$	4.14158	0.255867
$263$	−17.3834	−1.07191	−0.535954	−	0.844247i	$-0.680048\pi$
$263$	−17.3834	−1.07191	−0.535954	+	0.844247i	$0.680048\pi$
$264$	1.11762	0.0687848
$265$	−4.64405	−0.285282
$266$	−6.26639	−0.384217
$267$	−17.9451	−1.09822
$268$	0.409249	0.0249989
$269$	−4.16921	−0.254201	−0.127100	−	0.991890i	$-0.540567\pi$
$269$	−4.16921	−0.254201	−0.127100	+	0.991890i	$0.540567\pi$
$270$	−1.95360	−0.118892
$271$	−5.86774	−0.356440	−0.178220	−	0.983991i	$-0.557034\pi$
$271$	−5.86774	−0.356440	−0.178220	+	0.983991i	$0.557034\pi$
$272$	−4.18680	−0.253862
$273$	4.83856	0.292843
$274$	−23.5331	−1.42169
$275$	−1.29057	−0.0778241
$276$	−0.0133859	−0.000805737 0
$277$	−9.07319	−0.545155	−0.272578	−	0.962134i	$-0.587876\pi$
$277$	−9.07319	−0.545155	−0.272578	+	0.962134i	$0.587876\pi$
$278$	10.3873	0.622987
$279$	−0.651619	−0.0390114
$280$	−7.11522	−0.425215
$281$	−28.7023	−1.71224	−0.856118	−	0.516780i	$-0.827130\pi$
$281$	−28.7023	−1.71224	−0.856118	+	0.516780i	$0.827130\pi$
$282$	−1.08885	−0.0648402
$283$	10.8851	0.647053	0.323527	−	0.946219i	$-0.395131\pi$
$283$	10.8851	0.647053	0.323527	+	0.946219i	$0.395131\pi$
$284$	−0.768597	−0.0456078
$285$	−3.04655	−0.180462
$286$	1.48477	0.0877961
$287$	2.41936	0.142810
$288$	0.555149	0.0327125
$289$	1.00000	0.0588235
$290$	−18.8182	−1.10504
$291$	0.769383	0.0451021
$292$	−0.179460	−0.0105021
$293$	1.98532	0.115983	0.0579917	−	0.998317i	$-0.481530\pi$
$293$	1.98532	0.115983	0.0579917	+	0.998317i	$0.481530\pi$
$294$	4.82701	0.281517
$295$	1.05520	0.0614362
$296$	−2.29164	−0.133199
$297$	0.405704	0.0235413
$298$	−29.0814	−1.68464
$299$	0.344310	0.0199119
$300$	−0.312459	−0.0180398
$301$	10.7973	0.622346
$302$	21.9412	1.26257
$303$	−6.66083	−0.382655
$304$	9.45759	0.542430
$305$	−3.48447	−0.199520
$306$	−1.44853	−0.0828067
$307$	−7.86614	−0.448944	−0.224472	−	0.974480i	$-0.572066\pi$
$307$	−7.86614	−0.448944	−0.224472	+	0.974480i	$0.572066\pi$
$308$	−0.0763175	−0.00434859
$309$	2.36257	0.134402
$310$	1.27300	0.0723017
$311$	31.9062	1.80924	0.904619	−	0.426222i	$-0.140156\pi$
$311$	31.9062	1.80924	0.904619	+	0.426222i	$0.140156\pi$
$312$	−6.95998	−0.394031
$313$	23.6844	1.33872	0.669361	−	0.742938i	$-0.266568\pi$
$313$	23.6844	1.33872	0.669361	+	0.742938i	$0.266568\pi$
$314$	6.34942	0.358318
$315$	−2.58287	−0.145528
$316$	−0.0982249	−0.00552558
$317$	−16.9736	−0.953334	−0.476667	−	0.879084i	$-0.658155\pi$
$317$	−16.9736	−0.953334	−0.476667	+	0.879084i	$0.658155\pi$
$318$	4.98784	0.279704
$319$	3.90798	0.218805
$320$	10.2088	0.570689
$321$	14.0176	0.782385
$322$	−0.378047	−0.0210677
$323$	−2.25891	−0.125689
$324$	0.0982249	0.00545694
$325$	8.03700	0.445813
$326$	−12.0711	−0.668557
$327$	12.6333	0.698623
$328$	−3.48010	−0.192157
$329$	−1.43958	−0.0793667
$330$	−0.792583	−0.0436303
$331$	8.99725	0.494533	0.247267	−	0.968947i	$-0.420468\pi$
$331$	8.99725	0.494533	0.247267	+	0.968947i	$0.420468\pi$
$332$	−0.985261	−0.0540732
$333$	−0.831880	−0.0455868
$334$	29.5461	1.61669
$335$	5.61922	0.307011
$336$	8.01818	0.437427
$337$	2.64942	0.144323	0.0721616	−	0.997393i	$-0.477010\pi$
$337$	2.64942	0.144323	0.0721616	+	0.997393i	$0.477010\pi$
$338$	9.58445	0.521325
$339$	13.5991	0.738600
$340$	0.132474	0.00718442
$341$	−0.264364	−0.0143161
$342$	3.27208	0.176934
$343$	19.7876	1.06843
$344$	−15.5313	−0.837390
$345$	−0.183796	−0.00989524
$346$	22.1796	1.19238
$347$	−9.42943	−0.506198	−0.253099	−	0.967440i	$-0.581450\pi$
$347$	−9.42943	−0.506198	−0.253099	+	0.967440i	$0.581450\pi$
$348$	0.946159	0.0507195
$349$	−18.4375	−0.986938	−0.493469	−	0.869763i	$-0.664271\pi$
$349$	−18.4375	−0.986938	−0.493469	+	0.869763i	$0.664271\pi$
$350$	−8.82451	−0.471690
$351$	−2.52652	−0.134856
$352$	0.225226	0.0120046
$353$	−20.9625	−1.11572	−0.557862	−	0.829934i	$-0.688378\pi$
$353$	−20.9625	−1.11572	−0.557862	+	0.829934i	$0.688378\pi$
$354$	−1.13332	−0.0602351
$355$	−10.5533	−0.560109
$356$	−1.76265	−0.0934204
$357$	−1.91511	−0.101358
$358$	32.1288	1.69806
$359$	−31.2321	−1.64837	−0.824185	−	0.566321i	$-0.808366\pi$
$359$	−31.2321	−1.64837	−0.824185	+	0.566321i	$0.808366\pi$
$360$	3.71531	0.195814
$361$	−13.8973	−0.731439
$362$	25.1655	1.32267
$363$	−10.8354	−0.568711
$364$	0.475267	0.0249108
$365$	−2.46408	−0.128976
