LMFDB - Embedded newform 8042.2.a.c.1.10

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [8042,2,Mod(1,8042)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(8042, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("8042.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 8042 = 2 \cdot 4021 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	8042.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:	$64.2156933055$
Analytic rank:	$0$
Dimension:	$86$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.10
Character	$\chi$	$=$	8042.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.00000 q^{2} -2.53308 q^{3} +1.00000 q^{4} -2.12930 q^{5} +2.53308 q^{6} -1.20392 q^{7} -1.00000 q^{8} +3.41648 q^{9} +O(q^{10})$	\(q-1.00000 q^{2} -2.53308 q^{3} +1.00000 q^{4} -2.12930 q^{5} +2.53308 q^{6} -1.20392 q^{7} -1.00000 q^{8} +3.41648 q^{9} +2.12930 q^{10} -3.06628 q^{11} -2.53308 q^{12} +2.94048 q^{13} +1.20392 q^{14} +5.39369 q^{15} +1.00000 q^{16} -0.513898 q^{17} -3.41648 q^{18} +4.03318 q^{19} -2.12930 q^{20} +3.04963 q^{21} +3.06628 q^{22} +6.16231 q^{23} +2.53308 q^{24} -0.466073 q^{25} -2.94048 q^{26} -1.05499 q^{27} -1.20392 q^{28} +0.113495 q^{29} -5.39369 q^{30} +6.64630 q^{31} -1.00000 q^{32} +7.76713 q^{33} +0.513898 q^{34} +2.56351 q^{35} +3.41648 q^{36} +1.12473 q^{37} -4.03318 q^{38} -7.44846 q^{39} +2.12930 q^{40} +7.47821 q^{41} -3.04963 q^{42} +10.9649 q^{43} -3.06628 q^{44} -7.27473 q^{45} -6.16231 q^{46} -9.30504 q^{47} -2.53308 q^{48} -5.55057 q^{49} +0.466073 q^{50} +1.30174 q^{51} +2.94048 q^{52} -0.632478 q^{53} +1.05499 q^{54} +6.52904 q^{55} +1.20392 q^{56} -10.2163 q^{57} -0.113495 q^{58} -12.6898 q^{59} +5.39369 q^{60} +8.24791 q^{61} -6.64630 q^{62} -4.11318 q^{63} +1.00000 q^{64} -6.26117 q^{65} -7.76713 q^{66} +3.19595 q^{67} -0.513898 q^{68} -15.6096 q^{69} -2.56351 q^{70} -5.15906 q^{71} -3.41648 q^{72} -12.7258 q^{73} -1.12473 q^{74} +1.18060 q^{75} +4.03318 q^{76} +3.69156 q^{77} +7.44846 q^{78} +6.64324 q^{79} -2.12930 q^{80} -7.57709 q^{81} -7.47821 q^{82} +3.76008 q^{83} +3.04963 q^{84} +1.09424 q^{85} -10.9649 q^{86} -0.287492 q^{87} +3.06628 q^{88} -5.64721 q^{89} +7.27473 q^{90} -3.54011 q^{91} +6.16231 q^{92} -16.8356 q^{93} +9.30504 q^{94} -8.58785 q^{95} +2.53308 q^{96} +18.1952 q^{97} +5.55057 q^{98} -10.4759 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 86 q - 86 q^{2} + 12 q^{3} + 86 q^{4} - 4 q^{5} - 12 q^{6} + 35 q^{7} - 86 q^{8} + 72 q^{9}+O(q^{10}) $ 86 * q - 86 * q^2 + 12 * q^3 + 86 * q^4 - 4 * q^5 - 12 * q^6 + 35 * q^7 - 86 * q^8 + 72 * q^9	\( 86 q - 86 q^{2} + 12 q^{3} + 86 q^{4} - 4 q^{5} - 12 q^{6} + 35 q^{7} - 86 q^{8} + 72 q^{9} + 4 q^{10} + 13 q^{11} + 12 q^{12} + 45 q^{13} - 35 q^{14} + 17 q^{15} + 86 q^{16} + 5 q^{17} - 72 q^{18} + 47 q^{19} - 4 q^{20} + 15 q^{21} - 13 q^{22} + 6 q^{23} - 12 q^{24} + 112 q^{25} - 45 q^{26} + 51 q^{27} + 35 q^{28} - 14 q^{29} - 17 q^{30} + 24 q^{31} - 86 q^{32} + 43 q^{33} - 5 q^{34} + 42 q^{35} + 72 q^{36} + 61 q^{37} - 47 q^{38} + 20 q^{39} + 4 q^{40} - 16 q^{41} - 15 q^{42} + 72 q^{43} + 13 q^{44} + 6 q^{45} - 6 q^{46} + 11 q^{47} + 12 q^{48} + 89 q^{49} - 112 q^{50} + 56 q^{51} + 45 q^{52} - 7 q^{53} - 51 q^{54} + 48 q^{55} - 35 q^{56} + 65 q^{57} + 14 q^{58} + 24 q^{59} + 17 q^{60} + 31 q^{61} - 24 q^{62} + 98 q^{63} + 86 q^{64} - 9 q^{65} - 43 q^{66} + 157 q^{67} + 5 q^{68} + q^{69} - 42 q^{70} - 11 q^{71} - 72 q^{72} + 74 q^{73} - 61 q^{74} + 76 q^{75} + 47 q^{76} - 13 q^{77} - 20 q^{78} + 57 q^{79} - 4 q^{80} + 34 q^{81} + 16 q^{82} + 65 q^{83} + 15 q^{84} + 102 q^{85} - 72 q^{86} + 49 q^{87} - 13 q^{88} - 34 q^{89} - 6 q^{90} + 91 q^{91} + 6 q^{92} + 57 q^{93} - 11 q^{94} - 13 q^{95} - 12 q^{96} + 64 q^{97} - 89 q^{98} + 56 q^{99}+O(q^{100}) \) 86 * q - 86 * q^2 + 12 * q^3 + 86 * q^4 - 4 * q^5 - 12 * q^6 + 35 * q^7 - 86 * q^8 + 72 * q^9 + 4 * q^10 + 13 * q^11 + 12 * q^12 + 45 * q^13 - 35 * q^14 + 17 * q^15 + 86 * q^16 + 5 * q^17 - 72 * q^18 + 47 * q^19 - 4 * q^20 + 15 * q^21 - 13 * q^22 + 6 * q^23 - 12 * q^24 + 112 * q^25 - 45 * q^26 + 51 * q^27 + 35 * q^28 - 14 * q^29 - 17 * q^30 + 24 * q^31 - 86 * q^32 + 43 * q^33 - 5 * q^34 + 42 * q^35 + 72 * q^36 + 61 * q^37 - 47 * q^38 + 20 * q^39 + 4 * q^40 - 16 * q^41 - 15 * q^42 + 72 * q^43 + 13 * q^44 + 6 * q^45 - 6 * q^46 + 11 * q^47 + 12 * q^48 + 89 * q^49 - 112 * q^50 + 56 * q^51 + 45 * q^52 - 7 * q^53 - 51 * q^54 + 48 * q^55 - 35 * q^56 + 65 * q^57 + 14 * q^58 + 24 * q^59 + 17 * q^60 + 31 * q^61 - 24 * q^62 + 98 * q^63 + 86 * q^64 - 9 * q^65 - 43 * q^66 + 157 * q^67 + 5 * q^68 + q^69 - 42 * q^70 - 11 * q^71 - 72 * q^72 + 74 * q^73 - 61 * q^74 + 76 * q^75 + 47 * q^76 - 13 * q^77 - 20 * q^78 + 57 * q^79 - 4 * q^80 + 34 * q^81 + 16 * q^82 + 65 * q^83 + 15 * q^84 + 102 * q^85 - 72 * q^86 + 49 * q^87 - 13 * q^88 - 34 * q^89 - 6 * q^90 + 91 * q^91 + 6 * q^92 + 57 * q^93 - 11 * q^94 - 13 * q^95 - 12 * q^96 + 64 * q^97 - 89 * q^98 + 56 * 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
$3$	−2.53308	−1.46247	−0.731237	−	0.682124i	$-0.761056\pi$
$3$	−2.53308	−1.46247	−0.731237	+	0.682124i	$0.761056\pi$
$4$	1.00000	0.500000
$5$	−2.12930	−0.952253	−0.476126	−	0.879377i	$-0.657960\pi$
$5$	−2.12930	−0.952253	−0.476126	+	0.879377i	$0.657960\pi$
$6$	2.53308	1.03412
$7$	−1.20392	−0.455040	−0.227520	−	0.973773i	$-0.573062\pi$
$7$	−1.20392	−0.455040	−0.227520	+	0.973773i	$0.573062\pi$
$8$	−1.00000	−0.353553
$9$	3.41648	1.13883
$10$	2.12930	0.673344
$11$	−3.06628	−0.924519	−0.462260	−	0.886745i	$-0.652961\pi$
$11$	−3.06628	−0.924519	−0.462260	+	0.886745i	$0.652961\pi$
$12$	−2.53308	−0.731237
$13$	2.94048	0.815542	0.407771	−	0.913084i	$-0.366306\pi$
$13$	2.94048	0.815542	0.407771	+	0.913084i	$0.366306\pi$
$14$	1.20392	0.321762
$15$	5.39369	1.39264
$16$	1.00000	0.250000
$17$	−0.513898	−0.124639	−0.0623193	−	0.998056i	$-0.519850\pi$
$17$	−0.513898	−0.124639	−0.0623193	+	0.998056i	$0.519850\pi$
$18$	−3.41648	−0.805273
$19$	4.03318	0.925274	0.462637	−	0.886548i	$-0.346903\pi$
$19$	4.03318	0.925274	0.462637	+	0.886548i	$0.346903\pi$
$20$	−2.12930	−0.476126
$21$	3.04963	0.665483
$22$	3.06628	0.653734
$23$	6.16231	1.28493	0.642466	−	0.766315i	$-0.277912\pi$
$23$	6.16231	1.28493	0.642466	+	0.766315i	$0.277912\pi$
