LMFDB - Embedded newform 4011.2.a.l.1.8

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:	$28$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.8
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)

$f(q)$	$=$	$q-1.80294 q^{2} -1.00000 q^{3} +1.25060 q^{4} -3.82317 q^{5} +1.80294 q^{6} +1.00000 q^{7} +1.35113 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q-1.80294 q^{2} -1.00000 q^{3} +1.25060 q^{4} -3.82317 q^{5} +1.80294 q^{6} +1.00000 q^{7} +1.35113 q^{8} +1.00000 q^{9} +6.89294 q^{10} -1.43419 q^{11} -1.25060 q^{12} +6.02601 q^{13} -1.80294 q^{14} +3.82317 q^{15} -4.93720 q^{16} +3.50863 q^{17} -1.80294 q^{18} +2.91876 q^{19} -4.78124 q^{20} -1.00000 q^{21} +2.58576 q^{22} +0.715931 q^{23} -1.35113 q^{24} +9.61660 q^{25} -10.8645 q^{26} -1.00000 q^{27} +1.25060 q^{28} +7.30619 q^{29} -6.89294 q^{30} +2.00118 q^{31} +6.19922 q^{32} +1.43419 q^{33} -6.32585 q^{34} -3.82317 q^{35} +1.25060 q^{36} +5.89552 q^{37} -5.26236 q^{38} -6.02601 q^{39} -5.16559 q^{40} +1.30020 q^{41} +1.80294 q^{42} +1.13014 q^{43} -1.79360 q^{44} -3.82317 q^{45} -1.29078 q^{46} -2.43499 q^{47} +4.93720 q^{48} +1.00000 q^{49} -17.3382 q^{50} -3.50863 q^{51} +7.53611 q^{52} +6.26177 q^{53} +1.80294 q^{54} +5.48315 q^{55} +1.35113 q^{56} -2.91876 q^{57} -13.1726 q^{58} -9.03155 q^{59} +4.78124 q^{60} +8.11671 q^{61} -3.60801 q^{62} +1.00000 q^{63} -1.30243 q^{64} -23.0385 q^{65} -2.58576 q^{66} +4.55976 q^{67} +4.38788 q^{68} -0.715931 q^{69} +6.89294 q^{70} -2.53003 q^{71} +1.35113 q^{72} +9.24082 q^{73} -10.6293 q^{74} -9.61660 q^{75} +3.65020 q^{76} -1.43419 q^{77} +10.8645 q^{78} -16.9446 q^{79} +18.8757 q^{80} +1.00000 q^{81} -2.34419 q^{82} -6.95751 q^{83} -1.25060 q^{84} -13.4141 q^{85} -2.03758 q^{86} -7.30619 q^{87} -1.93778 q^{88} -1.56197 q^{89} +6.89294 q^{90} +6.02601 q^{91} +0.895342 q^{92} -2.00118 q^{93} +4.39014 q^{94} -11.1589 q^{95} -6.19922 q^{96} +9.54373 q^{97} -1.80294 q^{98} -1.43419 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 28 q - 6 q^{2} - 28 q^{3} + 34 q^{4} + 8 q^{5} + 6 q^{6} + 28 q^{7} - 15 q^{8} + 28 q^{9}+O(q^{10}) $ 28 * q - 6 * q^2 - 28 * q^3 + 34 * q^4 + 8 * q^5 + 6 * q^6 + 28 * q^7 - 15 * q^8 + 28 * q^9	\( 28 q - 6 q^{2} - 28 q^{3} + 34 q^{4} + 8 q^{5} + 6 q^{6} + 28 q^{7} - 15 q^{8} + 28 q^{9} + 4 q^{10} - 8 q^{11} - 34 q^{12} + 26 q^{13} - 6 q^{14} - 8 q^{15} + 62 q^{16} + 9 q^{17} - 6 q^{18} + 25 q^{19} + 20 q^{20} - 28 q^{21} + 3 q^{22} - 30 q^{23} + 15 q^{24} + 42 q^{25} + 25 q^{26} - 28 q^{27} + 34 q^{28} - 5 q^{29} - 4 q^{30} + 18 q^{31} - 26 q^{32} + 8 q^{33} + 30 q^{34} + 8 q^{35} + 34 q^{36} + 36 q^{37} - 2 q^{38} - 26 q^{39} + 28 q^{40} + 21 q^{41} + 6 q^{42} + 8 q^{43} - 20 q^{44} + 8 q^{45} + 24 q^{46} + 6 q^{47} - 62 q^{48} + 28 q^{49} - 48 q^{50} - 9 q^{51} + 54 q^{52} - 12 q^{53} + 6 q^{54} + 15 q^{55} - 15 q^{56} - 25 q^{57} + 19 q^{58} + 33 q^{59} - 20 q^{60} + 48 q^{61} + 28 q^{63} + 75 q^{64} + 21 q^{65} - 3 q^{66} + 27 q^{67} + 19 q^{68} + 30 q^{69} + 4 q^{70} - 45 q^{71} - 15 q^{72} + 61 q^{73} - 31 q^{74} - 42 q^{75} + 63 q^{76} - 8 q^{77} - 25 q^{78} + 35 q^{79} + 84 q^{80} + 28 q^{81} + 11 q^{82} + 43 q^{83} - 34 q^{84} + 43 q^{85} - q^{86} + 5 q^{87} - 27 q^{88} + 25 q^{89} + 4 q^{90} + 26 q^{91} - 102 q^{92} - 18 q^{93} + 55 q^{94} - 43 q^{95} + 26 q^{96} + 40 q^{97} - 6 q^{98} - 8 q^{99}+O(q^{100}) \) 28 * q - 6 * q^2 - 28 * q^3 + 34 * q^4 + 8 * q^5 + 6 * q^6 + 28 * q^7 - 15 * q^8 + 28 * q^9 + 4 * q^10 - 8 * q^11 - 34 * q^12 + 26 * q^13 - 6 * q^14 - 8 * q^15 + 62 * q^16 + 9 * q^17 - 6 * q^18 + 25 * q^19 + 20 * q^20 - 28 * q^21 + 3 * q^22 - 30 * q^23 + 15 * q^24 + 42 * q^25 + 25 * q^26 - 28 * q^27 + 34 * q^28 - 5 * q^29 - 4 * q^30 + 18 * q^31 - 26 * q^32 + 8 * q^33 + 30 * q^34 + 8 * q^35 + 34 * q^36 + 36 * q^37 - 2 * q^38 - 26 * q^39 + 28 * q^40 + 21 * q^41 + 6 * q^42 + 8 * q^43 - 20 * q^44 + 8 * q^45 + 24 * q^46 + 6 * q^47 - 62 * q^48 + 28 * q^49 - 48 * q^50 - 9 * q^51 + 54 * q^52 - 12 * q^53 + 6 * q^54 + 15 * q^55 - 15 * q^56 - 25 * q^57 + 19 * q^58 + 33 * q^59 - 20 * q^60 + 48 * q^61 + 28 * q^63 + 75 * q^64 + 21 * q^65 - 3 * q^66 + 27 * q^67 + 19 * q^68 + 30 * q^69 + 4 * q^70 - 45 * q^71 - 15 * q^72 + 61 * q^73 - 31 * q^74 - 42 * q^75 + 63 * q^76 - 8 * q^77 - 25 * q^78 + 35 * q^79 + 84 * q^80 + 28 * q^81 + 11 * q^82 + 43 * q^83 - 34 * q^84 + 43 * q^85 - q^86 + 5 * q^87 - 27 * q^88 + 25 * q^89 + 4 * q^90 + 26 * q^91 - 102 * q^92 - 18 * q^93 + 55 * q^94 - 43 * q^95 + 26 * q^96 + 40 * q^97 - 6 * q^98 - 8 * q^99

