LMFDB - Embedded newform 2006.2.a.n.1.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [2006,2,Mod(1,2006)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(2006, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("2006.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 2006 = 2 \cdot 17 \cdot 59 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	2006.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:	$16.0179906455$
Analytic rank:	$1$
Dimension:	$3$
Coefficient field:	3.3.229.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{3} - 4x - 1 $ x^3 - 4*x - 1
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.3
Root			$2.11491$ of defining polynomial
Character	$\chi$	$=$	2006.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.00000 q^{2} +2.47283 q^{3} +1.00000 q^{4} -2.47283 q^{5} -2.47283 q^{6} -3.22982 q^{7} -1.00000 q^{8} +3.11491 q^{9} +O(q^{10})$	\(q-1.00000 q^{2} +2.47283 q^{3} +1.00000 q^{4} -2.47283 q^{5} -2.47283 q^{6} -3.22982 q^{7} -1.00000 q^{8} +3.11491 q^{9} +2.47283 q^{10} +3.11491 q^{11} +2.47283 q^{12} +0.756981 q^{13} +3.22982 q^{14} -6.11491 q^{15} +1.00000 q^{16} -1.00000 q^{17} -3.11491 q^{18} +1.22982 q^{19} -2.47283 q^{20} -7.98680 q^{21} -3.11491 q^{22} +0.715853 q^{23} -2.47283 q^{24} +1.11491 q^{25} -0.756981 q^{26} +0.284147 q^{27} -3.22982 q^{28} -8.87189 q^{29} +6.11491 q^{30} -7.30359 q^{31} -1.00000 q^{32} +7.70265 q^{33} +1.00000 q^{34} +7.98680 q^{35} +3.11491 q^{36} +1.70265 q^{37} -1.22982 q^{38} +1.87189 q^{39} +2.47283 q^{40} +5.81756 q^{41} +7.98680 q^{42} -1.41226 q^{43} +3.11491 q^{44} -7.70265 q^{45} -0.715853 q^{46} -4.81756 q^{47} +2.47283 q^{48} +3.43171 q^{49} -1.11491 q^{50} -2.47283 q^{51} +0.756981 q^{52} +0.0954606 q^{53} -0.284147 q^{54} -7.70265 q^{55} +3.22982 q^{56} +3.04113 q^{57} +8.87189 q^{58} -1.00000 q^{59} -6.11491 q^{60} -13.0474 q^{61} +7.30359 q^{62} -10.0606 q^{63} +1.00000 q^{64} -1.87189 q^{65} -7.70265 q^{66} -8.81756 q^{67} -1.00000 q^{68} +1.77018 q^{69} -7.98680 q^{70} +10.3579 q^{71} -3.11491 q^{72} +1.30359 q^{73} -1.70265 q^{74} +2.75698 q^{75} +1.22982 q^{76} -10.0606 q^{77} -1.87189 q^{78} -9.41850 q^{79} -2.47283 q^{80} -8.64207 q^{81} -5.81756 q^{82} -3.11491 q^{83} -7.98680 q^{84} +2.47283 q^{85} +1.41226 q^{86} -21.9387 q^{87} -3.11491 q^{88} -8.58774 q^{89} +7.70265 q^{90} -2.44491 q^{91} +0.715853 q^{92} -18.0606 q^{93} +4.81756 q^{94} -3.04113 q^{95} -2.47283 q^{96} -5.57454 q^{97} -3.43171 q^{98} +9.70265 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 3 q - 3 q^{2} + 2 q^{3} + 3 q^{4} - 2 q^{5} - 2 q^{6} + 3 q^{7} - 3 q^{8} + 3 q^{9}+O(q^{10}) $ 3 * q - 3 * q^2 + 2 * q^3 + 3 * q^4 - 2 * q^5 - 2 * q^6 + 3 * q^7 - 3 * q^8 + 3 * q^9	\( 3 q - 3 q^{2} + 2 q^{3} + 3 q^{4} - 2 q^{5} - 2 q^{6} + 3 q^{7} - 3 q^{8} + 3 q^{9} + 2 q^{10} + 3 q^{11} + 2 q^{12} - 5 q^{13} - 3 q^{14} - 12 q^{15} + 3 q^{16} - 3 q^{17} - 3 q^{18} - 9 q^{19} - 2 q^{20} - 4 q^{21} - 3 q^{22} + 4 q^{23} - 2 q^{24} - 3 q^{25} + 5 q^{26} - q^{27} + 3 q^{28} - 13 q^{29} + 12 q^{30} - 12 q^{31} - 3 q^{32} + 5 q^{33} + 3 q^{34} + 4 q^{35} + 3 q^{36} - 13 q^{37} + 9 q^{38} - 8 q^{39} + 2 q^{40} - 7 q^{41} + 4 q^{42} - 16 q^{43} + 3 q^{44} - 5 q^{45} - 4 q^{46} + 10 q^{47} + 2 q^{48} + 14 q^{49} + 3 q^{50} - 2 q^{51} - 5 q^{52} + 2 q^{53} + q^{54} - 5 q^{55} - 3 q^{56} + 13 q^{58} - 3 q^{59} - 12 q^{60} - 2 q^{61} + 12 q^{62} - 13 q^{63} + 3 q^{64} + 8 q^{65} - 5 q^{66} - 2 q^{67} - 3 q^{68} + 18 q^{69} - 4 q^{70} + 32 q^{71} - 3 q^{72} - 6 q^{73} + 13 q^{74} + q^{75} - 9 q^{76} - 13 q^{77} + 8 q^{78} - 12 q^{79} - 2 q^{80} - 25 q^{81} + 7 q^{82} - 3 q^{83} - 4 q^{84} + 2 q^{85} + 16 q^{86} - 7 q^{87} - 3 q^{88} - 14 q^{89} + 5 q^{90} - 31 q^{91} + 4 q^{92} - 37 q^{93} - 10 q^{94} - 2 q^{96} + 15 q^{97} - 14 q^{98} + 11 q^{99}+O(q^{100}) \) 3 * q - 3 * q^2 + 2 * q^3 + 3 * q^4 - 2 * q^5 - 2 * q^6 + 3 * q^7 - 3 * q^8 + 3 * q^9 + 2 * q^10 + 3 * q^11 + 2 * q^12 - 5 * q^13 - 3 * q^14 - 12 * q^15 + 3 * q^16 - 3 * q^17 - 3 * q^18 - 9 * q^19 - 2 * q^20 - 4 * q^21 - 3 * q^22 + 4 * q^23 - 2 * q^24 - 3 * q^25 + 5 * q^26 - q^27 + 3 * q^28 - 13 * q^29 + 12 * q^30 - 12 * q^31 - 3 * q^32 + 5 * q^33 + 3 * q^34 + 4 * q^35 + 3 * q^36 - 13 * q^37 + 9 * q^38 - 8 * q^39 + 2 * q^40 - 7 * q^41 + 4 * q^42 - 16 * q^43 + 3 * q^44 - 5 * q^45 - 4 * q^46 + 10 * q^47 + 2 * q^48 + 14 * q^49 + 3 * q^50 - 2 * q^51 - 5 * q^52 + 2 * q^53 + q^54 - 5 * q^55 - 3 * q^56 + 13 * q^58 - 3 * q^59 - 12 * q^60 - 2 * q^61 + 12 * q^62 - 13 * q^63 + 3 * q^64 + 8 * q^65 - 5 * q^66 - 2 * q^67 - 3 * q^68 + 18 * q^69 - 4 * q^70 + 32 * q^71 - 3 * q^72 - 6 * q^73 + 13 * q^74 + q^75 - 9 * q^76 - 13 * q^77 + 8 * q^78 - 12 * q^79 - 2 * q^80 - 25 * q^81 + 7 * q^82 - 3 * q^83 - 4 * q^84 + 2 * q^85 + 16 * q^86 - 7 * q^87 - 3 * q^88 - 14 * q^89 + 5 * q^90 - 31 * q^91 + 4 * q^92 - 37 * q^93 - 10 * q^94 - 2 * q^96 + 15 * q^97 - 14 * q^98 + 11 * 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
$3$	2.47283	1.42769	0.713846	−	0.700303i	$-0.246952\pi$
$3$	2.47283	1.42769	0.713846	+	0.700303i	$0.246952\pi$
$4$	1.00000	0.500000
$5$	−2.47283	−1.10588	−0.552942	−	0.833219i	$-0.686495\pi$
$5$	−2.47283	−1.10588	−0.552942	+	0.833219i	$0.686495\pi$
$6$	−2.47283	−1.00953
$7$	−3.22982	−1.22076	−0.610378	−	0.792111i	$-0.708982\pi$
$7$	−3.22982	−1.22076	−0.610378	+	0.792111i	$0.708982\pi$
$8$	−1.00000	−0.353553
$9$	3.11491	1.03830
$10$	2.47283	0.781979
$11$	3.11491	0.939180	0.469590	−	0.882885i	$-0.344402\pi$
$11$	3.11491	0.939180	0.469590	+	0.882885i	$0.344402\pi$
$12$	2.47283	0.713846
$13$	0.756981	0.209949	0.104974	−	0.994475i	$-0.466524\pi$
$13$	0.756981	0.209949	0.104974	+	0.994475i	$0.466524\pi$
$14$	3.22982	0.863204
$15$	−6.11491	−1.57886
$16$	1.00000	0.250000
$17$	−1.00000	−0.242536
$17$	−1.00000	−0.242536
$18$	−3.11491	−0.734191
$19$	1.22982	0.282139	0.141069	−	0.990000i	$-0.454946\pi$
$19$	1.22982	0.282139	0.141069	+	0.990000i	$0.454946\pi$
$20$	−2.47283	−0.552942
$21$	−7.98680	−1.74286
$22$	−3.11491	−0.664101
$23$	0.715853	0.149266	0.0746328	−	0.997211i	$-0.476222\pi$
$23$	0.715853	0.149266	0.0746328	+	0.997211i	$0.476222\pi$
$24$	−2.47283	−0.504765
$25$	1.11491	0.222982
$26$	−0.756981	−0.148456
$27$	0.284147	0.0546842
