LMFDB - Embedded newform 717.2.a.d.1.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [717,2,Mod(1,717)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(717, 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("717.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 717 = 3 \cdot 239 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	717.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:	$5.72527382493$
Analytic rank:	$1$
Dimension:	$6$
Coefficient field:	6.6.1767625.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{6} - 7x^{4} - x^{3} + 11x^{2} + x - 1 $ x^6 - 7x^4 - x^3 + 11x^2 + x - 1
Coefficient ring:	$\Z[a_1, a_2]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.4
Root			$-1.94590$ of defining polynomial
Character	$\chi$	$=$	717.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+0.104133 q^{2} -1.00000 q^{3} -1.98916 q^{4} -0.431998 q^{5} -0.104133 q^{6} +2.76657 q^{7} -0.415402 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q+0.104133 q^{2} -1.00000 q^{3} -1.98916 q^{4} -0.431998 q^{5} -0.104133 q^{6} +2.76657 q^{7} -0.415402 q^{8} +1.00000 q^{9} -0.0449852 q^{10} -1.08824 q^{11} +1.98916 q^{12} -2.81084 q^{13} +0.288090 q^{14} +0.431998 q^{15} +3.93506 q^{16} +5.82744 q^{17} +0.104133 q^{18} -7.25266 q^{19} +0.859312 q^{20} -2.76657 q^{21} -0.113322 q^{22} -3.48861 q^{23} +0.415402 q^{24} -4.81338 q^{25} -0.292701 q^{26} -1.00000 q^{27} -5.50313 q^{28} -5.03919 q^{29} +0.0449852 q^{30} -2.02388 q^{31} +1.24057 q^{32} +1.08824 q^{33} +0.606828 q^{34} -1.19515 q^{35} -1.98916 q^{36} +2.08347 q^{37} -0.755240 q^{38} +2.81084 q^{39} +0.179453 q^{40} -5.40397 q^{41} -0.288090 q^{42} -5.91283 q^{43} +2.16468 q^{44} -0.431998 q^{45} -0.363279 q^{46} -0.795216 q^{47} -3.93506 q^{48} +0.653884 q^{49} -0.501230 q^{50} -5.82744 q^{51} +5.59121 q^{52} -3.47735 q^{53} -0.104133 q^{54} +0.470119 q^{55} -1.14924 q^{56} +7.25266 q^{57} -0.524745 q^{58} -9.03190 q^{59} -0.859312 q^{60} -10.4206 q^{61} -0.210753 q^{62} +2.76657 q^{63} -7.74093 q^{64} +1.21428 q^{65} +0.113322 q^{66} -3.98418 q^{67} -11.5917 q^{68} +3.48861 q^{69} -0.124454 q^{70} +10.9852 q^{71} -0.415402 q^{72} +1.10684 q^{73} +0.216957 q^{74} +4.81338 q^{75} +14.4267 q^{76} -3.01069 q^{77} +0.292701 q^{78} -0.409081 q^{79} -1.69994 q^{80} +1.00000 q^{81} -0.562731 q^{82} +15.0992 q^{83} +5.50313 q^{84} -2.51744 q^{85} -0.615719 q^{86} +5.03919 q^{87} +0.452058 q^{88} +14.2188 q^{89} -0.0449852 q^{90} -7.77639 q^{91} +6.93940 q^{92} +2.02388 q^{93} -0.0828081 q^{94} +3.13314 q^{95} -1.24057 q^{96} +12.5418 q^{97} +0.0680907 q^{98} -1.08824 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 6 q - 2 q^{2} - 6 q^{3} + 4 q^{4} + 5 q^{5} + 2 q^{6} - 9 q^{7} - 3 q^{8} + 6 q^{9}+O(q^{10}) $ 6 * q - 2 * q^2 - 6 * q^3 + 4 * q^4 + 5 * q^5 + 2 * q^6 - 9 * q^7 - 3 * q^8 + 6 * q^9	\( 6 q - 2 q^{2} - 6 q^{3} + 4 q^{4} + 5 q^{5} + 2 q^{6} - 9 q^{7} - 3 q^{8} + 6 q^{9} - 11 q^{10} - 13 q^{11} - 4 q^{12} - q^{13} - 5 q^{15} - 4 q^{16} + 11 q^{17} - 2 q^{18} - 22 q^{19} - q^{20} + 9 q^{21} - 2 q^{22} - 12 q^{23} + 3 q^{24} - q^{25} + 12 q^{26} - 6 q^{27} - 16 q^{28} + 11 q^{30} - 18 q^{31} + 7 q^{32} + 13 q^{33} - 3 q^{34} - 9 q^{35} + 4 q^{36} - 8 q^{37} - 5 q^{38} + q^{39} - 11 q^{40} + 10 q^{41} - 14 q^{43} - 4 q^{44} + 5 q^{45} - 18 q^{46} - 9 q^{47} + 4 q^{48} + 5 q^{49} + 4 q^{50} - 11 q^{51} - 16 q^{52} - 8 q^{53} + 2 q^{54} - 20 q^{55} + 11 q^{56} + 22 q^{57} - 15 q^{58} - 10 q^{59} + q^{60} - 12 q^{61} - 13 q^{62} - 9 q^{63} - 31 q^{64} - 11 q^{65} + 2 q^{66} - 36 q^{67} + 22 q^{68} + 12 q^{69} + q^{70} - 3 q^{71} - 3 q^{72} - 32 q^{73} + 9 q^{74} + q^{75} - 4 q^{76} + 6 q^{77} - 12 q^{78} - q^{79} - 7 q^{80} + 6 q^{81} + 7 q^{82} - 7 q^{83} + 16 q^{84} - 14 q^{85} + 45 q^{86} - 15 q^{88} + 17 q^{89} - 11 q^{90} - 23 q^{91} - 12 q^{92} + 18 q^{93} + 50 q^{94} - 7 q^{96} - 28 q^{97} + 13 q^{98} - 13 q^{99}+O(q^{100}) \) 6 * q - 2 * q^2 - 6 * q^3 + 4 * q^4 + 5 * q^5 + 2 * q^6 - 9 * q^7 - 3 * q^8 + 6 * q^9 - 11 * q^10 - 13 * q^11 - 4 * q^12 - q^13 - 5 * q^15 - 4 * q^16 + 11 * q^17 - 2 * q^18 - 22 * q^19 - q^20 + 9 * q^21 - 2 * q^22 - 12 * q^23 + 3 * q^24 - q^25 + 12 * q^26 - 6 * q^27 - 16 * q^28 + 11 * q^30 - 18 * q^31 + 7 * q^32 + 13 * q^33 - 3 * q^34 - 9 * q^35 + 4 * q^36 - 8 * q^37 - 5 * q^38 + q^39 - 11 * q^40 + 10 * q^41 - 14 * q^43 - 4 * q^44 + 5 * q^45 - 18 * q^46 - 9 * q^47 + 4 * q^48 + 5 * q^49 + 4 * q^50 - 11 * q^51 - 16 * q^52 - 8 * q^53 + 2 * q^54 - 20 * q^55 + 11 * q^56 + 22 * q^57 - 15 * q^58 - 10 * q^59 + q^60 - 12 * q^61 - 13 * q^62 - 9 * q^63 - 31 * q^64 - 11 * q^65 + 2 * q^66 - 36 * q^67 + 22 * q^68 + 12 * q^69 + q^70 - 3 * q^71 - 3 * q^72 - 32 * q^73 + 9 * q^74 + q^75 - 4 * q^76 + 6 * q^77 - 12 * q^78 - q^79 - 7 * q^80 + 6 * q^81 + 7 * q^82 - 7 * q^83 + 16 * q^84 - 14 * q^85 + 45 * q^86 - 15 * q^88 + 17 * q^89 - 11 * q^90 - 23 * q^91 - 12 * q^92 + 18 * q^93 + 50 * q^94 - 7 * q^96 - 28 * q^97 + 13 * q^98 - 13 * 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 $

$2$	0.104133	0.0736330	0.0368165	−	0.999322i	$-0.488278\pi$
$2$	0.104133	0.0736330	0.0368165	+	0.999322i	$0.488278\pi$
$3$	−1.00000	−0.577350
$3$	−1.00000	−0.577350
$4$	−1.98916	−0.994578
$5$	−0.431998	−0.193195	−0.0965977	−	0.995324i	$-0.530796\pi$
$5$	−0.431998	−0.193195	−0.0965977	+	0.995324i	$0.530796\pi$
$6$	−0.104133	−0.0425120
$7$	2.76657	1.04566	0.522832	−	0.852436i	$-0.324876\pi$
$7$	2.76657	1.04566	0.522832	+	0.852436i	$0.324876\pi$
$8$	−0.415402	−0.146867
$9$	1.00000	0.333333
$10$	−0.0449852	−0.0142256
$11$	−1.08824	−0.328117	−0.164059	−	0.986451i	$-0.552459\pi$
$11$	−1.08824	−0.328117	−0.164059	+	0.986451i	$0.552459\pi$
$12$	1.98916	0.574220
$13$	−2.81084	−0.779588	−0.389794	−	0.920902i	$-0.627454\pi$
$13$	−2.81084	−0.779588	−0.389794	+	0.920902i	$0.627454\pi$
$14$	0.288090	0.0769953
$15$	0.431998	0.111541
$16$	3.93506	0.983764
$17$	5.82744	1.41336	0.706681	−	0.707532i	$-0.250192\pi$
$17$	5.82744	1.41336	0.706681	+	0.707532i	$0.250192\pi$
$18$	0.104133	0.0245443
$19$	−7.25266	−1.66388	−0.831938	−	0.554869i	$-0.812768\pi$
$19$	−7.25266	−1.66388	−0.831938	+	0.554869i	$0.812768\pi$
$20$	0.859312	0.192148
$21$	−2.76657	−0.603714
$22$	−0.113322	−0.0241603
$23$	−3.48861	−0.727426	−0.363713	−	0.931511i	$-0.618491\pi$
$23$	−3.48861	−0.727426	−0.363713	+	0.931511i	$0.618491\pi$
