LMFDB - Embedded newform 8030.2.a.bd.1.12

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [8030,2,Mod(1,8030)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(8030, 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("8030.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 8030 = 2 \cdot 5 \cdot 11 \cdot 73 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	8030.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:	$64.1198728231$
Analytic rank:	$0$
Dimension:	$14$
Coefficient field:	$\mathbb{Q}[x]/(x^{14} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{14} - 6 x^{13} - 15 x^{12} + 143 x^{11} - 13 x^{10} - 1176 x^{9} + 1018 x^{8} + 4076 x^{7} + \cdots - 54 $ x^14 - 6x^13 - 15x^12 + 143x^11 - 13x^10 - 1176x^9 + 1018x^8 + 4076x^7 - 4865x^6 - 5483x^5 + 7607x^4 + 1210x^3 - 3153x^2 + 878*x - 54
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 2 $
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.12
Root			$2.86338$ of defining polynomial
Character	$\chi$	$=$	8030.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.00000 q^{2} +2.86338 q^{3} +1.00000 q^{4} -1.00000 q^{5} +2.86338 q^{6} +2.76153 q^{7} +1.00000 q^{8} +5.19896 q^{9} +O(q^{10})$	\(q+1.00000 q^{2} +2.86338 q^{3} +1.00000 q^{4} -1.00000 q^{5} +2.86338 q^{6} +2.76153 q^{7} +1.00000 q^{8} +5.19896 q^{9} -1.00000 q^{10} +1.00000 q^{11} +2.86338 q^{12} -2.67446 q^{13} +2.76153 q^{14} -2.86338 q^{15} +1.00000 q^{16} -2.89779 q^{17} +5.19896 q^{18} +1.41818 q^{19} -1.00000 q^{20} +7.90731 q^{21} +1.00000 q^{22} +6.20435 q^{23} +2.86338 q^{24} +1.00000 q^{25} -2.67446 q^{26} +6.29647 q^{27} +2.76153 q^{28} -1.29159 q^{29} -2.86338 q^{30} +5.43485 q^{31} +1.00000 q^{32} +2.86338 q^{33} -2.89779 q^{34} -2.76153 q^{35} +5.19896 q^{36} -8.25144 q^{37} +1.41818 q^{38} -7.65800 q^{39} -1.00000 q^{40} -0.280658 q^{41} +7.90731 q^{42} +6.92905 q^{43} +1.00000 q^{44} -5.19896 q^{45} +6.20435 q^{46} +10.7069 q^{47} +2.86338 q^{48} +0.626029 q^{49} +1.00000 q^{50} -8.29748 q^{51} -2.67446 q^{52} +12.2398 q^{53} +6.29647 q^{54} -1.00000 q^{55} +2.76153 q^{56} +4.06078 q^{57} -1.29159 q^{58} -8.36162 q^{59} -2.86338 q^{60} -6.83633 q^{61} +5.43485 q^{62} +14.3571 q^{63} +1.00000 q^{64} +2.67446 q^{65} +2.86338 q^{66} +9.94350 q^{67} -2.89779 q^{68} +17.7654 q^{69} -2.76153 q^{70} -3.96650 q^{71} +5.19896 q^{72} +1.00000 q^{73} -8.25144 q^{74} +2.86338 q^{75} +1.41818 q^{76} +2.76153 q^{77} -7.65800 q^{78} -2.15098 q^{79} -1.00000 q^{80} +2.43231 q^{81} -0.280658 q^{82} +4.18354 q^{83} +7.90731 q^{84} +2.89779 q^{85} +6.92905 q^{86} -3.69833 q^{87} +1.00000 q^{88} +10.2779 q^{89} -5.19896 q^{90} -7.38559 q^{91} +6.20435 q^{92} +15.5620 q^{93} +10.7069 q^{94} -1.41818 q^{95} +2.86338 q^{96} +2.68778 q^{97} +0.626029 q^{98} +5.19896 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 14 q + 14 q^{2} + 6 q^{3} + 14 q^{4} - 14 q^{5} + 6 q^{6} + 4 q^{7} + 14 q^{8} + 24 q^{9}+O(q^{10}) $ 14 * q + 14 * q^2 + 6 * q^3 + 14 * q^4 - 14 * q^5 + 6 * q^6 + 4 * q^7 + 14 * q^8 + 24 * q^9	\( 14 q + 14 q^{2} + 6 q^{3} + 14 q^{4} - 14 q^{5} + 6 q^{6} + 4 q^{7} + 14 q^{8} + 24 q^{9} - 14 q^{10} + 14 q^{11} + 6 q^{12} + 4 q^{13} + 4 q^{14} - 6 q^{15} + 14 q^{16} + 20 q^{17} + 24 q^{18} - 14 q^{20} + 25 q^{21} + 14 q^{22} - 4 q^{23} + 6 q^{24} + 14 q^{25} + 4 q^{26} + 21 q^{27} + 4 q^{28} + 7 q^{29} - 6 q^{30} + 8 q^{31} + 14 q^{32} + 6 q^{33} + 20 q^{34} - 4 q^{35} + 24 q^{36} + 17 q^{37} + 7 q^{39} - 14 q^{40} - 14 q^{41} + 25 q^{42} + 12 q^{43} + 14 q^{44} - 24 q^{45} - 4 q^{46} + 28 q^{47} + 6 q^{48} + 20 q^{49} + 14 q^{50} - 13 q^{51} + 4 q^{52} + 13 q^{53} + 21 q^{54} - 14 q^{55} + 4 q^{56} - 23 q^{57} + 7 q^{58} + 36 q^{59} - 6 q^{60} + 25 q^{61} + 8 q^{62} + 45 q^{63} + 14 q^{64} - 4 q^{65} + 6 q^{66} + 20 q^{68} - 7 q^{69} - 4 q^{70} + 17 q^{71} + 24 q^{72} + 14 q^{73} + 17 q^{74} + 6 q^{75} + 4 q^{77} + 7 q^{78} + 10 q^{79} - 14 q^{80} + 58 q^{81} - 14 q^{82} - 6 q^{83} + 25 q^{84} - 20 q^{85} + 12 q^{86} + 44 q^{87} + 14 q^{88} + 36 q^{89} - 24 q^{90} - 15 q^{91} - 4 q^{92} - 2 q^{93} + 28 q^{94} + 6 q^{96} - 19 q^{97} + 20 q^{98} + 24 q^{99}+O(q^{100}) \) 14 * q + 14 * q^2 + 6 * q^3 + 14 * q^4 - 14 * q^5 + 6 * q^6 + 4 * q^7 + 14 * q^8 + 24 * q^9 - 14 * q^10 + 14 * q^11 + 6 * q^12 + 4 * q^13 + 4 * q^14 - 6 * q^15 + 14 * q^16 + 20 * q^17 + 24 * q^18 - 14 * q^20 + 25 * q^21 + 14 * q^22 - 4 * q^23 + 6 * q^24 + 14 * q^25 + 4 * q^26 + 21 * q^27 + 4 * q^28 + 7 * q^29 - 6 * q^30 + 8 * q^31 + 14 * q^32 + 6 * q^33 + 20 * q^34 - 4 * q^35 + 24 * q^36 + 17 * q^37 + 7 * q^39 - 14 * q^40 - 14 * q^41 + 25 * q^42 + 12 * q^43 + 14 * q^44 - 24 * q^45 - 4 * q^46 + 28 * q^47 + 6 * q^48 + 20 * q^49 + 14 * q^50 - 13 * q^51 + 4 * q^52 + 13 * q^53 + 21 * q^54 - 14 * q^55 + 4 * q^56 - 23 * q^57 + 7 * q^58 + 36 * q^59 - 6 * q^60 + 25 * q^61 + 8 * q^62 + 45 * q^63 + 14 * q^64 - 4 * q^65 + 6 * q^66 + 20 * q^68 - 7 * q^69 - 4 * q^70 + 17 * q^71 + 24 * q^72 + 14 * q^73 + 17 * q^74 + 6 * q^75 + 4 * q^77 + 7 * q^78 + 10 * q^79 - 14 * q^80 + 58 * q^81 - 14 * q^82 - 6 * q^83 + 25 * q^84 - 20 * q^85 + 12 * q^86 + 44 * q^87 + 14 * q^88 + 36 * q^89 - 24 * q^90 - 15 * q^91 - 4 * q^92 - 2 * q^93 + 28 * q^94 + 6 * q^96 - 19 * q^97 + 20 * q^98 + 24 * q^99

Display 100 coefficients 10 coefficients

Coefficient data

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

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

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

$2$	1.00000	0.707107
$2$	1.00000	0.707107
$3$	2.86338	1.65317	0.826587	−	0.562808i	$-0.190279\pi$
$3$	2.86338	1.65317	0.826587	+	0.562808i	$0.190279\pi$
$4$	1.00000	0.500000
$5$	−1.00000	−0.447214
$5$	−1.00000	−0.447214
$6$	2.86338	1.16897
$7$	2.76153	1.04376	0.521879	−	0.853019i	$-0.325231\pi$
$7$	2.76153	1.04376	0.521879	+	0.853019i	$0.325231\pi$
$8$	1.00000	0.353553
$9$	5.19896	1.73299
$10$	−1.00000	−0.316228
$11$	1.00000	0.301511
$11$	1.00000	0.301511
$12$	2.86338	0.826587
$13$	−2.67446	−0.741761	−0.370881	−	0.928681i	$-0.620944\pi$
$13$	−2.67446	−0.741761	−0.370881	+	0.928681i	$0.620944\pi$
$14$	2.76153	0.738049
$15$	−2.86338	−0.739322
$16$	1.00000	0.250000
$17$	−2.89779	−0.702817	−0.351408	−	0.936222i	$-0.614297\pi$
$17$	−2.89779	−0.702817	−0.351408	+	0.936222i	$0.614297\pi$
