LMFDB - Embedded newform 4026.2.a.s.1.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [4026,2,Mod(1,4026)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(4026, 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("4026.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 4026 = 2 \cdot 3 \cdot 11 \cdot 61 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	4026.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:	$32.1477718538$
Analytic rank:	$0$
Dimension:	$4$
Coefficient field:	4.4.26825.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} - 2x^{3} - 5x^{2} + 5x + 5 $ x^4 - 2x^3 - 5x^2 + 5*x + 5
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.1
Root			$-0.696894$ of defining polynomial
Character	$\chi$	$=$	4026.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.00000 q^{2} -1.00000 q^{3} +1.00000 q^{4} -2.78091 q^{5} -1.00000 q^{6} -1.12055 q^{7} +1.00000 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q+1.00000 q^{2} -1.00000 q^{3} +1.00000 q^{4} -2.78091 q^{5} -1.00000 q^{6} -1.12055 q^{7} +1.00000 q^{8} +1.00000 q^{9} -2.78091 q^{10} -1.00000 q^{11} -1.00000 q^{12} -3.29524 q^{13} -1.12055 q^{14} +2.78091 q^{15} +1.00000 q^{16} -3.35725 q^{17} +1.00000 q^{18} +1.69689 q^{19} -2.78091 q^{20} +1.12055 q^{21} -1.00000 q^{22} +1.69689 q^{23} -1.00000 q^{24} +2.73343 q^{25} -3.29524 q^{26} -1.00000 q^{27} -1.12055 q^{28} -2.51434 q^{29} +2.78091 q^{30} +8.11269 q^{31} +1.00000 q^{32} +1.00000 q^{33} -3.35725 q^{34} +3.11615 q^{35} +1.00000 q^{36} -8.72557 q^{37} +1.69689 q^{38} +3.29524 q^{39} -2.78091 q^{40} +3.96346 q^{41} +1.12055 q^{42} -6.81744 q^{43} -1.00000 q^{44} -2.78091 q^{45} +1.69689 q^{46} +4.85398 q^{47} -1.00000 q^{48} -5.74437 q^{49} +2.73343 q^{50} +3.35725 q^{51} -3.29524 q^{52} +2.57634 q^{53} -1.00000 q^{54} +2.78091 q^{55} -1.12055 q^{56} -1.69689 q^{57} -2.51434 q^{58} +13.7985 q^{59} +2.78091 q^{60} -1.00000 q^{61} +8.11269 q^{62} -1.12055 q^{63} +1.00000 q^{64} +9.16376 q^{65} +1.00000 q^{66} -4.23670 q^{67} -3.35725 q^{68} -1.69689 q^{69} +3.11615 q^{70} -0.309777 q^{71} +1.00000 q^{72} +1.36165 q^{73} -8.72557 q^{74} -2.73343 q^{75} +1.69689 q^{76} +1.12055 q^{77} +3.29524 q^{78} +13.7774 q^{79} -2.78091 q^{80} +1.00000 q^{81} +3.96346 q^{82} +10.6824 q^{83} +1.12055 q^{84} +9.33619 q^{85} -6.81744 q^{86} +2.51434 q^{87} -1.00000 q^{88} +12.9489 q^{89} -2.78091 q^{90} +3.69249 q^{91} +1.69689 q^{92} -8.11269 q^{93} +4.85398 q^{94} -4.71890 q^{95} -1.00000 q^{96} +3.32511 q^{97} -5.74437 q^{98} -1.00000 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q + 4 q^{2} - 4 q^{3} + 4 q^{4} + 3 q^{5} - 4 q^{6} - 2 q^{7} + 4 q^{8} + 4 q^{9}+O(q^{10}) $ 4 * q + 4 * q^2 - 4 * q^3 + 4 * q^4 + 3 * q^5 - 4 * q^6 - 2 * q^7 + 4 * q^8 + 4 * q^9	\( 4 q + 4 q^{2} - 4 q^{3} + 4 q^{4} + 3 q^{5} - 4 q^{6} - 2 q^{7} + 4 q^{8} + 4 q^{9} + 3 q^{10} - 4 q^{11} - 4 q^{12} + 13 q^{13} - 2 q^{14} - 3 q^{15} + 4 q^{16} + 3 q^{17} + 4 q^{18} + 2 q^{19} + 3 q^{20} + 2 q^{21} - 4 q^{22} + 2 q^{23} - 4 q^{24} + 13 q^{25} + 13 q^{26} - 4 q^{27} - 2 q^{28} + 2 q^{29} - 3 q^{30} - q^{31} + 4 q^{32} + 4 q^{33} + 3 q^{34} + q^{35} + 4 q^{36} - 6 q^{37} + 2 q^{38} - 13 q^{39} + 3 q^{40} + 9 q^{41} + 2 q^{42} - 20 q^{43} - 4 q^{44} + 3 q^{45} + 2 q^{46} + 19 q^{47} - 4 q^{48} - 2 q^{49} + 13 q^{50} - 3 q^{51} + 13 q^{52} + 8 q^{53} - 4 q^{54} - 3 q^{55} - 2 q^{56} - 2 q^{57} + 2 q^{58} + 13 q^{59} - 3 q^{60} - 4 q^{61} - q^{62} - 2 q^{63} + 4 q^{64} + 36 q^{65} + 4 q^{66} - 3 q^{67} + 3 q^{68} - 2 q^{69} + q^{70} - q^{71} + 4 q^{72} - 2 q^{73} - 6 q^{74} - 13 q^{75} + 2 q^{76} + 2 q^{77} - 13 q^{78} + 19 q^{79} + 3 q^{80} + 4 q^{81} + 9 q^{82} + 12 q^{83} + 2 q^{84} + 27 q^{85} - 20 q^{86} - 2 q^{87} - 4 q^{88} + 19 q^{89} + 3 q^{90} + q^{91} + 2 q^{92} + q^{93} + 19 q^{94} + 5 q^{95} - 4 q^{96} - q^{97} - 2 q^{98} - 4 q^{99}+O(q^{100}) \) 4 * q + 4 * q^2 - 4 * q^3 + 4 * q^4 + 3 * q^5 - 4 * q^6 - 2 * q^7 + 4 * q^8 + 4 * q^9 + 3 * q^10 - 4 * q^11 - 4 * q^12 + 13 * q^13 - 2 * q^14 - 3 * q^15 + 4 * q^16 + 3 * q^17 + 4 * q^18 + 2 * q^19 + 3 * q^20 + 2 * q^21 - 4 * q^22 + 2 * q^23 - 4 * q^24 + 13 * q^25 + 13 * q^26 - 4 * q^27 - 2 * q^28 + 2 * q^29 - 3 * q^30 - q^31 + 4 * q^32 + 4 * q^33 + 3 * q^34 + q^35 + 4 * q^36 - 6 * q^37 + 2 * q^38 - 13 * q^39 + 3 * q^40 + 9 * q^41 + 2 * q^42 - 20 * q^43 - 4 * q^44 + 3 * q^45 + 2 * q^46 + 19 * q^47 - 4 * q^48 - 2 * q^49 + 13 * q^50 - 3 * q^51 + 13 * q^52 + 8 * q^53 - 4 * q^54 - 3 * q^55 - 2 * q^56 - 2 * q^57 + 2 * q^58 + 13 * q^59 - 3 * q^60 - 4 * q^61 - q^62 - 2 * q^63 + 4 * q^64 + 36 * q^65 + 4 * q^66 - 3 * q^67 + 3 * q^68 - 2 * q^69 + q^70 - q^71 + 4 * q^72 - 2 * q^73 - 6 * q^74 - 13 * q^75 + 2 * q^76 + 2 * q^77 - 13 * q^78 + 19 * q^79 + 3 * q^80 + 4 * q^81 + 9 * q^82 + 12 * q^83 + 2 * q^84 + 27 * q^85 - 20 * q^86 - 2 * q^87 - 4 * q^88 + 19 * q^89 + 3 * q^90 + q^91 + 2 * q^92 + q^93 + 19 * q^94 + 5 * q^95 - 4 * q^96 - q^97 - 2 * q^98 - 4 * q^99

Display 100 coefficients 10 coefficients

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$	$a_n / n^{(k-1)/2}$	$ \alpha_n $			$ \theta_n $
$p$	$a_p$	$a_p / p^{(k-1)/2}$	$ \alpha_p$			$ \theta_p $

$2$	1.00000	0.707107
$2$	1.00000	0.707107
$3$	−1.00000	−0.577350
$3$	−1.00000	−0.577350
$4$	1.00000	0.500000
$5$	−2.78091	−1.24366	−0.621829	−	0.783153i	$-0.713610\pi$
$5$	−2.78091	−1.24366	−0.621829	+	0.783153i	$0.713610\pi$
$6$	−1.00000	−0.408248
$7$	−1.12055	−0.423528	−0.211764	−	0.977321i	$-0.567921\pi$
$7$	−1.12055	−0.423528	−0.211764	+	0.977321i	$0.567921\pi$
$8$	1.00000	0.353553
$9$	1.00000	0.333333
$10$	−2.78091	−0.879399
$11$	−1.00000	−0.301511
$11$	−1.00000	−0.301511
$12$	−1.00000	−0.288675
$13$	−3.29524	−0.913936	−0.456968	−	0.889483i	$-0.651065\pi$
$13$	−3.29524	−0.913936	−0.456968	+	0.889483i	$0.651065\pi$
$14$	−1.12055	−0.299480
$15$	2.78091	0.718027
$16$	1.00000	0.250000
$17$	−3.35725	−0.814252	−0.407126	−	0.913372i	$-0.633469\pi$
$17$	−3.35725	−0.814252	−0.407126	+	0.913372i	$0.633469\pi$
$18$	1.00000	0.235702
$19$	1.69689	0.389294	0.194647	−	0.980873i	$-0.437644\pi$
$19$	1.69689	0.389294	0.194647	+	0.980873i	$0.437644\pi$
$20$	−2.78091	−0.621829
$21$	1.12055	0.244524
$22$	−1.00000	−0.213201
$23$	1.69689	0.353827	0.176913	−	0.984226i	$-0.443389\pi$
