LMFDB - Embedded newform 7942.2.a.bm.1.8

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [7942,2,Mod(1,7942)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(7942, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([0, 0]))

N = Newforms(chi, 2, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("7942.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 7942 = 2 \cdot 11 \cdot 19^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	7942.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:	$63.4171892853$
Analytic rank:	$1$
Dimension:	$8$
Coefficient field:	$\mathbb{Q}[x]/(x^{8} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} - 14x^{6} - 4x^{5} + 38x^{4} + 3x^{3} - 29x^{2} + 2x + 4 $ x^8 - 14x^6 - 4x^5 + 38x^4 + 3x^3 - 29x^2 + 2x + 4
Coefficient ring:	$\Z[a_1, \ldots, a_{17}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.8
Root			$1.25611$ of defining polynomial
Character	$\chi$	$=$	7942.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.00000 q^{2} +1.87414 q^{3} +1.00000 q^{4} +1.89996 q^{5} -1.87414 q^{6} -3.86154 q^{7} -1.00000 q^{8} +0.512419 q^{9} +O(q^{10})$	\(q-1.00000 q^{2} +1.87414 q^{3} +1.00000 q^{4} +1.89996 q^{5} -1.87414 q^{6} -3.86154 q^{7} -1.00000 q^{8} +0.512419 q^{9} -1.89996 q^{10} +1.00000 q^{11} +1.87414 q^{12} -3.71027 q^{13} +3.86154 q^{14} +3.56080 q^{15} +1.00000 q^{16} -1.72007 q^{17} -0.512419 q^{18} +1.89996 q^{20} -7.23709 q^{21} -1.00000 q^{22} +7.66828 q^{23} -1.87414 q^{24} -1.39014 q^{25} +3.71027 q^{26} -4.66209 q^{27} -3.86154 q^{28} +4.54820 q^{29} -3.56080 q^{30} +1.14967 q^{31} -1.00000 q^{32} +1.87414 q^{33} +1.72007 q^{34} -7.33678 q^{35} +0.512419 q^{36} +5.00660 q^{37} -6.95358 q^{39} -1.89996 q^{40} -0.967251 q^{41} +7.23709 q^{42} +0.985200 q^{43} +1.00000 q^{44} +0.973576 q^{45} -7.66828 q^{46} +2.49857 q^{47} +1.87414 q^{48} +7.91150 q^{49} +1.39014 q^{50} -3.22366 q^{51} -3.71027 q^{52} -0.759504 q^{53} +4.66209 q^{54} +1.89996 q^{55} +3.86154 q^{56} -4.54820 q^{58} -4.46795 q^{59} +3.56080 q^{60} +1.79311 q^{61} -1.14967 q^{62} -1.97873 q^{63} +1.00000 q^{64} -7.04937 q^{65} -1.87414 q^{66} -0.118803 q^{67} -1.72007 q^{68} +14.3715 q^{69} +7.33678 q^{70} +4.79857 q^{71} -0.512419 q^{72} -16.4002 q^{73} -5.00660 q^{74} -2.60533 q^{75} -3.86154 q^{77} +6.95358 q^{78} -13.2922 q^{79} +1.89996 q^{80} -10.2747 q^{81} +0.967251 q^{82} -8.51324 q^{83} -7.23709 q^{84} -3.26807 q^{85} -0.985200 q^{86} +8.52399 q^{87} -1.00000 q^{88} -1.27650 q^{89} -0.973576 q^{90} +14.3273 q^{91} +7.66828 q^{92} +2.15465 q^{93} -2.49857 q^{94} -1.87414 q^{96} -4.17503 q^{97} -7.91150 q^{98} +0.512419 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q - 8 q^{2} - 4 q^{3} + 8 q^{4} + q^{5} + 4 q^{6} + 4 q^{7} - 8 q^{8} + 6 q^{9}+O(q^{10}) $ 8 * q - 8 * q^2 - 4 * q^3 + 8 * q^4 + q^5 + 4 * q^6 + 4 * q^7 - 8 * q^8 + 6 * q^9	\( 8 q - 8 q^{2} - 4 q^{3} + 8 q^{4} + q^{5} + 4 q^{6} + 4 q^{7} - 8 q^{8} + 6 q^{9} - q^{10} + 8 q^{11} - 4 q^{12} - 12 q^{13} - 4 q^{14} + 9 q^{15} + 8 q^{16} + 7 q^{17} - 6 q^{18} + q^{20} - 13 q^{21} - 8 q^{22} - 6 q^{23} + 4 q^{24} + 5 q^{25} + 12 q^{26} - 22 q^{27} + 4 q^{28} + q^{29} - 9 q^{30} - 8 q^{31} - 8 q^{32} - 4 q^{33} - 7 q^{34} + 5 q^{35} + 6 q^{36} - 12 q^{37} + 10 q^{39} - q^{40} - 18 q^{41} + 13 q^{42} - 4 q^{43} + 8 q^{44} - 19 q^{45} + 6 q^{46} + 13 q^{47} - 4 q^{48} + 4 q^{49} - 5 q^{50} - 14 q^{51} - 12 q^{52} + 17 q^{53} + 22 q^{54} + q^{55} - 4 q^{56} - q^{58} - 26 q^{59} + 9 q^{60} - 7 q^{61} + 8 q^{62} + 13 q^{63} + 8 q^{64} - 36 q^{65} + 4 q^{66} - 6 q^{67} + 7 q^{68} - 19 q^{69} - 5 q^{70} + 3 q^{71} - 6 q^{72} + 5 q^{73} + 12 q^{74} - 30 q^{75} + 4 q^{77} - 10 q^{78} - 16 q^{79} + q^{80} + 8 q^{81} + 18 q^{82} - 21 q^{83} - 13 q^{84} - 10 q^{85} + 4 q^{86} - 29 q^{87} - 8 q^{88} - 16 q^{89} + 19 q^{90} - 31 q^{91} - 6 q^{92} + 20 q^{93} - 13 q^{94} + 4 q^{96} + 15 q^{97} - 4 q^{98} + 6 q^{99}+O(q^{100}) \) 8 * q - 8 * q^2 - 4 * q^3 + 8 * q^4 + q^5 + 4 * q^6 + 4 * q^7 - 8 * q^8 + 6 * q^9 - q^10 + 8 * q^11 - 4 * q^12 - 12 * q^13 - 4 * q^14 + 9 * q^15 + 8 * q^16 + 7 * q^17 - 6 * q^18 + q^20 - 13 * q^21 - 8 * q^22 - 6 * q^23 + 4 * q^24 + 5 * q^25 + 12 * q^26 - 22 * q^27 + 4 * q^28 + q^29 - 9 * q^30 - 8 * q^31 - 8 * q^32 - 4 * q^33 - 7 * q^34 + 5 * q^35 + 6 * q^36 - 12 * q^37 + 10 * q^39 - q^40 - 18 * q^41 + 13 * q^42 - 4 * q^43 + 8 * q^44 - 19 * q^45 + 6 * q^46 + 13 * q^47 - 4 * q^48 + 4 * q^49 - 5 * q^50 - 14 * q^51 - 12 * q^52 + 17 * q^53 + 22 * q^54 + q^55 - 4 * q^56 - q^58 - 26 * q^59 + 9 * q^60 - 7 * q^61 + 8 * q^62 + 13 * q^63 + 8 * q^64 - 36 * q^65 + 4 * q^66 - 6 * q^67 + 7 * q^68 - 19 * q^69 - 5 * q^70 + 3 * q^71 - 6 * q^72 + 5 * q^73 + 12 * q^74 - 30 * q^75 + 4 * q^77 - 10 * q^78 - 16 * q^79 + q^80 + 8 * q^81 + 18 * q^82 - 21 * q^83 - 13 * q^84 - 10 * q^85 + 4 * q^86 - 29 * q^87 - 8 * q^88 - 16 * q^89 + 19 * q^90 - 31 * q^91 - 6 * q^92 + 20 * q^93 - 13 * q^94 + 4 * q^96 + 15 * q^97 - 4 * q^98 + 6 * 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
$3$	1.87414	1.08204	0.541019	−	0.841010i	$-0.318039\pi$
$3$	1.87414	1.08204	0.541019	+	0.841010i	$0.318039\pi$
$4$	1.00000	0.500000
$5$	1.89996	0.849689	0.424845	−	0.905266i	$-0.360329\pi$
$5$	1.89996	0.849689	0.424845	+	0.905266i	$0.360329\pi$
$6$	−1.87414	−0.765116
$7$	−3.86154	−1.45953	−0.729763	−	0.683701i	$-0.760369\pi$
$7$	−3.86154	−1.45953	−0.729763	+	0.683701i	$0.760369\pi$
$8$	−1.00000	−0.353553
$9$	0.512419	0.170806
$10$	−1.89996	−0.600821
$11$	1.00000	0.301511
$11$	1.00000	0.301511
$12$	1.87414	0.541019
$13$	−3.71027	−1.02904	−0.514521	−	0.857478i	$-0.672030\pi$
$13$	−3.71027	−1.02904	−0.514521	+	0.857478i	$0.672030\pi$
$14$	3.86154	1.03204
$15$	3.56080	0.919396
$16$	1.00000	0.250000
$17$	−1.72007	−0.417178	−0.208589	−	0.978003i	$-0.566887\pi$
$17$	−1.72007	−0.417178	−0.208589	+	0.978003i	$0.566887\pi$
$18$	−0.512419	−0.120778
$19$	0	0
$19$	0	0
$20$	1.89996	0.424845
$21$	−7.23709	−1.57926
$22$	−1.00000	−0.213201
$23$	7.66828	1.59895	0.799473	−	0.600702i	$-0.205112\pi$
$23$	7.66828	1.59895	0.799473	+	0.600702i	$0.205112\pi$
$24$	−1.87414	−0.382558
$25$	−1.39014	−0.278028