$18$	5.19896	1.22541
$19$	1.41818	0.325352	0.162676	−	0.986680i	$-0.447987\pi$
$19$	1.41818	0.325352	0.162676	+	0.986680i	$0.447987\pi$
$20$	−1.00000	−0.223607
$21$	7.90731	1.72552
$22$	1.00000	0.213201
$23$	6.20435	1.29370	0.646849	−	0.762618i	$-0.276087\pi$
$23$	6.20435	1.29370	0.646849	+	0.762618i	$0.276087\pi$
$24$	2.86338	0.584486
$25$	1.00000	0.200000
$26$	−2.67446	−0.524504
$27$	6.29647	1.21176
$28$	2.76153	0.521879
$29$	−1.29159	−0.239843	−0.119922	−	0.992783i	$-0.538264\pi$
$29$	−1.29159	−0.239843	−0.119922	+	0.992783i	$0.538264\pi$
$30$	−2.86338	−0.522780
$31$	5.43485	0.976127	0.488064	−	0.872808i	$-0.337703\pi$
$31$	5.43485	0.976127	0.488064	+	0.872808i	$0.337703\pi$
$32$	1.00000	0.176777
$33$	2.86338	0.498451
$34$	−2.89779	−0.496967
$35$	−2.76153	−0.466783
$36$	5.19896	0.866493
$37$	−8.25144	−1.35653	−0.678264	−	0.734818i	$-0.737267\pi$
$37$	−8.25144	−1.35653	−0.678264	+	0.734818i	$0.737267\pi$
$38$	1.41818	0.230059
$39$	−7.65800	−1.22626
$40$	−1.00000	−0.158114
$41$	−0.280658	−0.0438315	−0.0219157	−	0.999760i	$-0.506977\pi$
$41$	−0.280658	−0.0438315	−0.0219157	+	0.999760i	$0.506977\pi$
$42$	7.90731	1.22012
$43$	6.92905	1.05667	0.528335	−	0.849036i	$-0.322817\pi$
$43$	6.92905	1.05667	0.528335	+	0.849036i	$0.322817\pi$
$44$	1.00000	0.150756
$45$	−5.19896	−0.775015
$46$	6.20435	0.914782
$47$	10.7069	1.56176	0.780882	−	0.624679i	$-0.214770\pi$
$47$	10.7069	1.56176	0.780882	+	0.624679i	$0.214770\pi$
$48$	2.86338	0.413294
$49$	0.626029	0.0894327
$50$	1.00000	0.141421
$51$	−8.29748	−1.16188
$52$	−2.67446	−0.370881
$53$	12.2398	1.68126	0.840631	−	0.541608i	$-0.182184\pi$
$53$	12.2398	1.68126	0.840631	+	0.541608i	$0.182184\pi$
$54$	6.29647	0.856841
$55$	−1.00000	−0.134840
$56$	2.76153	0.369025
$57$	4.06078	0.537864
$58$	−1.29159	−0.169595
$59$	−8.36162	−1.08859	−0.544295	−	0.838894i	$-0.683203\pi$
$59$	−8.36162	−1.08859	−0.544295	+	0.838894i	$0.683203\pi$
$60$	−2.86338	−0.369661
$61$	−6.83633	−0.875302	−0.437651	−	0.899145i	$-0.644189\pi$
$61$	−6.83633	−0.875302	−0.437651	+	0.899145i	$0.644189\pi$
$62$	5.43485	0.690226
$63$	14.3571	1.80882
$64$	1.00000	0.125000
$65$	2.67446	0.331726
$66$	2.86338	0.352458
$67$	9.94350	1.21479	0.607396	−	0.794399i	$-0.292214\pi$
$67$	9.94350	1.21479	0.607396	+	0.794399i	$0.292214\pi$
$68$	−2.89779	−0.351408
$69$	17.7654	2.13871
$70$	−2.76153	−0.330066
$71$	−3.96650	−0.470737	−0.235368	−	0.971906i	$-0.575630\pi$
$71$	−3.96650	−0.470737	−0.235368	+	0.971906i	$0.575630\pi$
$72$	5.19896	0.612703
$73$	1.00000	0.117041
$73$	1.00000	0.117041
$74$	−8.25144	−0.959210
$75$	2.86338	0.330635
$76$	1.41818	0.162676
$77$	2.76153	0.314705
$78$	−7.65800	−0.867097
$79$	−2.15098	−0.242005	−0.121002	−	0.992652i	$-0.538611\pi$
$79$	−2.15098	−0.242005	−0.121002	+	0.992652i	$0.538611\pi$
$80$	−1.00000	−0.111803
$81$	2.43231	0.270257
$82$	−0.280658	−0.0309935
$83$	4.18354	0.459203	0.229602	−	0.973285i	$-0.426258\pi$
$83$	4.18354	0.459203	0.229602	+	0.973285i	$0.426258\pi$
$84$	7.90731	0.862758
$85$	2.89779	0.314309
$86$	6.92905	0.747179
$87$	−3.69833	−0.396503
$88$	1.00000	0.106600
$89$	10.2779	1.08946	0.544728	−	0.838613i	$-0.316633\pi$
$89$	10.2779	1.08946	0.544728	+	0.838613i	$0.316633\pi$
$90$	−5.19896	−0.548019
$91$	−7.38559	−0.774220
$92$	6.20435	0.646849
$93$	15.5620	1.61371
$94$	10.7069	1.10433
$95$	−1.41818	−0.145502
$96$	2.86338	0.292243
$97$	2.68778	0.272902	0.136451	−	0.990647i	$-0.456430\pi$
$97$	2.68778	0.272902	0.136451	+	0.990647i	$0.456430\pi$
$98$	0.626029	0.0632385
$99$	5.19896	0.522515
$100$	1.00000	0.100000
$101$	8.83033	0.878651	0.439325	−	0.898328i	$-0.355218\pi$
$101$	8.83033	0.878651	0.439325	+	0.898328i	$0.355218\pi$
$102$	−8.29748	−0.821573
$103$	−4.77372	−0.470368	−0.235184	−	0.971951i	$-0.575569\pi$
$103$	−4.77372	−0.470368	−0.235184	+	0.971951i	$0.575569\pi$
$104$	−2.67446	−0.262252
$105$	−7.90731	−0.771674
$106$	12.2398	1.18883
$107$	−19.0550	−1.84211	−0.921056	−	0.389430i	$-0.872672\pi$
$107$	−19.0550	−1.84211	−0.921056	+	0.389430i	$0.872672\pi$
$108$	6.29647	0.605878
$109$	−16.3461	−1.56568	−0.782838	−	0.622226i	$-0.786229\pi$
$109$	−16.3461	−1.56568	−0.782838	+	0.622226i	$0.786229\pi$
$110$	−1.00000	−0.0953463
$111$	−23.6270	−2.24258
$112$	2.76153	0.260940
$113$	−12.0959	−1.13788	−0.568941	−	0.822378i	$-0.692647\pi$
$113$	−12.0959	−1.13788	−0.568941	+	0.822378i	$0.692647\pi$
$114$	4.06078	0.380327
$115$	−6.20435	−0.578559
$116$	−1.29159	−0.119922
$117$	−13.9044	−1.28546
$118$	−8.36162	−0.769749
$119$	−8.00232	−0.733571
$120$	−2.86338	−0.261390
$121$	1.00000	0.0909091
$122$	−6.83633	−0.618932
$123$	−0.803632	−0.0724611
$124$	5.43485	0.488064
$125$	−1.00000	−0.0894427
$126$	14.3571	1.27903
$127$	−0.0373438	−0.00331373	−0.00165686	−	0.999999i	$-0.500527\pi$
$127$	−0.0373438	−0.00331373	−0.00165686	+	0.999999i	$0.500527\pi$
$128$	1.00000	0.0883883
$129$	19.8405	1.74686
$130$	2.67446	0.234566
$131$	14.8916	1.30108	0.650542	−	0.759470i	$-0.274542\pi$
$131$	14.8916	1.30108	0.650542	+	0.759470i	$0.274542\pi$
$132$	2.86338	0.249225
$133$	3.91633	0.339589
$134$	9.94350	0.858988
$135$	−6.29647	−0.541914
$136$	−2.89779	−0.248483
$137$	15.3030	1.30742	0.653710	−	0.756745i	$-0.273212\pi$
$137$	15.3030	1.30742	0.653710	+	0.756745i	$0.273212\pi$
$138$	17.7654	1.51229
$139$	0.0730650	0.00619729	0.00309864	−	0.999995i	$-0.499014\pi$
$139$	0.0730650	0.00619729	0.00309864	+	0.999995i	$0.499014\pi$
$140$	−2.76153	−0.233392
$141$	30.6580	2.58187
$142$	−3.96650	−0.332861
$143$	−2.67446	−0.223649
$144$	5.19896	0.433247
$145$	1.29159	0.107261
$146$	1.00000	0.0827606
$147$	1.79256	0.147848
$148$	−8.25144	−0.678264
$149$	7.95747	0.651902	0.325951	−	0.945387i	$-0.394316\pi$
$149$	7.95747	0.651902	0.325951	+	0.945387i	$0.394316\pi$
$150$	2.86338	0.233794
$151$	6.47683	0.527077	0.263539	−	0.964649i	$-0.415110\pi$
$151$	6.47683	0.527077	0.263539	+	0.964649i	$0.415110\pi$
$152$	1.41818	0.115029
$153$	−15.0655	−1.21797
$154$	2.76153	0.222530
$155$	−5.43485	−0.436537
$156$	−7.65800	−0.613131
$157$	1.12980	0.0901679	0.0450839	−	0.998983i	$-0.485644\pi$
$157$	1.12980	0.0901679	0.0450839	+	0.998983i	$0.485644\pi$
$158$	−2.15098	−0.171123
$159$	35.0472	2.77942
$160$	−1.00000	−0.0790569
$161$	17.1335	1.35031
$162$	2.43231	0.191100
$163$	19.1260	1.49806	0.749032	−	0.662534i	$-0.230519\pi$