$23$	1.69689	0.353827	0.176913	+	0.984226i	$0.443389\pi$
$24$	−1.00000	−0.204124
$25$	2.73343	0.546687
$26$	−3.29524	−0.646251
$27$	−1.00000	−0.192450
$28$	−1.12055	−0.211764
$29$	−2.51434	−0.466901	−0.233451	−	0.972369i	$-0.575002\pi$
$29$	−2.51434	−0.466901	−0.233451	+	0.972369i	$0.575002\pi$
$30$	2.78091	0.507722
$31$	8.11269	1.45708	0.728541	−	0.685002i	$-0.240199\pi$
$31$	8.11269	1.45708	0.728541	+	0.685002i	$0.240199\pi$
$32$	1.00000	0.176777
$33$	1.00000	0.174078
$34$	−3.35725	−0.575763
$35$	3.11615	0.526725
$36$	1.00000	0.166667
$37$	−8.72557	−1.43448	−0.717238	−	0.696829i	$-0.754594\pi$
$37$	−8.72557	−1.43448	−0.717238	+	0.696829i	$0.754594\pi$
$38$	1.69689	0.275273
$39$	3.29524	0.527661
$40$	−2.78091	−0.439700
$41$	3.96346	0.618988	0.309494	−	0.950901i	$-0.399840\pi$
$41$	3.96346	0.618988	0.309494	+	0.950901i	$0.399840\pi$
$42$	1.12055	0.172905
$43$	−6.81744	−1.03965	−0.519825	−	0.854273i	$-0.674003\pi$
$43$	−6.81744	−1.03965	−0.519825	+	0.854273i	$0.674003\pi$
$44$	−1.00000	−0.150756
$45$	−2.78091	−0.414553
$46$	1.69689	0.250193
$47$	4.85398	0.708026	0.354013	−	0.935240i	$-0.384817\pi$
$47$	4.85398	0.708026	0.354013	+	0.935240i	$0.384817\pi$
$48$	−1.00000	−0.144338
$49$	−5.74437	−0.820624
$50$	2.73343	0.386566
$51$	3.35725	0.470109
$52$	−3.29524	−0.456968
$53$	2.57634	0.353888	0.176944	−	0.984221i	$-0.443379\pi$
$53$	2.57634	0.353888	0.176944	+	0.984221i	$0.443379\pi$
$54$	−1.00000	−0.136083
$55$	2.78091	0.374977
$56$	−1.12055	−0.149740
$57$	−1.69689	−0.224759
$58$	−2.51434	−0.330149
$59$	13.7985	1.79641	0.898206	−	0.439574i	$-0.144871\pi$
$59$	13.7985	1.79641	0.898206	+	0.439574i	$0.144871\pi$
$60$	2.78091	0.359013
$61$	−1.00000	−0.128037
$61$	−1.00000	−0.128037
$62$	8.11269	1.03031
$63$	−1.12055	−0.141176
$64$	1.00000	0.125000
$65$	9.16376	1.13662
$66$	1.00000	0.123091
$67$	−4.23670	−0.517595	−0.258797	−	0.965932i	$-0.583326\pi$
$67$	−4.23670	−0.517595	−0.258797	+	0.965932i	$0.583326\pi$
$68$	−3.35725	−0.407126
$69$	−1.69689	−0.204282
$70$	3.11615	0.372451
$71$	−0.309777	−0.0367637	−0.0183819	−	0.999831i	$-0.505851\pi$
$71$	−0.309777	−0.0367637	−0.0183819	+	0.999831i	$0.505851\pi$
$72$	1.00000	0.117851
$73$	1.36165	0.159369	0.0796847	−	0.996820i	$-0.474609\pi$
$73$	1.36165	0.159369	0.0796847	+	0.996820i	$0.474609\pi$
$74$	−8.72557	−1.01433
$75$	−2.73343	−0.315630
$76$	1.69689	0.194647
$77$	1.12055	0.127699
$78$	3.29524	0.373113
$79$	13.7774	1.55008	0.775042	−	0.631910i	$-0.217729\pi$
$79$	13.7774	1.55008	0.775042	+	0.631910i	$0.217729\pi$
$80$	−2.78091	−0.310915
$81$	1.00000	0.111111
$82$	3.96346	0.437691
$83$	10.6824	1.17254	0.586271	−	0.810115i	$-0.300595\pi$
$83$	10.6824	1.17254	0.586271	+	0.810115i	$0.300595\pi$
$84$	1.12055	0.122262
$85$	9.33619	1.01265
$86$	−6.81744	−0.735144
$87$	2.51434	0.269565
$88$	−1.00000	−0.106600
$89$	12.9489	1.37258	0.686292	−	0.727326i	$-0.259237\pi$
$89$	12.9489	1.37258	0.686292	+	0.727326i	$0.259237\pi$
$90$	−2.78091	−0.293133
$91$	3.69249	0.387078
$92$	1.69689	0.176913
$93$	−8.11269	−0.841247
$94$	4.85398	0.500650
$95$	−4.71890	−0.484149
$96$	−1.00000	−0.102062
$97$	3.32511	0.337614	0.168807	−	0.985649i	$-0.446009\pi$
$97$	3.32511	0.337614	0.168807	+	0.985649i	$0.446009\pi$
$98$	−5.74437	−0.580269
$99$	−1.00000	−0.100504
$100$	2.73343	0.273343
$101$	2.90491	0.289050	0.144525	−	0.989501i	$-0.453835\pi$
$101$	2.90491	0.289050	0.144525	+	0.989501i	$0.453835\pi$
$102$	3.35725	0.332417
$103$	−4.78091	−0.471077	−0.235538	−	0.971865i	$-0.575685\pi$
$103$	−4.78091	−0.471077	−0.235538	+	0.971865i	$0.575685\pi$
$104$	−3.29524	−0.323125
$105$	−3.11615	−0.304105
$106$	2.57634	0.250237
$107$	7.60943	0.735631	0.367815	−	0.929899i	$-0.380106\pi$
$107$	7.60943	0.735631	0.367815	+	0.929899i	$0.380106\pi$
$108$	−1.00000	−0.0962250
$109$	14.0828	1.34889	0.674445	−	0.738325i	$-0.264383\pi$
$109$	14.0828	1.34889	0.674445	+	0.738325i	$0.264383\pi$
$110$	2.78091	0.265149
$111$	8.72557	0.828195
$112$	−1.12055	−0.105882
$113$	2.22696	0.209494	0.104747	−	0.994499i	$-0.466597\pi$
$113$	2.22696	0.209494	0.104747	+	0.994499i	$0.466597\pi$
$114$	−1.69689	−0.158929
$115$	−4.71890	−0.440040
$116$	−2.51434	−0.233451
$117$	−3.29524	−0.304645
$118$	13.7985	1.27026
$119$	3.76197	0.344859
$120$	2.78091	0.253861
$121$	1.00000	0.0909091
$122$	−1.00000	−0.0905357
$123$	−3.96346	−0.357373
$124$	8.11269	0.728541
$125$	6.30311	0.563767
$126$	−1.12055	−0.0998266
$127$	−8.67796	−0.770044	−0.385022	−	0.922907i	$-0.625806\pi$
$127$	−8.67796	−0.770044	−0.385022	+	0.922907i	$0.625806\pi$
$128$	1.00000	0.0883883
$129$	6.81744	0.600243
$130$	9.16376	0.803715
$131$	−17.5319	−1.53177	−0.765886	−	0.642976i	$-0.777700\pi$
$131$	−17.5319	−1.53177	−0.765886	+	0.642976i	$0.777700\pi$
$132$	1.00000	0.0870388
$133$	−1.90146	−0.164877
$134$	−4.23670	−0.365995
$135$	2.78091	0.239342
$136$	−3.35725	−0.287882
$137$	−6.21790	−0.531231	−0.265616	−	0.964079i	$-0.585575\pi$
$137$	−6.21790	−0.531231	−0.265616	+	0.964079i	$0.585575\pi$
$138$	−1.69689	−0.144449
$139$	1.35498	0.114928	0.0574641	−	0.998348i	$-0.481699\pi$
$139$	1.35498	0.114928	0.0574641	+	0.998348i	$0.481699\pi$
$140$	3.11615	0.263362
$141$	−4.85398	−0.408779
$142$	−0.309777	−0.0259959
$143$	3.29524	0.275562
$144$	1.00000	0.0833333
$145$	6.99214	0.580665
$146$	1.36165	0.112691
$147$	5.74437	0.473787
$148$	−8.72557	−0.717238
$149$	6.75104	0.553066	0.276533	−	0.961004i	$-0.410814\pi$
$149$	6.75104	0.553066	0.276533	+	0.961004i	$0.410814\pi$
$150$	−2.73343	−0.223184
$151$	19.1967	1.56221	0.781103	−	0.624403i	$-0.214658\pi$
$151$	19.1967	1.56221	0.781103	+	0.624403i	$0.214658\pi$
$152$	1.69689	0.137636
$153$	−3.35725	−0.271417
$154$	1.12055	0.0902966
$155$	−22.5606	−1.81211
$156$	3.29524	0.263831
$157$	−1.36165	−0.108672	−0.0543359	−	0.998523i	$-0.517304\pi$
$157$	−1.36165	−0.108672	−0.0543359	+	0.998523i	$0.517304\pi$
$158$	13.7774	1.09607
$159$	−2.57634	−0.204317
$160$	−2.78091	−0.219850
$161$	−1.90146	−0.149856
$162$	1.00000	0.0785674
$163$	−2.82852	−0.221547	−0.110773	−	0.993846i	$-0.535333\pi$
$163$	−2.82852	−0.221547	−0.110773	+	0.993846i	$0.535333\pi$
$164$	3.96346	0.309494
$165$	−2.78091	−0.216493
$166$	10.6824	0.829112
$167$	11.2908	0.873711	0.436856	−	0.899532i	$-0.356092\pi$
