LMFDB - Embedded newform 1334.2.a.j.1.6

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1334,2,Mod(1,1334)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1334, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("1334.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1334 = 2 \cdot 23 \cdot 29 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1334.a (trivial)

Newform invariants

comment: select newform

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

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

Self dual:	yes
Analytic conductor:	$10.6520436296$
Analytic rank:	$0$
Dimension:	$9$
Coefficient field:	$\mathbb{Q}[x]/(x^{9} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{9} - 3x^{8} - 16x^{7} + 44x^{6} + 87x^{5} - 209x^{4} - 160x^{3} + 348x^{2} + 12x - 100 $ x^9 - 3x^8 - 16x^7 + 44x^6 + 87x^5 - 209x^4 - 160x^3 + 348x^2 + 12x - 100
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.6
Root			$-0.540845$ of defining polynomial
Character	$\chi$	$=$	1334.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.00000 q^{2} +0.540845 q^{3} +1.00000 q^{4} +1.92844 q^{5} -0.540845 q^{6} +2.85963 q^{7} -1.00000 q^{8} -2.70749 q^{9} +O(q^{10})$	\(q-1.00000 q^{2} +0.540845 q^{3} +1.00000 q^{4} +1.92844 q^{5} -0.540845 q^{6} +2.85963 q^{7} -1.00000 q^{8} -2.70749 q^{9} -1.92844 q^{10} +6.29002 q^{11} +0.540845 q^{12} -5.64221 q^{13} -2.85963 q^{14} +1.04298 q^{15} +1.00000 q^{16} +1.77271 q^{17} +2.70749 q^{18} +6.79435 q^{19} +1.92844 q^{20} +1.54662 q^{21} -6.29002 q^{22} -1.00000 q^{23} -0.540845 q^{24} -1.28113 q^{25} +5.64221 q^{26} -3.08686 q^{27} +2.85963 q^{28} +1.00000 q^{29} -1.04298 q^{30} +8.29002 q^{31} -1.00000 q^{32} +3.40193 q^{33} -1.77271 q^{34} +5.51462 q^{35} -2.70749 q^{36} +2.88726 q^{37} -6.79435 q^{38} -3.05156 q^{39} -1.92844 q^{40} +0.887256 q^{41} -1.54662 q^{42} -5.20833 q^{43} +6.29002 q^{44} -5.22122 q^{45} +1.00000 q^{46} -0.232048 q^{47} +0.540845 q^{48} +1.17749 q^{49} +1.28113 q^{50} +0.958760 q^{51} -5.64221 q^{52} -9.34341 q^{53} +3.08686 q^{54} +12.1299 q^{55} -2.85963 q^{56} +3.67469 q^{57} -1.00000 q^{58} +7.53517 q^{59} +1.04298 q^{60} +0.247217 q^{61} -8.29002 q^{62} -7.74241 q^{63} +1.00000 q^{64} -10.8806 q^{65} -3.40193 q^{66} +2.98728 q^{67} +1.77271 q^{68} -0.540845 q^{69} -5.51462 q^{70} +1.98043 q^{71} +2.70749 q^{72} -8.25722 q^{73} -2.88726 q^{74} -0.692893 q^{75} +6.79435 q^{76} +17.9871 q^{77} +3.05156 q^{78} +0.989179 q^{79} +1.92844 q^{80} +6.45295 q^{81} -0.887256 q^{82} -4.38757 q^{83} +1.54662 q^{84} +3.41856 q^{85} +5.20833 q^{86} +0.540845 q^{87} -6.29002 q^{88} -3.55699 q^{89} +5.22122 q^{90} -16.1346 q^{91} -1.00000 q^{92} +4.48361 q^{93} +0.232048 q^{94} +13.1025 q^{95} -0.540845 q^{96} -12.9895 q^{97} -1.17749 q^{98} -17.0302 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 9 q - 9 q^{2} - 3 q^{3} + 9 q^{4} + 5 q^{5} + 3 q^{6} + 6 q^{7} - 9 q^{8} + 14 q^{9}+O(q^{10}) $ 9 * q - 9 * q^2 - 3 * q^3 + 9 * q^4 + 5 * q^5 + 3 * q^6 + 6 * q^7 - 9 * q^8 + 14 * q^9	\( 9 q - 9 q^{2} - 3 q^{3} + 9 q^{4} + 5 q^{5} + 3 q^{6} + 6 q^{7} - 9 q^{8} + 14 q^{9} - 5 q^{10} - 3 q^{11} - 3 q^{12} + 13 q^{13} - 6 q^{14} - 3 q^{15} + 9 q^{16} + 2 q^{17} - 14 q^{18} + 16 q^{19} + 5 q^{20} + 8 q^{21} + 3 q^{22} - 9 q^{23} + 3 q^{24} + 20 q^{25} - 13 q^{26} - 21 q^{27} + 6 q^{28} + 9 q^{29} + 3 q^{30} + 15 q^{31} - 9 q^{32} + 13 q^{33} - 2 q^{34} + 14 q^{36} + 12 q^{37} - 16 q^{38} - 5 q^{39} - 5 q^{40} - 6 q^{41} - 8 q^{42} - 3 q^{43} - 3 q^{44} + 20 q^{45} + 9 q^{46} - 19 q^{47} - 3 q^{48} + 37 q^{49} - 20 q^{50} + 6 q^{51} + 13 q^{52} + 5 q^{53} + 21 q^{54} + q^{55} - 6 q^{56} - 20 q^{57} - 9 q^{58} + 12 q^{59} - 3 q^{60} + 12 q^{61} - 15 q^{62} + 6 q^{63} + 9 q^{64} + 19 q^{65} - 13 q^{66} - 6 q^{67} + 2 q^{68} + 3 q^{69} + 12 q^{71} - 14 q^{72} - 12 q^{74} + 16 q^{75} + 16 q^{76} + 34 q^{77} + 5 q^{78} + 29 q^{79} + 5 q^{80} + 5 q^{81} + 6 q^{82} + 24 q^{83} + 8 q^{84} + 12 q^{85} + 3 q^{86} - 3 q^{87} + 3 q^{88} - 2 q^{89} - 20 q^{90} + 58 q^{91} - 9 q^{92} + 7 q^{93} + 19 q^{94} + 6 q^{95} + 3 q^{96} + 12 q^{97} - 37 q^{98} - 20 q^{99}+O(q^{100}) \) 9 * q - 9 * q^2 - 3 * q^3 + 9 * q^4 + 5 * q^5 + 3 * q^6 + 6 * q^7 - 9 * q^8 + 14 * q^9 - 5 * q^10 - 3 * q^11 - 3 * q^12 + 13 * q^13 - 6 * q^14 - 3 * q^15 + 9 * q^16 + 2 * q^17 - 14 * q^18 + 16 * q^19 + 5 * q^20 + 8 * q^21 + 3 * q^22 - 9 * q^23 + 3 * q^24 + 20 * q^25 - 13 * q^26 - 21 * q^27 + 6 * q^28 + 9 * q^29 + 3 * q^30 + 15 * q^31 - 9 * q^32 + 13 * q^33 - 2 * q^34 + 14 * q^36 + 12 * q^37 - 16 * q^38 - 5 * q^39 - 5 * q^40 - 6 * q^41 - 8 * q^42 - 3 * q^43 - 3 * q^44 + 20 * q^45 + 9 * q^46 - 19 * q^47 - 3 * q^48 + 37 * q^49 - 20 * q^50 + 6 * q^51 + 13 * q^52 + 5 * q^53 + 21 * q^54 + q^55 - 6 * q^56 - 20 * q^57 - 9 * q^58 + 12 * q^59 - 3 * q^60 + 12 * q^61 - 15 * q^62 + 6 * q^63 + 9 * q^64 + 19 * q^65 - 13 * q^66 - 6 * q^67 + 2 * q^68 + 3 * q^69 + 12 * q^71 - 14 * q^72 - 12 * q^74 + 16 * q^75 + 16 * q^76 + 34 * q^77 + 5 * q^78 + 29 * q^79 + 5 * q^80 + 5 * q^81 + 6 * q^82 + 24 * q^83 + 8 * q^84 + 12 * q^85 + 3 * q^86 - 3 * q^87 + 3 * q^88 - 2 * q^89 - 20 * q^90 + 58 * q^91 - 9 * q^92 + 7 * q^93 + 19 * q^94 + 6 * q^95 + 3 * q^96 + 12 * q^97 - 37 * q^98 - 20 * q^99

