LMFDB - Embedded newform 8034.2.a.y.1.7

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [8034,2,Mod(1,8034)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(8034, 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("8034.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 8034 = 2 \cdot 3 \cdot 13 \cdot 103 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	8034.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:	$64.1518129839$
Analytic rank:	$0$
Dimension:	$13$
Coefficient field:	$\mathbb{Q}[x]/(x^{13} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{13} - 5 x^{12} - 25 x^{11} + 134 x^{10} + 196 x^{9} - 1151 x^{8} - 801 x^{7} + 4263 x^{6} + \cdots - 180 $ x^13 - 5x^12 - 25x^11 + 134x^10 + 196x^9 - 1151x^8 - 801x^7 + 4263x^6 + 2205x^5 - 6840x^4 - 3579x^3 + 3559x^2 + 1839x - 180
Coefficient ring:	$\Z[a_1, \ldots, a_{11}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.7
Root			$-0.723662$ of defining polynomial
Character	$\chi$	$=$	8034.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.00000 q^{2} -1.00000 q^{3} +1.00000 q^{4} +0.370604 q^{5} -1.00000 q^{6} -0.723662 q^{7} +1.00000 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q+1.00000 q^{2} -1.00000 q^{3} +1.00000 q^{4} +0.370604 q^{5} -1.00000 q^{6} -0.723662 q^{7} +1.00000 q^{8} +1.00000 q^{9} +0.370604 q^{10} +4.08485 q^{11} -1.00000 q^{12} +1.00000 q^{13} -0.723662 q^{14} -0.370604 q^{15} +1.00000 q^{16} +2.82780 q^{17} +1.00000 q^{18} +6.02179 q^{19} +0.370604 q^{20} +0.723662 q^{21} +4.08485 q^{22} +9.47630 q^{23} -1.00000 q^{24} -4.86265 q^{25} +1.00000 q^{26} -1.00000 q^{27} -0.723662 q^{28} +1.81973 q^{29} -0.370604 q^{30} +6.02179 q^{31} +1.00000 q^{32} -4.08485 q^{33} +2.82780 q^{34} -0.268192 q^{35} +1.00000 q^{36} +2.69606 q^{37} +6.02179 q^{38} -1.00000 q^{39} +0.370604 q^{40} -4.02235 q^{41} +0.723662 q^{42} -9.90584 q^{43} +4.08485 q^{44} +0.370604 q^{45} +9.47630 q^{46} -5.09292 q^{47} -1.00000 q^{48} -6.47631 q^{49} -4.86265 q^{50} -2.82780 q^{51} +1.00000 q^{52} +8.46008 q^{53} -1.00000 q^{54} +1.51386 q^{55} -0.723662 q^{56} -6.02179 q^{57} +1.81973 q^{58} -8.70338 q^{59} -0.370604 q^{60} -3.58234 q^{61} +6.02179 q^{62} -0.723662 q^{63} +1.00000 q^{64} +0.370604 q^{65} -4.08485 q^{66} +0.686569 q^{67} +2.82780 q^{68} -9.47630 q^{69} -0.268192 q^{70} +3.03612 q^{71} +1.00000 q^{72} +6.55392 q^{73} +2.69606 q^{74} +4.86265 q^{75} +6.02179 q^{76} -2.95605 q^{77} -1.00000 q^{78} -10.7053 q^{79} +0.370604 q^{80} +1.00000 q^{81} -4.02235 q^{82} +3.83880 q^{83} +0.723662 q^{84} +1.04799 q^{85} -9.90584 q^{86} -1.81973 q^{87} +4.08485 q^{88} +10.5725 q^{89} +0.370604 q^{90} -0.723662 q^{91} +9.47630 q^{92} -6.02179 q^{93} -5.09292 q^{94} +2.23170 q^{95} -1.00000 q^{96} -3.82498 q^{97} -6.47631 q^{98} +4.08485 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 13 q + 13 q^{2} - 13 q^{3} + 13 q^{4} + 3 q^{5} - 13 q^{6} + 5 q^{7} + 13 q^{8} + 13 q^{9}+O(q^{10}) $ 13 * q + 13 * q^2 - 13 * q^3 + 13 * q^4 + 3 * q^5 - 13 * q^6 + 5 * q^7 + 13 * q^8 + 13 * q^9	\( 13 q + 13 q^{2} - 13 q^{3} + 13 q^{4} + 3 q^{5} - 13 q^{6} + 5 q^{7} + 13 q^{8} + 13 q^{9} + 3 q^{10} + 8 q^{11} - 13 q^{12} + 13 q^{13} + 5 q^{14} - 3 q^{15} + 13 q^{16} - q^{17} + 13 q^{18} + 5 q^{19} + 3 q^{20} - 5 q^{21} + 8 q^{22} - 9 q^{23} - 13 q^{24} + 24 q^{25} + 13 q^{26} - 13 q^{27} + 5 q^{28} - q^{29} - 3 q^{30} + 5 q^{31} + 13 q^{32} - 8 q^{33} - q^{34} + 28 q^{35} + 13 q^{36} + 35 q^{37} + 5 q^{38} - 13 q^{39} + 3 q^{40} + 24 q^{41} - 5 q^{42} + 9 q^{43} + 8 q^{44} + 3 q^{45} - 9 q^{46} - 8 q^{47} - 13 q^{48} - 16 q^{49} + 24 q^{50} + q^{51} + 13 q^{52} + 32 q^{53} - 13 q^{54} - 4 q^{55} + 5 q^{56} - 5 q^{57} - q^{58} + 12 q^{59} - 3 q^{60} + 17 q^{61} + 5 q^{62} + 5 q^{63} + 13 q^{64} + 3 q^{65} - 8 q^{66} + 20 q^{67} - q^{68} + 9 q^{69} + 28 q^{70} + 16 q^{71} + 13 q^{72} + 46 q^{73} + 35 q^{74} - 24 q^{75} + 5 q^{76} - 7 q^{77} - 13 q^{78} + 17 q^{79} + 3 q^{80} + 13 q^{81} + 24 q^{82} + 13 q^{83} - 5 q^{84} + 11 q^{85} + 9 q^{86} + q^{87} + 8 q^{88} + 14 q^{89} + 3 q^{90} + 5 q^{91} - 9 q^{92} - 5 q^{93} - 8 q^{94} + 2 q^{95} - 13 q^{96} + 46 q^{97} - 16 q^{98} + 8 q^{99}+O(q^{100}) \) 13 * q + 13 * q^2 - 13 * q^3 + 13 * q^4 + 3 * q^5 - 13 * q^6 + 5 * q^7 + 13 * q^8 + 13 * q^9 + 3 * q^10 + 8 * q^11 - 13 * q^12 + 13 * q^13 + 5 * q^14 - 3 * q^15 + 13 * q^16 - q^17 + 13 * q^18 + 5 * q^19 + 3 * q^20 - 5 * q^21 + 8 * q^22 - 9 * q^23 - 13 * q^24 + 24 * q^25 + 13 * q^26 - 13 * q^27 + 5 * q^28 - q^29 - 3 * q^30 + 5 * q^31 + 13 * q^32 - 8 * q^33 - q^34 + 28 * q^35 + 13 * q^36 + 35 * q^37 + 5 * q^38 - 13 * q^39 + 3 * q^40 + 24 * q^41 - 5 * q^42 + 9 * q^43 + 8 * q^44 + 3 * q^45 - 9 * q^46 - 8 * q^47 - 13 * q^48 - 16 * q^49 + 24 * q^50 + q^51 + 13 * q^52 + 32 * q^53 - 13 * q^54 - 4 * q^55 + 5 * q^56 - 5 * q^57 - q^58 + 12 * q^59 - 3 * q^60 + 17 * q^61 + 5 * q^62 + 5 * q^63 + 13 * q^64 + 3 * q^65 - 8 * q^66 + 20 * q^67 - q^68 + 9 * q^69 + 28 * q^70 + 16 * q^71 + 13 * q^72 + 46 * q^73 + 35 * q^74 - 24 * q^75 + 5 * q^76 - 7 * q^77 - 13 * q^78 + 17 * q^79 + 3 * q^80 + 13 * q^81 + 24 * q^82 + 13 * q^83 - 5 * q^84 + 11 * q^85 + 9 * q^86 + q^87 + 8 * q^88 + 14 * q^89 + 3 * q^90 + 5 * q^91 - 9 * q^92 - 5 * q^93 - 8 * q^94 + 2 * q^95 - 13 * q^96 + 46 * q^97 - 16 * q^98 + 8 * 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
$5$	0.370604	0.165739	0.0828695	−	0.996560i	$-0.473592\pi$
$5$	0.370604	0.165739	0.0828695	+	0.996560i	$0.473592\pi$
$6$	−1.00000	−0.408248
$7$	−0.723662	−0.273518	−0.136759	−	0.990604i	$-0.543669\pi$
$7$	−0.723662	−0.273518	−0.136759	+	0.990604i	$0.543669\pi$
$8$	1.00000	0.353553
$9$	1.00000	0.333333
$10$	0.370604	0.117195
$11$	4.08485	1.23163	0.615815	−	0.787891i	$-0.288827\pi$
$11$	4.08485	1.23163	0.615815	+	0.787891i	$0.288827\pi$
$12$	−1.00000	−0.288675
$13$	1.00000	0.277350
$13$	1.00000	0.277350
$14$	−0.723662	−0.193407
$15$	−0.370604	−0.0956895
$16$	1.00000	0.250000
$17$	2.82780	0.685843	0.342922	−	0.939364i	$-0.388583\pi$
$17$	2.82780	0.685843	0.342922	+	0.939364i	$0.388583\pi$
$18$	1.00000	0.235702
$19$	6.02179	1.38149	0.690747	−	0.723096i	$-0.257282\pi$
$19$	6.02179	1.38149	0.690747	+	0.723096i	$0.257282\pi$
$20$	0.370604	0.0828695
$21$	0.723662	0.157916
$22$	4.08485	0.870894
$23$	9.47630	1.97595	0.987973	−	0.154628i	$-0.0494180\pi$