$167$	11.2908	0.873711	0.436856	+	0.899532i	$0.356092\pi$
$168$	1.12055	0.0864524
$169$	−2.14137	−0.164721
$170$	9.33619	0.716053
$171$	1.69689	0.129765
$172$	−6.81744	−0.519825
$173$	12.6824	0.964222	0.482111	−	0.876110i	$-0.339870\pi$
$173$	12.6824	0.964222	0.482111	+	0.876110i	$0.339870\pi$
$174$	2.51434	0.190612
$175$	−3.06295	−0.231537
$176$	−1.00000	−0.0753778
$177$	−13.7985	−1.03716
$178$	12.9489	0.970563
$179$	−17.6856	−1.32188	−0.660941	−	0.750438i	$-0.729843\pi$
$179$	−17.6856	−1.32188	−0.660941	+	0.750438i	$0.729843\pi$
$180$	−2.78091	−0.207276
$181$	8.99214	0.668380	0.334190	−	0.942506i	$-0.391537\pi$
$181$	8.99214	0.668380	0.334190	+	0.942506i	$0.391537\pi$
$182$	3.69249	0.273705
$183$	1.00000	0.0739221
$184$	1.69689	0.125097
$185$	24.2650	1.78400
$186$	−8.11269	−0.594851
$187$	3.35725	0.245506
$188$	4.85398	0.354013
$189$	1.12055	0.0815081
$190$	−4.71890	−0.342345
$191$	22.2508	1.61001	0.805007	−	0.593265i	$-0.202161\pi$
$191$	22.2508	1.61001	0.805007	+	0.593265i	$0.202161\pi$
$192$	−1.00000	−0.0721688
$193$	12.4778	0.898172	0.449086	−	0.893489i	$-0.351750\pi$
$193$	12.4778	0.898172	0.449086	+	0.893489i	$0.351750\pi$
$194$	3.32511	0.238729
$195$	−9.16376	−0.656231
$196$	−5.74437	−0.410312
$197$	−5.78412	−0.412101	−0.206051	−	0.978541i	$-0.566061\pi$
$197$	−5.78412	−0.412101	−0.206051	+	0.978541i	$0.566061\pi$
$198$	−1.00000	−0.0710669
$199$	−20.1523	−1.42856	−0.714279	−	0.699861i	$-0.753245\pi$
$199$	−20.1523	−1.42856	−0.714279	+	0.699861i	$0.753245\pi$
$200$	2.73343	0.193283
$201$	4.23670	0.298834
$202$	2.90491	0.204389
$203$	2.81744	0.197746
$204$	3.35725	0.235054
$205$	−11.0220	−0.769810
$206$	−4.78091	−0.333101
$207$	1.69689	0.117942
$208$	−3.29524	−0.228484
$209$	−1.69689	−0.117377
$210$	−3.11615	−0.215035
$211$	6.24110	0.429655	0.214828	−	0.976652i	$-0.431081\pi$
$211$	6.24110	0.429655	0.214828	+	0.976652i	$0.431081\pi$
$212$	2.57634	0.176944
$213$	0.309777	0.0212255
$214$	7.60943	0.520170
$215$	18.9587	1.29297
$216$	−1.00000	−0.0680414
$217$	−9.09068	−0.617116
$218$	14.0828	0.953809
$219$	−1.36165	−0.0920120
$220$	2.78091	0.187489
$221$	11.0630	0.744175
$222$	8.72557	0.585622
$223$	−18.5097	−1.23950	−0.619750	−	0.784799i	$-0.712766\pi$
$223$	−18.5097	−1.23950	−0.619750	+	0.784799i	$0.712766\pi$
$224$	−1.12055	−0.0748700
$225$	2.73343	0.182229
$226$	2.22696	0.148135
$227$	−12.3903	−0.822375	−0.411188	−	0.911551i	$-0.634886\pi$
$227$	−12.3903	−0.822375	−0.411188	+	0.911551i	$0.634886\pi$
$228$	−1.69689	−0.112380
$229$	2.36046	0.155984	0.0779918	−	0.996954i	$-0.475149\pi$
$229$	2.36046	0.155984	0.0779918	+	0.996954i	$0.475149\pi$
$230$	−4.71890	−0.311155
$231$	−1.12055	−0.0737268
$232$	−2.51434	−0.165074
$233$	13.2100	0.865419	0.432709	−	0.901534i	$-0.357558\pi$
$233$	13.2100	0.865419	0.432709	+	0.901534i	$0.357558\pi$
$234$	−3.29524	−0.215417
$235$	−13.4985	−0.880543
$236$	13.7985	0.898206
$237$	−13.7774	−0.894941
$238$	3.76197	0.243852
$239$	15.3935	0.995726	0.497863	−	0.867256i	$-0.334118\pi$
$239$	15.3935	0.995726	0.497863	+	0.867256i	$0.334118\pi$
$240$	2.78091	0.179507
$241$	7.57289	0.487812	0.243906	−	0.969799i	$-0.421571\pi$
$241$	7.57289	0.487812	0.243906	+	0.969799i	$0.421571\pi$
$242$	1.00000	0.0642824
$243$	−1.00000	−0.0641500
$244$	−1.00000	−0.0640184
$245$	15.9745	1.02058
$246$	−3.96346	−0.252701
$247$	−5.59168	−0.355790
$248$	8.11269	0.515156
$249$	−10.6824	−0.676967
$250$	6.30311	0.398643
$251$	10.0628	0.635159	0.317579	−	0.948232i	$-0.397130\pi$
$251$	10.0628	0.635159	0.317579	+	0.948232i	$0.397130\pi$
$252$	−1.12055	−0.0705881
$253$	−1.69689	−0.106683
$254$	−8.67796	−0.544503
$255$	−9.33619	−0.584655
$256$	1.00000	0.0625000
$257$	6.65916	0.415387	0.207694	−	0.978194i	$-0.433404\pi$
$257$	6.65916	0.415387	0.207694	+	0.978194i	$0.433404\pi$
$258$	6.81744	0.424436
$259$	9.77745	0.607541
$260$	9.16376	0.568312
$261$	−2.51434	−0.155634
$262$	−17.5319	−1.08313
$263$	−2.81971	−0.173871	−0.0869354	−	0.996214i	$-0.527707\pi$
$263$	−2.81971	−0.173871	−0.0869354	+	0.996214i	$0.527707\pi$
$264$	1.00000	0.0615457
$265$	−7.16457	−0.440116
$266$	−1.90146	−0.116586
$267$	−12.9489	−0.792462
$268$	−4.23670	−0.258797
$269$	3.96346	0.241656	0.120828	−	0.992673i	$-0.461445\pi$
$269$	3.96346	0.241656	0.120828	+	0.992673i	$0.461445\pi$
$270$	2.78091	0.169241
$271$	14.4687	0.878914	0.439457	−	0.898264i	$-0.355171\pi$
$271$	14.4687	0.878914	0.439457	+	0.898264i	$0.355171\pi$
$272$	−3.35725	−0.203563
$273$	−3.69249	−0.223480
$274$	−6.21790	−0.375637
$275$	−2.73343	−0.164832
$276$	−1.69689	−0.102141
$277$	−30.8280	−1.85227	−0.926137	−	0.377187i	$-0.876891\pi$
$277$	−30.8280	−1.85227	−0.926137	+	0.377187i	$0.876891\pi$
$278$	1.35498	0.0812664
$279$	8.11269	0.485694
$280$	3.11615	0.186225
$281$	−4.06281	−0.242367	−0.121183	−	0.992630i	$-0.538669\pi$
$281$	−4.06281	−0.242367	−0.121183	+	0.992630i	$0.538669\pi$
$282$	−4.85398	−0.289051
$283$	22.6713	1.34767	0.673834	−	0.738883i	$-0.264646\pi$
$283$	22.6713	1.34767	0.673834	+	0.738883i	$0.264646\pi$
$284$	−0.309777	−0.0183819
$285$	4.71890	0.279524
$286$	3.29524	0.194852
$287$	−4.44126	−0.262159
$288$	1.00000	0.0589256
$289$	−5.72889	−0.336993
$290$	6.99214	0.410592
$291$	−3.32511	−0.194922
$292$	1.36165	0.0796847
$293$	−2.63608	−0.154002	−0.0770008	−	0.997031i	$-0.524534\pi$
$293$	−2.63608	−0.154002	−0.0770008	+	0.997031i	$0.524534\pi$
$294$	5.74437	0.335018
$295$	−38.3723	−2.23412
$296$	−8.72557	−0.507164
$297$	1.00000	0.0580259
$298$	6.75104	0.391077
$299$	−5.59168	−0.323375
$300$	−2.73343	−0.157815
$301$	7.63929	0.440322
$302$	19.1967	1.10465
$303$	−2.90491	−0.166883
$304$	1.69689	0.0973235
$305$	2.78091	0.159234
$306$	−3.35725	−0.191921
$307$	2.63915	0.150624	0.0753122	−	0.997160i	$-0.476005\pi$
$307$	2.63915	0.150624	0.0753122	+	0.997160i	$0.476005\pi$
$308$	1.12055	0.0638493
$309$	4.78091	0.271976
$310$	−22.5606	−1.28136
$311$	−9.95986	−0.564772	−0.282386	−	0.959301i	$-0.591126\pi$
$311$	−9.95986	−0.564772	−0.282386	+	0.959301i	$0.591126\pi$
$312$	3.29524	0.186556
$313$	29.6812	1.67768	0.838839	−	0.544379i	$-0.183235\pi$
$313$	29.6812	1.67768	0.838839	+	0.544379i	$0.183235\pi$
$314$	−1.36165	−0.0768425
$315$	3.11615	0.175575
$316$	13.7774	0.775042
$317$	12.6115	0.708335	0.354168	−	0.935182i	$-0.384764\pi$