Display 100 coefficients 10 coefficients

Coefficient data

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

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

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

$2$	−1.00000	−0.707107
$2$	−1.00000	−0.707107
$3$	0.540845	0.312257	0.156128	−	0.987737i	$-0.450099\pi$
$3$	0.540845	0.312257	0.156128	+	0.987737i	$0.450099\pi$
$4$	1.00000	0.500000
$5$	1.92844	0.862423	0.431212	−	0.902251i	$-0.358086\pi$
$5$	1.92844	0.862423	0.431212	+	0.902251i	$0.358086\pi$
$6$	−0.540845	−0.220799
$7$	2.85963	1.08084	0.540419	−	0.841396i	$-0.318266\pi$
$7$	2.85963	1.08084	0.540419	+	0.841396i	$0.318266\pi$
$8$	−1.00000	−0.353553
$9$	−2.70749	−0.902496
$10$	−1.92844	−0.609825
$11$	6.29002	1.89651	0.948257	−	0.317504i	$-0.102845\pi$
$11$	6.29002	1.89651	0.948257	+	0.317504i	$0.102845\pi$
$12$	0.540845	0.156128
$13$	−5.64221	−1.56487	−0.782433	−	0.622734i	$-0.786022\pi$
$13$	−5.64221	−1.56487	−0.782433	+	0.622734i	$0.786022\pi$
$14$	−2.85963	−0.764269
$15$	1.04298	0.269297
$16$	1.00000	0.250000
$17$	1.77271	0.429945	0.214972	−	0.976620i	$-0.431034\pi$
$17$	1.77271	0.429945	0.214972	+	0.976620i	$0.431034\pi$
$18$	2.70749	0.638161
$19$	6.79435	1.55873	0.779365	−	0.626570i	$-0.215542\pi$
$19$	6.79435	1.55873	0.779365	+	0.626570i	$0.215542\pi$
$20$	1.92844	0.431212
$21$	1.54662	0.337499
$22$	−6.29002	−1.34104
$23$	−1.00000	−0.208514
$23$	−1.00000	−0.208514
$24$	−0.540845	−0.110399
$25$	−1.28113	−0.256226
$26$	5.64221	1.10653
$27$	−3.08686	−0.594067
$28$	2.85963	0.540419
$29$	1.00000	0.185695
$29$	1.00000	0.185695
$30$	−1.04298	−0.190422
$31$	8.29002	1.48893	0.744466	−	0.667660i	$-0.232704\pi$
$31$	8.29002	1.48893	0.744466	+	0.667660i	$0.232704\pi$
$32$	−1.00000	−0.176777
$33$	3.40193	0.592199
$34$	−1.77271	−0.304017
$35$	5.51462	0.932141
$36$	−2.70749	−0.451248
$37$	2.88726	0.474662	0.237331	−	0.971429i	$-0.423727\pi$
$37$	2.88726	0.474662	0.237331	+	0.971429i	$0.423727\pi$
$38$	−6.79435	−1.10219
$39$	−3.05156	−0.488640
$40$	−1.92844	−0.304913
$41$	0.887256	0.138566	0.0692830	−	0.997597i	$-0.477929\pi$
$41$	0.887256	0.138566	0.0692830	+	0.997597i	$0.477929\pi$
$42$	−1.54662	−0.238648
$43$	−5.20833	−0.794264	−0.397132	−	0.917762i	$-0.629994\pi$
$43$	−5.20833	−0.794264	−0.397132	+	0.917762i	$0.629994\pi$
$44$	6.29002	0.948257
$45$	−5.22122	−0.778333
$46$	1.00000	0.147442
$47$	−0.232048	−0.0338476	−0.0169238	−	0.999857i	$-0.505387\pi$
$47$	−0.232048	−0.0338476	−0.0169238	+	0.999857i	$0.505387\pi$
$48$	0.540845	0.0780642
$49$	1.17749	0.168213
$50$	1.28113	0.181179
$51$	0.958760	0.134253
$52$	−5.64221	−0.782433
$53$	−9.34341	−1.28342	−0.641708	−	0.766949i	$-0.721774\pi$
$53$	−9.34341	−1.28342	−0.641708	+	0.766949i	$0.721774\pi$
$54$	3.08686	0.420069
$55$	12.1299	1.63560
$56$	−2.85963	−0.382134
$57$	3.67469	0.486724
$58$	−1.00000	−0.131306
$59$	7.53517	0.980996	0.490498	−	0.871442i	$-0.336815\pi$
$59$	7.53517	0.980996	0.490498	+	0.871442i	$0.336815\pi$
$60$	1.04298	0.134649
$61$	0.247217	0.0316529	0.0158264	−	0.999875i	$-0.494962\pi$
$61$	0.247217	0.0316529	0.0158264	+	0.999875i	$0.494962\pi$
$62$	−8.29002	−1.05283
$63$	−7.74241	−0.975453
$64$	1.00000	0.125000
$65$	−10.8806	−1.34958
$66$	−3.40193	−0.418748
$67$	2.98728	0.364954	0.182477	−	0.983210i	$-0.441588\pi$
$67$	2.98728	0.364954	0.182477	+	0.983210i	$0.441588\pi$
$68$	1.77271	0.214972
$69$	−0.540845	−0.0651100
$70$	−5.51462	−0.659123
$71$	1.98043	0.235033	0.117517	−	0.993071i	$-0.462507\pi$
$71$	1.98043	0.235033	0.117517	+	0.993071i	$0.462507\pi$
$72$	2.70749	0.319080
$73$	−8.25722	−0.966435	−0.483218	−	0.875500i	$-0.660532\pi$
$73$	−8.25722	−0.966435	−0.483218	+	0.875500i	$0.660532\pi$
$74$	−2.88726	−0.335637
$75$	−0.692893	−0.0800084
$76$	6.79435	0.779365
$77$	17.9871	2.04983
$78$	3.05156	0.345521
$79$	0.989179	0.111291	0.0556456	−	0.998451i	$-0.482278\pi$
$79$	0.989179	0.111291	0.0556456	+	0.998451i	$0.482278\pi$
$80$	1.92844	0.215606
$81$	6.45295	0.716994
$82$	−0.887256	−0.0979810
$83$	−4.38757	−0.481599	−0.240799	−	0.970575i	$-0.577410\pi$
$83$	−4.38757	−0.481599	−0.240799	+	0.970575i	$0.577410\pi$
$84$	1.54662	0.168750
$85$	3.41856	0.370794
$86$	5.20833	0.561629
$87$	0.540845	0.0579846
$88$	−6.29002	−0.670519
$89$	−3.55699	−0.377040	−0.188520	−	0.982069i	$-0.560369\pi$
$89$	−3.55699	−0.377040	−0.188520	+	0.982069i	$0.560369\pi$
$90$	5.22122	0.550365
$91$	−16.1346	−1.69137
$92$	−1.00000	−0.104257
$93$	4.48361	0.464929
$94$	0.232048	0.0239339
$95$	13.1025	1.34429
$96$	−0.540845	−0.0551997
$97$	−12.9895	−1.31888	−0.659441	−	0.751756i	$-0.729207\pi$
$97$	−12.9895	−1.31888	−0.659441	+	0.751756i	$0.729207\pi$
$98$	−1.17749	−0.118944
$99$	−17.0302	−1.71160
$100$	−1.28113	−0.128113
$101$	−6.56183	−0.652926	−0.326463	−	0.945210i	$-0.605857\pi$
$101$	−6.56183	−0.652926	−0.326463	+	0.945210i	$0.605857\pi$
$102$	−0.958760	−0.0949313
$103$	19.8887	1.95969	0.979846	−	0.199753i	$-0.0640138\pi$
$103$	19.8887	1.95969	0.979846	+	0.199753i	$0.0640138\pi$
$104$	5.64221	0.553264
$105$	2.98255	0.291067
$106$	9.34341	0.907512
$107$	11.8904	1.14949	0.574745	−	0.818333i	$-0.305101\pi$
$107$	11.8904	1.14949	0.574745	+	0.818333i	$0.305101\pi$
$108$	−3.08686	−0.297034
$109$	17.2315	1.65048	0.825240	−	0.564782i	$-0.191040\pi$
$109$	17.2315	1.65048	0.825240	+	0.564782i	$0.191040\pi$
$110$	−12.1299	−1.15654
$111$	1.56156	0.148216
$112$	2.85963	0.270210
$113$	−5.34319	−0.502645	−0.251322	−	0.967903i	$-0.580865\pi$
$113$	−5.34319	−0.502645	−0.251322	+	0.967903i	$0.580865\pi$
$114$	−3.67469	−0.344166
$115$	−1.92844	−0.179828
$116$	1.00000	0.0928477
$117$	15.2762	1.41229
$118$	−7.53517	−0.693669
$119$	5.06929	0.464701
$120$	−1.04298	−0.0952110
$121$	28.5644	2.59676
$122$	−0.247217	−0.0223820
$123$	0.479868	0.0432682
$124$	8.29002	0.744466
$125$	−12.1128	−1.08340
$126$	7.74241	0.689749
$127$	18.6867	1.65818	0.829088	−	0.559118i	$-0.188860\pi$
$127$	18.6867	1.65818	0.829088	+	0.559118i	$0.188860\pi$
$128$	−1.00000	−0.0883883
$129$	−2.81690	−0.248014
$130$	10.8806	0.954295
$131$	−2.94772	−0.257544	−0.128772	−	0.991674i	$-0.541103\pi$
$131$	−2.94772	−0.257544	−0.128772	+	0.991674i	$0.541103\pi$
$132$	3.40193	0.296100
$133$	19.4293	1.68474
$134$	−2.98728	−0.258062
$135$	−5.95282	−0.512337
$136$	−1.77271	−0.152008
$137$	2.24879	0.192127	0.0960636	−	0.995375i	$-0.469375\pi$
$137$	2.24879	0.192127	0.0960636	+	0.995375i	$0.469375\pi$
$138$	0.540845	0.0460397
$139$	−10.2517	−0.869536	−0.434768	−	0.900543i	$-0.643170\pi$
$139$	−10.2517	−0.869536	−0.434768	+	0.900543i	$0.643170\pi$
$140$	5.51462	0.466070
$141$	−0.125502	−0.0105691
$142$	−1.98043	−0.166194
$143$	−35.4896	−2.96779
$144$	−2.70749	−0.225624
$145$	1.92844	0.160148
$146$	8.25722	0.683373
$147$	0.636839	0.0525256
$148$	2.88726	0.237331
