LMFDB - Embedded newform 6034.2.a.l.1.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [6034,2,Mod(1,6034)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(6034, 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("6034.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 6034 = 2 \cdot 7 \cdot 431 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	6034.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:	$48.1817325796$
Analytic rank:	$1$
Dimension:	$20$
Coefficient field:	$\mathbb{Q}[x]/(x^{20} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{20} - 3 x^{19} - 36 x^{18} + 97 x^{17} + 573 x^{16} - 1292 x^{15} - 5329 x^{14} + 9121 x^{13} + \cdots - 21776 $ x^20 - 3x^19 - 36x^18 + 97x^17 + 573x^16 - 1292x^15 - 5329x^14 + 9121x^13 + 31784x^12 - 36075x^11 - 124276x^10 + 74594x^9 + 312410x^8 - 47208x^7 - 477646x^6 - 101137x^5 + 391391x^4 + 205294x^3 - 112848x^2 - 109144*x - 21776
Coefficient ring:	$\Z[a_1, \ldots, a_{13}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.1
Root			$2.98166$ of defining polynomial
Character	$\chi$	$=$	6034.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.00000 q^{2} -2.98166 q^{3} +1.00000 q^{4} -1.98359 q^{5} -2.98166 q^{6} -1.00000 q^{7} +1.00000 q^{8} +5.89028 q^{9} +O(q^{10})$	\(q+1.00000 q^{2} -2.98166 q^{3} +1.00000 q^{4} -1.98359 q^{5} -2.98166 q^{6} -1.00000 q^{7} +1.00000 q^{8} +5.89028 q^{9} -1.98359 q^{10} -5.55852 q^{11} -2.98166 q^{12} -6.48754 q^{13} -1.00000 q^{14} +5.91438 q^{15} +1.00000 q^{16} +3.37713 q^{17} +5.89028 q^{18} +5.27632 q^{19} -1.98359 q^{20} +2.98166 q^{21} -5.55852 q^{22} +6.73897 q^{23} -2.98166 q^{24} -1.06538 q^{25} -6.48754 q^{26} -8.61783 q^{27} -1.00000 q^{28} +7.00943 q^{29} +5.91438 q^{30} -1.83909 q^{31} +1.00000 q^{32} +16.5736 q^{33} +3.37713 q^{34} +1.98359 q^{35} +5.89028 q^{36} +3.74109 q^{37} +5.27632 q^{38} +19.3436 q^{39} -1.98359 q^{40} +8.26578 q^{41} +2.98166 q^{42} +2.39817 q^{43} -5.55852 q^{44} -11.6839 q^{45} +6.73897 q^{46} +1.87585 q^{47} -2.98166 q^{48} +1.00000 q^{49} -1.06538 q^{50} -10.0694 q^{51} -6.48754 q^{52} -3.25729 q^{53} -8.61783 q^{54} +11.0258 q^{55} -1.00000 q^{56} -15.7322 q^{57} +7.00943 q^{58} -4.64958 q^{59} +5.91438 q^{60} -13.7219 q^{61} -1.83909 q^{62} -5.89028 q^{63} +1.00000 q^{64} +12.8686 q^{65} +16.5736 q^{66} -10.9873 q^{67} +3.37713 q^{68} -20.0933 q^{69} +1.98359 q^{70} +14.4915 q^{71} +5.89028 q^{72} -10.2156 q^{73} +3.74109 q^{74} +3.17660 q^{75} +5.27632 q^{76} +5.55852 q^{77} +19.3436 q^{78} +4.82681 q^{79} -1.98359 q^{80} +8.02456 q^{81} +8.26578 q^{82} +8.64763 q^{83} +2.98166 q^{84} -6.69883 q^{85} +2.39817 q^{86} -20.8997 q^{87} -5.55852 q^{88} -13.0342 q^{89} -11.6839 q^{90} +6.48754 q^{91} +6.73897 q^{92} +5.48353 q^{93} +1.87585 q^{94} -10.4660 q^{95} -2.98166 q^{96} +7.42890 q^{97} +1.00000 q^{98} -32.7412 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 20 q + 20 q^{2} - 3 q^{3} + 20 q^{4} - 10 q^{5} - 3 q^{6} - 20 q^{7} + 20 q^{8} + 21 q^{9}+O(q^{10}) $ 20 * q + 20 * q^2 - 3 * q^3 + 20 * q^4 - 10 * q^5 - 3 * q^6 - 20 * q^7 + 20 * q^8 + 21 * q^9	\( 20 q + 20 q^{2} - 3 q^{3} + 20 q^{4} - 10 q^{5} - 3 q^{6} - 20 q^{7} + 20 q^{8} + 21 q^{9} - 10 q^{10} - 17 q^{11} - 3 q^{12} - 23 q^{13} - 20 q^{14} - 3 q^{15} + 20 q^{16} - 21 q^{17} + 21 q^{18} - 22 q^{19} - 10 q^{20} + 3 q^{21} - 17 q^{22} + 15 q^{23} - 3 q^{24} - 23 q^{26} - 42 q^{27} - 20 q^{28} - 3 q^{29} - 3 q^{30} - 3 q^{31} + 20 q^{32} - 12 q^{33} - 21 q^{34} + 10 q^{35} + 21 q^{36} - 14 q^{37} - 22 q^{38} + q^{39} - 10 q^{40} - 37 q^{41} + 3 q^{42} - 5 q^{43} - 17 q^{44} - 55 q^{45} + 15 q^{46} - 29 q^{47} - 3 q^{48} + 20 q^{49} - 7 q^{51} - 23 q^{52} - 28 q^{53} - 42 q^{54} + 4 q^{55} - 20 q^{56} - 23 q^{57} - 3 q^{58} - 47 q^{59} - 3 q^{60} - 13 q^{61} - 3 q^{62} - 21 q^{63} + 20 q^{64} - 26 q^{65} - 12 q^{66} - 24 q^{67} - 21 q^{68} - 76 q^{69} + 10 q^{70} - 22 q^{71} + 21 q^{72} - 37 q^{73} - 14 q^{74} - 39 q^{75} - 22 q^{76} + 17 q^{77} + q^{78} + 25 q^{79} - 10 q^{80} - 36 q^{81} - 37 q^{82} - 33 q^{83} + 3 q^{84} - 2 q^{85} - 5 q^{86} - 26 q^{87} - 17 q^{88} - 71 q^{89} - 55 q^{90} + 23 q^{91} + 15 q^{92} - 49 q^{93} - 29 q^{94} - 14 q^{95} - 3 q^{96} - 51 q^{97} + 20 q^{98} - 10 q^{99}+O(q^{100}) \) 20 * q + 20 * q^2 - 3 * q^3 + 20 * q^4 - 10 * q^5 - 3 * q^6 - 20 * q^7 + 20 * q^8 + 21 * q^9 - 10 * q^10 - 17 * q^11 - 3 * q^12 - 23 * q^13 - 20 * q^14 - 3 * q^15 + 20 * q^16 - 21 * q^17 + 21 * q^18 - 22 * q^19 - 10 * q^20 + 3 * q^21 - 17 * q^22 + 15 * q^23 - 3 * q^24 - 23 * q^26 - 42 * q^27 - 20 * q^28 - 3 * q^29 - 3 * q^30 - 3 * q^31 + 20 * q^32 - 12 * q^33 - 21 * q^34 + 10 * q^35 + 21 * q^36 - 14 * q^37 - 22 * q^38 + q^39 - 10 * q^40 - 37 * q^41 + 3 * q^42 - 5 * q^43 - 17 * q^44 - 55 * q^45 + 15 * q^46 - 29 * q^47 - 3 * q^48 + 20 * q^49 - 7 * q^51 - 23 * q^52 - 28 * q^53 - 42 * q^54 + 4 * q^55 - 20 * q^56 - 23 * q^57 - 3 * q^58 - 47 * q^59 - 3 * q^60 - 13 * q^61 - 3 * q^62 - 21 * q^63 + 20 * q^64 - 26 * q^65 - 12 * q^66 - 24 * q^67 - 21 * q^68 - 76 * q^69 + 10 * q^70 - 22 * q^71 + 21 * q^72 - 37 * q^73 - 14 * q^74 - 39 * q^75 - 22 * q^76 + 17 * q^77 + q^78 + 25 * q^79 - 10 * q^80 - 36 * q^81 - 37 * q^82 - 33 * q^83 + 3 * q^84 - 2 * q^85 - 5 * q^86 - 26 * q^87 - 17 * q^88 - 71 * q^89 - 55 * q^90 + 23 * q^91 + 15 * q^92 - 49 * q^93 - 29 * q^94 - 14 * q^95 - 3 * q^96 - 51 * q^97 + 20 * q^98 - 10 * 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
$3$	−2.98166	−1.72146	−0.860730	−	0.509061i	$-0.829993\pi$
$3$	−2.98166	−1.72146	−0.860730	+	0.509061i	$0.829993\pi$
$4$	1.00000	0.500000
$5$	−1.98359	−0.887087	−0.443544	−	0.896253i	$-0.646279\pi$
$5$	−1.98359	−0.887087	−0.443544	+	0.896253i	$0.646279\pi$
$6$	−2.98166	−1.21726
$7$	−1.00000	−0.377964
$7$	−1.00000	−0.377964
$8$	1.00000	0.353553
$9$	5.89028	1.96343
$10$	−1.98359	−0.627265
$11$	−5.55852	−1.67596	−0.837978	−	0.545704i	$-0.816262\pi$
$11$	−5.55852	−1.67596	−0.837978	+	0.545704i	$0.816262\pi$
$12$	−2.98166	−0.860730
$13$	−6.48754	−1.79932	−0.899660	−	0.436592i	$-0.856185\pi$
$13$	−6.48754	−1.79932	−0.899660	+	0.436592i	$0.856185\pi$
$14$	−1.00000	−0.267261
$15$	5.91438	1.52709
$16$	1.00000	0.250000
$17$	3.37713	0.819074	0.409537	−	0.912293i	$-0.365690\pi$
$17$	3.37713	0.819074	0.409537	+	0.912293i	$0.365690\pi$
