LMFDB - Embedded newform 4006.2.a.h.1.19

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [4006,2,Mod(1,4006)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(4006, 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("4006.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 4006 = 2 \cdot 2003 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	4006.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:	$31.9880710497$
Analytic rank:	$0$
Dimension:	$42$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.19
Character	$\chi$	$=$	4006.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.00000 q^{2} -0.372757 q^{3} +1.00000 q^{4} +3.67312 q^{5} +0.372757 q^{6} -1.58044 q^{7} -1.00000 q^{8} -2.86105 q^{9} +O(q^{10})$	\(q-1.00000 q^{2} -0.372757 q^{3} +1.00000 q^{4} +3.67312 q^{5} +0.372757 q^{6} -1.58044 q^{7} -1.00000 q^{8} -2.86105 q^{9} -3.67312 q^{10} +4.52999 q^{11} -0.372757 q^{12} +0.887618 q^{13} +1.58044 q^{14} -1.36918 q^{15} +1.00000 q^{16} +4.72698 q^{17} +2.86105 q^{18} +3.99036 q^{19} +3.67312 q^{20} +0.589120 q^{21} -4.52999 q^{22} -0.0615527 q^{23} +0.372757 q^{24} +8.49183 q^{25} -0.887618 q^{26} +2.18475 q^{27} -1.58044 q^{28} +6.70317 q^{29} +1.36918 q^{30} -6.74091 q^{31} -1.00000 q^{32} -1.68859 q^{33} -4.72698 q^{34} -5.80515 q^{35} -2.86105 q^{36} +1.66615 q^{37} -3.99036 q^{38} -0.330865 q^{39} -3.67312 q^{40} -4.78498 q^{41} -0.589120 q^{42} +10.7939 q^{43} +4.52999 q^{44} -10.5090 q^{45} +0.0615527 q^{46} -6.44691 q^{47} -0.372757 q^{48} -4.50221 q^{49} -8.49183 q^{50} -1.76202 q^{51} +0.887618 q^{52} -4.13142 q^{53} -2.18475 q^{54} +16.6392 q^{55} +1.58044 q^{56} -1.48743 q^{57} -6.70317 q^{58} -2.76939 q^{59} -1.36918 q^{60} -1.94029 q^{61} +6.74091 q^{62} +4.52173 q^{63} +1.00000 q^{64} +3.26033 q^{65} +1.68859 q^{66} +7.36958 q^{67} +4.72698 q^{68} +0.0229442 q^{69} +5.80515 q^{70} -7.68364 q^{71} +2.86105 q^{72} -3.88097 q^{73} -1.66615 q^{74} -3.16538 q^{75} +3.99036 q^{76} -7.15939 q^{77} +0.330865 q^{78} +8.77117 q^{79} +3.67312 q^{80} +7.76878 q^{81} +4.78498 q^{82} -2.92081 q^{83} +0.589120 q^{84} +17.3628 q^{85} -10.7939 q^{86} -2.49865 q^{87} -4.52999 q^{88} +7.29561 q^{89} +10.5090 q^{90} -1.40283 q^{91} -0.0615527 q^{92} +2.51272 q^{93} +6.44691 q^{94} +14.6571 q^{95} +0.372757 q^{96} +9.38686 q^{97} +4.50221 q^{98} -12.9605 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 42 q - 42 q^{2} + 42 q^{4} + 27 q^{5} - 10 q^{7} - 42 q^{8} + 56 q^{9}+O(q^{10}) $ 42 * q - 42 * q^2 + 42 * q^4 + 27 * q^5 - 10 * q^7 - 42 * q^8 + 56 * q^9	\( 42 q - 42 q^{2} + 42 q^{4} + 27 q^{5} - 10 q^{7} - 42 q^{8} + 56 q^{9} - 27 q^{10} + 23 q^{11} + 15 q^{13} + 10 q^{14} + 6 q^{15} + 42 q^{16} + 14 q^{17} - 56 q^{18} - 4 q^{19} + 27 q^{20} + 26 q^{21} - 23 q^{22} + 12 q^{23} + 45 q^{25} - 15 q^{26} - 3 q^{27} - 10 q^{28} + 41 q^{29} - 6 q^{30} + 18 q^{31} - 42 q^{32} + 25 q^{33} - 14 q^{34} + 8 q^{35} + 56 q^{36} + 33 q^{37} + 4 q^{38} + 10 q^{39} - 27 q^{40} + 84 q^{41} - 26 q^{42} - 36 q^{43} + 23 q^{44} + 66 q^{45} - 12 q^{46} + 28 q^{47} + 58 q^{49} - 45 q^{50} + 17 q^{51} + 15 q^{52} + 68 q^{53} + 3 q^{54} - 28 q^{55} + 10 q^{56} - 9 q^{57} - 41 q^{58} + 59 q^{59} + 6 q^{60} + 41 q^{61} - 18 q^{62} - 28 q^{63} + 42 q^{64} + 44 q^{65} - 25 q^{66} + 14 q^{68} + 67 q^{69} - 8 q^{70} + 69 q^{71} - 56 q^{72} - 27 q^{73} - 33 q^{74} + 14 q^{75} - 4 q^{76} + 43 q^{77} - 10 q^{78} - 19 q^{79} + 27 q^{80} + 74 q^{81} - 84 q^{82} + 20 q^{83} + 26 q^{84} + 16 q^{85} + 36 q^{86} - 28 q^{87} - 23 q^{88} + 123 q^{89} - 66 q^{90} - 9 q^{91} + 12 q^{92} + 48 q^{93} - 28 q^{94} + 28 q^{95} + 10 q^{97} - 58 q^{98} + 75 q^{99}+O(q^{100}) \) 42 * q - 42 * q^2 + 42 * q^4 + 27 * q^5 - 10 * q^7 - 42 * q^8 + 56 * q^9 - 27 * q^10 + 23 * q^11 + 15 * q^13 + 10 * q^14 + 6 * q^15 + 42 * q^16 + 14 * q^17 - 56 * q^18 - 4 * q^19 + 27 * q^20 + 26 * q^21 - 23 * q^22 + 12 * q^23 + 45 * q^25 - 15 * q^26 - 3 * q^27 - 10 * q^28 + 41 * q^29 - 6 * q^30 + 18 * q^31 - 42 * q^32 + 25 * q^33 - 14 * q^34 + 8 * q^35 + 56 * q^36 + 33 * q^37 + 4 * q^38 + 10 * q^39 - 27 * q^40 + 84 * q^41 - 26 * q^42 - 36 * q^43 + 23 * q^44 + 66 * q^45 - 12 * q^46 + 28 * q^47 + 58 * q^49 - 45 * q^50 + 17 * q^51 + 15 * q^52 + 68 * q^53 + 3 * q^54 - 28 * q^55 + 10 * q^56 - 9 * q^57 - 41 * q^58 + 59 * q^59 + 6 * q^60 + 41 * q^61 - 18 * q^62 - 28 * q^63 + 42 * q^64 + 44 * q^65 - 25 * q^66 + 14 * q^68 + 67 * q^69 - 8 * q^70 + 69 * q^71 - 56 * q^72 - 27 * q^73 - 33 * q^74 + 14 * q^75 - 4 * q^76 + 43 * q^77 - 10 * q^78 - 19 * q^79 + 27 * q^80 + 74 * q^81 - 84 * q^82 + 20 * q^83 + 26 * q^84 + 16 * q^85 + 36 * q^86 - 28 * q^87 - 23 * q^88 + 123 * q^89 - 66 * q^90 - 9 * q^91 + 12 * q^92 + 48 * q^93 - 28 * q^94 + 28 * q^95 + 10 * q^97 - 58 * q^98 + 75 * 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
$3$	−0.372757	−0.215211	−0.107606	−	0.994194i	$-0.534318\pi$
$3$	−0.372757	−0.215211	−0.107606	+	0.994194i	$0.534318\pi$
$4$	1.00000	0.500000
$5$	3.67312	1.64267	0.821335	−	0.570446i	$-0.193230\pi$
$5$	3.67312	1.64267	0.821335	+	0.570446i	$0.193230\pi$
$6$	0.372757	0.152177
$7$	−1.58044	−0.597351	−0.298675	−	0.954355i	$-0.596545\pi$
$7$	−1.58044	−0.597351	−0.298675	+	0.954355i	$0.596545\pi$
$8$	−1.00000	−0.353553
$9$	−2.86105	−0.953684
$10$	−3.67312	−1.16154
$11$	4.52999	1.36584	0.682922	−	0.730491i	$-0.260709\pi$
$11$	4.52999	1.36584	0.682922	+	0.730491i	$0.260709\pi$
$12$	−0.372757	−0.107606
$13$	0.887618	0.246181	0.123090	−	0.992395i	$-0.460719\pi$
$13$	0.887618	0.246181	0.123090	+	0.992395i	$0.460719\pi$
$14$	1.58044	0.422391
$15$	−1.36918	−0.353521
$16$	1.00000	0.250000
$17$	4.72698	1.14646	0.573231	−	0.819394i	$-0.305690\pi$
$17$	4.72698	1.14646	0.573231	+	0.819394i	$0.305690\pi$
$18$	2.86105	0.674357
$19$	3.99036	0.915450	0.457725	−	0.889094i	$-0.348664\pi$
$19$	3.99036	0.915450	0.457725	+	0.889094i	$0.348664\pi$
$20$	3.67312	0.821335
$21$	0.589120	0.128557
$22$	−4.52999	−0.965798
$23$	−0.0615527	−0.0128346	−0.00641731	−	0.999979i	$-0.502043\pi$
$23$	−0.0615527	−0.0128346	−0.00641731	+	0.999979i	$0.502043\pi$
$24$	0.372757	0.0760886
$25$	8.49183	1.69837
$26$	−0.887618	−0.174076
$27$	2.18475	0.420455
$28$	−1.58044	−0.298675
$29$	6.70317	1.24475	0.622374	−	0.782720i	$-0.286168\pi$
