LMFDB - Embedded newform 671.2.a.b.1.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [671,2,Mod(1,671)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(671, 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("671.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 671 = 11 \cdot 61 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	671.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:	$5.35796197563$
Analytic rank:	$1$
Dimension:	$6$
Coefficient field:	6.6.2661761.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{6} - x^{5} - 6x^{4} + 3x^{3} + 9x^{2} - x - 1 $ x^6 - x^5 - 6x^4 + 3x^3 + 9*x^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			1.3
Root			$0.387870$ of defining polynomial
Character	$\chi$	$=$	671.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-0.255699 q^{2} -0.387870 q^{3} -1.93462 q^{4} +2.57819 q^{5} +0.0991779 q^{6} -0.612130 q^{7} +1.00608 q^{8} -2.84956 q^{9} +O(q^{10})$	\(q-0.255699 q^{2} -0.387870 q^{3} -1.93462 q^{4} +2.57819 q^{5} +0.0991779 q^{6} -0.612130 q^{7} +1.00608 q^{8} -2.84956 q^{9} -0.659240 q^{10} -1.00000 q^{11} +0.750379 q^{12} -3.42167 q^{13} +0.156521 q^{14} -1.00000 q^{15} +3.61198 q^{16} +1.40807 q^{17} +0.728629 q^{18} -0.203631 q^{19} -4.98781 q^{20} +0.237427 q^{21} +0.255699 q^{22} -7.26318 q^{23} -0.390227 q^{24} +1.64705 q^{25} +0.874917 q^{26} +2.26886 q^{27} +1.18424 q^{28} -2.39395 q^{29} +0.255699 q^{30} +0.0531881 q^{31} -2.93574 q^{32} +0.387870 q^{33} -0.360041 q^{34} -1.57819 q^{35} +5.51280 q^{36} -4.56986 q^{37} +0.0520683 q^{38} +1.32716 q^{39} +2.59386 q^{40} -12.5852 q^{41} -0.0607098 q^{42} +5.84108 q^{43} +1.93462 q^{44} -7.34669 q^{45} +1.85719 q^{46} +5.88284 q^{47} -1.40098 q^{48} -6.62530 q^{49} -0.421148 q^{50} -0.546146 q^{51} +6.61962 q^{52} -9.59867 q^{53} -0.580147 q^{54} -2.57819 q^{55} -0.615851 q^{56} +0.0789822 q^{57} +0.612130 q^{58} -6.40835 q^{59} +1.93462 q^{60} -1.00000 q^{61} -0.0136002 q^{62} +1.74430 q^{63} -6.47330 q^{64} -8.82169 q^{65} -0.0991779 q^{66} -6.19516 q^{67} -2.72407 q^{68} +2.81717 q^{69} +0.403541 q^{70} +6.32009 q^{71} -2.86688 q^{72} -3.28169 q^{73} +1.16851 q^{74} -0.638839 q^{75} +0.393948 q^{76} +0.612130 q^{77} -0.339354 q^{78} +6.61147 q^{79} +9.31236 q^{80} +7.66865 q^{81} +3.21803 q^{82} -6.24934 q^{83} -0.459330 q^{84} +3.63025 q^{85} -1.49356 q^{86} +0.928539 q^{87} -1.00608 q^{88} +1.31185 q^{89} +1.87854 q^{90} +2.09451 q^{91} +14.0515 q^{92} -0.0206301 q^{93} -1.50424 q^{94} -0.524998 q^{95} +1.13868 q^{96} +6.95579 q^{97} +1.69408 q^{98} +2.84956 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 6 q - q^{3} + 2 q^{4} - q^{5} - q^{6} - 5 q^{7} - 6 q^{8} - 5 q^{9}+O(q^{10}) $ 6 * q - q^3 + 2 * q^4 - q^5 - q^6 - 5 * q^7 - 6 * q^8 - 5 * q^9	\( 6 q - q^{3} + 2 q^{4} - q^{5} - q^{6} - 5 q^{7} - 6 q^{8} - 5 q^{9} - 7 q^{10} - 6 q^{11} - 6 q^{12} - 4 q^{13} + q^{14} - 6 q^{15} - 10 q^{16} - 5 q^{17} - 3 q^{19} - 6 q^{20} - 12 q^{21} - 3 q^{23} + 10 q^{24} - 11 q^{25} + q^{26} - 4 q^{27} + 4 q^{28} - q^{29} - 10 q^{31} + 3 q^{32} + q^{33} - 19 q^{34} + 7 q^{35} + 3 q^{36} - 19 q^{37} - 3 q^{38} + 8 q^{39} + 5 q^{40} - 7 q^{41} + q^{42} - 2 q^{43} - 2 q^{44} + 4 q^{45} - 7 q^{46} + 5 q^{47} + q^{48} - 25 q^{49} + 17 q^{50} - q^{51} + 2 q^{52} - 9 q^{53} - 11 q^{54} + q^{55} - 4 q^{56} + 11 q^{57} + 5 q^{58} - 5 q^{59} - 2 q^{60} - 6 q^{61} + 3 q^{62} + 12 q^{63} - 6 q^{64} - 11 q^{65} + q^{66} - 14 q^{67} + 18 q^{68} - 7 q^{69} + 7 q^{70} - 14 q^{71} - q^{72} - 14 q^{73} + 6 q^{74} + 6 q^{75} - 11 q^{76} + 5 q^{77} - 26 q^{78} + 5 q^{79} + 26 q^{80} - 14 q^{81} + q^{82} + 17 q^{83} - 3 q^{84} + 2 q^{85} - 7 q^{86} + 4 q^{87} + 6 q^{88} - 25 q^{89} + 22 q^{90} - 4 q^{91} + 35 q^{92} - q^{93} + 30 q^{94} + 3 q^{95} + 8 q^{96} - 24 q^{97} - 2 q^{98} + 5 q^{99}+O(q^{100}) \) 6 * q - q^3 + 2 * q^4 - q^5 - q^6 - 5 * q^7 - 6 * q^8 - 5 * q^9 - 7 * q^10 - 6 * q^11 - 6 * q^12 - 4 * q^13 + q^14 - 6 * q^15 - 10 * q^16 - 5 * q^17 - 3 * q^19 - 6 * q^20 - 12 * q^21 - 3 * q^23 + 10 * q^24 - 11 * q^25 + q^26 - 4 * q^27 + 4 * q^28 - q^29 - 10 * q^31 + 3 * q^32 + q^33 - 19 * q^34 + 7 * q^35 + 3 * q^36 - 19 * q^37 - 3 * q^38 + 8 * q^39 + 5 * q^40 - 7 * q^41 + q^42 - 2 * q^43 - 2 * q^44 + 4 * q^45 - 7 * q^46 + 5 * q^47 + q^48 - 25 * q^49 + 17 * q^50 - q^51 + 2 * q^52 - 9 * q^53 - 11 * q^54 + q^55 - 4 * q^56 + 11 * q^57 + 5 * q^58 - 5 * q^59 - 2 * q^60 - 6 * q^61 + 3 * q^62 + 12 * q^63 - 6 * q^64 - 11 * q^65 + q^66 - 14 * q^67 + 18 * q^68 - 7 * q^69 + 7 * q^70 - 14 * q^71 - q^72 - 14 * q^73 + 6 * q^74 + 6 * q^75 - 11 * q^76 + 5 * q^77 - 26 * q^78 + 5 * q^79 + 26 * q^80 - 14 * q^81 + q^82 + 17 * q^83 - 3 * q^84 + 2 * q^85 - 7 * q^86 + 4 * q^87 + 6 * q^88 - 25 * q^89 + 22 * q^90 - 4 * q^91 + 35 * q^92 - q^93 + 30 * q^94 + 3 * q^95 + 8 * q^96 - 24 * q^97 - 2 * q^98 + 5 * 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 $

$2$	−0.255699	−0.180807	−0.0904033	−	0.995905i	$-0.528816\pi$
$2$	−0.255699	−0.180807	−0.0904033	+	0.995905i	$0.528816\pi$
$3$	−0.387870	−0.223937	−0.111968	−	0.993712i	$-0.535716\pi$
$3$	−0.387870	−0.223937	−0.111968	+	0.993712i	$0.535716\pi$
$4$	−1.93462	−0.967309
$5$	2.57819	1.15300	0.576500	−	0.817097i	$-0.304418\pi$
$5$	2.57819	1.15300	0.576500	+	0.817097i	$0.304418\pi$
$6$	0.0991779	0.0404892
$7$	−0.612130	−0.231364	−0.115682	−	0.993286i	$-0.536905\pi$
$7$	−0.612130	−0.231364	−0.115682	+	0.993286i	$0.536905\pi$
$8$	1.00608	0.355702
$9$	−2.84956	−0.949852
$10$	−0.659240	−0.208470
$11$	−1.00000	−0.301511
$11$	−1.00000	−0.301511
$12$	0.750379	0.216616
$13$	−3.42167	−0.948999	−0.474500	−	0.880256i	$-0.657371\pi$
$13$	−3.42167	−0.948999	−0.474500	+	0.880256i	$0.657371\pi$
$14$	0.156521	0.0418321
$15$	−1.00000	−0.258199
$16$	3.61198	0.902996
$17$	1.40807	0.341506	0.170753	−	0.985314i	$-0.445380\pi$
$17$	1.40807	0.341506	0.170753	+	0.985314i	$0.445380\pi$
$18$	0.728629	0.171740
$19$	−0.203631	−0.0467161	−0.0233581	−	0.999727i	$-0.507436\pi$
$19$	−0.203631	−0.0467161	−0.0233581	+	0.999727i	$0.507436\pi$
$20$	−4.98781	−1.11531
$21$	0.237427	0.0518108
$22$	0.255699	0.0545152
$23$	−7.26318	−1.51448	−0.757239	−	0.653138i	$-0.773452\pi$
$23$	−7.26318	−1.51448	−0.757239	+	0.653138i	$0.773452\pi$
$24$	−0.390227	−0.0796548
$25$	1.64705	0.329409
$26$	0.874917	0.171585