$24$	0.415402	0.0847936
$25$	−4.81338	−0.962676
$26$	−0.292701	−0.0574034
$27$	−1.00000	−0.192450
$28$	−5.50313	−1.03999
$29$	−5.03919	−0.935754	−0.467877	−	0.883794i	$-0.654981\pi$
$29$	−5.03919	−0.935754	−0.467877	+	0.883794i	$0.654981\pi$
$30$	0.0449852	0.00821313
$31$	−2.02388	−0.363500	−0.181750	−	0.983345i	$-0.558176\pi$
$31$	−2.02388	−0.363500	−0.181750	+	0.983345i	$0.558176\pi$
$32$	1.24057	0.219304
$33$	1.08824	0.189439
$34$	0.606828	0.104070
$35$	−1.19515	−0.202017
$36$	−1.98916	−0.331526
$37$	2.08347	0.342520	0.171260	−	0.985226i	$-0.445216\pi$
$37$	2.08347	0.342520	0.171260	+	0.985226i	$0.445216\pi$
$38$	−0.755240	−0.122516
$39$	2.81084	0.450095
$40$	0.179453	0.0283740
$41$	−5.40397	−0.843959	−0.421979	−	0.906605i	$-0.638665\pi$
$41$	−5.40397	−0.843959	−0.421979	+	0.906605i	$0.638665\pi$
$42$	−0.288090	−0.0444533
$43$	−5.91283	−0.901698	−0.450849	−	0.892600i	$-0.648879\pi$
$43$	−5.91283	−0.901698	−0.450849	+	0.892600i	$0.648879\pi$
$44$	2.16468	0.326338
$45$	−0.431998	−0.0643985
$46$	−0.363279	−0.0535626
$47$	−0.795216	−0.115994	−0.0579971	−	0.998317i	$-0.518471\pi$
$47$	−0.795216	−0.115994	−0.0579971	+	0.998317i	$0.518471\pi$
$48$	−3.93506	−0.567976
$49$	0.653884	0.0934120
$50$	−0.501230	−0.0708847
$51$	−5.82744	−0.816005
$52$	5.59121	0.775361
$53$	−3.47735	−0.477650	−0.238825	−	0.971063i	$-0.576762\pi$
$53$	−3.47735	−0.477650	−0.238825	+	0.971063i	$0.576762\pi$
$54$	−0.104133	−0.0141707
$55$	0.470119	0.0633908
$56$	−1.14924	−0.153573
$57$	7.25266	0.960639
$58$	−0.524745	−0.0689024
$59$	−9.03190	−1.17585	−0.587927	−	0.808914i	$-0.700056\pi$
$59$	−9.03190	−1.17585	−0.587927	+	0.808914i	$0.700056\pi$
$60$	−0.859312	−0.110937
$61$	−10.4206	−1.33422	−0.667109	−	0.744961i	$-0.732468\pi$
$61$	−10.4206	−1.33422	−0.667109	+	0.744961i	$0.732468\pi$
$62$	−0.210753	−0.0267656
$63$	2.76657	0.348554
$64$	−7.74093	−0.967616
$65$	1.21428	0.150613
$66$	0.113322	0.0139489
$67$	−3.98418	−0.486745	−0.243373	−	0.969933i	$-0.578254\pi$
$67$	−3.98418	−0.486745	−0.243373	+	0.969933i	$0.578254\pi$
$68$	−11.5917	−1.40570
$69$	3.48861	0.419980
$70$	−0.124454	−0.0148752
$71$	10.9852	1.30370	0.651851	−	0.758347i	$-0.273993\pi$
$71$	10.9852	1.30370	0.651851	+	0.758347i	$0.273993\pi$
$72$	−0.415402	−0.0489556
$73$	1.10684	0.129546	0.0647729	−	0.997900i	$-0.479368\pi$
$73$	1.10684	0.129546	0.0647729	+	0.997900i	$0.479368\pi$
$74$	0.216957	0.0252208
$75$	4.81338	0.555801
$76$	14.4267	1.65485
$77$	−3.01069	−0.343100
$78$	0.292701	0.0331419
$79$	−0.409081	−0.0460252	−0.0230126	−	0.999735i	$-0.507326\pi$
$79$	−0.409081	−0.0460252	−0.0230126	+	0.999735i	$0.507326\pi$
$80$	−1.69994	−0.190059
$81$	1.00000	0.111111
$82$	−0.562731	−0.0621432
$83$	15.0992	1.65736	0.828679	−	0.559725i	$-0.189093\pi$
$83$	15.0992	1.65736	0.828679	+	0.559725i	$0.189093\pi$
$84$	5.50313	0.600441
$85$	−2.51744	−0.273055
$86$	−0.615719	−0.0663947
$87$	5.03919	0.540258
$88$	0.452058	0.0481895
$89$	14.2188	1.50719	0.753593	−	0.657342i	$-0.228319\pi$
$89$	14.2188	1.50719	0.753593	+	0.657342i	$0.228319\pi$
$90$	−0.0449852	−0.00474185
$91$	−7.77639	−0.815187
$92$	6.93940	0.723482
$93$	2.02388	0.209867
$94$	−0.0828081	−0.00854100
$95$	3.13314	0.321453
$96$	−1.24057	−0.126615
$97$	12.5418	1.27342	0.636712	−	0.771101i	$-0.280294\pi$
$97$	12.5418	1.27342	0.636712	+	0.771101i	$0.280294\pi$
$98$	0.0680907	0.00687820
$99$	−1.08824	−0.109372
$100$	9.57456	0.957456
$101$	4.71052	0.468714	0.234357	−	0.972151i	$-0.424702\pi$
$101$	4.71052	0.468714	0.234357	+	0.972151i	$0.424702\pi$
$102$	−0.606828	−0.0600849
$103$	−19.1362	−1.88555	−0.942775	−	0.333431i	$-0.891794\pi$
$103$	−19.1362	−1.88555	−0.942775	+	0.333431i	$0.891794\pi$
$104$	1.16763	0.114496
$105$	1.19515	0.116635
$106$	−0.362106	−0.0351708
$107$	6.40124	0.618831	0.309416	−	0.950927i	$-0.399867\pi$
$107$	6.40124	0.618831	0.309416	+	0.950927i	$0.399867\pi$
$108$	1.98916	0.191407
$109$	−2.95365	−0.282908	−0.141454	−	0.989945i	$-0.545178\pi$
$109$	−2.95365	−0.282908	−0.141454	+	0.989945i	$0.545178\pi$
$110$	0.0489548	0.00466765
$111$	−2.08347	−0.197754
$112$	10.8866	1.02869
$113$	0.888386	0.0835724	0.0417862	−	0.999127i	$-0.486695\pi$
$113$	0.888386	0.0835724	0.0417862	+	0.999127i	$0.486695\pi$
$114$	0.755240	0.0707347
$115$	1.50707	0.140535
$116$	10.0237	0.930680
$117$	−2.81084	−0.259863
$118$	−0.940517	−0.0865816
$119$	16.1220	1.47790
$120$	−0.179453	−0.0163817
$121$	−9.81573	−0.892339
$122$	−1.08512	−0.0982424
$123$	5.40397	0.487260
$124$	4.02582	0.361530
$125$	4.23936	0.379180
$126$	0.288090	0.0256651
$127$	−2.46764	−0.218968	−0.109484	−	0.993989i	$-0.534920\pi$
$127$	−2.46764	−0.218968	−0.109484	+	0.993989i	$0.534920\pi$
$128$	−3.28723	−0.290553
$129$	5.91283	0.520595
$130$	0.126446	0.0110901
$131$	−6.69156	−0.584644	−0.292322	−	0.956320i	$-0.594428\pi$
$131$	−6.69156	−0.584644	−0.292322	+	0.956320i	$0.594428\pi$
$132$	−2.16468	−0.188412
$133$	−20.0650	−1.73985
$134$	−0.414884	−0.0358405
$135$	0.431998	0.0371805
$136$	−2.42073	−0.207576
$137$	−6.91690	−0.590951	−0.295475	−	0.955350i	$-0.595478\pi$
$137$	−6.91690	−0.590951	−0.295475	+	0.955350i	$0.595478\pi$
$138$	0.363279	0.0309244
$139$	−9.48581	−0.804575	−0.402288	−	0.915513i	$-0.631785\pi$
$139$	−9.48581	−0.804575	−0.402288	+	0.915513i	$0.631785\pi$
$140$	2.37734	0.200922
$141$	0.795216	0.0669693
$142$	1.14392	0.0959955
$143$	3.05888	0.255796
$144$	3.93506	0.327921
$145$	2.17692	0.180783
$146$	0.115258	0.00953885
$147$	−0.653884	−0.0539314
$148$	−4.14434	−0.340663
$149$	7.32345	0.599961	0.299980	−	0.953945i	$-0.403020\pi$
$149$	7.32345	0.599961	0.299980	+	0.953945i	$0.403020\pi$
$150$	0.501230	0.0409253
$151$	−1.83931	−0.149681	−0.0748404	−	0.997196i	$-0.523845\pi$
$151$	−1.83931	−0.149681	−0.0748404	+	0.997196i	$0.523845\pi$
$152$	3.01277	0.244368
$153$	5.82744	0.471121
$154$	−0.313512	−0.0252635
$155$	0.874314	0.0702266
$156$	−5.59121	−0.447655
$157$	−1.48477	−0.118498	−0.0592488	−	0.998243i	$-0.518871\pi$
$157$	−1.48477	−0.118498	−0.0592488	+	0.998243i	$0.518871\pi$
$158$	−0.0425988	−0.00338897
$159$	3.47735	0.275771
$160$	−0.535925	−0.0423686
$161$	−9.65148	−0.760643
$162$	0.104133	0.00818145
$163$	9.95721	0.779909	0.389954	−	0.920834i	$-0.372491\pi$
$163$	9.95721	0.779909	0.389954	+	0.920834i	$0.372491\pi$
$164$	10.7493	0.839383
$165$	−0.470119	−0.0365987