$317$	12.6115	0.708335	0.354168	+	0.935182i	$0.384764\pi$
$318$	−2.57634	−0.144474
$319$	2.51434	0.140776
$320$	−2.78091	−0.155457
$321$	−7.60943	−0.424717
$322$	−1.90146	−0.105964
$323$	−5.69689	−0.316984
$324$	1.00000	0.0555556
$325$	−9.00733	−0.499637
$326$	−2.82852	−0.156657
$327$	−14.0828	−0.778782
$328$	3.96346	0.218845
$329$	−5.43914	−0.299869
$330$	−2.78091	−0.153084
$331$	−25.5417	−1.40390	−0.701949	−	0.712227i	$-0.747687\pi$
$331$	−25.5417	−1.40390	−0.701949	+	0.712227i	$0.747687\pi$
$332$	10.6824	0.586271
$333$	−8.72557	−0.478158
$334$	11.2908	0.617807
$335$	11.7819	0.643711
$336$	1.12055	0.0611311
$337$	12.1592	0.662355	0.331177	−	0.943569i	$-0.392554\pi$
$337$	12.1592	0.662355	0.331177	+	0.943569i	$0.392554\pi$
$338$	−2.14137	−0.116475
$339$	−2.22696	−0.120952
$340$	9.33619	0.506326
$341$	−8.11269	−0.439327
$342$	1.69689	0.0917575
$343$	14.2807	0.771086
$344$	−6.81744	−0.367572
$345$	4.71890	0.254057
$346$	12.6824	0.681808
$347$	11.6194	0.623763	0.311881	−	0.950121i	$-0.399041\pi$
$347$	11.6194	0.623763	0.311881	+	0.950121i	$0.399041\pi$
$348$	2.51434	0.134783
$349$	11.2916	0.604428	0.302214	−	0.953240i	$-0.402274\pi$
$349$	11.2916	0.604428	0.302214	+	0.953240i	$0.402274\pi$
$350$	−3.06295	−0.163722
$351$	3.29524	0.175887
$352$	−1.00000	−0.0533002
$353$	4.11188	0.218854	0.109427	−	0.993995i	$-0.465098\pi$
$353$	4.11188	0.218854	0.109427	+	0.993995i	$0.465098\pi$
$354$	−13.7985	−0.733382
$355$	0.861459	0.0457215
$356$	12.9489	0.686292
$357$	−3.76197	−0.199104
$358$	−17.6856	−0.934712
$359$	17.5693	0.927271	0.463636	−	0.886026i	$-0.346545\pi$
$359$	17.5693	0.927271	0.463636	+	0.886026i	$0.346545\pi$
$360$	−2.78091	−0.146567
$361$	−16.1206	−0.848450
$362$	8.99214	0.472616
$363$	−1.00000	−0.0524864
$364$	3.69249	0.193539
$365$	−3.78663	−0.198201
$366$	1.00000	0.0522708
$367$	32.6270	1.70312	0.851558	−	0.524260i	$-0.175658\pi$
$367$	32.6270	1.70312	0.851558	+	0.524260i	$0.175658\pi$
$368$	1.69689	0.0884567
$369$	3.96346	0.206329
$370$	24.2650	1.26148
$371$	−2.88692	−0.149882
$372$	−8.11269	−0.420623
$373$	−28.1346	−1.45675	−0.728376	−	0.685178i	$-0.759725\pi$
$373$	−28.1346	−1.45675	−0.728376	+	0.685178i	$0.759725\pi$
$374$	3.35725	0.173599
$375$	−6.30311	−0.325491
$376$	4.85398	0.250325
$377$	8.28536	0.426718
$378$	1.12055	0.0576349
$379$	2.45020	0.125858	0.0629290	−	0.998018i	$-0.479956\pi$
$379$	2.45020	0.125858	0.0629290	+	0.998018i	$0.479956\pi$
$380$	−4.71890	−0.242075
$381$	8.67796	0.444585
$382$	22.2508	1.13845
$383$	−22.4590	−1.14760	−0.573801	−	0.818995i	$-0.694532\pi$
$383$	−22.4590	−1.14760	−0.573801	+	0.818995i	$0.694532\pi$
$384$	−1.00000	−0.0510310
$385$	−3.11615	−0.158814
$386$	12.4778	0.635103
$387$	−6.81744	−0.346550
$388$	3.32511	0.168807
$389$	7.05628	0.357768	0.178884	−	0.983870i	$-0.442751\pi$
$389$	7.05628	0.357768	0.178884	+	0.983870i	$0.442751\pi$
$390$	−9.16376	−0.464025
$391$	−5.69689	−0.288104
$392$	−5.74437	−0.290134
$393$	17.5319	0.884369
$394$	−5.78412	−0.291400
$395$	−38.3138	−1.92778
$396$	−1.00000	−0.0502519
$397$	−4.62396	−0.232070	−0.116035	−	0.993245i	$-0.537018\pi$
$397$	−4.62396	−0.232070	−0.116035	+	0.993245i	$0.537018\pi$
$398$	−20.1523	−1.01014
$399$	1.90146	0.0951919
$400$	2.73343	0.136672
$401$	−7.58396	−0.378725	−0.189362	−	0.981907i	$-0.560642\pi$
$401$	−7.58396	−0.378725	−0.189362	+	0.981907i	$0.560642\pi$
$402$	4.23670	0.211307
$403$	−26.7333	−1.33168
$404$	2.90491	0.144525
$405$	−2.78091	−0.138184
$406$	2.81744	0.139827
$407$	8.72557	0.432511
$408$	3.35725	0.166209
$409$	−8.97334	−0.443703	−0.221852	−	0.975080i	$-0.571210\pi$
$409$	−8.97334	−0.443703	−0.221852	+	0.975080i	$0.571210\pi$
$410$	−11.0220	−0.544338
$411$	6.21790	0.306707
$412$	−4.78091	−0.235538
$413$	−15.4619	−0.760832
$414$	1.69689	0.0833978
$415$	−29.7066	−1.45824
$416$	−3.29524	−0.161563
$417$	−1.35498	−0.0663538
$418$	−1.69689	−0.0829978
$419$	−9.55821	−0.466949	−0.233475	−	0.972363i	$-0.575010\pi$
$419$	−9.55821	−0.466949	−0.233475	+	0.972363i	$0.575010\pi$
$420$	−3.11615	−0.152052
$421$	−5.39152	−0.262767	−0.131383	−	0.991332i	$-0.541942\pi$
$421$	−5.39152	−0.262767	−0.131383	+	0.991332i	$0.541942\pi$
$422$	6.24110	0.303812
$423$	4.85398	0.236009
$424$	2.57634	0.125118
$425$	−9.17682	−0.445141
$426$	0.309777	0.0150087
$427$	1.12055	0.0542273
$428$	7.60943	0.367815
$429$	−3.29524	−0.159096
$430$	18.9587	0.914268
$431$	13.7664	0.663103	0.331551	−	0.943437i	$-0.392428\pi$
$431$	13.7664	0.663103	0.331551	+	0.943437i	$0.392428\pi$
$432$	−1.00000	−0.0481125
$433$	−31.4077	−1.50936	−0.754679	−	0.656095i	$-0.772207\pi$
$433$	−31.4077	−1.50936	−0.754679	+	0.656095i	$0.772207\pi$
$434$	−9.09068	−0.436367
$435$	−6.99214	−0.335247
$436$	14.0828	0.674445
$437$	2.87945	0.137743
$438$	−1.36165	−0.0650623
$439$	−11.6382	−0.555461	−0.277731	−	0.960659i	$-0.589582\pi$
$439$	−11.6382	−0.555461	−0.277731	+	0.960659i	$0.589582\pi$
$440$	2.78091	0.132574
$441$	−5.74437	−0.273541
$442$	11.0630	0.526211
$443$	−20.3159	−0.965238	−0.482619	−	0.875830i	$-0.660314\pi$
$443$	−20.3159	−0.965238	−0.482619	+	0.875830i	$0.660314\pi$
$444$	8.72557	0.414097
$445$	−36.0097	−1.70703
$446$	−18.5097	−0.876459
$447$	−6.75104	−0.319313
$448$	−1.12055	−0.0529411
$449$	29.6266	1.39817	0.699084	−	0.715040i	$-0.253591\pi$
$449$	29.6266	1.39817	0.699084	+	0.715040i	$0.253591\pi$
$450$	2.73343	0.128855
$451$	−3.96346	−0.186632
$452$	2.22696	0.104747
$453$	−19.1967	−0.901940
$454$	−12.3903	−0.581507
$455$	−10.2685	−0.481393
$456$	−1.69689	−0.0794643
$457$	−2.98907	−0.139823	−0.0699114	−	0.997553i	$-0.522272\pi$
$457$	−2.98907	−0.139823	−0.0699114	+	0.997553i	$0.522272\pi$
$458$	2.36046	0.110297
$459$	3.35725	0.156703
$460$	−4.71890	−0.220020
$461$	−10.7585	−0.501074	−0.250537	−	0.968107i	$-0.580607\pi$
$461$	−10.7585	−0.501074	−0.250537	+	0.968107i	$0.580607\pi$
$462$	−1.12055	−0.0521328
$463$	−34.3970	−1.59856	−0.799282	−	0.600956i	$-0.794787\pi$
$463$	−34.3970	−1.59856	−0.799282	+	0.600956i	$0.794787\pi$
$464$	−2.51434	−0.116725
$465$	22.5606	1.04622
$466$	13.2100	0.611943
$467$	−9.75663	−0.451483	−0.225742	−	0.974187i	$-0.572480\pi$
$467$	−9.75663	−0.451483	−0.225742	+	0.974187i	$0.572480\pi$
$468$	−3.29524	−0.152323
$469$	4.74744	0.219216
$470$	−13.4985	−0.622638