$23$	9.47630	1.97595	0.987973	+	0.154628i	$0.0494180\pi$
$24$	−1.00000	−0.204124
$25$	−4.86265	−0.972531
$26$	1.00000	0.196116
$27$	−1.00000	−0.192450
$28$	−0.723662	−0.136759
$29$	1.81973	0.337916	0.168958	−	0.985623i	$-0.445960\pi$
$29$	1.81973	0.337916	0.168958	+	0.985623i	$0.445960\pi$
$30$	−0.370604	−0.0676627
$31$	6.02179	1.08155	0.540773	−	0.841169i	$-0.318132\pi$
$31$	6.02179	1.08155	0.540773	+	0.841169i	$0.318132\pi$
$32$	1.00000	0.176777
$33$	−4.08485	−0.711082
$34$	2.82780	0.484964
$35$	−0.268192	−0.0453327
$36$	1.00000	0.166667
$37$	2.69606	0.443229	0.221615	−	0.975134i	$-0.428867\pi$
$37$	2.69606	0.443229	0.221615	+	0.975134i	$0.428867\pi$
$38$	6.02179	0.976864
$39$	−1.00000	−0.160128
$40$	0.370604	0.0585976
$41$	−4.02235	−0.628186	−0.314093	−	0.949392i	$-0.601700\pi$
$41$	−4.02235	−0.628186	−0.314093	+	0.949392i	$0.601700\pi$
$42$	0.723662	0.111663
$43$	−9.90584	−1.51063	−0.755313	−	0.655364i	$-0.772515\pi$
$43$	−9.90584	−1.51063	−0.755313	+	0.655364i	$0.772515\pi$
$44$	4.08485	0.615815
$45$	0.370604	0.0552463
$46$	9.47630	1.39720
$47$	−5.09292	−0.742879	−0.371440	−	0.928457i	$-0.621136\pi$
$47$	−5.09292	−0.742879	−0.371440	+	0.928457i	$0.621136\pi$
$48$	−1.00000	−0.144338
$49$	−6.47631	−0.925188
$50$	−4.86265	−0.687683
$51$	−2.82780	−0.395972
$52$	1.00000	0.138675
$53$	8.46008	1.16208	0.581041	−	0.813874i	$-0.302646\pi$
$53$	8.46008	1.16208	0.581041	+	0.813874i	$0.302646\pi$
$54$	−1.00000	−0.136083
$55$	1.51386	0.204129
$56$	−0.723662	−0.0967033
$57$	−6.02179	−0.797606
$58$	1.81973	0.238943
$59$	−8.70338	−1.13308	−0.566542	−	0.824033i	$-0.691719\pi$
$59$	−8.70338	−1.13308	−0.566542	+	0.824033i	$0.691719\pi$
$60$	−0.370604	−0.0478447
$61$	−3.58234	−0.458672	−0.229336	−	0.973347i	$-0.573655\pi$
$61$	−3.58234	−0.458672	−0.229336	+	0.973347i	$0.573655\pi$
$62$	6.02179	0.764769
$63$	−0.723662	−0.0911728
$64$	1.00000	0.125000
$65$	0.370604	0.0459677
$66$	−4.08485	−0.502811
$67$	0.686569	0.0838777	0.0419389	−	0.999120i	$-0.486647\pi$
$67$	0.686569	0.0838777	0.0419389	+	0.999120i	$0.486647\pi$
$68$	2.82780	0.342922
$69$	−9.47630	−1.14081
$70$	−0.268192	−0.0320550
$71$	3.03612	0.360321	0.180160	−	0.983637i	$-0.442338\pi$
$71$	3.03612	0.360321	0.180160	+	0.983637i	$0.442338\pi$
$72$	1.00000	0.117851
$73$	6.55392	0.767079	0.383539	−	0.923525i	$-0.374705\pi$
$73$	6.55392	0.767079	0.383539	+	0.923525i	$0.374705\pi$
$74$	2.69606	0.313411
$75$	4.86265	0.561491
$76$	6.02179	0.690747
$77$	−2.95605	−0.336873
$78$	−1.00000	−0.113228
$79$	−10.7053	−1.20444	−0.602219	−	0.798331i	$-0.705717\pi$
$79$	−10.7053	−1.20444	−0.602219	+	0.798331i	$0.705717\pi$
$80$	0.370604	0.0414348
$81$	1.00000	0.111111
$82$	−4.02235	−0.444195
$83$	3.83880	0.421363	0.210681	−	0.977555i	$-0.432432\pi$
$83$	3.83880	0.421363	0.210681	+	0.977555i	$0.432432\pi$
$84$	0.723662	0.0789580
$85$	1.04799	0.113671
$86$	−9.90584	−1.06817
$87$	−1.81973	−0.195096
$88$	4.08485	0.435447
$89$	10.5725	1.12068	0.560342	−	0.828261i	$-0.310670\pi$
$89$	10.5725	1.12068	0.560342	+	0.828261i	$0.310670\pi$
$90$	0.370604	0.0390651
$91$	−0.723662	−0.0758603
$92$	9.47630	0.987973
$93$	−6.02179	−0.624431
$94$	−5.09292	−0.525295
$95$	2.23170	0.228968
$96$	−1.00000	−0.102062
$97$	−3.82498	−0.388368	−0.194184	−	0.980965i	$-0.562206\pi$
$97$	−3.82498	−0.388368	−0.194184	+	0.980965i	$0.562206\pi$
$98$	−6.47631	−0.654206
$99$	4.08485	0.410543
$100$	−4.86265	−0.486265
$101$	−18.4899	−1.83981	−0.919906	−	0.392139i	$-0.871735\pi$
$101$	−18.4899	−1.83981	−0.919906	+	0.392139i	$0.871735\pi$
$102$	−2.82780	−0.279994
$103$	1.00000	0.0985329
$103$	1.00000	0.0985329
$104$	1.00000	0.0980581
$105$	0.268192	0.0261728
$106$	8.46008	0.821716
$107$	7.96833	0.770328	0.385164	−	0.922848i	$-0.374145\pi$
$107$	7.96833	0.770328	0.385164	+	0.922848i	$0.374145\pi$
$108$	−1.00000	−0.0962250
$109$	−5.36157	−0.513545	−0.256773	−	0.966472i	$-0.582659\pi$
$109$	−5.36157	−0.513545	−0.256773	+	0.966472i	$0.582659\pi$
$110$	1.51386	0.144341
$111$	−2.69606	−0.255899
$112$	−0.723662	−0.0683796
$113$	−3.09054	−0.290734	−0.145367	−	0.989378i	$-0.546436\pi$
$113$	−3.09054	−0.290734	−0.145367	+	0.989378i	$0.546436\pi$
$114$	−6.02179	−0.563993
$115$	3.51195	0.327491
$116$	1.81973	0.168958
$117$	1.00000	0.0924500
$118$	−8.70338	−0.801211
$119$	−2.04637	−0.187591
$120$	−0.370604	−0.0338313
$121$	5.68603	0.516912
$122$	−3.58234	−0.324330
$123$	4.02235	0.362683
$124$	6.02179	0.540773
$125$	−3.65514	−0.326925
$126$	−0.723662	−0.0644689
$127$	8.00147	0.710016	0.355008	−	0.934863i	$-0.384478\pi$
$127$	8.00147	0.710016	0.355008	+	0.934863i	$0.384478\pi$
$128$	1.00000	0.0883883
$129$	9.90584	0.872160
$130$	0.370604	0.0325041
$131$	5.38636	0.470608	0.235304	−	0.971922i	$-0.424391\pi$
$131$	5.38636	0.470608	0.235304	+	0.971922i	$0.424391\pi$
$132$	−4.08485	−0.355541
$133$	−4.35774	−0.377864
$134$	0.686569	0.0593105
$135$	−0.370604	−0.0318965
$136$	2.82780	0.242482
$137$	10.8255	0.924883	0.462441	−	0.886650i	$-0.346974\pi$
$137$	10.8255	0.924883	0.462441	+	0.886650i	$0.346974\pi$
$138$	−9.47630	−0.806676
$139$	−9.27710	−0.786874	−0.393437	−	0.919352i	$-0.628714\pi$
$139$	−9.27710	−0.786874	−0.393437	+	0.919352i	$0.628714\pi$
$140$	−0.268192	−0.0226663
$141$	5.09292	0.428902
$142$	3.03612	0.254785
$143$	4.08485	0.341593
$144$	1.00000	0.0833333
$145$	0.674401	0.0560059
$146$	6.55392	0.542407
$147$	6.47631	0.534157
$148$	2.69606	0.221615
$149$	14.3341	1.17430	0.587149	−	0.809479i	$-0.300250\pi$
$149$	14.3341	1.17430	0.587149	+	0.809479i	$0.300250\pi$
$150$	4.86265	0.397034
$151$	0.229540	0.0186797	0.00933987	−	0.999956i	$-0.497027\pi$
$151$	0.229540	0.0186797	0.00933987	+	0.999956i	$0.497027\pi$
$152$	6.02179	0.488432
$153$	2.82780	0.228614
$154$	−2.95605	−0.238205
$155$	2.23170	0.179254
$156$	−1.00000	−0.0800641
$157$	20.3191	1.62164	0.810821	−	0.585294i	$-0.199021\pi$
$157$	20.3191	1.62164	0.810821	+	0.585294i	$0.199021\pi$
$158$	−10.7053	−0.851666
$159$	−8.46008	−0.670928
$160$	0.370604	0.0292988
$161$	−6.85764	−0.540457
$162$	1.00000	0.0785674
$163$	2.42839	0.190206	0.0951031	−	0.995467i	$-0.469682\pi$
$163$	2.42839	0.190206	0.0951031	+	0.995467i	$0.469682\pi$
$164$	−4.02235	−0.314093
$165$	−1.51386	−0.117854
$166$	3.83880	0.297949
$167$	13.5013	1.04476	0.522380	−	0.852713i	$-0.325044\pi$