$166$	1.57233	0.122036
$167$	−1.51314	−0.117090	−0.0585452	−	0.998285i	$-0.518646\pi$
$167$	−1.51314	−0.117090	−0.0585452	+	0.998285i	$0.518646\pi$
$168$	1.14924	0.0886655
$169$	−5.09915	−0.392242
$170$	−0.262149	−0.0201059
$171$	−7.25266	−0.554625
$172$	11.7615	0.896809
$173$	21.1660	1.60922	0.804612	−	0.593801i	$-0.202373\pi$
$173$	21.1660	1.60922	0.804612	+	0.593801i	$0.202373\pi$
$174$	0.524745	0.0397808
$175$	−13.3165	−1.00663
$176$	−4.28229	−0.322790
$177$	9.03190	0.678879
$178$	1.48064	0.110979
$179$	−23.4094	−1.74970	−0.874850	−	0.484394i	$-0.839040\pi$
$179$	−23.4094	−1.74970	−0.874850	+	0.484394i	$0.839040\pi$
$180$	0.859312	0.0640493
$181$	14.5477	1.08132	0.540660	−	0.841241i	$-0.318175\pi$
$181$	14.5477	1.08132	0.540660	+	0.841241i	$0.318175\pi$
$182$	−0.809777	−0.0600247
$183$	10.4206	0.770311
$184$	1.44918	0.106835
$185$	−0.900055	−0.0661733
$186$	0.210753	0.0154531
$187$	−6.34167	−0.463749
$188$	1.58181	0.115365
$189$	−2.76657	−0.201238
$190$	0.326262	0.0236696
$191$	24.9050	1.80206	0.901031	−	0.433755i	$-0.142812\pi$
$191$	24.9050	1.80206	0.901031	+	0.433755i	$0.142812\pi$
$192$	7.74093	0.558653
$193$	5.84285	0.420577	0.210289	−	0.977639i	$-0.432560\pi$
$193$	5.84285	0.420577	0.210289	+	0.977639i	$0.432560\pi$
$194$	1.30601	0.0937661
$195$	−1.21428	−0.0869564
$196$	−1.30068	−0.0929055
$197$	−16.2436	−1.15731	−0.578655	−	0.815572i	$-0.696422\pi$
$197$	−16.2436	−1.15731	−0.578655	+	0.815572i	$0.696422\pi$
$198$	−0.113322	−0.00805342
$199$	−22.7909	−1.61560	−0.807801	−	0.589455i	$-0.799343\pi$
$199$	−22.7909	−1.61560	−0.807801	+	0.589455i	$0.799343\pi$
$200$	1.99949	0.141385
$201$	3.98418	0.281023
$202$	0.490519	0.0345128
$203$	−13.9412	−0.978484
$204$	11.5917	0.811581
$205$	2.33451	0.163049
$206$	−1.99271	−0.138839
$207$	−3.48861	−0.242475
$208$	−11.0608	−0.766931
$209$	7.89265	0.545946
$210$	0.124454	0.00858817
$211$	18.5913	1.27988	0.639938	−	0.768427i	$-0.278960\pi$
$211$	18.5913	1.27988	0.639938	+	0.768427i	$0.278960\pi$
$212$	6.91698	0.475060
$213$	−10.9852	−0.752693
$214$	0.666579	0.0455664
$215$	2.55433	0.174204
$216$	0.415402	0.0282645
$217$	−5.59921	−0.380099
$218$	−0.307572	−0.0208314
$219$	−1.10684	−0.0747933
$220$	−0.935140	−0.0630471
$221$	−16.3800	−1.10184
$222$	−0.216957	−0.0145612
$223$	−12.7025	−0.850622	−0.425311	−	0.905047i	$-0.639835\pi$
$223$	−12.7025	−0.850622	−0.425311	+	0.905047i	$0.639835\pi$
$224$	3.43212	0.229318
$225$	−4.81338	−0.320892
$226$	0.0925102	0.00615369
$227$	−11.9490	−0.793086	−0.396543	−	0.918016i	$-0.629790\pi$
$227$	−11.9490	−0.793086	−0.396543	+	0.918016i	$0.629790\pi$
$228$	−14.4267	−0.955430
$229$	2.84730	0.188155	0.0940773	−	0.995565i	$-0.470010\pi$
$229$	2.84730	0.188155	0.0940773	+	0.995565i	$0.470010\pi$
$230$	0.156936	0.0103480
$231$	3.01069	0.198089
$232$	2.09329	0.137431
$233$	−4.49249	−0.294313	−0.147156	−	0.989113i	$-0.547012\pi$
$233$	−4.49249	−0.294313	−0.147156	+	0.989113i	$0.547012\pi$
$234$	−0.292701	−0.0191345
$235$	0.343532	0.0224096
$236$	17.9659	1.16948
$237$	0.409081	0.0265727
$238$	1.67883	0.108822
$239$	−1.00000	−0.0646846
$239$	−1.00000	−0.0646846
$240$	1.69994	0.109730
$241$	13.6633	0.880133	0.440067	−	0.897965i	$-0.354955\pi$
$241$	13.6633	0.880133	0.440067	+	0.897965i	$0.354955\pi$
$242$	−1.02214	−0.0657056
$243$	−1.00000	−0.0641500
$244$	20.7281	1.32698
$245$	−0.282477	−0.0180468
$246$	0.562731	0.0358784
$247$	20.3861	1.29714
$248$	0.840726	0.0533861
$249$	−15.0992	−0.956876
$250$	0.441457	0.0279202
$251$	−18.2147	−1.14970	−0.574850	−	0.818259i	$-0.694940\pi$
$251$	−18.2147	−1.14970	−0.574850	+	0.818259i	$0.694940\pi$
$252$	−5.50313	−0.346665
$253$	3.79646	0.238681
$254$	−0.256963	−0.0161233
$255$	2.51744	0.157648
$256$	15.1395	0.946222
$257$	4.82747	0.301129	0.150565	−	0.988600i	$-0.451891\pi$
$257$	4.82747	0.301129	0.150565	+	0.988600i	$0.451891\pi$
$258$	0.615719	0.0383330
$259$	5.76405	0.358161
$260$	−2.41539	−0.149796
$261$	−5.03919	−0.311918
$262$	−0.696811	−0.0430491
$263$	−0.934556	−0.0576272	−0.0288136	−	0.999585i	$-0.509173\pi$
$263$	−0.934556	−0.0576272	−0.0288136	+	0.999585i	$0.509173\pi$
$264$	−0.452058	−0.0278222
$265$	1.50221	0.0922799
$266$	−2.08942	−0.128111
$267$	−14.2188	−0.870174
$268$	7.92516	0.484106
$269$	22.8799	1.39501	0.697506	−	0.716579i	$-0.254293\pi$
$269$	22.8799	1.39501	0.697506	+	0.716579i	$0.254293\pi$
$270$	0.0449852	0.00273771
$271$	14.5729	0.885243	0.442621	−	0.896709i	$-0.354049\pi$
$271$	14.5729	0.885243	0.442621	+	0.896709i	$0.354049\pi$
$272$	22.9313	1.39041
$273$	7.77639	0.470648
$274$	−0.720276	−0.0435135
$275$	5.23812	0.315871
$276$	−6.93940	−0.417703
$277$	−6.42790	−0.386215	−0.193108	−	0.981178i	$-0.561857\pi$
$277$	−6.42790	−0.386215	−0.193108	+	0.981178i	$0.561857\pi$
$278$	−0.987783	−0.0592433
$279$	−2.02388	−0.121167
$280$	0.496468	0.0296697
$281$	−11.9766	−0.714462	−0.357231	−	0.934016i	$-0.616279\pi$
$281$	−11.9766	−0.714462	−0.357231	+	0.934016i	$0.616279\pi$
$282$	0.0828081	0.00493115
$283$	−18.4031	−1.09395	−0.546975	−	0.837149i	$-0.684221\pi$
$283$	−18.4031	−1.09395	−0.546975	+	0.837149i	$0.684221\pi$
$284$	−21.8513	−1.29663
$285$	−3.13314	−0.185591
$286$	0.318530	0.0188351
$287$	−14.9504	−0.882497
$288$	1.24057	0.0731014
$289$	16.9591	0.997592
$290$	0.226689	0.0133116
$291$	−12.5418	−0.735212
$292$	−2.20168	−0.128843
$293$	24.8968	1.45449	0.727244	−	0.686379i	$-0.240801\pi$
$293$	24.8968	1.45449	0.727244	+	0.686379i	$0.240801\pi$
$294$	−0.0680907	−0.00397113
$295$	3.90176	0.227170
$296$	−0.865477	−0.0503048
$297$	1.08824	0.0631462
$298$	0.762612	0.0441769
$299$	9.80595	0.567093
$300$	−9.57456	−0.552788
$301$	−16.3582	−0.942872
$302$	−0.191532	−0.0110214
$303$	−4.71052	−0.270612
$304$	−28.5396	−1.63686
$305$	4.50167	0.257765
$306$	0.606828	0.0346900
$307$	−3.67995	−0.210026	−0.105013	−	0.994471i	$-0.533488\pi$
$307$	−3.67995	−0.210026	−0.105013	+	0.994471i	$0.533488\pi$
$308$	5.98874	0.341240
$309$	19.1362	1.08862
$310$	0.0910448	0.00517100
$311$	−28.6157	−1.62265	−0.811324	−	0.584596i	$-0.801253\pi$
$311$	−28.6157	−1.62265	−0.811324	+	0.584596i	$0.801253\pi$
$312$	−1.16763	−0.0661041
$313$	14.3414	0.810622	0.405311	−	0.914179i	$-0.367163\pi$
$313$	14.3414	0.810622	0.405311	+	0.914179i	$0.367163\pi$
$314$	−0.154613	−0.00872534
$315$	−1.19515	−0.0673391
$316$	0.813726	0.0457757
