LMFDB - Embedded newform 4011.2.a.m.1.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [4011,2,Mod(1,4011)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(4011, 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("4011.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 4011 = 3 \cdot 7 \cdot 191 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	4011.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:	$32.0279962507$
Analytic rank:	$0$
Dimension:	$29$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.3
Character	$\chi$	$=$	4011.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-2.32184 q^{2} +1.00000 q^{3} +3.39092 q^{4} +1.73819 q^{5} -2.32184 q^{6} -1.00000 q^{7} -3.22949 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q-2.32184 q^{2} +1.00000 q^{3} +3.39092 q^{4} +1.73819 q^{5} -2.32184 q^{6} -1.00000 q^{7} -3.22949 q^{8} +1.00000 q^{9} -4.03578 q^{10} +4.22465 q^{11} +3.39092 q^{12} +0.457541 q^{13} +2.32184 q^{14} +1.73819 q^{15} +0.716504 q^{16} -7.83037 q^{17} -2.32184 q^{18} +5.51372 q^{19} +5.89405 q^{20} -1.00000 q^{21} -9.80895 q^{22} -1.27133 q^{23} -3.22949 q^{24} -1.97871 q^{25} -1.06233 q^{26} +1.00000 q^{27} -3.39092 q^{28} +8.13218 q^{29} -4.03578 q^{30} -3.47424 q^{31} +4.79538 q^{32} +4.22465 q^{33} +18.1808 q^{34} -1.73819 q^{35} +3.39092 q^{36} -1.49179 q^{37} -12.8020 q^{38} +0.457541 q^{39} -5.61346 q^{40} -12.5585 q^{41} +2.32184 q^{42} +9.72398 q^{43} +14.3255 q^{44} +1.73819 q^{45} +2.95183 q^{46} +10.0655 q^{47} +0.716504 q^{48} +1.00000 q^{49} +4.59424 q^{50} -7.83037 q^{51} +1.55148 q^{52} +5.02634 q^{53} -2.32184 q^{54} +7.34324 q^{55} +3.22949 q^{56} +5.51372 q^{57} -18.8816 q^{58} +8.18964 q^{59} +5.89405 q^{60} -10.5284 q^{61} +8.06661 q^{62} -1.00000 q^{63} -12.5671 q^{64} +0.795291 q^{65} -9.80895 q^{66} +7.01185 q^{67} -26.5522 q^{68} -1.27133 q^{69} +4.03578 q^{70} +6.60893 q^{71} -3.22949 q^{72} -11.4659 q^{73} +3.46369 q^{74} -1.97871 q^{75} +18.6966 q^{76} -4.22465 q^{77} -1.06233 q^{78} +16.4460 q^{79} +1.24542 q^{80} +1.00000 q^{81} +29.1588 q^{82} -0.738747 q^{83} -3.39092 q^{84} -13.6106 q^{85} -22.5775 q^{86} +8.13218 q^{87} -13.6435 q^{88} +14.9928 q^{89} -4.03578 q^{90} -0.457541 q^{91} -4.31099 q^{92} -3.47424 q^{93} -23.3705 q^{94} +9.58388 q^{95} +4.79538 q^{96} -8.34107 q^{97} -2.32184 q^{98} +4.22465 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 29 q + 6 q^{2} + 29 q^{3} + 40 q^{4} + 22 q^{5} + 6 q^{6} - 29 q^{7} + 15 q^{8} + 29 q^{9}+O(q^{10}) $ 29 * q + 6 * q^2 + 29 * q^3 + 40 * q^4 + 22 * q^5 + 6 * q^6 - 29 * q^7 + 15 * q^8 + 29 * q^9	\( 29 q + 6 q^{2} + 29 q^{3} + 40 q^{4} + 22 q^{5} + 6 q^{6} - 29 q^{7} + 15 q^{8} + 29 q^{9} + 11 q^{11} + 40 q^{12} + 13 q^{13} - 6 q^{14} + 22 q^{15} + 58 q^{16} + 17 q^{17} + 6 q^{18} + 3 q^{19} + 52 q^{20} - 29 q^{21} + 17 q^{22} + 36 q^{23} + 15 q^{24} + 57 q^{25} + 25 q^{26} + 29 q^{27} - 40 q^{28} + 20 q^{29} + 6 q^{31} + 46 q^{32} + 11 q^{33} + 18 q^{34} - 22 q^{35} + 40 q^{36} + 22 q^{37} + 8 q^{38} + 13 q^{39} + 6 q^{40} + 26 q^{41} - 6 q^{42} + 21 q^{43} + 22 q^{44} + 22 q^{45} + 28 q^{46} + 41 q^{47} + 58 q^{48} + 29 q^{49} + 18 q^{50} + 17 q^{51} + 2 q^{52} + 37 q^{53} + 6 q^{54} + 7 q^{55} - 15 q^{56} + 3 q^{57} + 9 q^{58} + 27 q^{59} + 52 q^{60} + 20 q^{61} - 12 q^{62} - 29 q^{63} + 59 q^{64} + 3 q^{65} + 17 q^{66} + 30 q^{67} + 33 q^{68} + 36 q^{69} + 68 q^{71} + 15 q^{72} + q^{73} + 21 q^{74} + 57 q^{75} + 11 q^{76} - 11 q^{77} + 25 q^{78} + 34 q^{79} + 110 q^{80} + 29 q^{81} - 49 q^{82} + 13 q^{83} - 40 q^{84} + 27 q^{85} + 35 q^{86} + 20 q^{87} + 17 q^{88} + 61 q^{89} - 13 q^{91} + 86 q^{92} + 6 q^{93} - 19 q^{94} + 25 q^{95} + 46 q^{96} - 3 q^{97} + 6 q^{98} + 11 q^{99}+O(q^{100}) \) 29 * q + 6 * q^2 + 29 * q^3 + 40 * q^4 + 22 * q^5 + 6 * q^6 - 29 * q^7 + 15 * q^8 + 29 * q^9 + 11 * q^11 + 40 * q^12 + 13 * q^13 - 6 * q^14 + 22 * q^15 + 58 * q^16 + 17 * q^17 + 6 * q^18 + 3 * q^19 + 52 * q^20 - 29 * q^21 + 17 * q^22 + 36 * q^23 + 15 * q^24 + 57 * q^25 + 25 * q^26 + 29 * q^27 - 40 * q^28 + 20 * q^29 + 6 * q^31 + 46 * q^32 + 11 * q^33 + 18 * q^34 - 22 * q^35 + 40 * q^36 + 22 * q^37 + 8 * q^38 + 13 * q^39 + 6 * q^40 + 26 * q^41 - 6 * q^42 + 21 * q^43 + 22 * q^44 + 22 * q^45 + 28 * q^46 + 41 * q^47 + 58 * q^48 + 29 * q^49 + 18 * q^50 + 17 * q^51 + 2 * q^52 + 37 * q^53 + 6 * q^54 + 7 * q^55 - 15 * q^56 + 3 * q^57 + 9 * q^58 + 27 * q^59 + 52 * q^60 + 20 * q^61 - 12 * q^62 - 29 * q^63 + 59 * q^64 + 3 * q^65 + 17 * q^66 + 30 * q^67 + 33 * q^68 + 36 * q^69 + 68 * q^71 + 15 * q^72 + q^73 + 21 * q^74 + 57 * q^75 + 11 * q^76 - 11 * q^77 + 25 * q^78 + 34 * q^79 + 110 * q^80 + 29 * q^81 - 49 * q^82 + 13 * q^83 - 40 * q^84 + 27 * q^85 + 35 * q^86 + 20 * q^87 + 17 * q^88 + 61 * q^89 - 13 * q^91 + 86 * q^92 + 6 * q^93 - 19 * q^94 + 25 * q^95 + 46 * q^96 - 3 * q^97 + 6 * q^98 + 11 * 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 $

$2$	−2.32184	−1.64179	−0.820893	−	0.571082i	$-0.806524\pi$
$2$	−2.32184	−1.64179	−0.820893	+	0.571082i	$0.806524\pi$
$3$	1.00000	0.577350
$3$	1.00000	0.577350
$4$	3.39092	1.69546
$5$	1.73819	0.777341	0.388670	−	0.921377i	$-0.372935\pi$
$5$	1.73819	0.777341	0.388670	+	0.921377i	$0.372935\pi$
$6$	−2.32184	−0.947885
$7$	−1.00000	−0.377964
$7$	−1.00000	−0.377964
$8$	−3.22949	−1.14180
$9$	1.00000	0.333333
$10$	−4.03578	−1.27623
$11$	4.22465	1.27378	0.636891	−	0.770954i	$-0.280220\pi$
$11$	4.22465	1.27378	0.636891	+	0.770954i	$0.280220\pi$
$12$	3.39092	0.978875
$13$	0.457541	0.126899	0.0634495	−	0.997985i	$-0.479790\pi$
$13$	0.457541	0.126899	0.0634495	+	0.997985i	$0.479790\pi$
$14$	2.32184	0.620537
$15$	1.73819	0.448798
$16$	0.716504	0.179126
$17$	−7.83037	−1.89914	−0.949572	−	0.313550i	$-0.898482\pi$
$17$	−7.83037	−1.89914	−0.949572	+	0.313550i	$0.898482\pi$
$18$	−2.32184	−0.547262
$19$	5.51372	1.26493	0.632467	−	0.774587i	$-0.282042\pi$
$19$	5.51372	1.26493	0.632467	+	0.774587i	$0.282042\pi$
$20$	5.89405	1.31795
$21$	−1.00000	−0.218218
$22$	−9.80895	−2.09128
$23$	−1.27133	−0.265091	−0.132546	−	0.991177i	$-0.542315\pi$
$23$	−1.27133	−0.265091	−0.132546	+	0.991177i	$0.542315\pi$
$24$	−3.22949	−0.659217
$25$	−1.97871	−0.395742
$26$	−1.06233	−0.208341
