LMFDB - Embedded newform 1342.2.a.i.1.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1342,2,Mod(1,1342)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1342, 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("1342.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1342 = 2 \cdot 11 \cdot 61 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1342.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:	$10.7159239513$
Analytic rank:	$0$
Dimension:	$4$
Coefficient field:	4.4.48396.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} - 2x^{3} - 7x^{2} + 6x + 6 $ x^4 - 2x^3 - 7x^2 + 6*x + 6
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.1
Root			$-2.08183$ of defining polynomial
Character	$\chi$	$=$	1342.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.00000 q^{2} -3.08183 q^{3} +1.00000 q^{4} -2.41585 q^{5} +3.08183 q^{6} +1.43287 q^{7} -1.00000 q^{8} +6.49768 q^{9} +O(q^{10})$	\(q-1.00000 q^{2} -3.08183 q^{3} +1.00000 q^{4} -2.41585 q^{5} +3.08183 q^{6} +1.43287 q^{7} -1.00000 q^{8} +6.49768 q^{9} +2.41585 q^{10} -1.00000 q^{11} -3.08183 q^{12} -4.84872 q^{13} -1.43287 q^{14} +7.44525 q^{15} +1.00000 q^{16} +6.84872 q^{17} -6.49768 q^{18} -8.01238 q^{19} -2.41585 q^{20} -4.41585 q^{21} +1.00000 q^{22} -2.16366 q^{23} +3.08183 q^{24} +0.836338 q^{25} +4.84872 q^{26} -10.7793 q^{27} +1.43287 q^{28} +0.718416 q^{29} -7.44525 q^{30} -6.21610 q^{31} -1.00000 q^{32} +3.08183 q^{33} -6.84872 q^{34} -3.46159 q^{35} +6.49768 q^{36} -6.04847 q^{37} +8.01238 q^{38} +14.9429 q^{39} +2.41585 q^{40} -12.3273 q^{41} +4.41585 q^{42} +9.91353 q^{43} -1.00000 q^{44} -15.6974 q^{45} +2.16366 q^{46} +1.76689 q^{47} -3.08183 q^{48} -4.94689 q^{49} -0.836338 q^{50} -21.1066 q^{51} -4.84872 q^{52} +10.1466 q^{53} +10.7793 q^{54} +2.41585 q^{55} -1.43287 q^{56} +24.6928 q^{57} -0.718416 q^{58} -5.99603 q^{59} +7.44525 q^{60} +1.00000 q^{61} +6.21610 q^{62} +9.31031 q^{63} +1.00000 q^{64} +11.7138 q^{65} -3.08183 q^{66} -1.18737 q^{67} +6.84872 q^{68} +6.66804 q^{69} +3.46159 q^{70} +5.94756 q^{71} -6.49768 q^{72} +11.7478 q^{73} +6.04847 q^{74} -2.57745 q^{75} -8.01238 q^{76} -1.43287 q^{77} -14.9429 q^{78} -13.6280 q^{79} -2.41585 q^{80} +13.7268 q^{81} +12.3273 q^{82} -3.04574 q^{83} -4.41585 q^{84} -16.5455 q^{85} -9.91353 q^{86} -2.21404 q^{87} +1.00000 q^{88} +18.2769 q^{89} +15.6974 q^{90} -6.94756 q^{91} -2.16366 q^{92} +19.1570 q^{93} -1.76689 q^{94} +19.3567 q^{95} +3.08183 q^{96} +2.94689 q^{97} +4.94689 q^{98} -6.49768 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q - 4 q^{2} - 2 q^{3} + 4 q^{4} + 2 q^{6} + 3 q^{7} - 4 q^{8} + 6 q^{9}+O(q^{10}) $ 4 * q - 4 * q^2 - 2 * q^3 + 4 * q^4 + 2 * q^6 + 3 * q^7 - 4 * q^8 + 6 * q^9	\( 4 q - 4 q^{2} - 2 q^{3} + 4 q^{4} + 2 q^{6} + 3 q^{7} - 4 q^{8} + 6 q^{9} - 4 q^{11} - 2 q^{12} - 7 q^{13} - 3 q^{14} - 6 q^{15} + 4 q^{16} + 15 q^{17} - 6 q^{18} + q^{19} - 8 q^{21} + 4 q^{22} + 12 q^{23} + 2 q^{24} + 24 q^{25} + 7 q^{26} - 8 q^{27} + 3 q^{28} + 18 q^{29} + 6 q^{30} - 20 q^{31} - 4 q^{32} + 2 q^{33} - 15 q^{34} + 22 q^{35} + 6 q^{36} - 7 q^{37} - q^{38} + 4 q^{39} - 8 q^{41} + 8 q^{42} + 10 q^{43} - 4 q^{44} - 38 q^{45} - 12 q^{46} + 5 q^{47} - 2 q^{48} + 3 q^{49} - 24 q^{50} - 8 q^{51} - 7 q^{52} + 13 q^{53} + 8 q^{54} - 3 q^{56} + 34 q^{57} - 18 q^{58} + 9 q^{59} - 6 q^{60} + 4 q^{61} + 20 q^{62} - 11 q^{63} + 4 q^{64} + 22 q^{65} - 2 q^{66} - 33 q^{67} + 15 q^{68} + 28 q^{69} - 22 q^{70} + 8 q^{71} - 6 q^{72} + 36 q^{73} + 7 q^{74} + 22 q^{75} + q^{76} - 3 q^{77} - 4 q^{78} - 7 q^{79} + 4 q^{81} + 8 q^{82} + 14 q^{83} - 8 q^{84} - 22 q^{85} - 10 q^{86} - 2 q^{87} + 4 q^{88} + 18 q^{89} + 38 q^{90} - 12 q^{91} + 12 q^{92} + 14 q^{93} - 5 q^{94} + 10 q^{95} + 2 q^{96} - 11 q^{97} - 3 q^{98} - 6 q^{99}+O(q^{100}) \) 4 * q - 4 * q^2 - 2 * q^3 + 4 * q^4 + 2 * q^6 + 3 * q^7 - 4 * q^8 + 6 * q^9 - 4 * q^11 - 2 * q^12 - 7 * q^13 - 3 * q^14 - 6 * q^15 + 4 * q^16 + 15 * q^17 - 6 * q^18 + q^19 - 8 * q^21 + 4 * q^22 + 12 * q^23 + 2 * q^24 + 24 * q^25 + 7 * q^26 - 8 * q^27 + 3 * q^28 + 18 * q^29 + 6 * q^30 - 20 * q^31 - 4 * q^32 + 2 * q^33 - 15 * q^34 + 22 * q^35 + 6 * q^36 - 7 * q^37 - q^38 + 4 * q^39 - 8 * q^41 + 8 * q^42 + 10 * q^43 - 4 * q^44 - 38 * q^45 - 12 * q^46 + 5 * q^47 - 2 * q^48 + 3 * q^49 - 24 * q^50 - 8 * q^51 - 7 * q^52 + 13 * q^53 + 8 * q^54 - 3 * q^56 + 34 * q^57 - 18 * q^58 + 9 * q^59 - 6 * q^60 + 4 * q^61 + 20 * q^62 - 11 * q^63 + 4 * q^64 + 22 * q^65 - 2 * q^66 - 33 * q^67 + 15 * q^68 + 28 * q^69 - 22 * q^70 + 8 * q^71 - 6 * q^72 + 36 * q^73 + 7 * q^74 + 22 * q^75 + q^76 - 3 * q^77 - 4 * q^78 - 7 * q^79 + 4 * q^81 + 8 * q^82 + 14 * q^83 - 8 * q^84 - 22 * q^85 - 10 * q^86 - 2 * q^87 + 4 * q^88 + 18 * q^89 + 38 * q^90 - 12 * q^91 + 12 * q^92 + 14 * q^93 - 5 * q^94 + 10 * q^95 + 2 * q^96 - 11 * q^97 - 3 * q^98 - 6 * q^99

Display 100 coefficients 10 coefficients

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$	$a_n / n^{(k-1)/2}$	$ \alpha_n $			$ \theta_n $
$p$	$a_p$	$a_p / p^{(k-1)/2}$	$ \alpha_p$			$ \theta_p $

$2$	−1.00000	−0.707107
$2$	−1.00000	−0.707107
$3$	−3.08183	−1.77930	−0.889648	−	0.456647i	$-0.849050\pi$
$3$	−3.08183	−1.77930	−0.889648	+	0.456647i	$0.849050\pi$
$4$	1.00000	0.500000
$5$	−2.41585	−1.08040	−0.540201	−	0.841536i	$-0.681652\pi$
$5$	−2.41585	−1.08040	−0.540201	+	0.841536i	$0.681652\pi$
$6$	3.08183	1.25815
$7$	1.43287	0.541573	0.270786	−	0.962639i	$-0.412716\pi$
$7$	1.43287	0.541573	0.270786	+	0.962639i	$0.412716\pi$
$8$	−1.00000	−0.353553
$9$	6.49768	2.16589
$10$	2.41585	0.763959
$11$	−1.00000	−0.301511
$11$	−1.00000	−0.301511
$12$	−3.08183	−0.889648
$13$	−4.84872	−1.34479	−0.672396	−	0.740191i	$-0.734735\pi$
$13$	−4.84872	−1.34479	−0.672396	+	0.740191i	$0.734735\pi$
$14$	−1.43287	−0.382950
$15$	7.44525	1.92235
$16$	1.00000	0.250000
$17$	6.84872	1.66106	0.830529	−	0.556975i	$-0.188038\pi$
$17$	6.84872	1.66106	0.830529	+	0.556975i	$0.188038\pi$
$18$	−6.49768	−1.53152
$19$	−8.01238	−1.83817	−0.919083	−	0.394064i	$-0.871069\pi$
$19$	−8.01238	−1.83817	−0.919083	+	0.394064i	$0.871069\pi$
$20$	−2.41585	−0.540201
$21$	−4.41585	−0.963618
$22$	1.00000	0.213201
$23$	−2.16366	−0.451155	−0.225577	−	0.974225i	$-0.572427\pi$