$29$	6.70317	1.24475	0.622374	+	0.782720i	$0.286168\pi$
$30$	1.36918	0.249977
$31$	−6.74091	−1.21070	−0.605352	−	0.795958i	$-0.706967\pi$
$31$	−6.74091	−1.21070	−0.605352	+	0.795958i	$0.706967\pi$
$32$	−1.00000	−0.176777
$33$	−1.68859	−0.293945
$34$	−4.72698	−0.810671
$35$	−5.80515	−0.981250
$36$	−2.86105	−0.476842
$37$	1.66615	0.273913	0.136956	−	0.990577i	$-0.456268\pi$
$37$	1.66615	0.273913	0.136956	+	0.990577i	$0.456268\pi$
$38$	−3.99036	−0.647321
$39$	−0.330865	−0.0529809
$40$	−3.67312	−0.580772
$41$	−4.78498	−0.747288	−0.373644	−	0.927572i	$-0.621892\pi$
$41$	−4.78498	−0.747288	−0.373644	+	0.927572i	$0.621892\pi$
$42$	−0.589120	−0.0909032
$43$	10.7939	1.64606	0.823029	−	0.568000i	$-0.192283\pi$
$43$	10.7939	1.64606	0.823029	+	0.568000i	$0.192283\pi$
$44$	4.52999	0.682922
$45$	−10.5090	−1.56659
$46$	0.0615527	0.00907544
$47$	−6.44691	−0.940378	−0.470189	−	0.882566i	$-0.655814\pi$
$47$	−6.44691	−0.940378	−0.470189	+	0.882566i	$0.655814\pi$
$48$	−0.372757	−0.0538028
$49$	−4.50221	−0.643172
$50$	−8.49183	−1.20093
$51$	−1.76202	−0.246731
$52$	0.887618	0.123090
$53$	−4.13142	−0.567494	−0.283747	−	0.958899i	$-0.591578\pi$
$53$	−4.13142	−0.567494	−0.283747	+	0.958899i	$0.591578\pi$
$54$	−2.18475	−0.297306
$55$	16.6392	2.24363
$56$	1.58044	0.211195
$57$	−1.48743	−0.197015
$58$	−6.70317	−0.880170
$59$	−2.76939	−0.360544	−0.180272	−	0.983617i	$-0.557698\pi$
$59$	−2.76939	−0.360544	−0.180272	+	0.983617i	$0.557698\pi$
$60$	−1.36918	−0.176760
$61$	−1.94029	−0.248429	−0.124215	−	0.992255i	$-0.539641\pi$
$61$	−1.94029	−0.248429	−0.124215	+	0.992255i	$0.539641\pi$
$62$	6.74091	0.856096
$63$	4.52173	0.569684
$64$	1.00000	0.125000
$65$	3.26033	0.404394
$66$	1.68859	0.207850
$67$	7.36958	0.900337	0.450169	−	0.892944i	$-0.351364\pi$
$67$	7.36958	0.900337	0.450169	+	0.892944i	$0.351364\pi$
$68$	4.72698	0.573231
$69$	0.0229442	0.00276215
$70$	5.80515	0.693849
$71$	−7.68364	−0.911880	−0.455940	−	0.890011i	$-0.650697\pi$
$71$	−7.68364	−0.911880	−0.455940	+	0.890011i	$0.650697\pi$
$72$	2.86105	0.337178
$73$	−3.88097	−0.454233	−0.227116	−	0.973868i	$-0.572930\pi$
$73$	−3.88097	−0.454233	−0.227116	+	0.973868i	$0.572930\pi$
$74$	−1.66615	−0.193685
$75$	−3.16538	−0.365507
$76$	3.99036	0.457725
$77$	−7.15939	−0.815888
$78$	0.330865	0.0374631
$79$	8.77117	0.986833	0.493417	−	0.869793i	$-0.335748\pi$
$79$	8.77117	0.986833	0.493417	+	0.869793i	$0.335748\pi$
$80$	3.67312	0.410668
$81$	7.76878	0.863198
$82$	4.78498	0.528413
$83$	−2.92081	−0.320601	−0.160301	−	0.987068i	$-0.551246\pi$
$83$	−2.92081	−0.320601	−0.160301	+	0.987068i	$0.551246\pi$
$84$	0.589120	0.0642783
$85$	17.3628	1.88326
$86$	−10.7939	−1.16394
$87$	−2.49865	−0.267884
$88$	−4.52999	−0.482899
$89$	7.29561	0.773333	0.386666	−	0.922220i	$-0.373627\pi$
$89$	7.29561	0.773333	0.386666	+	0.922220i	$0.373627\pi$
$90$	10.5090	1.10775
$91$	−1.40283	−0.147056
$92$	−0.0615527	−0.00641731
$93$	2.51272	0.260557
$94$	6.44691	0.664948
$95$	14.6571	1.50378
$96$	0.372757	0.0380443
$97$	9.38686	0.953092	0.476546	−	0.879150i	$-0.341889\pi$
$97$	9.38686	0.953092	0.476546	+	0.879150i	$0.341889\pi$
$98$	4.50221	0.454791
$99$	−12.9605	−1.30258
$100$	8.49183	0.849183
$101$	16.7339	1.66508	0.832540	−	0.553965i	$-0.186886\pi$
$101$	16.7339	1.66508	0.832540	+	0.553965i	$0.186886\pi$
$102$	1.76202	0.174466
$103$	−4.91607	−0.484395	−0.242197	−	0.970227i	$-0.577868\pi$
$103$	−4.91607	−0.484395	−0.242197	+	0.970227i	$0.577868\pi$
$104$	−0.887618	−0.0870381
$105$	2.16391	0.211176
$106$	4.13142	0.401279
$107$	−16.5520	−1.60015	−0.800073	−	0.599902i	$-0.795206\pi$
$107$	−16.5520	−1.60015	−0.800073	+	0.599902i	$0.795206\pi$
$108$	2.18475	0.210227
$109$	11.6252	1.11349	0.556747	−	0.830682i	$-0.312049\pi$
$109$	11.6252	1.11349	0.556747	+	0.830682i	$0.312049\pi$
$110$	−16.6392	−1.58649
$111$	−0.621067	−0.0589491
$112$	−1.58044	−0.149338
$113$	−4.06170	−0.382092	−0.191046	−	0.981581i	$-0.561188\pi$
$113$	−4.06170	−0.382092	−0.191046	+	0.981581i	$0.561188\pi$
$114$	1.48743	0.139311
$115$	−0.226090	−0.0210830
$116$	6.70317	0.622374
$117$	−2.53952	−0.234779
$118$	2.76939	0.254943
$119$	−7.47072	−0.684840
$120$	1.36918	0.124989
$121$	9.52083	0.865530
$122$	1.94029	0.175666
$123$	1.78363	0.160825
$124$	−6.74091	−0.605352
$125$	12.8259	1.14718
$126$	−4.52173	−0.402827
$127$	−3.15276	−0.279762	−0.139881	−	0.990168i	$-0.544672\pi$
$127$	−3.15276	−0.279762	−0.139881	+	0.990168i	$0.544672\pi$
$128$	−1.00000	−0.0883883
$129$	−4.02351	−0.354250
$130$	−3.26033	−0.285950
$131$	8.57842	0.749500	0.374750	−	0.927126i	$-0.377729\pi$
$131$	8.57842	0.749500	0.374750	+	0.927126i	$0.377729\pi$
$132$	−1.68859	−0.146972
$133$	−6.30652	−0.546845
$134$	−7.36958	−0.636635
$135$	8.02484	0.690668
$136$	−4.72698	−0.405336
$137$	16.7504	1.43108	0.715540	−	0.698571i	$-0.246181\pi$
$137$	16.7504	1.43108	0.715540	+	0.698571i	$0.246181\pi$
$138$	−0.0229442	−0.00195314
$139$	−10.6738	−0.905338	−0.452669	−	0.891679i	$-0.649528\pi$
$139$	−10.6738	−0.905338	−0.452669	+	0.891679i	$0.649528\pi$
$140$	−5.80515	−0.490625
$141$	2.40313	0.202380
$142$	7.68364	0.644796
$143$	4.02090	0.336245
$144$	−2.86105	−0.238421
$145$	24.6216	2.04471
$146$	3.88097	0.321191
$147$	1.67823	0.138418
$148$	1.66615	0.136956
$149$	−12.4622	−1.02094	−0.510470	−	0.859896i	$-0.670528\pi$
$149$	−12.4622	−1.02094	−0.510470	+	0.859896i	$0.670528\pi$
$150$	3.16538	0.258453
$151$	11.5028	0.936086	0.468043	−	0.883706i	$-0.344959\pi$
$151$	11.5028	0.936086	0.468043	+	0.883706i	$0.344959\pi$
$152$	−3.99036	−0.323661
$153$	−13.5242	−1.09336
$154$	7.15939	0.576920
$155$	−24.7602	−1.98879
$156$	−0.330865	−0.0264904
$157$	−0.267661	−0.0213616	−0.0106808	−	0.999943i	$-0.503400\pi$
$157$	−0.267661	−0.0213616	−0.0106808	+	0.999943i	$0.503400\pi$
$158$	−8.77117	−0.697796
$159$	1.54001	0.122131
$160$	−3.67312	−0.290386
$161$	0.0972804	0.00766677
$162$	−7.76878	−0.610373
$163$	−8.27837	−0.648412	−0.324206	−	0.945987i	$-0.605097\pi$
$163$	−8.27837	−0.648412	−0.324206	+	0.945987i	$0.605097\pi$
$164$	−4.78498	−0.373644
$165$	−6.20238	−0.482855
$166$	2.92081	0.226699
$167$	−6.34469	−0.490967	−0.245484	−	0.969401i	$-0.578947\pi$
$167$	−6.34469	−0.490967	−0.245484	+	0.969401i	$0.578947\pi$
$168$	−0.589120	−0.0454516
$169$	−12.2121	−0.939395