$26$	3.71027	0.727643
$27$	−4.66209	−0.897219
$28$	−3.86154	−0.729763
$29$	4.54820	0.844580	0.422290	−	0.906461i	$-0.361226\pi$
$29$	4.54820	0.844580	0.422290	+	0.906461i	$0.361226\pi$
$30$	−3.56080	−0.650111
$31$	1.14967	0.206487	0.103243	−	0.994656i	$-0.467078\pi$
$31$	1.14967	0.206487	0.103243	+	0.994656i	$0.467078\pi$
$32$	−1.00000	−0.176777
$33$	1.87414	0.326247
$34$	1.72007	0.294990
$35$	−7.33678	−1.24014
$36$	0.512419	0.0854031
$37$	5.00660	0.823079	0.411540	−	0.911392i	$-0.364991\pi$
$37$	5.00660	0.823079	0.411540	+	0.911392i	$0.364991\pi$
$38$	0	0
$39$	−6.95358	−1.11346
$40$	−1.89996	−0.300410
$41$	−0.967251	−0.151059	−0.0755296	−	0.997144i	$-0.524065\pi$
$41$	−0.967251	−0.151059	−0.0755296	+	0.997144i	$0.524065\pi$
$42$	7.23709	1.11671
$43$	0.985200	0.150242	0.0751208	−	0.997174i	$-0.476066\pi$
$43$	0.985200	0.150242	0.0751208	+	0.997174i	$0.476066\pi$
$44$	1.00000	0.150756
$45$	0.973576	0.145132
$46$	−7.66828	−1.13063
$47$	2.49857	0.364454	0.182227	−	0.983256i	$-0.441669\pi$
$47$	2.49857	0.364454	0.182227	+	0.983256i	$0.441669\pi$
$48$	1.87414	0.270509
$49$	7.91150	1.13021
$50$	1.39014	0.196596
$51$	−3.22366	−0.451403
$52$	−3.71027	−0.514521
$53$	−0.759504	−0.104326	−0.0521630	−	0.998639i	$-0.516612\pi$
$53$	−0.759504	−0.104326	−0.0521630	+	0.998639i	$0.516612\pi$
$54$	4.66209	0.634430
$55$	1.89996	0.256191
$56$	3.86154	0.516020
$57$	0	0
$58$	−4.54820	−0.597208
$59$	−4.46795	−0.581677	−0.290839	−	0.956772i	$-0.593934\pi$
$59$	−4.46795	−0.581677	−0.290839	+	0.956772i	$0.593934\pi$
$60$	3.56080	0.459698
$61$	1.79311	0.229584	0.114792	−	0.993390i	$-0.463380\pi$
$61$	1.79311	0.229584	0.114792	+	0.993390i	$0.463380\pi$
$62$	−1.14967	−0.146008
$63$	−1.97873	−0.249296
$64$	1.00000	0.125000
$65$	−7.04937	−0.874366
$66$	−1.87414	−0.230691
$67$	−0.118803	−0.0145141	−0.00725705	−	0.999974i	$-0.502310\pi$
$67$	−0.118803	−0.0145141	−0.00725705	+	0.999974i	$0.502310\pi$
$68$	−1.72007	−0.208589
$69$	14.3715	1.73012
$70$	7.33678	0.876913
$71$	4.79857	0.569485	0.284743	−	0.958604i	$-0.408092\pi$
$71$	4.79857	0.569485	0.284743	+	0.958604i	$0.408092\pi$
$72$	−0.512419	−0.0603891
$73$	−16.4002	−1.91950	−0.959752	−	0.280850i	$-0.909384\pi$
$73$	−16.4002	−1.91950	−0.959752	+	0.280850i	$0.909384\pi$
$74$	−5.00660	−0.582005
$75$	−2.60533	−0.300837
$76$	0	0
$77$	−3.86154	−0.440063
$78$	6.95358	0.787337
$79$	−13.2922	−1.49549	−0.747745	−	0.663986i	$-0.768864\pi$
$79$	−13.2922	−1.49549	−0.747745	+	0.663986i	$0.768864\pi$
$80$	1.89996	0.212422
$81$	−10.2747	−1.14163
$82$	0.967251	0.106815
$83$	−8.51324	−0.934450	−0.467225	−	0.884139i	$-0.654746\pi$
$83$	−8.51324	−0.934450	−0.467225	+	0.884139i	$0.654746\pi$
$84$	−7.23709	−0.789631
$85$	−3.26807	−0.354472
$86$	−0.985200	−0.106237
$87$	8.52399	0.913867
$88$	−1.00000	−0.106600
$89$	−1.27650	−0.135309	−0.0676544	−	0.997709i	$-0.521552\pi$
$89$	−1.27650	−0.135309	−0.0676544	+	0.997709i	$0.521552\pi$
$90$	−0.973576	−0.102624
$91$	14.3273	1.50191
$92$	7.66828	0.799473
$93$	2.15465	0.223426
$94$	−2.49857	−0.257708
$95$	0	0
$96$	−1.87414	−0.191279
$97$	−4.17503	−0.423910	−0.211955	−	0.977279i	$-0.567983\pi$
$97$	−4.17503	−0.423910	−0.211955	+	0.977279i	$0.567983\pi$
$98$	−7.91150	−0.799182
$99$	0.512419	0.0515000
$100$	−1.39014	−0.139014
$101$	10.7229	1.06696	0.533482	−	0.845811i	$-0.320883\pi$
$101$	10.7229	1.06696	0.533482	+	0.845811i	$0.320883\pi$
$102$	3.22366	0.319190
$103$	−18.6727	−1.83987	−0.919936	−	0.392069i	$-0.871760\pi$
$103$	−18.6727	−1.83987	−0.919936	+	0.392069i	$0.871760\pi$
$104$	3.71027	0.363822
$105$	−13.7502	−1.34188
$106$	0.759504	0.0737696
$107$	−0.915589	−0.0885134	−0.0442567	−	0.999020i	$-0.514092\pi$
$107$	−0.915589	−0.0885134	−0.0442567	+	0.999020i	$0.514092\pi$
$108$	−4.66209	−0.448610
$109$	0.261314	0.0250293	0.0125147	−	0.999922i	$-0.496016\pi$
$109$	0.261314	0.0250293	0.0125147	+	0.999922i	$0.496016\pi$
$110$	−1.89996	−0.181154
$111$	9.38309	0.890603
$112$	−3.86154	−0.364881
$113$	6.69829	0.630122	0.315061	−	0.949071i	$-0.397975\pi$
$113$	6.69829	0.630122	0.315061	+	0.949071i	$0.397975\pi$
$114$	0	0
$115$	14.5694	1.35861
$116$	4.54820	0.422290
$117$	−1.90121	−0.175767
$118$	4.46795	0.411308
$119$	6.64212	0.608882
$120$	−3.56080	−0.325056
$121$	1.00000	0.0909091
$122$	−1.79311	−0.162341
$123$	−1.81277	−0.163452
$124$	1.14967	0.103243
$125$	−12.1410	−1.08593
$126$	1.97873	0.176279
$127$	−13.3751	−1.18685	−0.593426	−	0.804889i	$-0.702225\pi$
$127$	−13.3751	−1.18685	−0.593426	+	0.804889i	$0.702225\pi$
$128$	−1.00000	−0.0883883
$129$	1.84641	0.162567
$130$	7.04937	0.618270
$131$	15.6258	1.36523	0.682615	−	0.730778i	$-0.260843\pi$
$131$	15.6258	1.36523	0.682615	+	0.730778i	$0.260843\pi$
$132$	1.87414	0.163123
$133$	0	0
$134$	0.118803	0.0102630
$135$	−8.85779	−0.762357
$136$	1.72007	0.147495
$137$	−16.5314	−1.41237	−0.706187	−	0.708025i	$-0.749586\pi$
$137$	−16.5314	−1.41237	−0.706187	+	0.708025i	$0.749586\pi$
$138$	−14.3715	−1.22338
$139$	−21.4746	−1.82145	−0.910727	−	0.413008i	$-0.864478\pi$
$139$	−21.4746	−1.82145	−0.910727	+	0.413008i	$0.864478\pi$
$140$	−7.33678	−0.620071
$141$	4.68269	0.394354
$142$	−4.79857	−0.402687
$143$	−3.71027	−0.310268
$144$	0.512419	0.0427016
$145$	8.64141	0.717630
$146$	16.4002	1.35729
$147$	14.8273	1.22293
$148$	5.00660	0.411540
$149$	18.2962	1.49889	0.749443	−	0.662068i	$-0.230321\pi$
$149$	18.2962	1.49889	0.749443	+	0.662068i	$0.230321\pi$
$150$	2.60533	0.212724
$151$	−14.3930	−1.17129	−0.585644	−	0.810569i	$-0.699158\pi$
$151$	−14.3930	−1.17129	−0.585644	+	0.810569i	$0.699158\pi$
$152$	0	0
$153$	−0.881396	−0.0712567
$154$	3.86154	0.311172
$155$	2.18433	0.175449
$156$	−6.95358	−0.556732
$157$	−13.0090	−1.03823	−0.519116	−	0.854704i	$-0.673739\pi$
$157$	−13.0090	−1.03823	−0.519116	+	0.854704i	$0.673739\pi$
$158$	13.2922	1.05747
$159$	−1.42342	−0.112885
$160$	−1.89996	−0.150205
$161$	−29.6114	−2.33370
$162$	10.2747	0.807255
$163$	14.7418	1.15467	0.577334	−	0.816508i	$-0.304093\pi$
$163$	14.7418	1.15467	0.577334	+	0.816508i	$0.304093\pi$
$164$	−0.967251	−0.0755296
$165$	3.56080	0.277208
$166$	8.51324	0.660756
$167$	2.18307	0.168931	0.0844655	−	0.996426i	$-0.473082\pi$