$23$	−2.16366	−0.451155	−0.225577	+	0.974225i	$0.572427\pi$
$24$	3.08183	0.629076
$25$	0.836338	0.167268
$26$	4.84872	0.950912
$27$	−10.7793	−2.07447
$28$	1.43287	0.270786
$29$	0.718416	0.133407	0.0667033	−	0.997773i	$-0.478752\pi$
$29$	0.718416	0.133407	0.0667033	+	0.997773i	$0.478752\pi$
$30$	−7.44525	−1.35931
$31$	−6.21610	−1.11644	−0.558222	−	0.829692i	$-0.688516\pi$
$31$	−6.21610	−1.11644	−0.558222	+	0.829692i	$0.688516\pi$
$32$	−1.00000	−0.176777
$33$	3.08183	0.536478
$34$	−6.84872	−1.17455
$35$	−3.46159	−0.585116
$36$	6.49768	1.08295
$37$	−6.04847	−0.994362	−0.497181	−	0.867647i	$-0.665632\pi$
$37$	−6.04847	−0.994362	−0.497181	+	0.867647i	$0.665632\pi$
$38$	8.01238	1.29978
$39$	14.9429	2.39278
$40$	2.41585	0.381980
$41$	−12.3273	−1.92520	−0.962602	−	0.270919i	$-0.912673\pi$
$41$	−12.3273	−1.92520	−0.962602	+	0.270919i	$0.912673\pi$
$42$	4.41585	0.681381
$43$	9.91353	1.51180	0.755900	−	0.654687i	$-0.227200\pi$
$43$	9.91353	1.51180	0.755900	+	0.654687i	$0.227200\pi$
$44$	−1.00000	−0.150756
$45$	−15.6974	−2.34004
$46$	2.16366	0.319015
$47$	1.76689	0.257727	0.128863	−	0.991662i	$-0.458867\pi$
$47$	1.76689	0.257727	0.128863	+	0.991662i	$0.458867\pi$
$48$	−3.08183	−0.444824
$49$	−4.94689	−0.706699
$50$	−0.836338	−0.118276
$51$	−21.1066	−2.95551
$52$	−4.84872	−0.672396
$53$	10.1466	1.39375	0.696875	−	0.717193i	$-0.254573\pi$
$53$	10.1466	1.39375	0.696875	+	0.717193i	$0.254573\pi$
$54$	10.7793	1.46687
$55$	2.41585	0.325753
$56$	−1.43287	−0.191475
$57$	24.6928	3.27064
$58$	−0.718416	−0.0943327
$59$	−5.99603	−0.780617	−0.390309	−	0.920684i	$-0.627632\pi$
$59$	−5.99603	−0.780617	−0.390309	+	0.920684i	$0.627632\pi$
$60$	7.44525	0.961177
$61$	1.00000	0.128037
$61$	1.00000	0.128037
$62$	6.21610	0.789445
$63$	9.31031	1.17299
$64$	1.00000	0.125000
$65$	11.7138	1.45292
$66$	−3.08183	−0.379347
$67$	−1.18737	−0.145061	−0.0725304	−	0.997366i	$-0.523107\pi$
$67$	−1.18737	−0.145061	−0.0725304	+	0.997366i	$0.523107\pi$
$68$	6.84872	0.830529
$69$	6.66804	0.802738
$70$	3.46159	0.413739
$71$	5.94756	0.705846	0.352923	−	0.935652i	$-0.385188\pi$
$71$	5.94756	0.705846	0.352923	+	0.935652i	$0.385188\pi$
$72$	−6.49768	−0.765759
$73$	11.7478	1.37498	0.687489	−	0.726195i	$-0.258713\pi$
$73$	11.7478	1.37498	0.687489	+	0.726195i	$0.258713\pi$
$74$	6.04847	0.703120
$75$	−2.57745	−0.297619
$76$	−8.01238	−0.919083
$77$	−1.43287	−0.163290
$78$	−14.9429	−1.69195
$79$	−13.6280	−1.53327	−0.766634	−	0.642084i	$-0.778070\pi$
$79$	−13.6280	−1.53327	−0.766634	+	0.642084i	$0.778070\pi$
$80$	−2.41585	−0.270100
$81$	13.7268	1.52520
$82$	12.3273	1.36133
$83$	−3.04574	−0.334313	−0.167157	−	0.985930i	$-0.553459\pi$
$83$	−3.04574	−0.334313	−0.167157	+	0.985930i	$0.553459\pi$
$84$	−4.41585	−0.481809
$85$	−16.5455	−1.79461
$86$	−9.91353	−1.06900
$87$	−2.21404	−0.237370
$88$	1.00000	0.106600
$89$	18.2769	1.93735	0.968676	−	0.248327i	$-0.0798807\pi$
$89$	18.2769	1.93735	0.968676	+	0.248327i	$0.0798807\pi$
$90$	15.6974	1.65465
$91$	−6.94756	−0.728303
$92$	−2.16366	−0.225577
$93$	19.1570	1.98648
$94$	−1.76689	−0.182240
$95$	19.3567	1.98596
$96$	3.08183	0.314538
$97$	2.94689	0.299212	0.149606	−	0.988746i	$-0.452200\pi$
$97$	2.94689	0.299212	0.149606	+	0.988746i	$0.452200\pi$
$98$	4.94689	0.499712
$99$	−6.49768	−0.653042
$100$	0.836338	0.0836338
$101$	18.7772	1.86840	0.934201	−	0.356747i	$-0.116114\pi$
$101$	18.7772	1.86840	0.934201	+	0.356747i	$0.116114\pi$
$102$	21.1066	2.08986
$103$	15.1466	1.49244	0.746222	−	0.665697i	$-0.231866\pi$
$103$	15.1466	1.49244	0.746222	+	0.665697i	$0.231866\pi$
$104$	4.84872	0.475456
$105$	10.6680	1.04109
$106$	−10.1466	−0.985530
$107$	6.39678	0.618400	0.309200	−	0.950997i	$-0.399939\pi$
$107$	6.39678	0.618400	0.309200	+	0.950997i	$0.399939\pi$
$108$	−10.7793	−1.03724
$109$	4.94689	0.473827	0.236913	−	0.971531i	$-0.423864\pi$
$109$	4.94689	0.473827	0.236913	+	0.971531i	$0.423864\pi$
$110$	−2.41585	−0.230342
$111$	18.6404	1.76926
$112$	1.43287	0.135393
$113$	−1.11725	−0.105102	−0.0525512	−	0.998618i	$-0.516735\pi$
$113$	−1.11725	−0.105102	−0.0525512	+	0.998618i	$0.516735\pi$
$114$	−24.6928	−2.31269
$115$	5.22709	0.487428
$116$	0.718416	0.0667033
$117$	−31.5054	−2.91268
$118$	5.99603	0.551980
$119$	9.81330	0.899583
$120$	−7.44525	−0.679655
$121$	1.00000	0.0909091
$122$	−1.00000	−0.0905357
$123$	37.9907	3.42551
$124$	−6.21610	−0.558222
$125$	10.0588	0.899685
$126$	−9.31031	−0.829428
$127$	−6.94293	−0.616085	−0.308043	−	0.951373i	$-0.599674\pi$
$127$	−6.94293	−0.616085	−0.308043	+	0.951373i	$0.599674\pi$
$128$	−1.00000	−0.0883883
$129$	−30.5518	−2.68994
$130$	−11.7138	−1.02737
$131$	−2.41858	−0.211312	−0.105656	−	0.994403i	$-0.533694\pi$
$131$	−2.41858	−0.211312	−0.105656	+	0.994403i	$0.533694\pi$
$132$	3.08183	0.268239
$133$	−11.4807	−0.995500
$134$	1.18737	0.102573
$135$	26.0411	2.24126
$136$	−6.84872	−0.587273
$137$	−1.41652	−0.121021	−0.0605107	−	0.998168i	$-0.519273\pi$
$137$	−1.41652	−0.121021	−0.0605107	+	0.998168i	$0.519273\pi$
$138$	−6.66804	−0.567621
$139$	−15.2455	−1.29311	−0.646553	−	0.762869i	$-0.723790\pi$
$139$	−15.2455	−1.29311	−0.646553	+	0.762869i	$0.723790\pi$
$140$	−3.46159	−0.292558
$141$	−5.44525	−0.458572
$142$	−5.94756	−0.499108
$143$	4.84872	0.405470
$144$	6.49768	0.541474
$145$	−1.73559	−0.144133
$146$	−11.7478	−0.972256
$147$	15.2455	1.25743
$148$	−6.04847	−0.497181
$149$	1.33402	0.109287	0.0546436	−	0.998506i	$-0.482598\pi$
$149$	1.33402	0.109287	0.0546436	+	0.998506i	$0.482598\pi$
$150$	2.57745	0.210448
$151$	−9.69471	−0.788944	−0.394472	−	0.918908i	$-0.629072\pi$
$151$	−9.69471	−0.788944	−0.394472	+	0.918908i	$0.629072\pi$
$152$	8.01238	0.649890
$153$	44.5008	3.59768
$154$	1.43287	0.115464
$155$	15.0172	1.20621
$156$	14.9429	1.19639
$157$	−15.9096	−1.26972	−0.634861	−	0.772626i	$-0.718943\pi$
$157$	−15.9096	−1.26972	−0.634861	+	0.772626i	$0.718943\pi$
$158$	13.6280	1.08418
$159$	−31.2703	−2.47989
$160$	2.41585	0.190990
$161$	−3.10024	−0.244333
$162$	−13.7268	−1.07848
$163$	13.3751	1.04762	0.523810	−	0.851835i	$-0.324510\pi$
$163$	13.3751	1.04762	0.523810	+	0.851835i	$0.324510\pi$
$164$	−12.3273	−0.962602
$165$	−7.44525	−0.579612
$166$	3.04574	0.236395
$167$	−21.9723	−1.70027	−0.850135	−	0.526565i	$-0.823480\pi$