$27$	2.26886	0.436643
$28$	1.18424	0.223800
$29$	−2.39395	−0.444545	−0.222272	−	0.974985i	$-0.571347\pi$
$29$	−2.39395	−0.444545	−0.222272	+	0.974985i	$0.571347\pi$
$30$	0.255699	0.0466841
$31$	0.0531881	0.00955287	0.00477644	−	0.999989i	$-0.498480\pi$
$31$	0.0531881	0.00955287	0.00477644	+	0.999989i	$0.498480\pi$
$32$	−2.93574	−0.518970
$33$	0.387870	0.0675194
$34$	−0.360041	−0.0617465
$35$	−1.57819	−0.266762
$36$	5.51280	0.918801
$37$	−4.56986	−0.751281	−0.375640	−	0.926766i	$-0.622577\pi$
$37$	−4.56986	−0.751281	−0.375640	+	0.926766i	$0.622577\pi$
$38$	0.0520683	0.00844659
$39$	1.32716	0.212516
$40$	2.59386	0.410125
$41$	−12.5852	−1.96548	−0.982742	−	0.184982i	$-0.940777\pi$
$41$	−12.5852	−1.96548	−0.982742	+	0.184982i	$0.940777\pi$
$42$	−0.0607098	−0.00936773
$43$	5.84108	0.890757	0.445378	−	0.895342i	$-0.353069\pi$
$43$	5.84108	0.890757	0.445378	+	0.895342i	$0.353069\pi$
$44$	1.93462	0.291655
$45$	−7.34669	−1.09518
$46$	1.85719	0.273828
$47$	5.88284	0.858100	0.429050	−	0.903281i	$-0.358848\pi$
$47$	5.88284	0.858100	0.429050	+	0.903281i	$0.358848\pi$
$48$	−1.40098	−0.202214
$49$	−6.62530	−0.946471
$50$	−0.421148	−0.0595594
$51$	−0.546146	−0.0764757
$52$	6.61962	0.917975
$53$	−9.59867	−1.31848	−0.659239	−	0.751933i	$-0.729122\pi$
$53$	−9.59867	−1.31848	−0.659239	+	0.751933i	$0.729122\pi$
$54$	−0.580147	−0.0789480
$55$	−2.57819	−0.347643
$56$	−0.615851	−0.0822966
$57$	0.0789822	0.0104615
$58$	0.612130	0.0803767
$59$	−6.40835	−0.834296	−0.417148	−	0.908838i	$-0.636970\pi$
$59$	−6.40835	−0.834296	−0.417148	+	0.908838i	$0.636970\pi$
$60$	1.93462	0.249758
$61$	−1.00000	−0.128037
$61$	−1.00000	−0.128037
$62$	−0.0136002	−0.00172722
$63$	1.74430	0.219761
$64$	−6.47330	−0.809162
$65$	−8.82169	−1.09420
$66$	−0.0991779	−0.0122080
$67$	−6.19516	−0.756859	−0.378429	−	0.925630i	$-0.623536\pi$
$67$	−6.19516	−0.756859	−0.378429	+	0.925630i	$0.623536\pi$
$68$	−2.72407	−0.330342
$69$	2.81717	0.339147
$70$	0.403541	0.0482324
$71$	6.32009	0.750057	0.375029	−	0.927013i	$-0.377633\pi$
$71$	6.32009	0.750057	0.375029	+	0.927013i	$0.377633\pi$
$72$	−2.86688	−0.337865
$73$	−3.28169	−0.384092	−0.192046	−	0.981386i	$-0.561512\pi$
$73$	−3.28169	−0.384092	−0.192046	+	0.981386i	$0.561512\pi$
$74$	1.16851	0.135836
$75$	−0.638839	−0.0737668
$76$	0.393948	0.0451889
$77$	0.612130	0.0697587
$78$	−0.339354	−0.0384242
$79$	6.61147	0.743848	0.371924	−	0.928263i	$-0.378698\pi$
$79$	6.61147	0.743848	0.371924	+	0.928263i	$0.378698\pi$
$80$	9.31236	1.04115
$81$	7.66865	0.852072
$82$	3.21803	0.355372
$83$	−6.24934	−0.685954	−0.342977	−	0.939344i	$-0.611435\pi$
$83$	−6.24934	−0.685954	−0.342977	+	0.939344i	$0.611435\pi$
$84$	−0.459330	−0.0501170
$85$	3.63025	0.393756
$86$	−1.49356	−0.161055
$87$	0.928539	0.0995499
$88$	−1.00608	−0.107248
$89$	1.31185	0.139056	0.0695278	−	0.997580i	$-0.477851\pi$
$89$	1.31185	0.139056	0.0695278	+	0.997580i	$0.477851\pi$
$90$	1.87854	0.198016
$91$	2.09451	0.219564
$92$	14.0515	1.46497
$93$	−0.0206301	−0.00213924
$94$	−1.50424	−0.155150
$95$	−0.524998	−0.0538637
$96$	1.13868	0.116216
$97$	6.95579	0.706253	0.353127	−	0.935576i	$-0.385119\pi$
$97$	6.95579	0.706253	0.353127	+	0.935576i	$0.385119\pi$
$98$	1.69408	0.171128
$99$	2.84956	0.286391
$100$	−3.18641	−0.318641
$101$	11.5315	1.14743	0.573715	−	0.819055i	$-0.305502\pi$
$101$	11.5315	1.14743	0.573715	+	0.819055i	$0.305502\pi$
$102$	0.139649	0.0138273
$103$	6.62334	0.652617	0.326308	−	0.945263i	$-0.394195\pi$
$103$	6.62334	0.652617	0.326308	+	0.945263i	$0.394195\pi$
$104$	−3.44246	−0.337561
$105$	0.612130	0.0597378
$106$	2.45437	0.238390
$107$	12.6721	1.22505	0.612527	−	0.790450i	$-0.290153\pi$
$107$	12.6721	1.22505	0.612527	+	0.790450i	$0.290153\pi$
$108$	−4.38939	−0.422369
$109$	1.55847	0.149274	0.0746372	−	0.997211i	$-0.476220\pi$
$109$	1.55847	0.149274	0.0746372	+	0.997211i	$0.476220\pi$
$110$	0.659240	0.0628561
$111$	1.77251	0.168239
$112$	−2.21100	−0.208920
$113$	−2.65849	−0.250090	−0.125045	−	0.992151i	$-0.539907\pi$
$113$	−2.65849	−0.250090	−0.125045	+	0.992151i	$0.539907\pi$
$114$	−0.0201957	−0.00189150
$115$	−18.7258	−1.74619
$116$	4.63137	0.430012
$117$	9.75023	0.901409
$118$	1.63861	0.150846
$119$	−0.861920	−0.0790120
$120$	−1.00608	−0.0918420
$121$	1.00000	0.0909091
$122$	0.255699	0.0231499
$123$	4.88143	0.440144
$124$	−0.102899	−0.00924058
$125$	−8.64454	−0.773191
$126$	−0.446016	−0.0397343
$127$	−3.38267	−0.300163	−0.150082	−	0.988674i	$-0.547954\pi$
$127$	−3.38267	−0.300163	−0.150082	+	0.988674i	$0.547954\pi$
$128$	7.52669	0.665272
$129$	−2.26558	−0.199473
$130$	2.25570	0.197838
$131$	4.33479	0.378733	0.189366	−	0.981907i	$-0.439357\pi$
$131$	4.33479	0.378733	0.189366	+	0.981907i	$0.439357\pi$
$132$	−0.750379	−0.0653121
$133$	0.124649	0.0108084
$134$	1.58410	0.136845
$135$	5.84956	0.503450
$136$	1.41662	0.121475
$137$	9.58242	0.818682	0.409341	−	0.912382i	$-0.365759\pi$
$137$	9.58242	0.818682	0.409341	+	0.912382i	$0.365759\pi$
$138$	−0.720347	−0.0613200
$139$	4.19490	0.355807	0.177903	−	0.984048i	$-0.443069\pi$
$139$	4.19490	0.355807	0.177903	+	0.984048i	$0.443069\pi$
$140$	3.05319	0.258041
$141$	−2.28177	−0.192160
$142$	−1.61604	−0.135615
$143$	3.42167	0.286134
$144$	−10.2926	−0.857713
$145$	−6.17204	−0.512560
$146$	0.839125	0.0694464
$147$	2.56975	0.211949
$148$	8.84094	0.726720
$149$	17.3443	1.42090	0.710450	−	0.703748i	$-0.248491\pi$
$149$	17.3443	1.42090	0.710450	+	0.703748i	$0.248491\pi$
$150$	0.163351	0.0133375
$151$	0.638485	0.0519591	0.0259796	−	0.999662i	$-0.491730\pi$
$151$	0.638485	0.0519591	0.0259796	+	0.999662i	$0.491730\pi$
$152$	−0.204869	−0.0166170
$153$	−4.01236	−0.324380
$154$	−0.156521	−0.0126128
$155$	0.137129	0.0110145
$156$	−2.56755	−0.205568
$157$	3.28910	0.262499	0.131249	−	0.991349i	$-0.458101\pi$
$157$	3.28910	0.262499	0.131249	+	0.991349i	$0.458101\pi$
$158$	−1.69055	−0.134493
$159$	3.72303	0.295256
$160$	−7.56888	−0.598373
$161$	4.44602	0.350395
$162$	−1.96087	−0.154060
$163$	−13.1124	−1.02704	−0.513522	−	0.858076i	$-0.671660\pi$
$163$	−13.1124	−1.02704	−0.513522	+	0.858076i	$0.671660\pi$
$164$	24.3476	1.90123
$165$	1.00000	0.0778499
$166$	1.59795	0.124025
$167$	10.4522	0.808819	0.404409	−	0.914578i	$-0.367477\pi$
$167$	10.4522	0.808819	0.404409	+	0.914578i	$0.367477\pi$
$168$	0.238870	0.0184292
$169$	−1.29221	−0.0994005