$167$	2.18307	0.168931	0.0844655	+	0.996426i	$0.473082\pi$
$168$	7.23709	0.558353
$169$	0.766074	0.0589288
$170$	3.26807	0.250649
$171$	0	0
$172$	0.985200	0.0751208
$173$	−24.9071	−1.89365	−0.946827	−	0.321742i	$-0.895732\pi$
$173$	−24.9071	−1.89365	−0.946827	+	0.321742i	$0.895732\pi$
$174$	−8.52399	−0.646202
$175$	5.36809	0.405790
$176$	1.00000	0.0753778
$177$	−8.37358	−0.629397
$178$	1.27650	0.0956778
$179$	−4.72427	−0.353109	−0.176554	−	0.984291i	$-0.556495\pi$
$179$	−4.72427	−0.353109	−0.176554	+	0.984291i	$0.556495\pi$
$180$	0.973576	0.0725661
$181$	−25.7541	−1.91429	−0.957145	−	0.289609i	$-0.906475\pi$
$181$	−25.7541	−1.91429	−0.957145	+	0.289609i	$0.906475\pi$
$182$	−14.3273	−1.06201
$183$	3.36055	0.248419
$184$	−7.66828	−0.565313
$185$	9.51235	0.699362
$186$	−2.15465	−0.157986
$187$	−1.72007	−0.125784
$188$	2.49857	0.182227
$189$	18.0028	1.30951
$190$	0	0
$191$	22.0927	1.59857	0.799286	−	0.600951i	$-0.205211\pi$
$191$	22.0927	1.59857	0.799286	+	0.600951i	$0.205211\pi$
$192$	1.87414	0.135255
$193$	−20.2621	−1.45850	−0.729248	−	0.684249i	$-0.760130\pi$
$193$	−20.2621	−1.45850	−0.729248	+	0.684249i	$0.760130\pi$
$194$	4.17503	0.299750
$195$	−13.2115	−0.946098
$196$	7.91150	0.565107
$197$	17.2012	1.22554	0.612769	−	0.790262i	$-0.290056\pi$
$197$	17.2012	1.22554	0.612769	+	0.790262i	$0.290056\pi$
$198$	−0.512419	−0.0364160
$199$	−24.8793	−1.76365	−0.881824	−	0.471579i	$-0.843684\pi$
$199$	−24.8793	−1.76365	−0.881824	+	0.471579i	$0.843684\pi$
$200$	1.39014	0.0982979
$201$	−0.222654	−0.0157048
$202$	−10.7229	−0.754457
$203$	−17.5631	−1.23269
$204$	−3.22366	−0.225701
$205$	−1.83774	−0.128353
$206$	18.6727	1.30099
$207$	3.92937	0.273110
$208$	−3.71027	−0.257261
$209$	0	0
$210$	13.7502	0.948854
$211$	−18.5060	−1.27401	−0.637004	−	0.770860i	$-0.719827\pi$
$211$	−18.5060	−1.27401	−0.637004	+	0.770860i	$0.719827\pi$
$212$	−0.759504	−0.0521630
$213$	8.99321	0.616205
$214$	0.915589	0.0625884
$215$	1.87184	0.127659
$216$	4.66209	0.317215
$217$	−4.43949	−0.301372
$218$	−0.261314	−0.0176984
$219$	−30.7364	−2.07698
$220$	1.89996	0.128095
$221$	6.38192	0.429294
$222$	−9.38309	−0.629752
$223$	−23.8106	−1.59448	−0.797238	−	0.603665i	$-0.793706\pi$
$223$	−23.8106	−1.59448	−0.797238	+	0.603665i	$0.793706\pi$
$224$	3.86154	0.258010
$225$	−0.712335	−0.0474890
$226$	−6.69829	−0.445563
$227$	−27.4134	−1.81949	−0.909747	−	0.415164i	$-0.863724\pi$
$227$	−27.4134	−1.81949	−0.909747	+	0.415164i	$0.863724\pi$
$228$	0	0
$229$	−7.56854	−0.500143	−0.250072	−	0.968227i	$-0.580454\pi$
$229$	−7.56854	−0.500143	−0.250072	+	0.968227i	$0.580454\pi$
$230$	−14.5694	−0.960680
$231$	−7.23709	−0.476165
$232$	−4.54820	−0.298604
$233$	27.4389	1.79758	0.898790	−	0.438379i	$-0.144447\pi$
$233$	27.4389	1.79758	0.898790	+	0.438379i	$0.144447\pi$
$234$	1.90121	0.124286
$235$	4.74720	0.309673
$236$	−4.46795	−0.290839
$237$	−24.9115	−1.61818
$238$	−6.64212	−0.430545
$239$	−16.7668	−1.08456	−0.542278	−	0.840199i	$-0.682438\pi$
$239$	−16.7668	−1.08456	−0.542278	+	0.840199i	$0.682438\pi$
$240$	3.56080	0.229849
$241$	−2.38796	−0.153822	−0.0769111	−	0.997038i	$-0.524506\pi$
$241$	−2.38796	−0.153822	−0.0769111	+	0.997038i	$0.524506\pi$
$242$	−1.00000	−0.0642824
$243$	−5.26998	−0.338069
$244$	1.79311	0.114792
$245$	15.0315	0.960330
$246$	1.81277	0.115578
$247$	0	0
$248$	−1.14967	−0.0730040
$249$	−15.9550	−1.01111
$250$	12.1410	0.767866
$251$	−10.1749	−0.642236	−0.321118	−	0.947039i	$-0.604059\pi$
$251$	−10.1749	−0.642236	−0.321118	+	0.947039i	$0.604059\pi$
$252$	−1.97873	−0.124648
$253$	7.66828	0.482100
$254$	13.3751	0.839230
$255$	−6.12484	−0.383552
$256$	1.00000	0.0625000
$257$	26.3318	1.64254	0.821268	−	0.570543i	$-0.193267\pi$
$257$	26.3318	1.64254	0.821268	+	0.570543i	$0.193267\pi$
$258$	−1.84641	−0.114952
$259$	−19.3332	−1.20131
$260$	−7.04937	−0.437183
$261$	2.33058	0.144259
$262$	−15.6258	−0.965363
$263$	−16.9397	−1.04455	−0.522274	−	0.852778i	$-0.674916\pi$
$263$	−16.9397	−1.04455	−0.522274	+	0.852778i	$0.674916\pi$
$264$	−1.87414	−0.115346
$265$	−1.44303	−0.0886446
$266$	0	0
$267$	−2.39235	−0.146409
$268$	−0.118803	−0.00725705
$269$	−2.32455	−0.141730	−0.0708652	−	0.997486i	$-0.522576\pi$
$269$	−2.32455	−0.141730	−0.0708652	+	0.997486i	$0.522576\pi$
$270$	8.85779	0.539068
$271$	20.8536	1.26676	0.633382	−	0.773839i	$-0.281666\pi$
$271$	20.8536	1.26676	0.633382	+	0.773839i	$0.281666\pi$
$272$	−1.72007	−0.104295
$273$	26.8515	1.62513
$274$	16.5314	0.998699
$275$	−1.39014	−0.0838287
$276$	14.3715	0.865060
$277$	1.70401	0.102384	0.0511919	−	0.998689i	$-0.483698\pi$
$277$	1.70401	0.102384	0.0511919	+	0.998689i	$0.483698\pi$
$278$	21.4746	1.28796
$279$	0.589112	0.0352692
$280$	7.33678	0.438457
$281$	−3.38766	−0.202091	−0.101046	−	0.994882i	$-0.532219\pi$
$281$	−3.38766	−0.202091	−0.101046	+	0.994882i	$0.532219\pi$
$282$	−4.68269	−0.278850
$283$	6.72599	0.399819	0.199909	−	0.979814i	$-0.435935\pi$
$283$	6.72599	0.399819	0.199909	+	0.979814i	$0.435935\pi$
$284$	4.79857	0.284743
$285$	0	0
$286$	3.71027	0.219393
$287$	3.73508	0.220475
$288$	−0.512419	−0.0301946
$289$	−14.0414	−0.825962
$290$	−8.64141	−0.507441
$291$	−7.82461	−0.458687
$292$	−16.4002	−0.959752
$293$	22.1111	1.29175	0.645873	−	0.763445i	$-0.276494\pi$
$293$	22.1111	1.29175	0.645873	+	0.763445i	$0.276494\pi$
$294$	−14.8273	−0.864745
$295$	−8.48893	−0.494245
$296$	−5.00660	−0.291003
$297$	−4.66209	−0.270522
$298$	−18.2962	−1.05987
$299$	−28.4513	−1.64538
$300$	−2.60533	−0.150419
$301$	−3.80439	−0.219281
$302$	14.3930	0.828225
$303$	20.0962	1.15450
$304$	0	0
$305$	3.40685	0.195075
$306$	0.881396	0.0503861
$307$	3.11344	0.177693	0.0888467	−	0.996045i	$-0.471682\pi$
$307$	3.11344	0.177693	0.0888467	+	0.996045i	$0.471682\pi$
$308$	−3.86154	−0.220032
$309$	−34.9953	−1.99081
$310$	−2.18433	−0.124061
$311$	−19.5190	−1.10682	−0.553412	−	0.832908i	$-0.686674\pi$
$311$	−19.5190	−1.10682	−0.553412	+	0.832908i	$0.686674\pi$
$312$	6.95358	0.393669
$313$	−3.10062	−0.175257	−0.0876287	−	0.996153i	$-0.527929\pi$
$313$	−3.10062	−0.175257	−0.0876287	+	0.996153i	$0.527929\pi$
$314$	13.0090	0.734141
$315$	−3.75950	−0.211824
$316$	−13.2922	−0.747745