$18$	5.89028	1.38835
$19$	5.27632	1.21047	0.605235	−	0.796047i	$-0.293079\pi$
$19$	5.27632	1.21047	0.605235	+	0.796047i	$0.293079\pi$
$20$	−1.98359	−0.443544
$21$	2.98166	0.650651
$22$	−5.55852	−1.18508
$23$	6.73897	1.40517	0.702587	−	0.711598i	$-0.252028\pi$
$23$	6.73897	1.40517	0.702587	+	0.711598i	$0.252028\pi$
$24$	−2.98166	−0.608628
$25$	−1.06538	−0.213076
$26$	−6.48754	−1.27231
$27$	−8.61783	−1.65850
$28$	−1.00000	−0.188982
$29$	7.00943	1.30162	0.650809	−	0.759241i	$-0.274430\pi$
$29$	7.00943	1.30162	0.650809	+	0.759241i	$0.274430\pi$
$30$	5.91438	1.07981
$31$	−1.83909	−0.330310	−0.165155	−	0.986268i	$-0.552812\pi$
$31$	−1.83909	−0.330310	−0.165155	+	0.986268i	$0.552812\pi$
$32$	1.00000	0.176777
$33$	16.5736	2.88509
$34$	3.37713	0.579173
$35$	1.98359	0.335287
$36$	5.89028	0.981713
$37$	3.74109	0.615032	0.307516	−	0.951543i	$-0.400502\pi$
$37$	3.74109	0.615032	0.307516	+	0.951543i	$0.400502\pi$
$38$	5.27632	0.855932
$39$	19.3436	3.09746
$40$	−1.98359	−0.313633
$41$	8.26578	1.29090	0.645449	−	0.763804i	$-0.276670\pi$
$41$	8.26578	1.29090	0.645449	+	0.763804i	$0.276670\pi$
$42$	2.98166	0.460080
$43$	2.39817	0.365717	0.182858	−	0.983139i	$-0.441465\pi$
$43$	2.39817	0.365717	0.182858	+	0.983139i	$0.441465\pi$
$44$	−5.55852	−0.837978
$45$	−11.6839	−1.74173
$46$	6.73897	0.993608
$47$	1.87585	0.273621	0.136811	−	0.990597i	$-0.456315\pi$
$47$	1.87585	0.273621	0.136811	+	0.990597i	$0.456315\pi$
$48$	−2.98166	−0.430365
$49$	1.00000	0.142857
$50$	−1.06538	−0.150668
$51$	−10.0694	−1.41000
$52$	−6.48754	−0.899660
$53$	−3.25729	−0.447424	−0.223712	−	0.974655i	$-0.571817\pi$
$53$	−3.25729	−0.447424	−0.223712	+	0.974655i	$0.571817\pi$
$54$	−8.61783	−1.17274
$55$	11.0258	1.48672
$56$	−1.00000	−0.133631
$57$	−15.7322	−2.08378
$58$	7.00943	0.920383
$59$	−4.64958	−0.605324	−0.302662	−	0.953098i	$-0.597875\pi$
$59$	−4.64958	−0.605324	−0.302662	+	0.953098i	$0.597875\pi$
$60$	5.91438	0.763543
$61$	−13.7219	−1.75691	−0.878456	−	0.477823i	$-0.841426\pi$
$61$	−13.7219	−1.75691	−0.878456	+	0.477823i	$0.841426\pi$
$62$	−1.83909	−0.233564
$63$	−5.89028	−0.742106
$64$	1.00000	0.125000
$65$	12.8686	1.59615
$66$	16.5736	2.04007
$67$	−10.9873	−1.34232	−0.671158	−	0.741314i	$-0.734203\pi$
$67$	−10.9873	−1.34232	−0.671158	+	0.741314i	$0.734203\pi$
$68$	3.37713	0.409537
$69$	−20.0933	−2.41895
$70$	1.98359	0.237084
$71$	14.4915	1.71983	0.859913	−	0.510441i	$-0.170518\pi$
$71$	14.4915	1.71983	0.859913	+	0.510441i	$0.170518\pi$
$72$	5.89028	0.694176
$73$	−10.2156	−1.19565	−0.597825	−	0.801627i	$-0.703968\pi$
$73$	−10.2156	−1.19565	−0.597825	+	0.801627i	$0.703968\pi$
$74$	3.74109	0.434893
$75$	3.17660	0.366803
$76$	5.27632	0.605235
$77$	5.55852	0.633452
$78$	19.3436	2.19023
$79$	4.82681	0.543058	0.271529	−	0.962430i	$-0.412471\pi$
$79$	4.82681	0.543058	0.271529	+	0.962430i	$0.412471\pi$
$80$	−1.98359	−0.221772
$81$	8.02456	0.891618
$82$	8.26578	0.912802
$83$	8.64763	0.949201	0.474601	−	0.880201i	$-0.342593\pi$
$83$	8.64763	0.949201	0.474601	+	0.880201i	$0.342593\pi$
$84$	2.98166	0.325325
$85$	−6.69883	−0.726590
$86$	2.39817	0.258601
$87$	−20.8997	−2.24068
$88$	−5.55852	−0.592540
$89$	−13.0342	−1.38163	−0.690813	−	0.723034i	$-0.742747\pi$
$89$	−13.0342	−1.38163	−0.690813	+	0.723034i	$0.742747\pi$
$90$	−11.6839	−1.23159
$91$	6.48754	0.680079
$92$	6.73897	0.702587
$93$	5.48353	0.568615
$94$	1.87585	0.193479
$95$	−10.4660	−1.07379
$96$	−2.98166	−0.304314
$97$	7.42890	0.754291	0.377145	−	0.926154i	$-0.376906\pi$
$97$	7.42890	0.754291	0.377145	+	0.926154i	$0.376906\pi$
$98$	1.00000	0.101015
$99$	−32.7412	−3.29062
$100$	−1.06538	−0.106538
$101$	−8.76512	−0.872162	−0.436081	−	0.899907i	$-0.643634\pi$
$101$	−8.76512	−0.872162	−0.436081	+	0.899907i	$0.643634\pi$
$102$	−10.0694	−0.997024
$103$	6.92313	0.682157	0.341078	−	0.940035i	$-0.389208\pi$
$103$	6.92313	0.682157	0.341078	+	0.940035i	$0.389208\pi$
$104$	−6.48754	−0.636155
$105$	−5.91438	−0.577184
$106$	−3.25729	−0.316376
$107$	15.6813	1.51596	0.757982	−	0.652276i	$-0.226186\pi$
$107$	15.6813	1.51596	0.757982	+	0.652276i	$0.226186\pi$
$108$	−8.61783	−0.829251
$109$	−13.2014	−1.26447	−0.632233	−	0.774778i	$-0.717862\pi$
$109$	−13.2014	−1.26447	−0.632233	+	0.774778i	$0.717862\pi$
$110$	11.0258	1.05127
$111$	−11.1547	−1.05875
$112$	−1.00000	−0.0944911
$113$	1.39060	0.130816	0.0654082	−	0.997859i	$-0.479165\pi$
$113$	1.39060	0.130816	0.0654082	+	0.997859i	$0.479165\pi$
$114$	−15.7322	−1.47345
$115$	−13.3673	−1.24651
$116$	7.00943	0.650809
$117$	−38.2134	−3.53283
$118$	−4.64958	−0.428029
$119$	−3.37713	−0.309581
$120$	5.91438	0.539906
$121$	19.8971	1.80883
$122$	−13.7219	−1.24232
$123$	−24.6457	−2.22223
$124$	−1.83909	−0.165155
$125$	12.0312	1.07610
$126$	−5.89028	−0.524748
$127$	8.79078	0.780055	0.390028	−	0.920803i	$-0.372465\pi$
$127$	8.79078	0.780055	0.390028	+	0.920803i	$0.372465\pi$
$128$	1.00000	0.0883883
$129$	−7.15051	−0.629567
$130$	12.8686	1.12865
$131$	−5.69261	−0.497366	−0.248683	−	0.968585i	$-0.579998\pi$
$131$	−5.69261	−0.497366	−0.248683	+	0.968585i	$0.579998\pi$
$132$	16.5736	1.44255
$133$	−5.27632	−0.457515
$134$	−10.9873	−0.949161
$135$	17.0942	1.47124
$136$	3.37713	0.289587
$137$	4.90022	0.418654	0.209327	−	0.977846i	$-0.432873\pi$
$137$	4.90022	0.418654	0.209327	+	0.977846i	$0.432873\pi$
$138$	−20.0933	−1.71046
$139$	−12.9972	−1.10240	−0.551202	−	0.834372i	$-0.685831\pi$
$139$	−12.9972	−1.10240	−0.551202	+	0.834372i	$0.685831\pi$
$140$	1.98359	0.167644
$141$	−5.59315	−0.471028
$142$	14.4915	1.21610
$143$	36.0611	3.01558
$144$	5.89028	0.490857
$145$	−13.9038	−1.15465
$146$	−10.2156	−0.845452
$147$	−2.98166	−0.245923
$148$	3.74109	0.307516
$149$	−14.7047	−1.20466	−0.602329	−	0.798248i	$-0.705761\pi$
$149$	−14.7047	−1.20466	−0.602329	+	0.798248i	$0.705761\pi$
$150$	3.17660	0.259369
$151$	12.9021	1.04996	0.524978	−	0.851116i	$-0.324074\pi$
$151$	12.9021	1.04996	0.524978	+	0.851116i	$0.324074\pi$
$152$	5.27632	0.427966
$153$	19.8922	1.60819
$154$	5.55852	0.447918
$155$	3.64799	0.293014
$156$	19.3436	1.54873
$157$	21.4218	1.70965	0.854823	−	0.518919i	$-0.173666\pi$
$157$	21.4218	1.70965	0.854823	+	0.518919i	$0.173666\pi$
$158$	4.82681	0.384000
$159$	9.71213	0.770222
$160$	−1.98359	−0.156816
$161$	−6.73897	−0.531106