$24$	2.53308	0.517062
$25$	−0.466073	−0.0932146
$26$	−2.94048	−0.576675
$27$	−1.05499	−0.203032
$28$	−1.20392	−0.227520
$29$	0.113495	0.0210755	0.0105378	−	0.999944i	$-0.496646\pi$
$29$	0.113495	0.0210755	0.0105378	+	0.999944i	$0.496646\pi$
$30$	−5.39369	−0.984748
$31$	6.64630	1.19371	0.596855	−	0.802349i	$-0.296417\pi$
$31$	6.64630	1.19371	0.596855	+	0.802349i	$0.296417\pi$
$32$	−1.00000	−0.176777
$33$	7.76713	1.35208
$34$	0.513898	0.0881328
$35$	2.56351	0.433313
$36$	3.41648	0.569414
$37$	1.12473	0.184904	0.0924522	−	0.995717i	$-0.470529\pi$
$37$	1.12473	0.184904	0.0924522	+	0.995717i	$0.470529\pi$
$38$	−4.03318	−0.654268
$39$	−7.44846	−1.19271
$40$	2.12930	0.336672
$41$	7.47821	1.16790	0.583950	−	0.811790i	$-0.301506\pi$
$41$	7.47821	1.16790	0.583950	+	0.811790i	$0.301506\pi$
$42$	−3.04963	−0.470568
$43$	10.9649	1.67212	0.836062	−	0.548634i	$-0.184852\pi$
$43$	10.9649	1.67212	0.836062	+	0.548634i	$0.184852\pi$
$44$	−3.06628	−0.462260
$45$	−7.27473	−1.08445
$46$	−6.16231	−0.908584
$47$	−9.30504	−1.35728	−0.678640	−	0.734471i	$-0.737430\pi$
$47$	−9.30504	−1.35728	−0.678640	+	0.734471i	$0.737430\pi$
$48$	−2.53308	−0.365618
$49$	−5.55057	−0.792939
$50$	0.466073	0.0659127
$51$	1.30174	0.182281
$52$	2.94048	0.407771
$53$	−0.632478	−0.0868775	−0.0434388	−	0.999056i	$-0.513831\pi$
$53$	−0.632478	−0.0868775	−0.0434388	+	0.999056i	$0.513831\pi$
$54$	1.05499	0.143566
$55$	6.52904	0.880376
$56$	1.20392	0.160881
$57$	−10.2163	−1.35319
$58$	−0.113495	−0.0149027
$59$	−12.6898	−1.65208	−0.826038	−	0.563615i	$-0.809410\pi$
$59$	−12.6898	−1.65208	−0.826038	+	0.563615i	$0.809410\pi$
$60$	5.39369	0.696322
$61$	8.24791	1.05604	0.528018	−	0.849233i	$-0.322935\pi$
$61$	8.24791	1.05604	0.528018	+	0.849233i	$0.322935\pi$
$62$	−6.64630	−0.844080
$63$	−4.11318	−0.518212
$64$	1.00000	0.125000
$65$	−6.26117	−0.776602
$66$	−7.76713	−0.956068
$67$	3.19595	0.390448	0.195224	−	0.980759i	$-0.437457\pi$
$67$	3.19595	0.390448	0.195224	+	0.980759i	$0.437457\pi$
$68$	−0.513898	−0.0623193
$69$	−15.6096	−1.87918
$70$	−2.56351	−0.306398
$71$	−5.15906	−0.612267	−0.306134	−	0.951989i	$-0.599035\pi$
$71$	−5.15906	−0.612267	−0.306134	+	0.951989i	$0.599035\pi$
$72$	−3.41648	−0.402637
$73$	−12.7258	−1.48945	−0.744723	−	0.667373i	$-0.767419\pi$
$73$	−12.7258	−1.48945	−0.744723	+	0.667373i	$0.767419\pi$
$74$	−1.12473	−0.130747
$75$	1.18060	0.136324
$76$	4.03318	0.462637
$77$	3.69156	0.420693
$78$	7.44846	0.843372
$79$	6.64324	0.747423	0.373712	−	0.927545i	$-0.378085\pi$
$79$	6.64324	0.747423	0.373712	+	0.927545i	$0.378085\pi$
$80$	−2.12930	−0.238063
$81$	−7.57709	−0.841899
$82$	−7.47821	−0.825830
$83$	3.76008	0.412723	0.206361	−	0.978476i	$-0.433838\pi$
$83$	3.76008	0.412723	0.206361	+	0.978476i	$0.433838\pi$
$84$	3.04963	0.332742
$85$	1.09424	0.118687
$86$	−10.9649	−1.18237
$87$	−0.287492	−0.0308224
$88$	3.06628	0.326867
$89$	−5.64721	−0.598603	−0.299301	−	0.954159i	$-0.596754\pi$
$89$	−5.64721	−0.598603	−0.299301	+	0.954159i	$0.596754\pi$
$90$	7.27473	0.766824
$91$	−3.54011	−0.371104
$92$	6.16231	0.642466
$93$	−16.8356	−1.74577
$94$	9.30504	0.959742
$95$	−8.58785	−0.881095
$96$	2.53308	0.258531
$97$	18.1952	1.84745	0.923723	−	0.383060i	$-0.125130\pi$
$97$	18.1952	1.84745	0.923723	+	0.383060i	$0.125130\pi$
$98$	5.55057	0.560693
$99$	−10.4759	−1.05287
$100$	−0.466073	−0.0466073
$101$	12.5521	1.24898	0.624492	−	0.781031i	$-0.285306\pi$
$101$	12.5521	1.24898	0.624492	+	0.781031i	$0.285306\pi$
$102$	−1.30174	−0.128892
$103$	−4.42601	−0.436107	−0.218054	−	0.975937i	$-0.569971\pi$
$103$	−4.42601	−0.436107	−0.218054	+	0.975937i	$0.569971\pi$
$104$	−2.94048	−0.288338
$105$	−6.49358	−0.633708
$106$	0.632478	0.0614317
$107$	−10.7491	−1.03916	−0.519579	−	0.854423i	$-0.673911\pi$
$107$	−10.7491	−1.03916	−0.519579	+	0.854423i	$0.673911\pi$
$108$	−1.05499	−0.101516
$109$	0.866909	0.0830348	0.0415174	−	0.999138i	$-0.486781\pi$
$109$	0.866909	0.0830348	0.0415174	+	0.999138i	$0.486781\pi$
$110$	−6.52904	−0.622520
$111$	−2.84903	−0.270418
$112$	−1.20392	−0.113760
$113$	18.6280	1.75238	0.876188	−	0.481969i	$-0.160078\pi$
$113$	18.6280	1.75238	0.876188	+	0.481969i	$0.160078\pi$
$114$	10.2163	0.956849
$115$	−13.1214	−1.22358
$116$	0.113495	0.0105378
$117$	10.0461	0.928762
$118$	12.6898	1.16819
$119$	0.618693	0.0567155
$120$	−5.39369	−0.492374
$121$	−1.59791	−0.145264
$122$	−8.24791	−0.746731
$123$	−18.9429	−1.70802
$124$	6.64630	0.596855
$125$	11.6389	1.04102
$126$	4.11318	0.366431
$127$	13.2106	1.17225	0.586124	−	0.810221i	$-0.300653\pi$
$127$	13.2106	1.17225	0.586124	+	0.810221i	$0.300653\pi$
$128$	−1.00000	−0.0883883
$129$	−27.7748	−2.44544
$130$	6.26117	0.549141
$131$	1.78277	0.155762	0.0778808	−	0.996963i	$-0.475185\pi$
$131$	1.78277	0.155762	0.0778808	+	0.996963i	$0.475185\pi$
$132$	7.76713	0.676042
$133$	−4.85563	−0.421036
$134$	−3.19595	−0.276088
$135$	2.24639	0.193338
$136$	0.513898	0.0440664
$137$	−17.1499	−1.46521	−0.732607	−	0.680652i	$-0.761697\pi$
$137$	−17.1499	−1.46521	−0.732607	+	0.680652i	$0.761697\pi$
$138$	15.6096	1.32878
$139$	−22.9002	−1.94237	−0.971185	−	0.238326i	$-0.923401\pi$
$139$	−22.9002	−1.94237	−0.971185	+	0.238326i	$0.923401\pi$
$140$	2.56351	0.216656
$141$	23.5704	1.98499
$142$	5.15906	0.432938
$143$	−9.01634	−0.753984
$144$	3.41648	0.284707
$145$	−0.241666	−0.0200692
$146$	12.7258	1.05320
$147$	14.0600	1.15965
$148$	1.12473	0.0924522
$149$	3.81534	0.312565	0.156282	−	0.987712i	$-0.450049\pi$
$149$	3.81534	0.312565	0.156282	+	0.987712i	$0.450049\pi$
$150$	−1.18060	−0.0963956
$151$	2.63594	0.214510	0.107255	−	0.994232i	$-0.465794\pi$
$151$	2.63594	0.214510	0.107255	+	0.994232i	$0.465794\pi$
$152$	−4.03318	−0.327134
$153$	−1.75572	−0.141942
$154$	−3.69156	−0.297475
$155$	−14.1520	−1.13671
$156$	−7.44846	−0.596354
$157$	−12.1405	−0.968915	−0.484458	−	0.874815i	$-0.660983\pi$
$157$	−12.1405	−0.968915	−0.484458	+	0.874815i	$0.660983\pi$
$158$	−6.64324	−0.528508
$159$	1.60212	0.127056
$160$	2.12930	0.168336
$161$	−7.41894	−0.584694
$162$	7.57709	0.595312
$163$	3.78720	0.296636	0.148318	−	0.988940i	$-0.452614\pi$
$163$	3.78720	0.296636	0.148318	+	0.988940i	$0.452614\pi$
$164$	7.47821	0.583950
$165$	−16.5386	−1.28753
$166$	−3.76008	−0.291839
$167$	0.835722	0.0646701	0.0323350	−	0.999477i	$-0.489706\pi$