$167$	−21.9723	−1.70027	−0.850135	+	0.526565i	$0.823480\pi$
$168$	4.41585	0.340690
$169$	10.5101	0.808466
$170$	16.5455	1.26898
$171$	−52.0619	−3.98127
$172$	9.91353	0.755900
$173$	8.91611	0.677879	0.338940	−	0.940808i	$-0.389932\pi$
$173$	8.91611	0.677879	0.338940	+	0.940808i	$0.389932\pi$
$174$	2.21404	0.167846
$175$	1.19836	0.0905875
$176$	−1.00000	−0.0753778
$177$	18.4788	1.38895
$178$	−18.2769	−1.36992
$179$	13.3608	0.998636	0.499318	−	0.866419i	$-0.333584\pi$
$179$	13.3608	0.998636	0.499318	+	0.866419i	$0.333584\pi$
$180$	−15.6974	−1.17002
$181$	−4.31031	−0.320383	−0.160191	−	0.987086i	$-0.551211\pi$
$181$	−4.31031	−0.320383	−0.160191	+	0.987086i	$0.551211\pi$
$182$	6.94756	0.514988
$183$	−3.08183	−0.227816
$184$	2.16366	0.159507
$185$	14.6122	1.07431
$186$	−19.1570	−1.40466
$187$	−6.84872	−0.500828
$188$	1.76689	0.128863
$189$	−15.4452	−1.12348
$190$	−19.3567	−1.40428
$191$	13.3504	0.965999	0.482999	−	0.875621i	$-0.339547\pi$
$191$	13.3504	0.965999	0.482999	+	0.875621i	$0.339547\pi$
$192$	−3.08183	−0.222412
$193$	14.7165	1.05932	0.529659	−	0.848211i	$-0.322320\pi$
$193$	14.7165	1.05932	0.529659	+	0.848211i	$0.322320\pi$
$194$	−2.94689	−0.211575
$195$	−36.0999	−2.58517
$196$	−4.94689	−0.353350
$197$	6.61751	0.471478	0.235739	−	0.971816i	$-0.424249\pi$
$197$	6.61751	0.471478	0.235739	+	0.971816i	$0.424249\pi$
$198$	6.49768	0.461770
$199$	−12.3313	−0.874142	−0.437071	−	0.899427i	$-0.643984\pi$
$199$	−12.3313	−0.874142	−0.437071	+	0.899427i	$0.643984\pi$
$200$	−0.836338	−0.0591380
$201$	3.65928	0.258106
$202$	−18.7772	−1.32116
$203$	1.02939	0.0722493
$204$	−21.1066	−1.47776
$205$	29.7810	2.07999
$206$	−15.1466	−1.05532
$207$	−14.0588	−0.977153
$208$	−4.84872	−0.336198
$209$	8.01238	0.554228
$210$	−10.6680	−0.736165
$211$	25.3227	1.74329	0.871643	−	0.490141i	$-0.163055\pi$
$211$	25.3227	1.74329	0.871643	+	0.490141i	$0.163055\pi$
$212$	10.1466	0.696875
$213$	−18.3294	−1.25591
$214$	−6.39678	−0.437275
$215$	−23.9496	−1.63335
$216$	10.7793	0.733436
$217$	−8.90684	−0.604636
$218$	−4.94689	−0.335046
$219$	−36.2048	−2.44649
$220$	2.41585	0.162877
$221$	−33.2075	−2.23378
$222$	−18.6404	−1.25106
$223$	−3.27952	−0.219613	−0.109807	−	0.993953i	$-0.535023\pi$
$223$	−3.27952	−0.219613	−0.109807	+	0.993953i	$0.535023\pi$
$224$	−1.43287	−0.0957374
$225$	5.43426	0.362284
$226$	1.11725	0.0743186
$227$	−14.5107	−0.963111	−0.481556	−	0.876416i	$-0.659928\pi$
$227$	−14.5107	−0.963111	−0.481556	+	0.876416i	$0.659928\pi$
$228$	24.6928	1.63532
$229$	27.0760	1.78923	0.894615	−	0.446838i	$-0.147450\pi$
$229$	27.0760	1.78923	0.894615	+	0.446838i	$0.147450\pi$
$230$	−5.22709	−0.344664
$231$	4.41585	0.290542
$232$	−0.718416	−0.0471663
$233$	20.0124	1.31105	0.655527	−	0.755171i	$-0.272446\pi$
$233$	20.0124	1.31105	0.655527	+	0.755171i	$0.272446\pi$
$234$	31.5054	2.05957
$235$	−4.26854	−0.278449
$236$	−5.99603	−0.390309
$237$	41.9991	2.72814
$238$	−9.81330	−0.636101
$239$	9.67769	0.625998	0.312999	−	0.949753i	$-0.398666\pi$
$239$	9.67769	0.625998	0.312999	+	0.949753i	$0.398666\pi$
$240$	7.44525	0.480589
$241$	1.94962	0.125586	0.0627932	−	0.998027i	$-0.479999\pi$
$241$	1.94962	0.125586	0.0627932	+	0.998027i	$0.479999\pi$
$242$	−1.00000	−0.0642824
$243$	−9.96597	−0.639317
$244$	1.00000	0.0640184
$245$	11.9510	0.763519
$246$	−37.9907	−2.42220
$247$	38.8498	2.47195
$248$	6.21610	0.394723
$249$	9.38646	0.594843
$250$	−10.0588	−0.636174
$251$	−11.6784	−0.737131	−0.368566	−	0.929602i	$-0.620151\pi$
$251$	−11.6784	−0.737131	−0.368566	+	0.929602i	$0.620151\pi$
$252$	9.31031	0.586494
$253$	2.16366	0.136028
$254$	6.94293	0.435638
$255$	50.9904	3.19314
$256$	1.00000	0.0625000
$257$	−8.91750	−0.556258	−0.278129	−	0.960544i	$-0.589714\pi$
$257$	−8.91750	−0.556258	−0.278129	+	0.960544i	$0.589714\pi$
$258$	30.5518	1.90207
$259$	−8.66665	−0.538519
$260$	11.7138	0.726458
$261$	4.66804	0.288944
$262$	2.41858	0.149420
$263$	11.9857	0.739071	0.369535	−	0.929217i	$-0.379517\pi$
$263$	11.9857	0.739071	0.369535	+	0.929217i	$0.379517\pi$
$264$	−3.08183	−0.189674
$265$	−24.5128	−1.50581
$266$	11.4807	0.703925
$267$	−56.3265	−3.44712
$268$	−1.18737	−0.0725304
$269$	16.1721	0.986029	0.493014	−	0.870021i	$-0.335895\pi$
$269$	16.1721	0.986029	0.493014	+	0.870021i	$0.335895\pi$
$270$	−26.0411	−1.58481
$271$	−15.2455	−0.926098	−0.463049	−	0.886333i	$-0.653245\pi$
$271$	−15.2455	−0.926098	−0.463049	+	0.886333i	$0.653245\pi$
$272$	6.84872	0.415264
$273$	21.4112	1.29587
$274$	1.41652	0.0855751
$275$	−0.836338	−0.0504331
$276$	6.66804	0.401369
$277$	−22.3521	−1.34301	−0.671503	−	0.741002i	$-0.734351\pi$
$277$	−22.3521	−1.34301	−0.671503	+	0.741002i	$0.734351\pi$
$278$	15.2455	0.914364
$279$	−40.3902	−2.41810
$280$	3.46159	0.206870
$281$	−4.78323	−0.285344	−0.142672	−	0.989770i	$-0.545569\pi$
$281$	−4.78323	−0.285344	−0.142672	+	0.989770i	$0.545569\pi$
$282$	5.44525	0.324260
$283$	28.6670	1.70408	0.852039	−	0.523478i	$-0.175366\pi$
$283$	28.6670	1.70408	0.852039	+	0.523478i	$0.175366\pi$
$284$	5.94756	0.352923
$285$	−59.6541	−3.53361
$286$	−4.84872	−0.286711
$287$	−17.6634	−1.04264
$288$	−6.49768	−0.382880
$289$	29.9049	1.75911
$290$	1.73559	0.101917
$291$	−9.08183	−0.532386
$292$	11.7478	0.687489
$293$	−13.4760	−0.787278	−0.393639	−	0.919265i	$-0.628784\pi$
$293$	−13.4760	−0.787278	−0.393639	+	0.919265i	$0.628784\pi$
$294$	−15.2455	−0.889135
$295$	14.4855	0.843380
$296$	6.04847	0.351560
$297$	10.7793	0.625476
$298$	−1.33402	−0.0772777
$299$	10.4910	0.606709
$300$	−2.57745	−0.148809
$301$	14.2048	0.818749
$302$	9.69471	0.557868
$303$	−57.8682	−3.32444
$304$	−8.01238	−0.459541
$305$	−2.41585	−0.138331
$306$	−44.5008	−2.54394
$307$	0.419250	0.0239279	0.0119639	−	0.999928i	$-0.496192\pi$
$307$	0.419250	0.0239279	0.0119639	+	0.999928i	$0.496192\pi$
$308$	−1.43287	−0.0816451
$309$	−46.6794	−2.65550
$310$	−15.0172	−0.852918
$311$	−4.81742	−0.273171	−0.136585	−	0.990628i	$-0.543613\pi$
$311$	−4.81742	−0.273171	−0.136585	+	0.990628i	$0.543613\pi$
$312$	−14.9429	−0.845977
$313$	−0.219497	−0.0124067	−0.00620336	−	0.999981i	$-0.501975\pi$
$313$	−0.219497	−0.0124067	−0.00620336	+	0.999981i	$0.501975\pi$
$314$	15.9096	0.897829
$315$	−22.4923	−1.26730
$316$	−13.6280	−0.766634