$162$	8.02456	0.630469
$163$	14.5557	1.14009	0.570047	−	0.821612i	$-0.306925\pi$
$163$	14.5557	1.14009	0.570047	+	0.821612i	$0.306925\pi$
$164$	8.26578	0.645449
$165$	−32.8752	−2.55933
$166$	8.64763	0.671186
$167$	−24.0150	−1.85833	−0.929167	−	0.369661i	$-0.879474\pi$
$167$	−24.0150	−1.85833	−0.929167	+	0.369661i	$0.879474\pi$
$168$	2.98166	0.230040
$169$	29.0882	2.23755
$170$	−6.69883	−0.513777
$171$	31.0790	2.37667
$172$	2.39817	0.182858
$173$	−1.99514	−0.151688	−0.0758440	−	0.997120i	$-0.524165\pi$
$173$	−1.99514	−0.151688	−0.0758440	+	0.997120i	$0.524165\pi$
$174$	−20.8997	−1.58440
$175$	1.06538	0.0805353
$176$	−5.55852	−0.418989
$177$	13.8635	1.04204
$178$	−13.0342	−0.976957
$179$	−23.3234	−1.74328	−0.871638	−	0.490150i	$-0.836942\pi$
$179$	−23.3234	−1.74328	−0.871638	+	0.490150i	$0.836942\pi$
$180$	−11.6839	−0.870865
$181$	−5.80122	−0.431201	−0.215601	−	0.976482i	$-0.569171\pi$
$181$	−5.80122	−0.431201	−0.215601	+	0.976482i	$0.569171\pi$
$182$	6.48754	0.480888
$183$	40.9141	3.02446
$184$	6.73897	0.496804
$185$	−7.42078	−0.545587
$186$	5.48353	0.402072
$187$	−18.7718	−1.37273
$188$	1.87585	0.136811
$189$	8.61783	0.626855
$190$	−10.4660	−0.759286
$191$	14.9085	1.07874	0.539372	−	0.842068i	$-0.318662\pi$
$191$	14.9085	1.07874	0.539372	+	0.842068i	$0.318662\pi$
$192$	−2.98166	−0.215183
$193$	−24.3145	−1.75020	−0.875098	−	0.483946i	$-0.839203\pi$
$193$	−24.3145	−1.75020	−0.875098	+	0.483946i	$0.839203\pi$
$194$	7.42890	0.533364
$195$	−38.3697	−2.74771
$196$	1.00000	0.0714286
$197$	−5.83060	−0.415413	−0.207707	−	0.978191i	$-0.566600\pi$
$197$	−5.83060	−0.415413	−0.207707	+	0.978191i	$0.566600\pi$
$198$	−32.7412	−2.32682
$199$	−23.9756	−1.69958	−0.849792	−	0.527118i	$-0.823273\pi$
$199$	−23.9756	−1.69958	−0.849792	+	0.527118i	$0.823273\pi$
$200$	−1.06538	−0.0753339
$201$	32.7605	2.31075
$202$	−8.76512	−0.616712
$203$	−7.00943	−0.491965
$204$	−10.0694	−0.705002
$205$	−16.3959	−1.14514
$206$	6.92313	0.482358
$207$	39.6944	2.75895
$208$	−6.48754	−0.449830
$209$	−29.3285	−2.02870
$210$	−5.91438	−0.408131
$211$	−11.8048	−0.812676	−0.406338	−	0.913723i	$-0.633195\pi$
$211$	−11.8048	−0.812676	−0.406338	+	0.913723i	$0.633195\pi$
$212$	−3.25729	−0.223712
$213$	−43.2087	−2.96061
$214$	15.6813	1.07195
$215$	−4.75697	−0.324423
$216$	−8.61783	−0.586369
$217$	1.83909	0.124845
$218$	−13.2014	−0.894113
$219$	30.4595	2.05826
$220$	11.0258	0.743359
$221$	−21.9093	−1.47378
$222$	−11.1547	−0.748651
$223$	−2.42061	−0.162096	−0.0810480	−	0.996710i	$-0.525827\pi$
$223$	−2.42061	−0.162096	−0.0810480	+	0.996710i	$0.525827\pi$
$224$	−1.00000	−0.0668153
$225$	−6.27540	−0.418360
$226$	1.39060	0.0925011
$227$	21.9615	1.45763	0.728817	−	0.684708i	$-0.240070\pi$
$227$	21.9615	1.45763	0.728817	+	0.684708i	$0.240070\pi$
$228$	−15.7322	−1.04189
$229$	15.7636	1.04169	0.520843	−	0.853653i	$-0.325618\pi$
$229$	15.7636	1.04169	0.520843	+	0.853653i	$0.325618\pi$
$230$	−13.3673	−0.881416
$231$	−16.5736	−1.09046
$232$	7.00943	0.460191
$233$	3.68653	0.241512	0.120756	−	0.992682i	$-0.461468\pi$
$233$	3.68653	0.241512	0.120756	+	0.992682i	$0.461468\pi$
$234$	−38.2134	−2.49809
$235$	−3.72092	−0.242726
$236$	−4.64958	−0.302662
$237$	−14.3919	−0.934853
$238$	−3.37713	−0.218907
$239$	−15.0585	−0.974056	−0.487028	−	0.873386i	$-0.661919\pi$
$239$	−15.0585	−0.974056	−0.487028	+	0.873386i	$0.661919\pi$
$240$	5.91438	0.381771
$241$	−4.34562	−0.279926	−0.139963	−	0.990157i	$-0.544698\pi$
$241$	−4.34562	−0.279926	−0.139963	+	0.990157i	$0.544698\pi$
$242$	19.8971	1.27903
$243$	1.92698	0.123616
$244$	−13.7219	−0.878456
$245$	−1.98359	−0.126727
$246$	−24.6457	−1.57135
$247$	−34.2303	−2.17802
$248$	−1.83909	−0.116782
$249$	−25.7843	−1.63401
$250$	12.0312	0.760921
$251$	−7.31608	−0.461787	−0.230893	−	0.972979i	$-0.574165\pi$
$251$	−7.31608	−0.461787	−0.230893	+	0.972979i	$0.574165\pi$
$252$	−5.89028	−0.371053
$253$	−37.4587	−2.35501
$254$	8.79078	0.551582
$255$	19.9736	1.25080
$256$	1.00000	0.0625000
$257$	−26.2045	−1.63459	−0.817296	−	0.576218i	$-0.804528\pi$
$257$	−26.2045	−1.63459	−0.817296	+	0.576218i	$0.804528\pi$
$258$	−7.15051	−0.445171
$259$	−3.74109	−0.232460
$260$	12.8686	0.798077
$261$	41.2875	2.55563
$262$	−5.69261	−0.351691
$263$	−5.04158	−0.310877	−0.155439	−	0.987846i	$-0.549679\pi$
$263$	−5.04158	−0.310877	−0.155439	+	0.987846i	$0.549679\pi$
$264$	16.5736	1.02003
$265$	6.46113	0.396904
$266$	−5.27632	−0.323512
$267$	38.8636	2.37841
$268$	−10.9873	−0.671158
$269$	−15.3059	−0.933216	−0.466608	−	0.884464i	$-0.654524\pi$
$269$	−15.3059	−0.933216	−0.466608	+	0.884464i	$0.654524\pi$
$270$	17.0942	1.04032
$271$	−12.2613	−0.744821	−0.372410	−	0.928068i	$-0.621469\pi$
$271$	−12.2613	−0.744821	−0.372410	+	0.928068i	$0.621469\pi$
$272$	3.37713	0.204769
$273$	−19.3436	−1.17073
$274$	4.90022	0.296033
$275$	5.92194	0.357107
$276$	−20.0933	−1.20948
$277$	22.0102	1.32246	0.661231	−	0.750182i	$-0.270034\pi$
$277$	22.0102	1.32246	0.661231	+	0.750182i	$0.270034\pi$
$278$	−12.9972	−0.779517
$279$	−10.8327	−0.648539
$280$	1.98359	0.118542
$281$	−14.7926	−0.882455	−0.441228	−	0.897395i	$-0.645457\pi$
$281$	−14.7926	−0.882455	−0.441228	+	0.897395i	$0.645457\pi$
$282$	−5.59315	−0.333067
$283$	3.41439	0.202964	0.101482	−	0.994837i	$-0.467642\pi$
$283$	3.41439	0.202964	0.101482	+	0.994837i	$0.467642\pi$
$284$	14.4915	0.859913
$285$	31.2061	1.84849
$286$	36.0611	2.13234
$287$	−8.26578	−0.487913
$288$	5.89028	0.347088
$289$	−5.59499	−0.329117
$290$	−13.9038	−0.816460
$291$	−22.1504	−1.29848
$292$	−10.2156	−0.597825
$293$	−11.8301	−0.691124	−0.345562	−	0.938396i	$-0.612312\pi$
$293$	−11.8301	−0.691124	−0.345562	+	0.938396i	$0.612312\pi$
$294$	−2.98166	−0.173894
$295$	9.22285	0.536975
$296$	3.74109	0.217447
$297$	47.9023	2.77957
$298$	−14.7047	−0.851822
$299$	−43.7194	−2.52836
$300$	3.17660	0.183401
$301$	−2.39817	−0.138228
$302$	12.9021	0.742431
$303$	26.1346	1.50139
$304$	5.27632	0.302618
$305$	27.2186	1.55853
$306$	19.8922	1.13716
$307$	13.0487	0.744731	0.372366	−	0.928086i	$-0.378547\pi$
$307$	13.0487	0.744731	0.372366	+	0.928086i	$0.378547\pi$
$308$	5.55852	0.316726
$309$	−20.6424	−1.17431
$310$	3.64799	0.207192
$311$	−13.4116	−0.760505	−0.380252	−	0.924883i	$-0.624163\pi$
$311$	−13.4116	−0.760505	−0.380252	+	0.924883i	$0.624163\pi$