$317$	−21.1255	−1.18653	−0.593263	−	0.805008i	$-0.702161\pi$
$317$	−21.1255	−1.18653	−0.593263	+	0.805008i	$0.702161\pi$
$318$	1.42342	0.0798215
$319$	4.54820	0.254650
$320$	1.89996	0.106211
$321$	−1.71595	−0.0957748
$322$	29.6114	1.65018
$323$	0	0
$324$	−10.2747	−0.570816
$325$	5.15780	0.286103
$326$	−14.7418	−0.816474
$327$	0.489740	0.0270827
$328$	0.967251	0.0534075
$329$	−9.64834	−0.531930
$330$	−3.56080	−0.196016
$331$	26.1232	1.43586	0.717932	−	0.696114i	$-0.245089\pi$
$331$	26.1232	1.43586	0.717932	+	0.696114i	$0.245089\pi$
$332$	−8.51324	−0.467225
$333$	2.56547	0.140587
$334$	−2.18307	−0.119452
$335$	−0.225721	−0.0123325
$336$	−7.23709	−0.394815
$337$	−11.9914	−0.653212	−0.326606	−	0.945161i	$-0.605905\pi$
$337$	−11.9914	−0.653212	−0.326606	+	0.945161i	$0.605905\pi$
$338$	−0.766074	−0.0416689
$339$	12.5536	0.681816
$340$	−3.26807	−0.177236
$341$	1.14967	0.0622581
$342$	0	0
$343$	−3.51979	−0.190051
$344$	−0.985200	−0.0531184
$345$	27.3052	1.47006
$346$	24.9071	1.33902
$347$	−14.1518	−0.759710	−0.379855	−	0.925046i	$-0.624026\pi$
$347$	−14.1518	−0.759710	−0.379855	+	0.925046i	$0.624026\pi$
$348$	8.52399	0.456934
$349$	9.11547	0.487940	0.243970	−	0.969783i	$-0.421550\pi$
$349$	9.11547	0.487940	0.243970	+	0.969783i	$0.421550\pi$
$350$	−5.36809	−0.286937
$351$	17.2976	0.923277
$352$	−1.00000	−0.0533002
$353$	9.05048	0.481708	0.240854	−	0.970561i	$-0.422572\pi$
$353$	9.05048	0.481708	0.240854	+	0.970561i	$0.422572\pi$
$354$	8.37358	0.445051
$355$	9.11710	0.483885
$356$	−1.27650	−0.0676544
$357$	12.4483	0.658834
$358$	4.72427	0.249685
$359$	23.4694	1.23867	0.619333	−	0.785128i	$-0.287403\pi$
$359$	23.4694	1.23867	0.619333	+	0.785128i	$0.287403\pi$
$360$	−0.973576	−0.0513120
$361$	0	0
$362$	25.7541	1.35361
$363$	1.87414	0.0983671
$364$	14.3273	0.750957
$365$	−31.1598	−1.63098
$366$	−3.36055	−0.175659
$367$	8.96543	0.467992	0.233996	−	0.972238i	$-0.424820\pi$
$367$	8.96543	0.467992	0.233996	+	0.972238i	$0.424820\pi$
$368$	7.66828	0.399736
$369$	−0.495638	−0.0258019
$370$	−9.51235	−0.494523
$371$	2.93286	0.152266
$372$	2.15465	0.111713
$373$	8.42369	0.436162	0.218081	−	0.975931i	$-0.430020\pi$
$373$	8.42369	0.436162	0.218081	+	0.975931i	$0.430020\pi$
$374$	1.72007	0.0889427
$375$	−22.7541	−1.17501
$376$	−2.49857	−0.128854
$377$	−16.8750	−0.869109
$378$	−18.0028	−0.925966
$379$	13.9231	0.715184	0.357592	−	0.933878i	$-0.383598\pi$
$379$	13.9231	0.715184	0.357592	+	0.933878i	$0.383598\pi$
$380$	0	0
$381$	−25.0669	−1.28422
$382$	−22.0927	−1.13036
$383$	−6.32105	−0.322990	−0.161495	−	0.986874i	$-0.551632\pi$
$383$	−6.32105	−0.322990	−0.161495	+	0.986874i	$0.551632\pi$
$384$	−1.87414	−0.0956396
$385$	−7.33678	−0.373917
$386$	20.2621	1.03131
$387$	0.504835	0.0256622
$388$	−4.17503	−0.211955
$389$	−32.2295	−1.63410	−0.817051	−	0.576565i	$-0.804393\pi$
$389$	−32.2295	−1.63410	−0.817051	+	0.576565i	$0.804393\pi$
$390$	13.2115	0.668992
$391$	−13.1900	−0.667046
$392$	−7.91150	−0.399591
$393$	29.2849	1.47723
$394$	−17.2012	−0.866586
$395$	−25.2547	−1.27070
$396$	0.512419	0.0257500
$397$	25.3339	1.27147	0.635737	−	0.771906i	$-0.280696\pi$
$397$	25.3339	1.27147	0.635737	+	0.771906i	$0.280696\pi$
$398$	24.8793	1.24709
$399$	0	0
$400$	−1.39014	−0.0695071
$401$	−0.765866	−0.0382455	−0.0191228	−	0.999817i	$-0.506087\pi$
$401$	−0.765866	−0.0382455	−0.0191228	+	0.999817i	$0.506087\pi$
$402$	0.222654	0.0111050
$403$	−4.26558	−0.212484
$404$	10.7229	0.533482
$405$	−19.5215	−0.970032
$406$	17.5631	0.871640
$407$	5.00660	0.248168
$408$	3.22366	0.159595
$409$	−11.2877	−0.558141	−0.279071	−	0.960271i	$-0.590026\pi$
$409$	−11.2877	−0.558141	−0.279071	+	0.960271i	$0.590026\pi$
$410$	1.83774	0.0907596
$411$	−30.9823	−1.52824
$412$	−18.6727	−0.919936
$413$	17.2532	0.848973
$414$	−3.92937	−0.193118
$415$	−16.1748	−0.793992
$416$	3.71027	0.181911
$417$	−40.2466	−1.97088
$418$	0	0
$419$	37.2698	1.82075	0.910375	−	0.413784i	$-0.135793\pi$
$419$	37.2698	1.82075	0.910375	+	0.413784i	$0.135793\pi$
$420$	−13.7502	−0.670941
$421$	−27.7213	−1.35106	−0.675528	−	0.737335i	$-0.736084\pi$
$421$	−27.7213	−1.35106	−0.675528	+	0.737335i	$0.736084\pi$
$422$	18.5060	0.900860
$423$	1.28032	0.0622511
$424$	0.759504	0.0368848
$425$	2.39114	0.115987
$426$	−8.99321	−0.435722
$427$	−6.92417	−0.335084
$428$	−0.915589	−0.0442567
$429$	−6.95358	−0.335722
$430$	−1.87184	−0.0902683
$431$	17.8243	0.858569	0.429284	−	0.903169i	$-0.358766\pi$
$431$	17.8243	0.858569	0.429284	+	0.903169i	$0.358766\pi$
$432$	−4.66209	−0.224305
$433$	14.9808	0.719931	0.359965	−	0.932966i	$-0.382789\pi$
$433$	14.9808	0.719931	0.359965	+	0.932966i	$0.382789\pi$
$434$	4.43949	0.213102
$435$	16.1953	0.776503
$436$	0.261314	0.0125147
$437$	0	0
$438$	30.7364	1.46864
$439$	31.7040	1.51315	0.756575	−	0.653907i	$-0.226871\pi$
$439$	31.7040	1.51315	0.756575	+	0.653907i	$0.226871\pi$
$440$	−1.89996	−0.0905772
$441$	4.05400	0.193048
$442$	−6.38192	−0.303557
$443$	−5.89147	−0.279912	−0.139956	−	0.990158i	$-0.544696\pi$
$443$	−5.89147	−0.279912	−0.139956	+	0.990158i	$0.544696\pi$
$444$	9.38309	0.445302
$445$	−2.42530	−0.114970
$446$	23.8106	1.12746
$447$	34.2898	1.62185
$448$	−3.86154	−0.182441
$449$	18.4598	0.871172	0.435586	−	0.900147i	$-0.356541\pi$
$449$	18.4598	0.871172	0.435586	+	0.900147i	$0.356541\pi$
$450$	0.712335	0.0335798
$451$	−0.967251	−0.0455461
$452$	6.69829	0.315061
$453$	−26.9746	−1.26738
$454$	27.4134	1.28658
$455$	27.2214	1.27616
$456$	0	0
$457$	3.32325	0.155455	0.0777275	−	0.996975i	$-0.475234\pi$
$457$	3.32325	0.155455	0.0777275	+	0.996975i	$0.475234\pi$
$458$	7.56854	0.353655
$459$	8.01912	0.374300
$460$	14.5694	0.679303
$461$	9.55543	0.445041	0.222520	−	0.974928i	$-0.428572\pi$
$461$	9.55543	0.445041	0.222520	+	0.974928i	$0.428572\pi$
$462$	7.23709	0.336700
$463$	26.0001	1.20833	0.604163	−	0.796861i	$-0.293508\pi$
$463$	26.0001	1.20833	0.604163	+	0.796861i	$0.293508\pi$
$464$	4.54820	0.211145
$465$	4.09375	0.189843
$466$	−27.4389	−1.27108
$467$	15.3284	0.709313	0.354657	−	0.934997i	$-0.384598\pi$
$467$	15.3284	0.709313	0.354657	+	0.934997i	$0.384598\pi$
$468$	−1.90121	−0.0878834
$469$	0.458762	0.0211837
$470$	−4.74720	−0.218972
