LMFDB - Embedded newform 134.2.a.a.1.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [134,2,Mod(1,134)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(134, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("134.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 134 = 2 \cdot 67 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	134.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:	$1.06999538709$
Analytic rank:	$0$
Dimension:	$3$
Coefficient field:	3.3.473.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{3} - 5x - 1 $ x^3 - 5*x - 1
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.3
Root			$2.33006$ of defining polynomial
Character	$\chi$	$=$	134.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.00000 q^{2} +2.42917 q^{3} +1.00000 q^{4} +3.33006 q^{5} -2.42917 q^{6} -4.66012 q^{7} -1.00000 q^{8} +2.90089 q^{9} +O(q^{10})$	\(q-1.00000 q^{2} +2.42917 q^{3} +1.00000 q^{4} +3.33006 q^{5} -2.42917 q^{6} -4.66012 q^{7} -1.00000 q^{8} +2.90089 q^{9} -3.33006 q^{10} -4.75923 q^{11} +2.42917 q^{12} +3.90089 q^{13} +4.66012 q^{14} +8.08929 q^{15} +1.00000 q^{16} -3.33006 q^{17} -2.90089 q^{18} +2.00000 q^{19} +3.33006 q^{20} -11.3202 q^{21} +4.75923 q^{22} -1.57083 q^{23} -2.42917 q^{24} +6.08929 q^{25} -3.90089 q^{26} -0.240768 q^{27} -4.66012 q^{28} -8.08929 q^{30} +6.46189 q^{31} -1.00000 q^{32} -11.5610 q^{33} +3.33006 q^{34} -15.5185 q^{35} +2.90089 q^{36} -7.51846 q^{37} -2.00000 q^{38} +9.47593 q^{39} -3.33006 q^{40} -5.05658 q^{41} +11.3202 q^{42} +3.13183 q^{43} -4.75923 q^{44} +9.66012 q^{45} +1.57083 q^{46} +4.75923 q^{47} +2.42917 q^{48} +14.7167 q^{49} -6.08929 q^{50} -8.08929 q^{51} +3.90089 q^{52} +0.627404 q^{53} +0.240768 q^{54} -15.8485 q^{55} +4.66012 q^{56} +4.85835 q^{57} -13.9804 q^{59} +8.08929 q^{60} +8.62740 q^{61} -6.46189 q^{62} -13.5185 q^{63} +1.00000 q^{64} +12.9902 q^{65} +11.5610 q^{66} +1.00000 q^{67} -3.33006 q^{68} -3.81581 q^{69} +15.5185 q^{70} +12.8485 q^{71} -2.90089 q^{72} +1.41935 q^{73} +7.51846 q^{74} +14.7919 q^{75} +2.00000 q^{76} +22.1786 q^{77} -9.47593 q^{78} +7.05658 q^{79} +3.33006 q^{80} -9.28752 q^{81} +5.05658 q^{82} -11.0566 q^{83} -11.3202 q^{84} -11.0893 q^{85} -3.13183 q^{86} +4.75923 q^{88} +3.76906 q^{89} -9.66012 q^{90} -18.1786 q^{91} -1.57083 q^{92} +15.6970 q^{93} -4.75923 q^{94} +6.66012 q^{95} -2.42917 q^{96} -14.1786 q^{97} -14.7167 q^{98} -13.8060 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 3 q - 3 q^{2} + q^{3} + 3 q^{4} + 3 q^{5} - q^{6} - 3 q^{8} + 8 q^{9}+O(q^{10}) $ 3 * q - 3 * q^2 + q^3 + 3 * q^4 + 3 * q^5 - q^6 - 3 * q^8 + 8 * q^9	$ 3 q - 3 q^{2} + q^{3} + 3 q^{4} + 3 q^{5} - q^{6} - 3 q^{8} + 8 q^{9} - 3 q^{10} - q^{11} + q^{12} + 11 q^{13} + 4 q^{15} + 3 q^{16} - 3 q^{17} - 8 q^{18} + 6 q^{19} + 3 q^{20} - 6 q^{21} + q^{22} - 11 q^{23} - q^{24} - 2 q^{25} - 11 q^{26} - 14 q^{27} - 4 q^{30} + 4 q^{31} - 3 q^{32} - 20 q^{33} + 3 q^{34} - 20 q^{35} + 8 q^{36} + 4 q^{37} - 6 q^{38} - 10 q^{39} - 3 q^{40} - 4 q^{41} + 6 q^{42} + q^{43} - q^{44} + 15 q^{45} + 11 q^{46} + q^{47} + q^{48} + 19 q^{49} + 2 q^{50} - 4 q^{51} + 11 q^{52} - 3 q^{53} + 14 q^{54} - 14 q^{55} + 2 q^{57} + 4 q^{60} + 21 q^{61} - 4 q^{62} - 14 q^{63} + 3 q^{64} + 18 q^{65} + 20 q^{66} + 3 q^{67} - 3 q^{68} + 13 q^{69} + 20 q^{70} + 5 q^{71} - 8 q^{72} - 23 q^{73} - 4 q^{74} + 22 q^{75} + 6 q^{76} + 26 q^{77} + 10 q^{78} + 10 q^{79} + 3 q^{80} - 9 q^{81} + 4 q^{82} - 22 q^{83} - 6 q^{84} - 13 q^{85} - q^{86} + q^{88} + 19 q^{89} - 15 q^{90} - 14 q^{91} - 11 q^{92} - 20 q^{93} - q^{94} + 6 q^{95} - q^{96} - 2 q^{97} - 19 q^{98} + 4 q^{99}+O(q^{100}) $ 3 * q - 3 * q^2 + q^3 + 3 * q^4 + 3 * q^5 - q^6 - 3 * q^8 + 8 * q^9 - 3 * q^10 - q^11 + q^12 + 11 * q^13 + 4 * q^15 + 3 * q^16 - 3 * q^17 - 8 * q^18 + 6 * q^19 + 3 * q^20 - 6 * q^21 + q^22 - 11 * q^23 - q^24 - 2 * q^25 - 11 * q^26 - 14 * q^27 - 4 * q^30 + 4 * q^31 - 3 * q^32 - 20 * q^33 + 3 * q^34 - 20 * q^35 + 8 * q^36 + 4 * q^37 - 6 * q^38 - 10 * q^39 - 3 * q^40 - 4 * q^41 + 6 * q^42 + q^43 - q^44 + 15 * q^45 + 11 * q^46 + q^47 + q^48 + 19 * q^49 + 2 * q^50 - 4 * q^51 + 11 * q^52 - 3 * q^53 + 14 * q^54 - 14 * q^55 + 2 * q^57 + 4 * q^60 + 21 * q^61 - 4 * q^62 - 14 * q^63 + 3 * q^64 + 18 * q^65 + 20 * q^66 + 3 * q^67 - 3 * q^68 + 13 * q^69 + 20 * q^70 + 5 * q^71 - 8 * q^72 - 23 * q^73 - 4 * q^74 + 22 * q^75 + 6 * q^76 + 26 * q^77 + 10 * q^78 + 10 * q^79 + 3 * q^80 - 9 * q^81 + 4 * q^82 - 22 * q^83 - 6 * q^84 - 13 * q^85 - q^86 + q^88 + 19 * q^89 - 15 * q^90 - 14 * q^91 - 11 * q^92 - 20 * q^93 - q^94 + 6 * q^95 - q^96 - 2 * q^97 - 19 * q^98 + 4 * q^99

Display 100 coefficients 10 coefficients

Coefficient data

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

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

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

$2$	−1.00000	−0.707107
$2$	−1.00000	−0.707107
$3$	2.42917	1.40248	0.701242	−	0.712923i	$-0.252629\pi$
$3$	2.42917	1.40248	0.701242	+	0.712923i	$0.252629\pi$
$4$	1.00000	0.500000
$5$	3.33006	1.48925	0.744624	−	0.667484i	$-0.232629\pi$
$5$	3.33006	1.48925	0.744624	+	0.667484i	$0.232629\pi$
$6$	−2.42917	−0.991706
$7$	−4.66012	−1.76136	−0.880679	−	0.473713i	$-0.842914\pi$
$7$	−4.66012	−1.76136	−0.880679	+	0.473713i	$0.842914\pi$
$8$	−1.00000	−0.353553
$9$	2.90089	0.966962
$10$	−3.33006	−1.05306
$11$	−4.75923	−1.43496	−0.717481	−	0.696578i	$-0.754705\pi$
$11$	−4.75923	−1.43496	−0.717481	+	0.696578i	$0.754705\pi$
$12$	2.42917	0.701242
$13$	3.90089	1.08191	0.540955	−	0.841051i	$-0.318063\pi$
$13$	3.90089	1.08191	0.540955	+	0.841051i	$0.318063\pi$
$14$	4.66012	1.24547
$15$	8.08929	2.08865
$16$	1.00000	0.250000
$17$	−3.33006	−0.807658	−0.403829	−	0.914835i	$-0.632321\pi$
$17$	−3.33006	−0.807658	−0.403829	+	0.914835i	$0.632321\pi$
$18$	−2.90089	−0.683745
$19$	2.00000	0.458831	0.229416	−	0.973329i	$-0.426318\pi$
$19$	2.00000	0.458831	0.229416	+	0.973329i	$0.426318\pi$
$20$	3.33006	0.744624
$21$	−11.3202	−2.47028
$22$	4.75923	1.01467
$23$	−1.57083	−0.327540	−0.163770	−	0.986499i	$-0.552365\pi$
$23$	−1.57083	−0.327540	−0.163770	+	0.986499i	$0.552365\pi$
$24$	−2.42917	−0.495853
$25$	6.08929	1.21786