$312$	19.3436	1.09512
$313$	−12.4329	−0.702747	−0.351374	−	0.936235i	$-0.614285\pi$
$313$	−12.4329	−0.702747	−0.351374	+	0.936235i	$0.614285\pi$
$314$	21.4218	1.20890
$315$	11.6839	0.658312
$316$	4.82681	0.271529
$317$	−11.6699	−0.655446	−0.327723	−	0.944774i	$-0.606281\pi$
$317$	−11.6699	−0.655446	−0.327723	+	0.944774i	$0.606281\pi$
$318$	9.71213	0.544629
$319$	−38.9620	−2.18145
$320$	−1.98359	−0.110886
$321$	−46.7561	−2.60967
$322$	−6.73897	−0.375548
$323$	17.8188	0.991466
$324$	8.02456	0.445809
$325$	6.91171	0.383393
$326$	14.5557	0.806168
$327$	39.3621	2.17673
$328$	8.26578	0.456401
$329$	−1.87585	−0.103419
$330$	−32.8752	−1.80972
$331$	15.7710	0.866850	0.433425	−	0.901190i	$-0.357305\pi$
$331$	15.7710	0.866850	0.433425	+	0.901190i	$0.357305\pi$
$332$	8.64763	0.474601
$333$	22.0361	1.20757
$334$	−24.0150	−1.31404
$335$	21.7943	1.19075
$336$	2.98166	0.162663
$337$	−6.13809	−0.334363	−0.167181	−	0.985926i	$-0.553467\pi$
$337$	−6.13809	−0.334363	−0.167181	+	0.985926i	$0.553467\pi$
$338$	29.0882	1.58219
$339$	−4.14628	−0.225195
$340$	−6.69883	−0.363295
$341$	10.2226	0.553584
$342$	31.0790	1.68056
$343$	−1.00000	−0.0539949
$344$	2.39817	0.129300
$345$	39.8568	2.14582
$346$	−1.99514	−0.107260
$347$	33.2389	1.78436	0.892179	−	0.451682i	$-0.149176\pi$
$347$	33.2389	1.78436	0.892179	+	0.451682i	$0.149176\pi$
$348$	−20.8997	−1.12034
$349$	20.7250	1.10938	0.554691	−	0.832056i	$-0.312837\pi$
$349$	20.7250	1.10938	0.554691	+	0.832056i	$0.312837\pi$
$350$	1.06538	0.0569471
$351$	55.9085	2.98417
$352$	−5.55852	−0.296270
$353$	17.3281	0.922284	0.461142	−	0.887326i	$-0.347440\pi$
$353$	17.3281	0.922284	0.461142	+	0.887326i	$0.347440\pi$
$354$	13.8635	0.736835
$355$	−28.7452	−1.52564
$356$	−13.0342	−0.690813
$357$	10.0694	0.532932
$358$	−23.3234	−1.23268
$359$	−29.9553	−1.58098	−0.790490	−	0.612475i	$-0.790174\pi$
$359$	−29.9553	−1.58098	−0.790490	+	0.612475i	$0.790174\pi$
$360$	−11.6839	−0.615795
$361$	8.83955	0.465240
$362$	−5.80122	−0.304905
$363$	−59.3263	−3.11382
$364$	6.48754	0.340039
$365$	20.2636	1.06064
$366$	40.9141	2.13861
$367$	6.18481	0.322845	0.161422	−	0.986885i	$-0.448392\pi$
$367$	6.18481	0.322845	0.161422	+	0.986885i	$0.448392\pi$
$368$	6.73897	0.351293
$369$	48.6877	2.53458
$370$	−7.42078	−0.385788
$371$	3.25729	0.169110
$372$	5.48353	0.284308
$373$	−14.2403	−0.737333	−0.368666	−	0.929562i	$-0.620186\pi$
$373$	−14.2403	−0.737333	−0.368666	+	0.929562i	$0.620186\pi$
$374$	−18.7718	−0.970668
$375$	−35.8730	−1.85247
$376$	1.87585	0.0967397
$377$	−45.4739	−2.34203
$378$	8.61783	0.443253
$379$	−0.0192138	−0.000986949 0	−0.000493474	−	1.00000i	$-0.500157\pi$
$379$	−0.0192138	−0.000986949 0	−0.000493474		1.00000i	$0.500157\pi$
$380$	−10.4660	−0.536897
$381$	−26.2111	−1.34283
$382$	14.9085	0.762787
$383$	−14.6925	−0.750752	−0.375376	−	0.926873i	$-0.622486\pi$
$383$	−14.6925	−0.750752	−0.375376	+	0.926873i	$0.622486\pi$
$384$	−2.98166	−0.152157
$385$	−11.0258	−0.561927
$386$	−24.3145	−1.23758
$387$	14.1259	0.718058
$388$	7.42890	0.377145
$389$	−16.8236	−0.852989	−0.426495	−	0.904490i	$-0.640252\pi$
$389$	−16.8236	−0.852989	−0.426495	+	0.904490i	$0.640252\pi$
$390$	−38.3697	−1.94293
$391$	22.7584	1.15094
$392$	1.00000	0.0505076
$393$	16.9734	0.856195
$394$	−5.83060	−0.293741
$395$	−9.57439	−0.481740
$396$	−32.7412	−1.64531
$397$	11.9277	0.598632	0.299316	−	0.954154i	$-0.403241\pi$
$397$	11.9277	0.598632	0.299316	+	0.954154i	$0.403241\pi$
$398$	−23.9756	−1.20179
$399$	15.7322	0.787594
$400$	−1.06538	−0.0532691
$401$	−3.68045	−0.183793	−0.0918964	−	0.995769i	$-0.529293\pi$
$401$	−3.68045	−0.183793	−0.0918964	+	0.995769i	$0.529293\pi$
$402$	32.7605	1.63394
$403$	11.9311	0.594333
$404$	−8.76512	−0.436081
$405$	−15.9174	−0.790943
$406$	−7.00943	−0.347872
$407$	−20.7949	−1.03077
$408$	−10.0694	−0.498512
$409$	8.56624	0.423573	0.211787	−	0.977316i	$-0.432072\pi$
$409$	8.56624	0.423573	0.211787	+	0.977316i	$0.432072\pi$
$410$	−16.3959	−0.809735
$411$	−14.6108	−0.720696
$412$	6.92313	0.341078
$413$	4.64958	0.228791
$414$	39.6944	1.95088
$415$	−17.1533	−0.842024
$416$	−6.48754	−0.318078
$417$	38.7531	1.89775
$418$	−29.3285	−1.43450
$419$	−9.80165	−0.478842	−0.239421	−	0.970916i	$-0.576958\pi$
$419$	−9.80165	−0.478842	−0.239421	+	0.970916i	$0.576958\pi$
$420$	−5.91438	−0.288592
$421$	−2.56212	−0.124870	−0.0624350	−	0.998049i	$-0.519887\pi$
$421$	−2.56212	−0.124870	−0.0624350	+	0.998049i	$0.519887\pi$
$422$	−11.8048	−0.574649
$423$	11.0493	0.537235
$424$	−3.25729	−0.158188
$425$	−3.59793	−0.174525
$426$	−43.2087	−2.09347
$427$	13.7219	0.664051
$428$	15.6813	0.757982
$429$	−107.522	−5.19120
$430$	−4.75697	−0.229401
$431$	1.00000	0.0481683
$431$	1.00000	0.0481683
$432$	−8.61783	−0.414625
$433$	15.2892	0.734753	0.367376	−	0.930072i	$-0.380256\pi$
$433$	15.2892	0.734753	0.367376	+	0.930072i	$0.380256\pi$
$434$	1.83909	0.0882790
$435$	41.4564	1.98768
$436$	−13.2014	−0.632233
$437$	35.5570	1.70092
$438$	30.4595	1.45541
$439$	30.3410	1.44809	0.724047	−	0.689750i	$-0.242280\pi$
$439$	30.3410	1.44809	0.724047	+	0.689750i	$0.242280\pi$
$440$	11.0258	0.525634
$441$	5.89028	0.280490
$442$	−21.9093	−1.04212
$443$	−4.50170	−0.213882	−0.106941	−	0.994265i	$-0.534106\pi$
$443$	−4.50170	−0.213882	−0.106941	+	0.994265i	$0.534106\pi$
$444$	−11.1547	−0.529376
$445$	25.8545	1.22562
$446$	−2.42061	−0.114619
$447$	43.8445	2.07377
$448$	−1.00000	−0.0472456
$449$	−39.3203	−1.85564	−0.927819	−	0.373030i	$-0.878319\pi$
$449$	−39.3203	−1.85564	−0.927819	+	0.373030i	$0.878319\pi$
$450$	−6.27540	−0.295825
$451$	−45.9454	−2.16349
$452$	1.39060	0.0654082
$453$	−38.4696	−1.80746
$454$	21.9615	1.03070
$455$	−12.8686	−0.603289
$456$	−15.7322	−0.736727
$457$	−11.5203	−0.538897	−0.269449	−	0.963015i	$-0.586841\pi$
$457$	−11.5203	−0.538897	−0.269449	+	0.963015i	$0.586841\pi$
$458$	15.7636	0.736583
$459$	−29.1035	−1.35844
$460$	−13.3673	−0.623256
$461$	−4.77516	−0.222401	−0.111201	−	0.993798i	$-0.535470\pi$
$461$	−4.77516	−0.222401	−0.111201	+	0.993798i	$0.535470\pi$
$462$	−16.5736	−0.771073
$463$	−21.5915	−1.00344	−0.501721	−	0.865030i	$-0.667300\pi$
$463$	−21.5915	−1.00344	−0.501721	+	0.865030i	$0.667300\pi$
$464$	7.00943	0.325405
$465$	−10.8771	−0.504411
$466$	3.68653	0.170775
$467$	31.4137	1.45365	0.726826	−	0.686822i	$-0.240995\pi$