$471$	−24.3808	−1.12341
$472$	4.46795	0.205654
$473$	0.985200	0.0452995
$474$	24.9115	1.14422
$475$	0	0
$476$	6.64212	0.304441
$477$	−0.389184	−0.0178195
$478$	16.7668	0.766897
$479$	−12.9024	−0.589525	−0.294762	−	0.955571i	$-0.595241\pi$
$479$	−12.9024	−0.589525	−0.294762	+	0.955571i	$0.595241\pi$
$480$	−3.56080	−0.162528
$481$	−18.5758	−0.846984
$482$	2.38796	0.108769
$483$	−55.4960	−2.52515
$484$	1.00000	0.0454545
$485$	−7.93240	−0.360192
$486$	5.26998	0.239051
$487$	−18.6727	−0.846141	−0.423070	−	0.906097i	$-0.639048\pi$
$487$	−18.6727	−0.846141	−0.423070	+	0.906097i	$0.639048\pi$
$488$	−1.79311	−0.0811704
$489$	27.6283	1.24940
$490$	−15.0315	−0.679056
$491$	10.2472	0.462451	0.231226	−	0.972900i	$-0.425726\pi$
$491$	10.2472	0.462451	0.231226	+	0.972900i	$0.425726\pi$
$492$	−1.81277	−0.0817259
$493$	−7.82323	−0.352340
$494$	0	0
$495$	0.973576	0.0437590
$496$	1.14967	0.0516217
$497$	−18.5299	−0.831178
$498$	15.9550	0.714963
$499$	−1.43321	−0.0641593	−0.0320796	−	0.999485i	$-0.510213\pi$
$499$	−1.43321	−0.0641593	−0.0320796	+	0.999485i	$0.510213\pi$
$500$	−12.1410	−0.542963
$501$	4.09139	0.182790
$502$	10.1749	0.454129
$503$	27.8210	1.24048	0.620238	−	0.784414i	$-0.287036\pi$
$503$	27.8210	1.24048	0.620238	+	0.784414i	$0.287036\pi$
$504$	1.97873	0.0881394
$505$	20.3730	0.906588
$506$	−7.66828	−0.340896
$507$	1.43573	0.0637632
$508$	−13.3751	−0.593426
$509$	−17.6644	−0.782962	−0.391481	−	0.920186i	$-0.628037\pi$
$509$	−17.6644	−0.782962	−0.391481	+	0.920186i	$0.628037\pi$
$510$	6.12484	0.271212
$511$	63.3302	2.80156
$512$	−1.00000	−0.0441942
$513$	0	0
$514$	−26.3318	−1.16145
$515$	−35.4774	−1.56332
$516$	1.84641	0.0812835
$517$	2.49857	0.109887
$518$	19.3332	0.849451
$519$	−46.6796	−2.04901
$520$	7.04937	0.309135
$521$	4.40856	0.193142	0.0965712	−	0.995326i	$-0.469212\pi$
$521$	4.40856	0.193142	0.0965712	+	0.995326i	$0.469212\pi$
$522$	−2.33058	−0.102007
$523$	−5.94050	−0.259760	−0.129880	−	0.991530i	$-0.541459\pi$
$523$	−5.94050	−0.259760	−0.129880	+	0.991530i	$0.541459\pi$
$524$	15.6258	0.682615
$525$	10.0606	0.439080
$526$	16.9397	0.738607
$527$	−1.97751	−0.0861418
$528$	1.87414	0.0815617
$529$	35.8024	1.55663
$530$	1.44303	0.0626812
$531$	−2.28946	−0.0993541
$532$	0	0
$533$	3.58876	0.155446
$534$	2.39235	0.103527
$535$	−1.73959	−0.0752088
$536$	0.118803	0.00513151
$537$	−8.85397	−0.382077
$538$	2.32455	0.100219
$539$	7.91150	0.340772
$540$	−8.85779	−0.381179
$541$	31.2893	1.34523	0.672616	−	0.739991i	$-0.265170\pi$
$541$	31.2893	1.34523	0.672616	+	0.739991i	$0.265170\pi$
$542$	−20.8536	−0.895737
$543$	−48.2670	−2.07133
$544$	1.72007	0.0737474
$545$	0.496486	0.0212671
$546$	−26.8515	−1.14914
$547$	−11.6841	−0.499574	−0.249787	−	0.968301i	$-0.580361\pi$
$547$	−11.6841	−0.499574	−0.249787	+	0.968301i	$0.580361\pi$
$548$	−16.5314	−0.706187
$549$	0.918824	0.0392145
$550$	1.39014	0.0592759
$551$	0	0
$552$	−14.3715	−0.611690
$553$	51.3284	2.18271
$554$	−1.70401	−0.0723963
$555$	17.8275	0.756736
$556$	−21.4746	−0.910727
$557$	−28.3336	−1.20053	−0.600266	−	0.799800i	$-0.704939\pi$
$557$	−28.3336	−1.20053	−0.600266	+	0.799800i	$0.704939\pi$
$558$	−0.589112	−0.0249391
$559$	−3.65535	−0.154605
$560$	−7.33678	−0.310036
$561$	−3.22366	−0.136103
$562$	3.38766	0.142900
$563$	12.2657	0.516936	0.258468	−	0.966020i	$-0.416782\pi$
$563$	12.2657	0.516936	0.258468	+	0.966020i	$0.416782\pi$
$564$	4.68269	0.197177
$565$	12.7265	0.535408
$566$	−6.72599	−0.282715
$567$	39.6761	1.66624
$568$	−4.79857	−0.201343
$569$	16.3531	0.685556	0.342778	−	0.939416i	$-0.388632\pi$
$569$	16.3531	0.685556	0.342778	+	0.939416i	$0.388632\pi$
$570$	0	0
$571$	33.3562	1.39592	0.697958	−	0.716139i	$-0.254092\pi$
$571$	33.3562	1.39592	0.697958	+	0.716139i	$0.254092\pi$
$572$	−3.71027	−0.155134
$573$	41.4049	1.72971
$574$	−3.73508	−0.155899
$575$	−10.6600	−0.444552
$576$	0.512419	0.0213508
$577$	−19.6504	−0.818056	−0.409028	−	0.912522i	$-0.634132\pi$
$577$	−19.6504	−0.818056	−0.409028	+	0.912522i	$0.634132\pi$
$578$	14.0414	0.584043
$579$	−37.9741	−1.57815
$580$	8.64141	0.358815
$581$	32.8742	1.36385
$582$	7.82461	0.324341
$583$	−0.759504	−0.0314555
$584$	16.4002	0.678647
$585$	−3.61223	−0.149347
$586$	−22.1111	−0.913402
$587$	22.1458	0.914056	0.457028	−	0.889452i	$-0.348914\pi$
$587$	22.1458	0.914056	0.457028	+	0.889452i	$0.348914\pi$
$588$	14.8273	0.611467
$589$	0	0
$590$	8.48893	0.349484
$591$	32.2376	1.32608
$592$	5.00660	0.205770
$593$	32.9251	1.35207	0.676037	−	0.736868i	$-0.263696\pi$
$593$	32.9251	1.35207	0.676037	+	0.736868i	$0.263696\pi$
$594$	4.66209	0.191288
$595$	12.6198	0.517361
$596$	18.2962	0.749443
$597$	−46.6274	−1.90833
$598$	28.4513	1.16346
$599$	43.2934	1.76892	0.884460	−	0.466616i	$-0.154527\pi$
$599$	43.2934	1.76892	0.884460	+	0.466616i	$0.154527\pi$
$600$	2.60533	0.106362
$601$	−23.6917	−0.966403	−0.483201	−	0.875509i	$-0.660526\pi$
$601$	−23.6917	−0.966403	−0.483201	+	0.875509i	$0.660526\pi$
$602$	3.80439	0.155055
$603$	−0.0608769	−0.00247910
$604$	−14.3930	−0.585644
$605$	1.89996	0.0772445
$606$	−20.0962	−0.816352
$607$	−24.4933	−0.994150	−0.497075	−	0.867707i	$-0.665593\pi$
$607$	−24.4933	−0.994150	−0.497075	+	0.867707i	$0.665593\pi$
$608$	0	0
$609$	−32.9157	−1.33381
$610$	−3.40685	−0.137939
$611$	−9.27037	−0.375039
$612$	−0.881396	−0.0356283
$613$	−18.3891	−0.742728	−0.371364	−	0.928487i	$-0.621110\pi$
$613$	−18.3891	−0.742728	−0.371364	+	0.928487i	$0.621110\pi$
$614$	−3.11344	−0.125648
$615$	−3.44419	−0.138883
$616$	3.86154	0.155586
$617$	−21.9560	−0.883915	−0.441958	−	0.897036i	$-0.645716\pi$
$617$	−21.9560	−0.883915	−0.441958	+	0.897036i	$0.645716\pi$
$618$	34.9953	1.40772
$619$	25.1717	1.01174	0.505868	−	0.862611i	$-0.331172\pi$
$619$	25.1717	1.01174	0.505868	+	0.862611i	$0.331172\pi$
$620$	2.18433	0.0877247
$621$	−35.7502	−1.43460
$622$	19.5190	0.782642
$623$	4.92926	0.197487
$624$	−6.95358	−0.278366
$625$	−16.1168	−0.644672
$626$	3.10062	0.123926
$627$	0	0
$628$	−13.0090	−0.519116
$629$	−8.61170	−0.343371
$630$	3.75950	0.149782
$631$	48.4480	1.92868	0.964342	−	0.264659i	$-0.0852595\pi$
$631$	48.4480	1.92868	0.964342	+	0.264659i	$0.0852595\pi$