$471$	1.36165	0.0627417
$472$	13.7985	0.635128
$473$	6.81744	0.313466
$474$	−13.7774	−0.632819
$475$	4.63835	0.212822
$476$	3.76197	0.172430
$477$	2.57634	0.117963
$478$	15.3935	0.704084
$479$	0.226957	0.0103699	0.00518496	−	0.999987i	$-0.498350\pi$
$479$	0.226957	0.0103699	0.00518496	+	0.999987i	$0.498350\pi$
$480$	2.78091	0.126930
$481$	28.7529	1.31102
$482$	7.57289	0.344935
$483$	1.90146	0.0865193
$484$	1.00000	0.0454545
$485$	−9.24682	−0.419877
$486$	−1.00000	−0.0453609
$487$	6.68236	0.302807	0.151403	−	0.988472i	$-0.451621\pi$
$487$	6.68236	0.302807	0.151403	+	0.988472i	$0.451621\pi$
$488$	−1.00000	−0.0452679
$489$	2.82852	0.127910
$490$	15.9745	0.721656
$491$	−39.3058	−1.77385	−0.886923	−	0.461918i	$-0.847161\pi$
$491$	−39.3058	−1.77385	−0.886923	+	0.461918i	$0.847161\pi$
$492$	−3.96346	−0.178687
$493$	8.44126	0.380175
$494$	−5.59168	−0.251582
$495$	2.78091	0.124992
$496$	8.11269	0.364270
$497$	0.347120	0.0155705
$498$	−10.6824	−0.478688
$499$	−20.6248	−0.923291	−0.461646	−	0.887064i	$-0.652741\pi$
$499$	−20.6248	−0.923291	−0.461646	+	0.887064i	$0.652741\pi$
$500$	6.30311	0.281883
$501$	−11.2908	−0.504437
$502$	10.0628	0.449125
$503$	17.1192	0.763308	0.381654	−	0.924305i	$-0.375355\pi$
$503$	17.1192	0.763308	0.381654	+	0.924305i	$0.375355\pi$
$504$	−1.12055	−0.0499133
$505$	−8.07829	−0.359479
$506$	−1.69689	−0.0754361
$507$	2.14137	0.0951014
$508$	−8.67796	−0.385022
$509$	15.9820	0.708390	0.354195	−	0.935172i	$-0.384755\pi$
$509$	15.9820	0.708390	0.354195	+	0.935172i	$0.384755\pi$
$510$	−9.33619	−0.413413
$511$	−1.52580	−0.0674975
$512$	1.00000	0.0441942
$513$	−1.69689	−0.0749197
$514$	6.65916	0.293723
$515$	13.2952	0.585858
$516$	6.81744	0.300121
$517$	−4.85398	−0.213478
$518$	9.77745	0.429596
$519$	−12.6824	−0.556694
$520$	9.16376	0.401858
$521$	16.0628	0.703724	0.351862	−	0.936052i	$-0.385549\pi$
$521$	16.0628	0.703724	0.351862	+	0.936052i	$0.385549\pi$
$522$	−2.51434	−0.110050
$523$	9.88133	0.432080	0.216040	−	0.976384i	$-0.430686\pi$
$523$	9.88133	0.432080	0.216040	+	0.976384i	$0.430686\pi$
$524$	−17.5319	−0.765886
$525$	3.06295	0.133678
$526$	−2.81971	−0.122945
$527$	−27.2363	−1.18643
$528$	1.00000	0.0435194
$529$	−20.1206	−0.874807
$530$	−7.16457	−0.311209
$531$	13.7985	0.598804
$532$	−1.90146	−0.0824386
$533$	−13.0606	−0.565716
$534$	−12.9489	−0.560355
$535$	−21.1611	−0.914874
$536$	−4.23670	−0.182997
$537$	17.6856	0.763189
$538$	3.96346	0.170877
$539$	5.74437	0.247427
$540$	2.78091	0.119671
$541$	1.91920	0.0825129	0.0412565	−	0.999149i	$-0.486864\pi$
$541$	1.91920	0.0825129	0.0412565	+	0.999149i	$0.486864\pi$
$542$	14.4687	0.621486
$543$	−8.99214	−0.385890
$544$	−3.35725	−0.143941
$545$	−39.1630	−1.67756
$546$	−3.69249	−0.158024
$547$	22.9301	0.980422	0.490211	−	0.871604i	$-0.336920\pi$
$547$	22.9301	0.980422	0.490211	+	0.871604i	$0.336920\pi$
$548$	−6.21790	−0.265616
$549$	−1.00000	−0.0426790
$550$	−2.73343	−0.116554
$551$	−4.26657	−0.181762
$552$	−1.69689	−0.0722246
$553$	−15.4383	−0.656505
$554$	−30.8280	−1.30976
$555$	−24.2650	−1.02999
$556$	1.35498	0.0574641
$557$	4.15670	0.176125	0.0880626	−	0.996115i	$-0.471932\pi$
$557$	4.15670	0.176125	0.0880626	+	0.996115i	$0.471932\pi$
$558$	8.11269	0.343438
$559$	22.4651	0.950174
$560$	3.11615	0.131681
$561$	−3.35725	−0.141743
$562$	−4.06281	−0.171379
$563$	−33.7859	−1.42390	−0.711952	−	0.702228i	$-0.752189\pi$
$563$	−33.7859	−1.42390	−0.711952	+	0.702228i	$0.752189\pi$
$564$	−4.85398	−0.204390
$565$	−6.19296	−0.260540
$566$	22.6713	0.952945
$567$	−1.12055	−0.0470587
$568$	−0.309777	−0.0129979
$569$	3.59528	0.150722	0.0753610	−	0.997156i	$-0.475989\pi$
$569$	3.59528	0.150722	0.0753610	+	0.997156i	$0.475989\pi$
$570$	4.71890	0.197653
$571$	1.93359	0.0809183	0.0404591	−	0.999181i	$-0.487118\pi$
$571$	1.93359	0.0809183	0.0404591	+	0.999181i	$0.487118\pi$
$572$	3.29524	0.137781
$573$	−22.2508	−0.929542
$574$	−4.44126	−0.185375
$575$	4.63835	0.193432
$576$	1.00000	0.0416667
$577$	3.71023	0.154459	0.0772296	−	0.997013i	$-0.475393\pi$
$577$	3.71023	0.154459	0.0772296	+	0.997013i	$0.475393\pi$
$578$	−5.72889	−0.238290
$579$	−12.4778	−0.518560
$580$	6.99214	0.290333
$581$	−11.9701	−0.496605
$582$	−3.32511	−0.137830
$583$	−2.57634	−0.106701
$584$	1.36165	0.0563456
$585$	9.16376	0.378875
$586$	−2.63608	−0.108896
$587$	−2.79889	−0.115523	−0.0577614	−	0.998330i	$-0.518396\pi$
$587$	−2.79889	−0.115523	−0.0577614	+	0.998330i	$0.518396\pi$
$588$	5.74437	0.236894
$589$	13.7664	0.567234
$590$	−38.3723	−1.57976
$591$	5.78412	0.237927
$592$	−8.72557	−0.358619
$593$	31.8171	1.30657	0.653285	−	0.757112i	$-0.273390\pi$
$593$	31.8171	1.30657	0.653285	+	0.757112i	$0.273390\pi$
$594$	1.00000	0.0410305
$595$	−10.4617	−0.428887
$596$	6.75104	0.276533
$597$	20.1523	0.824779
$598$	−5.59168	−0.228661
$599$	−14.3703	−0.587155	−0.293578	−	0.955935i	$-0.594846\pi$
$599$	−14.3703	−0.587155	−0.293578	+	0.955935i	$0.594846\pi$
$600$	−2.73343	−0.111592
$601$	−4.67104	−0.190536	−0.0952679	−	0.995452i	$-0.530371\pi$
$601$	−4.67104	−0.190536	−0.0952679	+	0.995452i	$0.530371\pi$
$602$	7.63929	0.311354
$603$	−4.23670	−0.172532
$604$	19.1967	0.781103
$605$	−2.78091	−0.113060
$606$	−2.90491	−0.118004
$607$	−30.1723	−1.22466	−0.612328	−	0.790604i	$-0.709767\pi$
$607$	−30.1723	−1.22466	−0.612328	+	0.790604i	$0.709767\pi$
$608$	1.69689	0.0688181
$609$	−2.81744	−0.114169
$610$	2.78091	0.112596
$611$	−15.9951	−0.647091
$612$	−3.35725	−0.135709
$613$	11.1699	0.451148	0.225574	−	0.974226i	$-0.427574\pi$
$613$	11.1699	0.451148	0.225574	+	0.974226i	$0.427574\pi$
$614$	2.63915	0.106507
$615$	11.0220	0.444450
$616$	1.12055	0.0451483
$617$	7.81932	0.314794	0.157397	−	0.987535i	$-0.449690\pi$
$617$	7.81932	0.314794	0.157397	+	0.987535i	$0.449690\pi$
$618$	4.78091	0.192316
$619$	44.1521	1.77462	0.887310	−	0.461173i	$-0.152571\pi$
$619$	44.1521	1.77462	0.887310	+	0.461173i	$0.152571\pi$
$620$	−22.5606	−0.906056
$621$	−1.69689	−0.0680940
$622$	−9.95986	−0.399354
$623$	−14.5099	−0.581328
$624$	3.29524	0.131915
$625$	−31.1955	−1.24782
$626$	29.6812	1.18630
$627$	1.69689	0.0677674
$628$	−1.36165	−0.0543359
$629$	29.2939	1.16802
$630$	3.11615	0.124150
$631$	0.356174	0.0141791	0.00708953	−	0.999975i	$-0.497743\pi$
