LMFDB - Embedded newform 1001.2.a.n.1.9

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1001,2,Mod(1,1001)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1001, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("1001.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1001 = 7 \cdot 11 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1001.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:	$7.99302524233$
Analytic rank:	$0$
Dimension:	$11$
Coefficient field:	$\mathbb{Q}[x]/(x^{11} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{11} - x^{10} - 18x^{9} + 15x^{8} + 117x^{7} - 78x^{6} - 326x^{5} + 167x^{4} + 348x^{3} - 143x^{2} - 74x + 24 $ x^11 - x^10 - 18x^9 + 15x^8 + 117x^7 - 78x^6 - 326x^5 + 167x^4 + 348x^3 - 143x^2 - 74*x + 24
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 2^{2} $
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.9
Root			$-1.72345$ of defining polynomial
Character	$\chi$	$=$	1001.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.72345 q^{2} +1.94436 q^{3} +0.970287 q^{4} +2.87921 q^{5} +3.35102 q^{6} +1.00000 q^{7} -1.77466 q^{8} +0.780553 q^{9} +O(q^{10})$	\(q+1.72345 q^{2} +1.94436 q^{3} +0.970287 q^{4} +2.87921 q^{5} +3.35102 q^{6} +1.00000 q^{7} -1.77466 q^{8} +0.780553 q^{9} +4.96218 q^{10} +1.00000 q^{11} +1.88659 q^{12} +1.00000 q^{13} +1.72345 q^{14} +5.59824 q^{15} -4.99912 q^{16} -1.03513 q^{17} +1.34525 q^{18} -3.77967 q^{19} +2.79366 q^{20} +1.94436 q^{21} +1.72345 q^{22} +4.81227 q^{23} -3.45059 q^{24} +3.28986 q^{25} +1.72345 q^{26} -4.31541 q^{27} +0.970287 q^{28} -2.49935 q^{29} +9.64829 q^{30} -3.70030 q^{31} -5.06642 q^{32} +1.94436 q^{33} -1.78400 q^{34} +2.87921 q^{35} +0.757361 q^{36} +3.10095 q^{37} -6.51408 q^{38} +1.94436 q^{39} -5.10962 q^{40} -3.08866 q^{41} +3.35102 q^{42} +2.77031 q^{43} +0.970287 q^{44} +2.24738 q^{45} +8.29371 q^{46} -1.01541 q^{47} -9.72011 q^{48} +1.00000 q^{49} +5.66991 q^{50} -2.01267 q^{51} +0.970287 q^{52} +1.70518 q^{53} -7.43741 q^{54} +2.87921 q^{55} -1.77466 q^{56} -7.34906 q^{57} -4.30751 q^{58} +12.6864 q^{59} +5.43190 q^{60} -11.8456 q^{61} -6.37729 q^{62} +0.780553 q^{63} +1.26650 q^{64} +2.87921 q^{65} +3.35102 q^{66} -2.26886 q^{67} -1.00437 q^{68} +9.35680 q^{69} +4.96218 q^{70} -11.5460 q^{71} -1.38522 q^{72} +3.92496 q^{73} +5.34435 q^{74} +6.39668 q^{75} -3.66737 q^{76} +1.00000 q^{77} +3.35102 q^{78} -7.80949 q^{79} -14.3935 q^{80} -10.7324 q^{81} -5.32317 q^{82} +1.39326 q^{83} +1.88659 q^{84} -2.98036 q^{85} +4.77450 q^{86} -4.85965 q^{87} -1.77466 q^{88} -6.58651 q^{89} +3.87325 q^{90} +1.00000 q^{91} +4.66928 q^{92} -7.19474 q^{93} -1.75000 q^{94} -10.8825 q^{95} -9.85096 q^{96} +15.1174 q^{97} +1.72345 q^{98} +0.780553 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 11 q - q^{2} + 2 q^{3} + 15 q^{4} + 7 q^{5} + 3 q^{6} + 11 q^{7} - 6 q^{8} + 15 q^{9}+O(q^{10}) $ 11 * q - q^2 + 2 * q^3 + 15 * q^4 + 7 * q^5 + 3 * q^6 + 11 * q^7 - 6 * q^8 + 15 * q^9	\( 11 q - q^{2} + 2 q^{3} + 15 q^{4} + 7 q^{5} + 3 q^{6} + 11 q^{7} - 6 q^{8} + 15 q^{9} + q^{10} + 11 q^{11} - 5 q^{12} + 11 q^{13} - q^{14} + 4 q^{15} + 15 q^{16} + 7 q^{17} - 17 q^{18} + 22 q^{19} + 6 q^{20} + 2 q^{21} - q^{22} + 3 q^{23} + 17 q^{24} + 10 q^{25} - q^{26} + 2 q^{27} + 15 q^{28} - 6 q^{29} - 40 q^{30} + 28 q^{31} - 23 q^{32} + 2 q^{33} + 19 q^{34} + 7 q^{35} + 48 q^{36} + q^{37} - 20 q^{38} + 2 q^{39} + 16 q^{40} - 4 q^{41} + 3 q^{42} - 8 q^{43} + 15 q^{44} + 12 q^{45} + 2 q^{46} + 22 q^{47} - 30 q^{48} + 11 q^{49} - 24 q^{50} - 27 q^{51} + 15 q^{52} + 9 q^{53} + 36 q^{54} + 7 q^{55} - 6 q^{56} - 34 q^{57} - 8 q^{58} - 2 q^{59} + 25 q^{60} + 8 q^{62} + 15 q^{63} - 10 q^{64} + 7 q^{65} + 3 q^{66} + 23 q^{67} + 24 q^{68} + 7 q^{69} + q^{70} + 3 q^{71} - 76 q^{72} + 29 q^{73} + 15 q^{74} + 36 q^{75} + 62 q^{76} + 11 q^{77} + 3 q^{78} + 26 q^{79} - 16 q^{80} + 7 q^{81} - 16 q^{82} + 9 q^{83} - 5 q^{84} - 31 q^{85} + 28 q^{86} + 13 q^{87} - 6 q^{88} + 9 q^{89} - 26 q^{90} + 11 q^{91} - 58 q^{92} - 24 q^{93} - 34 q^{94} - 14 q^{95} + 56 q^{96} + 40 q^{97} - q^{98} + 15 q^{99}+O(q^{100}) \) 11 * q - q^2 + 2 * q^3 + 15 * q^4 + 7 * q^5 + 3 * q^6 + 11 * q^7 - 6 * q^8 + 15 * q^9 + q^10 + 11 * q^11 - 5 * q^12 + 11 * q^13 - q^14 + 4 * q^15 + 15 * q^16 + 7 * q^17 - 17 * q^18 + 22 * q^19 + 6 * q^20 + 2 * q^21 - q^22 + 3 * q^23 + 17 * q^24 + 10 * q^25 - q^26 + 2 * q^27 + 15 * q^28 - 6 * q^29 - 40 * q^30 + 28 * q^31 - 23 * q^32 + 2 * q^33 + 19 * q^34 + 7 * q^35 + 48 * q^36 + q^37 - 20 * q^38 + 2 * q^39 + 16 * q^40 - 4 * q^41 + 3 * q^42 - 8 * q^43 + 15 * q^44 + 12 * q^45 + 2 * q^46 + 22 * q^47 - 30 * q^48 + 11 * q^49 - 24 * q^50 - 27 * q^51 + 15 * q^52 + 9 * q^53 + 36 * q^54 + 7 * q^55 - 6 * q^56 - 34 * q^57 - 8 * q^58 - 2 * q^59 + 25 * q^60 + 8 * q^62 + 15 * q^63 - 10 * q^64 + 7 * q^65 + 3 * q^66 + 23 * q^67 + 24 * q^68 + 7 * q^69 + q^70 + 3 * q^71 - 76 * q^72 + 29 * q^73 + 15 * q^74 + 36 * q^75 + 62 * q^76 + 11 * q^77 + 3 * q^78 + 26 * q^79 - 16 * q^80 + 7 * q^81 - 16 * q^82 + 9 * q^83 - 5 * q^84 - 31 * q^85 + 28 * q^86 + 13 * q^87 - 6 * q^88 + 9 * q^89 - 26 * q^90 + 11 * q^91 - 58 * q^92 - 24 * q^93 - 34 * q^94 - 14 * q^95 + 56 * q^96 + 40 * q^97 - q^98 + 15 * 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 $

$2$	1.72345	1.21866	0.609332	−	0.792915i	$-0.291438\pi$
$2$	1.72345	1.21866	0.609332	+	0.792915i	$0.291438\pi$
$3$	1.94436	1.12258	0.561290	−	0.827619i	$-0.310305\pi$
$3$	1.94436	1.12258	0.561290	+	0.827619i	$0.310305\pi$
$4$	0.970287	0.485144
$5$	2.87921	1.28762	0.643811	−	0.765184i	$-0.277352\pi$
$5$	2.87921	1.28762	0.643811	+	0.765184i	$0.277352\pi$
$6$	3.35102	1.36805
$7$	1.00000	0.377964
$7$	1.00000	0.377964
$8$	−1.77466	−0.627437
$9$	0.780553	0.260184
$10$	4.96218	1.56918
$11$	1.00000	0.301511
$11$	1.00000	0.301511
$12$	1.88659	0.544612
$13$	1.00000	0.277350
$13$	1.00000	0.277350
$14$	1.72345	0.460612
$15$	5.59824	1.44546
$16$	−4.99912	−1.24978
$17$	−1.03513	−0.251056	−0.125528	−	0.992090i	$-0.540062\pi$
$17$	−1.03513	−0.251056	−0.125528	+	0.992090i	$0.540062\pi$
$18$	1.34525	0.317077
$19$	−3.77967	−0.867116	−0.433558	−	0.901126i	$-0.642742\pi$
$19$	−3.77967	−0.867116	−0.433558	+	0.901126i	$0.642742\pi$
$20$	2.79366	0.624682
$21$	1.94436	0.424295
$22$	1.72345	0.367441