$27$	1.00000	0.192450
$28$	−3.39092	−0.640824
$29$	8.13218	1.51011	0.755054	−	0.655663i	$-0.227611\pi$
$29$	8.13218	1.51011	0.755054	+	0.655663i	$0.227611\pi$
$30$	−4.03578	−0.736830
$31$	−3.47424	−0.623991	−0.311996	−	0.950084i	$-0.600997\pi$
$31$	−3.47424	−0.623991	−0.311996	+	0.950084i	$0.600997\pi$
$32$	4.79538	0.847711
$33$	4.22465	0.735418
$34$	18.1808	3.11799
$35$	−1.73819	−0.293807
$36$	3.39092	0.565154
$37$	−1.49179	−0.245249	−0.122624	−	0.992453i	$-0.539131\pi$
$37$	−1.49179	−0.245249	−0.122624	+	0.992453i	$0.539131\pi$
$38$	−12.8020	−2.07675
$39$	0.457541	0.0732651
$40$	−5.61346	−0.887565
$41$	−12.5585	−1.96131	−0.980655	−	0.195747i	$-0.937287\pi$
$41$	−12.5585	−1.96131	−0.980655	+	0.195747i	$0.937287\pi$
$42$	2.32184	0.358267
$43$	9.72398	1.48289	0.741446	−	0.671012i	$-0.234140\pi$
$43$	9.72398	1.48289	0.741446	+	0.671012i	$0.234140\pi$
$44$	14.3255	2.15965
$45$	1.73819	0.259114
$46$	2.95183	0.435223
$47$	10.0655	1.46821	0.734103	−	0.679038i	$-0.237603\pi$
$47$	10.0655	1.46821	0.734103	+	0.679038i	$0.237603\pi$
$48$	0.716504	0.103419
$49$	1.00000	0.142857
$50$	4.59424	0.649723
$51$	−7.83037	−1.09647
$52$	1.55148	0.215152
$53$	5.02634	0.690421	0.345210	−	0.938525i	$-0.387808\pi$
$53$	5.02634	0.690421	0.345210	+	0.938525i	$0.387808\pi$
$54$	−2.32184	−0.315962
$55$	7.34324	0.990162
$56$	3.22949	0.431559
$57$	5.51372	0.730311
$58$	−18.8816	−2.47927
$59$	8.18964	1.06620	0.533100	−	0.846052i	$-0.321027\pi$
$59$	8.18964	1.06620	0.533100	+	0.846052i	$0.321027\pi$
$60$	5.89405	0.760919
$61$	−10.5284	−1.34802	−0.674012	−	0.738721i	$-0.735430\pi$
$61$	−10.5284	−1.34802	−0.674012	+	0.738721i	$0.735430\pi$
$62$	8.06661	1.02446
$63$	−1.00000	−0.125988
$64$	−12.5671	−1.57089
$65$	0.795291	0.0986437
$66$	−9.80895	−1.20740
$67$	7.01185	0.856634	0.428317	−	0.903629i	$-0.359107\pi$
$67$	7.01185	0.856634	0.428317	+	0.903629i	$0.359107\pi$
$68$	−26.5522	−3.21992
$69$	−1.27133	−0.153050
$70$	4.03578	0.482368
$71$	6.60893	0.784336	0.392168	−	0.919894i	$-0.371725\pi$
$71$	6.60893	0.784336	0.392168	+	0.919894i	$0.371725\pi$
$72$	−3.22949	−0.380599
$73$	−11.4659	−1.34198	−0.670991	−	0.741466i	$-0.734131\pi$
$73$	−11.4659	−1.34198	−0.670991	+	0.741466i	$0.734131\pi$
$74$	3.46369	0.402646
$75$	−1.97871	−0.228482
$76$	18.6966	2.14465
$77$	−4.22465	−0.481444
$78$	−1.06233	−0.120286
$79$	16.4460	1.85032	0.925160	−	0.379578i	$-0.123931\pi$
$79$	16.4460	1.85032	0.925160	+	0.379578i	$0.123931\pi$
$80$	1.24542	0.139242
$81$	1.00000	0.111111
$82$	29.1588	3.22005
$83$	−0.738747	−0.0810881	−0.0405440	−	0.999178i	$-0.512909\pi$
$83$	−0.738747	−0.0810881	−0.0405440	+	0.999178i	$0.512909\pi$
$84$	−3.39092	−0.369980
$85$	−13.6106	−1.47628
$86$	−22.5775	−2.43459
$87$	8.13218	0.871861
$88$	−13.6435	−1.45440
$89$	14.9928	1.58923	0.794615	−	0.607114i	$-0.207673\pi$
$89$	14.9928	1.58923	0.794615	+	0.607114i	$0.207673\pi$
$90$	−4.03578	−0.425409
$91$	−0.457541	−0.0479633
$92$	−4.31099	−0.449452
$93$	−3.47424	−0.360262
$94$	−23.3705	−2.41048
$95$	9.58388	0.983285
$96$	4.79538	0.489426
$97$	−8.34107	−0.846907	−0.423454	−	0.905918i	$-0.639182\pi$
$97$	−8.34107	−0.846907	−0.423454	+	0.905918i	$0.639182\pi$
$98$	−2.32184	−0.234541
$99$	4.22465	0.424594
$100$	−6.70964	−0.670964
$101$	14.6531	1.45803	0.729017	−	0.684495i	$-0.239977\pi$
$101$	14.6531	1.45803	0.729017	+	0.684495i	$0.239977\pi$
$102$	18.1808	1.80017
$103$	−6.69549	−0.659726	−0.329863	−	0.944029i	$-0.607003\pi$
$103$	−6.69549	−0.659726	−0.329863	+	0.944029i	$0.607003\pi$
$104$	−1.47762	−0.144893
$105$	−1.73819	−0.169630
$106$	−11.6703	−1.13352
$107$	2.85640	0.276138	0.138069	−	0.990423i	$-0.455910\pi$
$107$	2.85640	0.276138	0.138069	+	0.990423i	$0.455910\pi$
$108$	3.39092	0.326292
$109$	4.89998	0.469333	0.234666	−	0.972076i	$-0.424600\pi$
$109$	4.89998	0.469333	0.234666	+	0.972076i	$0.424600\pi$
$110$	−17.0498	−1.62563
$111$	−1.49179	−0.141594
$112$	−0.716504	−0.0677033
$113$	6.74370	0.634394	0.317197	−	0.948360i	$-0.397258\pi$
$113$	6.74370	0.634394	0.317197	+	0.948360i	$0.397258\pi$
$114$	−12.8020	−1.19901
$115$	−2.20981	−0.206066
$116$	27.5756	2.56033
$117$	0.457541	0.0422996
$118$	−19.0150	−1.75047
$119$	7.83037	0.717809
$120$	−5.61346	−0.512436
$121$	6.84770	0.622518
$122$	24.4452	2.21317
$123$	−12.5585	−1.13236
$124$	−11.7809	−1.05795
$125$	−12.1303	−1.08497
$126$	2.32184	0.206846
$127$	−15.4731	−1.37301	−0.686506	−	0.727124i	$-0.740856\pi$
$127$	−15.4731	−1.37301	−0.686506	+	0.727124i	$0.740856\pi$
$128$	19.5880	1.73135
$129$	9.72398	0.856149
$130$	−1.84653	−0.161952
$131$	15.8166	1.38190	0.690952	−	0.722901i	$-0.257192\pi$
$131$	15.8166	1.38190	0.690952	+	0.722901i	$0.257192\pi$
$132$	14.3255	1.24687
$133$	−5.51372	−0.478100
$134$	−16.2804	−1.40641
$135$	1.73819	0.149599
$136$	25.2881	2.16844
$137$	17.3527	1.48254	0.741271	−	0.671205i	$-0.234223\pi$
$137$	17.3527	1.48254	0.741271	+	0.671205i	$0.234223\pi$
$138$	2.95183	0.251276
$139$	2.28713	0.193992	0.0969958	−	0.995285i	$-0.469077\pi$
$139$	2.28713	0.193992	0.0969958	+	0.995285i	$0.469077\pi$
$140$	−5.89405	−0.498138
$141$	10.0655	0.847670
$142$	−15.3449	−1.28771
$143$	1.93295	0.161641
$144$	0.716504	0.0597087
$145$	14.1352	1.17387
$146$	26.6219	2.20325
$147$	1.00000	0.0824786
$148$	−5.05854	−0.415809
$149$	−7.85577	−0.643570	−0.321785	−	0.946813i	$-0.604283\pi$
$149$	−7.85577	−0.643570	−0.321785	+	0.946813i	$0.604283\pi$
$150$	4.59424	0.375118
$151$	12.6721	1.03124	0.515619	−	0.856818i	$-0.327562\pi$
$151$	12.6721	1.03124	0.515619	+	0.856818i	$0.327562\pi$
$152$	−17.8065	−1.44430
$153$	−7.83037	−0.633048
$154$	9.80895	0.790428
$155$	−6.03887	−0.485054
$156$	1.55148	0.124218
$157$	21.6003	1.72389	0.861946	−	0.507001i	$-0.169246\pi$
$157$	21.6003	1.72389	0.861946	+	0.507001i	$0.169246\pi$
$158$	−38.1849	−3.03783
$159$	5.02634	0.398615
$160$	8.33526	0.658960
$161$	1.27133	0.100195
$162$	−2.32184	−0.182421
$163$	5.31720	0.416475	0.208238	−	0.978078i	$-0.433227\pi$
$163$	5.31720	0.416475	0.208238	+	0.978078i	$0.433227\pi$
$164$	−42.5849	−3.32532
$165$	7.34324	0.571670
$166$	1.71525	0.133129
$167$	−9.99792	−0.773662	−0.386831	−	0.922151i	$-0.626430\pi$
$167$	−9.99792	−0.773662	−0.386831	+	0.922151i	$0.626430\pi$