$632$	13.2922	0.528736
$633$	−34.6830	−1.37853
$634$	21.1255	0.839001
$635$	−25.4122	−1.00845
$636$	−1.42342	−0.0564423
$637$	−29.3538	−1.16304
$638$	−4.54820	−0.180065
$639$	2.45888	0.0972716
$640$	−1.89996	−0.0751026
$641$	12.7584	0.503926	0.251963	−	0.967737i	$-0.418924\pi$
$641$	12.7584	0.503926	0.251963	+	0.967737i	$0.418924\pi$
$642$	1.71595	0.0677230
$643$	20.4685	0.807200	0.403600	−	0.914936i	$-0.367759\pi$
$643$	20.4685	0.807200	0.403600	+	0.914936i	$0.367759\pi$
$644$	−29.6114	−1.16685
$645$	3.50810	0.138131
$646$	0	0
$647$	28.9563	1.13839	0.569195	−	0.822203i	$-0.307255\pi$
$647$	28.9563	1.13839	0.569195	+	0.822203i	$0.307255\pi$
$648$	10.2747	0.403628
$649$	−4.46795	−0.175382
$650$	−5.15780	−0.202305
$651$	−8.32025	−0.326096
$652$	14.7418	0.577334
$653$	2.29448	0.0897900	0.0448950	−	0.998992i	$-0.485705\pi$
$653$	2.29448	0.0897900	0.0448950	+	0.998992i	$0.485705\pi$
$654$	−0.489740	−0.0191503
$655$	29.6884	1.16002
$656$	−0.967251	−0.0377648
$657$	−8.40379	−0.327863
$658$	9.64834	0.376132
$659$	4.57813	0.178338	0.0891692	−	0.996016i	$-0.471579\pi$
$659$	4.57813	0.178338	0.0891692	+	0.996016i	$0.471579\pi$
$660$	3.56080	0.138604
$661$	44.2688	1.72186	0.860929	−	0.508725i	$-0.169883\pi$
$661$	44.2688	1.72186	0.860929	+	0.508725i	$0.169883\pi$
$662$	−26.1232	−1.01531
$663$	11.9606	0.464513
$664$	8.51324	0.330378
$665$	0	0
$666$	−2.56547	−0.0994101
$667$	34.8769	1.35044
$668$	2.18307	0.0844655
$669$	−44.6245	−1.72528
$670$	0.225721	0.00872037
$671$	1.79311	0.0692223
$672$	7.23709	0.279177
$673$	27.3620	1.05473	0.527363	−	0.849640i	$-0.323181\pi$
$673$	27.3620	1.05473	0.527363	+	0.849640i	$0.323181\pi$
$674$	11.9914	0.461891
$675$	6.48097	0.249452
$676$	0.766074	0.0294644
$677$	−28.0836	−1.07934	−0.539670	−	0.841876i	$-0.681451\pi$
$677$	−28.0836	−1.07934	−0.539670	+	0.841876i	$0.681451\pi$
$678$	−12.5536	−0.482116
$679$	16.1221	0.618708
$680$	3.26807	0.125325
$681$	−51.3767	−1.96876
$682$	−1.14967	−0.0440231
$683$	−34.7365	−1.32916	−0.664578	−	0.747219i	$-0.731388\pi$
$683$	−34.7365	−1.32916	−0.664578	+	0.747219i	$0.731388\pi$
$684$	0	0
$685$	−31.4091	−1.20008
$686$	3.51979	0.134386
$687$	−14.1845	−0.541174
$688$	0.985200	0.0375604
$689$	2.81796	0.107356
$690$	−27.3052	−1.03949
$691$	34.1992	1.30100	0.650499	−	0.759507i	$-0.274560\pi$
$691$	34.1992	1.30100	0.650499	+	0.759507i	$0.274560\pi$
$692$	−24.9071	−0.946827
$693$	−1.97873	−0.0751656
$694$	14.1518	0.537196
$695$	−40.8010	−1.54767
$696$	−8.52399	−0.323101
$697$	1.66374	0.0630187
$698$	−9.11547	−0.345026
$699$	51.4244	1.94505
$700$	5.36809	0.202895
$701$	43.9079	1.65838	0.829189	−	0.558968i	$-0.188803\pi$
$701$	43.9079	1.65838	0.829189	+	0.558968i	$0.188803\pi$
$702$	−17.2976	−0.652855
$703$	0	0
$704$	1.00000	0.0376889
$705$	8.89693	0.335078
$706$	−9.05048	−0.340619
$707$	−41.4067	−1.55726
$708$	−8.37358	−0.314698
$709$	−7.30738	−0.274434	−0.137217	−	0.990541i	$-0.543816\pi$
$709$	−7.30738	−0.274434	−0.137217	+	0.990541i	$0.543816\pi$
$710$	−9.11710	−0.342159
$711$	−6.81118	−0.255439
$712$	1.27650	0.0478389
$713$	8.81598	0.330161
$714$	−12.4483	−0.465866
$715$	−7.04937	−0.263631
$716$	−4.72427	−0.176554
$717$	−31.4235	−1.17353
$718$	−23.4694	−0.875870
$719$	−41.5366	−1.54905	−0.774527	−	0.632540i	$-0.782012\pi$
$719$	−41.5366	−1.54905	−0.774527	+	0.632540i	$0.782012\pi$
$720$	0.973576	0.0362830
$721$	72.1052	2.68534
$722$	0	0
$723$	−4.47539	−0.166441
$724$	−25.7541	−0.957145
$725$	−6.32265	−0.234817
$726$	−1.87414	−0.0695560
$727$	−24.0311	−0.891263	−0.445632	−	0.895216i	$-0.647021\pi$
$727$	−24.0311	−0.891263	−0.445632	+	0.895216i	$0.647021\pi$
$728$	−14.3273	−0.531007
$729$	20.9473	0.775827
$730$	31.1598	1.15328
$731$	−1.69461	−0.0626775
$732$	3.36055	0.124210
$733$	−26.5618	−0.981081	−0.490541	−	0.871418i	$-0.663201\pi$
$733$	−26.5618	−0.981081	−0.490541	+	0.871418i	$0.663201\pi$
$734$	−8.96543	−0.330920
$735$	28.1713	1.03911
$736$	−7.66828	−0.282656
$737$	−0.118803	−0.00437616
$738$	0.495638	0.0182447
$739$	12.6391	0.464938	0.232469	−	0.972604i	$-0.425320\pi$
$739$	12.6391	0.464938	0.232469	+	0.972604i	$0.425320\pi$
$740$	9.51235	0.349681
$741$	0	0
$742$	−2.93286	−0.107669
$743$	−8.45781	−0.310287	−0.155144	−	0.987892i	$-0.549584\pi$
$743$	−8.45781	−0.310287	−0.155144	+	0.987892i	$0.549584\pi$
$744$	−2.15465	−0.0789932
$745$	34.7622	1.27359
$746$	−8.42369	−0.308413
$747$	−4.36234	−0.159610
$748$	−1.72007	−0.0628920
$749$	3.53559	0.129187
$750$	22.7541	0.830860
$751$	45.4340	1.65791	0.828955	−	0.559316i	$-0.188936\pi$
$751$	45.4340	1.65791	0.828955	+	0.559316i	$0.188936\pi$
$752$	2.49857	0.0911136
$753$	−19.0693	−0.694924
$754$	16.8750	0.614553
$755$	−27.3462	−0.995230
$756$	18.0028	0.654757
$757$	9.26363	0.336692	0.168346	−	0.985728i	$-0.446157\pi$
$757$	9.26363	0.336692	0.168346	+	0.985728i	$0.446157\pi$
$758$	−13.9231	−0.505712
$759$	14.3715	0.521651
$760$	0	0
$761$	−49.0890	−1.77947	−0.889737	−	0.456473i	$-0.849112\pi$
$761$	−49.0890	−1.77947	−0.889737	+	0.456473i	$0.849112\pi$
$762$	25.0669	0.908079
$763$	−1.00907	−0.0365309
$764$	22.0927	0.799286
$765$	−1.67462	−0.0605460
$766$	6.32105	0.228389
$767$	16.5773	0.598571
$768$	1.87414	0.0676274
$769$	−0.781101	−0.0281672	−0.0140836	−	0.999901i	$-0.504483\pi$
$769$	−0.781101	−0.0281672	−0.0140836	+	0.999901i	$0.504483\pi$
$770$	7.33678	0.264399
$771$	49.3497	1.77729
$772$	−20.2621	−0.729248
$773$	−5.31722	−0.191247	−0.0956235	−	0.995418i	$-0.530484\pi$
$773$	−5.31722	−0.191247	−0.0956235	+	0.995418i	$0.530484\pi$
$774$	−0.504835	−0.0181459
$775$	−1.59820	−0.0574092
$776$	4.17503	0.149875
$777$	−36.2332	−1.29986
$778$	32.2295	1.15548
$779$	0	0
$780$	−13.2115	−0.473049
$781$	4.79857	0.171706
$782$	13.1900	0.471673
$783$	−21.2041	−0.757773
$784$	7.91150	0.282553
$785$	−24.7166	−0.882174
$786$	−29.2849	−1.04456
$787$	43.5052	1.55079	0.775397	−	0.631474i	$-0.217550\pi$
$787$	43.5052	1.55079	0.775397	+	0.631474i	$0.217550\pi$
$788$	17.2012	0.612769
$789$	−31.7475	−1.13024
$790$	25.2547	0.898522
$791$	−25.8657	−0.919679
$792$	−0.512419	−0.0182080
$793$	−6.65292	−0.236252
$794$	−25.3339	−0.899067
$795$	−2.70445	−0.0959168