$317$	−24.7113	−1.38793	−0.693964	−	0.720010i	$-0.744137\pi$
$317$	−24.7113	−1.38793	−0.693964	+	0.720010i	$0.744137\pi$
$318$	0.362106	0.0203059
$319$	5.48386	0.307037
$320$	3.34407	0.186939
$321$	−6.40124	−0.357282
$322$	−1.00504	−0.0560084
$323$	−42.2645	−2.35166
$324$	−1.98916	−0.110509
$325$	13.5297	0.750490
$326$	1.03687	0.0574270
$327$	2.95365	0.163337
$328$	2.24482	0.123949
$329$	−2.20002	−0.121291
$330$	−0.0489548	−0.00269487
$331$	−30.5404	−1.67865	−0.839327	−	0.543627i	$-0.817051\pi$
$331$	−30.5404	−1.67865	−0.839327	+	0.543627i	$0.817051\pi$
$332$	−30.0348	−1.64837
$333$	2.08347	0.114173
$334$	−0.157568	−0.00862171
$335$	1.72116	0.0940370
$336$	−10.8866	−0.593912
$337$	26.8195	1.46095	0.730474	−	0.682940i	$-0.239299\pi$
$337$	26.8195	1.46095	0.730474	+	0.682940i	$0.239299\pi$
$338$	−0.530989	−0.0288820
$339$	−0.888386	−0.0482505
$340$	5.00759	0.271575
$341$	2.20248	0.119271
$342$	−0.755240	−0.0408387
$343$	−17.5569	−0.947986
$344$	2.45620	0.132429
$345$	−1.50707	−0.0811382
$346$	2.20408	0.118492
$347$	−9.11072	−0.489089	−0.244544	−	0.969638i	$-0.578638\pi$
$347$	−9.11072	−0.489089	−0.244544	+	0.969638i	$0.578638\pi$
$348$	−10.0237	−0.537329
$349$	31.8626	1.70557	0.852783	−	0.522265i	$-0.174913\pi$
$349$	31.8626	1.70557	0.852783	+	0.522265i	$0.174913\pi$
$350$	−1.38669	−0.0741215
$351$	2.81084	0.150032
$352$	−1.35004	−0.0719575
$353$	13.4752	0.717214	0.358607	−	0.933489i	$-0.383252\pi$
$353$	13.4752	0.717214	0.358607	+	0.933489i	$0.383252\pi$
$354$	0.940517	0.0499879
$355$	−4.74558	−0.251869
$356$	−28.2833	−1.49901
$357$	−16.1220	−0.853267
$358$	−2.43769	−0.128836
$359$	2.38673	0.125967	0.0629835	−	0.998015i	$-0.479938\pi$
$359$	2.38673	0.125967	0.0629835	+	0.998015i	$0.479938\pi$
$360$	0.179453	0.00945800
$361$	33.6011	1.76848
$362$	1.51489	0.0796208
$363$	9.81573	0.515192
$364$	15.4684	0.810767
$365$	−0.478153	−0.0250277
$366$	1.08512	0.0567203
$367$	1.65472	0.0863755	0.0431877	−	0.999067i	$-0.486249\pi$
$367$	1.65472	0.0863755	0.0431877	+	0.999067i	$0.486249\pi$
$368$	−13.7279	−0.715616
$369$	−5.40397	−0.281320
$370$	−0.0937252	−0.00487254
$371$	−9.62030	−0.499461
$372$	−4.02582	−0.208729
$373$	−6.13773	−0.317800	−0.158900	−	0.987295i	$-0.550795\pi$
$373$	−6.13773	−0.317800	−0.158900	+	0.987295i	$0.550795\pi$
$374$	−0.660376	−0.0341472
$375$	−4.23936	−0.218920
$376$	0.330334	0.0170357
$377$	14.1644	0.729503
$378$	−0.288090	−0.0148178
$379$	14.3037	0.734731	0.367365	−	0.930077i	$-0.380260\pi$
$379$	14.3037	0.734731	0.367365	+	0.930077i	$0.380260\pi$
$380$	−6.23230	−0.319710
$381$	2.46764	0.126421
$382$	2.59343	0.132691
$383$	18.2784	0.933981	0.466990	−	0.884262i	$-0.345338\pi$
$383$	18.2784	0.933981	0.466990	+	0.884262i	$0.345338\pi$
$384$	3.28723	0.167751
$385$	1.30061	0.0662854
$386$	0.608432	0.0309684
$387$	−5.91283	−0.300566
$388$	−24.9476	−1.26652
$389$	12.9086	0.654492	0.327246	−	0.944939i	$-0.393880\pi$
$389$	12.9086	0.654492	0.327246	+	0.944939i	$0.393880\pi$
$390$	−0.126446	−0.00640286
$391$	−20.3297	−1.02812
$392$	−0.271625	−0.0137191
$393$	6.69156	0.337544
$394$	−1.69149	−0.0852163
$395$	0.176722	0.00889186
$396$	2.16468	0.108779
$397$	−17.5435	−0.880484	−0.440242	−	0.897879i	$-0.645107\pi$
$397$	−17.5435	−0.880484	−0.440242	+	0.897879i	$0.645107\pi$
$398$	−2.37328	−0.118962
$399$	20.0650	1.00450
$400$	−18.9409	−0.947045
$401$	35.1950	1.75755	0.878777	−	0.477233i	$-0.158360\pi$
$401$	35.1950	1.75755	0.878777	+	0.477233i	$0.158360\pi$
$402$	0.414884	0.0206925
$403$	5.68883	0.283381
$404$	−9.36995	−0.466173
$405$	−0.431998	−0.0214662
$406$	−1.45174	−0.0720487
$407$	−2.26732	−0.112387
$408$	2.42073	0.119844
$409$	6.31266	0.312141	0.156070	−	0.987746i	$-0.450117\pi$
$409$	6.31266	0.312141	0.156070	+	0.987746i	$0.450117\pi$
$410$	0.243099	0.0120058
$411$	6.91690	0.341185
$412$	38.0650	1.87533
$413$	−24.9873	−1.22955
$414$	−0.363279	−0.0178542
$415$	−6.52284	−0.320194
$416$	−3.48706	−0.170967
$417$	9.48581	0.464522
$418$	0.821884	0.0401997
$419$	24.6530	1.20438	0.602190	−	0.798353i	$-0.294295\pi$
$419$	24.6530	1.20438	0.602190	+	0.798353i	$0.294295\pi$
$420$	−2.37734	−0.116002
$421$	−25.4233	−1.23906	−0.619529	−	0.784974i	$-0.712676\pi$
$421$	−25.4233	−1.23906	−0.619529	+	0.784974i	$0.712676\pi$
$422$	1.93596	0.0942411
$423$	−0.795216	−0.0386647
$424$	1.44450	0.0701510
$425$	−28.0497	−1.36061
$426$	−1.14392	−0.0554230
$427$	−28.8292	−1.39514
$428$	−12.7331	−0.615476
$429$	−3.05888	−0.147684
$430$	0.265990	0.0128272
$431$	−35.1475	−1.69299	−0.846497	−	0.532393i	$-0.821293\pi$
$431$	−35.1475	−1.69299	−0.846497	+	0.532393i	$0.821293\pi$
$432$	−3.93506	−0.189325
$433$	−28.5125	−1.37022	−0.685111	−	0.728439i	$-0.740246\pi$
$433$	−28.5125	−1.37022	−0.685111	+	0.728439i	$0.740246\pi$
$434$	−0.583061	−0.0279878
$435$	−2.17692	−0.104375
$436$	5.87527	0.281374
$437$	25.3017	1.21035
$438$	−0.115258	−0.00550725
$439$	19.6250	0.936648	0.468324	−	0.883557i	$-0.344858\pi$
$439$	19.6250	0.936648	0.468324	+	0.883557i	$0.344858\pi$
$440$	−0.195288	−0.00931000
$441$	0.653884	0.0311373
$442$	−1.70570	−0.0811318
$443$	−13.5449	−0.643539	−0.321770	−	0.946818i	$-0.604278\pi$
$443$	−13.5449	−0.643539	−0.321770	+	0.946818i	$0.604278\pi$
$444$	4.14434	0.196682
$445$	−6.14248	−0.291181
$446$	−1.32275	−0.0626338
$447$	−7.32345	−0.346387
$448$	−21.4158	−1.01180
$449$	31.3156	1.47787	0.738936	−	0.673775i	$-0.235328\pi$
$449$	31.3156	1.47787	0.738936	+	0.673775i	$0.235328\pi$
$450$	−0.501230	−0.0236282
$451$	5.88083	0.276917
$452$	−1.76714	−0.0831193
$453$	1.83931	0.0864182
$454$	−1.24429	−0.0583973
$455$	3.35938	0.157490
$456$	−3.01277	−0.141086
$457$	−11.7404	−0.549193	−0.274597	−	0.961560i	$-0.588544\pi$
$457$	−11.7404	−0.549193	−0.274597	+	0.961560i	$0.588544\pi$
$458$	0.296497	0.0138544
$459$	−5.82744	−0.272002
$460$	−2.99781	−0.139773
$461$	−0.0379172	−0.00176598	−0.000882990	−	1.00000i	$-0.500281\pi$
$461$	−0.0379172	−0.00176598	−0.000882990		1.00000i	$0.500281\pi$
$462$	0.313512	0.0145859
$463$	3.78515	0.175911	0.0879554	−	0.996124i	$-0.471967\pi$
$463$	3.78515	0.175911	0.0879554	+	0.996124i	$0.471967\pi$
$464$	−19.8295	−0.920561
$465$	−0.874314	−0.0405454
$466$	−0.467816	−0.0216711
$467$	32.5797	1.50761	0.753804	−	0.657099i	$-0.228217\pi$
$467$	32.5797	1.50761	0.753804	+	0.657099i	$0.228217\pi$
$468$	5.59121	0.258454
$469$	−11.0225	−0.508972
