LMFDB - Embedded newform 1334.2.a.j.1.1

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			1.1
Root			$3.18584$ 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)

$f(q)$	$=$	$q-1.00000 q^{2} -3.18584 q^{3} +1.00000 q^{4} -0.979916 q^{5} +3.18584 q^{6} +4.69416 q^{7} -1.00000 q^{8} +7.14956 q^{9} +O(q^{10})$	\(q-1.00000 q^{2} -3.18584 q^{3} +1.00000 q^{4} -0.979916 q^{5} +3.18584 q^{6} +4.69416 q^{7} -1.00000 q^{8} +7.14956 q^{9} +0.979916 q^{10} +3.33189 q^{11} -3.18584 q^{12} +5.77346 q^{13} -4.69416 q^{14} +3.12185 q^{15} +1.00000 q^{16} -2.62394 q^{17} -7.14956 q^{18} +7.07027 q^{19} -0.979916 q^{20} -14.9548 q^{21} -3.33189 q^{22} -1.00000 q^{23} +3.18584 q^{24} -4.03977 q^{25} -5.77346 q^{26} -13.2198 q^{27} +4.69416 q^{28} +1.00000 q^{29} -3.12185 q^{30} +5.33189 q^{31} -1.00000 q^{32} -10.6149 q^{33} +2.62394 q^{34} -4.59988 q^{35} +7.14956 q^{36} +3.47782 q^{37} -7.07027 q^{38} -18.3933 q^{39} +0.979916 q^{40} +1.47782 q^{41} +14.9548 q^{42} -9.70356 q^{43} +3.33189 q^{44} -7.00597 q^{45} +1.00000 q^{46} -7.25194 q^{47} -3.18584 q^{48} +15.0352 q^{49} +4.03977 q^{50} +8.35946 q^{51} +5.77346 q^{52} +13.2790 q^{53} +13.2198 q^{54} -3.26497 q^{55} -4.69416 q^{56} -22.5247 q^{57} -1.00000 q^{58} +1.40677 q^{59} +3.12185 q^{60} -0.994753 q^{61} -5.33189 q^{62} +33.5612 q^{63} +1.00000 q^{64} -5.65750 q^{65} +10.6149 q^{66} -0.381131 q^{67} -2.62394 q^{68} +3.18584 q^{69} +4.59988 q^{70} -12.9605 q^{71} -7.14956 q^{72} +11.0433 q^{73} -3.47782 q^{74} +12.8700 q^{75} +7.07027 q^{76} +15.6404 q^{77} +18.3933 q^{78} -10.4635 q^{79} -0.979916 q^{80} +20.6675 q^{81} -1.47782 q^{82} +5.47080 q^{83} -14.9548 q^{84} +2.57124 q^{85} +9.70356 q^{86} -3.18584 q^{87} -3.33189 q^{88} -5.89619 q^{89} +7.00597 q^{90} +27.1016 q^{91} -1.00000 q^{92} -16.9865 q^{93} +7.25194 q^{94} -6.92827 q^{95} +3.18584 q^{96} -3.33092 q^{97} -15.0352 q^{98} +23.8215 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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
$3$	−3.18584	−1.83934	−0.919672	−	0.392687i	$-0.871546\pi$
$3$	−3.18584	−1.83934	−0.919672	+	0.392687i	$0.871546\pi$
$4$	1.00000	0.500000
$5$	−0.979916	−0.438232	−0.219116	−	0.975699i	$-0.570317\pi$
$5$	−0.979916	−0.438232	−0.219116	+	0.975699i	$0.570317\pi$
$6$	3.18584	1.30061
$7$	4.69416	1.77423	0.887114	−	0.461551i	$-0.152707\pi$
$7$	4.69416	1.77423	0.887114	+	0.461551i	$0.152707\pi$
$8$	−1.00000	−0.353553
$9$	7.14956	2.38319
$10$	0.979916	0.309877
$11$	3.33189	1.00460	0.502301	−	0.864693i	$-0.332487\pi$
$11$	3.33189	1.00460	0.502301	+	0.864693i	$0.332487\pi$
$12$	−3.18584	−0.919672
$13$	5.77346	1.60127	0.800634	−	0.599153i	$-0.204496\pi$
$13$	5.77346	1.60127	0.800634	+	0.599153i	$0.204496\pi$
$14$	−4.69416	−1.25457
$15$	3.12185	0.806059
$16$	1.00000	0.250000
$17$	−2.62394	−0.636400	−0.318200	−	0.948024i	$-0.603078\pi$
$17$	−2.62394	−0.636400	−0.318200	+	0.948024i	$0.603078\pi$
$18$	−7.14956	−1.68517
$19$	7.07027	1.62203	0.811015	−	0.585025i	$-0.198915\pi$
$19$	7.07027	1.62203	0.811015	+	0.585025i	$0.198915\pi$
$20$	−0.979916	−0.219116
$21$	−14.9548	−3.26341
$22$	−3.33189	−0.710361
$23$	−1.00000	−0.208514
$23$	−1.00000	−0.208514
$24$	3.18584	0.650306
$25$	−4.03977	−0.807953
$26$	−5.77346	−1.13227
$27$	−13.2198	−2.54416
$28$	4.69416	0.887114
$29$	1.00000	0.185695
$29$	1.00000	0.185695
$30$	−3.12185	−0.569970
$31$	5.33189	0.957635	0.478818	−	0.877914i	$-0.341066\pi$
$31$	5.33189	0.957635	0.478818	+	0.877914i	$0.341066\pi$
$32$	−1.00000	−0.176777
$33$	−10.6149	−1.84781
$34$	2.62394	0.450003
$35$	−4.59988	−0.777522
$36$	7.14956	1.19159
$37$	3.47782	0.571751	0.285875	−	0.958267i	$-0.407716\pi$
$37$	3.47782	0.571751	0.285875	+	0.958267i	$0.407716\pi$
$38$	−7.07027	−1.14695
$39$	−18.3933	−2.94528
$40$	0.979916	0.154938
$41$	1.47782	0.230797	0.115399	−	0.993319i	$-0.463185\pi$
$41$	1.47782	0.230797	0.115399	+	0.993319i	$0.463185\pi$
$42$	14.9548	2.30758
$43$	−9.70356	−1.47978	−0.739890	−	0.672728i	$-0.765122\pi$
$43$	−9.70356	−1.47978	−0.739890	+	0.672728i	$0.765122\pi$
$44$	3.33189	0.502301
$45$	−7.00597	−1.04439
$46$	1.00000	0.147442
$47$	−7.25194	−1.05780	−0.528902	−	0.848683i	$-0.677396\pi$
$47$	−7.25194	−1.05780	−0.528902	+	0.848683i	$0.677396\pi$
$48$	−3.18584	−0.459836
$49$	15.0352	2.14788
$50$	4.03977	0.571309
$51$	8.35946	1.17056
$52$	5.77346	0.800634
$53$	13.2790	1.82402	0.912008	−	0.410172i	$-0.134531\pi$
$53$	13.2790	1.82402	0.912008	+	0.410172i	$0.134531\pi$
$54$	13.2198	1.79899
$55$	−3.26497	−0.440248
$56$	−4.69416	−0.627284
$57$	−22.5247	−2.98347
$58$	−1.00000	−0.131306
$59$	1.40677	0.183146	0.0915729	−	0.995798i	$-0.470811\pi$
$59$	1.40677	0.183146	0.0915729	+	0.995798i	$0.470811\pi$
$60$	3.12185	0.403029
$61$	−0.994753	−0.127365	−0.0636825	−	0.997970i	$-0.520285\pi$
$61$	−0.994753	−0.127365	−0.0636825	+	0.997970i	$0.520285\pi$
$62$	−5.33189	−0.677150
$63$	33.5612	4.22832
$64$	1.00000	0.125000
$65$	−5.65750	−0.701727
$66$	10.6149	1.30660
$67$	−0.381131	−0.0465625	−0.0232813	−	0.999729i	$-0.507411\pi$
$67$	−0.381131	−0.0465625	−0.0232813	+	0.999729i	$0.507411\pi$
$68$	−2.62394	−0.318200
$69$	3.18584	0.383530
$70$	4.59988	0.549791
$71$	−12.9605	−1.53812	−0.769062	−	0.639175i	$-0.779276\pi$
$71$	−12.9605	−1.53812	−0.769062	+	0.639175i	$0.779276\pi$
$72$	−7.14956	−0.842584
$73$	11.0433	1.29252	0.646259	−	0.763118i	$-0.276333\pi$
$73$	11.0433	1.29252	0.646259	+	0.763118i	$0.276333\pi$
$74$	−3.47782	−0.404289
$75$	12.8700	1.48610
$76$	7.07027	0.811015
$77$	15.6404	1.78239
$78$	18.3933	2.08263
