LMFDB - Embedded newform 273.4.a.d.1.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [273,4,Mod(1,273)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(273, base_ring=CyclotomicField(2))

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

N = Newforms(chi, 4, names="a")

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

chi := DirichletCharacter("273.1");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 273 = 3 \cdot 7 \cdot 13 $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	273.a (trivial)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	yes
Analytic conductor:	$16.1075214316$
Analytic rank:	$0$
Dimension:	$2$
Coefficient field:	$\Q(\sqrt{865}) $
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{2} - x - 216 $ x^2 - x - 216
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Fricke sign:	$+1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.1
Root			$15.2054$ of defining polynomial
Character	$\chi$	$=$	273.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.00000 q^{2} -3.00000 q^{3} -7.00000 q^{4} -12.2054 q^{5} -3.00000 q^{6} -7.00000 q^{7} -15.0000 q^{8} +9.00000 q^{9} +O(q^{10})$	\(q+1.00000 q^{2} -3.00000 q^{3} -7.00000 q^{4} -12.2054 q^{5} -3.00000 q^{6} -7.00000 q^{7} -15.0000 q^{8} +9.00000 q^{9} -12.2054 q^{10} -18.2054 q^{11} +21.0000 q^{12} -13.0000 q^{13} -7.00000 q^{14} +36.6163 q^{15} +41.0000 q^{16} +77.0272 q^{17} +9.00000 q^{18} -47.4381 q^{19} +85.4381 q^{20} +21.0000 q^{21} -18.2054 q^{22} +29.3837 q^{23} +45.0000 q^{24} +23.9728 q^{25} -13.0000 q^{26} -27.0000 q^{27} +49.0000 q^{28} +16.2054 q^{29} +36.6163 q^{30} +338.465 q^{31} +161.000 q^{32} +54.6163 q^{33} +77.0272 q^{34} +85.4381 q^{35} -63.0000 q^{36} +5.74015 q^{37} -47.4381 q^{38} +39.0000 q^{39} +183.082 q^{40} -140.876 q^{41} +21.0000 q^{42} -97.0816 q^{43} +127.438 q^{44} -109.849 q^{45} +29.3837 q^{46} +147.178 q^{47} -123.000 q^{48} +49.0000 q^{49} +23.9728 q^{50} -231.082 q^{51} +91.0000 q^{52} -176.465 q^{53} -27.0000 q^{54} +222.205 q^{55} +105.000 q^{56} +142.314 q^{57} +16.2054 q^{58} +359.287 q^{59} -256.314 q^{60} -691.903 q^{61} +338.465 q^{62} -63.0000 q^{63} -167.000 q^{64} +158.671 q^{65} +54.6163 q^{66} -350.876 q^{67} -539.190 q^{68} -88.1510 q^{69} +85.4381 q^{70} +481.039 q^{71} -135.000 q^{72} +979.299 q^{73} +5.74015 q^{74} -71.9184 q^{75} +332.067 q^{76} +127.438 q^{77} +39.0000 q^{78} -465.124 q^{79} -500.423 q^{80} +81.0000 q^{81} -140.876 q^{82} -342.163 q^{83} -147.000 q^{84} -940.151 q^{85} -97.0816 q^{86} -48.6163 q^{87} +273.082 q^{88} +747.039 q^{89} -109.849 q^{90} +91.0000 q^{91} -205.686 q^{92} -1015.40 q^{93} +147.178 q^{94} +579.003 q^{95} -483.000 q^{96} +722.109 q^{97} +49.0000 q^{98} -163.849 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 2 q + 2 q^{2} - 6 q^{3} - 14 q^{4} + 5 q^{5} - 6 q^{6} - 14 q^{7} - 30 q^{8} + 18 q^{9}+O(q^{10}) $ 2 * q + 2 * q^2 - 6 * q^3 - 14 * q^4 + 5 * q^5 - 6 * q^6 - 14 * q^7 - 30 * q^8 + 18 * q^9	\( 2 q + 2 q^{2} - 6 q^{3} - 14 q^{4} + 5 q^{5} - 6 q^{6} - 14 q^{7} - 30 q^{8} + 18 q^{9} + 5 q^{10} - 7 q^{11} + 42 q^{12} - 26 q^{13} - 14 q^{14} - 15 q^{15} + 82 q^{16} + 7 q^{17} + 18 q^{18} + 111 q^{19} - 35 q^{20} + 42 q^{21} - 7 q^{22} + 147 q^{23} + 90 q^{24} + 195 q^{25} - 26 q^{26} - 54 q^{27} + 98 q^{28} + 3 q^{29} - 15 q^{30} + 324 q^{31} + 322 q^{32} + 21 q^{33} + 7 q^{34} - 35 q^{35} - 126 q^{36} + 335 q^{37} + 111 q^{38} + 78 q^{39} - 75 q^{40} + 130 q^{41} + 42 q^{42} + 247 q^{43} + 49 q^{44} + 45 q^{45} + 147 q^{46} + 412 q^{47} - 246 q^{48} + 98 q^{49} + 195 q^{50} - 21 q^{51} + 182 q^{52} - 54 q^{54} + 415 q^{55} + 210 q^{56} - 333 q^{57} + 3 q^{58} + 248 q^{59} + 105 q^{60} - 825 q^{61} + 324 q^{62} - 126 q^{63} - 334 q^{64} - 65 q^{65} + 21 q^{66} - 290 q^{67} - 49 q^{68} - 441 q^{69} - 35 q^{70} - 332 q^{71} - 270 q^{72} + 341 q^{73} + 335 q^{74} - 585 q^{75} - 777 q^{76} + 49 q^{77} + 78 q^{78} - 1342 q^{79} + 205 q^{80} + 162 q^{81} + 130 q^{82} + 198 q^{83} - 294 q^{84} - 2145 q^{85} + 247 q^{86} - 9 q^{87} + 105 q^{88} + 200 q^{89} + 45 q^{90} + 182 q^{91} - 1029 q^{92} - 972 q^{93} + 412 q^{94} + 3305 q^{95} - 966 q^{96} + 856 q^{97} + 98 q^{98} - 63 q^{99}+O(q^{100}) \) 2 * q + 2 * q^2 - 6 * q^3 - 14 * q^4 + 5 * q^5 - 6 * q^6 - 14 * q^7 - 30 * q^8 + 18 * q^9 + 5 * q^10 - 7 * q^11 + 42 * q^12 - 26 * q^13 - 14 * q^14 - 15 * q^15 + 82 * q^16 + 7 * q^17 + 18 * q^18 + 111 * q^19 - 35 * q^20 + 42 * q^21 - 7 * q^22 + 147 * q^23 + 90 * q^24 + 195 * q^25 - 26 * q^26 - 54 * q^27 + 98 * q^28 + 3 * q^29 - 15 * q^30 + 324 * q^31 + 322 * q^32 + 21 * q^33 + 7 * q^34 - 35 * q^35 - 126 * q^36 + 335 * q^37 + 111 * q^38 + 78 * q^39 - 75 * q^40 + 130 * q^41 + 42 * q^42 + 247 * q^43 + 49 * q^44 + 45 * q^45 + 147 * q^46 + 412 * q^47 - 246 * q^48 + 98 * q^49 + 195 * q^50 - 21 * q^51 + 182 * q^52 - 54 * q^54 + 415 * q^55 + 210 * q^56 - 333 * q^57 + 3 * q^58 + 248 * q^59 + 105 * q^60 - 825 * q^61 + 324 * q^62 - 126 * q^63 - 334 * q^64 - 65 * q^65 + 21 * q^66 - 290 * q^67 - 49 * q^68 - 441 * q^69 - 35 * q^70 - 332 * q^71 - 270 * q^72 + 341 * q^73 + 335 * q^74 - 585 * q^75 - 777 * q^76 + 49 * q^77 + 78 * q^78 - 1342 * q^79 + 205 * q^80 + 162 * q^81 + 130 * q^82 + 198 * q^83 - 294 * q^84 - 2145 * q^85 + 247 * q^86 - 9 * q^87 + 105 * q^88 + 200 * q^89 + 45 * q^90 + 182 * q^91 - 1029 * q^92 - 972 * q^93 + 412 * q^94 + 3305 * q^95 - 966 * q^96 + 856 * q^97 + 98 * q^98 - 63 * 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	0.353553	0.176777	−	0.984251i	$-0.443433\pi$
$2$	1.00000	0.353553	0.176777	+	0.984251i	$0.443433\pi$
$3$	−3.00000	−0.577350
$3$	−3.00000	−0.577350
$4$	−7.00000	−0.875000
$5$	−12.2054	−1.09169	−0.545844	−	0.837887i	$-0.683791\pi$
$5$	−12.2054	−1.09169	−0.545844	+	0.837887i	$0.683791\pi$
$6$	−3.00000	−0.204124
$7$	−7.00000	−0.377964
$7$	−7.00000	−0.377964
$8$	−15.0000	−0.662913
$9$	9.00000	0.333333
$10$	−12.2054	−0.385970
$11$	−18.2054	−0.499013	−0.249507	−	0.968373i	$-0.580268\pi$
$11$	−18.2054	−0.499013	−0.249507	+	0.968373i	$0.580268\pi$
$12$	21.0000	0.505181
$13$	−13.0000	−0.277350
$13$	−13.0000	−0.277350
$14$	−7.00000	−0.133631
$15$	36.6163	0.630286
$16$	41.0000	0.640625
$17$	77.0272	1.09893	0.549466	−	0.835516i	$-0.314831\pi$
$17$	77.0272	1.09893	0.549466	+	0.835516i	$0.314831\pi$
$18$	9.00000	0.117851