$470$	0.0357729	0.00165008
$471$	1.48477	0.0684147
$472$	3.75187	0.172694
$473$	6.43459	0.295863
$474$	0.0425988	0.00195663
$475$	34.9098	1.60177
$476$	−32.0692	−1.46989
$477$	−3.47735	−0.159217
$478$	−0.104133	−0.00476292
$479$	−19.3874	−0.885833	−0.442917	−	0.896563i	$-0.646056\pi$
$479$	−19.3874	−0.885833	−0.442917	+	0.896563i	$0.646056\pi$
$480$	0.535925	0.0244615
$481$	−5.85631	−0.267025
$482$	1.42280	0.0648069
$483$	9.65148	0.439157
$484$	19.5250	0.887501
$485$	−5.41803	−0.246020
$486$	−0.104133	−0.00472356
$487$	4.84919	0.219738	0.109869	−	0.993946i	$-0.464957\pi$
$487$	4.84919	0.219738	0.109869	+	0.993946i	$0.464957\pi$
$488$	4.32873	0.195952
$489$	−9.95721	−0.450281
$490$	−0.0294151	−0.00132884
$491$	−24.7326	−1.11617	−0.558084	−	0.829784i	$-0.688463\pi$
$491$	−24.7326	−1.11617	−0.558084	+	0.829784i	$0.688463\pi$
$492$	−10.7493	−0.484618
$493$	−29.3656	−1.32256
$494$	2.12286	0.0955121
$495$	0.470119	0.0211303
$496$	−7.96410	−0.357599
$497$	30.3912	1.36323
$498$	−1.57233	−0.0704576
$499$	−13.0377	−0.583647	−0.291823	−	0.956472i	$-0.594262\pi$
$499$	−13.0377	−0.583647	−0.291823	+	0.956472i	$0.594262\pi$
$500$	−8.43275	−0.377124
$501$	1.51314	0.0676021
$502$	−1.89675	−0.0846559
$503$	−3.27894	−0.146201	−0.0731004	−	0.997325i	$-0.523289\pi$
$503$	−3.27894	−0.146201	−0.0731004	+	0.997325i	$0.523289\pi$
$504$	−1.14924	−0.0511911
$505$	−2.03493	−0.0905534
$506$	0.395336	0.0175748
$507$	5.09915	0.226461
$508$	4.90853	0.217781
$509$	19.1552	0.849040	0.424520	−	0.905419i	$-0.360443\pi$
$509$	19.1552	0.849040	0.424520	+	0.905419i	$0.360443\pi$
$510$	0.262149	0.0116081
$511$	3.06214	0.135461
$512$	8.15098	0.360226
$513$	7.25266	0.320213
$514$	0.502698	0.0221731
$515$	8.26682	0.364280
$516$	−11.7615	−0.517773
$517$	0.865388	0.0380597
$518$	0.600227	0.0263725
$519$	−21.1660	−0.929086
$520$	−0.504414	−0.0221200
$521$	−9.95719	−0.436232	−0.218116	−	0.975923i	$-0.569991\pi$
$521$	−9.95719	−0.436232	−0.218116	+	0.975923i	$0.569991\pi$
$522$	−0.524745	−0.0229675
$523$	23.4154	1.02389	0.511943	−	0.859020i	$-0.328926\pi$
$523$	23.4154	1.02389	0.511943	+	0.859020i	$0.328926\pi$
$524$	13.3106	0.581474
$525$	13.3165	0.581181
$526$	−0.0973180	−0.00424326
$527$	−11.7941	−0.513758
$528$	4.28229	0.186363
$529$	−10.8296	−0.470851
$530$	0.156429	0.00679484
$531$	−9.03190	−0.391951
$532$	39.9124	1.73042
$533$	15.1897	0.657940
$534$	−1.48064	−0.0640735
$535$	−2.76532	−0.119555
$536$	1.65504	0.0714867
$537$	23.4094	1.01019
$538$	2.38255	0.102719
$539$	−0.711584	−0.0306501
$540$	−0.859312	−0.0369789
$541$	15.9305	0.684904	0.342452	−	0.939535i	$-0.388743\pi$
$541$	15.9305	0.684904	0.342452	+	0.939535i	$0.388743\pi$
$542$	1.51752	0.0651831
$543$	−14.5477	−0.624300
$544$	7.22936	0.309956
$545$	1.27597	0.0546566
$546$	0.809777	0.0346553
$547$	33.0838	1.41456	0.707280	−	0.706934i	$-0.249922\pi$
$547$	33.0838	1.41456	0.707280	+	0.706934i	$0.249922\pi$
$548$	13.7588	0.587746
$549$	−10.4206	−0.444739
$550$	0.545460	0.0232585
$551$	36.5475	1.55698
$552$	−1.44918	−0.0616811
$553$	−1.13175	−0.0481269
$554$	−0.669355	−0.0284382
$555$	0.900055	0.0382052
$556$	18.8687	0.800213
$557$	−31.7597	−1.34570	−0.672851	−	0.739778i	$-0.734931\pi$
$557$	−31.7597	−1.34570	−0.672851	+	0.739778i	$0.734931\pi$
$558$	−0.210753	−0.00892188
$559$	16.6200	0.702953
$560$	−4.70299	−0.198737
$561$	6.34167	0.267745
$562$	−1.24715	−0.0526080
$563$	−33.8109	−1.42496	−0.712479	−	0.701694i	$-0.752428\pi$
$563$	−33.8109	−1.42496	−0.712479	+	0.701694i	$0.752428\pi$
$564$	−1.58181	−0.0666062
$565$	−0.383781	−0.0161458
$566$	−1.91636	−0.0805508
$567$	2.76657	0.116185
$568$	−4.56327	−0.191471
$569$	13.6032	0.570274	0.285137	−	0.958487i	$-0.407961\pi$
$569$	13.6032	0.570274	0.285137	+	0.958487i	$0.407961\pi$
$570$	−0.326262	−0.0136656
$571$	19.2244	0.804517	0.402259	−	0.915526i	$-0.368225\pi$
$571$	19.2244	0.804517	0.402259	+	0.915526i	$0.368225\pi$
$572$	−6.08459	−0.254410
$573$	−24.9050	−1.04042
$574$	−1.55683	−0.0649809
$575$	16.7920	0.700275
$576$	−7.74093	−0.322539
$577$	−30.1474	−1.25505	−0.627525	−	0.778596i	$-0.715932\pi$
$577$	−30.1474	−1.25505	−0.627525	+	0.778596i	$0.715932\pi$
$578$	1.76600	0.0734557
$579$	−5.84285	−0.242820
$580$	−4.33023	−0.179803
$581$	41.7730	1.73304
$582$	−1.30601	−0.0541359
$583$	3.78419	0.156725
$584$	−0.459783	−0.0190260
$585$	1.21428	0.0502043
$586$	2.59258	0.107098
$587$	−34.4451	−1.42170	−0.710850	−	0.703344i	$-0.751689\pi$
$587$	−34.4451	−1.42170	−0.710850	+	0.703344i	$0.751689\pi$
$588$	1.30068	0.0536390
$589$	14.6786	0.604819
$590$	0.406302	0.0167272
$591$	16.2436	0.668174
$592$	8.19856	0.336959
$593$	−18.4600	−0.758061	−0.379030	−	0.925384i	$-0.623742\pi$
$593$	−18.4600	−0.758061	−0.379030	+	0.925384i	$0.623742\pi$
$594$	0.113322	0.00464965
$595$	−6.96467	−0.285524
$596$	−14.5675	−0.596708
$597$	22.7909	0.932769
$598$	1.02112	0.0417567
$599$	−44.8094	−1.83086	−0.915432	−	0.402473i	$-0.868151\pi$
$599$	−44.8094	−1.83086	−0.915432	+	0.402473i	$0.868151\pi$
$600$	−1.99949	−0.0816287
$601$	−1.25830	−0.0513271	−0.0256636	−	0.999671i	$-0.508170\pi$
$601$	−1.25830	−0.0513271	−0.0256636	+	0.999671i	$0.508170\pi$
$602$	−1.70343	−0.0694265
$603$	−3.98418	−0.162248
$604$	3.65867	0.148869
$605$	4.24038	0.172396
$606$	−0.490519	−0.0199260
$607$	−24.6395	−1.00009	−0.500044	−	0.866000i	$-0.666683\pi$
$607$	−24.6395	−1.00009	−0.500044	+	0.866000i	$0.666683\pi$
$608$	−8.99746	−0.364895
$609$	13.9412	0.564928
$610$	0.468771	0.0189800
$611$	2.23523	0.0904277
$612$	−11.5917	−0.468566
$613$	1.92675	0.0778205	0.0389103	−	0.999243i	$-0.487611\pi$
$613$	1.92675	0.0778205	0.0389103	+	0.999243i	$0.487611\pi$
$614$	−0.383204	−0.0154648
$615$	−2.33451	−0.0941364
$616$	1.25065	0.0503900
$617$	25.5030	1.02671	0.513357	−	0.858175i	$-0.328402\pi$
$617$	25.5030	1.02671	0.513357	+	0.858175i	$0.328402\pi$
$618$	1.99271	0.0801585
$619$	−18.7143	−0.752190	−0.376095	−	0.926581i	$-0.622733\pi$
$619$	−18.7143	−0.752190	−0.376095	+	0.926581i	$0.622733\pi$
$620$	−1.73915	−0.0698459
$621$	3.48861	0.139993
$622$	−2.97984	−0.119481
$623$	39.3371	1.57601
$624$	11.0608	0.442788
$625$	22.2355	0.889420
$626$	1.49341	0.0596886
$627$	−7.89265	−0.315202
$628$	2.95344	0.117855
$629$	12.1413	0.484105
$630$	−0.124454	−0.00495838
$631$	−2.67027	−0.106302	−0.0531510	−	0.998586i	$-0.516926\pi$
