LMFDB - Embedded newform 4029.2.a.k.1.16

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [4029,2,Mod(1,4029)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(4029, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("4029.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 4029 = 3 \cdot 17 \cdot 79 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	4029.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:	$32.1717269744$
Analytic rank:	$0$
Dimension:	$31$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.16
Character	$\chi$	$=$	4029.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+0.0509119 q^{2} +1.00000 q^{3} -1.99741 q^{4} +3.95784 q^{5} +0.0509119 q^{6} +1.89285 q^{7} -0.203515 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q+0.0509119 q^{2} +1.00000 q^{3} -1.99741 q^{4} +3.95784 q^{5} +0.0509119 q^{6} +1.89285 q^{7} -0.203515 q^{8} +1.00000 q^{9} +0.201501 q^{10} +5.26878 q^{11} -1.99741 q^{12} -2.15571 q^{13} +0.0963686 q^{14} +3.95784 q^{15} +3.98445 q^{16} +1.00000 q^{17} +0.0509119 q^{18} +3.28525 q^{19} -7.90542 q^{20} +1.89285 q^{21} +0.268243 q^{22} -2.60175 q^{23} -0.203515 q^{24} +10.6645 q^{25} -0.109751 q^{26} +1.00000 q^{27} -3.78080 q^{28} +1.79464 q^{29} +0.201501 q^{30} +1.06539 q^{31} +0.609887 q^{32} +5.26878 q^{33} +0.0509119 q^{34} +7.49161 q^{35} -1.99741 q^{36} -6.27633 q^{37} +0.167258 q^{38} -2.15571 q^{39} -0.805482 q^{40} +8.76444 q^{41} +0.0963686 q^{42} -10.2465 q^{43} -10.5239 q^{44} +3.95784 q^{45} -0.132460 q^{46} +6.79563 q^{47} +3.98445 q^{48} -3.41711 q^{49} +0.542950 q^{50} +1.00000 q^{51} +4.30584 q^{52} -6.84440 q^{53} +0.0509119 q^{54} +20.8530 q^{55} -0.385225 q^{56} +3.28525 q^{57} +0.0913684 q^{58} -13.4533 q^{59} -7.90542 q^{60} +10.8439 q^{61} +0.0542410 q^{62} +1.89285 q^{63} -7.93786 q^{64} -8.53197 q^{65} +0.268243 q^{66} +10.6925 q^{67} -1.99741 q^{68} -2.60175 q^{69} +0.381412 q^{70} -0.635598 q^{71} -0.203515 q^{72} -3.45288 q^{73} -0.319540 q^{74} +10.6645 q^{75} -6.56198 q^{76} +9.97301 q^{77} -0.109751 q^{78} +1.00000 q^{79} +15.7698 q^{80} +1.00000 q^{81} +0.446214 q^{82} -12.9078 q^{83} -3.78080 q^{84} +3.95784 q^{85} -0.521670 q^{86} +1.79464 q^{87} -1.07228 q^{88} -6.91898 q^{89} +0.201501 q^{90} -4.08045 q^{91} +5.19675 q^{92} +1.06539 q^{93} +0.345978 q^{94} +13.0025 q^{95} +0.609887 q^{96} +2.23271 q^{97} -0.173972 q^{98} +5.26878 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 31 q + 4 q^{2} + 31 q^{3} + 34 q^{4} + 11 q^{5} + 4 q^{6} + 4 q^{7} + 12 q^{8} + 31 q^{9}+O(q^{10}) $ 31 * q + 4 * q^2 + 31 * q^3 + 34 * q^4 + 11 * q^5 + 4 * q^6 + 4 * q^7 + 12 * q^8 + 31 * q^9	\( 31 q + 4 q^{2} + 31 q^{3} + 34 q^{4} + 11 q^{5} + 4 q^{6} + 4 q^{7} + 12 q^{8} + 31 q^{9} + 5 q^{10} + 26 q^{11} + 34 q^{12} + 7 q^{13} + 19 q^{14} + 11 q^{15} + 40 q^{16} + 31 q^{17} + 4 q^{18} + 32 q^{19} + 23 q^{20} + 4 q^{21} + 2 q^{22} + 29 q^{23} + 12 q^{24} + 32 q^{25} + 13 q^{26} + 31 q^{27} - 13 q^{28} + 25 q^{29} + 5 q^{30} + 22 q^{31} + 28 q^{32} + 26 q^{33} + 4 q^{34} + 20 q^{35} + 34 q^{36} - 4 q^{37} + 19 q^{38} + 7 q^{39} - 3 q^{40} + 33 q^{41} + 19 q^{42} + 6 q^{43} + 30 q^{44} + 11 q^{45} - 11 q^{46} + 23 q^{47} + 40 q^{48} + 31 q^{49} + 6 q^{50} + 31 q^{51} - 7 q^{52} + 12 q^{53} + 4 q^{54} + 40 q^{56} + 32 q^{57} + 9 q^{58} + 27 q^{59} + 23 q^{60} - 4 q^{61} + 25 q^{62} + 4 q^{63} + 10 q^{64} + 54 q^{65} + 2 q^{66} + 34 q^{68} + 29 q^{69} - 59 q^{70} + 35 q^{71} + 12 q^{72} + 5 q^{73} + 48 q^{74} + 32 q^{75} + 32 q^{76} + 42 q^{77} + 13 q^{78} + 31 q^{79} + 24 q^{80} + 31 q^{81} + 5 q^{82} + 67 q^{83} - 13 q^{84} + 11 q^{85} - 20 q^{86} + 25 q^{87} - 7 q^{88} + 22 q^{89} + 5 q^{90} + 16 q^{91} + 57 q^{92} + 22 q^{93} + 45 q^{94} + 73 q^{95} + 28 q^{96} - 13 q^{97} - 19 q^{98} + 26 q^{99}+O(q^{100}) \) 31 * q + 4 * q^2 + 31 * q^3 + 34 * q^4 + 11 * q^5 + 4 * q^6 + 4 * q^7 + 12 * q^8 + 31 * q^9 + 5 * q^10 + 26 * q^11 + 34 * q^12 + 7 * q^13 + 19 * q^14 + 11 * q^15 + 40 * q^16 + 31 * q^17 + 4 * q^18 + 32 * q^19 + 23 * q^20 + 4 * q^21 + 2 * q^22 + 29 * q^23 + 12 * q^24 + 32 * q^25 + 13 * q^26 + 31 * q^27 - 13 * q^28 + 25 * q^29 + 5 * q^30 + 22 * q^31 + 28 * q^32 + 26 * q^33 + 4 * q^34 + 20 * q^35 + 34 * q^36 - 4 * q^37 + 19 * q^38 + 7 * q^39 - 3 * q^40 + 33 * q^41 + 19 * q^42 + 6 * q^43 + 30 * q^44 + 11 * q^45 - 11 * q^46 + 23 * q^47 + 40 * q^48 + 31 * q^49 + 6 * q^50 + 31 * q^51 - 7 * q^52 + 12 * q^53 + 4 * q^54 + 40 * q^56 + 32 * q^57 + 9 * q^58 + 27 * q^59 + 23 * q^60 - 4 * q^61 + 25 * q^62 + 4 * q^63 + 10 * q^64 + 54 * q^65 + 2 * q^66 + 34 * q^68 + 29 * q^69 - 59 * q^70 + 35 * q^71 + 12 * q^72 + 5 * q^73 + 48 * q^74 + 32 * q^75 + 32 * q^76 + 42 * q^77 + 13 * q^78 + 31 * q^79 + 24 * q^80 + 31 * q^81 + 5 * q^82 + 67 * q^83 - 13 * q^84 + 11 * q^85 - 20 * q^86 + 25 * q^87 - 7 * q^88 + 22 * q^89 + 5 * q^90 + 16 * q^91 + 57 * q^92 + 22 * q^93 + 45 * q^94 + 73 * q^95 + 28 * q^96 - 13 * q^97 - 19 * q^98 + 26 * 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 $

$2$	0.0509119	0.0360001	0.0180001	−	0.999838i	$-0.494270\pi$
$2$	0.0509119	0.0360001	0.0180001	+	0.999838i	$0.494270\pi$
$3$	1.00000	0.577350
$3$	1.00000	0.577350
$4$	−1.99741	−0.998704
$5$	3.95784	1.77000	0.885000	−	0.465590i	$-0.154158\pi$
$5$	3.95784	1.77000	0.885000	+	0.465590i	$0.154158\pi$
$6$	0.0509119	0.0207847
$7$	1.89285	0.715431	0.357715	−	0.933831i	$-0.383556\pi$
$7$	1.89285	0.715431	0.357715	+	0.933831i	$0.383556\pi$
$8$	−0.203515	−0.0719536
$9$	1.00000	0.333333
$10$	0.201501	0.0637202
$11$	5.26878	1.58860	0.794298	−	0.607528i	$-0.207839\pi$
$11$	5.26878	1.58860	0.794298	+	0.607528i	$0.207839\pi$
$12$	−1.99741	−0.576602
$13$	−2.15571	−0.597887	−0.298944	−	0.954271i	$-0.596634\pi$
$13$	−2.15571	−0.597887	−0.298944	+	0.954271i	$0.596634\pi$
$14$	0.0963686	0.0257556
$15$	3.95784	1.02191
$16$	3.98445	0.996114
$17$	1.00000	0.242536
$17$	1.00000	0.242536
$18$	0.0509119	0.0120000
$19$	3.28525	0.753688	0.376844	−	0.926277i	$-0.377009\pi$
$19$	3.28525	0.753688	0.376844	+	0.926277i	$0.377009\pi$
$20$	−7.90542	−1.76771
$21$	1.89285	0.413054
$22$	0.268243	0.0571897
$23$	−2.60175	−0.542501	−0.271251	−	0.962509i	$-0.587437\pi$
$23$	−2.60175	−0.542501	−0.271251	+	0.962509i	$0.587437\pi$
$24$	−0.203515	−0.0415424
$25$	10.6645	2.13290
$26$	−0.109751	−0.0215240
$27$	1.00000	0.192450