$28$	−3.22982	−0.610378
$29$	−8.87189	−1.64747	−0.823734	−	0.566976i	$-0.808113\pi$
$29$	−8.87189	−1.64747	−0.823734	+	0.566976i	$0.808113\pi$
$30$	6.11491	1.11642
$31$	−7.30359	−1.31176	−0.655882	−	0.754863i	$-0.727703\pi$
$31$	−7.30359	−1.31176	−0.655882	+	0.754863i	$0.727703\pi$
$32$	−1.00000	−0.176777
$33$	7.70265	1.34086
$34$	1.00000	0.171499
$35$	7.98680	1.35001
$36$	3.11491	0.519151
$37$	1.70265	0.279914	0.139957	−	0.990158i	$-0.455304\pi$
$37$	1.70265	0.279914	0.139957	+	0.990158i	$0.455304\pi$
$38$	−1.22982	−0.199502
$39$	1.87189	0.299742
$40$	2.47283	0.390989
$41$	5.81756	0.908550	0.454275	−	0.890862i	$-0.349898\pi$
$41$	5.81756	0.908550	0.454275	+	0.890862i	$0.349898\pi$
$42$	7.98680	1.23239
$43$	−1.41226	−0.215367	−0.107684	−	0.994185i	$-0.534343\pi$
$43$	−1.41226	−0.215367	−0.107684	+	0.994185i	$0.534343\pi$
$44$	3.11491	0.469590
$45$	−7.70265	−1.14824
$46$	−0.715853	−0.105547
$47$	−4.81756	−0.702713	−0.351356	−	0.936242i	$-0.614279\pi$
$47$	−4.81756	−0.702713	−0.351356	+	0.936242i	$0.614279\pi$
$48$	2.47283	0.356923
$49$	3.43171	0.490244
$50$	−1.11491	−0.157672
$51$	−2.47283	−0.346266
$52$	0.756981	0.104974
$53$	0.0954606	0.0131125	0.00655626	−	0.999979i	$-0.497913\pi$
$53$	0.0954606	0.0131125	0.00655626	+	0.999979i	$0.497913\pi$
$54$	−0.284147	−0.0386675
$55$	−7.70265	−1.03862
$56$	3.22982	0.431602
$57$	3.04113	0.402807
$58$	8.87189	1.16494
$59$	−1.00000	−0.130189
$59$	−1.00000	−0.130189
$60$	−6.11491	−0.789431
$61$	−13.0474	−1.67054	−0.835272	−	0.549836i	$-0.814690\pi$
$61$	−13.0474	−1.67054	−0.835272	+	0.549836i	$0.814690\pi$
$62$	7.30359	0.927557
$63$	−10.0606	−1.26751
$64$	1.00000	0.125000
$65$	−1.87189	−0.232179
$66$	−7.70265	−0.948131
$67$	−8.81756	−1.07724	−0.538618	−	0.842550i	$-0.681053\pi$
$67$	−8.81756	−1.07724	−0.538618	+	0.842550i	$0.681053\pi$
$68$	−1.00000	−0.121268
$69$	1.77018	0.213105
$70$	−7.98680	−0.954605
$71$	10.3579	1.22926	0.614630	−	0.788816i	$-0.289305\pi$
$71$	10.3579	1.22926	0.614630	+	0.788816i	$0.289305\pi$
$72$	−3.11491	−0.367095
$73$	1.30359	0.152574	0.0762871	−	0.997086i	$-0.475693\pi$
$73$	1.30359	0.152574	0.0762871	+	0.997086i	$0.475693\pi$
$74$	−1.70265	−0.197929
$75$	2.75698	0.318349
$76$	1.22982	0.141069
$77$	−10.0606	−1.14651
$78$	−1.87189	−0.211950
$79$	−9.41850	−1.05966	−0.529832	−	0.848103i	$-0.677745\pi$
$79$	−9.41850	−1.05966	−0.529832	+	0.848103i	$0.677745\pi$
$80$	−2.47283	−0.276471
$81$	−8.64207	−0.960230
$82$	−5.81756	−0.642442
$83$	−3.11491	−0.341906	−0.170953	−	0.985279i	$-0.554685\pi$
$83$	−3.11491	−0.341906	−0.170953	+	0.985279i	$0.554685\pi$
$84$	−7.98680	−0.871431
$85$	2.47283	0.268216
$86$	1.41226	0.152288
$87$	−21.9387	−2.35208
$88$	−3.11491	−0.332050
$89$	−8.58774	−0.910299	−0.455149	−	0.890415i	$-0.650414\pi$
$89$	−8.58774	−0.910299	−0.455149	+	0.890415i	$0.650414\pi$
$90$	7.70265	0.811930
$91$	−2.44491	−0.256296
$92$	0.715853	0.0746328
$93$	−18.0606	−1.87279
$94$	4.81756	0.496893
$95$	−3.04113	−0.312013
$96$	−2.47283	−0.252383
$97$	−5.57454	−0.566009	−0.283004	−	0.959119i	$-0.591331\pi$
$97$	−5.57454	−0.566009	−0.283004	+	0.959119i	$0.591331\pi$
$98$	−3.43171	−0.346655
$99$	9.70265	0.975153
$100$	1.11491	0.111491
$101$	−13.6157	−1.35481	−0.677405	−	0.735611i	$-0.736895\pi$
$101$	−13.6157	−1.35481	−0.677405	+	0.735611i	$0.736895\pi$
$102$	2.47283	0.244847
$103$	−3.07378	−0.302868	−0.151434	−	0.988467i	$-0.548389\pi$
$103$	−3.07378	−0.302868	−0.151434	+	0.988467i	$0.548389\pi$
$104$	−0.756981	−0.0742281
$105$	19.7500	1.92740
$106$	−0.0954606	−0.00927196
$107$	6.40530	0.619224	0.309612	−	0.950863i	$-0.399801\pi$
$107$	6.40530	0.619224	0.309612	+	0.950863i	$0.399801\pi$
$108$	0.284147	0.0273421
$109$	3.53341	0.338439	0.169220	−	0.985578i	$-0.445875\pi$
$109$	3.53341	0.338439	0.169220	+	0.985578i	$0.445875\pi$
$110$	7.70265	0.734419
$111$	4.21037	0.399630
$112$	−3.22982	−0.305189
$113$	14.2493	1.34046	0.670229	−	0.742154i	$-0.266196\pi$
$113$	14.2493	1.34046	0.670229	+	0.742154i	$0.266196\pi$
$114$	−3.04113	−0.284828
$115$	−1.77018	−0.165071
$116$	−8.87189	−0.823734
$117$	2.35793	0.217990
$118$	1.00000	0.0920575
$119$	3.22982	0.296077
$120$	6.11491	0.558212
$121$	−1.29735	−0.117941
$122$	13.0474	1.18125
$123$	14.3859	1.29713
$124$	−7.30359	−0.655882
$125$	9.60719	0.859293
$126$	10.0606	0.896267
$127$	−14.2841	−1.26751	−0.633757	−	0.773533i	$-0.718488\pi$
$127$	−14.2841	−1.26751	−0.633757	+	0.773533i	$0.718488\pi$
$128$	−1.00000	−0.0883883
$129$	−3.49228	−0.307478
$130$	1.87189	0.164176
$131$	−18.8370	−1.64580	−0.822898	−	0.568189i	$-0.807644\pi$
$131$	−18.8370	−1.64580	−0.822898	+	0.568189i	$0.807644\pi$
$132$	7.70265	0.670430
$133$	−3.97208	−0.344423
$134$	8.81756	0.761721
$135$	−0.702649	−0.0604744
$136$	1.00000	0.0857493
$137$	−0.472834	−0.0403969	−0.0201985	−	0.999796i	$-0.506430\pi$
$137$	−0.472834	−0.0403969	−0.0201985	+	0.999796i	$0.506430\pi$
$138$	−1.77018	−0.150688
$139$	3.15604	0.267691	0.133846	−	0.991002i	$-0.457267\pi$
$139$	3.15604	0.267691	0.133846	+	0.991002i	$0.457267\pi$
$140$	7.98680	0.675007
$141$	−11.9130	−1.00326
$142$	−10.3579	−0.869218
$143$	2.35793	0.197180
$144$	3.11491	0.259576
$145$	21.9387	1.82191
$146$	−1.30359	−0.107886
$147$	8.48604	0.699917
$148$	1.70265	0.139957
$149$	−3.98055	−0.326100	−0.163050	−	0.986618i	$-0.552133\pi$
$149$	−3.98055	−0.326100	−0.163050	+	0.986618i	$0.552133\pi$
$150$	−2.75698	−0.225107
$151$	19.1755	1.56048	0.780239	−	0.625481i	$-0.215097\pi$
$151$	19.1755	1.56048	0.780239	+	0.625481i	$0.215097\pi$
$152$	−1.22982	−0.0997512
$153$	−3.11491	−0.251825
$154$	10.0606	0.810704
$155$	18.0606	1.45066
$156$	1.87189	0.149871
$157$	0.466591	0.0372380	0.0186190	−	0.999827i	$-0.494073\pi$
$157$	0.466591	0.0372380	0.0186190	+	0.999827i	$0.494073\pi$
$158$	9.41850	0.749296
$159$	0.236058	0.0187206
$160$	2.47283	0.195495
$161$	−2.31207	−0.182217
$162$	8.64207	0.678985
$163$	−3.78963	−0.296827	−0.148413	−	0.988925i	$-0.547417\pi$
$163$	−3.78963	−0.296827	−0.148413	+	0.988925i	$0.547417\pi$
$164$	5.81756	0.454275
$165$	−19.0474	−1.48284
$166$	3.11491	0.241764
$167$	2.47283	0.191354	0.0956768	−	0.995412i	$-0.469498\pi$
$167$	2.47283	0.191354	0.0956768	+	0.995412i	$0.469498\pi$
$168$	7.98680	0.616195
$169$	−12.4270	−0.955922