$631$	−2.67027	−0.106302	−0.0531510	+	0.998586i	$0.516926\pi$
$632$	0.169933	0.00675957
$633$	−18.5913	−0.738937
$634$	−2.57326	−0.102197
$635$	1.06602	0.0423036
$636$	−6.91698	−0.274276
$637$	−1.83797	−0.0728229
$638$	0.571049	0.0226081
$639$	10.9852	0.434567
$640$	1.42008	0.0561335
$641$	−12.0848	−0.477320	−0.238660	−	0.971103i	$-0.576708\pi$
$641$	−12.0848	−0.477320	−0.238660	+	0.971103i	$0.576708\pi$
$642$	−0.666579	−0.0263078
$643$	43.4945	1.71525	0.857627	−	0.514272i	$-0.171938\pi$
$643$	43.4945	1.71525	0.857627	+	0.514272i	$0.171938\pi$
$644$	19.1983	0.756519
$645$	−2.55433	−0.100577
$646$	−4.40112	−0.173160
$647$	0.330370	0.0129882	0.00649409	−	0.999979i	$-0.497933\pi$
$647$	0.330370	0.0129882	0.00649409	+	0.999979i	$0.497933\pi$
$648$	−0.415402	−0.0163185
$649$	9.82889	0.385818
$650$	1.40888	0.0552609
$651$	5.59921	0.219450
$652$	−19.8064	−0.775680
$653$	−29.4599	−1.15285	−0.576427	−	0.817148i	$-0.695554\pi$
$653$	−29.4599	−1.15285	−0.576427	+	0.817148i	$0.695554\pi$
$654$	0.307572	0.0120270
$655$	2.89074	0.112951
$656$	−21.2649	−0.830256
$657$	1.10684	0.0431819
$658$	−0.229094	−0.00893101
$659$	42.6534	1.66154	0.830770	−	0.556616i	$-0.187900\pi$
$659$	42.6534	1.66154	0.830770	+	0.556616i	$0.187900\pi$
$660$	0.935140	0.0364003
$661$	44.7939	1.74228	0.871140	−	0.491034i	$-0.163381\pi$
$661$	44.7939	1.74228	0.871140	+	0.491034i	$0.163381\pi$
$662$	−3.18026	−0.123604
$663$	16.3800	0.636148
$664$	−6.27226	−0.243411
$665$	8.66803	0.336132
$666$	0.216957	0.00840693
$667$	17.5798	0.680692
$668$	3.00987	0.116455
$669$	12.7025	0.491107
$670$	0.179229	0.00692423
$671$	11.3401	0.437780
$672$	−3.43212	−0.132397
$673$	0.183092	0.00705769	0.00352885	−	0.999994i	$-0.498877\pi$
$673$	0.183092	0.00705769	0.00352885	+	0.999994i	$0.498877\pi$
$674$	2.79279	0.107574
$675$	4.81338	0.185267
$676$	10.1430	0.390116
$677$	−2.12245	−0.0815725	−0.0407862	−	0.999168i	$-0.512986\pi$
$677$	−2.12245	−0.0815725	−0.0407862	+	0.999168i	$0.512986\pi$
$678$	−0.0925102	−0.00355283
$679$	34.6976	1.33157
$680$	1.04575	0.0401027
$681$	11.9490	0.457889
$682$	0.229350	0.00878227
$683$	6.23555	0.238597	0.119298	−	0.992858i	$-0.461936\pi$
$683$	6.23555	0.238597	0.119298	+	0.992858i	$0.461936\pi$
$684$	14.4267	0.551618
$685$	2.98809	0.114169
$686$	−1.82825	−0.0698031
$687$	−2.84730	−0.108631
$688$	−23.2673	−0.887057
$689$	9.77428	0.372370
$690$	−0.156936	−0.00597445
$691$	29.0740	1.10603	0.553014	−	0.833172i	$-0.313478\pi$
$691$	29.0740	1.10603	0.553014	+	0.833172i	$0.313478\pi$
$692$	−42.1025	−1.60050
$693$	−3.01069	−0.114367
$694$	−0.948725	−0.0360131
$695$	4.09785	0.155440
$696$	−2.09329	−0.0793459
$697$	−31.4913	−1.19282
$698$	3.31794	0.125586
$699$	4.49249	0.169922
$700$	26.4886	1.00118
$701$	4.01876	0.151786	0.0758932	−	0.997116i	$-0.475819\pi$
$701$	4.01876	0.151786	0.0758932	+	0.997116i	$0.475819\pi$
$702$	0.292701	0.0110473
$703$	−15.1107	−0.569911
$704$	8.42400	0.317492
$705$	−0.343532	−0.0129382
$706$	1.40321	0.0528106
$707$	13.0320	0.490117
$708$	−17.9659	−0.675198
$709$	38.7677	1.45595	0.727975	−	0.685603i	$-0.240462\pi$
$709$	38.7677	1.45595	0.727975	+	0.685603i	$0.240462\pi$
$710$	−0.494171	−0.0185459
$711$	−0.409081	−0.0153417
$712$	−5.90650	−0.221356
$713$	7.06055	0.264420
$714$	−1.67883	−0.0628286
$715$	−1.32143	−0.0494187
$716$	46.5649	1.74021
$717$	1.00000	0.0373457
$718$	0.248537	0.00927533
$719$	36.1988	1.34999	0.674993	−	0.737824i	$-0.264146\pi$
$719$	36.1988	1.34999	0.674993	+	0.737824i	$0.264146\pi$
$720$	−1.69994	−0.0633529
$721$	−52.9416	−1.97165
$722$	3.49898	0.130219
$723$	−13.6633	−0.508145
$724$	−28.9376	−1.07546
$725$	24.2555	0.900827
$726$	1.02214	0.0379352
$727$	−9.24566	−0.342902	−0.171451	−	0.985193i	$-0.554846\pi$
$727$	−9.24566	−0.342902	−0.171451	+	0.985193i	$0.554846\pi$
$728$	3.23033	0.119724
$729$	1.00000	0.0370370
$730$	−0.0497914	−0.00184286
$731$	−34.4566	−1.27443
$732$	−20.7281	−0.766134
$733$	8.57554	0.316745	0.158372	−	0.987379i	$-0.449375\pi$
$733$	8.57554	0.316745	0.158372	+	0.987379i	$0.449375\pi$
$734$	0.172310	0.00636009
$735$	0.282477	0.0104193
$736$	−4.32788	−0.159528
$737$	4.33576	0.159710
$738$	−0.562731	−0.0207144
$739$	14.0883	0.518246	0.259123	−	0.965844i	$-0.416566\pi$
$739$	14.0883	0.518246	0.259123	+	0.965844i	$0.416566\pi$
$740$	1.79035	0.0658145
$741$	−20.3861	−0.748903
$742$	−1.00179	−0.0367768
$743$	−47.7553	−1.75197	−0.875986	−	0.482337i	$-0.839788\pi$
$743$	−47.7553	−1.75197	−0.875986	+	0.482337i	$0.839788\pi$
$744$	−0.840726	−0.0308225
$745$	−3.16372	−0.115910
$746$	−0.639139	−0.0234005
$747$	15.0992	0.552452
$748$	12.6146	0.461234
$749$	17.7095	0.647089
$750$	−0.441457	−0.0161197
$751$	24.4902	0.893662	0.446831	−	0.894618i	$-0.352553\pi$
$751$	24.4902	0.893662	0.446831	+	0.894618i	$0.352553\pi$
$752$	−3.12922	−0.114111
$753$	18.2147	0.663780
$754$	1.47498	0.0537155
$755$	0.794578	0.0289176
$756$	5.50313	0.200147
$757$	−18.3094	−0.665465	−0.332733	−	0.943021i	$-0.607971\pi$
$757$	−18.3094	−0.665465	−0.332733	+	0.943021i	$0.607971\pi$
$758$	1.48948	0.0541004
$759$	−3.79646	−0.137803
$760$	−1.30151	−0.0472108
$761$	−37.5505	−1.36120	−0.680602	−	0.732653i	$-0.738282\pi$
$761$	−37.5505	−1.36120	−0.680602	+	0.732653i	$0.738282\pi$
$762$	0.256963	0.00930878
$763$	−8.17146	−0.295827
$764$	−49.5399	−1.79229
$765$	−2.51744	−0.0910184
$766$	1.90338	0.0687718
$767$	25.3873	0.916681
$768$	−15.1395	−0.546301
$769$	−35.3202	−1.27368	−0.636839	−	0.770996i	$-0.719759\pi$
$769$	−35.3202	−1.27368	−0.636839	+	0.770996i	$0.719759\pi$
$770$	0.135437	0.00488080
$771$	−4.82747	−0.173857
$772$	−11.6223	−0.418297
$773$	−7.48572	−0.269243	−0.134621	−	0.990897i	$-0.542982\pi$
$773$	−7.48572	−0.269243	−0.134621	+	0.990897i	$0.542982\pi$
$774$	−0.615719	−0.0221316
$775$	9.74172	0.349933
$776$	−5.20988	−0.187024
$777$	−5.76405	−0.206784
$778$	1.34421	0.0481922
$779$	39.1932	1.40424
$780$	2.41539	0.0864849
$781$	−11.9545	−0.427767
$782$	−2.11699	−0.0757033
$783$	5.03919	0.180086
$784$	2.57307	0.0918953
$785$	0.641419	0.0228932
$786$	0.696811	0.0248544
$787$	−4.60088	−0.164004	−0.0820018	−	0.996632i	$-0.526131\pi$
$787$	−4.60088	−0.164004	−0.0820018	+	0.996632i	$0.526131\pi$
$788$	32.3111	1.15104
$789$	0.934556	0.0332711
$790$	0.0184026	0.000654735 0
$791$	2.45778	0.0873886
$792$	0.452058	0.0160632
$793$	29.2906	1.04014