$149$	−17.1250	−1.40294	−0.701468	−	0.712701i	$-0.747472\pi$
$149$	−17.1250	−1.40294	−0.701468	+	0.712701i	$0.747472\pi$
$150$	0.692893	0.0565745
$151$	5.76208	0.468912	0.234456	−	0.972127i	$-0.424669\pi$
$151$	5.76208	0.468912	0.234456	+	0.972127i	$0.424669\pi$
$152$	−6.79435	−0.551095
$153$	−4.79958	−0.388023
$154$	−17.9871	−1.44945
$155$	15.9868	1.28409
$156$	−3.05156	−0.244320
$157$	11.7218	0.935504	0.467752	−	0.883860i	$-0.345064\pi$
$157$	11.7218	0.935504	0.467752	+	0.883860i	$0.345064\pi$
$158$	−0.989179	−0.0786948
$159$	−5.05333	−0.400755
$160$	−1.92844	−0.152456
$161$	−2.85963	−0.225370
$162$	−6.45295	−0.506991
$163$	−9.50612	−0.744577	−0.372288	−	0.928117i	$-0.621427\pi$
$163$	−9.50612	−0.744577	−0.372288	+	0.928117i	$0.621427\pi$
$164$	0.887256	0.0692830
$165$	6.56040	0.510726
$166$	4.38757	0.340542
$167$	−17.7997	−1.37738	−0.688689	−	0.725056i	$-0.741814\pi$
$167$	−17.7997	−1.37738	−0.688689	+	0.725056i	$0.741814\pi$
$168$	−1.54662	−0.119324
$169$	18.8345	1.44881
$170$	−3.41856	−0.262191
$171$	−18.3956	−1.40675
$172$	−5.20833	−0.397132
$173$	16.9509	1.28875	0.644376	−	0.764709i	$-0.277117\pi$
$173$	16.9509	1.28875	0.644376	+	0.764709i	$0.277117\pi$
$174$	−0.540845	−0.0410013
$175$	−3.66356	−0.276939
$176$	6.29002	0.474128
$177$	4.07536	0.306323
$178$	3.55699	0.266608
$179$	−4.79210	−0.358178	−0.179089	−	0.983833i	$-0.557315\pi$
$179$	−4.79210	−0.358178	−0.179089	+	0.983833i	$0.557315\pi$
$180$	−5.22122	−0.389167
$181$	12.3081	0.914851	0.457426	−	0.889248i	$-0.348772\pi$
$181$	12.3081	0.914851	0.457426	+	0.889248i	$0.348772\pi$
$182$	16.1346	1.19598
$183$	0.133706	0.00988383
$184$	1.00000	0.0737210
$185$	5.56789	0.409359
$186$	−4.48361	−0.328755
$187$	11.1504	0.815396
$188$	−0.232048	−0.0169238
$189$	−8.82729	−0.642091
$190$	−13.1025	−0.950554
$191$	11.0527	0.799742	0.399871	−	0.916571i	$-0.369055\pi$
$191$	11.0527	0.799742	0.399871	+	0.916571i	$0.369055\pi$
$192$	0.540845	0.0390321
$193$	3.96216	0.285203	0.142601	−	0.989780i	$-0.454453\pi$
$193$	3.96216	0.285203	0.142601	+	0.989780i	$0.454453\pi$
$194$	12.9895	0.932591
$195$	−5.88474	−0.421415
$196$	1.17749	0.0841064
$197$	−20.8810	−1.48771	−0.743855	−	0.668341i	$-0.767005\pi$
$197$	−20.8810	−1.48771	−0.743855	+	0.668341i	$0.767005\pi$
$198$	17.0302	1.21028
$199$	−24.4407	−1.73256	−0.866279	−	0.499561i	$-0.833495\pi$
$199$	−24.4407	−1.73256	−0.866279	+	0.499561i	$0.833495\pi$
$200$	1.28113	0.0905896
$201$	1.61565	0.113959
$202$	6.56183	0.461688
$203$	2.85963	0.200707
$204$	0.958760	0.0671266
$205$	1.71102	0.119503
$206$	−19.8887	−1.38571
$207$	2.70749	0.188183
$208$	−5.64221	−0.391217
$209$	42.7366	2.95615
$210$	−2.98255	−0.205816
$211$	−16.9963	−1.17007	−0.585037	−	0.811007i	$-0.698920\pi$
$211$	−16.9963	−1.17007	−0.585037	+	0.811007i	$0.698920\pi$
$212$	−9.34341	−0.641708
$213$	1.07110	0.0733907
$214$	−11.8904	−0.812812
$215$	−10.0439	−0.684991
$216$	3.08686	0.210034
$217$	23.7064	1.60930
$218$	−17.2315	−1.16707
$219$	−4.46588	−0.301776
$220$	12.1299	0.817799
$221$	−10.0020	−0.672806
$222$	−1.56156	−0.104805
$223$	11.6594	0.780773	0.390386	−	0.920651i	$-0.372341\pi$
$223$	11.6594	0.780773	0.390386	+	0.920651i	$0.372341\pi$
$224$	−2.85963	−0.191067
$225$	3.46865	0.231243
$226$	5.34319	0.355423
$227$	12.3421	0.819172	0.409586	−	0.912272i	$-0.365673\pi$
$227$	12.3421	0.819172	0.409586	+	0.912272i	$0.365673\pi$
$228$	3.67469	0.243362
$229$	6.98390	0.461509	0.230755	−	0.973012i	$-0.425881\pi$
$229$	6.98390	0.461509	0.230755	+	0.973012i	$0.425881\pi$
$230$	1.92844	0.127157
$231$	9.72825	0.640072
$232$	−1.00000	−0.0656532
$233$	15.1565	0.992937	0.496469	−	0.868055i	$-0.334630\pi$
$233$	15.1565	0.992937	0.496469	+	0.868055i	$0.334630\pi$
$234$	−15.2762	−0.998637
$235$	−0.447489	−0.0291910
$236$	7.53517	0.490498
$237$	0.534992	0.0347515
$238$	−5.06929	−0.328593
$239$	0.863547	0.0558582	0.0279291	−	0.999610i	$-0.491109\pi$
$239$	0.863547	0.0558582	0.0279291	+	0.999610i	$0.491109\pi$
$240$	1.04298	0.0673244
$241$	3.79238	0.244289	0.122144	−	0.992512i	$-0.461023\pi$
$241$	3.79238	0.244289	0.122144	+	0.992512i	$0.461023\pi$
$242$	−28.5644	−1.83619
$243$	12.7506	0.817953
$244$	0.247217	0.0158264
$245$	2.27071	0.145071
$246$	−0.479868	−0.0305952
$247$	−38.3351	−2.43921
$248$	−8.29002	−0.526417
$249$	−2.37300	−0.150382
$250$	12.1128	0.766079
$251$	−16.9126	−1.06751	−0.533756	−	0.845639i	$-0.679220\pi$
$251$	−16.9126	−1.06751	−0.533756	+	0.845639i	$0.679220\pi$
$252$	−7.74241	−0.487726
$253$	−6.29002	−0.395450
$254$	−18.6867	−1.17251
$255$	1.84891	0.115783
$256$	1.00000	0.0625000
$257$	−10.1388	−0.632439	−0.316219	−	0.948686i	$-0.602414\pi$
$257$	−10.1388	−0.632439	−0.316219	+	0.948686i	$0.602414\pi$
$258$	2.81690	0.175373
$259$	8.25649	0.513033
$260$	−10.8806	−0.674789
$261$	−2.70749	−0.167589
$262$	2.94772	0.182111
$263$	−26.7733	−1.65091	−0.825456	−	0.564466i	$-0.809082\pi$
$263$	−26.7733	−1.65091	−0.825456	+	0.564466i	$0.809082\pi$
$264$	−3.40193	−0.209374
$265$	−18.0182	−1.10685
$266$	−19.4293	−1.19129
$267$	−1.92378	−0.117733
$268$	2.98728	0.182477
$269$	−28.3866	−1.73076	−0.865380	−	0.501116i	$-0.832923\pi$
$269$	−28.3866	−1.73076	−0.865380	+	0.501116i	$0.832923\pi$
$270$	5.95282	0.362277
$271$	19.9796	1.21368	0.606838	−	0.794825i	$-0.292438\pi$
$271$	19.9796	1.21368	0.606838	+	0.794825i	$0.292438\pi$
$272$	1.77271	0.107486
$273$	−8.72633	−0.528141
$274$	−2.24879	−0.135854
$275$	−8.05834	−0.485936
$276$	−0.540845	−0.0325550
$277$	4.71512	0.283304	0.141652	−	0.989917i	$-0.454759\pi$
$277$	4.71512	0.283304	0.141652	+	0.989917i	$0.454759\pi$
$278$	10.2517	0.614855
$279$	−22.4451	−1.34375
$280$	−5.51462	−0.329561
$281$	−24.9993	−1.49133	−0.745667	−	0.666318i	$-0.767869\pi$
$281$	−24.9993	−1.49133	−0.745667	+	0.666318i	$0.767869\pi$
$282$	0.125502	0.00747351
$283$	−31.1291	−1.85043	−0.925217	−	0.379437i	$-0.876118\pi$
$283$	−31.1291	−1.85043	−0.925217	+	0.379437i	$0.876118\pi$
$284$	1.98043	0.117517
$285$	7.08640	0.419762
$286$	35.4896	2.09855
$287$	2.53722	0.149768
$288$	2.70749	0.159540
$289$	−13.8575	−0.815147
$290$	−1.92844	−0.113242
$291$	−7.02529	−0.411830
$292$	−8.25722	−0.483218
$293$	−4.36720	−0.255135	−0.127567	−	0.991830i	$-0.540717\pi$
$293$	−4.36720	−0.255135	−0.127567	+	0.991830i	$0.540717\pi$
$294$	−0.636839	−0.0371412
$295$	14.5311	0.846034
$296$	−2.88726	−0.167818
$297$	−19.4164	−1.12666
$298$	17.1250	0.992026
$299$	5.64221	0.326297
$300$	−0.692893	−0.0400042
$301$	−14.8939	−0.858471
$302$	−5.76208	−0.331571
$303$	−3.54893	−0.203881
$304$	6.79435	0.389683
$305$	0.476742	0.0272982
$306$	4.79958	0.274374
$307$	1.25222	0.0714679	0.0357340	−	0.999361i	$-0.488623\pi$
$307$	1.25222	0.0714679	0.0357340	+	0.999361i	$0.488623\pi$
$308$	17.9871	1.02491
$309$	10.7567	0.611927