$19$	−47.4381	−0.572792	−0.286396	−	0.958111i	$-0.592457\pi$
$19$	−47.4381	−0.572792	−0.286396	+	0.958111i	$0.592457\pi$
$20$	85.4381	0.955227
$21$	21.0000	0.218218
$22$	−18.2054	−0.176428
$23$	29.3837	0.266388	0.133194	−	0.991090i	$-0.457477\pi$
$23$	29.3837	0.266388	0.133194	+	0.991090i	$0.457477\pi$
$24$	45.0000	0.382733
$25$	23.9728	0.191782
$26$	−13.0000	−0.0980581
$27$	−27.0000	−0.192450
$28$	49.0000	0.330719
$29$	16.2054	0.103768	0.0518840	−	0.998653i	$-0.483477\pi$
$29$	16.2054	0.103768	0.0518840	+	0.998653i	$0.483477\pi$
$30$	36.6163	0.222840
$31$	338.465	1.96097	0.980486	−	0.196587i	$-0.0629857\pi$
$31$	338.465	1.96097	0.980486	+	0.196587i	$0.0629857\pi$
$32$	161.000	0.889408
$33$	54.6163	0.288106
$34$	77.0272	0.388531
$35$	85.4381	0.412619
$36$	−63.0000	−0.291667
$37$	5.74015	0.0255047	0.0127524	−	0.999919i	$-0.495941\pi$
$37$	5.74015	0.0255047	0.0127524	+	0.999919i	$0.495941\pi$
$38$	−47.4381	−0.202512
$39$	39.0000	0.160128
$40$	183.082	0.723694
$41$	−140.876	−0.536614	−0.268307	−	0.963333i	$-0.586464\pi$
$41$	−140.876	−0.536614	−0.268307	+	0.963333i	$0.586464\pi$
$42$	21.0000	0.0771517
$43$	−97.0816	−0.344298	−0.172149	−	0.985071i	$-0.555071\pi$
$43$	−97.0816	−0.344298	−0.172149	+	0.985071i	$0.555071\pi$
$44$	127.438	0.436637
$45$	−109.849	−0.363896
$46$	29.3837	0.0941823
$47$	147.178	0.456769	0.228385	−	0.973571i	$-0.426656\pi$
$47$	147.178	0.456769	0.228385	+	0.973571i	$0.426656\pi$
$48$	−123.000	−0.369865
$49$	49.0000	0.142857
$50$	23.9728	0.0678053
$51$	−231.082	−0.634469
$52$	91.0000	0.242681
$53$	−176.465	−0.457347	−0.228673	−	0.973503i	$-0.573439\pi$
$53$	−176.465	−0.457347	−0.228673	+	0.973503i	$0.573439\pi$
$54$	−27.0000	−0.0680414
$55$	222.205	0.544767
$56$	105.000	0.250557
$57$	142.314	0.330701
$58$	16.2054	0.0366876
$59$	359.287	0.792800	0.396400	−	0.918078i	$-0.370259\pi$
$59$	359.287	0.792800	0.396400	+	0.918078i	$0.370259\pi$
$60$	−256.314	−0.551500
$61$	−691.903	−1.45228	−0.726141	−	0.687546i	$-0.758688\pi$
$61$	−691.903	−1.45228	−0.726141	+	0.687546i	$0.758688\pi$
$62$	338.465	0.693309
$63$	−63.0000	−0.125988
$64$	−167.000	−0.326172
$65$	158.671	0.302780
$66$	54.6163	0.101861
$67$	−350.876	−0.639796	−0.319898	−	0.947452i	$-0.603649\pi$
$67$	−350.876	−0.639796	−0.319898	+	0.947452i	$0.603649\pi$
$68$	−539.190	−0.961565
$69$	−88.1510	−0.153799
$70$	85.4381	0.145883
$71$	481.039	0.804069	0.402034	−	0.915625i	$-0.368303\pi$
$71$	481.039	0.804069	0.402034	+	0.915625i	$0.368303\pi$
$72$	−135.000	−0.220971
$73$	979.299	1.57011	0.785057	−	0.619424i	$-0.212634\pi$
$73$	979.299	1.57011	0.785057	+	0.619424i	$0.212634\pi$
$74$	5.74015	0.00901728
$75$	−71.9184	−0.110726
$76$	332.067	0.501193
$77$	127.438	0.188609
$78$	39.0000	0.0566139
$79$	−465.124	−0.662412	−0.331206	−	0.943559i	$-0.607455\pi$
$79$	−465.124	−0.662412	−0.331206	+	0.943559i	$0.607455\pi$
$80$	−500.423	−0.699363
$81$	81.0000	0.111111
$82$	−140.876	−0.189722
$83$	−342.163	−0.452498	−0.226249	−	0.974070i	$-0.572646\pi$
$83$	−342.163	−0.452498	−0.226249	+	0.974070i	$0.572646\pi$
$84$	−147.000	−0.190941
$85$	−940.151	−1.19969
$86$	−97.0816	−0.121728
$87$	−48.6163	−0.0599105
$88$	273.082	0.330802
$89$	747.039	0.889731	0.444865	−	0.895598i	$-0.353252\pi$
$89$	747.039	0.889731	0.444865	+	0.895598i	$0.353252\pi$
$90$	−109.849	−0.128657
$91$	91.0000	0.104828
$92$	−205.686	−0.233089
$93$	−1015.40	−1.13217
$94$	147.178	0.161492
$95$	579.003	0.625310
$96$	−483.000	−0.513500
$97$	722.109	0.755866	0.377933	−	0.925833i	$-0.376635\pi$
$97$	722.109	0.755866	0.377933	+	0.925833i	$0.376635\pi$
$98$	49.0000	0.0505076
$99$	−163.849	−0.166338
$100$	−167.810	−0.167810
$101$	1468.16	1.44641	0.723206	−	0.690632i	$-0.242668\pi$
$101$	1468.16	1.44641	0.723206	+	0.690632i	$0.242668\pi$
$102$	−231.082	−0.224319
$103$	−1029.71	−0.985052	−0.492526	−	0.870298i	$-0.663926\pi$
$103$	−1029.71	−0.985052	−0.492526	+	0.870298i	$0.663926\pi$
$104$	195.000	0.183859
$105$	−256.314	−0.238226
$106$	−176.465	−0.161696
$107$	1024.30	0.925449	0.462724	−	0.886502i	$-0.346872\pi$
$107$	1024.30	0.925449	0.462724	+	0.886502i	$0.346872\pi$
$108$	189.000	0.168394
$109$	−204.810	−0.179974	−0.0899871	−	0.995943i	$-0.528683\pi$
$109$	−204.810	−0.179974	−0.0899871	+	0.995943i	$0.528683\pi$
$110$	222.205	0.192604
$111$	−17.2204	−0.0147252
$112$	−287.000	−0.242133
$113$	−791.426	−0.658859	−0.329430	−	0.944180i	$-0.606856\pi$
$113$	−791.426	−0.658859	−0.329430	+	0.944180i	$0.606856\pi$
$114$	142.314	0.116921
$115$	−358.641	−0.290812
$116$	−113.438	−0.0907971
$117$	−117.000	−0.0924500
$118$	359.287	0.280297
$119$	−539.190	−0.415357
$120$	−549.245	−0.417825
$121$	−999.562	−0.750986
$122$	−691.903	−0.513459
$123$	422.629	0.309814
$124$	−2369.26	−1.71585
$125$	1233.08	0.882321
$126$	−63.0000	−0.0445435
$127$	−773.064	−0.540144	−0.270072	−	0.962840i	$-0.587048\pi$
$127$	−773.064	−0.540144	−0.270072	+	0.962840i	$0.587048\pi$
$128$	−1455.00	−1.00473
$129$	291.245	0.198780
$130$	158.671	0.107049
$131$	2535.27	1.69090	0.845448	−	0.534057i	$-0.179333\pi$
$131$	2535.27	1.69090	0.845448	+	0.534057i	$0.179333\pi$
$132$	−382.314	−0.252092
$133$	332.067	0.216495
$134$	−350.876	−0.226202
$135$	329.547	0.210095
$136$	−1155.41	−0.728496
$137$	1847.52	1.15215	0.576073	−	0.817398i	$-0.304584\pi$
$137$	1847.52	1.15215	0.576073	+	0.817398i	$0.304584\pi$
$138$	−88.1510	−0.0543762
$139$	−1839.12	−1.12224	−0.561122	−	0.827733i	$-0.689630\pi$
$139$	−1839.12	−1.12224	−0.561122	+	0.827733i	$0.689630\pi$
$140$	−598.067	−0.361042
$141$	−441.535	−0.263716
$142$	481.039	0.284281
$143$	236.671	0.138401
$144$	369.000	0.213542
$145$	−197.795	−0.113282
$146$	979.299	0.555119
$147$	−147.000	−0.0824786
$148$	−40.1810	−0.0223166
$149$	−1246.02	−0.685089	−0.342545	−	0.939502i	$-0.611289\pi$
$149$	−1246.02	−0.685089	−0.342545	+	0.939502i	$0.611289\pi$
$150$	−71.9184	−0.0391474
$151$	1655.38	0.892137	0.446069	−	0.894999i	$-0.352824\pi$
$151$	1655.38	0.892137	0.446069	+	0.894999i	$0.352824\pi$
$152$	711.571	0.379711
$153$	693.245	0.366311
$154$	127.438	0.0666835
$155$	−4131.12	−2.14077
$156$	−273.000	−0.140112
$157$	497.849	0.253074	0.126537	−	0.991962i	$-0.459614\pi$
$157$	497.849	0.253074	0.126537	+	0.991962i	$0.459614\pi$
$158$	−465.124	−0.234198
$159$	529.396	0.264049
$160$	−1965.08	−0.970956
$161$	−205.686	−0.100685
$162$	81.0000	0.0392837
$163$	133.668	0.0642312	0.0321156	−	0.999484i	$-0.489776\pi$