$794$	−1.82686	−0.0648327
$795$	−1.50221	−0.0532778
$796$	45.3346	1.60684
$797$	−4.86780	−0.172426	−0.0862132	−	0.996277i	$-0.527477\pi$
$797$	−4.86780	−0.172426	−0.0862132	+	0.996277i	$0.527477\pi$
$798$	2.08942	0.0739647
$799$	−4.63408	−0.163942
$800$	−5.97134	−0.211119
$801$	14.2188	0.502395
$802$	3.66495	0.129414
$803$	−1.20451	−0.0425062
$804$	−7.92516	−0.279499
$805$	4.16942	0.146953
$806$	0.592393	0.0208662
$807$	−22.8799	−0.805411
$808$	−1.95676	−0.0688385
$809$	−29.9137	−1.05171	−0.525855	−	0.850574i	$-0.676255\pi$
$809$	−29.9137	−1.05171	−0.525855	+	0.850574i	$0.676255\pi$
$810$	−0.0449852	−0.00158062
$811$	32.8629	1.15397	0.576986	−	0.816754i	$-0.304229\pi$
$811$	32.8629	1.15397	0.576986	+	0.816754i	$0.304229\pi$
$812$	27.7313	0.973178
$813$	−14.5729	−0.511095
$814$	−0.236102	−0.00827538
$815$	−4.30150	−0.150675
$816$	−22.9313	−0.802756
$817$	42.8837	1.50031
$818$	0.657355	0.0229839
$819$	−7.77639	−0.271729
$820$	−4.64370	−0.162165
$821$	−3.75765	−0.131143	−0.0655715	−	0.997848i	$-0.520887\pi$
$821$	−3.75765	−0.131143	−0.0655715	+	0.997848i	$0.520887\pi$
$822$	0.720276	0.0251225
$823$	−28.8183	−1.00454	−0.502271	−	0.864710i	$-0.667502\pi$
$823$	−28.8183	−1.00454	−0.502271	+	0.864710i	$0.667502\pi$
$824$	7.94923	0.276925
$825$	−5.23812	−0.182368
$826$	−2.60200	−0.0905352
$827$	−55.3088	−1.92328	−0.961638	−	0.274322i	$-0.911547\pi$
$827$	−55.3088	−1.92328	−0.961638	+	0.274322i	$0.911547\pi$
$828$	6.93940	0.241161
$829$	35.2389	1.22390	0.611949	−	0.790897i	$-0.290386\pi$
$829$	35.2389	1.22390	0.611949	+	0.790897i	$0.290386\pi$
$830$	−0.679242	−0.0235768
$831$	6.42790	0.222981
$832$	21.7585	0.754342
$833$	3.81047	0.132025
$834$	0.987783	0.0342041
$835$	0.653674	0.0226213
$836$	−15.6997	−0.542986
$837$	2.02388	0.0699557
$838$	2.56719	0.0886821
$839$	18.9566	0.654454	0.327227	−	0.944946i	$-0.393886\pi$
$839$	18.9566	0.654454	0.327227	+	0.944946i	$0.393886\pi$
$840$	−0.496468	−0.0171298
$841$	−3.60658	−0.124365
$842$	−2.64740	−0.0912355
$843$	11.9766	0.412495
$844$	−36.9809	−1.27294
$845$	2.20282	0.0757794
$846$	−0.0828081	−0.00284700
$847$	−27.1559	−0.933086
$848$	−13.6836	−0.469895
$849$	18.4031	0.631592
$850$	−2.92089	−0.100186
$851$	−7.26841	−0.249158
$852$	21.8513	0.748612
$853$	−5.80817	−0.198868	−0.0994339	−	0.995044i	$-0.531703\pi$
$853$	−5.80817	−0.198868	−0.0994339	+	0.995044i	$0.531703\pi$
$854$	−3.00206	−0.102728
$855$	3.13314	0.107151
$856$	−2.65909	−0.0908858
$857$	20.8413	0.711924	0.355962	−	0.934500i	$-0.384153\pi$
$857$	20.8413	0.711924	0.355962	+	0.934500i	$0.384153\pi$
$858$	−0.318530	−0.0108744
$859$	20.6840	0.705728	0.352864	−	0.935675i	$-0.385208\pi$
$859$	20.6840	0.705728	0.352864	+	0.935675i	$0.385208\pi$
$860$	−5.08096	−0.173259
$861$	14.9504	0.509510
$862$	−3.66000	−0.124660
$863$	−32.6930	−1.11288	−0.556441	−	0.830887i	$-0.687834\pi$
$863$	−32.6930	−1.11288	−0.556441	+	0.830887i	$0.687834\pi$
$864$	−1.24057	−0.0422051
$865$	−9.14369	−0.310895
$866$	−2.96908	−0.100894
$867$	−16.9591	−0.575960
$868$	11.1377	0.378038
$869$	0.445179	0.0151017
$870$	−0.226689	−0.00768547
$871$	11.1989	0.379461
$872$	1.22695	0.0415498
$873$	12.5418	0.424475
$874$	2.63474	0.0891214
$875$	11.7285	0.396495
$876$	2.20168	0.0743878
$877$	31.3932	1.06007	0.530036	−	0.847975i	$-0.322178\pi$
$877$	31.3932	1.06007	0.530036	+	0.847975i	$0.322178\pi$
$878$	2.04360	0.0689682
$879$	−24.8968	−0.839749
$880$	1.84994	0.0623616
$881$	54.7572	1.84482	0.922409	−	0.386214i	$-0.126217\pi$
$881$	54.7572	1.84482	0.922409	+	0.386214i	$0.126217\pi$
$882$	0.0680907	0.00229273
$883$	−44.9140	−1.51148	−0.755738	−	0.654874i	$-0.772722\pi$
$883$	−44.9140	−1.51148	−0.755738	+	0.654874i	$0.772722\pi$
$884$	32.5824	1.09587
$885$	−3.90176	−0.131156
$886$	−1.41047	−0.0473857
$887$	−29.8624	−1.00268	−0.501340	−	0.865250i	$-0.667159\pi$
$887$	−29.8624	−1.00268	−0.501340	+	0.865250i	$0.667159\pi$
$888$	0.865477	0.0290435
$889$	−6.82690	−0.228967
$890$	−0.639634	−0.0214406
$891$	−1.08824	−0.0364575
$892$	25.2672	0.846010
$893$	5.76744	0.193000
$894$	−0.762612	−0.0255056
$895$	10.1128	0.338034
$896$	−9.09433	−0.303820
$897$	−9.80595	−0.327411
$898$	3.26098	0.108820
$899$	10.1987	0.340147
$900$	9.57456	0.319152
$901$	−20.2640	−0.675093
$902$	0.612387	0.0203903
$903$	16.3582	0.544367
$904$	−0.369038	−0.0122740
$905$	−6.28456	−0.208906
$906$	0.191532	0.00636323
$907$	−5.00636	−0.166234	−0.0831168	−	0.996540i	$-0.526487\pi$
$907$	−5.00636	−0.166234	−0.0831168	+	0.996540i	$0.526487\pi$
$908$	23.7685	0.788786
$909$	4.71052	0.156238
$910$	0.349822	0.0115965
$911$	32.0748	1.06269	0.531343	−	0.847157i	$-0.321688\pi$
$911$	32.0748	1.06269	0.531343	+	0.847157i	$0.321688\pi$
$912$	28.5396	0.945042
$913$	−16.4316	−0.543808
$914$	−1.22256	−0.0404388
$915$	−4.50167	−0.148821
$916$	−5.66371	−0.187134
$917$	−18.5126	−0.611341
$918$	−0.606828	−0.0200283
$919$	−24.0569	−0.793565	−0.396783	−	0.917913i	$-0.629873\pi$
$919$	−24.0569	−0.793565	−0.396783	+	0.917913i	$0.629873\pi$
$920$	−0.626042	−0.0206400
$921$	3.67995	0.121258
$922$	−0.00394842	−0.000130034 0
$923$	−30.8777	−1.01635
$924$	−5.98874	−0.197015
$925$	−10.0285	−0.329736
$926$	0.394158	0.0129528
$927$	−19.1362	−0.628516
$928$	−6.25148	−0.205215
$929$	−39.0700	−1.28184	−0.640922	−	0.767606i	$-0.721448\pi$
$929$	−39.0700	−1.28184	−0.640922	+	0.767606i	$0.721448\pi$
$930$	−0.0910448	−0.00298548
$931$	−4.74240	−0.155426
$932$	8.93627	0.292717
$933$	28.6157	0.936837
$934$	3.39262	0.111010
$935$	2.73959	0.0895941
$936$	1.16763	0.0381652
$937$	−4.37686	−0.142986	−0.0714929	−	0.997441i	$-0.522776\pi$
$937$	−4.37686	−0.142986	−0.0714929	+	0.997441i	$0.522776\pi$
$938$	−1.14780	−0.0374771
$939$	−14.3414	−0.468013
$940$	−0.683339	−0.0222881
$941$	42.0947	1.37225	0.686123	−	0.727485i	$-0.259311\pi$
$941$	42.0947	1.37225	0.686123	+	0.727485i	$0.259311\pi$
$942$	0.154613	0.00503758
$943$	18.8524	0.613918
$944$	−35.5410	−1.15676
$945$	1.19515	0.0388783
$946$	0.670052	0.0217853
$947$	28.4050	0.923037	0.461519	−	0.887131i	$-0.347305\pi$
$947$	28.4050	0.923037	0.461519	+	0.887131i	$0.347305\pi$
$948$	−0.813726	−0.0264286
$949$	−3.11115	−0.100992
$950$	3.63526	0.117943
$951$	24.7113	0.801320
$952$	−6.69711	−0.217055
$953$	−17.0187	−0.551289	−0.275645	−	0.961260i	$-0.588891\pi$
$953$	−17.0187	−0.551289	−0.275645	+	0.961260i	$0.588891\pi$