$366$	3.74243	0.195620
$367$	−20.9974	−1.09606	−0.548028	−	0.836460i	$-0.684621\pi$
$367$	−20.9974	−1.09606	−0.548028	+	0.836460i	$0.684621\pi$
$368$	0.570570	0.0297430
$369$	−1.26330	−0.0657649
$370$	1.62516	0.0844881
$371$	6.59447	0.342368
$372$	−0.0640052	−0.00331851
$373$	−1.68138	−0.0870584	−0.0435292	−	0.999052i	$-0.513860\pi$
$373$	−1.68138	−0.0870584	−0.0435292	+	0.999052i	$0.513860\pi$
$374$	−0.587672	−0.0303878
$375$	−11.0336	−0.569775
$376$	2.07075	0.106791
$377$	−24.3369	−1.25341
$378$	2.77408	0.142683
$379$	6.02638	0.309555	0.154777	−	0.987949i	$-0.450534\pi$
$379$	6.02638	0.309555	0.154777	+	0.987949i	$0.450534\pi$
$380$	−0.299247	−0.0153510
$381$	−12.4223	−0.636415
$382$	−12.7803	−0.653896
$383$	−19.1046	−0.976198	−0.488099	−	0.872788i	$-0.662310\pi$
$383$	−19.1046	−0.976198	−0.488099	+	0.872788i	$0.662310\pi$
$384$	−12.0748	−0.616192
$385$	−1.04788	−0.0534050
$386$	−5.10048	−0.259608
$387$	−5.63796	−0.286594
$388$	0.0755726	0.00383662
$389$	−1.98114	−0.100448	−0.0502240	−	0.998738i	$-0.515994\pi$
$389$	−1.98114	−0.100448	−0.0502240	+	0.998738i	$0.515994\pi$
$390$	4.93581	0.249934
$391$	−0.136278	−0.00689189
$392$	−9.17989	−0.463654
$393$	−2.85917	−0.144226
$394$	−16.9449	−0.853670
$395$	−1.34868	−0.0678596
$396$	0.0398502	0.00200255
$397$	−9.96113	−0.499935	−0.249967	−	0.968254i	$-0.580420\pi$
$397$	−9.96113	−0.499935	−0.249967	+	0.968254i	$0.580420\pi$
$398$	11.1828	0.560545
$399$	4.32605	0.216573
$400$	13.3185	0.665923
$401$	16.8059	0.839245	0.419622	−	0.907699i	$-0.362162\pi$
$401$	16.8059	0.839245	0.419622	+	0.907699i	$0.362162\pi$
$402$	−6.03521	−0.301009
$403$	1.64633	0.0820094
$404$	−0.654259	−0.0325506
$405$	1.34868	0.0670166
$406$	26.7216	1.32617
$407$	−0.337497	−0.0167291
$408$	2.75477	0.136381
$409$	6.33196	0.313095	0.156548	−	0.987670i	$-0.449964\pi$
$409$	6.33196	0.313095	0.156548	+	0.987670i	$0.449964\pi$
$410$	2.46799	0.121885
$411$	16.2463	0.801370
$412$	0.232063	0.0114329
$413$	−1.49837	−0.0737299
$414$	0.197402	0.00970180
$415$	−13.5282	−0.664072
$416$	−1.40260	−0.0687679
$417$	−7.17092	−0.351162
$418$	1.32750	0.0649300
$419$	−23.1647	−1.13167	−0.565834	−	0.824519i	$-0.691446\pi$
$419$	−23.1647	−1.13167	−0.565834	+	0.824519i	$0.691446\pi$
$420$	−0.253702	−0.0123794
$421$	7.56737	0.368811	0.184406	−	0.982850i	$-0.440964\pi$
$421$	7.56737	0.368811	0.184406	+	0.982850i	$0.440964\pi$
$422$	−27.2519	−1.32660
$423$	0.751697	0.0365488
$424$	−9.48576	−0.460669
$425$	−3.18106	−0.154304
$426$	11.3345	0.549159
$427$	4.94790	0.239446
$428$	1.37687	0.0665538
$429$	−1.02502	−0.0494884
$430$	11.0143	0.531158
$431$	6.56899	0.316417	0.158209	−	0.987406i	$-0.449428\pi$
$431$	6.56899	0.316417	0.158209	+	0.987406i	$0.449428\pi$
$432$	−4.18680	−0.201438
$433$	8.33993	0.400792	0.200396	−	0.979715i	$-0.435777\pi$
$433$	8.33993	0.400792	0.200396	+	0.979715i	$0.435777\pi$
$434$	−1.80764	−0.0867697
$435$	12.9913	0.622885
$436$	1.24091	0.0594286
$437$	0.307840	0.0147260
$438$	2.64650	0.126455
$439$	−39.5397	−1.88713	−0.943564	−	0.331190i	$-0.892550\pi$
$439$	−39.5397	−1.88713	−0.943564	+	0.331190i	$0.892550\pi$
$440$	1.50732	0.0718584
$441$	−3.33236	−0.158684
$442$	3.65973	0.174076
$443$	−5.01188	−0.238122	−0.119061	−	0.992887i	$-0.537988\pi$
$443$	−5.01188	−0.238122	−0.119061	+	0.992887i	$0.537988\pi$
$444$	−0.0817114	−0.00387785
$445$	−24.2022	−1.14729
$446$	15.2810	0.723576
$447$	20.0766	0.949588
$448$	−14.4963	−0.684887
$449$	−18.2191	−0.859814	−0.429907	−	0.902873i	$-0.641454\pi$
$449$	−18.2191	−0.859814	−0.429907	+	0.902873i	$0.641454\pi$
$450$	4.60784	0.217216
$451$	−0.512527	−0.0241339
$452$	1.33577	0.0628292
$453$	−15.1473	−0.711681
$454$	4.20162	0.197192
$455$	6.52568	0.305929
$456$	−6.22276	−0.291408
$457$	−16.4830	−0.771042	−0.385521	−	0.922699i	$-0.625978\pi$
$457$	−16.4830	−0.771042	−0.385521	+	0.922699i	$0.625978\pi$
$458$	−15.8165	−0.739058
$459$	1.00000	0.0466760
$460$	−0.0180533	−0.000841741 0
$461$	−5.68616	−0.264831	−0.132415	−	0.991194i	$-0.542273\pi$
$461$	−5.68616	−0.264831	−0.132415	+	0.991194i	$0.542273\pi$
$462$	1.12546	0.0523610
$463$	25.7603	1.19718	0.598591	−	0.801055i	$-0.295727\pi$
$463$	25.7603	1.19718	0.598591	+	0.801055i	$0.295727\pi$
$464$	−40.3297	−1.87226
$465$	−0.878827	−0.0407546