$167$	13.5013	1.04476	0.522380	+	0.852713i	$0.325044\pi$
$168$	0.723662	0.0558317
$169$	1.00000	0.0769231
$170$	1.04799	0.0803775
$171$	6.02179	0.460498
$172$	−9.90584	−0.755313
$173$	−7.09134	−0.539145	−0.269572	−	0.962980i	$-0.586882\pi$
$173$	−7.09134	−0.539145	−0.269572	+	0.962980i	$0.586882\pi$
$174$	−1.81973	−0.137954
$175$	3.51892	0.266005
$176$	4.08485	0.307907
$177$	8.70338	0.654186
$178$	10.5725	0.792443
$179$	6.85207	0.512148	0.256074	−	0.966657i	$-0.417571\pi$
$179$	6.85207	0.512148	0.256074	+	0.966657i	$0.417571\pi$
$180$	0.370604	0.0276232
$181$	−5.74020	−0.426666	−0.213333	−	0.976980i	$-0.568432\pi$
$181$	−5.74020	−0.426666	−0.213333	+	0.976980i	$0.568432\pi$
$182$	−0.723662	−0.0536414
$183$	3.58234	0.264814
$184$	9.47630	0.698602
$185$	0.999170	0.0734604
$186$	−6.02179	−0.441539
$187$	11.5512	0.844705
$188$	−5.09292	−0.371440
$189$	0.723662	0.0526386
$190$	2.23170	0.161904
$191$	1.39059	0.100620	0.0503098	−	0.998734i	$-0.483979\pi$
$191$	1.39059	0.100620	0.0503098	+	0.998734i	$0.483979\pi$
$192$	−1.00000	−0.0721688
$193$	12.2587	0.882398	0.441199	−	0.897409i	$-0.354553\pi$
$193$	12.2587	0.882398	0.441199	+	0.897409i	$0.354553\pi$
$194$	−3.82498	−0.274618
$195$	−0.370604	−0.0265395
$196$	−6.47631	−0.462594
$197$	6.36281	0.453332	0.226666	−	0.973973i	$-0.427217\pi$
$197$	6.36281	0.453332	0.226666	+	0.973973i	$0.427217\pi$
$198$	4.08485	0.290298
$199$	−9.00503	−0.638349	−0.319175	−	0.947696i	$-0.603406\pi$
$199$	−9.00503	−0.638349	−0.319175	+	0.947696i	$0.603406\pi$
$200$	−4.86265	−0.343841
$201$	−0.686569	−0.0484268
$202$	−18.4899	−1.30094
$203$	−1.31687	−0.0924263
$204$	−2.82780	−0.197986
$205$	−1.49070	−0.104115
$206$	1.00000	0.0696733
$207$	9.47630	0.658648
$208$	1.00000	0.0693375
$209$	24.5981	1.70149
$210$	0.268192	0.0185070
$211$	21.4330	1.47551	0.737753	−	0.675070i	$-0.235887\pi$
$211$	21.4330	1.47551	0.737753	+	0.675070i	$0.235887\pi$
$212$	8.46008	0.581041
$213$	−3.03612	−0.208031
$214$	7.96833	0.544704
$215$	−3.67114	−0.250370
$216$	−1.00000	−0.0680414
$217$	−4.35774	−0.295823
$218$	−5.36157	−0.363131
$219$	−6.55392	−0.442873
$220$	1.51386	0.102065
$221$	2.82780	0.190219
$222$	−2.69606	−0.180948
$223$	−2.33444	−0.156326	−0.0781630	−	0.996941i	$-0.524905\pi$
$223$	−2.33444	−0.156326	−0.0781630	+	0.996941i	$0.524905\pi$
$224$	−0.723662	−0.0483517
$225$	−4.86265	−0.324177
$226$	−3.09054	−0.205580
$227$	−13.3759	−0.887790	−0.443895	−	0.896079i	$-0.646404\pi$
$227$	−13.3759	−0.887790	−0.443895	+	0.896079i	$0.646404\pi$
$228$	−6.02179	−0.398803
$229$	0.0526342	0.00347816	0.00173908	−	0.999998i	$-0.499446\pi$
$229$	0.0526342	0.00347816	0.00173908	+	0.999998i	$0.499446\pi$
$230$	3.51195	0.231571
$231$	2.95605	0.194494
$232$	1.81973	0.119471
$233$	−4.80383	−0.314709	−0.157355	−	0.987542i	$-0.550297\pi$
$233$	−4.80383	−0.314709	−0.157355	+	0.987542i	$0.550297\pi$
$234$	1.00000	0.0653720
$235$	−1.88746	−0.123124
$236$	−8.70338	−0.566542
$237$	10.7053	0.695383
$238$	−2.04637	−0.132647
$239$	2.37617	0.153702	0.0768508	−	0.997043i	$-0.475513\pi$
$239$	2.37617	0.153702	0.0768508	+	0.997043i	$0.475513\pi$
$240$	−0.370604	−0.0239224
$241$	−19.4337	−1.25184	−0.625918	−	0.779889i	$-0.715276\pi$
$241$	−19.4337	−1.25184	−0.625918	+	0.779889i	$0.715276\pi$
$242$	5.68603	0.365512
$243$	−1.00000	−0.0641500
$244$	−3.58234	−0.229336
$245$	−2.40015	−0.153340
$246$	4.02235	0.256456
$247$	6.02179	0.383158
$248$	6.02179	0.382384
$249$	−3.83880	−0.243274
$250$	−3.65514	−0.231171
$251$	29.8758	1.88574	0.942871	−	0.333159i	$-0.108114\pi$
$251$	29.8758	1.88574	0.942871	+	0.333159i	$0.108114\pi$
$252$	−0.723662	−0.0455864
$253$	38.7093	2.43363
$254$	8.00147	0.502057
$255$	−1.04799	−0.0656280
$256$	1.00000	0.0625000
$257$	−13.4299	−0.837736	−0.418868	−	0.908047i	$-0.637573\pi$
$257$	−13.4299	−0.837736	−0.418868	+	0.908047i	$0.637573\pi$
$258$	9.90584	0.616710
$259$	−1.95103	−0.121231
$260$	0.370604	0.0229839
$261$	1.81973	0.112639
$262$	5.38636	0.332770
$263$	−22.2144	−1.36980	−0.684898	−	0.728639i	$-0.740153\pi$
$263$	−22.2144	−1.36980	−0.684898	+	0.728639i	$0.740153\pi$
$264$	−4.08485	−0.251405
$265$	3.13534	0.192602
$266$	−4.35774	−0.267190
$267$	−10.5725	−0.647027
$268$	0.686569	0.0419389
$269$	26.5687	1.61992	0.809960	−	0.586485i	$-0.199489\pi$
$269$	26.5687	1.61992	0.809960	+	0.586485i	$0.199489\pi$
$270$	−0.370604	−0.0225542
$271$	17.6921	1.07472	0.537360	−	0.843353i	$-0.319422\pi$
$271$	17.6921	1.07472	0.537360	+	0.843353i	$0.319422\pi$
$272$	2.82780	0.171461
$273$	0.723662	0.0437980
$274$	10.8255	0.653991
$275$	−19.8632	−1.19780
$276$	−9.47630	−0.570406
$277$	−3.70776	−0.222778	−0.111389	−	0.993777i	$-0.535530\pi$
$277$	−3.70776	−0.222778	−0.111389	+	0.993777i	$0.535530\pi$
$278$	−9.27710	−0.556404
$279$	6.02179	0.360515
$280$	−0.268192	−0.0160275
$281$	−12.1669	−0.725814	−0.362907	−	0.931825i	$-0.618216\pi$
$281$	−12.1669	−0.725814	−0.362907	+	0.931825i	$0.618216\pi$
$282$	5.09292	0.303279
$283$	−0.358585	−0.0213157	−0.0106578	−	0.999943i	$-0.503393\pi$
$283$	−0.358585	−0.0213157	−0.0106578	+	0.999943i	$0.503393\pi$
$284$	3.03612	0.180160
$285$	−2.23170	−0.132194
$286$	4.08485	0.241542
$287$	2.91082	0.171820
$288$	1.00000	0.0589256
$289$	−9.00352	−0.529619
$290$	0.674401	0.0396022
$291$	3.82498	0.224224
$292$	6.55392	0.383539
$293$	3.44414	0.201209	0.100604	−	0.994927i	$-0.467922\pi$
$293$	3.44414	0.201209	0.100604	+	0.994927i	$0.467922\pi$
$294$	6.47631	0.377706
$295$	−3.22551	−0.187796
$296$	2.69606	0.156705
$297$	−4.08485	−0.237027
$298$	14.3341	0.830354
$299$	9.47630	0.548029
$300$	4.86265	0.280745
$301$	7.16847	0.413184
$302$	0.229540	0.0132086
$303$	18.4899	1.06222
$304$	6.02179	0.345374
$305$	−1.32763	−0.0760199
$306$	2.82780	0.161655
$307$	13.0229	0.743258	0.371629	−	0.928381i	$-0.378799\pi$
$307$	13.0229	0.743258	0.371629	+	0.928381i	$0.378799\pi$
$308$	−2.95605	−0.168437
$309$	−1.00000	−0.0568880
$310$	2.23170	0.126752
$311$	−5.23865	−0.297057	−0.148528	−	0.988908i	$-0.547454\pi$
$311$	−5.23865	−0.297057	−0.148528	+	0.988908i	$0.547454\pi$
$312$	−1.00000	−0.0566139
$313$	−4.99104	−0.282110	−0.141055	−	0.990002i	$-0.545049\pi$
$313$	−4.99104	−0.282110	−0.141055	+	0.990002i	$0.545049\pi$
$314$	20.3191	1.14667
$315$	−0.268192	−0.0151109
$316$	−10.7053	−0.602219