$163$	133.668	0.0642312	0.0321156	+	0.999484i	$0.489776\pi$
$164$	986.133	0.469537
$165$	−666.616	−0.314521
$166$	−342.163	−0.159982
$167$	2127.52	0.985824	0.492912	−	0.870079i	$-0.335932\pi$
$167$	2127.52	0.985824	0.492912	+	0.870079i	$0.335932\pi$
$168$	−315.000	−0.144659
$169$	169.000	0.0769231
$170$	−940.151	−0.424155
$171$	−426.943	−0.190931
$172$	679.571	0.301261
$173$	2153.40	0.946356	0.473178	−	0.880967i	$-0.343107\pi$
$173$	2153.40	0.946356	0.473178	+	0.880967i	$0.343107\pi$
$174$	−48.6163	−0.0211816
$175$	−167.810	−0.0724869
$176$	−746.423	−0.319680
$177$	−1077.86	−0.457723
$178$	747.039	0.314567
$179$	3204.11	1.33791	0.668956	−	0.743302i	$-0.266741\pi$
$179$	3204.11	1.33791	0.668956	+	0.743302i	$0.266741\pi$
$180$	768.943	0.318409
$181$	−2702.27	−1.10971	−0.554856	−	0.831946i	$-0.687227\pi$
$181$	−2702.27	−1.10971	−0.554856	+	0.831946i	$0.687227\pi$
$182$	91.0000	0.0370625
$183$	2075.71	0.838475
$184$	−440.755	−0.176592
$185$	−70.0610	−0.0278432
$186$	−1015.40	−0.400282
$187$	−1402.31	−0.548382
$188$	−1030.25	−0.399673
$189$	189.000	0.0727393
$190$	579.003	0.221080
$191$	−1420.91	−0.538291	−0.269146	−	0.963099i	$-0.586741\pi$
$191$	−1420.91	−0.538291	−0.269146	+	0.963099i	$0.586741\pi$
$192$	501.000	0.188315
$193$	−1187.62	−0.442936	−0.221468	−	0.975168i	$-0.571085\pi$
$193$	−1187.62	−0.442936	−0.221468	+	0.975168i	$0.571085\pi$
$194$	722.109	0.267239
$195$	−476.012	−0.174810
$196$	−343.000	−0.125000
$197$	−99.5103	−0.0359889	−0.0179945	−	0.999838i	$-0.505728\pi$
$197$	−99.5103	−0.0359889	−0.0179945	+	0.999838i	$0.505728\pi$
$198$	−163.849	−0.0588093
$199$	3213.54	1.14473	0.572367	−	0.819998i	$-0.306025\pi$
$199$	3213.54	1.14473	0.572367	+	0.819998i	$0.306025\pi$
$200$	−359.592	−0.127135
$201$	1052.63	0.369387
$202$	1468.16	0.511384
$203$	−113.438	−0.0392207
$204$	1617.57	0.555160
$205$	1719.46	0.585815
$206$	−1029.71	−0.348268
$207$	264.453	0.0887959
$208$	−533.000	−0.177677
$209$	863.631	0.285831
$210$	−256.314	−0.0842255
$211$	651.547	0.212580	0.106290	−	0.994335i	$-0.466103\pi$
$211$	651.547	0.212580	0.106290	+	0.994335i	$0.466103\pi$
$212$	1235.26	0.400178
$213$	−1443.12	−0.464229
$214$	1024.30	0.327196
$215$	1184.92	0.375866
$216$	405.000	0.127578
$217$	−2369.26	−0.741178
$218$	−204.810	−0.0636305
$219$	−2937.90	−0.906506
$220$	−1555.44	−0.476671
$221$	−1001.35	−0.304789
$222$	−17.2204	−0.00520613
$223$	6535.96	1.96269	0.981347	−	0.192247i	$-0.0615776\pi$
$223$	6535.96	1.96269	0.981347	+	0.192247i	$0.0615776\pi$
$224$	−1127.00	−0.336165
$225$	215.755	0.0639275
$226$	−791.426	−0.232942
$227$	62.3321	0.0182252	0.00911261	−	0.999958i	$-0.497099\pi$
$227$	62.3321	0.0182252	0.00911261	+	0.999958i	$0.497099\pi$
$228$	−996.200	−0.289364
$229$	−2746.98	−0.792688	−0.396344	−	0.918102i	$-0.629721\pi$
$229$	−2746.98	−0.792688	−0.396344	+	0.918102i	$0.629721\pi$
$230$	−358.641	−0.102818
$231$	−382.314	−0.108894
$232$	−243.082	−0.0687892
$233$	3356.86	0.943844	0.471922	−	0.881640i	$-0.343560\pi$
$233$	3356.86	0.943844	0.471922	+	0.881640i	$0.343560\pi$
$234$	−117.000	−0.0326860
$235$	−1796.38	−0.498649
$236$	−2515.01	−0.693700
$237$	1395.37	0.382444
$238$	−539.190	−0.146851
$239$	2318.41	0.627469	0.313735	−	0.949511i	$-0.398420\pi$
$239$	2318.41	0.627469	0.313735	+	0.949511i	$0.398420\pi$
$240$	1501.27	0.403777
$241$	566.266	0.151354	0.0756772	−	0.997132i	$-0.475888\pi$
$241$	566.266	0.151354	0.0756772	+	0.997132i	$0.475888\pi$
$242$	−999.562	−0.265514
$243$	−243.000	−0.0641500
$244$	4843.32	1.27075
$245$	−598.067	−0.155955
$246$	422.629	0.109536
$247$	616.695	0.158864
$248$	−5076.98	−1.29995
$249$	1026.49	0.261250
$250$	1233.08	0.311948
$251$	5865.95	1.47512	0.737561	−	0.675281i	$-0.235977\pi$
$251$	5865.95	1.47512	0.737561	+	0.675281i	$0.235977\pi$
$252$	441.000	0.110240
$253$	−534.943	−0.132931
$254$	−773.064	−0.190970
$255$	2820.45	0.692642
$256$	−119.000	−0.0290527
$257$	5312.51	1.28944	0.644719	−	0.764420i	$-0.276974\pi$
$257$	5312.51	1.28944	0.644719	+	0.764420i	$0.276974\pi$
$258$	291.245	0.0702795
$259$	−40.1810	−0.00963988
$260$	−1110.70	−0.264932
$261$	145.849	0.0345894
$262$	2535.27	0.597822
$263$	−212.544	−0.0498328	−0.0249164	−	0.999690i	$-0.507932\pi$
$263$	−212.544	−0.0498328	−0.0249164	+	0.999690i	$0.507932\pi$
$264$	−819.245	−0.190989
$265$	2153.84	0.499280
$266$	332.067	0.0765425
$267$	−2241.12	−0.513686
$268$	2456.13	0.559822
$269$	4037.17	0.915057	0.457529	−	0.889195i	$-0.348735\pi$
$269$	4037.17	0.915057	0.457529	+	0.889195i	$0.348735\pi$
$270$	329.547	0.0742799
$271$	8214.42	1.84129	0.920646	−	0.390397i	$-0.127662\pi$
$271$	8214.42	1.84129	0.920646	+	0.390397i	$0.127662\pi$
$272$	3158.12	0.704003
$273$	−273.000	−0.0605228
$274$	1847.52	0.407345
$275$	−436.435	−0.0957020
$276$	617.057	0.134574
$277$	6323.63	1.37166	0.685831	−	0.727761i	$-0.259439\pi$
$277$	6323.63	1.37166	0.685831	+	0.727761i	$0.259439\pi$
$278$	−1839.12	−0.396773
$279$	3046.19	0.653658
$280$	−1281.57	−0.273530
$281$	−7356.07	−1.56166	−0.780830	−	0.624744i	$-0.785203\pi$
$281$	−7356.07	−1.56166	−0.780830	+	0.624744i	$0.785203\pi$
$282$	−441.535	−0.0932376
$283$	526.416	0.110573	0.0552866	−	0.998471i	$-0.482393\pi$
$283$	526.416	0.110573	0.0552866	+	0.998471i	$0.482393\pi$
$284$	−3367.28	−0.703560
$285$	−1737.01	−0.361023
$286$	236.671	0.0489323
$287$	986.133	0.202821
$288$	1449.00	0.296469
$289$	1020.19	0.207651
$290$	−197.795	−0.0400514
$291$	−2166.33	−0.436400
$292$	−6855.09	−1.37385
$293$	3336.53	0.665262	0.332631	−	0.943057i	$-0.392064\pi$
$293$	3336.53	0.665262	0.332631	+	0.943057i	$0.392064\pi$
$294$	−147.000	−0.0291606
$295$	−4385.26	−0.865490
$296$	−86.1022	−0.0169074
$297$	491.547	0.0960352
$298$	−1246.02	−0.242216
$299$	−381.988	−0.0738827
$300$	503.429	0.0968849
$301$	679.571	0.130132
$302$	1655.38	0.315418
$303$	−4404.49	−0.835087
$304$	−1944.96	−0.366945
$305$	8444.99	1.58544
$306$	693.245	0.129510
$307$	7385.10	1.37293	0.686466	−	0.727162i	$-0.259161\pi$
$307$	7385.10	1.37293	0.686466	+	0.727162i	$0.259161\pi$
$308$	−892.067	−0.165033
$309$	3089.13	0.568720
$310$	−4131.12	−0.756877
$311$	−6593.51	−1.20220	−0.601099	−	0.799174i	$-0.705270\pi$
$311$	−6593.51	−1.20220	−0.601099	+	0.799174i	$0.705270\pi$
$312$	−585.000	−0.106151
$313$	−10937.3	−1.97513	−0.987565	−	0.157213i	$-0.949749\pi$
$313$	−10937.3	−1.97513	−0.987565	+	0.157213i	$0.949749\pi$