$79$	−10.4635	−1.17723	−0.588617	−	0.808412i	$-0.700327\pi$
$79$	−10.4635	−1.17723	−0.588617	+	0.808412i	$0.700327\pi$
$80$	−0.979916	−0.109558
$81$	20.6675	2.29639
$82$	−1.47782	−0.163198
$83$	5.47080	0.600499	0.300249	−	0.953861i	$-0.402930\pi$
$83$	5.47080	0.600499	0.300249	+	0.953861i	$0.402930\pi$
$84$	−14.9548	−1.63171
$85$	2.57124	0.278891
$86$	9.70356	1.04636
$87$	−3.18584	−0.341558
$88$	−3.33189	−0.355180
$89$	−5.89619	−0.624995	−0.312498	−	0.949919i	$-0.601166\pi$
$89$	−5.89619	−0.624995	−0.312498	+	0.949919i	$0.601166\pi$
$90$	7.00597	0.738494
$91$	27.1016	2.84101
$92$	−1.00000	−0.104257
$93$	−16.9865	−1.76142
$94$	7.25194	0.747981
$95$	−6.92827	−0.710825
$96$	3.18584	0.325153
$97$	−3.33092	−0.338203	−0.169102	−	0.985599i	$-0.554087\pi$
$97$	−3.33092	−0.338203	−0.169102	+	0.985599i	$0.554087\pi$
$98$	−15.0352	−1.51878
$99$	23.8215	2.39415
$100$	−4.03977	−0.403977
$101$	11.2435	1.11877	0.559383	−	0.828909i	$-0.311038\pi$
$101$	11.2435	1.11877	0.559383	+	0.828909i	$0.311038\pi$
$102$	−8.35946	−0.827710
$103$	−19.2239	−1.89418	−0.947092	−	0.320963i	$-0.895993\pi$
$103$	−19.2239	−1.89418	−0.947092	+	0.320963i	$0.895993\pi$
$104$	−5.77346	−0.566134
$105$	14.6545	1.43013
$106$	−13.2790	−1.28977
$107$	8.26427	0.798938	0.399469	−	0.916747i	$-0.369195\pi$
$107$	8.26427	0.798938	0.399469	+	0.916747i	$0.369195\pi$
$108$	−13.2198	−1.27208
$109$	13.4361	1.28695	0.643473	−	0.765469i	$-0.277493\pi$
$109$	13.4361	1.28695	0.643473	+	0.765469i	$0.277493\pi$
$110$	3.26497	0.311303
$111$	−11.0798	−1.05165
$112$	4.69416	0.443557
$113$	10.3906	0.977470	0.488735	−	0.872432i	$-0.337459\pi$
$113$	10.3906	0.977470	0.488735	+	0.872432i	$0.337459\pi$
$114$	22.5247	2.10963
$115$	0.979916	0.0913776
$116$	1.00000	0.0928477
$117$	41.2777	3.81612
$118$	−1.40677	−0.129504
$119$	−12.3172	−1.12912
$120$	−3.12185	−0.284985
$121$	0.101476	0.00922509
$122$	0.994753	0.0900607
$123$	−4.70811	−0.424516
$124$	5.33189	0.478818
$125$	8.85821	0.792302
$126$	−33.5612	−2.98987
$127$	−18.7546	−1.66420	−0.832102	−	0.554622i	$-0.812863\pi$
$127$	−18.7546	−1.66420	−0.832102	+	0.554622i	$0.812863\pi$
$128$	−1.00000	−0.0883883
$129$	30.9140	2.72182
$130$	5.65750	0.496196
$131$	−6.37544	−0.557025	−0.278512	−	0.960433i	$-0.589841\pi$
$131$	−6.37544	−0.557025	−0.278512	+	0.960433i	$0.589841\pi$
$132$	−10.6149	−0.923904
$133$	33.1890	2.87785
$134$	0.381131	0.0329247
$135$	12.9543	1.11493
$136$	2.62394	0.225001
$137$	−15.0265	−1.28380	−0.641902	−	0.766787i	$-0.721854\pi$
$137$	−15.0265	−1.28380	−0.641902	+	0.766787i	$0.721854\pi$
$138$	−3.18584	−0.271197
$139$	−0.141102	−0.0119681	−0.00598405	−	0.999982i	$-0.501905\pi$
$139$	−0.141102	−0.0119681	−0.00598405	+	0.999982i	$0.501905\pi$
$140$	−4.59988	−0.388761
$141$	23.1035	1.94567
$142$	12.9605	1.08762
$143$	19.2365	1.60864
$144$	7.14956	0.595797
$145$	−0.979916	−0.0813776
$146$	−11.0433	−0.913948
$147$	−47.8996	−3.95069
$148$	3.47782	0.285875
$149$	11.7160	0.959814	0.479907	−	0.877319i	$-0.340670\pi$
$149$	11.7160	0.959814	0.479907	+	0.877319i	$0.340670\pi$
$150$	−12.8700	−1.05083
$151$	17.5889	1.43136	0.715682	−	0.698426i	$-0.246116\pi$
$151$	17.5889	1.43136	0.715682	+	0.698426i	$0.246116\pi$
$152$	−7.07027	−0.573474
$153$	−18.7601	−1.51666
$154$	−15.6404	−1.26034
$155$	−5.22480	−0.419666
$156$	−18.3933	−1.47264
$157$	−9.07550	−0.724304	−0.362152	−	0.932119i	$-0.617958\pi$
$157$	−9.07550	−0.724304	−0.362152	+	0.932119i	$0.617958\pi$
$158$	10.4635	0.832430
$159$	−42.3049	−3.35499
$160$	0.979916	0.0774691
$161$	−4.69416	−0.369952
$162$	−20.6675	−1.62380
$163$	−11.5361	−0.903576	−0.451788	−	0.892125i	$-0.649214\pi$
$163$	−11.5361	−0.903576	−0.451788	+	0.892125i	$0.649214\pi$
$164$	1.47782	0.115399
$165$	10.4017	0.809768
$166$	−5.47080	−0.424617
$167$	25.5706	1.97871	0.989357	−	0.145510i	$-0.0464824\pi$
$167$	25.5706	1.97871	0.989357	+	0.145510i	$0.0464824\pi$
$168$	14.9548	1.15379
$169$	20.3328	1.56406
$170$	−2.57124	−0.197205
$171$	50.5493	3.86560
$172$	−9.70356	−0.739890
$173$	−9.01333	−0.685271	−0.342636	−	0.939468i	$-0.611320\pi$
$173$	−9.01333	−0.685271	−0.342636	+	0.939468i	$0.611320\pi$
$174$	3.18584	0.241518
$175$	−18.9633	−1.43349
$176$	3.33189	0.251150
$177$	−4.48174	−0.336868
$178$	5.89619	0.441938
$179$	−7.64646	−0.571523	−0.285762	−	0.958301i	$-0.592247\pi$
$179$	−7.64646	−0.571523	−0.285762	+	0.958301i	$0.592247\pi$
$180$	−7.00597	−0.522194
$181$	−4.09681	−0.304514	−0.152257	−	0.988341i	$-0.548654\pi$
$181$	−4.09681	−0.304514	−0.152257	+	0.988341i	$0.548654\pi$
$182$	−27.1016	−2.00890
$183$	3.16912	0.234268
$184$	1.00000	0.0737210
$185$	−3.40797	−0.250559
$186$	16.9865	1.24551
$187$	−8.74269	−0.639329
$188$	−7.25194	−0.528902
$189$	−62.0560	−4.51391
$190$	6.92827	0.502629
$191$	0.283875	0.0205405	0.0102702	−	0.999947i	$-0.496731\pi$
$191$	0.283875	0.0205405	0.0102702	+	0.999947i	$0.496731\pi$
$192$	−3.18584	−0.229918
$193$	−16.6214	−1.19643	−0.598216	−	0.801335i	$-0.704124\pi$
$193$	−16.6214	−1.19643	−0.598216	+	0.801335i	$0.704124\pi$
$194$	3.33092	0.239146
$195$	18.0239	1.29072
$196$	15.0352	1.07394
$197$	−15.0646	−1.07331	−0.536655	−	0.843802i	$-0.680312\pi$
$197$	−15.0646	−1.07331	−0.536655	+	0.843802i	$0.680312\pi$
$198$	−23.8215	−1.69292
$199$	6.48967	0.460041	0.230020	−	0.973186i	$-0.426121\pi$
$199$	6.48967	0.460041	0.230020	+	0.973186i	$0.426121\pi$
$200$	4.03977	0.285655
$201$	1.21422	0.0856445
$202$	−11.2435	−0.791087
$203$	4.69416	0.329466
$204$	8.35946	0.585279
$205$	−1.44814	−0.101143
$206$	19.2239	1.33939
$207$	−7.14956	−0.496929