$168$	3.22949	0.249161
$169$	−12.7907	−0.983897
$170$	31.6017	2.42374
$171$	5.51372	0.421645
$172$	32.9732	2.51419
$173$	−0.984500	−0.0748501	−0.0374251	−	0.999299i	$-0.511916\pi$
$173$	−0.984500	−0.0748501	−0.0374251	+	0.999299i	$0.511916\pi$
$174$	−18.8816	−1.43141
$175$	1.97871	0.149576
$176$	3.02698	0.228167
$177$	8.18964	0.615571
$178$	−34.8107	−2.60918
$179$	18.1740	1.35839	0.679195	−	0.733958i	$-0.262329\pi$
$179$	18.1740	1.35839	0.679195	+	0.733958i	$0.262329\pi$
$180$	5.89405	0.439317
$181$	−4.62237	−0.343578	−0.171789	−	0.985134i	$-0.554955\pi$
$181$	−4.62237	−0.343578	−0.171789	+	0.985134i	$0.554955\pi$
$182$	1.06233	0.0787454
$183$	−10.5284	−0.778281
$184$	4.10576	0.302680
$185$	−2.59301	−0.190642
$186$	8.06661	0.591472
$187$	−33.0806	−2.41909
$188$	34.1314	2.48929
$189$	−1.00000	−0.0727393
$190$	−22.2522	−1.61434
$191$	−1.00000	−0.0723575
$191$	−1.00000	−0.0723575
$192$	−12.5671	−0.906951
$193$	−11.3521	−0.817142	−0.408571	−	0.912727i	$-0.633973\pi$
$193$	−11.3521	−0.817142	−0.408571	+	0.912727i	$0.633973\pi$
$194$	19.3666	1.39044
$195$	0.795291	0.0569520
$196$	3.39092	0.242209
$197$	9.17940	0.654005	0.327002	−	0.945024i	$-0.393961\pi$
$197$	9.17940	0.654005	0.327002	+	0.945024i	$0.393961\pi$
$198$	−9.80895	−0.697092
$199$	−23.3691	−1.65659	−0.828296	−	0.560291i	$-0.810689\pi$
$199$	−23.3691	−1.65659	−0.828296	+	0.560291i	$0.810689\pi$
$200$	6.39022	0.451857
$201$	7.01185	0.494578
$202$	−34.0220	−2.39378
$203$	−8.13218	−0.570767
$204$	−26.5522	−1.85902
$205$	−21.8290	−1.52461
$206$	15.5458	1.08313
$207$	−1.27133	−0.0883637
$208$	0.327830	0.0227309
$209$	23.2936	1.61125
$210$	4.03578	0.278495
$211$	20.3194	1.39885	0.699423	−	0.714708i	$-0.253441\pi$
$211$	20.3194	1.39885	0.699423	+	0.714708i	$0.253441\pi$
$212$	17.0439	1.17058
$213$	6.60893	0.452836
$214$	−6.63209	−0.453360
$215$	16.9021	1.15271
$216$	−3.22949	−0.219739
$217$	3.47424	0.235847
$218$	−11.3769	−0.770544
$219$	−11.4659	−0.774793
$220$	24.9003	1.67878
$221$	−3.58271	−0.240999
$222$	3.46369	0.232468
$223$	−10.2921	−0.689208	−0.344604	−	0.938748i	$-0.611987\pi$
$223$	−10.2921	−0.689208	−0.344604	+	0.938748i	$0.611987\pi$
$224$	−4.79538	−0.320405
$225$	−1.97871	−0.131914
$226$	−15.6578	−1.04154
$227$	−19.7245	−1.30916	−0.654580	−	0.755993i	$-0.727154\pi$
$227$	−19.7245	−1.30916	−0.654580	+	0.755993i	$0.727154\pi$
$228$	18.6966	1.23821
$229$	−7.97412	−0.526944	−0.263472	−	0.964667i	$-0.584868\pi$
$229$	−7.97412	−0.526944	−0.263472	+	0.964667i	$0.584868\pi$
$230$	5.13082	0.338316
$231$	−4.22465	−0.277962
$232$	−26.2628	−1.72424
$233$	9.76680	0.639845	0.319922	−	0.947444i	$-0.396343\pi$
$233$	9.76680	0.639845	0.319922	+	0.947444i	$0.396343\pi$
$234$	−1.06233	−0.0694470
$235$	17.4957	1.14130
$236$	27.7704	1.80770
$237$	16.4460	1.06828
$238$	−18.1808	−1.17849
$239$	2.59293	0.167723	0.0838614	−	0.996477i	$-0.473275\pi$
$239$	2.59293	0.167723	0.0838614	+	0.996477i	$0.473275\pi$
$240$	1.24542	0.0803914
$241$	3.97348	0.255955	0.127977	−	0.991777i	$-0.459152\pi$
$241$	3.97348	0.255955	0.127977	+	0.991777i	$0.459152\pi$
$242$	−15.8992	−1.02204
$243$	1.00000	0.0641500
$244$	−35.7010	−2.28552
$245$	1.73819	0.111049
$246$	29.1588	1.85910
$247$	2.52275	0.160519
$248$	11.2200	0.712472
$249$	−0.738747	−0.0468162
$250$	28.1646	1.78128
$251$	−0.648261	−0.0409179	−0.0204589	−	0.999791i	$-0.506513\pi$
$251$	−0.648261	−0.0409179	−0.0204589	+	0.999791i	$0.506513\pi$
$252$	−3.39092	−0.213608
$253$	−5.37094	−0.337668
$254$	35.9259	2.25419
$255$	−13.6106	−0.852331
$256$	−20.3458	−1.27162
$257$	−29.3544	−1.83108	−0.915538	−	0.402231i	$-0.868235\pi$
$257$	−29.3544	−1.83108	−0.915538	+	0.402231i	$0.868235\pi$
$258$	−22.5775	−1.40561
$259$	1.49179	0.0926953
$260$	2.69677	0.167246
$261$	8.13218	0.503369
$262$	−36.7236	−2.26879
$263$	−23.7412	−1.46394	−0.731972	−	0.681335i	$-0.761400\pi$
$263$	−23.7412	−1.46394	−0.731972	+	0.681335i	$0.761400\pi$
$264$	−13.6435	−0.839698
$265$	8.73671	0.536692
$266$	12.8020	0.784939
$267$	14.9928	0.917543
$268$	23.7766	1.45239
$269$	14.0679	0.857738	0.428869	−	0.903367i	$-0.358912\pi$
$269$	14.0679	0.857738	0.428869	+	0.903367i	$0.358912\pi$
$270$	−4.03578	−0.245610
$271$	−17.2490	−1.04781	−0.523903	−	0.851778i	$-0.675524\pi$
$271$	−17.2490	−1.04781	−0.523903	+	0.851778i	$0.675524\pi$
$272$	−5.61049	−0.340186
$273$	−0.457541	−0.0276916
$274$	−40.2902	−2.43402
$275$	−8.35936	−0.504088
$276$	−4.31099	−0.259491
$277$	−13.0195	−0.782266	−0.391133	−	0.920334i	$-0.627917\pi$
$277$	−13.0195	−0.782266	−0.391133	+	0.920334i	$0.627917\pi$
$278$	−5.31033	−0.318493
$279$	−3.47424	−0.207997
$280$	5.61346	0.335468
$281$	−22.8942	−1.36576	−0.682878	−	0.730533i	$-0.739272\pi$
$281$	−22.8942	−1.36576	−0.682878	+	0.730533i	$0.739272\pi$
$282$	−23.3705	−1.39169
$283$	13.5343	0.804529	0.402265	−	0.915523i	$-0.368223\pi$
$283$	13.5343	0.804529	0.402265	+	0.915523i	$0.368223\pi$
$284$	22.4104	1.32981
$285$	9.58388	0.567700
$286$	−4.48799	−0.265381
$287$	12.5585	0.741305
$288$	4.79538	0.282570
$289$	44.3147	2.60675
$290$	−32.8197	−1.92724
$291$	−8.34107	−0.488962
$292$	−38.8799	−2.27528
$293$	−14.6766	−0.857415	−0.428707	−	0.903443i	$-0.641031\pi$
$293$	−14.6766	−0.857415	−0.428707	+	0.903443i	$0.641031\pi$
$294$	−2.32184	−0.135412
$295$	14.2351	0.828801
$296$	4.81772	0.280024
$297$	4.22465	0.245139
$298$	18.2398	1.05660
$299$	−0.581686	−0.0336398
$300$	−6.70964	−0.387381
$301$	−9.72398	−0.560481
$302$	−29.4225	−1.69307
$303$	14.6531	0.841797
$304$	3.95061	0.226583
$305$	−18.3003	−1.04787
$306$	18.1808	1.03933
$307$	−31.6711	−1.80756	−0.903782	−	0.427994i	$-0.859221\pi$
$307$	−31.6711	−1.80756	−0.903782	+	0.427994i	$0.859221\pi$
$308$	−14.3255	−0.816269
$309$	−6.69549	−0.380893
$310$	14.0213	0.796355
$311$	6.94333	0.393720	0.196860	−	0.980432i	$-0.436926\pi$
$311$	6.94333	0.393720	0.196860	+	0.980432i	$0.436926\pi$
$312$	−1.47762	−0.0836539
$313$	−7.58453	−0.428703	−0.214352	−	0.976757i	$-0.568764\pi$
$313$	−7.58453	−0.428703	−0.214352	+	0.976757i	$0.568764\pi$
$314$	−50.1523	−2.83026
$315$	−1.73819	−0.0979357
$316$	55.7671	3.13714
$317$	15.5672	0.874340	0.437170	−	0.899379i	$-0.355981\pi$
$317$	15.5672	0.874340	0.437170	+	0.899379i	$0.355981\pi$