$314$	497.849	0.0894753
$315$	768.943	0.137540
$316$	3255.87	0.579610
$317$	−6295.38	−1.11541	−0.557703	−	0.830041i	$-0.688317\pi$
$317$	−6295.38	−1.11541	−0.557703	+	0.830041i	$0.688317\pi$
$318$	529.396	0.0933555
$319$	−295.027	−0.0517817
$320$	2038.31	0.356078
$321$	−3072.91	−0.534308
$322$	−205.686	−0.0355976
$323$	−3654.02	−0.629459
$324$	−567.000	−0.0972222
$325$	−311.646	−0.0531909
$326$	133.668	0.0227091
$327$	614.429	0.103908
$328$	2113.14	0.355728
$329$	−1030.25	−0.172643
$330$	−666.616	−0.111200
$331$	−1865.44	−0.309770	−0.154885	−	0.987933i	$-0.549501\pi$
$331$	−1865.44	−0.309770	−0.154885	+	0.987933i	$0.549501\pi$
$332$	2395.14	0.395935
$333$	51.6613	0.00850157
$334$	2127.52	0.348541
$335$	4282.60	0.698458
$336$	861.000	0.139796
$337$	−7358.07	−1.18938	−0.594688	−	0.803957i	$-0.702724\pi$
$337$	−7358.07	−1.18938	−0.594688	+	0.803957i	$0.702724\pi$
$338$	169.000	0.0271964
$339$	2374.28	0.380393
$340$	6581.06	1.04973
$341$	−6161.91	−0.978552
$342$	−426.943	−0.0675042
$343$	−343.000	−0.0539949
$344$	1456.22	0.228239
$345$	1075.92	0.167901
$346$	2153.40	0.334588
$347$	−1723.82	−0.266684	−0.133342	−	0.991070i	$-0.542571\pi$
$347$	−1723.82	−0.266684	−0.133342	+	0.991070i	$0.542571\pi$
$348$	340.314	0.0524217
$349$	−190.822	−0.0292678	−0.0146339	−	0.999893i	$-0.504658\pi$
$349$	−190.822	−0.0292678	−0.0146339	+	0.999893i	$0.504658\pi$
$350$	−167.810	−0.0256280
$351$	351.000	0.0533761
$352$	−2931.08	−0.443826
$353$	−7558.00	−1.13958	−0.569790	−	0.821790i	$-0.692975\pi$
$353$	−7558.00	−1.13958	−0.569790	+	0.821790i	$0.692975\pi$
$354$	−1077.86	−0.161830
$355$	−5871.30	−0.877792
$356$	−5229.28	−0.778514
$357$	1617.57	0.239807
$358$	3204.11	0.473024
$359$	3888.94	0.571728	0.285864	−	0.958270i	$-0.407719\pi$
$359$	3888.94	0.571728	0.285864	+	0.958270i	$0.407719\pi$
$360$	1647.73	0.241231
$361$	−4608.63	−0.671910
$362$	−2702.27	−0.392342
$363$	2998.69	0.433582
$364$	−637.000	−0.0917249
$365$	−11952.8	−1.71407
$366$	2075.71	0.296446
$367$	5063.43	0.720188	0.360094	−	0.932916i	$-0.382745\pi$
$367$	5063.43	0.720188	0.360094	+	0.932916i	$0.382745\pi$
$368$	1204.73	0.170655
$369$	−1267.89	−0.178871
$370$	−70.0610	−0.00984405
$371$	1235.26	0.172861
$372$	7107.77	0.990647
$373$	−6753.21	−0.937448	−0.468724	−	0.883345i	$-0.655286\pi$
$373$	−6753.21	−0.937448	−0.468724	+	0.883345i	$0.655286\pi$
$374$	−1402.31	−0.193882
$375$	−3699.24	−0.509408
$376$	−2207.67	−0.302798
$377$	−210.671	−0.0287801
$378$	189.000	0.0257172
$379$	11692.6	1.58472	0.792358	−	0.610057i	$-0.208853\pi$
$379$	11692.6	1.58472	0.792358	+	0.610057i	$0.208853\pi$
$380$	−4053.02	−0.547146
$381$	2319.19	0.311852
$382$	−1420.91	−0.190315
$383$	−13706.3	−1.82862	−0.914310	−	0.405016i	$-0.867266\pi$
$383$	−13706.3	−1.82862	−0.914310	+	0.405016i	$0.867266\pi$
$384$	4365.00	0.580079
$385$	−1555.44	−0.205903
$386$	−1187.62	−0.156602
$387$	−873.735	−0.114766
$388$	−5054.76	−0.661383
$389$	−175.812	−0.0229153	−0.0114576	−	0.999934i	$-0.503647\pi$
$389$	−175.812	−0.0229153	−0.0114576	+	0.999934i	$0.503647\pi$
$390$	−476.012	−0.0618047
$391$	2263.34	0.292742
$392$	−735.000	−0.0947018
$393$	−7605.81	−0.976240
$394$	−99.5103	−0.0127240
$395$	5677.04	0.723147
$396$	1146.94	0.145546
$397$	1482.27	0.187387	0.0936937	−	0.995601i	$-0.470133\pi$
$397$	1482.27	0.187387	0.0936937	+	0.995601i	$0.470133\pi$
$398$	3213.54	0.404724
$399$	−996.200	−0.124993
$400$	982.885	0.122861
$401$	−5658.45	−0.704662	−0.352331	−	0.935876i	$-0.614611\pi$
$401$	−5658.45	−0.704662	−0.352331	+	0.935876i	$0.614611\pi$
$402$	1052.63	0.130598
$403$	−4400.05	−0.543876
$404$	−10277.1	−1.26561
$405$	−988.641	−0.121299
$406$	−113.438	−0.0138666
$407$	−104.502	−0.0127272
$408$	3466.22	0.420597
$409$	−6758.62	−0.817096	−0.408548	−	0.912737i	$-0.633965\pi$
$409$	−6758.62	−0.817096	−0.408548	+	0.912737i	$0.633965\pi$
$410$	1719.46	0.207117
$411$	−5542.55	−0.665192
$412$	7207.97	0.861920
$413$	−2515.01	−0.299650
$414$	264.453	0.0313941
$415$	4176.25	0.493986
$416$	−2093.00	−0.246677
$417$	5517.35	0.647928
$418$	863.631	0.101056
$419$	−8973.79	−1.04630	−0.523149	−	0.852241i	$-0.675243\pi$
$419$	−8973.79	−1.04630	−0.523149	+	0.852241i	$0.675243\pi$
$420$	1794.20	0.208448
$421$	−14101.7	−1.63248	−0.816242	−	0.577711i	$-0.803946\pi$
$421$	−14101.7	−1.63248	−0.816242	+	0.577711i	$0.803946\pi$
$422$	651.547	0.0751583
$423$	1324.60	0.152256
$424$	2646.98	0.303181
$425$	1846.56	0.210756
$426$	−1443.12	−0.164130
$427$	4843.32	0.548911
$428$	−7170.11	−0.809768
$429$	−710.012	−0.0799061
$430$	1184.92	0.132889
$431$	9959.24	1.11304	0.556519	−	0.830835i	$-0.312136\pi$
$431$	9959.24	1.11304	0.556519	+	0.830835i	$0.312136\pi$
$432$	−1107.00	−0.123288
$433$	−666.411	−0.0739623	−0.0369811	−	0.999316i	$-0.511774\pi$
$433$	−666.411	−0.0739623	−0.0369811	+	0.999316i	$0.511774\pi$
$434$	−2369.26	−0.262046
$435$	593.384	0.0654036
$436$	1433.67	0.157478
$437$	−1393.91	−0.152585
$438$	−2937.90	−0.320498
$439$	4238.93	0.460850	0.230425	−	0.973090i	$-0.425988\pi$
$439$	4238.93	0.460850	0.230425	+	0.973090i	$0.425988\pi$
$440$	−3333.08	−0.361133
$441$	441.000	0.0476190
$442$	−1001.35	−0.107759
$443$	−12735.3	−1.36585	−0.682927	−	0.730487i	$-0.739293\pi$
$443$	−12735.3	−1.36585	−0.682927	+	0.730487i	$0.739293\pi$
$444$	120.543	0.0128845
$445$	−9117.95	−0.971308
$446$	6535.96	0.693917
$447$	3738.07	0.395536
$448$	1169.00	0.123281
$449$	−5212.79	−0.547899	−0.273949	−	0.961744i	$-0.588330\pi$
$449$	−5212.79	−0.547899	−0.273949	+	0.961744i	$0.588330\pi$
$450$	215.755	0.0226018
$451$	2564.71	0.267777
$452$	5539.98	0.576502
$453$	−4966.13	−0.515076
$454$	62.3321	0.00644359
$455$	−1110.70	−0.114440
$456$	−2134.71	−0.219226
$457$	8561.26	0.876322	0.438161	−	0.898897i	$-0.355630\pi$
$457$	8561.26	0.876322	0.438161	+	0.898897i	$0.355630\pi$
$458$	−2746.98	−0.280257
$459$	−2079.73	−0.211490
$460$	2510.49	0.254461
$461$	−4086.27	−0.412834	−0.206417	−	0.978464i	$-0.566180\pi$
$461$	−4086.27	−0.412834	−0.206417	+	0.978464i	$0.566180\pi$
$462$	−382.314	−0.0384997
$463$	16016.4	1.60766	0.803831	−	0.594858i	$-0.202792\pi$
$463$	16016.4	1.60766	0.803831	+	0.594858i	$0.202792\pi$
$464$	664.423	0.0664764
$465$	12393.4	1.23597
$466$	3356.86	0.333699
$467$	−8700.48	−0.862120	−0.431060	−	0.902323i	$-0.641860\pi$
$467$	−8700.48	−0.862120	−0.431060	+	0.902323i	$0.641860\pi$