$163$	19.1260	1.49806	0.749032	+	0.662534i	$0.230519\pi$
$164$	−0.280658	−0.0219157
$165$	−2.86338	−0.222914
$166$	4.18354	0.324706
$167$	−8.45081	−0.653944	−0.326972	−	0.945034i	$-0.606028\pi$
$167$	−8.45081	−0.653944	−0.326972	+	0.945034i	$0.606028\pi$
$168$	7.90731	0.610062
$169$	−5.84727	−0.449790
$170$	2.89779	0.222250
$171$	7.37305	0.563831
$172$	6.92905	0.528335
$173$	−23.1241	−1.75809	−0.879045	−	0.476738i	$-0.841819\pi$
$173$	−23.1241	−1.75809	−0.879045	+	0.476738i	$0.841819\pi$
$174$	−3.69833	−0.280370
$175$	2.76153	0.208752
$176$	1.00000	0.0753778
$177$	−23.9425	−1.79963
$178$	10.2779	0.770361
$179$	−16.8579	−1.26002	−0.630011	−	0.776586i	$-0.716950\pi$
$179$	−16.8579	−1.26002	−0.630011	+	0.776586i	$0.716950\pi$
$180$	−5.19896	−0.387508
$181$	3.50346	0.260410	0.130205	−	0.991487i	$-0.458436\pi$
$181$	3.50346	0.260410	0.130205	+	0.991487i	$0.458436\pi$
$182$	−7.38559	−0.547456
$183$	−19.5750	−1.44703
$184$	6.20435	0.457391
$185$	8.25144	0.606658
$186$	15.5620	1.14106
$187$	−2.89779	−0.211907
$188$	10.7069	0.780882
$189$	17.3879	1.26478
$190$	−1.41818	−0.102885
$191$	−20.7076	−1.49835	−0.749175	−	0.662372i	$-0.769550\pi$
$191$	−20.7076	−1.49835	−0.749175	+	0.662372i	$0.769550\pi$
$192$	2.86338	0.206647
$193$	−13.3206	−0.958837	−0.479418	−	0.877586i	$-0.659152\pi$
$193$	−13.3206	−0.958837	−0.479418	+	0.877586i	$0.659152\pi$
$194$	2.68778	0.192971
$195$	7.65800	0.548401
$196$	0.626029	0.0447164
$197$	7.95910	0.567063	0.283531	−	0.958963i	$-0.408494\pi$
$197$	7.95910	0.567063	0.283531	+	0.958963i	$0.408494\pi$
$198$	5.19896	0.369474
$199$	4.55398	0.322823	0.161412	−	0.986887i	$-0.448395\pi$
$199$	4.55398	0.322823	0.161412	+	0.986887i	$0.448395\pi$
$200$	1.00000	0.0707107
$201$	28.4721	2.00826
$202$	8.83033	0.621300
$203$	−3.56677	−0.250338
$204$	−8.29748	−0.580940
$205$	0.280658	0.0196020
$206$	−4.77372	−0.332601
$207$	32.2562	2.24196
$208$	−2.67446	−0.185440
$209$	1.41818	0.0980974
$210$	−7.90731	−0.545656
$211$	1.43040	0.0984726	0.0492363	−	0.998787i	$-0.484321\pi$
$211$	1.43040	0.0984726	0.0492363	+	0.998787i	$0.484321\pi$
$212$	12.2398	0.840631
$213$	−11.3576	−0.778210
$214$	−19.0550	−1.30257
$215$	−6.92905	−0.472557
$216$	6.29647	0.428420
$217$	15.0085	1.01884
$218$	−16.3461	−1.10710
$219$	2.86338	0.193489
$220$	−1.00000	−0.0674200
$221$	7.75001	0.521322
$222$	−23.6270	−1.58574
$223$	10.8430	0.726098	0.363049	−	0.931770i	$-0.381736\pi$
$223$	10.8430	0.726098	0.363049	+	0.931770i	$0.381736\pi$
$224$	2.76153	0.184512
$225$	5.19896	0.346597
$226$	−12.0959	−0.804604
$227$	−2.60765	−0.173076	−0.0865380	−	0.996249i	$-0.527580\pi$
$227$	−2.60765	−0.173076	−0.0865380	+	0.996249i	$0.527580\pi$
$228$	4.06078	0.268932
$229$	7.60166	0.502332	0.251166	−	0.967944i	$-0.419186\pi$
$229$	7.60166	0.502332	0.251166	+	0.967944i	$0.419186\pi$
$230$	−6.20435	−0.409103
$231$	7.90731	0.520263
$232$	−1.29159	−0.0847974
$233$	11.8859	0.778672	0.389336	−	0.921096i	$-0.372705\pi$
$233$	11.8859	0.778672	0.389336	+	0.921096i	$0.372705\pi$
$234$	−13.9044	−0.908959
$235$	−10.7069	−0.698442
$236$	−8.36162	−0.544295
$237$	−6.15909	−0.400076
$238$	−8.00232	−0.518713
$239$	−10.8642	−0.702744	−0.351372	−	0.936236i	$-0.614285\pi$
$239$	−10.8642	−0.702744	−0.351372	+	0.936236i	$0.614285\pi$
$240$	−2.86338	−0.184831
$241$	−23.9779	−1.54455	−0.772277	−	0.635286i	$-0.780882\pi$
$241$	−23.9779	−1.54455	−0.772277	+	0.635286i	$0.780882\pi$
$242$	1.00000	0.0642824
$243$	−11.9248	−0.764974
$244$	−6.83633	−0.437651
$245$	−0.626029	−0.0399955
$246$	−0.803632	−0.0512377
$247$	−3.79286	−0.241334
$248$	5.43485	0.345113
$249$	11.9791	0.759143
$250$	−1.00000	−0.0632456
$251$	−22.1056	−1.39529	−0.697647	−	0.716442i	$-0.745769\pi$
$251$	−22.1056	−1.39529	−0.697647	+	0.716442i	$0.745769\pi$
$252$	14.3571	0.904410
$253$	6.20435	0.390064
$254$	−0.0373438	−0.00234316
$255$	8.29748	0.519608
$256$	1.00000	0.0625000
$257$	−21.9777	−1.37093	−0.685466	−	0.728104i	$-0.740402\pi$
$257$	−21.9777	−1.37093	−0.685466	+	0.728104i	$0.740402\pi$
$258$	19.8405	1.23522
$259$	−22.7866	−1.41589
$260$	2.67446	0.165863
$261$	−6.71495	−0.415645
$262$	14.8916	0.920006
$263$	−17.9406	−1.10626	−0.553132	−	0.833094i	$-0.686567\pi$
$263$	−17.9406	−1.10626	−0.553132	+	0.833094i	$0.686567\pi$
$264$	2.86338	0.176229
$265$	−12.2398	−0.751883
$266$	3.91633	0.240126
$267$	29.4296	1.80106
$268$	9.94350	0.607396
$269$	25.3229	1.54396	0.771982	−	0.635645i	$-0.219266\pi$
$269$	25.3229	1.54396	0.771982	+	0.635645i	$0.219266\pi$
$270$	−6.29647	−0.383191
$271$	1.10829	0.0673236	0.0336618	−	0.999433i	$-0.489283\pi$
$271$	1.10829	0.0673236	0.0336618	+	0.999433i	$0.489283\pi$
$272$	−2.89779	−0.175704
$273$	−21.1478	−1.27992
$274$	15.3030	0.924486
$275$	1.00000	0.0603023
$276$	17.7654	1.06935
$277$	23.8712	1.43428	0.717142	−	0.696927i	$-0.245450\pi$
$277$	23.8712	1.43428	0.717142	+	0.696927i	$0.245450\pi$
$278$	0.0730650	0.00438214
$279$	28.2556	1.69162
$280$	−2.76153	−0.165033
$281$	10.5179	0.627447	0.313723	−	0.949514i	$-0.398424\pi$
$281$	10.5179	0.627447	0.313723	+	0.949514i	$0.398424\pi$
$282$	30.6580	1.82566
$283$	2.88914	0.171742	0.0858708	−	0.996306i	$-0.472633\pi$
$283$	2.88914	0.171742	0.0858708	+	0.996306i	$0.472633\pi$
$284$	−3.96650	−0.235368
$285$	−4.06078	−0.240540
$286$	−2.67446	−0.158144
$287$	−0.775045	−0.0457495
$288$	5.19896	0.306352
$289$	−8.60283	−0.506049
$290$	1.29159	0.0758451
$291$	7.69613	0.451155
$292$	1.00000	0.0585206
$293$	−15.2982	−0.893730	−0.446865	−	0.894601i	$-0.647460\pi$
$293$	−15.2982	−0.893730	−0.446865	+	0.894601i	$0.647460\pi$
$294$	1.79256	0.104544
$295$	8.36162	0.486832
$296$	−8.25144	−0.479605
$297$	6.29647	0.365358
$298$	7.95747	0.460964
$299$	−16.5933	−0.959614
$300$	2.86338	0.165317
$301$	19.1348	1.10291
$302$	6.47683	0.372700
$303$	25.2846	1.45256
$304$	1.41818	0.0813381
$305$	6.83633	0.391447
$306$	−15.0655	−0.861237
$307$	−0.325591	−0.0185825	−0.00929124	−	0.999957i	$-0.502958\pi$
$307$	−0.325591	−0.0185825	−0.00929124	+	0.999957i	$0.502958\pi$
$308$	2.76153	0.157353
$309$	−13.6690	−0.777601
$310$	−5.43485	−0.308679
$311$	−21.0557	−1.19396	−0.596981	−	0.802255i	$-0.703633\pi$
$311$	−21.0557	−1.19396	−0.596981	+	0.802255i	$0.703633\pi$
$312$	−7.65800	−0.433549
$313$	−27.5843	−1.55916	−0.779578	−	0.626306i	$-0.784566\pi$