$631$	0.356174	0.0141791	0.00708953	+	0.999975i	$0.497743\pi$
$632$	13.7774	0.548037
$633$	−6.24110	−0.248062
$634$	12.6115	0.500869
$635$	24.1326	0.957672
$636$	−2.57634	−0.102159
$637$	18.9291	0.749998
$638$	2.51434	0.0995436
$639$	−0.309777	−0.0122546
$640$	−2.78091	−0.109925
$641$	−27.0796	−1.06958	−0.534790	−	0.844985i	$-0.679609\pi$
$641$	−27.0796	−1.06958	−0.534790	+	0.844985i	$0.679609\pi$
$642$	−7.60943	−0.300320
$643$	35.0415	1.38190	0.690951	−	0.722902i	$-0.257192\pi$
$643$	35.0415	1.38190	0.690951	+	0.722902i	$0.257192\pi$
$644$	−1.90146	−0.0749279
$645$	−18.9587	−0.746497
$646$	−5.69689	−0.224141
$647$	27.0340	1.06282	0.531408	−	0.847116i	$-0.321663\pi$
$647$	27.0340	1.06282	0.531408	+	0.847116i	$0.321663\pi$
$648$	1.00000	0.0392837
$649$	−13.7985	−0.541639
$650$	−9.00733	−0.353297
$651$	9.09068	0.356292
$652$	−2.82852	−0.110773
$653$	3.08094	0.120567	0.0602833	−	0.998181i	$-0.480800\pi$
$653$	3.08094	0.120567	0.0602833	+	0.998181i	$0.480800\pi$
$654$	−14.0828	−0.550682
$655$	48.7547	1.90500
$656$	3.96346	0.154747
$657$	1.36165	0.0531231
$658$	−5.43914	−0.212040
$659$	−32.5614	−1.26841	−0.634206	−	0.773164i	$-0.718673\pi$
$659$	−32.5614	−1.26841	−0.634206	+	0.773164i	$0.718673\pi$
$660$	−2.78091	−0.108247
$661$	29.7692	1.15789	0.578944	−	0.815367i	$-0.303465\pi$
$661$	29.7692	1.15789	0.578944	+	0.815367i	$0.303465\pi$
$662$	−25.5417	−0.992706
$663$	−11.0630	−0.429649
$664$	10.6824	0.414556
$665$	5.28777	0.205051
$666$	−8.72557	−0.338109
$667$	−4.26657	−0.165202
$668$	11.2908	0.436856
$669$	18.5097	0.715626
$670$	11.7819	0.455173
$671$	1.00000	0.0386046
$672$	1.12055	0.0432262
$673$	−42.8380	−1.65128	−0.825641	−	0.564195i	$-0.809186\pi$
$673$	−42.8380	−1.65128	−0.825641	+	0.564195i	$0.809186\pi$
$674$	12.1592	0.468355
$675$	−2.73343	−0.105210
$676$	−2.14137	−0.0823603
$677$	25.9998	0.999252	0.499626	−	0.866241i	$-0.333471\pi$
$677$	25.9998	0.999252	0.499626	+	0.866241i	$0.333471\pi$
$678$	−2.22696	−0.0855258
$679$	−3.72596	−0.142989
$680$	9.33619	0.358026
$681$	12.3903	0.474799
$682$	−8.11269	−0.310651
$683$	6.34247	0.242688	0.121344	−	0.992611i	$-0.461280\pi$
$683$	6.34247	0.242688	0.121344	+	0.992611i	$0.461280\pi$
$684$	1.69689	0.0648824
$685$	17.2914	0.660670
$686$	14.2807	0.545240
$687$	−2.36046	−0.0900572
$688$	−6.81744	−0.259913
$689$	−8.48968	−0.323431
$690$	4.71890	0.179645
$691$	−51.0659	−1.94264	−0.971319	−	0.237779i	$-0.923581\pi$
$691$	−51.0659	−1.94264	−0.971319	+	0.237779i	$0.923581\pi$
$692$	12.6824	0.482111
$693$	1.12055	0.0425662
$694$	11.6194	0.441067
$695$	−3.76808	−0.142931
$696$	2.51434	0.0953058
$697$	−13.3063	−0.504013
$698$	11.2916	0.427395
$699$	−13.2100	−0.499650
$700$	−3.06295	−0.115769
$701$	20.8048	0.785786	0.392893	−	0.919584i	$-0.371474\pi$
$701$	20.8048	0.785786	0.392893	+	0.919584i	$0.371474\pi$
$702$	3.29524	0.124371
$703$	−14.8064	−0.558433
$704$	−1.00000	−0.0376889
$705$	13.4985	0.508382
$706$	4.11188	0.154753
$707$	−3.25510	−0.122421
$708$	−13.7985	−0.518580
$709$	21.9778	0.825395	0.412698	−	0.910868i	$-0.364587\pi$
$709$	21.9778	0.825395	0.412698	+	0.910868i	$0.364587\pi$
$710$	0.861459	0.0323300
$711$	13.7774	0.516695
$712$	12.9489	0.485282
$713$	13.7664	0.515555
$714$	−3.76197	−0.140788
$715$	−9.16376	−0.342705
$716$	−17.6856	−0.660941
$717$	−15.3935	−0.574882
$718$	17.5693	0.655680
$719$	33.4985	1.24928	0.624641	−	0.780912i	$-0.285245\pi$
$719$	33.4985	1.24928	0.624641	+	0.780912i	$0.285245\pi$
$720$	−2.78091	−0.103638
$721$	5.35725	0.199514
$722$	−16.1206	−0.599945
$723$	−7.57289	−0.281639
$724$	8.99214	0.334190
$725$	−6.87278	−0.255249
$726$	−1.00000	−0.0371135
$727$	14.5658	0.540217	0.270108	−	0.962830i	$-0.412940\pi$
$727$	14.5658	0.540217	0.270108	+	0.962830i	$0.412940\pi$
$728$	3.69249	0.136853
$729$	1.00000	0.0370370
$730$	−3.78663	−0.140149
$731$	22.8879	0.846538
$732$	1.00000	0.0369611
$733$	−14.3562	−0.530257	−0.265129	−	0.964213i	$-0.585414\pi$
$733$	−14.3562	−0.530257	−0.265129	+	0.964213i	$0.585414\pi$
$734$	32.6270	1.20429
$735$	−15.9745	−0.589230
$736$	1.69689	0.0625483
$737$	4.23670	0.156061
$738$	3.96346	0.145897
$739$	−20.1559	−0.741447	−0.370723	−	0.928743i	$-0.620890\pi$
$739$	−20.1559	−0.741447	−0.370723	+	0.928743i	$0.620890\pi$
$740$	24.2650	0.891999
$741$	5.59168	0.205415
$742$	−2.88692	−0.105982
$743$	−30.0064	−1.10083	−0.550415	−	0.834892i	$-0.685530\pi$
$743$	−30.0064	−1.10083	−0.550415	+	0.834892i	$0.685530\pi$
$744$	−8.11269	−0.297426
$745$	−18.7740	−0.687826
$746$	−28.1346	−1.03008
$747$	10.6824	0.390847
$748$	3.35725	0.122753
$749$	−8.52675	−0.311561
$750$	−6.30311	−0.230157
$751$	−4.39393	−0.160337	−0.0801684	−	0.996781i	$-0.525546\pi$
$751$	−4.39393	−0.160337	−0.0801684	+	0.996781i	$0.525546\pi$
$752$	4.85398	0.177007
$753$	−10.0628	−0.366709
$754$	8.28536	0.301735
$755$	−53.3842	−1.94285
$756$	1.12055	0.0407540
$757$	−0.419396	−0.0152432	−0.00762160	−	0.999971i	$-0.502426\pi$
$757$	−0.419396	−0.0152432	−0.00762160	+	0.999971i	$0.502426\pi$
$758$	2.45020	0.0889951
$759$	1.69689	0.0615933
$760$	−4.71890	−0.171173
$761$	−11.3174	−0.410255	−0.205128	−	0.978735i	$-0.565761\pi$
$761$	−11.3174	−0.410255	−0.205128	+	0.978735i	$0.565761\pi$
$762$	8.67796	0.314369
$763$	−15.7805	−0.571293
$764$	22.2508	0.805007
$765$	9.33619	0.337551
$766$	−22.4590	−0.811477
$767$	−45.4694	−1.64181
$768$	−1.00000	−0.0360844
$769$	28.1122	1.01375	0.506875	−	0.862019i	$-0.330801\pi$
$769$	28.1122	1.01375	0.506875	+	0.862019i	$0.330801\pi$
$770$	−3.11615	−0.112298
$771$	−6.65916	−0.239824
$772$	12.4778	0.449086
$773$	−6.98135	−0.251102	−0.125551	−	0.992087i	$-0.540070\pi$
$773$	−6.98135	−0.251102	−0.125551	+	0.992087i	$0.540070\pi$
$774$	−6.81744	−0.245048
$775$	22.1755	0.796567
$776$	3.32511	0.119365
$777$	−9.77745	−0.350764
$778$	7.05628	0.252980
$779$	6.72557	0.240969
$780$	−9.16376	−0.328115
$781$	0.309777	0.0110847
$782$	−5.69689	−0.203721
$783$	2.51434	0.0898551
$784$	−5.74437	−0.205156
$785$	3.78663	0.135151
$786$	17.5319	0.625344
$787$	−27.8669	−0.993349	−0.496675	−	0.867937i	$-0.665446\pi$
$787$	−27.8669	−0.993349	−0.496675	+	0.867937i	$0.665446\pi$
$788$	−5.78412	−0.206051
$789$	2.81971	0.100384
$790$	−38.3138	−1.36314
$791$	−2.49542	−0.0887269
$792$	−1.00000	−0.0355335
$793$	3.29524	0.117018
$794$	−4.62396	−0.164098