$468$	819.000	0.0808938
$469$	2456.13	0.241820
$470$	−1796.38	−0.176299
$471$	−1493.55	−0.146113
$472$	−5389.31	−0.525557
$473$	1767.41	0.171809
$474$	1395.37	0.135214
$475$	−1137.22	−0.109851
$476$	3774.33	0.363438
$477$	−1588.19	−0.152449
$478$	2318.41	0.221844
$479$	12040.5	1.14853	0.574265	−	0.818670i	$-0.305288\pi$
$479$	12040.5	1.14853	0.574265	+	0.818670i	$0.305288\pi$
$480$	5895.23	0.560581
$481$	−74.6219	−0.00707373
$482$	566.266	0.0535119
$483$	617.057	0.0581306
$484$	6996.93	0.657112
$485$	−8813.66	−0.825170
$486$	−243.000	−0.0226805
$487$	3540.38	0.329424	0.164712	−	0.986342i	$-0.447330\pi$
$487$	3540.38	0.329424	0.164712	+	0.986342i	$0.447330\pi$
$488$	10378.6	0.962735
$489$	−401.004	−0.0370839
$490$	−598.067	−0.0551386
$491$	2773.40	0.254912	0.127456	−	0.991844i	$-0.459319\pi$
$491$	2773.40	0.254912	0.127456	+	0.991844i	$0.459319\pi$
$492$	−2958.40	−0.271087
$493$	1248.26	0.114034
$494$	616.695	0.0561669
$495$	1999.85	0.181589
$496$	13877.1	1.25625
$497$	−3367.28	−0.303909
$498$	1026.49	0.0923657
$499$	3676.21	0.329799	0.164899	−	0.986310i	$-0.447270\pi$
$499$	3676.21	0.329799	0.164899	+	0.986310i	$0.447270\pi$
$500$	−8631.57	−0.772031
$501$	−6382.57	−0.569166
$502$	5865.95	0.521534
$503$	−15765.8	−1.39754	−0.698770	−	0.715346i	$-0.746269\pi$
$503$	−15765.8	−1.39754	−0.698770	+	0.715346i	$0.746269\pi$
$504$	945.000	0.0835191
$505$	−17919.6	−1.57903
$506$	−534.943	−0.0469982
$507$	−507.000	−0.0444116
$508$	5411.45	0.472626
$509$	11455.9	0.997588	0.498794	−	0.866721i	$-0.333776\pi$
$509$	11455.9	0.997588	0.498794	+	0.866721i	$0.333776\pi$
$510$	2820.45	0.244886
$511$	−6855.09	−0.593447
$512$	11521.0	0.994455
$513$	1280.83	0.110234
$514$	5312.51	0.455885
$515$	12568.1	1.07537
$516$	−2038.71	−0.173933
$517$	−2679.44	−0.227934
$518$	−40.1810	−0.00340821
$519$	−6460.19	−0.546379
$520$	−2380.06	−0.200717
$521$	−17206.8	−1.44692	−0.723458	−	0.690369i	$-0.757448\pi$
$521$	−17206.8	−1.44692	−0.723458	+	0.690369i	$0.757448\pi$
$522$	145.849	0.0122292
$523$	1829.81	0.152987	0.0764934	−	0.997070i	$-0.475628\pi$
$523$	1829.81	0.152987	0.0764934	+	0.997070i	$0.475628\pi$
$524$	−17746.9	−1.47953
$525$	503.429	0.0418503
$526$	−212.544	−0.0176186
$527$	26071.0	2.15498
$528$	2239.27	0.184568
$529$	−11303.6	−0.929038
$530$	2153.84	0.176522
$531$	3233.58	0.264267
$532$	−2324.47	−0.189433
$533$	1831.39	0.148830
$534$	−2241.12	−0.181615
$535$	−12502.1	−1.01030
$536$	5263.14	0.424129
$537$	−9612.33	−0.772444
$538$	4037.17	0.323522
$539$	−892.067	−0.0712876
$540$	−2306.83	−0.183833
$541$	2004.71	0.159315	0.0796575	−	0.996822i	$-0.474617\pi$
$541$	2004.71	0.159315	0.0796575	+	0.996822i	$0.474617\pi$
$542$	8214.42	0.650995
$543$	8106.80	0.640693
$544$	12401.4	0.977399
$545$	2499.79	0.196476
$546$	−273.000	−0.0213980
$547$	21533.5	1.68319	0.841595	−	0.540109i	$-0.181617\pi$
$547$	21533.5	1.68319	0.841595	+	0.540109i	$0.181617\pi$
$548$	−12932.6	−1.00813
$549$	−6227.13	−0.484094
$550$	−436.435	−0.0338358
$551$	−768.755	−0.0594375
$552$	1322.27	0.101955
$553$	3255.87	0.250368
$554$	6323.63	0.484956
$555$	210.183	0.0160753
$556$	12873.8	0.981964
$557$	24095.3	1.83295	0.916474	−	0.400094i	$-0.131022\pi$
$557$	24095.3	1.83295	0.916474	+	0.400094i	$0.131022\pi$
$558$	3046.19	0.231103
$559$	1262.06	0.0954910
$560$	3502.96	0.264334
$561$	4206.94	0.316608
$562$	−7356.07	−0.552130
$563$	16303.1	1.22042	0.610209	−	0.792241i	$-0.291086\pi$
$563$	16303.1	1.22042	0.610209	+	0.792241i	$0.291086\pi$
$564$	3090.74	0.230751
$565$	9659.70	0.719269
$566$	526.416	0.0390935
$567$	−567.000	−0.0419961
$568$	−7215.59	−0.533027
$569$	18614.2	1.37144	0.685720	−	0.727866i	$-0.259488\pi$
$569$	18614.2	1.37144	0.685720	+	0.727866i	$0.259488\pi$
$570$	−1737.01	−0.127641
$571$	−17578.6	−1.28834	−0.644170	−	0.764882i	$-0.722797\pi$
$571$	−17578.6	−1.28834	−0.644170	+	0.764882i	$0.722797\pi$
$572$	−1656.70	−0.121101
$573$	4262.74	0.310783
$574$	986.133	0.0717080
$575$	704.409	0.0510885
$576$	−1503.00	−0.108724
$577$	−9786.72	−0.706112	−0.353056	−	0.935602i	$-0.614857\pi$
$577$	−9786.72	−0.706112	−0.353056	+	0.935602i	$0.614857\pi$
$578$	1020.19	0.0734158
$579$	3562.86	0.255729
$580$	1384.56	0.0991221
$581$	2395.14	0.171028
$582$	−2166.33	−0.154291
$583$	3212.63	0.228222
$584$	−14689.5	−1.04085
$585$	1428.04	0.100927
$586$	3336.53	0.235206
$587$	−20676.2	−1.45383	−0.726915	−	0.686727i	$-0.759047\pi$
$587$	−20676.2	−1.45383	−0.726915	+	0.686727i	$0.759047\pi$
$588$	1029.00	0.0721688
$589$	−16056.1	−1.12323
$590$	−4385.26	−0.305997
$591$	298.531	0.0207782
$592$	235.346	0.0163390
$593$	21885.8	1.51558	0.757792	−	0.652497i	$-0.226278\pi$
$593$	21885.8	1.51558	0.757792	+	0.652497i	$0.226278\pi$
$594$	491.547	0.0339536
$595$	6581.06	0.453440
$596$	8722.17	0.599453
$597$	−9640.62	−0.660912
$598$	−381.988	−0.0261215
$599$	15022.3	1.02470	0.512349	−	0.858777i	$-0.328775\pi$
$599$	15022.3	1.02470	0.512349	+	0.858777i	$0.328775\pi$
$600$	1078.78	0.0734014
$601$	−4302.43	−0.292013	−0.146006	−	0.989284i	$-0.546642\pi$
$601$	−4302.43	−0.292013	−0.146006	+	0.989284i	$0.546642\pi$
$602$	679.571	0.0460087
$603$	−3157.89	−0.213265
$604$	−11587.6	−0.780620
$605$	12200.1	0.819842
$606$	−4404.49	−0.295248
$607$	−12007.7	−0.802930	−0.401465	−	0.915874i	$-0.631499\pi$
$607$	−12007.7	−0.802930	−0.401465	+	0.915874i	$0.631499\pi$
$608$	−7637.53	−0.509445
$609$	340.314	0.0226441
$610$	8444.99	0.560537
$611$	−1913.32	−0.126685
$612$	−4852.71	−0.320522
$613$	−6494.87	−0.427937	−0.213968	−	0.976841i	$-0.568639\pi$
$613$	−6494.87	−0.427937	−0.213968	+	0.976841i	$0.568639\pi$
$614$	7385.10	0.485404
$615$	−5158.37	−0.338220
$616$	−1911.57	−0.125031
$617$	23753.6	1.54989	0.774946	−	0.632027i	$-0.217777\pi$
$617$	23753.6	1.54989	0.774946	+	0.632027i	$0.217777\pi$
$618$	3089.13	0.201073
$619$	−23340.2	−1.51554	−0.757772	−	0.652519i	$-0.773712\pi$
$619$	−23340.2	−1.51554	−0.757772	+	0.652519i	$0.773712\pi$
$620$	28917.8	1.87317
$621$	−793.359	−0.0512664
$622$	−6593.51	−0.425041
$623$	−5229.28	−0.336287
$624$	1599.00	0.102582
$625$	−18046.9	−1.15500
$626$	−10937.3	−0.698314
$627$	−2590.89	−0.165024
$628$	−3484.94	−0.221440
$629$	442.147	0.0280279
$630$	768.943	0.0486276
$631$	2734.75	0.172534	0.0862668	−	0.996272i	$-0.472506\pi$
$631$	2734.75	0.172534	0.0862668	+	0.996272i	$0.472506\pi$
$632$	6976.86	0.439121