$170$	−2.47283	−0.189658
$171$	3.83076	0.292946
$172$	−1.41226	−0.107684
$173$	6.47908	0.492595	0.246298	−	0.969194i	$-0.420786\pi$
$173$	6.47908	0.492595	0.246298	+	0.969194i	$0.420786\pi$
$174$	21.9387	1.66317
$175$	−3.60095	−0.272206
$176$	3.11491	0.234795
$177$	−2.47283	−0.185870
$178$	8.58774	0.643678
$179$	22.6678	1.69427	0.847134	−	0.531379i	$-0.178326\pi$
$179$	22.6678	1.69427	0.847134	+	0.531379i	$0.178326\pi$
$180$	−7.70265	−0.574122
$181$	19.3098	1.43529	0.717644	−	0.696410i	$-0.245220\pi$
$181$	19.3098	1.43529	0.717644	+	0.696410i	$0.245220\pi$
$182$	2.44491	0.181229
$183$	−32.2640	−2.38502
$184$	−0.715853	−0.0527734
$185$	−4.21037	−0.309552
$186$	18.0606	1.32427
$187$	−3.11491	−0.227785
$188$	−4.81756	−0.351356
$189$	−0.917743	−0.0667560
$190$	3.04113	0.220627
$191$	−10.9045	−0.789025	−0.394512	−	0.918891i	$-0.629086\pi$
$191$	−10.9045	−0.789025	−0.394512	+	0.918891i	$0.629086\pi$
$192$	2.47283	0.178461
$193$	22.8649	1.64585	0.822927	−	0.568147i	$-0.192340\pi$
$193$	22.8649	1.64585	0.822927	+	0.568147i	$0.192340\pi$
$194$	5.57454	0.400228
$195$	−4.62887	−0.331480
$196$	3.43171	0.245122
$197$	11.7849	0.839640	0.419820	−	0.907607i	$-0.362093\pi$
$197$	11.7849	0.839640	0.419820	+	0.907607i	$0.362093\pi$
$198$	−9.70265	−0.689537
$199$	−25.3991	−1.80049	−0.900246	−	0.435382i	$-0.856613\pi$
$199$	−25.3991	−1.80049	−0.900246	+	0.435382i	$0.856613\pi$
$200$	−1.11491	−0.0788359
$201$	−21.8044	−1.53796
$202$	13.6157	0.957995
$203$	28.6546	2.01116
$204$	−2.47283	−0.173133
$205$	−14.3859	−1.00475
$206$	3.07378	0.214160
$207$	2.22982	0.154983
$208$	0.756981	0.0524872
$209$	3.83076	0.264979
$210$	−19.7500	−1.36288
$211$	−8.79811	−0.605687	−0.302843	−	0.953040i	$-0.597936\pi$
$211$	−8.79811	−0.605687	−0.302843	+	0.953040i	$0.597936\pi$
$212$	0.0954606	0.00655626
$213$	25.6134	1.75500
$214$	−6.40530	−0.437857
$215$	3.49228	0.238172
$216$	−0.284147	−0.0193338
$217$	23.5893	1.60134
$218$	−3.53341	−0.239313
$219$	3.22357	0.217829
$220$	−7.70265	−0.519312
$221$	−0.756981	−0.0509201
$222$	−4.21037	−0.282581
$223$	22.0342	1.47552	0.737759	−	0.675065i	$-0.235884\pi$
$223$	22.0342	1.47552	0.737759	+	0.675065i	$0.235884\pi$
$224$	3.22982	0.215801
$225$	3.47283	0.231522
$226$	−14.2493	−0.947847
$227$	17.4247	1.15652	0.578260	−	0.815852i	$-0.303732\pi$
$227$	17.4247	1.15652	0.578260	+	0.815852i	$0.303732\pi$
$228$	3.04113	0.201404
$229$	−1.28415	−0.0848588	−0.0424294	−	0.999099i	$-0.513510\pi$
$229$	−1.28415	−0.0848588	−0.0424294	+	0.999099i	$0.513510\pi$
$230$	1.77018	0.116723
$231$	−24.8781	−1.63686
$232$	8.87189	0.582468
$233$	−5.85021	−0.383260	−0.191630	−	0.981467i	$-0.561377\pi$
$233$	−5.85021	−0.383260	−0.191630	+	0.981467i	$0.561377\pi$
$234$	−2.35793	−0.154142
$235$	11.9130	0.777120
$236$	−1.00000	−0.0650945
$237$	−23.2904	−1.51287
$238$	−3.22982	−0.209358
$239$	5.54661	0.358781	0.179390	−	0.983778i	$-0.442588\pi$
$239$	5.54661	0.358781	0.179390	+	0.983778i	$0.442588\pi$
$240$	−6.11491	−0.394716
$241$	−13.0411	−0.840053	−0.420026	−	0.907512i	$-0.637979\pi$
$241$	−13.0411	−0.840053	−0.420026	+	0.907512i	$0.637979\pi$
$242$	1.29735	0.0833969
$243$	−22.2229	−1.42560
$244$	−13.0474	−0.835272
$245$	−8.48604	−0.542153
$246$	−14.3859	−0.917208
$247$	0.930947	0.0592347
$248$	7.30359	0.463779
$249$	−7.70265	−0.488136
$250$	−9.60719	−0.607612
$251$	−11.9651	−0.755231	−0.377616	−	0.925962i	$-0.623256\pi$
$251$	−11.9651	−0.755231	−0.377616	+	0.925962i	$0.623256\pi$
$252$	−10.0606	−0.633757
$253$	2.22982	0.140187
$254$	14.2841	0.896267
$255$	6.11491	0.382930
$256$	1.00000	0.0625000
$257$	−9.47908	−0.591289	−0.295644	−	0.955298i	$-0.595534\pi$
$257$	−9.47908	−0.591289	−0.295644	+	0.955298i	$0.595534\pi$
$258$	3.49228	0.217420
$259$	−5.49924	−0.341706
$260$	−1.87189	−0.116090
$261$	−27.6351	−1.71057
$262$	18.8370	1.16375
$263$	−0.194930	−0.0120199	−0.00600994	−	0.999982i	$-0.501913\pi$
$263$	−0.194930	−0.0120199	−0.00600994	+	0.999982i	$0.501913\pi$
$264$	−7.70265	−0.474065
$265$	−0.236058	−0.0145009
$266$	3.97208	0.243544
$267$	−21.2361	−1.29963
$268$	−8.81756	−0.538618
$269$	23.7174	1.44607	0.723037	−	0.690810i	$-0.242746\pi$
$269$	23.7174	1.44607	0.723037	+	0.690810i	$0.242746\pi$
$270$	0.702649	0.0427619
$271$	−31.1964	−1.89505	−0.947525	−	0.319683i	$-0.896424\pi$
$271$	−31.1964	−1.89505	−0.947525	+	0.319683i	$0.896424\pi$
$272$	−1.00000	−0.0606339
$273$	−6.04585	−0.365912
$274$	0.472834	0.0285649
$275$	3.47283	0.209420
$276$	1.77018	0.106553
$277$	−14.2166	−0.854193	−0.427097	−	0.904206i	$-0.640464\pi$
$277$	−14.2166	−0.854193	−0.427097	+	0.904206i	$0.640464\pi$
$278$	−3.15604	−0.189286
$279$	−22.7500	−1.36201
$280$	−7.98680	−0.477302
$281$	4.55286	0.271601	0.135800	−	0.990736i	$-0.456639\pi$
$281$	4.55286	0.271601	0.135800	+	0.990736i	$0.456639\pi$
$282$	11.9130	0.709410
$283$	−10.1692	−0.604499	−0.302249	−	0.953229i	$-0.597738\pi$
$283$	−10.1692	−0.604499	−0.302249	+	0.953229i	$0.597738\pi$
$284$	10.3579	0.614630
$285$	−7.52021	−0.445459
$286$	−2.35793	−0.139427
$287$	−18.7896	−1.10912
$288$	−3.11491	−0.183548
$289$	1.00000	0.0588235
$290$	−21.9387	−1.28829
$291$	−13.7849	−0.808085
$292$	1.30359	0.0762871
$293$	5.37961	0.314280	0.157140	−	0.987576i	$-0.449773\pi$
$293$	5.37961	0.314280	0.157140	+	0.987576i	$0.449773\pi$
$294$	−8.48604	−0.494916
$295$	2.47283	0.143974
$296$	−1.70265	−0.0989645
$297$	0.885092	0.0513583
$298$	3.98055	0.230587
$299$	0.541887	0.0313381
$300$	2.75698	0.159174
$301$	4.56133	0.262911
$302$	−19.1755	−1.10343
$303$	−33.6693	−1.93425
$304$	1.22982	0.0705347
$305$	32.2640	1.84743
$306$	3.11491	0.178067
$307$	−3.71585	−0.212075	−0.106037	−	0.994362i	$-0.533816\pi$
$307$	−3.71585	−0.212075	−0.106037	+	0.994362i	$0.533816\pi$
$308$	−10.0606	−0.573254
$309$	−7.60095	−0.432403
$310$	−18.0606	−1.02577
$311$	16.2577	0.921892	0.460946	−	0.887428i	$-0.347510\pi$
$311$	16.2577	0.921892	0.460946	+	0.887428i	$0.347510\pi$
$312$	−1.87189	−0.105975
$313$	13.7243	0.775745	0.387873	−	0.921713i	$-0.373210\pi$
$313$	13.7243	0.775745	0.387873	+	0.921713i	$0.373210\pi$
$314$	−0.466591	−0.0263312
$315$	24.8781	1.40172
$316$	−9.41850	−0.529832
$317$	25.0279	1.40571	0.702854	−	0.711334i	$-0.251909\pi$
$317$	25.0279	1.40571	0.702854	+	0.711334i	$0.251909\pi$