$28$	−3.78080	−0.714504
$29$	1.79464	0.333256	0.166628	−	0.986020i	$-0.446712\pi$
$29$	1.79464	0.333256	0.166628	+	0.986020i	$0.446712\pi$
$30$	0.201501	0.0367889
$31$	1.06539	0.191350	0.0956749	−	0.995413i	$-0.469499\pi$
$31$	1.06539	0.191350	0.0956749	+	0.995413i	$0.469499\pi$
$32$	0.609887	0.107814
$33$	5.26878	0.917176
$34$	0.0509119	0.00873131
$35$	7.49161	1.26631
$36$	−1.99741	−0.332901
$37$	−6.27633	−1.03182	−0.515911	−	0.856642i	$-0.672547\pi$
$37$	−6.27633	−1.03182	−0.515911	+	0.856642i	$0.672547\pi$
$38$	0.167258	0.0271328
$39$	−2.15571	−0.345190
$40$	−0.805482	−0.127358
$41$	8.76444	1.36878	0.684388	−	0.729118i	$-0.260070\pi$
$41$	8.76444	1.36878	0.684388	+	0.729118i	$0.260070\pi$
$42$	0.0963686	0.0148700
$43$	−10.2465	−1.56258	−0.781291	−	0.624167i	$-0.785438\pi$
$43$	−10.2465	−1.56258	−0.781291	+	0.624167i	$0.785438\pi$
$44$	−10.5239	−1.58654
$45$	3.95784	0.590000
$46$	−0.132460	−0.0195301
$47$	6.79563	0.991244	0.495622	−	0.868538i	$-0.334940\pi$
$47$	6.79563	0.991244	0.495622	+	0.868538i	$0.334940\pi$
$48$	3.98445	0.575106
$49$	−3.41711	−0.488159
$50$	0.542950	0.0767847
$51$	1.00000	0.140028
$52$	4.30584	0.597113
$53$	−6.84440	−0.940150	−0.470075	−	0.882626i	$-0.655773\pi$
$53$	−6.84440	−0.940150	−0.470075	+	0.882626i	$0.655773\pi$
$54$	0.0509119	0.00692823
$55$	20.8530	2.81182
$56$	−0.385225	−0.0514778
$57$	3.28525	0.435142
$58$	0.0913684	0.0119973
$59$	−13.4533	−1.75147	−0.875736	−	0.482791i	$-0.839623\pi$
$59$	−13.4533	−1.75147	−0.875736	+	0.482791i	$0.839623\pi$
$60$	−7.90542	−1.02059
$61$	10.8439	1.38842	0.694210	−	0.719773i	$-0.255754\pi$
$61$	10.8439	1.38842	0.694210	+	0.719773i	$0.255754\pi$
$62$	0.0542410	0.00688862
$63$	1.89285	0.238477
$64$	−7.93786	−0.992232
$65$	−8.53197	−1.05826
$66$	0.268243	0.0330185
$67$	10.6925	1.30630	0.653150	−	0.757228i	$-0.273447\pi$
$67$	10.6925	1.30630	0.653150	+	0.757228i	$0.273447\pi$
$68$	−1.99741	−0.242221
$69$	−2.60175	−0.313213
$70$	0.381412	0.0455874
$71$	−0.635598	−0.0754316	−0.0377158	−	0.999289i	$-0.512008\pi$
$71$	−0.635598	−0.0754316	−0.0377158	+	0.999289i	$0.512008\pi$
$72$	−0.203515	−0.0239845
$73$	−3.45288	−0.404129	−0.202064	−	0.979372i	$-0.564765\pi$
$73$	−3.45288	−0.404129	−0.202064	+	0.979372i	$0.564765\pi$
$74$	−0.319540	−0.0371457
$75$	10.6645	1.23143
$76$	−6.56198	−0.752711
$77$	9.97301	1.13653
$78$	−0.109751	−0.0124269
$79$	1.00000	0.112509
$79$	1.00000	0.112509
$80$	15.7698	1.76312
$81$	1.00000	0.111111
$82$	0.446214	0.0492761
$83$	−12.9078	−1.41682	−0.708410	−	0.705801i	$-0.750587\pi$
$83$	−12.9078	−1.41682	−0.708410	+	0.705801i	$0.750587\pi$
$84$	−3.78080	−0.412519
$85$	3.95784	0.429288
$86$	−0.521670	−0.0562531
$87$	1.79464	0.192405
$88$	−1.07228	−0.114305
$89$	−6.91898	−0.733411	−0.366705	−	0.930337i	$-0.619514\pi$
$89$	−6.91898	−0.733411	−0.366705	+	0.930337i	$0.619514\pi$
$90$	0.201501	0.0212401
$91$	−4.08045	−0.427747
$92$	5.19675	0.541798
$93$	1.06539	0.110476
$94$	0.345978	0.0356849
$95$	13.0025	1.33403
$96$	0.609887	0.0622463
$97$	2.23271	0.226697	0.113349	−	0.993555i	$-0.463842\pi$
$97$	2.23271	0.226697	0.113349	+	0.993555i	$0.463842\pi$
$98$	−0.173972	−0.0175738
$99$	5.26878	0.529532
$100$	−21.3014	−2.13014
$101$	−7.71317	−0.767490	−0.383745	−	0.923439i	$-0.625366\pi$
$101$	−7.71317	−0.767490	−0.383745	+	0.923439i	$0.625366\pi$
$102$	0.0509119	0.00504103
$103$	6.30662	0.621410	0.310705	−	0.950506i	$-0.399435\pi$
$103$	6.30662	0.621410	0.310705	+	0.950506i	$0.399435\pi$
$104$	0.438721	0.0430201
$105$	7.49161	0.731106
$106$	−0.348461	−0.0338455
$107$	−18.0287	−1.74290	−0.871450	−	0.490484i	$-0.836820\pi$
$107$	−18.0287	−1.74290	−0.871450	+	0.490484i	$0.836820\pi$
$108$	−1.99741	−0.192201
$109$	15.0394	1.44051	0.720256	−	0.693709i	$-0.244024\pi$
$109$	15.0394	1.44051	0.720256	+	0.693709i	$0.244024\pi$
$110$	1.06166	0.101226
$111$	−6.27633	−0.595723
$112$	7.54198	0.712650
$113$	−1.47464	−0.138722	−0.0693610	−	0.997592i	$-0.522096\pi$
$113$	−1.47464	−0.138722	−0.0693610	+	0.997592i	$0.522096\pi$
$114$	0.167258	0.0156652
$115$	−10.2973	−0.960228
$116$	−3.58462	−0.332824
$117$	−2.15571	−0.199296
$118$	−0.684933	−0.0630532
$119$	1.89285	0.173517
$120$	−0.805482	−0.0735301
$121$	16.7600	1.52364
$122$	0.552083	0.0499833
$123$	8.76444	0.790263
$124$	−2.12802	−0.191102
$125$	22.4192	2.00524
$126$	0.0963686	0.00858520
$127$	−3.07151	−0.272553	−0.136276	−	0.990671i	$-0.543514\pi$
$127$	−3.07151	−0.272553	−0.136276	+	0.990671i	$0.543514\pi$
$128$	−1.62391	−0.143534
$129$	−10.2465	−0.902157
$130$	−0.434379	−0.0380975
$131$	7.42141	0.648412	0.324206	−	0.945987i	$-0.394903\pi$
$131$	7.42141	0.648412	0.324206	+	0.945987i	$0.394903\pi$
$132$	−10.5239	−0.915988
$133$	6.21849	0.539211
$134$	0.544377	0.0470270
$135$	3.95784	0.340637
$136$	−0.203515	−0.0174513
$137$	−20.7596	−1.77361	−0.886805	−	0.462144i	$-0.847080\pi$
$137$	−20.7596	−1.77361	−0.886805	+	0.462144i	$0.847080\pi$
$138$	−0.132460	−0.0112757
$139$	−6.99991	−0.593725	−0.296862	−	0.954920i	$-0.595940\pi$
$139$	−6.99991	−0.593725	−0.296862	+	0.954920i	$0.595940\pi$
$140$	−14.9638	−1.26467
$141$	6.79563	0.572295
$142$	−0.0323595	−0.00271555
$143$	−11.3580	−0.949802
$144$	3.98445	0.332038
$145$	7.10289	0.589863
$146$	−0.175792	−0.0145487
$147$	−3.41711	−0.281839
$148$	12.5364	1.03049
$149$	−2.52004	−0.206449	−0.103225	−	0.994658i	$-0.532916\pi$
$149$	−2.52004	−0.206449	−0.103225	+	0.994658i	$0.532916\pi$
$150$	0.542950	0.0443317
$151$	2.39953	0.195271	0.0976357	−	0.995222i	$-0.468872\pi$
$151$	2.39953	0.195271	0.0976357	+	0.995222i	$0.468872\pi$
$152$	−0.668599	−0.0542305
$153$	1.00000	0.0808452
$154$	0.507745	0.0409152
$155$	4.21665	0.338689
$156$	4.30584	0.344743
$157$	−7.13021	−0.569053	−0.284526	−	0.958668i	$-0.591836\pi$
$157$	−7.13021	−0.569053	−0.284526	+	0.958668i	$0.591836\pi$
$158$	0.0509119	0.00405033
$159$	−6.84440	−0.542796
$160$	2.41384	0.190830
$161$	−4.92472	−0.388122
$162$	0.0509119	0.00400001
$163$	9.18135	0.719139	0.359570	−	0.933118i	$-0.382924\pi$
$163$	9.18135	0.719139	0.359570	+	0.933118i	$0.382924\pi$
$164$	−17.5062	−1.36700
$165$	20.8530	1.62340
$166$	−0.657162	−0.0510057
$167$	11.7414	0.908574	0.454287	−	0.890855i	$-0.349894\pi$
$167$	11.7414	0.908574	0.454287	+	0.890855i	$0.349894\pi$
$168$	−0.385225	−0.0297207
$169$	−8.35290	−0.642531