$317$	−2.41585	−0.135688	−0.0678439	−	0.997696i	$-0.521612\pi$
$317$	−2.41585	−0.135688	−0.0678439	+	0.997696i	$0.521612\pi$
$318$	31.2703	1.75355
$319$	−0.718416	−0.0402236
$320$	−2.41585	−0.135050
$321$	−19.7138	−1.10032
$322$	3.10024	0.172770
$323$	−54.8745	−3.05330
$324$	13.7268	0.762602
$325$	−4.05517	−0.224940
$326$	−13.3751	−0.740780
$327$	−15.2455	−0.843078
$328$	12.3273	0.680663
$329$	2.53171	0.139578
$330$	7.44525	0.409847
$331$	−19.8324	−1.09009	−0.545043	−	0.838408i	$-0.683487\pi$
$331$	−19.8324	−1.09009	−0.545043	+	0.838408i	$0.683487\pi$
$332$	−3.04574	−0.167157
$333$	−39.3010	−2.15368
$334$	21.9723	1.20227
$335$	2.86852	0.156724
$336$	−4.41585	−0.240904
$337$	21.3779	1.16453	0.582263	−	0.813000i	$-0.302167\pi$
$337$	21.3779	1.16453	0.582263	+	0.813000i	$0.302167\pi$
$338$	−10.5101	−0.571672
$339$	3.44318	0.187008
$340$	−16.5455	−0.897305
$341$	6.21610	0.336621
$342$	52.0619	2.81519
$343$	−17.1183	−0.924301
$344$	−9.91353	−0.534502
$345$	−16.1090	−0.867279
$346$	−8.91611	−0.479333
$347$	1.34846	0.0723892	0.0361946	−	0.999345i	$-0.488476\pi$
$347$	1.34846	0.0723892	0.0361946	+	0.999345i	$0.488476\pi$
$348$	−2.21404	−0.118685
$349$	29.9567	1.60355	0.801773	−	0.597629i	$-0.203890\pi$
$349$	29.9567	1.60355	0.801773	+	0.597629i	$0.203890\pi$
$350$	−1.19836	−0.0640551
$351$	52.2656	2.78973
$352$	1.00000	0.0533002
$353$	−8.37579	−0.445799	−0.222899	−	0.974841i	$-0.571552\pi$
$353$	−8.37579	−0.445799	−0.222899	+	0.974841i	$0.571552\pi$
$354$	−18.4788	−0.982135
$355$	−14.3684	−0.762597
$356$	18.2769	0.968676
$357$	−30.2429	−1.60063
$358$	−13.3608	−0.706142
$359$	7.98092	0.421217	0.210609	−	0.977570i	$-0.432455\pi$
$359$	7.98092	0.421217	0.210609	+	0.977570i	$0.432455\pi$
$360$	15.6974	0.827327
$361$	45.1982	2.37885
$362$	4.31031	0.226545
$363$	−3.08183	−0.161754
$364$	−6.94756	−0.364151
$365$	−28.3810	−1.48553
$366$	3.08183	0.161090
$367$	−18.4937	−0.965364	−0.482682	−	0.875796i	$-0.660337\pi$
$367$	−18.4937	−0.965364	−0.482682	+	0.875796i	$0.660337\pi$
$368$	−2.16366	−0.112789
$369$	−80.0990	−4.16979
$370$	−14.6122	−0.759652
$371$	14.5388	0.754816
$372$	19.1570	0.993242
$373$	−21.8284	−1.13023	−0.565116	−	0.825011i	$-0.691169\pi$
$373$	−21.8284	−1.13023	−0.565116	+	0.825011i	$0.691169\pi$
$374$	6.84872	0.354139
$375$	−30.9995	−1.60081
$376$	−1.76689	−0.0911202
$377$	−3.48340	−0.179404
$378$	15.4452	0.794418
$379$	5.14474	0.264268	0.132134	−	0.991232i	$-0.457817\pi$
$379$	5.14474	0.264268	0.132134	+	0.991232i	$0.457817\pi$
$380$	19.3567	0.992979
$381$	21.3969	1.09620
$382$	−13.3504	−0.683064
$383$	−10.6206	−0.542688	−0.271344	−	0.962482i	$-0.587468\pi$
$383$	−10.6206	−0.542688	−0.271344	+	0.962482i	$0.587468\pi$
$384$	3.08183	0.157269
$385$	3.46159	0.176419
$386$	−14.7165	−0.749051
$387$	64.4150	3.27440
$388$	2.94689	0.149606
$389$	12.7812	0.648031	0.324016	−	0.946052i	$-0.394967\pi$
$389$	12.7812	0.648031	0.324016	+	0.946052i	$0.394967\pi$
$390$	36.0999	1.82799
$391$	−14.8183	−0.749394
$392$	4.94689	0.249856
$393$	7.45366	0.375987
$394$	−6.61751	−0.333385
$395$	32.9232	1.65655
$396$	−6.49768	−0.326521
$397$	0.224512	0.0112679	0.00563396	−	0.999984i	$-0.498207\pi$
$397$	0.224512	0.0112679	0.00563396	+	0.999984i	$0.498207\pi$
$398$	12.3313	0.618112
$399$	35.3815	1.77129
$400$	0.836338	0.0418169
$401$	−13.3404	−0.666186	−0.333093	−	0.942894i	$-0.608092\pi$
$401$	−13.3404	−0.666186	−0.333093	+	0.942894i	$0.608092\pi$
$402$	−3.65928	−0.182508
$403$	30.1401	1.50139
$404$	18.7772	0.934201
$405$	−33.1620	−1.64783
$406$	−1.02939	−0.0510880
$407$	6.04847	0.299812
$408$	21.1066	1.04493
$409$	−0.585541	−0.0289531	−0.0144766	−	0.999895i	$-0.504608\pi$
$409$	−0.585541	−0.0289531	−0.0144766	+	0.999895i	$0.504608\pi$
$410$	−29.7810	−1.47078
$411$	4.36548	0.215333
$412$	15.1466	0.746222
$413$	−8.59151	−0.422761
$414$	14.0588	0.690952
$415$	7.35806	0.361193
$416$	4.84872	0.237728
$417$	46.9840	2.30082
$418$	−8.01238	−0.391898
$419$	14.6082	0.713659	0.356830	−	0.934169i	$-0.383858\pi$
$419$	14.6082	0.713659	0.356830	+	0.934169i	$0.383858\pi$
$420$	10.6680	0.520547
$421$	−21.8761	−1.06617	−0.533087	−	0.846061i	$-0.678968\pi$
$421$	−21.8761	−1.06617	−0.533087	+	0.846061i	$0.678968\pi$
$422$	−25.3227	−1.23269
$423$	11.4807	0.558209
$424$	−10.1466	−0.492765
$425$	5.72784	0.277841
$426$	18.3294	0.888062
$427$	1.43287	0.0693413
$428$	6.39678	0.309200
$429$	−14.9429	−0.721451
$430$	23.9496	1.15495
$431$	33.2991	1.60396	0.801981	−	0.597349i	$-0.203779\pi$
$431$	33.2991	1.60396	0.801981	+	0.597349i	$0.203779\pi$
$432$	−10.7793	−0.518618
$433$	38.8976	1.86930	0.934649	−	0.355572i	$-0.115714\pi$
$433$	38.8976	1.86930	0.934649	+	0.355572i	$0.115714\pi$
$434$	8.90684	0.427542
$435$	5.34879	0.256455
$436$	4.94689	0.236913
$437$	17.3361	0.829297
$438$	36.2048	1.72993
$439$	23.9001	1.14069	0.570346	−	0.821405i	$-0.306809\pi$
$439$	23.9001	1.14069	0.570346	+	0.821405i	$0.306809\pi$
$440$	−2.41585	−0.115171
$441$	−32.1433	−1.53064
$442$	33.2075	1.57952
$443$	12.5775	0.597573	0.298786	−	0.954320i	$-0.403418\pi$
$443$	12.5775	0.597573	0.298786	+	0.954320i	$0.403418\pi$
$444$	18.6404	0.884632
$445$	−44.1544	−2.09312
$446$	3.27952	0.155290
$447$	−4.11123	−0.194454
$448$	1.43287	0.0676966
$449$	−0.458482	−0.0216371	−0.0108186	−	0.999941i	$-0.503444\pi$
$449$	−0.458482	−0.0216371	−0.0108186	+	0.999941i	$0.503444\pi$
$450$	−5.43426	−0.256173
$451$	12.3273	0.580471
$452$	−1.11725	−0.0525512
$453$	29.8774	1.40376
$454$	14.5107	0.681022
$455$	16.7843	0.786859
$456$	−24.6928	−1.15635
$457$	38.9024	1.81978	0.909888	−	0.414854i	$-0.136168\pi$
$457$	38.9024	1.81978	0.909888	+	0.414854i	$0.136168\pi$
$458$	−27.0760	−1.26518
$459$	−73.8241	−3.44582
$460$	5.22709	0.243714
$461$	0.821897	0.0382796	0.0191398	−	0.999817i	$-0.493907\pi$
$461$	0.821897	0.0382796	0.0191398	+	0.999817i	$0.493907\pi$
$462$	−4.41585	−0.205444
$463$	−21.6661	−1.00691	−0.503455	−	0.864021i	$-0.667938\pi$
$463$	−21.6661	−1.00691	−0.503455	+	0.864021i	$0.667938\pi$
$464$	0.718416	0.0333516
$465$	−46.2804	−2.14620
$466$	−20.0124	−0.927056
$467$	4.26714	0.197460	0.0987299	−	0.995114i	$-0.468522\pi$
$467$	4.26714	0.197460	0.0987299	+	0.995114i	$0.468522\pi$
$468$	−31.5054	−1.45634