$318$	−0.236058	−0.0132375
$319$	−27.6351	−1.54727
$320$	−2.47283	−0.138236
$321$	15.8392	0.884060
$322$	2.31207	0.128847
$323$	−1.22982	−0.0684287
$324$	−8.64207	−0.480115
$325$	0.843964	0.0468147
$326$	3.78963	0.209888
$327$	8.73753	0.483187
$328$	−5.81756	−0.321221
$329$	15.5598	0.857840
$330$	19.0474	1.04852
$331$	−8.43394	−0.463571	−0.231786	−	0.972767i	$-0.574457\pi$
$331$	−8.43394	−0.463571	−0.231786	+	0.972767i	$0.574457\pi$
$332$	−3.11491	−0.170953
$333$	5.30359	0.290635
$334$	−2.47283	−0.135307
$335$	21.8044	1.19130
$336$	−7.98680	−0.435715
$337$	14.6072	0.795704	0.397852	−	0.917450i	$-0.369756\pi$
$337$	14.6072	0.795704	0.397852	+	0.917450i	$0.369756\pi$
$338$	12.4270	0.675939
$339$	35.2361	1.91376
$340$	2.47283	0.134108
$341$	−22.7500	−1.23198
$342$	−3.83076	−0.207144
$343$	11.5249	0.622288
$344$	1.41226	0.0761439
$345$	−4.37737	−0.235670
$346$	−6.47908	−0.348317
$347$	−12.4185	−0.666660	−0.333330	−	0.942810i	$-0.608172\pi$
$347$	−12.4185	−0.666660	−0.333330	+	0.942810i	$0.608172\pi$
$348$	−21.9387	−1.17604
$349$	−5.29111	−0.283227	−0.141613	−	0.989922i	$-0.545229\pi$
$349$	−5.29111	−0.283227	−0.141613	+	0.989922i	$0.545229\pi$
$350$	3.60095	0.192479
$351$	0.215094	0.0114809
$352$	−3.11491	−0.166025
$353$	28.3704	1.51000	0.755002	−	0.655722i	$-0.227636\pi$
$353$	28.3704	1.51000	0.755002	+	0.655722i	$0.227636\pi$
$354$	2.47283	0.131430
$355$	−25.6134	−1.35942
$356$	−8.58774	−0.455149
$357$	7.98680	0.422706
$358$	−22.6678	−1.19803
$359$	−22.9861	−1.21316	−0.606579	−	0.795023i	$-0.707459\pi$
$359$	−22.9861	−1.21316	−0.606579	+	0.795023i	$0.707459\pi$
$360$	7.70265	0.405965
$361$	−17.4876	−0.920398
$362$	−19.3098	−1.01490
$363$	−3.20813	−0.168383
$364$	−2.44491	−0.128148
$365$	−3.22357	−0.168729
$366$	32.2640	1.68647
$367$	−3.63511	−0.189751	−0.0948757	−	0.995489i	$-0.530245\pi$
$367$	−3.63511	−0.189751	−0.0948757	+	0.995489i	$0.530245\pi$
$368$	0.715853	0.0373164
$369$	18.1212	0.943349
$370$	4.21037	0.218887
$371$	−0.308320	−0.0160072
$372$	−18.0606	−0.936397
$373$	1.72906	0.0895272	0.0447636	−	0.998998i	$-0.485747\pi$
$373$	1.72906	0.0895272	0.0447636	+	0.998998i	$0.485747\pi$
$374$	3.11491	0.161068
$375$	23.7570	1.22681
$376$	4.81756	0.248447
$377$	−6.71585	−0.345884
$378$	0.917743	0.0472036
$379$	19.7353	1.01373	0.506867	−	0.862024i	$-0.330803\pi$
$379$	19.7353	1.01373	0.506867	+	0.862024i	$0.330803\pi$
$380$	−3.04113	−0.156007
$381$	−35.3223	−1.80962
$382$	10.9045	0.557925
$383$	29.0474	1.48425	0.742126	−	0.670261i	$-0.233818\pi$
$383$	29.0474	1.48425	0.742126	+	0.670261i	$0.233818\pi$
$384$	−2.47283	−0.126191
$385$	24.8781	1.26791
$386$	−22.8649	−1.16379
$387$	−4.39905	−0.223617
$388$	−5.57454	−0.283004
$389$	11.6810	0.592249	0.296124	−	0.955149i	$-0.404306\pi$
$389$	11.6810	0.592249	0.296124	+	0.955149i	$0.404306\pi$
$390$	4.62887	0.234392
$391$	−0.715853	−0.0362022
$392$	−3.43171	−0.173327
$393$	−46.5808	−2.34969
$394$	−11.7849	−0.593715
$395$	23.2904	1.17187
$396$	9.70265	0.487576
$397$	27.0474	1.35747	0.678734	−	0.734384i	$-0.262529\pi$
$397$	27.0474	1.35747	0.678734	+	0.734384i	$0.262529\pi$
$398$	25.3991	1.27314
$399$	−9.82228	−0.491729
$400$	1.11491	0.0557454
$401$	−18.4791	−0.922801	−0.461401	−	0.887192i	$-0.652653\pi$
$401$	−18.4791	−0.922801	−0.461401	+	0.887192i	$0.652653\pi$
$402$	21.8044	1.08750
$403$	−5.52868	−0.275403
$404$	−13.6157	−0.677405
$405$	21.3704	1.06190
$406$	−28.6546	−1.42210
$407$	5.30359	0.262889
$408$	2.47283	0.122424
$409$	−18.3796	−0.908813	−0.454407	−	0.890794i	$-0.650149\pi$
$409$	−18.3796	−0.908813	−0.454407	+	0.890794i	$0.650149\pi$
$410$	14.3859	0.710467
$411$	−1.16924	−0.0576743
$412$	−3.07378	−0.151434
$413$	3.22982	0.158929
$414$	−2.22982	−0.109589
$415$	7.70265	0.378108
$416$	−0.756981	−0.0371141
$417$	7.80435	0.382181
$418$	−3.83076	−0.187369
$419$	25.5070	1.24610	0.623049	−	0.782183i	$-0.285894\pi$
$419$	25.5070	1.24610	0.623049	+	0.782183i	$0.285894\pi$
$420$	19.7500	0.963702
$421$	24.4138	1.18985	0.594927	−	0.803780i	$-0.297181\pi$
$421$	24.4138	1.18985	0.594927	+	0.803780i	$0.297181\pi$
$422$	8.79811	0.428285
$423$	−15.0062	−0.729629
$424$	−0.0954606	−0.00463598
$425$	−1.11491	−0.0540810
$426$	−25.6134	−1.24097
$427$	42.1406	2.03933
$428$	6.40530	0.309612
$429$	5.83076	0.281512
$430$	−3.49228	−0.168413
$431$	20.9673	1.00996	0.504981	−	0.863131i	$-0.331500\pi$
$431$	20.9673	1.00996	0.504981	+	0.863131i	$0.331500\pi$
$432$	0.284147	0.0136710
$433$	−7.17620	−0.344866	−0.172433	−	0.985021i	$-0.555163\pi$
$433$	−7.17620	−0.344866	−0.172433	+	0.985021i	$0.555163\pi$
$434$	−23.5893	−1.13232
$435$	54.2508	2.60113
$436$	3.53341	0.169220
$437$	0.880366	0.0421136
$438$	−3.22357	−0.154028
$439$	−4.16701	−0.198880	−0.0994402	−	0.995044i	$-0.531705\pi$
$439$	−4.16701	−0.198880	−0.0994402	+	0.995044i	$0.531705\pi$
$440$	7.70265	0.367209
$441$	10.6894	0.509021
$442$	0.756981	0.0360059
$443$	2.02641	0.0962775	0.0481388	−	0.998841i	$-0.484671\pi$
$443$	2.02641	0.0962775	0.0481388	+	0.998841i	$0.484671\pi$
$444$	4.21037	0.199815
$445$	21.2361	1.00669
$446$	−22.0342	−1.04335
$447$	−9.84325	−0.465570
$448$	−3.22982	−0.152594
$449$	5.06058	0.238823	0.119412	−	0.992845i	$-0.461899\pi$
$449$	5.06058	0.238823	0.119412	+	0.992845i	$0.461899\pi$
$450$	−3.47283	−0.163711
$451$	18.1212	0.853292
$452$	14.2493	0.670229
$453$	47.4178	2.22788
$454$	−17.4247	−0.817784
$455$	6.04585	0.283434
$456$	−3.04113	−0.142414
$457$	−5.21661	−0.244023	−0.122011	−	0.992529i	$-0.538934\pi$
$457$	−5.21661	−0.244023	−0.122011	+	0.992529i	$0.538934\pi$
$458$	1.28415	0.0600043
$459$	−0.284147	−0.0132629
$460$	−1.77018	−0.0825353
$461$	−38.8689	−1.81031	−0.905153	−	0.425085i	$-0.860244\pi$
$461$	−38.8689	−1.81031	−0.905153	+	0.425085i	$0.860244\pi$
$462$	24.8781	1.15744
$463$	−9.61343	−0.446774	−0.223387	−	0.974730i	$-0.571711\pi$
$463$	−9.61343	−0.446774	−0.223387	+	0.974730i	$0.571711\pi$
$464$	−8.87189	−0.411867
$465$	44.6608	2.07110
$466$	5.85021	0.271006
$467$	15.1949	0.703137	0.351569	−	0.936162i	$-0.385648\pi$
$467$	15.1949	0.703137	0.351569	+	0.936162i	$0.385648\pi$
$468$	2.35793	0.108995
$469$	28.4791	1.31504
$470$	−11.9130	−0.549507
$471$	1.15380	0.0531644
$472$	1.00000	0.0460287
$473$	−4.39905	−0.202269