$170$	−0.928253	−0.0711938
$171$	0.580258	0.0443734
$172$	−11.3003	−0.861637
$173$	−8.03982	−0.611256	−0.305628	−	0.952151i	$-0.598866\pi$
$173$	−8.03982	−0.611256	−0.305628	+	0.952151i	$0.598866\pi$
$174$	−0.237427	−0.0179993
$175$	−1.00821	−0.0762133
$176$	−3.61198	−0.272263
$177$	2.48560	0.186829
$178$	−0.335438	−0.0251422
$179$	10.6526	0.796211	0.398106	−	0.917340i	$-0.369668\pi$
$179$	10.6526	0.796211	0.398106	+	0.917340i	$0.369668\pi$
$180$	14.2130	1.05938
$181$	−14.5583	−1.08211	−0.541056	−	0.840987i	$-0.681975\pi$
$181$	−14.5583	−1.08211	−0.541056	+	0.840987i	$0.681975\pi$
$182$	−0.535563	−0.0396986
$183$	0.387870	0.0286721
$184$	−7.30733	−0.538704
$185$	−11.7820	−0.866227
$186$	0.00527509	0.000386788 0
$187$	−1.40807	−0.102968
$188$	−11.3810	−0.830048
$189$	−1.38884	−0.101023
$190$	0.134242	0.00973891
$191$	−3.29039	−0.238084	−0.119042	−	0.992889i	$-0.537982\pi$
$191$	−3.29039	−0.238084	−0.119042	+	0.992889i	$0.537982\pi$
$192$	2.51080	0.181201
$193$	−5.76630	−0.415067	−0.207534	−	0.978228i	$-0.566544\pi$
$193$	−5.76630	−0.415067	−0.207534	+	0.978228i	$0.566544\pi$
$194$	−1.77859	−0.127695
$195$	3.42167	0.245031
$196$	12.8174	0.915530
$197$	−27.1123	−1.93167	−0.965835	−	0.259156i	$-0.916555\pi$
$197$	−27.1123	−1.93167	−0.965835	+	0.259156i	$0.916555\pi$
$198$	−0.728629	−0.0517814
$199$	2.66595	0.188984	0.0944920	−	0.995526i	$-0.469877\pi$
$199$	2.66595	0.188984	0.0944920	+	0.995526i	$0.469877\pi$
$200$	1.65706	0.117172
$201$	2.40291	0.169488
$202$	−2.94860	−0.207463
$203$	1.46541	0.102852
$204$	1.05658	0.0739756
$205$	−32.4471	−2.26620
$206$	−1.69358	−0.117997
$207$	20.6969	1.43853
$208$	−12.3590	−0.856942
$209$	0.203631	0.0140854
$210$	−0.156521	−0.0108010
$211$	8.96358	0.617078	0.308539	−	0.951212i	$-0.400160\pi$
$211$	8.96358	0.617078	0.308539	+	0.951212i	$0.400160\pi$
$212$	18.5698	1.27538
$213$	−2.45137	−0.167965
$214$	−3.24023	−0.221498
$215$	15.0594	1.02704
$216$	2.28266	0.155315
$217$	−0.0325581	−0.00221019
$218$	−0.398500	−0.0269898
$219$	1.27287	0.0860123
$220$	4.98781	0.336278
$221$	−4.81793	−0.324089
$222$	−0.453229	−0.0304188
$223$	−15.6150	−1.04565	−0.522827	−	0.852439i	$-0.675123\pi$
$223$	−15.6150	−1.04565	−0.522827	+	0.852439i	$0.675123\pi$
$224$	1.79705	0.120071
$225$	−4.69335	−0.312890
$226$	0.679773	0.0452179
$227$	16.0398	1.06460	0.532300	−	0.846556i	$-0.321328\pi$
$227$	16.0398	1.06460	0.532300	+	0.846556i	$0.321328\pi$
$228$	−0.152800	−0.0101195
$229$	8.27916	0.547102	0.273551	−	0.961857i	$-0.411802\pi$
$229$	8.27916	0.547102	0.273551	+	0.961857i	$0.411802\pi$
$230$	4.78818	0.315723
$231$	−0.237427	−0.0156215
$232$	−2.40850	−0.158126
$233$	20.0364	1.31263	0.656316	−	0.754486i	$-0.272114\pi$
$233$	20.0364	1.31263	0.656316	+	0.754486i	$0.272114\pi$
$234$	−2.49313	−0.162981
$235$	15.1670	0.989389
$236$	12.3977	0.807022
$237$	−2.56439	−0.166575
$238$	0.220392	0.0142859
$239$	10.0194	0.648099	0.324049	−	0.946040i	$-0.394956\pi$
$239$	10.0194	0.648099	0.324049	+	0.946040i	$0.394956\pi$
$240$	−3.61198	−0.233152
$241$	−12.1860	−0.784967	−0.392483	−	0.919759i	$-0.628384\pi$
$241$	−12.1860	−0.784967	−0.392483	+	0.919759i	$0.628384\pi$
$242$	−0.255699	−0.0164370
$243$	−9.78103	−0.627453
$244$	1.93462	0.123851
$245$	−17.0813	−1.09128
$246$	−1.24818	−0.0795809
$247$	0.696757	0.0443336
$248$	0.0535114	0.00339798
$249$	2.42393	0.153610
$250$	2.21040	0.139798
$251$	−5.52638	−0.348822	−0.174411	−	0.984673i	$-0.555802\pi$
$251$	−5.52638	−0.348822	−0.174411	+	0.984673i	$0.555802\pi$
$252$	−3.37456	−0.212577
$253$	7.26318	0.456632
$254$	0.864945	0.0542715
$255$	−1.40807	−0.0881765
$256$	11.0220	0.688877
$257$	−9.77286	−0.609615	−0.304807	−	0.952414i	$-0.598592\pi$
$257$	−9.77286	−0.609615	−0.304807	+	0.952414i	$0.598592\pi$
$258$	0.579307	0.0360660
$259$	2.79735	0.173819
$260$	17.0666	1.05843
$261$	6.82169	0.422252
$262$	−1.10840	−0.0684774
$263$	1.83879	0.113384	0.0566922	−	0.998392i	$-0.481945\pi$
$263$	1.83879	0.113384	0.0566922	+	0.998392i	$0.481945\pi$
$264$	0.390227	0.0240168
$265$	−24.7472	−1.52021
$266$	−0.0318726	−0.00195423
$267$	−0.508826	−0.0311396
$268$	11.9853	0.732116
$269$	−31.1609	−1.89991	−0.949956	−	0.312385i	$-0.898872\pi$
$269$	−31.1609	−1.89991	−0.949956	+	0.312385i	$0.898872\pi$
$270$	−1.49573	−0.0910270
$271$	−25.9407	−1.57579	−0.787893	−	0.615812i	$-0.788828\pi$
$271$	−25.9407	−1.57579	−0.787893	+	0.615812i	$0.788828\pi$
$272$	5.08591	0.308378
$273$	−0.812395	−0.0491684
$274$	−2.45022	−0.148023
$275$	−1.64705	−0.0993206
$276$	−5.45014	−0.328060
$277$	25.5694	1.53632	0.768158	−	0.640260i	$-0.221173\pi$
$277$	25.5694	1.53632	0.768158	+	0.640260i	$0.221173\pi$
$278$	−1.07263	−0.0643322
$279$	−0.151563	−0.00907382
$280$	−1.58778	−0.0948880
$281$	15.3493	0.915662	0.457831	−	0.889039i	$-0.348626\pi$
$281$	15.3493	0.915662	0.457831	+	0.889039i	$0.348626\pi$
$282$	0.583447	0.0347438
$283$	16.8362	1.00081	0.500405	−	0.865792i	$-0.333185\pi$
$283$	16.8362	1.00081	0.500405	+	0.865792i	$0.333185\pi$
$284$	−12.2270	−0.725537
$285$	0.203631	0.0120621
$286$	−0.874917	−0.0517349
$287$	7.70381	0.454741
$288$	8.36555	0.492945
$289$	−15.0174	−0.883374
$290$	1.57819	0.0926743
$291$	−2.69794	−0.158156
$292$	6.34881	0.371536
$293$	−17.8943	−1.04539	−0.522697	−	0.852518i	$-0.675074\pi$
$293$	−17.8943	−1.04539	−0.522697	+	0.852518i	$0.675074\pi$
$294$	−0.657083	−0.0383219
$295$	−16.5219	−0.961944
$296$	−4.59764	−0.267232
$297$	−2.26886	−0.131653
$298$	−4.43492	−0.256908
$299$	24.8522	1.43724
$300$	1.23591	0.0713553
$301$	−3.57551	−0.206089
$302$	−0.163260	−0.00939456
$303$	−4.47272	−0.256951
$304$	−0.735511	−0.0421845
$305$	−2.57819	−0.147627
$306$	1.02596	0.0586501
$307$	−8.12384	−0.463652	−0.231826	−	0.972757i	$-0.574470\pi$
$307$	−8.12384	−0.463652	−0.231826	+	0.972757i	$0.574470\pi$
$308$	−1.18424	−0.0674783
$309$	−2.56899	−0.146145
$310$	−0.0350638	−0.00199149
$311$	1.16185	0.0658826	0.0329413	−	0.999457i	$-0.489513\pi$
$311$	1.16185	0.0658826	0.0329413	+	0.999457i	$0.489513\pi$
$312$	1.33523	0.0755923
$313$	6.84024	0.386633	0.193317	−	0.981136i	$-0.438076\pi$
$313$	6.84024	0.386633	0.193317	+	0.981136i	$0.438076\pi$
$314$	−0.841019	−0.0474615
$315$	4.49713	0.253385
$316$	−12.7907	−0.719531
$317$	22.1528	1.24422	0.622111	−	0.782929i	$-0.286275\pi$