$167$	0.835722	0.0646701	0.0323350	+	0.999477i	$0.489706\pi$
$168$	−3.04963	−0.235284
$169$	−4.35359	−0.334891
$170$	−1.09424	−0.0839247
$171$	13.7793	1.05373
$172$	10.9649	0.836062
$173$	−17.9559	−1.36516	−0.682580	−	0.730811i	$-0.739142\pi$
$173$	−17.9559	−1.36516	−0.682580	+	0.730811i	$0.739142\pi$
$174$	0.287492	0.0217947
$175$	0.561116	0.0424163
$176$	−3.06628	−0.231130
$177$	32.1443	2.41612
$178$	5.64721	0.423276
$179$	−15.0728	−1.12659	−0.563297	−	0.826254i	$-0.690467\pi$
$179$	−15.0728	−1.12659	−0.563297	+	0.826254i	$0.690467\pi$
$180$	−7.27473	−0.542226
$181$	−0.830708	−0.0617460	−0.0308730	−	0.999523i	$-0.509829\pi$
$181$	−0.830708	−0.0617460	−0.0308730	+	0.999523i	$0.509829\pi$
$182$	3.54011	0.262410
$183$	−20.8926	−1.54443
$184$	−6.16231	−0.454292
$185$	−2.39489	−0.176076
$186$	16.8356	1.23445
$187$	1.57576	0.115231
$188$	−9.30504	−0.678640
$189$	1.27012	0.0923878
$190$	8.58785	0.623028
$191$	1.57893	0.114247	0.0571237	−	0.998367i	$-0.481807\pi$
$191$	1.57893	0.114247	0.0571237	+	0.998367i	$0.481807\pi$
$192$	−2.53308	−0.182809
$193$	2.09273	0.150638	0.0753190	−	0.997159i	$-0.476003\pi$
$193$	2.09273	0.150638	0.0753190	+	0.997159i	$0.476003\pi$
$194$	−18.1952	−1.30634
$195$	15.8600	1.13576
$196$	−5.55057	−0.396470
$197$	13.2338	0.942868	0.471434	−	0.881901i	$-0.343737\pi$
$197$	13.2338	0.942868	0.471434	+	0.881901i	$0.343737\pi$
$198$	10.4759	0.744490
$199$	12.5057	0.886502	0.443251	−	0.896397i	$-0.353825\pi$
$199$	12.5057	0.886502	0.443251	+	0.896397i	$0.353825\pi$
$200$	0.466073	0.0329564
$201$	−8.09560	−0.571019
$202$	−12.5521	−0.883165
$203$	−0.136639	−0.00959020
$204$	1.30174	0.0911403
$205$	−15.9234	−1.11214
$206$	4.42601	0.308375
$207$	21.0534	1.46332
$208$	2.94048	0.203885
$209$	−12.3669	−0.855433
$210$	6.49358	0.448099
$211$	−21.2655	−1.46397	−0.731987	−	0.681319i	$-0.761407\pi$
$211$	−21.2655	−1.46397	−0.731987	+	0.681319i	$0.761407\pi$
$212$	−0.632478	−0.0434388
$213$	13.0683	0.895425
$214$	10.7491	0.734795
$215$	−23.3475	−1.59229
$216$	1.05499	0.0717828
$217$	−8.00162	−0.543185
$218$	−0.866909	−0.0587145
$219$	32.2355	2.17828
$220$	6.52904	0.440188
$221$	−1.51111	−0.101648
$222$	2.84903	0.191214
$223$	−10.1800	−0.681705	−0.340853	−	0.940117i	$-0.610716\pi$
$223$	−10.1800	−0.681705	−0.340853	+	0.940117i	$0.610716\pi$
$224$	1.20392	0.0804404
$225$	−1.59233	−0.106155
$226$	−18.6280	−1.23912
$227$	9.15917	0.607916	0.303958	−	0.952686i	$-0.401692\pi$
$227$	9.15917	0.607916	0.303958	+	0.952686i	$0.401692\pi$
$228$	−10.2163	−0.676594
$229$	−7.22664	−0.477549	−0.238775	−	0.971075i	$-0.576746\pi$
$229$	−7.22664	−0.477549	−0.238775	+	0.971075i	$0.576746\pi$
$230$	13.1214	0.865201
$231$	−9.35102	−0.615252
$232$	−0.113495	−0.00745133
$233$	−11.1930	−0.733277	−0.366639	−	0.930363i	$-0.619491\pi$
$233$	−11.1930	−0.733277	−0.366639	+	0.930363i	$0.619491\pi$
$234$	−10.0461	−0.656734
$235$	19.8132	1.29247
$236$	−12.6898	−0.826038
$237$	−16.8278	−1.09309
$238$	−0.618693	−0.0401039
$239$	13.4255	0.868423	0.434212	−	0.900811i	$-0.357027\pi$
$239$	13.4255	0.868423	0.434212	+	0.900811i	$0.357027\pi$
$240$	5.39369	0.348161
$241$	−12.9413	−0.833621	−0.416810	−	0.908993i	$-0.636852\pi$
$241$	−12.9413	−0.833621	−0.416810	+	0.908993i	$0.636852\pi$
$242$	1.59791	0.102717
$243$	22.3583	1.43429
$244$	8.24791	0.528018
$245$	11.8188	0.755078
$246$	18.9429	1.20775
$247$	11.8595	0.754600
$248$	−6.64630	−0.422040
$249$	−9.52458	−0.603596
$250$	−11.6389	−0.736110
$251$	29.1185	1.83795	0.918973	−	0.394321i	$-0.129020\pi$
$251$	29.1185	1.83795	0.918973	+	0.394321i	$0.129020\pi$
$252$	−4.11318	−0.259106
$253$	−18.8954	−1.18794
$254$	−13.2106	−0.828904
$255$	−2.77181	−0.173577
$256$	1.00000	0.0625000
$257$	−1.53352	−0.0956582	−0.0478291	−	0.998856i	$-0.515230\pi$
$257$	−1.53352	−0.0956582	−0.0478291	+	0.998856i	$0.515230\pi$
$258$	27.7748	1.72919
$259$	−1.35409	−0.0841388
$260$	−6.26117	−0.388301
$261$	0.387755	0.0240014
$262$	−1.78277	−0.110140
$263$	10.5843	0.652659	0.326329	−	0.945256i	$-0.394188\pi$
$263$	10.5843	0.652659	0.326329	+	0.945256i	$0.394188\pi$
$264$	−7.76713	−0.478034
$265$	1.34674	0.0827294
$266$	4.85563	0.297718
$267$	14.3048	0.875440
$268$	3.19595	0.195224
$269$	−16.9355	−1.03257	−0.516287	−	0.856415i	$-0.672686\pi$
$269$	−16.9355	−1.03257	−0.516287	+	0.856415i	$0.672686\pi$
$270$	−2.24639	−0.136711
$271$	28.2892	1.71845	0.859223	−	0.511602i	$-0.170948\pi$
$271$	28.2892	1.71845	0.859223	+	0.511602i	$0.170948\pi$
$272$	−0.513898	−0.0311596
$273$	8.96736	0.542729
$274$	17.1499	1.03606
$275$	1.42911	0.0861787
$276$	−15.6096	−0.939589
$277$	1.00398	0.0603234	0.0301617	−	0.999545i	$-0.490398\pi$
$277$	1.00398	0.0603234	0.0301617	+	0.999545i	$0.490398\pi$
$278$	22.9002	1.37346
$279$	22.7070	1.35943
$280$	−2.56351	−0.153199
$281$	−22.4590	−1.33979	−0.669896	−	0.742455i	$-0.733662\pi$
$281$	−22.4590	−1.33979	−0.669896	+	0.742455i	$0.733662\pi$
$282$	−23.5704	−1.40360
$283$	10.6085	0.630609	0.315305	−	0.948991i	$-0.397893\pi$
$283$	10.6085	0.630609	0.315305	+	0.948991i	$0.397893\pi$
$284$	−5.15906	−0.306134
$285$	21.7537	1.28858
$286$	9.01634	0.533147
$287$	−9.00318	−0.531441
$288$	−3.41648	−0.201318
$289$	−16.7359	−0.984465
$290$	0.241666	0.0141911
$291$	−46.0900	−2.70184
$292$	−12.7258	−0.744723
$293$	−2.18696	−0.127763	−0.0638817	−	0.997957i	$-0.520348\pi$
$293$	−2.18696	−0.127763	−0.0638817	+	0.997957i	$0.520348\pi$
$294$	−14.0600	−0.819998
$295$	27.0205	1.57319
$296$	−1.12473	−0.0653736
$297$	3.23489	0.187707
$298$	−3.81534	−0.221016
$299$	18.1201	1.04792
$300$	1.18060	0.0681620
$301$	−13.2008	−0.760883
$302$	−2.63594	−0.151681
$303$	−31.7955	−1.82661
$304$	4.03318	0.231318
$305$	−17.5623	−1.00561
$306$	1.75572	0.100368
$307$	24.8860	1.42032	0.710160	−	0.704040i	$-0.248622\pi$
$307$	24.8860	1.42032	0.710160	+	0.704040i	$0.248622\pi$
$308$	3.69156	0.210346
$309$	11.2114	0.637795
$310$	14.1520	0.803778
$311$	−2.33950	−0.132661	−0.0663303	−	0.997798i	$-0.521129\pi$
$311$	−2.33950	−0.132661	−0.0663303	+	0.997798i	$0.521129\pi$
$312$	7.44846	0.421686
$313$	−9.59628	−0.542414	−0.271207	−	0.962521i	$-0.587423\pi$
$313$	−9.59628	−0.542414	−0.271207	+	0.962521i	$0.587423\pi$
$314$	12.1405	0.685126
$315$	8.75820	0.493469
$316$	6.64324	0.373712
$317$	32.5612	1.82882	0.914411	−	0.404788i	$-0.132655\pi$