$208$	5.77346	0.400317
$209$	23.5573	1.62950
$210$	−14.6545	−1.01126
$211$	15.6305	1.07605	0.538025	−	0.842929i	$-0.319170\pi$
$211$	15.6305	1.07605	0.538025	+	0.842929i	$0.319170\pi$
$212$	13.2790	0.912008
$213$	41.2899	2.82914
$214$	−8.26427	−0.564934
$215$	9.50867	0.648486
$216$	13.2198	0.899495
$217$	25.0288	1.69906
$218$	−13.4361	−0.910009
$219$	−35.1821	−2.37739
$220$	−3.26497	−0.220124
$221$	−15.1492	−1.01905
$222$	11.0798	0.743626
$223$	−7.42659	−0.497322	−0.248661	−	0.968591i	$-0.579990\pi$
$223$	−7.42659	−0.497322	−0.248661	+	0.968591i	$0.579990\pi$
$224$	−4.69416	−0.313642
$225$	−28.8826	−1.92550
$226$	−10.3906	−0.691175
$227$	6.06296	0.402413	0.201206	−	0.979549i	$-0.435514\pi$
$227$	6.06296	0.402413	0.201206	+	0.979549i	$0.435514\pi$
$228$	−22.5247	−1.49174
$229$	−5.89206	−0.389358	−0.194679	−	0.980867i	$-0.562367\pi$
$229$	−5.89206	−0.389358	−0.194679	+	0.980867i	$0.562367\pi$
$230$	−0.979916	−0.0646137
$231$	−49.8279	−3.27843
$232$	−1.00000	−0.0656532
$233$	−12.8371	−0.840988	−0.420494	−	0.907295i	$-0.638143\pi$
$233$	−12.8371	−0.840988	−0.420494	+	0.907295i	$0.638143\pi$
$234$	−41.2777	−2.69841
$235$	7.10629	0.463563
$236$	1.40677	0.0915729
$237$	33.3350	2.16534
$238$	12.3172	0.798407
$239$	−18.7164	−1.21067	−0.605333	−	0.795972i	$-0.706960\pi$
$239$	−18.7164	−1.21067	−0.605333	+	0.795972i	$0.706960\pi$
$240$	3.12185	0.201515
$241$	12.7298	0.819998	0.409999	−	0.912086i	$-0.365529\pi$
$241$	12.7298	0.819998	0.409999	+	0.912086i	$0.365529\pi$
$242$	−0.101476	−0.00652312
$243$	−26.1840	−1.67970
$244$	−0.994753	−0.0636825
$245$	−14.7332	−0.941270
$246$	4.70811	0.300178
$247$	40.8199	2.59731
$248$	−5.33189	−0.338575
$249$	−17.4291	−1.10452
$250$	−8.85821	−0.560242
$251$	−4.52790	−0.285799	−0.142899	−	0.989737i	$-0.545643\pi$
$251$	−4.52790	−0.285799	−0.142899	+	0.989737i	$0.545643\pi$
$252$	33.5612	2.11416
$253$	−3.33189	−0.209474
$254$	18.7546	1.17677
$255$	−8.19157	−0.512976
$256$	1.00000	0.0625000
$257$	23.9500	1.49396	0.746980	−	0.664846i	$-0.231503\pi$
$257$	23.9500	1.49396	0.746980	+	0.664846i	$0.231503\pi$
$258$	−30.9140	−1.92462
$259$	16.3255	1.01442
$260$	−5.65750	−0.350863
$261$	7.14956	0.442547
$262$	6.37544	0.393876
$263$	4.85242	0.299213	0.149606	−	0.988746i	$-0.452199\pi$
$263$	4.85242	0.299213	0.149606	+	0.988746i	$0.452199\pi$
$264$	10.6149	0.653299
$265$	−13.0123	−0.799342
$266$	−33.1890	−2.03495
$267$	18.7843	1.14958
$268$	−0.381131	−0.0232813
$269$	2.54563	0.155210	0.0776048	−	0.996984i	$-0.475273\pi$
$269$	2.54563	0.155210	0.0776048	+	0.996984i	$0.475273\pi$
$270$	−12.9543	−0.788375
$271$	25.5912	1.55455	0.777277	−	0.629158i	$-0.216600\pi$
$271$	25.5912	1.55455	0.777277	+	0.629158i	$0.216600\pi$
$272$	−2.62394	−0.159100
$273$	−86.3412	−5.22560
$274$	15.0265	0.907786
$275$	−13.4600	−0.811671
$276$	3.18584	0.191765
$277$	−4.61390	−0.277222	−0.138611	−	0.990347i	$-0.544264\pi$
$277$	−4.61390	−0.277222	−0.138611	+	0.990347i	$0.544264\pi$
$278$	0.141102	0.00846272
$279$	38.1207	2.28222
$280$	4.59988	0.274896
$281$	17.1955	1.02580	0.512898	−	0.858450i	$-0.328572\pi$
$281$	17.1955	1.02580	0.512898	+	0.858450i	$0.328572\pi$
$282$	−23.1035	−1.37579
$283$	−20.9622	−1.24608	−0.623038	−	0.782192i	$-0.714102\pi$
$283$	−20.9622	−1.24608	−0.623038	+	0.782192i	$0.714102\pi$
$284$	−12.9605	−0.769062
$285$	22.0723	1.30745
$286$	−19.2365	−1.13748
$287$	6.93715	0.409487
$288$	−7.14956	−0.421292
$289$	−10.1149	−0.594995
$290$	0.979916	0.0575426
$291$	10.6118	0.622072
$292$	11.0433	0.646259
$293$	5.53341	0.323265	0.161633	−	0.986851i	$-0.448324\pi$
$293$	5.53341	0.323265	0.161633	+	0.986851i	$0.448324\pi$
$294$	47.8996	2.79356
$295$	−1.37852	−0.0802603
$296$	−3.47782	−0.202144
$297$	−44.0470	−2.55587
$298$	−11.7160	−0.678691
$299$	−5.77346	−0.333888
$300$	12.8700	0.743052
$301$	−45.5501	−2.62546
$302$	−17.5889	−1.01213
$303$	−35.8198	−2.05780
$304$	7.07027	0.405508
$305$	0.974774	0.0558154
$306$	18.7601	1.07244
$307$	−7.14811	−0.407964	−0.203982	−	0.978975i	$-0.565388\pi$
$307$	−7.14811	−0.407964	−0.203982	+	0.978975i	$0.565388\pi$
$308$	15.6404	0.891196
$309$	61.2441	3.48406
$310$	5.22480	0.296749
$311$	24.2888	1.37729	0.688646	−	0.725098i	$-0.258206\pi$
$311$	24.2888	1.37729	0.688646	+	0.725098i	$0.258206\pi$
$312$	18.3933	1.04132
$313$	−14.2356	−0.804641	−0.402320	−	0.915499i	$-0.631796\pi$
$313$	−14.2356	−0.804641	−0.402320	+	0.915499i	$0.631796\pi$
$314$	9.07550	0.512160
$315$	−32.8872	−1.85298
$316$	−10.4635	−0.588617
$317$	−18.7373	−1.05239	−0.526197	−	0.850363i	$-0.676383\pi$
$317$	−18.7373	−1.05239	−0.526197	+	0.850363i	$0.676383\pi$
$318$	42.3049	2.37234
$319$	3.33189	0.186550
$320$	−0.979916	−0.0547789
$321$	−26.3286	−1.46952
$322$	4.69416	0.261596
$323$	−18.5520	−1.03226
$324$	20.6675	1.14820
$325$	−23.3234	−1.29375
$326$	11.5361	0.638925
$327$	−42.8053	−2.36714
$328$	−1.47782	−0.0815992
$329$	−34.0418	−1.87679
$330$	−10.4017	−0.572593
$331$	22.7079	1.24814	0.624070	−	0.781368i	$-0.285478\pi$
$331$	22.7079	1.24814	0.624070	+	0.781368i	$0.285478\pi$
$332$	5.47080	0.300249
$333$	24.8649	1.36259
$334$	−25.5706	−1.39916
$335$	0.373476	0.0204052
$336$	−14.9548	−0.815854
$337$	8.63338	0.470290	0.235145	−	0.971960i	$-0.424443\pi$
$337$	8.63338	0.470290	0.235145	+	0.971960i	$0.424443\pi$
$338$	−20.3328	−1.10596
$339$	−33.1029	−1.79790
$340$	2.57124	0.139445
$341$	17.7653	0.962042
$342$	−50.5493	−2.73339
$343$	37.7184	2.03660
$344$	9.70356	0.523181
$345$	−3.12185	−0.168075
$346$	9.01333	0.484560
$347$	4.26119	0.228753	0.114376	−	0.993437i	$-0.463513\pi$