$317$	−7.85669	−0.441276	−0.220638	−	0.975356i	$-0.570814\pi$
$317$	−7.85669	−0.441276	−0.220638	+	0.975356i	$0.570814\pi$
$318$	−8.46008	−0.474418
$319$	7.43335	0.416188
$320$	0.370604	0.0207174
$321$	−7.96833	−0.444749
$322$	−6.85764	−0.382161
$323$	17.0285	0.947489
$324$	1.00000	0.0555556
$325$	−4.86265	−0.269731
$326$	2.42839	0.134496
$327$	5.36157	0.296495
$328$	−4.02235	−0.222097
$329$	3.68555	0.203191
$330$	−1.51386	−0.0833354
$331$	−18.6316	−1.02409	−0.512044	−	0.858959i	$-0.671111\pi$
$331$	−18.6316	−1.02409	−0.512044	+	0.858959i	$0.671111\pi$
$332$	3.83880	0.210681
$333$	2.69606	0.147743
$334$	13.5013	0.738757
$335$	0.254445	0.0139018
$336$	0.723662	0.0394790
$337$	2.88003	0.156885	0.0784427	−	0.996919i	$-0.475005\pi$
$337$	2.88003	0.156885	0.0784427	+	0.996919i	$0.475005\pi$
$338$	1.00000	0.0543928
$339$	3.09054	0.167855
$340$	1.04799	0.0568355
$341$	24.5981	1.33206
$342$	6.02179	0.325621
$343$	9.75229	0.526574
$344$	−9.90584	−0.534087
$345$	−3.51195	−0.189077
$346$	−7.09134	−0.381233
$347$	−28.3732	−1.52315	−0.761576	−	0.648076i	$-0.775574\pi$
$347$	−28.3732	−1.52315	−0.761576	+	0.648076i	$0.775574\pi$
$348$	−1.81973	−0.0975480
$349$	−2.45320	−0.131317	−0.0656584	−	0.997842i	$-0.520915\pi$
$349$	−2.45320	−0.131317	−0.0656584	+	0.997842i	$0.520915\pi$
$350$	3.51892	0.188094
$351$	−1.00000	−0.0533761
$352$	4.08485	0.217723
$353$	−24.8206	−1.32107	−0.660534	−	0.750796i	$-0.729670\pi$
$353$	−24.8206	−1.32107	−0.660534	+	0.750796i	$0.729670\pi$
$354$	8.70338	0.462579
$355$	1.12520	0.0597192
$356$	10.5725	0.560342
$357$	2.04637	0.108306
$358$	6.85207	0.362143
$359$	27.0311	1.42665	0.713324	−	0.700834i	$-0.247189\pi$
$359$	27.0311	1.42665	0.713324	+	0.700834i	$0.247189\pi$
$360$	0.370604	0.0195325
$361$	17.2620	0.908526
$362$	−5.74020	−0.301698
$363$	−5.68603	−0.298439
$364$	−0.723662	−0.0379302
$365$	2.42891	0.127135
$366$	3.58234	0.187252
$367$	−7.25592	−0.378756	−0.189378	−	0.981904i	$-0.560647\pi$
$367$	−7.25592	−0.378756	−0.189378	+	0.981904i	$0.560647\pi$
$368$	9.47630	0.493986
$369$	−4.02235	−0.209395
$370$	0.999170	0.0519444
$371$	−6.12224	−0.317851
$372$	−6.02179	−0.312215
$373$	−29.3118	−1.51771	−0.758855	−	0.651260i	$-0.774241\pi$
$373$	−29.3118	−1.51771	−0.758855	+	0.651260i	$0.774241\pi$
$374$	11.5512	0.597297
$375$	3.65514	0.188750
$376$	−5.09292	−0.262647
$377$	1.81973	0.0937211
$378$	0.723662	0.0372211
$379$	−11.0218	−0.566152	−0.283076	−	0.959097i	$-0.591355\pi$
$379$	−11.0218	−0.566152	−0.283076	+	0.959097i	$0.591355\pi$
$380$	2.23170	0.114484
$381$	−8.00147	−0.409928
$382$	1.39059	0.0711488
$383$	−33.0155	−1.68701	−0.843506	−	0.537120i	$-0.819512\pi$
$383$	−33.0155	−1.68701	−0.843506	+	0.537120i	$0.819512\pi$
$384$	−1.00000	−0.0510310
$385$	−1.09552	−0.0558331
$386$	12.2587	0.623950
$387$	−9.90584	−0.503542
$388$	−3.82498	−0.194184
$389$	23.2651	1.17959	0.589794	−	0.807553i	$-0.299209\pi$
$389$	23.2651	1.17959	0.589794	+	0.807553i	$0.299209\pi$
$390$	−0.370604	−0.0187663
$391$	26.7971	1.35519
$392$	−6.47631	−0.327103
$393$	−5.38636	−0.271706
$394$	6.36281	0.320554
$395$	−3.96742	−0.199622
$396$	4.08485	0.205272
$397$	−9.59816	−0.481718	−0.240859	−	0.970560i	$-0.577429\pi$
$397$	−9.59816	−0.481718	−0.240859	+	0.970560i	$0.577429\pi$
$398$	−9.00503	−0.451381
$399$	4.35774	0.218160
$400$	−4.86265	−0.243133
$401$	−13.4287	−0.670595	−0.335297	−	0.942112i	$-0.608837\pi$
$401$	−13.4287	−0.670595	−0.335297	+	0.942112i	$0.608837\pi$
$402$	−0.686569	−0.0342429
$403$	6.02179	0.299967
$404$	−18.4899	−0.919906
$405$	0.370604	0.0184154
$406$	−1.31687	−0.0653553
$407$	11.0130	0.545895
$408$	−2.82780	−0.139997
$409$	4.95578	0.245047	0.122524	−	0.992466i	$-0.460901\pi$
$409$	4.95578	0.245047	0.122524	+	0.992466i	$0.460901\pi$
$410$	−1.49070	−0.0736204
$411$	−10.8255	−0.533981
$412$	1.00000	0.0492665
$413$	6.29830	0.309919
$414$	9.47630	0.465735
$415$	1.42267	0.0698363
$416$	1.00000	0.0490290
$417$	9.27710	0.454302
$418$	24.5981	1.20313
$419$	−37.9125	−1.85215	−0.926075	−	0.377341i	$-0.876839\pi$
$419$	−37.9125	−1.85215	−0.926075	+	0.377341i	$0.876839\pi$
$420$	0.268192	0.0130864
$421$	15.1376	0.737762	0.368881	−	0.929477i	$-0.379741\pi$
$421$	15.1376	0.737762	0.368881	+	0.929477i	$0.379741\pi$
$422$	21.4330	1.04334
$423$	−5.09292	−0.247626
$424$	8.46008	0.410858
$425$	−13.7506	−0.667004
$426$	−3.03612	−0.147100
$427$	2.59240	0.125455
$428$	7.96833	0.385164
$429$	−4.08485	−0.197219
$430$	−3.67114	−0.177038
$431$	5.62624	0.271006	0.135503	−	0.990777i	$-0.456735\pi$
$431$	5.62624	0.271006	0.135503	+	0.990777i	$0.456735\pi$
$432$	−1.00000	−0.0481125
$433$	30.4790	1.46473	0.732364	−	0.680913i	$-0.238417\pi$
$433$	30.4790	1.46473	0.732364	+	0.680913i	$0.238417\pi$
$434$	−4.35774	−0.209178
$435$	−0.674401	−0.0323350
$436$	−5.36157	−0.256773
$437$	57.0643	2.72976
$438$	−6.55392	−0.313159
$439$	−2.73082	−0.130335	−0.0651675	−	0.997874i	$-0.520758\pi$
$439$	−2.73082	−0.130335	−0.0651675	+	0.997874i	$0.520758\pi$
$440$	1.51386	0.0721705
$441$	−6.47631	−0.308396
$442$	2.82780	0.134505
$443$	−35.1315	−1.66915	−0.834574	−	0.550895i	$-0.814286\pi$
$443$	−35.1315	−1.66915	−0.834574	+	0.550895i	$0.814286\pi$
$444$	−2.69606	−0.127949
$445$	3.91821	0.185741
$446$	−2.33444	−0.110539
$447$	−14.3341	−0.677982
$448$	−0.723662	−0.0341898
$449$	20.7905	0.981164	0.490582	−	0.871395i	$-0.336784\pi$
$449$	20.7905	0.981164	0.490582	+	0.871395i	$0.336784\pi$
$450$	−4.86265	−0.229228
$451$	−16.4307	−0.773693
$452$	−3.09054	−0.145367
$453$	−0.229540	−0.0107848
$454$	−13.3759	−0.627762
$455$	−0.268192	−0.0125730
$456$	−6.02179	−0.281996
$457$	33.1262	1.54958	0.774789	−	0.632220i	$-0.217856\pi$
$457$	33.1262	1.54958	0.774789	+	0.632220i	$0.217856\pi$
$458$	0.0526342	0.00245943
$459$	−2.82780	−0.131991
$460$	3.51195	0.163746
$461$	25.5852	1.19162	0.595810	−	0.803125i	$-0.296831\pi$
$461$	25.5852	1.19162	0.595810	+	0.803125i	$0.296831\pi$
$462$	2.95605	0.137528
$463$	29.6878	1.37971	0.689854	−	0.723949i	$-0.257675\pi$
$463$	29.6878	1.37971	0.689854	+	0.723949i	$0.257675\pi$
$464$	1.81973	0.0844791
$465$	−2.23170	−0.103493
$466$	−4.80383	−0.222533
$467$	−25.8056	−1.19414	−0.597071	−	0.802189i	$-0.703669\pi$
$467$	−25.8056	−1.19414	−0.597071	+	0.802189i	$0.703669\pi$
$468$	1.00000	0.0462250
$469$	−0.496843	−0.0229421
$470$	−1.88746	−0.0870619