$23$	4.81227	1.00343	0.501713	−	0.865034i	$-0.332703\pi$
$23$	4.81227	1.00343	0.501713	+	0.865034i	$0.332703\pi$
$24$	−3.45059	−0.704348
$25$	3.28986	0.657972
$26$	1.72345	0.337997
$27$	−4.31541	−0.830502
$28$	0.970287	0.183367
$29$	−2.49935	−0.464118	−0.232059	−	0.972702i	$-0.574546\pi$
$29$	−2.49935	−0.464118	−0.232059	+	0.972702i	$0.574546\pi$
$30$	9.64829	1.76153
$31$	−3.70030	−0.664594	−0.332297	−	0.943175i	$-0.607824\pi$
$31$	−3.70030	−0.664594	−0.332297	+	0.943175i	$0.607824\pi$
$32$	−5.06642	−0.895625
$33$	1.94436	0.338470
$34$	−1.78400	−0.305953
$35$	2.87921	0.486676
$36$	0.757361	0.126227
$37$	3.10095	0.509794	0.254897	−	0.966968i	$-0.417958\pi$
$37$	3.10095	0.509794	0.254897	+	0.966968i	$0.417958\pi$
$38$	−6.51408	−1.05672
$39$	1.94436	0.311347
$40$	−5.10962	−0.807902
$41$	−3.08866	−0.482368	−0.241184	−	0.970479i	$-0.577536\pi$
$41$	−3.08866	−0.482368	−0.241184	+	0.970479i	$0.577536\pi$
$42$	3.35102	0.517073
$43$	2.77031	0.422469	0.211234	−	0.977435i	$-0.432252\pi$
$43$	2.77031	0.422469	0.211234	+	0.977435i	$0.432252\pi$
$44$	0.970287	0.146276
$45$	2.24738	0.335019
$46$	8.29371	1.22284
$47$	−1.01541	−0.148112	−0.0740561	−	0.997254i	$-0.523594\pi$
$47$	−1.01541	−0.148112	−0.0740561	+	0.997254i	$0.523594\pi$
$48$	−9.72011	−1.40298
$49$	1.00000	0.142857
$50$	5.66991	0.801847
$51$	−2.01267	−0.281830
$52$	0.970287	0.134555
$53$	1.70518	0.234224	0.117112	−	0.993119i	$-0.462636\pi$
$53$	1.70518	0.234224	0.117112	+	0.993119i	$0.462636\pi$
$54$	−7.43741	−1.01210
$55$	2.87921	0.388233
$56$	−1.77466	−0.237149
$57$	−7.34906	−0.973406
$58$	−4.30751	−0.565604
$59$	12.6864	1.65163	0.825816	−	0.563940i	$-0.190715\pi$
$59$	12.6864	1.65163	0.825816	+	0.563940i	$0.190715\pi$
$60$	5.43190	0.701255
$61$	−11.8456	−1.51668	−0.758338	−	0.651862i	$-0.773988\pi$
$61$	−11.8456	−1.51668	−0.758338	+	0.651862i	$0.773988\pi$
$62$	−6.37729	−0.809917
$63$	0.780553	0.0983404
$64$	1.26650	0.158313
$65$	2.87921	0.357122
$66$	3.35102	0.412482
$67$	−2.26886	−0.277185	−0.138593	−	0.990349i	$-0.544258\pi$
$67$	−2.26886	−0.277185	−0.138593	+	0.990349i	$0.544258\pi$
$68$	−1.00437	−0.121798
$69$	9.35680	1.12643
$70$	4.96218	0.593094
$71$	−11.5460	−1.37026	−0.685128	−	0.728423i	$-0.740254\pi$
$71$	−11.5460	−1.37026	−0.685128	+	0.728423i	$0.740254\pi$
$72$	−1.38522	−0.163249
$73$	3.92496	0.459382	0.229691	−	0.973264i	$-0.426228\pi$
$73$	3.92496	0.459382	0.229691	+	0.973264i	$0.426228\pi$
$74$	5.34435	0.621268
$75$	6.39668	0.738625
$76$	−3.66737	−0.420676
$77$	1.00000	0.113961
$78$	3.35102	0.379428
$79$	−7.80949	−0.878636	−0.439318	−	0.898332i	$-0.644780\pi$
$79$	−7.80949	−0.878636	−0.439318	+	0.898332i	$0.644780\pi$
$80$	−14.3935	−1.60924
$81$	−10.7324	−1.19249
$82$	−5.32317	−0.587845
$83$	1.39326	0.152930	0.0764650	−	0.997072i	$-0.475637\pi$
$83$	1.39326	0.152930	0.0764650	+	0.997072i	$0.475637\pi$
$84$	1.88659	0.205844
$85$	−2.98036	−0.323265
$86$	4.77450	0.514848
$87$	−4.85965	−0.521009
$88$	−1.77466	−0.189179
$89$	−6.58651	−0.698168	−0.349084	−	0.937091i	$-0.613507\pi$
$89$	−6.58651	−0.698168	−0.349084	+	0.937091i	$0.613507\pi$
$90$	3.87325	0.408276
$91$	1.00000	0.104828
$92$	4.66928	0.486806
$93$	−7.19474	−0.746059
$94$	−1.75000	−0.180499
$95$	−10.8825	−1.11652
$96$	−9.85096	−1.00541
$97$	15.1174	1.53494	0.767472	−	0.641082i	$-0.221514\pi$
$97$	15.1174	1.53494	0.767472	+	0.641082i	$0.221514\pi$
$98$	1.72345	0.174095
$99$	0.780553	0.0784485
$100$	3.19211	0.319211
$101$	10.4474	1.03955	0.519775	−	0.854303i	$-0.326016\pi$
$101$	10.4474	1.03955	0.519775	+	0.854303i	$0.326016\pi$
$102$	−3.46874	−0.343457
$103$	9.02391	0.889152	0.444576	−	0.895741i	$-0.353354\pi$
$103$	9.02391	0.889152	0.444576	+	0.895741i	$0.353354\pi$
$104$	−1.77466	−0.174020
$105$	5.59824	0.546332
$106$	2.93879	0.285441
$107$	2.89837	0.280196	0.140098	−	0.990138i	$-0.455258\pi$
$107$	2.89837	0.280196	0.140098	+	0.990138i	$0.455258\pi$
$108$	−4.18719	−0.402913
$109$	−15.6973	−1.50353	−0.751764	−	0.659432i	$-0.770797\pi$
$109$	−15.6973	−1.50353	−0.751764	+	0.659432i	$0.770797\pi$
$110$	4.96218	0.473126
$111$	6.02939	0.572284
$112$	−4.99912	−0.472372
$113$	15.2593	1.43547	0.717737	−	0.696314i	$-0.245178\pi$
$113$	15.2593	1.43547	0.717737	+	0.696314i	$0.245178\pi$
$114$	−12.6657	−1.18626
$115$	13.8555	1.29203
$116$	−2.42509	−0.225164
$117$	0.780553	0.0721621
$118$	21.8644	2.01279
$119$	−1.03513	−0.0948902
$120$	−9.93497	−0.906934
$121$	1.00000	0.0909091
$122$	−20.4153	−1.84832
$123$	−6.00549	−0.541497
$124$	−3.59036	−0.322424
$125$	−4.92386	−0.440403
$126$	1.34525	0.119844
$127$	16.2764	1.44430	0.722148	−	0.691739i	$-0.243155\pi$
$127$	16.2764	1.44430	0.722148	+	0.691739i	$0.243155\pi$
$128$	12.3156	1.08856
$129$	5.38650	0.474255
$130$	4.96218	0.435212
$131$	−11.9570	−1.04469	−0.522345	−	0.852734i	$-0.674943\pi$
$131$	−11.9570	−1.04469	−0.522345	+	0.852734i	$0.674943\pi$
$132$	1.88659	0.164207
$133$	−3.77967	−0.327739
$134$	−3.91027	−0.337796
$135$	−12.4250	−1.06937
$136$	1.83700	0.157522
$137$	−8.62065	−0.736512	−0.368256	−	0.929725i	$-0.620045\pi$
$137$	−8.62065	−0.736512	−0.368256	+	0.929725i	$0.620045\pi$
$138$	16.1260	1.37274
$139$	8.50892	0.721717	0.360859	−	0.932621i	$-0.382484\pi$
$139$	8.50892	0.721717	0.360859	+	0.932621i	$0.382484\pi$
$140$	2.79366	0.236108
$141$	−1.97432	−0.166268
$142$	−19.8990	−1.66988
$143$	1.00000	0.0836242
$144$	−3.90208	−0.325173
$145$	−7.19616	−0.597609
$146$	6.76448	0.559833
$147$	1.94436	0.160368
$148$	3.00882	0.247323
$149$	18.5684	1.52118	0.760591	−	0.649231i	$-0.224909\pi$
$149$	18.5684	1.52118	0.760591	+	0.649231i	$0.224909\pi$
$150$	11.0244	0.900137
$151$	−12.2923	−1.00033	−0.500167	−	0.865929i	$-0.666728\pi$
$151$	−12.2923	−1.00033	−0.500167	+	0.865929i	$0.666728\pi$
$152$	6.70763	0.544061
$153$	−0.807974	−0.0653208
$154$	1.72345	0.138880
$155$	−10.6540	−0.855746
$156$	1.88659	0.151048
$157$	−3.69196	−0.294650	−0.147325	−	0.989088i	$-0.547066\pi$
$157$	−3.69196	−0.294650	−0.147325	+	0.989088i	$0.547066\pi$
$158$	−13.4593	−1.07076
$159$	3.31549	0.262935
$160$	−14.5873	−1.15323
$161$	4.81227	0.379260
$162$	−18.4968	−1.45324
$163$	−12.1805	−0.954049	−0.477025	−	0.878890i	$-0.658285\pi$
$163$	−12.1805	−0.954049	−0.477025	+	0.878890i	$0.658285\pi$
$164$	−2.99689	−0.234018
$165$	5.59824	0.435822