$347$	4.26119	0.228753	0.114376	+	0.993437i	$0.463513\pi$
$348$	−3.18584	−0.170779
$349$	−10.4398	−0.558828	−0.279414	−	0.960171i	$-0.590140\pi$
$349$	−10.4398	−0.558828	−0.279414	+	0.960171i	$0.590140\pi$
$350$	18.9633	1.01363
$351$	−76.3241	−4.07388
$352$	−3.33189	−0.177590
$353$	19.5476	1.04041	0.520206	−	0.854041i	$-0.325855\pi$
$353$	19.5476	1.04041	0.520206	+	0.854041i	$0.325855\pi$
$354$	4.48174	0.238202
$355$	12.7002	0.674054
$356$	−5.89619	−0.312498
$357$	39.2407	2.07684
$358$	7.64646	0.404128
$359$	−34.2876	−1.80963	−0.904816	−	0.425803i	$-0.859992\pi$
$359$	−34.2876	−1.80963	−0.904816	+	0.425803i	$0.859992\pi$
$360$	7.00597	0.369247
$361$	30.9887	1.63098
$362$	4.09681	0.215324
$363$	−0.323286	−0.0169681
$364$	27.1016	1.42051
$365$	−10.8215	−0.566422
$366$	−3.16912	−0.165653
$367$	11.5181	0.601242	0.300621	−	0.953744i	$-0.402806\pi$
$367$	11.5181	0.601242	0.300621	+	0.953744i	$0.402806\pi$
$368$	−1.00000	−0.0521286
$369$	10.5658	0.550033
$370$	3.40797	0.177172
$371$	62.3340	3.23622
$372$	−16.9865	−0.880710
$373$	−19.0788	−0.987863	−0.493932	−	0.869501i	$-0.664441\pi$
$373$	−19.0788	−0.987863	−0.493932	+	0.869501i	$0.664441\pi$
$374$	8.74269	0.452074
$375$	−28.2208	−1.45732
$376$	7.25194	0.373990
$377$	5.77346	0.297348
$378$	62.0560	3.19182
$379$	−12.1486	−0.624034	−0.312017	−	0.950077i	$-0.601005\pi$
$379$	−12.1486	−0.624034	−0.312017	+	0.950077i	$0.601005\pi$
$380$	−6.92827	−0.355413
$381$	59.7492	3.06105
$382$	−0.283875	−0.0145243
$383$	3.69469	0.188790	0.0943950	−	0.995535i	$-0.469908\pi$
$383$	3.69469	0.188790	0.0943950	+	0.995535i	$0.469908\pi$
$384$	3.18584	0.162577
$385$	−15.3263	−0.781101
$386$	16.6214	0.846005
$387$	−69.3762	−3.52659
$388$	−3.33092	−0.169102
$389$	−3.25392	−0.164981	−0.0824903	−	0.996592i	$-0.526287\pi$
$389$	−3.25392	−0.164981	−0.0824903	+	0.996592i	$0.526287\pi$
$390$	−18.0239	−0.912675
$391$	2.62394	0.132699
$392$	−15.0352	−0.759391
$393$	20.3111	1.02456
$394$	15.0646	0.758945
$395$	10.2533	0.515901
$396$	23.8215	1.19708
$397$	−3.94724	−0.198106	−0.0990531	−	0.995082i	$-0.531581\pi$
$397$	−3.94724	−0.198106	−0.0990531	+	0.995082i	$0.531581\pi$
$398$	−6.48967	−0.325298
$399$	−105.735	−5.29336
$400$	−4.03977	−0.201988
$401$	−9.01622	−0.450249	−0.225124	−	0.974330i	$-0.572279\pi$
$401$	−9.01622	−0.450249	−0.225124	+	0.974330i	$0.572279\pi$
$402$	−1.21422	−0.0605598
$403$	30.7834	1.53343
$404$	11.2435	0.559383
$405$	−20.2525	−1.00635
$406$	−4.69416	−0.232967
$407$	11.5877	0.574382
$408$	−8.35946	−0.413855
$409$	16.6053	0.821081	0.410540	−	0.911842i	$-0.365340\pi$
$409$	16.6053	0.821081	0.410540	+	0.911842i	$0.365340\pi$
$410$	1.44814	0.0715187
$411$	47.8721	2.36136
$412$	−19.2239	−0.947092
$413$	6.60361	0.324942
$414$	7.14956	0.351382
$415$	−5.36092	−0.263157
$416$	−5.77346	−0.283067
$417$	0.449527	0.0220135
$418$	−23.5573	−1.15223
$419$	6.53196	0.319107	0.159553	−	0.987189i	$-0.448995\pi$
$419$	6.53196	0.319107	0.159553	+	0.987189i	$0.448995\pi$
$420$	14.6545	0.715066
$421$	37.6144	1.83321	0.916607	−	0.399790i	$-0.130917\pi$
$421$	37.6144	1.83321	0.916607	+	0.399790i	$0.130917\pi$
$422$	−15.6305	−0.760883
$423$	−51.8482	−2.52095
$424$	−13.2790	−0.644887
$425$	10.6001	0.514181
$426$	−41.2899	−2.00050
$427$	−4.66953	−0.225975
$428$	8.26427	0.399469
$429$	−61.2844	−2.95884
$430$	−9.50867	−0.458549
$431$	−28.9630	−1.39510	−0.697549	−	0.716537i	$-0.745726\pi$
$431$	−28.9630	−1.39510	−0.697549	+	0.716537i	$0.745726\pi$
$432$	−13.2198	−0.636039
$433$	35.4925	1.70566	0.852831	−	0.522186i	$-0.174883\pi$
$433$	35.4925	1.70566	0.852831	+	0.522186i	$0.174883\pi$
$434$	−25.0288	−1.20142
$435$	3.12185	0.149681
$436$	13.4361	0.643473
$437$	−7.07027	−0.338217
$438$	35.1821	1.68107
$439$	11.9694	0.571268	0.285634	−	0.958339i	$-0.407796\pi$
$439$	11.9694	0.571268	0.285634	+	0.958339i	$0.407796\pi$
$440$	3.26497	0.155651
$441$	107.495	5.11880
$442$	15.1492	0.720575
$443$	36.6786	1.74265	0.871326	−	0.490705i	$-0.163261\pi$
$443$	36.6786	1.74265	0.871326	+	0.490705i	$0.163261\pi$
$444$	−11.0798	−0.525823
$445$	5.77777	0.273893
$446$	7.42659	0.351659
$447$	−37.3253	−1.76543
$448$	4.69416	0.221778
$449$	10.2367	0.483100	0.241550	−	0.970388i	$-0.422344\pi$
$449$	10.2367	0.483100	0.241550	+	0.970388i	$0.422344\pi$
$450$	28.8826	1.36154
$451$	4.92394	0.231859
$452$	10.3906	0.488735
$453$	−56.0354	−2.63277
$454$	−6.06296	−0.284549
$455$	−26.5572	−1.24502
$456$	22.5247	1.05482
$457$	10.5771	0.494774	0.247387	−	0.968917i	$-0.420428\pi$
$457$	10.5771	0.494774	0.247387	+	0.968917i	$0.420428\pi$
$458$	5.89206	0.275318
$459$	34.6881	1.61910
$460$	0.979916	0.0456888
$461$	17.0250	0.792935	0.396467	−	0.918049i	$-0.370236\pi$
$461$	17.0250	0.792935	0.396467	+	0.918049i	$0.370236\pi$
$462$	49.8279	2.31820
$463$	−20.5603	−0.955517	−0.477758	−	0.878491i	$-0.658551\pi$
$463$	−20.5603	−0.955517	−0.477758	+	0.878491i	$0.658551\pi$
$464$	1.00000	0.0464238
$465$	16.6454	0.771910
$466$	12.8371	0.594668
$467$	−1.74109	−0.0805681	−0.0402841	−	0.999188i	$-0.512826\pi$
$467$	−1.74109	−0.0805681	−0.0402841	+	0.999188i	$0.512826\pi$
$468$	41.2777	1.90806
$469$	−1.78909	−0.0826125
$470$	−7.10629	−0.327789
$471$	28.9131	1.33224
$472$	−1.40677	−0.0647518
$473$	−32.3312	−1.48659
$474$	−33.3350	−1.53113
$475$	−28.5622	−1.31052
$476$	−12.3172	−0.564559
$477$	94.9393	4.34697
$478$	18.7164	0.856070
$479$	−29.9983	−1.37066	−0.685328	−	0.728235i	$-0.740341\pi$
$479$	−29.9983	−1.37066	−0.685328	+	0.728235i	$0.740341\pi$
$480$	−3.12185	−0.142492
$481$	20.0791	0.915527