$26$	−3.90089	−0.765026
$27$	−0.240768	−0.0463357
$28$	−4.66012	−0.880679
$29$	0	0		−	1.00000i	$-0.5\pi$
$29$	0	0			1.00000i	$0.5\pi$
$30$	−8.08929	−1.47690
$31$	6.46189	1.16059	0.580295	−	0.814407i	$-0.302937\pi$
$31$	6.46189	1.16059	0.580295	+	0.814407i	$0.302937\pi$
$32$	−1.00000	−0.176777
$33$	−11.5610	−2.01251
$34$	3.33006	0.571100
$35$	−15.5185	−2.62310
$36$	2.90089	0.483481
$37$	−7.51846	−1.23603	−0.618014	−	0.786167i	$-0.712063\pi$
$37$	−7.51846	−1.23603	−0.618014	+	0.786167i	$0.712063\pi$
$38$	−2.00000	−0.324443
$39$	9.47593	1.51736
$40$	−3.33006	−0.526529
$41$	−5.05658	−0.789705	−0.394852	−	0.918745i	$-0.629204\pi$
$41$	−5.05658	−0.789705	−0.394852	+	0.918745i	$0.629204\pi$
$42$	11.3202	1.74675
$43$	3.13183	0.477599	0.238800	−	0.971069i	$-0.423246\pi$
$43$	3.13183	0.477599	0.238800	+	0.971069i	$0.423246\pi$
$44$	−4.75923	−0.717481
$45$	9.66012	1.44005
$46$	1.57083	0.231606
$47$	4.75923	0.694205	0.347103	−	0.937827i	$-0.387166\pi$
$47$	4.75923	0.694205	0.347103	+	0.937827i	$0.387166\pi$
$48$	2.42917	0.350621
$49$	14.7167	2.10238
$50$	−6.08929	−0.861156
$51$	−8.08929	−1.13273
$52$	3.90089	0.540955
$53$	0.627404	0.0861805	0.0430903	−	0.999071i	$-0.486280\pi$
$53$	0.627404	0.0861805	0.0430903	+	0.999071i	$0.486280\pi$
$54$	0.240768	0.0327643
$55$	−15.8485	−2.13701
$56$	4.66012	0.622734
$57$	4.85835	0.643504
$58$	0	0
$59$	−13.9804	−1.82009	−0.910043	−	0.414513i	$-0.863952\pi$
$59$	−13.9804	−1.82009	−0.910043	+	0.414513i	$0.863952\pi$
$60$	8.08929	1.04432
$61$	8.62740	1.10463	0.552313	−	0.833637i	$-0.313745\pi$
$61$	8.62740	1.10463	0.552313	+	0.833637i	$0.313745\pi$
$62$	−6.46189	−0.820661
$63$	−13.5185	−1.70317
$64$	1.00000	0.125000
$65$	12.9902	1.61123
$66$	11.5610	1.42306
$67$	1.00000	0.122169
$67$	1.00000	0.122169
$68$	−3.33006	−0.403829
$69$	−3.81581	−0.459370
$70$	15.5185	1.85481
$71$	12.8485	1.52484	0.762420	−	0.647083i	$-0.224011\pi$
$71$	12.8485	1.52484	0.762420	+	0.647083i	$0.224011\pi$
$72$	−2.90089	−0.341873
$73$	1.41935	0.166122	0.0830612	−	0.996544i	$-0.473530\pi$
$73$	1.41935	0.166122	0.0830612	+	0.996544i	$0.473530\pi$
$74$	7.51846	0.874004
$75$	14.7919	1.70803
$76$	2.00000	0.229416
$77$	22.1786	2.52748
$78$	−9.47593	−1.07294
$79$	7.05658	0.793927	0.396963	−	0.917834i	$-0.370064\pi$
$79$	7.05658	0.793927	0.396963	+	0.917834i	$0.370064\pi$
$80$	3.33006	0.372312
$81$	−9.28752	−1.03195
$82$	5.05658	0.558406
$83$	−11.0566	−1.21362	−0.606809	−	0.794848i	$-0.707551\pi$
$83$	−11.0566	−1.21362	−0.606809	+	0.794848i	$0.707551\pi$
$84$	−11.3202	−1.23514
$85$	−11.0893	−1.20280
$86$	−3.13183	−0.337714
$87$	0	0
$88$	4.75923	0.507336
$89$	3.76906	0.399519	0.199760	−	0.979845i	$-0.435984\pi$
$89$	3.76906	0.399519	0.199760	+	0.979845i	$0.435984\pi$
$90$	−9.66012	−1.01827
$91$	−18.1786	−1.90563
$92$	−1.57083	−0.163770
$93$	15.6970	1.62771
$94$	−4.75923	−0.490877
$95$	6.66012	0.683314
$96$	−2.42917	−0.247927
$97$	−14.1786	−1.43962	−0.719808	−	0.694173i	$-0.755770\pi$
$97$	−14.1786	−1.43962	−0.719808	+	0.694173i	$0.755770\pi$
$98$	−14.7167	−1.48661
$99$	−13.8060	−1.38755
$100$	6.08929	0.608929
$101$	3.76906	0.375035	0.187518	−	0.982261i	$-0.439956\pi$
$101$	3.76906	0.375035	0.187518	+	0.982261i	$0.439956\pi$
$102$	8.08929	0.800959
$103$	0.712479	0.0702026	0.0351013	−	0.999384i	$-0.488825\pi$
$103$	0.712479	0.0702026	0.0351013	+	0.999384i	$0.488825\pi$
$104$	−3.90089	−0.382513
$105$	−37.6970	−3.67886
$106$	−0.627404	−0.0609388
$107$	8.26366	0.798878	0.399439	−	0.916760i	$-0.369205\pi$
$107$	8.26366	0.798878	0.399439	+	0.916760i	$0.369205\pi$
$108$	−0.240768	−0.0231679
$109$	−1.61336	−0.154532	−0.0772661	−	0.997011i	$-0.524619\pi$
$109$	−1.61336	−0.154532	−0.0772661	+	0.997011i	$0.524619\pi$
$110$	15.8485	1.51110
$111$	−18.2637	−1.73351
$112$	−4.66012	−0.440340
$113$	5.71669	0.537781	0.268891	−	0.963171i	$-0.413343\pi$
$113$	5.71669	0.537781	0.268891	+	0.963171i	$0.413343\pi$
$114$	−4.85835	−0.455026
$115$	−5.23094	−0.487788
$116$	0	0
$117$	11.3160	1.04617
$118$	13.9804	1.28700
$119$	15.5185	1.42258
$120$	−8.08929	−0.738448
$121$	11.6503	1.05912
$122$	−8.62740	−0.781088
$123$	−12.2833	−1.10755
$124$	6.46189	0.580295
$125$	3.62740	0.324445
$126$	13.5185	1.20432
$127$	−5.79195	−0.513952	−0.256976	−	0.966418i	$-0.582726\pi$
$127$	−5.79195	−0.513952	−0.256976	+	0.966418i	$0.582726\pi$
$128$	−1.00000	−0.0883883
$129$	7.60776	0.669826
$130$	−12.9902	−1.13931
$131$	14.5750	1.27343	0.636714	−	0.771100i	$-0.280293\pi$
$131$	14.5750	1.27343	0.636714	+	0.771100i	$0.280293\pi$
$132$	−11.5610	−1.00626
$133$	−9.32023	−0.808167
$134$	−1.00000	−0.0863868
$135$	−0.801770	−0.0690054
$136$	3.33006	0.285550
$137$	−0.660117	−0.0563976	−0.0281988	−	0.999602i	$-0.508977\pi$
$137$	−0.660117	−0.0563976	−0.0281988	+	0.999602i	$0.508977\pi$
$138$	3.81581	0.324823
$139$	15.0369	1.27542	0.637708	−	0.770278i	$-0.279883\pi$
$139$	15.0369	1.27542	0.637708	+	0.770278i	$0.279883\pi$
$140$	−15.5185	−1.31155
$141$	11.5610	0.973612
$142$	−12.8485	−1.07822
$143$	−18.5652	−1.55250
$144$	2.90089	0.241740
$145$	0	0
$146$	−1.41935	−0.117466
$147$	35.7494	2.94856
$148$	−7.51846	−0.618014
$149$	6.00000	0.491539	0.245770	−	0.969328i	$-0.420959\pi$
$149$	6.00000	0.491539	0.245770	+	0.969328i	$0.420959\pi$
$150$	−14.7919	−1.20776
$151$	17.8812	1.45515	0.727577	−	0.686026i	$-0.240646\pi$
$151$	17.8812	1.45515	0.727577	+	0.686026i	$0.240646\pi$
$152$	−2.00000	−0.162221
$153$	−9.66012	−0.780974
$154$	−22.1786	−1.78720
$155$	21.5185	1.72840
$156$	9.47593	0.758681
$157$	18.1786	1.45081	0.725404	−	0.688323i	$-0.241653\pi$
$157$	18.1786	1.45081	0.725404	+	0.688323i	$0.241653\pi$
$158$	−7.05658	−0.561391
$159$	1.52407	0.120867
$160$	−3.33006	−0.263264
$161$	7.32023	0.576915
$162$	9.28752	0.729697
$163$	−3.33988	−0.261600	−0.130800	−	0.991409i	$-0.541755\pi$
$163$	−3.33988	−0.261600	−0.130800	+	0.991409i	$0.541755\pi$
$164$	−5.05658	−0.394852
$165$	−38.4988	−2.99713
$166$	11.0566	0.858157
$167$	−12.9575	−1.00268	−0.501339	−	0.865251i	$-0.667159\pi$
$167$	−12.9575	−1.00268	−0.501339	+	0.865251i	$0.667159\pi$
$168$	11.3202	0.873375
$169$	2.21690	0.170531
$170$	11.0893	0.850510
$171$	5.80177	0.443672
$172$	3.13183	0.238800