$166$	2.40122	0.186371
$167$	10.6257	0.822242	0.411121	−	0.911581i	$-0.365137\pi$
$167$	10.6257	0.822242	0.411121	+	0.911581i	$0.365137\pi$
$168$	−3.45059	−0.266219
$169$	1.00000	0.0769231
$170$	−5.13651	−0.393952
$171$	−2.95023	−0.225610
$172$	2.68800	0.204958
$173$	−23.6962	−1.80159	−0.900796	−	0.434242i	$-0.857016\pi$
$173$	−23.6962	−1.80159	−0.900796	+	0.434242i	$0.857016\pi$
$174$	−8.37537	−0.634936
$175$	3.28986	0.248690
$176$	−4.99912	−0.376823
$177$	24.6670	1.85409
$178$	−11.3515	−0.850833
$179$	11.3529	0.848557	0.424279	−	0.905532i	$-0.360528\pi$
$179$	11.3529	0.848557	0.424279	+	0.905532i	$0.360528\pi$
$180$	2.18060	0.162532
$181$	−17.5961	−1.30791	−0.653953	−	0.756535i	$-0.726891\pi$
$181$	−17.5961	−1.30791	−0.653953	+	0.756535i	$0.726891\pi$
$182$	1.72345	0.127751
$183$	−23.0322	−1.70259
$184$	−8.54014	−0.629587
$185$	8.92830	0.656422
$186$	−12.3998	−0.909196
$187$	−1.03513	−0.0756962
$188$	−0.985236	−0.0718557
$189$	−4.31541	−0.313900
$190$	−18.7554	−1.36066
$191$	0.551266	0.0398882	0.0199441	−	0.999801i	$-0.493651\pi$
$191$	0.551266	0.0398882	0.0199441	+	0.999801i	$0.493651\pi$
$192$	2.46254	0.177719
$193$	−3.94413	−0.283905	−0.141952	−	0.989874i	$-0.545338\pi$
$193$	−3.94413	−0.283905	−0.141952	+	0.989874i	$0.545338\pi$
$194$	26.0542	1.87058
$195$	5.59824	0.400898
$196$	0.970287	0.0693062
$197$	−13.0818	−0.932041	−0.466021	−	0.884774i	$-0.654313\pi$
$197$	−13.0818	−0.932041	−0.466021	+	0.884774i	$0.654313\pi$
$198$	1.34525	0.0956024
$199$	12.7655	0.904923	0.452462	−	0.891784i	$-0.350546\pi$
$199$	12.7655	0.904923	0.452462	+	0.891784i	$0.350546\pi$
$200$	−5.83838	−0.412836
$201$	−4.41149	−0.311162
$202$	18.0055	1.26686
$203$	−2.49935	−0.175420
$204$	−1.95287	−0.136728
$205$	−8.89292	−0.621108
$206$	15.5523	1.08358
$207$	3.75623	0.261076
$208$	−4.99912	−0.346626
$209$	−3.77967	−0.261445
$210$	9.64829	0.665795
$211$	−20.0586	−1.38089	−0.690444	−	0.723385i	$-0.742585\pi$
$211$	−20.0586	−1.38089	−0.690444	+	0.723385i	$0.742585\pi$
$212$	1.65451	0.113632
$213$	−22.4496	−1.53822
$214$	4.99520	0.341465
$215$	7.97631	0.543980
$216$	7.65839	0.521088
$217$	−3.70030	−0.251193
$218$	−27.0535	−1.83230
$219$	7.63156	0.515693
$220$	2.79366	0.188349
$221$	−1.03513	−0.0696304
$222$	10.3914	0.697422
$223$	10.7719	0.721338	0.360669	−	0.932694i	$-0.382548\pi$
$223$	10.7719	0.721338	0.360669	+	0.932694i	$0.382548\pi$
$224$	−5.06642	−0.338514
$225$	2.56791	0.171194
$226$	26.2987	1.74936
$227$	−1.46581	−0.0972891	−0.0486445	−	0.998816i	$-0.515490\pi$
$227$	−1.46581	−0.0972891	−0.0486445	+	0.998816i	$0.515490\pi$
$228$	−7.13070	−0.472242
$229$	22.7162	1.50113	0.750563	−	0.660799i	$-0.229782\pi$
$229$	22.7162	1.50113	0.750563	+	0.660799i	$0.229782\pi$
$230$	23.8793	1.57456
$231$	1.94436	0.127930
$232$	4.43550	0.291205
$233$	13.9802	0.915872	0.457936	−	0.888985i	$-0.348589\pi$
$233$	13.9802	0.915872	0.457936	+	0.888985i	$0.348589\pi$
$234$	1.34525	0.0879414
$235$	−2.92357	−0.190713
$236$	12.3095	0.801279
$237$	−15.1845	−0.986339
$238$	−1.78400	−0.115639
$239$	−3.50685	−0.226839	−0.113420	−	0.993547i	$-0.536180\pi$
$239$	−3.50685	−0.226839	−0.113420	+	0.993547i	$0.536180\pi$
$240$	−27.9862	−1.80650
$241$	−9.78814	−0.630510	−0.315255	−	0.949007i	$-0.602090\pi$
$241$	−9.78814	−0.630510	−0.315255	+	0.949007i	$0.602090\pi$
$242$	1.72345	0.110788
$243$	−7.92145	−0.508161
$244$	−11.4937	−0.735806
$245$	2.87921	0.183946
$246$	−10.3502	−0.659903
$247$	−3.77967	−0.240495
$248$	6.56678	0.416991
$249$	2.70900	0.171676
$250$	−8.48604	−0.536704
$251$	14.0207	0.884977	0.442489	−	0.896774i	$-0.354096\pi$
$251$	14.0207	0.884977	0.442489	+	0.896774i	$0.354096\pi$
$252$	0.757361	0.0477092
$253$	4.81227	0.302545
$254$	28.0516	1.76011
$255$	−5.79490	−0.362891
$256$	18.6923	1.16827
$257$	24.6752	1.53919	0.769597	−	0.638530i	$-0.220457\pi$
$257$	24.6752	1.53919	0.769597	+	0.638530i	$0.220457\pi$
$258$	9.28337	0.577957
$259$	3.10095	0.192684
$260$	2.79366	0.173256
$261$	−1.95088	−0.120756
$262$	−20.6073	−1.27313
$263$	7.25020	0.447067	0.223533	−	0.974696i	$-0.428241\pi$
$263$	7.25020	0.447067	0.223533	+	0.974696i	$0.428241\pi$
$264$	−3.45059	−0.212369
$265$	4.90957	0.301592
$266$	−6.51408	−0.399404
$267$	−12.8066	−0.783749
$268$	−2.20145	−0.134475
$269$	14.6971	0.896097	0.448048	−	0.894009i	$-0.352119\pi$
$269$	14.6971	0.896097	0.448048	+	0.894009i	$0.352119\pi$
$270$	−21.4139	−1.30321
$271$	4.61422	0.280294	0.140147	−	0.990131i	$-0.455242\pi$
$271$	4.61422	0.280294	0.140147	+	0.990131i	$0.455242\pi$
$272$	5.17474	0.313765
$273$	1.94436	0.117678
$274$	−14.8573	−0.897561
$275$	3.28986	0.198386
$276$	9.07878	0.546479
$277$	−25.0313	−1.50399	−0.751993	−	0.659171i	$-0.770907\pi$
$277$	−25.0313	−1.50399	−0.751993	+	0.659171i	$0.770907\pi$
$278$	14.6647	0.879531
$279$	−2.88828	−0.172917
$280$	−5.10962	−0.305358
$281$	−13.0057	−0.775855	−0.387927	−	0.921690i	$-0.626809\pi$
$281$	−13.0057	−0.775855	−0.387927	+	0.921690i	$0.626809\pi$
$282$	−3.40264	−0.202625
$283$	2.68107	0.159373	0.0796864	−	0.996820i	$-0.474608\pi$
$283$	2.68107	0.159373	0.0796864	+	0.996820i	$0.474608\pi$
$284$	−11.2029	−0.664771
$285$	−21.1595	−1.25338
$286$	1.72345	0.101910
$287$	−3.08866	−0.182318
$288$	−3.95461	−0.233027
$289$	−15.9285	−0.936971
$290$	−12.4022	−0.728285
$291$	29.3938	1.72310
$292$	3.80834	0.222866
$293$	15.9085	0.929385	0.464693	−	0.885472i	$-0.346165\pi$
$293$	15.9085	0.929385	0.464693	+	0.885472i	$0.346165\pi$
$294$	3.35102	0.195435
$295$	36.5269	2.12668
$296$	−5.50314	−0.319864
$297$	−4.31541	−0.250406
$298$	32.0017	1.85381
$299$	4.81227	0.278301
$300$	6.20662	0.358339
$301$	2.77031	0.159678
$302$	−21.1852	−1.21907
$303$	20.3135	1.16698
$304$	18.8950	1.08370
$305$	−34.1060	−1.95291
$306$	−1.39250	−0.0796042
$307$	27.0504	1.54385	0.771925	−	0.635714i	$-0.219294\pi$
$307$	27.0504	1.54385	0.771925	+	0.635714i	$0.219294\pi$
$308$	0.970287	0.0552873
$309$	17.5458	0.998144
$310$	−18.3616	−1.04287
$311$	−17.7956	−1.00910	−0.504548	−	0.863384i	$-0.668341\pi$
$311$	−17.7956	−1.00910	−0.504548	+	0.863384i	$0.668341\pi$
$312$	−3.45059	−0.195351
$313$	−22.8496	−1.29153	−0.645767	−	0.763534i	$-0.723462\pi$
$313$	−22.8496	−1.29153	−0.645767	+	0.763534i	$0.723462\pi$
$314$	−6.36291	−0.359080
$315$	2.24738	0.126625