Display 100 coefficients 10 coefficients

Coefficient data

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

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

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

$2$	−1.80294	−1.27487	−0.637436	−	0.770503i	$-0.720005\pi$
$2$	−1.80294	−1.27487	−0.637436	+	0.770503i	$0.720005\pi$
$3$	−1.00000	−0.577350
$3$	−1.00000	−0.577350
$4$	1.25060	0.625298
$5$	−3.82317	−1.70977	−0.854886	−	0.518816i	$-0.826373\pi$
$5$	−3.82317	−1.70977	−0.854886	+	0.518816i	$0.826373\pi$
$6$	1.80294	0.736048
$7$	1.00000	0.377964
$7$	1.00000	0.377964
$8$	1.35113	0.477697
$9$	1.00000	0.333333
$10$	6.89294	2.17974
$11$	−1.43419	−0.432425	−0.216213	−	0.976346i	$-0.569370\pi$
$11$	−1.43419	−0.432425	−0.216213	+	0.976346i	$0.569370\pi$
$12$	−1.25060	−0.361016
$13$	6.02601	1.67132	0.835658	−	0.549250i	$-0.185087\pi$
$13$	6.02601	1.67132	0.835658	+	0.549250i	$0.185087\pi$
$14$	−1.80294	−0.481856
$15$	3.82317	0.987137
$16$	−4.93720	−1.23430
$17$	3.50863	0.850967	0.425483	−	0.904966i	$-0.360104\pi$
$17$	3.50863	0.850967	0.425483	+	0.904966i	$0.360104\pi$
$18$	−1.80294	−0.424957
$19$	2.91876	0.669610	0.334805	−	0.942287i	$-0.391330\pi$
$19$	2.91876	0.669610	0.334805	+	0.942287i	$0.391330\pi$
$20$	−4.78124	−1.06912
$21$	−1.00000	−0.218218
$22$	2.58576	0.551287
$23$	0.715931	0.149282	0.0746410	−	0.997210i	$-0.476219\pi$
$23$	0.715931	0.149282	0.0746410	+	0.997210i	$0.476219\pi$
$24$	−1.35113	−0.275798
$25$	9.61660	1.92332
$26$	−10.8645	−2.13071
$27$	−1.00000	−0.192450
$28$	1.25060	0.236341
$29$	7.30619	1.35673	0.678363	−	0.734727i	$-0.262690\pi$
$29$	7.30619	1.35673	0.678363	+	0.734727i	$0.262690\pi$
$30$	−6.89294	−1.25847
$31$	2.00118	0.359423	0.179711	−	0.983719i	$-0.442484\pi$
$31$	2.00118	0.359423	0.179711	+	0.983719i	$0.442484\pi$
$32$	6.19922	1.09588
$33$	1.43419	0.249661
$34$	−6.32585	−1.08487
$35$	−3.82317	−0.646233
$36$	1.25060	0.208433
$37$	5.89552	0.969218	0.484609	−	0.874731i	$-0.338962\pi$
$37$	5.89552	0.969218	0.484609	+	0.874731i	$0.338962\pi$
$38$	−5.26236	−0.853667
$39$	−6.02601	−0.964935
$40$	−5.16559	−0.816752
$41$	1.30020	0.203058	0.101529	−	0.994833i	$-0.467627\pi$
$41$	1.30020	0.203058	0.101529	+	0.994833i	$0.467627\pi$
$42$	1.80294	0.278200
$43$	1.13014	0.172345	0.0861724	−	0.996280i	$-0.472536\pi$
$43$	1.13014	0.172345	0.0861724	+	0.996280i	$0.472536\pi$
$44$	−1.79360	−0.270395
$45$	−3.82317	−0.569924
$46$	−1.29078	−0.190315
$47$	−2.43499	−0.355179	−0.177590	−	0.984105i	$-0.556830\pi$
$47$	−2.43499	−0.355179	−0.177590	+	0.984105i	$0.556830\pi$
$48$	4.93720	0.712624
$49$	1.00000	0.142857
$50$	−17.3382	−2.45199
$51$	−3.50863	−0.491306
$52$	7.53611	1.04507
$53$	6.26177	0.860121	0.430060	−	0.902800i	$-0.358492\pi$
$53$	6.26177	0.860121	0.430060	+	0.902800i	$0.358492\pi$
$54$	1.80294	0.245349
$55$	5.48315	0.739348
$56$	1.35113	0.180552
$57$	−2.91876	−0.386600
$58$	−13.1726	−1.72965
$59$	−9.03155	−1.17581	−0.587904	−	0.808931i	$-0.700047\pi$
$59$	−9.03155	−1.17581	−0.587904	+	0.808931i	$0.700047\pi$
$60$	4.78124	0.617255
$61$	8.11671	1.03924	0.519619	−	0.854398i	$-0.326074\pi$
$61$	8.11671	1.03924	0.519619	+	0.854398i	$0.326074\pi$
$62$	−3.60801	−0.458218
$63$	1.00000	0.125988
$64$	−1.30243	−0.162804
$65$	−23.0385	−2.85757
$66$	−2.58576	−0.318286
$67$	4.55976	0.557063	0.278532	−	0.960427i	$-0.410152\pi$
$67$	4.55976	0.557063	0.278532	+	0.960427i	$0.410152\pi$
$68$	4.38788	0.532108
$69$	−0.715931	−0.0861880
$70$	6.89294	0.823864
$71$	−2.53003	−0.300259	−0.150130	−	0.988666i	$-0.547969\pi$
$71$	−2.53003	−0.300259	−0.150130	+	0.988666i	$0.547969\pi$
$72$	1.35113	0.159232
$73$	9.24082	1.08156	0.540778	−	0.841165i	$-0.318130\pi$
$73$	9.24082	1.08156	0.540778	+	0.841165i	$0.318130\pi$
$74$	−10.6293	−1.23563
$75$	−9.61660	−1.11043
$76$	3.65020	0.418706
$77$	−1.43419	−0.163441
$78$	10.8645	1.23017
$79$	−16.9446	−1.90642	−0.953211	−	0.302307i	$-0.902243\pi$
$79$	−16.9446	−1.90642	−0.953211	+	0.302307i	$0.902243\pi$
$80$	18.8757	2.11037
$81$	1.00000	0.111111
$82$	−2.34419	−0.258872
$83$	−6.95751	−0.763686	−0.381843	−	0.924227i	$-0.624711\pi$