$310$	−15.9868	−0.907989
$311$	−33.7559	−1.91412	−0.957061	−	0.289886i	$-0.906383\pi$
$311$	−33.7559	−1.91412	−0.957061	+	0.289886i	$0.906383\pi$
$312$	3.05156	0.172760
$313$	6.01143	0.339786	0.169893	−	0.985463i	$-0.445658\pi$
$313$	6.01143	0.339786	0.169893	+	0.985463i	$0.445658\pi$
$314$	−11.7218	−0.661501
$315$	−14.9308	−0.841253
$316$	0.989179	0.0556456
$317$	−20.4559	−1.14892	−0.574459	−	0.818533i	$-0.694788\pi$
$317$	−20.4559	−1.14892	−0.574459	+	0.818533i	$0.694788\pi$
$318$	5.05333	0.283377
$319$	6.29002	0.352174
$320$	1.92844	0.107803
$321$	6.43087	0.358936
$322$	2.85963	0.159361
$323$	12.0444	0.670168
$324$	6.45295	0.358497
$325$	7.22841	0.400960
$326$	9.50612	0.526495
$327$	9.31957	0.515374
$328$	−0.887256	−0.0489905
$329$	−0.663570	−0.0365838
$330$	−6.56040	−0.361138
$331$	1.68995	0.0928883	0.0464441	−	0.998921i	$-0.485211\pi$
$331$	1.68995	0.0928883	0.0464441	+	0.998921i	$0.485211\pi$
$332$	−4.38757	−0.240799
$333$	−7.81721	−0.428380
$334$	17.7997	0.973954
$335$	5.76078	0.314745
$336$	1.54662	0.0843748
$337$	3.59157	0.195645	0.0978225	−	0.995204i	$-0.468812\pi$
$337$	3.59157	0.195645	0.0978225	+	0.995204i	$0.468812\pi$
$338$	−18.8345	−1.02446
$339$	−2.88983	−0.156954
$340$	3.41856	0.185397
$341$	52.1445	2.82378
$342$	18.3956	0.994721
$343$	−16.6502	−0.899028
$344$	5.20833	0.280815
$345$	−1.04298	−0.0561524
$346$	−16.9509	−0.911286
$347$	−0.586509	−0.0314855	−0.0157427	−	0.999876i	$-0.505011\pi$
$347$	−0.586509	−0.0314855	−0.0157427	+	0.999876i	$0.505011\pi$
$348$	0.540845	0.0289923
$349$	5.91855	0.316813	0.158406	−	0.987374i	$-0.449364\pi$
$349$	5.91855	0.316813	0.158406	+	0.987374i	$0.449364\pi$
$350$	3.66356	0.195826
$351$	17.4167	0.929636
$352$	−6.29002	−0.335259
$353$	−22.7245	−1.20950	−0.604752	−	0.796414i	$-0.706728\pi$
$353$	−22.7245	−1.20950	−0.604752	+	0.796414i	$0.706728\pi$
$354$	−4.07536	−0.216603
$355$	3.81913	0.202698
$356$	−3.55699	−0.188520
$357$	2.74170	0.145106
$358$	4.79210	0.253270
$359$	−7.74311	−0.408666	−0.204333	−	0.978901i	$-0.565503\pi$
$359$	−7.74311	−0.408666	−0.204333	+	0.978901i	$0.565503\pi$
$360$	5.22122	0.275182
$361$	27.1632	1.42964
$362$	−12.3081	−0.646898
$363$	15.4489	0.810857
$364$	−16.1346	−0.845684
$365$	−15.9235	−0.833476
$366$	−0.133706	−0.00698892
$367$	8.78249	0.458442	0.229221	−	0.973374i	$-0.426382\pi$
$367$	8.78249	0.458442	0.229221	+	0.973374i	$0.426382\pi$
$368$	−1.00000	−0.0521286
$369$	−2.40223	−0.125055
$370$	−5.56789	−0.289461
$371$	−26.7187	−1.38717
$372$	4.48361	0.232465
$373$	−13.1379	−0.680255	−0.340127	−	0.940379i	$-0.610470\pi$
$373$	−13.1379	−0.680255	−0.340127	+	0.940379i	$0.610470\pi$
$374$	−11.1504	−0.576572
$375$	−6.55112	−0.338299
$376$	0.232048	0.0119669
$377$	−5.64221	−0.290588
$378$	8.82729	0.454027
$379$	−15.1436	−0.777876	−0.388938	−	0.921264i	$-0.627158\pi$
$379$	−15.1436	−0.777876	−0.388938	+	0.921264i	$0.627158\pi$
$380$	13.1025	0.672143
$381$	10.1066	0.517777
$382$	−11.0527	−0.565503
$383$	22.1344	1.13102	0.565508	−	0.824743i	$-0.308680\pi$
$383$	22.1344	1.13102	0.565508	+	0.824743i	$0.308680\pi$
$384$	−0.540845	−0.0275999
$385$	34.6871	1.76782
$386$	−3.96216	−0.201669
$387$	14.1015	0.716820
$388$	−12.9895	−0.659441
$389$	29.8175	1.51181	0.755905	−	0.654681i	$-0.227197\pi$
$389$	29.8175	1.51181	0.755905	+	0.654681i	$0.227197\pi$
$390$	5.88474	0.297985
$391$	−1.77271	−0.0896497
$392$	−1.17749	−0.0594722
$393$	−1.59426	−0.0804197
$394$	20.8810	1.05197
$395$	1.90757	0.0959802
$396$	−17.0302	−0.855798
$397$	−37.4428	−1.87920	−0.939600	−	0.342273i	$-0.888803\pi$
$397$	−37.4428	−1.87920	−0.939600	+	0.342273i	$0.888803\pi$
$398$	24.4407	1.22510
$399$	10.5083	0.526071
$400$	−1.28113	−0.0640565
$401$	−4.71877	−0.235644	−0.117822	−	0.993035i	$-0.537591\pi$
$401$	−4.71877	−0.235644	−0.117822	+	0.993035i	$0.537591\pi$
$402$	−1.61565	−0.0805815
$403$	−46.7740	−2.32998
$404$	−6.56183	−0.326463
$405$	12.4441	0.618352
$406$	−2.85963	−0.141921
$407$	18.1609	0.900203
$408$	−0.958760	−0.0474657
$409$	16.6786	0.824705	0.412353	−	0.911024i	$-0.364707\pi$
$409$	16.6786	0.824705	0.412353	+	0.911024i	$0.364707\pi$
$410$	−1.71102	−0.0845011
$411$	1.21625	0.0599930
$412$	19.8887	0.979846
$413$	21.5478	1.06030
$414$	−2.70749	−0.133066
$415$	−8.46116	−0.415342
$416$	5.64221	0.276632
$417$	−5.54456	−0.271518
$418$	−42.7366	−2.09032
$419$	−11.0217	−0.538447	−0.269224	−	0.963078i	$-0.586767\pi$
$419$	−11.0217	−0.538447	−0.269224	+	0.963078i	$0.586767\pi$
$420$	2.98255	0.145534
$421$	−39.9287	−1.94601	−0.973003	−	0.230793i	$-0.925868\pi$
$421$	−39.9287	−1.94601	−0.973003	+	0.230793i	$0.925868\pi$
$422$	16.9963	0.827367
$423$	0.628266	0.0305473
$424$	9.34341	0.453756
$425$	−2.27107	−0.110163
$426$	−1.07110	−0.0518951
$427$	0.706949	0.0342117
$428$	11.8904	0.574745
$429$	−19.1944	−0.926713
$430$	10.0439	0.484362
$431$	−9.48910	−0.457074	−0.228537	−	0.973535i	$-0.573394\pi$
$431$	−9.48910	−0.457074	−0.228537	+	0.973535i	$0.573394\pi$
$432$	−3.08686	−0.148517
$433$	−6.51636	−0.313156	−0.156578	−	0.987666i	$-0.550046\pi$
$433$	−6.51636	−0.313156	−0.156578	+	0.987666i	$0.550046\pi$
$434$	−23.7064	−1.13794
$435$	1.04298	0.0500073
$436$	17.2315	0.825240
$437$	−6.79435	−0.325018
$438$	4.46588	0.213388
$439$	−12.0552	−0.575364	−0.287682	−	0.957726i	$-0.592885\pi$
$439$	−12.0552	−0.575364	−0.287682	+	0.957726i	$0.592885\pi$
$440$	−12.1299	−0.578271
$441$	−3.18804	−0.151811
$442$	10.0020	0.475746
$443$	0.260591	0.0123811	0.00619053	−	0.999981i	$-0.498029\pi$
$443$	0.260591	0.0123811	0.00619053	+	0.999981i	$0.498029\pi$
$444$	1.56156	0.0741082
$445$	−6.85943	−0.325168
$446$	−11.6594	−0.552090
$447$	−9.26197	−0.438076
$448$	2.85963	0.135105
$449$	−15.5515	−0.733922	−0.366961	−	0.930236i	$-0.619602\pi$
$449$	−15.5515	−0.733922	−0.366961	+	0.930236i	$0.619602\pi$
$450$	−3.46865	−0.163514
$451$	5.58086	0.262792
$452$	−5.34319	−0.251322
$453$	3.11639	0.146421
$454$	−12.3421	−0.579242
$455$	−31.1146	−1.45868
$456$	−3.67469	−0.172083
$457$	−14.5755	−0.681815	−0.340908	−	0.940097i	$-0.610734\pi$
$457$	−14.5755	−0.681815	−0.340908	+	0.940097i	$0.610734\pi$
$458$	−6.98390	−0.326336
$459$	−5.47211	−0.255416
$460$	−1.92844	−0.0899138
$461$	−10.7188	−0.499223	−0.249612	−	0.968346i	$-0.580303\pi$
$461$	−10.7188	−0.499223	−0.249612	+	0.968346i	$0.580303\pi$
$462$	−9.72825	−0.452599
$463$	15.7933	0.733978	0.366989	−	0.930225i	$-0.380389\pi$
$463$	15.7933	0.733978	0.366989	+	0.930225i	$0.380389\pi$
$464$	1.00000	0.0464238
$465$	8.64637	0.400966
$466$	−15.1565	−0.702113
$467$	−24.1124	−1.11579	−0.557895	−	0.829912i	$-0.688391\pi$
$467$	−24.1124	−1.11579	−0.557895	+	0.829912i	$0.688391\pi$
$468$	15.2762	0.706143
$469$	8.54252	0.394457
$470$	0.447489	0.0206411
$471$	6.33969	0.292117
$472$	−7.53517	−0.346834
$473$	−32.7606	−1.50633