$170$	−17.3628	−1.33167
$171$	−11.4166	−0.873050
$172$	10.7939	0.823029
$173$	16.7708	1.27506	0.637528	−	0.770427i	$-0.279957\pi$
$173$	16.7708	1.27506	0.637528	+	0.770427i	$0.279957\pi$
$174$	2.49865	0.189422
$175$	−13.4208	−1.01452
$176$	4.52999	0.341461
$177$	1.03231	0.0775931
$178$	−7.29561	−0.546829
$179$	−1.21117	−0.0905274	−0.0452637	−	0.998975i	$-0.514413\pi$
$179$	−1.21117	−0.0905274	−0.0452637	+	0.998975i	$0.514413\pi$
$180$	−10.5090	−0.783294
$181$	14.1834	1.05424	0.527121	−	0.849790i	$-0.323271\pi$
$181$	14.1834	1.05424	0.527121	+	0.849790i	$0.323271\pi$
$182$	1.40283	0.103984
$183$	0.723257	0.0534647
$184$	0.0615527	0.00453772
$185$	6.11996	0.449948
$186$	−2.51272	−0.184242
$187$	21.4132	1.56589
$188$	−6.44691	−0.470189
$189$	−3.45286	−0.251159
$190$	−14.6571	−1.06334
$191$	−10.4523	−0.756303	−0.378151	−	0.925744i	$-0.623440\pi$
$191$	−10.4523	−0.756303	−0.378151	+	0.925744i	$0.623440\pi$
$192$	−0.372757	−0.0269014
$193$	−1.21994	−0.0878129	−0.0439065	−	0.999036i	$-0.513980\pi$
$193$	−1.21994	−0.0878129	−0.0439065	+	0.999036i	$0.513980\pi$
$194$	−9.38686	−0.673938
$195$	−1.21531	−0.0870301
$196$	−4.50221	−0.321586
$197$	6.91233	0.492483	0.246241	−	0.969209i	$-0.420804\pi$
$197$	6.91233	0.492483	0.246241	+	0.969209i	$0.420804\pi$
$198$	12.9605	0.921066
$199$	15.0257	1.06514	0.532570	−	0.846386i	$-0.321226\pi$
$199$	15.0257	1.06514	0.532570	+	0.846386i	$0.321226\pi$
$200$	−8.49183	−0.600463
$201$	−2.74706	−0.193763
$202$	−16.7339	−1.17739
$203$	−10.5940	−0.743551
$204$	−1.76202	−0.123366
$205$	−17.5758	−1.22755
$206$	4.91607	0.342519
$207$	0.176105	0.0122402
$208$	0.887618	0.0615452
$209$	18.0763	1.25036
$210$	−2.16391	−0.149324
$211$	3.69475	0.254357	0.127179	−	0.991880i	$-0.459408\pi$
$211$	3.69475	0.254357	0.127179	+	0.991880i	$0.459408\pi$
$212$	−4.13142	−0.283747
$213$	2.86413	0.196247
$214$	16.5520	1.13147
$215$	39.6474	2.70393
$216$	−2.18475	−0.148653
$217$	10.6536	0.723214
$218$	−11.6252	−0.787360
$219$	1.44666	0.0977560
$220$	16.6392	1.12182
$221$	4.19575	0.282237
$222$	0.621067	0.0416833
$223$	12.6592	0.847726	0.423863	−	0.905726i	$-0.360674\pi$
$223$	12.6592	0.847726	0.423863	+	0.905726i	$0.360674\pi$
$224$	1.58044	0.105598
$225$	−24.2956	−1.61970
$226$	4.06170	0.270180
$227$	−12.9313	−0.858279	−0.429139	−	0.903238i	$-0.641183\pi$
$227$	−12.9313	−0.858279	−0.429139	+	0.903238i	$0.641183\pi$
$228$	−1.48743	−0.0985076
$229$	−5.02821	−0.332273	−0.166137	−	0.986103i	$-0.553129\pi$
$229$	−5.02821	−0.332273	−0.166137	+	0.986103i	$0.553129\pi$
$230$	0.226090	0.0149080
$231$	2.66871	0.175588
$232$	−6.70317	−0.440085
$233$	−16.0991	−1.05468	−0.527342	−	0.849653i	$-0.676811\pi$
$233$	−16.0991	−1.05468	−0.527342	+	0.849653i	$0.676811\pi$
$234$	2.53952	0.166014
$235$	−23.6803	−1.54473
$236$	−2.76939	−0.180272
$237$	−3.26951	−0.212378
$238$	7.47072	0.484255
$239$	−14.8472	−0.960385	−0.480193	−	0.877163i	$-0.659433\pi$
$239$	−14.8472	−0.960385	−0.480193	+	0.877163i	$0.659433\pi$
$240$	−1.36918	−0.0883802
$241$	3.93252	0.253316	0.126658	−	0.991946i	$-0.459575\pi$
$241$	3.93252	0.253316	0.126658	+	0.991946i	$0.459575\pi$
$242$	−9.52083	−0.612022
$243$	−9.45010	−0.606224
$244$	−1.94029	−0.124215
$245$	−16.5371	−1.05652
$246$	−1.78363	−0.113720
$247$	3.54191	0.225366
$248$	6.74091	0.428048
$249$	1.08875	0.0689969
$250$	−12.8259	−0.811181
$251$	11.8161	0.745828	0.372914	−	0.927866i	$-0.378359\pi$
$251$	11.8161	0.745828	0.372914	+	0.927866i	$0.378359\pi$
$252$	4.52173	0.284842
$253$	−0.278833	−0.0175301
$254$	3.15276	0.197822
$255$	−6.47210	−0.405298
$256$	1.00000	0.0625000
$257$	13.1439	0.819892	0.409946	−	0.912110i	$-0.365548\pi$
$257$	13.1439	0.819892	0.409946	+	0.912110i	$0.365548\pi$
$258$	4.02351	0.250493
$259$	−2.63325	−0.163622
$260$	3.26033	0.202197
$261$	−19.1781	−1.18710
$262$	−8.57842	−0.529977
$263$	−3.35306	−0.206759	−0.103379	−	0.994642i	$-0.532966\pi$
$263$	−3.35306	−0.206759	−0.103379	+	0.994642i	$0.532966\pi$
$264$	1.68859	0.103925
$265$	−15.1752	−0.932206
$266$	6.30652	0.386678
$267$	−2.71949	−0.166430
$268$	7.36958	0.450169
$269$	26.9626	1.64394	0.821971	−	0.569530i	$-0.192875\pi$
$269$	26.9626	1.64394	0.821971	+	0.569530i	$0.192875\pi$
$270$	−8.02484	−0.488376
$271$	24.6008	1.49439	0.747195	−	0.664605i	$-0.231400\pi$
$271$	24.6008	1.49439	0.747195	+	0.664605i	$0.231400\pi$
$272$	4.72698	0.286616
$273$	0.522913	0.0316482
$274$	−16.7504	−1.01193
$275$	38.4679	2.31970
$276$	0.0229442	0.00138108
$277$	−22.2340	−1.33591	−0.667955	−	0.744202i	$-0.732830\pi$
$277$	−22.2340	−1.33591	−0.667955	+	0.744202i	$0.732830\pi$
$278$	10.6738	0.640171
$279$	19.2861	1.15463
$280$	5.80515	0.346924
$281$	3.05179	0.182054	0.0910271	−	0.995848i	$-0.470985\pi$
$281$	3.05179	0.182054	0.0910271	+	0.995848i	$0.470985\pi$
$282$	−2.40313	−0.143104
$283$	−9.46357	−0.562551	−0.281275	−	0.959627i	$-0.590757\pi$
$283$	−9.46357	−0.562551	−0.281275	+	0.959627i	$0.590757\pi$
$284$	−7.68364	−0.455940
$285$	−5.46352	−0.323631
$286$	−4.02090	−0.237761
$287$	7.56238	0.446393
$288$	2.86105	0.168589
$289$	5.34438	0.314375
$290$	−24.6216	−1.44583
$291$	−3.49902	−0.205116
$292$	−3.88097	−0.227116
$293$	33.8101	1.97521	0.987603	−	0.156975i	$-0.0501743\pi$
$293$	33.8101	1.97521	0.987603	+	0.156975i	$0.0501743\pi$
$294$	−1.67823	−0.0978762
$295$	−10.1723	−0.592255
$296$	−1.66615	−0.0968427
$297$	9.89689	0.574276
$298$	12.4622	0.721913
$299$	−0.0546352	−0.00315964
$300$	−3.16538	−0.182754
$301$	−17.0592	−0.983273
$302$	−11.5028	−0.661913
$303$	−6.23766	−0.358344
$304$	3.99036	0.228863
$305$	−7.12693	−0.408087
$306$	13.5242	0.773124
$307$	−10.7688	−0.614609	−0.307304	−	0.951611i	$-0.599427\pi$
$307$	−10.7688	−0.614609	−0.307304	+	0.951611i	$0.599427\pi$
$308$	−7.15939	−0.407944
$309$	1.83250	0.104247
$310$	24.7602	1.40628
$311$	2.35849	0.133738	0.0668690	−	0.997762i	$-0.478699\pi$
$311$	2.35849	0.133738	0.0668690	+	0.997762i	$0.478699\pi$
$312$	0.330865	0.0187316
$313$	−9.27919	−0.524491	−0.262245	−	0.965001i	$-0.584463\pi$
$313$	−9.27919	−0.524491	−0.262245	+	0.965001i	$0.584463\pi$
$314$	0.267661	0.0151050
$315$	16.6088	0.935803
$316$	8.77117	0.493417
$317$	1.84833	0.103813	0.0519063	−	0.998652i	$-0.483470\pi$
$317$	1.84833	0.103813	0.0519063	+	0.998652i	$0.483470\pi$