$467$	31.4137	1.45365	0.726826	+	0.686822i	$0.240995\pi$
$468$	−38.2134	−1.76642
$469$	10.9873	0.507348
$470$	−3.72092	−0.171633
$471$	−63.8725	−2.94309
$472$	−4.64958	−0.214014
$473$	−13.3302	−0.612925
$474$	−14.3919	−0.661041
$475$	−5.62130	−0.257923
$476$	−3.37713	−0.154791
$477$	−19.1864	−0.878484
$478$	−15.0585	−0.688761
$479$	−1.66244	−0.0759589	−0.0379794	−	0.999279i	$-0.512092\pi$
$479$	−1.66244	−0.0759589	−0.0379794	+	0.999279i	$0.512092\pi$
$480$	5.91438	0.269953
$481$	−24.2705	−1.10664
$482$	−4.34562	−0.197938
$483$	20.0933	0.914277
$484$	19.8971	0.904413
$485$	−14.7359	−0.669122
$486$	1.92698	0.0874097
$487$	−0.363217	−0.0164589	−0.00822947	−	0.999966i	$-0.502620\pi$
$487$	−0.363217	−0.0164589	−0.00822947	+	0.999966i	$0.502620\pi$
$488$	−13.7219	−0.621162
$489$	−43.4002	−1.96263
$490$	−1.98359	−0.0896093
$491$	28.0585	1.26626	0.633131	−	0.774044i	$-0.281769\pi$
$491$	28.0585	1.26626	0.633131	+	0.774044i	$0.281769\pi$
$492$	−24.6457	−1.11111
$493$	23.6718	1.06612
$494$	−34.2303	−1.54010
$495$	64.9451	2.91906
$496$	−1.83909	−0.0825774
$497$	−14.4915	−0.650033
$498$	−25.7843	−1.15542
$499$	19.5241	0.874020	0.437010	−	0.899457i	$-0.356037\pi$
$499$	19.5241	0.874020	0.437010	+	0.899457i	$0.356037\pi$
$500$	12.0312	0.538052
$501$	71.6044	3.19905
$502$	−7.31608	−0.326533
$503$	1.68872	0.0752963	0.0376481	−	0.999291i	$-0.488013\pi$
$503$	1.68872	0.0752963	0.0376481	+	0.999291i	$0.488013\pi$
$504$	−5.89028	−0.262374
$505$	17.3864	0.773684
$506$	−37.4587	−1.66524
$507$	−86.7309	−3.85186
$508$	8.79078	0.390028
$509$	−14.2521	−0.631713	−0.315856	−	0.948807i	$-0.602292\pi$
$509$	−14.2521	−0.631713	−0.315856	+	0.948807i	$0.602292\pi$
$510$	19.9736	0.884447
$511$	10.2156	0.451913
$512$	1.00000	0.0441942
$513$	−45.4704	−2.00757
$514$	−26.2045	−1.15583
$515$	−13.7326	−0.605132
$516$	−7.15051	−0.314783
$517$	−10.4270	−0.458577
$518$	−3.74109	−0.164374
$519$	5.94884	0.261125
$520$	12.8686	0.564325
$521$	37.7936	1.65577	0.827885	−	0.560898i	$-0.189544\pi$
$521$	37.7936	1.65577	0.827885	+	0.560898i	$0.189544\pi$
$522$	41.2875	1.80710
$523$	−40.3303	−1.76352	−0.881760	−	0.471698i	$-0.843641\pi$
$523$	−40.3303	−1.76352	−0.881760	+	0.471698i	$0.843641\pi$
$524$	−5.69261	−0.248683
$525$	−3.17660	−0.138638
$526$	−5.04158	−0.219823
$527$	−6.21084	−0.270548
$528$	16.5736	0.721273
$529$	22.4138	0.974512
$530$	6.46113	0.280653
$531$	−27.3873	−1.18851
$532$	−5.27632	−0.228757
$533$	−53.6245	−2.32274
$534$	38.8636	1.68179
$535$	−31.1051	−1.34479
$536$	−10.9873	−0.474581
$537$	69.5425	3.00098
$538$	−15.3059	−0.659883
$539$	−5.55852	−0.239422
$540$	17.0942	0.735618
$541$	32.8604	1.41278	0.706390	−	0.707823i	$-0.250322\pi$
$541$	32.8604	1.41278	0.706390	+	0.707823i	$0.250322\pi$
$542$	−12.2613	−0.526668
$543$	17.2973	0.742296
$544$	3.37713	0.144793
$545$	26.1862	1.12169
$546$	−19.3436	−0.827830
$547$	−37.3889	−1.59864	−0.799318	−	0.600909i	$-0.794806\pi$
$547$	−37.3889	−1.59864	−0.799318	+	0.600909i	$0.794806\pi$
$548$	4.90022	0.209327
$549$	−80.8260	−3.44957
$550$	5.92194	0.252512
$551$	36.9840	1.57557
$552$	−20.0933	−0.855228
$553$	−4.82681	−0.205257
$554$	22.0102	0.935122
$555$	22.1262	0.939206
$556$	−12.9972	−0.551202
$557$	−20.3242	−0.861164	−0.430582	−	0.902551i	$-0.641692\pi$
$557$	−20.3242	−0.861164	−0.430582	+	0.902551i	$0.641692\pi$
$558$	−10.8327	−0.458586
$559$	−15.5582	−0.658041
$560$	1.98359	0.0838219
$561$	55.9712	2.36310
$562$	−14.7926	−0.623990
$563$	8.99196	0.378966	0.189483	−	0.981884i	$-0.439319\pi$
$563$	8.99196	0.378966	0.189483	+	0.981884i	$0.439319\pi$
$564$	−5.59315	−0.235514
$565$	−2.75837	−0.116045
$566$	3.41439	0.143517
$567$	−8.02456	−0.337000
$568$	14.4915	0.608050
$569$	−33.3672	−1.39882	−0.699412	−	0.714718i	$-0.746555\pi$
$569$	−33.3672	−1.39882	−0.699412	+	0.714718i	$0.746555\pi$
$570$	31.2061	1.30708
$571$	18.0889	0.756998	0.378499	−	0.925602i	$-0.376440\pi$
$571$	18.0889	0.756998	0.378499	+	0.925602i	$0.376440\pi$
$572$	36.0611	1.50779
$573$	−44.4521	−1.85702
$574$	−8.26578	−0.345007
$575$	−7.17958	−0.299409
$576$	5.89028	0.245428
$577$	−32.8432	−1.36728	−0.683640	−	0.729819i	$-0.739604\pi$
$577$	−32.8432	−1.36728	−0.683640	+	0.729819i	$0.739604\pi$
$578$	−5.59499	−0.232721
$579$	72.4975	3.01289
$580$	−13.9038	−0.577324
$581$	−8.64763	−0.358764
$582$	−22.1504	−0.918165
$583$	18.1057	0.749862
$584$	−10.2156	−0.422726
$585$	75.7997	3.13393
$586$	−11.8301	−0.488699
$587$	−41.0629	−1.69485	−0.847425	−	0.530916i	$-0.821848\pi$
$587$	−41.0629	−1.69485	−0.847425	+	0.530916i	$0.821848\pi$
$588$	−2.98166	−0.122961
$589$	−9.70361	−0.399830
$590$	9.22285	0.379699
$591$	17.3849	0.715117
$592$	3.74109	0.153758
$593$	−23.0989	−0.948560	−0.474280	−	0.880374i	$-0.657292\pi$
$593$	−23.0989	−0.948560	−0.474280	+	0.880374i	$0.657292\pi$
$594$	47.9023	1.96546
$595$	6.69883	0.274625
$596$	−14.7047	−0.602329
$597$	71.4870	2.92577
$598$	−43.7194	−1.78782
$599$	−42.5187	−1.73727	−0.868633	−	0.495457i	$-0.835001\pi$
$599$	−42.5187	−1.73727	−0.868633	+	0.495457i	$0.835001\pi$
$600$	3.17660	0.129684
$601$	38.8633	1.58527	0.792634	−	0.609698i	$-0.208709\pi$
$601$	38.8633	1.58527	0.792634	+	0.609698i	$0.208709\pi$
$602$	−2.39817	−0.0977419
$603$	−64.7185	−2.63554
$604$	12.9021	0.524978
$605$	−39.4676	−1.60459
$606$	26.1346	1.06164
$607$	45.0730	1.82946	0.914729	−	0.404068i	$-0.132404\pi$
$607$	45.0730	1.82946	0.914729	+	0.404068i	$0.132404\pi$
$608$	5.27632	0.213983
$609$	20.8997	0.846899
$610$	27.2186	1.10205
$611$	−12.1697	−0.492332
$612$	19.8922	0.804096
$613$	1.62506	0.0656357	0.0328178	−	0.999461i	$-0.489552\pi$
$613$	1.62506	0.0656357	0.0328178	+	0.999461i	$0.489552\pi$
$614$	13.0487	0.526604
$615$	48.8869	1.97131
$616$	5.55852	0.223959
$617$	−34.6119	−1.39342	−0.696712	−	0.717351i	$-0.745355\pi$
$617$	−34.6119	−1.39342	−0.696712	+	0.717351i	$0.745355\pi$
$618$	−20.6424	−0.830360
$619$	3.96944	0.159545	0.0797726	−	0.996813i	$-0.474581\pi$
$619$	3.96944	0.159545	0.0797726	+	0.996813i	$0.474581\pi$
$620$	3.64799	0.146507
$621$	−58.0753	−2.33048
$622$	−13.4116	−0.537758
$623$	13.0342	0.522205
$624$	19.3436	0.774364
$625$	−18.5381	−0.741522
$626$	−12.4329	−0.496918
$627$	87.4476	3.49232
$628$	21.4218	0.854823
$629$	12.6342	0.503757
$630$	11.6839	0.465497