$317$	32.5612	1.82882	0.914411	+	0.404788i	$0.132655\pi$
$318$	−1.60212	−0.0898422
$319$	−0.348008	−0.0194847
$320$	−2.12930	−0.119032
$321$	27.2284	1.51974
$322$	7.41894	0.413441
$323$	−2.07264	−0.115325
$324$	−7.57709	−0.420949
$325$	−1.37048	−0.0760205
$326$	−3.78720	−0.209754
$327$	−2.19595	−0.121436
$328$	−7.47821	−0.412915
$329$	11.2025	0.617616
$330$	16.5386	0.910419
$331$	29.2281	1.60652	0.803260	−	0.595629i	$-0.203097\pi$
$331$	29.2281	1.60652	0.803260	+	0.595629i	$0.203097\pi$
$332$	3.76008	0.206361
$333$	3.84262	0.210574
$334$	−0.835722	−0.0457287
$335$	−6.80515	−0.371805
$336$	3.04963	0.166371
$337$	−4.99392	−0.272036	−0.136018	−	0.990706i	$-0.543431\pi$
$337$	−4.99392	−0.272036	−0.136018	+	0.990706i	$0.543431\pi$
$338$	4.35359	0.236804
$339$	−47.1862	−2.56280
$340$	1.09424	0.0593437
$341$	−20.3794	−1.10361
$342$	−13.7793	−0.745098
$343$	15.1099	0.815858
$344$	−10.9649	−0.591185
$345$	33.2376	1.78945
$346$	17.9559	0.965314
$347$	1.46788	0.0787997	0.0393999	−	0.999224i	$-0.487455\pi$
$347$	1.46788	0.0787997	0.0393999	+	0.999224i	$0.487455\pi$
$348$	−0.287492	−0.0154112
$349$	−6.77065	−0.362425	−0.181212	−	0.983444i	$-0.558002\pi$
$349$	−6.77065	−0.362425	−0.181212	+	0.983444i	$0.558002\pi$
$350$	−0.561116	−0.0299929
$351$	−3.10217	−0.165582
$352$	3.06628	0.163433
$353$	−29.8279	−1.58758	−0.793790	−	0.608192i	$-0.791895\pi$
$353$	−29.8279	−1.58758	−0.793790	+	0.608192i	$0.791895\pi$
$354$	−32.1443	−1.70845
$355$	10.9852	0.583033
$356$	−5.64721	−0.299301
$357$	−1.56720	−0.0829449
$358$	15.0728	0.796623
$359$	2.57061	0.135672	0.0678358	−	0.997696i	$-0.478391\pi$
$359$	2.57061	0.135672	0.0678358	+	0.997696i	$0.478391\pi$
$360$	7.27473	0.383412
$361$	−2.73349	−0.143868
$362$	0.830708	0.0436610
$363$	4.04763	0.212445
$364$	−3.54011	−0.185552
$365$	27.0972	1.41833
$366$	20.8926	1.09207
$367$	24.4069	1.27403	0.637014	−	0.770852i	$-0.280169\pi$
$367$	24.4069	1.27403	0.637014	+	0.770852i	$0.280169\pi$
$368$	6.16231	0.321233
$369$	25.5492	1.33004
$370$	2.39489	0.124504
$371$	0.761454	0.0395327
$372$	−16.8356	−0.872884
$373$	−15.3279	−0.793650	−0.396825	−	0.917894i	$-0.629888\pi$
$373$	−15.3279	−0.793650	−0.396825	+	0.917894i	$0.629888\pi$
$374$	−1.57576	−0.0814804
$375$	−29.4823	−1.52246
$376$	9.30504	0.479871
$377$	0.333730	0.0171880
$378$	−1.27012	−0.0653280
$379$	−22.1185	−1.13615	−0.568075	−	0.822976i	$-0.692312\pi$
$379$	−22.1185	−1.13615	−0.568075	+	0.822976i	$0.692312\pi$
$380$	−8.58785	−0.440547
$381$	−33.4634	−1.71438
$382$	−1.57893	−0.0807851
$383$	−20.8364	−1.06469	−0.532345	−	0.846528i	$-0.678689\pi$
$383$	−20.8364	−1.06469	−0.532345	+	0.846528i	$0.678689\pi$
$384$	2.53308	0.129266
$385$	−7.86045	−0.400606
$386$	−2.09273	−0.106517
$387$	37.4613	1.90426
$388$	18.1952	0.923723
$389$	−5.44060	−0.275849	−0.137925	−	0.990443i	$-0.544043\pi$
$389$	−5.44060	−0.275849	−0.137925	+	0.990443i	$0.544043\pi$
$390$	−15.8600	−0.803104
$391$	−3.16680	−0.160152
$392$	5.55057	0.280346
$393$	−4.51591	−0.227797
$394$	−13.2338	−0.666708
$395$	−14.1455	−0.711736
$396$	−10.4759	−0.526434
$397$	−23.7638	−1.19267	−0.596337	−	0.802735i	$-0.703378\pi$
$397$	−23.7638	−1.19267	−0.596337	+	0.802735i	$0.703378\pi$
$398$	−12.5057	−0.626852
$399$	12.2997	0.615754
$400$	−0.466073	−0.0233037
$401$	3.18365	0.158984	0.0794918	−	0.996836i	$-0.474670\pi$
$401$	3.18365	0.158984	0.0794918	+	0.996836i	$0.474670\pi$
$402$	8.09560	0.403772
$403$	19.5433	0.973521
$404$	12.5521	0.624492
$405$	16.1339	0.801700
$406$	0.136639	0.00678130
$407$	−3.44874	−0.170948
$408$	−1.30174	−0.0644459
$409$	28.8154	1.42483	0.712414	−	0.701760i	$-0.247602\pi$
$409$	28.8154	1.42483	0.712414	+	0.701760i	$0.247602\pi$
$410$	15.9234	0.786399
$411$	43.4420	2.14284
$412$	−4.42601	−0.218054
$413$	15.2776	0.751759
$414$	−21.0534	−1.03472
$415$	−8.00635	−0.393016
$416$	−2.94048	−0.144169
$417$	58.0080	2.84066
$418$	12.3669	0.604883
$419$	25.0695	1.22473	0.612363	−	0.790577i	$-0.290219\pi$
$419$	25.0695	1.22473	0.612363	+	0.790577i	$0.290219\pi$
$420$	−6.49358	−0.316854
$421$	21.7468	1.05987	0.529936	−	0.848038i	$-0.322216\pi$
$421$	21.7468	1.05987	0.529936	+	0.848038i	$0.322216\pi$
$422$	21.2655	1.03519
$423$	−31.7905	−1.54571
$424$	0.632478	0.0307159
$425$	0.239514	0.0116181
$426$	−13.0683	−0.633161
$427$	−9.92984	−0.480539
$428$	−10.7491	−0.519579
$429$	22.8391	1.10268
$430$	23.3475	1.12592
$431$	−10.2615	−0.494279	−0.247139	−	0.968980i	$-0.579491\pi$
$431$	−10.2615	−0.494279	−0.247139	+	0.968980i	$0.579491\pi$
$432$	−1.05499	−0.0507581
$433$	17.4472	0.838458	0.419229	−	0.907881i	$-0.362300\pi$
$433$	17.4472	0.838458	0.419229	+	0.907881i	$0.362300\pi$
$434$	8.00162	0.384090
$435$	0.612158	0.0293507
$436$	0.866909	0.0415174
$437$	24.8537	1.18891
$438$	−32.2355	−1.54027
$439$	−38.6564	−1.84497	−0.922484	−	0.386036i	$-0.873844\pi$
$439$	−38.6564	−1.84497	−0.922484	+	0.386036i	$0.873844\pi$
$440$	−6.52904	−0.311260
$441$	−18.9634	−0.903021
$442$	1.51111	0.0718760
$443$	28.1368	1.33682	0.668411	−	0.743793i	$-0.266975\pi$
$443$	28.1368	1.33682	0.668411	+	0.743793i	$0.266975\pi$
$444$	−2.84903	−0.135209
$445$	12.0246	0.570021
$446$	10.1800	0.482038
$447$	−9.66454	−0.457117
$448$	−1.20392	−0.0568799
$449$	−21.8623	−1.03174	−0.515872	−	0.856666i	$-0.672532\pi$
$449$	−21.8623	−1.03174	−0.515872	+	0.856666i	$0.672532\pi$
$450$	1.59233	0.0750632
$451$	−22.9303	−1.07975
$452$	18.6280	0.876188
$453$	−6.67704	−0.313715
$454$	−9.15917	−0.429861
$455$	7.53795	0.353385
$456$	10.2163	0.478424
$457$	12.9541	0.605966	0.302983	−	0.952996i	$-0.402017\pi$
$457$	12.9541	0.605966	0.302983	+	0.952996i	$0.402017\pi$
$458$	7.22664	0.337678
$459$	0.542156	0.0253057
$460$	−13.1214	−0.611790
$461$	−15.9404	−0.742417	−0.371209	−	0.928549i	$-0.621057\pi$
$461$	−15.9404	−0.742417	−0.371209	+	0.928549i	$0.621057\pi$
$462$	9.35102	0.435049
$463$	39.4991	1.83568	0.917840	−	0.396951i	$-0.129932\pi$
$463$	39.4991	1.83568	0.917840	+	0.396951i	$0.129932\pi$
$464$	0.113495	0.00526888
$465$	35.8480	1.66241
$466$	11.1930	0.518505
$467$	32.1352	1.48704	0.743519	−	0.668715i	$-0.233155\pi$
$467$	32.1352	1.48704	0.743519	+	0.668715i	$0.233155\pi$
$468$	10.0461	0.464381
$469$	−3.84768	−0.177669
$470$	−19.8132	−0.913917
$471$	30.7528	1.41701