$170$	0.201501	0.0154544
$171$	3.28525	0.251229
$172$	20.4665	1.56056
$173$	−17.3164	−1.31654	−0.658270	−	0.752782i	$-0.728711\pi$
$173$	−17.3164	−1.31654	−0.658270	+	0.752782i	$0.728711\pi$
$174$	0.0913684	0.00692662
$175$	20.1863	1.52594
$176$	20.9932	1.58242
$177$	−13.4533	−1.01121
$178$	−0.352258	−0.0264029
$179$	23.2880	1.74063	0.870314	−	0.492497i	$-0.163916\pi$
$179$	23.2880	1.74063	0.870314	+	0.492497i	$0.163916\pi$
$180$	−7.90542	−0.589236
$181$	1.61698	0.120189	0.0600946	−	0.998193i	$-0.480860\pi$
$181$	1.61698	0.120189	0.0600946	+	0.998193i	$0.480860\pi$
$182$	−0.207743	−0.0153989
$183$	10.8439	0.801604
$184$	0.529496	0.0390349
$185$	−24.8407	−1.82633
$186$	0.0542410	0.00397714
$187$	5.26878	0.385291
$188$	−13.5736	−0.989960
$189$	1.89285	0.137685
$190$	0.661981	0.0480252
$191$	−8.53278	−0.617410	−0.308705	−	0.951158i	$-0.599896\pi$
$191$	−8.53278	−0.617410	−0.308705	+	0.951158i	$0.599896\pi$
$192$	−7.93786	−0.572866
$193$	−21.0273	−1.51358	−0.756790	−	0.653658i	$-0.773233\pi$
$193$	−21.0273	−1.51358	−0.756790	+	0.653658i	$0.773233\pi$
$194$	0.113671	0.00816113
$195$	−8.53197	−0.610987
$196$	6.82537	0.487526
$197$	18.1465	1.29288	0.646441	−	0.762964i	$-0.276256\pi$
$197$	18.1465	1.29288	0.646441	+	0.762964i	$0.276256\pi$
$198$	0.268243	0.0190632
$199$	−8.58119	−0.608305	−0.304152	−	0.952623i	$-0.598373\pi$
$199$	−8.58119	−0.608305	−0.304152	+	0.952623i	$0.598373\pi$
$200$	−2.17039	−0.153470
$201$	10.6925	0.754193
$202$	−0.392692	−0.0276297
$203$	3.39698	0.238422
$204$	−1.99741	−0.139847
$205$	34.6883	2.42273
$206$	0.321082	0.0223708
$207$	−2.60175	−0.180834
$208$	−8.58934	−0.595564
$209$	17.3092	1.19731
$210$	0.381412	0.0263199
$211$	24.2509	1.66950	0.834749	−	0.550631i	$-0.185613\pi$
$211$	24.2509	1.66950	0.834749	+	0.550631i	$0.185613\pi$
$212$	13.6711	0.938932
$213$	−0.635598	−0.0435505
$214$	−0.917875	−0.0627446
$215$	−40.5542	−2.76577
$216$	−0.203515	−0.0138475
$217$	2.01663	0.136898
$218$	0.765683	0.0518586
$219$	−3.45288	−0.233324
$220$	−41.6519	−2.80817
$221$	−2.15571	−0.145009
$222$	−0.319540	−0.0214461
$223$	−9.47539	−0.634519	−0.317260	−	0.948339i	$-0.602763\pi$
$223$	−9.47539	−0.634519	−0.317260	+	0.948339i	$0.602763\pi$
$224$	1.15443	0.0771333
$225$	10.6645	0.710967
$226$	−0.0750764	−0.00499401
$227$	−15.6787	−1.04063	−0.520317	−	0.853973i	$-0.674186\pi$
$227$	−15.6787	−1.04063	−0.520317	+	0.853973i	$0.674186\pi$
$228$	−6.56198	−0.434578
$229$	18.9379	1.25145	0.625727	−	0.780042i	$-0.284802\pi$
$229$	18.9379	1.25145	0.625727	+	0.780042i	$0.284802\pi$
$230$	−0.524255	−0.0345683
$231$	9.97301	0.656176
$232$	−0.365237	−0.0239790
$233$	28.1117	1.84166	0.920829	−	0.389967i	$-0.127514\pi$
$233$	28.1117	1.84166	0.920829	+	0.389967i	$0.127514\pi$
$234$	−0.109751	−0.00717467
$235$	26.8960	1.75450
$236$	26.8717	1.74920
$237$	1.00000	0.0649570
$238$	0.0963686	0.00624665
$239$	24.0586	1.55622	0.778110	−	0.628128i	$-0.216179\pi$
$239$	24.0586	1.55622	0.778110	+	0.628128i	$0.216179\pi$
$240$	15.7698	1.01794
$241$	11.1814	0.720258	0.360129	−	0.932902i	$-0.382733\pi$
$241$	11.1814	0.720258	0.360129	+	0.932902i	$0.382733\pi$
$242$	0.853284	0.0548511
$243$	1.00000	0.0641500
$244$	−21.6597	−1.38662
$245$	−13.5244	−0.864042
$246$	0.446214	0.0284496
$247$	−7.08205	−0.450620
$248$	−0.216823	−0.0137683
$249$	−12.9078	−0.818001
$250$	1.14140	0.0721888
$251$	13.3467	0.842437	0.421218	−	0.906959i	$-0.361603\pi$
$251$	13.3467	0.842437	0.421218	+	0.906959i	$0.361603\pi$
$252$	−3.78080	−0.238168
$253$	−13.7080	−0.861816
$254$	−0.156377	−0.00981194
$255$	3.95784	0.247850
$256$	15.7930	0.987065
$257$	16.1906	1.00994	0.504971	−	0.863137i	$-0.331503\pi$
$257$	16.1906	1.00994	0.504971	+	0.863137i	$0.331503\pi$
$258$	−0.521670	−0.0324778
$259$	−11.8802	−0.738197
$260$	17.0418	1.05689
$261$	1.79464	0.111085
$262$	0.377838	0.0233429
$263$	−17.8736	−1.10214	−0.551068	−	0.834460i	$-0.685779\pi$
$263$	−17.8736	−1.10214	−0.551068	+	0.834460i	$0.685779\pi$
$264$	−1.07228	−0.0659941
$265$	−27.0890	−1.66407
$266$	0.316595	0.0194117
$267$	−6.91898	−0.423435
$268$	−21.3573	−1.30461
$269$	15.7614	0.960992	0.480496	−	0.876997i	$-0.340457\pi$
$269$	15.7614	0.960992	0.480496	+	0.876997i	$0.340457\pi$
$270$	0.201501	0.0122630
$271$	−17.7427	−1.07779	−0.538897	−	0.842372i	$-0.681159\pi$
$271$	−17.7427	−1.07779	−0.538897	+	0.842372i	$0.681159\pi$
$272$	3.98445	0.241593
$273$	−4.08045	−0.246960
$274$	−1.05691	−0.0638502
$275$	56.1889	3.38832
$276$	5.19675	0.312807
$277$	−14.7538	−0.886471	−0.443235	−	0.896405i	$-0.646169\pi$
$277$	−14.7538	−0.886471	−0.443235	+	0.896405i	$0.646169\pi$
$278$	−0.356378	−0.0213742
$279$	1.06539	0.0637833
$280$	−1.52466	−0.0911158
$281$	−32.3269	−1.92846	−0.964230	−	0.265066i	$-0.914606\pi$
$281$	−32.3269	−1.92846	−0.964230	+	0.265066i	$0.914606\pi$
$282$	0.345978	0.0206027
$283$	−15.7050	−0.933565	−0.466782	−	0.884372i	$-0.654587\pi$
$283$	−15.7050	−0.933565	−0.466782	+	0.884372i	$0.654587\pi$
$284$	1.26955	0.0753339
$285$	13.0025	0.770201
$286$	−0.578256	−0.0341930
$287$	16.5898	0.979264
$288$	0.609887	0.0359379
$289$	1.00000	0.0588235
$290$	0.361622	0.0212352
$291$	2.23271	0.130884
$292$	6.89681	0.403605
$293$	−10.2116	−0.596570	−0.298285	−	0.954477i	$-0.596415\pi$
$293$	−10.2116	−0.596570	−0.298285	+	0.954477i	$0.596415\pi$
$294$	−0.173972	−0.0101462
$295$	−53.2461	−3.10011
$296$	1.27733	0.0742433
$297$	5.26878	0.305725
$298$	−0.128300	−0.00743221
$299$	5.60862	0.324355
$300$	−21.3014	−1.22984
$301$	−19.3952	−1.11792
$302$	0.122165	0.00702979
$303$	−7.71317	−0.443110
$304$	13.0899	0.750758
$305$	42.9185	2.45750
$306$	0.0509119	0.00291044
$307$	−10.2616	−0.585660	−0.292830	−	0.956165i	$-0.594597\pi$
$307$	−10.2616	−0.585660	−0.292830	+	0.956165i	$0.594597\pi$
$308$	−19.9202	−1.13506
$309$	6.30662	0.358771
$310$	0.214677	0.0121929
$311$	−3.07625	−0.174438	−0.0872191	−	0.996189i	$-0.527798\pi$
$311$	−3.07625	−0.174438	−0.0872191	+	0.996189i	$0.527798\pi$
$312$	0.438721	0.0248377
$313$	−6.77918	−0.383182	−0.191591	−	0.981475i	$-0.561365\pi$
$313$	−6.77918	−0.383182	−0.191591	+	0.981475i	$0.561365\pi$
$314$	−0.363012	−0.0204860
$315$	7.49161	0.422104
$316$	−1.99741	−0.112363
$317$	27.8869	1.56628	0.783142	−	0.621842i	$-0.213616\pi$
$317$	27.8869	1.56628	0.783142	+	0.621842i	$0.213616\pi$
$318$	−0.348461	−0.0195407