$795$	7.16457	0.254101
$796$	−20.1523	−0.714279
$797$	44.1268	1.56305	0.781526	−	0.623872i	$-0.214441\pi$
$797$	44.1268	1.56305	0.781526	+	0.623872i	$0.214441\pi$
$798$	1.90146	0.0673108
$799$	−16.2960	−0.576512
$800$	2.73343	0.0966415
$801$	12.9489	0.457528
$802$	−7.58396	−0.267799
$803$	−1.36165	−0.0480517
$804$	4.23670	0.149417
$805$	5.28777	0.186369
$806$	−26.7333	−0.941640
$807$	−3.96346	−0.139520
$808$	2.90491	0.102194
$809$	9.89863	0.348017	0.174009	−	0.984744i	$-0.444328\pi$
$809$	9.89863	0.348017	0.174009	+	0.984744i	$0.444328\pi$
$810$	−2.78091	−0.0977110
$811$	−6.34632	−0.222849	−0.111425	−	0.993773i	$-0.535541\pi$
$811$	−6.34632	−0.222849	−0.111425	+	0.993773i	$0.535541\pi$
$812$	2.81744	0.0988729
$813$	−14.4687	−0.507441
$814$	8.72557	0.305831
$815$	7.86585	0.275529
$816$	3.35725	0.117527
$817$	−11.5685	−0.404730
$818$	−8.97334	−0.313746
$819$	3.69249	0.129026
$820$	−11.0220	−0.384905
$821$	−3.80235	−0.132703	−0.0663515	−	0.997796i	$-0.521136\pi$
$821$	−3.80235	−0.132703	−0.0663515	+	0.997796i	$0.521136\pi$
$822$	6.21790	0.216874
$823$	21.9752	0.766008	0.383004	−	0.923747i	$-0.374890\pi$
$823$	21.9752	0.766008	0.383004	+	0.923747i	$0.374890\pi$
$824$	−4.78091	−0.166551
$825$	2.73343	0.0951659
$826$	−15.4619	−0.537989
$827$	48.6576	1.69199	0.845995	−	0.533191i	$-0.179007\pi$
$827$	48.6576	1.69199	0.845995	+	0.533191i	$0.179007\pi$
$828$	1.69689	0.0589711
$829$	24.0311	0.834634	0.417317	−	0.908761i	$-0.362970\pi$
$829$	24.0311	0.834634	0.417317	+	0.908761i	$0.362970\pi$
$830$	−29.7066	−1.03113
$831$	30.8280	1.06941
$832$	−3.29524	−0.114242
$833$	19.2853	0.668195
$834$	−1.35498	−0.0469192
$835$	−31.3988	−1.08660
$836$	−1.69689	−0.0586883
$837$	−8.11269	−0.280416
$838$	−9.55821	−0.330183
$839$	−12.5331	−0.432692	−0.216346	−	0.976317i	$-0.569414\pi$
$839$	−12.5331	−0.432692	−0.216346	+	0.976317i	$0.569414\pi$
$840$	−3.11615	−0.107517
$841$	−22.6781	−0.782003
$842$	−5.39152	−0.185804
$843$	4.06281	0.139931
$844$	6.24110	0.214828
$845$	5.95494	0.204856
$846$	4.85398	0.166883
$847$	−1.12055	−0.0385026
$848$	2.57634	0.0884720
$849$	−22.6713	−0.778077
$850$	−9.17682	−0.314762
$851$	−14.8064	−0.507556
$852$	0.309777	0.0106128
$853$	14.4799	0.495784	0.247892	−	0.968788i	$-0.420262\pi$
$853$	14.4799	0.495784	0.247892	+	0.968788i	$0.420262\pi$
$854$	1.12055	0.0383445
$855$	−4.71890	−0.161383
$856$	7.60943	0.260085
$857$	49.8000	1.70114	0.850568	−	0.525865i	$-0.176258\pi$
$857$	49.8000	1.70114	0.850568	+	0.525865i	$0.176258\pi$
$858$	−3.29524	−0.112498
$859$	1.17577	0.0401167	0.0200583	−	0.999799i	$-0.493615\pi$
$859$	1.17577	0.0401167	0.0200583	+	0.999799i	$0.493615\pi$
$860$	18.9587	0.646485
$861$	4.44126	0.151358
$862$	13.7664	0.468885
$863$	28.2982	0.963282	0.481641	−	0.876369i	$-0.340041\pi$
$863$	28.2982	0.963282	0.481641	+	0.876369i	$0.340041\pi$
$864$	−1.00000	−0.0340207
$865$	−35.2684	−1.19916
$866$	−31.4077	−1.06728
$867$	5.72889	0.194563
$868$	−9.09068	−0.308558
$869$	−13.7774	−0.467368
$870$	−6.99214	−0.237056
$871$	13.9610	0.473049
$872$	14.0828	0.476904
$873$	3.32511	0.112538
$874$	2.87945	0.0973988
$875$	−7.06295	−0.238771
$876$	−1.36165	−0.0460060
$877$	25.3338	0.855462	0.427731	−	0.903906i	$-0.359313\pi$
$877$	25.3338	0.855462	0.427731	+	0.903906i	$0.359313\pi$
$878$	−11.6382	−0.392770
$879$	2.63608	0.0889128
$880$	2.78091	0.0937443
$881$	−14.5241	−0.489329	−0.244664	−	0.969608i	$-0.578678\pi$
$881$	−14.5241	−0.489329	−0.244664	+	0.969608i	$0.578678\pi$
$882$	−5.74437	−0.193423
$883$	45.1694	1.52007	0.760036	−	0.649881i	$-0.225181\pi$
$883$	45.1694	1.52007	0.760036	+	0.649881i	$0.225181\pi$
$884$	11.0630	0.372087
$885$	38.3723	1.28987
$886$	−20.3159	−0.682527
$887$	14.2420	0.478201	0.239100	−	0.970995i	$-0.423148\pi$
$887$	14.2420	0.478201	0.239100	+	0.970995i	$0.423148\pi$
$888$	8.72557	0.292811
$889$	9.72409	0.326136
$890$	−36.0097	−1.20705
$891$	−1.00000	−0.0335013
$892$	−18.5097	−0.619750
$893$	8.23670	0.275631
$894$	−6.75104	−0.225788
$895$	49.1819	1.64397
$896$	−1.12055	−0.0374350
$897$	5.59168	0.186701
$898$	29.6266	0.988654
$899$	−20.3980	−0.680313
$900$	2.73343	0.0911145
$901$	−8.64942	−0.288154
$902$	−3.96346	−0.131969
$903$	−7.63929	−0.254220
$904$	2.22696	0.0740675
$905$	−25.0063	−0.831237
$906$	−19.1967	−0.637768
$907$	7.28672	0.241952	0.120976	−	0.992655i	$-0.461398\pi$
$907$	7.28672	0.241952	0.120976	+	0.992655i	$0.461398\pi$
$908$	−12.3903	−0.411188
$909$	2.90491	0.0963499
$910$	−10.2685	−0.340396
$911$	−10.1736	−0.337068	−0.168534	−	0.985696i	$-0.553903\pi$
$911$	−10.1736	−0.337068	−0.168534	+	0.985696i	$0.553903\pi$
$912$	−1.69689	−0.0561898
$913$	−10.6824	−0.353535
$914$	−2.98907	−0.0988696
$915$	−2.78091	−0.0919339
$916$	2.36046	0.0779918
$917$	19.6454	0.648749
$918$	3.35725	0.110806
$919$	−4.41248	−0.145554	−0.0727772	−	0.997348i	$-0.523186\pi$
$919$	−4.41248	−0.145554	−0.0727772	+	0.997348i	$0.523186\pi$
$920$	−4.71890	−0.155578
$921$	−2.63915	−0.0869630
$922$	−10.7585	−0.354313
$923$	1.02079	0.0335997
$924$	−1.12055	−0.0368634
$925$	−23.8508	−0.784209
$926$	−34.3970	−1.13036
$927$	−4.78091	−0.157026
$928$	−2.51434	−0.0825372
$929$	0.0741274	0.00243204	0.00121602	−	0.999999i	$-0.499613\pi$
$929$	0.0741274	0.00243204	0.00121602	+	0.999999i	$0.499613\pi$
$930$	22.5606	0.739792
$931$	−9.74758	−0.319464
$932$	13.2100	0.432709
$933$	9.95986	0.326071
$934$	−9.75663	−0.319247
$935$	−9.33619	−0.305326
$936$	−3.29524	−0.107708
$937$	13.9964	0.457242	0.228621	−	0.973515i	$-0.426578\pi$
$937$	13.9964	0.457242	0.228621	+	0.973515i	$0.426578\pi$
$938$	4.74744	0.155009
$939$	−29.6812	−0.968608
$940$	−13.4985	−0.440272
$941$	−7.29298	−0.237744	−0.118872	−	0.992910i	$-0.537928\pi$
$941$	−7.29298	−0.237744	−0.118872	+	0.992910i	$0.537928\pi$
$942$	1.36165	0.0443651
$943$	6.72557	0.219015
$944$	13.7985	0.449103
$945$	−3.11615	−0.101368
$946$	6.81744	0.221654
$947$	−16.8218	−0.546637	−0.273318	−	0.961924i	$-0.588121\pi$
$947$	−16.8218	−0.546637	−0.273318	+	0.961924i	$0.588121\pi$
$948$	−13.7774	−0.447471
$949$	−4.48698	−0.145654
$950$	4.63835	0.150488
$951$	−12.6115	−0.408957
$952$	3.76197	0.121926
$953$	11.3672	0.368221	0.184110	−	0.982906i	$-0.441060\pi$
$953$	11.3672	0.368221	0.184110	+	0.982906i	$0.441060\pi$