$474$	−0.534992	−0.0245730
$475$	−8.70445	−0.399388
$476$	5.06929	0.232351
$477$	25.2972	1.15828
$478$	−0.863547	−0.0394977
$479$	32.1741	1.47007	0.735036	−	0.678028i	$-0.237165\pi$
$479$	32.1741	1.47007	0.735036	+	0.678028i	$0.237165\pi$
$480$	−1.04298	−0.0476055
$481$	−16.2905	−0.742783
$482$	−3.79238	−0.172738
$483$	−1.54662	−0.0703735
$484$	28.5644	1.29838
$485$	−25.0494	−1.13743
$486$	−12.7506	−0.578380
$487$	−4.34903	−0.197073	−0.0985367	−	0.995133i	$-0.531416\pi$
$487$	−4.34903	−0.197073	−0.0985367	+	0.995133i	$0.531416\pi$
$488$	−0.247217	−0.0111910
$489$	−5.14133	−0.232499
$490$	−2.27071	−0.102580
$491$	21.2102	0.957202	0.478601	−	0.878033i	$-0.341144\pi$
$491$	21.2102	0.957202	0.478601	+	0.878033i	$0.341144\pi$
$492$	0.479868	0.0216341
$493$	1.77271	0.0798388
$494$	38.3351	1.72478
$495$	−32.8416	−1.47612
$496$	8.29002	0.372233
$497$	5.66329	0.254033
$498$	2.37300	0.106336
$499$	28.9512	1.29603	0.648016	−	0.761627i	$-0.275599\pi$
$499$	28.9512	1.29603	0.648016	+	0.761627i	$0.275599\pi$
$500$	−12.1128	−0.541699
$501$	−9.62685	−0.430096
$502$	16.9126	0.754845
$503$	−8.15056	−0.363416	−0.181708	−	0.983353i	$-0.558163\pi$
$503$	−8.15056	−0.363416	−0.181708	+	0.983353i	$0.558163\pi$
$504$	7.74241	0.344875
$505$	−12.6541	−0.563099
$506$	6.29002	0.279626
$507$	10.1865	0.452400
$508$	18.6867	0.829088
$509$	34.4247	1.52585	0.762925	−	0.646487i	$-0.223763\pi$
$509$	34.4247	1.52585	0.762925	+	0.646487i	$0.223763\pi$
$510$	−1.84891	−0.0818710
$511$	−23.6126	−1.04456
$512$	−1.00000	−0.0441942
$513$	−20.9732	−0.925991
$514$	10.1388	0.447202
$515$	38.3541	1.69008
$516$	−2.81690	−0.124007
$517$	−1.45958	−0.0641925
$518$	−8.25649	−0.362769
$519$	9.16780	0.402422
$520$	10.8806	0.477148
$521$	−20.0474	−0.878290	−0.439145	−	0.898416i	$-0.644719\pi$
$521$	−20.0474	−0.878290	−0.439145	+	0.898416i	$0.644719\pi$
$522$	2.70749	0.118503
$523$	6.09225	0.266396	0.133198	−	0.991089i	$-0.457475\pi$
$523$	6.09225	0.266396	0.133198	+	0.991089i	$0.457475\pi$
$524$	−2.94772	−0.128772
$525$	−1.98142	−0.0864762
$526$	26.7733	1.16737
$527$	14.6958	0.640159
$528$	3.40193	0.148050
$529$	1.00000	0.0434783
$530$	18.0182	0.782660
$531$	−20.4014	−0.885345
$532$	19.4293	0.842369
$533$	−5.00608	−0.216837
$534$	1.92378	0.0832501
$535$	22.9299	0.991347
$536$	−2.98728	−0.129031
$537$	−2.59178	−0.111844
$538$	28.3866	1.22383
$539$	7.40644	0.319018
$540$	−5.95282	−0.256169
$541$	−39.1783	−1.68441	−0.842204	−	0.539159i	$-0.818742\pi$
$541$	−39.1783	−1.68441	−0.842204	+	0.539159i	$0.818742\pi$
$542$	−19.9796	−0.858199
$543$	6.65675	0.285669
$544$	−1.77271	−0.0760042
$545$	33.2299	1.42341
$546$	8.72633	0.373452
$547$	26.7187	1.14241	0.571204	−	0.820808i	$-0.306477\pi$
$547$	26.7187	1.14241	0.571204	+	0.820808i	$0.306477\pi$
$548$	2.24879	0.0960636
$549$	−0.669337	−0.0285666
$550$	8.05834	0.343609
$551$	6.79435	0.289449
$552$	0.540845	0.0230199
$553$	2.82869	0.120288
$554$	−4.71512	−0.200326
$555$	3.01136	0.127825
$556$	−10.2517	−0.434768
$557$	37.8143	1.60224	0.801122	−	0.598501i	$-0.204237\pi$
$557$	37.8143	1.60224	0.801122	+	0.598501i	$0.204237\pi$
$558$	22.4451	0.950178
$559$	29.3865	1.24292
$560$	5.51462	0.233035
$561$	6.03062	0.254613
$562$	24.9993	1.05453
$563$	32.7537	1.38040	0.690202	−	0.723617i	$-0.257522\pi$
$563$	32.7537	1.38040	0.690202	+	0.723617i	$0.257522\pi$
$564$	−0.125502	−0.00528457
$565$	−10.3040	−0.433492
$566$	31.1291	1.30846
$567$	18.4530	0.774955
$568$	−1.98043	−0.0830968
$569$	−38.8248	−1.62762	−0.813809	−	0.581132i	$-0.802610\pi$
$569$	−38.8248	−1.62762	−0.813809	+	0.581132i	$0.802610\pi$
$570$	−7.08640	−0.296817
$571$	21.9239	0.917488	0.458744	−	0.888568i	$-0.348299\pi$
$571$	21.9239	0.917488	0.458744	+	0.888568i	$0.348299\pi$
$572$	−35.4896	−1.48390
$573$	5.97777	0.249725
$574$	−2.53722	−0.105902
$575$	1.28113	0.0534269
$576$	−2.70749	−0.112812
$577$	7.91268	0.329409	0.164705	−	0.986343i	$-0.447333\pi$
$577$	7.91268	0.329409	0.164705	+	0.986343i	$0.447333\pi$
$578$	13.8575	0.576396
$579$	2.14292	0.0890565
$580$	1.92844	0.0800740
$581$	−12.5468	−0.520531
$582$	7.02529	0.291208
$583$	−58.7703	−2.43402
$584$	8.25722	0.341686
$585$	29.4592	1.21799
$586$	4.36720	0.180408
$587$	21.4898	0.886977	0.443489	−	0.896280i	$-0.353741\pi$
$587$	21.4898	0.886977	0.443489	+	0.896280i	$0.353741\pi$
$588$	0.636839	0.0262628
$589$	56.3253	2.32084
$590$	−14.5311	−0.598236
$591$	−11.2934	−0.464548
$592$	2.88726	0.118665
$593$	−31.6608	−1.30015	−0.650077	−	0.759868i	$-0.725264\pi$
$593$	−31.6608	−1.30015	−0.650077	+	0.759868i	$0.725264\pi$
$594$	19.4164	0.796666
$595$	9.77581	0.400769
$596$	−17.1250	−0.701468
$597$	−13.2186	−0.541003
$598$	−5.64221	−0.230727
$599$	−27.2881	−1.11496	−0.557480	−	0.830190i	$-0.688232\pi$
$599$	−27.2881	−1.11496	−0.557480	+	0.830190i	$0.688232\pi$
$600$	0.692893	0.0282872
$601$	16.5730	0.676025	0.338013	−	0.941142i	$-0.390245\pi$
$601$	16.5730	0.676025	0.338013	+	0.941142i	$0.390245\pi$
$602$	14.8939	0.607031
$603$	−8.08802	−0.329370
$604$	5.76208	0.234456
$605$	55.0847	2.23951
$606$	3.54893	0.144165
$607$	7.35123	0.298377	0.149189	−	0.988809i	$-0.452334\pi$
$607$	7.35123	0.298377	0.149189	+	0.988809i	$0.452334\pi$
$608$	−6.79435	−0.275547
$609$	1.54662	0.0626720
$610$	−0.476742	−0.0193027
$611$	1.30926	0.0529670
$612$	−4.79958	−0.194012
$613$	10.4520	0.422152	0.211076	−	0.977470i	$-0.432303\pi$
$613$	10.4520	0.422152	0.211076	+	0.977470i	$0.432303\pi$
$614$	−1.25222	−0.0505354
$615$	0.925394	0.0373155
$616$	−17.9871	−0.724723
$617$	−6.54737	−0.263587	−0.131794	−	0.991277i	$-0.542074\pi$
$617$	−6.54737	−0.263587	−0.131794	+	0.991277i	$0.542074\pi$
$618$	−10.7567	−0.432698
$619$	−24.6852	−0.992182	−0.496091	−	0.868271i	$-0.665232\pi$
$619$	−24.6852	−0.992182	−0.496091	+	0.868271i	$0.665232\pi$
$620$	15.9868	0.642045
$621$	3.08686	0.123872
$622$	33.7559	1.35349
$623$	−10.1717	−0.407520
$624$	−3.05156	−0.122160
$625$	−16.9530	−0.678122
$626$	−6.01143	−0.240265
$627$	23.1139	0.923079
$628$	11.7218	0.467752
$629$	5.11826	0.204078
$630$	14.9308	0.594856
$631$	−30.4144	−1.21078	−0.605389	−	0.795930i	$-0.706983\pi$
$631$	−30.4144	−1.21078	−0.605389	+	0.795930i	$0.706983\pi$
$632$	−0.989179	−0.0393474
$633$	−9.19236	−0.365363
$634$	20.4559	0.812408
$635$	36.0361	1.43005
$636$	−5.05333	−0.200378
$637$	−6.64364	−0.263231
$638$	−6.29002	−0.249024
$639$	−5.36198	−0.212117
$640$	−1.92844	−0.0762282
$641$	−0.162981	−0.00643737	−0.00321869	−	0.999995i	$-0.501025\pi$
$641$	−0.162981	−0.00643737	−0.00321869	+	0.999995i	$0.501025\pi$
$642$	−6.43087	−0.253806
$643$	13.3998	0.528436	0.264218	−	0.964463i	$-0.414886\pi$
$643$	13.3998	0.528436	0.264218	+	0.964463i	$0.414886\pi$
$644$	−2.85963	−0.112685
$645$	−5.43221	−0.213893
$646$	−12.0444	−0.473881