$319$	9.45555	0.529409
$320$	−31.4168	−1.75625
$321$	−18.0287	−1.00626
$322$	−0.250727	−0.0139724
$323$	3.28525	0.182796
$324$	−1.99741	−0.110967
$325$	−22.9896	−1.27524
$326$	0.467440	0.0258891
$327$	15.0394	0.831680
$328$	−1.78370	−0.0984883
$329$	12.8631	0.709167
$330$	1.06166	0.0584427
$331$	28.0154	1.53986	0.769932	−	0.638126i	$-0.220290\pi$
$331$	28.0154	1.53986	0.769932	+	0.638126i	$0.220290\pi$
$332$	25.7822	1.41498
$333$	−6.27633	−0.343941
$334$	0.597775	0.0327088
$335$	42.3193	2.31215
$336$	7.54198	0.411449
$337$	−26.2695	−1.43099	−0.715495	−	0.698618i	$-0.753799\pi$
$337$	−26.2695	−1.43099	−0.715495	+	0.698618i	$0.753799\pi$
$338$	−0.425262	−0.0231312
$339$	−1.47464	−0.0800912
$340$	−7.90542	−0.428732
$341$	5.61330	0.303978
$342$	0.167258	0.00904428
$343$	−19.7180	−1.06467
$344$	2.08533	0.112433
$345$	−10.2973	−0.554388
$346$	−0.881609	−0.0473956
$347$	−1.44253	−0.0774390	−0.0387195	−	0.999250i	$-0.512328\pi$
$347$	−1.44253	−0.0774390	−0.0387195	+	0.999250i	$0.512328\pi$
$348$	−3.58462	−0.192156
$349$	17.5904	0.941595	0.470797	−	0.882241i	$-0.343966\pi$
$349$	17.5904	0.941595	0.470797	+	0.882241i	$0.343966\pi$
$350$	1.02772	0.0549342
$351$	−2.15571	−0.115063
$352$	3.21336	0.171273
$353$	35.2617	1.87679	0.938394	−	0.345566i	$-0.112313\pi$
$353$	35.2617	1.87679	0.938394	+	0.345566i	$0.112313\pi$
$354$	−0.684933	−0.0364038
$355$	−2.51560	−0.133514
$356$	13.8200	0.732460
$357$	1.89285	0.100180
$358$	1.18564	0.0626628
$359$	27.6109	1.45725	0.728623	−	0.684915i	$-0.240161\pi$
$359$	27.6109	1.45725	0.728623	+	0.684915i	$0.240161\pi$
$360$	−0.805482	−0.0424526
$361$	−8.20715	−0.431955
$362$	0.0823235	0.00432683
$363$	16.7600	0.879673
$364$	8.15032	0.427193
$365$	−13.6659	−0.715308
$366$	0.552083	0.0288579
$367$	−12.7400	−0.665022	−0.332511	−	0.943099i	$-0.607896\pi$
$367$	−12.7400	−0.665022	−0.332511	+	0.943099i	$0.607896\pi$
$368$	−10.3665	−0.540393
$369$	8.76444	0.456258
$370$	−1.26469	−0.0657480
$371$	−12.9554	−0.672612
$372$	−2.12802	−0.110333
$373$	14.7130	0.761808	0.380904	−	0.924615i	$-0.375613\pi$
$373$	14.7130	0.761808	0.380904	+	0.924615i	$0.375613\pi$
$374$	0.268243	0.0138705
$375$	22.4192	1.15772
$376$	−1.38302	−0.0713236
$377$	−3.86873	−0.199250
$378$	0.0963686	0.00495667
$379$	4.68446	0.240625	0.120312	−	0.992736i	$-0.461610\pi$
$379$	4.68446	0.240625	0.120312	+	0.992736i	$0.461610\pi$
$380$	−25.9713	−1.33230
$381$	−3.07151	−0.157358
$382$	−0.434420	−0.0222269
$383$	27.1546	1.38753	0.693767	−	0.720199i	$-0.255950\pi$
$383$	27.1546	1.38753	0.693767	+	0.720199i	$0.255950\pi$
$384$	−1.62391	−0.0828696
$385$	39.4716	2.01166
$386$	−1.07054	−0.0544891
$387$	−10.2465	−0.520861
$388$	−4.45963	−0.226404
$389$	−7.35108	−0.372715	−0.186357	−	0.982482i	$-0.559668\pi$
$389$	−7.35108	−0.372715	−0.186357	+	0.982482i	$0.559668\pi$
$390$	−0.434379	−0.0219956
$391$	−2.60175	−0.131576
$392$	0.695435	0.0351248
$393$	7.42141	0.374361
$394$	0.923871	0.0465439
$395$	3.95784	0.199141
$396$	−10.5239	−0.528846
$397$	1.86641	0.0936722	0.0468361	−	0.998903i	$-0.485086\pi$
$397$	1.86641	0.0936722	0.0468361	+	0.998903i	$0.485086\pi$
$398$	−0.436884	−0.0218990
$399$	6.21849	0.311314
$400$	42.4923	2.12461
$401$	15.5893	0.778491	0.389246	−	0.921134i	$-0.372736\pi$
$401$	15.5893	0.778491	0.389246	+	0.921134i	$0.372736\pi$
$402$	0.544377	0.0271510
$403$	−2.29668	−0.114406
$404$	15.4064	0.766495
$405$	3.95784	0.196667
$406$	0.172947	0.00858321
$407$	−33.0686	−1.63915
$408$	−0.203515	−0.0100755
$409$	19.8656	0.982291	0.491145	−	0.871078i	$-0.336578\pi$
$409$	19.8656	0.982291	0.491145	+	0.871078i	$0.336578\pi$
$410$	1.76604	0.0872187
$411$	−20.7596	−1.02399
$412$	−12.5969	−0.620605
$413$	−25.4651	−1.25306
$414$	−0.132460	−0.00651004
$415$	−51.0872	−2.50777
$416$	−1.31474	−0.0644605
$417$	−6.99991	−0.342787
$418$	0.881246	0.0431031
$419$	24.8173	1.21241	0.606203	−	0.795310i	$-0.292692\pi$
$419$	24.8173	1.21241	0.606203	+	0.795310i	$0.292692\pi$
$420$	−14.9638	−0.730158
$421$	0.949942	0.0462974	0.0231487	−	0.999732i	$-0.492631\pi$
$421$	0.949942	0.0462974	0.0231487	+	0.999732i	$0.492631\pi$
$422$	1.23466	0.0601021
$423$	6.79563	0.330415
$424$	1.39294	0.0676472
$425$	10.6645	0.517305
$426$	−0.0323595	−0.00156782
$427$	20.5259	0.993318
$428$	36.0107	1.74064
$429$	−11.3580	−0.548368
$430$	−2.06469	−0.0995681
$431$	−37.6436	−1.81323	−0.906613	−	0.421962i	$-0.861341\pi$
$431$	−37.6436	−1.81323	−0.906613	+	0.421962i	$0.861341\pi$
$432$	3.98445	0.191702
$433$	26.7637	1.28618	0.643090	−	0.765791i	$-0.277652\pi$
$433$	26.7637	1.28618	0.643090	+	0.765791i	$0.277652\pi$
$434$	0.102670	0.00492833
$435$	7.10289	0.340558
$436$	−30.0398	−1.43864
$437$	−8.54738	−0.408877
$438$	−0.175792	−0.00839969
$439$	36.4366	1.73902	0.869512	−	0.493912i	$-0.164433\pi$
$439$	36.4366	1.73902	0.869512	+	0.493912i	$0.164433\pi$
$440$	−4.24391	−0.202320
$441$	−3.41711	−0.162720
$442$	−0.109751	−0.00522034
$443$	11.0897	0.526889	0.263444	−	0.964675i	$-0.415141\pi$
$443$	11.0897	0.526889	0.263444	+	0.964675i	$0.415141\pi$
$444$	12.5364	0.594951
$445$	−27.3842	−1.29814
$446$	−0.482410	−0.0228428
$447$	−2.52004	−0.119194
$448$	−15.0252	−0.709873
$449$	−14.4035	−0.679745	−0.339872	−	0.940472i	$-0.610384\pi$
$449$	−14.4035	−0.679745	−0.339872	+	0.940472i	$0.610384\pi$
$450$	0.542950	0.0255949
$451$	46.1779	2.17443
$452$	2.94545	0.138542
$453$	2.39953	0.112740
$454$	−0.798234	−0.0374630
$455$	−16.1498	−0.757112
$456$	−0.668599	−0.0313100
$457$	2.53031	0.118363	0.0591815	−	0.998247i	$-0.481151\pi$
$457$	2.53031	0.118363	0.0591815	+	0.998247i	$0.481151\pi$
$458$	0.964166	0.0450525
$459$	1.00000	0.0466760
$460$	20.5679	0.958983
$461$	−26.2235	−1.22135	−0.610675	−	0.791881i	$-0.709102\pi$
$461$	−26.2235	−1.22135	−0.610675	+	0.791881i	$0.709102\pi$
$462$	0.507745	0.0236224
$463$	−33.4646	−1.55523	−0.777617	−	0.628739i	$-0.783572\pi$
$463$	−33.4646	−1.55523	−0.777617	+	0.628739i	$0.783572\pi$
$464$	7.15066	0.331961
$465$	4.21665	0.195542
$466$	1.43122	0.0662999
$467$	−8.60118	−0.398015	−0.199008	−	0.979998i	$-0.563772\pi$
$467$	−8.60118	−0.398015	−0.199008	+	0.979998i	$0.563772\pi$
$468$	4.30584	0.199038
$469$	20.2394	0.934567
$470$	1.36933	0.0631623
$471$	−7.13021	−0.328543
$472$	2.73796	0.126025
$473$	−53.9867	−2.48231
$474$	0.0509119	0.00233846
$475$	35.0356	1.60754