$313$	−27.5843	−1.55916	−0.779578	+	0.626306i	$0.784566\pi$
$314$	1.12980	0.0637583
$315$	−14.3571	−0.808929
$316$	−2.15098	−0.121002
$317$	−7.40562	−0.415941	−0.207971	−	0.978135i	$-0.566686\pi$
$317$	−7.40562	−0.415941	−0.207971	+	0.978135i	$0.566686\pi$
$318$	35.0472	1.96535
$319$	−1.29159	−0.0723154
$320$	−1.00000	−0.0559017
$321$	−54.5616	−3.04533
$322$	17.1335	0.954812
$323$	−4.10958	−0.228663
$324$	2.43231	0.135128
$325$	−2.67446	−0.148352
$326$	19.1260	1.05929
$327$	−46.8052	−2.58834
$328$	−0.280658	−0.0154968
$329$	29.5674	1.63010
$330$	−2.86338	−0.157624
$331$	5.76601	0.316929	0.158464	−	0.987365i	$-0.449346\pi$
$331$	5.76601	0.316929	0.158464	+	0.987365i	$0.449346\pi$
$332$	4.18354	0.229602
$333$	−42.8989	−2.35084
$334$	−8.45081	−0.462408
$335$	−9.94350	−0.543272
$336$	7.90731	0.431379
$337$	−27.3756	−1.49124	−0.745621	−	0.666370i	$-0.767847\pi$
$337$	−27.3756	−1.49124	−0.745621	+	0.666370i	$0.767847\pi$
$338$	−5.84727	−0.318050
$339$	−34.6351	−1.88112
$340$	2.89779	0.157155
$341$	5.43485	0.294313
$342$	7.37305	0.398689
$343$	−17.6019	−0.950413
$344$	6.92905	0.373589
$345$	−17.7654	−0.956459
$346$	−23.1241	−1.24316
$347$	−26.7271	−1.43478	−0.717392	−	0.696670i	$-0.754664\pi$
$347$	−26.7271	−1.43478	−0.717392	+	0.696670i	$0.754664\pi$
$348$	−3.69833	−0.198251
$349$	−4.74482	−0.253985	−0.126992	−	0.991904i	$-0.540532\pi$
$349$	−4.74482	−0.253985	−0.126992	+	0.991904i	$0.540532\pi$
$350$	2.76153	0.147610
$351$	−16.8396	−0.898833
$352$	1.00000	0.0533002
$353$	−14.9754	−0.797059	−0.398530	−	0.917155i	$-0.630479\pi$
$353$	−14.9754	−0.797059	−0.398530	+	0.917155i	$0.630479\pi$
$354$	−23.9425	−1.27253
$355$	3.96650	0.210520
$356$	10.2779	0.544728
$357$	−22.9137	−1.21272
$358$	−16.8579	−0.890970
$359$	−11.6615	−0.615468	−0.307734	−	0.951472i	$-0.599571\pi$
$359$	−11.6615	−0.615468	−0.307734	+	0.951472i	$0.599571\pi$
$360$	−5.19896	−0.274009
$361$	−16.9888	−0.894146
$362$	3.50346	0.184138
$363$	2.86338	0.150289
$364$	−7.38559	−0.387110
$365$	−1.00000	−0.0523424
$366$	−19.5750	−1.02320
$367$	28.6751	1.49683	0.748415	−	0.663231i	$-0.230815\pi$
$367$	28.6751	1.49683	0.748415	+	0.663231i	$0.230815\pi$
$368$	6.20435	0.323424
$369$	−1.45913	−0.0759593
$370$	8.25144	0.428972
$371$	33.8005	1.75483
$372$	15.5620	0.806855
$373$	27.4683	1.42225	0.711126	−	0.703064i	$-0.248185\pi$
$373$	27.4683	1.42225	0.711126	+	0.703064i	$0.248185\pi$
$374$	−2.89779	−0.149841
$375$	−2.86338	−0.147864
$376$	10.7069	0.552167
$377$	3.45432	0.177906
$378$	17.3879	0.894335
$379$	21.4556	1.10210	0.551049	−	0.834473i	$-0.314228\pi$
$379$	21.4556	1.10210	0.551049	+	0.834473i	$0.314228\pi$
$380$	−1.41818	−0.0727510
$381$	−0.106930	−0.00547817
$382$	−20.7076	−1.05949
$383$	−0.164314	−0.00839606	−0.00419803	−	0.999991i	$-0.501336\pi$
$383$	−0.164314	−0.00839606	−0.00419803	+	0.999991i	$0.501336\pi$
$384$	2.86338	0.146121
$385$	−2.76153	−0.140740
$386$	−13.3206	−0.678000
$387$	36.0239	1.83120
$388$	2.68778	0.136451
$389$	−32.4186	−1.64369	−0.821844	−	0.569712i	$-0.807055\pi$
$389$	−32.4186	−1.64369	−0.821844	+	0.569712i	$0.807055\pi$
$390$	7.65800	0.387778
$391$	−17.9789	−0.909232
$392$	0.626029	0.0316192
$393$	42.6403	2.15092
$394$	7.95910	0.400974
$395$	2.15098	0.108228
$396$	5.19896	0.261258
$397$	1.55405	0.0779957	0.0389978	−	0.999239i	$-0.487583\pi$
$397$	1.55405	0.0779957	0.0389978	+	0.999239i	$0.487583\pi$
$398$	4.55398	0.228270
$399$	11.2140	0.561400
$400$	1.00000	0.0500000
$401$	−17.2082	−0.859338	−0.429669	−	0.902986i	$-0.641370\pi$
$401$	−17.2082	−0.859338	−0.429669	+	0.902986i	$0.641370\pi$
$402$	28.4721	1.42006
$403$	−14.5353	−0.724053
$404$	8.83033	0.439325
$405$	−2.43231	−0.120863
$406$	−3.56677	−0.177016
$407$	−8.25144	−0.409009
$408$	−8.29748	−0.410786
$409$	−2.35645	−0.116519	−0.0582594	−	0.998301i	$-0.518555\pi$
$409$	−2.35645	−0.116519	−0.0582594	+	0.998301i	$0.518555\pi$
$410$	0.280658	0.0138607
$411$	43.8182	2.16139
$412$	−4.77372	−0.235184
$413$	−23.0908	−1.13623
$414$	32.2562	1.58531
$415$	−4.18354	−0.205362
$416$	−2.67446	−0.131126
$417$	0.209213	0.0102452
$418$	1.41818	0.0693653
$419$	31.6240	1.54493	0.772466	−	0.635057i	$-0.219023\pi$
$419$	31.6240	1.54493	0.772466	+	0.635057i	$0.219023\pi$
$420$	−7.90731	−0.385837
$421$	18.8591	0.919137	0.459568	−	0.888142i	$-0.348004\pi$
$421$	18.8591	0.919137	0.459568	+	0.888142i	$0.348004\pi$
$422$	1.43040	0.0696306
$423$	55.6648	2.70652
$424$	12.2398	0.594416
$425$	−2.89779	−0.140563
$426$	−11.3576	−0.550278
$427$	−18.8787	−0.913604
$428$	−19.0550	−0.921056
$429$	−7.65800	−0.369732
$430$	−6.92905	−0.334148
$431$	11.8446	0.570536	0.285268	−	0.958448i	$-0.407917\pi$
$431$	11.8446	0.570536	0.285268	+	0.958448i	$0.407917\pi$
$432$	6.29647	0.302939
$433$	39.6603	1.90595	0.952977	−	0.303042i	$-0.0980021\pi$
$433$	39.6603	1.90595	0.952977	+	0.303042i	$0.0980021\pi$
$434$	15.0085	0.720430
$435$	3.69833	0.177321
$436$	−16.3461	−0.782838
$437$	8.79887	0.420907
$438$	2.86338	0.136818
$439$	18.5158	0.883712	0.441856	−	0.897086i	$-0.354320\pi$
$439$	18.5158	0.883712	0.441856	+	0.897086i	$0.354320\pi$
$440$	−1.00000	−0.0476731
$441$	3.25470	0.154986
$442$	7.75001	0.368631
$443$	1.01390	0.0481718	0.0240859	−	0.999710i	$-0.492332\pi$
$443$	1.01390	0.0481718	0.0240859	+	0.999710i	$0.492332\pi$
$444$	−23.6270	−1.12129
$445$	−10.2779	−0.487219
$446$	10.8430	0.513429
$447$	22.7853	1.07771
$448$	2.76153	0.130470
$449$	−11.8503	−0.559252	−0.279626	−	0.960109i	$-0.590210\pi$
$449$	−11.8503	−0.559252	−0.279626	+	0.960109i	$0.590210\pi$
$450$	5.19896	0.245081
$451$	−0.280658	−0.0132157
$452$	−12.0959	−0.568941
$453$	18.5457	0.871351
$454$	−2.60765	−0.122383
$455$	7.38559	0.346242
$456$	4.06078	0.190164
$457$	7.88552	0.368869	0.184434	−	0.982845i	$-0.440955\pi$
$457$	7.88552	0.368869	0.184434	+	0.982845i	$0.440955\pi$
$458$	7.60166	0.355202
$459$	−18.2458	−0.851642
$460$	−6.20435	−0.289279
$461$	8.07673	0.376171	0.188086	−	0.982153i	$-0.439772\pi$
$461$	8.07673	0.376171	0.188086	+	0.982153i	$0.439772\pi$
$462$	7.90731	0.367881
$463$	−16.4185	−0.763034	−0.381517	−	0.924362i	$-0.624598\pi$
$463$	−16.4185	−0.763034	−0.381517	+	0.924362i	$0.624598\pi$
$464$	−1.29159	−0.0599608
$465$	−15.5620	−0.721673
$466$	11.8859	0.550604
$467$	8.52752	0.394607	0.197303	−	0.980342i	$-0.436782\pi$