$472$	12.6898	0.584097
$473$	−33.6214	−1.54591
$474$	16.8278	0.772929
$475$	−1.87976	−0.0862491
$476$	0.618693	0.0283577
$477$	−2.16085	−0.0989386
$478$	−13.4255	−0.614068
$479$	11.1418	0.509081	0.254541	−	0.967062i	$-0.418076\pi$
$479$	11.1418	0.509081	0.254541	+	0.967062i	$0.418076\pi$
$480$	−5.39369	−0.246187
$481$	3.30724	0.150797
$482$	12.9413	0.589459
$483$	18.7928	0.855100
$484$	−1.59791	−0.0726322
$485$	−38.7432	−1.75924
$486$	−22.3583	−1.01419
$487$	−17.9409	−0.812978	−0.406489	−	0.913656i	$-0.633247\pi$
$487$	−17.9409	−0.812978	−0.406489	+	0.913656i	$0.633247\pi$
$488$	−8.24791	−0.373365
$489$	−9.59327	−0.433823
$490$	−11.8188	−0.533921
$491$	−40.9212	−1.84675	−0.923375	−	0.383900i	$-0.874581\pi$
$491$	−40.9212	−1.84675	−0.923375	+	0.383900i	$0.874581\pi$
$492$	−18.9429	−0.854011
$493$	−0.0583250	−0.00262682
$494$	−11.8595	−0.533583
$495$	22.3064	1.00260
$496$	6.64630	0.298427
$497$	6.21110	0.278606
$498$	9.52458	0.426807
$499$	−23.3987	−1.04747	−0.523734	−	0.851882i	$-0.675462\pi$
$499$	−23.3987	−1.04747	−0.523734	+	0.851882i	$0.675462\pi$
$500$	11.6389	0.520508
$501$	−2.11695	−0.0945783
$502$	−29.1185	−1.29962
$503$	3.38932	0.151122	0.0755612	−	0.997141i	$-0.475925\pi$
$503$	3.38932	0.151122	0.0755612	+	0.997141i	$0.475925\pi$
$504$	4.11318	0.183216
$505$	−26.7273	−1.18935
$506$	18.8954	0.840003
$507$	11.0280	0.489770
$508$	13.2106	0.586124
$509$	−14.7430	−0.653470	−0.326735	−	0.945116i	$-0.605948\pi$
$509$	−14.7430	−0.653470	−0.326735	+	0.945116i	$0.605948\pi$
$510$	2.77181	0.122738
$511$	15.3209	0.677757
$512$	−1.00000	−0.0441942
$513$	−4.25495	−0.187861
$514$	1.53352	0.0676406
$515$	9.42431	0.415285
$516$	−27.7748	−1.22272
$517$	28.5319	1.25483
$518$	1.35409	0.0594951
$519$	45.4837	1.99651
$520$	6.26117	0.274570
$521$	−14.9116	−0.653290	−0.326645	−	0.945147i	$-0.605918\pi$
$521$	−14.9116	−0.653290	−0.326645	+	0.945147i	$0.605918\pi$
$522$	−0.387755	−0.0169716
$523$	27.1952	1.18916	0.594582	−	0.804035i	$-0.297318\pi$
$523$	27.1952	1.18916	0.594582	+	0.804035i	$0.297318\pi$
$524$	1.78277	0.0778808
$525$	−1.42135	−0.0620328
$526$	−10.5843	−0.461499
$527$	−3.41552	−0.148782
$528$	7.76713	0.338021
$529$	14.9741	0.651048
$530$	−1.34674	−0.0584985
$531$	−43.3546	−1.88143
$532$	−4.85563	−0.210518
$533$	21.9895	0.952472
$534$	−14.3048	−0.619030
$535$	22.8881	0.989540
$536$	−3.19595	−0.138044
$537$	38.1806	1.64762
$538$	16.9355	0.730141
$539$	17.0196	0.733087
$540$	2.24639	0.0966691
$541$	−12.4078	−0.533452	−0.266726	−	0.963772i	$-0.585942\pi$
$541$	−12.4078	−0.533452	−0.266726	+	0.963772i	$0.585942\pi$
$542$	−28.2892	−1.21512
$543$	2.10425	0.0903019
$544$	0.513898	0.0220332
$545$	−1.84591	−0.0790701
$546$	−8.96736	−0.383768
$547$	11.2214	0.479793	0.239896	−	0.970798i	$-0.422887\pi$
$547$	11.2214	0.479793	0.239896	+	0.970798i	$0.422887\pi$
$548$	−17.1499	−0.732607
$549$	28.1789	1.20264
$550$	−1.42911	−0.0609376
$551$	0.457746	0.0195006
$552$	15.6096	0.664390
$553$	−7.99794	−0.340107
$554$	−1.00398	−0.0426551
$555$	6.06644	0.257506
$556$	−22.9002	−0.971185
$557$	−10.8678	−0.460483	−0.230242	−	0.973133i	$-0.573952\pi$
$557$	−10.8678	−0.460483	−0.230242	+	0.973133i	$0.573952\pi$
$558$	−22.7070	−0.961262
$559$	32.2419	1.36369
$560$	2.56351	0.108328
$561$	−3.99151	−0.168522
$562$	22.4590	0.947377
$563$	0.670584	0.0282618	0.0141309	−	0.999900i	$-0.495502\pi$
$563$	0.670584	0.0282618	0.0141309	+	0.999900i	$0.495502\pi$
$564$	23.5704	0.992493
$565$	−39.6647	−1.66871
$566$	−10.6085	−0.445908
$567$	9.12222	0.383097
$568$	5.15906	0.216469
$569$	21.5616	0.903910	0.451955	−	0.892041i	$-0.350727\pi$
$569$	21.5616	0.903910	0.451955	+	0.892041i	$0.350727\pi$
$570$	−21.7537	−0.911162
$571$	14.8583	0.621799	0.310899	−	0.950443i	$-0.399370\pi$
$571$	14.8583	0.621799	0.310899	+	0.950443i	$0.399370\pi$
$572$	−9.01634	−0.376992
$573$	−3.99956	−0.167084
$574$	9.00318	0.375785
$575$	−2.87209	−0.119774
$576$	3.41648	0.142354
$577$	40.0292	1.66644	0.833219	−	0.552943i	$-0.186495\pi$
$577$	40.0292	1.66644	0.833219	+	0.552943i	$0.186495\pi$
$578$	16.7359	0.696122
$579$	−5.30105	−0.220304
$580$	−0.241666	−0.0100346
$581$	−4.52684	−0.187805
$582$	46.0900	1.91049
$583$	1.93936	0.0803200
$584$	12.7258	0.526599
$585$	−21.3912	−0.884416
$586$	2.18696	0.0903423
$587$	−4.78535	−0.197512	−0.0987562	−	0.995112i	$-0.531486\pi$
$587$	−4.78535	−0.197512	−0.0987562	+	0.995112i	$0.531486\pi$
$588$	14.0600	0.579826
$589$	26.8057	1.10451
$590$	−27.0205	−1.11242
$591$	−33.5222	−1.37892
$592$	1.12473	0.0462261
$593$	−4.00197	−0.164341	−0.0821707	−	0.996618i	$-0.526185\pi$
$593$	−4.00197	−0.164341	−0.0821707	+	0.996618i	$0.526185\pi$
$594$	−3.23489	−0.132729
$595$	−1.31738	−0.0540075
$596$	3.81534	0.156282
$597$	−31.6778	−1.29649
$598$	−18.1201	−0.740988
$599$	−5.02840	−0.205455	−0.102727	−	0.994710i	$-0.532757\pi$
$599$	−5.02840	−0.205455	−0.102727	+	0.994710i	$0.532757\pi$
$600$	−1.18060	−0.0481978
$601$	4.88081	0.199093	0.0995463	−	0.995033i	$-0.468261\pi$
$601$	4.88081	0.199093	0.0995463	+	0.995033i	$0.468261\pi$
$602$	13.2008	0.538026
$603$	10.9189	0.444653
$604$	2.63594	0.107255
$605$	3.40243	0.138328
$606$	31.7955	1.29161
$607$	−28.6821	−1.16417	−0.582086	−	0.813127i	$-0.697763\pi$
$607$	−28.6821	−1.16417	−0.582086	+	0.813127i	$0.697763\pi$
$608$	−4.03318	−0.163567
$609$	0.346118	0.0140254
$610$	17.5623	0.711077
$611$	−27.3613	−1.10692
$612$	−1.75572	−0.0709710
$613$	27.9728	1.12981	0.564906	−	0.825156i	$-0.308913\pi$
$613$	27.9728	1.12981	0.564906	+	0.825156i	$0.308913\pi$
$614$	−24.8860	−1.00432
$615$	40.3351	1.62647
$616$	−3.69156	−0.148737
$617$	7.45984	0.300322	0.150161	−	0.988662i	$-0.452021\pi$
$617$	7.45984	0.300322	0.150161	+	0.988662i	$0.452021\pi$
$618$	−11.2114	−0.450990
$619$	40.5111	1.62828	0.814140	−	0.580669i	$-0.197209\pi$
$619$	40.5111	1.62828	0.814140	+	0.580669i	$0.197209\pi$
$620$	−14.1520	−0.568357
$621$	−6.50116	−0.260883
$622$	2.33950	0.0938052
$623$	6.79879	0.272388
$624$	−7.44846	−0.298177
$625$	−22.4524	−0.898096
$626$	9.59628	0.383545
$627$	31.3262	1.25105
$628$	−12.1405	−0.484458
$629$	−0.577996	−0.0230462
$630$	−8.75820	−0.348935
$631$	37.8225	1.50569	0.752844	−	0.658199i	$-0.228681\pi$
$631$	37.8225	1.50569	0.752844	+	0.658199i	$0.228681\pi$
$632$	−6.64324	−0.264254