$317$	22.1528	1.24422	0.622111	+	0.782929i	$0.286275\pi$
$318$	−0.951976	−0.0533842
$319$	2.39395	0.134035
$320$	−16.6894	−0.932964
$321$	−4.91510	−0.274334
$322$	−1.13684	−0.0633538
$323$	−0.286726	−0.0159538
$324$	−14.8359	−0.824217
$325$	−5.63564	−0.312609
$326$	3.35284	0.185696
$327$	−0.604483	−0.0334280
$328$	−12.6617	−0.699127
$329$	−3.60106	−0.198533
$330$	−0.255699	−0.0140758
$331$	−27.0138	−1.48481	−0.742406	−	0.669950i	$-0.766315\pi$
$331$	−27.0138	−1.48481	−0.742406	+	0.669950i	$0.766315\pi$
$332$	12.0901	0.663530
$333$	13.0221	0.713606
$334$	−2.67263	−0.146240
$335$	−15.9723	−0.872658
$336$	0.857581	0.0467849
$337$	−21.5409	−1.17341	−0.586703	−	0.809802i	$-0.699574\pi$
$337$	−21.5409	−1.17341	−0.586703	+	0.809802i	$0.699574\pi$
$338$	0.330416	0.0179723
$339$	1.03115	0.0560042
$340$	−7.02316	−0.380884
$341$	−0.0531881	−0.00288030
$342$	−0.148371	−0.00802301
$343$	8.34046	0.450342
$344$	5.87659	0.316844
$345$	7.26318	0.391037
$346$	2.05578	0.110519
$347$	30.1500	1.61854	0.809268	−	0.587439i	$-0.199864\pi$
$347$	30.1500	1.61854	0.809268	+	0.587439i	$0.199864\pi$
$348$	−1.79637	−0.0962955
$349$	−17.8950	−0.957896	−0.478948	−	0.877843i	$-0.658982\pi$
$349$	−17.8950	−0.957896	−0.478948	+	0.877843i	$0.658982\pi$
$350$	0.257798	0.0137799
$351$	−7.76330	−0.414374
$352$	2.93574	0.156475
$353$	10.5889	0.563591	0.281795	−	0.959475i	$-0.409070\pi$
$353$	10.5889	0.563591	0.281795	+	0.959475i	$0.409070\pi$
$354$	−0.635567	−0.0337800
$355$	16.2944	0.864816
$356$	−2.53792	−0.134510
$357$	0.334312	0.0176937
$358$	−2.72386	−0.143960
$359$	−25.5353	−1.34770	−0.673851	−	0.738867i	$-0.735361\pi$
$359$	−25.5353	−1.34770	−0.673851	+	0.738867i	$0.735361\pi$
$360$	−7.39135	−0.389558
$361$	−18.9585	−0.997818
$362$	3.72255	0.195653
$363$	−0.387870	−0.0203579
$364$	−4.05207	−0.212386
$365$	−8.46080	−0.442859
$366$	−0.0991779	−0.00518411
$367$	−9.97211	−0.520540	−0.260270	−	0.965536i	$-0.583812\pi$
$367$	−9.97211	−0.520540	−0.260270	+	0.965536i	$0.583812\pi$
$368$	−26.2345	−1.36757
$369$	35.8624	1.86692
$370$	3.01264	0.156619
$371$	5.87564	0.305048
$372$	0.0399113	0.00206930
$373$	8.07049	0.417874	0.208937	−	0.977929i	$-0.433000\pi$
$373$	8.07049	0.417874	0.208937	+	0.977929i	$0.433000\pi$
$374$	0.360041	0.0186173
$375$	3.35295	0.173146
$376$	5.91859	0.305228
$377$	8.19129	0.421873
$378$	0.355126	0.0182657
$379$	−37.0910	−1.90524	−0.952619	−	0.304167i	$-0.901622\pi$
$379$	−37.0910	−1.90524	−0.952619	+	0.304167i	$0.901622\pi$
$380$	1.01567	0.0521028
$381$	1.31203	0.0672175
$382$	0.841349	0.0430472
$383$	−8.46421	−0.432501	−0.216250	−	0.976338i	$-0.569383\pi$
$383$	−8.46421	−0.432501	−0.216250	+	0.976338i	$0.569383\pi$
$384$	−2.91937	−0.148979
$385$	1.57819	0.0804318
$386$	1.47444	0.0750469
$387$	−16.6445	−0.846088
$388$	−13.4568	−0.683165
$389$	−36.2250	−1.83668	−0.918340	−	0.395793i	$-0.870470\pi$
$389$	−36.2250	−1.83668	−0.918340	+	0.395793i	$0.870470\pi$
$390$	−0.874917	−0.0443031
$391$	−10.2270	−0.517203
$392$	−6.66557	−0.336662
$393$	−1.68133	−0.0848121
$394$	6.93259	0.349259
$395$	17.0456	0.857657
$396$	−5.51280	−0.277029
$397$	19.6836	0.987889	0.493945	−	0.869493i	$-0.335555\pi$
$397$	19.6836	0.987889	0.493945	+	0.869493i	$0.335555\pi$
$398$	−0.681680	−0.0341695
$399$	−0.0483474	−0.00242040
$400$	5.94910	0.297455
$401$	18.4542	0.921559	0.460779	−	0.887515i	$-0.347570\pi$
$401$	18.4542	0.921559	0.460779	+	0.887515i	$0.347570\pi$
$402$	−0.614423	−0.0306446
$403$	−0.181992	−0.00906567
$404$	−22.3091	−1.10992
$405$	19.7712	0.982439
$406$	−0.374704	−0.0185962
$407$	4.56986	0.226520
$408$	−0.549465	−0.0272026
$409$	19.8932	0.983655	0.491827	−	0.870693i	$-0.336329\pi$
$409$	19.8932	0.983655	0.491827	+	0.870693i	$0.336329\pi$
$410$	8.29669	0.409744
$411$	−3.71673	−0.183333
$412$	−12.8136	−0.631282
$413$	3.92275	0.193026
$414$	−5.29217	−0.260096
$415$	−16.1120	−0.790905
$416$	10.0451	0.492502
$417$	−1.62707	−0.0796781
$418$	−0.0520683	−0.00254674
$419$	−32.7776	−1.60129	−0.800644	−	0.599140i	$-0.795509\pi$
$419$	−32.7776	−1.60129	−0.800644	+	0.599140i	$0.795509\pi$
$420$	−1.18424	−0.0577849
$421$	−33.2262	−1.61935	−0.809674	−	0.586880i	$-0.800356\pi$
$421$	−33.2262	−1.61935	−0.809674	+	0.586880i	$0.800356\pi$
$422$	−2.29198	−0.111572
$423$	−16.7635	−0.815068
$424$	−9.65701	−0.468986
$425$	2.31915	0.112495
$426$	0.626814	0.0303692
$427$	0.612130	0.0296231
$428$	−24.5156	−1.18501
$429$	−1.32716	−0.0640759
$430$	−3.85068	−0.185696
$431$	18.8007	0.905599	0.452800	−	0.891612i	$-0.350425\pi$
$431$	18.8007	0.905599	0.452800	+	0.891612i	$0.350425\pi$
$432$	8.19510	0.394287
$433$	−33.6821	−1.61866	−0.809330	−	0.587355i	$-0.800169\pi$
$433$	−33.6821	−1.61866	−0.809330	+	0.587355i	$0.800169\pi$
$434$	0.00832507	0.000399616 0
$435$	2.39395	0.114781
$436$	−3.01505	−0.144395
$437$	1.47901	0.0707506
$438$	−0.325471	−0.0155516
$439$	−39.1396	−1.86803	−0.934015	−	0.357233i	$-0.883720\pi$
$439$	−39.1396	−1.86803	−0.934015	+	0.357233i	$0.883720\pi$
$440$	−2.59386	−0.123657
$441$	18.8792	0.899008
$442$	1.23194	0.0585974
$443$	29.5803	1.40540	0.702702	−	0.711484i	$-0.251977\pi$
$443$	29.5803	1.40540	0.702702	+	0.711484i	$0.251977\pi$
$444$	−3.42913	−0.162739
$445$	3.38219	0.160331
$446$	3.99273	0.189061
$447$	−6.72732	−0.318191
$448$	3.96250	0.187211
$449$	9.93300	0.468767	0.234384	−	0.972144i	$-0.424693\pi$
$449$	9.93300	0.468767	0.234384	+	0.972144i	$0.424693\pi$
$450$	1.20009	0.0565726
$451$	12.5852	0.592616
$452$	5.14316	0.241914
$453$	−0.247649	−0.0116356
$454$	−4.10137	−0.192487
$455$	5.40003	0.253157
$456$	0.0794623	0.00372116
$457$	7.03130	0.328910	0.164455	−	0.986385i	$-0.447413\pi$
$457$	7.03130	0.328910	0.164455	+	0.986385i	$0.447413\pi$
$458$	−2.11697	−0.0989197
$459$	3.19471	0.149116
$460$	36.2274	1.68911
$461$	−18.0250	−0.839507	−0.419753	−	0.907638i	$-0.637883\pi$
$461$	−18.0250	−0.839507	−0.419753	+	0.907638i	$0.637883\pi$
$462$	0.0607098	0.00282448
$463$	36.2219	1.68337	0.841687	−	0.539965i	$-0.181563\pi$
$463$	36.2219	1.68337	0.841687	+	0.539965i	$0.181563\pi$
$464$	−8.64690	−0.401422
$465$	−0.0531881	−0.00246654
$466$	−5.12330	−0.237332
$467$	−11.6127	−0.537370	−0.268685	−	0.963228i	$-0.586589\pi$
$467$	−11.6127	−0.537370	−0.268685	+	0.963228i	$0.586589\pi$
$468$	−18.8630	−0.871941
$469$	3.79224	0.175110
$470$	−3.87820	−0.178888
$471$	−1.27574	−0.0587830