$466$	−11.5761	−0.536252
$467$	28.7030	1.32822	0.664108	−	0.747637i	$-0.268812\pi$
$467$	28.7030	1.32822	0.664108	+	0.747637i	$0.268812\pi$
$468$	−0.248167	−0.0114715
$469$	−7.97920	−0.368445
$470$	−1.46852	−0.0677376
$471$	−4.38337	−0.201975
$472$	2.15531	0.0992064
$473$	−2.28734	−0.105172
$474$	1.44853	0.0665330
$475$	7.18571	0.329703
$476$	−0.188111	−0.00862207
$477$	−3.44340	−0.157662
$478$	24.9438	1.14090
$479$	−31.5184	−1.44011	−0.720057	−	0.693915i	$-0.755884\pi$
$479$	−31.5184	−1.44011	−0.720057	+	0.693915i	$0.755884\pi$
$480$	0.748720	0.0341742
$481$	2.10176	0.0958321
$482$	−26.0920	−1.18846
$483$	0.260987	0.0118753
$484$	−1.06431	−0.0483776
$485$	1.03765	0.0471174
$486$	−1.44853	−0.0657064
$487$	32.2971	1.46352	0.731760	−	0.681562i	$-0.238699\pi$
$487$	32.2971	1.46352	0.731760	+	0.681562i	$0.238699\pi$
$488$	−7.11726	−0.322183
$489$	8.33338	0.376848
$490$	6.51010	0.294096
$491$	−25.2771	−1.14074	−0.570371	−	0.821387i	$-0.693200\pi$
$491$	−25.2771	−1.14074	−0.570371	+	0.821387i	$0.693200\pi$
$492$	−0.124088	−0.00559430
$493$	9.63258	0.433830
$494$	−8.26698	−0.371949
$495$	0.547166	0.0245933
$496$	2.72820	0.122500
$497$	14.9855	0.672190
$498$	14.5297	0.651090
$499$	−5.26990	−0.235913	−0.117957	−	0.993019i	$-0.537634\pi$
$499$	−5.26990	−0.235913	−0.117957	+	0.993019i	$0.537634\pi$
$500$	−1.08378	−0.0484681
$501$	−20.3974	−0.911288
$502$	−10.5483	−0.470794
$503$	−27.4414	−1.22355	−0.611776	−	0.791031i	$-0.709545\pi$
$503$	−27.4414	−1.22355	−0.611776	+	0.791031i	$0.709545\pi$
$504$	−5.27568	−0.234997
$505$	−8.98334	−0.399753
$506$	0.0800870	0.00356030
$507$	−6.61670	−0.293858
$508$	−1.22018	−0.0541368
$509$	19.3599	0.858114	0.429057	−	0.903277i	$-0.358846\pi$
$509$	19.3599	0.858114	0.429057	+	0.903277i	$0.358846\pi$
$510$	−1.95360	−0.0865069
$511$	3.49896	0.154785
$512$	20.7430	0.916722
$513$	−2.25891	−0.0997331
$514$	38.2659	1.68784
$515$	3.18635	0.140408
$516$	−0.553788	−0.0243792
$517$	0.304967	0.0134124
$518$	−2.30770	−0.101395
$519$	−15.3119	−0.672117
$520$	−9.38680	−0.411638
$521$	16.1041	0.705534	0.352767	−	0.935711i	$-0.385241\pi$
$521$	16.1041	0.705534	0.352767	+	0.935711i	$0.385241\pi$
$522$	−13.9530	−0.610708
$523$	−34.8084	−1.52206	−0.761032	−	0.648714i	$-0.775307\pi$
$523$	−34.8084	−1.52206	−0.761032	+	0.648714i	$0.775307\pi$
$524$	−0.280841	−0.0122686
$525$	6.09207	0.265880
$526$	25.1803	1.09791
$527$	−0.651619	−0.0283850
$528$	−1.69860	−0.0739222
$529$	−22.9814	−0.999193
$530$	6.72702	0.292203
$531$	0.782394	0.0339530
$532$	0.424926	0.0184229
$533$	3.19176	0.138250
$534$	25.9939	1.12487
$535$	18.9053	0.817345
$536$	11.4776	0.495757
$537$	−22.1804	−0.957153
$538$	6.03920	0.260368
$539$	−1.35195	−0.0582327
$540$	0.132474	0.00570078
$541$	2.31348	0.0994644	0.0497322	−	0.998763i	$-0.484163\pi$
$541$	2.31348	0.0994644	0.0497322	+	0.998763i	$0.484163\pi$
$542$	8.49957	0.365088
$543$	−17.3732	−0.745555
$544$	0.555149	0.0238018
$545$	17.0383	0.729841
$546$	−7.00877	−0.299948
$547$	−13.8086	−0.590412	−0.295206	−	0.955434i	$-0.595388\pi$
$547$	−13.8086	−0.590412	−0.295206	+	0.955434i	$0.595388\pi$
$548$	1.59579	0.0681687
$549$	−2.58361	−0.110266
$550$	1.86942	0.0797123
$551$	−21.7591	−0.926968
$552$	−0.375415	−0.0159787
$553$	1.91511	0.0814387
$554$	13.1427	0.558382
$555$	−1.12194	−0.0476238
$556$	−0.704363	−0.0298717
$557$	−0.0109203	−0.000462709 0	−0.000231354	−	1.00000i	$-0.500074\pi$
$557$	−0.0109203	−0.000462709 0	−0.000231354		1.00000i	$0.500074\pi$
$558$	0.943886	0.0399579
$559$	14.2444	0.602475
$560$	10.8140	0.456974
$561$	0.405704	0.0171288
$562$	41.5760	1.75378
$563$	−18.5235	−0.780674	−0.390337	−	0.920672i	$-0.627642\pi$
$563$	−18.5235	−0.780674	−0.390337	+	0.920672i	$0.627642\pi$
$564$	0.0738354	0.00310903
$565$	18.3408	0.771604
$566$	−15.7674	−0.662752
$567$	−1.91511	−0.0804270
$568$	−21.5557	−0.904457
$569$	33.1773	1.39086	0.695432	−	0.718592i	$-0.255213\pi$
$569$	33.1773	1.39086	0.695432	+	0.718592i	$0.255213\pi$
$570$	4.41300	0.184840
$571$	31.2570	1.30807	0.654033	−	0.756466i	$-0.273076\pi$
$571$	31.2570	1.30807	0.654033	+	0.756466i	$0.273076\pi$
$572$	−0.100682	−0.00420974
$573$	8.82296	0.368584
$574$	−3.50450	−0.146275
$575$	0.433509	0.0180786
$576$	7.56946	0.315394
$577$	−2.54102	−0.105784	−0.0528920	−	0.998600i	$-0.516844\pi$