$83$	−6.95751	−0.763686	−0.381843	+	0.924227i	$0.624711\pi$
$84$	−1.25060	−0.136451
$85$	−13.4141	−1.45496
$86$	−2.03758	−0.219717
$87$	−7.30619	−0.783306
$88$	−1.93778	−0.206568
$89$	−1.56197	−0.165568	−0.0827841	−	0.996568i	$-0.526381\pi$
$89$	−1.56197	−0.165568	−0.0827841	+	0.996568i	$0.526381\pi$
$90$	6.89294	0.726580
$91$	6.02601	0.631698
$92$	0.895342	0.0933458
$93$	−2.00118	−0.207513
$94$	4.39014	0.452808
$95$	−11.1589	−1.14488
$96$	−6.19922	−0.632706
$97$	9.54373	0.969019	0.484510	−	0.874786i	$-0.338998\pi$
$97$	9.54373	0.969019	0.484510	+	0.874786i	$0.338998\pi$
$98$	−1.80294	−0.182125
$99$	−1.43419	−0.144142
$100$	12.0265	1.20265
$101$	−4.49383	−0.447153	−0.223577	−	0.974686i	$-0.571773\pi$
$101$	−4.49383	−0.447153	−0.223577	+	0.974686i	$0.571773\pi$
$102$	6.32585	0.626352
$103$	0.283173	0.0279018	0.0139509	−	0.999903i	$-0.495559\pi$
$103$	0.283173	0.0279018	0.0139509	+	0.999903i	$0.495559\pi$
$104$	8.14193	0.798382
$105$	3.82317	0.373103
$106$	−11.2896	−1.09654
$107$	−12.5051	−1.20892	−0.604459	−	0.796636i	$-0.706611\pi$
$107$	−12.5051	−1.20892	−0.604459	+	0.796636i	$0.706611\pi$
$108$	−1.25060	−0.120339
$109$	−8.78451	−0.841404	−0.420702	−	0.907199i	$-0.638216\pi$
$109$	−8.78451	−0.841404	−0.420702	+	0.907199i	$0.638216\pi$
$110$	−9.88580	−0.942575
$111$	−5.89552	−0.559578
$112$	−4.93720	−0.466522
$113$	0.732957	0.0689508	0.0344754	−	0.999406i	$-0.489024\pi$
$113$	0.732957	0.0689508	0.0344754	+	0.999406i	$0.489024\pi$
$114$	5.26236	0.492865
$115$	−2.73712	−0.255238
$116$	9.13710	0.848358
$117$	6.02601	0.557105
$118$	16.2833	1.49900
$119$	3.50863	0.321635
$120$	5.16559	0.471552
$121$	−8.94309	−0.813008
$122$	−14.6340	−1.32490
$123$	−1.30020	−0.117235
$124$	2.50267	0.224746
$125$	−17.6500	−1.57867
$126$	−1.80294	−0.160619
$127$	−0.564097	−0.0500555	−0.0250278	−	0.999687i	$-0.507967\pi$
$127$	−0.564097	−0.0500555	−0.0250278	+	0.999687i	$0.507967\pi$
$128$	−10.0502	−0.888324
$129$	−1.13014	−0.0995033
$130$	41.5370	3.64303
$131$	6.99339	0.611016	0.305508	−	0.952190i	$-0.401174\pi$
$131$	6.99339	0.611016	0.305508	+	0.952190i	$0.401174\pi$
$132$	1.79360	0.156113
$133$	2.91876	0.253089
$134$	−8.22098	−0.710184
$135$	3.82317	0.329046
$136$	4.74061	0.406504
$137$	14.7816	1.26288	0.631438	−	0.775426i	$-0.282465\pi$
$137$	14.7816	1.26288	0.631438	+	0.775426i	$0.282465\pi$
$138$	1.29078	0.109879
$139$	1.33612	0.113328	0.0566641	−	0.998393i	$-0.481954\pi$
$139$	1.33612	0.113328	0.0566641	+	0.998393i	$0.481954\pi$
$140$	−4.78124	−0.404088
$141$	2.43499	0.205063
$142$	4.56150	0.382792
$143$	−8.64246	−0.722719
$144$	−4.93720	−0.411433
$145$	−27.9328	−2.31969
$146$	−16.6607	−1.37885
$147$	−1.00000	−0.0824786
$148$	7.37292	0.606050
$149$	−2.49576	−0.204461	−0.102230	−	0.994761i	$-0.532598\pi$
$149$	−2.49576	−0.204461	−0.102230	+	0.994761i	$0.532598\pi$
$150$	17.3382	1.41565
$151$	−7.80909	−0.635495	−0.317748	−	0.948175i	$-0.602926\pi$
$151$	−7.80909	−0.635495	−0.317748	+	0.948175i	$0.602926\pi$
$152$	3.94363	0.319870
$153$	3.50863	0.283656
$154$	2.58576	0.208367
$155$	−7.65084	−0.614531
$156$	−7.53611	−0.603372
$157$	7.98020	0.636890	0.318445	−	0.947941i	$-0.396839\pi$
$157$	7.98020	0.636890	0.318445	+	0.947941i	$0.396839\pi$
$158$	30.5502	2.43044
$159$	−6.26177	−0.496591
$160$	−23.7007	−1.87370
$161$	0.715931	0.0564233
$162$	−1.80294	−0.141652
$163$	−0.907386	−0.0710719	−0.0355360	−	0.999368i	$-0.511314\pi$
$163$	−0.907386	−0.0710719	−0.0355360	+	0.999368i	$0.511314\pi$
$164$	1.62603	0.126972
$165$	−5.48315	−0.426863
$166$	12.5440	0.973602
$167$	7.42540	0.574595	0.287297	−	0.957841i	$-0.407243\pi$
$167$	7.42540	0.574595	0.287297	+	0.957841i	$0.407243\pi$
$168$	−1.35113	−0.104242
$169$	23.3128	1.79330
$170$	24.1848	1.85489
$171$	2.91876	0.223203
$172$	1.41335	0.107767
$173$	4.08709	0.310735	0.155368	−	0.987857i	$-0.450344\pi$
$173$	4.08709	0.310735	0.155368	+	0.987857i	$0.450344\pi$
$174$	13.1726	0.998615
$175$	9.61660	0.726946
$176$	7.08090	0.533743
$177$	9.03155	0.678853
$178$	2.81613	0.211078
$179$	14.3472	1.07236	0.536182	−	0.844103i	$-0.319866\pi$
$179$	14.3472	1.07236	0.536182	+	0.844103i	$0.319866\pi$
$180$	−4.78124	−0.356373
$181$	−2.10090	−0.156159	−0.0780793	−	0.996947i	$-0.524879\pi$
$181$	−2.10090	−0.156159	−0.0780793	+	0.996947i	$0.524879\pi$
$182$	−10.8645	−0.805334