$469$	−1.70135	−0.0785609
$470$	4.26854	0.196893
$471$	49.0306	2.25921
$472$	5.99603	0.275990
$473$	−9.91353	−0.455825
$474$	−41.9991	−1.92908
$475$	−6.70106	−0.307466
$476$	9.81330	0.449792
$477$	65.9297	3.01871
$478$	−9.67769	−0.442647
$479$	−24.2463	−1.10784	−0.553921	−	0.832569i	$-0.686869\pi$
$479$	−24.2463	−1.10784	−0.553921	+	0.832569i	$0.686869\pi$
$480$	−7.44525	−0.339827
$481$	29.3273	1.33721
$482$	−1.94962	−0.0888030
$483$	9.55441	0.434741
$484$	1.00000	0.0454545
$485$	−7.11926	−0.323269
$486$	9.96597	0.452066
$487$	−17.5377	−0.794711	−0.397355	−	0.917665i	$-0.630072\pi$
$487$	−17.5377	−0.794711	−0.397355	+	0.917665i	$0.630072\pi$
$488$	−1.00000	−0.0452679
$489$	−41.2199	−1.86403
$490$	−11.9510	−0.539889
$491$	−20.4760	−0.924070	−0.462035	−	0.886862i	$-0.652881\pi$
$491$	−20.4760	−0.924070	−0.462035	+	0.886862i	$0.652881\pi$
$492$	37.9907	1.71275
$493$	4.92023	0.221596
$494$	−38.8498	−1.74793
$495$	15.6974	0.705547
$496$	−6.21610	−0.279111
$497$	8.52206	0.382267
$498$	−9.38646	−0.420617
$499$	−10.9232	−0.488989	−0.244494	−	0.969651i	$-0.578622\pi$
$499$	−10.9232	−0.488989	−0.244494	+	0.969651i	$0.578622\pi$
$500$	10.0588	0.449843
$501$	67.7150	3.02528
$502$	11.6784	0.521231
$503$	−14.9522	−0.666686	−0.333343	−	0.942806i	$-0.608177\pi$
$503$	−14.9522	−0.666686	−0.333343	+	0.942806i	$0.608177\pi$
$504$	−9.31031	−0.414714
$505$	−45.3629	−2.01862
$506$	−2.16366	−0.0961865
$507$	−32.3902	−1.43850
$508$	−6.94293	−0.308043
$509$	29.2709	1.29741	0.648705	−	0.761040i	$-0.275311\pi$
$509$	29.2709	1.29741	0.648705	+	0.761040i	$0.275311\pi$
$510$	−50.9904	−2.25789
$511$	16.8330	0.744650
$512$	−1.00000	−0.0441942
$513$	86.3676	3.81322
$514$	8.91750	0.393334
$515$	−36.5920	−1.61244
$516$	−30.5518	−1.34497
$517$	−1.76689	−0.0777076
$518$	8.66665	0.380791
$519$	−27.4779	−1.20615
$520$	−11.7138	−0.513683
$521$	−16.7050	−0.731860	−0.365930	−	0.930642i	$-0.619249\pi$
$521$	−16.7050	−0.731860	−0.365930	+	0.930642i	$0.619249\pi$
$522$	−4.66804	−0.204315
$523$	36.1805	1.58206	0.791031	−	0.611776i	$-0.209545\pi$
$523$	36.1805	1.58206	0.791031	+	0.611776i	$0.209545\pi$
$524$	−2.41858	−0.105656
$525$	−3.69314	−0.161182
$526$	−11.9857	−0.522602
$527$	−42.5723	−1.85448
$528$	3.08183	0.134119
$529$	−18.3186	−0.796459
$530$	24.5128	1.06477
$531$	−38.9603	−1.69073
$532$	−11.4807	−0.497750
$533$	59.7717	2.58900
$534$	56.3265	2.43748
$535$	−15.4537	−0.668120
$536$	1.18737	0.0512867
$537$	−41.1759	−1.77687
$538$	−16.1721	−0.697228
$539$	4.94689	0.213078
$540$	26.0411	1.12063
$541$	0.155249	0.00667467	0.00333733	−	0.999994i	$-0.498938\pi$
$541$	0.155249	0.00667467	0.00333733	+	0.999994i	$0.498938\pi$
$542$	15.2455	0.654850
$543$	13.2836	0.570056
$544$	−6.84872	−0.293636
$545$	−11.9510	−0.511923
$546$	−21.4112	−0.916315
$547$	−14.9904	−0.640941	−0.320471	−	0.947258i	$-0.603841\pi$
$547$	−14.9904	−0.640941	−0.320471	+	0.947258i	$0.603841\pi$
$548$	−1.41652	−0.0605107
$549$	6.49768	0.277314
$550$	0.836338	0.0356616
$551$	−5.75622	−0.245223
$552$	−6.66804	−0.283811
$553$	−19.5271	−0.830376
$554$	22.3521	0.949649
$555$	−45.0323	−1.91152
$556$	−15.2455	−0.646553
$557$	37.0760	1.57096	0.785479	−	0.618888i	$-0.212416\pi$
$557$	37.0760	1.57096	0.785479	+	0.618888i	$0.212416\pi$
$558$	40.3902	1.70985
$559$	−48.0679	−2.03306
$560$	−3.46159	−0.146279
$561$	21.1066	0.891121
$562$	4.78323	0.201768
$563$	1.49165	0.0628658	0.0314329	−	0.999506i	$-0.489993\pi$
$563$	1.49165	0.0628658	0.0314329	+	0.999506i	$0.489993\pi$
$564$	−5.44525	−0.229286
$565$	2.69912	0.113553
$566$	−28.6670	−1.20497
$567$	19.6687	0.826008
$568$	−5.94756	−0.249554
$569$	21.7045	0.909900	0.454950	−	0.890517i	$-0.349657\pi$
$569$	21.7045	0.909900	0.454950	+	0.890517i	$0.349657\pi$
$570$	59.6541	2.49864
$571$	41.3638	1.73102	0.865510	−	0.500891i	$-0.166994\pi$
$571$	41.3638	1.73102	0.865510	+	0.500891i	$0.166994\pi$
$572$	4.84872	0.202735
$573$	−41.1436	−1.71880
$574$	17.6634	0.737256
$575$	−1.80955	−0.0754636
$576$	6.49768	0.270737
$577$	−20.2211	−0.841816	−0.420908	−	0.907103i	$-0.638288\pi$
$577$	−20.2211	−0.841816	−0.420908	+	0.907103i	$0.638288\pi$
$578$	−29.9049	−1.24388
$579$	−45.3538	−1.88484
$580$	−1.73559	−0.0720663
$581$	−4.36414	−0.181055
$582$	9.08183	0.376454
$583$	−10.1466	−0.420231
$584$	−11.7478	−0.486128
$585$	76.1124	3.14686
$586$	13.4760	0.556690
$587$	21.5082	0.887737	0.443868	−	0.896092i	$-0.353606\pi$
$587$	21.5082	0.887737	0.443868	+	0.896092i	$0.353606\pi$
$588$	15.2455	0.628714
$589$	49.8057	2.05221
$590$	−14.4855	−0.596360
$591$	−20.3940	−0.838899
$592$	−6.04847	−0.248591
$593$	−1.82056	−0.0747614	−0.0373807	−	0.999301i	$-0.511901\pi$
$593$	−1.82056	−0.0747614	−0.0373807	+	0.999301i	$0.511901\pi$
$594$	−10.7793	−0.442279
$595$	−23.7075	−0.971911
$596$	1.33402	0.0546436
$597$	38.0030	1.55536
$598$	−10.4910	−0.429008
$599$	−7.50108	−0.306486	−0.153243	−	0.988189i	$-0.548972\pi$
$599$	−7.50108	−0.306486	−0.153243	+	0.988189i	$0.548972\pi$
$600$	2.57745	0.105224
$601$	36.1217	1.47343	0.736717	−	0.676201i	$-0.236375\pi$
$601$	36.1217	1.47343	0.736717	+	0.676201i	$0.236375\pi$
$602$	−14.2048	−0.578943
$603$	−7.71517	−0.314186
$604$	−9.69471	−0.394472
$605$	−2.41585	−0.0982183
$606$	57.8682	2.35073
$607$	46.7503	1.89753	0.948767	−	0.315976i	$-0.102332\pi$
$607$	46.7503	1.89753	0.948767	+	0.315976i	$0.102332\pi$
$608$	8.01238	0.324945
$609$	−3.17242	−0.128553
$610$	2.41585	0.0978150
$611$	−8.56713	−0.346589
$612$	44.5008	1.79884
$613$	−5.18737	−0.209516	−0.104758	−	0.994498i	$-0.533407\pi$
$613$	−5.18737	−0.209516	−0.104758	+	0.994498i	$0.533407\pi$
$614$	−0.419250	−0.0169196
$615$	−91.7800	−3.70093
$616$	1.43287	0.0577318
$617$	8.88754	0.357799	0.178899	−	0.983867i	$-0.442746\pi$
$617$	8.88754	0.357799	0.178899	+	0.983867i	$0.442746\pi$
$618$	46.6794	1.87772
$619$	33.1393	1.33198	0.665990	−	0.745961i	$-0.268009\pi$
$619$	33.1393	1.33198	0.665990	+	0.745961i	$0.268009\pi$
$620$	15.0172	0.603104
$621$	23.3227	0.935907
$622$	4.81742	0.193161
$623$	26.1884	1.04922
$624$	14.9429	0.598196
$625$	−28.4822	−1.13929
$626$	0.219497	0.00877288
$627$	−24.6928	−0.986135
$628$	−15.9096	−0.634861
$629$	−41.4243	−1.65169
$630$	22.4923	0.896116