$577$	−2.54102	−0.105784	−0.0528920	+	0.998600i	$0.516844\pi$
$578$	−1.44853	−0.0602507
$579$	3.52116	0.146334
$580$	1.27607	0.0529858
$581$	19.2098	0.796957
$582$	−1.11447	−0.0461963
$583$	−1.39700	−0.0578578
$584$	−5.03305	−0.208269
$585$	−3.40747	−0.140882
$586$	−2.87578	−0.118797
$587$	−11.7563	−0.485234	−0.242617	−	0.970122i	$-0.578006\pi$
$587$	−11.7563	−0.485234	−0.242617	+	0.970122i	$0.578006\pi$
$588$	−0.327321	−0.0134985
$589$	1.47195	0.0606504
$590$	−1.52848	−0.0629267
$591$	11.6980	0.481192
$592$	3.48292	0.143147
$593$	29.7746	1.22269	0.611347	−	0.791363i	$-0.290628\pi$
$593$	29.7746	1.22269	0.611347	+	0.791363i	$0.290628\pi$
$594$	−0.587672	−0.0241125
$595$	−2.58287	−0.105887
$596$	1.97202	0.0807770
$597$	−7.72016	−0.315965
$598$	−0.498741	−0.0203950
$599$	16.7409	0.684014	0.342007	−	0.939697i	$-0.388893\pi$
$599$	16.7409	0.684014	0.342007	+	0.939697i	$0.388893\pi$
$600$	−8.76307	−0.357751
$601$	−37.2082	−1.51775	−0.758877	−	0.651234i	$-0.774252\pi$
$601$	−37.2082	−1.51775	−0.758877	+	0.651234i	$0.774252\pi$
$602$	−15.6402	−0.637445
$603$	4.16645	0.169671
$604$	−1.48784	−0.0605393
$605$	−14.6135	−0.594124
$606$	9.64837	0.391938
$607$	5.42394	0.220151	0.110076	−	0.993923i	$-0.464891\pi$
$607$	5.42394	0.220151	0.110076	+	0.993923i	$0.464891\pi$
$608$	−1.25403	−0.0508576
$609$	−18.4474	−0.747528
$610$	5.04735	0.204361
$611$	−1.89918	−0.0768325
$612$	0.0982249	0.00397051
$613$	1.54025	0.0622101	0.0311050	−	0.999516i	$-0.490097\pi$
$613$	1.54025	0.0622101	0.0311050	+	0.999516i	$0.490097\pi$
$614$	11.3943	0.459837
$615$	−1.70379	−0.0687035
$616$	−2.14036	−0.0862377
$617$	44.1671	1.77810	0.889050	−	0.457809i	$-0.151366\pi$
$617$	44.1671	1.77810	0.889050	+	0.457809i	$0.151366\pi$
$618$	−3.42224	−0.137663
$619$	−26.8696	−1.07998	−0.539990	−	0.841671i	$-0.681572\pi$
$619$	−26.8696	−1.07998	−0.539990	+	0.841671i	$0.681572\pi$
$620$	−0.0863226	−0.00346680
$621$	−0.136278	−0.00546866
$622$	−46.2170	−1.85313
$623$	34.3668	1.37688
$624$	10.5780	0.423460
$625$	1.02440	0.0409760
$626$	−34.3074	−1.37120
$627$	−0.916447	−0.0365994
$628$	−0.430556	−0.0171811
$629$	−0.831880	−0.0331692
$630$	3.74136	0.149059
$631$	−6.65404	−0.264893	−0.132446	−	0.991190i	$-0.542283\pi$
$631$	−6.65404	−0.264893	−0.132446	+	0.991190i	$0.542283\pi$
$632$	−2.75477	−0.109579
$633$	18.8135	0.747770
$634$	24.5867	0.976464
$635$	−16.7538	−0.664853
$636$	−0.338227	−0.0134116
$637$	8.41928	0.333584
$638$	−5.66080	−0.224113
$639$	−7.82487	−0.309547
$640$	−16.2851	−0.643726
$641$	−4.62632	−0.182729	−0.0913644	−	0.995818i	$-0.529123\pi$
$641$	−4.62632	−0.182729	−0.0913644	+	0.995818i	$0.529123\pi$
$642$	−20.3048	−0.801367
$643$	−0.540081	−0.0212987	−0.0106494	−	0.999943i	$-0.503390\pi$
$643$	−0.540081	−0.0212987	−0.0106494	+	0.999943i	$0.503390\pi$
$644$	0.0256355	0.00101018
$645$	−7.60382	−0.299400
$646$	3.27208	0.128738
$647$	−15.3217	−0.602358	−0.301179	−	0.953568i	$-0.597380\pi$
$647$	−15.3217	−0.602358	−0.301179	+	0.953568i	$0.597380\pi$
$648$	2.75477	0.108218
$649$	0.317420	0.0124598
$650$	−11.6418	−0.456629
$651$	1.24792	0.0489098
$652$	0.818545	0.0320567
$653$	−38.6865	−1.51392	−0.756960	−	0.653461i	$-0.773316\pi$
$653$	−38.6865	−1.51392	−0.756960	+	0.653461i	$0.773316\pi$
$654$	−18.2997	−0.715573
$655$	−3.85611	−0.150671
$656$	5.28919	0.206508
$657$	−1.82703	−0.0712793
$658$	2.08527	0.0812923
$659$	19.5923	0.763208	0.381604	−	0.924326i	$-0.375372\pi$
$659$	19.5923	0.763208	0.381604	+	0.924326i	$0.375372\pi$
$660$	0.0537453	0.00209203
$661$	41.8244	1.62678	0.813390	−	0.581719i	$-0.197620\pi$
$661$	41.8244	1.62678	0.813390	+	0.581719i	$0.197620\pi$
$662$	−13.0327	−0.506532
$663$	−2.52652	−0.0981219
$664$	−27.6322	−1.07234
$665$	5.83446	0.226251
$666$	1.20500	0.0466928
$667$	−1.31271	−0.0508284
$668$	−2.00353	−0.0775190
$669$	−10.5494	−0.407861
$670$	−8.13958	−0.314459
$671$	−1.04818	−0.0404646
$672$	−1.06317	−0.0410127
$673$	−3.03089	−0.116832	−0.0584161	−	0.998292i	$-0.518605\pi$
$673$	−3.03089	−0.116832	−0.0584161	+	0.998292i	$0.518605\pi$
$674$	−3.83775	−0.147825
$675$	−3.18106	−0.122439
$676$	−0.649924	−0.0249971
$677$	35.8392	1.37741	0.688705	−	0.725041i	$-0.258179\pi$
$677$	35.8392	1.37741	0.688705	+	0.725041i	$0.258179\pi$