$471$	−20.3191	−0.936255
$472$	−8.70338	−0.400605
$473$	−40.4639	−1.86053
$474$	10.7053	0.491710
$475$	−29.2819	−1.34355
$476$	−2.04637	−0.0937954
$477$	8.46008	0.387361
$478$	2.37617	0.108684
$479$	30.0058	1.37100	0.685499	−	0.728073i	$-0.259584\pi$
$479$	30.0058	1.37100	0.685499	+	0.728073i	$0.259584\pi$
$480$	−0.370604	−0.0169157
$481$	2.69606	0.122930
$482$	−19.4337	−0.885182
$483$	6.85764	0.312033
$484$	5.68603	0.258456
$485$	−1.41755	−0.0643678
$486$	−1.00000	−0.0453609
$487$	−14.9303	−0.676558	−0.338279	−	0.941046i	$-0.609845\pi$
$487$	−14.9303	−0.676558	−0.338279	+	0.941046i	$0.609845\pi$
$488$	−3.58234	−0.162165
$489$	−2.42839	−0.109816
$490$	−2.40015	−0.108428
$491$	29.0275	1.30999	0.654996	−	0.755632i	$-0.272670\pi$
$491$	29.0275	1.30999	0.654996	+	0.755632i	$0.272670\pi$
$492$	4.02235	0.181342
$493$	5.14585	0.231758
$494$	6.02179	0.270933
$495$	1.51386	0.0680430
$496$	6.02179	0.270387
$497$	−2.19712	−0.0985544
$498$	−3.83880	−0.172021
$499$	−22.8181	−1.02148	−0.510739	−	0.859736i	$-0.670628\pi$
$499$	−22.8181	−1.02148	−0.510739	+	0.859736i	$0.670628\pi$
$500$	−3.65514	−0.163463
$501$	−13.5013	−0.603193
$502$	29.8758	1.33342
$503$	17.4326	0.777283	0.388642	−	0.921389i	$-0.372944\pi$
$503$	17.4326	0.777283	0.388642	+	0.921389i	$0.372944\pi$
$504$	−0.723662	−0.0322344
$505$	−6.85242	−0.304929
$506$	38.7093	1.72084
$507$	−1.00000	−0.0444116
$508$	8.00147	0.355008
$509$	−5.02336	−0.222657	−0.111328	−	0.993784i	$-0.535511\pi$
$509$	−5.02336	−0.222657	−0.111328	+	0.993784i	$0.535511\pi$
$510$	−1.04799	−0.0464060
$511$	−4.74282	−0.209810
$512$	1.00000	0.0441942
$513$	−6.02179	−0.265869
$514$	−13.4299	−0.592369
$515$	0.370604	0.0163308
$516$	9.90584	0.436080
$517$	−20.8038	−0.914952
$518$	−1.95103	−0.0857235
$519$	7.09134	0.311275
$520$	0.370604	0.0162521
$521$	33.7354	1.47798	0.738988	−	0.673718i	$-0.235304\pi$
$521$	33.7354	1.47798	0.738988	+	0.673718i	$0.235304\pi$
$522$	1.81973	0.0796476
$523$	−17.5589	−0.767796	−0.383898	−	0.923375i	$-0.625419\pi$
$523$	−17.5589	−0.767796	−0.383898	+	0.923375i	$0.625419\pi$
$524$	5.38636	0.235304
$525$	−3.51892	−0.153578
$526$	−22.2144	−0.968592
$527$	17.0285	0.741771
$528$	−4.08485	−0.177770
$529$	66.8003	2.90436
$530$	3.13534	0.136190
$531$	−8.70338	−0.377694
$532$	−4.35774	−0.188932
$533$	−4.02235	−0.174228
$534$	−10.5725	−0.457517
$535$	2.95309	0.127673
$536$	0.686569	0.0296552
$537$	−6.85207	−0.295689
$538$	26.5687	1.14546
$539$	−26.4548	−1.13949
$540$	−0.370604	−0.0159482
$541$	−10.1962	−0.438367	−0.219184	−	0.975684i	$-0.570339\pi$
$541$	−10.1962	−0.438367	−0.219184	+	0.975684i	$0.570339\pi$
$542$	17.6921	0.759941
$543$	5.74020	0.246335
$544$	2.82780	0.121241
$545$	−1.98702	−0.0851145
$546$	0.723662	0.0309699
$547$	14.5042	0.620157	0.310078	−	0.950711i	$-0.399645\pi$
$547$	14.5042	0.620157	0.310078	+	0.950711i	$0.399645\pi$
$548$	10.8255	0.462441
$549$	−3.58234	−0.152891
$550$	−19.8632	−0.846971
$551$	10.9581	0.466829
$552$	−9.47630	−0.403338
$553$	7.74700	0.329436
$554$	−3.70776	−0.157528
$555$	−0.999170	−0.0424124
$556$	−9.27710	−0.393437
$557$	−31.2280	−1.32317	−0.661587	−	0.749868i	$-0.730117\pi$
$557$	−31.2280	−1.32317	−0.661587	+	0.749868i	$0.730117\pi$
$558$	6.02179	0.254923
$559$	−9.90584	−0.418972
$560$	−0.268192	−0.0113332
$561$	−11.5512	−0.487691
$562$	−12.1669	−0.513228
$563$	33.0082	1.39113	0.695565	−	0.718464i	$-0.255154\pi$
$563$	33.0082	1.39113	0.695565	+	0.718464i	$0.255154\pi$
$564$	5.09292	0.214451
$565$	−1.14537	−0.0481859
$566$	−0.358585	−0.0150724
$567$	−0.723662	−0.0303909
$568$	3.03612	0.127393
$569$	−1.56523	−0.0656180	−0.0328090	−	0.999462i	$-0.510445\pi$
$569$	−1.56523	−0.0656180	−0.0328090	+	0.999462i	$0.510445\pi$
$570$	−2.23170	−0.0934756
$571$	1.20520	0.0504362	0.0252181	−	0.999682i	$-0.491972\pi$
$571$	1.20520	0.0504362	0.0252181	+	0.999682i	$0.491972\pi$
$572$	4.08485	0.170796
$573$	−1.39059	−0.0580928
$574$	2.91082	0.121495
$575$	−46.0800	−1.92167
$576$	1.00000	0.0416667
$577$	46.1035	1.91931	0.959656	−	0.281177i	$-0.0907247\pi$
$577$	46.1035	1.91931	0.959656	+	0.281177i	$0.0907247\pi$
$578$	−9.00352	−0.374497
$579$	−12.2587	−0.509453
$580$	0.674401	0.0280030
$581$	−2.77799	−0.115250
$582$	3.82498	0.158551
$583$	34.5582	1.43125
$584$	6.55392	0.271203
$585$	0.370604	0.0153226
$586$	3.44414	0.142276
$587$	−8.91285	−0.367873	−0.183936	−	0.982938i	$-0.558884\pi$
$587$	−8.91285	−0.367873	−0.183936	+	0.982938i	$0.558884\pi$
$588$	6.47631	0.267079
$589$	36.2620	1.49415
$590$	−3.22551	−0.132792
$591$	−6.36281	−0.261731
$592$	2.69606	0.110807
$593$	−29.5270	−1.21253	−0.606265	−	0.795263i	$-0.707333\pi$
$593$	−29.5270	−1.21253	−0.606265	+	0.795263i	$0.707333\pi$
$594$	−4.08485	−0.167604
$595$	−0.758394	−0.0310911
$596$	14.3341	0.587149
$597$	9.00503	0.368551
$598$	9.47630	0.387515
$599$	−4.01418	−0.164015	−0.0820075	−	0.996632i	$-0.526133\pi$
$599$	−4.01418	−0.164015	−0.0820075	+	0.996632i	$0.526133\pi$
$600$	4.86265	0.198517
$601$	44.4925	1.81489	0.907443	−	0.420175i	$-0.138031\pi$
$601$	44.4925	1.81489	0.907443	+	0.420175i	$0.138031\pi$
$602$	7.16847	0.292165
$603$	0.686569	0.0279592
$604$	0.229540	0.00933987
$605$	2.10726	0.0856724
$606$	18.4899	0.751100
$607$	−34.5936	−1.40411	−0.702056	−	0.712122i	$-0.747734\pi$
$607$	−34.5936	−1.40411	−0.702056	+	0.712122i	$0.747734\pi$
$608$	6.02179	0.244216
$609$	1.31687	0.0533624
$610$	−1.32763	−0.0537542
$611$	−5.09292	−0.206038
$612$	2.82780	0.114307
$613$	16.0416	0.647915	0.323958	−	0.946072i	$-0.394986\pi$
$613$	16.0416	0.647915	0.323958	+	0.946072i	$0.394986\pi$
$614$	13.0229	0.525563
$615$	1.49070	0.0601108
$616$	−2.95605	−0.119103
$617$	15.4935	0.623744	0.311872	−	0.950124i	$-0.399044\pi$
$617$	15.4935	0.623744	0.311872	+	0.950124i	$0.399044\pi$
$618$	−1.00000	−0.0402259
$619$	−19.4932	−0.783497	−0.391748	−	0.920072i	$-0.628130\pi$
$619$	−19.4932	−0.783497	−0.391748	+	0.920072i	$0.628130\pi$
$620$	2.23170	0.0896272
$621$	−9.47630	−0.380271
$622$	−5.23865	−0.210051
$623$	−7.65092	−0.306528
$624$	−1.00000	−0.0400320
$625$	22.9587	0.918346
$626$	−4.99104	−0.199482
$627$	−24.5981	−0.982355
$628$	20.3191	0.810821
$629$	7.62393	0.303986
$630$	−0.268192	−0.0106850
$631$	−12.0807	−0.480926	−0.240463	−	0.970658i	$-0.577299\pi$
$631$	−12.0807	−0.480926	−0.240463	+	0.970658i	$0.577299\pi$