$474$	23.2904	1.06976
$475$	1.37113	0.0629118
$476$	3.22982	0.148038
$477$	0.297351	0.0136148
$478$	−5.54661	−0.253696
$479$	14.9457	0.682885	0.341442	−	0.939903i	$-0.389085\pi$
$479$	14.9457	0.682885	0.341442	+	0.939903i	$0.389085\pi$
$480$	6.11491	0.279106
$481$	1.28887	0.0587676
$482$	13.0411	0.594007
$483$	−5.71737	−0.260149
$484$	−1.29735	−0.0589705
$485$	13.7849	0.625940
$486$	22.2229	1.00805
$487$	−25.6700	−1.16322	−0.581609	−	0.813468i	$-0.697577\pi$
$487$	−25.6700	−1.16322	−0.581609	+	0.813468i	$0.697577\pi$
$488$	13.0474	0.590627
$489$	−9.37113	−0.423777
$490$	8.48604	0.383360
$491$	29.1600	1.31597	0.657987	−	0.753029i	$-0.271408\pi$
$491$	29.1600	1.31597	0.657987	+	0.753029i	$0.271408\pi$
$492$	14.3859	0.648564
$493$	8.87189	0.399570
$494$	−0.930947	−0.0418853
$495$	−23.9930	−1.07841
$496$	−7.30359	−0.327941
$497$	−33.4542	−1.50063
$498$	7.70265	0.345164
$499$	−13.2493	−0.593118	−0.296559	−	0.955014i	$-0.595839\pi$
$499$	−13.2493	−0.593118	−0.296559	+	0.955014i	$0.595839\pi$
$500$	9.60719	0.429647
$501$	6.11491	0.273194
$502$	11.9651	0.534029
$503$	−4.81532	−0.214705	−0.107352	−	0.994221i	$-0.534237\pi$
$503$	−4.81532	−0.214705	−0.107352	+	0.994221i	$0.534237\pi$
$504$	10.0606	0.448134
$505$	33.6693	1.49826
$506$	−2.22982	−0.0991274
$507$	−30.7299	−1.36476
$508$	−14.2841	−0.633757
$509$	27.1880	1.20509	0.602543	−	0.798087i	$-0.294154\pi$
$509$	27.1880	1.20509	0.602543	+	0.798087i	$0.294154\pi$
$510$	−6.11491	−0.270773
$511$	−4.21037	−0.186256
$512$	−1.00000	−0.0441942
$513$	0.349449	0.0154285
$514$	9.47908	0.418104
$515$	7.60095	0.334938
$516$	−3.49228	−0.153739
$517$	−15.0062	−0.659974
$518$	5.49924	0.241623
$519$	16.0217	0.703274
$520$	1.87189	0.0820878
$521$	−3.17548	−0.139120	−0.0695602	−	0.997578i	$-0.522160\pi$
$521$	−3.17548	−0.139120	−0.0695602	+	0.997578i	$0.522160\pi$
$522$	27.6351	1.20956
$523$	−16.5529	−0.723806	−0.361903	−	0.932216i	$-0.617873\pi$
$523$	−16.5529	−0.723806	−0.361903	+	0.932216i	$0.617873\pi$
$524$	−18.8370	−0.822898
$525$	−8.90454	−0.388626
$526$	0.194930	0.00849934
$527$	7.30359	0.318150
$528$	7.70265	0.335215
$529$	−22.4876	−0.977720
$530$	0.236058	0.0102537
$531$	−3.11491	−0.135175
$532$	−3.97208	−0.172211
$533$	4.40378	0.190749
$534$	21.2361	0.918974
$535$	−15.8392	−0.684790
$536$	8.81756	0.380860
$537$	56.0536	2.41889
$538$	−23.7174	−1.02253
$539$	10.6894	0.460427
$540$	−0.702649	−0.0302372
$541$	−16.8976	−0.726484	−0.363242	−	0.931695i	$-0.618330\pi$
$541$	−16.8976	−0.726484	−0.363242	+	0.931695i	$0.618330\pi$
$542$	31.1964	1.34000
$543$	47.7500	2.04915
$544$	1.00000	0.0428746
$545$	−8.73753	−0.374275
$546$	6.04585	0.258739
$547$	18.3657	0.785260	0.392630	−	0.919697i	$-0.371565\pi$
$547$	18.3657	0.785260	0.392630	+	0.919697i	$0.371565\pi$
$548$	−0.472834	−0.0201985
$549$	−40.6414	−1.73453
$550$	−3.47283	−0.148082
$551$	−10.9108	−0.464815
$552$	−1.77018	−0.0753441
$553$	30.4200	1.29359
$554$	14.2166	0.604006
$555$	−10.4115	−0.441945
$556$	3.15604	0.133846
$557$	14.6282	0.619815	0.309907	−	0.950767i	$-0.399702\pi$
$557$	14.6282	0.619815	0.309907	+	0.950767i	$0.399702\pi$
$558$	22.7500	0.963085
$559$	−1.06905	−0.0452161
$560$	7.98680	0.337504
$561$	−7.70265	−0.325206
$562$	−4.55286	−0.192051
$563$	17.8627	0.752823	0.376411	−	0.926453i	$-0.377158\pi$
$563$	17.8627	0.752823	0.376411	+	0.926453i	$0.377158\pi$
$564$	−11.9130	−0.501629
$565$	−35.2361	−1.48239
$566$	10.1692	0.427445
$567$	27.9123	1.17221
$568$	−10.3579	−0.434609
$569$	5.33000	0.223445	0.111723	−	0.993739i	$-0.464363\pi$
$569$	5.33000	0.223445	0.111723	+	0.993739i	$0.464363\pi$
$570$	7.52021	0.314987
$571$	−24.4549	−1.02341	−0.511703	−	0.859162i	$-0.670985\pi$
$571$	−24.4549	−1.02341	−0.511703	+	0.859162i	$0.670985\pi$
$572$	2.35793	0.0985899
$573$	−26.9651	−1.12648
$574$	18.7896	0.784264
$575$	0.798110	0.0332835
$576$	3.11491	0.129788
$577$	−4.30359	−0.179161	−0.0895805	−	0.995980i	$-0.528553\pi$
$577$	−4.30359	−0.179161	−0.0895805	+	0.995980i	$0.528553\pi$
$578$	−1.00000	−0.0415945
$579$	56.5412	2.34977
$580$	21.9387	0.910955
$581$	10.0606	0.417383
$582$	13.7849	0.571403
$583$	0.297351	0.0123150
$584$	−1.30359	−0.0539431
$585$	−5.83076	−0.241072
$586$	−5.37961	−0.222230
$587$	−37.4931	−1.54751	−0.773753	−	0.633488i	$-0.781623\pi$
$587$	−37.4931	−1.54751	−0.773753	+	0.633488i	$0.781623\pi$
$588$	8.48604	0.349958
$589$	−8.98207	−0.370100
$590$	−2.47283	−0.101805
$591$	29.1421	1.19875
$592$	1.70265	0.0699784
$593$	−28.3859	−1.16567	−0.582834	−	0.812592i	$-0.698056\pi$
$593$	−28.3859	−1.16567	−0.582834	+	0.812592i	$0.698056\pi$
$594$	−0.885092	−0.0363158
$595$	−7.98680	−0.327427
$596$	−3.98055	−0.163050
$597$	−62.8076	−2.57055
$598$	−0.541887	−0.0221594
$599$	−5.49300	−0.224438	−0.112219	−	0.993684i	$-0.535796\pi$
$599$	−5.49300	−0.224438	−0.112219	+	0.993684i	$0.535796\pi$
$600$	−2.75698	−0.112553
$601$	−28.7695	−1.17353	−0.586766	−	0.809757i	$-0.699599\pi$
$601$	−28.7695	−1.17353	−0.586766	+	0.809757i	$0.699599\pi$
$602$	−4.56133	−0.185906
$603$	−27.4659	−1.11850
$604$	19.1755	0.780239
$605$	3.20813	0.130429
$606$	33.6693	1.36772
$607$	1.06530	0.0432392	0.0216196	−	0.999766i	$-0.493118\pi$
$607$	1.06530	0.0432392	0.0216196	+	0.999766i	$0.493118\pi$
$608$	−1.22982	−0.0498756
$609$	70.8580	2.87131
$610$	−32.2640	−1.30633
$611$	−3.64680	−0.147534
$612$	−3.11491	−0.125913
$613$	−45.6212	−1.84262	−0.921311	−	0.388826i	$-0.872881\pi$
$613$	−45.6212	−1.84262	−0.921311	+	0.388826i	$0.872881\pi$
$614$	3.71585	0.149960
$615$	−35.5738	−1.43447
$616$	10.0606	0.405352
$617$	−35.7842	−1.44062	−0.720309	−	0.693654i	$-0.756000\pi$
$617$	−35.7842	−1.44062	−0.720309	+	0.693654i	$0.756000\pi$
$618$	7.60095	0.305755
$619$	16.6615	0.669683	0.334842	−	0.942274i	$-0.391317\pi$
$619$	16.6615	0.669683	0.334842	+	0.942274i	$0.391317\pi$
$620$	18.0606	0.725330
$621$	0.203408	0.00816247
$622$	−16.2577	−0.651876
$623$	27.7368	1.11125
$624$	1.87189	0.0749355
$625$	−29.3315	−1.17326
$626$	−13.7243	−0.548535
$627$	9.47283	0.378309
$628$	0.466591	0.0186190
$629$	−1.70265	−0.0678891
$630$	−24.8781	−0.991168
$631$	25.1972	1.00308	0.501542	−	0.865134i	$-0.332766\pi$
$631$	25.1972	1.00308	0.501542	+	0.865134i	$0.332766\pi$
$632$	9.41850	0.374648
$633$	−21.7563	−0.864734