$796$	−24.8793	−0.881824
$797$	−24.7787	−0.877706	−0.438853	−	0.898559i	$-0.644615\pi$
$797$	−24.7787	−0.877706	−0.438853	+	0.898559i	$0.644615\pi$
$798$	0	0
$799$	−4.29772	−0.152042
$800$	1.39014	0.0491490
$801$	−0.654103	−0.0231116
$802$	0.765866	0.0270437
$803$	−16.4002	−0.578752
$804$	−0.222654	−0.00785240
$805$	−56.2605	−1.98292
$806$	4.26558	0.150249
$807$	−4.35655	−0.153358
$808$	−10.7229	−0.377229
$809$	−0.561785	−0.0197513	−0.00987565	−	0.999951i	$-0.503144\pi$
$809$	−0.561785	−0.0197513	−0.00987565	+	0.999951i	$0.503144\pi$
$810$	19.5215	0.685916
$811$	−21.1625	−0.743115	−0.371557	−	0.928410i	$-0.621176\pi$
$811$	−21.1625	−0.743115	−0.371557	+	0.928410i	$0.621176\pi$
$812$	−17.5631	−0.616343
$813$	39.0826	1.37069
$814$	−5.00660	−0.175481
$815$	28.0089	0.981109
$816$	−3.22366	−0.112851
$817$	0	0
$818$	11.2877	0.394666
$819$	7.34160	0.256536
$820$	−1.83774	−0.0641767
$821$	−22.1945	−0.774592	−0.387296	−	0.921955i	$-0.626591\pi$
$821$	−22.1945	−0.774592	−0.387296	+	0.921955i	$0.626591\pi$
$822$	30.9823	1.08063
$823$	−17.0037	−0.592713	−0.296357	−	0.955077i	$-0.595772\pi$
$823$	−17.0037	−0.592713	−0.296357	+	0.955077i	$0.595772\pi$
$824$	18.6727	0.650493
$825$	−2.60533	−0.0907059
$826$	−17.2532	−0.600314
$827$	41.1301	1.43024	0.715118	−	0.699004i	$-0.246373\pi$
$827$	41.1301	1.43024	0.715118	+	0.699004i	$0.246373\pi$
$828$	3.92937	0.136555
$829$	−45.4222	−1.57758	−0.788789	−	0.614664i	$-0.789292\pi$
$829$	−45.4222	−1.57758	−0.788789	+	0.614664i	$0.789292\pi$
$830$	16.1748	0.561437
$831$	3.19355	0.110783
$832$	−3.71027	−0.128630
$833$	−13.6083	−0.471501
$834$	40.2466	1.39363
$835$	4.14775	0.143539
$836$	0	0
$837$	−5.35986	−0.185264
$838$	−37.2698	−1.28746
$839$	−7.31344	−0.252488	−0.126244	−	0.991999i	$-0.540292\pi$
$839$	−7.31344	−0.252488	−0.126244	+	0.991999i	$0.540292\pi$
$840$	13.7502	0.474427
$841$	−8.31387	−0.286685
$842$	27.7213	0.955340
$843$	−6.34897	−0.218670
$844$	−18.5060	−0.637004
$845$	1.45551	0.0500712
$846$	−1.28032	−0.0440182
$847$	−3.86154	−0.132684
$848$	−0.759504	−0.0260815
$849$	12.6055	0.432619
$850$	−2.39114	−0.0820155
$851$	38.3920	1.31606
$852$	8.99321	0.308102
$853$	−31.9482	−1.09389	−0.546943	−	0.837170i	$-0.684208\pi$
$853$	−31.9482	−1.09389	−0.546943	+	0.837170i	$0.684208\pi$
$854$	6.92417	0.236940
$855$	0	0
$856$	0.915589	0.0312942
$857$	−34.8573	−1.19070	−0.595351	−	0.803466i	$-0.702987\pi$
$857$	−34.8573	−1.19070	−0.595351	+	0.803466i	$0.702987\pi$
$858$	6.95358	0.237391
$859$	−0.187794	−0.00640744	−0.00320372	−	0.999995i	$-0.501020\pi$
$859$	−0.187794	−0.00640744	−0.00320372	+	0.999995i	$0.501020\pi$
$860$	1.87184	0.0638293
$861$	7.00008	0.238562
$862$	−17.8243	−0.607100
$863$	31.3518	1.06723	0.533613	−	0.845729i	$-0.320834\pi$
$863$	31.3518	1.06723	0.533613	+	0.845729i	$0.320834\pi$
$864$	4.66209	0.158607
$865$	−47.3226	−1.60902
$866$	−14.9808	−0.509068
$867$	−26.3155	−0.893722
$868$	−4.43949	−0.150686
$869$	−13.2922	−0.450907
$870$	−16.1953	−0.549071
$871$	0.440791	0.0149356
$872$	−0.261314	−0.00884920
$873$	−2.13936	−0.0724065
$874$	0	0
$875$	46.8831	1.58494
$876$	−30.7364	−1.03849
$877$	−36.5171	−1.23309	−0.616547	−	0.787318i	$-0.711469\pi$
$877$	−36.5171	−1.23309	−0.616547	+	0.787318i	$0.711469\pi$
$878$	−31.7040	−1.06996
$879$	41.4395	1.39772
$880$	1.89996	0.0640477
$881$	−35.8749	−1.20866	−0.604328	−	0.796735i	$-0.706558\pi$
$881$	−35.8749	−1.20866	−0.604328	+	0.796735i	$0.706558\pi$
$882$	−4.05400	−0.136505
$883$	41.7157	1.40385	0.701923	−	0.712253i	$-0.252325\pi$
$883$	41.7157	1.40385	0.701923	+	0.712253i	$0.252325\pi$
$884$	6.38192	0.214647
$885$	−15.9095	−0.534792
$886$	5.89147	0.197928
$887$	−2.94032	−0.0987262	−0.0493631	−	0.998781i	$-0.515719\pi$
$887$	−2.94032	−0.0987262	−0.0493631	+	0.998781i	$0.515719\pi$
$888$	−9.38309	−0.314876
$889$	51.6486	1.73224
$890$	2.42530	0.0812963
$891$	−10.2747	−0.344215
$892$	−23.8106	−0.797238
$893$	0	0
$894$	−34.2898	−1.14682
$895$	−8.97594	−0.300033
$896$	3.86154	0.129005
$897$	−53.3219	−1.78037
$898$	−18.4598	−0.616012
$899$	5.22892	0.174394
$900$	−0.712335	−0.0237445
$901$	1.30640	0.0435225
$902$	0.967251	0.0322059
$903$	−7.12998	−0.237271
$904$	−6.69829	−0.222782
$905$	−48.9319	−1.62655
$906$	26.9746	0.896171
$907$	24.3903	0.809865	0.404933	−	0.914347i	$-0.367295\pi$
$907$	24.3903	0.809865	0.404933	+	0.914347i	$0.367295\pi$
$908$	−27.4134	−0.909747
$909$	5.49459	0.182244
$910$	−27.2214	−0.902381
$911$	−33.4489	−1.10821	−0.554106	−	0.832446i	$-0.686940\pi$
$911$	−33.4489	−1.10821	−0.554106	+	0.832446i	$0.686940\pi$
$912$	0	0
$913$	−8.51324	−0.281747
$914$	−3.32325	−0.109923
$915$	6.38492	0.211079
$916$	−7.56854	−0.250072
$917$	−60.3395	−1.99259
$918$	−8.01912	−0.264670
$919$	−20.0702	−0.662055	−0.331027	−	0.943621i	$-0.607395\pi$
$919$	−20.0702	−0.662055	−0.331027	+	0.943621i	$0.607395\pi$
$920$	−14.5694	−0.480340
$921$	5.83503	0.192271
$922$	−9.55543	−0.314691
$923$	−17.8040	−0.586025
$924$	−7.23709	−0.238083
$925$	−6.95988	−0.228839
$926$	−26.0001	−0.854416
$927$	−9.56822	−0.314262
$928$	−4.54820	−0.149302
$929$	−47.9540	−1.57332	−0.786660	−	0.617386i	$-0.788192\pi$
$929$	−47.9540	−1.57332	−0.786660	+	0.617386i	$0.788192\pi$
$930$	−4.09375	−0.134239
$931$	0	0
$932$	27.4389	0.898790
$933$	−36.5815	−1.19763
$934$	−15.3284	−0.501560
$935$	−3.26807	−0.106877
$936$	1.90121	0.0621430
$937$	−29.1547	−0.952442	−0.476221	−	0.879326i	$-0.657994\pi$
$937$	−29.1547	−0.952442	−0.476221	+	0.879326i	$0.657994\pi$
$938$	−0.458762	−0.0149791
$939$	−5.81101	−0.189635
$940$	4.74720	0.154836
$941$	−36.8233	−1.20040	−0.600202	−	0.799848i	$-0.704913\pi$
$941$	−36.8233	−1.20040	−0.600202	+	0.799848i	$0.704913\pi$
$942$	24.3808	0.794368
$943$	−7.41715	−0.241536
$944$	−4.46795	−0.145419
$945$	34.2047	1.11268
$946$	−0.985200	−0.0320316
$947$	−30.3240	−0.985398	−0.492699	−	0.870200i	$-0.663990\pi$
$947$	−30.3240	−0.985398	−0.492699	+	0.870200i	$0.663990\pi$
$948$	−24.9115	−0.809089
$949$	60.8493	1.97525
$950$	0	0
$951$	−39.5923	−1.28387
$952$	−6.64212	−0.215272
$953$	13.7466	0.445294	0.222647	−	0.974899i	$-0.428530\pi$
$953$	13.7466	0.445294	0.222647	+	0.974899i	$0.428530\pi$