$472$	−6.44730	−0.296761
$473$	−5.84108	−0.268573
$474$	0.655711	0.0301178
$475$	−0.335390	−0.0153887
$476$	1.66749	0.0764291
$477$	27.3520	1.25236
$478$	−2.56194	−0.117181
$479$	18.7772	0.857952	0.428976	−	0.903316i	$-0.358874\pi$
$479$	18.7772	0.857952	0.428976	+	0.903316i	$0.358874\pi$
$480$	2.93574	0.133997
$481$	15.6365	0.712965
$482$	3.11594	0.141927
$483$	−1.72447	−0.0784663
$484$	−1.93462	−0.0879372
$485$	17.9333	0.814310
$486$	2.50100	0.113448
$487$	7.97337	0.361308	0.180654	−	0.983547i	$-0.442179\pi$
$487$	7.97337	0.361308	0.180654	+	0.983547i	$0.442179\pi$
$488$	−1.00608	−0.0455430
$489$	5.08591	0.229993
$490$	4.36766	0.197311
$491$	20.8249	0.939816	0.469908	−	0.882715i	$-0.344287\pi$
$491$	20.8249	0.939816	0.469908	+	0.882715i	$0.344287\pi$
$492$	−9.44370	−0.425755
$493$	−3.37083	−0.151815
$494$	−0.178160	−0.00801580
$495$	7.34669	0.330209
$496$	0.192115	0.00862620
$497$	−3.86872	−0.173536
$498$	−0.619797	−0.0277737
$499$	−11.6631	−0.522112	−0.261056	−	0.965324i	$-0.584071\pi$
$499$	−11.6631	−0.522112	−0.261056	+	0.965324i	$0.584071\pi$
$500$	16.7239	0.747915
$501$	−4.05411	−0.181124
$502$	1.41309	0.0630693
$503$	28.7658	1.28260	0.641302	−	0.767288i	$-0.278394\pi$
$503$	28.7658	1.28260	0.641302	+	0.767288i	$0.278394\pi$
$504$	1.75490	0.0781696
$505$	29.7304	1.32299
$506$	−1.85719	−0.0825622
$507$	0.501207	0.0222594
$508$	6.54417	0.290351
$509$	−27.8375	−1.23388	−0.616939	−	0.787011i	$-0.711627\pi$
$509$	−27.8375	−1.23388	−0.616939	+	0.787011i	$0.711627\pi$
$510$	0.360041	0.0159429
$511$	2.00882	0.0888650
$512$	−17.8717	−0.789825
$513$	−0.462011	−0.0203983
$514$	2.49891	0.110222
$515$	17.0762	0.752467
$516$	4.38303	0.192952
$517$	−5.88284	−0.258727
$518$	−0.715280	−0.0314276
$519$	3.11840	0.136883
$520$	−8.87531	−0.389208
$521$	17.5787	0.770136	0.385068	−	0.922888i	$-0.374178\pi$
$521$	17.5787	0.770136	0.385068	+	0.922888i	$0.374178\pi$
$522$	−1.74430	−0.0763460
$523$	41.3439	1.80784	0.903921	−	0.427699i	$-0.140676\pi$
$523$	41.3439	1.80784	0.903921	+	0.427699i	$0.140676\pi$
$524$	−8.38617	−0.366351
$525$	0.391053	0.0170669
$526$	−0.470176	−0.0205006
$527$	0.0748924	0.00326236
$528$	1.40098	0.0609697
$529$	29.7538	1.29365
$530$	6.32783	0.274863
$531$	18.2610	0.792458
$532$	−0.241148	−0.0104551
$533$	43.0625	1.86524
$534$	0.130106	0.00563025
$535$	32.6709	1.41249
$536$	−6.23281	−0.269217
$537$	−4.13181	−0.178301
$538$	7.96781	0.343516
$539$	6.62530	0.285372
$540$	−11.3167	−0.486991
$541$	7.52316	0.323446	0.161723	−	0.986836i	$-0.448295\pi$
$541$	7.52316	0.323446	0.161723	+	0.986836i	$0.448295\pi$
$542$	6.63302	0.284913
$543$	5.64673	0.242324
$544$	−4.13371	−0.177231
$545$	4.01803	0.172113
$546$	0.207729	0.00888997
$547$	−3.25607	−0.139220	−0.0696098	−	0.997574i	$-0.522175\pi$
$547$	−3.25607	−0.139220	−0.0696098	+	0.997574i	$0.522175\pi$
$548$	−18.5383	−0.791918
$549$	2.84956	0.121616
$550$	0.421148	0.0179578
$551$	0.487482	0.0207674
$552$	2.83429	0.120635
$553$	−4.04708	−0.172099
$554$	−6.53807	−0.277776
$555$	4.56986	0.193980
$556$	−8.11553	−0.344175
$557$	33.4936	1.41917	0.709585	−	0.704619i	$-0.248882\pi$
$557$	33.4936	1.41917	0.709585	+	0.704619i	$0.248882\pi$
$558$	0.0387544	0.00164061
$559$	−19.9862	−0.845328
$560$	−5.70038	−0.240885
$561$	0.546146	0.0230583
$562$	−3.92480	−0.165558
$563$	−18.0683	−0.761488	−0.380744	−	0.924680i	$-0.624332\pi$
$563$	−18.0683	−0.761488	−0.380744	+	0.924680i	$0.624332\pi$
$564$	4.41436	0.185878
$565$	−6.85408	−0.288353
$566$	−4.30501	−0.180953
$567$	−4.69421	−0.197138
$568$	6.35851	0.266797
$569$	−31.6306	−1.32602	−0.663012	−	0.748608i	$-0.730722\pi$
$569$	−31.6306	−1.32602	−0.663012	+	0.748608i	$0.730722\pi$
$570$	−0.0520683	−0.00218090
$571$	−20.0983	−0.841086	−0.420543	−	0.907273i	$-0.638160\pi$
$571$	−20.0983	−0.841086	−0.420543	+	0.907273i	$0.638160\pi$
$572$	−6.61962	−0.276780
$573$	1.27624	0.0533157
$574$	−1.96986	−0.0822202
$575$	−11.9628	−0.498883
$576$	18.4460	0.768585
$577$	7.24260	0.301513	0.150757	−	0.988571i	$-0.451829\pi$
$577$	7.24260	0.301513	0.150757	+	0.988571i	$0.451829\pi$
$578$	3.83992	0.159720
$579$	2.23657	0.0929487
$580$	11.9405	0.495804
$581$	3.82541	0.158705
$582$	0.689860	0.0285956
$583$	9.59867	0.397536
$584$	−3.30163	−0.136623
$585$	25.1379	1.03932
$586$	4.57555	0.189014
$587$	−9.38457	−0.387343	−0.193671	−	0.981066i	$-0.562040\pi$
$587$	−9.38457	−0.387343	−0.193671	+	0.981066i	$0.562040\pi$
$588$	−4.97149	−0.205021
$589$	−0.0108307	−0.000446273 0
$590$	4.22464	0.173926
$591$	10.5160	0.432572
$592$	−16.5063	−0.678403
$593$	−33.6305	−1.38104	−0.690520	−	0.723313i	$-0.742618\pi$
$593$	−33.6305	−1.38104	−0.690520	+	0.723313i	$0.742618\pi$
$594$	0.580147	0.0238037
$595$	−2.22219	−0.0911009
$596$	−33.5546	−1.37445
$597$	−1.03404	−0.0423204
$598$	−6.35468	−0.259862
$599$	13.9904	0.571631	0.285816	−	0.958285i	$-0.407736\pi$
$599$	13.9904	0.571631	0.285816	+	0.958285i	$0.407736\pi$
$600$	−0.642722	−0.0262390
$601$	−3.36481	−0.137254	−0.0686268	−	0.997642i	$-0.521862\pi$
$601$	−3.36481	−0.137254	−0.0686268	+	0.997642i	$0.521862\pi$
$602$	0.914254	0.0372622
$603$	17.6535	0.718904
$604$	−1.23522	−0.0502605
$605$	2.57819	0.104818
$606$	1.14367	0.0464585
$607$	39.2298	1.59229	0.796144	−	0.605107i	$-0.206870\pi$
$607$	39.2298	1.59229	0.796144	+	0.605107i	$0.206870\pi$
$608$	0.597807	0.0242443
$609$	−0.568387	−0.0230322
$610$	0.659240	0.0266919
$611$	−20.1291	−0.814336
$612$	7.76239	0.313776
$613$	24.2559	0.979687	0.489844	−	0.871810i	$-0.337054\pi$
$613$	24.2559	0.979687	0.489844	+	0.871810i	$0.337054\pi$
$614$	2.07726	0.0838314
$615$	12.5852	0.507486
$616$	0.615851	0.0248134
$617$	−18.3022	−0.736820	−0.368410	−	0.929663i	$-0.620098\pi$
$617$	−18.3022	−0.736820	−0.368410	+	0.929663i	$0.620098\pi$
$618$	0.656889	0.0264239
$619$	21.9917	0.883920	0.441960	−	0.897035i	$-0.354283\pi$
$619$	21.9917	0.883920	0.441960	+	0.897035i	$0.354283\pi$
$620$	−0.265292	−0.0106544
$621$	−16.4792	−0.661287
$622$	−0.297085	−0.0119120
$623$	−0.803022	−0.0321724
$624$	4.79368	0.191901
$625$	−30.5225	−1.22090
$626$	−1.74904	−0.0699059
$627$	−0.0789822	−0.00315425
$628$	−6.36315	−0.253917
$629$	−6.43466	−0.256567
$630$	−1.14991	−0.0458136
$631$	10.1923	0.405750	0.202875	−	0.979205i	$-0.434972\pi$
$631$	10.1923	0.405750	0.202875	+	0.979205i	$0.434972\pi$