$482$	−12.7298	−0.579826
$483$	14.9548	0.680469
$484$	0.101476	0.00461254
$485$	3.26402	0.148211
$486$	26.1840	1.18773
$487$	−4.12152	−0.186764	−0.0933820	−	0.995630i	$-0.529768\pi$
$487$	−4.12152	−0.186764	−0.0933820	+	0.995630i	$0.529768\pi$
$488$	0.994753	0.0450303
$489$	36.7521	1.66199
$490$	14.7332	0.665578
$491$	2.19086	0.0988722	0.0494361	−	0.998777i	$-0.484258\pi$
$491$	2.19086	0.0988722	0.0494361	+	0.998777i	$0.484258\pi$
$492$	−4.70811	−0.212258
$493$	−2.62394	−0.118177
$494$	−40.8199	−1.83657
$495$	−23.3431	−1.04919
$496$	5.33189	0.239409
$497$	−60.8385	−2.72898
$498$	17.4291	0.781016
$499$	−23.2127	−1.03914	−0.519572	−	0.854427i	$-0.673908\pi$
$499$	−23.2127	−1.03914	−0.519572	+	0.854427i	$0.673908\pi$
$500$	8.85821	0.396151
$501$	−81.4638	−3.63954
$502$	4.52790	0.202090
$503$	−3.89714	−0.173765	−0.0868823	−	0.996219i	$-0.527690\pi$
$503$	−3.89714	−0.173765	−0.0868823	+	0.996219i	$0.527690\pi$
$504$	−33.5612	−1.49494
$505$	−11.0176	−0.490279
$506$	3.33189	0.148120
$507$	−64.7770	−2.87685
$508$	−18.7546	−0.832102
$509$	24.3774	1.08051	0.540254	−	0.841502i	$-0.318328\pi$
$509$	24.3774	1.08051	0.540254	+	0.841502i	$0.318328\pi$
$510$	8.19157	0.362729
$511$	51.8390	2.29322
$512$	−1.00000	−0.0441942
$513$	−93.4677	−4.12670
$514$	−23.9500	−1.05639
$515$	18.8378	0.830091
$516$	30.9140	1.36091
$517$	−24.1627	−1.06267
$518$	−16.3255	−0.717300
$519$	28.7150	1.26045
$520$	5.65750	0.248098
$521$	13.5036	0.591603	0.295801	−	0.955249i	$-0.404413\pi$
$521$	13.5036	0.591603	0.295801	+	0.955249i	$0.404413\pi$
$522$	−7.14956	−0.312928
$523$	−17.7590	−0.776547	−0.388273	−	0.921544i	$-0.626928\pi$
$523$	−17.7590	−0.776547	−0.388273	+	0.921544i	$0.626928\pi$
$524$	−6.37544	−0.278512
$525$	60.4141	2.63669
$526$	−4.85242	−0.211575
$527$	−13.9906	−0.609439
$528$	−10.6149	−0.461952
$529$	1.00000	0.0434783
$530$	13.0123	0.565220
$531$	10.0578	0.436471
$532$	33.1890	1.43893
$533$	8.53215	0.369568
$534$	−18.7843	−0.812877
$535$	−8.09829	−0.350120
$536$	0.381131	0.0164623
$537$	24.3604	1.05123
$538$	−2.54563	−0.109750
$539$	50.0955	2.15777
$540$	12.9543	0.557465
$541$	−10.8834	−0.467912	−0.233956	−	0.972247i	$-0.575167\pi$
$541$	−10.8834	−0.467912	−0.233956	+	0.972247i	$0.575167\pi$
$542$	−25.5912	−1.09924
$543$	13.0518	0.560106
$544$	2.62394	0.112501
$545$	−13.1663	−0.563981
$546$	86.3412	3.69506
$547$	18.8336	0.805269	0.402634	−	0.915361i	$-0.368095\pi$
$547$	18.8336	0.805269	0.402634	+	0.915361i	$0.368095\pi$
$548$	−15.0265	−0.641902
$549$	−7.11205	−0.303535
$550$	13.4600	0.573938
$551$	7.07027	0.301204
$552$	−3.18584	−0.135598
$553$	−49.1173	−2.08868
$554$	4.61390	0.196026
$555$	10.8573	0.460865
$556$	−0.141102	−0.00598405
$557$	−44.7812	−1.89744	−0.948721	−	0.316115i	$-0.897622\pi$
$557$	−44.7812	−1.89744	−0.948721	+	0.316115i	$0.897622\pi$
$558$	−38.1207	−1.61378
$559$	−56.0231	−2.36952
$560$	−4.59988	−0.194381
$561$	27.8528	1.17595
$562$	−17.1955	−0.725347
$563$	12.2449	0.516061	0.258030	−	0.966137i	$-0.416927\pi$
$563$	12.2449	0.516061	0.258030	+	0.966137i	$0.416927\pi$
$564$	23.1035	0.972833
$565$	−10.1820	−0.428358
$566$	20.9622	0.881108
$567$	97.0168	4.07432
$568$	12.9605	0.543809
$569$	25.5856	1.07260	0.536302	−	0.844026i	$-0.319821\pi$
$569$	25.5856	1.07260	0.536302	+	0.844026i	$0.319821\pi$
$570$	−22.0723	−0.924508
$571$	4.44652	0.186081	0.0930406	−	0.995662i	$-0.470341\pi$
$571$	4.44652	0.186081	0.0930406	+	0.995662i	$0.470341\pi$
$572$	19.2365	0.804319
$573$	−0.904379	−0.0377810
$574$	−6.93715	−0.289551
$575$	4.03977	0.168470
$576$	7.14956	0.297898
$577$	29.8592	1.24305	0.621527	−	0.783393i	$-0.286513\pi$
$577$	29.8592	1.24305	0.621527	+	0.783393i	$0.286513\pi$
$578$	10.1149	0.420725
$579$	52.9530	2.20065
$580$	−0.979916	−0.0406888
$581$	25.6808	1.06542
$582$	−10.6118	−0.439872
$583$	44.2443	1.83241
$584$	−11.0433	−0.456974
$585$	−40.4487	−1.67235
$586$	−5.53341	−0.228583
$587$	−16.2014	−0.668703	−0.334351	−	0.942449i	$-0.608517\pi$
$587$	−16.2014	−0.668703	−0.334351	+	0.942449i	$0.608517\pi$
$588$	−47.8996	−1.97535
$589$	37.6979	1.55331
$590$	1.37852	0.0567526
$591$	47.9935	1.97419
$592$	3.47782	0.142938
$593$	6.48659	0.266372	0.133186	−	0.991091i	$-0.457479\pi$
$593$	6.48659	0.266372	0.133186	+	0.991091i	$0.457479\pi$
$594$	44.0470	1.80727
$595$	12.0698	0.494815
$596$	11.7160	0.479907
$597$	−20.6750	−0.846173
$598$	5.77346	0.236094
$599$	2.33125	0.0952522	0.0476261	−	0.998865i	$-0.484834\pi$
$599$	2.33125	0.0952522	0.0476261	+	0.998865i	$0.484834\pi$
$600$	−12.8700	−0.525417
$601$	10.2826	0.419434	0.209717	−	0.977762i	$-0.432746\pi$
$601$	10.2826	0.419434	0.209717	+	0.977762i	$0.432746\pi$
$602$	45.5501	1.85648
$603$	−2.72492	−0.110967
$604$	17.5889	0.715682
$605$	−0.0994379	−0.00404273
$606$	35.8198	1.45508
$607$	0.896449	0.0363857	0.0181929	−	0.999834i	$-0.494209\pi$
$607$	0.896449	0.0363857	0.0181929	+	0.999834i	$0.494209\pi$
$608$	−7.07027	−0.286737
$609$	−14.9548	−0.606001
$610$	−0.974774	−0.0394674
$611$	−41.8688	−1.69383
$612$	−18.7601	−0.758330
$613$	−19.5628	−0.790136	−0.395068	−	0.918652i	$-0.629279\pi$
$613$	−19.5628	−0.790136	−0.395068	+	0.918652i	$0.629279\pi$
$614$	7.14811	0.288474
$615$	4.61355	0.186036
$616$	−15.6404	−0.630171
$617$	7.99319	0.321794	0.160897	−	0.986971i	$-0.448561\pi$
$617$	7.99319	0.321794	0.160897	+	0.986971i	$0.448561\pi$
$618$	−61.2441	−2.46360
$619$	−14.2149	−0.571344	−0.285672	−	0.958327i	$-0.592217\pi$
$619$	−14.2149	−0.571344	−0.285672	+	0.958327i	$0.592217\pi$
$620$	−5.22480	−0.209833
$621$	13.2198	0.530493