$316$	−7.57745	−0.426265
$317$	21.4245	1.20332	0.601660	−	0.798752i	$-0.294506\pi$
$317$	21.4245	1.20332	0.601660	+	0.798752i	$0.294506\pi$
$318$	5.71408	0.320430
$319$	−2.49935	−0.139937
$320$	3.64653	0.203847
$321$	5.63548	0.314542
$322$	8.29371	0.462190
$323$	3.91245	0.217695
$324$	−10.4135	−0.578528
$325$	3.28986	0.182489
$326$	−20.9925	−1.16267
$327$	−30.5213	−1.68783
$328$	5.48133	0.302656
$329$	−1.01541	−0.0559811
$330$	9.64829	0.531121
$331$	27.9542	1.53650	0.768250	−	0.640150i	$-0.221128\pi$
$331$	27.9542	1.53650	0.768250	+	0.640150i	$0.221128\pi$
$332$	1.35186	0.0741931
$333$	2.42046	0.132640
$334$	18.3129	1.00204
$335$	−6.53253	−0.356910
$336$	−9.72011	−0.530275
$337$	−18.4576	−1.00545	−0.502725	−	0.864446i	$-0.667669\pi$
$337$	−18.4576	−1.00545	−0.502725	+	0.864446i	$0.667669\pi$
$338$	1.72345	0.0937434
$339$	29.6696	1.61143
$340$	−2.89180	−0.156830
$341$	−3.70030	−0.200383
$342$	−5.08458	−0.274943
$343$	1.00000	0.0539949
$344$	−4.91636	−0.265073
$345$	26.9402	1.45041
$346$	−40.8394	−2.19554
$347$	−2.70175	−0.145037	−0.0725187	−	0.997367i	$-0.523104\pi$
$347$	−2.70175	−0.145037	−0.0725187	+	0.997367i	$0.523104\pi$
$348$	−4.71526	−0.252764
$349$	−19.0171	−1.01796	−0.508980	−	0.860778i	$-0.669977\pi$
$349$	−19.0171	−1.01796	−0.508980	+	0.860778i	$0.669977\pi$
$350$	5.66991	0.303070
$351$	−4.31541	−0.230340
$352$	−5.06642	−0.270041
$353$	−1.19490	−0.0635980	−0.0317990	−	0.999494i	$-0.510124\pi$
$353$	−1.19490	−0.0635980	−0.0317990	+	0.999494i	$0.510124\pi$
$354$	42.5124	2.25951
$355$	−33.2433	−1.76437
$356$	−6.39081	−0.338712
$357$	−2.01267	−0.106522
$358$	19.5662	1.03411
$359$	−2.19748	−0.115979	−0.0579893	−	0.998317i	$-0.518469\pi$
$359$	−2.19748	−0.115979	−0.0579893	+	0.998317i	$0.518469\pi$
$360$	−3.98833	−0.210203
$361$	−4.71409	−0.248110
$362$	−30.3260	−1.59390
$363$	1.94436	0.102053
$364$	0.970287	0.0508569
$365$	11.3008	0.591511
$366$	−39.6949	−2.07488
$367$	16.6210	0.867611	0.433805	−	0.901007i	$-0.357171\pi$
$367$	16.6210	0.867611	0.433805	+	0.901007i	$0.357171\pi$
$368$	−24.0571	−1.25406
$369$	−2.41087	−0.125505
$370$	15.3875	0.799958
$371$	1.70518	0.0885284
$372$	−6.98096	−0.361946
$373$	25.9831	1.34536	0.672678	−	0.739935i	$-0.265144\pi$
$373$	25.9831	1.34536	0.672678	+	0.739935i	$0.265144\pi$
$374$	−1.78400	−0.0922483
$375$	−9.57378	−0.494388
$376$	1.80200	0.0929311
$377$	−2.49935	−0.128723
$378$	−7.43741	−0.382539
$379$	−7.62905	−0.391878	−0.195939	−	0.980616i	$-0.562775\pi$
$379$	−7.62905	−0.391878	−0.195939	+	0.980616i	$0.562775\pi$
$380$	−10.5591	−0.541672
$381$	31.6472	1.62134
$382$	0.950081	0.0486104
$383$	−3.76269	−0.192265	−0.0961323	−	0.995369i	$-0.530647\pi$
$383$	−3.76269	−0.192265	−0.0961323	+	0.995369i	$0.530647\pi$
$384$	23.9460	1.22199
$385$	2.87921	0.146738
$386$	−6.79752	−0.345984
$387$	2.16238	0.109920
$388$	14.6683	0.744669
$389$	−25.0146	−1.26829	−0.634145	−	0.773214i	$-0.718648\pi$
$389$	−25.0146	−1.26829	−0.634145	+	0.773214i	$0.718648\pi$
$390$	9.64829	0.488560
$391$	−4.98132	−0.251916
$392$	−1.77466	−0.0896339
$393$	−23.2488	−1.17275
$394$	−22.5459	−1.13585
$395$	−22.4852	−1.13135
$396$	0.757361	0.0380588
$397$	32.6317	1.63774	0.818869	−	0.573981i	$-0.194601\pi$
$397$	32.6317	1.63774	0.818869	+	0.573981i	$0.194601\pi$
$398$	22.0008	1.10280
$399$	−7.34906	−0.367913
$400$	−16.4464	−0.822319
$401$	7.33420	0.366253	0.183126	−	0.983089i	$-0.441378\pi$
$401$	7.33420	0.366253	0.183126	+	0.983089i	$0.441378\pi$
$402$	−7.60299	−0.379203
$403$	−3.70030	−0.184325
$404$	10.1369	0.504331
$405$	−30.9008	−1.53547
$406$	−4.30751	−0.213778
$407$	3.10095	0.153709
$408$	3.57181	0.176831
$409$	−3.76552	−0.186193	−0.0930966	−	0.995657i	$-0.529677\pi$
$409$	−3.76552	−0.186193	−0.0930966	+	0.995657i	$0.529677\pi$
$410$	−15.3265	−0.756923
$411$	−16.7617	−0.826793
$412$	8.75579	0.431367
$413$	12.6864	0.624258
$414$	6.47368	0.318164
$415$	4.01149	0.196916
$416$	−5.06642	−0.248402
$417$	16.5444	0.810185
$418$	−6.51408	−0.318614
$419$	−10.3298	−0.504644	−0.252322	−	0.967643i	$-0.581194\pi$
$419$	−10.3298	−0.504644	−0.252322	+	0.967643i	$0.581194\pi$
$420$	5.43190	0.265050
$421$	16.9650	0.826825	0.413413	−	0.910544i	$-0.364337\pi$
$421$	16.9650	0.826825	0.413413	+	0.910544i	$0.364337\pi$
$422$	−34.5700	−1.68284
$423$	−0.792578	−0.0385365
$424$	−3.02611	−0.146961
$425$	−3.40543	−0.165188
$426$	−38.6908	−1.87458
$427$	−11.8456	−0.573249
$428$	2.81225	0.135935
$429$	1.94436	0.0938748
$430$	13.7468	0.662929
$431$	−24.1799	−1.16471	−0.582353	−	0.812936i	$-0.697868\pi$
$431$	−24.1799	−1.16471	−0.582353	+	0.812936i	$0.697868\pi$
$432$	21.5733	1.03794
$433$	19.1566	0.920608	0.460304	−	0.887761i	$-0.347740\pi$
$433$	19.1566	0.920608	0.460304	+	0.887761i	$0.347740\pi$
$434$	−6.37729	−0.306120
$435$	−13.9920	−0.670863
$436$	−15.2309	−0.729427
$437$	−18.1888	−0.870087
$438$	13.1526	0.628457
$439$	40.0714	1.91250	0.956252	−	0.292545i	$-0.0945021\pi$
$439$	40.0714	1.91250	0.956252	+	0.292545i	$0.0945021\pi$
$440$	−5.10962	−0.243592
$441$	0.780553	0.0371692
$442$	−1.78400	−0.0848561
$443$	−15.2894	−0.726420	−0.363210	−	0.931707i	$-0.618319\pi$
$443$	−15.2894	−0.726420	−0.363210	+	0.931707i	$0.618319\pi$
$444$	5.85024	0.277640
$445$	−18.9639	−0.898977
$446$	18.5648	0.879069
$447$	36.1037	1.70765
$448$	1.26650	0.0598367
$449$	6.65972	0.314292	0.157146	−	0.987575i	$-0.449771\pi$
$449$	6.65972	0.314292	0.157146	+	0.987575i	$0.449771\pi$
$450$	4.42567	0.208628
$451$	−3.08866	−0.145440
$452$	14.8059	0.696411
$453$	−23.9007	−1.12295
$454$	−2.52625	−0.118563
$455$	2.87921	0.134980
$456$	13.0421	0.610751
$457$	2.84735	0.133193	0.0665967	−	0.997780i	$-0.478786\pi$
$457$	2.84735	0.133193	0.0665967	+	0.997780i	$0.478786\pi$
$458$	39.1502	1.82937
$459$	4.46702	0.208502
$460$	13.4438	0.626823
$461$	26.4112	1.23009	0.615045	−	0.788492i	$-0.289138\pi$
$461$	26.4112	1.23009	0.615045	+	0.788492i	$0.289138\pi$
$462$	3.35102	0.155904
$463$	18.2720	0.849172	0.424586	−	0.905388i	$-0.360420\pi$
$463$	18.2720	0.849172	0.424586	+	0.905388i	$0.360420\pi$
$464$	12.4946	0.580045
$465$	−20.7152	−0.960643
$466$	24.0942	1.11614
$467$	4.52674	0.209472	0.104736	−	0.994500i	$-0.466600\pi$
$467$	4.52674	0.209472	0.104736	+	0.994500i	$0.466600\pi$
$468$	0.757361	0.0350090
$469$	−2.26886	−0.104766