$173$	−23.4988	−1.78658	−0.893291	−	0.449479i	$-0.851610\pi$
$173$	−23.4988	−1.78658	−0.893291	+	0.449479i	$0.851610\pi$
$174$	0	0
$175$	−28.3768	−2.14509
$176$	−4.75923	−0.358741
$177$	−33.9607	−2.55264
$178$	−3.76906	−0.282503
$179$	5.96729	0.446016	0.223008	−	0.974817i	$-0.428412\pi$
$179$	5.96729	0.446016	0.223008	+	0.974817i	$0.428412\pi$
$180$	9.66012	0.720023
$181$	6.17858	0.459250	0.229625	−	0.973279i	$-0.426250\pi$
$181$	6.17858	0.459250	0.229625	+	0.973279i	$0.426250\pi$
$182$	18.1786	1.34749
$183$	20.9575	1.54922
$184$	1.57083	0.115803
$185$	−25.0369	−1.84075
$186$	−15.6970	−1.15096
$187$	15.8485	1.15896
$188$	4.75923	0.347103
$189$	1.12200	0.0816139
$190$	−6.66012	−0.483176
$191$	−1.32023	−0.0955288	−0.0477644	−	0.998859i	$-0.515210\pi$
$191$	−1.32023	−0.0955288	−0.0477644	+	0.998859i	$0.515210\pi$
$192$	2.42917	0.175311
$193$	14.4095	1.03722	0.518610	−	0.855011i	$-0.326450\pi$
$193$	14.4095	1.03722	0.518610	+	0.855011i	$0.326450\pi$
$194$	14.1786	1.01796
$195$	31.5554	2.25973
$196$	14.7167	1.05119
$197$	2.18419	0.155617	0.0778086	−	0.996968i	$-0.475208\pi$
$197$	2.18419	0.155617	0.0778086	+	0.996968i	$0.475208\pi$
$198$	13.8060	0.981149
$199$	−5.79195	−0.410580	−0.205290	−	0.978701i	$-0.565814\pi$
$199$	−5.79195	−0.410580	−0.205290	+	0.978701i	$0.565814\pi$
$200$	−6.08929	−0.430578
$201$	2.42917	0.171341
$202$	−3.76906	−0.265190
$203$	0	0
$204$	−8.08929	−0.566364
$205$	−16.8387	−1.17607
$206$	−0.712479	−0.0496408
$207$	−4.55679	−0.316719
$208$	3.90089	0.270478
$209$	−9.51846	−0.658406
$210$	37.6970	2.60134
$211$	0.396460	0.0272934	0.0136467	−	0.999907i	$-0.495656\pi$
$211$	0.396460	0.0272934	0.0136467	+	0.999907i	$0.495656\pi$
$212$	0.627404	0.0430903
$213$	31.2113	2.13856
$214$	−8.26366	−0.564892
$215$	10.4292	0.711264
$216$	0.240768	0.0163822
$217$	−30.1132	−2.04421
$218$	1.61336	0.109271
$219$	3.44785	0.232984
$220$	−15.8485	−1.06851
$221$	−12.9902	−0.873814
$222$	18.2637	1.22578
$223$	−16.8485	−1.12826	−0.564130	−	0.825686i	$-0.690788\pi$
$223$	−16.8485	−1.12826	−0.564130	+	0.825686i	$0.690788\pi$
$224$	4.66012	0.311367
$225$	17.6643	1.17762
$226$	−5.71669	−0.380269
$227$	−19.9804	−1.32614	−0.663071	−	0.748556i	$-0.730747\pi$
$227$	−19.9804	−1.32614	−0.663071	+	0.748556i	$0.730747\pi$
$228$	4.85835	0.321752
$229$	−11.3202	−0.748062	−0.374031	−	0.927416i	$-0.622025\pi$
$229$	−11.3202	−0.748062	−0.374031	+	0.927416i	$0.622025\pi$
$230$	5.23094	0.344918
$231$	53.8756	3.54476
$232$	0	0
$233$	9.23516	0.605015	0.302508	−	0.953147i	$-0.402176\pi$
$233$	9.23516	0.605015	0.302508	+	0.953147i	$0.402176\pi$
$234$	−11.3160	−0.739751
$235$	15.8485	1.03384
$236$	−13.9804	−0.910043
$237$	17.1417	1.11347
$238$	−15.5185	−1.00591
$239$	−13.5381	−0.875708	−0.437854	−	0.899046i	$-0.644261\pi$
$239$	−13.5381	−0.875708	−0.437854	+	0.899046i	$0.644261\pi$
$240$	8.08929	0.522162
$241$	−30.3431	−1.95457	−0.977286	−	0.211924i	$-0.932027\pi$
$241$	−30.3431	−1.95457	−0.977286	+	0.211924i	$0.932027\pi$
$242$	−11.6503	−0.748909
$243$	−21.8387	−1.40095
$244$	8.62740	0.552313
$245$	49.0075	3.13097
$246$	12.2833	0.783155
$247$	7.80177	0.496415
$248$	−6.46189	−0.410330
$249$	−26.8583	−1.70208
$250$	−3.62740	−0.229417
$251$	−7.50864	−0.473941	−0.236971	−	0.971517i	$-0.576155\pi$
$251$	−7.50864	−0.473941	−0.236971	+	0.971517i	$0.576155\pi$
$252$	−13.5185	−0.851583
$253$	7.47593	0.470008
$254$	5.79195	0.363419
$255$	−26.9378	−1.68691
$256$	1.00000	0.0625000
$257$	−11.7027	−0.729992	−0.364996	−	0.931009i	$-0.618930\pi$
$257$	−11.7027	−0.729992	−0.364996	+	0.931009i	$0.618930\pi$
$258$	−7.60776	−0.473638
$259$	35.0369	2.17709
$260$	12.9902	0.805617
$261$	0	0
$262$	−14.5750	−0.900449
$263$	−16.1459	−0.995597	−0.497798	−	0.867293i	$-0.665858\pi$
$263$	−16.1459	−0.995597	−0.497798	+	0.867293i	$0.665858\pi$
$264$	11.5610	0.711531
$265$	2.08929	0.128344
$266$	9.32023	0.571460
$267$	9.15569	0.560319
$268$	1.00000	0.0610847
$269$	7.32023	0.446323	0.223161	−	0.974782i	$-0.428362\pi$
$269$	7.32023	0.446323	0.223161	+	0.974782i	$0.428362\pi$
$270$	0.801770	0.0487942
$271$	32.4422	1.97073	0.985363	−	0.170470i	$-0.0545286\pi$
$271$	32.4422	1.97073	0.985363	+	0.170470i	$0.0545286\pi$
$272$	−3.33006	−0.201914
$273$	−44.1589	−2.67262
$274$	0.660117	0.0398792
$275$	−28.9804	−1.74758
$276$	−3.81581	−0.229685
$277$	−18.5750	−1.11607	−0.558033	−	0.829819i	$-0.688444\pi$
$277$	−18.5750	−1.11607	−0.558033	+	0.829819i	$0.688444\pi$
$278$	−15.0369	−0.901855
$279$	18.7452	1.12225
$280$	15.5185	0.927406
$281$	4.01965	0.239792	0.119896	−	0.992786i	$-0.461744\pi$
$281$	4.01965	0.239792	0.119896	+	0.992786i	$0.461744\pi$
$282$	−11.5610	−0.688448
$283$	−31.3006	−1.86063	−0.930313	−	0.366766i	$-0.880465\pi$
$283$	−31.3006	−1.86063	−0.930313	+	0.366766i	$0.880465\pi$
$284$	12.8485	0.762420
$285$	16.1786	0.958337
$286$	18.5652	1.09778
$287$	23.5642	1.39095
$288$	−2.90089	−0.170936
$289$	−5.91071	−0.347689
$290$	0	0
$291$	−34.4422	−2.01904
$292$	1.41935	0.0830612
$293$	25.9804	1.51779	0.758894	−	0.651214i	$-0.225740\pi$
$293$	25.9804	1.51779	0.758894	+	0.651214i	$0.225740\pi$
$294$	−35.7494	−2.08495
$295$	−46.5554	−2.71056
$296$	7.51846	0.437002
$297$	1.14587	0.0664900
$298$	−6.00000	−0.347571
$299$	−6.12761	−0.354369
$300$	14.7919	0.854013
$301$	−14.5947	−0.841224
$302$	−17.8812	−1.02895
$303$	9.15569	0.525981
$304$	2.00000	0.114708
$305$	28.7298	1.64506
$306$	9.66012	0.552232
$307$	−2.39646	−0.136773	−0.0683866	−	0.997659i	$-0.521785\pi$
$307$	−2.39646	−0.136773	−0.0683866	+	0.997659i	$0.521785\pi$
$308$	22.1786	1.26374
$309$	1.73073	0.0984581
$310$	−21.5185	−1.22217
$311$	−0.594690	−0.0337218	−0.0168609	−	0.999858i	$-0.505367\pi$
$311$	−0.594690	−0.0337218	−0.0168609	+	0.999858i	$0.505367\pi$
$312$	−9.47593	−0.536469
$313$	10.1982	0.576438	0.288219	−	0.957565i	$-0.406937\pi$
$313$	10.1982	0.576438	0.288219	+	0.957565i	$0.406937\pi$
$314$	−18.1786	−1.02588
$315$	−45.0173	−2.53644
$316$	7.05658	0.396963
$317$	4.01965	0.225766	0.112883	−	0.993608i	$-0.463991\pi$
$317$	4.01965	0.225766	0.112883	+	0.993608i	$0.463991\pi$
$318$	−1.52407	−0.0854657
$319$	0	0
$320$	3.33006	0.186156
$321$	20.0739	1.12041
$322$	−7.32023	−0.407941