$954$	0.389184	0.0126003
$955$	41.9753	1.35829
$956$	−16.7668	−0.542278
$957$	8.52399	0.275541
$958$	12.9024	0.416857
$959$	63.8367	2.06140
$960$	3.56080	0.114924
$961$	−29.6783	−0.957363
$962$	18.5758	0.598908
$963$	−0.469165	−0.0151186
$964$	−2.38796	−0.0769111
$965$	−38.4972	−1.23927
$966$	55.4960	1.78555
$967$	−28.6687	−0.921922	−0.460961	−	0.887420i	$-0.652495\pi$
$967$	−28.6687	−0.921922	−0.460961	+	0.887420i	$0.652495\pi$
$968$	−1.00000	−0.0321412
$969$	0	0
$970$	7.93240	0.254694
$971$	19.6291	0.629928	0.314964	−	0.949104i	$-0.398007\pi$
$971$	19.6291	0.629928	0.314964	+	0.949104i	$0.398007\pi$
$972$	−5.26998	−0.169035
$973$	82.9252	2.65846
$974$	18.6727	0.598312
$975$	9.66646	0.309574
$976$	1.79311	0.0573961
$977$	41.5820	1.33033	0.665163	−	0.746698i	$-0.268362\pi$
$977$	41.5820	1.33033	0.665163	+	0.746698i	$0.268362\pi$
$978$	−27.6283	−0.883456
$979$	−1.27650	−0.0407971
$980$	15.0315	0.480165
$981$	0.133902	0.00427516
$982$	−10.2472	−0.327002
$983$	−13.3094	−0.424503	−0.212252	−	0.977215i	$-0.568080\pi$
$983$	−13.3094	−0.424503	−0.212252	+	0.977215i	$0.568080\pi$
$984$	1.81277	0.0577890
$985$	32.6817	1.04133
$986$	7.82323	0.249142
$987$	−18.0824	−0.575569
$988$	0	0
$989$	7.55478	0.240228
$990$	−0.973576	−0.0309423
$991$	−41.2203	−1.30941	−0.654703	−	0.755886i	$-0.727206\pi$
$991$	−41.2203	−1.30941	−0.654703	+	0.755886i	$0.727206\pi$
$992$	−1.14967	−0.0365020
$993$	48.9587	1.55366
$994$	18.5299	0.587732
$995$	−47.2698	−1.49855
$996$	−15.9550	−0.505555
$997$	−3.25112	−0.102964	−0.0514820	−	0.998674i	$-0.516394\pi$
$997$	−3.25112	−0.102964	−0.0514820	+	0.998674i	$0.516394\pi$
$998$	1.43321	0.0453674
$999$	−23.3412	−0.738483

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	7942.2.a.bm.1.8	✓	8
19.18	odd	2		7942.2.a.br.1.1	yes	8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
7942.2.a.bm.1.8	✓	8	1.1	even	1	trivial
7942.2.a.br.1.1	yes	8	19.18	odd	2

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:	\( N \)	\(=\)	\( 7942 = 2 \cdot 11 \cdot 19^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	7942.a (trivial)

\(f(q)\)	\(=\)	\(q-1.00000 q^{2} +1.87414 q^{3} +1.00000 q^{4} +1.89996 q^{5} -1.87414 q^{6} -3.86154 q^{7} -1.00000 q^{8} +0.512419 q^{9} +O(q^{10})\)	\(q-1.00000 q^{2} +1.87414 q^{3} +1.00000 q^{4} +1.89996 q^{5} -1.87414 q^{6} -3.86154 q^{7} -1.00000 q^{8} +0.512419 q^{9} -1.89996 q^{10} +1.00000 q^{11} +1.87414 q^{12} -3.71027 q^{13} +3.86154 q^{14} +3.56080 q^{15} +1.00000 q^{16} -1.72007 q^{17} -0.512419 q^{18} +1.89996 q^{20} -7.23709 q^{21} -1.00000 q^{22} +7.66828 q^{23} -1.87414 q^{24} -1.39014 q^{25} +3.71027 q^{26} -4.66209 q^{27} -3.86154 q^{28} +4.54820 q^{29} -3.56080 q^{30} +1.14967 q^{31} -1.00000 q^{32} +1.87414 q^{33} +1.72007 q^{34} -7.33678 q^{35} +0.512419 q^{36} +5.00660 q^{37} -6.95358 q^{39} -1.89996 q^{40} -0.967251 q^{41} +7.23709 q^{42} +0.985200 q^{43} +1.00000 q^{44} +0.973576 q^{45} -7.66828 q^{46} +2.49857 q^{47} +1.87414 q^{48} +7.91150 q^{49} +1.39014 q^{50} -3.22366 q^{51} -3.71027 q^{52} -0.759504 q^{53} +4.66209 q^{54} +1.89996 q^{55} +3.86154 q^{56} -4.54820 q^{58} -4.46795 q^{59} +3.56080 q^{60} +1.79311 q^{61} -1.14967 q^{62} -1.97873 q^{63} +1.00000 q^{64} -7.04937 q^{65} -1.87414 q^{66} -0.118803 q^{67} -1.72007 q^{68} +14.3715 q^{69} +7.33678 q^{70} +4.79857 q^{71} -0.512419 q^{72} -16.4002 q^{73} -5.00660 q^{74} -2.60533 q^{75} -3.86154 q^{77} +6.95358 q^{78} -13.2922 q^{79} +1.89996 q^{80} -10.2747 q^{81} +0.967251 q^{82} -8.51324 q^{83} -7.23709 q^{84} -3.26807 q^{85} -0.985200 q^{86} +8.52399 q^{87} -1.00000 q^{88} -1.27650 q^{89} -0.973576 q^{90} +14.3273 q^{91} +7.66828 q^{92} +2.15465 q^{93} -2.49857 q^{94} -1.87414 q^{96} -4.17503 q^{97} -7.91150 q^{98} +0.512419 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q - 8 q^{2} - 4 q^{3} + 8 q^{4} + q^{5} + 4 q^{6} + 4 q^{7} - 8 q^{8} + 6 q^{9}+O(q^{10}) \) 8 * q - 8 * q^2 - 4 * q^3 + 8 * q^4 + q^5 + 4 * q^6 + 4 * q^7 - 8 * q^8 + 6 * q^9	\( 8 q - 8 q^{2} - 4 q^{3} + 8 q^{4} + q^{5} + 4 q^{6} + 4 q^{7} - 8 q^{8} + 6 q^{9} - q^{10} + 8 q^{11} - 4 q^{12} - 12 q^{13} - 4 q^{14} + 9 q^{15} + 8 q^{16} + 7 q^{17} - 6 q^{18} + q^{20} - 13 q^{21} - 8 q^{22} - 6 q^{23} + 4 q^{24} + 5 q^{25} + 12 q^{26} - 22 q^{27} + 4 q^{28} + q^{29} - 9 q^{30} - 8 q^{31} - 8 q^{32} - 4 q^{33} - 7 q^{34} + 5 q^{35} + 6 q^{36} - 12 q^{37} + 10 q^{39} - q^{40} - 18 q^{41} + 13 q^{42} - 4 q^{43} + 8 q^{44} - 19 q^{45} + 6 q^{46} + 13 q^{47} - 4 q^{48} + 4 q^{49} - 5 q^{50} - 14 q^{51} - 12 q^{52} + 17 q^{53} + 22 q^{54} + q^{55} - 4 q^{56} - q^{58} - 26 q^{59} + 9 q^{60} - 7 q^{61} + 8 q^{62} + 13 q^{63} + 8 q^{64} - 36 q^{65} + 4 q^{66} - 6 q^{67} + 7 q^{68} - 19 q^{69} - 5 q^{70} + 3 q^{71} - 6 q^{72} + 5 q^{73} + 12 q^{74} - 30 q^{75} + 4 q^{77} - 10 q^{78} - 16 q^{79} + q^{80} + 8 q^{81} + 18 q^{82} - 21 q^{83} - 13 q^{84} - 10 q^{85} + 4 q^{86} - 29 q^{87} - 8 q^{88} - 16 q^{89} + 19 q^{90} - 31 q^{91} - 6 q^{92} + 20 q^{93} - 13 q^{94} + 4 q^{96} + 15 q^{97} - 4 q^{98} + 6 q^{99}+O(q^{100}) \) 8 * q - 8 * q^2 - 4 * q^3 + 8 * q^4 + q^5 + 4 * q^6 + 4 * q^7 - 8 * q^8 + 6 * q^9 - q^10 + 8 * q^11 - 4 * q^12 - 12 * q^13 - 4 * q^14 + 9 * q^15 + 8 * q^16 + 7 * q^17 - 6 * q^18 + q^20 - 13 * q^21 - 8 * q^22 - 6 * q^23 + 4 * q^24 + 5 * q^25 + 12 * q^26 - 22 * q^27 + 4 * q^28 + q^29 - 9 * q^30 - 8 * q^31 - 8 * q^32 - 4 * q^33 - 7 * q^34 + 5 * q^35 + 6 * q^36 - 12 * q^37 + 10 * q^39 - q^40 - 18 * q^41 + 13 * q^42 - 4 * q^43 + 8 * q^44 - 19 * q^45 + 6 * q^46 + 13 * q^47 - 4 * q^48 + 4 * q^49 - 5 * q^50 - 14 * q^51 - 12 * q^52 + 17 * q^53 + 22 * q^54 + q^55 - 4 * q^56 - q^58 - 26 * q^59 + 9 * q^60 - 7 * q^61 + 8 * q^62 + 13 * q^63 + 8 * q^64 - 36 * q^65 + 4 * q^66 - 6 * q^67 + 7 * q^68 - 19 * q^69 - 5 * q^70 + 3 * q^71 - 6 * q^72 + 5 * q^73 + 12 * q^74 - 30 * q^75 + 4 * q^77 - 10 * q^78 - 16 * q^79 + q^80 + 8 * q^81 + 18 * q^82 - 21 * q^83 - 13 * q^84 - 10 * q^85 + 4 * q^86 - 29 * q^87 - 8 * q^88 - 16 * q^89 + 19 * q^90 - 31 * q^91 - 6 * q^92 + 20 * q^93 - 13 * q^94 + 4 * q^96 + 15 * q^97 - 4 * q^98 + 6 * q^99

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