$632$	−10.7053	−0.425833
$633$	−21.4330	−0.851884
$634$	−7.85669	−0.312029
$635$	2.96538	0.117677
$636$	−8.46008	−0.335464
$637$	−6.47631	−0.256601
$638$	7.43335	0.294289
$639$	3.03612	0.120107
$640$	0.370604	0.0146494
$641$	16.8112	0.664002	0.332001	−	0.943279i	$-0.392276\pi$
$641$	16.8112	0.664002	0.332001	+	0.943279i	$0.392276\pi$
$642$	−7.96833	−0.314485
$643$	−25.4631	−1.00417	−0.502083	−	0.864819i	$-0.667433\pi$
$643$	−25.4631	−1.00417	−0.502083	+	0.864819i	$0.667433\pi$
$644$	−6.85764	−0.270229
$645$	3.67114	0.144551
$646$	17.0285	0.669976
$647$	−0.0447601	−0.00175970	−0.000879850	−	1.00000i	$-0.500280\pi$
$647$	−0.0447601	−0.00175970	−0.000879850		1.00000i	$0.500280\pi$
$648$	1.00000	0.0392837
$649$	−35.5520	−1.39554
$650$	−4.86265	−0.190729
$651$	4.35774	0.170793
$652$	2.42839	0.0951031
$653$	−5.67608	−0.222122	−0.111061	−	0.993814i	$-0.535425\pi$
$653$	−5.67608	−0.222122	−0.111061	+	0.993814i	$0.535425\pi$
$654$	5.36157	0.209654
$655$	1.99620	0.0779982
$656$	−4.02235	−0.157047
$657$	6.55392	0.255693
$658$	3.68555	0.143678
$659$	−19.8522	−0.773333	−0.386666	−	0.922220i	$-0.626373\pi$
$659$	−19.8522	−0.773333	−0.386666	+	0.922220i	$0.626373\pi$
$660$	−1.51386	−0.0589270
$661$	37.1773	1.44603	0.723014	−	0.690833i	$-0.242756\pi$
$661$	37.1773	1.44603	0.723014	+	0.690833i	$0.242756\pi$
$662$	−18.6316	−0.724139
$663$	−2.82780	−0.109823
$664$	3.83880	0.148974
$665$	−1.61500	−0.0626268
$666$	2.69606	0.104470
$667$	17.2444	0.667704
$668$	13.5013	0.522380
$669$	2.33444	0.0902548
$670$	0.254445	0.00983006
$671$	−14.6333	−0.564914
$672$	0.723662	0.0279159
$673$	−43.1632	−1.66382	−0.831910	−	0.554911i	$-0.812752\pi$
$673$	−43.1632	−1.66382	−0.831910	+	0.554911i	$0.812752\pi$
$674$	2.88003	0.110935
$675$	4.86265	0.187164
$676$	1.00000	0.0384615
$677$	−35.0499	−1.34708	−0.673539	−	0.739152i	$-0.735227\pi$
$677$	−35.0499	−1.34708	−0.673539	+	0.739152i	$0.735227\pi$
$678$	3.09054	0.118692
$679$	2.76799	0.106226
$680$	1.04799	0.0401888
$681$	13.3759	0.512566
$682$	24.5981	0.941912
$683$	−43.7178	−1.67281	−0.836407	−	0.548108i	$-0.815348\pi$
$683$	−43.7178	−1.67281	−0.836407	+	0.548108i	$0.815348\pi$
$684$	6.02179	0.230249
$685$	4.01196	0.153289
$686$	9.75229	0.372344
$687$	−0.0526342	−0.00200812
$688$	−9.90584	−0.377656
$689$	8.46008	0.322304
$690$	−3.51195	−0.133698
$691$	46.2703	1.76021	0.880103	−	0.474784i	$-0.157474\pi$
$691$	46.2703	1.76021	0.880103	+	0.474784i	$0.157474\pi$
$692$	−7.09134	−0.269572
$693$	−2.95605	−0.112291
$694$	−28.3732	−1.07703
$695$	−3.43813	−0.130416
$696$	−1.81973	−0.0689769
$697$	−11.3744	−0.430837
$698$	−2.45320	−0.0928550
$699$	4.80383	0.181697
$700$	3.51892	0.133002
$701$	34.7635	1.31300	0.656500	−	0.754326i	$-0.272036\pi$
$701$	34.7635	1.31300	0.656500	+	0.754326i	$0.272036\pi$
$702$	−1.00000	−0.0377426
$703$	16.2351	0.612319
$704$	4.08485	0.153954
$705$	1.88746	0.0710857
$706$	−24.8206	−0.934137
$707$	13.3804	0.503222
$708$	8.70338	0.327093
$709$	13.6284	0.511825	0.255912	−	0.966700i	$-0.417624\pi$
$709$	13.6284	0.511825	0.255912	+	0.966700i	$0.417624\pi$
$710$	1.12520	0.0422279
$711$	−10.7053	−0.401479
$712$	10.5725	0.396222
$713$	57.0643	2.13708
$714$	2.04637	0.0765836
$715$	1.51386	0.0566152
$716$	6.85207	0.256074
$717$	−2.37617	−0.0887397
$718$	27.0311	1.00879
$719$	−23.3360	−0.870284	−0.435142	−	0.900362i	$-0.643302\pi$
$719$	−23.3360	−0.870284	−0.435142	+	0.900362i	$0.643302\pi$
$720$	0.370604	0.0138116
$721$	−0.723662	−0.0269506
$722$	17.2620	0.642425
$723$	19.4337	0.722748
$724$	−5.74020	−0.213333
$725$	−8.84874	−0.328634
$726$	−5.68603	−0.211028
$727$	−39.9831	−1.48289	−0.741446	−	0.671012i	$-0.765860\pi$
$727$	−39.9831	−1.48289	−0.741446	+	0.671012i	$0.765860\pi$
$728$	−0.723662	−0.0268207
$729$	1.00000	0.0370370
$730$	2.42891	0.0898980
$731$	−28.0118	−1.03605
$732$	3.58234	0.132407
$733$	23.4395	0.865758	0.432879	−	0.901452i	$-0.357498\pi$
$733$	23.4395	0.865758	0.432879	+	0.901452i	$0.357498\pi$
$734$	−7.25592	−0.267821
$735$	2.40015	0.0885307
$736$	9.47630	0.349301
$737$	2.80453	0.103306
$738$	−4.02235	−0.148065
$739$	−37.2913	−1.37178	−0.685891	−	0.727705i	$-0.740587\pi$
$739$	−37.2913	−1.37178	−0.685891	+	0.727705i	$0.740587\pi$
$740$	0.999170	0.0367302
$741$	−6.02179	−0.221216
$742$	−6.12224	−0.224754
$743$	−23.8287	−0.874191	−0.437096	−	0.899415i	$-0.643993\pi$
$743$	−23.8287	−0.874191	−0.437096	+	0.899415i	$0.643993\pi$
$744$	−6.02179	−0.220770
$745$	5.31229	0.194627
$746$	−29.3118	−1.07318
$747$	3.83880	0.140454
$748$	11.5512	0.422352
$749$	−5.76637	−0.210699
$750$	3.65514	0.133467
$751$	23.1756	0.845690	0.422845	−	0.906202i	$-0.361031\pi$
$751$	23.1756	0.845690	0.422845	+	0.906202i	$0.361031\pi$
$752$	−5.09292	−0.185720
$753$	−29.8758	−1.08873
$754$	1.81973	0.0662708
$755$	0.0850686	0.00309596
$756$	0.723662	0.0263193
$757$	25.9737	0.944029	0.472015	−	0.881591i	$-0.343527\pi$
$757$	25.9737	0.944029	0.472015	+	0.881591i	$0.343527\pi$
$758$	−11.0218	−0.400330
$759$	−38.7093	−1.40506
$760$	2.23170	0.0809522
$761$	12.3720	0.448483	0.224242	−	0.974534i	$-0.428010\pi$
$761$	12.3720	0.448483	0.224242	+	0.974534i	$0.428010\pi$
$762$	−8.00147	−0.289863
$763$	3.87996	0.140464
$764$	1.39059	0.0503098
$765$	1.04799	0.0378903
$766$	−33.0155	−1.19290
$767$	−8.70338	−0.314261
$768$	−1.00000	−0.0360844
$769$	45.3228	1.63438	0.817191	−	0.576367i	$-0.195530\pi$
$769$	45.3228	1.63438	0.817191	+	0.576367i	$0.195530\pi$
$770$	−1.09552	−0.0394799
$771$	13.4299	0.483667
$772$	12.2587	0.441199
$773$	−38.0245	−1.36765	−0.683823	−	0.729648i	$-0.739684\pi$
$773$	−38.0245	−1.36765	−0.683823	+	0.729648i	$0.739684\pi$
$774$	−9.90584	−0.356058
$775$	−29.2819	−1.05184
$776$	−3.82498	−0.137309
$777$	1.95103	0.0699930
$778$	23.2651	0.834095
$779$	−24.2218	−0.867836
$780$	−0.370604	−0.0132697
$781$	12.4021	0.443782
$782$	26.7971	0.958263
$783$	−1.81973	−0.0650320
$784$	−6.47631	−0.231297
$785$	7.53034	0.268769
$786$	−5.38636	−0.192125
$787$	−42.4035	−1.51152	−0.755761	−	0.654847i	$-0.772733\pi$
$787$	−42.4035	−1.51152	−0.755761	+	0.654847i	$0.772733\pi$
$788$	6.36281	0.226666
$789$	22.2144	0.790852
$790$	−3.96742	−0.141154
$791$	2.23651	0.0795210
$792$	4.08485	0.145149
$793$	−3.58234	−0.127213
$794$	−9.59816	−0.340626
$795$	−3.13534	−0.111199
$796$	−9.00503	−0.319175