$183$	−8.11671	−0.600005
$184$	0.967316	0.0713115
$185$	−22.5396	−1.65714
$186$	3.60801	0.264552
$187$	−5.03204	−0.367980
$188$	−3.04519	−0.222093
$189$	−1.00000	−0.0727393
$190$	20.1189	1.45958
$191$	−1.00000	−0.0723575
$191$	−1.00000	−0.0723575
$192$	1.30243	0.0939950
$193$	−12.2764	−0.883677	−0.441838	−	0.897095i	$-0.645674\pi$
$193$	−12.2764	−0.883677	−0.441838	+	0.897095i	$0.645674\pi$
$194$	−17.2068	−1.23538
$195$	23.0385	1.64982
$196$	1.25060	0.0893283
$197$	15.8690	1.13062	0.565311	−	0.824878i	$-0.308756\pi$
$197$	15.8690	1.13062	0.565311	+	0.824878i	$0.308756\pi$
$198$	2.58576	0.183762
$199$	21.7195	1.53965	0.769827	−	0.638252i	$-0.220342\pi$
$199$	21.7195	1.53965	0.769827	+	0.638252i	$0.220342\pi$
$200$	12.9933	0.918763
$201$	−4.55976	−0.321621
$202$	8.10212	0.570063
$203$	7.30619	0.512794
$204$	−4.38788	−0.307213
$205$	−4.97089	−0.347182
$206$	−0.510544	−0.0355713
$207$	0.715931	0.0497607
$208$	−29.7516	−2.06291
$209$	−4.18607	−0.289556
$210$	−6.89294	−0.475658
$211$	−12.2607	−0.844064	−0.422032	−	0.906581i	$-0.638683\pi$
$211$	−12.2607	−0.844064	−0.422032	+	0.906581i	$0.638683\pi$
$212$	7.83095	0.537832
$213$	2.53003	0.173355
$214$	22.5460	1.54122
$215$	−4.32071	−0.294670
$216$	−1.35113	−0.0919327
$217$	2.00118	0.135849
$218$	15.8380	1.07268
$219$	−9.24082	−0.624437
$220$	6.85722	0.462313
$221$	21.1430	1.42223
$222$	10.6293	0.713390
$223$	−18.1670	−1.21655	−0.608276	−	0.793726i	$-0.708139\pi$
$223$	−18.1670	−1.21655	−0.608276	+	0.793726i	$0.708139\pi$
$224$	6.19922	0.414203
$225$	9.61660	0.641107
$226$	−1.32148	−0.0879034
$227$	9.04176	0.600122	0.300061	−	0.953920i	$-0.402993\pi$
$227$	9.04176	0.600122	0.300061	+	0.953920i	$0.402993\pi$
$228$	−3.65020	−0.241740
$229$	9.38181	0.619967	0.309984	−	0.950742i	$-0.399676\pi$
$229$	9.38181	0.619967	0.309984	+	0.950742i	$0.399676\pi$
$230$	4.93487	0.325396
$231$	1.43419	0.0943629
$232$	9.87161	0.648103
$233$	16.6386	1.09003	0.545016	−	0.838426i	$-0.316524\pi$
$233$	16.6386	1.09003	0.545016	+	0.838426i	$0.316524\pi$
$234$	−10.8645	−0.710238
$235$	9.30935	0.607275
$236$	−11.2948	−0.735230
$237$	16.9446	1.10067
$238$	−6.32585	−0.410044
$239$	−1.78688	−0.115584	−0.0577920	−	0.998329i	$-0.518406\pi$
$239$	−1.78688	−0.115584	−0.0577920	+	0.998329i	$0.518406\pi$
$240$	−18.8757	−1.21842
$241$	23.4733	1.51205	0.756025	−	0.654543i	$-0.227139\pi$
$241$	23.4733	1.51205	0.756025	+	0.654543i	$0.227139\pi$
$242$	16.1239	1.03648
$243$	−1.00000	−0.0641500
$244$	10.1507	0.649834
$245$	−3.82317	−0.244253
$246$	2.34419	0.149460
$247$	17.5885	1.11913
$248$	2.70385	0.171695
$249$	6.95751	0.440914
$250$	31.8219	2.01260
$251$	12.8620	0.811842	0.405921	−	0.913908i	$-0.366951\pi$
$251$	12.8620	0.811842	0.405921	+	0.913908i	$0.366951\pi$
$252$	1.25060	0.0787802
$253$	−1.02678	−0.0645533
$254$	1.01703	0.0638144
$255$	13.4141	0.840021
$256$	20.7249	1.29530
$257$	−20.4966	−1.27854	−0.639271	−	0.768982i	$-0.720764\pi$
$257$	−20.4966	−1.27854	−0.639271	+	0.768982i	$0.720764\pi$
$258$	2.03758	0.126854
$259$	5.89552	0.366330
$260$	−28.8118	−1.78683
$261$	7.30619	0.452242
$262$	−12.6087	−0.778967
$263$	−26.5195	−1.63526	−0.817631	−	0.575743i	$-0.804713\pi$
$263$	−26.5195	−1.63526	−0.817631	+	0.575743i	$0.804713\pi$
$264$	1.93778	0.119262
$265$	−23.9398	−1.47061
$266$	−5.26236	−0.322656
$267$	1.56197	0.0955908
$268$	5.70242	0.348331
$269$	−17.9988	−1.09741	−0.548704	−	0.836017i	$-0.684878\pi$
$269$	−17.9988	−1.09741	−0.548704	+	0.836017i	$0.684878\pi$
$270$	−6.89294	−0.419491
$271$	12.9460	0.786414	0.393207	−	0.919450i	$-0.371366\pi$
$271$	12.9460	0.786414	0.393207	+	0.919450i	$0.371366\pi$
$272$	−17.3228	−1.05035
$273$	−6.02601	−0.364711
$274$	−26.6503	−1.61001
$275$	−13.7920	−0.831692
$276$	−0.895342	−0.0538932
$277$	−19.0936	−1.14722	−0.573611	−	0.819128i	$-0.694458\pi$
$277$	−19.0936	−1.14722	−0.573611	+	0.819128i	$0.694458\pi$
$278$	−2.40894	−0.144479
$279$	2.00118	0.119808
$280$	−5.16559	−0.308703
$281$	14.1429	0.843694	0.421847	−	0.906667i	$-0.361382\pi$
$281$	14.1429	0.843694	0.421847	+	0.906667i	$0.361382\pi$
$282$	−4.39014	−0.261429
$283$	14.0331	0.834184	0.417092	−	0.908864i	$-0.363049\pi$
$283$	14.0331	0.834184	0.417092	+	0.908864i	$0.363049\pi$
$284$	−3.16405	−0.187752
$285$	11.1589	0.660997
$286$	15.5819	0.921374
$287$	1.30020	0.0767486