$318$	−1.54001	−0.0863597
$319$	30.3653	1.70013
$320$	3.67312	0.205334
$321$	6.16989	0.344369
$322$	−0.0972804	−0.00542122
$323$	18.8623	1.04953
$324$	7.76878	0.431599
$325$	7.53749	0.418105
$326$	8.27837	0.458496
$327$	−4.33338	−0.239636
$328$	4.78498	0.264206
$329$	10.1890	0.561735
$330$	6.20238	0.341430
$331$	−7.88679	−0.433497	−0.216749	−	0.976227i	$-0.569545\pi$
$331$	−7.88679	−0.433497	−0.216749	+	0.976227i	$0.569545\pi$
$332$	−2.92081	−0.160301
$333$	−4.76693	−0.261226
$334$	6.34469	0.347166
$335$	27.0694	1.47896
$336$	0.589120	0.0321391
$337$	7.35742	0.400784	0.200392	−	0.979716i	$-0.435778\pi$
$337$	7.35742	0.400784	0.200392	+	0.979716i	$0.435778\pi$
$338$	12.2121	0.664253
$339$	1.51403	0.0822306
$340$	17.3628	0.941630
$341$	−30.5363	−1.65363
$342$	11.4166	0.617340
$343$	18.1786	0.981550
$344$	−10.7939	−0.581969
$345$	0.0842767	0.00453731
$346$	−16.7708	−0.901601
$347$	−14.2735	−0.766242	−0.383121	−	0.923698i	$-0.625151\pi$
$347$	−14.2735	−0.766242	−0.383121	+	0.923698i	$0.625151\pi$
$348$	−2.49865	−0.133942
$349$	−7.34434	−0.393134	−0.196567	−	0.980490i	$-0.562979\pi$
$349$	−7.34434	−0.393134	−0.196567	+	0.980490i	$0.562979\pi$
$350$	13.4208	0.717374
$351$	1.93922	0.103508
$352$	−4.52999	−0.241449
$353$	−11.6276	−0.618875	−0.309438	−	0.950920i	$-0.600141\pi$
$353$	−11.6276	−0.618875	−0.309438	+	0.950920i	$0.600141\pi$
$354$	−1.03231	−0.0548666
$355$	−28.2229	−1.49792
$356$	7.29561	0.386666
$357$	2.78476	0.147385
$358$	1.21117	0.0640125
$359$	7.10599	0.375040	0.187520	−	0.982261i	$-0.439955\pi$
$359$	7.10599	0.375040	0.187520	+	0.982261i	$0.439955\pi$
$360$	10.5090	0.553873
$361$	−3.07706	−0.161951
$362$	−14.1834	−0.745462
$363$	−3.54896	−0.186272
$364$	−1.40283	−0.0735281
$365$	−14.2553	−0.746155
$366$	−0.723257	−0.0378053
$367$	−33.4986	−1.74861	−0.874307	−	0.485374i	$-0.838683\pi$
$367$	−33.4986	−1.74861	−0.874307	+	0.485374i	$0.838683\pi$
$368$	−0.0615527	−0.00320865
$369$	13.6901	0.712677
$370$	−6.11996	−0.318161
$371$	6.52947	0.338993
$372$	2.51272	0.130278
$373$	26.2005	1.35661	0.678306	−	0.734779i	$-0.262714\pi$
$373$	26.2005	1.35661	0.678306	+	0.734779i	$0.262714\pi$
$374$	−21.4132	−1.10725
$375$	−4.78094	−0.246887
$376$	6.44691	0.332474
$377$	5.94985	0.306433
$378$	3.45286	0.177596
$379$	14.0970	0.724115	0.362057	−	0.932156i	$-0.382074\pi$
$379$	14.0970	0.724115	0.362057	+	0.932156i	$0.382074\pi$
$380$	14.6571	0.751891
$381$	1.17521	0.0602080
$382$	10.4523	0.534787
$383$	13.8043	0.705365	0.352682	−	0.935743i	$-0.385270\pi$
$383$	13.8043	0.705365	0.352682	+	0.935743i	$0.385270\pi$
$384$	0.372757	0.0190222
$385$	−26.2973	−1.34023
$386$	1.21994	0.0620931
$387$	−30.8820	−1.56982
$388$	9.38686	0.476546
$389$	34.1625	1.73211	0.866055	−	0.499949i	$-0.166648\pi$
$389$	34.1625	1.73211	0.866055	+	0.499949i	$0.166648\pi$
$390$	1.21531	0.0615396
$391$	−0.290958	−0.0147144
$392$	4.50221	0.227396
$393$	−3.19766	−0.161301
$394$	−6.91233	−0.348238
$395$	32.2176	1.62104
$396$	−12.9605	−0.651292
$397$	7.70258	0.386581	0.193291	−	0.981142i	$-0.438084\pi$
$397$	7.70258	0.386581	0.193291	+	0.981142i	$0.438084\pi$
$398$	−15.0257	−0.753168
$399$	2.35080	0.117687
$400$	8.49183	0.424591
$401$	29.4298	1.46965	0.734827	−	0.678254i	$-0.237263\pi$
$401$	29.4298	1.46965	0.734827	+	0.678254i	$0.237263\pi$
$402$	2.74706	0.137011
$403$	−5.98335	−0.298052
$404$	16.7339	0.832540
$405$	28.5357	1.41795
$406$	10.5940	0.525770
$407$	7.54763	0.374122
$408$	1.76202	0.0872328
$409$	11.8114	0.584035	0.292018	−	0.956413i	$-0.405673\pi$
$409$	11.8114	0.584035	0.292018	+	0.956413i	$0.405673\pi$
$410$	17.5758	0.868008
$411$	−6.24381	−0.307985
$412$	−4.91607	−0.242197
$413$	4.37686	0.215371
$414$	−0.176105	−0.00865511
$415$	−10.7285	−0.526642
$416$	−0.887618	−0.0435190
$417$	3.97872	0.194839
$418$	−18.0763	−0.884140
$419$	4.28821	0.209493	0.104746	−	0.994499i	$-0.466597\pi$
$419$	4.28821	0.209493	0.104746	+	0.994499i	$0.466597\pi$
$420$	2.16391	0.105588
$421$	32.0762	1.56330	0.781649	−	0.623719i	$-0.214379\pi$
$421$	32.0762	1.56330	0.781649	+	0.623719i	$0.214379\pi$
$422$	−3.69475	−0.179858
$423$	18.4449	0.896824
$424$	4.13142	0.200639
$425$	40.1407	1.94711
$426$	−2.86413	−0.138767
$427$	3.06652	0.148399
$428$	−16.5520	−0.800073
$429$	−1.49882	−0.0723636
$430$	−39.6474	−1.91197
$431$	27.6575	1.33221	0.666107	−	0.745856i	$-0.267959\pi$
$431$	27.6575	1.33221	0.666107	+	0.745856i	$0.267959\pi$
$432$	2.18475	0.105114
$433$	−5.21969	−0.250842	−0.125421	−	0.992104i	$-0.540028\pi$
$433$	−5.21969	−0.250842	−0.125421	+	0.992104i	$0.540028\pi$
$434$	−10.6536	−0.511390
$435$	−9.17785	−0.440044
$436$	11.6252	0.556747
$437$	−0.245617	−0.0117495
$438$	−1.44666	−0.0691239
$439$	38.2659	1.82633	0.913167	−	0.407586i	$-0.133629\pi$
$439$	38.2659	1.82633	0.913167	+	0.407586i	$0.133629\pi$
$440$	−16.6392	−0.793244
$441$	12.8810	0.613383
$442$	−4.19575	−0.199572
$443$	−5.86406	−0.278610	−0.139305	−	0.990250i	$-0.544487\pi$
$443$	−5.86406	−0.278610	−0.139305	+	0.990250i	$0.544487\pi$
$444$	−0.621067	−0.0294745
$445$	26.7976	1.27033
$446$	−12.6592	−0.599433
$447$	4.64535	0.219718
$448$	−1.58044	−0.0746688
$449$	−17.4784	−0.824856	−0.412428	−	0.910990i	$-0.635319\pi$
$449$	−17.4784	−0.824856	−0.412428	+	0.910990i	$0.635319\pi$
$450$	24.2956	1.14530
$451$	−21.6759	−1.02068
$452$	−4.06170	−0.191046
$453$	−4.28775	−0.201456
$454$	12.9313	0.606895
$455$	−5.15276	−0.241565
$456$	1.48743	0.0696554
$457$	−0.524754	−0.0245470	−0.0122735	−	0.999925i	$-0.503907\pi$
$457$	−0.524754	−0.0245470	−0.0122735	+	0.999925i	$0.503907\pi$
$458$	5.02821	0.234953
$459$	10.3273	0.482035
$460$	−0.226090	−0.0105415
$461$	−13.2889	−0.618925	−0.309463	−	0.950912i	$-0.600149\pi$
$461$	−13.2889	−0.618925	−0.309463	+	0.950912i	$0.600149\pi$
$462$	−2.66871	−0.124160
$463$	−13.7608	−0.639517	−0.319758	−	0.947499i	$-0.603602\pi$
$463$	−13.7608	−0.639517	−0.319758	+	0.947499i	$0.603602\pi$
$464$	6.70317	0.311187
$465$	9.22952	0.428009
$466$	16.0991	0.745775
$467$	−24.7435	−1.14499	−0.572496	−	0.819907i	$-0.694025\pi$
$467$	−24.7435	−1.14499	−0.572496	+	0.819907i	$0.694025\pi$
$468$	−2.53952	−0.117389
$469$	−11.6472	−0.537817
$470$	23.6803	1.09229
$471$	0.0997723	0.00459726
$472$	2.76939	0.127472
$473$	48.8964	2.24826