$318$	−11.6703	−0.654440
$319$	34.3556	1.92355
$320$	−21.8439	−1.22111
$321$	2.85640	0.159429
$322$	−2.95183	−0.164499
$323$	−43.1745	−2.40229
$324$	3.39092	0.188385
$325$	−0.905339	−0.0502192
$326$	−12.3457	−0.683763
$327$	4.89998	0.270969
$328$	40.5576	2.23942
$329$	−10.0655	−0.554930
$330$	−17.0498	−0.938560
$331$	−1.06943	−0.0587810	−0.0293905	−	0.999568i	$-0.509357\pi$
$331$	−1.06943	−0.0587810	−0.0293905	+	0.999568i	$0.509357\pi$
$332$	−2.50503	−0.137482
$333$	−1.49179	−0.0817495
$334$	23.2135	1.27019
$335$	12.1879	0.665896
$336$	−0.716504	−0.0390885
$337$	2.24900	0.122511	0.0612555	−	0.998122i	$-0.480490\pi$
$337$	2.24900	0.122511	0.0612555	+	0.998122i	$0.480490\pi$
$338$	29.6978	1.61535
$339$	6.74370	0.366268
$340$	−46.1526	−2.50298
$341$	−14.6775	−0.794829
$342$	−12.8020	−0.692251
$343$	−1.00000	−0.0539949
$344$	−31.4035	−1.69316
$345$	−2.20981	−0.118972
$346$	2.28585	0.122888
$347$	30.3004	1.62661	0.813305	−	0.581838i	$-0.197666\pi$
$347$	30.3004	1.62661	0.813305	+	0.581838i	$0.197666\pi$
$348$	27.5756	1.47821
$349$	−15.0980	−0.808179	−0.404089	−	0.914719i	$-0.632412\pi$
$349$	−15.0980	−0.808179	−0.404089	+	0.914719i	$0.632412\pi$
$350$	−4.59424	−0.245572
$351$	0.457541	0.0244217
$352$	20.2588	1.07980
$353$	25.8575	1.37626	0.688129	−	0.725589i	$-0.258432\pi$
$353$	25.8575	1.37626	0.688129	+	0.725589i	$0.258432\pi$
$354$	−19.0150	−1.01064
$355$	11.4876	0.609696
$356$	50.8393	2.69448
$357$	7.83037	0.414427
$358$	−42.1971	−2.23019
$359$	22.4343	1.18404	0.592018	−	0.805925i	$-0.298332\pi$
$359$	22.4343	1.18404	0.592018	+	0.805925i	$0.298332\pi$
$360$	−5.61346	−0.295855
$361$	11.4011	0.600060
$362$	10.7324	0.564081
$363$	6.84770	0.359411
$364$	−1.55148	−0.0813199
$365$	−19.9299	−1.04318
$366$	24.4452	1.27777
$367$	6.79265	0.354574	0.177287	−	0.984159i	$-0.443268\pi$
$367$	6.79265	0.354574	0.177287	+	0.984159i	$0.443268\pi$
$368$	−0.910915	−0.0474847
$369$	−12.5585	−0.653770
$370$	6.02054	0.312993
$371$	−5.02634	−0.260955
$372$	−11.7809	−0.610809
$373$	12.1335	0.628247	0.314123	−	0.949382i	$-0.398289\pi$
$373$	12.1335	0.628247	0.314123	+	0.949382i	$0.398289\pi$
$374$	76.8077	3.97163
$375$	−12.1303	−0.626406
$376$	−32.5065	−1.67639
$377$	3.72080	0.191631
$378$	2.32184	0.119422
$379$	15.4165	0.791893	0.395947	−	0.918273i	$-0.370416\pi$
$379$	15.4165	0.791893	0.395947	+	0.918273i	$0.370416\pi$
$380$	32.4982	1.66712
$381$	−15.4731	−0.792709
$382$	2.32184	0.118795
$383$	24.6669	1.26042	0.630209	−	0.776426i	$-0.282969\pi$
$383$	24.6669	1.26042	0.630209	+	0.776426i	$0.282969\pi$
$384$	19.5880	0.999594
$385$	−7.34324	−0.374246
$386$	26.3577	1.34157
$387$	9.72398	0.494298
$388$	−28.2839	−1.43590
$389$	18.9234	0.959454	0.479727	−	0.877418i	$-0.340736\pi$
$389$	18.9234	0.959454	0.479727	+	0.877418i	$0.340736\pi$
$390$	−1.84653	−0.0935029
$391$	9.95500	0.503446
$392$	−3.22949	−0.163114
$393$	15.8166	0.797842
$394$	−21.3130	−1.07374
$395$	28.5862	1.43833
$396$	14.3255	0.719882
$397$	10.2384	0.513848	0.256924	−	0.966432i	$-0.417291\pi$
$397$	10.2384	0.513848	0.256924	+	0.966432i	$0.417291\pi$
$398$	54.2592	2.71977
$399$	−5.51372	−0.276031
$400$	−1.41775	−0.0708877
$401$	36.7147	1.83345	0.916724	−	0.399522i	$-0.130824\pi$
$401$	36.7147	1.83345	0.916724	+	0.399522i	$0.130824\pi$
$402$	−16.2804	−0.811991
$403$	−1.58960	−0.0791839
$404$	49.6874	2.47204
$405$	1.73819	0.0863712
$406$	18.8816	0.937077
$407$	−6.30229	−0.312393
$408$	25.2881	1.25195
$409$	26.0882	1.28998	0.644988	−	0.764193i	$-0.276862\pi$
$409$	26.0882	1.28998	0.644988	+	0.764193i	$0.276862\pi$
$410$	50.6834	2.50307
$411$	17.3527	0.855947
$412$	−22.7039	−1.11854
$413$	−8.18964	−0.402986
$414$	2.95183	0.145074
$415$	−1.28408	−0.0630330
$416$	2.19408	0.107574
$417$	2.28713	0.112001
$418$	−54.0839	−2.64533
$419$	9.12623	0.445846	0.222923	−	0.974836i	$-0.428440\pi$
$419$	9.12623	0.445846	0.222923	+	0.974836i	$0.428440\pi$
$420$	−5.89405	−0.287600
$421$	10.1758	0.495937	0.247969	−	0.968768i	$-0.420237\pi$
$421$	10.1758	0.495937	0.247969	+	0.968768i	$0.420237\pi$
$422$	−47.1783	−2.29660
$423$	10.0655	0.489402
$424$	−16.2325	−0.788321
$425$	15.4940	0.751570
$426$	−15.3449	−0.743460
$427$	10.5284	0.509505
$428$	9.68582	0.468182
$429$	1.93295	0.0933237
$430$	−39.2439	−1.89251
$431$	−20.9767	−1.01041	−0.505206	−	0.862999i	$-0.668584\pi$
$431$	−20.9767	−1.01041	−0.505206	+	0.862999i	$0.668584\pi$
$432$	0.716504	0.0344728
$433$	40.3941	1.94122	0.970608	−	0.240666i	$-0.0773660\pi$
$433$	40.3941	1.94122	0.970608	+	0.240666i	$0.0773660\pi$
$434$	−8.06661	−0.387210
$435$	14.1352	0.677733
$436$	16.6154	0.795735
$437$	−7.00978	−0.335323
$438$	26.6219	1.27204
$439$	−8.08400	−0.385828	−0.192914	−	0.981216i	$-0.561794\pi$
$439$	−8.08400	−0.385828	−0.192914	+	0.981216i	$0.561794\pi$
$440$	−23.7149	−1.13056
$441$	1.00000	0.0476190
$442$	8.31847	0.395669
$443$	−7.23856	−0.343915	−0.171957	−	0.985104i	$-0.555009\pi$
$443$	−7.23856	−0.343915	−0.171957	+	0.985104i	$0.555009\pi$
$444$	−5.05854	−0.240068
$445$	26.0602	1.23537
$446$	23.8965	1.13153
$447$	−7.85577	−0.371565
$448$	12.5671	0.593739
$449$	−35.0380	−1.65355	−0.826773	−	0.562536i	$-0.809826\pi$
$449$	−35.0380	−1.65355	−0.826773	+	0.562536i	$0.809826\pi$
$450$	4.59424	0.216574
$451$	−53.0553	−2.49828
$452$	22.8674	1.07559
$453$	12.6721	0.595385
$454$	45.7970	2.14936
$455$	−0.795291	−0.0372838
$456$	−17.8065	−0.833867
$457$	8.45987	0.395736	0.197868	−	0.980229i	$-0.436598\pi$
$457$	8.45987	0.395736	0.197868	+	0.980229i	$0.436598\pi$
$458$	18.5146	0.865130
$459$	−7.83037	−0.365490
$460$	−7.49330	−0.349377
$461$	−19.0393	−0.886747	−0.443373	−	0.896337i	$-0.646218\pi$
$461$	−19.0393	−0.886747	−0.443373	+	0.896337i	$0.646218\pi$
$462$	9.80895	0.456354
$463$	−7.40002	−0.343908	−0.171954	−	0.985105i	$-0.555008\pi$
$463$	−7.40002	−0.343908	−0.171954	+	0.985105i	$0.555008\pi$
$464$	5.82674	0.270500
$465$	−6.03887	−0.280046
$466$	−22.6769	−1.05049
$467$	−31.3155	−1.44911	−0.724555	−	0.689217i	$-0.757955\pi$
$467$	−31.3155	−1.44911	−0.724555	+	0.689217i	$0.757955\pi$
$468$	1.55148	0.0717174
$469$	−7.01185	−0.323777
$470$	−40.6223	−1.87376
$471$	21.6003	0.995289
$472$	−26.4484	−1.21738
$473$	41.0804	1.88888
$474$	−38.1849	−1.75389