$954$	2.57634	0.0834122
$955$	−61.8775	−2.00231
$956$	15.3935	0.497863
$957$	−2.51434	−0.0812770
$958$	0.226957	0.00733264
$959$	6.96748	0.224992
$960$	2.78091	0.0897533
$961$	34.8157	1.12309
$962$	28.7529	0.927030
$963$	7.60943	0.245210
$964$	7.57289	0.243906
$965$	−34.6996	−1.11702
$966$	1.90146	0.0611784
$967$	0.215881	0.00694228	0.00347114	−	0.999994i	$-0.498895\pi$
$967$	0.215881	0.00694228	0.00347114	+	0.999994i	$0.498895\pi$
$968$	1.00000	0.0321412
$969$	5.69689	0.183011
$970$	−9.24682	−0.296898
$971$	50.6075	1.62407	0.812035	−	0.583608i	$-0.198360\pi$
$971$	50.6075	1.62407	0.812035	+	0.583608i	$0.198360\pi$
$972$	−1.00000	−0.0320750
$973$	−1.51833	−0.0486753
$974$	6.68236	0.214117
$975$	9.00733	0.288465
$976$	−1.00000	−0.0320092
$977$	−48.1918	−1.54179	−0.770896	−	0.636961i	$-0.780191\pi$
$977$	−48.1918	−1.54179	−0.770896	+	0.636961i	$0.780191\pi$
$978$	2.82852	0.0904461
$979$	−12.9489	−0.413850
$980$	15.9745	0.510288
$981$	14.0828	0.449630
$982$	−39.3058	−1.25430
$983$	−48.3946	−1.54355	−0.771774	−	0.635897i	$-0.780630\pi$
$983$	−48.3946	−1.54355	−0.771774	+	0.635897i	$0.780630\pi$
$984$	−3.96346	−0.126350
$985$	16.0851	0.512513
$986$	8.44126	0.268824
$987$	5.43914	0.173130
$988$	−5.59168	−0.177895
$989$	−11.5685	−0.367856
$990$	2.78091	0.0883830
$991$	38.2837	1.21612	0.608060	−	0.793891i	$-0.291948\pi$
$991$	38.2837	1.21612	0.608060	+	0.793891i	$0.291948\pi$
$992$	8.11269	0.257578
$993$	25.5417	0.810541
$994$	0.347120	0.0110100
$995$	56.0416	1.77664
$996$	−10.6824	−0.338484
$997$	−47.2161	−1.49535	−0.747674	−	0.664066i	$-0.768829\pi$
$997$	−47.2161	−1.49535	−0.747674	+	0.664066i	$0.768829\pi$
$998$	−20.6248	−0.652865
$999$	8.72557	0.276065

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	4026.2.a.s.1.1	✓	4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
4026.2.a.s.1.1	✓	4	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:	\( N \)	\(=\)	\( 4026 = 2 \cdot 3 \cdot 11 \cdot 61 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	4026.a (trivial)

\(f(q)\)	\(=\)	\(q+1.00000 q^{2} -1.00000 q^{3} +1.00000 q^{4} -2.78091 q^{5} -1.00000 q^{6} -1.12055 q^{7} +1.00000 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q+1.00000 q^{2} -1.00000 q^{3} +1.00000 q^{4} -2.78091 q^{5} -1.00000 q^{6} -1.12055 q^{7} +1.00000 q^{8} +1.00000 q^{9} -2.78091 q^{10} -1.00000 q^{11} -1.00000 q^{12} -3.29524 q^{13} -1.12055 q^{14} +2.78091 q^{15} +1.00000 q^{16} -3.35725 q^{17} +1.00000 q^{18} +1.69689 q^{19} -2.78091 q^{20} +1.12055 q^{21} -1.00000 q^{22} +1.69689 q^{23} -1.00000 q^{24} +2.73343 q^{25} -3.29524 q^{26} -1.00000 q^{27} -1.12055 q^{28} -2.51434 q^{29} +2.78091 q^{30} +8.11269 q^{31} +1.00000 q^{32} +1.00000 q^{33} -3.35725 q^{34} +3.11615 q^{35} +1.00000 q^{36} -8.72557 q^{37} +1.69689 q^{38} +3.29524 q^{39} -2.78091 q^{40} +3.96346 q^{41} +1.12055 q^{42} -6.81744 q^{43} -1.00000 q^{44} -2.78091 q^{45} +1.69689 q^{46} +4.85398 q^{47} -1.00000 q^{48} -5.74437 q^{49} +2.73343 q^{50} +3.35725 q^{51} -3.29524 q^{52} +2.57634 q^{53} -1.00000 q^{54} +2.78091 q^{55} -1.12055 q^{56} -1.69689 q^{57} -2.51434 q^{58} +13.7985 q^{59} +2.78091 q^{60} -1.00000 q^{61} +8.11269 q^{62} -1.12055 q^{63} +1.00000 q^{64} +9.16376 q^{65} +1.00000 q^{66} -4.23670 q^{67} -3.35725 q^{68} -1.69689 q^{69} +3.11615 q^{70} -0.309777 q^{71} +1.00000 q^{72} +1.36165 q^{73} -8.72557 q^{74} -2.73343 q^{75} +1.69689 q^{76} +1.12055 q^{77} +3.29524 q^{78} +13.7774 q^{79} -2.78091 q^{80} +1.00000 q^{81} +3.96346 q^{82} +10.6824 q^{83} +1.12055 q^{84} +9.33619 q^{85} -6.81744 q^{86} +2.51434 q^{87} -1.00000 q^{88} +12.9489 q^{89} -2.78091 q^{90} +3.69249 q^{91} +1.69689 q^{92} -8.11269 q^{93} +4.85398 q^{94} -4.71890 q^{95} -1.00000 q^{96} +3.32511 q^{97} -5.74437 q^{98} -1.00000 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q + 4 q^{2} - 4 q^{3} + 4 q^{4} + 3 q^{5} - 4 q^{6} - 2 q^{7} + 4 q^{8} + 4 q^{9}+O(q^{10}) \) 4 * q + 4 * q^2 - 4 * q^3 + 4 * q^4 + 3 * q^5 - 4 * q^6 - 2 * q^7 + 4 * q^8 + 4 * q^9	\( 4 q + 4 q^{2} - 4 q^{3} + 4 q^{4} + 3 q^{5} - 4 q^{6} - 2 q^{7} + 4 q^{8} + 4 q^{9} + 3 q^{10} - 4 q^{11} - 4 q^{12} + 13 q^{13} - 2 q^{14} - 3 q^{15} + 4 q^{16} + 3 q^{17} + 4 q^{18} + 2 q^{19} + 3 q^{20} + 2 q^{21} - 4 q^{22} + 2 q^{23} - 4 q^{24} + 13 q^{25} + 13 q^{26} - 4 q^{27} - 2 q^{28} + 2 q^{29} - 3 q^{30} - q^{31} + 4 q^{32} + 4 q^{33} + 3 q^{34} + q^{35} + 4 q^{36} - 6 q^{37} + 2 q^{38} - 13 q^{39} + 3 q^{40} + 9 q^{41} + 2 q^{42} - 20 q^{43} - 4 q^{44} + 3 q^{45} + 2 q^{46} + 19 q^{47} - 4 q^{48} - 2 q^{49} + 13 q^{50} - 3 q^{51} + 13 q^{52} + 8 q^{53} - 4 q^{54} - 3 q^{55} - 2 q^{56} - 2 q^{57} + 2 q^{58} + 13 q^{59} - 3 q^{60} - 4 q^{61} - q^{62} - 2 q^{63} + 4 q^{64} + 36 q^{65} + 4 q^{66} - 3 q^{67} + 3 q^{68} - 2 q^{69} + q^{70} - q^{71} + 4 q^{72} - 2 q^{73} - 6 q^{74} - 13 q^{75} + 2 q^{76} + 2 q^{77} - 13 q^{78} + 19 q^{79} + 3 q^{80} + 4 q^{81} + 9 q^{82} + 12 q^{83} + 2 q^{84} + 27 q^{85} - 20 q^{86} - 2 q^{87} - 4 q^{88} + 19 q^{89} + 3 q^{90} + q^{91} + 2 q^{92} + q^{93} + 19 q^{94} + 5 q^{95} - 4 q^{96} - q^{97} - 2 q^{98} - 4 q^{99}+O(q^{100}) \) 4 * q + 4 * q^2 - 4 * q^3 + 4 * q^4 + 3 * q^5 - 4 * q^6 - 2 * q^7 + 4 * q^8 + 4 * q^9 + 3 * q^10 - 4 * q^11 - 4 * q^12 + 13 * q^13 - 2 * q^14 - 3 * q^15 + 4 * q^16 + 3 * q^17 + 4 * q^18 + 2 * q^19 + 3 * q^20 + 2 * q^21 - 4 * q^22 + 2 * q^23 - 4 * q^24 + 13 * q^25 + 13 * q^26 - 4 * q^27 - 2 * q^28 + 2 * q^29 - 3 * q^30 - q^31 + 4 * q^32 + 4 * q^33 + 3 * q^34 + q^35 + 4 * q^36 - 6 * q^37 + 2 * q^38 - 13 * q^39 + 3 * q^40 + 9 * q^41 + 2 * q^42 - 20 * q^43 - 4 * q^44 + 3 * q^45 + 2 * q^46 + 19 * q^47 - 4 * q^48 - 2 * q^49 + 13 * q^50 - 3 * q^51 + 13 * q^52 + 8 * q^53 - 4 * q^54 - 3 * q^55 - 2 * q^56 - 2 * q^57 + 2 * q^58 + 13 * q^59 - 3 * q^60 - 4 * q^61 - q^62 - 2 * q^63 + 4 * q^64 + 36 * q^65 + 4 * q^66 - 3 * q^67 + 3 * q^68 - 2 * q^69 + q^70 - q^71 + 4 * q^72 - 2 * q^73 - 6 * q^74 - 13 * q^75 + 2 * q^76 + 2 * q^77 - 13 * q^78 + 19 * q^79 + 3 * q^80 + 4 * q^81 + 9 * q^82 + 12 * q^83 + 2 * q^84 + 27 * q^85 - 20 * q^86 - 2 * q^87 - 4 * q^88 + 19 * q^89 + 3 * q^90 + q^91 + 2 * q^92 + q^93 + 19 * q^94 + 5 * q^95 - 4 * q^96 - q^97 - 2 * q^98 - 4 * q^99

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