$631$	−10.1389	−0.403623	−0.201812	−	0.979424i	$-0.564683\pi$
$631$	−10.1389	−0.403623	−0.201812	+	0.979424i	$0.564683\pi$
$632$	13.6280	0.542092
$633$	−78.0402	−3.10182
$634$	2.41585	0.0959457
$635$	16.7731	0.665619
$636$	−31.2703	−1.23995
$637$	23.9861	0.950364
$638$	0.718416	0.0284424
$639$	38.6454	1.52879
$640$	2.41585	0.0954949
$641$	−37.2001	−1.46932	−0.734658	−	0.678437i	$-0.762658\pi$
$641$	−37.2001	−1.46932	−0.734658	+	0.678437i	$0.762658\pi$
$642$	19.7138	0.778041
$643$	−16.5155	−0.651309	−0.325654	−	0.945489i	$-0.605585\pi$
$643$	−16.5155	−0.651309	−0.325654	+	0.945489i	$0.605585\pi$
$644$	−3.10024	−0.122166
$645$	73.8087	2.90621
$646$	54.8745	2.15901
$647$	21.4813	0.844518	0.422259	−	0.906475i	$-0.361237\pi$
$647$	21.4813	0.844518	0.422259	+	0.906475i	$0.361237\pi$
$648$	−13.7268	−0.539241
$649$	5.99603	0.235365
$650$	4.05517	0.159057
$651$	27.4494	1.07583
$652$	13.3751	0.523810
$653$	−3.71239	−0.145277	−0.0726385	−	0.997358i	$-0.523142\pi$
$653$	−3.71239	−0.145277	−0.0726385	+	0.997358i	$0.523142\pi$
$654$	15.2455	0.596146
$655$	5.84293	0.228302
$656$	−12.3273	−0.481301
$657$	76.3335	2.97806
$658$	−2.53171	−0.0986964
$659$	−27.1563	−1.05786	−0.528930	−	0.848666i	$-0.677406\pi$
$659$	−27.1563	−1.05786	−0.528930	+	0.848666i	$0.677406\pi$
$660$	−7.44525	−0.289806
$661$	−6.27060	−0.243898	−0.121949	−	0.992536i	$-0.538914\pi$
$661$	−6.27060	−0.243898	−0.121949	+	0.992536i	$0.538914\pi$
$662$	19.8324	0.770807
$663$	102.340	3.97455
$664$	3.04574	0.118198
$665$	27.7356	1.07554
$666$	39.3010	1.52288
$667$	−1.55441	−0.0601870
$668$	−21.9723	−0.850135
$669$	10.1069	0.390757
$670$	−2.86852	−0.110820
$671$	−1.00000	−0.0386046
$672$	4.41585	0.170345
$673$	−29.9560	−1.15472	−0.577359	−	0.816490i	$-0.695917\pi$
$673$	−29.9560	−1.15472	−0.577359	+	0.816490i	$0.695917\pi$
$674$	−21.3779	−0.823444
$675$	−9.01511	−0.346992
$676$	10.5101	0.404233
$677$	−9.67975	−0.372023	−0.186012	−	0.982548i	$-0.559556\pi$
$677$	−9.67975	−0.372023	−0.186012	+	0.982548i	$0.559556\pi$
$678$	−3.44318	−0.132235
$679$	4.22251	0.162045
$680$	16.5455	0.634490
$681$	44.7196	1.71366
$682$	−6.21610	−0.238027
$683$	33.8766	1.29625	0.648126	−	0.761533i	$-0.275553\pi$
$683$	33.8766	1.29625	0.648126	+	0.761533i	$0.275553\pi$
$684$	−52.0619	−1.99064
$685$	3.42210	0.130752
$686$	17.1183	0.653580
$687$	−83.4435	−3.18357
$688$	9.91353	0.377950
$689$	−49.1982	−1.87430
$690$	16.1090	0.613259
$691$	−5.85183	−0.222614	−0.111307	−	0.993786i	$-0.535504\pi$
$691$	−5.85183	−0.222614	−0.111307	+	0.993786i	$0.535504\pi$
$692$	8.91611	0.338940
$693$	−9.31031	−0.353669
$694$	−1.34846	−0.0511869
$695$	36.8308	1.39707
$696$	2.21404	0.0839229
$697$	−84.4264	−3.19788
$698$	−29.9567	−1.13388
$699$	−61.6748	−2.33275
$700$	1.19836	0.0452938
$701$	−26.9861	−1.01925	−0.509625	−	0.860396i	$-0.670216\pi$
$701$	−26.9861	−1.01925	−0.509625	+	0.860396i	$0.670216\pi$
$702$	−52.2656	−1.97264
$703$	48.4626	1.82780
$704$	−1.00000	−0.0376889
$705$	13.1549	0.495442
$706$	8.37579	0.315227
$707$	26.9052	1.01188
$708$	18.4788	0.694474
$709$	−22.8080	−0.856572	−0.428286	−	0.903643i	$-0.640882\pi$
$709$	−22.8080	−0.856572	−0.428286	+	0.903643i	$0.640882\pi$
$710$	14.3684	0.539238
$711$	−88.5503	−3.32090
$712$	−18.2769	−0.684958
$713$	13.4495	0.503689
$714$	30.2429	1.13181
$715$	−11.7138	−0.438071
$716$	13.3608	0.499318
$717$	−29.8250	−1.11384
$718$	−7.98092	−0.297845
$719$	0.241527	0.00900743	0.00450371	−	0.999990i	$-0.498566\pi$
$719$	0.241527	0.00900743	0.00450371	+	0.999990i	$0.498566\pi$
$720$	−15.6974	−0.585009
$721$	21.7031	0.808266
$722$	−45.1982	−1.68210
$723$	−6.00841	−0.223455
$724$	−4.31031	−0.160191
$725$	0.600839	0.0223146
$726$	3.08183	0.114377
$727$	5.75724	0.213524	0.106762	−	0.994285i	$-0.465952\pi$
$727$	5.75724	0.213524	0.106762	+	0.994285i	$0.465952\pi$
$728$	6.94756	0.257494
$729$	−10.4671	−0.387669
$730$	28.3810	1.05043
$731$	67.8950	2.51119
$732$	−3.08183	−0.113908
$733$	41.1333	1.51929	0.759646	−	0.650337i	$-0.225372\pi$
$733$	41.1333	1.51929	0.759646	+	0.650337i	$0.225372\pi$
$734$	18.4937	0.682616
$735$	−36.8308	−1.35853
$736$	2.16366	0.0797536
$737$	1.18737	0.0437375
$738$	80.0990	2.94849
$739$	9.64366	0.354748	0.177374	−	0.984144i	$-0.443240\pi$
$739$	9.64366	0.354748	0.177374	+	0.984144i	$0.443240\pi$
$740$	14.6122	0.537155
$741$	−119.728	−4.39833
$742$	−14.5388	−0.533736
$743$	44.3096	1.62556	0.812782	−	0.582569i	$-0.197952\pi$
$743$	44.3096	1.62556	0.812782	+	0.582569i	$0.197952\pi$
$744$	−19.1570	−0.702328
$745$	−3.22279	−0.118074
$746$	21.8284	0.799195
$747$	−19.7903	−0.724088
$748$	−6.84872	−0.250414
$749$	9.16572	0.334908
$750$	30.9995	1.13194
$751$	−22.5973	−0.824585	−0.412293	−	0.911051i	$-0.635272\pi$
$751$	−22.5973	−0.824585	−0.412293	+	0.911051i	$0.635272\pi$
$752$	1.76689	0.0644317
$753$	35.9907	1.31158
$754$	3.48340	0.126858
$755$	23.4210	0.852376
$756$	−15.4452	−0.561738
$757$	−32.7763	−1.19128	−0.595638	−	0.803253i	$-0.703101\pi$
$757$	−32.7763	−1.19128	−0.595638	+	0.803253i	$0.703101\pi$
$758$	−5.14474	−0.186865
$759$	−6.66804	−0.242035
$760$	−19.3567	−0.702142
$761$	5.74920	0.208408	0.104204	−	0.994556i	$-0.466770\pi$
$761$	5.74920	0.208408	0.104204	+	0.994556i	$0.466770\pi$
$762$	−21.3969	−0.775129
$763$	7.08824	0.256611
$764$	13.3504	0.482999
$765$	−107.507	−3.88693
$766$	10.6206	0.383739
$767$	29.0731	1.04977
$768$	−3.08183	−0.111206
$769$	−38.2551	−1.37952	−0.689758	−	0.724040i	$-0.742283\pi$
$769$	−38.2551	−1.37952	−0.689758	+	0.724040i	$0.742283\pi$
$770$	−3.46159	−0.124747
$771$	27.4822	0.989748
$772$	14.7165	0.529659
$773$	−11.6500	−0.419022	−0.209511	−	0.977806i	$-0.567187\pi$
$773$	−11.6500	−0.419022	−0.209511	+	0.977806i	$0.567187\pi$
$774$	−64.4150	−2.31535
$775$	−5.19876	−0.186745
$776$	−2.94689	−0.105787
$777$	26.7091	0.958185
$778$	−12.7812	−0.458227
$779$	98.7712	3.53885
$780$	−36.0999	−1.29258
$781$	−5.94756	−0.212821
$782$	14.8183	0.529902
$783$	−7.74400	−0.276748
$784$	−4.94689	−0.176675
$785$	38.4352	1.37181
$786$	−7.45366	−0.265863
$787$	−47.1498	−1.68071	−0.840354	−	0.542039i	$-0.817653\pi$
$787$	−47.1498	−1.68071	−0.840354	+	0.542039i	$0.817653\pi$
$788$	6.61751	0.235739
$789$	−36.9379	−1.31503
$790$	−32.9232	−1.17135
$791$	−1.60087	−0.0569205