$475$	−10.9101	−0.500587
$476$	26.5522	1.21702
$477$	5.02634	0.230140
$478$	−6.02036	−0.275365
$479$	16.5301	0.755281	0.377641	−	0.925952i	$-0.376735\pi$
$479$	16.5301	0.755281	0.377641	+	0.925952i	$0.376735\pi$
$480$	8.33526	0.380451
$481$	−0.682554	−0.0311218
$482$	−9.22578	−0.420223
$483$	1.27133	0.0578476
$484$	23.2200	1.05546
$485$	−14.4983	−0.658335
$486$	−2.32184	−0.105321
$487$	25.7226	1.16560	0.582802	−	0.812614i	$-0.301956\pi$
$487$	25.7226	1.16560	0.582802	+	0.812614i	$0.301956\pi$
$488$	34.0014	1.53917
$489$	5.31720	0.240452
$490$	−4.03578	−0.182318
$491$	19.1504	0.864243	0.432122	−	0.901815i	$-0.357765\pi$
$491$	19.1504	0.864243	0.432122	+	0.901815i	$0.357765\pi$
$492$	−42.5849	−1.91988
$493$	−63.6779	−2.86791
$494$	−5.85742	−0.263538
$495$	7.34324	0.330054
$496$	−2.48931	−0.111773
$497$	−6.60893	−0.296451
$498$	1.71525	0.0768622
$499$	23.4814	1.05117	0.525586	−	0.850741i	$-0.323846\pi$
$499$	23.4814	1.05117	0.525586	+	0.850741i	$0.323846\pi$
$500$	−41.1329	−1.83952
$501$	−9.99792	−0.446674
$502$	1.50516	0.0671784
$503$	35.1985	1.56943	0.784713	−	0.619859i	$-0.212810\pi$
$503$	35.1985	1.56943	0.784713	+	0.619859i	$0.212810\pi$
$504$	3.22949	0.143853
$505$	25.4698	1.13339
$506$	12.4704	0.554379
$507$	−12.7907	−0.568053
$508$	−52.4679	−2.32789
$509$	28.9664	1.28391	0.641956	−	0.766742i	$-0.278123\pi$
$509$	28.9664	1.28391	0.641956	+	0.766742i	$0.278123\pi$
$510$	31.6017	1.39935
$511$	11.4659	0.507221
$512$	8.06380	0.356373
$513$	5.51372	0.243437
$514$	68.1561	3.00623
$515$	−11.6380	−0.512832
$516$	32.9732	1.45157
$517$	42.5233	1.87017
$518$	−3.46369	−0.152186
$519$	−0.984500	−0.0432147
$520$	−2.56838	−0.112631
$521$	34.3862	1.50649	0.753244	−	0.657742i	$-0.228488\pi$
$521$	34.3862	1.50649	0.753244	+	0.657742i	$0.228488\pi$
$522$	−18.8816	−0.826424
$523$	9.36676	0.409580	0.204790	−	0.978806i	$-0.434349\pi$
$523$	9.36676	0.409580	0.204790	+	0.978806i	$0.434349\pi$
$524$	53.6329	2.34296
$525$	1.97871	0.0863579
$526$	55.1231	2.40348
$527$	27.2046	1.18505
$528$	3.02698	0.131733
$529$	−21.3837	−0.929727
$530$	−20.2852	−0.881133
$531$	8.18964	0.355400
$532$	−18.6966	−0.810601
$533$	−5.74603	−0.248888
$534$	−34.8107	−1.50641
$535$	4.96495	0.214654
$536$	−22.6447	−0.978103
$537$	18.1740	0.784267
$538$	−32.6635	−1.40822
$539$	4.22465	0.181969
$540$	5.89405	0.253640
$541$	−28.9034	−1.24265	−0.621327	−	0.783551i	$-0.713406\pi$
$541$	−28.9034	−1.24265	−0.621327	+	0.783551i	$0.713406\pi$
$542$	40.0495	1.72027
$543$	−4.62237	−0.198365
$544$	−37.5496	−1.60992
$545$	8.51707	0.364831
$546$	1.06233	0.0454637
$547$	7.06380	0.302026	0.151013	−	0.988532i	$-0.451746\pi$
$547$	7.06380	0.302026	0.151013	+	0.988532i	$0.451746\pi$
$548$	58.8417	2.51359
$549$	−10.5284	−0.449341
$550$	19.4091	0.827605
$551$	44.8386	1.91019
$552$	4.10576	0.174753
$553$	−16.4460	−0.699355
$554$	30.2291	1.28431
$555$	−2.59301	−0.110067
$556$	7.75547	0.328905
$557$	−20.8408	−0.883055	−0.441528	−	0.897248i	$-0.645563\pi$
$557$	−20.8408	−0.883055	−0.441528	+	0.897248i	$0.645563\pi$
$558$	8.06661	0.341487
$559$	4.44912	0.188178
$560$	−1.24542	−0.0526285
$561$	−33.0806	−1.39666
$562$	53.1566	2.24228
$563$	−7.37212	−0.310698	−0.155349	−	0.987860i	$-0.549650\pi$
$563$	−7.37212	−0.310698	−0.155349	+	0.987860i	$0.549650\pi$
$564$	34.1314	1.43719
$565$	11.7218	0.493140
$566$	−31.4244	−1.32086
$567$	−1.00000	−0.0419961
$568$	−21.3435	−0.895553
$569$	−42.5565	−1.78406	−0.892030	−	0.451975i	$-0.850719\pi$
$569$	−42.5565	−1.78406	−0.892030	+	0.451975i	$0.850719\pi$
$570$	−22.2522	−0.932042
$571$	−1.88368	−0.0788298	−0.0394149	−	0.999223i	$-0.512549\pi$
$571$	−1.88368	−0.0788298	−0.0394149	+	0.999223i	$0.512549\pi$
$572$	6.55448	0.274057
$573$	−1.00000	−0.0417756
$574$	−29.1588	−1.21706
$575$	2.51560	0.104908
$576$	−12.5671	−0.523628
$577$	12.7457	0.530609	0.265305	−	0.964165i	$-0.414527\pi$
$577$	12.7457	0.530609	0.265305	+	0.964165i	$0.414527\pi$
$578$	−102.891	−4.27972
$579$	−11.3521	−0.471777
$580$	47.9315	1.99025
$581$	0.738747	0.0306484
$582$	19.3666	0.802771
$583$	21.2345	0.879445
$584$	37.0290	1.53227
$585$	0.795291	0.0328812
$586$	34.0766	1.40769
$587$	1.74675	0.0720959	0.0360480	−	0.999350i	$-0.488523\pi$
$587$	1.74675	0.0720959	0.0360480	+	0.999350i	$0.488523\pi$
$588$	3.39092	0.139839
$589$	−19.1560	−0.789309
$590$	−33.0516	−1.36071
$591$	9.17940	0.377590
$592$	−1.06887	−0.0439304
$593$	20.9659	0.860967	0.430483	−	0.902598i	$-0.358343\pi$
$593$	20.9659	0.860967	0.430483	+	0.902598i	$0.358343\pi$
$594$	−9.80895	−0.402466
$595$	13.6106	0.557982
$596$	−26.6383	−1.09115
$597$	−23.3691	−0.956433
$598$	1.35058	0.0552293
$599$	−12.4582	−0.509028	−0.254514	−	0.967069i	$-0.581915\pi$
$599$	−12.4582	−0.509028	−0.254514	+	0.967069i	$0.581915\pi$
$600$	6.39022	0.260880
$601$	30.0200	1.22454	0.612270	−	0.790648i	$-0.290256\pi$
$601$	30.0200	1.22454	0.612270	+	0.790648i	$0.290256\pi$
$602$	22.5775	0.920189
$603$	7.01185	0.285545
$604$	42.9700	1.74842
$605$	11.9026	0.483909
$606$	−34.0220	−1.38205
$607$	19.9026	0.807822	0.403911	−	0.914798i	$-0.367650\pi$
$607$	19.9026	0.807822	0.403911	+	0.914798i	$0.367650\pi$
$608$	26.4404	1.07230
$609$	−8.13218	−0.329532
$610$	42.4903	1.72038
$611$	4.60538	0.186314
$612$	−26.5522	−1.07331
$613$	11.9298	0.481838	0.240919	−	0.970545i	$-0.422551\pi$
$613$	11.9298	0.481838	0.240919	+	0.970545i	$0.422551\pi$
$614$	73.5350	2.96763
$615$	−21.8290	−0.880231
$616$	13.6435	0.549711
$617$	−45.5843	−1.83516	−0.917578	−	0.397556i	$-0.869858\pi$
$617$	−45.5843	−1.83516	−0.917578	+	0.397556i	$0.869858\pi$
$618$	15.5458	0.625345
$619$	−45.3762	−1.82382	−0.911911	−	0.410388i	$-0.865393\pi$
$619$	−45.3762	−1.82382	−0.911911	+	0.410388i	$0.865393\pi$
$620$	−20.4773	−0.822390
$621$	−1.27133	−0.0510168
$622$	−16.1213	−0.646404
$623$	−14.9928	−0.600673
$624$	0.327830	0.0131237
$625$	−11.1912	−0.447647
$626$	17.6100	0.703839
$627$	23.2936	0.930256
$628$	73.2449	2.92279
$629$	11.6813	0.465762
$630$	4.03578	0.160789
$631$	−35.7025	−1.42130	−0.710648	−	0.703548i	$-0.751598\pi$
$631$	−35.7025	−1.42130	−0.710648	+	0.703548i	$0.751598\pi$
$632$	−53.1122	−2.11269
$633$	20.3194	0.807624
$634$	−36.1444	−1.43548
$635$	−26.8950	−1.06730
$636$	17.0439	0.675835