$323$	−6.66012	−0.370579
$324$	−9.28752	−0.515973
$325$	23.7536	1.31761
$326$	3.33988	0.184979
$327$	−3.91914	−0.216729
$328$	5.05658	0.279203
$329$	−22.1786	−1.22274
$330$	38.4988	2.11929
$331$	22.1688	1.21851	0.609253	−	0.792976i	$-0.291470\pi$
$331$	22.1688	1.21851	0.609253	+	0.792976i	$0.291470\pi$
$332$	−11.0566	−0.606809
$333$	−21.8102	−1.19519
$334$	12.9575	0.709001
$335$	3.33006	0.181941
$336$	−11.3202	−0.617569
$337$	−17.3857	−0.947057	−0.473529	−	0.880778i	$-0.657020\pi$
$337$	−17.3857	−0.947057	−0.473529	+	0.880778i	$0.657020\pi$
$338$	−2.21690	−0.120584
$339$	13.8868	0.754230
$340$	−11.0893	−0.601401
$341$	−30.7536	−1.66540
$342$	−5.80177	−0.313724
$343$	−35.9607	−1.94170
$344$	−3.13183	−0.168857
$345$	−12.7069	−0.684115
$346$	23.4988	1.26330
$347$	5.24498	0.281565	0.140783	−	0.990041i	$-0.455038\pi$
$347$	5.24498	0.281565	0.140783	+	0.990041i	$0.455038\pi$
$348$	0	0
$349$	1.93457	0.103555	0.0517776	−	0.998659i	$-0.483511\pi$
$349$	1.93457	0.103555	0.0517776	+	0.998659i	$0.483511\pi$
$350$	28.3768	1.51680
$351$	−0.939206	−0.0501311
$352$	4.75923	0.253668
$353$	17.7167	0.942965	0.471482	−	0.881876i	$-0.343719\pi$
$353$	17.7167	0.942965	0.471482	+	0.881876i	$0.343719\pi$
$354$	33.9607	1.80499
$355$	42.7863	2.27086
$356$	3.76906	0.199760
$357$	37.6970	1.99514
$358$	−5.96729	−0.315381
$359$	14.6405	0.772694	0.386347	−	0.922353i	$-0.373737\pi$
$359$	14.6405	0.772694	0.386347	+	0.922353i	$0.373737\pi$
$360$	−9.66012	−0.509133
$361$	−15.0000	−0.789474
$362$	−6.17858	−0.324739
$363$	28.3006	1.48540
$364$	−18.1786	−0.952817
$365$	4.72652	0.247397
$366$	−20.9575	−1.09546
$367$	18.4619	0.963703	0.481851	−	0.876253i	$-0.339965\pi$
$367$	18.4619	0.963703	0.481851	+	0.876253i	$0.339965\pi$
$368$	−1.57083	−0.0818850
$369$	−14.6685	−0.763614
$370$	25.0369	1.30161
$371$	−2.92377	−0.151795
$372$	15.6970	0.813854
$373$	−0.495575	−0.0256599	−0.0128299	−	0.999918i	$-0.504084\pi$
$373$	−0.495575	−0.0256599	−0.0128299	+	0.999918i	$0.504084\pi$
$374$	−15.8485	−0.819508
$375$	8.81159	0.455029
$376$	−4.75923	−0.245439
$377$	0	0
$378$	−1.12200	−0.0577097
$379$	−30.2777	−1.55526	−0.777630	−	0.628722i	$-0.783578\pi$
$379$	−30.2777	−1.55526	−0.777630	+	0.628722i	$0.783578\pi$
$380$	6.66012	0.341657
$381$	−14.0696	−0.720810
$382$	1.32023	0.0675491
$383$	−10.6798	−0.545711	−0.272855	−	0.962055i	$-0.587968\pi$
$383$	−10.6798	−0.545711	−0.272855	+	0.962055i	$0.587968\pi$
$384$	−2.42917	−0.123963
$385$	73.8560	3.76405
$386$	−14.4095	−0.733426
$387$	9.08508	0.461820
$388$	−14.1786	−0.719808
$389$	−25.6970	−1.30289	−0.651446	−	0.758695i	$-0.725837\pi$
$389$	−25.6970	−1.30289	−0.651446	+	0.758695i	$0.725837\pi$
$390$	−31.5554	−1.59787
$391$	5.23094	0.264540
$392$	−14.7167	−0.743305
$393$	35.4053	1.78596
$394$	−2.18419	−0.110038
$395$	23.4988	1.18235
$396$	−13.8060	−0.693777
$397$	−20.1786	−1.01273	−0.506367	−	0.862318i	$-0.669012\pi$
$397$	−20.1786	−1.01273	−0.506367	+	0.862318i	$0.669012\pi$
$398$	5.79195	0.290324
$399$	−22.6405	−1.13344
$400$	6.08929	0.304465
$401$	19.3857	0.968074	0.484037	−	0.875048i	$-0.339170\pi$
$401$	19.3857	0.968074	0.484037	+	0.875048i	$0.339170\pi$
$402$	−2.42917	−0.121156
$403$	25.2071	1.25565
$404$	3.76906	0.187518
$405$	−30.9280	−1.53682
$406$	0	0
$407$	35.7821	1.77365
$408$	8.08929	0.400480
$409$	11.8018	0.583560	0.291780	−	0.956485i	$-0.405752\pi$
$409$	11.8018	0.583560	0.291780	+	0.956485i	$0.405752\pi$
$410$	16.8387	0.831604
$411$	−1.60354	−0.0790968
$412$	0.712479	0.0351013
$413$	65.1501	3.20583
$414$	4.55679	0.223954
$415$	−36.8191	−1.80738
$416$	−3.90089	−0.191257
$417$	36.5273	1.78875
$418$	9.51846	0.465563
$419$	−23.1220	−1.12958	−0.564792	−	0.825233i	$-0.691044\pi$
$419$	−23.1220	−1.12958	−0.564792	+	0.825233i	$0.691044\pi$
$420$	−37.6970	−1.83943
$421$	−31.9607	−1.55767	−0.778835	−	0.627229i	$-0.784189\pi$
$421$	−31.9607	−1.55767	−0.778835	+	0.627229i	$0.784189\pi$
$422$	−0.396460	−0.0192994
$423$	13.8060	0.671270
$424$	−0.627404	−0.0304694
$425$	−20.2777	−0.983613
$426$	−31.2113	−1.51219
$427$	−40.2047	−1.94564
$428$	8.26366	0.399439
$429$	−45.0981	−2.17736
$430$	−10.4292	−0.502939
$431$	−37.6830	−1.81513	−0.907563	−	0.419915i	$-0.862060\pi$
$431$	−37.6830	−1.81513	−0.907563	+	0.419915i	$0.862060\pi$
$432$	−0.240768	−0.0115839
$433$	28.5750	1.37323	0.686614	−	0.727022i	$-0.259096\pi$
$433$	28.5750	1.37323	0.686614	+	0.727022i	$0.259096\pi$
$434$	30.1132	1.44548
$435$	0	0
$436$	−1.61336	−0.0772661
$437$	−3.14165	−0.150286
$438$	−3.44785	−0.164745
$439$	17.1089	0.816565	0.408283	−	0.912856i	$-0.366128\pi$
$439$	17.1089	0.816565	0.408283	+	0.912856i	$0.366128\pi$
$440$	15.8485	0.755549
$441$	42.6914	2.03293
$442$	12.9902	0.617880
$443$	0.362773	0.0172358	0.00861792	−	0.999963i	$-0.497257\pi$
$443$	0.362773	0.0172358	0.00861792	+	0.999963i	$0.497257\pi$
$444$	−18.2637	−0.866755
$445$	12.5512	0.594983
$446$	16.8485	0.797801
$447$	14.5750	0.689376
$448$	−4.66012	−0.220170
$449$	−2.00982	−0.0948494	−0.0474247	−	0.998875i	$-0.515101\pi$
$449$	−2.00982	−0.0948494	−0.0474247	+	0.998875i	$0.515101\pi$
$450$	−17.6643	−0.832705
$451$	24.0654	1.13320
$452$	5.71669	0.268891
$453$	43.4366	2.04083
$454$	19.9804	0.937724
$455$	−60.5357	−2.83796
$456$	−4.85835	−0.227513
$457$	10.7634	0.503493	0.251746	−	0.967793i	$-0.418995\pi$
$457$	10.7634	0.503493	0.251746	+	0.967793i	$0.418995\pi$
$458$	11.3202	0.528960
$459$	0.801770	0.0374234
$460$	−5.23094	−0.243894
$461$	−0.660117	−0.0307447	−0.0153724	−	0.999882i	$-0.504893\pi$
$461$	−0.660117	−0.0307447	−0.0153724	+	0.999882i	$0.504893\pi$
$462$	−53.8756	−2.50652
$463$	13.7821	0.640510	0.320255	−	0.947331i	$-0.396231\pi$
$463$	13.7821	0.640510	0.320255	+	0.947331i	$0.396231\pi$
$464$	0	0
$465$	52.2721	2.42406
$466$	−9.23516	−0.427811
$467$	36.4703	1.68765	0.843823	−	0.536622i	$-0.180300\pi$
$467$	36.4703	1.68765	0.843823	+	0.536622i	$0.180300\pi$
$468$	11.3160	0.523083
$469$	−4.66012	−0.215184
$470$	−15.8485	−0.731038
$471$	44.1589	2.03474
$472$	13.9804	0.643498
$473$	−14.9051	−0.685337
$474$	−17.1417	−0.787342
$475$	12.1786	0.558792
$476$	15.5185	0.711288
$477$	1.82003	0.0833333
$478$	13.5381	0.619219
$479$	21.3146	0.973890	0.486945	−	0.873433i	$-0.338111\pi$