$634$	−25.0279	−0.993986
$635$	35.3223	1.40172
$636$	0.236058	0.00936032
$637$	2.59774	0.102926
$638$	27.6351	1.09408
$639$	32.2640	1.27634
$640$	2.47283	0.0977473
$641$	−21.5551	−0.851375	−0.425687	−	0.904870i	$-0.639968\pi$
$641$	−21.5551	−0.851375	−0.425687	+	0.904870i	$0.639968\pi$
$642$	−15.8392	−0.625125
$643$	−15.7717	−0.621975	−0.310988	−	0.950414i	$-0.600660\pi$
$643$	−15.7717	−0.621975	−0.310988	+	0.950414i	$0.600660\pi$
$644$	−2.31207	−0.0911084
$645$	8.63583	0.340035
$646$	1.22982	0.0483864
$647$	−42.2966	−1.66285	−0.831426	−	0.555635i	$-0.812475\pi$
$647$	−42.2966	−1.66285	−0.831426	+	0.555635i	$0.812475\pi$
$648$	8.64207	0.339493
$649$	−3.11491	−0.122271
$650$	−0.843964	−0.0331030
$651$	58.3323	2.28622
$652$	−3.78963	−0.148413
$653$	19.2757	0.754315	0.377158	−	0.926149i	$-0.376902\pi$
$653$	19.2757	0.754315	0.377158	+	0.926149i	$0.376902\pi$
$654$	−8.73753	−0.341665
$655$	46.5808	1.82006
$656$	5.81756	0.227137
$657$	4.06058	0.158418
$658$	−15.5598	−0.606585
$659$	13.0257	0.507409	0.253704	−	0.967282i	$-0.418351\pi$
$659$	13.0257	0.507409	0.253704	+	0.967282i	$0.418351\pi$
$660$	−19.0474	−0.741418
$661$	−15.5947	−0.606564	−0.303282	−	0.952901i	$-0.598082\pi$
$661$	−15.5947	−0.606564	−0.303282	+	0.952901i	$0.598082\pi$
$662$	8.43394	0.327794
$663$	−1.87189	−0.0726981
$664$	3.11491	0.120882
$665$	9.82228	0.380892
$666$	−5.30359	−0.205510
$667$	−6.35097	−0.245910
$668$	2.47283	0.0956768
$669$	54.4868	2.10658
$670$	−21.8044	−0.842376
$671$	−40.6414	−1.56894
$672$	7.98680	0.308097
$673$	23.0496	0.888497	0.444249	−	0.895904i	$-0.353471\pi$
$673$	23.0496	0.888497	0.444249	+	0.895904i	$0.353471\pi$
$674$	−14.6072	−0.562648
$675$	0.316798	0.0121936
$676$	−12.4270	−0.477961
$677$	−11.6810	−0.448936	−0.224468	−	0.974481i	$-0.572064\pi$
$677$	−11.6810	−0.448936	−0.224468	+	0.974481i	$0.572064\pi$
$678$	−35.2361	−1.35323
$679$	18.0047	0.690958
$680$	−2.47283	−0.0948289
$681$	43.0885	1.65115
$682$	22.7500	0.871143
$683$	8.60023	0.329079	0.164539	−	0.986371i	$-0.447386\pi$
$683$	8.60023	0.329079	0.164539	+	0.986371i	$0.447386\pi$
$684$	3.83076	0.146473
$685$	1.16924	0.0446744
$686$	−11.5249	−0.440024
$687$	−3.17548	−0.121152
$688$	−1.41226	−0.0538419
$689$	0.0722619	0.00275296
$690$	4.37737	0.166644
$691$	50.4721	1.92005	0.960025	−	0.279915i	$-0.0903062\pi$
$691$	50.4721	1.92005	0.960025	+	0.279915i	$0.0903062\pi$
$692$	6.47908	0.246298
$693$	−31.3378	−1.19042
$694$	12.4185	0.471400
$695$	−7.80435	−0.296036
$696$	21.9387	0.831585
$697$	−5.81756	−0.220356
$698$	5.29111	0.200271
$699$	−14.4666	−0.547177
$700$	−3.60095	−0.136103
$701$	−26.3293	−0.994443	−0.497222	−	0.867624i	$-0.665646\pi$
$701$	−26.3293	−0.994443	−0.497222	+	0.867624i	$0.665646\pi$
$702$	−0.215094	−0.00811820
$703$	2.09394	0.0789746
$704$	3.11491	0.117397
$705$	29.4589	1.10949
$706$	−28.3704	−1.06773
$707$	43.9761	1.65389
$708$	−2.47283	−0.0929348
$709$	−6.34249	−0.238197	−0.119099	−	0.992882i	$-0.538000\pi$
$709$	−6.34249	−0.238197	−0.119099	+	0.992882i	$0.538000\pi$
$710$	25.6134	0.961255
$711$	−29.3378	−1.10025
$712$	8.58774	0.321839
$713$	−5.22830	−0.195801
$714$	−7.98680	−0.298898
$715$	−5.83076	−0.218058
$716$	22.6678	0.847134
$717$	13.7159	0.512228
$718$	22.9861	0.857833
$719$	11.6157	0.433191	0.216596	−	0.976261i	$-0.430505\pi$
$719$	11.6157	0.433191	0.216596	+	0.976261i	$0.430505\pi$
$720$	−7.70265	−0.287061
$721$	9.92774	0.369728
$722$	17.4876	0.650819
$723$	−32.2485	−1.19934
$724$	19.3098	0.717644
$725$	−9.89134	−0.367355
$726$	3.20813	0.119065
$727$	49.3502	1.83030	0.915150	−	0.403114i	$-0.132072\pi$
$727$	49.3502	1.83030	0.915150	+	0.403114i	$0.132072\pi$
$728$	2.44491	0.0906144
$729$	−29.0272	−1.07508
$730$	3.22357	0.119310
$731$	1.41226	0.0522343
$732$	−32.2640	−1.19251
$733$	−17.6685	−0.652600	−0.326300	−	0.945266i	$-0.605802\pi$
$733$	−17.6685	−0.652600	−0.326300	+	0.945266i	$0.605802\pi$
$734$	3.63511	0.134174
$735$	−20.9846	−0.774027
$736$	−0.715853	−0.0263867
$737$	−27.4659	−1.01172
$738$	−18.1212	−0.667049
$739$	4.08922	0.150424	0.0752121	−	0.997168i	$-0.476037\pi$
$739$	4.08922	0.150424	0.0752121	+	0.997168i	$0.476037\pi$
$740$	−4.21037	−0.154776
$741$	2.30208	0.0845689
$742$	0.308320	0.0113188
$743$	12.8804	0.472535	0.236267	−	0.971688i	$-0.424076\pi$
$743$	12.8804	0.472535	0.236267	+	0.971688i	$0.424076\pi$
$744$	18.0606	0.662133
$745$	9.84325	0.360629
$746$	−1.72906	−0.0633053
$747$	−9.70265	−0.355001
$748$	−3.11491	−0.113892
$749$	−20.6879	−0.755920
$750$	−23.7570	−0.867482
$751$	22.3315	0.814889	0.407444	−	0.913230i	$-0.366420\pi$
$751$	22.3315	0.814889	0.407444	+	0.913230i	$0.366420\pi$
$752$	−4.81756	−0.175678
$753$	−29.5877	−1.07824
$754$	6.71585	0.244577
$755$	−47.4178	−1.72571
$756$	−0.917743	−0.0333780
$757$	−4.98608	−0.181222	−0.0906111	−	0.995886i	$-0.528882\pi$
$757$	−4.98608	−0.181222	−0.0906111	+	0.995886i	$0.528882\pi$
$758$	−19.7353	−0.716818
$759$	5.51396	0.200144
$760$	3.04113	0.110313
$761$	4.83299	0.175196	0.0875980	−	0.996156i	$-0.472081\pi$
$761$	4.83299	0.175196	0.0875980	+	0.996156i	$0.472081\pi$
$762$	35.3223	1.27959
$763$	−11.4123	−0.413151
$764$	−10.9045	−0.394512
$765$	7.70265	0.278490
$766$	−29.0474	−1.04952
$767$	−0.756981	−0.0273330
$768$	2.47283	0.0892307
$769$	16.9170	0.610044	0.305022	−	0.952345i	$-0.401336\pi$
$769$	16.9170	0.610044	0.305022	+	0.952345i	$0.401336\pi$
$770$	−24.8781	−0.896546
$771$	−23.4402	−0.844178
$772$	22.8649	0.822927
$773$	−7.96111	−0.286341	−0.143171	−	0.989698i	$-0.545730\pi$
$773$	−7.96111	−0.286341	−0.143171	+	0.989698i	$0.545730\pi$
$774$	4.39905	0.158121
$775$	−8.14283	−0.292499
$776$	5.57454	0.200114
$777$	−13.5987	−0.487851
$778$	−11.6810	−0.418783
$779$	7.15452	0.256337
$780$	−4.62887	−0.165740
$781$	32.2640	1.15450
$782$	0.715853	0.0255988
$783$	−2.52092	−0.0900904
$784$	3.43171	0.122561
$785$	−1.15380	−0.0411809
$786$	46.5808	1.66148
$787$	12.8517	0.458114	0.229057	−	0.973413i	$-0.426436\pi$
$787$	12.8517	0.458114	0.229057	+	0.973413i	$0.426436\pi$
$788$	11.7849	0.419820
$789$	−0.482029	−0.0171607
$790$	−23.2904	−0.828635
$791$	−46.0225	−1.63637
$792$	−9.70265	−0.344769
$793$	−9.87661	−0.350729
$794$	−27.0474	−0.959875
$795$	−0.583733	−0.0207029
$796$	−25.3991	−0.900246