$622$	−24.2888	−0.973892
$623$	−27.6777	−1.10888
$624$	−18.3933	−0.736321
$625$	11.5185	0.460741
$626$	14.2356	0.568967
$627$	−75.0499	−2.99720
$628$	−9.07550	−0.362152
$629$	−9.12562	−0.363862
$630$	32.8872	1.31026
$631$	−23.9261	−0.952483	−0.476241	−	0.879315i	$-0.658001\pi$
$631$	−23.9261	−0.952483	−0.476241	+	0.879315i	$0.658001\pi$
$632$	10.4635	0.416215
$633$	−49.7964	−1.97923
$634$	18.7373	0.744155
$635$	18.3780	0.729307
$636$	−42.3049	−1.67750
$637$	86.8049	3.43934
$638$	−3.33189	−0.131911
$639$	−92.6616	−3.66564
$640$	0.979916	0.0387346
$641$	−11.9748	−0.472977	−0.236488	−	0.971634i	$-0.575997\pi$
$641$	−11.9748	−0.472977	−0.236488	+	0.971634i	$0.575997\pi$
$642$	26.3286	1.03911
$643$	12.6090	0.497248	0.248624	−	0.968600i	$-0.420022\pi$
$643$	12.6090	0.497248	0.248624	+	0.968600i	$0.420022\pi$
$644$	−4.69416	−0.184976
$645$	−30.2931	−1.19279
$646$	18.5520	0.729918
$647$	−12.8998	−0.507145	−0.253573	−	0.967316i	$-0.581606\pi$
$647$	−12.8998	−0.507145	−0.253573	+	0.967316i	$0.581606\pi$
$648$	−20.6675	−0.811898
$649$	4.68720	0.183989
$650$	23.3234	0.914820
$651$	−79.7375	−3.12516
$652$	−11.5361	−0.451788
$653$	15.5009	0.606595	0.303298	−	0.952896i	$-0.401912\pi$
$653$	15.5009	0.606595	0.303298	+	0.952896i	$0.401912\pi$
$654$	42.8053	1.67382
$655$	6.24739	0.244106
$656$	1.47782	0.0576993
$657$	78.9546	3.08031
$658$	34.0418	1.32709
$659$	−33.8087	−1.31700	−0.658501	−	0.752580i	$-0.728809\pi$
$659$	−33.8087	−1.31700	−0.658501	+	0.752580i	$0.728809\pi$
$660$	10.4017	0.404884
$661$	17.6468	0.686383	0.343191	−	0.939265i	$-0.388492\pi$
$661$	17.6468	0.686383	0.343191	+	0.939265i	$0.388492\pi$
$662$	−22.7079	−0.882569
$663$	48.2630	1.87438
$664$	−5.47080	−0.212308
$665$	−32.5224	−1.26117
$666$	−24.8649	−0.963496
$667$	−1.00000	−0.0387202
$668$	25.5706	0.989357
$669$	23.6599	0.914746
$670$	−0.373476	−0.0144286
$671$	−3.31440	−0.127951
$672$	14.9548	0.576896
$673$	−36.5045	−1.40714	−0.703572	−	0.710624i	$-0.748413\pi$
$673$	−36.5045	−1.40714	−0.703572	+	0.710624i	$0.748413\pi$
$674$	−8.63338	−0.332545
$675$	53.4050	2.05556
$676$	20.3328	0.782031
$677$	−6.60065	−0.253684	−0.126842	−	0.991923i	$-0.540484\pi$
$677$	−6.60065	−0.253684	−0.126842	+	0.991923i	$0.540484\pi$
$678$	33.1029	1.27131
$679$	−15.6359	−0.600050
$680$	−2.57124	−0.0986027
$681$	−19.3156	−0.740175
$682$	−17.7653	−0.680267
$683$	−25.3876	−0.971428	−0.485714	−	0.874118i	$-0.661440\pi$
$683$	−25.3876	−0.971428	−0.485714	+	0.874118i	$0.661440\pi$
$684$	50.5493	1.93280
$685$	14.7247	0.562603
$686$	−37.7184	−1.44010
$687$	18.7712	0.716164
$688$	−9.70356	−0.369945
$689$	76.6660	2.92074
$690$	3.12185	0.118847
$691$	−29.4923	−1.12194	−0.560969	−	0.827836i	$-0.689571\pi$
$691$	−29.4923	−1.12194	−0.560969	+	0.827836i	$0.689571\pi$
$692$	−9.01333	−0.342636
$693$	111.822	4.24777
$694$	−4.26119	−0.161753
$695$	0.138268	0.00524480
$696$	3.18584	0.120759
$697$	−3.87773	−0.146879
$698$	10.4398	0.395151
$699$	40.8970	1.54687
$700$	−18.9633	−0.716746
$701$	28.5131	1.07693	0.538463	−	0.842649i	$-0.319005\pi$
$701$	28.5131	1.07693	0.538463	+	0.842649i	$0.319005\pi$
$702$	76.3241	2.88067
$703$	24.5891	0.927397
$704$	3.33189	0.125575
$705$	−22.6395	−0.852653
$706$	−19.5476	−0.735682
$707$	52.7786	1.98495
$708$	−4.48174	−0.168434
$709$	−38.9629	−1.46328	−0.731642	−	0.681689i	$-0.761246\pi$
$709$	−38.9629	−1.46328	−0.731642	+	0.681689i	$0.761246\pi$
$710$	−12.7002	−0.476628
$711$	−74.8093	−2.80557
$712$	5.89619	0.220969
$713$	−5.33189	−0.199681
$714$	−39.2407	−1.46855
$715$	−18.8502	−0.704956
$716$	−7.64646	−0.285762
$717$	59.6275	2.22683
$718$	34.2876	1.27960
$719$	−10.5054	−0.391785	−0.195892	−	0.980625i	$-0.562760\pi$
$719$	−10.5054	−0.391785	−0.195892	+	0.980625i	$0.562760\pi$
$720$	−7.00597	−0.261097
$721$	−90.2400	−3.36071
$722$	−30.9887	−1.15328
$723$	−40.5551	−1.50826
$724$	−4.09681	−0.152257
$725$	−4.03977	−0.150033
$726$	0.323286	0.0119983
$727$	14.4246	0.534978	0.267489	−	0.963561i	$-0.413806\pi$
$727$	14.4246	0.534978	0.267489	+	0.963561i	$0.413806\pi$
$728$	−27.1016	−1.00445
$729$	21.4152	0.793156
$730$	10.8215	0.400521
$731$	25.4616	0.941732
$732$	3.16912	0.117134
$733$	2.24795	0.0830300	0.0415150	−	0.999138i	$-0.486782\pi$
$733$	2.24795	0.0830300	0.0415150	+	0.999138i	$0.486782\pi$
$734$	−11.5181	−0.425143
$735$	46.9376	1.73132
$736$	1.00000	0.0368605
$737$	−1.26988	−0.0467768
$738$	−10.5658	−0.388932
$739$	18.6586	0.686368	0.343184	−	0.939268i	$-0.388495\pi$
$739$	18.6586	0.686368	0.343184	+	0.939268i	$0.388495\pi$
$740$	−3.40797	−0.125280
$741$	−130.046	−4.77734
$742$	−62.3340	−2.28835
$743$	−11.8302	−0.434007	−0.217004	−	0.976171i	$-0.569628\pi$
$743$	−11.8302	−0.434007	−0.217004	+	0.976171i	$0.569628\pi$
$744$	16.9865	0.622756
$745$	−11.4807	−0.420621
$746$	19.0788	0.698525
$747$	39.1138	1.43110
$748$	−8.74269	−0.319664
$749$	38.7939	1.41750
$750$	28.2208	1.03048
$751$	5.44424	0.198663	0.0993315	−	0.995054i	$-0.468330\pi$
$751$	5.44424	0.198663	0.0993315	+	0.995054i	$0.468330\pi$
$752$	−7.25194	−0.264451
$753$	14.4252	0.525682
$754$	−5.77346	−0.210257
$755$	−17.2356	−0.627269
$756$	−62.0560	−2.25696
$757$	27.7931	1.01016	0.505079	−	0.863073i	$-0.331463\pi$
$757$	27.7931	1.01016	0.505079	+	0.863073i	$0.331463\pi$
$758$	12.1486	0.441259
$759$	10.6149	0.385295
$760$	6.92827	0.251315
$761$	6.90749	0.250396	0.125198	−	0.992132i	$-0.460043\pi$
$761$	6.90749	0.250396	0.125198	+	0.992132i	$0.460043\pi$
$762$	−59.7492	−2.16449
$763$	63.0713	2.28334
$764$	0.283875	0.0102702
$765$	18.3833	0.664648
$766$	−3.69469	−0.133495