$479$	21.3146	0.973890	0.486945	+	0.873433i	$0.338111\pi$
$480$	−8.08929	−0.369224
$481$	−29.3287	−1.33727
$482$	30.3431	1.38209
$483$	17.7821	0.809115
$484$	11.6503	0.529559
$485$	−47.2155	−2.14395
$486$	21.8387	0.990624
$487$	−9.40531	−0.426195	−0.213098	−	0.977031i	$-0.568355\pi$
$487$	−9.40531	−0.426195	−0.213098	+	0.977031i	$0.568355\pi$
$488$	−8.62740	−0.390544
$489$	−8.11315	−0.366890
$490$	−49.0075	−2.21393
$491$	−34.4900	−1.55651	−0.778255	−	0.627948i	$-0.783895\pi$
$491$	−34.4900	−1.55651	−0.778255	+	0.627948i	$0.783895\pi$
$492$	−12.2833	−0.553774
$493$	0	0
$494$	−7.80177	−0.351018
$495$	−45.9747	−2.06641
$496$	6.46189	0.290147
$497$	−59.8756	−2.68579
$498$	26.8583	1.20355
$499$	27.2875	1.22156	0.610779	−	0.791801i	$-0.290857\pi$
$499$	27.2875	1.22156	0.610779	+	0.791801i	$0.290857\pi$
$500$	3.62740	0.162222
$501$	−31.4759	−1.40624
$502$	7.50864	0.335127
$503$	1.91492	0.0853823	0.0426911	−	0.999088i	$-0.486407\pi$
$503$	1.91492	0.0853823	0.0426911	+	0.999088i	$0.486407\pi$
$504$	13.5185	0.602160
$505$	12.5512	0.558520
$506$	−7.47593	−0.332346
$507$	5.38524	0.239167
$508$	−5.79195	−0.256976
$509$	42.0935	1.86576	0.932881	−	0.360185i	$-0.117286\pi$
$509$	42.0935	1.86576	0.932881	+	0.360185i	$0.117286\pi$
$510$	26.9378	1.19283
$511$	−6.61434	−0.292601
$512$	−1.00000	−0.0441942
$513$	−0.481535	−0.0212603
$514$	11.7027	0.516182
$515$	2.37260	0.104549
$516$	7.60776	0.334913
$517$	−22.6503	−0.996159
$518$	−35.0369	−1.53943
$519$	−57.0827	−2.50565
$520$	−12.9902	−0.569657
$521$	−38.7994	−1.69983	−0.849916	−	0.526918i	$-0.823348\pi$
$521$	−38.7994	−1.69983	−0.849916	+	0.526918i	$0.823348\pi$
$522$	0	0
$523$	8.15893	0.356765	0.178383	−	0.983961i	$-0.442914\pi$
$523$	8.15893	0.356765	0.178383	+	0.983961i	$0.442914\pi$
$524$	14.5750	0.636714
$525$	−68.9322	−3.00845
$526$	16.1459	0.703993
$527$	−21.5185	−0.937359
$528$	−11.5610	−0.503128
$529$	−20.5325	−0.892718
$530$	−2.08929	−0.0907530
$531$	−40.5554	−1.75995
$532$	−9.32023	−0.404083
$533$	−19.7251	−0.854390
$534$	−9.15569	−0.396206
$535$	27.5185	1.18973
$536$	−1.00000	−0.0431934
$537$	14.4956	0.625530
$538$	−7.32023	−0.315598
$539$	−70.0402	−3.01684
$540$	−0.801770	−0.0345027
$541$	−41.0510	−1.76492	−0.882460	−	0.470388i	$-0.844114\pi$
$541$	−41.0510	−1.76492	−0.882460	+	0.470388i	$0.844114\pi$
$542$	−32.4422	−1.39351
$543$	15.0089	0.644091
$544$	3.33006	0.142775
$545$	−5.37260	−0.230137
$546$	44.1589	1.88983
$547$	21.2253	0.907530	0.453765	−	0.891121i	$-0.350081\pi$
$547$	21.2253	0.907530	0.453765	+	0.891121i	$0.350081\pi$
$548$	−0.660117	−0.0281988
$549$	25.0271	1.06813
$550$	28.9804	1.23573
$551$	0	0
$552$	3.81581	0.162412
$553$	−32.8845	−1.39839
$554$	18.5750	0.789178
$555$	−60.8191	−2.58162
$556$	15.0369	0.637708
$557$	12.0654	0.511229	0.255614	−	0.966779i	$-0.417722\pi$
$557$	12.0654	0.511229	0.255614	+	0.966779i	$0.417722\pi$
$558$	−18.7452	−0.793547
$559$	12.2169	0.516720
$560$	−15.5185	−0.655775
$561$	38.4988	1.62542
$562$	−4.01965	−0.169559
$563$	18.8050	0.792537	0.396268	−	0.918135i	$-0.370305\pi$
$563$	18.8050	0.792537	0.396268	+	0.918135i	$0.370305\pi$
$564$	11.5610	0.486806
$565$	19.0369	0.800890
$566$	31.3006	1.31566
$567$	43.2809	1.81763
$568$	−12.8485	−0.539112
$569$	14.0131	0.587458	0.293729	−	0.955889i	$-0.405104\pi$
$569$	14.0131	0.587458	0.293729	+	0.955889i	$0.405104\pi$
$570$	−16.1786	−0.677646
$571$	−13.2071	−0.552699	−0.276350	−	0.961057i	$-0.589125\pi$
$571$	−13.2071	−0.552699	−0.276350	+	0.961057i	$0.589125\pi$
$572$	−18.5652	−0.776251
$573$	−3.20708	−0.133978
$574$	−23.5642	−0.983553
$575$	−9.56522	−0.398897
$576$	2.90089	0.120870
$577$	−4.37681	−0.182209	−0.0911045	−	0.995841i	$-0.529040\pi$
$577$	−4.37681	−0.182209	−0.0911045	+	0.995841i	$0.529040\pi$
$578$	5.91071	0.245853
$579$	35.0032	1.45469
$580$	0	0
$581$	51.5249	2.13762
$582$	34.4422	1.42768
$583$	−2.98596	−0.123666
$584$	−1.41935	−0.0587331
$585$	37.6830	1.55800
$586$	−25.9804	−1.07324
$587$	38.3245	1.58182	0.790910	−	0.611933i	$-0.209608\pi$
$587$	38.3245	1.58182	0.790910	+	0.611933i	$0.209608\pi$
$588$	35.7494	1.47428
$589$	12.9238	0.532515
$590$	46.5554	1.91666
$591$	5.30578	0.218251
$592$	−7.51846	−0.309007
$593$	−11.1220	−0.456726	−0.228363	−	0.973576i	$-0.573337\pi$
$593$	−11.1220	−0.456726	−0.228363	+	0.973576i	$0.573337\pi$
$594$	−1.14587	−0.0470156
$595$	51.6774	2.11857
$596$	6.00000	0.245770
$597$	−14.0696	−0.575832
$598$	6.12761	0.250577
$599$	−39.3660	−1.60845	−0.804226	−	0.594324i	$-0.797420\pi$
$599$	−39.3660	−1.60845	−0.804226	+	0.594324i	$0.797420\pi$
$600$	−14.7919	−0.603879
$601$	−21.9083	−0.893660	−0.446830	−	0.894619i	$-0.647447\pi$
$601$	−21.9083	−0.893660	−0.446830	+	0.894619i	$0.647447\pi$
$602$	14.5947	0.594835
$603$	2.90089	0.118133
$604$	17.8812	0.727577
$605$	38.7962	1.57729
$606$	−9.15569	−0.371925
$607$	10.2777	0.417159	0.208579	−	0.978005i	$-0.433116\pi$
$607$	10.2777	0.417159	0.208579	+	0.978005i	$0.433116\pi$
$608$	−2.00000	−0.0811107
$609$	0	0
$610$	−28.7298	−1.16323
$611$	18.5652	0.751068
$612$	−9.66012	−0.390487
$613$	−32.8387	−1.32634	−0.663171	−	0.748468i	$-0.730790\pi$
$613$	−32.8387	−1.32634	−0.663171	+	0.748468i	$0.730790\pi$
$614$	2.39646	0.0967133
$615$	−40.9041	−1.64941
$616$	−22.1786	−0.893601
$617$	9.96070	0.401003	0.200501	−	0.979693i	$-0.435743\pi$
$617$	9.96070	0.401003	0.200501	+	0.979693i	$0.435743\pi$
$618$	−1.73073	−0.0696204
$619$	11.1417	0.447821	0.223910	−	0.974610i	$-0.428118\pi$
$619$	11.1417	0.447821	0.223910	+	0.974610i	$0.428118\pi$
$620$	21.5185	0.864202
$621$	0.378204	0.0151768
$622$	0.594690	0.0238449
$623$	−17.5642	−0.703697
$624$	9.47593	0.379341
$625$	−18.3670	−0.734680
$626$	−10.1982	−0.407603
$627$	−23.1220	−0.923404
$628$	18.1786	0.725404
$629$	25.0369	0.998288
$630$	45.0173	1.79353
$631$	−13.8018	−0.549440	−0.274720	−	0.961524i	$-0.588585\pi$
$631$	−13.8018	−0.549440	−0.274720	+	0.961524i	$0.588585\pi$
$632$	−7.05658	−0.280696
$633$	0.963070	0.0382786
$634$	−4.01965	−0.159641
$635$	−19.2875	−0.765402
$636$	1.52407	0.0604334
$637$	57.4081	2.27459
$638$	0	0
$639$	37.2721	1.47446
$640$	−3.33006	−0.131632
$641$	12.6601	0.500045	0.250022	−	0.968240i	$-0.419562\pi$