$678$	−19.6986	−0.756520
$679$	−1.47345	−0.0565459
$680$	3.71531	0.142476
$681$	−2.90062	−0.111152
$682$	0.382938	0.0146635
$683$	−6.65115	−0.254499	−0.127250	−	0.991871i	$-0.540615\pi$
$683$	−6.65115	−0.254499	−0.127250	+	0.991871i	$0.540615\pi$
$684$	−0.221881	−0.00848382
$685$	21.9111	0.837179
$686$	−28.6628	−1.09435
$687$	10.9191	0.416588
$688$	23.6050	0.899933
$689$	8.69981	0.331436
$690$	0.266233	0.0101353
$691$	−19.3570	−0.736377	−0.368188	−	0.929751i	$-0.620022\pi$
$691$	−19.3570	−0.736377	−0.368188	+	0.929751i	$0.620022\pi$
$692$	−1.50401	−0.0571738
$693$	−0.776967	−0.0295145
$694$	13.6588	0.518480
$695$	−9.67130	−0.366853
$696$	26.5355	1.00583
$697$	−1.26330	−0.0478510
$698$	26.7072	1.01088
$699$	7.99164	0.302272
$700$	0.598393	0.0226171
$701$	2.64962	0.100075	0.0500374	−	0.998747i	$-0.484066\pi$
$701$	2.64962	0.100075	0.0500374	+	0.998747i	$0.484066\pi$
$702$	3.65973	0.138128
$703$	1.87914	0.0708731
$704$	3.07096	0.115741
$705$	1.01380	0.0381820
$706$	30.3648	1.14279
$707$	12.7562	0.479746
$708$	0.0768506	0.00288822
$709$	9.34289	0.350880	0.175440	−	0.984490i	$-0.443865\pi$
$709$	9.34289	0.350880	0.175440	+	0.984490i	$0.443865\pi$
$710$	15.2867	0.573698
$711$	−1.00000	−0.0375029
$712$	−49.4345	−1.85264
$713$	0.0888014	0.00332564
$714$	2.77408	0.103817
$715$	−1.38243	−0.0516998
$716$	−2.17866	−0.0814205
$717$	−17.2202	−0.643098
$718$	45.2405	1.68836
$719$	5.98329	0.223139	0.111569	−	0.993757i	$-0.464412\pi$
$719$	5.98329	0.223139	0.111569	+	0.993757i	$0.464412\pi$
$720$	−5.64667	−0.210439
$721$	−4.52457	−0.168504
$722$	20.1307	0.749185
$723$	18.0128	0.669902
$724$	−1.70648	−0.0634209
$725$	−30.6418	−1.13801
$726$	15.6954	0.582509
$727$	−24.6171	−0.912996	−0.456498	−	0.889724i	$-0.650896\pi$
$727$	−24.6171	−0.912996	−0.456498	+	0.889724i	$0.650896\pi$
$728$	13.3291	0.494010
$729$	1.00000	0.0370370
$730$	3.56929	0.132105
$731$	−5.63796	−0.208527
$732$	−0.253775	−0.00937980
$733$	16.1986	0.598307	0.299154	−	0.954205i	$-0.403296\pi$
$733$	16.1986	0.598307	0.299154	+	0.954205i	$0.403296\pi$
$734$	30.4153	1.12265
$735$	−4.49430	−0.165775
$736$	−0.0756548	−0.00278867
$737$	1.69035	0.0622647
$738$	1.82992	0.0673604
$739$	−14.5495	−0.535212	−0.267606	−	0.963528i	$-0.586233\pi$
$739$	−14.5495	−0.535212	−0.267606	+	0.963528i	$0.586233\pi$
$740$	−0.110203	−0.00405113
$741$	5.70717	0.209658
$742$	−9.55226	−0.350675
$743$	33.2994	1.22164	0.610819	−	0.791770i	$-0.290840\pi$
$743$	33.2994	1.22164	0.610819	+	0.791770i	$0.290840\pi$
$744$	−1.79506	−0.0658101
$745$	27.0769	0.992021
$746$	2.43552	0.0891706
$747$	−10.0307	−0.367003
$748$	0.0398502	0.00145707
$749$	−26.8452	−0.980901
$750$	15.9825	0.583599
$751$	−1.69056	−0.0616894	−0.0308447	−	0.999524i	$-0.509820\pi$
$751$	−1.69056	−0.0616894	−0.0308447	+	0.999524i	$0.509820\pi$
$752$	−3.14721	−0.114767
$753$	7.28210	0.265375
$754$	35.2526	1.28382
$755$	−20.4289	−0.743482
$756$	−0.188111	−0.00684154
$757$	−16.5780	−0.602536	−0.301268	−	0.953539i	$-0.597410\pi$
$757$	−16.5780	−0.602536	−0.301268	+	0.953539i	$0.597410\pi$
$758$	−8.72937	−0.317065
$759$	−0.0552886	−0.00200685
$760$	−8.39253	−0.304429
$761$	−12.5063	−0.453351	−0.226676	−	0.973970i	$-0.572786\pi$
$761$	−12.5063	−0.453351	−0.226676	+	0.973970i	$0.572786\pi$
$762$	17.9940	0.651855
$763$	−24.1941	−0.875887
$764$	0.866634	0.0313537
$765$	1.34868	0.0487617
$766$	27.6735	0.999882
$767$	−1.97673	−0.0713757
$768$	2.35180	0.0848634
$769$	−35.5836	−1.28318	−0.641589	−	0.767048i	$-0.721725\pi$
$769$	−35.5836	−1.28318	−0.641589	+	0.767048i	$0.721725\pi$
$770$	1.51788	0.0547007
$771$	−26.4171	−0.951390
$772$	0.345865	0.0124480
$773$	31.1512	1.12043	0.560216	−	0.828347i	$-0.310718\pi$
$773$	31.1512	1.12043	0.560216	+	0.828347i	$0.310718\pi$
$774$	8.16673	0.293547
$775$	2.07284	0.0744585
$776$	2.11947	0.0760847
$777$	1.59314	0.0571536
$778$	2.86974	0.102885
$779$	2.85368	0.102244
$780$	−0.334699	−0.0119841
$781$	−3.17458	−0.113595
$782$	0.197402	0.00705910
$783$	9.63258	0.344240
$784$	13.9519	0.498283
$785$	−5.91177	−0.211000
$786$	4.14158	0.147725
$787$	−6.76912	−0.241293	−0.120647	−	0.992696i	$-0.538497\pi$
$787$	−6.76912	−0.241293	−0.120647	+	0.992696i	$0.538497\pi$
$788$	1.14904	0.0409327
$789$	−17.3834	−0.618867
$790$	1.95360	0.0695060