$474$	3.26951	0.150174
$475$	33.8854	1.55477
$476$	−7.47072	−0.342420
$477$	11.8202	0.541210
$478$	14.8472	0.679095
$479$	−8.85228	−0.404471	−0.202236	−	0.979337i	$-0.564821\pi$
$479$	−8.85228	−0.404471	−0.202236	+	0.979337i	$0.564821\pi$
$480$	1.36918	0.0624943
$481$	1.47890	0.0674320
$482$	−3.93252	−0.179122
$483$	−0.0362619	−0.00164997
$484$	9.52083	0.432765
$485$	34.4791	1.56562
$486$	9.45010	0.428665
$487$	−22.4568	−1.01761	−0.508807	−	0.860881i	$-0.669913\pi$
$487$	−22.4568	−1.01761	−0.508807	+	0.860881i	$0.669913\pi$
$488$	1.94029	0.0878330
$489$	3.08582	0.139545
$490$	16.5371	0.747072
$491$	−5.14304	−0.232102	−0.116051	−	0.993243i	$-0.537024\pi$
$491$	−5.14304	−0.232102	−0.116051	+	0.993243i	$0.537024\pi$
$492$	1.78363	0.0804124
$493$	31.6858	1.42706
$494$	−3.54191	−0.159358
$495$	−47.6057	−2.13972
$496$	−6.74091	−0.302676
$497$	12.1435	0.544712
$498$	−1.08875	−0.0487882
$499$	9.51548	0.425971	0.212986	−	0.977055i	$-0.431681\pi$
$499$	9.51548	0.425971	0.212986	+	0.977055i	$0.431681\pi$
$500$	12.8259	0.573592
$501$	2.36503	0.105662
$502$	−11.8161	−0.527380
$503$	14.3371	0.639260	0.319630	−	0.947542i	$-0.396441\pi$
$503$	14.3371	0.639260	0.319630	+	0.947542i	$0.396441\pi$
$504$	−4.52173	−0.201414
$505$	61.4655	2.73518
$506$	0.278833	0.0123956
$507$	4.55216	0.202168
$508$	−3.15276	−0.139881
$509$	−36.1574	−1.60265	−0.801324	−	0.598230i	$-0.795871\pi$
$509$	−36.1574	−1.60265	−0.801324	+	0.598230i	$0.795871\pi$
$510$	6.47210	0.286589
$511$	6.13364	0.271336
$512$	−1.00000	−0.0441942
$513$	8.71792	0.384905
$514$	−13.1439	−0.579751
$515$	−18.0573	−0.795701
$516$	−4.02351	−0.177125
$517$	−29.2044	−1.28441
$518$	2.63325	0.115698
$519$	−6.25141	−0.274406
$520$	−3.26033	−0.142975
$521$	13.6417	0.597654	0.298827	−	0.954307i	$-0.403405\pi$
$521$	13.6417	0.597654	0.298827	+	0.954307i	$0.403405\pi$
$522$	19.1781	0.839404
$523$	−27.2497	−1.19155	−0.595774	−	0.803152i	$-0.703155\pi$
$523$	−27.2497	−1.19155	−0.595774	+	0.803152i	$0.703155\pi$
$524$	8.57842	0.374750
$525$	5.00271	0.218336
$526$	3.35306	0.146201
$527$	−31.8642	−1.38803
$528$	−1.68859	−0.0734862
$529$	−22.9962	−0.999835
$530$	15.1752	0.659169
$531$	7.92337	0.343845
$532$	−6.30652	−0.273422
$533$	−4.24723	−0.183968
$534$	2.71949	0.117684
$535$	−60.7977	−2.62851
$536$	−7.36958	−0.318317
$537$	0.451473	0.0194825
$538$	−26.9626	−1.16244
$539$	−20.3950	−0.878473
$540$	8.02484	0.345334
$541$	10.5337	0.452881	0.226441	−	0.974025i	$-0.427291\pi$
$541$	10.5337	0.452881	0.226441	+	0.974025i	$0.427291\pi$
$542$	−24.6008	−1.05669
$543$	−5.28695	−0.226885
$544$	−4.72698	−0.202668
$545$	42.7009	1.82910
$546$	−0.522913	−0.0223786
$547$	−15.2794	−0.653299	−0.326650	−	0.945146i	$-0.605920\pi$
$547$	−15.2794	−0.653299	−0.326650	+	0.945146i	$0.605920\pi$
$548$	16.7504	0.715540
$549$	5.55128	0.236923
$550$	−38.4679	−1.64028
$551$	26.7480	1.13950
$552$	−0.0229442	−0.000976569 0
$553$	−13.8623	−0.589485
$554$	22.2340	0.944631
$555$	−2.28125	−0.0968339
$556$	−10.6738	−0.452669
$557$	−37.3534	−1.58271	−0.791357	−	0.611355i	$-0.790625\pi$
$557$	−37.3534	−1.58271	−0.791357	+	0.611355i	$0.790625\pi$
$558$	−19.2861	−0.816446
$559$	9.58087	0.405228
$560$	−5.80515	−0.245313
$561$	−7.98192	−0.336997
$562$	−3.05179	−0.128732
$563$	1.70280	0.0717643	0.0358821	−	0.999356i	$-0.488576\pi$
$563$	1.70280	0.0717643	0.0358821	+	0.999356i	$0.488576\pi$
$564$	2.40313	0.101190
$565$	−14.9191	−0.627652
$566$	9.46357	0.397783
$567$	−12.2781	−0.515632
$568$	7.68364	0.322398
$569$	42.5661	1.78446	0.892231	−	0.451579i	$-0.149139\pi$
$569$	42.5661	1.78446	0.892231	+	0.451579i	$0.149139\pi$
$570$	5.46352	0.228842
$571$	−35.8237	−1.49917	−0.749587	−	0.661905i	$-0.769748\pi$
$571$	−35.8237	−1.49917	−0.749587	+	0.661905i	$0.769748\pi$
$572$	4.02090	0.168122
$573$	3.89617	0.162765
$574$	−7.56238	−0.315648
$575$	−0.522694	−0.0217979
$576$	−2.86105	−0.119211
$577$	−24.1849	−1.00683	−0.503416	−	0.864044i	$-0.667924\pi$
$577$	−24.1849	−1.00683	−0.503416	+	0.864044i	$0.667924\pi$
$578$	−5.34438	−0.222297
$579$	0.454739	0.0188983
$580$	24.6216	1.02235
$581$	4.61618	0.191511
$582$	3.49902	0.145039
$583$	−18.7153	−0.775109
$584$	3.88097	0.160596
$585$	−9.32797	−0.385664
$586$	−33.8101	−1.39668
$587$	−2.95764	−0.122075	−0.0610375	−	0.998135i	$-0.519441\pi$
$587$	−2.95764	−0.122075	−0.0610375	+	0.998135i	$0.519441\pi$
$588$	1.67823	0.0692089
$589$	−26.8986	−1.10834
$590$	10.1723	0.418787
$591$	−2.57662	−0.105988
$592$	1.66615	0.0684782
$593$	5.77896	0.237313	0.118657	−	0.992935i	$-0.462141\pi$
$593$	5.77896	0.237313	0.118657	+	0.992935i	$0.462141\pi$
$594$	−9.89689	−0.406074
$595$	−27.4409	−1.12497
$596$	−12.4622	−0.510470
$597$	−5.60092	−0.229230
$598$	0.0546352	0.00223420
$599$	0.831272	0.0339648	0.0169824	−	0.999856i	$-0.494594\pi$
$599$	0.831272	0.0339648	0.0169824	+	0.999856i	$0.494594\pi$
$600$	3.16538	0.129226
$601$	37.4395	1.52719	0.763595	−	0.645696i	$-0.223433\pi$
$601$	37.4395	1.52719	0.763595	+	0.645696i	$0.223433\pi$
$602$	17.0592	0.695279
$603$	−21.0848	−0.858637
$604$	11.5028	0.468043
$605$	34.9712	1.42178
$606$	6.23766	0.253387
$607$	−37.4080	−1.51834	−0.759171	−	0.650891i	$-0.774395\pi$
$607$	−37.4080	−1.51834	−0.759171	+	0.650891i	$0.774395\pi$
$608$	−3.99036	−0.161830
$609$	3.94897	0.160020
$610$	7.12693	0.288561
$611$	−5.72239	−0.231503
$612$	−13.5242	−0.546681
$613$	29.8480	1.20555	0.602774	−	0.797912i	$-0.294062\pi$
$613$	29.8480	1.20555	0.602774	+	0.797912i	$0.294062\pi$
$614$	10.7688	0.434594
$615$	6.55150	0.264182
$616$	7.15939	0.288460
$617$	17.0818	0.687689	0.343845	−	0.939027i	$-0.388271\pi$
$617$	17.0818	0.687689	0.343845	+	0.939027i	$0.388271\pi$
$618$	−1.83250	−0.0737139
$619$	8.73718	0.351177	0.175588	−	0.984464i	$-0.443817\pi$
$619$	8.73718	0.351177	0.175588	+	0.984464i	$0.443817\pi$
$620$	−24.7602	−0.994393
$621$	−0.134477	−0.00539637
$622$	−2.35849	−0.0945670
$623$	−11.5303	−0.461951
$624$	−0.330865	−0.0132452
$625$	4.65197	0.186079
$626$	9.27919	0.370871
$627$	−6.73806	−0.269092
$628$	−0.267661	−0.0106808
$629$	7.87584	0.314030
$630$	−16.6088	−0.661712
$631$	40.4150	1.60890	0.804449	−	0.594022i	$-0.202461\pi$
$631$	40.4150	1.60890	0.804449	+	0.594022i	$0.202461\pi$
$632$	−8.77117	−0.348898
$633$	−1.37724	−0.0547405