$633$	53.8670	2.14102
$634$	−32.5612	−1.29317
$635$	−28.1293	−1.11628
$636$	1.60212	0.0635280
$637$	−16.3213	−0.646675
$638$	0.348008	0.0137778
$639$	−17.6258	−0.697267
$640$	2.12930	0.0841680
$641$	16.3878	0.647278	0.323639	−	0.946181i	$-0.395094\pi$
$641$	16.3878	0.647278	0.323639	+	0.946181i	$0.395094\pi$
$642$	−27.2284	−1.07462
$643$	21.6475	0.853692	0.426846	−	0.904324i	$-0.359625\pi$
$643$	21.6475	0.853692	0.426846	+	0.904324i	$0.359625\pi$
$644$	−7.41894	−0.292347
$645$	59.1410	2.32868
$646$	2.07264	0.0815470
$647$	−11.1367	−0.437830	−0.218915	−	0.975744i	$-0.570252\pi$
$647$	−11.1367	−0.437830	−0.218915	+	0.975744i	$0.570252\pi$
$648$	7.57709	0.297656
$649$	38.9106	1.52737
$650$	1.37048	0.0537546
$651$	20.2687	0.794394
$652$	3.78720	0.148318
$653$	−13.0889	−0.512207	−0.256104	−	0.966649i	$-0.582439\pi$
$653$	−13.0889	−0.512207	−0.256104	+	0.966649i	$0.582439\pi$
$654$	2.19595	0.0858684
$655$	−3.79606	−0.148325
$656$	7.47821	0.291975
$657$	−43.4776	−1.69622
$658$	−11.2025	−0.436721
$659$	2.78635	0.108541	0.0542704	−	0.998526i	$-0.482717\pi$
$659$	2.78635	0.108541	0.0542704	+	0.998526i	$0.482717\pi$
$660$	−16.5386	−0.643763
$661$	45.7348	1.77888	0.889438	−	0.457056i	$-0.151096\pi$
$661$	45.7348	1.77888	0.889438	+	0.457056i	$0.151096\pi$
$662$	−29.2281	−1.13598
$663$	3.82775	0.148657
$664$	−3.76008	−0.145920
$665$	10.3391	0.400933
$666$	−3.84262	−0.148899
$667$	0.699393	0.0270806
$668$	0.835722	0.0323350
$669$	25.7868	0.996976
$670$	6.80515	0.262906
$671$	−25.2904	−0.976326
$672$	−3.04963	−0.117642
$673$	−25.1312	−0.968736	−0.484368	−	0.874864i	$-0.660950\pi$
$673$	−25.1312	−0.968736	−0.484368	+	0.874864i	$0.660950\pi$
$674$	4.99392	0.192359
$675$	0.491702	0.0189256
$676$	−4.35359	−0.167446
$677$	19.2415	0.739512	0.369756	−	0.929129i	$-0.379441\pi$
$677$	19.2415	0.739512	0.369756	+	0.929129i	$0.379441\pi$
$678$	47.1862	1.81218
$679$	−21.9056	−0.840661
$680$	−1.09424	−0.0419623
$681$	−23.2009	−0.889060
$682$	20.3794	0.780368
$683$	42.2614	1.61709	0.808544	−	0.588435i	$-0.200256\pi$
$683$	42.2614	1.61709	0.808544	+	0.588435i	$0.200256\pi$
$684$	13.7793	0.526864
$685$	36.5173	1.39525
$686$	−15.1099	−0.576899
$687$	18.3056	0.698403
$688$	10.9649	0.418031
$689$	−1.85979	−0.0708523
$690$	−33.2376	−1.26533
$691$	33.6529	1.28022	0.640109	−	0.768284i	$-0.278889\pi$
$691$	33.6529	1.28022	0.640109	+	0.768284i	$0.278889\pi$
$692$	−17.9559	−0.682580
$693$	12.6122	0.479097
$694$	−1.46788	−0.0557198
$695$	48.7615	1.84963
$696$	0.287492	0.0108974
$697$	−3.84304	−0.145565
$698$	6.77065	0.256273
$699$	28.3527	1.07240
$700$	0.561116	0.0212082
$701$	12.2484	0.462614	0.231307	−	0.972881i	$-0.425700\pi$
$701$	12.2484	0.462614	0.231307	+	0.972881i	$0.425700\pi$
$702$	3.10217	0.117084
$703$	4.53623	0.171087
$704$	−3.06628	−0.115565
$705$	−50.1885	−1.89021
$706$	29.8279	1.12259
$707$	−15.1118	−0.568337
$708$	32.1443	1.20806
$709$	9.34150	0.350827	0.175414	−	0.984495i	$-0.443874\pi$
$709$	9.34150	0.350827	0.175414	+	0.984495i	$0.443874\pi$
$710$	−10.9852	−0.412267
$711$	22.6965	0.851186
$712$	5.64721	0.211638
$713$	40.9566	1.53384
$714$	1.56720	0.0586509
$715$	19.1985	0.717983
$716$	−15.0728	−0.563297
$717$	−34.0078	−1.27005
$718$	−2.57061	−0.0959343
$719$	−14.8460	−0.553663	−0.276832	−	0.960918i	$-0.589284\pi$
$719$	−14.8460	−0.553663	−0.276832	+	0.960918i	$0.589284\pi$
$720$	−7.27473	−0.271113
$721$	5.32856	0.198446
$722$	2.73349	0.101730
$723$	32.7813	1.21915
$724$	−0.830708	−0.0308730
$725$	−0.0528971	−0.00196455
$726$	−4.04763	−0.150222
$727$	19.9246	0.738963	0.369482	−	0.929238i	$-0.379535\pi$
$727$	19.9246	0.738963	0.369482	+	0.929238i	$0.379535\pi$
$728$	3.54011	0.131205
$729$	−33.9041	−1.25571
$730$	−27.0972	−1.00291
$731$	−5.63482	−0.208411
$732$	−20.8926	−0.772213
$733$	14.8687	0.549189	0.274594	−	0.961560i	$-0.411456\pi$
$733$	14.8687	0.549189	0.274594	+	0.961560i	$0.411456\pi$
$734$	−24.4069	−0.900874
$735$	−29.9381	−1.10428
$736$	−6.16231	−0.227146
$737$	−9.79969	−0.360976
$738$	−25.5492	−0.940479
$739$	39.0133	1.43513	0.717565	−	0.696492i	$-0.245257\pi$
$739$	39.0133	1.43513	0.717565	+	0.696492i	$0.245257\pi$
$740$	−2.39489	−0.0880378
$741$	−30.0410	−1.10358
$742$	−0.761454	−0.0279539
$743$	30.8331	1.13116	0.565578	−	0.824695i	$-0.308653\pi$
$743$	30.8331	1.13116	0.565578	+	0.824695i	$0.308653\pi$
$744$	16.8356	0.617223
$745$	−8.12400	−0.297640
$746$	15.3279	0.561195
$747$	12.8463	0.470020
$748$	1.57576	0.0576154
$749$	12.9411	0.472858
$750$	29.4823	1.07654
$751$	−34.8453	−1.27152	−0.635762	−	0.771885i	$-0.719314\pi$
$751$	−34.8453	−1.27152	−0.635762	+	0.771885i	$0.719314\pi$
$752$	−9.30504	−0.339320
$753$	−73.7595	−2.68795
$754$	−0.333730	−0.0121537
$755$	−5.61271	−0.204267
$756$	1.27012	0.0461939
$757$	41.4239	1.50558	0.752789	−	0.658261i	$-0.228708\pi$
$757$	41.4239	1.50558	0.752789	+	0.658261i	$0.228708\pi$
$758$	22.1185	0.803380
$759$	47.8635	1.73734
$760$	8.58785	0.311514
$761$	−6.14816	−0.222871	−0.111435	−	0.993772i	$-0.535545\pi$
$761$	−6.14816	−0.222871	−0.111435	+	0.993772i	$0.535545\pi$
$762$	33.4634	1.21225
$763$	−1.04369	−0.0377841
$764$	1.57893	0.0571237
$765$	3.73847	0.135165
$766$	20.8364	0.752849
$767$	−37.3142	−1.34734
$768$	−2.53308	−0.0914046
$769$	−49.1402	−1.77204	−0.886020	−	0.463647i	$-0.846541\pi$
$769$	−49.1402	−1.77204	−0.886020	+	0.463647i	$0.846541\pi$
$770$	7.86045	0.283271
$771$	3.88452	0.139898
$772$	2.09273	0.0753190
$773$	40.0773	1.44148	0.720741	−	0.693205i	$-0.243802\pi$
$773$	40.0773	1.44148	0.720741	+	0.693205i	$0.243802\pi$
$774$	−37.4613	−1.34652
$775$	−3.09766	−0.111271
$776$	−18.1952	−0.653171
$777$	3.43000	0.123051
$778$	5.44060	0.195055
$779$	30.1609	1.08063
$780$	15.8600	0.567880
$781$	15.8191	0.566053
$782$	3.16680	0.113245
$783$	−0.119736	−0.00427902
$784$	−5.55057	−0.198235
$785$	25.8507	0.922652
$786$	4.51591	0.161077
$787$	−53.7358	−1.91547	−0.957737	−	0.287645i	$-0.907128\pi$
$787$	−53.7358	−1.91547	−0.957737	+	0.287645i	$0.907128\pi$
$788$	13.2338	0.471434
$789$	−26.8110	−0.954496
$790$	14.1455	0.503273
$791$	−22.4267	−0.797401
$792$	10.4759	0.372245
$793$	24.2528	0.861242
$794$	23.7638	0.843347
$795$	−3.41139	−0.120990
$796$	12.5057	0.443251
$797$	23.6070	0.836204	0.418102	−	0.908400i	$-0.362695\pi$