$631$	5.07142	0.201890	0.100945	−	0.994892i	$-0.467813\pi$
$631$	5.07142	0.201890	0.100945	+	0.994892i	$0.467813\pi$
$632$	4.82681	0.192000
$633$	35.1979	1.39899
$634$	−11.6699	−0.463470
$635$	−17.4373	−0.691977
$636$	9.71213	0.385111
$637$	−6.48754	−0.257046
$638$	−38.9620	−1.54252
$639$	85.3590	3.37675
$640$	−1.98359	−0.0784082
$641$	−8.12652	−0.320978	−0.160489	−	0.987038i	$-0.551307\pi$
$641$	−8.12652	−0.320978	−0.160489	+	0.987038i	$0.551307\pi$
$642$	−46.7561	−1.84532
$643$	41.3799	1.63186	0.815931	−	0.578149i	$-0.196225\pi$
$643$	41.3799	1.63186	0.815931	+	0.578149i	$0.196225\pi$
$644$	−6.73897	−0.265553
$645$	14.1837	0.558481
$646$	17.8188	0.701072
$647$	2.18079	0.0857357	0.0428678	−	0.999081i	$-0.486351\pi$
$647$	2.18079	0.0857357	0.0428678	+	0.999081i	$0.486351\pi$
$648$	8.02456	0.315235
$649$	25.8448	1.01450
$650$	6.91171	0.271099
$651$	−5.48353	−0.214916
$652$	14.5557	0.570047
$653$	−18.7517	−0.733811	−0.366905	−	0.930258i	$-0.619583\pi$
$653$	−18.7517	−0.733811	−0.366905	+	0.930258i	$0.619583\pi$
$654$	39.3621	1.53918
$655$	11.2918	0.441207
$656$	8.26578	0.322724
$657$	−60.1729	−2.34757
$658$	−1.87585	−0.0731283
$659$	6.47340	0.252168	0.126084	−	0.992020i	$-0.459759\pi$
$659$	6.47340	0.252168	0.126084	+	0.992020i	$0.459759\pi$
$660$	−32.8752	−1.27966
$661$	0.283461	0.0110254	0.00551268	−	0.999985i	$-0.498245\pi$
$661$	0.283461	0.0110254	0.00551268	+	0.999985i	$0.498245\pi$
$662$	15.7710	0.612956
$663$	65.3259	2.53705
$664$	8.64763	0.335593
$665$	10.4660	0.405856
$666$	22.0361	0.853881
$667$	47.2364	1.82900
$668$	−24.0150	−0.929167
$669$	7.21743	0.279042
$670$	21.7943	0.841989
$671$	76.2735	2.94451
$672$	2.98166	0.115020
$673$	41.2082	1.58846	0.794229	−	0.607619i	$-0.207875\pi$
$673$	41.2082	1.58846	0.794229	+	0.607619i	$0.207875\pi$
$674$	−6.13809	−0.236430
$675$	9.18128	0.353388
$676$	29.0882	1.11878
$677$	3.31268	0.127317	0.0636584	−	0.997972i	$-0.479723\pi$
$677$	3.31268	0.127317	0.0636584	+	0.997972i	$0.479723\pi$
$678$	−4.14628	−0.159237
$679$	−7.42890	−0.285095
$680$	−6.69883	−0.256888
$681$	−65.4816	−2.50926
$682$	10.2226	0.391443
$683$	19.9460	0.763212	0.381606	−	0.924325i	$-0.375371\pi$
$683$	19.9460	0.763212	0.381606	+	0.924325i	$0.375371\pi$
$684$	31.0790	1.18834
$685$	−9.72000	−0.371382
$686$	−1.00000	−0.0381802
$687$	−47.0015	−1.79322
$688$	2.39817	0.0914292
$689$	21.1318	0.805058
$690$	39.8568	1.51732
$691$	−2.20915	−0.0840400	−0.0420200	−	0.999117i	$-0.513379\pi$
$691$	−2.20915	−0.0840400	−0.0420200	+	0.999117i	$0.513379\pi$
$692$	−1.99514	−0.0758440
$693$	32.7412	1.24374
$694$	33.2389	1.26173
$695$	25.7810	0.977929
$696$	−20.8997	−0.792202
$697$	27.9146	1.05734
$698$	20.7250	0.784451
$699$	−10.9920	−0.415754
$700$	1.06538	0.0402677
$701$	5.78779	0.218602	0.109301	−	0.994009i	$-0.465139\pi$
$701$	5.78779	0.218602	0.109301	+	0.994009i	$0.465139\pi$
$702$	55.9085	2.11013
$703$	19.7392	0.744478
$704$	−5.55852	−0.209494
$705$	11.0945	0.417843
$706$	17.3281	0.652154
$707$	8.76512	0.329646
$708$	13.8635	0.521021
$709$	16.0817	0.603960	0.301980	−	0.953314i	$-0.402352\pi$
$709$	16.0817	0.603960	0.301980	+	0.953314i	$0.402352\pi$
$710$	−28.7452	−1.07879
$711$	28.4312	1.06625
$712$	−13.0342	−0.488478
$713$	−12.3936	−0.464142
$714$	10.0694	0.376840
$715$	−71.5303	−2.67508
$716$	−23.3234	−0.871638
$717$	44.8994	1.67680
$718$	−29.9553	−1.11792
$719$	16.7088	0.623133	0.311567	−	0.950224i	$-0.399146\pi$
$719$	16.7088	0.623133	0.311567	+	0.950224i	$0.399146\pi$
$720$	−11.6839	−0.435433
$721$	−6.92313	−0.257831
$722$	8.83955	0.328974
$723$	12.9572	0.481882
$724$	−5.80122	−0.215601
$725$	−7.46772	−0.277344
$726$	−59.3263	−2.20181
$727$	19.0615	0.706953	0.353477	−	0.935443i	$-0.384999\pi$
$727$	19.0615	0.706953	0.353477	+	0.935443i	$0.384999\pi$
$728$	6.48754	0.240444
$729$	−29.8193	−1.10442
$730$	20.2636	0.749989
$731$	8.09892	0.299549
$732$	40.9141	1.51223
$733$	−34.9721	−1.29173	−0.645863	−	0.763453i	$-0.723502\pi$
$733$	−34.9721	−1.29173	−0.645863	+	0.763453i	$0.723502\pi$
$734$	6.18481	0.228286
$735$	5.91438	0.218155
$736$	6.73897	0.248402
$737$	61.0733	2.24966
$738$	48.6877	1.79222
$739$	−28.6401	−1.05354	−0.526771	−	0.850007i	$-0.676598\pi$
$739$	−28.6401	−1.05354	−0.526771	+	0.850007i	$0.676598\pi$
$740$	−7.42078	−0.272793
$741$	102.063	3.74938
$742$	3.25729	0.119579
$743$	41.1032	1.50793	0.753966	−	0.656914i	$-0.228139\pi$
$743$	41.1032	1.50793	0.753966	+	0.656914i	$0.228139\pi$
$744$	5.48353	0.201036
$745$	29.1681	1.06864
$746$	−14.2403	−0.521373
$747$	50.9370	1.86369
$748$	−18.7718	−0.686366
$749$	−15.6813	−0.572980
$750$	−35.8730	−1.30990
$751$	−18.6553	−0.680742	−0.340371	−	0.940291i	$-0.610553\pi$
$751$	−18.6553	−0.680742	−0.340371	+	0.940291i	$0.610553\pi$
$752$	1.87585	0.0684053
$753$	21.8140	0.794948
$754$	−45.4739	−1.65606
$755$	−25.5924	−0.931403
$756$	8.61783	0.313427
$757$	−16.3696	−0.594961	−0.297481	−	0.954728i	$-0.596146\pi$
$757$	−16.3696	−0.594961	−0.297481	+	0.954728i	$0.596146\pi$
$758$	−0.0192138	−0.000697878 0
$759$	111.689	4.05405
$760$	−10.4660	−0.379643
$761$	−23.9833	−0.869395	−0.434698	−	0.900576i	$-0.643145\pi$
$761$	−23.9833	−0.869395	−0.434698	+	0.900576i	$0.643145\pi$
$762$	−26.2111	−0.949527
$763$	13.2014	0.477923
$764$	14.9085	0.539372
$765$	−39.4580	−1.42661
$766$	−14.6925	−0.530862
$767$	30.1643	1.08917
$768$	−2.98166	−0.107591
$769$	−26.0804	−0.940484	−0.470242	−	0.882537i	$-0.655833\pi$
$769$	−26.0804	−0.940484	−0.470242	+	0.882537i	$0.655833\pi$
$770$	−11.0258	−0.397342
$771$	78.1328	2.81389
$772$	−24.3145	−0.875098
$773$	−9.97718	−0.358854	−0.179427	−	0.983771i	$-0.557424\pi$
$773$	−9.97718	−0.358854	−0.179427	+	0.983771i	$0.557424\pi$
$774$	14.1259	0.507744
$775$	1.95933	0.0703812
$776$	7.42890	0.266682
$777$	11.1547	0.400171
$778$	−16.8236	−0.603155
$779$	43.6129	1.56259
$780$	−38.3697	−1.37386
$781$	−80.5513	−2.88235
$782$	22.7584	0.813838
$783$	−60.4060	−2.15874
$784$	1.00000	0.0357143
$785$	−42.4920	−1.51661
$786$	16.9734	0.605422
$787$	−29.1787	−1.04011	−0.520055	−	0.854133i	$-0.674088\pi$
$787$	−29.1787	−1.04011	−0.520055	+	0.854133i	$0.674088\pi$
$788$	−5.83060	−0.207707
$789$	15.0323	0.535163
$790$	−9.57439	−0.340642
$791$	−1.39060	−0.0494439
$792$	−32.7412	−1.16341
$793$	89.0215	3.16125
$794$	11.9277	0.423297