$637$	0.457541	0.0181284
$638$	−79.7681	−3.15805
$639$	6.60893	0.261445
$640$	34.0475	1.34585
$641$	0.172459	0.00681171	0.00340586	−	0.999994i	$-0.498916\pi$
$641$	0.172459	0.00681171	0.00340586	+	0.999994i	$0.498916\pi$
$642$	−6.63209	−0.261748
$643$	−17.0301	−0.671600	−0.335800	−	0.941933i	$-0.609007\pi$
$643$	−17.0301	−0.671600	−0.335800	+	0.941933i	$0.609007\pi$
$644$	4.31099	0.169877
$645$	16.9021	0.665519
$646$	100.244	3.94405
$647$	−30.5489	−1.20100	−0.600501	−	0.799624i	$-0.705032\pi$
$647$	−30.5489	−1.20100	−0.600501	+	0.799624i	$0.705032\pi$
$648$	−3.22949	−0.126866
$649$	34.5984	1.35811
$650$	2.10205	0.0824492
$651$	3.47424	0.136166
$652$	18.0302	0.706117
$653$	−27.1788	−1.06359	−0.531795	−	0.846873i	$-0.678482\pi$
$653$	−27.1788	−1.06359	−0.531795	+	0.846873i	$0.678482\pi$
$654$	−11.3769	−0.444874
$655$	27.4922	1.07421
$656$	−8.99822	−0.351322
$657$	−11.4659	−0.447327
$658$	23.3705	0.911076
$659$	−34.5575	−1.34617	−0.673085	−	0.739565i	$-0.735031\pi$
$659$	−34.5575	−1.34617	−0.673085	+	0.739565i	$0.735031\pi$
$660$	24.9003	0.969244
$661$	35.6360	1.38608	0.693041	−	0.720898i	$-0.256271\pi$
$661$	35.6360	1.38608	0.693041	+	0.720898i	$0.256271\pi$
$662$	2.48303	0.0965059
$663$	−3.58271	−0.139141
$664$	2.38578	0.0925861
$665$	−9.58388	−0.371647
$666$	3.46369	0.134215
$667$	−10.3387	−0.400316
$668$	−33.9022	−1.31171
$669$	−10.2921	−0.397914
$670$	−28.2983	−1.09326
$671$	−44.4788	−1.71709
$672$	−4.79538	−0.184986
$673$	12.6836	0.488916	0.244458	−	0.969660i	$-0.421390\pi$
$673$	12.6836	0.488916	0.244458	+	0.969660i	$0.421390\pi$
$674$	−5.22182	−0.201137
$675$	−1.97871	−0.0761605
$676$	−43.3721	−1.66816
$677$	−17.7334	−0.681548	−0.340774	−	0.940145i	$-0.610689\pi$
$677$	−17.7334	−0.681548	−0.340774	+	0.940145i	$0.610689\pi$
$678$	−15.6578	−0.601333
$679$	8.34107	0.320101
$680$	43.9554	1.68561
$681$	−19.7245	−0.755844
$682$	34.0786	1.30494
$683$	−17.2866	−0.661452	−0.330726	−	0.943727i	$-0.607294\pi$
$683$	−17.2866	−0.661452	−0.330726	+	0.943727i	$0.607294\pi$
$684$	18.6966	0.714882
$685$	30.1623	1.15244
$686$	2.32184	0.0886481
$687$	−7.97412	−0.304232
$688$	6.96727	0.265625
$689$	2.29975	0.0876137
$690$	5.13082	0.195327
$691$	−26.0204	−0.989861	−0.494931	−	0.868933i	$-0.664807\pi$
$691$	−26.0204	−0.989861	−0.494931	+	0.868933i	$0.664807\pi$
$692$	−3.33836	−0.126905
$693$	−4.22465	−0.160481
$694$	−70.3525	−2.67054
$695$	3.97545	0.150798
$696$	−26.2628	−0.995488
$697$	98.3377	3.72481
$698$	35.0551	1.32686
$699$	9.76680	0.369414
$700$	6.70964	0.253601
$701$	−45.4685	−1.71732	−0.858661	−	0.512544i	$-0.828703\pi$
$701$	−45.4685	−1.71732	−0.858661	+	0.512544i	$0.828703\pi$
$702$	−1.06233	−0.0400952
$703$	−8.22531	−0.310223
$704$	−53.0916	−2.00096
$705$	17.4957	0.658928
$706$	−60.0369	−2.25952
$707$	−14.6531	−0.551085
$708$	27.7704	1.04368
$709$	28.1621	1.05765	0.528824	−	0.848731i	$-0.322633\pi$
$709$	28.1621	1.05765	0.528824	+	0.848731i	$0.322633\pi$
$710$	−26.6722	−1.00099
$711$	16.4460	0.616773
$712$	−48.4190	−1.81458
$713$	4.41691	0.165415
$714$	−18.1808	−0.680401
$715$	3.35983	0.125650
$716$	61.6267	2.30310
$717$	2.59293	0.0968348
$718$	−52.0887	−1.94393
$719$	30.1008	1.12257	0.561285	−	0.827622i	$-0.310307\pi$
$719$	30.1008	1.12257	0.561285	+	0.827622i	$0.310307\pi$
$720$	1.24542	0.0464140
$721$	6.69549	0.249353
$722$	−26.4716	−0.985171
$723$	3.97348	0.147775
$724$	−15.6741	−0.582523
$725$	−16.0912	−0.597612
$726$	−15.8992	−0.590076
$727$	−39.6298	−1.46979	−0.734893	−	0.678183i	$-0.762768\pi$
$727$	−39.6298	−1.46979	−0.734893	+	0.678183i	$0.762768\pi$
$728$	1.47762	0.0547644
$729$	1.00000	0.0370370
$730$	46.2739	1.71267
$731$	−76.1424	−2.81623
$732$	−35.7010	−1.31955
$733$	31.0782	1.14790	0.573949	−	0.818891i	$-0.305411\pi$
$733$	31.0782	1.14790	0.573949	+	0.818891i	$0.305411\pi$
$734$	−15.7714	−0.582134
$735$	1.73819	0.0641140
$736$	−6.09652	−0.224721
$737$	29.6226	1.09116
$738$	29.1588	1.07335
$739$	−9.30321	−0.342224	−0.171112	−	0.985252i	$-0.554736\pi$
$739$	−9.30321	−0.342224	−0.171112	+	0.985252i	$0.554736\pi$
$740$	−8.79268	−0.323225
$741$	2.52275	0.0926756
$742$	11.6703	0.428431
$743$	32.4444	1.19027	0.595135	−	0.803626i	$-0.297099\pi$
$743$	32.4444	1.19027	0.595135	+	0.803626i	$0.297099\pi$
$744$	11.2200	0.411346
$745$	−13.6548	−0.500273
$746$	−28.1719	−1.03145
$747$	−0.738747	−0.0270294
$748$	−112.174	−4.10148
$749$	−2.85640	−0.104371
$750$	28.1646	1.02842
$751$	37.1283	1.35483	0.677415	−	0.735601i	$-0.263100\pi$
$751$	37.1283	1.35483	0.677415	+	0.735601i	$0.263100\pi$
$752$	7.21199	0.262994
$753$	−0.648261	−0.0236239
$754$	−8.63909	−0.314617
$755$	22.0264	0.801623
$756$	−3.39092	−0.123327
$757$	15.0827	0.548189	0.274095	−	0.961703i	$-0.411622\pi$
$757$	15.0827	0.548189	0.274095	+	0.961703i	$0.411622\pi$
$758$	−35.7946	−1.30012
$759$	−5.37094	−0.194953
$760$	−30.9510	−1.12271
$761$	−8.53406	−0.309359	−0.154680	−	0.987965i	$-0.549435\pi$
$761$	−8.53406	−0.309359	−0.154680	+	0.987965i	$0.549435\pi$
$762$	35.9259	1.30146
$763$	−4.89998	−0.177391
$764$	−3.39092	−0.122679
$765$	−13.6106	−0.492094
$766$	−57.2724	−2.06934
$767$	3.74709	0.135300
$768$	−20.3458	−0.734167
$769$	−5.01214	−0.180742	−0.0903711	−	0.995908i	$-0.528805\pi$
$769$	−5.01214	−0.180742	−0.0903711	+	0.995908i	$0.528805\pi$
$770$	17.0498	0.614432
$771$	−29.3544	−1.05717
$772$	−38.4941	−1.38543
$773$	−36.5900	−1.31605	−0.658025	−	0.752996i	$-0.728608\pi$
$773$	−36.5900	−1.31605	−0.658025	+	0.752996i	$0.728608\pi$
$774$	−22.5775	−0.811531
$775$	6.87450	0.246939
$776$	26.9374	0.966996
$777$	1.49179	0.0535176
$778$	−43.9370	−1.57522
$779$	−69.2441	−2.48093
$780$	2.69677	0.0965598
$781$	27.9204	0.999072
$782$	−23.1139	−0.826551
$783$	8.13218	0.290620
$784$	0.716504	0.0255894
$785$	37.5453	1.34005
$786$	−36.7236	−1.30989
$787$	−14.2385	−0.507549	−0.253775	−	0.967263i	$-0.581672\pi$
$787$	−14.2385	−0.507549	−0.253775	+	0.967263i	$0.581672\pi$
$788$	31.1266	1.10884
$789$	−23.7412	−0.845209
$790$	−66.3725	−2.36143
$791$	−6.74370	−0.239778
$792$	−13.6435	−0.484800
$793$	−4.81717	−0.171063
$794$	−23.7718	−0.843629
$795$	8.73671	0.309859
$796$	−79.2428	−2.80868
$797$	12.0441	0.426623	0.213311	−	0.976984i	$-0.431575\pi$