$797$	23.6070	0.836204	0.418102	+	0.908400i	$0.362695\pi$
$798$	−12.2997	−0.435404
$799$	4.78184	0.169169
$800$	0.466073	0.0164782
$801$	−19.2936	−0.681706
$802$	−3.18365	−0.112418
$803$	39.0210	1.37702
$804$	−8.09560	−0.285510
$805$	15.7972	0.556777
$806$	−19.5433	−0.688383
$807$	42.8989	1.51011
$808$	−12.5521	−0.441583
$809$	−53.7426	−1.88949	−0.944745	−	0.327806i	$-0.893691\pi$
$809$	−53.7426	−1.88949	−0.944745	+	0.327806i	$0.893691\pi$
$810$	−16.1339	−0.566888
$811$	7.63651	0.268154	0.134077	−	0.990971i	$-0.457193\pi$
$811$	7.63651	0.268154	0.134077	+	0.990971i	$0.457193\pi$
$812$	−0.136639	−0.00479510
$813$	−71.6587	−2.51318
$814$	3.44874	0.120878
$815$	−8.06409	−0.282473
$816$	1.30174	0.0455701
$817$	44.2232	1.54717
$818$	−28.8154	−1.00751
$819$	−12.0947	−0.422624
$820$	−15.9234	−0.556068
$821$	12.1277	0.423261	0.211630	−	0.977350i	$-0.432123\pi$
$821$	12.1277	0.423261	0.211630	+	0.977350i	$0.432123\pi$
$822$	−43.4420	−1.51521
$823$	−20.9603	−0.730630	−0.365315	−	0.930884i	$-0.619039\pi$
$823$	−20.9603	−0.730630	−0.365315	+	0.930884i	$0.619039\pi$
$824$	4.42601	0.154187
$825$	−3.62005	−0.126034
$826$	−15.2776	−0.531574
$827$	14.3923	0.500469	0.250235	−	0.968185i	$-0.419492\pi$
$827$	14.3923	0.500469	0.250235	+	0.968185i	$0.419492\pi$
$828$	21.0534	0.731658
$829$	15.1220	0.525210	0.262605	−	0.964903i	$-0.415418\pi$
$829$	15.1220	0.525210	0.262605	+	0.964903i	$0.415418\pi$
$830$	8.00635	0.277905
$831$	−2.54316	−0.0882213
$832$	2.94048	0.101943
$833$	2.85243	0.0988308
$834$	−58.0080	−2.00865
$835$	−1.77950	−0.0615823
$836$	−12.3669	−0.427717
$837$	−7.01176	−0.242362
$838$	−25.0695	−0.866012
$839$	20.6046	0.711349	0.355675	−	0.934610i	$-0.384251\pi$
$839$	20.6046	0.711349	0.355675	+	0.934610i	$0.384251\pi$
$840$	6.49358	0.224050
$841$	−28.9871	−0.999556
$842$	−21.7468	−0.749443
$843$	56.8905	1.95941
$844$	−21.2655	−0.731987
$845$	9.27010	0.318901
$846$	31.7905	1.09298
$847$	1.92376	0.0661011
$848$	−0.632478	−0.0217194
$849$	−26.8721	−0.922249
$850$	−0.239514	−0.00821527
$851$	6.93093	0.237589
$852$	13.0683	0.447712
$853$	−38.1574	−1.30648	−0.653242	−	0.757150i	$-0.726591\pi$
$853$	−38.1574	−1.30648	−0.653242	+	0.757150i	$0.726591\pi$
$854$	9.92984	0.339792
$855$	−29.3403	−1.00342
$856$	10.7491	0.367398
$857$	14.0341	0.479396	0.239698	−	0.970848i	$-0.422952\pi$
$857$	14.0341	0.479396	0.239698	+	0.970848i	$0.422952\pi$
$858$	−22.8391	−0.779714
$859$	−23.4889	−0.801432	−0.400716	−	0.916202i	$-0.631239\pi$
$859$	−23.4889	−0.801432	−0.400716	+	0.916202i	$0.631239\pi$
$860$	−23.3475	−0.796143
$861$	22.8058	0.777218
$862$	10.2615	0.349508
$863$	7.95156	0.270674	0.135337	−	0.990800i	$-0.456788\pi$
$863$	7.95156	0.270674	0.135337	+	0.990800i	$0.456788\pi$
$864$	1.05499	0.0358914
$865$	38.2335	1.29998
$866$	−17.4472	−0.592879
$867$	42.3934	1.43975
$868$	−8.00162	−0.271593
$869$	−20.3701	−0.691007
$870$	−0.612158	−0.0207541
$871$	9.39763	0.318427
$872$	−0.866909	−0.0293572
$873$	62.1638	2.10392
$874$	−24.8537	−0.840689
$875$	−14.0123	−0.473704
$876$	32.2355	1.08914
$877$	−15.2971	−0.516546	−0.258273	−	0.966072i	$-0.583153\pi$
$877$	−15.2971	−0.516546	−0.258273	+	0.966072i	$0.583153\pi$
$878$	38.6564	1.30459
$879$	5.53973	0.186851
$880$	6.52904	0.220094
$881$	−53.1095	−1.78931	−0.894653	−	0.446762i	$-0.852577\pi$
$881$	−53.1095	−1.78931	−0.894653	+	0.446762i	$0.852577\pi$
$882$	18.9634	0.638532
$883$	−33.1576	−1.11584	−0.557920	−	0.829894i	$-0.688401\pi$
$883$	−33.1576	−1.11584	−0.557920	+	0.829894i	$0.688401\pi$
$884$	−1.51111	−0.0508240
$885$	−68.4450	−2.30075
$886$	−28.1368	−0.945275
$887$	−30.1350	−1.01184	−0.505918	−	0.862582i	$-0.668846\pi$
$887$	−30.1350	−1.01184	−0.505918	+	0.862582i	$0.668846\pi$
$888$	2.84903	0.0956071
$889$	−15.9045	−0.533419
$890$	−12.0246	−0.403066
$891$	23.2335	0.778351
$892$	−10.1800	−0.340853
$893$	−37.5289	−1.25586
$894$	9.66454	0.323231
$895$	32.0946	1.07280
$896$	1.20392	0.0402202
$897$	−45.8998	−1.53255
$898$	21.8623	0.729553
$899$	0.754323	0.0251581
$900$	−1.59233	−0.0530777
$901$	0.325029	0.0108283
$902$	22.9303	0.763496
$903$	33.4387	1.11277
$904$	−18.6280	−0.619559
$905$	1.76883	0.0587978
$906$	6.67704	0.221830
$907$	28.3830	0.942441	0.471220	−	0.882016i	$-0.343814\pi$
$907$	28.3830	0.942441	0.471220	+	0.882016i	$0.343814\pi$
$908$	9.15917	0.303958
$909$	42.8842	1.42238
$910$	−7.53795	−0.249881
$911$	−31.4396	−1.04164	−0.520820	−	0.853667i	$-0.674374\pi$
$911$	−31.4396	−1.04164	−0.520820	+	0.853667i	$0.674374\pi$
$912$	−10.2163	−0.338297
$913$	−11.5295	−0.381570
$914$	−12.9541	−0.428483
$915$	44.4867	1.47068
$916$	−7.22664	−0.238775
$917$	−2.14632	−0.0708777
$918$	−0.542156	−0.0178938
$919$	−27.8992	−0.920309	−0.460155	−	0.887839i	$-0.652206\pi$
$919$	−27.8992	−0.920309	−0.460155	+	0.887839i	$0.652206\pi$
$920$	13.1214	0.432601
$921$	−63.0382	−2.07718
$922$	15.9404	0.524968
$923$	−15.1701	−0.499330
$924$	−9.35102	−0.307626
$925$	−0.524206	−0.0172358
$926$	−39.4991	−1.29802
$927$	−15.1214	−0.496651
$928$	−0.113495	−0.00372566
$929$	−1.36636	−0.0448289	−0.0224144	−	0.999749i	$-0.507135\pi$
$929$	−1.36636	−0.0448289	−0.0224144	+	0.999749i	$0.507135\pi$
$930$	−35.8480	−1.17550
$931$	−22.3864	−0.733686
$932$	−11.1930	−0.366639
$933$	5.92613	0.194013
$934$	−32.1352	−1.05149
$935$	−3.35526	−0.109729
$936$	−10.0461	−0.328367
$937$	−7.59756	−0.248201	−0.124101	−	0.992270i	$-0.539605\pi$
$937$	−7.59756	−0.248201	−0.124101	+	0.992270i	$0.539605\pi$
$938$	3.84768	0.125631
$939$	24.3081	0.793266
$940$	19.8132	0.646237
$941$	9.74433	0.317656	0.158828	−	0.987306i	$-0.449228\pi$
$941$	9.74433	0.317656	0.158828	+	0.987306i	$0.449228\pi$
$942$	−30.7528	−1.00198
$943$	46.0831	1.50067
$944$	−12.6898	−0.413019
$945$	−2.70447	−0.0879765
$946$	33.6214	1.09312
$947$	43.7432	1.42146	0.710732	−	0.703463i	$-0.248364\pi$
$947$	43.7432	1.42146	0.710732	+	0.703463i	$0.248364\pi$
$948$	−16.8278	−0.546543
$949$	−37.4201	−1.21471
$950$	1.87976	0.0609873
$951$	−82.4801	−2.67460
$952$	−0.618693	−0.0200519
$953$	1.73391	0.0561670	0.0280835	−	0.999606i	$-0.491060\pi$
$953$	1.73391	0.0561670	0.0280835	+	0.999606i	$0.491060\pi$
$954$	2.16085	0.0699602
$955$	−3.36202	−0.108792
$956$	13.4255	0.434212
$957$	0.881533	0.0284959
$958$	−11.1418	−0.359975
$959$	20.6471	0.666730
$960$	5.39369	0.174081