$467$	8.52752	0.394607	0.197303	+	0.980342i	$0.436782\pi$
$468$	−13.9044	−0.642731
$469$	27.4593	1.26795
$470$	−10.7069	−0.493873
$471$	3.23505	0.149063
$472$	−8.36162	−0.384875
$473$	6.92905	0.318598
$474$	−6.15909	−0.282897
$475$	1.41818	0.0650704
$476$	−8.00232	−0.366786
$477$	63.6341	2.91360
$478$	−10.8642	−0.496915
$479$	−38.1980	−1.74531	−0.872656	−	0.488336i	$-0.837604\pi$
$479$	−38.1980	−1.74531	−0.872656	+	0.488336i	$0.837604\pi$
$480$	−2.86338	−0.130695
$481$	22.0681	1.00622
$482$	−23.9779	−1.09216
$483$	49.0597	2.23230
$484$	1.00000	0.0454545
$485$	−2.68778	−0.122046
$486$	−11.9248	−0.540918
$487$	−15.0082	−0.680085	−0.340042	−	0.940410i	$-0.610441\pi$
$487$	−15.0082	−0.680085	−0.340042	+	0.940410i	$0.610441\pi$
$488$	−6.83633	−0.309466
$489$	54.7650	2.47656
$490$	−0.626029	−0.0282811
$491$	−14.1624	−0.639140	−0.319570	−	0.947563i	$-0.603538\pi$
$491$	−14.1624	−0.639140	−0.319570	+	0.947563i	$0.603538\pi$
$492$	−0.803632	−0.0362305
$493$	3.74277	0.168566
$494$	−3.79286	−0.170649
$495$	−5.19896	−0.233676
$496$	5.43485	0.244032
$497$	−10.9536	−0.491336
$498$	11.9791	0.536795
$499$	−26.5044	−1.18650	−0.593251	−	0.805018i	$-0.702156\pi$
$499$	−26.5044	−1.18650	−0.593251	+	0.805018i	$0.702156\pi$
$500$	−1.00000	−0.0447214
$501$	−24.1979	−1.08108
$502$	−22.1056	−0.986621
$503$	41.3662	1.84443	0.922214	−	0.386679i	$-0.126378\pi$
$503$	41.3662	1.84443	0.922214	+	0.386679i	$0.126378\pi$
$504$	14.3571	0.639515
$505$	−8.83033	−0.392944
$506$	6.20435	0.275817
$507$	−16.7430	−0.743582
$508$	−0.0373438	−0.00165686
$509$	5.82097	0.258010	0.129005	−	0.991644i	$-0.458822\pi$
$509$	5.82097	0.258010	0.129005	+	0.991644i	$0.458822\pi$
$510$	8.29748	0.367418
$511$	2.76153	0.122163
$512$	1.00000	0.0441942
$513$	8.92951	0.394247
$514$	−21.9777	−0.969396
$515$	4.77372	0.210355
$516$	19.8405	0.873430
$517$	10.7069	0.470890
$518$	−22.7866	−1.00118
$519$	−66.2131	−2.90643
$520$	2.67446	0.117283
$521$	25.2972	1.10829	0.554144	−	0.832421i	$-0.313046\pi$
$521$	25.2972	1.10829	0.554144	+	0.832421i	$0.313046\pi$
$522$	−6.71495	−0.293905
$523$	43.3520	1.89565	0.947826	−	0.318788i	$-0.103276\pi$
$523$	43.3520	1.89565	0.947826	+	0.318788i	$0.103276\pi$
$524$	14.8916	0.650542
$525$	7.90731	0.345103
$526$	−17.9406	−0.782246
$527$	−15.7490	−0.686039
$528$	2.86338	0.124613
$529$	15.4940	0.673652
$530$	−12.2398	−0.531662
$531$	−43.4717	−1.88651
$532$	3.91633	0.169795
$533$	0.750609	0.0325125
$534$	29.4296	1.27354
$535$	19.0550	0.823818
$536$	9.94350	0.429494
$537$	−48.2708	−2.08304
$538$	25.3229	1.09175
$539$	0.626029	0.0269650
$540$	−6.29647	−0.270957
$541$	−2.49694	−0.107352	−0.0536760	−	0.998558i	$-0.517094\pi$
$541$	−2.49694	−0.107352	−0.0536760	+	0.998558i	$0.517094\pi$
$542$	1.10829	0.0476049
$543$	10.0318	0.430504
$544$	−2.89779	−0.124242
$545$	16.3461	0.700191
$546$	−21.1478	−0.905041
$547$	−20.0870	−0.858856	−0.429428	−	0.903101i	$-0.641285\pi$
$547$	−20.0870	−0.858856	−0.429428	+	0.903101i	$0.641285\pi$
$548$	15.3030	0.653710
$549$	−35.5418	−1.51689
$550$	1.00000	0.0426401
$551$	−1.83171	−0.0780335
$552$	17.7654	0.756147
$553$	−5.94000	−0.252595
$554$	23.8712	1.01419
$555$	23.6270	1.00291
$556$	0.0730650	0.00309864
$557$	7.52468	0.318831	0.159416	−	0.987212i	$-0.449039\pi$
$557$	7.52468	0.318831	0.159416	+	0.987212i	$0.449039\pi$
$558$	28.2556	1.19615
$559$	−18.5315	−0.783797
$560$	−2.76153	−0.116696
$561$	−8.29748	−0.350320
$562$	10.5179	0.443672
$563$	−6.60822	−0.278503	−0.139252	−	0.990257i	$-0.544470\pi$
$563$	−6.60822	−0.278503	−0.139252	+	0.990257i	$0.544470\pi$
$564$	30.6580	1.29093
$565$	12.0959	0.508877
$566$	2.88914	0.121440
$567$	6.71689	0.282083
$568$	−3.96650	−0.166431
$569$	0.0811422	0.00340166	0.00170083	−	0.999999i	$-0.499459\pi$
$569$	0.0811422	0.00340166	0.00170083	+	0.999999i	$0.499459\pi$
$570$	−4.06078	−0.170088
$571$	−9.50800	−0.397897	−0.198949	−	0.980010i	$-0.563753\pi$
$571$	−9.50800	−0.397897	−0.198949	+	0.980010i	$0.563753\pi$
$572$	−2.67446	−0.111825
$573$	−59.2938	−2.47703
$574$	−0.775045	−0.0323498
$575$	6.20435	0.258739
$576$	5.19896	0.216623
$577$	30.7101	1.27848	0.639238	−	0.769009i	$-0.279250\pi$
$577$	30.7101	1.27848	0.639238	+	0.769009i	$0.279250\pi$
$578$	−8.60283	−0.357830
$579$	−38.1419	−1.58512
$580$	1.29159	0.0536306
$581$	11.5530	0.479297
$582$	7.69613	0.319015
$583$	12.2398	0.506920
$584$	1.00000	0.0413803
$585$	13.9044	0.574876
$586$	−15.2982	−0.631962
$587$	−25.9390	−1.07062	−0.535308	−	0.844657i	$-0.679804\pi$
$587$	−25.9390	−1.07062	−0.535308	+	0.844657i	$0.679804\pi$
$588$	1.79256	0.0739240
$589$	7.70758	0.317585
$590$	8.36162	0.344242
$591$	22.7900	0.937454
$592$	−8.25144	−0.339132
$593$	−5.40013	−0.221757	−0.110878	−	0.993834i	$-0.535366\pi$
$593$	−5.40013	−0.221757	−0.110878	+	0.993834i	$0.535366\pi$
$594$	6.29647	0.258347
$595$	8.00232	0.328063
$596$	7.95747	0.325951
$597$	13.0398	0.533683
$598$	−16.5933	−0.678550
$599$	10.5303	0.430254	0.215127	−	0.976586i	$-0.430983\pi$
$599$	10.5303	0.430254	0.215127	+	0.976586i	$0.430983\pi$
$600$	2.86338	0.116897
$601$	−26.2774	−1.07188	−0.535939	−	0.844257i	$-0.680042\pi$
$601$	−26.2774	−1.07188	−0.535939	+	0.844257i	$0.680042\pi$
$602$	19.1348	0.779874
$603$	51.6959	2.10522
$604$	6.47683	0.263539
$605$	−1.00000	−0.0406558
$606$	25.2846	1.02712
$607$	−25.1311	−1.02004	−0.510019	−	0.860163i	$-0.670362\pi$
$607$	−25.1311	−1.02004	−0.510019	+	0.860163i	$0.670362\pi$
$608$	1.41818	0.0575147
$609$	−10.2130	−0.413853
$610$	6.83633	0.276795
$611$	−28.6352	−1.15846
$612$	−15.0655	−0.608986
$613$	29.6638	1.19811	0.599054	−	0.800709i	$-0.295544\pi$
$613$	29.6638	1.19811	0.599054	+	0.800709i	$0.295544\pi$
$614$	−0.325591	−0.0131398
$615$	0.803632	0.0324056
$616$	2.76153	0.111265
$617$	−38.0150	−1.53043	−0.765213	−	0.643777i	$-0.777367\pi$
$617$	−38.0150	−1.53043	−0.765213	+	0.643777i	$0.777367\pi$
$618$	−13.6690	−0.549847
$619$	21.1315	0.849347	0.424673	−	0.905347i	$-0.360389\pi$
$619$	21.1315	0.849347	0.424673	+	0.905347i	$0.360389\pi$
$620$	−5.43485	−0.218269
$621$	39.0655	1.56764
$622$	−21.0557	−0.844258
$623$	28.3827	1.13713
$624$	−7.65800	−0.306565
$625$	1.00000	0.0400000
$626$	−27.5843	−1.10249
$627$	4.06078	0.162172
$628$	1.12980	0.0450839
$629$	23.9109	0.953390
$630$	−14.3571	−0.571999