$647$	6.83236	0.268608	0.134304	−	0.990940i	$-0.457120\pi$
$647$	6.83236	0.268608	0.134304	+	0.990940i	$0.457120\pi$
$648$	−6.45295	−0.253496
$649$	47.3964	1.86047
$650$	−7.22841	−0.283521
$651$	12.8215	0.502514
$652$	−9.50612	−0.372288
$653$	17.2467	0.674916	0.337458	−	0.941341i	$-0.390433\pi$
$653$	17.2467	0.674916	0.337458	+	0.941341i	$0.390433\pi$
$654$	−9.31957	−0.364424
$655$	−5.68449	−0.222112
$656$	0.887256	0.0346415
$657$	22.3563	0.872204
$658$	0.663570	0.0258687
$659$	41.6546	1.62263	0.811316	−	0.584607i	$-0.198751\pi$
$659$	41.6546	1.62263	0.811316	+	0.584607i	$0.198751\pi$
$660$	6.56040	0.255363
$661$	22.7970	0.886699	0.443349	−	0.896349i	$-0.353790\pi$
$661$	22.7970	0.886699	0.443349	+	0.896349i	$0.353790\pi$
$662$	−1.68995	−0.0656819
$663$	−5.40952	−0.210088
$664$	4.38757	0.170271
$665$	37.4682	1.45296
$666$	7.81721	0.302911
$667$	−1.00000	−0.0387202
$668$	−17.7997	−0.688689
$669$	6.30594	0.243802
$670$	−5.76078	−0.222558
$671$	1.55500	0.0600301
$672$	−1.54662	−0.0596620
$673$	−22.8150	−0.879455	−0.439728	−	0.898131i	$-0.644925\pi$
$673$	−22.8150	−0.879455	−0.439728	+	0.898131i	$0.644925\pi$
$674$	−3.59157	−0.138342
$675$	3.95468	0.152216
$676$	18.8345	0.724404
$677$	3.13741	0.120580	0.0602901	−	0.998181i	$-0.480797\pi$
$677$	3.13741	0.120580	0.0602901	+	0.998181i	$0.480797\pi$
$678$	2.88983	0.110983
$679$	−37.1451	−1.42550
$680$	−3.41856	−0.131096
$681$	6.67514	0.255792
$682$	−52.1445	−1.99671
$683$	−48.0946	−1.84029	−0.920144	−	0.391581i	$-0.871928\pi$
$683$	−48.0946	−1.84029	−0.920144	+	0.391581i	$0.871928\pi$
$684$	−18.3956	−0.703374
$685$	4.33665	0.165695
$686$	16.6502	0.635709
$687$	3.77721	0.144109
$688$	−5.20833	−0.198566
$689$	52.7175	2.00838
$690$	1.04298	0.0397057
$691$	−11.1775	−0.425213	−0.212607	−	0.977138i	$-0.568195\pi$
$691$	−11.1775	−0.425213	−0.212607	+	0.977138i	$0.568195\pi$
$692$	16.9509	0.644376
$693$	−48.7000	−1.84996
$694$	0.586509	0.0222636
$695$	−19.7697	−0.749908
$696$	−0.540845	−0.0205007
$697$	1.57285	0.0595758
$698$	−5.91855	−0.224021
$699$	8.19733	0.310051
$700$	−3.66356	−0.138470
$701$	−37.8835	−1.43084	−0.715421	−	0.698694i	$-0.753765\pi$
$701$	−37.8835	−1.43084	−0.715421	+	0.698694i	$0.753765\pi$
$702$	−17.4167	−0.657352
$703$	19.6170	0.739870
$704$	6.29002	0.237064
$705$	−0.242022	−0.00911508
$706$	22.7245	0.855249
$707$	−18.7644	−0.705708
$708$	4.07536	0.153161
$709$	7.18965	0.270013	0.135006	−	0.990845i	$-0.456894\pi$
$709$	7.18965	0.270013	0.135006	+	0.990845i	$0.456894\pi$
$710$	−3.81913	−0.143329
$711$	−2.67819	−0.100440
$712$	3.55699	0.133304
$713$	−8.29002	−0.310464
$714$	−2.74170	−0.102605
$715$	−68.4395	−2.55949
$716$	−4.79210	−0.179089
$717$	0.467045	0.0174421
$718$	7.74311	0.288970
$719$	−24.6994	−0.921131	−0.460566	−	0.887626i	$-0.652353\pi$
$719$	−24.6994	−0.921131	−0.460566	+	0.887626i	$0.652353\pi$
$720$	−5.22122	−0.194583
$721$	56.8744	2.11811
$722$	−27.1632	−1.01091
$723$	2.05109	0.0762808
$724$	12.3081	0.457426
$725$	−1.28113	−0.0475800
$726$	−15.4489	−0.573363
$727$	−7.26861	−0.269578	−0.134789	−	0.990874i	$-0.543036\pi$
$727$	−7.26861	−0.269578	−0.134789	+	0.990874i	$0.543036\pi$
$728$	16.1346	0.597989
$729$	−12.4627	−0.461583
$730$	15.9235	0.589357
$731$	−9.23286	−0.341490
$732$	0.133706	0.00494192
$733$	−39.9789	−1.47666	−0.738328	−	0.674442i	$-0.764384\pi$
$733$	−39.9789	−1.47666	−0.738328	+	0.674442i	$0.764384\pi$
$734$	−8.78249	−0.324167
$735$	1.22810	0.0452993
$736$	1.00000	0.0368605
$737$	18.7901	0.692141
$738$	2.40223	0.0884275
$739$	49.2506	1.81171	0.905857	−	0.423584i	$-0.139228\pi$
$739$	49.2506	1.81171	0.905857	+	0.423584i	$0.139228\pi$
$740$	5.56789	0.204680
$741$	−20.7333	−0.761659
$742$	26.7187	0.980875
$743$	37.3742	1.37113	0.685564	−	0.728012i	$-0.259556\pi$
$743$	37.3742	1.37113	0.685564	+	0.728012i	$0.259556\pi$
$744$	−4.48361	−0.164377
$745$	−33.0245	−1.20992
$746$	13.1379	0.481013
$747$	11.8793	0.434641
$748$	11.1504	0.407698
$749$	34.0022	1.24241
$750$	6.55112	0.239213
$751$	22.6237	0.825551	0.412776	−	0.910833i	$-0.364559\pi$
$751$	22.6237	0.825551	0.412776	+	0.910833i	$0.364559\pi$
$752$	−0.232048	−0.00846190
$753$	−9.14707	−0.333338
$754$	5.64221	0.205477
$755$	11.1118	0.404400
$756$	−8.82729	−0.321045
$757$	13.7389	0.499349	0.249674	−	0.968330i	$-0.419676\pi$
$757$	13.7389	0.499349	0.249674	+	0.968330i	$0.419676\pi$
$758$	15.1436	0.550041
$759$	−3.40193	−0.123482
$760$	−13.1025	−0.475277
$761$	17.8746	0.647953	0.323976	−	0.946065i	$-0.394980\pi$
$761$	17.8746	0.647953	0.323976	+	0.946065i	$0.394980\pi$
$762$	−10.1066	−0.366124
$763$	49.2758	1.78390
$764$	11.0527	0.399871
$765$	−9.25570	−0.334640
$766$	−22.1344	−0.799749
$767$	−42.5150	−1.53513
$768$	0.540845	0.0195160
$769$	1.52522	0.0550008	0.0275004	−	0.999622i	$-0.491245\pi$
$769$	1.52522	0.0550008	0.0275004	+	0.999622i	$0.491245\pi$
$770$	−34.6871	−1.25004
$771$	−5.48350	−0.197483
$772$	3.96216	0.142601
$773$	10.1053	0.363462	0.181731	−	0.983348i	$-0.441830\pi$
$773$	10.1053	0.363462	0.181731	+	0.983348i	$0.441830\pi$
$774$	−14.1015	−0.506868
$775$	−10.6206	−0.381503
$776$	12.9895	0.466295
$777$	4.46548	0.160198
$778$	−29.8175	−1.06901
$779$	6.02833	0.215987
$780$	−5.88474	−0.210707
$781$	12.4569	0.445744
$782$	1.77271	0.0633919
$783$	−3.08686	−0.110316
$784$	1.17749	0.0420532
$785$	22.6048	0.806800
$786$	1.59426	0.0568653
$787$	24.7433	0.882003	0.441002	−	0.897506i	$-0.354623\pi$
$787$	24.7433	0.882003	0.441002	+	0.897506i	$0.354623\pi$
$788$	−20.8810	−0.743855
$789$	−14.4802	−0.515509
$790$	−1.90757	−0.0678682
$791$	−15.2795	−0.543278
$792$	17.0302	0.605140
$793$	−1.39485	−0.0495326
$794$	37.4428	1.32880
$795$	−9.74503	−0.345621
$796$	−24.4407	−0.866279
$797$	−50.3873	−1.78481	−0.892404	−	0.451237i	$-0.850983\pi$
$797$	−50.3873	−1.78481	−0.892404	+	0.451237i	$0.850983\pi$
$798$	−10.5083	−0.371988
$799$	−0.411353	−0.0145526
$800$	1.28113	0.0452948
$801$	9.63051	0.340277
$802$	4.71877	0.166626
$803$	−51.9381	−1.83286
$804$	1.61565	0.0569797
$805$	−5.51462	−0.194365
$806$	46.7740	1.64754
$807$	−15.3527	−0.540441
$808$	6.56183	0.230844
$809$	27.4114	0.963732	0.481866	−	0.876245i	$-0.339959\pi$
$809$	27.4114	0.963732	0.481866	+	0.876245i	$0.339959\pi$
$810$	−12.4441	−0.437241
$811$	−47.4855	−1.66744	−0.833720	−	0.552187i	$-0.813794\pi$
$811$	−47.4855	−1.66744	−0.833720	+	0.552187i	$0.813794\pi$
$812$	2.85963	0.100353
$813$	10.8059	0.378979
$814$	−18.1609	−0.636540
$815$	−18.3319	−0.642140
$816$	0.958760	0.0335633
$817$	−35.3873	−1.23804
$818$	−16.6786	−0.583155
$819$	43.6843	1.52645
$820$	1.71102	0.0597513
$821$	−16.8928	−0.589562	−0.294781	−	0.955565i	$-0.595247\pi$
$821$	−16.8928	−0.589562	−0.294781	+	0.955565i	$0.595247\pi$
$822$	−1.21625	−0.0424215
$823$	1.69807	0.0591910	0.0295955	−	0.999562i	$-0.490578\pi$