$797$	−34.6678	−1.22800	−0.613998	−	0.789308i	$-0.710440\pi$
$797$	−34.6678	−1.22800	−0.613998	+	0.789308i	$0.710440\pi$
$798$	9.82228	0.347705
$799$	4.81756	0.170433
$800$	−1.11491	−0.0394179
$801$	−26.7500	−0.945166
$802$	18.4791	0.652519
$803$	4.06058	0.143295
$804$	−21.8044	−0.768980
$805$	5.71737	0.201511
$806$	5.52868	0.194740
$807$	58.6491	2.06455
$808$	13.6157	0.478997
$809$	−9.14211	−0.321420	−0.160710	−	0.987002i	$-0.551378\pi$
$809$	−9.14211	−0.321420	−0.160710	+	0.987002i	$0.551378\pi$
$810$	−21.3704	−0.750880
$811$	−10.0459	−0.352758	−0.176379	−	0.984322i	$-0.556438\pi$
$811$	−10.0459	−0.352758	−0.176379	+	0.984322i	$0.556438\pi$
$812$	28.6546	1.00558
$813$	−77.1436	−2.70555
$814$	−5.30359	−0.185891
$815$	9.37113	0.328256
$816$	−2.47283	−0.0865665
$817$	−1.73682	−0.0607635
$818$	18.3796	0.642628
$819$	−7.61567	−0.266113
$820$	−14.3859	−0.502376
$821$	−53.3719	−1.86269	−0.931347	−	0.364134i	$-0.881365\pi$
$821$	−53.3719	−1.86269	−0.931347	+	0.364134i	$0.881365\pi$
$822$	1.16924	0.0407819
$823$	6.93871	0.241868	0.120934	−	0.992661i	$-0.461411\pi$
$823$	6.93871	0.241868	0.120934	+	0.992661i	$0.461411\pi$
$824$	3.07378	0.107080
$825$	8.58774	0.298987
$826$	−3.22982	−0.112380
$827$	38.1700	1.32730	0.663651	−	0.748042i	$-0.269006\pi$
$827$	38.1700	1.32730	0.663651	+	0.748042i	$0.269006\pi$
$828$	2.22982	0.0774914
$829$	−3.52940	−0.122581	−0.0612906	−	0.998120i	$-0.519522\pi$
$829$	−3.52940	−0.122581	−0.0612906	+	0.998120i	$0.519522\pi$
$830$	−7.70265	−0.267363
$831$	−35.1553	−1.21952
$832$	0.756981	0.0262436
$833$	−3.43171	−0.118902
$834$	−7.80435	−0.270243
$835$	−6.11491	−0.211615
$836$	3.83076	0.132490
$837$	−2.07530	−0.0717327
$838$	−25.5070	−0.881125
$839$	−27.5870	−0.952410	−0.476205	−	0.879334i	$-0.657988\pi$
$839$	−27.5870	−0.952410	−0.476205	+	0.879334i	$0.657988\pi$
$840$	−19.7500	−0.681440
$841$	49.7104	1.71415
$842$	−24.4138	−0.841354
$843$	11.2585	0.387762
$844$	−8.79811	−0.302843
$845$	30.7299	1.05714
$846$	15.0062	0.515925
$847$	4.19020	0.143977
$848$	0.0954606	0.00327813
$849$	−25.1468	−0.863037
$850$	1.11491	0.0382410
$851$	1.21885	0.0417815
$852$	25.6134	0.877502
$853$	−51.9534	−1.77885	−0.889426	−	0.457080i	$-0.848895\pi$
$853$	−51.9534	−1.77885	−0.889426	+	0.457080i	$0.848895\pi$
$854$	−42.1406	−1.44202
$855$	−9.47283	−0.323964
$856$	−6.40530	−0.218929
$857$	1.98751	0.0678922	0.0339461	−	0.999424i	$-0.489193\pi$
$857$	1.98751	0.0678922	0.0339461	+	0.999424i	$0.489193\pi$
$858$	−5.83076	−0.199059
$859$	−3.73602	−0.127471	−0.0637356	−	0.997967i	$-0.520301\pi$
$859$	−3.73602	−0.127471	−0.0637356	+	0.997967i	$0.520301\pi$
$860$	3.49228	0.119086
$861$	−46.4636	−1.58348
$862$	−20.9673	−0.714151
$863$	23.4270	0.797464	0.398732	−	0.917068i	$-0.369450\pi$
$863$	23.4270	0.797464	0.398732	+	0.917068i	$0.369450\pi$
$864$	−0.284147	−0.00966689
$865$	−16.0217	−0.544754
$866$	7.17620	0.243857
$867$	2.47283	0.0839818
$868$	23.5893	0.800672
$869$	−29.3378	−0.995215
$870$	−54.2508	−1.83927
$871$	−6.67472	−0.226164
$872$	−3.53341	−0.119656
$873$	−17.3642	−0.587688
$874$	−0.880366	−0.0297788
$875$	−31.0294	−1.04899
$876$	3.22357	0.108914
$877$	−14.9736	−0.505622	−0.252811	−	0.967516i	$-0.581355\pi$
$877$	−14.9736	−0.505622	−0.252811	+	0.967516i	$0.581355\pi$
$878$	4.16701	0.140630
$879$	13.3029	0.448695
$880$	−7.70265	−0.259656
$881$	22.1645	0.746741	0.373371	−	0.927682i	$-0.378202\pi$
$881$	22.1645	0.746741	0.373371	+	0.927682i	$0.378202\pi$
$882$	−10.6894	−0.359932
$883$	−26.9038	−0.905386	−0.452693	−	0.891667i	$-0.649537\pi$
$883$	−26.9038	−0.905386	−0.452693	+	0.891667i	$0.649537\pi$
$884$	−0.756981	−0.0254600
$885$	6.11491	0.205550
$886$	−2.02641	−0.0680785
$887$	49.3400	1.65667	0.828337	−	0.560229i	$-0.189287\pi$
$887$	49.3400	1.65667	0.828337	+	0.560229i	$0.189287\pi$
$888$	−4.21037	−0.141291
$889$	46.1352	1.54732
$890$	−21.2361	−0.711834
$891$	−26.9193	−0.901829
$892$	22.0342	0.737759
$893$	−5.92470	−0.198263
$894$	9.84325	0.329207
$895$	−56.0536	−1.87367
$896$	3.22982	0.107901
$897$	1.34000	0.0447412
$898$	−5.06058	−0.168874
$899$	64.7967	2.16109
$900$	3.47283	0.115761
$901$	−0.0954606	−0.00318025
$902$	−18.1212	−0.603368
$903$	11.2794	0.375356
$904$	−14.2493	−0.473923
$905$	−47.7500	−1.58726
$906$	−47.4178	−1.57535
$907$	−25.1359	−0.834623	−0.417311	−	0.908764i	$-0.637028\pi$
$907$	−25.1359	−0.834623	−0.417311	+	0.908764i	$0.637028\pi$
$908$	17.4247	0.578260
$909$	−42.4115	−1.40670
$910$	−6.04585	−0.200418
$911$	4.53564	0.150273	0.0751363	−	0.997173i	$-0.476061\pi$
$911$	4.53564	0.150273	0.0751363	+	0.997173i	$0.476061\pi$
$912$	3.04113	0.100702
$913$	−9.70265	−0.321111
$914$	5.21661	0.172550
$915$	79.7835	2.63756
$916$	−1.28415	−0.0424294
$917$	60.8400	2.00912
$918$	0.284147	0.00937826
$919$	22.1576	0.730910	0.365455	−	0.930829i	$-0.380913\pi$
$919$	22.1576	0.730910	0.365455	+	0.930829i	$0.380913\pi$
$920$	1.77018	0.0583613
$921$	−9.18869	−0.302778
$922$	38.8689	1.28008
$923$	7.84076	0.258082
$924$	−24.8781	−0.818430
$925$	1.89830	0.0624156
$926$	9.61343	0.315917
$927$	−9.57454	−0.314469
$928$	8.87189	0.291234
$929$	−17.2772	−0.566846	−0.283423	−	0.958995i	$-0.591470\pi$
$929$	−17.2772	−0.566846	−0.283423	+	0.958995i	$0.591470\pi$
$930$	−44.6608	−1.46449
$931$	4.22036	0.138317
$932$	−5.85021	−0.191630
$933$	40.2027	1.31618
$934$	−15.1949	−0.497193
$935$	7.70265	0.251904
$936$	−2.35793	−0.0770712
$937$	47.1010	1.53872	0.769361	−	0.638814i	$-0.220575\pi$
$937$	47.1010	1.53872	0.769361	+	0.638814i	$0.220575\pi$
$938$	−28.4791	−0.929875
$939$	33.9380	1.10752
$940$	11.9130	0.388560
$941$	−32.1964	−1.04957	−0.524787	−	0.851234i	$-0.675855\pi$
$941$	−32.1964	−1.04957	−0.524787	+	0.851234i	$0.675855\pi$
$942$	−1.15380	−0.0375929
$943$	4.16451	0.135615
$944$	−1.00000	−0.0325472
$945$	2.26943	0.0738244
$946$	4.39905	0.143026
$947$	−27.0342	−0.878492	−0.439246	−	0.898367i	$-0.644754\pi$
$947$	−27.0342	−0.878492	−0.439246	+	0.898367i	$0.644754\pi$
$948$	−23.2904	−0.756437
$949$	0.986796	0.0320328
$950$	−1.37113	−0.0444853
$951$	61.8899	2.00692
$952$	−3.22982	−0.104679
$953$	1.95415	0.0633010	0.0316505	−	0.999499i	$-0.489924\pi$
$953$	1.95415	0.0633010	0.0316505	+	0.999499i	$0.489924\pi$
$954$	−0.297351	−0.00962709