$797$	12.0441	0.426623	0.213311	+	0.976984i	$0.431575\pi$
$798$	12.8020	0.453184
$799$	−78.8167	−2.78834
$800$	−9.48865	−0.335474
$801$	14.9928	0.529743
$802$	−85.2456	−3.01013
$803$	−48.4394	−1.70939
$804$	23.7766	0.838537
$805$	2.20981	0.0778857
$806$	3.69080	0.130003
$807$	14.0679	0.495215
$808$	−47.3219	−1.66478
$809$	−19.7254	−0.693506	−0.346753	−	0.937956i	$-0.612716\pi$
$809$	−19.7254	−0.693506	−0.346753	+	0.937956i	$0.612716\pi$
$810$	−4.03578	−0.141803
$811$	13.5643	0.476306	0.238153	−	0.971228i	$-0.423458\pi$
$811$	13.5643	0.476306	0.238153	+	0.971228i	$0.423458\pi$
$812$	−27.5756	−0.967713
$813$	−17.2490	−0.604951
$814$	14.6329	0.512882
$815$	9.24228	0.323743
$816$	−5.61049	−0.196407
$817$	53.6153	1.87576
$818$	−60.5724	−2.11786
$819$	−0.457541	−0.0159878
$820$	−74.0205	−2.58491
$821$	−9.74642	−0.340152	−0.170076	−	0.985431i	$-0.554401\pi$
$821$	−9.74642	−0.340152	−0.170076	+	0.985431i	$0.554401\pi$
$822$	−40.2902	−1.40528
$823$	−17.9618	−0.626110	−0.313055	−	0.949735i	$-0.601352\pi$
$823$	−17.9618	−0.626110	−0.313055	+	0.949735i	$0.601352\pi$
$824$	21.6230	0.753273
$825$	−8.35936	−0.291035
$826$	19.0150	0.661616
$827$	14.1842	0.493234	0.246617	−	0.969113i	$-0.420681\pi$
$827$	14.1842	0.493234	0.246617	+	0.969113i	$0.420681\pi$
$828$	−4.31099	−0.149817
$829$	49.8560	1.73157	0.865786	−	0.500415i	$-0.166819\pi$
$829$	49.8560	1.73157	0.865786	+	0.500415i	$0.166819\pi$
$830$	2.98142	0.103487
$831$	−13.0195	−0.451642
$832$	−5.74995	−0.199344
$833$	−7.83037	−0.271306
$834$	−5.31033	−0.183882
$835$	−17.3782	−0.601399
$836$	78.9867	2.73181
$837$	−3.47424	−0.120087
$838$	−21.1896	−0.731983
$839$	19.1627	0.661569	0.330785	−	0.943706i	$-0.392687\pi$
$839$	19.1627	0.661569	0.330785	+	0.943706i	$0.392687\pi$
$840$	5.61346	0.193683
$841$	37.1323	1.28042
$842$	−23.6265	−0.814223
$843$	−22.8942	−0.788519
$844$	68.9015	2.37169
$845$	−22.2325	−0.764823
$846$	−23.3705	−0.803494
$847$	−6.84770	−0.235290
$848$	3.60139	0.123672
$849$	13.5343	0.464495
$850$	−35.9746	−1.23392
$851$	1.89656	0.0650132
$852$	22.4104	0.767766
$853$	11.9536	0.409282	0.204641	−	0.978837i	$-0.434397\pi$
$853$	11.9536	0.409282	0.204641	+	0.978837i	$0.434397\pi$
$854$	−24.4452	−0.836498
$855$	9.58388	0.327762
$856$	−9.22471	−0.315294
$857$	−42.9884	−1.46846	−0.734228	−	0.678903i	$-0.762456\pi$
$857$	−42.9884	−1.46846	−0.734228	+	0.678903i	$0.762456\pi$
$858$	−4.48799	−0.153218
$859$	−19.8412	−0.676972	−0.338486	−	0.940971i	$-0.609915\pi$
$859$	−19.8412	−0.676972	−0.338486	+	0.940971i	$0.609915\pi$
$860$	57.3136	1.95438
$861$	12.5585	0.427993
$862$	48.7045	1.65888
$863$	40.3368	1.37308	0.686540	−	0.727092i	$-0.259129\pi$
$863$	40.3368	1.37308	0.686540	+	0.727092i	$0.259129\pi$
$864$	4.79538	0.163142
$865$	−1.71124	−0.0581840
$866$	−93.7884	−3.18706
$867$	44.3147	1.50501
$868$	11.7809	0.399869
$869$	69.4786	2.35690
$870$	−32.8197	−1.11269
$871$	3.20821	0.108706
$872$	−15.8244	−0.535883
$873$	−8.34107	−0.282302
$874$	16.2755	0.550529
$875$	12.1303	0.410079
$876$	−38.8799	−1.31363
$877$	−36.1376	−1.22028	−0.610140	−	0.792293i	$-0.708887\pi$
$877$	−36.1376	−1.22028	−0.610140	+	0.792293i	$0.708887\pi$
$878$	18.7697	0.633447
$879$	−14.6766	−0.495029
$880$	5.26146	0.177364
$881$	21.1662	0.713106	0.356553	−	0.934275i	$-0.383952\pi$
$881$	21.1662	0.713106	0.356553	+	0.934275i	$0.383952\pi$
$882$	−2.32184	−0.0781803
$883$	−18.8870	−0.635598	−0.317799	−	0.948158i	$-0.602944\pi$
$883$	−18.8870	−0.635598	−0.317799	+	0.948158i	$0.602944\pi$
$884$	−12.1487	−0.408605
$885$	14.2351	0.478508
$886$	16.8068	0.564634
$887$	−4.41551	−0.148258	−0.0741291	−	0.997249i	$-0.523618\pi$
$887$	−4.41551	−0.148258	−0.0741291	+	0.997249i	$0.523618\pi$
$888$	4.81772	0.161672
$889$	15.4731	0.518950
$890$	−60.5076	−2.02822
$891$	4.22465	0.141531
$892$	−34.8996	−1.16852
$893$	55.4985	1.85719
$894$	18.2398	0.610030
$895$	31.5898	1.05593
$896$	−19.5880	−0.654388
$897$	−0.581686	−0.0194219
$898$	81.3525	2.71477
$899$	−28.2531	−0.942294
$900$	−6.70964	−0.223655
$901$	−39.3581	−1.31121
$902$	123.186	4.10164
$903$	−9.72398	−0.323594
$904$	−21.7787	−0.724349
$905$	−8.03454	−0.267077
$906$	−29.4225	−0.977495
$907$	18.4935	0.614067	0.307034	−	0.951699i	$-0.400664\pi$
$907$	18.4935	0.614067	0.307034	+	0.951699i	$0.400664\pi$
$908$	−66.8842	−2.21963
$909$	14.6531	0.486012
$910$	1.84653	0.0612120
$911$	8.20277	0.271770	0.135885	−	0.990725i	$-0.456612\pi$
$911$	8.20277	0.271770	0.135885	+	0.990725i	$0.456612\pi$
$912$	3.95061	0.130818
$913$	−3.12095	−0.103288
$914$	−19.6424	−0.649714
$915$	−18.3003	−0.604990
$916$	−27.0396	−0.893414
$917$	−15.8166	−0.522310
$918$	18.1808	0.600057
$919$	38.6448	1.27478	0.637388	−	0.770543i	$-0.280015\pi$
$919$	38.6448	1.27478	0.637388	+	0.770543i	$0.280015\pi$
$920$	7.13657	0.235286
$921$	−31.6711	−1.04360
$922$	44.2060	1.45585
$923$	3.02385	0.0995314
$924$	−14.3255	−0.471273
$925$	2.95182	0.0970551
$926$	17.1816	0.564623
$927$	−6.69549	−0.219909
$928$	38.9968	1.28013
$929$	11.2883	0.370358	0.185179	−	0.982705i	$-0.440714\pi$
$929$	11.2883	0.370358	0.185179	+	0.982705i	$0.440714\pi$
$930$	14.0213	0.459776
$931$	5.51372	0.180705
$932$	33.1185	1.08483
$933$	6.94333	0.227314
$934$	72.7095	2.37913
$935$	−57.5003	−1.88046
$936$	−1.47762	−0.0482976
$937$	8.39037	0.274101	0.137051	−	0.990564i	$-0.456238\pi$
$937$	8.39037	0.274101	0.137051	+	0.990564i	$0.456238\pi$
$938$	16.2804	0.531573
$939$	−7.58453	−0.247512
$940$	59.3267	1.93502
$941$	26.1578	0.852721	0.426360	−	0.904553i	$-0.359796\pi$
$941$	26.1578	0.852721	0.426360	+	0.904553i	$0.359796\pi$
$942$	−50.1523	−1.63405
$943$	15.9660	0.519926
$944$	5.86791	0.190984
$945$	−1.73819	−0.0565432
$946$	−95.3820	−3.10114
$947$	30.6591	0.996286	0.498143	−	0.867095i	$-0.334015\pi$
$947$	30.6591	0.996286	0.498143	+	0.867095i	$0.334015\pi$
$948$	55.7671	1.81123
$949$	−5.24611	−0.170296
$950$	25.3313	0.821857
$951$	15.5672	0.504800
$952$	−25.2881	−0.819592
$953$	5.01368	0.162409	0.0812046	−	0.996697i	$-0.474123\pi$
$953$	5.01368	0.162409	0.0812046	+	0.996697i	$0.474123\pi$
$954$	−11.6703	−0.377841
$955$	−1.73819	−0.0562464
$956$	8.79242	0.284367
$957$	34.3556	1.11056
$958$	−38.3803	−1.24001
$959$	−17.3527	−0.560349
$960$	−21.8439	−0.705010