$797$	−14.8520	−0.526086	−0.263043	−	0.964784i	$-0.584726\pi$
$797$	−14.8520	−0.526086	−0.263043	+	0.964784i	$0.584726\pi$
$798$	4.35774	0.154262
$799$	−14.4018	−0.509499
$800$	−4.86265	−0.171921
$801$	10.5725	0.373561
$802$	−13.4287	−0.474182
$803$	26.7718	0.944757
$804$	−0.686569	−0.0242134
$805$	−2.54147	−0.0895749
$806$	6.02179	0.212109
$807$	−26.5687	−0.935262
$808$	−18.4899	−0.650472
$809$	−6.71887	−0.236223	−0.118111	−	0.993000i	$-0.537684\pi$
$809$	−6.71887	−0.236223	−0.118111	+	0.993000i	$0.537684\pi$
$810$	0.370604	0.0130217
$811$	−7.07233	−0.248343	−0.124172	−	0.992261i	$-0.539627\pi$
$811$	−7.07233	−0.248343	−0.124172	+	0.992261i	$0.539627\pi$
$812$	−1.31687	−0.0462132
$813$	−17.6921	−0.620489
$814$	11.0130	0.386006
$815$	0.899971	0.0315246
$816$	−2.82780	−0.0989930
$817$	−59.6509	−2.08692
$818$	4.95578	0.173275
$819$	−0.723662	−0.0252868
$820$	−1.49070	−0.0520575
$821$	22.7604	0.794342	0.397171	−	0.917745i	$-0.369992\pi$
$821$	22.7604	0.794342	0.397171	+	0.917745i	$0.369992\pi$
$822$	−10.8255	−0.377582
$823$	−17.9065	−0.624182	−0.312091	−	0.950052i	$-0.601029\pi$
$823$	−17.9065	−0.624182	−0.312091	+	0.950052i	$0.601029\pi$
$824$	1.00000	0.0348367
$825$	19.8632	0.691549
$826$	6.29830	0.219146
$827$	−19.1316	−0.665271	−0.332635	−	0.943056i	$-0.607938\pi$
$827$	−19.1316	−0.665271	−0.332635	+	0.943056i	$0.607938\pi$
$828$	9.47630	0.329324
$829$	−11.8760	−0.412470	−0.206235	−	0.978502i	$-0.566121\pi$
$829$	−11.8760	−0.412470	−0.206235	+	0.978502i	$0.566121\pi$
$830$	1.42267	0.0493817
$831$	3.70776	0.128621
$832$	1.00000	0.0346688
$833$	−18.3137	−0.634534
$834$	9.27710	0.321240
$835$	5.00363	0.173158
$836$	24.5981	0.850745
$837$	−6.02179	−0.208144
$838$	−37.9125	−1.30967
$839$	−4.29993	−0.148450	−0.0742250	−	0.997242i	$-0.523648\pi$
$839$	−4.29993	−0.148450	−0.0742250	+	0.997242i	$0.523648\pi$
$840$	0.268192	0.00925349
$841$	−25.6886	−0.885813
$842$	15.1376	0.521677
$843$	12.1669	0.419049
$844$	21.4330	0.737753
$845$	0.370604	0.0127492
$846$	−5.09292	−0.175098
$847$	−4.11476	−0.141385
$848$	8.46008	0.290520
$849$	0.358585	0.0123066
$850$	−13.7506	−0.471643
$851$	25.5487	0.875797
$852$	−3.03612	−0.104016
$853$	7.08607	0.242623	0.121311	−	0.992615i	$-0.461290\pi$
$853$	7.08607	0.242623	0.121311	+	0.992615i	$0.461290\pi$
$854$	2.59240	0.0887102
$855$	2.23170	0.0763225
$856$	7.96833	0.272352
$857$	−16.2998	−0.556792	−0.278396	−	0.960466i	$-0.589803\pi$
$857$	−16.2998	−0.556792	−0.278396	+	0.960466i	$0.589803\pi$
$858$	−4.08485	−0.139455
$859$	−1.64787	−0.0562246	−0.0281123	−	0.999605i	$-0.508950\pi$
$859$	−1.64787	−0.0562246	−0.0281123	+	0.999605i	$0.508950\pi$
$860$	−3.67114	−0.125185
$861$	−2.91082	−0.0992006
$862$	5.62624	0.191630
$863$	−30.2864	−1.03096	−0.515480	−	0.856902i	$-0.672386\pi$
$863$	−30.2864	−1.03096	−0.515480	+	0.856902i	$0.672386\pi$
$864$	−1.00000	−0.0340207
$865$	−2.62808	−0.0893573
$866$	30.4790	1.03572
$867$	9.00352	0.305776
$868$	−4.35774	−0.147911
$869$	−43.7295	−1.48342
$870$	−0.674401	−0.0228643
$871$	0.686569	0.0232635
$872$	−5.36157	−0.181566
$873$	−3.82498	−0.129456
$874$	57.0643	1.93023
$875$	2.64508	0.0894201
$876$	−6.55392	−0.221437
$877$	41.2853	1.39410	0.697052	−	0.717020i	$-0.254495\pi$
$877$	41.2853	1.39410	0.697052	+	0.717020i	$0.254495\pi$
$878$	−2.73082	−0.0921608
$879$	−3.44414	−0.116168
$880$	1.51386	0.0510323
$881$	−21.8732	−0.736928	−0.368464	−	0.929642i	$-0.620116\pi$
$881$	−21.8732	−0.736928	−0.368464	+	0.929642i	$0.620116\pi$
$882$	−6.47631	−0.218069
$883$	8.68687	0.292337	0.146168	−	0.989260i	$-0.453306\pi$
$883$	8.68687	0.292337	0.146168	+	0.989260i	$0.453306\pi$
$884$	2.82780	0.0951094
$885$	3.22551	0.108424
$886$	−35.1315	−1.18027
$887$	−18.9403	−0.635954	−0.317977	−	0.948099i	$-0.603003\pi$
$887$	−18.9403	−0.635954	−0.317977	+	0.948099i	$0.603003\pi$
$888$	−2.69606	−0.0904738
$889$	−5.79036	−0.194202
$890$	3.91821	0.131339
$891$	4.08485	0.136848
$892$	−2.33444	−0.0781630
$893$	−30.6685	−1.02628
$894$	−14.3341	−0.479405
$895$	2.53940	0.0848829
$896$	−0.723662	−0.0241758
$897$	−9.47630	−0.316404
$898$	20.7905	0.693788
$899$	10.9581	0.365472
$900$	−4.86265	−0.162088
$901$	23.9235	0.797006
$902$	−16.4307	−0.547083
$903$	−7.16847	−0.238552
$904$	−3.09054	−0.102790
$905$	−2.12734	−0.0707151
$906$	−0.229540	−0.00762597
$907$	−6.71764	−0.223056	−0.111528	−	0.993761i	$-0.535574\pi$
$907$	−6.71764	−0.223056	−0.111528	+	0.993761i	$0.535574\pi$
$908$	−13.3759	−0.443895
$909$	−18.4899	−0.613271
$910$	−0.268192	−0.00889047
$911$	−51.2339	−1.69746	−0.848728	−	0.528830i	$-0.822631\pi$
$911$	−51.2339	−1.69746	−0.848728	+	0.528830i	$0.822631\pi$
$912$	−6.02179	−0.199402
$913$	15.6809	0.518963
$914$	33.1262	1.09572
$915$	1.32763	0.0438901
$916$	0.0526342	0.00173908
$917$	−3.89790	−0.128720
$918$	−2.82780	−0.0933315
$919$	38.8813	1.28258	0.641288	−	0.767300i	$-0.278400\pi$
$919$	38.8813	1.28258	0.641288	+	0.767300i	$0.278400\pi$
$920$	3.51195	0.115786
$921$	−13.0229	−0.429120
$922$	25.5852	0.842603
$923$	3.03612	0.0999350
$924$	2.95605	0.0972470
$925$	−13.1100	−0.431054
$926$	29.6878	0.975601
$927$	1.00000	0.0328443
$928$	1.81973	0.0597357
$929$	0.998295	0.0327530	0.0163765	−	0.999866i	$-0.494787\pi$
$929$	0.998295	0.0327530	0.0163765	+	0.999866i	$0.494787\pi$
$930$	−2.23170	−0.0731803
$931$	−38.9990	−1.27814
$932$	−4.80383	−0.157355
$933$	5.23865	0.171506
$934$	−25.8056	−0.844386
$935$	4.28091	0.140001
$936$	1.00000	0.0326860
$937$	−33.1948	−1.08443	−0.542214	−	0.840240i	$-0.682414\pi$
$937$	−33.1948	−1.08443	−0.542214	+	0.840240i	$0.682414\pi$
$938$	−0.496843	−0.0162225
$939$	4.99104	0.162876
$940$	−1.88746	−0.0615620
$941$	−41.6847	−1.35888	−0.679442	−	0.733730i	$-0.737778\pi$
$941$	−41.6847	−1.35888	−0.679442	+	0.733730i	$0.737778\pi$
$942$	−20.3191	−0.662033
$943$	−38.1170	−1.24126
$944$	−8.70338	−0.283271
$945$	0.268192	0.00872428
$946$	−40.4639	−1.31559
$947$	3.85439	0.125251	0.0626254	−	0.998037i	$-0.480053\pi$
$947$	3.85439	0.125251	0.0626254	+	0.998037i	$0.480053\pi$
$948$	10.7053	0.347691
$949$	6.55392	0.212749
$950$	−29.2819	−0.950030
$951$	7.85669	0.254771
$952$	−2.04637	−0.0663233
$953$	9.67653	0.313453	0.156727	−	0.987642i	$-0.449906\pi$
$953$	9.67653	0.313453	0.156727	+	0.987642i	$0.449906\pi$
$954$	8.46008	0.273905
$955$	0.515358	0.0166766
$956$	2.37617	0.0768508