$470$	−5.03863	−0.232415
$471$	−7.17851	−0.330768
$472$	−22.5141	−1.03630
$473$	2.77031	0.127379
$474$	−26.1698	−1.20202
$475$	−12.4346	−0.570538
$476$	−1.00437	−0.0460354
$477$	1.33098	0.0609415
$478$	−6.04389	−0.276441
$479$	−8.24909	−0.376911	−0.188455	−	0.982082i	$-0.560348\pi$
$479$	−8.24909	−0.376911	−0.188455	+	0.982082i	$0.560348\pi$
$480$	−28.3630	−1.29459
$481$	3.10095	0.141391
$482$	−16.8694	−0.768380
$483$	9.35680	0.425749
$484$	0.970287	0.0441040
$485$	43.5263	1.97643
$486$	−13.6522	−0.619278
$487$	20.4246	0.925527	0.462763	−	0.886482i	$-0.346858\pi$
$487$	20.4246	0.925527	0.462763	+	0.886482i	$0.346858\pi$
$488$	21.0219	0.951619
$489$	−23.6833	−1.07100
$490$	4.96218	0.224169
$491$	37.6909	1.70097	0.850483	−	0.526003i	$-0.176310\pi$
$491$	37.6909	1.70097	0.850483	+	0.526003i	$0.176310\pi$
$492$	−5.82705	−0.262704
$493$	2.58715	0.116520
$494$	−6.51408	−0.293082
$495$	2.24738	0.101012
$496$	18.4982	0.830596
$497$	−11.5460	−0.517908
$498$	4.66884	0.209216
$499$	35.5360	1.59081	0.795404	−	0.606080i	$-0.207259\pi$
$499$	35.5360	1.59081	0.795404	+	0.606080i	$0.207259\pi$
$500$	−4.77756	−0.213659
$501$	20.6602	0.923032
$502$	24.1640	1.07849
$503$	−4.37096	−0.194892	−0.0974458	−	0.995241i	$-0.531067\pi$
$503$	−4.37096	−0.194892	−0.0974458	+	0.995241i	$0.531067\pi$
$504$	−1.38522	−0.0617024
$505$	30.0801	1.33855
$506$	8.29371	0.368700
$507$	1.94436	0.0863523
$508$	15.7928	0.700691
$509$	4.03288	0.178754	0.0893772	−	0.995998i	$-0.471512\pi$
$509$	4.03288	0.178754	0.0893772	+	0.995998i	$0.471512\pi$
$510$	−9.98724	−0.442242
$511$	3.92496	0.173630
$512$	7.58415	0.335175
$513$	16.3108	0.720141
$514$	42.5265	1.87576
$515$	25.9817	1.14489
$516$	5.22645	0.230082
$517$	−1.01541	−0.0446575
$518$	5.34435	0.234817
$519$	−46.0741	−2.02243
$520$	−5.10962	−0.224072
$521$	−10.7797	−0.472267	−0.236134	−	0.971721i	$-0.575880\pi$
$521$	−10.7797	−0.472267	−0.236134	+	0.971721i	$0.575880\pi$
$522$	−3.36224	−0.147161
$523$	23.9060	1.04533	0.522667	−	0.852537i	$-0.324937\pi$
$523$	23.9060	1.04533	0.522667	+	0.852537i	$0.324937\pi$
$524$	−11.6017	−0.506825
$525$	6.39668	0.279174
$526$	12.4954	0.544824
$527$	3.83029	0.166850
$528$	−9.72011	−0.423013
$529$	0.157900	0.00686521
$530$	8.46141	0.367540
$531$	9.90242	0.429729
$532$	−3.66737	−0.159001
$533$	−3.08866	−0.133785
$534$	−22.0715	−0.955128
$535$	8.34501	0.360786
$536$	4.02645	0.173916
$537$	22.0742	0.952573
$538$	25.3297	1.09204
$539$	1.00000	0.0430730
$540$	−12.0558	−0.518800
$541$	40.2380	1.72996	0.864982	−	0.501802i	$-0.167330\pi$
$541$	40.2380	1.72996	0.864982	+	0.501802i	$0.167330\pi$
$542$	7.95239	0.341585
$543$	−34.2132	−1.46823
$544$	5.24440	0.224852
$545$	−45.1958	−1.93598
$546$	3.35102	0.143410
$547$	−4.01979	−0.171874	−0.0859369	−	0.996301i	$-0.527388\pi$
$547$	−4.01979	−0.171874	−0.0859369	+	0.996301i	$0.527388\pi$
$548$	−8.36451	−0.357314
$549$	−9.24613	−0.394615
$550$	5.66991	0.241766
$551$	9.44672	0.402444
$552$	−16.6051	−0.706762
$553$	−7.80949	−0.332093
$554$	−43.1403	−1.83285
$555$	17.3599	0.736886
$556$	8.25610	0.350137
$557$	−12.8281	−0.543545	−0.271773	−	0.962362i	$-0.587610\pi$
$557$	−12.8281	−0.543545	−0.271773	+	0.962362i	$0.587610\pi$
$558$	−4.97781	−0.210728
$559$	2.77031	0.117172
$560$	−14.3935	−0.608237
$561$	−2.01267	−0.0849750
$562$	−22.4147	−0.945507
$563$	−6.18807	−0.260796	−0.130398	−	0.991462i	$-0.541626\pi$
$563$	−6.18807	−0.260796	−0.130398	+	0.991462i	$0.541626\pi$
$564$	−1.91566	−0.0806637
$565$	43.9347	1.84835
$566$	4.62069	0.194222
$567$	−10.7324	−0.450718
$568$	20.4902	0.859750
$569$	−37.7901	−1.58424	−0.792121	−	0.610364i	$-0.791023\pi$
$569$	−37.7901	−1.58424	−0.792121	+	0.610364i	$0.791023\pi$
$570$	−36.4674	−1.52745
$571$	−22.2849	−0.932592	−0.466296	−	0.884629i	$-0.654412\pi$
$571$	−22.2849	−0.932592	−0.466296	+	0.884629i	$0.654412\pi$
$572$	0.970287	0.0405698
$573$	1.07186	0.0447777
$574$	−5.32317	−0.222185
$575$	15.8317	0.660226
$576$	0.988573	0.0411905
$577$	31.8317	1.32517	0.662585	−	0.748987i	$-0.269459\pi$
$577$	31.8317	1.32517	0.662585	+	0.748987i	$0.269459\pi$
$578$	−27.4520	−1.14185
$579$	−7.66882	−0.318705
$580$	−6.98235	−0.289926
$581$	1.39326	0.0578021
$582$	50.6589	2.09988
$583$	1.70518	0.0706213
$584$	−6.96547	−0.288233
$585$	2.24738	0.0929176
$586$	27.4176	1.13261
$587$	−5.99885	−0.247599	−0.123800	−	0.992307i	$-0.539508\pi$
$587$	−5.99885	−0.247599	−0.123800	+	0.992307i	$0.539508\pi$
$588$	1.88659	0.0778018
$589$	13.9859	0.576280
$590$	62.9524	2.59171
$591$	−25.4358	−1.04629
$592$	−15.5020	−0.637130
$593$	3.90931	0.160536	0.0802681	−	0.996773i	$-0.474422\pi$
$593$	3.90931	0.160536	0.0802681	+	0.996773i	$0.474422\pi$
$594$	−7.43741	−0.305161
$595$	−2.98036	−0.122183
$596$	18.0167	0.737992
$597$	24.8208	1.01585
$598$	8.29371	0.339155
$599$	−4.07150	−0.166357	−0.0831786	−	0.996535i	$-0.526507\pi$
$599$	−4.07150	−0.166357	−0.0831786	+	0.996535i	$0.526507\pi$
$600$	−11.3519	−0.463441
$601$	−42.7755	−1.74485	−0.872425	−	0.488747i	$-0.837454\pi$
$601$	−42.7755	−1.74485	−0.872425	+	0.488747i	$0.837454\pi$
$602$	4.77450	0.194594
$603$	−1.77096	−0.0721193
$604$	−11.9271	−0.485306
$605$	2.87921	0.117057
$606$	35.0093	1.42215
$607$	7.75409	0.314729	0.157364	−	0.987541i	$-0.449700\pi$
$607$	7.75409	0.314729	0.157364	+	0.987541i	$0.449700\pi$
$608$	19.1494	0.776610
$609$	−4.85965	−0.196923
$610$	−58.7801	−2.37994
$611$	−1.01541	−0.0410789
$612$	−0.783967	−0.0316900
$613$	28.4076	1.14737	0.573686	−	0.819075i	$-0.305513\pi$
$613$	28.4076	1.14737	0.573686	+	0.819075i	$0.305513\pi$
$614$	46.6201	1.88143
$615$	−17.2911	−0.697243
$616$	−1.77466	−0.0715031
$617$	−18.3782	−0.739880	−0.369940	−	0.929056i	$-0.620622\pi$
$617$	−18.3782	−0.739880	−0.369940	+	0.929056i	$0.620622\pi$
$618$	30.2393	1.21640
$619$	−24.0955	−0.968482	−0.484241	−	0.874935i	$-0.660904\pi$
$619$	−24.0955	−0.968482	−0.484241	+	0.874935i	$0.660904\pi$
$620$	−10.3374	−0.415160
$621$	−20.7669	−0.833348
$622$	−30.6698	−1.22975
$623$	−6.58651	−0.263883
$624$	−9.72011	−0.389116
$625$	−30.6261	−1.22504
$626$	−39.3801	−1.57395
$627$	−7.34906	−0.293493
$628$	−3.58226	−0.142948
$629$	−3.20989	−0.127987
$630$	3.87325	0.154314
$631$	23.1221	0.920477	0.460239	−	0.887795i	$-0.347764\pi$
$631$	23.1221	0.920477	0.460239	+	0.887795i	$0.347764\pi$