$823$	1.69807	0.0591910	0.0295955	+	0.999562i	$0.490578\pi$
$824$	−19.8887	−0.692856
$825$	−4.35831	−0.151737
$826$	−21.5478	−0.749744
$827$	−14.4507	−0.502501	−0.251250	−	0.967922i	$-0.580842\pi$
$827$	−14.4507	−0.502501	−0.251250	+	0.967922i	$0.580842\pi$
$828$	2.70749	0.0940917
$829$	35.8016	1.24344	0.621720	−	0.783239i	$-0.286434\pi$
$829$	35.8016	1.24344	0.621720	+	0.783239i	$0.286434\pi$
$830$	8.46116	0.293691
$831$	2.55015	0.0884636
$832$	−5.64221	−0.195608
$833$	2.08735	0.0723222
$834$	5.54456	0.191993
$835$	−34.3255	−1.18788
$836$	42.7366	1.47808
$837$	−25.5902	−0.884526
$838$	11.0217	0.380740
$839$	27.0211	0.932871	0.466436	−	0.884555i	$-0.345538\pi$
$839$	27.0211	0.932871	0.466436	+	0.884555i	$0.345538\pi$
$840$	−2.98255	−0.102908
$841$	1.00000	0.0344828
$842$	39.9287	1.37603
$843$	−13.5208	−0.465679
$844$	−16.9963	−0.585037
$845$	36.3211	1.24949
$846$	−0.628266	−0.0216002
$847$	81.6837	2.80668
$848$	−9.34341	−0.320854
$849$	−16.8360	−0.577811
$850$	2.27107	0.0778971
$851$	−2.88726	−0.0989739
$852$	1.07110	0.0366954
$853$	30.9685	1.06034	0.530171	−	0.847891i	$-0.322128\pi$
$853$	30.9685	1.06034	0.530171	+	0.847891i	$0.322128\pi$
$854$	−0.706949	−0.0241913
$855$	−35.4748	−1.21321
$856$	−11.8904	−0.406406
$857$	−17.7171	−0.605205	−0.302602	−	0.953117i	$-0.597855\pi$
$857$	−17.7171	−0.605205	−0.302602	+	0.953117i	$0.597855\pi$
$858$	19.1944	0.655285
$859$	20.5639	0.701630	0.350815	−	0.936445i	$-0.385905\pi$
$859$	20.5639	0.701630	0.350815	+	0.936445i	$0.385905\pi$
$860$	−10.0439	−0.342496
$861$	1.37224	0.0467660
$862$	9.48910	0.323200
$863$	51.1102	1.73981	0.869906	−	0.493218i	$-0.164179\pi$
$863$	51.1102	1.73981	0.869906	+	0.493218i	$0.164179\pi$
$864$	3.08686	0.105017
$865$	32.6887	1.11145
$866$	6.51636	0.221435
$867$	−7.49476	−0.254535
$868$	23.7064	0.804648
$869$	6.22196	0.211065
$870$	−1.04298	−0.0353605
$871$	−16.8548	−0.571105
$872$	−17.2315	−0.583533
$873$	35.1689	1.19029
$874$	6.79435	0.229822
$875$	−34.6380	−1.17098
$876$	−4.46588	−0.150888
$877$	40.7280	1.37529	0.687643	−	0.726049i	$-0.258645\pi$
$877$	40.7280	1.37529	0.687643	+	0.726049i	$0.258645\pi$
$878$	12.0552	0.406843
$879$	−2.36198	−0.0796676
$880$	12.1299	0.408899
$881$	−19.7915	−0.666793	−0.333396	−	0.942787i	$-0.608195\pi$
$881$	−19.7915	−0.666793	−0.333396	+	0.942787i	$0.608195\pi$
$882$	3.18804	0.107347
$883$	−27.1187	−0.912618	−0.456309	−	0.889821i	$-0.650829\pi$
$883$	−27.1187	−0.912618	−0.456309	+	0.889821i	$0.650829\pi$
$884$	−10.0020	−0.336403
$885$	7.85907	0.264180
$886$	−0.260591	−0.00875474
$887$	−28.6657	−0.962500	−0.481250	−	0.876583i	$-0.659817\pi$
$887$	−28.6657	−0.962500	−0.481250	+	0.876583i	$0.659817\pi$
$888$	−1.56156	−0.0524024
$889$	53.4371	1.79222
$890$	6.85943	0.229929
$891$	40.5892	1.35979
$892$	11.6594	0.390386
$893$	−1.57661	−0.0527593
$894$	9.26197	0.309767
$895$	−9.24126	−0.308901
$896$	−2.85963	−0.0955336
$897$	3.05156	0.101889
$898$	15.5515	0.518961
$899$	8.29002	0.276488
$900$	3.46865	0.115622
$901$	−16.5631	−0.551798
$902$	−5.58086	−0.185822
$903$	−8.05529	−0.268063
$904$	5.34319	0.177712
$905$	23.7353	0.788989
$906$	−3.11639	−0.103535
$907$	−59.0442	−1.96053	−0.980265	−	0.197686i	$-0.936657\pi$
$907$	−59.0442	−1.96053	−0.980265	+	0.197686i	$0.936657\pi$
$908$	12.3421	0.409586
$909$	17.7661	0.589263
$910$	31.1146	1.03144
$911$	36.1162	1.19658	0.598291	−	0.801279i	$-0.295847\pi$
$911$	36.1162	1.19658	0.598291	+	0.801279i	$0.295847\pi$
$912$	3.67469	0.121681
$913$	−27.5979	−0.913359
$914$	14.5755	0.482116
$915$	0.257844	0.00852404
$916$	6.98390	0.230755
$917$	−8.42940	−0.278363
$918$	5.47211	0.180606
$919$	42.9496	1.41678	0.708388	−	0.705823i	$-0.249423\pi$
$919$	42.9496	1.41678	0.708388	+	0.705823i	$0.249423\pi$
$920$	1.92844	0.0635787
$921$	0.677256	0.0223163
$922$	10.7188	0.353004
$923$	−11.1740	−0.367796
$924$	9.72825	0.320036
$925$	−3.69895	−0.121621
$926$	−15.7933	−0.519001
$927$	−53.8484	−1.76861
$928$	−1.00000	−0.0328266
$929$	19.5141	0.640237	0.320118	−	0.947378i	$-0.396277\pi$
$929$	19.5141	0.640237	0.320118	+	0.947378i	$0.396277\pi$
$930$	−8.64637	−0.283526
$931$	8.00028	0.262199
$932$	15.1565	0.496469
$933$	−18.2567	−0.597698
$934$	24.1124	0.788982
$935$	21.5028	0.703217
$936$	−15.2762	−0.499318
$937$	−20.7231	−0.676995	−0.338497	−	0.940967i	$-0.609919\pi$
$937$	−20.7231	−0.676995	−0.338497	+	0.940967i	$0.609919\pi$
$938$	−8.54252	−0.278923
$939$	3.25125	0.106100
$940$	−0.447489	−0.0145955
$941$	17.6658	0.575890	0.287945	−	0.957647i	$-0.407028\pi$
$941$	17.6658	0.575890	0.287945	+	0.957647i	$0.407028\pi$
$942$	−6.33969	−0.206558
$943$	−0.887256	−0.0288930
$944$	7.53517	0.245249
$945$	−17.0229	−0.553754
$946$	32.7606	1.06514
$947$	−36.7870	−1.19542	−0.597709	−	0.801713i	$-0.703922\pi$
$947$	−36.7870	−1.19542	−0.597709	+	0.801713i	$0.703922\pi$
$948$	0.534992	0.0173757
$949$	46.5890	1.51234
$950$	8.70445	0.282410
$951$	−11.0635	−0.358758
$952$	−5.06929	−0.164297
$953$	7.14111	0.231323	0.115662	−	0.993289i	$-0.463101\pi$
$953$	7.14111	0.231323	0.115662	+	0.993289i	$0.463101\pi$
$954$	−25.2972	−0.819026
$955$	21.3143	0.689716
$956$	0.863547	0.0279291
$957$	3.40193	0.109969
$958$	−32.1741	−1.03950
$959$	6.43072	0.207659
$960$	1.04298	0.0336622
$961$	37.7245	1.21692
$962$	16.2905	0.525227
$963$	−32.1932	−1.03741
$964$	3.79238	0.122144
$965$	7.64078	0.245966
$966$	1.54662	0.0497616
$967$	46.2927	1.48867	0.744336	−	0.667805i	$-0.232766\pi$
$967$	46.2927	1.48867	0.744336	+	0.667805i	$0.232766\pi$
$968$	−28.5644	−0.918095
$969$	6.51415	0.209265
$970$	25.0494	0.804288
$971$	−2.64236	−0.0847974	−0.0423987	−	0.999101i	$-0.513500\pi$
$971$	−2.64236	−0.0847974	−0.0423987	+	0.999101i	$0.513500\pi$
$972$	12.7506	0.408977
$973$	−29.3160	−0.939828
$974$	4.34903	0.139352
$975$	3.90944	0.125202
$976$	0.247217	0.00791322
$977$	−38.5554	−1.23350	−0.616748	−	0.787160i	$-0.711550\pi$
$977$	−38.5554	−1.23350	−0.616748	+	0.787160i	$0.711550\pi$
$978$	5.14133	0.164402
$979$	−22.3736	−0.715062
$980$	2.27071	0.0725353
$981$	−46.6541	−1.48955
$982$	−21.2102	−0.676844
$983$	17.8126	0.568132	0.284066	−	0.958805i	$-0.408316\pi$
$983$	17.8126	0.568132	0.284066	+	0.958805i	$0.408316\pi$
$984$	−0.479868	−0.0152976
$985$	−40.2677	−1.28304
$986$	−1.77271	−0.0564545
$987$	−0.358888	−0.0114235
$988$	−38.3351	−1.21960
$989$	5.20833	0.165615
$990$	32.8416	1.04377
$991$	28.9854	0.920752	0.460376	−	0.887724i	$-0.347715\pi$
$991$	28.9854	0.920752	0.460376	+	0.887724i	$0.347715\pi$
$992$	−8.29002	−0.263209
$993$	0.914003	0.0290050
$994$	−5.66329	−0.179629
$995$	−47.1324	−1.49420
$996$	−2.37300	−0.0751912
$997$	31.8617	1.00907	0.504536	−	0.863391i	$-0.331664\pi$
$997$	31.8617	1.00907	0.504536	+	0.863391i	$0.331664\pi$
$998$	−28.9512	−0.916433
$999$	−8.91257	−0.281981