$957$	−7.43335	−0.240286
$958$	30.0058	0.969442
$959$	−7.83398	−0.252972
$960$	−0.370604	−0.0119612
$961$	5.26200	0.169742
$962$	2.69606	0.0869245
$963$	7.96833	0.256776
$964$	−19.4337	−0.625918
$965$	4.54311	0.146248
$966$	6.85764	0.220641
$967$	−17.0933	−0.549683	−0.274842	−	0.961490i	$-0.588625\pi$
$967$	−17.0933	−0.549683	−0.274842	+	0.961490i	$0.588625\pi$
$968$	5.68603	0.182756
$969$	−17.0285	−0.547033
$970$	−1.41755	−0.0455149
$971$	20.3727	0.653792	0.326896	−	0.945060i	$-0.393997\pi$
$971$	20.3727	0.653792	0.326896	+	0.945060i	$0.393997\pi$
$972$	−1.00000	−0.0320750
$973$	6.71348	0.215224
$974$	−14.9303	−0.478399
$975$	4.86265	0.155730
$976$	−3.58234	−0.114668
$977$	33.3650	1.06744	0.533721	−	0.845661i	$-0.320793\pi$
$977$	33.3650	1.06744	0.533721	+	0.845661i	$0.320793\pi$
$978$	−2.42839	−0.0776514
$979$	43.1872	1.38027
$980$	−2.40015	−0.0766699
$981$	−5.36157	−0.171182
$982$	29.0275	0.926304
$983$	7.14727	0.227962	0.113981	−	0.993483i	$-0.463640\pi$
$983$	7.14727	0.227962	0.113981	+	0.993483i	$0.463640\pi$
$984$	4.02235	0.128228
$985$	2.35808	0.0751348
$986$	5.14585	0.163877
$987$	−3.68555	−0.117312
$988$	6.02179	0.191579
$989$	−93.8707	−2.98491
$990$	1.51386	0.0481137
$991$	43.3331	1.37652	0.688261	−	0.725463i	$-0.258374\pi$
$991$	43.3331	1.37652	0.688261	+	0.725463i	$0.258374\pi$
$992$	6.02179	0.191192
$993$	18.6316	0.591257
$994$	−2.19712	−0.0696885
$995$	−3.33730	−0.105799
$996$	−3.83880	−0.121637
$997$	−38.0042	−1.20360	−0.601802	−	0.798645i	$-0.705550\pi$
$997$	−38.0042	−1.20360	−0.601802	+	0.798645i	$0.705550\pi$
$998$	−22.8181	−0.722294
$999$	−2.69606	−0.0852996

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	8034.2.a.y.1.7	✓	13

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
8034.2.a.y.1.7	✓	13	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:	\( N \)	\(=\)	\( 8034 = 2 \cdot 3 \cdot 13 \cdot 103 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	8034.a (trivial)

\(f(q)\)	\(=\)	\(q+1.00000 q^{2} -1.00000 q^{3} +1.00000 q^{4} +0.370604 q^{5} -1.00000 q^{6} -0.723662 q^{7} +1.00000 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q+1.00000 q^{2} -1.00000 q^{3} +1.00000 q^{4} +0.370604 q^{5} -1.00000 q^{6} -0.723662 q^{7} +1.00000 q^{8} +1.00000 q^{9} +0.370604 q^{10} +4.08485 q^{11} -1.00000 q^{12} +1.00000 q^{13} -0.723662 q^{14} -0.370604 q^{15} +1.00000 q^{16} +2.82780 q^{17} +1.00000 q^{18} +6.02179 q^{19} +0.370604 q^{20} +0.723662 q^{21} +4.08485 q^{22} +9.47630 q^{23} -1.00000 q^{24} -4.86265 q^{25} +1.00000 q^{26} -1.00000 q^{27} -0.723662 q^{28} +1.81973 q^{29} -0.370604 q^{30} +6.02179 q^{31} +1.00000 q^{32} -4.08485 q^{33} +2.82780 q^{34} -0.268192 q^{35} +1.00000 q^{36} +2.69606 q^{37} +6.02179 q^{38} -1.00000 q^{39} +0.370604 q^{40} -4.02235 q^{41} +0.723662 q^{42} -9.90584 q^{43} +4.08485 q^{44} +0.370604 q^{45} +9.47630 q^{46} -5.09292 q^{47} -1.00000 q^{48} -6.47631 q^{49} -4.86265 q^{50} -2.82780 q^{51} +1.00000 q^{52} +8.46008 q^{53} -1.00000 q^{54} +1.51386 q^{55} -0.723662 q^{56} -6.02179 q^{57} +1.81973 q^{58} -8.70338 q^{59} -0.370604 q^{60} -3.58234 q^{61} +6.02179 q^{62} -0.723662 q^{63} +1.00000 q^{64} +0.370604 q^{65} -4.08485 q^{66} +0.686569 q^{67} +2.82780 q^{68} -9.47630 q^{69} -0.268192 q^{70} +3.03612 q^{71} +1.00000 q^{72} +6.55392 q^{73} +2.69606 q^{74} +4.86265 q^{75} +6.02179 q^{76} -2.95605 q^{77} -1.00000 q^{78} -10.7053 q^{79} +0.370604 q^{80} +1.00000 q^{81} -4.02235 q^{82} +3.83880 q^{83} +0.723662 q^{84} +1.04799 q^{85} -9.90584 q^{86} -1.81973 q^{87} +4.08485 q^{88} +10.5725 q^{89} +0.370604 q^{90} -0.723662 q^{91} +9.47630 q^{92} -6.02179 q^{93} -5.09292 q^{94} +2.23170 q^{95} -1.00000 q^{96} -3.82498 q^{97} -6.47631 q^{98} +4.08485 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 13 q + 13 q^{2} - 13 q^{3} + 13 q^{4} + 3 q^{5} - 13 q^{6} + 5 q^{7} + 13 q^{8} + 13 q^{9}+O(q^{10}) \) 13 * q + 13 * q^2 - 13 * q^3 + 13 * q^4 + 3 * q^5 - 13 * q^6 + 5 * q^7 + 13 * q^8 + 13 * q^9	\( 13 q + 13 q^{2} - 13 q^{3} + 13 q^{4} + 3 q^{5} - 13 q^{6} + 5 q^{7} + 13 q^{8} + 13 q^{9} + 3 q^{10} + 8 q^{11} - 13 q^{12} + 13 q^{13} + 5 q^{14} - 3 q^{15} + 13 q^{16} - q^{17} + 13 q^{18} + 5 q^{19} + 3 q^{20} - 5 q^{21} + 8 q^{22} - 9 q^{23} - 13 q^{24} + 24 q^{25} + 13 q^{26} - 13 q^{27} + 5 q^{28} - q^{29} - 3 q^{30} + 5 q^{31} + 13 q^{32} - 8 q^{33} - q^{34} + 28 q^{35} + 13 q^{36} + 35 q^{37} + 5 q^{38} - 13 q^{39} + 3 q^{40} + 24 q^{41} - 5 q^{42} + 9 q^{43} + 8 q^{44} + 3 q^{45} - 9 q^{46} - 8 q^{47} - 13 q^{48} - 16 q^{49} + 24 q^{50} + q^{51} + 13 q^{52} + 32 q^{53} - 13 q^{54} - 4 q^{55} + 5 q^{56} - 5 q^{57} - q^{58} + 12 q^{59} - 3 q^{60} + 17 q^{61} + 5 q^{62} + 5 q^{63} + 13 q^{64} + 3 q^{65} - 8 q^{66} + 20 q^{67} - q^{68} + 9 q^{69} + 28 q^{70} + 16 q^{71} + 13 q^{72} + 46 q^{73} + 35 q^{74} - 24 q^{75} + 5 q^{76} - 7 q^{77} - 13 q^{78} + 17 q^{79} + 3 q^{80} + 13 q^{81} + 24 q^{82} + 13 q^{83} - 5 q^{84} + 11 q^{85} + 9 q^{86} + q^{87} + 8 q^{88} + 14 q^{89} + 3 q^{90} + 5 q^{91} - 9 q^{92} - 5 q^{93} - 8 q^{94} + 2 q^{95} - 13 q^{96} + 46 q^{97} - 16 q^{98} + 8 q^{99}+O(q^{100}) \) 13 * q + 13 * q^2 - 13 * q^3 + 13 * q^4 + 3 * q^5 - 13 * q^6 + 5 * q^7 + 13 * q^8 + 13 * q^9 + 3 * q^10 + 8 * q^11 - 13 * q^12 + 13 * q^13 + 5 * q^14 - 3 * q^15 + 13 * q^16 - q^17 + 13 * q^18 + 5 * q^19 + 3 * q^20 - 5 * q^21 + 8 * q^22 - 9 * q^23 - 13 * q^24 + 24 * q^25 + 13 * q^26 - 13 * q^27 + 5 * q^28 - q^29 - 3 * q^30 + 5 * q^31 + 13 * q^32 - 8 * q^33 - q^34 + 28 * q^35 + 13 * q^36 + 35 * q^37 + 5 * q^38 - 13 * q^39 + 3 * q^40 + 24 * q^41 - 5 * q^42 + 9 * q^43 + 8 * q^44 + 3 * q^45 - 9 * q^46 - 8 * q^47 - 13 * q^48 - 16 * q^49 + 24 * q^50 + q^51 + 13 * q^52 + 32 * q^53 - 13 * q^54 - 4 * q^55 + 5 * q^56 - 5 * q^57 - q^58 + 12 * q^59 - 3 * q^60 + 17 * q^61 + 5 * q^62 + 5 * q^63 + 13 * q^64 + 3 * q^65 - 8 * q^66 + 20 * q^67 - q^68 + 9 * q^69 + 28 * q^70 + 16 * q^71 + 13 * q^72 + 46 * q^73 + 35 * q^74 - 24 * q^75 + 5 * q^76 - 7 * q^77 - 13 * q^78 + 17 * q^79 + 3 * q^80 + 13 * q^81 + 24 * q^82 + 13 * q^83 - 5 * q^84 + 11 * q^85 + 9 * q^86 + q^87 + 8 * q^88 + 14 * q^89 + 3 * q^90 + 5 * q^91 - 9 * q^92 - 5 * q^93 - 8 * q^94 + 2 * q^95 - 13 * q^96 + 46 * q^97 - 16 * q^98 + 8 * q^99

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