$961$	13.1732	0.424943
$962$	−3.30724	−0.106630
$963$	−36.7242	−1.18342
$964$	−12.9413	−0.416810
$965$	−4.45605	−0.143445
$966$	−18.7928	−0.604647
$967$	45.9708	1.47832	0.739161	−	0.673529i	$-0.235222\pi$
$967$	45.9708	1.47832	0.739161	+	0.673529i	$0.235222\pi$
$968$	1.59791	0.0513587
$969$	5.25016	0.168659
$970$	38.7432	1.24397
$971$	−14.1606	−0.454437	−0.227218	−	0.973844i	$-0.572963\pi$
$971$	−14.1606	−0.454437	−0.227218	+	0.973844i	$0.572963\pi$
$972$	22.3583	0.717143
$973$	27.5701	0.883855
$974$	17.9409	0.574862
$975$	3.47153	0.111178
$976$	8.24791	0.264009
$977$	43.6485	1.39644	0.698220	−	0.715883i	$-0.253976\pi$
$977$	43.6485	1.39644	0.698220	+	0.715883i	$0.253976\pi$
$978$	9.59327	0.306759
$979$	17.3159	0.553420
$980$	11.8188	0.377539
$981$	2.96178	0.0945624
$982$	40.9212	1.30585
$983$	33.2087	1.05919	0.529597	−	0.848250i	$-0.322343\pi$
$983$	33.2087	1.05919	0.529597	+	0.848250i	$0.322343\pi$
$984$	18.9429	0.603877
$985$	−28.1787	−0.897849
$986$	0.0583250	0.00185745
$987$	−28.3769	−0.903247
$988$	11.8595	0.377300
$989$	67.5689	2.14857
$990$	−22.3064	−0.708943
$991$	−3.34825	−0.106361	−0.0531803	−	0.998585i	$-0.516936\pi$
$991$	−3.34825	−0.106361	−0.0531803	+	0.998585i	$0.516936\pi$
$992$	−6.64630	−0.211020
$993$	−74.0370	−2.34949
$994$	−6.21110	−0.197004
$995$	−26.6283	−0.844174
$996$	−9.52458	−0.301798
$997$	−56.1298	−1.77765	−0.888825	−	0.458247i	$-0.848477\pi$
$997$	−56.1298	−1.77765	−0.888825	+	0.458247i	$0.848477\pi$
$998$	23.3987	0.740672
$999$	−1.18658	−0.0375416

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	8042.2.a.c.1.10	✓	86

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
8042.2.a.c.1.10	✓	86	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:	\( N \)	\(=\)	\( 8042 = 2 \cdot 4021 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	8042.a (trivial)

\(f(q)\)	\(=\)	\(q-1.00000 q^{2} -2.53308 q^{3} +1.00000 q^{4} -2.12930 q^{5} +2.53308 q^{6} -1.20392 q^{7} -1.00000 q^{8} +3.41648 q^{9} +O(q^{10})\)	\(q-1.00000 q^{2} -2.53308 q^{3} +1.00000 q^{4} -2.12930 q^{5} +2.53308 q^{6} -1.20392 q^{7} -1.00000 q^{8} +3.41648 q^{9} +2.12930 q^{10} -3.06628 q^{11} -2.53308 q^{12} +2.94048 q^{13} +1.20392 q^{14} +5.39369 q^{15} +1.00000 q^{16} -0.513898 q^{17} -3.41648 q^{18} +4.03318 q^{19} -2.12930 q^{20} +3.04963 q^{21} +3.06628 q^{22} +6.16231 q^{23} +2.53308 q^{24} -0.466073 q^{25} -2.94048 q^{26} -1.05499 q^{27} -1.20392 q^{28} +0.113495 q^{29} -5.39369 q^{30} +6.64630 q^{31} -1.00000 q^{32} +7.76713 q^{33} +0.513898 q^{34} +2.56351 q^{35} +3.41648 q^{36} +1.12473 q^{37} -4.03318 q^{38} -7.44846 q^{39} +2.12930 q^{40} +7.47821 q^{41} -3.04963 q^{42} +10.9649 q^{43} -3.06628 q^{44} -7.27473 q^{45} -6.16231 q^{46} -9.30504 q^{47} -2.53308 q^{48} -5.55057 q^{49} +0.466073 q^{50} +1.30174 q^{51} +2.94048 q^{52} -0.632478 q^{53} +1.05499 q^{54} +6.52904 q^{55} +1.20392 q^{56} -10.2163 q^{57} -0.113495 q^{58} -12.6898 q^{59} +5.39369 q^{60} +8.24791 q^{61} -6.64630 q^{62} -4.11318 q^{63} +1.00000 q^{64} -6.26117 q^{65} -7.76713 q^{66} +3.19595 q^{67} -0.513898 q^{68} -15.6096 q^{69} -2.56351 q^{70} -5.15906 q^{71} -3.41648 q^{72} -12.7258 q^{73} -1.12473 q^{74} +1.18060 q^{75} +4.03318 q^{76} +3.69156 q^{77} +7.44846 q^{78} +6.64324 q^{79} -2.12930 q^{80} -7.57709 q^{81} -7.47821 q^{82} +3.76008 q^{83} +3.04963 q^{84} +1.09424 q^{85} -10.9649 q^{86} -0.287492 q^{87} +3.06628 q^{88} -5.64721 q^{89} +7.27473 q^{90} -3.54011 q^{91} +6.16231 q^{92} -16.8356 q^{93} +9.30504 q^{94} -8.58785 q^{95} +2.53308 q^{96} +18.1952 q^{97} +5.55057 q^{98} -10.4759 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 86 q - 86 q^{2} + 12 q^{3} + 86 q^{4} - 4 q^{5} - 12 q^{6} + 35 q^{7} - 86 q^{8} + 72 q^{9}+O(q^{10}) \) 86 * q - 86 * q^2 + 12 * q^3 + 86 * q^4 - 4 * q^5 - 12 * q^6 + 35 * q^7 - 86 * q^8 + 72 * q^9	\( 86 q - 86 q^{2} + 12 q^{3} + 86 q^{4} - 4 q^{5} - 12 q^{6} + 35 q^{7} - 86 q^{8} + 72 q^{9} + 4 q^{10} + 13 q^{11} + 12 q^{12} + 45 q^{13} - 35 q^{14} + 17 q^{15} + 86 q^{16} + 5 q^{17} - 72 q^{18} + 47 q^{19} - 4 q^{20} + 15 q^{21} - 13 q^{22} + 6 q^{23} - 12 q^{24} + 112 q^{25} - 45 q^{26} + 51 q^{27} + 35 q^{28} - 14 q^{29} - 17 q^{30} + 24 q^{31} - 86 q^{32} + 43 q^{33} - 5 q^{34} + 42 q^{35} + 72 q^{36} + 61 q^{37} - 47 q^{38} + 20 q^{39} + 4 q^{40} - 16 q^{41} - 15 q^{42} + 72 q^{43} + 13 q^{44} + 6 q^{45} - 6 q^{46} + 11 q^{47} + 12 q^{48} + 89 q^{49} - 112 q^{50} + 56 q^{51} + 45 q^{52} - 7 q^{53} - 51 q^{54} + 48 q^{55} - 35 q^{56} + 65 q^{57} + 14 q^{58} + 24 q^{59} + 17 q^{60} + 31 q^{61} - 24 q^{62} + 98 q^{63} + 86 q^{64} - 9 q^{65} - 43 q^{66} + 157 q^{67} + 5 q^{68} + q^{69} - 42 q^{70} - 11 q^{71} - 72 q^{72} + 74 q^{73} - 61 q^{74} + 76 q^{75} + 47 q^{76} - 13 q^{77} - 20 q^{78} + 57 q^{79} - 4 q^{80} + 34 q^{81} + 16 q^{82} + 65 q^{83} + 15 q^{84} + 102 q^{85} - 72 q^{86} + 49 q^{87} - 13 q^{88} - 34 q^{89} - 6 q^{90} + 91 q^{91} + 6 q^{92} + 57 q^{93} - 11 q^{94} - 13 q^{95} - 12 q^{96} + 64 q^{97} - 89 q^{98} + 56 q^{99}+O(q^{100}) \) 86 * q - 86 * q^2 + 12 * q^3 + 86 * q^4 - 4 * q^5 - 12 * q^6 + 35 * q^7 - 86 * q^8 + 72 * q^9 + 4 * q^10 + 13 * q^11 + 12 * q^12 + 45 * q^13 - 35 * q^14 + 17 * q^15 + 86 * q^16 + 5 * q^17 - 72 * q^18 + 47 * q^19 - 4 * q^20 + 15 * q^21 - 13 * q^22 + 6 * q^23 - 12 * q^24 + 112 * q^25 - 45 * q^26 + 51 * q^27 + 35 * q^28 - 14 * q^29 - 17 * q^30 + 24 * q^31 - 86 * q^32 + 43 * q^33 - 5 * q^34 + 42 * q^35 + 72 * q^36 + 61 * q^37 - 47 * q^38 + 20 * q^39 + 4 * q^40 - 16 * q^41 - 15 * q^42 + 72 * q^43 + 13 * q^44 + 6 * q^45 - 6 * q^46 + 11 * q^47 + 12 * q^48 + 89 * q^49 - 112 * q^50 + 56 * q^51 + 45 * q^52 - 7 * q^53 - 51 * q^54 + 48 * q^55 - 35 * q^56 + 65 * q^57 + 14 * q^58 + 24 * q^59 + 17 * q^60 + 31 * q^61 - 24 * q^62 + 98 * q^63 + 86 * q^64 - 9 * q^65 - 43 * q^66 + 157 * q^67 + 5 * q^68 + q^69 - 42 * q^70 - 11 * q^71 - 72 * q^72 + 74 * q^73 - 61 * q^74 + 76 * q^75 + 47 * q^76 - 13 * q^77 - 20 * q^78 + 57 * q^79 - 4 * q^80 + 34 * q^81 + 16 * q^82 + 65 * q^83 + 15 * q^84 + 102 * q^85 - 72 * q^86 + 49 * q^87 - 13 * q^88 - 34 * q^89 - 6 * q^90 + 91 * q^91 + 6 * q^92 + 57 * q^93 - 11 * q^94 - 13 * q^95 - 12 * q^96 + 64 * q^97 - 89 * q^98 + 56 * q^99

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