$632$	13.8592	0.551289
$633$	−39.0012	−1.55016
$634$	36.9241	1.46644
$635$	46.8632	1.85971
$636$	3.21698	0.127561
$637$	1.00000	0.0396214
$638$	−4.30751	−0.170536
$639$	−9.01225	−0.356519
$640$	35.4592	1.40165
$641$	−38.2805	−1.51199	−0.755994	−	0.654578i	$-0.772846\pi$
$641$	−38.2805	−1.51199	−0.755994	+	0.654578i	$0.772846\pi$
$642$	9.71249	0.383321
$643$	46.6257	1.83874	0.919369	−	0.393397i	$-0.128700\pi$
$643$	46.6257	1.83874	0.919369	+	0.393397i	$0.128700\pi$
$644$	4.66928	0.183995
$645$	15.5089	0.610661
$646$	6.74292	0.265297
$647$	−44.7530	−1.75942	−0.879711	−	0.475509i	$-0.842264\pi$
$647$	−44.7530	−1.75942	−0.879711	+	0.475509i	$0.842264\pi$
$648$	19.0464	0.748212
$649$	12.6864	0.497986
$650$	5.66991	0.222392
$651$	−7.19474	−0.281984
$652$	−11.8186	−0.462851
$653$	0.202996	0.00794384	0.00397192	−	0.999992i	$-0.498736\pi$
$653$	0.202996	0.00794384	0.00397192	+	0.999992i	$0.498736\pi$
$654$	−52.6019	−2.05690
$655$	−34.4268	−1.34517
$656$	15.4406	0.602854
$657$	3.06364	0.119524
$658$	−1.75000	−0.0682222
$659$	−19.7867	−0.770779	−0.385389	−	0.922754i	$-0.625933\pi$
$659$	−19.7867	−0.770779	−0.385389	+	0.922754i	$0.625933\pi$
$660$	5.43190	0.211436
$661$	−31.3250	−1.21840	−0.609201	−	0.793016i	$-0.708510\pi$
$661$	−31.3250	−1.21840	−0.609201	+	0.793016i	$0.708510\pi$
$662$	48.1777	1.87248
$663$	−2.01267	−0.0781656
$664$	−2.47256	−0.0959540
$665$	−10.8825	−0.422004
$666$	4.17155	0.161644
$667$	−12.0275	−0.465708
$668$	10.3100	0.398905
$669$	20.9444	0.809759
$670$	−11.2585	−0.434954
$671$	−11.8456	−0.457295
$672$	−9.85096	−0.380009
$673$	21.2057	0.817419	0.408710	−	0.912665i	$-0.365979\pi$
$673$	21.2057	0.817419	0.408710	+	0.912665i	$0.365979\pi$
$674$	−31.8108	−1.22531
$675$	−14.1971	−0.546447
$676$	0.970287	0.0373187
$677$	−11.8192	−0.454249	−0.227124	−	0.973866i	$-0.572932\pi$
$677$	−11.8192	−0.454249	−0.227124	+	0.973866i	$0.572932\pi$
$678$	51.1342	1.96380
$679$	15.1174	0.580154
$680$	5.28912	0.202829
$681$	−2.85006	−0.109215
$682$	−6.37729	−0.244199
$683$	5.78690	0.221430	0.110715	−	0.993852i	$-0.464686\pi$
$683$	5.78690	0.221430	0.110715	+	0.993852i	$0.464686\pi$
$684$	−2.86257	−0.109453
$685$	−24.8207	−0.948349
$686$	1.72345	0.0658017
$687$	44.1685	1.68513
$688$	−13.8491	−0.527993
$689$	1.70518	0.0649621
$690$	46.4301	1.76757
$691$	−16.2134	−0.616787	−0.308393	−	0.951259i	$-0.599791\pi$
$691$	−16.2134	−0.616787	−0.308393	+	0.951259i	$0.599791\pi$
$692$	−22.9922	−0.874031
$693$	0.780553	0.0296507
$694$	−4.65633	−0.176752
$695$	24.4990	0.929299
$696$	8.62423	0.326901
$697$	3.19717	0.121101
$698$	−32.7750	−1.24055
$699$	27.1826	1.02814
$700$	3.19211	0.120650
$701$	−27.6708	−1.04511	−0.522555	−	0.852606i	$-0.675021\pi$
$701$	−27.6708	−1.04511	−0.522555	+	0.852606i	$0.675021\pi$
$702$	−7.43741	−0.280707
$703$	−11.7206	−0.442050
$704$	1.26650	0.0477331
$705$	−5.68448	−0.214090
$706$	−2.05935	−0.0775046
$707$	10.4474	0.392913
$708$	23.9341	0.899499
$709$	−9.31849	−0.349963	−0.174982	−	0.984572i	$-0.555987\pi$
$709$	−9.31849	−0.349963	−0.174982	+	0.984572i	$0.555987\pi$
$710$	−57.2933	−2.15018
$711$	−6.09572	−0.228607
$712$	11.6888	0.438057
$713$	−17.8068	−0.666871
$714$	−3.46874	−0.129814
$715$	2.87921	0.107676
$716$	11.0156	0.411672
$717$	−6.81860	−0.254645
$718$	−3.78725	−0.141339
$719$	42.3895	1.58086	0.790430	−	0.612552i	$-0.209857\pi$
$719$	42.3895	1.58086	0.790430	+	0.612552i	$0.209857\pi$
$720$	−11.2349	−0.418700
$721$	9.02391	0.336068
$722$	−8.12452	−0.302363
$723$	−19.0317	−0.707797
$724$	−17.0732	−0.634522
$725$	−8.22251	−0.305376
$726$	3.35102	0.124368
$727$	17.6216	0.653549	0.326775	−	0.945102i	$-0.394038\pi$
$727$	17.6216	0.653549	0.326775	+	0.945102i	$0.394038\pi$
$728$	−1.77466	−0.0657733
$729$	16.7950	0.622037
$730$	19.4764	0.720853
$731$	−2.86763	−0.106063
$732$	−22.3478	−0.826000
$733$	42.1457	1.55669	0.778343	−	0.627839i	$-0.216060\pi$
$733$	42.1457	1.55669	0.778343	+	0.627839i	$0.216060\pi$
$734$	28.6455	1.05733
$735$	5.59824	0.206494
$736$	−24.3810	−0.898694
$737$	−2.26886	−0.0835745
$738$	−4.15501	−0.152948
$739$	18.6080	0.684506	0.342253	−	0.939608i	$-0.388810\pi$
$739$	18.6080	0.684506	0.342253	+	0.939608i	$0.388810\pi$
$740$	8.66302	0.318459
$741$	−7.34906	−0.269974
$742$	2.93879	0.107886
$743$	6.81625	0.250064	0.125032	−	0.992153i	$-0.460097\pi$
$743$	6.81625	0.250064	0.125032	+	0.992153i	$0.460097\pi$
$744$	12.7682	0.468105
$745$	53.4623	1.95871
$746$	44.7807	1.63954
$747$	1.08751	0.0397900
$748$	−1.00437	−0.0367235
$749$	2.89837	0.105904
$750$	−16.4999	−0.602493
$751$	−40.2134	−1.46741	−0.733704	−	0.679469i	$-0.762210\pi$
$751$	−40.2134	−1.46741	−0.733704	+	0.679469i	$0.762210\pi$
$752$	5.07613	0.185108
$753$	27.2613	0.993457
$754$	−4.30751	−0.156870
$755$	−35.3921	−1.28805
$756$	−4.18719	−0.152287
$757$	−19.9894	−0.726526	−0.363263	−	0.931687i	$-0.618337\pi$
$757$	−19.9894	−0.726526	−0.363263	+	0.931687i	$0.618337\pi$
$758$	−13.1483	−0.477568
$759$	9.35680	0.339630
$760$	19.3127	0.700545
$761$	24.0360	0.871304	0.435652	−	0.900115i	$-0.356518\pi$
$761$	24.0360	0.871304	0.435652	+	0.900115i	$0.356518\pi$
$762$	54.5425	1.97587
$763$	−15.6973	−0.568280
$764$	0.534887	0.0193515
$765$	−2.32633	−0.0841085
$766$	−6.48482	−0.234306
$767$	12.6864	0.458080
$768$	36.3447	1.31148
$769$	13.0814	0.471729	0.235864	−	0.971786i	$-0.424208\pi$
$769$	13.0814	0.471729	0.235864	+	0.971786i	$0.424208\pi$
$770$	4.96218	0.178825
$771$	47.9775	1.72787
$772$	−3.82694	−0.137735
$773$	5.98717	0.215343	0.107672	−	0.994187i	$-0.465660\pi$
$773$	5.98717	0.215343	0.107672	+	0.994187i	$0.465660\pi$
$774$	3.72675	0.133955
$775$	−12.1735	−0.437284
$776$	−26.8283	−0.963081
$777$	6.02939	0.216303
$778$	−43.1115	−1.54562
$779$	11.6741	0.418269
$780$	5.43190	0.194493
$781$	−11.5460	−0.413148
$782$	−8.58507	−0.307001
$783$	10.7857	0.385451
$784$	−4.99912	−0.178540
$785$	−10.6299	−0.379398
$786$	−40.0682	−1.42919
$787$	−14.3995	−0.513287	−0.256644	−	0.966506i	$-0.582617\pi$
$787$	−14.3995	−0.513287	−0.256644	+	0.966506i	$0.582617\pi$
$788$	−12.6931	−0.452174
$789$	14.0970	0.501868
$790$	−38.7521	−1.37874
$791$	15.2593	0.542558
$792$	−1.38522	−0.0492215
$793$	−11.8456	−0.420650
$794$	56.2392	1.99585
$795$	9.54599	0.338561
$796$	12.3862	0.439018