$954$	−0.362106	−0.0117236
$955$	−10.7589	−0.348150
$956$	1.98916	0.0643339
$957$	−5.48386	−0.177268
$958$	−2.01886	−0.0652266
$959$	−19.1361	−0.617935
$960$	−3.34407	−0.107929
$961$	−26.9039	−0.867867
$962$	−0.609834	−0.0196618
$963$	6.40124	0.206277
$964$	−27.1785	−0.875361
$965$	−2.52410	−0.0812536
$966$	1.00504	0.0323365
$967$	9.67491	0.311124	0.155562	−	0.987826i	$-0.450281\pi$
$967$	9.67491	0.311124	0.155562	+	0.987826i	$0.450281\pi$
$968$	4.07747	0.131055
$969$	42.2645	1.35773
$970$	−0.564194	−0.0181152
$971$	−34.6807	−1.11296	−0.556478	−	0.830862i	$-0.687848\pi$
$971$	−34.6807	−1.11296	−0.556478	+	0.830862i	$0.687848\pi$
$972$	1.98916	0.0638022
$973$	−26.2431	−0.841315
$974$	0.504960	0.0161800
$975$	−13.5297	−0.433296
$976$	−41.0055	−1.31255
$977$	−24.2830	−0.776882	−0.388441	−	0.921474i	$-0.626986\pi$
$977$	−24.2830	−0.776882	−0.388441	+	0.921474i	$0.626986\pi$
$978$	−1.03687	−0.0331555
$979$	−15.4735	−0.494534
$980$	0.561890	0.0179489
$981$	−2.95365	−0.0943028
$982$	−2.57548	−0.0821869
$983$	28.0091	0.893351	0.446675	−	0.894696i	$-0.352608\pi$
$983$	28.0091	0.893351	0.446675	+	0.894696i	$0.352608\pi$
$984$	−2.24482	−0.0715623
$985$	7.01722	0.223587
$986$	−3.05792	−0.0973840
$987$	2.20002	0.0700273
$988$	−40.5512	−1.29010
$989$	20.6276	0.655918
$990$	0.0489548	0.00155588
$991$	−0.266294	−0.00845912	−0.00422956	−	0.999991i	$-0.501346\pi$
$991$	−0.266294	−0.00845912	−0.00422956	+	0.999991i	$0.501346\pi$
$992$	−2.51078	−0.0797172
$993$	30.5404	0.969171
$994$	3.16473	0.100379
$995$	9.84562	0.312127
$996$	30.0348	0.951688
$997$	−45.0714	−1.42743	−0.713713	−	0.700439i	$-0.752988\pi$
$997$	−45.0714	−1.42743	−0.713713	+	0.700439i	$0.752988\pi$
$998$	−1.35765	−0.0429757
$999$	−2.08347	−0.0659180

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	717.2.a.d.1.4	✓	6
3.2	odd	2		2151.2.a.e.1.3		6

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
717.2.a.d.1.4	✓	6	1.1	even	1	trivial
2151.2.a.e.1.3		6	3.2	odd	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 717 = 3 \cdot 239 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	717.a (trivial)

\(f(q)\)	\(=\)	\(q+0.104133 q^{2} -1.00000 q^{3} -1.98916 q^{4} -0.431998 q^{5} -0.104133 q^{6} +2.76657 q^{7} -0.415402 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q+0.104133 q^{2} -1.00000 q^{3} -1.98916 q^{4} -0.431998 q^{5} -0.104133 q^{6} +2.76657 q^{7} -0.415402 q^{8} +1.00000 q^{9} -0.0449852 q^{10} -1.08824 q^{11} +1.98916 q^{12} -2.81084 q^{13} +0.288090 q^{14} +0.431998 q^{15} +3.93506 q^{16} +5.82744 q^{17} +0.104133 q^{18} -7.25266 q^{19} +0.859312 q^{20} -2.76657 q^{21} -0.113322 q^{22} -3.48861 q^{23} +0.415402 q^{24} -4.81338 q^{25} -0.292701 q^{26} -1.00000 q^{27} -5.50313 q^{28} -5.03919 q^{29} +0.0449852 q^{30} -2.02388 q^{31} +1.24057 q^{32} +1.08824 q^{33} +0.606828 q^{34} -1.19515 q^{35} -1.98916 q^{36} +2.08347 q^{37} -0.755240 q^{38} +2.81084 q^{39} +0.179453 q^{40} -5.40397 q^{41} -0.288090 q^{42} -5.91283 q^{43} +2.16468 q^{44} -0.431998 q^{45} -0.363279 q^{46} -0.795216 q^{47} -3.93506 q^{48} +0.653884 q^{49} -0.501230 q^{50} -5.82744 q^{51} +5.59121 q^{52} -3.47735 q^{53} -0.104133 q^{54} +0.470119 q^{55} -1.14924 q^{56} +7.25266 q^{57} -0.524745 q^{58} -9.03190 q^{59} -0.859312 q^{60} -10.4206 q^{61} -0.210753 q^{62} +2.76657 q^{63} -7.74093 q^{64} +1.21428 q^{65} +0.113322 q^{66} -3.98418 q^{67} -11.5917 q^{68} +3.48861 q^{69} -0.124454 q^{70} +10.9852 q^{71} -0.415402 q^{72} +1.10684 q^{73} +0.216957 q^{74} +4.81338 q^{75} +14.4267 q^{76} -3.01069 q^{77} +0.292701 q^{78} -0.409081 q^{79} -1.69994 q^{80} +1.00000 q^{81} -0.562731 q^{82} +15.0992 q^{83} +5.50313 q^{84} -2.51744 q^{85} -0.615719 q^{86} +5.03919 q^{87} +0.452058 q^{88} +14.2188 q^{89} -0.0449852 q^{90} -7.77639 q^{91} +6.93940 q^{92} +2.02388 q^{93} -0.0828081 q^{94} +3.13314 q^{95} -1.24057 q^{96} +12.5418 q^{97} +0.0680907 q^{98} -1.08824 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 6 q - 2 q^{2} - 6 q^{3} + 4 q^{4} + 5 q^{5} + 2 q^{6} - 9 q^{7} - 3 q^{8} + 6 q^{9}+O(q^{10}) \) 6 * q - 2 * q^2 - 6 * q^3 + 4 * q^4 + 5 * q^5 + 2 * q^6 - 9 * q^7 - 3 * q^8 + 6 * q^9	\( 6 q - 2 q^{2} - 6 q^{3} + 4 q^{4} + 5 q^{5} + 2 q^{6} - 9 q^{7} - 3 q^{8} + 6 q^{9} - 11 q^{10} - 13 q^{11} - 4 q^{12} - q^{13} - 5 q^{15} - 4 q^{16} + 11 q^{17} - 2 q^{18} - 22 q^{19} - q^{20} + 9 q^{21} - 2 q^{22} - 12 q^{23} + 3 q^{24} - q^{25} + 12 q^{26} - 6 q^{27} - 16 q^{28} + 11 q^{30} - 18 q^{31} + 7 q^{32} + 13 q^{33} - 3 q^{34} - 9 q^{35} + 4 q^{36} - 8 q^{37} - 5 q^{38} + q^{39} - 11 q^{40} + 10 q^{41} - 14 q^{43} - 4 q^{44} + 5 q^{45} - 18 q^{46} - 9 q^{47} + 4 q^{48} + 5 q^{49} + 4 q^{50} - 11 q^{51} - 16 q^{52} - 8 q^{53} + 2 q^{54} - 20 q^{55} + 11 q^{56} + 22 q^{57} - 15 q^{58} - 10 q^{59} + q^{60} - 12 q^{61} - 13 q^{62} - 9 q^{63} - 31 q^{64} - 11 q^{65} + 2 q^{66} - 36 q^{67} + 22 q^{68} + 12 q^{69} + q^{70} - 3 q^{71} - 3 q^{72} - 32 q^{73} + 9 q^{74} + q^{75} - 4 q^{76} + 6 q^{77} - 12 q^{78} - q^{79} - 7 q^{80} + 6 q^{81} + 7 q^{82} - 7 q^{83} + 16 q^{84} - 14 q^{85} + 45 q^{86} - 15 q^{88} + 17 q^{89} - 11 q^{90} - 23 q^{91} - 12 q^{92} + 18 q^{93} + 50 q^{94} - 7 q^{96} - 28 q^{97} + 13 q^{98} - 13 q^{99}+O(q^{100}) \) 6 * q - 2 * q^2 - 6 * q^3 + 4 * q^4 + 5 * q^5 + 2 * q^6 - 9 * q^7 - 3 * q^8 + 6 * q^9 - 11 * q^10 - 13 * q^11 - 4 * q^12 - q^13 - 5 * q^15 - 4 * q^16 + 11 * q^17 - 2 * q^18 - 22 * q^19 - q^20 + 9 * q^21 - 2 * q^22 - 12 * q^23 + 3 * q^24 - q^25 + 12 * q^26 - 6 * q^27 - 16 * q^28 + 11 * q^30 - 18 * q^31 + 7 * q^32 + 13 * q^33 - 3 * q^34 - 9 * q^35 + 4 * q^36 - 8 * q^37 - 5 * q^38 + q^39 - 11 * q^40 + 10 * q^41 - 14 * q^43 - 4 * q^44 + 5 * q^45 - 18 * q^46 - 9 * q^47 + 4 * q^48 + 5 * q^49 + 4 * q^50 - 11 * q^51 - 16 * q^52 - 8 * q^53 + 2 * q^54 - 20 * q^55 + 11 * q^56 + 22 * q^57 - 15 * q^58 - 10 * q^59 + q^60 - 12 * q^61 - 13 * q^62 - 9 * q^63 - 31 * q^64 - 11 * q^65 + 2 * q^66 - 36 * q^67 + 22 * q^68 + 12 * q^69 + q^70 - 3 * q^71 - 3 * q^72 - 32 * q^73 + 9 * q^74 + q^75 - 4 * q^76 + 6 * q^77 - 12 * q^78 - q^79 - 7 * q^80 + 6 * q^81 + 7 * q^82 - 7 * q^83 + 16 * q^84 - 14 * q^85 + 45 * q^86 - 15 * q^88 + 17 * q^89 - 11 * q^90 - 23 * q^91 - 12 * q^92 + 18 * q^93 + 50 * q^94 - 7 * q^96 - 28 * q^97 + 13 * q^98 - 13 * q^99

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