$791$	−26.0437	−0.926007
$792$	1.11762	0.0397129
$793$	6.52755	0.231800
$794$	14.4289	0.512064
$795$	−4.64405	−0.164707
$796$	−0.758312	−0.0268777
$797$	39.5495	1.40092	0.700458	−	0.713694i	$-0.252979\pi$
$797$	39.5495	1.40092	0.700458	+	0.713694i	$0.252979\pi$
$798$	−6.26639	−0.221828
$799$	0.751697	0.0265931
$800$	−1.76596	−0.0624362
$801$	−17.9451	−0.634058
$802$	−24.3437	−0.859607
$803$	−0.741234	−0.0261576
$804$	0.409249	0.0144331
$805$	0.351989	0.0124060
$806$	−2.38475	−0.0839991
$807$	−4.16921	−0.146763
$808$	−18.3490	−0.645517
$809$	−52.1533	−1.83361	−0.916807	−	0.399331i	$-0.869242\pi$
$809$	−52.1533	−1.83361	−0.916807	+	0.399331i	$0.869242\pi$
$810$	−1.95360	−0.0686425
$811$	10.3811	0.364529	0.182264	−	0.983250i	$-0.441657\pi$
$811$	10.3811	0.364529	0.182264	+	0.983250i	$0.441657\pi$
$812$	−1.81200	−0.0635886
$813$	−5.86774	−0.205791
$814$	0.488873	0.0171350
$815$	11.2391	0.393688
$816$	−4.18680	−0.146567
$817$	12.7356	0.445563
$818$	−9.17201	−0.320692
$819$	4.83856	0.169073
$820$	−0.167355	−0.00584428
$821$	27.0239	0.943142	0.471571	−	0.881828i	$-0.343687\pi$
$821$	27.0239	0.943142	0.471571	+	0.881828i	$0.343687\pi$
$822$	−23.5331	−0.820812
$823$	2.18433	0.0761411	0.0380705	−	0.999275i	$-0.487879\pi$
$823$	2.18433	0.0761411	0.0380705	+	0.999275i	$0.487879\pi$
$824$	6.50833	0.226728
$825$	−1.29057	−0.0449318
$826$	2.17042	0.0755187
$827$	2.06511	0.0718108	0.0359054	−	0.999355i	$-0.488568\pi$
$827$	2.06511	0.0718108	0.0359054	+	0.999355i	$0.488568\pi$
$828$	−0.0133859	−0.000465193 0
$829$	51.3504	1.78347	0.891737	−	0.452554i	$-0.149487\pi$
$829$	51.3504	1.78347	0.891737	+	0.452554i	$0.149487\pi$
$830$	19.5959	0.680184
$831$	−9.07319	−0.314746
$832$	−19.1244	−0.663019
$833$	−3.33236	−0.115459
$834$	10.3873	0.359681
$835$	−27.5096	−0.952009
$836$	−0.0900179	−0.00311333
$837$	−0.651619	−0.0225232
$838$	33.5546	1.15912
$839$	−38.3422	−1.32372	−0.661861	−	0.749627i	$-0.730233\pi$
$839$	−38.3422	−1.32372	−0.661861	+	0.749627i	$0.730233\pi$
$840$	−7.11522	−0.245498
$841$	63.7866	2.19954
$842$	−10.9615	−0.377759
$843$	−28.7023	−0.988560
$844$	1.84796	0.0636093
$845$	−8.92382	−0.306989
$846$	−1.08885	−0.0374355
$847$	20.7510	0.713012
$848$	14.4168	0.495075
$849$	10.8851	0.373576
$850$	4.60784	0.158048
$851$	0.113367	0.00388618
$852$	−0.768597	−0.0263317
$853$	0.223305	0.00764581	0.00382291	−	0.999993i	$-0.498783\pi$
$853$	0.223305	0.00764581	0.00382291	+	0.999993i	$0.498783\pi$
$854$	−7.16716	−0.245255
$855$	−3.04655	−0.104190
$856$	38.6152	1.31984
$857$	25.9459	0.886295	0.443147	−	0.896449i	$-0.353862\pi$
$857$	25.9459	0.886295	0.443147	+	0.896449i	$0.353862\pi$
$858$	1.48477	0.0506891
$859$	−12.1152	−0.413365	−0.206683	−	0.978408i	$-0.566267\pi$
$859$	−12.1152	−0.413365	−0.206683	+	0.978408i	$0.566267\pi$
$860$	−0.746884	−0.0254685
$861$	2.41936	0.0824515
$862$	−9.51535	−0.324094
$863$	50.4500	1.71734	0.858670	−	0.512529i	$-0.171291\pi$
$863$	50.4500	1.71734	0.858670	+	0.512529i	$0.171291\pi$
$864$	0.555149	0.0188866
$865$	−20.6509	−0.702150
$866$	−12.0806	−0.410515
$867$	1.00000	0.0339618
$868$	0.122577	0.00416053
$869$	−0.405704	−0.0137626
$870$	−18.8182	−0.637997
$871$	−10.5266	−0.356681
$872$	34.8018	1.17854
$873$	0.769383	0.0260397
$874$	−0.445913	−0.0150832
$875$	21.1306	0.714345
$876$	−0.179460	−0.00606339
$877$	24.3051	0.820725	0.410363	−	0.911922i	$-0.365402\pi$
$877$	24.3051	0.820725	0.410363	+	0.911922i	$0.365402\pi$
$878$	57.2743	1.93291
$879$	1.98532	0.0669630
$880$	−2.29087	−0.0772254
$881$	26.0822	0.878732	0.439366	−	0.898308i	$-0.355203\pi$
$881$	26.0822	0.878732	0.439366	+	0.898308i	$0.355203\pi$
$882$	4.82701	0.162534
$883$	−53.6955	−1.80700	−0.903498	−	0.428592i	$-0.859010\pi$
$883$	−53.6955	−1.80700	−0.903498	+	0.428592i	$0.859010\pi$
$884$	−0.248167	−0.00834677
$885$	1.05520	0.0354702
$886$	7.25984	0.243899
$887$	7.25030	0.243441	0.121721	−	0.992564i	$-0.461159\pi$
$887$	7.25030	0.243441	0.121721	+	0.992564i	$0.461159\pi$
$888$	−2.29164	−0.0769024
$889$	23.7901	0.797894
$890$	35.0575	1.17513
$891$	0.405704	0.0135916
$892$	−1.03621	−0.0346948
$893$	−1.69801	−0.0568219
$894$	−29.0814	−0.972627
$895$	−29.9143	−0.999924
$896$	23.1246	0.772540
$897$	0.344310	0.0114962
$898$	26.3909	0.880674
$899$	−6.27677	−0.209342