$288$	6.19922	0.365293
$289$	−4.68954	−0.275855
$290$	50.3612	2.95731
$291$	−9.54373	−0.559464
$292$	11.5565	0.676295
$293$	−3.42960	−0.200360	−0.100180	−	0.994969i	$-0.531942\pi$
$293$	−3.42960	−0.200360	−0.100180	+	0.994969i	$0.531942\pi$
$294$	1.80294	0.105150
$295$	34.5291	2.01036
$296$	7.96561	0.462992
$297$	1.43419	0.0832203
$298$	4.49971	0.260661
$299$	4.31421	0.249497
$300$	−12.0265	−0.694350
$301$	1.13014	0.0651402
$302$	14.0793	0.810175
$303$	4.49383	0.258164
$304$	−14.4105	−0.826500
$305$	−31.0315	−1.77686
$306$	−6.32585	−0.361625
$307$	17.8012	1.01597	0.507983	−	0.861367i	$-0.330391\pi$
$307$	17.8012	1.01597	0.507983	+	0.861367i	$0.330391\pi$
$308$	−1.79360	−0.102200
$309$	−0.283173	−0.0161091
$310$	13.7940	0.783448
$311$	−26.5219	−1.50392	−0.751960	−	0.659209i	$-0.770891\pi$
$311$	−26.5219	−1.50392	−0.751960	+	0.659209i	$0.770891\pi$
$312$	−8.14193	−0.460946
$313$	−34.1314	−1.92922	−0.964609	−	0.263683i	$-0.915063\pi$
$313$	−34.1314	−1.92922	−0.964609	+	0.263683i	$0.915063\pi$
$314$	−14.3878	−0.811953
$315$	−3.82317	−0.215411
$316$	−21.1909	−1.19208
$317$	15.6255	0.877616	0.438808	−	0.898581i	$-0.355401\pi$
$317$	15.6255	0.877616	0.438808	+	0.898581i	$0.355401\pi$
$318$	11.2896	0.633090
$319$	−10.4785	−0.586682
$320$	4.97942	0.278358
$321$	12.5051	0.697969
$322$	−1.29078	−0.0719325
$323$	10.2408	0.569816
$324$	1.25060	0.0694776
$325$	57.9498	3.21447
$326$	1.63596	0.0906076
$327$	8.78451	0.485785
$328$	1.75674	0.0969999
$329$	−2.43499	−0.134245
$330$	9.88580	0.544196
$331$	27.4095	1.50656	0.753281	−	0.657699i	$-0.228470\pi$
$331$	27.4095	1.50656	0.753281	+	0.657699i	$0.228470\pi$
$332$	−8.70104	−0.477532
$333$	5.89552	0.323073
$334$	−13.3876	−0.732535
$335$	−17.4327	−0.952451
$336$	4.93720	0.269346
$337$	18.3291	0.998451	0.499225	−	0.866472i	$-0.333618\pi$
$337$	18.3291	0.998451	0.499225	+	0.866472i	$0.333618\pi$
$338$	−42.0317	−2.28622
$339$	−0.732957	−0.0398088
$340$	−16.7756	−0.909784
$341$	−2.87008	−0.155423
$342$	−5.26236	−0.284556
$343$	1.00000	0.0539949
$344$	1.52697	0.0823285
$345$	2.73712	0.147362
$346$	−7.36878	−0.396148
$347$	−10.1300	−0.543806	−0.271903	−	0.962325i	$-0.587653\pi$
$347$	−10.1300	−0.543806	−0.271903	+	0.962325i	$0.587653\pi$
$348$	−9.13710	−0.489800
$349$	17.9786	0.962370	0.481185	−	0.876619i	$-0.340207\pi$
$349$	17.9786	0.962370	0.481185	+	0.876619i	$0.340207\pi$
$350$	−17.3382	−0.926764
$351$	−6.02601	−0.321645
$352$	−8.89088	−0.473885
$353$	20.2004	1.07516	0.537580	−	0.843213i	$-0.319339\pi$
$353$	20.2004	1.07516	0.537580	+	0.843213i	$0.319339\pi$
$354$	−16.2833	−0.865450
$355$	9.67273	0.513375
$356$	−1.95339	−0.103530
$357$	−3.50863	−0.185696
$358$	−25.8672	−1.36713
$359$	32.8045	1.73136	0.865678	−	0.500601i	$-0.166888\pi$
$359$	32.8045	1.73136	0.865678	+	0.500601i	$0.166888\pi$
$360$	−5.16559	−0.272251
$361$	−10.4808	−0.551622
$362$	3.78780	0.199082
$363$	8.94309	0.469391
$364$	7.53611	0.395000
$365$	−35.3292	−1.84921
$366$	14.6340	0.764929
$367$	−28.9121	−1.50920	−0.754600	−	0.656185i	$-0.772169\pi$
$367$	−28.9121	−1.50920	−0.754600	+	0.656185i	$0.772169\pi$
$368$	−3.53470	−0.184259
$369$	1.30020	0.0676859
$370$	40.6375	2.11264
$371$	6.26177	0.325095
$372$	−2.50267	−0.129757
$373$	−8.70130	−0.450536	−0.225268	−	0.974297i	$-0.572326\pi$
$373$	−8.70130	−0.450536	−0.225268	+	0.974297i	$0.572326\pi$
$374$	9.07248	0.469127
$375$	17.6500	0.911443
$376$	−3.28998	−0.169668
$377$	44.0272	2.26752
$378$	1.80294	0.0927333
$379$	−25.2117	−1.29504	−0.647518	−	0.762050i	$-0.724193\pi$
$379$	−25.2117	−1.29504	−0.647518	+	0.762050i	$0.724193\pi$
$380$	−13.9553	−0.715892
$381$	0.564097	0.0288996
$382$	1.80294	0.0922465
$383$	14.1140	0.721193	0.360596	−	0.932722i	$-0.382573\pi$
$383$	14.1140	0.721193	0.360596	+	0.932722i	$0.382573\pi$
$384$	10.0502	0.512874
$385$	5.48315	0.279447
$386$	22.1337	1.12657
$387$	1.13014	0.0574483
$388$	11.9354	0.605926
$389$	−4.49201	−0.227754	−0.113877	−	0.993495i	$-0.536327\pi$
$389$	−4.49201	−0.227754	−0.113877	+	0.993495i	$0.536327\pi$
$390$	−41.5370	−2.10331
$391$	2.51194	0.127034
$392$	1.35113	0.0682424
$393$	−6.99339	−0.352770
$394$	−28.6109	−1.44140
$395$	64.7822	3.25955
$396$	−1.79360	−0.0901316
$397$	2.03154	0.101960	0.0509800	−	0.998700i	$-0.483766\pi$
$397$	2.03154	0.101960	0.0509800	+	0.998700i	$0.483766\pi$