$476$	−3.78080	−0.173293
$477$	−6.84440	−0.313383
$478$	1.22487	0.0560241
$479$	−22.0804	−1.00888	−0.504439	−	0.863447i	$-0.668301\pi$
$479$	−22.0804	−1.00888	−0.504439	+	0.863447i	$0.668301\pi$
$480$	2.41384	0.110176
$481$	13.5300	0.616914
$482$	0.569267	0.0259294
$483$	−4.92472	−0.224082
$484$	−33.4766	−1.52166
$485$	8.83671	0.401255
$486$	0.0509119	0.00230941
$487$	−3.82625	−0.173384	−0.0866920	−	0.996235i	$-0.527630\pi$
$487$	−3.82625	−0.173384	−0.0866920	+	0.996235i	$0.527630\pi$
$488$	−2.20690	−0.0999018
$489$	9.18135	0.415195
$490$	−0.688552	−0.0311056
$491$	−17.9562	−0.810353	−0.405177	−	0.914238i	$-0.632790\pi$
$491$	−17.9562	−0.810353	−0.405177	+	0.914238i	$0.632790\pi$
$492$	−17.5062	−0.789239
$493$	1.79464	0.0808264
$494$	−0.360561	−0.0162224
$495$	20.8530	0.937272
$496$	4.24500	0.190606
$497$	−1.20309	−0.0539661
$498$	−0.657162	−0.0294481
$499$	−20.8933	−0.935311	−0.467656	−	0.883911i	$-0.654901\pi$
$499$	−20.8933	−0.935311	−0.467656	+	0.883911i	$0.654901\pi$
$500$	−44.7804	−2.00264
$501$	11.7414	0.524566
$502$	0.679506	0.0303278
$503$	−36.3950	−1.62277	−0.811386	−	0.584511i	$-0.801286\pi$
$503$	−36.3950	−1.62277	−0.811386	+	0.584511i	$0.801286\pi$
$504$	−0.385225	−0.0171593
$505$	−30.5275	−1.35846
$506$	−0.697901	−0.0310255
$507$	−8.35290	−0.370965
$508$	6.13507	0.272200
$509$	−27.7110	−1.22827	−0.614133	−	0.789202i	$-0.710494\pi$
$509$	−27.7110	−1.22827	−0.614133	+	0.789202i	$0.710494\pi$
$510$	0.201501	0.00892262
$511$	−6.53579	−0.289126
$512$	4.05186	0.179069
$513$	3.28525	0.145047
$514$	0.824293	0.0363580
$515$	24.9606	1.09990
$516$	20.4665	0.900988
$517$	35.8047	1.57469
$518$	−0.604841	−0.0265752
$519$	−17.3164	−0.760104
$520$	1.73639	0.0761457
$521$	15.1921	0.665580	0.332790	−	0.943001i	$-0.392010\pi$
$521$	15.1921	0.665580	0.332790	+	0.943001i	$0.392010\pi$
$522$	0.0913684	0.00399909
$523$	−13.9690	−0.610822	−0.305411	−	0.952221i	$-0.598794\pi$
$523$	−13.9690	−0.610822	−0.305411	+	0.952221i	$0.598794\pi$
$524$	−14.8236	−0.647571
$525$	20.1863	0.881004
$526$	−0.909980	−0.0396770
$527$	1.06539	0.0464091
$528$	20.9932	0.913612
$529$	−16.2309	−0.705692
$530$	−1.37915	−0.0599066
$531$	−13.4533	−0.583824
$532$	−12.4209	−0.538512
$533$	−18.8936	−0.818374
$534$	−0.352258	−0.0152437
$535$	−71.3547	−3.08493
$536$	−2.17610	−0.0939930
$537$	23.2880	1.00495
$538$	0.802444	0.0345958
$539$	−18.0040	−0.775487
$540$	−7.90542	−0.340195
$541$	−2.79015	−0.119958	−0.0599790	−	0.998200i	$-0.519103\pi$
$541$	−2.79015	−0.119958	−0.0599790	+	0.998200i	$0.519103\pi$
$542$	−0.903316	−0.0388007
$543$	1.61698	0.0693913
$544$	0.609887	0.0261487
$545$	59.5235	2.54971
$546$	−0.207743	−0.00889059
$547$	13.7464	0.587755	0.293877	−	0.955843i	$-0.405054\pi$
$547$	13.7464	0.587755	0.293877	+	0.955843i	$0.405054\pi$
$548$	41.4653	1.77131
$549$	10.8439	0.462807
$550$	2.86068	0.121980
$551$	5.89583	0.251171
$552$	0.529496	0.0225368
$553$	1.89285	0.0804922
$554$	−0.751144	−0.0319131
$555$	−24.8407	−1.05443
$556$	13.9817	0.592955
$557$	20.9519	0.887762	0.443881	−	0.896086i	$-0.353601\pi$
$557$	20.9519	0.887762	0.443881	+	0.896086i	$0.353601\pi$
$558$	0.0542410	0.00229621
$559$	22.0886	0.934248
$560$	29.8500	1.26139
$561$	5.26878	0.222448
$562$	−1.64582	−0.0694248
$563$	42.8573	1.80622	0.903109	−	0.429411i	$-0.141279\pi$
$563$	42.8573	1.80622	0.903109	+	0.429411i	$0.141279\pi$
$564$	−13.5736	−0.571553
$565$	−5.83637	−0.245538
$566$	−0.799570	−0.0336084
$567$	1.89285	0.0794923
$568$	0.129354	0.00542758
$569$	4.96177	0.208008	0.104004	−	0.994577i	$-0.466834\pi$
$569$	4.96177	0.208008	0.104004	+	0.994577i	$0.466834\pi$
$570$	0.661981	0.0277273
$571$	4.32863	0.181147	0.0905737	−	0.995890i	$-0.471130\pi$
$571$	4.32863	0.181147	0.0905737	+	0.995890i	$0.471130\pi$
$572$	22.6865	0.948571
$573$	−8.53278	−0.356462
$574$	0.844617	0.0352536
$575$	−27.7463	−1.15710
$576$	−7.93786	−0.330744
$577$	−40.8018	−1.69860	−0.849301	−	0.527909i	$-0.822976\pi$
$577$	−40.8018	−1.69860	−0.849301	+	0.527909i	$0.822976\pi$
$578$	0.0509119	0.00211765
$579$	−21.0273	−0.873866
$580$	−14.1874	−0.589099
$581$	−24.4326	−1.01364
$582$	0.113671	0.00471183
$583$	−36.0616	−1.49352
$584$	0.702714	0.0290785
$585$	−8.53197	−0.352754
$586$	−0.519893	−0.0214766
$587$	−36.6535	−1.51285	−0.756427	−	0.654079i	$-0.773057\pi$
$587$	−36.6535	−1.51285	−0.756427	+	0.654079i	$0.773057\pi$
$588$	6.82537	0.281473
$589$	3.50007	0.144218
$590$	−2.71086	−0.111604
$591$	18.1465	0.746446
$592$	−25.0078	−1.02781
$593$	1.21468	0.0498807	0.0249404	−	0.999689i	$-0.492060\pi$
$593$	1.21468	0.0498807	0.0249404	+	0.999689i	$0.492060\pi$
$594$	0.268243	0.0110062
$595$	7.49161	0.307126
$596$	5.03354	0.206182
$597$	−8.58119	−0.351205
$598$	0.285545	0.0116768
$599$	10.0949	0.412466	0.206233	−	0.978503i	$-0.433879\pi$
$599$	10.0949	0.412466	0.206233	+	0.978503i	$0.433879\pi$
$600$	−2.17039	−0.0886059
$601$	−17.6006	−0.717943	−0.358972	−	0.933348i	$-0.616873\pi$
$601$	−17.6006	−0.717943	−0.358972	+	0.933348i	$0.616873\pi$
$602$	−0.987444	−0.0402452
$603$	10.6925	0.435433
$604$	−4.79285	−0.195018
$605$	66.3335	2.69684
$606$	−0.392692	−0.0159520
$607$	−7.07116	−0.287010	−0.143505	−	0.989650i	$-0.545837\pi$
$607$	−7.07116	−0.287010	−0.143505	+	0.989650i	$0.545837\pi$
$608$	2.00363	0.0812579
$609$	3.39698	0.137653
$610$	2.18506	0.0884704
$611$	−14.6494	−0.592652
$612$	−1.99741	−0.0807404
$613$	−24.6259	−0.994631	−0.497315	−	0.867570i	$-0.665681\pi$
$613$	−24.6259	−0.994631	−0.497315	+	0.867570i	$0.665681\pi$
$614$	−0.522436	−0.0210838
$615$	34.6883	1.39877
$616$	−2.02966	−0.0817774
$617$	−44.2311	−1.78068	−0.890338	−	0.455300i	$-0.849532\pi$
$617$	−44.2311	−1.78068	−0.890338	+	0.455300i	$0.849532\pi$
$618$	0.321082	0.0129158
$619$	−21.7895	−0.875794	−0.437897	−	0.899025i	$-0.644277\pi$
$619$	−21.7895	−0.875794	−0.437897	+	0.899025i	$0.644277\pi$
$620$	−8.42236	−0.338250
$621$	−2.60175	−0.104404
$622$	−0.156618	−0.00627979
$623$	−13.0966	−0.524705
$624$	−8.58934	−0.343849
$625$	35.4092	1.41637
$626$	−0.345141	−0.0137946
$627$	17.3092	0.691264
$628$	14.2419	0.568315
$629$	−6.27633	−0.250254
$630$	0.381412	0.0151958
$631$	−16.6559	−0.663062	−0.331531	−	0.943444i	$-0.607565\pi$
$631$	−16.6559	−0.663062	−0.331531	+	0.943444i	$0.607565\pi$
$632$	−0.203515	−0.00809541
$633$	24.2509	0.963885
$634$	1.41977	0.0563865