$641$	12.6601	0.500045	0.250022	+	0.968240i	$0.419562\pi$
$642$	−20.0739	−0.792252
$643$	−36.7340	−1.44865	−0.724323	−	0.689460i	$-0.757848\pi$
$643$	−36.7340	−1.44865	−0.724323	+	0.689460i	$0.757848\pi$
$644$	7.32023	0.288458
$645$	25.3343	0.997536
$646$	6.66012	0.262039
$647$	−23.8756	−0.938648	−0.469324	−	0.883026i	$-0.655502\pi$
$647$	−23.8756	−0.938648	−0.469324	+	0.883026i	$0.655502\pi$
$648$	9.28752	0.364848
$649$	66.5357	2.61176
$650$	−23.7536	−0.931694
$651$	−73.1501	−2.86698
$652$	−3.33988	−0.130800
$653$	1.47268	0.0576306	0.0288153	−	0.999585i	$-0.490827\pi$
$653$	1.47268	0.0576306	0.0288153	+	0.999585i	$0.490827\pi$
$654$	3.91914	0.153251
$655$	48.5357	1.89645
$656$	−5.05658	−0.197426
$657$	4.11737	0.160634
$658$	22.1786	0.864611
$659$	21.9607	0.855468	0.427734	−	0.903905i	$-0.359312\pi$
$659$	21.9607	0.855468	0.427734	+	0.903905i	$0.359312\pi$
$660$	−38.4988	−1.49856
$661$	−27.6250	−1.07449	−0.537245	−	0.843426i	$-0.680535\pi$
$661$	−27.6250	−1.07449	−0.537245	+	0.843426i	$0.680535\pi$
$662$	−22.1688	−0.861613
$663$	−31.5554	−1.22551
$664$	11.0566	0.429078
$665$	−31.0369	−1.20356
$666$	21.8102	0.845128
$667$	0	0
$668$	−12.9575	−0.501339
$669$	−40.9280	−1.58237
$670$	−3.33006	−0.128651
$671$	−41.0598	−1.58510
$672$	11.3202	0.436688
$673$	15.0089	0.578549	0.289274	−	0.957246i	$-0.406586\pi$
$673$	15.0089	0.578549	0.289274	+	0.957246i	$0.406586\pi$
$674$	17.3857	0.669671
$675$	−1.46610	−0.0564304
$676$	2.21690	0.0852655
$677$	40.8527	1.57010	0.785049	−	0.619433i	$-0.212638\pi$
$677$	40.8527	1.57010	0.785049	+	0.619433i	$0.212638\pi$
$678$	−13.8868	−0.533321
$679$	66.0739	2.53568
$680$	11.0893	0.425255
$681$	−48.5357	−1.85989
$682$	30.7536	1.17762
$683$	43.6395	1.66982	0.834909	−	0.550387i	$-0.185520\pi$
$683$	43.6395	1.66982	0.834909	+	0.550387i	$0.185520\pi$
$684$	5.80177	0.221836
$685$	−2.19823	−0.0839901
$686$	35.9607	1.37299
$687$	−27.4988	−1.04915
$688$	3.13183	0.119400
$689$	2.44743	0.0932396
$690$	12.7069	0.483742
$691$	−22.6601	−0.862031	−0.431016	−	0.902344i	$-0.641845\pi$
$691$	−22.6601	−0.862031	−0.431016	+	0.902344i	$0.641845\pi$
$692$	−23.4988	−0.893291
$693$	64.3375	2.44398
$694$	−5.24498	−0.199097
$695$	50.0739	1.89941
$696$	0	0
$697$	16.8387	0.637811
$698$	−1.93457	−0.0732246
$699$	22.4338	0.848525
$700$	−28.3768	−1.07254
$701$	−4.67977	−0.176752	−0.0883761	−	0.996087i	$-0.528168\pi$
$701$	−4.67977	−0.176752	−0.0883761	+	0.996087i	$0.528168\pi$
$702$	0.939206	0.0354481
$703$	−15.0369	−0.567129
$704$	−4.75923	−0.179370
$705$	38.4988	1.44995
$706$	−17.7167	−0.666777
$707$	−17.5642	−0.660571
$708$	−33.9607	−1.27632
$709$	−12.5096	−0.469808	−0.234904	−	0.972019i	$-0.575478\pi$
$709$	−12.5096	−0.469808	−0.234904	+	0.972019i	$0.575478\pi$
$710$	−42.7863	−1.60574
$711$	20.4703	0.767697
$712$	−3.76906	−0.141251
$713$	−10.1505	−0.380139
$714$	−37.6970	−1.41078
$715$	−61.8233	−2.31206
$716$	5.96729	0.223008
$717$	−32.8864	−1.22817
$718$	−14.6405	−0.546377
$719$	−22.5849	−0.842273	−0.421137	−	0.906997i	$-0.638369\pi$
$719$	−22.5849	−0.842273	−0.421137	+	0.906997i	$0.638369\pi$
$720$	9.66012	0.360011
$721$	−3.32023	−0.123652
$722$	15.0000	0.558242
$723$	−73.7087	−2.74126
$724$	6.17858	0.229625
$725$	0	0
$726$	−28.3006	−1.05033
$727$	−49.3287	−1.82950	−0.914749	−	0.404021i	$-0.867612\pi$
$727$	−49.3287	−1.82950	−0.914749	+	0.404021i	$0.867612\pi$
$728$	18.1786	0.673743
$729$	−25.1874	−0.932868
$730$	−4.72652	−0.174936
$731$	−10.4292	−0.385737
$732$	20.9575	0.774610
$733$	−4.25383	−0.157119	−0.0785595	−	0.996909i	$-0.525032\pi$
$733$	−4.25383	−0.157119	−0.0785595	+	0.996909i	$0.525032\pi$
$734$	−18.4619	−0.681441
$735$	119.048	4.39114
$736$	1.57083	0.0579014
$737$	−4.75923	−0.175309
$738$	14.6685	0.539957
$739$	37.4661	1.37821	0.689106	−	0.724660i	$-0.258003\pi$
$739$	37.4661	1.37821	0.689106	+	0.724660i	$0.258003\pi$
$740$	−25.0369	−0.920376
$741$	18.9519	0.696214
$742$	2.92377	0.107335
$743$	3.59793	0.131995	0.0659977	−	0.997820i	$-0.478977\pi$
$743$	3.59793	0.131995	0.0659977	+	0.997820i	$0.478977\pi$
$744$	−15.6970	−0.575482
$745$	19.9804	0.732023
$746$	0.495575	0.0181443
$747$	−32.0739	−1.17352
$748$	15.8485	0.579479
$749$	−38.5096	−1.40711
$750$	−8.81159	−0.321754
$751$	46.3245	1.69040	0.845202	−	0.534448i	$-0.179480\pi$
$751$	46.3245	1.69040	0.845202	+	0.534448i	$0.179480\pi$
$752$	4.75923	0.173551
$753$	−18.2398	−0.664695
$754$	0	0
$755$	59.5456	2.16709
$756$	1.12200	0.0408069
$757$	19.3104	0.701849	0.350924	−	0.936404i	$-0.385867\pi$
$757$	19.3104	0.701849	0.350924	+	0.936404i	$0.385867\pi$
$758$	30.2777	1.09974
$759$	18.1603	0.659178
$760$	−6.66012	−0.241588
$761$	−0.283305	−0.0102698	−0.00513490	−	0.999987i	$-0.501634\pi$
$761$	−0.283305	−0.0102698	−0.00513490	+	0.999987i	$0.501634\pi$
$762$	14.0696	0.509689
$763$	7.51846	0.272187
$764$	−1.32023	−0.0477644
$765$	−32.1688	−1.16306
$766$	10.6798	0.385876
$767$	−54.5357	−1.96917
$768$	2.42917	0.0876553
$769$	28.9519	1.04403	0.522015	−	0.852936i	$-0.325180\pi$
$769$	28.9519	1.04403	0.522015	+	0.852936i	$0.325180\pi$
$770$	−73.8560	−2.66158
$771$	−28.4278	−1.02380
$772$	14.4095	0.518610
$773$	−2.57504	−0.0926178	−0.0463089	−	0.998927i	$-0.514746\pi$
$773$	−2.57504	−0.0926178	−0.0463089	+	0.998927i	$0.514746\pi$
$774$	−9.08508	−0.326556
$775$	39.3483	1.41343
$776$	14.1786	0.508981
$777$	85.1108	3.05333
$778$	25.6970	0.921284
$779$	−10.1132	−0.362341
$780$	31.5554	1.12986
$781$	−61.1491	−2.18809
$782$	−5.23094	−0.187058
$783$	0	0
$784$	14.7167	0.525596
$785$	60.5357	2.16061
$786$	−35.4053	−1.26287
$787$	30.4759	1.08635	0.543175	−	0.839620i	$-0.317222\pi$
$787$	30.4759	1.08635	0.543175	+	0.839620i	$0.317222\pi$
$788$	2.18419	0.0778086
$789$	−39.2211	−1.39631
$790$	−23.4988	−0.836050
$791$	−26.6405	−0.947226
$792$	13.8060	0.490574
$793$	33.6545	1.19511
$794$	20.1786	0.716111
$795$	5.07525	0.180001
$796$	−5.79195	−0.205290
$797$	−33.8298	−1.19831	−0.599157	−	0.800631i	$-0.704498\pi$
$797$	−33.8298	−1.19831	−0.599157	+	0.800631i	$0.704498\pi$
$798$	22.6405	0.801464
$799$	−15.8485	−0.560680
$800$	−6.08929	−0.215289
$801$	10.9336	0.386320
$802$	−19.3857	−0.684532
$803$	−6.75502	−0.238379