$633$	−1954.64	−0.122733
$634$	−6295.38	−0.394356
$635$	9435.59	0.589669
$636$	−3705.77	−0.231043
$637$	−637.000	−0.0396214
$638$	−295.027	−0.0183076
$639$	4329.35	0.268023
$640$	17758.9	1.09685
$641$	−1078.75	−0.0664713	−0.0332356	−	0.999448i	$-0.510581\pi$
$641$	−1078.75	−0.0664713	−0.0332356	+	0.999448i	$0.510581\pi$
$642$	−3072.91	−0.188906
$643$	7612.25	0.466871	0.233435	−	0.972372i	$-0.425003\pi$
$643$	7612.25	0.466871	0.233435	+	0.972372i	$0.425003\pi$
$644$	1439.80	0.0880995
$645$	−3554.77	−0.217006
$646$	−3654.02	−0.222547
$647$	22595.8	1.37300	0.686502	−	0.727127i	$-0.259145\pi$
$647$	22595.8	1.37300	0.686502	+	0.727127i	$0.259145\pi$
$648$	−1215.00	−0.0736570
$649$	−6540.98	−0.395618
$650$	−311.646	−0.0188058
$651$	7107.77	0.427919
$652$	−935.676	−0.0562023
$653$	19539.7	1.17098	0.585488	−	0.810681i	$-0.300903\pi$
$653$	19539.7	1.17098	0.585488	+	0.810681i	$0.300903\pi$
$654$	614.429	0.0367371
$655$	−30944.1	−1.84593
$656$	−5775.92	−0.343768
$657$	8813.69	0.523371
$658$	−1030.25	−0.0610384
$659$	−32704.0	−1.93318	−0.966592	−	0.256322i	$-0.917489\pi$
$659$	−32704.0	−1.93318	−0.966592	+	0.256322i	$0.917489\pi$
$660$	4666.31	0.275206
$661$	1575.20	0.0926900	0.0463450	−	0.998925i	$-0.485243\pi$
$661$	1575.20	0.0926900	0.0463450	+	0.998925i	$0.485243\pi$
$662$	−1865.44	−0.109520
$663$	3004.06	0.175970
$664$	5132.45	0.299966
$665$	−4053.02	−0.236345
$666$	51.6613	0.00300576
$667$	476.175	0.0276426
$668$	−14892.7	−0.862596
$669$	−19607.9	−1.13316
$670$	4282.60	0.246942
$671$	12596.4	0.724708
$672$	3381.00	0.194085
$673$	7869.07	0.450714	0.225357	−	0.974276i	$-0.427645\pi$
$673$	7869.07	0.450714	0.225357	+	0.974276i	$0.427645\pi$
$674$	−7358.07	−0.420508
$675$	−647.265	−0.0369085
$676$	−1183.00	−0.0673077
$677$	13225.8	0.750824	0.375412	−	0.926858i	$-0.377501\pi$
$677$	13225.8	0.750824	0.375412	+	0.926858i	$0.377501\pi$
$678$	2374.28	0.134489
$679$	−5054.76	−0.285691
$680$	14102.3	0.795290
$681$	−186.996	−0.0105223
$682$	−6161.91	−0.345970
$683$	7585.94	0.424990	0.212495	−	0.977162i	$-0.431841\pi$
$683$	7585.94	0.424990	0.212495	+	0.977162i	$0.431841\pi$
$684$	2988.60	0.167064
$685$	−22549.8	−1.25778
$686$	−343.000	−0.0190901
$687$	8240.94	0.457659
$688$	−3980.35	−0.220566
$689$	2294.05	0.126845
$690$	1075.92	0.0593618
$691$	24731.4	1.36155	0.680773	−	0.732494i	$-0.261644\pi$
$691$	24731.4	1.36155	0.680773	+	0.732494i	$0.261644\pi$
$692$	−15073.8	−0.828062
$693$	1146.94	0.0628698
$694$	−1723.82	−0.0942872
$695$	22447.2	1.22514
$696$	729.245	0.0397155
$697$	−10851.3	−0.589702
$698$	−190.822	−0.0103477
$699$	−10070.6	−0.544928
$700$	1174.67	0.0634261
$701$	−6209.82	−0.334582	−0.167291	−	0.985908i	$-0.553502\pi$
$701$	−6209.82	−0.334582	−0.167291	+	0.985908i	$0.553502\pi$
$702$	351.000	0.0188713
$703$	−272.302	−0.0146089
$704$	3040.31	0.162764
$705$	5389.13	0.287895
$706$	−7558.00	−0.402902
$707$	−10277.1	−0.546693
$708$	7545.03	0.400508
$709$	18720.8	0.991642	0.495821	−	0.868425i	$-0.334867\pi$
$709$	18720.8	0.991642	0.495821	+	0.868425i	$0.334867\pi$
$710$	−5871.30	−0.310346
$711$	−4186.11	−0.220804
$712$	−11205.6	−0.589814
$713$	9945.35	0.522379
$714$	1617.57	0.0847844
$715$	−2888.67	−0.151091
$716$	−22428.8	−1.17067
$717$	−6955.22	−0.362270
$718$	3888.94	0.202137
$719$	−8441.95	−0.437874	−0.218937	−	0.975739i	$-0.570259\pi$
$719$	−8441.95	−0.437874	−0.218937	+	0.975739i	$0.570259\pi$
$720$	−4503.81	−0.233121
$721$	7207.97	0.372315
$722$	−4608.63	−0.237556
$723$	−1698.80	−0.0873846
$724$	18915.9	0.970998
$725$	388.490	0.0199009
$726$	2998.69	0.153294
$727$	19068.4	0.972776	0.486388	−	0.873743i	$-0.338314\pi$
$727$	19068.4	0.972776	0.486388	+	0.873743i	$0.338314\pi$
$728$	−1365.00	−0.0694921
$729$	729.000	0.0370370
$730$	−11952.8	−0.606017
$731$	−7477.93	−0.378360
$732$	−14530.0	−0.733666
$733$	−7568.57	−0.381380	−0.190690	−	0.981650i	$-0.561073\pi$
$733$	−7568.57	−0.381380	−0.190690	+	0.981650i	$0.561073\pi$
$734$	5063.43	0.254625
$735$	1794.20	0.0900409
$736$	4730.77	0.236927
$737$	6387.86	0.319267
$738$	−1267.89	−0.0632405
$739$	−17018.2	−0.847123	−0.423562	−	0.905867i	$-0.639220\pi$
$739$	−17018.2	−0.847123	−0.423562	+	0.905867i	$0.639220\pi$
$740$	490.427	0.0243628
$741$	−1850.09	−0.0917201
$742$	1235.26	0.0611155
$743$	−6200.01	−0.306132	−0.153066	−	0.988216i	$-0.548915\pi$
$743$	−6200.01	−0.306132	−0.153066	+	0.988216i	$0.548915\pi$
$744$	15230.9	0.750529
$745$	15208.3	0.747904
$746$	−6753.21	−0.331438
$747$	−3079.47	−0.150833
$748$	9816.20	0.479834
$749$	−7170.11	−0.349787
$750$	−3699.24	−0.180103
$751$	6344.75	0.308287	0.154143	−	0.988049i	$-0.450738\pi$
$751$	6344.75	0.308287	0.154143	+	0.988049i	$0.450738\pi$
$752$	6034.31	0.292618
$753$	−17597.9	−0.851662
$754$	−210.671	−0.0101753
$755$	−20204.6	−0.973936
$756$	−1323.00	−0.0636469
$757$	24728.6	1.18729	0.593643	−	0.804728i	$-0.297689\pi$
$757$	24728.6	1.18729	0.593643	+	0.804728i	$0.297689\pi$
$758$	11692.6	0.560281
$759$	1604.83	0.0767478
$760$	−8685.04	−0.414526
$761$	12922.5	0.615559	0.307779	−	0.951458i	$-0.400414\pi$
$761$	12922.5	0.615559	0.307779	+	0.951458i	$0.400414\pi$
$762$	2319.19	0.110256
$763$	1433.67	0.0680239
$764$	9946.39	0.471005
$765$	−8461.36	−0.399897
$766$	−13706.3	−0.646515
$767$	−4670.73	−0.219883
$768$	357.000	0.0167736
$769$	6736.32	0.315888	0.157944	−	0.987448i	$-0.449513\pi$
$769$	6736.32	0.315888	0.157944	+	0.987448i	$0.449513\pi$
$770$	−1555.44	−0.0727975
$771$	−15937.5	−0.744457
$772$	8313.33	0.387569
$773$	−19662.0	−0.914866	−0.457433	−	0.889244i	$-0.651231\pi$
$773$	−19662.0	−0.914866	−0.457433	+	0.889244i	$0.651231\pi$
$774$	−873.735	−0.0405759
$775$	8113.96	0.376080
$776$	−10831.6	−0.501073
$777$	120.543	0.00556558
$778$	−175.812	−0.00810177
$779$	6682.90	0.307368
$780$	3332.09	0.152959
$781$	−8757.53	−0.401241
$782$	2263.34	0.103500
$783$	−437.547	−0.0199702
$784$	2009.00	0.0915179
$785$	−6076.47	−0.276278
$786$	−7605.81	−0.345153
$787$	21001.9	0.951255	0.475627	−	0.879647i	$-0.342221\pi$
$787$	21001.9	0.951255	0.475627	+	0.879647i	$0.342221\pi$
$788$	696.572	0.0314903
$789$	637.632	0.0287710
$790$	5677.04	0.255671
$791$	5539.98	0.249025
$792$	2457.73	0.110267
$793$	8994.74	0.402790
$794$	1482.27	0.0662515
$795$	−6461.51	−0.288259
$796$	−22494.8	−1.00164
$797$	−1342.23	−0.0596538	−0.0298269	−	0.999555i	$-0.509496\pi$