$635$	−12.1566	−0.482419
$636$	13.6711	0.542093
$637$	7.36632	0.291864
$638$	0.481400	0.0190588
$639$	−0.635598	−0.0251439
$640$	−6.42716	−0.254056
$641$	39.3415	1.55390	0.776949	−	0.629564i	$-0.216766\pi$
$641$	39.3415	1.55390	0.776949	+	0.629564i	$0.216766\pi$
$642$	−0.917875	−0.0362256
$643$	−29.6872	−1.17075	−0.585374	−	0.810763i	$-0.699052\pi$
$643$	−29.6872	−1.17075	−0.585374	+	0.810763i	$0.699052\pi$
$644$	9.83667	0.387619
$645$	−40.5542	−1.59682
$646$	0.167258	0.00658068
$647$	10.7626	0.423123	0.211562	−	0.977365i	$-0.432145\pi$
$647$	10.7626	0.423123	0.211562	+	0.977365i	$0.432145\pi$
$648$	−0.203515	−0.00799484
$649$	−70.8825	−2.78238
$650$	−1.17044	−0.0459086
$651$	2.01663	0.0790378
$652$	−18.3389	−0.718207
$653$	−41.0151	−1.60505	−0.802523	−	0.596621i	$-0.796510\pi$
$653$	−41.0151	−1.60505	−0.802523	+	0.596621i	$0.796510\pi$
$654$	0.765683	0.0299406
$655$	29.3728	1.14769
$656$	34.9215	1.36346
$657$	−3.45288	−0.134710
$658$	0.654885	0.0255301
$659$	−41.0426	−1.59879	−0.799397	−	0.600804i	$-0.794847\pi$
$659$	−41.0426	−1.59879	−0.799397	+	0.600804i	$0.794847\pi$
$660$	−41.6519	−1.62130
$661$	−14.7998	−0.575645	−0.287822	−	0.957684i	$-0.592931\pi$
$661$	−14.7998	−0.575645	−0.287822	+	0.957684i	$0.592931\pi$
$662$	1.42632	0.0554353
$663$	−2.15571	−0.0837210
$664$	2.62695	0.101945
$665$	24.6118	0.954404
$666$	−0.319540	−0.0123819
$667$	−4.66919	−0.180792
$668$	−23.4523	−0.907397
$669$	−9.47539	−0.366340
$670$	2.15456	0.0832378
$671$	57.1341	2.20564
$672$	1.15443	0.0445329
$673$	50.4582	1.94502	0.972510	−	0.232862i	$-0.0748092\pi$
$673$	50.4582	1.94502	0.972510	+	0.232862i	$0.0748092\pi$
$674$	−1.33743	−0.0515158
$675$	10.6645	0.410477
$676$	16.6841	0.641698
$677$	−16.6894	−0.641425	−0.320713	−	0.947177i	$-0.603922\pi$
$677$	−16.6894	−0.641425	−0.320713	+	0.947177i	$0.603922\pi$
$678$	−0.0750764	−0.00288329
$679$	4.22619	0.162186
$680$	−0.805482	−0.0308888
$681$	−15.6787	−0.600811
$682$	0.285784	0.0109432
$683$	17.3496	0.663865	0.331932	−	0.943303i	$-0.392299\pi$
$683$	17.3496	0.663865	0.331932	+	0.943303i	$0.392299\pi$
$684$	−6.56198	−0.250904
$685$	−82.1631	−3.13929
$686$	−1.00388	−0.0383284
$687$	18.9379	0.722528
$688$	−40.8269	−1.55651
$689$	14.7546	0.562104
$690$	−0.524255	−0.0199580
$691$	−31.5049	−1.19850	−0.599251	−	0.800562i	$-0.704535\pi$
$691$	−31.5049	−1.19850	−0.599251	+	0.800562i	$0.704535\pi$
$692$	34.5879	1.31483
$693$	9.97301	0.378843
$694$	−0.0734418	−0.00278781
$695$	−27.7045	−1.05089
$696$	−0.365237	−0.0138443
$697$	8.76444	0.331977
$698$	0.895562	0.0338975
$699$	28.1117	1.06328
$700$	−40.3203	−1.52397
$701$	−16.8050	−0.634715	−0.317357	−	0.948306i	$-0.602795\pi$
$701$	−16.8050	−0.634715	−0.317357	+	0.948306i	$0.602795\pi$
$702$	−0.109751	−0.00414230
$703$	−20.6193	−0.777672
$704$	−41.8228	−1.57626
$705$	26.8960	1.01296
$706$	1.79524	0.0675646
$707$	−14.5999	−0.549086
$708$	26.8717	1.00990
$709$	−34.7618	−1.30551	−0.652753	−	0.757571i	$-0.726386\pi$
$709$	−34.7618	−1.30551	−0.652753	+	0.757571i	$0.726386\pi$
$710$	−0.128074	−0.00480652
$711$	1.00000	0.0375029
$712$	1.40812	0.0527715
$713$	−2.77188	−0.103808
$714$	0.0963686	0.00360650
$715$	−44.9531	−1.68115
$716$	−46.5157	−1.73837
$717$	24.0586	0.898484
$718$	1.40572	0.0524610
$719$	2.59739	0.0968663	0.0484332	−	0.998826i	$-0.484577\pi$
$719$	2.59739	0.0968663	0.0484332	+	0.998826i	$0.484577\pi$
$720$	15.7698	0.587707
$721$	11.9375	0.444576
$722$	−0.417841	−0.0155504
$723$	11.1814	0.415841
$724$	−3.22977	−0.120034
$725$	19.1389	0.710802
$726$	0.853284	0.0316683
$727$	27.1767	1.00793	0.503964	−	0.863724i	$-0.331874\pi$
$727$	27.1767	1.00793	0.503964	+	0.863724i	$0.331874\pi$
$728$	0.830434	0.0307779
$729$	1.00000	0.0370370
$730$	−0.695759	−0.0257512
$731$	−10.2465	−0.378982
$732$	−21.6597	−0.800565
$733$	11.0733	0.409001	0.204501	−	0.978866i	$-0.434443\pi$
$733$	11.0733	0.409001	0.204501	+	0.978866i	$0.434443\pi$
$734$	−0.648617	−0.0239409
$735$	−13.5244	−0.498855
$736$	−1.58677	−0.0584891
$737$	56.3366	2.07518
$738$	0.446214	0.0164254
$739$	39.7289	1.46145	0.730725	−	0.682672i	$-0.239182\pi$
$739$	39.7289	1.46145	0.730725	+	0.682672i	$0.239182\pi$
$740$	49.6171	1.82396
$741$	−7.08205	−0.260166
$742$	−0.659585	−0.0242141
$743$	10.0844	0.369959	0.184980	−	0.982742i	$-0.440778\pi$
$743$	10.0844	0.369959	0.184980	+	0.982742i	$0.440778\pi$
$744$	−0.216823	−0.00794913
$745$	−9.97391	−0.365416
$746$	0.749064	0.0274252
$747$	−12.9078	−0.472273
$748$	−10.5239	−0.384792
$749$	−34.1257	−1.24692
$750$	1.14140	0.0416782
$751$	13.6380	0.497659	0.248830	−	0.968547i	$-0.419954\pi$
$751$	13.6380	0.497659	0.248830	+	0.968547i	$0.419954\pi$
$752$	27.0769	0.987392
$753$	13.3467	0.486381
$754$	−0.196964	−0.00717301
$755$	9.49698	0.345630
$756$	−3.78080	−0.137506
$757$	4.64496	0.168824	0.0844119	−	0.996431i	$-0.473099\pi$
$757$	4.64496	0.168824	0.0844119	+	0.996431i	$0.473099\pi$
$758$	0.238495	0.00866251
$759$	−13.7080	−0.497570
$760$	−2.64621	−0.0959881
$761$	25.3506	0.918958	0.459479	−	0.888189i	$-0.348036\pi$
$761$	25.3506	0.918958	0.459479	+	0.888189i	$0.348036\pi$
$762$	−0.156377	−0.00566492
$763$	28.4673	1.03059
$764$	17.0434	0.616610
$765$	3.95784	0.143096
$766$	1.38249	0.0499514
$767$	29.0015	1.04718
$768$	15.7930	0.569882
$769$	26.6305	0.960322	0.480161	−	0.877180i	$-0.340578\pi$
$769$	26.6305	0.960322	0.480161	+	0.877180i	$0.340578\pi$
$770$	2.00957	0.0724200
$771$	16.1906	0.583090
$772$	42.0001	1.51162
$773$	−0.763296	−0.0274538	−0.0137269	−	0.999906i	$-0.504370\pi$
$773$	−0.763296	−0.0274538	−0.0137269	+	0.999906i	$0.504370\pi$
$774$	−0.521670	−0.0187510
$775$	11.3619	0.408130
$776$	−0.454391	−0.0163117
$777$	−11.8802	−0.426198
$778$	−0.374257	−0.0134178
$779$	28.7934	1.03163
$780$	17.0418	0.610195
$781$	−3.34883	−0.119830
$782$	−0.132460	−0.00473675
$783$	1.79464	0.0641351
$784$	−13.6153	−0.486262
$785$	−28.2202	−1.00722
$786$	0.377838	0.0134770
$787$	11.1190	0.396351	0.198175	−	0.980167i	$-0.436498\pi$
$787$	11.1190	0.396351	0.198175	+	0.980167i	$0.436498\pi$
$788$	−36.2459	−1.29121
$789$	−17.8736	−0.636318
$790$	0.201501	0.00716909
$791$	−2.79127	−0.0992460
$792$	−1.07228	−0.0381017
$793$	−23.3763	−0.830119
$794$	0.0950222	0.00337221
$795$	−27.0890	−0.960749
$796$	17.1401	0.607516
$797$	−46.4224	−1.64436	−0.822182	−	0.569224i	$-0.807244\pi$