$398$	−39.1590	−1.96286
$399$	−2.91876	−0.146121
$400$	−47.4791	−2.37395
$401$	−24.2529	−1.21113	−0.605565	−	0.795796i	$-0.707053\pi$
$401$	−24.2529	−1.21113	−0.605565	+	0.795796i	$0.707053\pi$
$402$	8.22098	0.410025
$403$	12.0591	0.600709
$404$	−5.61998	−0.279604
$405$	−3.82317	−0.189975
$406$	−13.1726	−0.653747
$407$	−8.45531	−0.419114
$408$	−4.74061	−0.234695
$409$	25.9213	1.28173	0.640864	−	0.767654i	$-0.278576\pi$
$409$	25.9213	1.28173	0.640864	+	0.767654i	$0.278576\pi$
$410$	8.96223	0.442613
$411$	−14.7816	−0.729122
$412$	0.354135	0.0174470
$413$	−9.03155	−0.444413
$414$	−1.29078	−0.0634385
$415$	26.5997	1.30573
$416$	37.3566	1.83156
$417$	−1.33612	−0.0654300
$418$	7.54723	0.369147
$419$	−13.6983	−0.669206	−0.334603	−	0.942359i	$-0.608602\pi$
$419$	−13.6983	−0.669206	−0.334603	+	0.942359i	$0.608602\pi$
$420$	4.78124	0.233301
$421$	2.60641	0.127029	0.0635143	−	0.997981i	$-0.479769\pi$
$421$	2.60641	0.127029	0.0635143	+	0.997981i	$0.479769\pi$
$422$	22.1054	1.07607
$423$	−2.43499	−0.118393
$424$	8.46047	0.410877
$425$	33.7410	1.63668
$426$	−4.56150	−0.221005
$427$	8.11671	0.392795
$428$	−15.6389	−0.755934
$429$	8.64246	0.417262
$430$	7.78999	0.375667
$431$	15.0472	0.724798	0.362399	−	0.932023i	$-0.381958\pi$
$431$	15.0472	0.724798	0.362399	+	0.932023i	$0.381958\pi$
$432$	4.93720	0.237541
$433$	−3.07671	−0.147857	−0.0739285	−	0.997264i	$-0.523554\pi$
$433$	−3.07671	−0.147857	−0.0739285	+	0.997264i	$0.523554\pi$
$434$	−3.60801	−0.173190
$435$	27.9328	1.33927
$436$	−10.9859	−0.526128
$437$	2.08963	0.0999607
$438$	16.6607	0.796077
$439$	19.4805	0.929752	0.464876	−	0.885376i	$-0.346099\pi$
$439$	19.4805	0.929752	0.464876	+	0.885376i	$0.346099\pi$
$440$	7.40845	0.353184
$441$	1.00000	0.0476190
$442$	−38.1196	−1.81317
$443$	−15.5812	−0.740287	−0.370143	−	0.928975i	$-0.620691\pi$
$443$	−15.5812	−0.740287	−0.370143	+	0.928975i	$0.620691\pi$
$444$	−7.37292	−0.349903
$445$	5.97166	0.283084
$446$	32.7540	1.55095
$447$	2.49576	0.118045
$448$	−1.30243	−0.0615342
$449$	10.0899	0.476173	0.238086	−	0.971244i	$-0.423480\pi$
$449$	10.0899	0.476173	0.238086	+	0.971244i	$0.423480\pi$
$450$	−17.3382	−0.817329
$451$	−1.86474	−0.0878072
$452$	0.916634	0.0431148
$453$	7.80909	0.366903
$454$	−16.3018	−0.765079
$455$	−23.0385	−1.08006
$456$	−3.94363	−0.184677
$457$	−12.9750	−0.606943	−0.303471	−	0.952841i	$-0.598146\pi$
$457$	−12.9750	−0.606943	−0.303471	+	0.952841i	$0.598146\pi$
$458$	−16.9148	−0.790379
$459$	−3.50863	−0.163769
$460$	−3.42304	−0.159600
$461$	8.13569	0.378917	0.189458	−	0.981889i	$-0.439327\pi$
$461$	8.13569	0.378917	0.189458	+	0.981889i	$0.439327\pi$
$462$	−2.58576	−0.120301
$463$	−12.5721	−0.584277	−0.292138	−	0.956376i	$-0.594367\pi$
$463$	−12.5721	−0.584277	−0.292138	+	0.956376i	$0.594367\pi$
$464$	−36.0721	−1.67461
$465$	7.65084	0.354799
$466$	−29.9984	−1.38965
$467$	39.6273	1.83373	0.916866	−	0.399196i	$-0.130711\pi$
$467$	39.6273	1.83373	0.916866	+	0.399196i	$0.130711\pi$
$468$	7.53611	0.348357
$469$	4.55976	0.210550
$470$	−16.7842	−0.774198
$471$	−7.98020	−0.367708
$472$	−12.2028	−0.561679
$473$	−1.62084	−0.0745262
$474$	−30.5502	−1.40322
$475$	28.0686	1.28787
$476$	4.38788	0.201118
$477$	6.26177	0.286707
$478$	3.22165	0.147355
$479$	−37.3723	−1.70759	−0.853793	−	0.520613i	$-0.825704\pi$
$479$	−37.3723	−1.70759	−0.853793	+	0.520613i	$0.825704\pi$
$480$	23.7007	1.08178
$481$	35.5265	1.61987
$482$	−42.3210	−1.92767
$483$	−0.715931	−0.0325760
$484$	−11.1842	−0.508373
$485$	−36.4873	−1.65680
$486$	1.80294	0.0817831
$487$	8.59444	0.389451	0.194726	−	0.980858i	$-0.437618\pi$
$487$	8.59444	0.389451	0.194726	+	0.980858i	$0.437618\pi$
$488$	10.9667	0.496441
$489$	0.907386	0.0410334
$490$	6.89294	0.311391
$491$	28.8687	1.30283	0.651413	−	0.758723i	$-0.274177\pi$
$491$	28.8687	1.30283	0.651413	+	0.758723i	$0.274177\pi$
$492$	−1.62603	−0.0733071
$493$	25.6347	1.15453
$494$	−31.7110	−1.42675
$495$	5.48315	0.246449
$496$	−9.88023	−0.443635
$497$	−2.53003	−0.113487
$498$	−12.5440	−0.562109
$499$	−21.0192	−0.940949	−0.470475	−	0.882414i	$-0.655917\pi$
$499$	−21.0192	−0.940949	−0.470475	+	0.882414i	$0.655917\pi$
$500$	−22.0731	−0.987137
$501$	−7.42540	−0.331742
$502$	−23.1894	−1.03499
$503$	20.4230	0.910619	0.455309	−	0.890333i	$-0.349529\pi$
$503$	20.4230	0.910619	0.455309	+	0.890333i	$0.349529\pi$