$632$	6.65165	0.264589
$633$	−3.47670	−0.138186
$634$	−5.66444	−0.224964
$635$	−8.72115	−0.346088
$636$	−7.20264	−0.285603
$637$	22.6695	0.898200
$638$	−0.612130	−0.0242345
$639$	−18.0095	−0.712443
$640$	19.4052	0.767059
$641$	19.9024	0.786096	0.393048	−	0.919518i	$-0.371421\pi$
$641$	19.9024	0.786096	0.393048	+	0.919518i	$0.371421\pi$
$642$	1.25679	0.0496015
$643$	0.0479357	0.00189040	0.000945199	−	1.00000i	$-0.499699\pi$
$643$	0.0479357	0.00189040	0.000945199		1.00000i	$0.499699\pi$
$644$	−8.60134	−0.338940
$645$	−5.84108	−0.229992
$646$	0.0733155	0.00288456
$647$	−49.4868	−1.94553	−0.972764	−	0.231797i	$-0.925539\pi$
$647$	−49.4868	−1.94553	−0.972764	+	0.231797i	$0.925539\pi$
$648$	7.71526	0.303084
$649$	6.40835	0.251550
$650$	1.44103	0.0565218
$651$	0.0126283	0.000494942 0
$652$	25.3675	0.993469
$653$	−9.18379	−0.359389	−0.179695	−	0.983722i	$-0.557511\pi$
$653$	−9.18379	−0.359389	−0.179695	+	0.983722i	$0.557511\pi$
$654$	0.154566	0.00604400
$655$	11.1759	0.436679
$656$	−45.4577	−1.77482
$657$	9.35135	0.364831
$658$	0.920789	0.0358961
$659$	7.08141	0.275853	0.137926	−	0.990442i	$-0.455956\pi$
$659$	7.08141	0.275853	0.137926	+	0.990442i	$0.455956\pi$
$660$	−1.93462	−0.0753049
$661$	−10.4058	−0.404737	−0.202369	−	0.979309i	$-0.564864\pi$
$661$	−10.4058	−0.404737	−0.202369	+	0.979309i	$0.564864\pi$
$662$	6.90740	0.268464
$663$	1.86873	0.0725754
$664$	−6.28733	−0.243996
$665$	0.321368	0.0124621
$666$	−3.32974	−0.129025
$667$	17.3877	0.673254
$668$	−20.2211	−0.782378
$669$	6.05657	0.234160
$670$	4.08410	0.157782
$671$	1.00000	0.0386046
$672$	−0.697023	−0.0268882
$673$	−40.1794	−1.54880	−0.774401	−	0.632695i	$-0.781949\pi$
$673$	−40.1794	−1.54880	−0.774401	+	0.632695i	$0.781949\pi$
$674$	5.50798	0.212160
$675$	3.73693	0.143834
$676$	2.49993	0.0961510
$677$	18.6790	0.717893	0.358947	−	0.933358i	$-0.383136\pi$
$677$	18.6790	0.717893	0.358947	+	0.933358i	$0.383136\pi$
$678$	−0.263663	−0.0101259
$679$	−4.25785	−0.163401
$680$	3.65232	0.140060
$681$	−6.22136	−0.238403
$682$	0.0136002	0.000520777 0
$683$	9.25871	0.354275	0.177137	−	0.984186i	$-0.443316\pi$
$683$	9.25871	0.354275	0.177137	+	0.984186i	$0.443316\pi$
$684$	−1.12258	−0.0429228
$685$	24.7053	0.943940
$686$	−2.13265	−0.0814249
$687$	−3.21123	−0.122516
$688$	21.0979	0.804350
$689$	32.8434	1.25124
$690$	−1.85719	−0.0707020
$691$	−45.4874	−1.73042	−0.865210	−	0.501409i	$-0.832815\pi$
$691$	−45.4874	−1.73042	−0.865210	+	0.501409i	$0.832815\pi$
$692$	15.5540	0.591274
$693$	−1.74430	−0.0662605
$694$	−7.70933	−0.292642
$695$	10.8152	0.410245
$696$	0.934184	0.0354101
$697$	−17.7208	−0.671224
$698$	4.57573	0.173194
$699$	−7.77153	−0.293946
$700$	1.95050	0.0737218
$701$	−26.8238	−1.01312	−0.506561	−	0.862204i	$-0.669084\pi$
$701$	−26.8238	−1.01312	−0.506561	+	0.862204i	$0.669084\pi$
$702$	1.98507	0.0749216
$703$	0.930565	0.0350969
$704$	6.47330	0.243972
$705$	−5.88284	−0.221560
$706$	−2.70757	−0.101901
$707$	−7.05879	−0.265473
$708$	−4.80869	−0.180722
$709$	0.539792	0.0202723	0.0101362	−	0.999949i	$-0.496774\pi$
$709$	0.539792	0.0202723	0.0101362	+	0.999949i	$0.496774\pi$
$710$	−4.16646	−0.156364
$711$	−18.8397	−0.706546
$712$	1.31982	0.0494624
$713$	−0.386315	−0.0144676
$714$	−0.0854834	−0.00319914
$715$	8.82169	0.329913
$716$	−20.6087	−0.770182
$717$	−3.88621	−0.145133
$718$	6.52936	0.243674
$719$	2.57964	0.0962043	0.0481021	−	0.998842i	$-0.484683\pi$
$719$	2.57964	0.0962043	0.0481021	+	0.998842i	$0.484683\pi$
$720$	−26.5361	−0.988943
$721$	−4.05435	−0.150992
$722$	4.84768	0.180412
$723$	4.72656	0.175783
$724$	28.1648	1.04674
$725$	−3.94294	−0.146437
$726$	0.0991779	0.00368084
$727$	24.8297	0.920881	0.460441	−	0.887690i	$-0.347691\pi$
$727$	24.8297	0.920881	0.460441	+	0.887690i	$0.347691\pi$
$728$	2.10724	0.0780994
$729$	−19.2122	−0.711562
$730$	2.16342	0.0800718
$731$	8.22463	0.304199
$732$	−0.750379	−0.0277348
$733$	8.79860	0.324984	0.162492	−	0.986710i	$-0.448047\pi$
$733$	8.79860	0.324984	0.162492	+	0.986710i	$0.448047\pi$
$734$	2.54986	0.0941170
$735$	6.62530	0.244378
$736$	21.3228	0.785969
$737$	6.19516	0.228202
$738$	−9.16997	−0.337551
$739$	−28.3258	−1.04198	−0.520991	−	0.853562i	$-0.674437\pi$
$739$	−28.3258	−1.04198	−0.520991	+	0.853562i	$0.674437\pi$
$740$	22.7936	0.837909
$741$	−0.270251	−0.00992791
$742$	−1.50240	−0.0551547
$743$	5.53136	0.202926	0.101463	−	0.994839i	$-0.467648\pi$
$743$	5.53136	0.202926	0.101463	+	0.994839i	$0.467648\pi$
$744$	−0.0207555	−0.000760932 0
$745$	44.7168	1.63830
$746$	−2.06362	−0.0755544
$747$	17.8079	0.651555
$748$	2.72407	0.0996018
$749$	−7.75695	−0.283433
$750$	−0.857347	−0.0313059
$751$	−0.217887	−0.00795082	−0.00397541	−	0.999992i	$-0.501265\pi$
$751$	−0.217887	−0.00795082	−0.00397541	+	0.999992i	$0.501265\pi$
$752$	21.2487	0.774860
$753$	2.14351	0.0781140
$754$	−2.09451	−0.0762774
$755$	1.64613	0.0599089
$756$	2.68688	0.0977208
$757$	2.02867	0.0737331	0.0368666	−	0.999320i	$-0.488262\pi$
$757$	2.02867	0.0737331	0.0368666	+	0.999320i	$0.488262\pi$
$758$	9.48414	0.344480
$759$	−2.81717	−0.102257
$760$	−0.528190	−0.0191595
$761$	−11.7113	−0.424535	−0.212268	−	0.977212i	$-0.568085\pi$
$761$	−11.7113	−0.424535	−0.212268	+	0.977212i	$0.568085\pi$
$762$	−0.335486	−0.0121534
$763$	−0.953988	−0.0345367
$764$	6.36564	0.230301
$765$	−10.3446	−0.374010
$766$	2.16429	0.0781990
$767$	21.9272	0.791747
$768$	−4.27511	−0.154265
$769$	27.9145	1.00662	0.503312	−	0.864105i	$-0.332115\pi$
$769$	27.9145	1.00662	0.503312	+	0.864105i	$0.332115\pi$
$770$	−0.403541	−0.0145426
$771$	3.79060	0.136515
$772$	11.1556	0.401498
$773$	−9.18520	−0.330369	−0.165184	−	0.986263i	$-0.552822\pi$
$773$	−9.18520	−0.330369	−0.165184	+	0.986263i	$0.552822\pi$
$774$	4.25599	0.152978
$775$	0.0876033	0.00314680
$776$	6.99807	0.251216
$777$	−1.08501	−0.0389244
$778$	9.26270	0.332084
$779$	2.56274	0.0918198
$780$	−6.61962	−0.237020
$781$	−6.32009	−0.226151
$782$	2.61504	0.0935138
$783$	−5.43154	−0.194108
$784$	−23.9305	−0.854659
$785$	8.47991	0.302661
$786$	0.429916	0.0153346
$787$	−32.1181	−1.14489	−0.572444	−	0.819944i	$-0.694005\pi$
$787$	−32.1181	−1.14489	−0.572444	+	0.819944i	$0.694005\pi$
$788$	52.4519	1.86852
$789$	−0.713209	−0.0253909
$790$	−4.35854	−0.155070
$791$	1.62734	0.0578616
$792$	2.86688	0.101870
$793$	3.42167	0.121507