$797$	−46.4224	−1.64436	−0.822182	+	0.569224i	$0.807244\pi$
$798$	0.316595	0.0112073
$799$	6.79563	0.240412
$800$	6.50415	0.229956
$801$	−6.91898	−0.244470
$802$	0.793679	0.0280258
$803$	−18.1924	−0.641998
$804$	−21.3573	−0.753215
$805$	−19.4913	−0.686977
$806$	−0.116928	−0.00411862
$807$	15.7614	0.554829
$808$	1.56975	0.0552236
$809$	−42.7065	−1.50148	−0.750741	−	0.660597i	$-0.770303\pi$
$809$	−42.7065	−1.50148	−0.750741	+	0.660597i	$0.770303\pi$
$810$	0.201501	0.00708003
$811$	−28.4024	−0.997343	−0.498672	−	0.866791i	$-0.666179\pi$
$811$	−28.4024	−0.997343	−0.498672	+	0.866791i	$0.666179\pi$
$812$	−6.78516	−0.238113
$813$	−17.7427	−0.622265
$814$	−1.68358	−0.0590096
$815$	36.3383	1.27288
$816$	3.98445	0.139484
$817$	−33.6624	−1.17770
$818$	1.01139	0.0353626
$819$	−4.08045	−0.142582
$820$	−69.2866	−2.41959
$821$	17.2823	0.603156	0.301578	−	0.953441i	$-0.402487\pi$
$821$	17.2823	0.603156	0.301578	+	0.953441i	$0.402487\pi$
$822$	−1.05691	−0.0368639
$823$	−28.3635	−0.988688	−0.494344	−	0.869266i	$-0.664592\pi$
$823$	−28.3635	−0.988688	−0.494344	+	0.869266i	$0.664592\pi$
$824$	−1.28350	−0.0447127
$825$	56.1889	1.95625
$826$	−1.29648	−0.0451102
$827$	42.4452	1.47597	0.737983	−	0.674820i	$-0.235779\pi$
$827$	42.4452	1.47597	0.737983	+	0.674820i	$0.235779\pi$
$828$	5.19675	0.180599
$829$	−32.3382	−1.12315	−0.561576	−	0.827425i	$-0.689805\pi$
$829$	−32.3382	−1.12315	−0.561576	+	0.827425i	$0.689805\pi$
$830$	−2.60094	−0.0902801
$831$	−14.7538	−0.511804
$832$	17.1118	0.593243
$833$	−3.41711	−0.118396
$834$	−0.356378	−0.0123404
$835$	46.4705	1.60818
$836$	−34.5736	−1.19575
$837$	1.06539	0.0368253
$838$	1.26350	0.0436468
$839$	13.1367	0.453530	0.226765	−	0.973950i	$-0.427185\pi$
$839$	13.1367	0.453530	0.226765	+	0.973950i	$0.427185\pi$
$840$	−1.52466	−0.0526057
$841$	−25.7793	−0.888940
$842$	0.0483633	0.00166671
$843$	−32.3269	−1.11340
$844$	−48.4389	−1.66733
$845$	−33.0595	−1.13728
$846$	0.345978	0.0118950
$847$	31.7242	1.09006
$848$	−27.2712	−0.936496
$849$	−15.7050	−0.538994
$850$	0.542950	0.0186230
$851$	16.3294	0.559765
$852$	1.26955	0.0434940
$853$	−23.1614	−0.793030	−0.396515	−	0.918028i	$-0.629781\pi$
$853$	−23.1614	−0.793030	−0.396515	+	0.918028i	$0.629781\pi$
$854$	1.04501	0.0357596
$855$	13.0025	0.444676
$856$	3.66912	0.125408
$857$	−20.1442	−0.688113	−0.344056	−	0.938949i	$-0.611801\pi$
$857$	−20.1442	−0.688113	−0.344056	+	0.938949i	$0.611801\pi$
$858$	−0.578256	−0.0197413
$859$	9.63077	0.328598	0.164299	−	0.986411i	$-0.447464\pi$
$859$	9.63077	0.328598	0.164299	+	0.986411i	$0.447464\pi$
$860$	81.0032	2.76219
$861$	16.5898	0.565378
$862$	−1.91650	−0.0652764
$863$	25.8298	0.879257	0.439629	−	0.898180i	$-0.355110\pi$
$863$	25.8298	0.879257	0.439629	+	0.898180i	$0.355110\pi$
$864$	0.609887	0.0207488
$865$	−68.5355	−2.33028
$866$	1.36259	0.0463026
$867$	1.00000	0.0339618
$868$	−4.02803	−0.136720
$869$	5.26878	0.178731
$870$	0.361622	0.0122601
$871$	−23.0500	−0.781021
$872$	−3.06075	−0.103650
$873$	2.23271	0.0755658
$874$	−0.435163	−0.0147196
$875$	42.4363	1.43461
$876$	6.89681	0.233022
$877$	−0.660738	−0.0223116	−0.0111558	−	0.999938i	$-0.503551\pi$
$877$	−0.660738	−0.0223116	−0.0111558	+	0.999938i	$0.503551\pi$
$878$	1.85506	0.0626051
$879$	−10.2116	−0.344430
$880$	83.0878	2.80089
$881$	25.7400	0.867203	0.433601	−	0.901105i	$-0.357243\pi$
$881$	25.7400	0.867203	0.433601	+	0.901105i	$0.357243\pi$
$882$	−0.173972	−0.00585793
$883$	42.7441	1.43846	0.719228	−	0.694775i	$-0.244496\pi$
$883$	42.7441	1.43846	0.719228	+	0.694775i	$0.244496\pi$
$884$	4.30584	0.144821
$885$	−53.2461	−1.78985
$886$	0.564599	0.0189681
$887$	−41.2625	−1.38546	−0.692729	−	0.721198i	$-0.743592\pi$
$887$	−41.2625	−1.38546	−0.692729	+	0.721198i	$0.743592\pi$
$888$	1.27733	0.0428644
$889$	−5.81392	−0.194993
$890$	−1.39418	−0.0467331
$891$	5.26878	0.176511
$892$	18.9262	0.633697
$893$	22.3253	0.747089
$894$	−0.128300	−0.00429099
$895$	92.1703	3.08091
$896$	−3.07381	−0.102689
$897$	5.60862	0.187266
$898$	−0.733311	−0.0244709
$899$	1.91199	0.0637685
$900$	−21.3014	−0.710046
$901$	−6.84440	−0.228020
$902$	2.35100	0.0782798
$903$	−19.3952	−0.645431
$904$	0.300111	0.00998155
$905$	6.39976	0.212735
$906$	0.122165	0.00405865
$907$	16.0894	0.534241	0.267120	−	0.963663i	$-0.413928\pi$
$907$	16.0894	0.534241	0.267120	+	0.963663i	$0.413928\pi$
$908$	31.3168	1.03929
$909$	−7.71317	−0.255830
$910$	−0.822214	−0.0272561
$911$	36.7375	1.21717	0.608584	−	0.793489i	$-0.291738\pi$
$911$	36.7375	1.21717	0.608584	+	0.793489i	$0.291738\pi$
$912$	13.0899	0.433451
$913$	−68.0086	−2.25075
$914$	0.128823	0.00426109
$915$	42.9185	1.41884
$916$	−37.8268	−1.24983
$917$	14.0476	0.463894
$918$	0.0509119	0.00168034
$919$	−3.82043	−0.126024	−0.0630122	−	0.998013i	$-0.520071\pi$
$919$	−3.82043	−0.126024	−0.0630122	+	0.998013i	$0.520071\pi$
$920$	2.09566	0.0690918
$921$	−10.2616	−0.338131
$922$	−1.33509	−0.0439688
$923$	1.37017	0.0450996
$924$	−19.9202	−0.655326
$925$	−66.9340	−2.20078
$926$	−1.70375	−0.0559886
$927$	6.30662	0.207137
$928$	1.09453	0.0359296
$929$	−27.1946	−0.892227	−0.446113	−	0.894976i	$-0.647192\pi$
$929$	−27.1946	−0.892227	−0.446113	+	0.894976i	$0.647192\pi$
$930$	0.214677	0.00703955
$931$	−11.2261	−0.367919
$932$	−56.1505	−1.83927
$933$	−3.07625	−0.100712
$934$	−0.437902	−0.0143286
$935$	20.8530	0.681966
$936$	0.438721	0.0143400
$937$	34.9947	1.14323	0.571613	−	0.820523i	$-0.306318\pi$
$937$	34.9947	1.14323	0.571613	+	0.820523i	$0.306318\pi$
$938$	1.03042	0.0336445
$939$	−6.77918	−0.221230
$940$	−53.7223	−1.75223
$941$	−12.8381	−0.418509	−0.209255	−	0.977861i	$-0.567104\pi$
$941$	−12.8381	−0.418509	−0.209255	+	0.977861i	$0.567104\pi$
$942$	−0.363012	−0.0118276
$943$	−22.8028	−0.742563
$944$	−53.6041	−1.74466
$945$	7.49161	0.243702
$946$	−2.74856	−0.0893635
$947$	14.2263	0.462292	0.231146	−	0.972919i	$-0.425752\pi$
$947$	14.2263	0.462292	0.231146	+	0.972919i	$0.425752\pi$
$948$	−1.99741	−0.0648728
$949$	7.44342	0.241624
$950$	1.78373	0.0578717
$951$	27.8869	0.904295
$952$	−0.385225	−0.0124852
$953$	−5.76547	−0.186762	−0.0933810	−	0.995630i	$-0.529767\pi$
$953$	−5.76547	−0.186762	−0.0933810	+	0.995630i	$0.529767\pi$
$954$	−0.348461	−0.0112818
$955$	−33.7714	−1.09282
$956$	−48.0548	−1.55420
$957$	9.45555	0.305655
$958$	−1.12415	−0.0363197
$959$	−39.2948	−1.26889