$792$	6.49768	0.230885
$793$	−4.84872	−0.172183
$794$	−0.224512	−0.00796763
$795$	75.5443	2.67928
$796$	−12.3313	−0.437071
$797$	−13.7424	−0.486779	−0.243390	−	0.969929i	$-0.578259\pi$
$797$	−13.7424	−0.486779	−0.243390	+	0.969929i	$0.578259\pi$
$798$	−35.3815	−1.25249
$799$	12.1009	0.428099
$800$	−0.836338	−0.0295690
$801$	118.758	4.19610
$802$	13.3404	0.471065
$803$	−11.7478	−0.414571
$804$	3.65928	0.129053
$805$	7.48971	0.263978
$806$	−30.1401	−1.06164
$807$	−49.8396	−1.75444
$808$	−18.7772	−0.660580
$809$	9.56647	0.336339	0.168169	−	0.985758i	$-0.446214\pi$
$809$	9.56647	0.336339	0.168169	+	0.985758i	$0.446214\pi$
$810$	33.1620	1.16519
$811$	−38.3244	−1.34575	−0.672876	−	0.739755i	$-0.734941\pi$
$811$	−38.3244	−1.34575	−0.672876	+	0.739755i	$0.734941\pi$
$812$	1.02939	0.0361247
$813$	46.9840	1.64780
$814$	−6.04847	−0.211999
$815$	−32.3123	−1.13185
$816$	−21.1066	−0.738878
$817$	−79.4310	−2.77894
$818$	0.585541	0.0204730
$819$	−45.1431	−1.57743
$820$	29.7810	1.04000
$821$	−29.8913	−1.04321	−0.521607	−	0.853186i	$-0.674667\pi$
$821$	−29.8913	−1.04321	−0.521607	+	0.853186i	$0.674667\pi$
$822$	−4.36548	−0.152263
$823$	5.16417	0.180012	0.0900059	−	0.995941i	$-0.471311\pi$
$823$	5.16417	0.180012	0.0900059	+	0.995941i	$0.471311\pi$
$824$	−15.1466	−0.527658
$825$	2.57745	0.0897354
$826$	8.59151	0.298937
$827$	19.4169	0.675192	0.337596	−	0.941291i	$-0.390386\pi$
$827$	19.4169	0.675192	0.337596	+	0.941291i	$0.390386\pi$
$828$	−14.0588	−0.488577
$829$	46.2023	1.60467	0.802336	−	0.596873i	$-0.203590\pi$
$829$	46.2023	1.60467	0.802336	+	0.596873i	$0.203590\pi$
$830$	−7.35806	−0.255402
$831$	68.8853	2.38961
$832$	−4.84872	−0.168099
$833$	−33.8799	−1.17387
$834$	−46.9840	−1.62692
$835$	53.0819	1.83697
$836$	8.01238	0.277114
$837$	67.0050	2.31603
$838$	−14.6082	−0.504633
$839$	−36.5826	−1.26297	−0.631486	−	0.775387i	$-0.717555\pi$
$839$	−36.5826	−1.26297	−0.631486	+	0.775387i	$0.717555\pi$
$840$	−10.6680	−0.368082
$841$	−28.4839	−0.982203
$842$	21.8761	0.753898
$843$	14.7411	0.507711
$844$	25.3227	0.871643
$845$	−25.3907	−0.873468
$846$	−11.4807	−0.394713
$847$	1.43287	0.0492339
$848$	10.1466	0.348437
$849$	−88.3469	−3.03206
$850$	−5.72784	−0.196463
$851$	13.0868	0.448611
$852$	−18.3294	−0.627954
$853$	−14.1984	−0.486144	−0.243072	−	0.970008i	$-0.578155\pi$
$853$	−14.1984	−0.486144	−0.243072	+	0.970008i	$0.578155\pi$
$854$	−1.43287	−0.0490317
$855$	125.774	4.30137
$856$	−6.39678	−0.218637
$857$	27.2845	0.932022	0.466011	−	0.884779i	$-0.345691\pi$
$857$	27.2845	0.932022	0.466011	+	0.884779i	$0.345691\pi$
$858$	14.9429	0.510143
$859$	54.9493	1.87485	0.937423	−	0.348194i	$-0.113205\pi$
$859$	54.9493	1.87485	0.937423	+	0.348194i	$0.113205\pi$
$860$	−23.9496	−0.816675
$861$	54.4356	1.85516
$862$	−33.2991	−1.13417
$863$	−4.34104	−0.147771	−0.0738854	−	0.997267i	$-0.523540\pi$
$863$	−4.34104	−0.147771	−0.0738854	+	0.997267i	$0.523540\pi$
$864$	10.7793	0.366718
$865$	−21.5400	−0.732382
$866$	−38.8976	−1.32179
$867$	−92.1619	−3.12998
$868$	−8.90684	−0.302318
$869$	13.6280	0.462298
$870$	−5.34879	−0.181341
$871$	5.75724	0.195077
$872$	−4.94689	−0.167523
$873$	19.1480	0.648061
$874$	−17.3361	−0.586402
$875$	14.4129	0.487245
$876$	−36.2048	−1.22325
$877$	25.1892	0.850580	0.425290	−	0.905057i	$-0.360172\pi$
$877$	25.1892	0.850580	0.425290	+	0.905057i	$0.360172\pi$
$878$	−23.9001	−0.806591
$879$	41.5309	1.40080
$880$	2.41585	0.0814383
$881$	−3.79714	−0.127929	−0.0639644	−	0.997952i	$-0.520374\pi$
$881$	−3.79714	−0.127929	−0.0639644	+	0.997952i	$0.520374\pi$
$882$	32.1433	1.08232
$883$	−25.7005	−0.864892	−0.432446	−	0.901660i	$-0.642349\pi$
$883$	−25.7005	−0.864892	−0.432446	+	0.901660i	$0.642349\pi$
$884$	−33.2075	−1.11689
$885$	−44.6419	−1.50062
$886$	−12.5775	−0.422548
$887$	−11.9486	−0.401195	−0.200598	−	0.979674i	$-0.564288\pi$
$887$	−11.9486	−0.401195	−0.200598	+	0.979674i	$0.564288\pi$
$888$	−18.6404	−0.625530
$889$	−9.94829	−0.333655
$890$	44.1544	1.48006
$891$	−13.7268	−0.459866
$892$	−3.27952	−0.109807
$893$	−14.1570	−0.473745
$894$	4.11123	0.137500
$895$	−32.2778	−1.07893
$896$	−1.43287	−0.0478687
$897$	−32.3314	−1.07952
$898$	0.458482	0.0152998
$899$	−4.46575	−0.148941
$900$	5.43426	0.181142
$901$	69.4915	2.31510
$902$	−12.3273	−0.410455
$903$	−43.7767	−1.45680
$904$	1.11725	0.0371593
$905$	10.4131	0.346142
$906$	−29.8774	−0.992612
$907$	−9.70435	−0.322228	−0.161114	−	0.986936i	$-0.551509\pi$
$907$	−9.70435	−0.322228	−0.161114	+	0.986936i	$0.551509\pi$
$908$	−14.5107	−0.481556
$909$	122.008	4.04676
$910$	−16.7843	−0.556393
$911$	2.66407	0.0882647	0.0441324	−	0.999026i	$-0.485948\pi$
$911$	2.66407	0.0882647	0.0441324	+	0.999026i	$0.485948\pi$
$912$	24.6928	0.817660
$913$	3.04574	0.100799
$914$	−38.9024	−1.28678
$915$	7.44525	0.246132
$916$	27.0760	0.894615
$917$	−3.46550	−0.114441
$918$	73.8241	2.43656
$919$	−11.7591	−0.387898	−0.193949	−	0.981012i	$-0.562130\pi$
$919$	−11.7591	−0.387898	−0.193949	+	0.981012i	$0.562130\pi$
$920$	−5.22709	−0.172332
$921$	−1.29206	−0.0425748
$922$	−0.821897	−0.0270677
$923$	−28.8381	−0.949216
$924$	4.41585	0.145271
$925$	−5.05857	−0.166325
$926$	21.6661	0.711993
$927$	98.4181	3.23247
$928$	−0.718416	−0.0235832
$929$	−13.3884	−0.439258	−0.219629	−	0.975583i	$-0.570485\pi$
$929$	−13.3884	−0.439258	−0.219629	+	0.975583i	$0.570485\pi$
$930$	46.2804	1.51759
$931$	39.6364	1.29903
$932$	20.0124	0.655527
$933$	14.8465	0.486052
$934$	−4.26714	−0.139625
$935$	16.5455	0.541095
$936$	31.5054	1.02979
$937$	−42.8308	−1.39922	−0.699611	−	0.714524i	$-0.746644\pi$
$937$	−42.8308	−1.39922	−0.699611	+	0.714524i	$0.746644\pi$
$938$	1.70135	0.0555509
$939$	0.676454	0.0220752
$940$	−4.26854	−0.139224
$941$	13.5054	0.440263	0.220131	−	0.975470i	$-0.429351\pi$
$941$	13.5054	0.440263	0.220131	+	0.975470i	$0.429351\pi$
$942$	−49.0306	−1.59750
$943$	26.6722	0.868565
$944$	−5.99603	−0.195154
$945$	37.3134	1.21381
$946$	9.91353	0.322317
$947$	−26.8826	−0.873568	−0.436784	−	0.899567i	$-0.643883\pi$
$947$	−26.8826	−0.873568	−0.436784	+	0.899567i	$0.643883\pi$
$948$	41.9991	1.36407
$949$	−56.9618	−1.84906
$950$	6.70106	0.217411
$951$	7.44525	0.241429
$952$	−9.81330	−0.318051
$953$	−17.0779	−0.553206	−0.276603	−	0.960984i	$-0.589209\pi$