$504$	1.35113	0.0601841
$505$	17.1807	0.764530
$506$	1.85123	0.0822972
$507$	−23.3128	−1.03536
$508$	−0.705458	−0.0312996
$509$	−14.8921	−0.660080	−0.330040	−	0.943967i	$-0.607062\pi$
$509$	−14.8921	−0.660080	−0.330040	+	0.943967i	$0.607062\pi$
$510$	−24.1848	−1.07092
$511$	9.24082	0.408790
$512$	−17.2652	−0.763022
$513$	−2.91876	−0.128867
$514$	36.9541	1.62998
$515$	−1.08262	−0.0477058
$516$	−1.41335	−0.0622193
$517$	3.49224	0.153588
$518$	−10.6293	−0.467024
$519$	−4.08709	−0.179403
$520$	−31.1279	−1.36505
$521$	40.7737	1.78633	0.893163	−	0.449733i	$-0.148481\pi$
$521$	40.7737	1.78633	0.893163	+	0.449733i	$0.148481\pi$
$522$	−13.1726	−0.576550
$523$	−32.9265	−1.43978	−0.719888	−	0.694091i	$-0.755807\pi$
$523$	−32.9265	−1.43978	−0.719888	+	0.694091i	$0.755807\pi$
$524$	8.74592	0.382067
$525$	−9.61660	−0.419703
$526$	47.8131	2.08475
$527$	7.02139	0.305857
$528$	−7.08090	−0.308156
$529$	−22.4874	−0.977715
$530$	43.1620	1.87484
$531$	−9.03155	−0.391936
$532$	3.65020	0.158256
$533$	7.83504	0.339373
$534$	−2.81613	−0.121866
$535$	47.8092	2.06697
$536$	6.16082	0.266107
$537$	−14.3472	−0.619129
$538$	32.4508	1.39905
$539$	−1.43419	−0.0617750
$540$	4.78124	0.205752
$541$	−22.0749	−0.949072	−0.474536	−	0.880236i	$-0.657384\pi$
$541$	−22.0749	−0.949072	−0.474536	+	0.880236i	$0.657384\pi$
$542$	−23.3409	−1.00258
$543$	2.10090	0.0901582
$544$	21.7508	0.932556
$545$	33.5846	1.43861
$546$	10.8645	0.464960
$547$	21.5325	0.920664	0.460332	−	0.887747i	$-0.347730\pi$
$547$	21.5325	0.920664	0.460332	+	0.887747i	$0.347730\pi$
$548$	18.4858	0.789675
$549$	8.11671	0.346413
$550$	24.8663	1.06030
$551$	21.3250	0.908477
$552$	−0.967316	−0.0411717
$553$	−16.9446	−0.720560
$554$	34.4246	1.46256
$555$	22.5396	0.956751
$556$	1.67095	0.0708639
$557$	−23.1922	−0.982684	−0.491342	−	0.870967i	$-0.663493\pi$
$557$	−23.1922	−0.982684	−0.491342	+	0.870967i	$0.663493\pi$
$558$	−3.60801	−0.152739
$559$	6.81024	0.288042
$560$	18.8757	0.797646
$561$	5.03204	0.212453
$562$	−25.4988	−1.07560
$563$	38.1102	1.60615	0.803077	−	0.595875i	$-0.203195\pi$
$563$	38.1102	1.60615	0.803077	+	0.595875i	$0.203195\pi$
$564$	3.04519	0.128225
$565$	−2.80222	−0.117890
$566$	−25.3009	−1.06348
$567$	1.00000	0.0419961
$568$	−3.41840	−0.143433
$569$	19.8782	0.833338	0.416669	−	0.909058i	$-0.363197\pi$
$569$	19.8782	0.833338	0.416669	+	0.909058i	$0.363197\pi$
$570$	−20.1189	−0.842686
$571$	−6.95764	−0.291168	−0.145584	−	0.989346i	$-0.546506\pi$
$571$	−6.95764	−0.291168	−0.145584	+	0.989346i	$0.546506\pi$
$572$	−10.8082	−0.451915
$573$	1.00000	0.0417756
$574$	−2.34419	−0.0978446
$575$	6.88482	0.287117
$576$	−1.30243	−0.0542681
$577$	−17.5112	−0.729002	−0.364501	−	0.931203i	$-0.618760\pi$
$577$	−17.5112	−0.729002	−0.364501	+	0.931203i	$0.618760\pi$
$578$	8.45497	0.351680
$579$	12.2764	0.510191
$580$	−34.9326	−1.45050
$581$	−6.95751	−0.288646
$582$	17.2068	0.713244
$583$	−8.98058	−0.371938
$584$	12.4855	0.516656
$585$	−23.0385	−0.952523
$586$	6.18337	0.255433
$587$	−24.8271	−1.02472	−0.512362	−	0.858770i	$-0.671229\pi$
$587$	−24.8271	−1.02472	−0.512362	+	0.858770i	$0.671229\pi$
$588$	−1.25060	−0.0515737
$589$	5.84097	0.240673
$590$	−62.2539	−2.56295
$591$	−15.8690	−0.652765
$592$	−29.1074	−1.19631
$593$	−3.14628	−0.129202	−0.0646011	−	0.997911i	$-0.520578\pi$
$593$	−3.14628	−0.129202	−0.0646011	+	0.997911i	$0.520578\pi$
$594$	−2.58576	−0.106095
$595$	−13.4141	−0.549923
$596$	−3.12119	−0.127849
$597$	−21.7195	−0.888920
$598$	−7.77827	−0.318077
$599$	−2.44423	−0.0998685	−0.0499342	−	0.998753i	$-0.515901\pi$
$599$	−2.44423	−0.0998685	−0.0499342	+	0.998753i	$0.515901\pi$
$600$	−12.9933	−0.530448
$601$	−37.9444	−1.54779	−0.773893	−	0.633317i	$-0.781693\pi$
$601$	−37.9444	−1.54779	−0.773893	+	0.633317i	$0.781693\pi$
$602$	−2.03758	−0.0830454
$603$	4.55976	0.185688
$604$	−9.76603	−0.397374
$605$	34.1909	1.39006
$606$	−8.10212	−0.329126
$607$	8.79884	0.357134	0.178567	−	0.983928i	$-0.442854\pi$
$607$	8.79884	0.357134	0.178567	+	0.983928i	$0.442854\pi$
$608$	18.0941	0.733811
$609$	−7.30619	−0.296062
$610$	55.9480	2.26527
$611$	−14.6733	−0.593617
$612$	4.38788	0.177369
$613$	−2.20733	−0.0891532	−0.0445766	−	0.999006i	$-0.514194\pi$
$613$	−2.20733	−0.0891532	−0.0445766	+	0.999006i	$0.514194\pi$
$614$	−32.0945	−1.29523