$634$	−1.84833	−0.0734067
$635$	−11.5805	−0.459557
$636$	1.54001	0.0610655
$637$	−3.99624	−0.158337
$638$	−30.3653	−1.20217
$639$	21.9833	0.869645
$640$	−3.67312	−0.145193
$641$	0.176468	0.00697006	0.00348503	−	0.999994i	$-0.498891\pi$
$641$	0.176468	0.00697006	0.00348503	+	0.999994i	$0.498891\pi$
$642$	−6.16989	−0.243506
$643$	10.8652	0.428480	0.214240	−	0.976781i	$-0.431273\pi$
$643$	10.8652	0.428480	0.214240	+	0.976781i	$0.431273\pi$
$644$	0.0972804	0.00383338
$645$	−14.7788	−0.581916
$646$	−18.8623	−0.742129
$647$	−46.1864	−1.81578	−0.907888	−	0.419214i	$-0.862306\pi$
$647$	−46.1864	−1.81578	−0.907888	+	0.419214i	$0.862306\pi$
$648$	−7.76878	−0.305186
$649$	−12.5453	−0.492447
$650$	−7.53749	−0.295645
$651$	−3.97121	−0.155644
$652$	−8.27837	−0.324206
$653$	−32.8074	−1.28385	−0.641927	−	0.766766i	$-0.721865\pi$
$653$	−32.8074	−1.28385	−0.641927	+	0.766766i	$0.721865\pi$
$654$	4.33338	0.169449
$655$	31.5096	1.23118
$656$	−4.78498	−0.186822
$657$	11.1037	0.433195
$658$	−10.1890	−0.397207
$659$	−32.0733	−1.24940	−0.624700	−	0.780865i	$-0.714779\pi$
$659$	−32.0733	−1.24940	−0.624700	+	0.780865i	$0.714779\pi$
$660$	−6.20238	−0.241427
$661$	14.3909	0.559742	0.279871	−	0.960038i	$-0.409708\pi$
$661$	14.3909	0.559742	0.279871	+	0.960038i	$0.409708\pi$
$662$	7.88679	0.306529
$663$	−1.56400	−0.0607406
$664$	2.92081	0.113350
$665$	−23.1646	−0.898286
$666$	4.76693	0.184715
$667$	−0.412598	−0.0159759
$668$	−6.34469	−0.245484
$669$	−4.71882	−0.182440
$670$	−27.0694	−1.04578
$671$	−8.78951	−0.339315
$672$	−0.589120	−0.0227258
$673$	−42.4147	−1.63497	−0.817484	−	0.575951i	$-0.804632\pi$
$673$	−42.4147	−1.63497	−0.817484	+	0.575951i	$0.804632\pi$
$674$	−7.35742	−0.283397
$675$	18.5525	0.714086
$676$	−12.2121	−0.469698
$677$	18.7499	0.720617	0.360309	−	0.932833i	$-0.382671\pi$
$677$	18.7499	0.720617	0.360309	+	0.932833i	$0.382671\pi$
$678$	−1.51403	−0.0581458
$679$	−14.8354	−0.569330
$680$	−17.3628	−0.665833
$681$	4.82022	0.184711
$682$	30.5363	1.16929
$683$	26.6001	1.01782	0.508912	−	0.860818i	$-0.330048\pi$
$683$	26.6001	1.01782	0.508912	+	0.860818i	$0.330048\pi$
$684$	−11.4166	−0.436525
$685$	61.5261	2.35079
$686$	−18.1786	−0.694061
$687$	1.87430	0.0715089
$688$	10.7939	0.411514
$689$	−3.66712	−0.139706
$690$	−0.0842767	−0.00320836
$691$	−43.1965	−1.64327	−0.821636	−	0.570012i	$-0.806938\pi$
$691$	−43.1965	−1.64327	−0.821636	+	0.570012i	$0.806938\pi$
$692$	16.7708	0.637528
$693$	20.4834	0.778099
$694$	14.2735	0.541815
$695$	−39.2061	−1.48717
$696$	2.49865	0.0947112
$697$	−22.6185	−0.856738
$698$	7.34434	0.277987
$699$	6.00103	0.226980
$700$	−13.4208	−0.507260
$701$	−26.1115	−0.986219	−0.493109	−	0.869967i	$-0.664140\pi$
$701$	−26.1115	−0.986219	−0.493109	+	0.869967i	$0.664140\pi$
$702$	−1.93922	−0.0731911
$703$	6.64851	0.250753
$704$	4.52999	0.170731
$705$	8.82698	0.332443
$706$	11.6276	0.437611
$707$	−26.4469	−0.994637
$708$	1.03231	0.0387966
$709$	−10.5982	−0.398025	−0.199012	−	0.979997i	$-0.563773\pi$
$709$	−10.5982	−0.398025	−0.199012	+	0.979997i	$0.563773\pi$
$710$	28.2229	1.05919
$711$	−25.0948	−0.941127
$712$	−7.29561	−0.273414
$713$	0.414921	0.0155389
$714$	−2.78476	−0.104217
$715$	14.7693	0.552339
$716$	−1.21117	−0.0452637
$717$	5.53439	0.206686
$718$	−7.10599	−0.265193
$719$	−39.6412	−1.47837	−0.739184	−	0.673504i	$-0.764789\pi$
$719$	−39.6412	−1.47837	−0.739184	+	0.673504i	$0.764789\pi$
$720$	−10.5090	−0.391647
$721$	7.76956	0.289354
$722$	3.07706	0.114516
$723$	−1.46587	−0.0545165
$724$	14.1834	0.527121
$725$	56.9222	2.11404
$726$	3.54896	0.131714
$727$	18.6524	0.691779	0.345889	−	0.938275i	$-0.387577\pi$
$727$	18.6524	0.691779	0.345889	+	0.938275i	$0.387577\pi$
$728$	1.40283	0.0519922
$729$	−19.7837	−0.732731
$730$	14.2553	0.527611
$731$	51.0227	1.88714
$732$	0.723257	0.0267324
$733$	−52.6568	−1.94492	−0.972462	−	0.233062i	$-0.925125\pi$
$733$	−52.6568	−1.94492	−0.972462	+	0.233062i	$0.925125\pi$
$734$	33.4986	1.23646
$735$	6.16433	0.227375
$736$	0.0615527	0.00226886
$737$	33.3841	1.22972
$738$	−13.6901	−0.503939
$739$	8.85884	0.325878	0.162939	−	0.986636i	$-0.447903\pi$
$739$	8.85884	0.325878	0.162939	+	0.986636i	$0.447903\pi$
$740$	6.11996	0.224974
$741$	−1.32027	−0.0485013
$742$	−6.52947	−0.239704
$743$	38.5266	1.41340	0.706702	−	0.707511i	$-0.250182\pi$
$743$	38.5266	1.41340	0.706702	+	0.707511i	$0.250182\pi$
$744$	−2.51272	−0.0921208
$745$	−45.7750	−1.67707
$746$	−26.2005	−0.959270
$747$	8.35660	0.305752
$748$	21.4132	0.782944
$749$	26.1595	0.955849
$750$	4.78094	0.174575
$751$	9.10715	0.332325	0.166162	−	0.986098i	$-0.446862\pi$
$751$	9.10715	0.332325	0.166162	+	0.986098i	$0.446862\pi$
$752$	−6.44691	−0.235094
$753$	−4.40454	−0.160511
$754$	−5.94985	−0.216681
$755$	42.2512	1.53768
$756$	−3.45286	−0.125579
$757$	−48.4752	−1.76186	−0.880930	−	0.473247i	$-0.843082\pi$
$757$	−48.4752	−1.76186	−0.880930	+	0.473247i	$0.843082\pi$
$758$	−14.0970	−0.512027
$759$	0.103937	0.00377267
$760$	−14.6571	−0.531668
$761$	−34.1414	−1.23762	−0.618812	−	0.785539i	$-0.712386\pi$
$761$	−34.1414	−1.23762	−0.618812	+	0.785539i	$0.712386\pi$
$762$	−1.17521	−0.0425735
$763$	−18.3730	−0.665147
$764$	−10.4523	−0.378151
$765$	−49.6759	−1.79603
$766$	−13.8043	−0.498768
$767$	−2.45816	−0.0887590
$768$	−0.372757	−0.0134507
$769$	−9.24588	−0.333415	−0.166708	−	0.986006i	$-0.553314\pi$
$769$	−9.24588	−0.333415	−0.166708	+	0.986006i	$0.553314\pi$
$770$	26.2973	0.947689
$771$	−4.89946	−0.176450
$772$	−1.21994	−0.0439065
$773$	12.6170	0.453803	0.226901	−	0.973918i	$-0.427140\pi$
$773$	12.6170	0.453803	0.226901	+	0.973918i	$0.427140\pi$
$774$	30.8820	1.11003
$775$	−57.2426	−2.05622
$776$	−9.38686	−0.336969
$777$	0.981560	0.0352133
$778$	−34.1625	−1.22479
$779$	−19.0938	−0.684105
$780$	−1.21531	−0.0435150
$781$	−34.8068	−1.24549
$782$	0.290958	0.0104047
$783$	14.6447	0.523360
$784$	−4.50221	−0.160793
$785$	−0.983150	−0.0350901
$786$	3.19766	0.114057
$787$	−49.5327	−1.76565	−0.882826	−	0.469701i	$-0.844362\pi$
$787$	−49.5327	−1.76565	−0.882826	+	0.469701i	$0.844362\pi$
$788$	6.91233	0.246241
$789$	1.24988	0.0444968
$790$	−32.2176	−1.14625
$791$	6.41928	0.228243
$792$	12.9605	0.460533
$793$	−1.72224	−0.0611585
$794$	−7.70258	−0.273354
$795$	5.65666	0.200621
$796$	15.0257	0.532570