$804$	2.42917	0.0856704
$805$	24.3768	0.859170
$806$	−25.2071	−0.887882
$807$	17.7821	0.625960
$808$	−3.76906	−0.132595
$809$	−10.5554	−0.371108	−0.185554	−	0.982634i	$-0.559408\pi$
$809$	−10.5554	−0.371108	−0.185554	+	0.982634i	$0.559408\pi$
$810$	30.9280	1.08670
$811$	−16.3160	−0.572933	−0.286466	−	0.958090i	$-0.592481\pi$
$811$	−16.3160	−0.572933	−0.286466	+	0.958090i	$0.592481\pi$
$812$	0	0
$813$	78.8078	2.76391
$814$	−35.7821	−1.25416
$815$	−11.1220	−0.389587
$816$	−8.08929	−0.283182
$817$	6.26366	0.219138
$818$	−11.8018	−0.412639
$819$	−52.7340	−1.84267
$820$	−16.8387	−0.588033
$821$	44.7059	1.56025	0.780123	−	0.625626i	$-0.215156\pi$
$821$	44.7059	1.56025	0.780123	+	0.625626i	$0.215156\pi$
$822$	1.60354	0.0559299
$823$	11.4390	0.398738	0.199369	−	0.979924i	$-0.436111\pi$
$823$	11.4390	0.398738	0.199369	+	0.979924i	$0.436111\pi$
$824$	−0.712479	−0.0248204
$825$	−70.3983	−2.45095
$826$	−65.1501	−2.26686
$827$	−5.05658	−0.175834	−0.0879172	−	0.996128i	$-0.528021\pi$
$827$	−5.05658	−0.175834	−0.0879172	+	0.996128i	$0.528021\pi$
$828$	−4.55679	−0.158359
$829$	50.7536	1.76275	0.881373	−	0.472421i	$-0.156620\pi$
$829$	50.7536	1.76275	0.881373	+	0.472421i	$0.156620\pi$
$830$	36.8191	1.27801
$831$	−45.1220	−1.56527
$832$	3.90089	0.135239
$833$	−49.0075	−1.69801
$834$	−36.5273	−1.26484
$835$	−43.1491	−1.49324
$836$	−9.51846	−0.329203
$837$	−1.55581	−0.0537768
$838$	23.1220	0.798736
$839$	43.4184	1.49897	0.749484	−	0.662022i	$-0.230301\pi$
$839$	43.4184	1.49897	0.749484	+	0.662022i	$0.230301\pi$
$840$	37.6970	1.30067
$841$	−29.0000	−1.00000
$842$	31.9607	1.10144
$843$	9.76442	0.336305
$844$	0.396460	0.0136467
$845$	7.38242	0.253963
$846$	−13.8060	−0.474660
$847$	−54.2917	−1.86549
$848$	0.627404	0.0215451
$849$	−76.0346	−2.60950
$850$	20.2777	0.695519
$851$	11.8102	0.404849
$852$	31.2113	1.06928
$853$	−1.20708	−0.0413296	−0.0206648	−	0.999786i	$-0.506578\pi$
$853$	−1.20708	−0.0413296	−0.0206648	+	0.999786i	$0.506578\pi$
$854$	40.2047	1.37578
$855$	19.3202	0.660738
$856$	−8.26366	−0.282446
$857$	10.8387	0.370243	0.185121	−	0.982716i	$-0.440732\pi$
$857$	10.8387	0.370243	0.185121	+	0.982716i	$0.440732\pi$
$858$	45.0981	1.53963
$859$	−24.0739	−0.821389	−0.410695	−	0.911773i	$-0.634714\pi$
$859$	−24.0739	−0.821389	−0.410695	+	0.911773i	$0.634714\pi$
$860$	10.4292	0.355632
$861$	57.2416	1.95079
$862$	37.6830	1.28349
$863$	46.8668	1.59536	0.797682	−	0.603078i	$-0.206059\pi$
$863$	46.8668	1.59536	0.797682	+	0.603078i	$0.206059\pi$
$864$	0.240768	0.00819108
$865$	−78.2524	−2.66066
$866$	−28.5750	−0.971019
$867$	−14.3581	−0.487628
$868$	−30.1132	−1.02211
$869$	−33.5839	−1.13926
$870$	0	0
$871$	3.90089	0.132176
$872$	1.61336	0.0546354
$873$	−41.1304	−1.39205
$874$	3.14165	0.106268
$875$	−16.9041	−0.571464
$876$	3.44785	0.116492
$877$	7.40531	0.250060	0.125030	−	0.992153i	$-0.460097\pi$
$877$	7.40531	0.250060	0.125030	+	0.992153i	$0.460097\pi$
$878$	−17.1089	−0.577399
$879$	63.1108	2.12867
$880$	−15.8485	−0.534254
$881$	30.4095	1.02452	0.512261	−	0.858830i	$-0.328808\pi$
$881$	30.4095	1.02452	0.512261	+	0.858830i	$0.328808\pi$
$882$	−42.6914	−1.43750
$883$	1.32584	0.0446182	0.0223091	−	0.999751i	$-0.492898\pi$
$883$	1.32584	0.0446182	0.0223091	+	0.999751i	$0.492898\pi$
$884$	−12.9902	−0.436907
$885$	−113.091	−3.80152
$886$	−0.362773	−0.0121876
$887$	−46.7157	−1.56856	−0.784280	−	0.620407i	$-0.786968\pi$
$887$	−46.7157	−1.56856	−0.784280	+	0.620407i	$0.786968\pi$
$888$	18.2637	0.612888
$889$	26.9911	0.905254
$890$	−12.5512	−0.420716
$891$	44.2015	1.48081
$892$	−16.8485	−0.564130
$893$	9.51846	0.318523
$894$	−14.5750	−0.487462
$895$	19.8714	0.664228
$896$	4.66012	0.155684
$897$	−14.8850	−0.496997
$898$	2.00982	0.0670687
$899$	0	0
$900$	17.6643	0.588811
$901$	−2.08929	−0.0696044
$902$	−24.0654	−0.801291
$903$	−35.4530	−1.17980
$904$	−5.71669	−0.190134
$905$	20.5750	0.683938
$906$	−43.4366	−1.44309
$907$	2.75362	0.0914326	0.0457163	−	0.998954i	$-0.485443\pi$
$907$	2.75362	0.0914326	0.0457163	+	0.998954i	$0.485443\pi$
$908$	−19.9804	−0.663071
$909$	10.9336	0.362645
$910$	60.5357	2.00674
$911$	22.5600	0.747447	0.373724	−	0.927540i	$-0.378081\pi$
$911$	22.5600	0.747447	0.373724	+	0.927540i	$0.378081\pi$
$912$	4.85835	0.160876
$913$	52.6208	1.74150
$914$	−10.7634	−0.356023
$915$	69.7896	2.30717
$916$	−11.3202	−0.374031
$917$	−67.9214	−2.24296
$918$	−0.801770	−0.0264624
$919$	32.7536	1.08044	0.540221	−	0.841523i	$-0.318341\pi$
$919$	32.7536	1.08044	0.540221	+	0.841523i	$0.318341\pi$
$920$	5.23094	0.172459
$921$	−5.82142	−0.191822
$922$	0.660117	0.0217398
$923$	50.1206	1.64974
$924$	53.8756	1.77238
$925$	−45.7821	−1.50531
$926$	−13.7821	−0.452909
$927$	2.06682	0.0678832
$928$	0	0
$929$	−24.9434	−0.818367	−0.409184	−	0.912452i	$-0.634186\pi$
$929$	−24.9434	−0.818367	−0.409184	+	0.912452i	$0.634186\pi$
$930$	−52.2721	−1.71407
$931$	29.4334	0.964640
$932$	9.23516	0.302508
$933$	−1.44461	−0.0472943
$934$	−36.4703	−1.19335
$935$	52.7765	1.72598
$936$	−11.3160	−0.369876
$937$	28.3572	0.926388	0.463194	−	0.886257i	$-0.346703\pi$
$937$	28.3572	0.926388	0.463194	+	0.886257i	$0.346703\pi$
$938$	4.66012	0.152158
$939$	24.7733	0.808445
$940$	15.8485	0.516922
$941$	16.2440	0.529540	0.264770	−	0.964312i	$-0.414704\pi$
$941$	16.2440	0.529540	0.264770	+	0.964312i	$0.414704\pi$
$942$	−44.1589	−1.43878
$943$	7.94300	0.258660
$944$	−13.9804	−0.455022
$945$	3.73634	0.121543
$946$	14.9051	0.484607
$947$	−18.6601	−0.606372	−0.303186	−	0.952931i	$-0.598050\pi$
$947$	−18.6601	−0.606372	−0.303186	+	0.952931i	$0.598050\pi$
$948$	17.1417	0.556735
$949$	5.53672	0.179730
$950$	−12.1786	−0.395125
$951$	9.76442	0.316633
$952$	−15.5185	−0.502956
$953$	−46.7003	−1.51277	−0.756385	−	0.654126i	$-0.773036\pi$
$953$	−46.7003	−1.51277	−0.756385	+	0.654126i	$0.773036\pi$
$954$	−1.82003	−0.0589255
$955$	−4.39646	−0.142266
$956$	−13.5381	−0.437854
$957$	0	0
$958$	−21.3146	−0.688644
$959$	3.07623	0.0993365
$960$	8.08929	0.261081
$961$	10.7560	0.346967
$962$	29.3287	0.945594
$963$	23.9719	0.772484
$964$	−30.3431	−0.977286
$965$	47.9846	1.54468
$966$	−17.7821	−0.572130
$967$	−2.58487	−0.0831237	−0.0415618	−	0.999136i	$-0.513233\pi$