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1334.2.a.j.1.6	✓	9

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1334.2.a.j.1.6	✓	9	1.1	even	1	trivial

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 1334 = 2 \cdot 23 \cdot 29 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1334.a (trivial)

\(f(q)\)	\(=\)	\(q-1.00000 q^{2} +0.540845 q^{3} +1.00000 q^{4} +1.92844 q^{5} -0.540845 q^{6} +2.85963 q^{7} -1.00000 q^{8} -2.70749 q^{9} +O(q^{10})\)	\(q-1.00000 q^{2} +0.540845 q^{3} +1.00000 q^{4} +1.92844 q^{5} -0.540845 q^{6} +2.85963 q^{7} -1.00000 q^{8} -2.70749 q^{9} -1.92844 q^{10} +6.29002 q^{11} +0.540845 q^{12} -5.64221 q^{13} -2.85963 q^{14} +1.04298 q^{15} +1.00000 q^{16} +1.77271 q^{17} +2.70749 q^{18} +6.79435 q^{19} +1.92844 q^{20} +1.54662 q^{21} -6.29002 q^{22} -1.00000 q^{23} -0.540845 q^{24} -1.28113 q^{25} +5.64221 q^{26} -3.08686 q^{27} +2.85963 q^{28} +1.00000 q^{29} -1.04298 q^{30} +8.29002 q^{31} -1.00000 q^{32} +3.40193 q^{33} -1.77271 q^{34} +5.51462 q^{35} -2.70749 q^{36} +2.88726 q^{37} -6.79435 q^{38} -3.05156 q^{39} -1.92844 q^{40} +0.887256 q^{41} -1.54662 q^{42} -5.20833 q^{43} +6.29002 q^{44} -5.22122 q^{45} +1.00000 q^{46} -0.232048 q^{47} +0.540845 q^{48} +1.17749 q^{49} +1.28113 q^{50} +0.958760 q^{51} -5.64221 q^{52} -9.34341 q^{53} +3.08686 q^{54} +12.1299 q^{55} -2.85963 q^{56} +3.67469 q^{57} -1.00000 q^{58} +7.53517 q^{59} +1.04298 q^{60} +0.247217 q^{61} -8.29002 q^{62} -7.74241 q^{63} +1.00000 q^{64} -10.8806 q^{65} -3.40193 q^{66} +2.98728 q^{67} +1.77271 q^{68} -0.540845 q^{69} -5.51462 q^{70} +1.98043 q^{71} +2.70749 q^{72} -8.25722 q^{73} -2.88726 q^{74} -0.692893 q^{75} +6.79435 q^{76} +17.9871 q^{77} +3.05156 q^{78} +0.989179 q^{79} +1.92844 q^{80} +6.45295 q^{81} -0.887256 q^{82} -4.38757 q^{83} +1.54662 q^{84} +3.41856 q^{85} +5.20833 q^{86} +0.540845 q^{87} -6.29002 q^{88} -3.55699 q^{89} +5.22122 q^{90} -16.1346 q^{91} -1.00000 q^{92} +4.48361 q^{93} +0.232048 q^{94} +13.1025 q^{95} -0.540845 q^{96} -12.9895 q^{97} -1.17749 q^{98} -17.0302 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 9 q - 9 q^{2} - 3 q^{3} + 9 q^{4} + 5 q^{5} + 3 q^{6} + 6 q^{7} - 9 q^{8} + 14 q^{9}+O(q^{10}) \) 9 * q - 9 * q^2 - 3 * q^3 + 9 * q^4 + 5 * q^5 + 3 * q^6 + 6 * q^7 - 9 * q^8 + 14 * q^9	\( 9 q - 9 q^{2} - 3 q^{3} + 9 q^{4} + 5 q^{5} + 3 q^{6} + 6 q^{7} - 9 q^{8} + 14 q^{9} - 5 q^{10} - 3 q^{11} - 3 q^{12} + 13 q^{13} - 6 q^{14} - 3 q^{15} + 9 q^{16} + 2 q^{17} - 14 q^{18} + 16 q^{19} + 5 q^{20} + 8 q^{21} + 3 q^{22} - 9 q^{23} + 3 q^{24} + 20 q^{25} - 13 q^{26} - 21 q^{27} + 6 q^{28} + 9 q^{29} + 3 q^{30} + 15 q^{31} - 9 q^{32} + 13 q^{33} - 2 q^{34} + 14 q^{36} + 12 q^{37} - 16 q^{38} - 5 q^{39} - 5 q^{40} - 6 q^{41} - 8 q^{42} - 3 q^{43} - 3 q^{44} + 20 q^{45} + 9 q^{46} - 19 q^{47} - 3 q^{48} + 37 q^{49} - 20 q^{50} + 6 q^{51} + 13 q^{52} + 5 q^{53} + 21 q^{54} + q^{55} - 6 q^{56} - 20 q^{57} - 9 q^{58} + 12 q^{59} - 3 q^{60} + 12 q^{61} - 15 q^{62} + 6 q^{63} + 9 q^{64} + 19 q^{65} - 13 q^{66} - 6 q^{67} + 2 q^{68} + 3 q^{69} + 12 q^{71} - 14 q^{72} - 12 q^{74} + 16 q^{75} + 16 q^{76} + 34 q^{77} + 5 q^{78} + 29 q^{79} + 5 q^{80} + 5 q^{81} + 6 q^{82} + 24 q^{83} + 8 q^{84} + 12 q^{85} + 3 q^{86} - 3 q^{87} + 3 q^{88} - 2 q^{89} - 20 q^{90} + 58 q^{91} - 9 q^{92} + 7 q^{93} + 19 q^{94} + 6 q^{95} + 3 q^{96} + 12 q^{97} - 37 q^{98} - 20 q^{99}+O(q^{100}) \) 9 * q - 9 * q^2 - 3 * q^3 + 9 * q^4 + 5 * q^5 + 3 * q^6 + 6 * q^7 - 9 * q^8 + 14 * q^9 - 5 * q^10 - 3 * q^11 - 3 * q^12 + 13 * q^13 - 6 * q^14 - 3 * q^15 + 9 * q^16 + 2 * q^17 - 14 * q^18 + 16 * q^19 + 5 * q^20 + 8 * q^21 + 3 * q^22 - 9 * q^23 + 3 * q^24 + 20 * q^25 - 13 * q^26 - 21 * q^27 + 6 * q^28 + 9 * q^29 + 3 * q^30 + 15 * q^31 - 9 * q^32 + 13 * q^33 - 2 * q^34 + 14 * q^36 + 12 * q^37 - 16 * q^38 - 5 * q^39 - 5 * q^40 - 6 * q^41 - 8 * q^42 - 3 * q^43 - 3 * q^44 + 20 * q^45 + 9 * q^46 - 19 * q^47 - 3 * q^48 + 37 * q^49 - 20 * q^50 + 6 * q^51 + 13 * q^52 + 5 * q^53 + 21 * q^54 + q^55 - 6 * q^56 - 20 * q^57 - 9 * q^58 + 12 * q^59 - 3 * q^60 + 12 * q^61 - 15 * q^62 + 6 * q^63 + 9 * q^64 + 19 * q^65 - 13 * q^66 - 6 * q^67 + 2 * q^68 + 3 * q^69 + 12 * q^71 - 14 * q^72 - 12 * q^74 + 16 * q^75 + 16 * q^76 + 34 * q^77 + 5 * q^78 + 29 * q^79 + 5 * q^80 + 5 * q^81 + 6 * q^82 + 24 * q^83 + 8 * q^84 + 12 * q^85 + 3 * q^86 - 3 * q^87 + 3 * q^88 - 2 * q^89 - 20 * q^90 + 58 * q^91 - 9 * q^92 + 7 * q^93 + 19 * q^94 + 6 * q^95 + 3 * q^96 + 12 * q^97 - 37 * q^98 - 20 * q^99

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