$797$	−14.1400	−0.500863	−0.250432	−	0.968134i	$-0.580573\pi$
$797$	−14.1400	−0.500863	−0.250432	+	0.968134i	$0.580573\pi$
$798$	−2.35080	−0.0832174
$799$	−30.4744	−1.07811
$800$	−8.49183	−0.300231
$801$	−20.8731	−0.737515
$802$	−29.4298	−1.03920
$803$	−17.5808	−0.620411
$804$	−2.74706	−0.0968813
$805$	0.357323	0.0125940
$806$	5.98335	0.210755
$807$	−10.0505	−0.353795
$808$	−16.7339	−0.588695
$809$	32.7812	1.15253	0.576263	−	0.817264i	$-0.304510\pi$
$809$	32.7812	1.15253	0.576263	+	0.817264i	$0.304510\pi$
$810$	−28.5357	−1.00264
$811$	−24.1097	−0.846605	−0.423303	−	0.905988i	$-0.639129\pi$
$811$	−24.1097	−0.846605	−0.423303	+	0.905988i	$0.639129\pi$
$812$	−10.5940	−0.371775
$813$	−9.17010	−0.321610
$814$	−7.54763	−0.264544
$815$	−30.4075	−1.06513
$816$	−1.76202	−0.0616829
$817$	43.0716	1.50688
$818$	−11.8114	−0.412975
$819$	4.01356	0.140245
$820$	−17.5758	−0.613774
$821$	−17.6557	−0.616188	−0.308094	−	0.951356i	$-0.599691\pi$
$821$	−17.6557	−0.616188	−0.308094	+	0.951356i	$0.599691\pi$
$822$	6.24381	0.217778
$823$	47.1098	1.64215	0.821073	−	0.570823i	$-0.193376\pi$
$823$	47.1098	1.64215	0.821073	+	0.570823i	$0.193376\pi$
$824$	4.91607	0.171259
$825$	−14.3392	−0.499226
$826$	−4.37686	−0.152290
$827$	0.355903	0.0123760	0.00618798	−	0.999981i	$-0.498030\pi$
$827$	0.355903	0.0123760	0.00618798	+	0.999981i	$0.498030\pi$
$828$	0.176105	0.00612009
$829$	24.7370	0.859150	0.429575	−	0.903031i	$-0.358663\pi$
$829$	24.7370	0.859150	0.429575	+	0.903031i	$0.358663\pi$
$830$	10.7285	0.372392
$831$	8.28786	0.287503
$832$	0.887618	0.0307726
$833$	−21.2819	−0.737373
$834$	−3.97872	−0.137772
$835$	−23.3048	−0.806497
$836$	18.0763	0.625181
$837$	−14.7272	−0.509046
$838$	−4.28821	−0.148134
$839$	−8.88849	−0.306865	−0.153432	−	0.988159i	$-0.549033\pi$
$839$	−8.88849	−0.306865	−0.153432	+	0.988159i	$0.549033\pi$
$840$	−2.16391	−0.0746620
$841$	15.9325	0.549397
$842$	−32.0762	−1.10542
$843$	−1.13757	−0.0391801
$844$	3.69475	0.127179
$845$	−44.8567	−1.54312
$846$	−18.4449	−0.634150
$847$	−15.0471	−0.517025
$848$	−4.13142	−0.141874
$849$	3.52761	0.121067
$850$	−40.1407	−1.37682
$851$	−0.102556	−0.00351556
$852$	2.86413	0.0981234
$853$	−1.65675	−0.0567261	−0.0283630	−	0.999598i	$-0.509029\pi$
$853$	−1.65675	−0.0567261	−0.0283630	+	0.999598i	$0.509029\pi$
$854$	−3.06652	−0.104934
$855$	−41.9346	−1.43413
$856$	16.5520	0.565737
$857$	−14.2207	−0.485769	−0.242885	−	0.970055i	$-0.578094\pi$
$857$	−14.2207	−0.485769	−0.242885	+	0.970055i	$0.578094\pi$
$858$	1.49882	0.0511688
$859$	−15.8223	−0.539850	−0.269925	−	0.962881i	$-0.586999\pi$
$859$	−15.8223	−0.539850	−0.269925	+	0.962881i	$0.586999\pi$
$860$	39.6474	1.35196
$861$	−2.81893	−0.0960688
$862$	−27.6575	−0.942018
$863$	−25.6385	−0.872745	−0.436373	−	0.899766i	$-0.643737\pi$
$863$	−25.6385	−0.872745	−0.436373	+	0.899766i	$0.643737\pi$
$864$	−2.18475	−0.0743266
$865$	61.6010	2.09450
$866$	5.21969	0.177372
$867$	−1.99215	−0.0676571
$868$	10.6536	0.361607
$869$	39.7333	1.34786
$870$	9.17785	0.311158
$871$	6.54137	0.221646
$872$	−11.6252	−0.393680
$873$	−26.8563	−0.908948
$874$	0.245617	0.00830812
$875$	−20.2706	−0.685271
$876$	1.44666	0.0488780
$877$	−17.7820	−0.600456	−0.300228	−	0.953868i	$-0.597063\pi$
$877$	−17.7820	−0.600456	−0.300228	+	0.953868i	$0.597063\pi$
$878$	−38.2659	−1.29141
$879$	−12.6029	−0.425086
$880$	16.6392	0.560908
$881$	−17.7306	−0.597359	−0.298680	−	0.954353i	$-0.596546\pi$
$881$	−17.7306	−0.597359	−0.298680	+	0.954353i	$0.596546\pi$
$882$	−12.8810	−0.433727
$883$	25.8180	0.868844	0.434422	−	0.900709i	$-0.356953\pi$
$883$	25.8180	0.868844	0.434422	+	0.900709i	$0.356953\pi$
$884$	4.19575	0.141118
$885$	3.79180	0.127460
$886$	5.86406	0.197007
$887$	9.07809	0.304813	0.152406	−	0.988318i	$-0.451298\pi$
$887$	9.07809	0.304813	0.152406	+	0.988318i	$0.451298\pi$
$888$	0.621067	0.0208416
$889$	4.98275	0.167116
$890$	−26.7976	−0.898259
$891$	35.1925	1.17899
$892$	12.6592	0.423863
$893$	−25.7254	−0.860869
$894$	−4.64535	−0.155364
$895$	−4.44879	−0.148707
$896$	1.58044	0.0527988
$897$	0.0203656	0.000679989 0
$898$	17.4784	0.583261
$899$	−45.1855	−1.50702
$900$	−24.2956	−0.809852
$901$	−19.5292	−0.650611
$902$	21.6759	0.721729
$903$	6.35892	0.211611
$904$	4.06170	0.135090
$905$	52.0973	1.73177
$906$	4.28775	0.142451
$907$	−13.4034	−0.445051	−0.222526	−	0.974927i	$-0.571430\pi$
$907$	−13.4034	−0.445051	−0.222526	+	0.974927i	$0.571430\pi$
$908$	−12.9313	−0.429139
$909$	−47.8764	−1.58796
$910$	5.15276	0.170812
$911$	−19.7883	−0.655615	−0.327808	−	0.944745i	$-0.606310\pi$
$911$	−19.7883	−0.655615	−0.327808	+	0.944745i	$0.606310\pi$
$912$	−1.48743	−0.0492538
$913$	−13.2313	−0.437891
$914$	0.524754	0.0173573
$915$	2.65661	0.0878249
$916$	−5.02821	−0.166137
$917$	−13.5577	−0.447714
$918$	−10.3273	−0.340850
$919$	−44.8465	−1.47935	−0.739675	−	0.672964i	$-0.765021\pi$
$919$	−44.8465	−1.47935	−0.739675	+	0.672964i	$0.765021\pi$
$920$	0.226090	0.00745398
$921$	4.01415	0.132271
$922$	13.2889	0.437646
$923$	−6.82013	−0.224487
$924$	2.66871	0.0877941
$925$	14.1486	0.465204
$926$	13.7608	0.452207
$927$	14.0651	0.461960
$928$	−6.70317	−0.220042
$929$	−24.9444	−0.818400	−0.409200	−	0.912445i	$-0.634192\pi$
$929$	−24.9444	−0.818400	−0.409200	+	0.912445i	$0.634192\pi$
$930$	−9.22952	−0.302648
$931$	−17.9654	−0.588792
$932$	−16.0991	−0.527342
$933$	−0.879145	−0.0287819
$934$	24.7435	0.809632
$935$	78.6533	2.57224
$936$	2.53952	0.0830068
$937$	29.6796	0.969591	0.484795	−	0.874628i	$-0.338894\pi$
$937$	29.6796	0.969591	0.484795	+	0.874628i	$0.338894\pi$
$938$	11.6472	0.380294
$939$	3.45888	0.112876
$940$	−23.6803	−0.772365
$941$	14.7494	0.480816	0.240408	−	0.970672i	$-0.422719\pi$
$941$	14.7494	0.480816	0.240408	+	0.970672i	$0.422719\pi$
$942$	−0.0997723	−0.00325076
$943$	0.294528	0.00959116
$944$	−2.76939	−0.0901360
$945$	−12.6828	−0.412571
$946$	−48.8964	−1.58976
$947$	42.9789	1.39663	0.698313	−	0.715793i	$-0.253934\pi$
$947$	42.9789	1.39663	0.698313	+	0.715793i	$0.253934\pi$
$948$	−3.26951	−0.106189
$949$	−3.44482	−0.111823
$950$	−33.8854	−1.09939
$951$	−0.688978	−0.0223417
$952$	7.47072	0.242127
$953$	59.9835	1.94306	0.971528	−	0.236924i	$-0.0761393\pi$
$953$	59.9835	1.94306	0.971528	+	0.236924i	$0.0761393\pi$
$954$	−11.8202	−0.382693