$953$	−17.0779	−0.553206	−0.276603	+	0.960984i	$0.589209\pi$
$954$	−65.9297	−2.13455
$955$	−32.2525	−1.04367
$956$	9.67769	0.312999
$957$	2.21404	0.0715697
$958$	24.2463	0.783363
$959$	−2.02968	−0.0655419
$960$	7.44525	0.240294
$961$	7.63988	0.246448
$962$	−29.3273	−0.945551
$963$	41.5642	1.33939
$964$	1.94962	0.0627932
$965$	−35.5529	−1.14449
$966$	−9.55441	−0.307408
$967$	−13.9778	−0.449495	−0.224748	−	0.974417i	$-0.572156\pi$
$967$	−13.9778	−0.449495	−0.224748	+	0.974417i	$0.572156\pi$
$968$	−1.00000	−0.0321412
$969$	169.114	5.43272
$970$	7.11926	0.228586
$971$	2.73978	0.0879236	0.0439618	−	0.999033i	$-0.486002\pi$
$971$	2.73978	0.0879236	0.0439618	+	0.999033i	$0.486002\pi$
$972$	−9.96597	−0.319659
$973$	−21.8448	−0.700311
$974$	17.5377	0.561945
$975$	12.4973	0.400235
$976$	1.00000	0.0320092
$977$	−32.6419	−1.04431	−0.522153	−	0.852852i	$-0.674871\pi$
$977$	−32.6419	−1.04431	−0.522153	+	0.852852i	$0.674871\pi$
$978$	41.2199	1.31807
$979$	−18.2769	−0.584134
$980$	11.9510	0.381759
$981$	32.1433	1.02626
$982$	20.4760	0.653416
$983$	17.4855	0.557700	0.278850	−	0.960335i	$-0.410047\pi$
$983$	17.4855	0.557700	0.278850	+	0.960335i	$0.410047\pi$
$984$	−37.9907	−1.21110
$985$	−15.9869	−0.509386
$986$	−4.92023	−0.156692
$987$	−7.80231	−0.248350
$988$	38.8498	1.23598
$989$	−21.4495	−0.682056
$990$	−15.6974	−0.498897
$991$	11.8093	0.375136	0.187568	−	0.982252i	$-0.439940\pi$
$991$	11.8093	0.375136	0.187568	+	0.982252i	$0.439940\pi$
$992$	6.21610	0.197361
$993$	61.1200	1.93959
$994$	−8.52206	−0.270303
$995$	29.7906	0.944424
$996$	9.38646	0.297421
$997$	−37.5422	−1.18897	−0.594486	−	0.804106i	$-0.702645\pi$
$997$	−37.5422	−1.18897	−0.594486	+	0.804106i	$0.702645\pi$
$998$	10.9232	0.345767
$999$	65.1981	2.06278

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1342.2.a.i.1.1	✓	4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1342.2.a.i.1.1	✓	4	1.1	even	1	trivial

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 1342 = 2 \cdot 11 \cdot 61 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1342.a (trivial)

\(f(q)\)	\(=\)	\(q-1.00000 q^{2} -3.08183 q^{3} +1.00000 q^{4} -2.41585 q^{5} +3.08183 q^{6} +1.43287 q^{7} -1.00000 q^{8} +6.49768 q^{9} +O(q^{10})\)	\(q-1.00000 q^{2} -3.08183 q^{3} +1.00000 q^{4} -2.41585 q^{5} +3.08183 q^{6} +1.43287 q^{7} -1.00000 q^{8} +6.49768 q^{9} +2.41585 q^{10} -1.00000 q^{11} -3.08183 q^{12} -4.84872 q^{13} -1.43287 q^{14} +7.44525 q^{15} +1.00000 q^{16} +6.84872 q^{17} -6.49768 q^{18} -8.01238 q^{19} -2.41585 q^{20} -4.41585 q^{21} +1.00000 q^{22} -2.16366 q^{23} +3.08183 q^{24} +0.836338 q^{25} +4.84872 q^{26} -10.7793 q^{27} +1.43287 q^{28} +0.718416 q^{29} -7.44525 q^{30} -6.21610 q^{31} -1.00000 q^{32} +3.08183 q^{33} -6.84872 q^{34} -3.46159 q^{35} +6.49768 q^{36} -6.04847 q^{37} +8.01238 q^{38} +14.9429 q^{39} +2.41585 q^{40} -12.3273 q^{41} +4.41585 q^{42} +9.91353 q^{43} -1.00000 q^{44} -15.6974 q^{45} +2.16366 q^{46} +1.76689 q^{47} -3.08183 q^{48} -4.94689 q^{49} -0.836338 q^{50} -21.1066 q^{51} -4.84872 q^{52} +10.1466 q^{53} +10.7793 q^{54} +2.41585 q^{55} -1.43287 q^{56} +24.6928 q^{57} -0.718416 q^{58} -5.99603 q^{59} +7.44525 q^{60} +1.00000 q^{61} +6.21610 q^{62} +9.31031 q^{63} +1.00000 q^{64} +11.7138 q^{65} -3.08183 q^{66} -1.18737 q^{67} +6.84872 q^{68} +6.66804 q^{69} +3.46159 q^{70} +5.94756 q^{71} -6.49768 q^{72} +11.7478 q^{73} +6.04847 q^{74} -2.57745 q^{75} -8.01238 q^{76} -1.43287 q^{77} -14.9429 q^{78} -13.6280 q^{79} -2.41585 q^{80} +13.7268 q^{81} +12.3273 q^{82} -3.04574 q^{83} -4.41585 q^{84} -16.5455 q^{85} -9.91353 q^{86} -2.21404 q^{87} +1.00000 q^{88} +18.2769 q^{89} +15.6974 q^{90} -6.94756 q^{91} -2.16366 q^{92} +19.1570 q^{93} -1.76689 q^{94} +19.3567 q^{95} +3.08183 q^{96} +2.94689 q^{97} +4.94689 q^{98} -6.49768 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q - 4 q^{2} - 2 q^{3} + 4 q^{4} + 2 q^{6} + 3 q^{7} - 4 q^{8} + 6 q^{9}+O(q^{10}) \) 4 * q - 4 * q^2 - 2 * q^3 + 4 * q^4 + 2 * q^6 + 3 * q^7 - 4 * q^8 + 6 * q^9	\( 4 q - 4 q^{2} - 2 q^{3} + 4 q^{4} + 2 q^{6} + 3 q^{7} - 4 q^{8} + 6 q^{9} - 4 q^{11} - 2 q^{12} - 7 q^{13} - 3 q^{14} - 6 q^{15} + 4 q^{16} + 15 q^{17} - 6 q^{18} + q^{19} - 8 q^{21} + 4 q^{22} + 12 q^{23} + 2 q^{24} + 24 q^{25} + 7 q^{26} - 8 q^{27} + 3 q^{28} + 18 q^{29} + 6 q^{30} - 20 q^{31} - 4 q^{32} + 2 q^{33} - 15 q^{34} + 22 q^{35} + 6 q^{36} - 7 q^{37} - q^{38} + 4 q^{39} - 8 q^{41} + 8 q^{42} + 10 q^{43} - 4 q^{44} - 38 q^{45} - 12 q^{46} + 5 q^{47} - 2 q^{48} + 3 q^{49} - 24 q^{50} - 8 q^{51} - 7 q^{52} + 13 q^{53} + 8 q^{54} - 3 q^{56} + 34 q^{57} - 18 q^{58} + 9 q^{59} - 6 q^{60} + 4 q^{61} + 20 q^{62} - 11 q^{63} + 4 q^{64} + 22 q^{65} - 2 q^{66} - 33 q^{67} + 15 q^{68} + 28 q^{69} - 22 q^{70} + 8 q^{71} - 6 q^{72} + 36 q^{73} + 7 q^{74} + 22 q^{75} + q^{76} - 3 q^{77} - 4 q^{78} - 7 q^{79} + 4 q^{81} + 8 q^{82} + 14 q^{83} - 8 q^{84} - 22 q^{85} - 10 q^{86} - 2 q^{87} + 4 q^{88} + 18 q^{89} + 38 q^{90} - 12 q^{91} + 12 q^{92} + 14 q^{93} - 5 q^{94} + 10 q^{95} + 2 q^{96} - 11 q^{97} - 3 q^{98} - 6 q^{99}+O(q^{100}) \) 4 * q - 4 * q^2 - 2 * q^3 + 4 * q^4 + 2 * q^6 + 3 * q^7 - 4 * q^8 + 6 * q^9 - 4 * q^11 - 2 * q^12 - 7 * q^13 - 3 * q^14 - 6 * q^15 + 4 * q^16 + 15 * q^17 - 6 * q^18 + q^19 - 8 * q^21 + 4 * q^22 + 12 * q^23 + 2 * q^24 + 24 * q^25 + 7 * q^26 - 8 * q^27 + 3 * q^28 + 18 * q^29 + 6 * q^30 - 20 * q^31 - 4 * q^32 + 2 * q^33 - 15 * q^34 + 22 * q^35 + 6 * q^36 - 7 * q^37 - q^38 + 4 * q^39 - 8 * q^41 + 8 * q^42 + 10 * q^43 - 4 * q^44 - 38 * q^45 - 12 * q^46 + 5 * q^47 - 2 * q^48 + 3 * q^49 - 24 * q^50 - 8 * q^51 - 7 * q^52 + 13 * q^53 + 8 * q^54 - 3 * q^56 + 34 * q^57 - 18 * q^58 + 9 * q^59 - 6 * q^60 + 4 * q^61 + 20 * q^62 - 11 * q^63 + 4 * q^64 + 22 * q^65 - 2 * q^66 - 33 * q^67 + 15 * q^68 + 28 * q^69 - 22 * q^70 + 8 * q^71 - 6 * q^72 + 36 * q^73 + 7 * q^74 + 22 * q^75 + q^76 - 3 * q^77 - 4 * q^78 - 7 * q^79 + 4 * q^81 + 8 * q^82 + 14 * q^83 - 8 * q^84 - 22 * q^85 - 10 * q^86 - 2 * q^87 + 4 * q^88 + 18 * q^89 + 38 * q^90 - 12 * q^91 + 12 * q^92 + 14 * q^93 - 5 * q^94 + 10 * q^95 + 2 * q^96 - 11 * q^97 - 3 * q^98 - 6 * q^99

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