$795$	−19.2649	−0.683254
$796$	−23.9756	−0.849792
$797$	12.4443	0.440798	0.220399	−	0.975410i	$-0.429264\pi$
$797$	12.4443	0.440798	0.220399	+	0.975410i	$0.429264\pi$
$798$	15.7322	0.556913
$799$	6.33500	0.224116
$800$	−1.06538	−0.0376669
$801$	−76.7753	−2.71272
$802$	−3.68045	−0.129961
$803$	56.7837	2.00385
$804$	32.7605	1.15537
$805$	13.3673	0.471137
$806$	11.9311	0.420257
$807$	45.6369	1.60649
$808$	−8.76512	−0.308356
$809$	38.6150	1.35763	0.678816	−	0.734308i	$-0.262493\pi$
$809$	38.6150	1.35763	0.678816	+	0.734308i	$0.262493\pi$
$810$	−15.9174	−0.559281
$811$	41.9673	1.47367	0.736836	−	0.676072i	$-0.236319\pi$
$811$	41.9673	1.47367	0.736836	+	0.676072i	$0.236319\pi$
$812$	−7.00943	−0.245983
$813$	36.5590	1.28218
$814$	−20.7949	−0.728861
$815$	−28.8726	−1.01136
$816$	−10.0694	−0.352501
$817$	12.6535	0.442689
$818$	8.56624	0.299512
$819$	38.2134	1.33529
$820$	−16.3959	−0.572569
$821$	−22.1582	−0.773326	−0.386663	−	0.922221i	$-0.626372\pi$
$821$	−22.1582	−0.773326	−0.386663	+	0.922221i	$0.626372\pi$
$822$	−14.6108	−0.509609
$823$	9.31155	0.324580	0.162290	−	0.986743i	$-0.448112\pi$
$823$	9.31155	0.324580	0.162290	+	0.986743i	$0.448112\pi$
$824$	6.92313	0.241179
$825$	−17.6572	−0.614745
$826$	4.64958	0.161780
$827$	−10.9730	−0.381567	−0.190784	−	0.981632i	$-0.561103\pi$
$827$	−10.9730	−0.381567	−0.190784	+	0.981632i	$0.561103\pi$
$828$	39.6944	1.37948
$829$	−16.1871	−0.562200	−0.281100	−	0.959679i	$-0.590699\pi$
$829$	−16.1871	−0.562200	−0.281100	+	0.959679i	$0.590699\pi$
$830$	−17.1533	−0.595401
$831$	−65.6267	−2.27657
$832$	−6.48754	−0.224915
$833$	3.37713	0.117011
$834$	38.7531	1.34191
$835$	47.6358	1.64850
$836$	−29.3285	−1.01435
$837$	15.8489	0.547819
$838$	−9.80165	−0.338592
$839$	−26.4670	−0.913744	−0.456872	−	0.889533i	$-0.651030\pi$
$839$	−26.4670	−0.913744	−0.456872	+	0.889533i	$0.651030\pi$
$840$	−5.91438	−0.204065
$841$	20.1321	0.694210
$842$	−2.56212	−0.0882964
$843$	44.1066	1.51911
$844$	−11.8048	−0.406338
$845$	−57.6989	−1.98490
$846$	11.0493	0.379883
$847$	−19.8971	−0.683672
$848$	−3.25729	−0.111856
$849$	−10.1805	−0.349395
$850$	−3.59793	−0.123408
$851$	25.2111	0.864226
$852$	−43.2087	−1.48031
$853$	20.9872	0.718589	0.359294	−	0.933224i	$-0.383017\pi$
$853$	20.9872	0.718589	0.359294	+	0.933224i	$0.383017\pi$
$854$	13.7219	0.469555
$855$	−61.6479	−2.10831
$856$	15.6813	0.535974
$857$	−5.53472	−0.189063	−0.0945313	−	0.995522i	$-0.530135\pi$
$857$	−5.53472	−0.189063	−0.0945313	+	0.995522i	$0.530135\pi$
$858$	−107.522	−3.67073
$859$	−41.4820	−1.41535	−0.707673	−	0.706540i	$-0.750255\pi$
$859$	−41.4820	−1.41535	−0.707673	+	0.706540i	$0.750255\pi$
$860$	−4.75697	−0.162211
$861$	24.6457	0.839924
$862$	1.00000	0.0340601
$863$	−30.6260	−1.04252	−0.521261	−	0.853397i	$-0.674538\pi$
$863$	−30.6260	−1.04252	−0.521261	+	0.853397i	$0.674538\pi$
$864$	−8.61783	−0.293184
$865$	3.95754	0.134560
$866$	15.2892	0.519549
$867$	16.6823	0.566562
$868$	1.83909	0.0624227
$869$	−26.8299	−0.910141
$870$	41.4564	1.40550
$871$	71.2808	2.41526
$872$	−13.2014	−0.447056
$873$	43.7583	1.48099
$874$	35.5570	1.20273
$875$	−12.0312	−0.406729
$876$	30.4595	1.02913
$877$	−30.4544	−1.02837	−0.514185	−	0.857679i	$-0.671906\pi$
$877$	−30.4544	−1.02837	−0.514185	+	0.857679i	$0.671906\pi$
$878$	30.3410	1.02396
$879$	35.2734	1.18974
$880$	11.0258	0.371680
$881$	−50.0664	−1.68678	−0.843389	−	0.537303i	$-0.819443\pi$
$881$	−50.0664	−1.68678	−0.843389	+	0.537303i	$0.819443\pi$
$882$	5.89028	0.198336
$883$	−46.0473	−1.54962	−0.774808	−	0.632197i	$-0.782153\pi$
$883$	−46.0473	−1.54962	−0.774808	+	0.632197i	$0.782153\pi$
$884$	−21.9093	−0.736888
$885$	−27.4994	−0.924382
$886$	−4.50170	−0.151238
$887$	−1.05805	−0.0355257	−0.0177628	−	0.999842i	$-0.505654\pi$
$887$	−1.05805	−0.0355257	−0.0177628	+	0.999842i	$0.505654\pi$
$888$	−11.1547	−0.374326
$889$	−8.79078	−0.294833
$890$	25.8545	0.866646
$891$	−44.6047	−1.49431
$892$	−2.42061	−0.0810480
$893$	9.89760	0.331211
$894$	43.8445	1.46638
$895$	46.2641	1.54644
$896$	−1.00000	−0.0334077
$897$	130.356	4.35246
$898$	−39.3203	−1.31213
$899$	−12.8909	−0.429937
$900$	−6.27540	−0.209180
$901$	−11.0003	−0.366473
$902$	−45.9454	−1.52982
$903$	7.15051	0.237954
$904$	1.39060	0.0462506
$905$	11.5072	0.382513
$906$	−38.4696	−1.27807
$907$	34.0800	1.13161	0.565804	−	0.824540i	$-0.308566\pi$
$907$	34.0800	1.13161	0.565804	+	0.824540i	$0.308566\pi$
$908$	21.9615	0.728817
$909$	−51.6290	−1.71243
$910$	−12.8686	−0.426590
$911$	53.6465	1.77739	0.888695	−	0.458499i	$-0.151613\pi$
$911$	53.6465	1.77739	0.888695	+	0.458499i	$0.151613\pi$
$912$	−15.7322	−0.520944
$913$	−48.0680	−1.59082
$914$	−11.5203	−0.381058
$915$	−81.1566	−2.68296
$916$	15.7636	0.520843
$917$	5.69261	0.187987
$918$	−29.1035	−0.960559
$919$	31.0228	1.02335	0.511674	−	0.859180i	$-0.329026\pi$
$919$	31.0228	1.02335	0.511674	+	0.859180i	$0.329026\pi$
$920$	−13.3673	−0.440708
$921$	−38.9069	−1.28203
$922$	−4.77516	−0.157262
$923$	−94.0142	−3.09452
$924$	−16.5736	−0.545231
$925$	−3.98569	−0.131049
$926$	−21.5915	−0.709540
$927$	40.7792	1.33936
$928$	7.00943	0.230096
$929$	41.3209	1.35569	0.677847	−	0.735203i	$-0.262913\pi$
$929$	41.3209	1.35569	0.677847	+	0.735203i	$0.262913\pi$
$930$	−10.8771	−0.356673
$931$	5.27632	0.172924
$932$	3.68653	0.120756
$933$	39.9889	1.30918
$934$	31.4137	1.02789
$935$	37.2356	1.21773
$936$	−38.2134	−1.24904
$937$	−20.8242	−0.680297	−0.340149	−	0.940372i	$-0.610477\pi$
$937$	−20.8242	−0.680297	−0.340149	+	0.940372i	$0.610477\pi$
$938$	10.9873	0.358749
$939$	37.0706	1.20975
$940$	−3.72092	−0.121363
$941$	17.7875	0.579855	0.289928	−	0.957049i	$-0.406369\pi$
$941$	17.7875	0.579855	0.289928	+	0.957049i	$0.406369\pi$
$942$	−63.8725	−2.08108
$943$	55.7028	1.81393
$944$	−4.64958	−0.151331
$945$	−17.0942	−0.556075
$946$	−13.3302	−0.433403
$947$	−44.5737	−1.44845	−0.724225	−	0.689564i	$-0.757802\pi$
$947$	−44.5737	−1.44845	−0.724225	+	0.689564i	$0.757802\pi$
$948$	−14.3919	−0.467427
$949$	66.2743	2.15135
$950$	−5.62130	−0.182379
$951$	34.7956	1.12832
$952$	−3.37713	−0.109453
$953$	−8.26816	−0.267832	−0.133916	−	0.990993i	$-0.542755\pi$
$953$	−8.26816	−0.267832	−0.133916	+	0.990993i	$0.542755\pi$
$954$	−19.1864	−0.621182
$955$	−29.5724	−0.956940
$956$	−15.0585	−0.487028