$797$	14.6705	0.519656	0.259828	−	0.965655i	$-0.416334\pi$
$797$	14.6705	0.519656	0.259828	+	0.965655i	$0.416334\pi$
$798$	−12.6657	−0.448363
$799$	1.05108	0.0371844
$800$	−16.6678	−0.589296
$801$	−5.14112	−0.181652
$802$	12.6401	0.446339
$803$	3.92496	0.138509
$804$	−4.28041	−0.150959
$805$	13.8555	0.488343
$806$	−6.37729	−0.224631
$807$	28.5765	1.00594
$808$	−18.5405	−0.652252
$809$	−16.1263	−0.566969	−0.283485	−	0.958977i	$-0.591491\pi$
$809$	−16.1263	−0.566969	−0.283485	+	0.958977i	$0.591491\pi$
$810$	−53.2561	−1.87123
$811$	−22.8313	−0.801715	−0.400857	−	0.916140i	$-0.631288\pi$
$811$	−22.8313	−0.801715	−0.400857	+	0.916140i	$0.631288\pi$
$812$	−2.42509	−0.0851040
$813$	8.97173	0.314652
$814$	5.34435	0.187319
$815$	−35.0702	−1.22846
$816$	10.0616	0.352226
$817$	−10.4709	−0.366329
$818$	−6.48970	−0.226907
$819$	0.780553	0.0272747
$820$	−8.62869	−0.301327
$821$	−27.6232	−0.964057	−0.482029	−	0.876155i	$-0.660100\pi$
$821$	−27.6232	−0.964057	−0.482029	+	0.876155i	$0.660100\pi$
$822$	−28.8880	−1.00758
$823$	9.96213	0.347258	0.173629	−	0.984811i	$-0.444451\pi$
$823$	9.96213	0.347258	0.173629	+	0.984811i	$0.444451\pi$
$824$	−16.0144	−0.557887
$825$	6.39668	0.222704
$826$	21.8644	0.760761
$827$	33.3161	1.15851	0.579257	−	0.815145i	$-0.303343\pi$
$827$	33.3161	1.15851	0.579257	+	0.815145i	$0.303343\pi$
$828$	3.64462	0.126659
$829$	−15.3982	−0.534803	−0.267401	−	0.963585i	$-0.586165\pi$
$829$	−15.3982	−0.534803	−0.267401	+	0.963585i	$0.586165\pi$
$830$	6.91361	0.239975
$831$	−48.6700	−1.68834
$832$	1.26650	0.0439081
$833$	−1.03513	−0.0358651
$834$	28.5135	0.987343
$835$	30.5937	1.05874
$836$	−3.66737	−0.126839
$837$	15.9683	0.551946
$838$	−17.8029	−0.614992
$839$	23.6333	0.815914	0.407957	−	0.913001i	$-0.366241\pi$
$839$	23.6333	0.815914	0.407957	+	0.913001i	$0.366241\pi$
$840$	−9.93497	−0.342789
$841$	−22.7532	−0.784595
$842$	29.2384	1.00762
$843$	−25.2878	−0.870958
$844$	−19.4626	−0.669930
$845$	2.87921	0.0990479
$846$	−1.36597	−0.0469630
$847$	1.00000	0.0343604
$848$	−8.52438	−0.292729
$849$	5.21297	0.178909
$850$	−5.86910	−0.201308
$851$	14.9226	0.511541
$852$	−21.7826	−0.746258
$853$	8.42663	0.288522	0.144261	−	0.989540i	$-0.453919\pi$
$853$	8.42663	0.288522	0.144261	+	0.989540i	$0.453919\pi$
$854$	−20.4153	−0.698599
$855$	−8.49434	−0.290500
$856$	−5.14362	−0.175805
$857$	−40.1845	−1.37268	−0.686338	−	0.727283i	$-0.740783\pi$
$857$	−40.1845	−1.37268	−0.686338	+	0.727283i	$0.740783\pi$
$858$	3.35102	0.114402
$859$	−29.9007	−1.02020	−0.510099	−	0.860116i	$-0.670391\pi$
$859$	−29.9007	−1.02020	−0.510099	+	0.860116i	$0.670391\pi$
$860$	7.73932	0.263909
$861$	−6.00549	−0.204667
$862$	−41.6729	−1.41939
$863$	−31.5382	−1.07357	−0.536786	−	0.843718i	$-0.680362\pi$
$863$	−31.5382	−1.07357	−0.536786	+	0.843718i	$0.680362\pi$
$864$	21.8637	0.743818
$865$	−68.2265	−2.31977
$866$	33.0155	1.12191
$867$	−30.9708	−1.05182
$868$	−3.59036	−0.121865
$869$	−7.80949	−0.264919
$870$	−24.1145	−0.817557
$871$	−2.26886	−0.0768774
$872$	27.8574	0.943369
$873$	11.8000	0.399368
$874$	−31.3475	−1.06034
$875$	−4.92386	−0.166457
$876$	7.40480	0.250185
$877$	−27.2502	−0.920174	−0.460087	−	0.887874i	$-0.652182\pi$
$877$	−27.2502	−0.920174	−0.460087	+	0.887874i	$0.652182\pi$
$878$	69.0611	2.33070
$879$	30.9320	1.04331
$880$	−14.3935	−0.485205
$881$	−13.0723	−0.440415	−0.220208	−	0.975453i	$-0.570674\pi$
$881$	−13.0723	−0.440415	−0.220208	+	0.975453i	$0.570674\pi$
$882$	1.34525	0.0452968
$883$	25.2435	0.849512	0.424756	−	0.905308i	$-0.360360\pi$
$883$	25.2435	0.849512	0.424756	+	0.905308i	$0.360360\pi$
$884$	−1.00437	−0.0337807
$885$	71.0216	2.38736
$886$	−26.3505	−0.885262
$887$	46.8983	1.57469	0.787345	−	0.616512i	$-0.211455\pi$
$887$	46.8983	1.57469	0.787345	+	0.616512i	$0.211455\pi$
$888$	−10.7001	−0.359072
$889$	16.2764	0.545892
$890$	−32.6835	−1.09555
$891$	−10.7324	−0.359549
$892$	10.4518	0.349953
$893$	3.83790	0.128430
$894$	62.2231	2.08105
$895$	32.6875	1.09262
$896$	12.3156	0.411435
$897$	9.35680	0.312414
$898$	11.4777	0.383016
$899$	9.24836	0.308450
$900$	2.49161	0.0830536
$901$	−1.76508	−0.0588034
$902$	−5.32317	−0.177242
$903$	5.38650	0.179251
$904$	−27.0801	−0.900670
$905$	−50.6628	−1.68409
$906$	−41.1917	−1.36850
$907$	32.5039	1.07928	0.539638	−	0.841897i	$-0.318561\pi$
$907$	32.5039	1.07928	0.539638	+	0.841897i	$0.318561\pi$
$908$	−1.42225	−0.0471992
$909$	8.15471	0.270475
$910$	4.96218	0.164495
$911$	15.8733	0.525905	0.262952	−	0.964809i	$-0.415304\pi$
$911$	15.8733	0.525905	0.262952	+	0.964809i	$0.415304\pi$
$912$	36.7388	1.21654
$913$	1.39326	0.0461102
$914$	4.90727	0.162318
$915$	−66.3145	−2.19229
$916$	22.0412	0.728262
$917$	−11.9570	−0.394855
$918$	7.69869	0.254095
$919$	9.14281	0.301593	0.150797	−	0.988565i	$-0.451816\pi$
$919$	9.14281	0.301593	0.150797	+	0.988565i	$0.451816\pi$
$920$	−24.5889	−0.810671
$921$	52.5959	1.73309
$922$	45.5184	1.49907
$923$	−11.5460	−0.380041
$924$	1.88659	0.0620643
$925$	10.2017	0.335430
$926$	31.4909	1.03486
$927$	7.04364	0.231343
$928$	12.6628	0.415676
$929$	−32.5858	−1.06911	−0.534553	−	0.845135i	$-0.679520\pi$
$929$	−32.5858	−1.06911	−0.534553	+	0.845135i	$0.679520\pi$
$930$	−35.7016	−1.17070
$931$	−3.77967	−0.123874
$932$	13.5648	0.444329
$933$	−34.6011	−1.13279
$934$	7.80162	0.255277
$935$	−2.98036	−0.0974681
$936$	−1.38522	−0.0452772
$937$	−19.3244	−0.631302	−0.315651	−	0.948875i	$-0.602223\pi$
$937$	−19.3244	−0.631302	−0.315651	+	0.948875i	$0.602223\pi$
$938$	−3.91027	−0.127675
$939$	−44.4279	−1.44985
$940$	−2.83670	−0.0925230
$941$	−39.2795	−1.28047	−0.640237	−	0.768177i	$-0.721164\pi$
$941$	−39.2795	−1.28047	−0.640237	+	0.768177i	$0.721164\pi$
$942$	−12.3718	−0.403096
$943$	−14.8635	−0.484021
$944$	−63.4209	−2.06417
$945$	−12.4250	−0.404185
$946$	4.77450	0.155232
$947$	−46.0788	−1.49736	−0.748679	−	0.662932i	$-0.769312\pi$
$947$	−46.0788	−1.49736	−0.748679	+	0.662932i	$0.769312\pi$
$948$	−14.7333	−0.478516
$949$	3.92496	0.127410
$950$	−21.4304	−0.695294
$951$	41.6570	1.35082
$952$	1.83700	0.0595377
$953$	−36.2870	−1.17545	−0.587725	−	0.809061i	$-0.699976\pi$
$953$	−36.2870	−1.17545	−0.587725	+	0.809061i	$0.699976\pi$
$954$	2.29388	0.0742672
$955$	1.58721	0.0513610
$956$	−3.40265	−0.110050
$957$	−4.85965	−0.157090
$958$	−14.2169	−0.459328
$959$	−8.62065	−0.278375