$794$	−5.03307	−0.178617
$795$	9.59867	0.340430
$796$	−5.15759	−0.182806
$797$	15.0591	0.533421	0.266710	−	0.963777i	$-0.414063\pi$
$797$	15.0591	0.533421	0.266710	+	0.963777i	$0.414063\pi$
$798$	0.0123624	0.000437624 0
$799$	8.28342	0.293046
$800$	−4.83530	−0.170954
$801$	−3.73819	−0.132082
$802$	−4.71872	−0.166624
$803$	3.28169	0.115808
$804$	−4.64872	−0.163948
$805$	11.4627	0.404006
$806$	0.0465352	0.00163913
$807$	12.0863	0.425460
$808$	11.6016	0.408143
$809$	−54.0343	−1.89974	−0.949872	−	0.312640i	$-0.898786\pi$
$809$	−54.0343	−1.89974	−0.949872	+	0.312640i	$0.898786\pi$
$810$	−5.05548	−0.177631
$811$	44.6275	1.56708	0.783541	−	0.621340i	$-0.213412\pi$
$811$	44.6275	1.56708	0.783541	+	0.621340i	$0.213412\pi$
$812$	−2.83501	−0.0994892
$813$	10.0616	0.352876
$814$	−1.16851	−0.0409562
$815$	−33.8063	−1.18418
$816$	−1.97267	−0.0690572
$817$	−1.18943	−0.0416127
$818$	−5.08667	−0.177851
$819$	−5.96841	−0.208553
$820$	62.7727	2.19212
$821$	34.8941	1.21781	0.608906	−	0.793242i	$-0.291609\pi$
$821$	34.8941	1.21781	0.608906	+	0.793242i	$0.291609\pi$
$822$	0.950365	0.0331478
$823$	−52.5148	−1.83055	−0.915276	−	0.402828i	$-0.868027\pi$
$823$	−52.5148	−1.83055	−0.915276	+	0.402828i	$0.868027\pi$
$824$	6.66360	0.232137
$825$	0.638839	0.0222415
$826$	−1.00304	−0.0349003
$827$	−28.3336	−0.985255	−0.492627	−	0.870240i	$-0.663963\pi$
$827$	−28.3336	−0.985255	−0.492627	+	0.870240i	$0.663963\pi$
$828$	−40.0405	−1.39150
$829$	18.0396	0.626541	0.313270	−	0.949664i	$-0.398575\pi$
$829$	18.0396	0.626541	0.313270	+	0.949664i	$0.398575\pi$
$830$	4.11982	0.143001
$831$	−9.91759	−0.344037
$832$	22.1495	0.767894
$833$	−9.32885	−0.323225
$834$	0.416041	0.0144063
$835$	26.9478	0.932568
$836$	−0.393948	−0.0136250
$837$	0.120677	0.00417120
$838$	8.38120	0.289524
$839$	12.0729	0.416804	0.208402	−	0.978043i	$-0.433174\pi$
$839$	12.0729	0.416804	0.208402	+	0.978043i	$0.433174\pi$
$840$	0.615851	0.0212489
$841$	−23.2690	−0.802380
$842$	8.49592	0.292789
$843$	−5.95352	−0.205050
$844$	−17.3411	−0.596905
$845$	−3.33155	−0.114609
$846$	4.28641	0.147370
$847$	−0.612130	−0.0210331
$848$	−34.6702	−1.19058
$849$	−6.53026	−0.224118
$850$	−0.593004	−0.0203399
$851$	33.1917	1.13780
$852$	4.74247	0.162474
$853$	−38.2147	−1.30845	−0.654223	−	0.756301i	$-0.727004\pi$
$853$	−38.2147	−1.30845	−0.654223	+	0.756301i	$0.727004\pi$
$854$	−0.156521	−0.00535605
$855$	1.49601	0.0511626
$856$	12.7491	0.435755
$857$	−10.5010	−0.358708	−0.179354	−	0.983785i	$-0.557401\pi$
$857$	−10.5010	−0.358708	−0.179354	+	0.983785i	$0.557401\pi$
$858$	0.339354	0.0115853
$859$	4.74295	0.161827	0.0809136	−	0.996721i	$-0.474216\pi$
$859$	4.74295	0.161827	0.0809136	+	0.996721i	$0.474216\pi$
$860$	−29.1342	−0.993468
$861$	−2.98807	−0.101833
$862$	−4.80733	−0.163738
$863$	33.1953	1.12998	0.564990	−	0.825098i	$-0.308880\pi$
$863$	33.1953	1.12998	0.564990	+	0.825098i	$0.308880\pi$
$864$	−6.66079	−0.226605
$865$	−20.7282	−0.704779
$866$	8.61249	0.292664
$867$	5.82477	0.197820
$868$	0.0629875	0.00213793
$869$	−6.61147	−0.224279
$870$	−0.612130	−0.0207532
$871$	21.1978	0.718259
$872$	1.56794	0.0530973
$873$	−19.8209	−0.670836
$874$	−0.378181	−0.0127922
$875$	5.29159	0.178888
$876$	−2.46251	−0.0832005
$877$	−17.8534	−0.602865	−0.301433	−	0.953487i	$-0.597465\pi$
$877$	−17.8534	−0.602865	−0.301433	+	0.953487i	$0.597465\pi$
$878$	10.0080	0.337752
$879$	6.94064	0.234102
$880$	−9.31236	−0.313920
$881$	−2.05381	−0.0691945	−0.0345973	−	0.999401i	$-0.511015\pi$
$881$	−2.05381	−0.0691945	−0.0345973	+	0.999401i	$0.511015\pi$
$882$	−4.82739	−0.162547
$883$	−41.0417	−1.38116	−0.690582	−	0.723254i	$-0.742646\pi$
$883$	−41.0417	−1.38116	−0.690582	+	0.723254i	$0.742646\pi$
$884$	9.32085	0.313494
$885$	6.40835	0.215414
$886$	−7.56367	−0.254106
$887$	−12.9169	−0.433707	−0.216853	−	0.976204i	$-0.569579\pi$
$887$	−12.9169	−0.433707	−0.216853	+	0.976204i	$0.569579\pi$
$888$	1.78328	0.0598431
$889$	2.07063	0.0694468
$890$	−0.864823	−0.0289889
$891$	−7.66865	−0.256909
$892$	30.2090	1.01147
$893$	−1.19793	−0.0400871
$894$	1.72017	0.0575311
$895$	27.4643	0.918032
$896$	−4.60732	−0.153920
$897$	−9.63940	−0.321850
$898$	−2.53986	−0.0847563
$899$	−0.127330	−0.00424668
$900$	9.07984	0.302661
$901$	−13.5156	−0.450268
$902$	−3.21803	−0.107149
$903$	1.38683	0.0461508
$904$	−2.67465	−0.0889575
$905$	−37.5341	−1.24768
$906$	0.0633236	0.00210378
$907$	55.6732	1.84860	0.924299	−	0.381669i	$-0.124650\pi$
$907$	55.6732	1.84860	0.924299	+	0.381669i	$0.124650\pi$
$908$	−31.0309	−1.02980
$909$	−32.8597	−1.08989
$910$	−1.38078	−0.0457725
$911$	−4.52472	−0.149911	−0.0749553	−	0.997187i	$-0.523881\pi$
$911$	−4.52472	−0.149911	−0.0749553	+	0.997187i	$0.523881\pi$
$912$	0.285282	0.00944664
$913$	6.24934	0.206823
$914$	−1.79790	−0.0594691
$915$	1.00000	0.0330590
$916$	−16.0170	−0.529217
$917$	−2.65346	−0.0876249
$918$	−0.816885	−0.0269612
$919$	−8.69042	−0.286670	−0.143335	−	0.989674i	$-0.545783\pi$
$919$	−8.69042	−0.286670	−0.143335	+	0.989674i	$0.545783\pi$
$920$	−18.8397	−0.621125
$921$	3.15099	0.103829
$922$	4.60897	0.151788
$923$	−21.6252	−0.711804
$924$	0.459330	0.0151108
$925$	−7.52677	−0.247479
$926$	−9.26191	−0.304365
$927$	−18.8736	−0.619890
$928$	7.02800	0.230706
$929$	23.7701	0.779873	0.389936	−	0.920842i	$-0.372497\pi$
$929$	23.7701	0.779873	0.389936	+	0.920842i	$0.372497\pi$
$930$	0.0136002	0.000445967 0
$931$	1.34912	0.0442155
$932$	−38.7629	−1.26972
$933$	−0.450647	−0.0147535
$934$	2.96935	0.0971601
$935$	−3.63025	−0.118722
$936$	9.80950	0.320633
$937$	−7.10500	−0.232110	−0.116055	−	0.993243i	$-0.537025\pi$
$937$	−7.10500	−0.232110	−0.116055	+	0.993243i	$0.537025\pi$
$938$	−0.969674	−0.0316610
$939$	−2.65312	−0.0865814
$940$	−29.3424	−0.957045
$941$	45.9788	1.49887	0.749433	−	0.662080i	$-0.230326\pi$
$941$	45.9788	1.49887	0.749433	+	0.662080i	$0.230326\pi$
$942$	0.326206	0.0106284
$943$	91.4089	2.97668
$944$	−23.1469	−0.753366
$945$	−3.58069	−0.116480
$946$	1.49356	0.0485598
$947$	−20.8365	−0.677097	−0.338548	−	0.940949i	$-0.609936\pi$
$947$	−20.8365	−0.677097	−0.338548	+	0.940949i	$0.609936\pi$
$948$	4.96111	0.161129
$949$	11.2288	0.364503
$950$	0.0857588	0.00278238
$951$	−8.59238	−0.278627
$952$	−0.867159	−0.0281048
$953$	20.9542	0.678772	0.339386	−	0.940647i	$-0.389781\pi$
$953$	20.9542	0.678772	0.339386	+	0.940647i	$0.389781\pi$