$957$	116.171	3.75529
$958$	−1.66244	−0.0537110
$959$	−4.90022	−0.158236
$960$	5.91438	0.190886
$961$	−27.6178	−0.890895
$962$	−24.2705	−0.782511
$963$	92.3670	2.97648
$964$	−4.34562	−0.139963
$965$	48.2299	1.55258
$966$	20.0933	0.646492
$967$	34.6365	1.11383	0.556917	−	0.830568i	$-0.311984\pi$
$967$	34.6365	1.11383	0.556917	+	0.830568i	$0.311984\pi$
$968$	19.8971	0.639517
$969$	−53.1296	−1.70677
$970$	−14.7359	−0.473140
$971$	56.4722	1.81228	0.906139	−	0.422980i	$-0.139016\pi$
$971$	56.4722	1.81228	0.906139	+	0.422980i	$0.139016\pi$
$972$	1.92698	0.0618080
$973$	12.9972	0.416670
$974$	−0.363217	−0.0116382
$975$	−20.6083	−0.659995
$976$	−13.7219	−0.439228
$977$	12.6941	0.406120	0.203060	−	0.979166i	$-0.434911\pi$
$977$	12.6941	0.406120	0.203060	+	0.979166i	$0.434911\pi$
$978$	−43.4002	−1.38779
$979$	72.4510	2.31554
$980$	−1.98359	−0.0633634
$981$	−77.7601	−2.48269
$982$	28.0585	0.895383
$983$	24.7977	0.790925	0.395463	−	0.918482i	$-0.370584\pi$
$983$	24.7977	0.790925	0.395463	+	0.918482i	$0.370584\pi$
$984$	−24.6457	−0.785677
$985$	11.5655	0.368508
$986$	23.6718	0.753862
$987$	5.59315	0.178032
$988$	−34.2303	−1.08901
$989$	16.1612	0.513895
$990$	64.9451	2.06409
$991$	−6.06236	−0.192577	−0.0962885	−	0.995353i	$-0.530697\pi$
$991$	−6.06236	−0.192577	−0.0962885	+	0.995353i	$0.530697\pi$
$992$	−1.83909	−0.0583911
$993$	−47.0236	−1.49225
$994$	−14.4915	−0.459643
$995$	47.5577	1.50768
$996$	−25.7843	−0.817006
$997$	14.7140	0.465996	0.232998	−	0.972477i	$-0.425146\pi$
$997$	14.7140	0.465996	0.232998	+	0.972477i	$0.425146\pi$
$998$	19.5241	0.618025
$999$	−32.2401	−1.02003

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	6034.2.a.l.1.1	✓	20

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
6034.2.a.l.1.1	✓	20	1.1	even	1	trivial

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 6034 = 2 \cdot 7 \cdot 431 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	6034.a (trivial)

\(f(q)\)	\(=\)	\(q+1.00000 q^{2} -2.98166 q^{3} +1.00000 q^{4} -1.98359 q^{5} -2.98166 q^{6} -1.00000 q^{7} +1.00000 q^{8} +5.89028 q^{9} +O(q^{10})\)	\(q+1.00000 q^{2} -2.98166 q^{3} +1.00000 q^{4} -1.98359 q^{5} -2.98166 q^{6} -1.00000 q^{7} +1.00000 q^{8} +5.89028 q^{9} -1.98359 q^{10} -5.55852 q^{11} -2.98166 q^{12} -6.48754 q^{13} -1.00000 q^{14} +5.91438 q^{15} +1.00000 q^{16} +3.37713 q^{17} +5.89028 q^{18} +5.27632 q^{19} -1.98359 q^{20} +2.98166 q^{21} -5.55852 q^{22} +6.73897 q^{23} -2.98166 q^{24} -1.06538 q^{25} -6.48754 q^{26} -8.61783 q^{27} -1.00000 q^{28} +7.00943 q^{29} +5.91438 q^{30} -1.83909 q^{31} +1.00000 q^{32} +16.5736 q^{33} +3.37713 q^{34} +1.98359 q^{35} +5.89028 q^{36} +3.74109 q^{37} +5.27632 q^{38} +19.3436 q^{39} -1.98359 q^{40} +8.26578 q^{41} +2.98166 q^{42} +2.39817 q^{43} -5.55852 q^{44} -11.6839 q^{45} +6.73897 q^{46} +1.87585 q^{47} -2.98166 q^{48} +1.00000 q^{49} -1.06538 q^{50} -10.0694 q^{51} -6.48754 q^{52} -3.25729 q^{53} -8.61783 q^{54} +11.0258 q^{55} -1.00000 q^{56} -15.7322 q^{57} +7.00943 q^{58} -4.64958 q^{59} +5.91438 q^{60} -13.7219 q^{61} -1.83909 q^{62} -5.89028 q^{63} +1.00000 q^{64} +12.8686 q^{65} +16.5736 q^{66} -10.9873 q^{67} +3.37713 q^{68} -20.0933 q^{69} +1.98359 q^{70} +14.4915 q^{71} +5.89028 q^{72} -10.2156 q^{73} +3.74109 q^{74} +3.17660 q^{75} +5.27632 q^{76} +5.55852 q^{77} +19.3436 q^{78} +4.82681 q^{79} -1.98359 q^{80} +8.02456 q^{81} +8.26578 q^{82} +8.64763 q^{83} +2.98166 q^{84} -6.69883 q^{85} +2.39817 q^{86} -20.8997 q^{87} -5.55852 q^{88} -13.0342 q^{89} -11.6839 q^{90} +6.48754 q^{91} +6.73897 q^{92} +5.48353 q^{93} +1.87585 q^{94} -10.4660 q^{95} -2.98166 q^{96} +7.42890 q^{97} +1.00000 q^{98} -32.7412 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 20 q + 20 q^{2} - 3 q^{3} + 20 q^{4} - 10 q^{5} - 3 q^{6} - 20 q^{7} + 20 q^{8} + 21 q^{9}+O(q^{10}) \) 20 * q + 20 * q^2 - 3 * q^3 + 20 * q^4 - 10 * q^5 - 3 * q^6 - 20 * q^7 + 20 * q^8 + 21 * q^9	\( 20 q + 20 q^{2} - 3 q^{3} + 20 q^{4} - 10 q^{5} - 3 q^{6} - 20 q^{7} + 20 q^{8} + 21 q^{9} - 10 q^{10} - 17 q^{11} - 3 q^{12} - 23 q^{13} - 20 q^{14} - 3 q^{15} + 20 q^{16} - 21 q^{17} + 21 q^{18} - 22 q^{19} - 10 q^{20} + 3 q^{21} - 17 q^{22} + 15 q^{23} - 3 q^{24} - 23 q^{26} - 42 q^{27} - 20 q^{28} - 3 q^{29} - 3 q^{30} - 3 q^{31} + 20 q^{32} - 12 q^{33} - 21 q^{34} + 10 q^{35} + 21 q^{36} - 14 q^{37} - 22 q^{38} + q^{39} - 10 q^{40} - 37 q^{41} + 3 q^{42} - 5 q^{43} - 17 q^{44} - 55 q^{45} + 15 q^{46} - 29 q^{47} - 3 q^{48} + 20 q^{49} - 7 q^{51} - 23 q^{52} - 28 q^{53} - 42 q^{54} + 4 q^{55} - 20 q^{56} - 23 q^{57} - 3 q^{58} - 47 q^{59} - 3 q^{60} - 13 q^{61} - 3 q^{62} - 21 q^{63} + 20 q^{64} - 26 q^{65} - 12 q^{66} - 24 q^{67} - 21 q^{68} - 76 q^{69} + 10 q^{70} - 22 q^{71} + 21 q^{72} - 37 q^{73} - 14 q^{74} - 39 q^{75} - 22 q^{76} + 17 q^{77} + q^{78} + 25 q^{79} - 10 q^{80} - 36 q^{81} - 37 q^{82} - 33 q^{83} + 3 q^{84} - 2 q^{85} - 5 q^{86} - 26 q^{87} - 17 q^{88} - 71 q^{89} - 55 q^{90} + 23 q^{91} + 15 q^{92} - 49 q^{93} - 29 q^{94} - 14 q^{95} - 3 q^{96} - 51 q^{97} + 20 q^{98} - 10 q^{99}+O(q^{100}) \) 20 * q + 20 * q^2 - 3 * q^3 + 20 * q^4 - 10 * q^5 - 3 * q^6 - 20 * q^7 + 20 * q^8 + 21 * q^9 - 10 * q^10 - 17 * q^11 - 3 * q^12 - 23 * q^13 - 20 * q^14 - 3 * q^15 + 20 * q^16 - 21 * q^17 + 21 * q^18 - 22 * q^19 - 10 * q^20 + 3 * q^21 - 17 * q^22 + 15 * q^23 - 3 * q^24 - 23 * q^26 - 42 * q^27 - 20 * q^28 - 3 * q^29 - 3 * q^30 - 3 * q^31 + 20 * q^32 - 12 * q^33 - 21 * q^34 + 10 * q^35 + 21 * q^36 - 14 * q^37 - 22 * q^38 + q^39 - 10 * q^40 - 37 * q^41 + 3 * q^42 - 5 * q^43 - 17 * q^44 - 55 * q^45 + 15 * q^46 - 29 * q^47 - 3 * q^48 + 20 * q^49 - 7 * q^51 - 23 * q^52 - 28 * q^53 - 42 * q^54 + 4 * q^55 - 20 * q^56 - 23 * q^57 - 3 * q^58 - 47 * q^59 - 3 * q^60 - 13 * q^61 - 3 * q^62 - 21 * q^63 + 20 * q^64 - 26 * q^65 - 12 * q^66 - 24 * q^67 - 21 * q^68 - 76 * q^69 + 10 * q^70 - 22 * q^71 + 21 * q^72 - 37 * q^73 - 14 * q^74 - 39 * q^75 - 22 * q^76 + 17 * q^77 + q^78 + 25 * q^79 - 10 * q^80 - 36 * q^81 - 37 * q^82 - 33 * q^83 + 3 * q^84 - 2 * q^85 - 5 * q^86 - 26 * q^87 - 17 * q^88 - 71 * q^89 - 55 * q^90 + 23 * q^91 + 15 * q^92 - 49 * q^93 - 29 * q^94 - 14 * q^95 - 3 * q^96 - 51 * q^97 + 20 * q^98 - 10 * q^99

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