$767$	8.12192	0.293266
$768$	−3.18584	−0.114959
$769$	−31.3733	−1.13135	−0.565675	−	0.824628i	$-0.691384\pi$
$769$	−31.3733	−1.13135	−0.565675	+	0.824628i	$0.691384\pi$
$770$	15.3263	0.552321
$771$	−76.3008	−2.74791
$772$	−16.6214	−0.598216
$773$	20.1484	0.724688	0.362344	−	0.932045i	$-0.381977\pi$
$773$	20.1484	0.724688	0.362344	+	0.932045i	$0.381977\pi$
$774$	69.3762	2.49368
$775$	−21.5396	−0.773724
$776$	3.33092	0.119573
$777$	−52.0103	−1.86586
$778$	3.25392	0.116659
$779$	10.4486	0.374360
$780$	18.0239	0.645358
$781$	−43.1828	−1.54520
$782$	−2.62394	−0.0938321
$783$	−13.2198	−0.472438
$784$	15.0352	0.536971
$785$	8.89322	0.317413
$786$	−20.3111	−0.724474
$787$	−14.3958	−0.513154	−0.256577	−	0.966524i	$-0.582595\pi$
$787$	−14.3958	−0.513154	−0.256577	+	0.966524i	$0.582595\pi$
$788$	−15.0646	−0.536655
$789$	−15.4590	−0.550356
$790$	−10.2533	−0.364797
$791$	48.7754	1.73425
$792$	−23.8215	−0.846461
$793$	−5.74316	−0.203946
$794$	3.94724	0.140082
$795$	41.4552	1.47026
$796$	6.48967	0.230020
$797$	−2.66222	−0.0943008	−0.0471504	−	0.998888i	$-0.515014\pi$
$797$	−2.66222	−0.0943008	−0.0471504	+	0.998888i	$0.515014\pi$
$798$	105.735	3.74297
$799$	19.0287	0.673187
$800$	4.03977	0.142827
$801$	−42.1552	−1.48948
$802$	9.01622	0.318374
$803$	36.7950	1.29847
$804$	1.21422	0.0428222
$805$	4.59988	0.162125
$806$	−30.7834	−1.08430
$807$	−8.10996	−0.285484
$808$	−11.2435	−0.395544
$809$	−9.64912	−0.339245	−0.169623	−	0.985509i	$-0.554255\pi$
$809$	−9.64912	−0.339245	−0.169623	+	0.985509i	$0.554255\pi$
$810$	20.2525	0.711599
$811$	6.42998	0.225787	0.112893	−	0.993607i	$-0.463988\pi$
$811$	6.42998	0.225787	0.112893	+	0.993607i	$0.463988\pi$
$812$	4.69416	0.164733
$813$	−81.5294	−2.85936
$814$	−11.5877	−0.406149
$815$	11.3044	0.395976
$816$	8.35946	0.292640
$817$	−68.6068	−2.40025
$818$	−16.6053	−0.580592
$819$	193.764	6.77067
$820$	−1.44814	−0.0505713
$821$	−52.1852	−1.82128	−0.910638	−	0.413204i	$-0.864410\pi$
$821$	−52.1852	−1.82128	−0.910638	+	0.413204i	$0.864410\pi$
$822$	−47.8721	−1.66973
$823$	10.3845	0.361982	0.180991	−	0.983485i	$-0.442069\pi$
$823$	10.3845	0.361982	0.180991	+	0.983485i	$0.442069\pi$
$824$	19.2239	0.669695
$825$	42.8815	1.49294
$826$	−6.60361	−0.229769
$827$	26.3549	0.916450	0.458225	−	0.888836i	$-0.348485\pi$
$827$	26.3549	0.916450	0.458225	+	0.888836i	$0.348485\pi$
$828$	−7.14956	−0.248464
$829$	36.5508	1.26946	0.634730	−	0.772734i	$-0.281111\pi$
$829$	36.5508	1.26946	0.634730	+	0.772734i	$0.281111\pi$
$830$	5.36092	0.186080
$831$	14.6991	0.509907
$832$	5.77346	0.200159
$833$	−39.4515	−1.36691
$834$	−0.449527	−0.0155659
$835$	−25.0570	−0.867135
$836$	23.5573	0.814748
$837$	−70.4866	−2.43637
$838$	−6.53196	−0.225643
$839$	−57.3328	−1.97935	−0.989675	−	0.143332i	$-0.954218\pi$
$839$	−57.3328	−1.97935	−0.989675	+	0.143332i	$0.954218\pi$
$840$	−14.6545	−0.505628
$841$	1.00000	0.0344828
$842$	−37.6144	−1.29628
$843$	−54.7819	−1.88679
$844$	15.6305	0.538025
$845$	−19.9244	−0.685422
$846$	51.8482	1.78258
$847$	0.476345	0.0163674
$848$	13.2790	0.456004
$849$	66.7823	2.29196
$850$	−10.6001	−0.363581
$851$	−3.47782	−0.119218
$852$	41.2899	1.41457
$853$	−20.0963	−0.688086	−0.344043	−	0.938954i	$-0.611797\pi$
$853$	−20.0963	−0.688086	−0.344043	+	0.938954i	$0.611797\pi$
$854$	4.66953	0.159788
$855$	−49.5341	−1.69403
$856$	−8.26427	−0.282467
$857$	−6.51504	−0.222549	−0.111275	−	0.993790i	$-0.535493\pi$
$857$	−6.51504	−0.222549	−0.111275	+	0.993790i	$0.535493\pi$
$858$	61.2844	2.09222
$859$	50.8193	1.73393	0.866967	−	0.498366i	$-0.166067\pi$
$859$	50.8193	1.73393	0.866967	+	0.498366i	$0.166067\pi$
$860$	9.50867	0.324243
$861$	−22.1006	−0.753187
$862$	28.9630	0.986484
$863$	27.9907	0.952816	0.476408	−	0.879224i	$-0.341938\pi$
$863$	27.9907	0.952816	0.476408	+	0.879224i	$0.341938\pi$
$864$	13.2198	0.449748
$865$	8.83231	0.300307
$866$	−35.4925	−1.20609
$867$	32.2245	1.09440
$868$	25.0288	0.849531
$869$	−34.8632	−1.18265
$870$	−3.12185	−0.105841
$871$	−2.20044	−0.0745591
$872$	−13.4361	−0.455004
$873$	−23.8146	−0.806002
$874$	7.07027	0.239155
$875$	41.5819	1.40572
$876$	−35.1821	−1.18869
$877$	−23.5381	−0.794826	−0.397413	−	0.917640i	$-0.630092\pi$
$877$	−23.5381	−0.794826	−0.397413	+	0.917640i	$0.630092\pi$
$878$	−11.9694	−0.403947
$879$	−17.6285	−0.594596
$880$	−3.26497	−0.110062
$881$	−0.0274587	−0.000925108 0	−0.000462554	−	1.00000i	$-0.500147\pi$
$881$	−0.0274587	−0.000925108 0	−0.000462554		1.00000i	$0.500147\pi$
$882$	−107.495	−3.61954
$883$	−15.4353	−0.519440	−0.259720	−	0.965684i	$-0.583630\pi$
$883$	−15.4353	−0.519440	−0.259720	+	0.965684i	$0.583630\pi$
$884$	−15.1492	−0.509524
$885$	4.39173	0.147626
$886$	−36.6786	−1.23224
$887$	−34.1952	−1.14816	−0.574082	−	0.818798i	$-0.694641\pi$
$887$	−34.1952	−1.14816	−0.574082	+	0.818798i	$0.694641\pi$
$888$	11.0798	0.371813
$889$	−88.0373	−2.95268
$890$	−5.77777	−0.193671
$891$	68.8619	2.30696
$892$	−7.42659	−0.248661
$893$	−51.2732	−1.71579
$894$	37.3253	1.24835
$895$	7.49289	0.250460
$896$	−4.69416	−0.156821
$897$	18.3933	0.614134
$898$	−10.2367	−0.341604
$899$	5.33189	0.177828
$900$	−28.8826	−0.962752
$901$	−34.8435	−1.16080
$902$	−4.92394	−0.163949
$903$	145.115	4.82913
$904$	−10.3906	−0.345588
$905$	4.01453	0.133448
$906$	56.0354	1.86165
$907$	41.1851	1.36753	0.683765	−	0.729702i	$-0.260341\pi$
$907$	41.1851	1.36753	0.683765	+	0.729702i	$0.260341\pi$
$908$	6.06296	0.201206
$909$	80.3858	2.66623
$910$	26.5572	0.880364
$911$	−31.4237	−1.04111	−0.520556	−	0.853828i	$-0.674275\pi$