$631$	−11.6640	−0.464336	−0.232168	−	0.972676i	$-0.574582\pi$
$631$	−11.6640	−0.464336	−0.232168	+	0.972676i	$0.574582\pi$
$632$	−2.15098	−0.0855616
$633$	4.09577	0.162792
$634$	−7.40562	−0.294115
$635$	0.0373438	0.00148194
$636$	35.0472	1.38971
$637$	−1.67429	−0.0663377
$638$	−1.29159	−0.0511347
$639$	−20.6217	−0.815780
$640$	−1.00000	−0.0395285
$641$	34.6296	1.36779	0.683894	−	0.729581i	$-0.260285\pi$
$641$	34.6296	1.36779	0.683894	+	0.729581i	$0.260285\pi$
$642$	−54.5616	−2.15338
$643$	26.3096	1.03755	0.518775	−	0.854911i	$-0.326388\pi$
$643$	26.3096	1.03755	0.518775	+	0.854911i	$0.326388\pi$
$644$	17.1335	0.675154
$645$	−19.8405	−0.781220
$646$	−4.10958	−0.161689
$647$	−25.9613	−1.02065	−0.510323	−	0.859983i	$-0.670474\pi$
$647$	−25.9613	−1.02065	−0.510323	+	0.859983i	$0.670474\pi$
$648$	2.43231	0.0955502
$649$	−8.36162	−0.328222
$650$	−2.67446	−0.104901
$651$	42.9750	1.68432
$652$	19.1260	0.749032
$653$	−7.24983	−0.283708	−0.141854	−	0.989888i	$-0.545306\pi$
$653$	−7.24983	−0.283708	−0.141854	+	0.989888i	$0.545306\pi$
$654$	−46.8052	−1.83023
$655$	−14.8916	−0.581863
$656$	−0.280658	−0.0109579
$657$	5.19896	0.202831
$658$	29.5674	1.15266
$659$	12.1321	0.472601	0.236300	−	0.971680i	$-0.424065\pi$
$659$	12.1321	0.472601	0.236300	+	0.971680i	$0.424065\pi$
$660$	−2.86338	−0.111457
$661$	21.2584	0.826857	0.413428	−	0.910537i	$-0.364331\pi$
$661$	21.2584	0.826857	0.413428	+	0.910537i	$0.364331\pi$
$662$	5.76601	0.224102
$663$	22.1913	0.861837
$664$	4.18354	0.162353
$665$	−3.91633	−0.151869
$666$	−42.8989	−1.66230
$667$	−8.01351	−0.310284
$668$	−8.45081	−0.326972
$669$	31.0475	1.20037
$670$	−9.94350	−0.384151
$671$	−6.83633	−0.263913
$672$	7.90731	0.305031
$673$	38.2309	1.47369	0.736846	−	0.676060i	$-0.236314\pi$
$673$	38.2309	1.47369	0.736846	+	0.676060i	$0.236314\pi$
$674$	−27.3756	−1.05447
$675$	6.29647	0.242351
$676$	−5.84727	−0.224895
$677$	2.00720	0.0771429	0.0385714	−	0.999256i	$-0.487719\pi$
$677$	2.00720	0.0771429	0.0385714	+	0.999256i	$0.487719\pi$
$678$	−34.6351	−1.33015
$679$	7.42236	0.284844
$680$	2.89779	0.111125
$681$	−7.46670	−0.286125
$682$	5.43485	0.208111
$683$	7.91103	0.302707	0.151354	−	0.988480i	$-0.451637\pi$
$683$	7.91103	0.302707	0.151354	+	0.988480i	$0.451637\pi$
$684$	7.37305	0.281916
$685$	−15.3030	−0.584696
$686$	−17.6019	−0.672043
$687$	21.7665	0.830442
$688$	6.92905	0.264168
$689$	−32.7348	−1.24709
$690$	−17.7654	−0.676319
$691$	−37.2940	−1.41873	−0.709366	−	0.704840i	$-0.751019\pi$
$691$	−37.2940	−1.41873	−0.709366	+	0.704840i	$0.751019\pi$
$692$	−23.1241	−0.879045
$693$	14.3571	0.545380
$694$	−26.7271	−1.01455
$695$	−0.0730650	−0.00277151
$696$	−3.69833	−0.140185
$697$	0.813288	0.0308055
$698$	−4.74482	−0.179594
$699$	34.0339	1.28728
$700$	2.76153	0.104376
$701$	39.6303	1.49681	0.748407	−	0.663239i	$-0.230819\pi$
$701$	39.6303	1.49681	0.748407	+	0.663239i	$0.230819\pi$
$702$	−16.8396	−0.635571
$703$	−11.7020	−0.441349
$704$	1.00000	0.0376889
$705$	−30.6580	−1.15465
$706$	−14.9754	−0.563606
$707$	24.3852	0.917099
$708$	−23.9425	−0.899815
$709$	49.7548	1.86858	0.934290	−	0.356515i	$-0.116035\pi$
$709$	49.7548	1.86858	0.934290	+	0.356515i	$0.116035\pi$
$710$	3.96650	0.148860
$711$	−11.1829	−0.419391
$712$	10.2779	0.385181
$713$	33.7197	1.26281
$714$	−22.9137	−0.857524
$715$	2.67446	0.100019
$716$	−16.8579	−0.630011
$717$	−31.1082	−1.16176
$718$	−11.6615	−0.435202
$719$	−10.0066	−0.373182	−0.186591	−	0.982438i	$-0.559744\pi$
$719$	−10.0066	−0.373182	−0.186591	+	0.982438i	$0.559744\pi$
$720$	−5.19896	−0.193754
$721$	−13.1827	−0.490951
$722$	−16.9888	−0.632257
$723$	−68.6580	−2.55342
$724$	3.50346	0.130205
$725$	−1.29159	−0.0479686
$726$	2.86338	0.106270
$727$	−36.1123	−1.33933	−0.669665	−	0.742664i	$-0.733562\pi$
$727$	−36.1123	−1.33933	−0.669665	+	0.742664i	$0.733562\pi$
$728$	−7.38559	−0.273728
$729$	−41.4421	−1.53489
$730$	−1.00000	−0.0370117
$731$	−20.0789	−0.742645
$732$	−19.5750	−0.723514
$733$	−14.4343	−0.533143	−0.266572	−	0.963815i	$-0.585891\pi$
$733$	−14.4343	−0.533143	−0.266572	+	0.963815i	$0.585891\pi$
$734$	28.6751	1.05842
$735$	−1.79256	−0.0661196
$736$	6.20435	0.228696
$737$	9.94350	0.366274
$738$	−1.45913	−0.0537114
$739$	−48.3475	−1.77849	−0.889245	−	0.457431i	$-0.848770\pi$
$739$	−48.3475	−1.77849	−0.889245	+	0.457431i	$0.848770\pi$
$740$	8.25144	0.303329
$741$	−10.8604	−0.398967
$742$	33.8005	1.24085
$743$	−29.3947	−1.07839	−0.539193	−	0.842182i	$-0.681271\pi$
$743$	−29.3947	−1.07839	−0.539193	+	0.842182i	$0.681271\pi$
$744$	15.5620	0.570532
$745$	−7.95747	−0.291539
$746$	27.4683	1.00568
$747$	21.7501	0.795793
$748$	−2.89779	−0.105954
$749$	−52.6208	−1.92272
$750$	−2.86338	−0.104556
$751$	−38.5812	−1.40785	−0.703923	−	0.710276i	$-0.748570\pi$
$751$	−38.5812	−1.40785	−0.703923	+	0.710276i	$0.748570\pi$
$752$	10.7069	0.390441
$753$	−63.2968	−2.30666
$754$	3.45432	0.125799
$755$	−6.47683	−0.235716
$756$	17.3879	0.632390
$757$	−25.4394	−0.924611	−0.462305	−	0.886721i	$-0.652978\pi$
$757$	−25.4394	−0.924611	−0.462305	+	0.886721i	$0.652978\pi$
$758$	21.4556	0.779301
$759$	17.7654	0.644845
$760$	−1.41818	−0.0514427
$761$	−24.9330	−0.903822	−0.451911	−	0.892063i	$-0.649258\pi$
$761$	−24.9330	−0.903822	−0.451911	+	0.892063i	$0.649258\pi$
$762$	−0.106930	−0.00387365
$763$	−45.1403	−1.63419
$764$	−20.7076	−0.749175
$765$	15.0655	0.544694
$766$	−0.164314	−0.00593691
$767$	22.3628	0.807474
$768$	2.86338	0.103323
$769$	33.9595	1.22461	0.612306	−	0.790621i	$-0.290242\pi$
$769$	33.9595	1.22461	0.612306	+	0.790621i	$0.290242\pi$
$770$	−2.76153	−0.0995185
$771$	−62.9306	−2.26639
$772$	−13.3206	−0.479418
$773$	37.7168	1.35658	0.678289	−	0.734796i	$-0.262722\pi$
$773$	37.7168	1.35658	0.678289	+	0.734796i	$0.262722\pi$
$774$	36.0239	1.29485
$775$	5.43485	0.195225
$776$	2.68778	0.0964855
$777$	−65.2466	−2.34071
$778$	−32.4186	−1.16226
$779$	−0.398023	−0.0142607
$780$	7.65800	0.274200
$781$	−3.96650	−0.141932
$782$	−17.9789	−0.642924
$783$	−8.13248	−0.290631
$784$	0.626029	0.0223582
$785$	−1.12980	−0.0403243
$786$	42.6403	1.52093
$787$	−34.4745	−1.22888	−0.614441	−	0.788963i	$-0.710618\pi$
$787$	−34.4745	−1.22888	−0.614441	+	0.788963i	$0.710618\pi$
$788$	7.95910	0.283531
$789$	−51.3707	−1.82885
$790$	2.15098	0.0765286
$791$	−33.4030	−1.18768
$792$	5.19896	0.184737