$961$	−18.9297	−0.610635
$962$	1.58478	0.0510953
$963$	2.85640	0.0920461
$964$	13.4738	0.433961
$965$	−19.7321	−0.635198
$966$	−2.95183	−0.0949734
$967$	−6.77626	−0.217910	−0.108955	−	0.994047i	$-0.534750\pi$
$967$	−6.77626	−0.217910	−0.108955	+	0.994047i	$0.534750\pi$
$968$	−22.1146	−0.710790
$969$	−43.1745	−1.38696
$970$	33.6627	1.08085
$971$	−20.6505	−0.662705	−0.331352	−	0.943507i	$-0.607505\pi$
$971$	−20.6505	−0.662705	−0.331352	+	0.943507i	$0.607505\pi$
$972$	3.39092	0.108764
$973$	−2.28713	−0.0733219
$974$	−59.7237	−1.91367
$975$	−0.905339	−0.0289941
$976$	−7.54364	−0.241466
$977$	−21.5720	−0.690148	−0.345074	−	0.938575i	$-0.612146\pi$
$977$	−21.5720	−0.690148	−0.345074	+	0.938575i	$0.612146\pi$
$978$	−12.3457	−0.394771
$979$	63.3393	2.02433
$980$	5.89405	0.188279
$981$	4.89998	0.156444
$982$	−44.4640	−1.41890
$983$	36.2175	1.15516	0.577579	−	0.816335i	$-0.303998\pi$
$983$	36.2175	1.15516	0.577579	+	0.816335i	$0.303998\pi$
$984$	40.5576	1.29293
$985$	15.9555	0.508384
$986$	147.850	4.70849
$987$	−10.0655	−0.320389
$988$	8.55445	0.272153
$989$	−12.3624	−0.393102
$990$	−17.0498	−0.541878
$991$	−45.6893	−1.45137	−0.725684	−	0.688028i	$-0.758477\pi$
$991$	−45.6893	−1.45137	−0.725684	+	0.688028i	$0.758477\pi$
$992$	−16.6603	−0.528964
$993$	−1.06943	−0.0339372
$994$	15.3449	0.486709
$995$	−40.6198	−1.28774
$996$	−2.50503	−0.0793750
$997$	−43.0930	−1.36477	−0.682385	−	0.730993i	$-0.739057\pi$
$997$	−43.0930	−1.36477	−0.682385	+	0.730993i	$0.739057\pi$
$998$	−54.5200	−1.72580
$999$	−1.49179	−0.0471981

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	4011.2.a.m.1.3	✓	29

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
4011.2.a.m.1.3	✓	29	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:	\( N \)	\(=\)	\( 4011 = 3 \cdot 7 \cdot 191 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	4011.a (trivial)

\(f(q)\)	\(=\)	\(q-2.32184 q^{2} +1.00000 q^{3} +3.39092 q^{4} +1.73819 q^{5} -2.32184 q^{6} -1.00000 q^{7} -3.22949 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q-2.32184 q^{2} +1.00000 q^{3} +3.39092 q^{4} +1.73819 q^{5} -2.32184 q^{6} -1.00000 q^{7} -3.22949 q^{8} +1.00000 q^{9} -4.03578 q^{10} +4.22465 q^{11} +3.39092 q^{12} +0.457541 q^{13} +2.32184 q^{14} +1.73819 q^{15} +0.716504 q^{16} -7.83037 q^{17} -2.32184 q^{18} +5.51372 q^{19} +5.89405 q^{20} -1.00000 q^{21} -9.80895 q^{22} -1.27133 q^{23} -3.22949 q^{24} -1.97871 q^{25} -1.06233 q^{26} +1.00000 q^{27} -3.39092 q^{28} +8.13218 q^{29} -4.03578 q^{30} -3.47424 q^{31} +4.79538 q^{32} +4.22465 q^{33} +18.1808 q^{34} -1.73819 q^{35} +3.39092 q^{36} -1.49179 q^{37} -12.8020 q^{38} +0.457541 q^{39} -5.61346 q^{40} -12.5585 q^{41} +2.32184 q^{42} +9.72398 q^{43} +14.3255 q^{44} +1.73819 q^{45} +2.95183 q^{46} +10.0655 q^{47} +0.716504 q^{48} +1.00000 q^{49} +4.59424 q^{50} -7.83037 q^{51} +1.55148 q^{52} +5.02634 q^{53} -2.32184 q^{54} +7.34324 q^{55} +3.22949 q^{56} +5.51372 q^{57} -18.8816 q^{58} +8.18964 q^{59} +5.89405 q^{60} -10.5284 q^{61} +8.06661 q^{62} -1.00000 q^{63} -12.5671 q^{64} +0.795291 q^{65} -9.80895 q^{66} +7.01185 q^{67} -26.5522 q^{68} -1.27133 q^{69} +4.03578 q^{70} +6.60893 q^{71} -3.22949 q^{72} -11.4659 q^{73} +3.46369 q^{74} -1.97871 q^{75} +18.6966 q^{76} -4.22465 q^{77} -1.06233 q^{78} +16.4460 q^{79} +1.24542 q^{80} +1.00000 q^{81} +29.1588 q^{82} -0.738747 q^{83} -3.39092 q^{84} -13.6106 q^{85} -22.5775 q^{86} +8.13218 q^{87} -13.6435 q^{88} +14.9928 q^{89} -4.03578 q^{90} -0.457541 q^{91} -4.31099 q^{92} -3.47424 q^{93} -23.3705 q^{94} +9.58388 q^{95} +4.79538 q^{96} -8.34107 q^{97} -2.32184 q^{98} +4.22465 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 29 q + 6 q^{2} + 29 q^{3} + 40 q^{4} + 22 q^{5} + 6 q^{6} - 29 q^{7} + 15 q^{8} + 29 q^{9}+O(q^{10}) \) 29 * q + 6 * q^2 + 29 * q^3 + 40 * q^4 + 22 * q^5 + 6 * q^6 - 29 * q^7 + 15 * q^8 + 29 * q^9	\( 29 q + 6 q^{2} + 29 q^{3} + 40 q^{4} + 22 q^{5} + 6 q^{6} - 29 q^{7} + 15 q^{8} + 29 q^{9} + 11 q^{11} + 40 q^{12} + 13 q^{13} - 6 q^{14} + 22 q^{15} + 58 q^{16} + 17 q^{17} + 6 q^{18} + 3 q^{19} + 52 q^{20} - 29 q^{21} + 17 q^{22} + 36 q^{23} + 15 q^{24} + 57 q^{25} + 25 q^{26} + 29 q^{27} - 40 q^{28} + 20 q^{29} + 6 q^{31} + 46 q^{32} + 11 q^{33} + 18 q^{34} - 22 q^{35} + 40 q^{36} + 22 q^{37} + 8 q^{38} + 13 q^{39} + 6 q^{40} + 26 q^{41} - 6 q^{42} + 21 q^{43} + 22 q^{44} + 22 q^{45} + 28 q^{46} + 41 q^{47} + 58 q^{48} + 29 q^{49} + 18 q^{50} + 17 q^{51} + 2 q^{52} + 37 q^{53} + 6 q^{54} + 7 q^{55} - 15 q^{56} + 3 q^{57} + 9 q^{58} + 27 q^{59} + 52 q^{60} + 20 q^{61} - 12 q^{62} - 29 q^{63} + 59 q^{64} + 3 q^{65} + 17 q^{66} + 30 q^{67} + 33 q^{68} + 36 q^{69} + 68 q^{71} + 15 q^{72} + q^{73} + 21 q^{74} + 57 q^{75} + 11 q^{76} - 11 q^{77} + 25 q^{78} + 34 q^{79} + 110 q^{80} + 29 q^{81} - 49 q^{82} + 13 q^{83} - 40 q^{84} + 27 q^{85} + 35 q^{86} + 20 q^{87} + 17 q^{88} + 61 q^{89} - 13 q^{91} + 86 q^{92} + 6 q^{93} - 19 q^{94} + 25 q^{95} + 46 q^{96} - 3 q^{97} + 6 q^{98} + 11 q^{99}+O(q^{100}) \) 29 * q + 6 * q^2 + 29 * q^3 + 40 * q^4 + 22 * q^5 + 6 * q^6 - 29 * q^7 + 15 * q^8 + 29 * q^9 + 11 * q^11 + 40 * q^12 + 13 * q^13 - 6 * q^14 + 22 * q^15 + 58 * q^16 + 17 * q^17 + 6 * q^18 + 3 * q^19 + 52 * q^20 - 29 * q^21 + 17 * q^22 + 36 * q^23 + 15 * q^24 + 57 * q^25 + 25 * q^26 + 29 * q^27 - 40 * q^28 + 20 * q^29 + 6 * q^31 + 46 * q^32 + 11 * q^33 + 18 * q^34 - 22 * q^35 + 40 * q^36 + 22 * q^37 + 8 * q^38 + 13 * q^39 + 6 * q^40 + 26 * q^41 - 6 * q^42 + 21 * q^43 + 22 * q^44 + 22 * q^45 + 28 * q^46 + 41 * q^47 + 58 * q^48 + 29 * q^49 + 18 * q^50 + 17 * q^51 + 2 * q^52 + 37 * q^53 + 6 * q^54 + 7 * q^55 - 15 * q^56 + 3 * q^57 + 9 * q^58 + 27 * q^59 + 52 * q^60 + 20 * q^61 - 12 * q^62 - 29 * q^63 + 59 * q^64 + 3 * q^65 + 17 * q^66 + 30 * q^67 + 33 * q^68 + 36 * q^69 + 68 * q^71 + 15 * q^72 + q^73 + 21 * q^74 + 57 * q^75 + 11 * q^76 - 11 * q^77 + 25 * q^78 + 34 * q^79 + 110 * q^80 + 29 * q^81 - 49 * q^82 + 13 * q^83 - 40 * q^84 + 27 * q^85 + 35 * q^86 + 20 * q^87 + 17 * q^88 + 61 * q^89 - 13 * q^91 + 86 * q^92 + 6 * q^93 - 19 * q^94 + 25 * q^95 + 46 * q^96 - 3 * q^97 + 6 * q^98 + 11 * q^99

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