$967$	−2.58487	−0.0831237	−0.0415618	+	0.999136i	$0.513233\pi$
$968$	−11.6503	−0.374455
$969$	−16.1786	−0.519731
$970$	47.2155	1.51600
$971$	−17.2155	−0.552472	−0.276236	−	0.961090i	$-0.589087\pi$
$971$	−17.2155	−0.552472	−0.276236	+	0.961090i	$0.589087\pi$
$972$	−21.8387	−0.700477
$973$	−70.0739	−2.24646
$974$	9.40531	0.301366
$975$	57.7017	1.84793
$976$	8.62740	0.276156
$977$	30.1309	0.963971	0.481986	−	0.876179i	$-0.339916\pi$
$977$	30.1309	0.963971	0.481986	+	0.876179i	$0.339916\pi$
$978$	8.11315	0.259430
$979$	−17.9378	−0.573295
$980$	49.0075	1.56549
$981$	−4.68018	−0.149427
$982$	34.4900	1.10062
$983$	−23.8756	−0.761514	−0.380757	−	0.924675i	$-0.624337\pi$
$983$	−23.8756	−0.761514	−0.380757	+	0.924675i	$0.624337\pi$
$984$	12.2833	0.391577
$985$	7.27348	0.231752
$986$	0	0
$987$	−53.8756	−1.71488
$988$	7.80177	0.248207
$989$	−4.91956	−0.156433
$990$	45.9747	1.46117
$991$	16.5470	0.525632	0.262816	−	0.964846i	$-0.415349\pi$
$991$	16.5470	0.525632	0.262816	+	0.964846i	$0.415349\pi$
$992$	−6.46189	−0.205165
$993$	53.8518	1.70893
$994$	59.8756	1.89914
$995$	−19.2875	−0.611456
$996$	−26.8583	−0.851039
$997$	−49.5465	−1.56915	−0.784577	−	0.620031i	$-0.787120\pi$
$997$	−49.5465	−1.56915	−0.784577	+	0.620031i	$0.787120\pi$
$998$	−27.2875	−0.863771
$999$	1.81020	0.0572723

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	134.2.a.a.1.3	✓	3
3.2	odd	2		1206.2.a.o.1.1		3
4.3	odd	2		1072.2.a.j.1.1		3
5.2	odd	4		3350.2.c.i.2949.1		6
5.3	odd	4		3350.2.c.i.2949.6		6
5.4	even	2		3350.2.a.m.1.1		3
7.6	odd	2		6566.2.a.z.1.1		3
8.3	odd	2		4288.2.a.u.1.3		3
8.5	even	2		4288.2.a.t.1.1		3
12.11	even	2		9648.2.a.bk.1.1		3
67.66	odd	2		8978.2.a.i.1.1		3

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
134.2.a.a.1.3	✓	3	1.1	even	1	trivial
1072.2.a.j.1.1		3	4.3	odd	2
1206.2.a.o.1.1		3	3.2	odd	2
3350.2.a.m.1.1		3	5.4	even	2
3350.2.c.i.2949.1		6	5.2	odd	4
3350.2.c.i.2949.6		6	5.3	odd	4
4288.2.a.t.1.1		3	8.5	even	2
4288.2.a.u.1.3		3	8.3	odd	2
6566.2.a.z.1.1		3	7.6	odd	2
8978.2.a.i.1.1		3	67.66	odd	2
9648.2.a.bk.1.1		3	12.11	even	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:	\( N \)	\(=\)	\( 134 = 2 \cdot 67 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	134.a (trivial)

\(f(q)\)	\(=\)	\(q-1.00000 q^{2} +2.42917 q^{3} +1.00000 q^{4} +3.33006 q^{5} -2.42917 q^{6} -4.66012 q^{7} -1.00000 q^{8} +2.90089 q^{9} +O(q^{10})\)	\(q-1.00000 q^{2} +2.42917 q^{3} +1.00000 q^{4} +3.33006 q^{5} -2.42917 q^{6} -4.66012 q^{7} -1.00000 q^{8} +2.90089 q^{9} -3.33006 q^{10} -4.75923 q^{11} +2.42917 q^{12} +3.90089 q^{13} +4.66012 q^{14} +8.08929 q^{15} +1.00000 q^{16} -3.33006 q^{17} -2.90089 q^{18} +2.00000 q^{19} +3.33006 q^{20} -11.3202 q^{21} +4.75923 q^{22} -1.57083 q^{23} -2.42917 q^{24} +6.08929 q^{25} -3.90089 q^{26} -0.240768 q^{27} -4.66012 q^{28} -8.08929 q^{30} +6.46189 q^{31} -1.00000 q^{32} -11.5610 q^{33} +3.33006 q^{34} -15.5185 q^{35} +2.90089 q^{36} -7.51846 q^{37} -2.00000 q^{38} +9.47593 q^{39} -3.33006 q^{40} -5.05658 q^{41} +11.3202 q^{42} +3.13183 q^{43} -4.75923 q^{44} +9.66012 q^{45} +1.57083 q^{46} +4.75923 q^{47} +2.42917 q^{48} +14.7167 q^{49} -6.08929 q^{50} -8.08929 q^{51} +3.90089 q^{52} +0.627404 q^{53} +0.240768 q^{54} -15.8485 q^{55} +4.66012 q^{56} +4.85835 q^{57} -13.9804 q^{59} +8.08929 q^{60} +8.62740 q^{61} -6.46189 q^{62} -13.5185 q^{63} +1.00000 q^{64} +12.9902 q^{65} +11.5610 q^{66} +1.00000 q^{67} -3.33006 q^{68} -3.81581 q^{69} +15.5185 q^{70} +12.8485 q^{71} -2.90089 q^{72} +1.41935 q^{73} +7.51846 q^{74} +14.7919 q^{75} +2.00000 q^{76} +22.1786 q^{77} -9.47593 q^{78} +7.05658 q^{79} +3.33006 q^{80} -9.28752 q^{81} +5.05658 q^{82} -11.0566 q^{83} -11.3202 q^{84} -11.0893 q^{85} -3.13183 q^{86} +4.75923 q^{88} +3.76906 q^{89} -9.66012 q^{90} -18.1786 q^{91} -1.57083 q^{92} +15.6970 q^{93} -4.75923 q^{94} +6.66012 q^{95} -2.42917 q^{96} -14.1786 q^{97} -14.7167 q^{98} -13.8060 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 3 q - 3 q^{2} + q^{3} + 3 q^{4} + 3 q^{5} - q^{6} - 3 q^{8} + 8 q^{9}+O(q^{10}) \) 3 * q - 3 * q^2 + q^3 + 3 * q^4 + 3 * q^5 - q^6 - 3 * q^8 + 8 * q^9	\( 3 q - 3 q^{2} + q^{3} + 3 q^{4} + 3 q^{5} - q^{6} - 3 q^{8} + 8 q^{9} - 3 q^{10} - q^{11} + q^{12} + 11 q^{13} + 4 q^{15} + 3 q^{16} - 3 q^{17} - 8 q^{18} + 6 q^{19} + 3 q^{20} - 6 q^{21} + q^{22} - 11 q^{23} - q^{24} - 2 q^{25} - 11 q^{26} - 14 q^{27} - 4 q^{30} + 4 q^{31} - 3 q^{32} - 20 q^{33} + 3 q^{34} - 20 q^{35} + 8 q^{36} + 4 q^{37} - 6 q^{38} - 10 q^{39} - 3 q^{40} - 4 q^{41} + 6 q^{42} + q^{43} - q^{44} + 15 q^{45} + 11 q^{46} + q^{47} + q^{48} + 19 q^{49} + 2 q^{50} - 4 q^{51} + 11 q^{52} - 3 q^{53} + 14 q^{54} - 14 q^{55} + 2 q^{57} + 4 q^{60} + 21 q^{61} - 4 q^{62} - 14 q^{63} + 3 q^{64} + 18 q^{65} + 20 q^{66} + 3 q^{67} - 3 q^{68} + 13 q^{69} + 20 q^{70} + 5 q^{71} - 8 q^{72} - 23 q^{73} - 4 q^{74} + 22 q^{75} + 6 q^{76} + 26 q^{77} + 10 q^{78} + 10 q^{79} + 3 q^{80} - 9 q^{81} + 4 q^{82} - 22 q^{83} - 6 q^{84} - 13 q^{85} - q^{86} + q^{88} + 19 q^{89} - 15 q^{90} - 14 q^{91} - 11 q^{92} - 20 q^{93} - q^{94} + 6 q^{95} - q^{96} - 2 q^{97} - 19 q^{98} + 4 q^{99}+O(q^{100}) \) 3 * q - 3 * q^2 + q^3 + 3 * q^4 + 3 * q^5 - q^6 - 3 * q^8 + 8 * q^9 - 3 * q^10 - q^11 + q^12 + 11 * q^13 + 4 * q^15 + 3 * q^16 - 3 * q^17 - 8 * q^18 + 6 * q^19 + 3 * q^20 - 6 * q^21 + q^22 - 11 * q^23 - q^24 - 2 * q^25 - 11 * q^26 - 14 * q^27 - 4 * q^30 + 4 * q^31 - 3 * q^32 - 20 * q^33 + 3 * q^34 - 20 * q^35 + 8 * q^36 + 4 * q^37 - 6 * q^38 - 10 * q^39 - 3 * q^40 - 4 * q^41 + 6 * q^42 + q^43 - q^44 + 15 * q^45 + 11 * q^46 + q^47 + q^48 + 19 * q^49 + 2 * q^50 - 4 * q^51 + 11 * q^52 - 3 * q^53 + 14 * q^54 - 14 * q^55 + 2 * q^57 + 4 * q^60 + 21 * q^61 - 4 * q^62 - 14 * q^63 + 3 * q^64 + 18 * q^65 + 20 * q^66 + 3 * q^67 - 3 * q^68 + 13 * q^69 + 20 * q^70 + 5 * q^71 - 8 * q^72 - 23 * q^73 - 4 * q^74 + 22 * q^75 + 6 * q^76 + 26 * q^77 + 10 * q^78 + 10 * q^79 + 3 * q^80 - 9 * q^81 + 4 * q^82 - 22 * q^83 - 6 * q^84 - 13 * q^85 - q^86 + q^88 + 19 * q^89 - 15 * q^90 - 14 * q^91 - 11 * q^92 - 20 * q^93 - q^94 + 6 * q^95 - q^96 - 2 * q^97 - 19 * q^98 + 4 * q^99

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