$793$	18.2835	0.649265
$794$	1.55405	0.0551513
$795$	−35.0472	−1.24299
$796$	4.55398	0.161412
$797$	−38.5827	−1.36667	−0.683335	−	0.730105i	$-0.739471\pi$
$797$	−38.5827	−1.36667	−0.683335	+	0.730105i	$0.739471\pi$
$798$	11.2140	0.396970
$799$	−31.0264	−1.09763
$800$	1.00000	0.0353553
$801$	53.4344	1.88801
$802$	−17.2082	−0.607644
$803$	1.00000	0.0352892
$804$	28.4721	1.00413
$805$	−17.1335	−0.603876
$806$	−14.5353	−0.511983
$807$	72.5091	2.55244
$808$	8.83033	0.310650
$809$	−28.8050	−1.01273	−0.506365	−	0.862320i	$-0.669011\pi$
$809$	−28.8050	−1.01273	−0.506365	+	0.862320i	$0.669011\pi$
$810$	−2.43231	−0.0854627
$811$	17.4454	0.612592	0.306296	−	0.951936i	$-0.400910\pi$
$811$	17.4454	0.612592	0.306296	+	0.951936i	$0.400910\pi$
$812$	−3.56677	−0.125169
$813$	3.17345	0.111298
$814$	−8.25144	−0.289213
$815$	−19.1260	−0.669954
$816$	−8.29748	−0.290470
$817$	9.82662	0.343790
$818$	−2.35645	−0.0823912
$819$	−38.3974	−1.34171
$820$	0.280658	0.00980101
$821$	13.0900	0.456845	0.228423	−	0.973562i	$-0.426643\pi$
$821$	13.0900	0.456845	0.228423	+	0.973562i	$0.426643\pi$
$822$	43.8182	1.52834
$823$	36.8766	1.28544	0.642719	−	0.766102i	$-0.277806\pi$
$823$	36.8766	1.28544	0.642719	+	0.766102i	$0.277806\pi$
$824$	−4.77372	−0.166300
$825$	2.86338	0.0996902
$826$	−23.0908	−0.803433
$827$	9.81884	0.341435	0.170717	−	0.985320i	$-0.445392\pi$
$827$	9.81884	0.341435	0.170717	+	0.985320i	$0.445392\pi$
$828$	32.2562	1.12098
$829$	30.6177	1.06340	0.531698	−	0.846934i	$-0.321554\pi$
$829$	30.6177	1.06340	0.531698	+	0.846934i	$0.321554\pi$
$830$	−4.18354	−0.145213
$831$	68.3525	2.37112
$832$	−2.67446	−0.0927202
$833$	−1.81410	−0.0628548
$834$	0.209213	0.00724445
$835$	8.45081	0.292452
$836$	1.41818	0.0490487
$837$	34.2203	1.18283
$838$	31.6240	1.09243
$839$	−26.8973	−0.928597	−0.464298	−	0.885679i	$-0.653693\pi$
$839$	−26.8973	−0.928597	−0.464298	+	0.885679i	$0.653693\pi$
$840$	−7.90731	−0.272828
$841$	−27.3318	−0.942475
$842$	18.8591	0.649928
$843$	30.1169	1.03728
$844$	1.43040	0.0492363
$845$	5.84727	0.201152
$846$	55.6648	1.91380
$847$	2.76153	0.0948872
$848$	12.2398	0.420315
$849$	8.27272	0.283919
$850$	−2.89779	−0.0993933
$851$	−51.1948	−1.75494
$852$	−11.3576	−0.389105
$853$	37.4309	1.28161	0.640804	−	0.767704i	$-0.278601\pi$
$853$	37.4309	1.28161	0.640804	+	0.767704i	$0.278601\pi$
$854$	−18.8787	−0.646016
$855$	−7.37305	−0.252153
$856$	−19.0550	−0.651285
$857$	0.754660	0.0257787	0.0128893	−	0.999917i	$-0.495897\pi$
$857$	0.754660	0.0257787	0.0128893	+	0.999917i	$0.495897\pi$
$858$	−7.65800	−0.261440
$859$	35.0512	1.19593	0.597966	−	0.801521i	$-0.295976\pi$
$859$	35.0512	1.19593	0.597966	+	0.801521i	$0.295976\pi$
$860$	−6.92905	−0.236279
$861$	−2.21925	−0.0756319
$862$	11.8446	0.403430
$863$	−30.9224	−1.05261	−0.526305	−	0.850296i	$-0.676423\pi$
$863$	−30.9224	−1.05261	−0.526305	+	0.850296i	$0.676423\pi$
$864$	6.29647	0.214210
$865$	23.1241	0.786242
$866$	39.6603	1.34771
$867$	−24.6332	−0.836587
$868$	15.0085	0.509421
$869$	−2.15098	−0.0729672
$870$	3.69833	0.125385
$871$	−26.5935	−0.901086
$872$	−16.3461	−0.553550
$873$	13.9736	0.472936
$874$	8.79887	0.297626
$875$	−2.76153	−0.0933566
$876$	2.86338	0.0967447
$877$	−39.9122	−1.34774	−0.673870	−	0.738850i	$-0.735369\pi$
$877$	−39.9122	−1.34774	−0.673870	+	0.738850i	$0.735369\pi$
$878$	18.5158	0.624878
$879$	−43.8046	−1.47749
$880$	−1.00000	−0.0337100
$881$	−42.3260	−1.42600	−0.712999	−	0.701165i	$-0.752664\pi$
$881$	−42.3260	−1.42600	−0.712999	+	0.701165i	$0.752664\pi$
$882$	3.25470	0.109591
$883$	31.8892	1.07316	0.536578	−	0.843851i	$-0.319717\pi$
$883$	31.8892	1.07316	0.536578	+	0.843851i	$0.319717\pi$
$884$	7.75001	0.260661
$885$	23.9425	0.804819
$886$	1.01390	0.0340626
$887$	−5.46502	−0.183497	−0.0917487	−	0.995782i	$-0.529246\pi$
$887$	−5.46502	−0.183497	−0.0917487	+	0.995782i	$0.529246\pi$
$888$	−23.6270	−0.792871
$889$	−0.103126	−0.00345873
$890$	−10.2779	−0.344516
$891$	2.43231	0.0814855
$892$	10.8430	0.363049
$893$	15.1843	0.508123
$894$	22.7853	0.762054
$895$	16.8579	0.563499
$896$	2.76153	0.0922561
$897$	−47.5129	−1.58641
$898$	−11.8503	−0.395451
$899$	−7.01962	−0.234117
$900$	5.19896	0.173299
$901$	−35.4683	−1.18162
$902$	−0.280658	−0.00934490
$903$	54.7901	1.82330
$904$	−12.0959	−0.402302
$905$	−3.50346	−0.116459
$906$	18.5457	0.616138
$907$	20.7784	0.689934	0.344967	−	0.938615i	$-0.387890\pi$
$907$	20.7784	0.689934	0.344967	+	0.938615i	$0.387890\pi$
$908$	−2.60765	−0.0865380
$909$	45.9085	1.52269
$910$	7.38559	0.244830
$911$	33.2969	1.10318	0.551588	−	0.834117i	$-0.314022\pi$
$911$	33.2969	1.10318	0.551588	+	0.834117i	$0.314022\pi$
$912$	4.06078	0.134466
$913$	4.18354	0.138455
$914$	7.88552	0.260830
$915$	19.5750	0.647130
$916$	7.60166	0.251166
$917$	41.1235	1.35802
$918$	−18.2458	−0.602202
$919$	−3.36961	−0.111153	−0.0555766	−	0.998454i	$-0.517700\pi$
$919$	−3.36961	−0.111153	−0.0555766	+	0.998454i	$0.517700\pi$
$920$	−6.20435	−0.204551
$921$	−0.932293	−0.0307201
$922$	8.07673	0.265993
$923$	10.6082	0.349174
$924$	7.90731	0.260131
$925$	−8.25144	−0.271306
$926$	−16.4185	−0.539546
$927$	−24.8184	−0.815142
$928$	−1.29159	−0.0423987
$929$	26.0504	0.854686	0.427343	−	0.904090i	$-0.359450\pi$
$929$	26.0504	0.854686	0.427343	+	0.904090i	$0.359450\pi$
$930$	−15.5620	−0.510300
$931$	0.887820	0.0290971
$932$	11.8859	0.389336
$933$	−60.2907	−1.97383
$934$	8.52752	0.279029
$935$	2.89779	0.0947678
$936$	−13.9044	−0.454480
$937$	−37.0495	−1.21036	−0.605178	−	0.796090i	$-0.706898\pi$
$937$	−37.0495	−1.21036	−0.605178	+	0.796090i	$0.706898\pi$
$938$	27.4593	0.896576
$939$	−78.9843	−2.57756
$940$	−10.7069	−0.349221
$941$	32.0785	1.04573	0.522865	−	0.852416i	$-0.324863\pi$
$941$	32.0785	1.04573	0.522865	+	0.852416i	$0.324863\pi$
$942$	3.23505	0.105404
$943$	−1.74130	−0.0567046
$944$	−8.36162	−0.272147
$945$	−17.3879	−0.565627
$946$	6.92905	0.225283
$947$	0.535468	0.0174004	0.00870018	−	0.999962i	$-0.497231\pi$
$947$	0.535468	0.0174004	0.00870018	+	0.999962i	$0.497231\pi$
$948$	−6.15909	−0.200038
$949$	−2.67446	−0.0868166
$950$	1.41818	0.0460118
$951$	−21.2051	−0.687624
$952$	−8.00232	−0.259357
$953$	−45.0797	−1.46028	−0.730138	−	0.683300i	$-0.760544\pi$
$953$	−45.0797	−1.46028	−0.730138	+	0.683300i	$0.760544\pi$
$954$	63.6341	2.06023