$797$	−1342.23	−0.0596538	−0.0298269	+	0.999555i	$0.509496\pi$
$798$	−996.200	−0.0441918
$799$	11336.7	0.501958
$800$	3859.62	0.170573
$801$	6723.35	0.296577
$802$	−5658.45	−0.249136
$803$	−17828.6	−0.783508
$804$	−7368.40	−0.323213
$805$	2510.49	0.109917
$806$	−4400.05	−0.192289
$807$	−12111.5	−0.528309
$808$	−22022.4	−0.958845
$809$	−34653.1	−1.50598	−0.752990	−	0.658031i	$-0.771389\pi$
$809$	−34653.1	−1.50598	−0.752990	+	0.658031i	$0.771389\pi$
$810$	−988.641	−0.0428855
$811$	−41124.8	−1.78062	−0.890312	−	0.455352i	$-0.849514\pi$
$811$	−41124.8	−1.78062	−0.890312	+	0.455352i	$0.849514\pi$
$812$	794.067	0.0343181
$813$	−24643.3	−1.06307
$814$	−104.502	−0.00449974
$815$	−1631.48	−0.0701204
$816$	−9474.35	−0.406456
$817$	4605.37	0.197211
$818$	−6758.62	−0.288887
$819$	819.000	0.0349428
$820$	−12036.2	−0.512588
$821$	−20499.4	−0.871417	−0.435708	−	0.900088i	$-0.643502\pi$
$821$	−20499.4	−0.871417	−0.435708	+	0.900088i	$0.643502\pi$
$822$	−5542.55	−0.235181
$823$	−968.022	−0.0410002	−0.0205001	−	0.999790i	$-0.506526\pi$
$823$	−968.022	−0.0410002	−0.0205001	+	0.999790i	$0.506526\pi$
$824$	15445.7	0.653003
$825$	1309.31	0.0552536
$826$	−2515.01	−0.105942
$827$	45106.3	1.89661	0.948306	−	0.317357i	$-0.102795\pi$
$827$	45106.3	1.89661	0.948306	+	0.317357i	$0.102795\pi$
$828$	−1851.17	−0.0776965
$829$	31972.7	1.33952	0.669758	−	0.742580i	$-0.266398\pi$
$829$	31972.7	1.33952	0.669758	+	0.742580i	$0.266398\pi$
$830$	4176.25	0.174650
$831$	−18970.9	−0.791929
$832$	2171.00	0.0904638
$833$	3774.33	0.156990
$834$	5517.35	0.229077
$835$	−25967.4	−1.07621
$836$	−6045.42	−0.250102
$837$	−9138.56	−0.377389
$838$	−8973.79	−0.369922
$839$	−41799.7	−1.72001	−0.860004	−	0.510288i	$-0.829539\pi$
$839$	−41799.7	−1.72001	−0.860004	+	0.510288i	$0.829539\pi$
$840$	3844.71	0.157923
$841$	−24126.4	−0.989232
$842$	−14101.7	−0.577170
$843$	22068.2	0.901624
$844$	−4560.83	−0.186007
$845$	−2062.72	−0.0839760
$846$	1324.60	0.0538308
$847$	6996.93	0.283846
$848$	−7235.08	−0.292988
$849$	−1579.25	−0.0638395
$850$	1846.56	0.0745134
$851$	168.667	0.00679415
$852$	10101.8	0.406201
$853$	10280.9	0.412674	0.206337	−	0.978481i	$-0.433846\pi$
$853$	10280.9	0.412674	0.206337	+	0.978481i	$0.433846\pi$
$854$	4843.32	0.194069
$855$	5211.03	0.208437
$856$	−15364.5	−0.613492
$857$	−865.418	−0.0344949	−0.0172474	−	0.999851i	$-0.505490\pi$
$857$	−865.418	−0.0344949	−0.0172474	+	0.999851i	$0.505490\pi$
$858$	−710.012	−0.0282511
$859$	−22766.2	−0.904275	−0.452137	−	0.891948i	$-0.649338\pi$
$859$	−22766.2	−0.904275	−0.452137	+	0.891948i	$0.649338\pi$
$860$	−8294.47	−0.328883
$861$	−2958.40	−0.117099
$862$	9959.24	0.393519
$863$	15314.1	0.604053	0.302027	−	0.953300i	$-0.402337\pi$
$863$	15314.1	0.604053	0.302027	+	0.953300i	$0.402337\pi$
$864$	−4347.00	−0.171167
$865$	−26283.1	−1.03313
$866$	−666.411	−0.0261496
$867$	−3060.57	−0.119887
$868$	16584.8	0.648531
$869$	8467.78	0.330552
$870$	593.384	0.0231237
$871$	4561.39	0.177448
$872$	3072.14	0.119307
$873$	6498.98	0.251955
$874$	−1393.91	−0.0539469
$875$	−8631.57	−0.333486
$876$	20565.3	0.793192
$877$	31491.0	1.21252	0.606258	−	0.795268i	$-0.292670\pi$
$877$	31491.0	1.21252	0.606258	+	0.795268i	$0.292670\pi$
$878$	4238.93	0.162935
$879$	−10009.6	−0.384089
$880$	9110.42	0.348991
$881$	−38358.4	−1.46689	−0.733443	−	0.679751i	$-0.762088\pi$
$881$	−38358.4	−1.46689	−0.733443	+	0.679751i	$0.762088\pi$
$882$	441.000	0.0168359
$883$	18034.4	0.687322	0.343661	−	0.939094i	$-0.388333\pi$
$883$	18034.4	0.687322	0.343661	+	0.939094i	$0.388333\pi$
$884$	7009.48	0.266690
$885$	13155.8	0.499691
$886$	−12735.3	−0.482902
$887$	40849.3	1.54632	0.773159	−	0.634212i	$-0.218675\pi$
$887$	40849.3	1.54632	0.773159	+	0.634212i	$0.218675\pi$
$888$	258.307	0.00976149
$889$	5411.45	0.204155
$890$	−9117.95	−0.343409
$891$	−1474.64	−0.0554459
$892$	−45751.8	−1.71736
$893$	−6981.85	−0.261634
$894$	3738.07	0.139843
$895$	−39107.6	−1.46058
$896$	10185.0	0.379751
$897$	1145.96	0.0426562
$898$	−5212.79	−0.193712
$899$	5484.98	0.203486
$900$	−1510.29	−0.0559365
$901$	−13592.6	−0.502593
$902$	2564.71	0.0946736
$903$	−2038.71	−0.0751320
$904$	11871.4	0.436766
$905$	32982.4	1.21146
$906$	−4966.13	−0.182107
$907$	26987.2	0.987977	0.493989	−	0.869468i	$-0.335538\pi$
$907$	26987.2	0.987977	0.493989	+	0.869468i	$0.335538\pi$
$908$	−436.324	−0.0159471
$909$	13213.5	0.482138
$910$	−1110.70	−0.0404606
$911$	38833.4	1.41230	0.706152	−	0.708060i	$-0.250429\pi$
$911$	38833.4	1.41230	0.706152	+	0.708060i	$0.250429\pi$
$912$	5834.88	0.211856
$913$	6229.23	0.225802
$914$	8561.26	0.309826
$915$	−25335.0	−0.915353
$916$	19228.9	0.693602
$917$	−17746.9	−0.639099
$918$	−2079.73	−0.0747728
$919$	37889.4	1.36002	0.680009	−	0.733204i	$-0.261976\pi$
$919$	37889.4	1.36002	0.680009	+	0.733204i	$0.261976\pi$
$920$	5379.61	0.192783
$921$	−22155.3	−0.792662
$922$	−4086.27	−0.145959
$923$	−6253.51	−0.223009
$924$	2676.20	0.0952819
$925$	137.607	0.00489135
$926$	16016.4	0.568394
$927$	−9267.39	−0.328351
$928$	2609.08	0.0922922
$929$	3047.98	0.107644	0.0538218	−	0.998551i	$-0.482860\pi$
$929$	3047.98	0.107644	0.0538218	+	0.998551i	$0.482860\pi$
$930$	12393.4	0.436983
$931$	−2324.47	−0.0818274
$932$	−23498.1	−0.825863
$933$	19780.5	0.694090
$934$	−8700.48	−0.304806
$935$	17115.9	0.598662
$936$	1755.00	0.0612863
$937$	−25664.2	−0.894785	−0.447393	−	0.894338i	$-0.647647\pi$
$937$	−25664.2	−0.894785	−0.447393	+	0.894338i	$0.647647\pi$
$938$	2456.13	0.0854964
$939$	32812.0	1.14034
$940$	12574.6	0.436318
$941$	−49331.9	−1.70901	−0.854503	−	0.519447i	$-0.826138\pi$
$941$	−49331.9	−1.70901	−0.854503	+	0.519447i	$0.826138\pi$
$942$	−1493.55	−0.0516586
$943$	−4139.46	−0.142947
$944$	14730.8	0.507887
$945$	−2306.83	−0.0794086
$946$	1767.41	0.0607437
$947$	46571.8	1.59808	0.799039	−	0.601279i	$-0.205342\pi$
$947$	46571.8	1.59808	0.799039	+	0.601279i	$0.205342\pi$
$948$	−9767.60	−0.334638
$949$	−12730.9	−0.435471
$950$	−1137.22	−0.0388383
$951$	18886.1	0.643980
$952$	8087.86	0.275346
$953$	33788.5	1.14850	0.574249	−	0.818681i	$-0.305294\pi$
$953$	33788.5	1.14850	0.574249	+	0.818681i	$0.305294\pi$
$954$	−1588.19	−0.0538988
$955$	17342.9	0.587646
$956$	−16228.8	−0.549036
$957$	885.082	0.0298962
$958$	12040.5	0.406067
$959$	−12932.6	−0.435470
$960$	−6114.93	−0.205582
$961$	84767.8	2.84541
$962$	−74.6219	−0.00250094
$963$	9218.72	0.308483
$964$	−3963.87	−0.132435