$900$	−0.312459	−0.0104153
$901$	−3.44340	−0.114716
$902$	0.742408	0.0247195
$903$	10.7973	0.359312
$904$	37.4623	1.24598
$905$	−23.4309	−0.778870
$906$	21.9412	0.728948
$907$	34.8248	1.15634	0.578170	−	0.815916i	$-0.303767\pi$
$907$	34.8248	1.15634	0.578170	+	0.815916i	$0.303767\pi$
$908$	−0.284913	−0.00945517
$909$	−6.66083	−0.220926
$910$	−9.45261	−0.313351
$911$	17.8065	0.589957	0.294978	−	0.955504i	$-0.404688\pi$
$911$	17.8065	0.589957	0.294978	+	0.955504i	$0.404688\pi$
$912$	9.45759	0.313172
$913$	−4.06948	−0.134680
$914$	23.8760	0.789749
$915$	−3.48447	−0.115193
$916$	1.07252	0.0354372
$917$	5.47561	0.180821
$918$	−1.44853	−0.0478085
$919$	44.5812	1.47060	0.735299	−	0.677743i	$-0.237042\pi$
$919$	44.5812	1.47060	0.735299	+	0.677743i	$0.237042\pi$
$920$	−0.506316	−0.0166927
$921$	−7.86614	−0.259198
$922$	8.23654	0.271256
$923$	19.7697	0.650727
$924$	−0.0763175	−0.00251066
$925$	2.64626	0.0870084
$926$	−37.3144	−1.22623
$927$	2.36257	0.0775969
$928$	5.34752	0.175541
$929$	−40.3879	−1.32508	−0.662541	−	0.749025i	$-0.730522\pi$
$929$	−40.3879	−1.32508	−0.662541	+	0.749025i	$0.730522\pi$
$930$	1.27300	0.0417434
$931$	7.52749	0.246704
$932$	0.784978	0.0257128
$933$	31.9062	1.04456
$934$	−41.5770	−1.36044
$935$	0.547166	0.0178942
$936$	−6.95998	−0.227494
$937$	45.0270	1.47097	0.735484	−	0.677543i	$-0.236955\pi$
$937$	45.0270	1.47097	0.735484	+	0.677543i	$0.236955\pi$
$938$	11.5581	0.377385
$939$	23.6844	0.772911
$940$	0.0995805	0.00324796
$941$	10.6087	0.345833	0.172917	−	0.984936i	$-0.444681\pi$
$941$	10.6087	0.345833	0.172917	+	0.984936i	$0.444681\pi$
$942$	6.34942	0.206875
$943$	0.172160	0.00560632
$944$	−3.27573	−0.106616
$945$	−2.58287	−0.0840208
$946$	3.31327	0.107724
$947$	28.3082	0.919893	0.459946	−	0.887947i	$-0.347869\pi$
$947$	28.3082	0.919893	0.459946	+	0.887947i	$0.347869\pi$
$948$	−0.0982249	−0.00319020
$949$	4.61603	0.149843
$950$	−10.4087	−0.337702
$951$	−16.9736	−0.550408
$952$	−5.27568	−0.170986
$953$	−21.9713	−0.711719	−0.355860	−	0.934539i	$-0.615812\pi$
$953$	−21.9713	−0.711719	−0.355860	+	0.934539i	$0.615812\pi$
$954$	4.98784	0.161487
$955$	11.8994	0.385054
$956$	−1.69145	−0.0547053
$957$	3.90798	0.126327
$958$	45.6552	1.47505
$959$	−31.1134	−1.00470
$960$	10.2088	0.329487
$961$	−30.5754	−0.986303
$962$	−3.04446	−0.0981572
$963$	14.0176	0.451710
$964$	1.76930	0.0569854
$965$	4.74892	0.152873
$966$	−0.378047	−0.0121635
$967$	35.8497	1.15285	0.576425	−	0.817150i	$-0.304447\pi$
$967$	35.8497	1.15285	0.576425	+	0.817150i	$0.304447\pi$
$968$	−29.8490	−0.959384
$969$	−2.25891	−0.0725665
$970$	−1.50307	−0.0482606
$971$	22.2834	0.715108	0.357554	−	0.933892i	$-0.383611\pi$
$971$	22.2834	0.715108	0.357554	+	0.933892i	$0.383611\pi$
$972$	0.0982249	0.00315056
$973$	13.7331	0.440263
$974$	−46.7831	−1.49903
$975$	8.03700	0.257390
$976$	10.8171	0.346246
$977$	−6.37061	−0.203814	−0.101907	−	0.994794i	$-0.532494\pi$
$977$	−6.37061	−0.203814	−0.101907	+	0.994794i	$0.532494\pi$
$978$	−12.0711	−0.385991
$979$	−7.28039	−0.232682
$980$	−0.441452	−0.0141017
$981$	12.6333	0.403350
$982$	36.6146	1.16842
$983$	30.3614	0.968379	0.484190	−	0.874963i	$-0.339114\pi$
$983$	30.3614	0.968379	0.484190	+	0.874963i	$0.339114\pi$
$984$	−3.48010	−0.110942
$985$	15.7769	0.502694
$986$	−13.9530	−0.444355
$987$	−1.43958	−0.0458224
$988$	0.560586	0.0178346
$989$	0.768331	0.0244315
$990$	−0.792583	−0.0251900
$991$	51.9780	1.65114	0.825568	−	0.564303i	$-0.190855\pi$
$991$	51.9780	1.65114	0.825568	+	0.564303i	$0.190855\pi$
$992$	−0.361746	−0.0114854
$993$	8.99725	0.285519
$994$	−21.7068	−0.688499
$995$	−10.4120	−0.330084
$996$	−0.985261	−0.0312192
$997$	−11.1613	−0.353482	−0.176741	−	0.984257i	$-0.556556\pi$
$997$	−11.1613	−0.353482	−0.176741	+	0.984257i	$0.556556\pi$
$998$	7.63359	0.241637
$999$	−0.831880	−0.0263195

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	4029.2.a.e.1.8	✓	18

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
4029.2.a.e.1.8	✓	18	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:	\( N \)	\(=\)	\( 4029 = 3 \cdot 17 \cdot 79 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	4029.a (trivial)