$955$	−38.3926	−1.24236
$956$	−14.8472	−0.480193
$957$	−11.3189	−0.365887
$958$	8.85228	0.286004
$959$	−26.4730	−0.854857
$960$	−1.36918	−0.0441901
$961$	14.4399	0.465802
$962$	−1.47890	−0.0476817
$963$	47.3563	1.52603
$964$	3.93252	0.126658
$965$	−4.48097	−0.144248
$966$	0.0362619	0.00116671
$967$	21.5305	0.692375	0.346188	−	0.938165i	$-0.387476\pi$
$967$	21.5305	0.692375	0.346188	+	0.938165i	$0.387476\pi$
$968$	−9.52083	−0.306011
$969$	−7.03107	−0.225870
$970$	−34.4791	−1.10706
$971$	51.7586	1.66101	0.830507	−	0.557008i	$-0.188051\pi$
$971$	51.7586	1.66101	0.830507	+	0.557008i	$0.188051\pi$
$972$	−9.45010	−0.303112
$973$	16.8693	0.540804
$974$	22.4568	0.719561
$975$	−2.80965	−0.0899809
$976$	−1.94029	−0.0621073
$977$	−30.8801	−0.987943	−0.493971	−	0.869478i	$-0.664455\pi$
$977$	−30.8801	−0.987943	−0.493971	+	0.869478i	$0.664455\pi$
$978$	−3.08582	−0.0986736
$979$	33.0490	1.05625
$980$	−16.5371	−0.528260
$981$	−33.2604	−1.06192
$982$	5.14304	0.164121
$983$	44.8341	1.42999	0.714993	−	0.699131i	$-0.246430\pi$
$983$	44.8341	1.42999	0.714993	+	0.699131i	$0.246430\pi$
$984$	−1.78363	−0.0568602
$985$	25.3898	0.808987
$986$	−31.6858	−1.00908
$987$	−3.79800	−0.120892
$988$	3.54191	0.112683
$989$	−0.664394	−0.0211265
$990$	47.6057	1.51301
$991$	−29.9946	−0.952811	−0.476406	−	0.879226i	$-0.658061\pi$
$991$	−29.9946	−0.952811	−0.476406	+	0.879226i	$0.658061\pi$
$992$	6.74091	0.214024
$993$	2.93985	0.0932934
$994$	−12.1435	−0.385170
$995$	55.1911	1.74968
$996$	1.08875	0.0344985
$997$	−31.3304	−0.992243	−0.496121	−	0.868253i	$-0.665243\pi$
$997$	−31.3304	−0.992243	−0.496121	+	0.868253i	$0.665243\pi$
$998$	−9.51548	−0.301207
$999$	3.64011	0.115168

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	4006.2.a.h.1.19	✓	42

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
4006.2.a.h.1.19	✓	42	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:	\( N \)	\(=\)	\( 4006 = 2 \cdot 2003 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	4006.a (trivial)

\(f(q)\)	\(=\)	\(q-1.00000 q^{2} -0.372757 q^{3} +1.00000 q^{4} +3.67312 q^{5} +0.372757 q^{6} -1.58044 q^{7} -1.00000 q^{8} -2.86105 q^{9} +O(q^{10})\)	\(q-1.00000 q^{2} -0.372757 q^{3} +1.00000 q^{4} +3.67312 q^{5} +0.372757 q^{6} -1.58044 q^{7} -1.00000 q^{8} -2.86105 q^{9} -3.67312 q^{10} +4.52999 q^{11} -0.372757 q^{12} +0.887618 q^{13} +1.58044 q^{14} -1.36918 q^{15} +1.00000 q^{16} +4.72698 q^{17} +2.86105 q^{18} +3.99036 q^{19} +3.67312 q^{20} +0.589120 q^{21} -4.52999 q^{22} -0.0615527 q^{23} +0.372757 q^{24} +8.49183 q^{25} -0.887618 q^{26} +2.18475 q^{27} -1.58044 q^{28} +6.70317 q^{29} +1.36918 q^{30} -6.74091 q^{31} -1.00000 q^{32} -1.68859 q^{33} -4.72698 q^{34} -5.80515 q^{35} -2.86105 q^{36} +1.66615 q^{37} -3.99036 q^{38} -0.330865 q^{39} -3.67312 q^{40} -4.78498 q^{41} -0.589120 q^{42} +10.7939 q^{43} +4.52999 q^{44} -10.5090 q^{45} +0.0615527 q^{46} -6.44691 q^{47} -0.372757 q^{48} -4.50221 q^{49} -8.49183 q^{50} -1.76202 q^{51} +0.887618 q^{52} -4.13142 q^{53} -2.18475 q^{54} +16.6392 q^{55} +1.58044 q^{56} -1.48743 q^{57} -6.70317 q^{58} -2.76939 q^{59} -1.36918 q^{60} -1.94029 q^{61} +6.74091 q^{62} +4.52173 q^{63} +1.00000 q^{64} +3.26033 q^{65} +1.68859 q^{66} +7.36958 q^{67} +4.72698 q^{68} +0.0229442 q^{69} +5.80515 q^{70} -7.68364 q^{71} +2.86105 q^{72} -3.88097 q^{73} -1.66615 q^{74} -3.16538 q^{75} +3.99036 q^{76} -7.15939 q^{77} +0.330865 q^{78} +8.77117 q^{79} +3.67312 q^{80} +7.76878 q^{81} +4.78498 q^{82} -2.92081 q^{83} +0.589120 q^{84} +17.3628 q^{85} -10.7939 q^{86} -2.49865 q^{87} -4.52999 q^{88} +7.29561 q^{89} +10.5090 q^{90} -1.40283 q^{91} -0.0615527 q^{92} +2.51272 q^{93} +6.44691 q^{94} +14.6571 q^{95} +0.372757 q^{96} +9.38686 q^{97} +4.50221 q^{98} -12.9605 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 42 q - 42 q^{2} + 42 q^{4} + 27 q^{5} - 10 q^{7} - 42 q^{8} + 56 q^{9}+O(q^{10}) \) 42 * q - 42 * q^2 + 42 * q^4 + 27 * q^5 - 10 * q^7 - 42 * q^8 + 56 * q^9	\( 42 q - 42 q^{2} + 42 q^{4} + 27 q^{5} - 10 q^{7} - 42 q^{8} + 56 q^{9} - 27 q^{10} + 23 q^{11} + 15 q^{13} + 10 q^{14} + 6 q^{15} + 42 q^{16} + 14 q^{17} - 56 q^{18} - 4 q^{19} + 27 q^{20} + 26 q^{21} - 23 q^{22} + 12 q^{23} + 45 q^{25} - 15 q^{26} - 3 q^{27} - 10 q^{28} + 41 q^{29} - 6 q^{30} + 18 q^{31} - 42 q^{32} + 25 q^{33} - 14 q^{34} + 8 q^{35} + 56 q^{36} + 33 q^{37} + 4 q^{38} + 10 q^{39} - 27 q^{40} + 84 q^{41} - 26 q^{42} - 36 q^{43} + 23 q^{44} + 66 q^{45} - 12 q^{46} + 28 q^{47} + 58 q^{49} - 45 q^{50} + 17 q^{51} + 15 q^{52} + 68 q^{53} + 3 q^{54} - 28 q^{55} + 10 q^{56} - 9 q^{57} - 41 q^{58} + 59 q^{59} + 6 q^{60} + 41 q^{61} - 18 q^{62} - 28 q^{63} + 42 q^{64} + 44 q^{65} - 25 q^{66} + 14 q^{68} + 67 q^{69} - 8 q^{70} + 69 q^{71} - 56 q^{72} - 27 q^{73} - 33 q^{74} + 14 q^{75} - 4 q^{76} + 43 q^{77} - 10 q^{78} - 19 q^{79} + 27 q^{80} + 74 q^{81} - 84 q^{82} + 20 q^{83} + 26 q^{84} + 16 q^{85} + 36 q^{86} - 28 q^{87} - 23 q^{88} + 123 q^{89} - 66 q^{90} - 9 q^{91} + 12 q^{92} + 48 q^{93} - 28 q^{94} + 28 q^{95} + 10 q^{97} - 58 q^{98} + 75 q^{99}+O(q^{100}) \) 42 * q - 42 * q^2 + 42 * q^4 + 27 * q^5 - 10 * q^7 - 42 * q^8 + 56 * q^9 - 27 * q^10 + 23 * q^11 + 15 * q^13 + 10 * q^14 + 6 * q^15 + 42 * q^16 + 14 * q^17 - 56 * q^18 - 4 * q^19 + 27 * q^20 + 26 * q^21 - 23 * q^22 + 12 * q^23 + 45 * q^25 - 15 * q^26 - 3 * q^27 - 10 * q^28 + 41 * q^29 - 6 * q^30 + 18 * q^31 - 42 * q^32 + 25 * q^33 - 14 * q^34 + 8 * q^35 + 56 * q^36 + 33 * q^37 + 4 * q^38 + 10 * q^39 - 27 * q^40 + 84 * q^41 - 26 * q^42 - 36 * q^43 + 23 * q^44 + 66 * q^45 - 12 * q^46 + 28 * q^47 + 58 * q^49 - 45 * q^50 + 17 * q^51 + 15 * q^52 + 68 * q^53 + 3 * q^54 - 28 * q^55 + 10 * q^56 - 9 * q^57 - 41 * q^58 + 59 * q^59 + 6 * q^60 + 41 * q^61 - 18 * q^62 - 28 * q^63 + 42 * q^64 + 44 * q^65 - 25 * q^66 + 14 * q^68 + 67 * q^69 - 8 * q^70 + 69 * q^71 - 56 * q^72 - 27 * q^73 - 33 * q^74 + 14 * q^75 - 4 * q^76 + 43 * q^77 - 10 * q^78 - 19 * q^79 + 27 * q^80 + 74 * q^81 - 84 * q^82 + 20 * q^83 + 26 * q^84 + 16 * q^85 + 36 * q^86 - 28 * q^87 - 23 * q^88 + 123 * q^89 - 66 * q^90 - 9 * q^91 + 12 * q^92 + 48 * q^93 - 28 * q^94 + 28 * q^95 + 10 * q^97 - 58 * q^98 + 75 * q^99

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