$955$	20.7076	0.670083
$956$	−10.8642	−0.351372
$957$	−3.69833	−0.119550
$958$	−38.1980	−1.23412
$959$	42.2595	1.36463
$960$	−2.86338	−0.0924153
$961$	−1.46244	−0.0471755
$962$	22.0681	0.711505
$963$	−99.0660	−3.19236
$964$	−23.9779	−0.772277
$965$	13.3206	0.428805
$966$	49.0597	1.57847
$967$	−37.7518	−1.21402	−0.607008	−	0.794696i	$-0.707630\pi$
$967$	−37.7518	−1.21402	−0.607008	+	0.794696i	$0.707630\pi$
$968$	1.00000	0.0321412
$969$	−11.7673	−0.378020
$970$	−2.68778	−0.0862993
$971$	−34.9633	−1.12202	−0.561012	−	0.827807i	$-0.689588\pi$
$971$	−34.9633	−1.12202	−0.561012	+	0.827807i	$0.689588\pi$
$972$	−11.9248	−0.382487
$973$	0.201771	0.00646848
$974$	−15.0082	−0.480893
$975$	−7.65800	−0.245252
$976$	−6.83633	−0.218825
$977$	−29.4822	−0.943220	−0.471610	−	0.881807i	$-0.656327\pi$
$977$	−29.4822	−0.943220	−0.471610	+	0.881807i	$0.656327\pi$
$978$	54.7650	1.75119
$979$	10.2779	0.328483
$980$	−0.626029	−0.0199978
$981$	−84.9829	−2.71330
$982$	−14.1624	−0.451940
$983$	−8.70007	−0.277489	−0.138745	−	0.990328i	$-0.544307\pi$
$983$	−8.70007	−0.277489	−0.138745	+	0.990328i	$0.544307\pi$
$984$	−0.803632	−0.0256189
$985$	−7.95910	−0.253598
$986$	3.74277	0.119194
$987$	84.6629	2.69485
$988$	−3.79286	−0.120667
$989$	42.9903	1.36701
$990$	−5.19896	−0.165234
$991$	43.4833	1.38129	0.690647	−	0.723192i	$-0.257326\pi$
$991$	43.4833	1.38129	0.690647	+	0.723192i	$0.257326\pi$
$992$	5.43485	0.172557
$993$	16.5103	0.523939
$994$	−10.9536	−0.347427
$995$	−4.55398	−0.144371
$996$	11.9791	0.379571
$997$	−6.20181	−0.196413	−0.0982066	−	0.995166i	$-0.531311\pi$
$997$	−6.20181	−0.196413	−0.0982066	+	0.995166i	$0.531311\pi$
$998$	−26.5044	−0.838983
$999$	−51.9549	−1.64378

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	8030.2.a.bd.1.12	✓	14

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
8030.2.a.bd.1.12	✓	14	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:	\( N \)	\(=\)	\( 8030 = 2 \cdot 5 \cdot 11 \cdot 73 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	8030.a (trivial)

\(f(q)\)	\(=\)	\(q+1.00000 q^{2} +2.86338 q^{3} +1.00000 q^{4} -1.00000 q^{5} +2.86338 q^{6} +2.76153 q^{7} +1.00000 q^{8} +5.19896 q^{9} +O(q^{10})\)	\(q+1.00000 q^{2} +2.86338 q^{3} +1.00000 q^{4} -1.00000 q^{5} +2.86338 q^{6} +2.76153 q^{7} +1.00000 q^{8} +5.19896 q^{9} -1.00000 q^{10} +1.00000 q^{11} +2.86338 q^{12} -2.67446 q^{13} +2.76153 q^{14} -2.86338 q^{15} +1.00000 q^{16} -2.89779 q^{17} +5.19896 q^{18} +1.41818 q^{19} -1.00000 q^{20} +7.90731 q^{21} +1.00000 q^{22} +6.20435 q^{23} +2.86338 q^{24} +1.00000 q^{25} -2.67446 q^{26} +6.29647 q^{27} +2.76153 q^{28} -1.29159 q^{29} -2.86338 q^{30} +5.43485 q^{31} +1.00000 q^{32} +2.86338 q^{33} -2.89779 q^{34} -2.76153 q^{35} +5.19896 q^{36} -8.25144 q^{37} +1.41818 q^{38} -7.65800 q^{39} -1.00000 q^{40} -0.280658 q^{41} +7.90731 q^{42} +6.92905 q^{43} +1.00000 q^{44} -5.19896 q^{45} +6.20435 q^{46} +10.7069 q^{47} +2.86338 q^{48} +0.626029 q^{49} +1.00000 q^{50} -8.29748 q^{51} -2.67446 q^{52} +12.2398 q^{53} +6.29647 q^{54} -1.00000 q^{55} +2.76153 q^{56} +4.06078 q^{57} -1.29159 q^{58} -8.36162 q^{59} -2.86338 q^{60} -6.83633 q^{61} +5.43485 q^{62} +14.3571 q^{63} +1.00000 q^{64} +2.67446 q^{65} +2.86338 q^{66} +9.94350 q^{67} -2.89779 q^{68} +17.7654 q^{69} -2.76153 q^{70} -3.96650 q^{71} +5.19896 q^{72} +1.00000 q^{73} -8.25144 q^{74} +2.86338 q^{75} +1.41818 q^{76} +2.76153 q^{77} -7.65800 q^{78} -2.15098 q^{79} -1.00000 q^{80} +2.43231 q^{81} -0.280658 q^{82} +4.18354 q^{83} +7.90731 q^{84} +2.89779 q^{85} +6.92905 q^{86} -3.69833 q^{87} +1.00000 q^{88} +10.2779 q^{89} -5.19896 q^{90} -7.38559 q^{91} +6.20435 q^{92} +15.5620 q^{93} +10.7069 q^{94} -1.41818 q^{95} +2.86338 q^{96} +2.68778 q^{97} +0.626029 q^{98} +5.19896 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 14 q + 14 q^{2} + 6 q^{3} + 14 q^{4} - 14 q^{5} + 6 q^{6} + 4 q^{7} + 14 q^{8} + 24 q^{9}+O(q^{10}) \) 14 * q + 14 * q^2 + 6 * q^3 + 14 * q^4 - 14 * q^5 + 6 * q^6 + 4 * q^7 + 14 * q^8 + 24 * q^9	\( 14 q + 14 q^{2} + 6 q^{3} + 14 q^{4} - 14 q^{5} + 6 q^{6} + 4 q^{7} + 14 q^{8} + 24 q^{9} - 14 q^{10} + 14 q^{11} + 6 q^{12} + 4 q^{13} + 4 q^{14} - 6 q^{15} + 14 q^{16} + 20 q^{17} + 24 q^{18} - 14 q^{20} + 25 q^{21} + 14 q^{22} - 4 q^{23} + 6 q^{24} + 14 q^{25} + 4 q^{26} + 21 q^{27} + 4 q^{28} + 7 q^{29} - 6 q^{30} + 8 q^{31} + 14 q^{32} + 6 q^{33} + 20 q^{34} - 4 q^{35} + 24 q^{36} + 17 q^{37} + 7 q^{39} - 14 q^{40} - 14 q^{41} + 25 q^{42} + 12 q^{43} + 14 q^{44} - 24 q^{45} - 4 q^{46} + 28 q^{47} + 6 q^{48} + 20 q^{49} + 14 q^{50} - 13 q^{51} + 4 q^{52} + 13 q^{53} + 21 q^{54} - 14 q^{55} + 4 q^{56} - 23 q^{57} + 7 q^{58} + 36 q^{59} - 6 q^{60} + 25 q^{61} + 8 q^{62} + 45 q^{63} + 14 q^{64} - 4 q^{65} + 6 q^{66} + 20 q^{68} - 7 q^{69} - 4 q^{70} + 17 q^{71} + 24 q^{72} + 14 q^{73} + 17 q^{74} + 6 q^{75} + 4 q^{77} + 7 q^{78} + 10 q^{79} - 14 q^{80} + 58 q^{81} - 14 q^{82} - 6 q^{83} + 25 q^{84} - 20 q^{85} + 12 q^{86} + 44 q^{87} + 14 q^{88} + 36 q^{89} - 24 q^{90} - 15 q^{91} - 4 q^{92} - 2 q^{93} + 28 q^{94} + 6 q^{96} - 19 q^{97} + 20 q^{98} + 24 q^{99}+O(q^{100}) \) 14 * q + 14 * q^2 + 6 * q^3 + 14 * q^4 - 14 * q^5 + 6 * q^6 + 4 * q^7 + 14 * q^8 + 24 * q^9 - 14 * q^10 + 14 * q^11 + 6 * q^12 + 4 * q^13 + 4 * q^14 - 6 * q^15 + 14 * q^16 + 20 * q^17 + 24 * q^18 - 14 * q^20 + 25 * q^21 + 14 * q^22 - 4 * q^23 + 6 * q^24 + 14 * q^25 + 4 * q^26 + 21 * q^27 + 4 * q^28 + 7 * q^29 - 6 * q^30 + 8 * q^31 + 14 * q^32 + 6 * q^33 + 20 * q^34 - 4 * q^35 + 24 * q^36 + 17 * q^37 + 7 * q^39 - 14 * q^40 - 14 * q^41 + 25 * q^42 + 12 * q^43 + 14 * q^44 - 24 * q^45 - 4 * q^46 + 28 * q^47 + 6 * q^48 + 20 * q^49 + 14 * q^50 - 13 * q^51 + 4 * q^52 + 13 * q^53 + 21 * q^54 - 14 * q^55 + 4 * q^56 - 23 * q^57 + 7 * q^58 + 36 * q^59 - 6 * q^60 + 25 * q^61 + 8 * q^62 + 45 * q^63 + 14 * q^64 - 4 * q^65 + 6 * q^66 + 20 * q^68 - 7 * q^69 - 4 * q^70 + 17 * q^71 + 24 * q^72 + 14 * q^73 + 17 * q^74 + 6 * q^75 + 4 * q^77 + 7 * q^78 + 10 * q^79 - 14 * q^80 + 58 * q^81 - 14 * q^82 - 6 * q^83 + 25 * q^84 - 20 * q^85 + 12 * q^86 + 44 * q^87 + 14 * q^88 + 36 * q^89 - 24 * q^90 - 15 * q^91 - 4 * q^92 - 2 * q^93 + 28 * q^94 + 6 * q^96 - 19 * q^97 + 20 * q^98 + 24 * q^99

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