$960$	−31.4168	−1.01397
$961$	−29.8649	−0.963385
$962$	0.688836	0.0222090
$963$	−18.0287	−0.580967
$964$	−22.3338	−0.719325
$965$	−83.2228	−2.67904
$966$	−0.250727	−0.00806700
$967$	44.3428	1.42597	0.712984	−	0.701181i	$-0.247343\pi$
$967$	44.3428	1.42597	0.712984	+	0.701181i	$0.247343\pi$
$968$	−3.41092	−0.109631
$969$	3.28525	0.105537
$970$	0.449894	0.0144452
$971$	46.5023	1.49233	0.746165	−	0.665761i	$-0.231893\pi$
$971$	46.5023	1.49233	0.746165	+	0.665761i	$0.231893\pi$
$972$	−1.99741	−0.0640669
$973$	−13.2498	−0.424769
$974$	−0.194802	−0.00624185
$975$	−22.9896	−0.736257
$976$	43.2070	1.38302
$977$	1.00688	0.0322129	0.0161064	−	0.999870i	$-0.494873\pi$
$977$	1.00688	0.0322129	0.0161064	+	0.999870i	$0.494873\pi$
$978$	0.467440	0.0149471
$979$	−36.4546	−1.16509
$980$	27.0137	0.862922
$981$	15.0394	0.480170
$982$	−0.914185	−0.0291728
$983$	−7.22420	−0.230416	−0.115208	−	0.993341i	$-0.536753\pi$
$983$	−7.22420	−0.230416	−0.115208	+	0.993341i	$0.536753\pi$
$984$	−1.78370	−0.0568622
$985$	71.8209	2.28840
$986$	0.0913684	0.00290976
$987$	12.8631	0.409438
$988$	14.1458	0.450036
$989$	26.6589	0.847703
$990$	1.06166	0.0337419
$991$	−27.3165	−0.867738	−0.433869	−	0.900976i	$-0.642852\pi$
$991$	−27.3165	−0.867738	−0.433869	+	0.900976i	$0.642852\pi$
$992$	0.649768	0.0206301
$993$	28.0154	0.889041
$994$	−0.0612517	−0.00194279
$995$	−33.9630	−1.07670
$996$	25.7822	0.816941
$997$	−36.6981	−1.16224	−0.581120	−	0.813818i	$-0.697385\pi$
$997$	−36.6981	−1.16224	−0.581120	+	0.813818i	$0.697385\pi$
$998$	−1.06372	−0.0336713
$999$	−6.27633	−0.198574

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	4029.2.a.k.1.16	✓	31

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
4029.2.a.k.1.16	✓	31	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:	\( N \)	\(=\)	\( 4029 = 3 \cdot 17 \cdot 79 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	4029.a (trivial)

\(f(q)\)	\(=\)	\(q+0.0509119 q^{2} +1.00000 q^{3} -1.99741 q^{4} +3.95784 q^{5} +0.0509119 q^{6} +1.89285 q^{7} -0.203515 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q+0.0509119 q^{2} +1.00000 q^{3} -1.99741 q^{4} +3.95784 q^{5} +0.0509119 q^{6} +1.89285 q^{7} -0.203515 q^{8} +1.00000 q^{9} +0.201501 q^{10} +5.26878 q^{11} -1.99741 q^{12} -2.15571 q^{13} +0.0963686 q^{14} +3.95784 q^{15} +3.98445 q^{16} +1.00000 q^{17} +0.0509119 q^{18} +3.28525 q^{19} -7.90542 q^{20} +1.89285 q^{21} +0.268243 q^{22} -2.60175 q^{23} -0.203515 q^{24} +10.6645 q^{25} -0.109751 q^{26} +1.00000 q^{27} -3.78080 q^{28} +1.79464 q^{29} +0.201501 q^{30} +1.06539 q^{31} +0.609887 q^{32} +5.26878 q^{33} +0.0509119 q^{34} +7.49161 q^{35} -1.99741 q^{36} -6.27633 q^{37} +0.167258 q^{38} -2.15571 q^{39} -0.805482 q^{40} +8.76444 q^{41} +0.0963686 q^{42} -10.2465 q^{43} -10.5239 q^{44} +3.95784 q^{45} -0.132460 q^{46} +6.79563 q^{47} +3.98445 q^{48} -3.41711 q^{49} +0.542950 q^{50} +1.00000 q^{51} +4.30584 q^{52} -6.84440 q^{53} +0.0509119 q^{54} +20.8530 q^{55} -0.385225 q^{56} +3.28525 q^{57} +0.0913684 q^{58} -13.4533 q^{59} -7.90542 q^{60} +10.8439 q^{61} +0.0542410 q^{62} +1.89285 q^{63} -7.93786 q^{64} -8.53197 q^{65} +0.268243 q^{66} +10.6925 q^{67} -1.99741 q^{68} -2.60175 q^{69} +0.381412 q^{70} -0.635598 q^{71} -0.203515 q^{72} -3.45288 q^{73} -0.319540 q^{74} +10.6645 q^{75} -6.56198 q^{76} +9.97301 q^{77} -0.109751 q^{78} +1.00000 q^{79} +15.7698 q^{80} +1.00000 q^{81} +0.446214 q^{82} -12.9078 q^{83} -3.78080 q^{84} +3.95784 q^{85} -0.521670 q^{86} +1.79464 q^{87} -1.07228 q^{88} -6.91898 q^{89} +0.201501 q^{90} -4.08045 q^{91} +5.19675 q^{92} +1.06539 q^{93} +0.345978 q^{94} +13.0025 q^{95} +0.609887 q^{96} +2.23271 q^{97} -0.173972 q^{98} +5.26878 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 31 q + 4 q^{2} + 31 q^{3} + 34 q^{4} + 11 q^{5} + 4 q^{6} + 4 q^{7} + 12 q^{8} + 31 q^{9}+O(q^{10}) \) 31 * q + 4 * q^2 + 31 * q^3 + 34 * q^4 + 11 * q^5 + 4 * q^6 + 4 * q^7 + 12 * q^8 + 31 * q^9	\( 31 q + 4 q^{2} + 31 q^{3} + 34 q^{4} + 11 q^{5} + 4 q^{6} + 4 q^{7} + 12 q^{8} + 31 q^{9} + 5 q^{10} + 26 q^{11} + 34 q^{12} + 7 q^{13} + 19 q^{14} + 11 q^{15} + 40 q^{16} + 31 q^{17} + 4 q^{18} + 32 q^{19} + 23 q^{20} + 4 q^{21} + 2 q^{22} + 29 q^{23} + 12 q^{24} + 32 q^{25} + 13 q^{26} + 31 q^{27} - 13 q^{28} + 25 q^{29} + 5 q^{30} + 22 q^{31} + 28 q^{32} + 26 q^{33} + 4 q^{34} + 20 q^{35} + 34 q^{36} - 4 q^{37} + 19 q^{38} + 7 q^{39} - 3 q^{40} + 33 q^{41} + 19 q^{42} + 6 q^{43} + 30 q^{44} + 11 q^{45} - 11 q^{46} + 23 q^{47} + 40 q^{48} + 31 q^{49} + 6 q^{50} + 31 q^{51} - 7 q^{52} + 12 q^{53} + 4 q^{54} + 40 q^{56} + 32 q^{57} + 9 q^{58} + 27 q^{59} + 23 q^{60} - 4 q^{61} + 25 q^{62} + 4 q^{63} + 10 q^{64} + 54 q^{65} + 2 q^{66} + 34 q^{68} + 29 q^{69} - 59 q^{70} + 35 q^{71} + 12 q^{72} + 5 q^{73} + 48 q^{74} + 32 q^{75} + 32 q^{76} + 42 q^{77} + 13 q^{78} + 31 q^{79} + 24 q^{80} + 31 q^{81} + 5 q^{82} + 67 q^{83} - 13 q^{84} + 11 q^{85} - 20 q^{86} + 25 q^{87} - 7 q^{88} + 22 q^{89} + 5 q^{90} + 16 q^{91} + 57 q^{92} + 22 q^{93} + 45 q^{94} + 73 q^{95} + 28 q^{96} - 13 q^{97} - 19 q^{98} + 26 q^{99}+O(q^{100}) \) 31 * q + 4 * q^2 + 31 * q^3 + 34 * q^4 + 11 * q^5 + 4 * q^6 + 4 * q^7 + 12 * q^8 + 31 * q^9 + 5 * q^10 + 26 * q^11 + 34 * q^12 + 7 * q^13 + 19 * q^14 + 11 * q^15 + 40 * q^16 + 31 * q^17 + 4 * q^18 + 32 * q^19 + 23 * q^20 + 4 * q^21 + 2 * q^22 + 29 * q^23 + 12 * q^24 + 32 * q^25 + 13 * q^26 + 31 * q^27 - 13 * q^28 + 25 * q^29 + 5 * q^30 + 22 * q^31 + 28 * q^32 + 26 * q^33 + 4 * q^34 + 20 * q^35 + 34 * q^36 - 4 * q^37 + 19 * q^38 + 7 * q^39 - 3 * q^40 + 33 * q^41 + 19 * q^42 + 6 * q^43 + 30 * q^44 + 11 * q^45 - 11 * q^46 + 23 * q^47 + 40 * q^48 + 31 * q^49 + 6 * q^50 + 31 * q^51 - 7 * q^52 + 12 * q^53 + 4 * q^54 + 40 * q^56 + 32 * q^57 + 9 * q^58 + 27 * q^59 + 23 * q^60 - 4 * q^61 + 25 * q^62 + 4 * q^63 + 10 * q^64 + 54 * q^65 + 2 * q^66 + 34 * q^68 + 29 * q^69 - 59 * q^70 + 35 * q^71 + 12 * q^72 + 5 * q^73 + 48 * q^74 + 32 * q^75 + 32 * q^76 + 42 * q^77 + 13 * q^78 + 31 * q^79 + 24 * q^80 + 31 * q^81 + 5 * q^82 + 67 * q^83 - 13 * q^84 + 11 * q^85 - 20 * q^86 + 25 * q^87 - 7 * q^88 + 22 * q^89 + 5 * q^90 + 16 * q^91 + 57 * q^92 + 22 * q^93 + 45 * q^94 + 73 * q^95 + 28 * q^96 - 13 * q^97 - 19 * q^98 + 26 * q^99

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