$911$	−31.4237	−1.04111	−0.520556	+	0.853828i	$0.674275\pi$
$912$	−22.5247	−0.745868
$913$	18.2281	0.603262
$914$	−10.5771	−0.349858
$915$	−3.10547	−0.102664
$916$	−5.89206	−0.194679
$917$	−29.9274	−0.988289
$918$	−34.6881	−1.14488
$919$	−11.7432	−0.387372	−0.193686	−	0.981064i	$-0.562044\pi$
$919$	−11.7432	−0.387372	−0.193686	+	0.981064i	$0.562044\pi$
$920$	−0.979916	−0.0323069
$921$	22.7727	0.750387
$922$	−17.0250	−0.560690
$923$	−74.8266	−2.46295
$924$	−49.8279	−1.63922
$925$	−14.0496	−0.461948
$926$	20.5603	0.675652
$927$	−137.442	−4.51419
$928$	−1.00000	−0.0328266
$929$	10.5995	0.347760	0.173880	−	0.984767i	$-0.444370\pi$
$929$	10.5995	0.347760	0.173880	+	0.984767i	$0.444370\pi$
$930$	−16.6454	−0.545823
$931$	106.303	3.48393
$932$	−12.8371	−0.420494
$933$	−77.3802	−2.53331
$934$	1.74109	0.0569703
$935$	8.56710	0.280174
$936$	−41.2777	−1.34920
$937$	3.73957	0.122166	0.0610832	−	0.998133i	$-0.480545\pi$
$937$	3.73957	0.122166	0.0610832	+	0.998133i	$0.480545\pi$
$938$	1.78909	0.0584158
$939$	45.3522	1.48001
$940$	7.10629	0.231782
$941$	2.17585	0.0709306	0.0354653	−	0.999371i	$-0.488709\pi$
$941$	2.17585	0.0709306	0.0354653	+	0.999371i	$0.488709\pi$
$942$	−28.9131	−0.942039
$943$	−1.47782	−0.0481246
$944$	1.40677	0.0457864
$945$	60.8097	1.97814
$946$	32.3312	1.05118
$947$	11.9474	0.388238	0.194119	−	0.980978i	$-0.437815\pi$
$947$	11.9474	0.388238	0.194119	+	0.980978i	$0.437815\pi$
$948$	33.3350	1.08267
$949$	63.7579	2.06967
$950$	28.5622	0.926681
$951$	59.6941	1.93571
$952$	12.3172	0.399204
$953$	−23.7038	−0.767843	−0.383921	−	0.923366i	$-0.625427\pi$
$953$	−23.7038	−0.767843	−0.383921	+	0.923366i	$0.625427\pi$
$954$	−94.9393	−3.07377
$955$	−0.278173	−0.00900148
$956$	−18.7164	−0.605333
$957$	−10.6149	−0.343129
$958$	29.9983	0.969200
$959$	−70.5370	−2.27776
$960$	3.12185	0.100757
$961$	−2.57097	−0.0829346
$962$	−20.0791	−0.647375
$963$	59.0859	1.90402
$964$	12.7298	0.409999
$965$	16.2875	0.524314
$966$	−14.9548	−0.481164
$967$	13.2171	0.425034	0.212517	−	0.977157i	$-0.431834\pi$
$967$	13.2171	0.425034	0.212517	+	0.977157i	$0.431834\pi$
$968$	−0.101476	−0.00326156
$969$	59.1036	1.89868
$970$	−3.26402	−0.104801
$971$	−31.6920	−1.01704	−0.508522	−	0.861049i	$-0.669808\pi$
$971$	−31.6920	−1.01704	−0.508522	+	0.861049i	$0.669808\pi$
$972$	−26.1840	−0.839851
$973$	−0.662355	−0.0212341
$974$	4.12152	0.132062
$975$	74.3046	2.37965
$976$	−0.994753	−0.0318413
$977$	−1.22949	−0.0393347	−0.0196674	−	0.999807i	$-0.506261\pi$
$977$	−1.22949	−0.0393347	−0.0196674	+	0.999807i	$0.506261\pi$
$978$	−36.7521	−1.17520
$979$	−19.6455	−0.627871
$980$	−14.7332	−0.470635
$981$	96.0623	3.06703
$982$	−2.19086	−0.0699132
$983$	53.0685	1.69262	0.846311	−	0.532690i	$-0.178819\pi$
$983$	53.0685	1.69262	0.846311	+	0.532690i	$0.178819\pi$
$984$	4.70811	0.150089
$985$	14.7621	0.470359
$986$	2.62394	0.0835634
$987$	108.452	3.45206
$988$	40.8199	1.29865
$989$	9.70356	0.308555
$990$	23.3431	0.741892
$991$	4.90457	0.155799	0.0778994	−	0.996961i	$-0.475179\pi$
$991$	4.90457	0.155799	0.0778994	+	0.996961i	$0.475179\pi$
$992$	−5.33189	−0.169288
$993$	−72.3438	−2.29576
$994$	60.8385	1.92968
$995$	−6.35933	−0.201604
$996$	−17.4291	−0.552262
$997$	53.4599	1.69309	0.846546	−	0.532316i	$-0.178678\pi$
$997$	53.4599	1.69309	0.846546	+	0.532316i	$0.178678\pi$
$998$	23.2127	0.734785
$999$	−45.9762	−1.45462

Twists

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

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1334.2.a.j.1.1	✓	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)

\(f(q)\)	\(=\)	\(q-1.00000 q^{2} -3.18584 q^{3} +1.00000 q^{4} -0.979916 q^{5} +3.18584 q^{6} +4.69416 q^{7} -1.00000 q^{8} +7.14956 q^{9} +O(q^{10})\)	\(q-1.00000 q^{2} -3.18584 q^{3} +1.00000 q^{4} -0.979916 q^{5} +3.18584 q^{6} +4.69416 q^{7} -1.00000 q^{8} +7.14956 q^{9} +0.979916 q^{10} +3.33189 q^{11} -3.18584 q^{12} +5.77346 q^{13} -4.69416 q^{14} +3.12185 q^{15} +1.00000 q^{16} -2.62394 q^{17} -7.14956 q^{18} +7.07027 q^{19} -0.979916 q^{20} -14.9548 q^{21} -3.33189 q^{22} -1.00000 q^{23} +3.18584 q^{24} -4.03977 q^{25} -5.77346 q^{26} -13.2198 q^{27} +4.69416 q^{28} +1.00000 q^{29} -3.12185 q^{30} +5.33189 q^{31} -1.00000 q^{32} -10.6149 q^{33} +2.62394 q^{34} -4.59988 q^{35} +7.14956 q^{36} +3.47782 q^{37} -7.07027 q^{38} -18.3933 q^{39} +0.979916 q^{40} +1.47782 q^{41} +14.9548 q^{42} -9.70356 q^{43} +3.33189 q^{44} -7.00597 q^{45} +1.00000 q^{46} -7.25194 q^{47} -3.18584 q^{48} +15.0352 q^{49} +4.03977 q^{50} +8.35946 q^{51} +5.77346 q^{52} +13.2790 q^{53} +13.2198 q^{54} -3.26497 q^{55} -4.69416 q^{56} -22.5247 q^{57} -1.00000 q^{58} +1.40677 q^{59} +3.12185 q^{60} -0.994753 q^{61} -5.33189 q^{62} +33.5612 q^{63} +1.00000 q^{64} -5.65750 q^{65} +10.6149 q^{66} -0.381131 q^{67} -2.62394 q^{68} +3.18584 q^{69} +4.59988 q^{70} -12.9605 q^{71} -7.14956 q^{72} +11.0433 q^{73} -3.47782 q^{74} +12.8700 q^{75} +7.07027 q^{76} +15.6404 q^{77} +18.3933 q^{78} -10.4635 q^{79} -0.979916 q^{80} +20.6675 q^{81} -1.47782 q^{82} +5.47080 q^{83} -14.9548 q^{84} +2.57124 q^{85} +9.70356 q^{86} -3.18584 q^{87} -3.33189 q^{88} -5.89619 q^{89} +7.00597 q^{90} +27.1016 q^{91} -1.00000 q^{92} -16.9865 q^{93} +7.25194 q^{94} -6.92827 q^{95} +3.18584 q^{96} -3.33092 q^{97} -15.0352 q^{98} +23.8215 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 9 q - 9 q^{2} - 3 q^{3} + 9 q^{4} + 5 q^{5} + 3 q^{6} + 6 q^{7} - 9 q^{8} + 14 q^{9}+O(q^{10}) \) 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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