$954$	−6.99387	−0.226435
$955$	−8.48323	−0.274511
$956$	−19.3836	−0.626912
$957$	−0.928539	−0.0300154
$958$	−4.80131	−0.155123
$959$	−5.86569	−0.189413
$960$	6.47330	0.208925
$961$	−30.9972	−0.999909
$962$	−3.99825	−0.128909
$963$	−36.1097	−1.16362
$964$	23.5752	0.759305
$965$	−14.8666	−0.478573
$966$	0.440947	0.0141872
$967$	38.0634	1.22404	0.612018	−	0.790844i	$-0.290358\pi$
$967$	38.0634	1.22404	0.612018	+	0.790844i	$0.290358\pi$
$968$	1.00608	0.0323366
$969$	0.111212	0.00357265
$970$	−4.58553	−0.147233
$971$	49.6232	1.59248	0.796242	−	0.604978i	$-0.206818\pi$
$971$	49.6232	1.59248	0.796242	+	0.604978i	$0.206818\pi$
$972$	18.9226	0.606941
$973$	−2.56783	−0.0823207
$974$	−2.03878	−0.0653268
$975$	2.18589	0.0700046
$976$	−3.61198	−0.115617
$977$	−33.6245	−1.07574	−0.537872	−	0.843027i	$-0.680772\pi$
$977$	−33.6245	−1.07574	−0.537872	+	0.843027i	$0.680772\pi$
$978$	−1.30046	−0.0415842
$979$	−1.31185	−0.0419268
$980$	33.0457	1.05561
$981$	−4.44095	−0.141789
$982$	−5.32492	−0.169925
$983$	−54.9738	−1.75339	−0.876697	−	0.481044i	$-0.840258\pi$
$983$	−54.9738	−1.75339	−0.876697	+	0.481044i	$0.840258\pi$
$984$	4.91110	0.156560
$985$	−69.9005	−2.22722
$986$	0.861920	0.0274491
$987$	1.39674	0.0444588
$988$	−1.34796	−0.0428843
$989$	−42.4249	−1.34903
$990$	−1.87854	−0.0597040
$991$	−27.4333	−0.871447	−0.435724	−	0.900081i	$-0.643507\pi$
$991$	−27.4333	−0.871447	−0.435724	+	0.900081i	$0.643507\pi$
$992$	−0.156146	−0.00495765
$993$	10.4778	0.332504
$994$	0.989229	0.0313764
$995$	6.87331	0.217899
$996$	−4.68938	−0.148589
$997$	−46.4094	−1.46980	−0.734900	−	0.678176i	$-0.762771\pi$
$997$	−46.4094	−1.46980	−0.734900	+	0.678176i	$0.762771\pi$
$998$	2.98224	0.0944012
$999$	−10.3684	−0.328042

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	671.2.a.b.1.3	✓	6
3.2	odd	2		6039.2.a.b.1.4		6
11.10	odd	2		7381.2.a.h.1.4		6

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
671.2.a.b.1.3	✓	6	1.1	even	1	trivial
6039.2.a.b.1.4		6	3.2	odd	2
7381.2.a.h.1.4		6	11.10	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:	\( N \)	\(=\)	\( 671 = 11 \cdot 61 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	671.a (trivial)

\(f(q)\)	\(=\)	\(q-0.255699 q^{2} -0.387870 q^{3} -1.93462 q^{4} +2.57819 q^{5} +0.0991779 q^{6} -0.612130 q^{7} +1.00608 q^{8} -2.84956 q^{9} +O(q^{10})\)	\(q-0.255699 q^{2} -0.387870 q^{3} -1.93462 q^{4} +2.57819 q^{5} +0.0991779 q^{6} -0.612130 q^{7} +1.00608 q^{8} -2.84956 q^{9} -0.659240 q^{10} -1.00000 q^{11} +0.750379 q^{12} -3.42167 q^{13} +0.156521 q^{14} -1.00000 q^{15} +3.61198 q^{16} +1.40807 q^{17} +0.728629 q^{18} -0.203631 q^{19} -4.98781 q^{20} +0.237427 q^{21} +0.255699 q^{22} -7.26318 q^{23} -0.390227 q^{24} +1.64705 q^{25} +0.874917 q^{26} +2.26886 q^{27} +1.18424 q^{28} -2.39395 q^{29} +0.255699 q^{30} +0.0531881 q^{31} -2.93574 q^{32} +0.387870 q^{33} -0.360041 q^{34} -1.57819 q^{35} +5.51280 q^{36} -4.56986 q^{37} +0.0520683 q^{38} +1.32716 q^{39} +2.59386 q^{40} -12.5852 q^{41} -0.0607098 q^{42} +5.84108 q^{43} +1.93462 q^{44} -7.34669 q^{45} +1.85719 q^{46} +5.88284 q^{47} -1.40098 q^{48} -6.62530 q^{49} -0.421148 q^{50} -0.546146 q^{51} +6.61962 q^{52} -9.59867 q^{53} -0.580147 q^{54} -2.57819 q^{55} -0.615851 q^{56} +0.0789822 q^{57} +0.612130 q^{58} -6.40835 q^{59} +1.93462 q^{60} -1.00000 q^{61} -0.0136002 q^{62} +1.74430 q^{63} -6.47330 q^{64} -8.82169 q^{65} -0.0991779 q^{66} -6.19516 q^{67} -2.72407 q^{68} +2.81717 q^{69} +0.403541 q^{70} +6.32009 q^{71} -2.86688 q^{72} -3.28169 q^{73} +1.16851 q^{74} -0.638839 q^{75} +0.393948 q^{76} +0.612130 q^{77} -0.339354 q^{78} +6.61147 q^{79} +9.31236 q^{80} +7.66865 q^{81} +3.21803 q^{82} -6.24934 q^{83} -0.459330 q^{84} +3.63025 q^{85} -1.49356 q^{86} +0.928539 q^{87} -1.00608 q^{88} +1.31185 q^{89} +1.87854 q^{90} +2.09451 q^{91} +14.0515 q^{92} -0.0206301 q^{93} -1.50424 q^{94} -0.524998 q^{95} +1.13868 q^{96} +6.95579 q^{97} +1.69408 q^{98} +2.84956 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 6 q - q^{3} + 2 q^{4} - q^{5} - q^{6} - 5 q^{7} - 6 q^{8} - 5 q^{9}+O(q^{10}) \) 6 * q - q^3 + 2 * q^4 - q^5 - q^6 - 5 * q^7 - 6 * q^8 - 5 * q^9	\( 6 q - q^{3} + 2 q^{4} - q^{5} - q^{6} - 5 q^{7} - 6 q^{8} - 5 q^{9} - 7 q^{10} - 6 q^{11} - 6 q^{12} - 4 q^{13} + q^{14} - 6 q^{15} - 10 q^{16} - 5 q^{17} - 3 q^{19} - 6 q^{20} - 12 q^{21} - 3 q^{23} + 10 q^{24} - 11 q^{25} + q^{26} - 4 q^{27} + 4 q^{28} - q^{29} - 10 q^{31} + 3 q^{32} + q^{33} - 19 q^{34} + 7 q^{35} + 3 q^{36} - 19 q^{37} - 3 q^{38} + 8 q^{39} + 5 q^{40} - 7 q^{41} + q^{42} - 2 q^{43} - 2 q^{44} + 4 q^{45} - 7 q^{46} + 5 q^{47} + q^{48} - 25 q^{49} + 17 q^{50} - q^{51} + 2 q^{52} - 9 q^{53} - 11 q^{54} + q^{55} - 4 q^{56} + 11 q^{57} + 5 q^{58} - 5 q^{59} - 2 q^{60} - 6 q^{61} + 3 q^{62} + 12 q^{63} - 6 q^{64} - 11 q^{65} + q^{66} - 14 q^{67} + 18 q^{68} - 7 q^{69} + 7 q^{70} - 14 q^{71} - q^{72} - 14 q^{73} + 6 q^{74} + 6 q^{75} - 11 q^{76} + 5 q^{77} - 26 q^{78} + 5 q^{79} + 26 q^{80} - 14 q^{81} + q^{82} + 17 q^{83} - 3 q^{84} + 2 q^{85} - 7 q^{86} + 4 q^{87} + 6 q^{88} - 25 q^{89} + 22 q^{90} - 4 q^{91} + 35 q^{92} - q^{93} + 30 q^{94} + 3 q^{95} + 8 q^{96} - 24 q^{97} - 2 q^{98} + 5 q^{99}+O(q^{100}) \) 6 * q - q^3 + 2 * q^4 - q^5 - q^6 - 5 * q^7 - 6 * q^8 - 5 * q^9 - 7 * q^10 - 6 * q^11 - 6 * q^12 - 4 * q^13 + q^14 - 6 * q^15 - 10 * q^16 - 5 * q^17 - 3 * q^19 - 6 * q^20 - 12 * q^21 - 3 * q^23 + 10 * q^24 - 11 * q^25 + q^26 - 4 * q^27 + 4 * q^28 - q^29 - 10 * q^31 + 3 * q^32 + q^33 - 19 * q^34 + 7 * q^35 + 3 * q^36 - 19 * q^37 - 3 * q^38 + 8 * q^39 + 5 * q^40 - 7 * q^41 + q^42 - 2 * q^43 - 2 * q^44 + 4 * q^45 - 7 * q^46 + 5 * q^47 + q^48 - 25 * q^49 + 17 * q^50 - q^51 + 2 * q^52 - 9 * q^53 - 11 * q^54 + q^55 - 4 * q^56 + 11 * q^57 + 5 * q^58 - 5 * q^59 - 2 * q^60 - 6 * q^61 + 3 * q^62 + 12 * q^63 - 6 * q^64 - 11 * q^65 + q^66 - 14 * q^67 + 18 * q^68 - 7 * q^69 + 7 * q^70 - 14 * q^71 - q^72 - 14 * q^73 + 6 * q^74 + 6 * q^75 - 11 * q^76 + 5 * q^77 - 26 * q^78 + 5 * q^79 + 26 * q^80 - 14 * q^81 + q^82 + 17 * q^83 - 3 * q^84 + 2 * q^85 - 7 * q^86 + 4 * q^87 + 6 * q^88 - 25 * q^89 + 22 * q^90 - 4 * q^91 + 35 * q^92 - q^93 + 30 * q^94 + 3 * q^95 + 8 * q^96 - 24 * q^97 - 2 * q^98 + 5 * q^99

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