$960$	7.09019	0.228835
$961$	−17.3078	−0.558315
$962$	5.34435	0.172309
$963$	2.26233	0.0729025
$964$	−9.49731	−0.305888
$965$	−11.3560	−0.365562
$966$	16.1260	0.518845
$967$	5.48989	0.176543	0.0882715	−	0.996096i	$-0.471866\pi$
$967$	5.48989	0.176543	0.0882715	+	0.996096i	$0.471866\pi$
$968$	−1.77466	−0.0570397
$969$	7.60723	0.244379
$970$	75.0156	2.40860
$971$	−54.5126	−1.74939	−0.874696	−	0.484672i	$-0.838939\pi$
$971$	−54.5126	−1.74939	−0.874696	+	0.484672i	$0.838939\pi$
$972$	−7.68608	−0.246531
$973$	8.50892	0.272783
$974$	35.2008	1.12791
$975$	6.39668	0.204858
$976$	59.2176	1.89551
$977$	−53.4887	−1.71126	−0.855628	−	0.517592i	$-0.826829\pi$
$977$	−53.4887	−1.71126	−0.855628	+	0.517592i	$0.826829\pi$
$978$	−40.8170	−1.30518
$979$	−6.58651	−0.210506
$980$	2.79366	0.0892403
$981$	−12.2526	−0.391194
$982$	64.9584	2.07291
$983$	−21.0796	−0.672336	−0.336168	−	0.941802i	$-0.609131\pi$
$983$	−21.0796	−0.672336	−0.336168	+	0.941802i	$0.609131\pi$
$984$	10.6577	0.339755
$985$	−37.6653	−1.20012
$986$	4.45884	0.141998
$987$	−1.97432	−0.0628433
$988$	−3.66737	−0.116674
$989$	13.3315	0.423916
$990$	3.87325	0.123100
$991$	−35.9904	−1.14327	−0.571636	−	0.820507i	$-0.693691\pi$
$991$	−35.9904	−1.14327	−0.571636	+	0.820507i	$0.693691\pi$
$992$	18.7473	0.595227
$993$	54.3531	1.72484
$994$	−19.8990	−0.631156
$995$	36.7546	1.16520
$996$	2.62851	0.0832876
$997$	16.6810	0.528291	0.264146	−	0.964483i	$-0.414910\pi$
$997$	16.6810	0.528291	0.264146	+	0.964483i	$0.414910\pi$
$998$	61.2445	1.93866
$999$	−13.3819	−0.423385

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1001.2.a.n.1.9	✓	11
3.2	odd	2		9009.2.a.bs.1.3		11
7.6	odd	2		7007.2.a.w.1.9		11

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1001.2.a.n.1.9	✓	11	1.1	even	1	trivial
7007.2.a.w.1.9		11	7.6	odd	2
9009.2.a.bs.1.3		11	3.2	odd	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 1001 = 7 \cdot 11 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1001.a (trivial)

\(f(q)\)	\(=\)	\(q+1.72345 q^{2} +1.94436 q^{3} +0.970287 q^{4} +2.87921 q^{5} +3.35102 q^{6} +1.00000 q^{7} -1.77466 q^{8} +0.780553 q^{9} +O(q^{10})\)	\(q+1.72345 q^{2} +1.94436 q^{3} +0.970287 q^{4} +2.87921 q^{5} +3.35102 q^{6} +1.00000 q^{7} -1.77466 q^{8} +0.780553 q^{9} +4.96218 q^{10} +1.00000 q^{11} +1.88659 q^{12} +1.00000 q^{13} +1.72345 q^{14} +5.59824 q^{15} -4.99912 q^{16} -1.03513 q^{17} +1.34525 q^{18} -3.77967 q^{19} +2.79366 q^{20} +1.94436 q^{21} +1.72345 q^{22} +4.81227 q^{23} -3.45059 q^{24} +3.28986 q^{25} +1.72345 q^{26} -4.31541 q^{27} +0.970287 q^{28} -2.49935 q^{29} +9.64829 q^{30} -3.70030 q^{31} -5.06642 q^{32} +1.94436 q^{33} -1.78400 q^{34} +2.87921 q^{35} +0.757361 q^{36} +3.10095 q^{37} -6.51408 q^{38} +1.94436 q^{39} -5.10962 q^{40} -3.08866 q^{41} +3.35102 q^{42} +2.77031 q^{43} +0.970287 q^{44} +2.24738 q^{45} +8.29371 q^{46} -1.01541 q^{47} -9.72011 q^{48} +1.00000 q^{49} +5.66991 q^{50} -2.01267 q^{51} +0.970287 q^{52} +1.70518 q^{53} -7.43741 q^{54} +2.87921 q^{55} -1.77466 q^{56} -7.34906 q^{57} -4.30751 q^{58} +12.6864 q^{59} +5.43190 q^{60} -11.8456 q^{61} -6.37729 q^{62} +0.780553 q^{63} +1.26650 q^{64} +2.87921 q^{65} +3.35102 q^{66} -2.26886 q^{67} -1.00437 q^{68} +9.35680 q^{69} +4.96218 q^{70} -11.5460 q^{71} -1.38522 q^{72} +3.92496 q^{73} +5.34435 q^{74} +6.39668 q^{75} -3.66737 q^{76} +1.00000 q^{77} +3.35102 q^{78} -7.80949 q^{79} -14.3935 q^{80} -10.7324 q^{81} -5.32317 q^{82} +1.39326 q^{83} +1.88659 q^{84} -2.98036 q^{85} +4.77450 q^{86} -4.85965 q^{87} -1.77466 q^{88} -6.58651 q^{89} +3.87325 q^{90} +1.00000 q^{91} +4.66928 q^{92} -7.19474 q^{93} -1.75000 q^{94} -10.8825 q^{95} -9.85096 q^{96} +15.1174 q^{97} +1.72345 q^{98} +0.780553 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 11 q - q^{2} + 2 q^{3} + 15 q^{4} + 7 q^{5} + 3 q^{6} + 11 q^{7} - 6 q^{8} + 15 q^{9}+O(q^{10}) \) 11 * q - q^2 + 2 * q^3 + 15 * q^4 + 7 * q^5 + 3 * q^6 + 11 * q^7 - 6 * q^8 + 15 * q^9	\( 11 q - q^{2} + 2 q^{3} + 15 q^{4} + 7 q^{5} + 3 q^{6} + 11 q^{7} - 6 q^{8} + 15 q^{9} + q^{10} + 11 q^{11} - 5 q^{12} + 11 q^{13} - q^{14} + 4 q^{15} + 15 q^{16} + 7 q^{17} - 17 q^{18} + 22 q^{19} + 6 q^{20} + 2 q^{21} - q^{22} + 3 q^{23} + 17 q^{24} + 10 q^{25} - q^{26} + 2 q^{27} + 15 q^{28} - 6 q^{29} - 40 q^{30} + 28 q^{31} - 23 q^{32} + 2 q^{33} + 19 q^{34} + 7 q^{35} + 48 q^{36} + q^{37} - 20 q^{38} + 2 q^{39} + 16 q^{40} - 4 q^{41} + 3 q^{42} - 8 q^{43} + 15 q^{44} + 12 q^{45} + 2 q^{46} + 22 q^{47} - 30 q^{48} + 11 q^{49} - 24 q^{50} - 27 q^{51} + 15 q^{52} + 9 q^{53} + 36 q^{54} + 7 q^{55} - 6 q^{56} - 34 q^{57} - 8 q^{58} - 2 q^{59} + 25 q^{60} + 8 q^{62} + 15 q^{63} - 10 q^{64} + 7 q^{65} + 3 q^{66} + 23 q^{67} + 24 q^{68} + 7 q^{69} + q^{70} + 3 q^{71} - 76 q^{72} + 29 q^{73} + 15 q^{74} + 36 q^{75} + 62 q^{76} + 11 q^{77} + 3 q^{78} + 26 q^{79} - 16 q^{80} + 7 q^{81} - 16 q^{82} + 9 q^{83} - 5 q^{84} - 31 q^{85} + 28 q^{86} + 13 q^{87} - 6 q^{88} + 9 q^{89} - 26 q^{90} + 11 q^{91} - 58 q^{92} - 24 q^{93} - 34 q^{94} - 14 q^{95} + 56 q^{96} + 40 q^{97} - q^{98} + 15 q^{99}+O(q^{100}) \) 11 * q - q^2 + 2 * q^3 + 15 * q^4 + 7 * q^5 + 3 * q^6 + 11 * q^7 - 6 * q^8 + 15 * q^9 + q^10 + 11 * q^11 - 5 * q^12 + 11 * q^13 - q^14 + 4 * q^15 + 15 * q^16 + 7 * q^17 - 17 * q^18 + 22 * q^19 + 6 * q^20 + 2 * q^21 - q^22 + 3 * q^23 + 17 * q^24 + 10 * q^25 - q^26 + 2 * q^27 + 15 * q^28 - 6 * q^29 - 40 * q^30 + 28 * q^31 - 23 * q^32 + 2 * q^33 + 19 * q^34 + 7 * q^35 + 48 * q^36 + q^37 - 20 * q^38 + 2 * q^39 + 16 * q^40 - 4 * q^41 + 3 * q^42 - 8 * q^43 + 15 * q^44 + 12 * q^45 + 2 * q^46 + 22 * q^47 - 30 * q^48 + 11 * q^49 - 24 * q^50 - 27 * q^51 + 15 * q^52 + 9 * q^53 + 36 * q^54 + 7 * q^55 - 6 * q^56 - 34 * q^57 - 8 * q^58 - 2 * q^59 + 25 * q^60 + 8 * q^62 + 15 * q^63 - 10 * q^64 + 7 * q^65 + 3 * q^66 + 23 * q^67 + 24 * q^68 + 7 * q^69 + q^70 + 3 * q^71 - 76 * q^72 + 29 * q^73 + 15 * q^74 + 36 * q^75 + 62 * q^76 + 11 * q^77 + 3 * q^78 + 26 * q^79 - 16 * q^80 + 7 * q^81 - 16 * q^82 + 9 * q^83 - 5 * q^84 - 31 * q^85 + 28 * q^86 + 13 * q^87 - 6 * q^88 + 9 * q^89 - 26 * q^90 + 11 * q^91 - 58 * q^92 - 24 * q^93 - 34 * q^94 - 14 * q^95 + 56 * q^96 + 40 * q^97 - q^98 + 15 * q^99

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