\(f(q)\)	\(=\)	\(q-1.44853 q^{2} +1.00000 q^{3} +0.0982249 q^{4} +1.34868 q^{5} -1.44853 q^{6} -1.91511 q^{7} +2.75477 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q-1.44853 q^{2} +1.00000 q^{3} +0.0982249 q^{4} +1.34868 q^{5} -1.44853 q^{6} -1.91511 q^{7} +2.75477 q^{8} +1.00000 q^{9} -1.95360 q^{10} +0.405704 q^{11} +0.0982249 q^{12} -2.52652 q^{13} +2.77408 q^{14} +1.34868 q^{15} -4.18680 q^{16} +1.00000 q^{17} -1.44853 q^{18} -2.25891 q^{19} +0.132474 q^{20} -1.91511 q^{21} -0.587672 q^{22} -0.136278 q^{23} +2.75477 q^{24} -3.18106 q^{25} +3.65973 q^{26} +1.00000 q^{27} -0.188111 q^{28} +9.63258 q^{29} -1.95360 q^{30} -0.651619 q^{31} +0.555149 q^{32} +0.405704 q^{33} -1.44853 q^{34} -2.58287 q^{35} +0.0982249 q^{36} -0.831880 q^{37} +3.27208 q^{38} -2.52652 q^{39} +3.71531 q^{40} -1.26330 q^{41} +2.77408 q^{42} -5.63796 q^{43} +0.0398502 q^{44} +1.34868 q^{45} +0.197402 q^{46} +0.751697 q^{47} -4.18680 q^{48} -3.33236 q^{49} +4.60784 q^{50} +1.00000 q^{51} -0.248167 q^{52} -3.44340 q^{53} -1.44853 q^{54} +0.547166 q^{55} -5.27568 q^{56} -2.25891 q^{57} -13.9530 q^{58} +0.782394 q^{59} +0.132474 q^{60} -2.58361 q^{61} +0.943886 q^{62} -1.91511 q^{63} +7.56946 q^{64} -3.40747 q^{65} -0.587672 q^{66} +4.16645 q^{67} +0.0982249 q^{68} -0.136278 q^{69} +3.74136 q^{70} -7.82487 q^{71} +2.75477 q^{72} -1.82703 q^{73} +1.20500 q^{74} -3.18106 q^{75} -0.221881 q^{76} -0.776967 q^{77} +3.65973 q^{78} -1.00000 q^{79} -5.64667 q^{80} +1.00000 q^{81} +1.82992 q^{82} -10.0307 q^{83} -0.188111 q^{84} +1.34868 q^{85} +8.16673 q^{86} +9.63258 q^{87} +1.11762 q^{88} -17.9451 q^{89} -1.95360 q^{90} +4.83856 q^{91} -0.0133859 q^{92} -0.651619 q^{93} -1.08885 q^{94} -3.04655 q^{95} +0.555149 q^{96} +0.769383 q^{97} +4.82701 q^{98} +0.405704 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 18 q - 6 q^{2} + 18 q^{3} + 20 q^{4} - 5 q^{5} - 6 q^{6} - 13 q^{7} - 12 q^{8} + 18 q^{9}+O(q^{10}) \) 18 * q - 6 * q^2 + 18 * q^3 + 20 * q^4 - 5 * q^5 - 6 * q^6 - 13 * q^7 - 12 * q^8 + 18 * q^9	\( 18 q - 6 q^{2} + 18 q^{3} + 20 q^{4} - 5 q^{5} - 6 q^{6} - 13 q^{7} - 12 q^{8} + 18 q^{9} - 15 q^{10} - 27 q^{11} + 20 q^{12} - 4 q^{13} - 5 q^{14} - 5 q^{15} + 16 q^{16} + 18 q^{17} - 6 q^{18} - 30 q^{19} - 16 q^{20} - 13 q^{21} + 13 q^{22} - 21 q^{23} - 12 q^{24} + 13 q^{25} - 20 q^{26} + 18 q^{27} - 33 q^{28} - 47 q^{29} - 15 q^{30} - 18 q^{31} - 45 q^{32} - 27 q^{33} - 6 q^{34} - 17 q^{35} + 20 q^{36} + q^{37} + 5 q^{38} - 4 q^{39} - 12 q^{40} - 18 q^{41} - 5 q^{42} - 39 q^{43} - 34 q^{44} - 5 q^{45} - 7 q^{46} + 16 q^{48} + 15 q^{49} - 23 q^{50} + 18 q^{51} + 5 q^{52} - 9 q^{53} - 6 q^{54} + q^{55} - 24 q^{56} - 30 q^{57} + 41 q^{58} - 42 q^{59} - 16 q^{60} - 43 q^{61} - 54 q^{62} - 13 q^{63} + 22 q^{64} - 25 q^{65} + 13 q^{66} + 20 q^{68} - 21 q^{69} + 17 q^{70} + 9 q^{71} - 12 q^{72} + 19 q^{73} - 30 q^{74} + 13 q^{75} - 17 q^{76} - 14 q^{77} - 20 q^{78} - 18 q^{79} + 36 q^{80} + 18 q^{81} - 3 q^{82} - 61 q^{83} - 33 q^{84} - 5 q^{85} - 24 q^{86} - 47 q^{87} - 25 q^{88} + 10 q^{89} - 15 q^{90} - 52 q^{91} - 74 q^{92} - 18 q^{93} + 31 q^{94} - 37 q^{95} - 45 q^{96} - 9 q^{97} + 27 q^{98} - 27 q^{99}+O(q^{100}) \) 18 * q - 6 * q^2 + 18 * q^3 + 20 * q^4 - 5 * q^5 - 6 * q^6 - 13 * q^7 - 12 * q^8 + 18 * q^9 - 15 * q^10 - 27 * q^11 + 20 * q^12 - 4 * q^13 - 5 * q^14 - 5 * q^15 + 16 * q^16 + 18 * q^17 - 6 * q^18 - 30 * q^19 - 16 * q^20 - 13 * q^21 + 13 * q^22 - 21 * q^23 - 12 * q^24 + 13 * q^25 - 20 * q^26 + 18 * q^27 - 33 * q^28 - 47 * q^29 - 15 * q^30 - 18 * q^31 - 45 * q^32 - 27 * q^33 - 6 * q^34 - 17 * q^35 + 20 * q^36 + q^37 + 5 * q^38 - 4 * q^39 - 12 * q^40 - 18 * q^41 - 5 * q^42 - 39 * q^43 - 34 * q^44 - 5 * q^45 - 7 * q^46 + 16 * q^48 + 15 * q^49 - 23 * q^50 + 18 * q^51 + 5 * q^52 - 9 * q^53 - 6 * q^54 + q^55 - 24 * q^56 - 30 * q^57 + 41 * q^58 - 42 * q^59 - 16 * q^60 - 43 * q^61 - 54 * q^62 - 13 * q^63 + 22 * q^64 - 25 * q^65 + 13 * q^66 + 20 * q^68 - 21 * q^69 + 17 * q^70 + 9 * q^71 - 12 * q^72 + 19 * q^73 - 30 * q^74 + 13 * q^75 - 17 * q^76 - 14 * q^77 - 20 * q^78 - 18 * q^79 + 36 * q^80 + 18 * q^81 - 3 * q^82 - 61 * q^83 - 33 * q^84 - 5 * q^85 - 24 * q^86 - 47 * q^87 - 25 * q^88 + 10 * q^89 - 15 * q^90 - 52 * q^91 - 74 * q^92 - 18 * q^93 + 31 * q^94 - 37 * q^95 - 45 * q^96 - 9 * q^97 + 27 * q^98 - 27 * q^99

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