$955$	26.9651	0.872571
$956$	5.54661	0.179390
$957$	−68.3370	−2.20902
$958$	−14.9457	−0.482873
$959$	1.52717	0.0493148
$960$	−6.11491	−0.197358
$961$	22.3425	0.720725
$962$	−1.28887	−0.0415549
$963$	19.9519	0.642941
$964$	−13.0411	−0.420026
$965$	−56.5412	−1.82012
$966$	5.71737	0.183953
$967$	−18.0078	−0.579091	−0.289545	−	0.957164i	$-0.593504\pi$
$967$	−18.0078	−0.579091	−0.289545	+	0.957164i	$0.593504\pi$
$968$	1.29735	0.0416984
$969$	−3.04113	−0.0976951
$970$	−13.7849	−0.442607
$971$	−14.6762	−0.470983	−0.235492	−	0.971876i	$-0.575670\pi$
$971$	−14.6762	−0.470983	−0.235492	+	0.971876i	$0.575670\pi$
$972$	−22.2229	−0.712798
$973$	−10.1934	−0.326786
$974$	25.6700	0.822520
$975$	2.08698	0.0668369
$976$	−13.0474	−0.417636
$977$	37.5481	1.20127	0.600636	−	0.799523i	$-0.294914\pi$
$977$	37.5481	1.20127	0.600636	+	0.799523i	$0.294914\pi$
$978$	9.37113	0.299656
$979$	−26.7500	−0.854934
$980$	−8.48604	−0.271077
$981$	11.0062	0.351402
$982$	−29.1600	−0.930534
$983$	−26.3921	−0.841777	−0.420889	−	0.907112i	$-0.638282\pi$
$983$	−26.3921	−0.841777	−0.420889	+	0.907112i	$0.638282\pi$
$984$	−14.3859	−0.458604
$985$	−29.1421	−0.928545
$986$	−8.87189	−0.282538
$987$	38.4768	1.22473
$988$	0.930947	0.0296174
$989$	−1.01097	−0.0321469
$990$	23.9930	0.762549
$991$	−29.5048	−0.937250	−0.468625	−	0.883397i	$-0.655250\pi$
$991$	−29.5048	−0.937250	−0.468625	+	0.883397i	$0.655250\pi$
$992$	7.30359	0.231889
$993$	−20.8557	−0.661837
$994$	33.4542	1.06110
$995$	62.8076	1.99114
$996$	−7.70265	−0.244068
$997$	−18.2074	−0.576635	−0.288317	−	0.957535i	$-0.593096\pi$
$997$	−18.2074	−0.576635	−0.288317	+	0.957535i	$0.593096\pi$
$998$	13.2493	0.419398
$999$	0.483803	0.0153069

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	2006.2.a.n.1.3	✓	3

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
2006.2.a.n.1.3	✓	3	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:	\( N \)	\(=\)	\( 2006 = 2 \cdot 17 \cdot 59 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	2006.a (trivial)

\(f(q)\)	\(=\)	\(q-1.00000 q^{2} +2.47283 q^{3} +1.00000 q^{4} -2.47283 q^{5} -2.47283 q^{6} -3.22982 q^{7} -1.00000 q^{8} +3.11491 q^{9} +O(q^{10})\)	\(q-1.00000 q^{2} +2.47283 q^{3} +1.00000 q^{4} -2.47283 q^{5} -2.47283 q^{6} -3.22982 q^{7} -1.00000 q^{8} +3.11491 q^{9} +2.47283 q^{10} +3.11491 q^{11} +2.47283 q^{12} +0.756981 q^{13} +3.22982 q^{14} -6.11491 q^{15} +1.00000 q^{16} -1.00000 q^{17} -3.11491 q^{18} +1.22982 q^{19} -2.47283 q^{20} -7.98680 q^{21} -3.11491 q^{22} +0.715853 q^{23} -2.47283 q^{24} +1.11491 q^{25} -0.756981 q^{26} +0.284147 q^{27} -3.22982 q^{28} -8.87189 q^{29} +6.11491 q^{30} -7.30359 q^{31} -1.00000 q^{32} +7.70265 q^{33} +1.00000 q^{34} +7.98680 q^{35} +3.11491 q^{36} +1.70265 q^{37} -1.22982 q^{38} +1.87189 q^{39} +2.47283 q^{40} +5.81756 q^{41} +7.98680 q^{42} -1.41226 q^{43} +3.11491 q^{44} -7.70265 q^{45} -0.715853 q^{46} -4.81756 q^{47} +2.47283 q^{48} +3.43171 q^{49} -1.11491 q^{50} -2.47283 q^{51} +0.756981 q^{52} +0.0954606 q^{53} -0.284147 q^{54} -7.70265 q^{55} +3.22982 q^{56} +3.04113 q^{57} +8.87189 q^{58} -1.00000 q^{59} -6.11491 q^{60} -13.0474 q^{61} +7.30359 q^{62} -10.0606 q^{63} +1.00000 q^{64} -1.87189 q^{65} -7.70265 q^{66} -8.81756 q^{67} -1.00000 q^{68} +1.77018 q^{69} -7.98680 q^{70} +10.3579 q^{71} -3.11491 q^{72} +1.30359 q^{73} -1.70265 q^{74} +2.75698 q^{75} +1.22982 q^{76} -10.0606 q^{77} -1.87189 q^{78} -9.41850 q^{79} -2.47283 q^{80} -8.64207 q^{81} -5.81756 q^{82} -3.11491 q^{83} -7.98680 q^{84} +2.47283 q^{85} +1.41226 q^{86} -21.9387 q^{87} -3.11491 q^{88} -8.58774 q^{89} +7.70265 q^{90} -2.44491 q^{91} +0.715853 q^{92} -18.0606 q^{93} +4.81756 q^{94} -3.04113 q^{95} -2.47283 q^{96} -5.57454 q^{97} -3.43171 q^{98} +9.70265 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 3 q - 3 q^{2} + 2 q^{3} + 3 q^{4} - 2 q^{5} - 2 q^{6} + 3 q^{7} - 3 q^{8} + 3 q^{9}+O(q^{10}) \) 3 * q - 3 * q^2 + 2 * q^3 + 3 * q^4 - 2 * q^5 - 2 * q^6 + 3 * q^7 - 3 * q^8 + 3 * q^9	\( 3 q - 3 q^{2} + 2 q^{3} + 3 q^{4} - 2 q^{5} - 2 q^{6} + 3 q^{7} - 3 q^{8} + 3 q^{9} + 2 q^{10} + 3 q^{11} + 2 q^{12} - 5 q^{13} - 3 q^{14} - 12 q^{15} + 3 q^{16} - 3 q^{17} - 3 q^{18} - 9 q^{19} - 2 q^{20} - 4 q^{21} - 3 q^{22} + 4 q^{23} - 2 q^{24} - 3 q^{25} + 5 q^{26} - q^{27} + 3 q^{28} - 13 q^{29} + 12 q^{30} - 12 q^{31} - 3 q^{32} + 5 q^{33} + 3 q^{34} + 4 q^{35} + 3 q^{36} - 13 q^{37} + 9 q^{38} - 8 q^{39} + 2 q^{40} - 7 q^{41} + 4 q^{42} - 16 q^{43} + 3 q^{44} - 5 q^{45} - 4 q^{46} + 10 q^{47} + 2 q^{48} + 14 q^{49} + 3 q^{50} - 2 q^{51} - 5 q^{52} + 2 q^{53} + q^{54} - 5 q^{55} - 3 q^{56} + 13 q^{58} - 3 q^{59} - 12 q^{60} - 2 q^{61} + 12 q^{62} - 13 q^{63} + 3 q^{64} + 8 q^{65} - 5 q^{66} - 2 q^{67} - 3 q^{68} + 18 q^{69} - 4 q^{70} + 32 q^{71} - 3 q^{72} - 6 q^{73} + 13 q^{74} + q^{75} - 9 q^{76} - 13 q^{77} + 8 q^{78} - 12 q^{79} - 2 q^{80} - 25 q^{81} + 7 q^{82} - 3 q^{83} - 4 q^{84} + 2 q^{85} + 16 q^{86} - 7 q^{87} - 3 q^{88} - 14 q^{89} + 5 q^{90} - 31 q^{91} + 4 q^{92} - 37 q^{93} - 10 q^{94} - 2 q^{96} + 15 q^{97} - 14 q^{98} + 11 q^{99}+O(q^{100}) \) 3 * q - 3 * q^2 + 2 * q^3 + 3 * q^4 - 2 * q^5 - 2 * q^6 + 3 * q^7 - 3 * q^8 + 3 * q^9 + 2 * q^10 + 3 * q^11 + 2 * q^12 - 5 * q^13 - 3 * q^14 - 12 * q^15 + 3 * q^16 - 3 * q^17 - 3 * q^18 - 9 * q^19 - 2 * q^20 - 4 * q^21 - 3 * q^22 + 4 * q^23 - 2 * q^24 - 3 * q^25 + 5 * q^26 - q^27 + 3 * q^28 - 13 * q^29 + 12 * q^30 - 12 * q^31 - 3 * q^32 + 5 * q^33 + 3 * q^34 + 4 * q^35 + 3 * q^36 - 13 * q^37 + 9 * q^38 - 8 * q^39 + 2 * q^40 - 7 * q^41 + 4 * q^42 - 16 * q^43 + 3 * q^44 - 5 * q^45 - 4 * q^46 + 10 * q^47 + 2 * q^48 + 14 * q^49 + 3 * q^50 - 2 * q^51 - 5 * q^52 + 2 * q^53 + q^54 - 5 * q^55 - 3 * q^56 + 13 * q^58 - 3 * q^59 - 12 * q^60 - 2 * q^61 + 12 * q^62 - 13 * q^63 + 3 * q^64 + 8 * q^65 - 5 * q^66 - 2 * q^67 - 3 * q^68 + 18 * q^69 - 4 * q^70 + 32 * q^71 - 3 * q^72 - 6 * q^73 + 13 * q^74 + q^75 - 9 * q^76 - 13 * q^77 + 8 * q^78 - 12 * q^79 - 2 * q^80 - 25 * q^81 + 7 * q^82 - 3 * q^83 - 4 * q^84 + 2 * q^85 + 16 * q^86 - 7 * q^87 - 3 * q^88 - 14 * q^89 + 5 * q^90 - 31 * q^91 + 4 * q^92 - 37 * q^93 - 10 * q^94 - 2 * q^96 + 15 * q^97 - 14 * q^98 + 11 * q^99

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