$965$	14495.4	0.483548
$966$	617.057	0.0205523
$967$	−5212.87	−0.173355	−0.0866776	−	0.996236i	$-0.527625\pi$
$967$	−5212.87	−0.173355	−0.0866776	+	0.996236i	$0.527625\pi$
$968$	14993.4	0.497838
$969$	10962.1	0.363418
$970$	−8813.66	−0.291742
$971$	21325.5	0.704807	0.352404	−	0.935848i	$-0.385364\pi$
$971$	21325.5	0.704807	0.352404	+	0.935848i	$0.385364\pi$
$972$	1701.00	0.0561313
$973$	12873.8	0.424169
$974$	3540.38	0.116469
$975$	934.939	0.0307098
$976$	−28368.0	−0.930368
$977$	24212.2	0.792853	0.396427	−	0.918066i	$-0.370250\pi$
$977$	24212.2	0.792853	0.396427	+	0.918066i	$0.370250\pi$
$978$	−401.004	−0.0131111
$979$	−13600.2	−0.443987
$980$	4186.47	0.136461
$981$	−1843.29	−0.0599914
$982$	2773.40	0.0901250
$983$	2974.98	0.0965281	0.0482641	−	0.998835i	$-0.484631\pi$
$983$	2974.98	0.0965281	0.0482641	+	0.998835i	$0.484631\pi$
$984$	−6339.43	−0.205380
$985$	1214.57	0.0392887
$986$	1248.26	0.0403171
$987$	3090.74	0.0996752
$988$	−4316.87	−0.139006
$989$	−2852.61	−0.0917168
$990$	1999.85	0.0642014
$991$	17227.5	0.552219	0.276109	−	0.961126i	$-0.410955\pi$
$991$	17227.5	0.552219	0.276109	+	0.961126i	$0.410955\pi$
$992$	54492.9	1.74410
$993$	5596.32	0.178846
$994$	−3367.28	−0.107448
$995$	−39222.7	−1.24969
$996$	−7185.43	−0.228593
$997$	14380.7	0.456813	0.228406	−	0.973566i	$-0.426648\pi$
$997$	14380.7	0.456813	0.228406	+	0.973566i	$0.426648\pi$
$998$	3676.21	0.116601
$999$	−154.984	−0.00490838

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	273.4.a.d.1.1	✓	2
3.2	odd	2		819.4.a.d.1.2		2
7.6	odd	2		1911.4.a.g.1.2		2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
273.4.a.d.1.1	✓	2	1.1	even	1	trivial
819.4.a.d.1.2		2	3.2	odd	2
1911.4.a.g.1.2		2	7.6	odd	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 273 = 3 \cdot 7 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	273.a (trivial)

\(f(q)\)	\(=\)	\(q+1.00000 q^{2} -3.00000 q^{3} -7.00000 q^{4} -12.2054 q^{5} -3.00000 q^{6} -7.00000 q^{7} -15.0000 q^{8} +9.00000 q^{9} +O(q^{10})\)	\(q+1.00000 q^{2} -3.00000 q^{3} -7.00000 q^{4} -12.2054 q^{5} -3.00000 q^{6} -7.00000 q^{7} -15.0000 q^{8} +9.00000 q^{9} -12.2054 q^{10} -18.2054 q^{11} +21.0000 q^{12} -13.0000 q^{13} -7.00000 q^{14} +36.6163 q^{15} +41.0000 q^{16} +77.0272 q^{17} +9.00000 q^{18} -47.4381 q^{19} +85.4381 q^{20} +21.0000 q^{21} -18.2054 q^{22} +29.3837 q^{23} +45.0000 q^{24} +23.9728 q^{25} -13.0000 q^{26} -27.0000 q^{27} +49.0000 q^{28} +16.2054 q^{29} +36.6163 q^{30} +338.465 q^{31} +161.000 q^{32} +54.6163 q^{33} +77.0272 q^{34} +85.4381 q^{35} -63.0000 q^{36} +5.74015 q^{37} -47.4381 q^{38} +39.0000 q^{39} +183.082 q^{40} -140.876 q^{41} +21.0000 q^{42} -97.0816 q^{43} +127.438 q^{44} -109.849 q^{45} +29.3837 q^{46} +147.178 q^{47} -123.000 q^{48} +49.0000 q^{49} +23.9728 q^{50} -231.082 q^{51} +91.0000 q^{52} -176.465 q^{53} -27.0000 q^{54} +222.205 q^{55} +105.000 q^{56} +142.314 q^{57} +16.2054 q^{58} +359.287 q^{59} -256.314 q^{60} -691.903 q^{61} +338.465 q^{62} -63.0000 q^{63} -167.000 q^{64} +158.671 q^{65} +54.6163 q^{66} -350.876 q^{67} -539.190 q^{68} -88.1510 q^{69} +85.4381 q^{70} +481.039 q^{71} -135.000 q^{72} +979.299 q^{73} +5.74015 q^{74} -71.9184 q^{75} +332.067 q^{76} +127.438 q^{77} +39.0000 q^{78} -465.124 q^{79} -500.423 q^{80} +81.0000 q^{81} -140.876 q^{82} -342.163 q^{83} -147.000 q^{84} -940.151 q^{85} -97.0816 q^{86} -48.6163 q^{87} +273.082 q^{88} +747.039 q^{89} -109.849 q^{90} +91.0000 q^{91} -205.686 q^{92} -1015.40 q^{93} +147.178 q^{94} +579.003 q^{95} -483.000 q^{96} +722.109 q^{97} +49.0000 q^{98} -163.849 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q + 2 q^{2} - 6 q^{3} - 14 q^{4} + 5 q^{5} - 6 q^{6} - 14 q^{7} - 30 q^{8} + 18 q^{9}+O(q^{10}) \) 2 * q + 2 * q^2 - 6 * q^3 - 14 * q^4 + 5 * q^5 - 6 * q^6 - 14 * q^7 - 30 * q^8 + 18 * q^9	\( 2 q + 2 q^{2} - 6 q^{3} - 14 q^{4} + 5 q^{5} - 6 q^{6} - 14 q^{7} - 30 q^{8} + 18 q^{9} + 5 q^{10} - 7 q^{11} + 42 q^{12} - 26 q^{13} - 14 q^{14} - 15 q^{15} + 82 q^{16} + 7 q^{17} + 18 q^{18} + 111 q^{19} - 35 q^{20} + 42 q^{21} - 7 q^{22} + 147 q^{23} + 90 q^{24} + 195 q^{25} - 26 q^{26} - 54 q^{27} + 98 q^{28} + 3 q^{29} - 15 q^{30} + 324 q^{31} + 322 q^{32} + 21 q^{33} + 7 q^{34} - 35 q^{35} - 126 q^{36} + 335 q^{37} + 111 q^{38} + 78 q^{39} - 75 q^{40} + 130 q^{41} + 42 q^{42} + 247 q^{43} + 49 q^{44} + 45 q^{45} + 147 q^{46} + 412 q^{47} - 246 q^{48} + 98 q^{49} + 195 q^{50} - 21 q^{51} + 182 q^{52} - 54 q^{54} + 415 q^{55} + 210 q^{56} - 333 q^{57} + 3 q^{58} + 248 q^{59} + 105 q^{60} - 825 q^{61} + 324 q^{62} - 126 q^{63} - 334 q^{64} - 65 q^{65} + 21 q^{66} - 290 q^{67} - 49 q^{68} - 441 q^{69} - 35 q^{70} - 332 q^{71} - 270 q^{72} + 341 q^{73} + 335 q^{74} - 585 q^{75} - 777 q^{76} + 49 q^{77} + 78 q^{78} - 1342 q^{79} + 205 q^{80} + 162 q^{81} + 130 q^{82} + 198 q^{83} - 294 q^{84} - 2145 q^{85} + 247 q^{86} - 9 q^{87} + 105 q^{88} + 200 q^{89} + 45 q^{90} + 182 q^{91} - 1029 q^{92} - 972 q^{93} + 412 q^{94} + 3305 q^{95} - 966 q^{96} + 856 q^{97} + 98 q^{98} - 63 q^{99}+O(q^{100}) \) 2 * q + 2 * q^2 - 6 * q^3 - 14 * q^4 + 5 * q^5 - 6 * q^6 - 14 * q^7 - 30 * q^8 + 18 * q^9 + 5 * q^10 - 7 * q^11 + 42 * q^12 - 26 * q^13 - 14 * q^14 - 15 * q^15 + 82 * q^16 + 7 * q^17 + 18 * q^18 + 111 * q^19 - 35 * q^20 + 42 * q^21 - 7 * q^22 + 147 * q^23 + 90 * q^24 + 195 * q^25 - 26 * q^26 - 54 * q^27 + 98 * q^28 + 3 * q^29 - 15 * q^30 + 324 * q^31 + 322 * q^32 + 21 * q^33 + 7 * q^34 - 35 * q^35 - 126 * q^36 + 335 * q^37 + 111 * q^38 + 78 * q^39 - 75 * q^40 + 130 * q^41 + 42 * q^42 + 247 * q^43 + 49 * q^44 + 45 * q^45 + 147 * q^46 + 412 * q^47 - 246 * q^48 + 98 * q^49 + 195 * q^50 - 21 * q^51 + 182 * q^52 - 54 * q^54 + 415 * q^55 + 210 * q^56 - 333 * q^57 + 3 * q^58 + 248 * q^59 + 105 * q^60 - 825 * q^61 + 324 * q^62 - 126 * q^63 - 334 * q^64 - 65 * q^65 + 21 * q^66 - 290 * q^67 - 49 * q^68 - 441 * q^69 - 35 * q^70 - 332 * q^71 - 270 * q^72 + 341 * q^73 + 335 * q^74 - 585 * q^75 - 777 * q^76 + 49 * q^77 + 78 * q^78 - 1342 * q^79 + 205 * q^80 + 162 * q^81 + 130 * q^82 + 198 * q^83 - 294 * q^84 - 2145 * q^85 + 247 * q^86 - 9 * q^87 + 105 * q^88 + 200 * q^89 + 45 * q^90 + 182 * q^91 - 1029 * q^92 - 972 * q^93 + 412 * q^94 + 3305 * q^95 - 966 * q^96 + 856 * q^97 + 98 * q^98 - 63 * q^99

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