$615$	4.97089	0.200446
$616$	−1.93778	−0.0780754
$617$	−18.0439	−0.726419	−0.363209	−	0.931708i	$-0.618319\pi$
$617$	−18.0439	−0.726419	−0.363209	+	0.931708i	$0.618319\pi$
$618$	0.510544	0.0205371
$619$	42.1014	1.69220	0.846098	−	0.533027i	$-0.178946\pi$
$619$	42.1014	1.69220	0.846098	+	0.533027i	$0.178946\pi$
$620$	−9.56812	−0.384265
$621$	−0.715931	−0.0287293
$622$	47.8175	1.91731
$623$	−1.56197	−0.0625789
$624$	29.7516	1.19102
$625$	19.3960	0.775838
$626$	61.5368	2.45951
$627$	4.18607	0.167175
$628$	9.98002	0.398246
$629$	20.6852	0.824772
$630$	6.89294	0.274621
$631$	29.4535	1.17253	0.586263	−	0.810121i	$-0.300599\pi$
$631$	29.4535	1.17253	0.586263	+	0.810121i	$0.300599\pi$
$632$	−22.8944	−0.910691
$633$	12.2607	0.487320
$634$	−28.1719	−1.11885
$635$	2.15664	0.0855835
$636$	−7.83095	−0.310517
$637$	6.02601	0.238759
$638$	18.8921	0.747945
$639$	−2.53003	−0.100086
$640$	38.4237	1.51883
$641$	−19.9022	−0.786090	−0.393045	−	0.919519i	$-0.628578\pi$
$641$	−19.9022	−0.786090	−0.393045	+	0.919519i	$0.628578\pi$
$642$	−22.5460	−0.889821
$643$	27.9422	1.10193	0.550966	−	0.834528i	$-0.314259\pi$
$643$	27.9422	1.10193	0.550966	+	0.834528i	$0.314259\pi$
$644$	0.895342	0.0352814
$645$	4.32071	0.170128
$646$	−18.4636	−0.726442
$647$	−28.8467	−1.13408	−0.567040	−	0.823690i	$-0.691911\pi$
$647$	−28.8467	−1.13408	−0.567040	+	0.823690i	$0.691911\pi$
$648$	1.35113	0.0530774
$649$	12.9530	0.508449
$650$	−104.480	−4.09804
$651$	−2.00118	−0.0784324
$652$	−1.13477	−0.0444412
$653$	13.4409	0.525983	0.262992	−	0.964798i	$-0.415291\pi$
$653$	13.4409	0.525983	0.262992	+	0.964798i	$0.415291\pi$
$654$	−15.8380	−0.619313
$655$	−26.7369	−1.04470
$656$	−6.41936	−0.250634
$657$	9.24082	0.360519
$658$	4.39014	0.171145
$659$	17.8620	0.695803	0.347902	−	0.937531i	$-0.386894\pi$
$659$	17.8620	0.695803	0.347902	+	0.937531i	$0.386894\pi$
$660$	−6.85722	−0.266917
$661$	28.4397	1.10618	0.553088	−	0.833123i	$-0.313449\pi$
$661$	28.4397	1.10618	0.553088	+	0.833123i	$0.313449\pi$
$662$	−49.4177	−1.92067
$663$	−21.1430	−0.821127
$664$	−9.40050	−0.364810
$665$	−11.1589	−0.432724
$666$	−10.6293	−0.411876
$667$	5.23073	0.202535
$668$	9.28618	0.359293
$669$	18.1670	0.702377
$670$	31.4302	1.21425
$671$	−11.6409	−0.449393
$672$	−6.19922	−0.239140
$673$	−27.1462	−1.04641	−0.523204	−	0.852208i	$-0.675263\pi$
$673$	−27.1462	−1.04641	−0.523204	+	0.852208i	$0.675263\pi$
$674$	−33.0463	−1.27290
$675$	−9.61660	−0.370143
$676$	29.1550	1.12135
$677$	−3.00821	−0.115615	−0.0578075	−	0.998328i	$-0.518411\pi$
$677$	−3.00821	−0.115615	−0.0578075	+	0.998328i	$0.518411\pi$
$678$	1.32148	0.0507511
$679$	9.54373	0.366255
$680$	−18.1241	−0.695029
$681$	−9.04176	−0.346481
$682$	5.17458	0.198145
$683$	−17.9768	−0.687864	−0.343932	−	0.938994i	$-0.611759\pi$
$683$	−17.9768	−0.687864	−0.343932	+	0.938994i	$0.611759\pi$
$684$	3.65020	0.139569
$685$	−56.5125	−2.15923
$686$	−1.80294	−0.0688366
$687$	−9.38181	−0.357938
$688$	−5.57973	−0.212725
$689$	37.7335	1.43753
$690$	−4.93487	−0.187867
$691$	31.1979	1.18682	0.593412	−	0.804899i	$-0.297781\pi$
$691$	31.1979	1.18682	0.593412	+	0.804899i	$0.297781\pi$
$692$	5.11130	0.194302
$693$	−1.43419	−0.0544805
$694$	18.2638	0.693283
$695$	−5.10820	−0.193765
$696$	−9.87161	−0.374183
$697$	4.56193	0.172795
$698$	−32.4143	−1.22690
$699$	−16.6386	−0.629330
$700$	12.0265	0.454558
$701$	21.0603	0.795436	0.397718	−	0.917508i	$-0.369802\pi$
$701$	21.0603	0.795436	0.397718	+	0.917508i	$0.369802\pi$
$702$	10.8645	0.410056
$703$	17.2076	0.648998
$704$	1.86794	0.0704006
$705$	−9.30935	−0.350611
$706$	−36.4201	−1.37069
$707$	−4.49383	−0.169008
$708$	11.2948	0.424485
$709$	−49.3062	−1.85174	−0.925868	−	0.377848i	$-0.876664\pi$
$709$	−49.3062	−1.85174	−0.925868	+	0.377848i	$0.876664\pi$
$710$	−17.4394	−0.654487
$711$	−16.9446	−0.635474
$712$	−2.11042	−0.0790913
$713$	1.43271	0.0536553
$714$	6.32585	0.236739
$715$	33.0416	1.23568
$716$	17.9426	0.670547
$717$	1.78688	0.0667324
$718$	−59.1446	−2.20726
$719$	50.7127	1.89127	0.945633	−	0.325236i	$-0.105444\pi$
$719$	50.7127	1.89127	0.945633	+	0.325236i	$0.105444\pi$
$720$	18.8757	0.703457
$721$	0.283173	0.0105459
$722$	18.8963	0.703248
$723$	−23.4733	−0.872982
$724$	−2.62738	−0.0976458
$725$	70.2607	2.60942
$726$	−16.1239	−0.598413
$727$	−26.0433	−0.965892	−0.482946	−	0.875650i	$-0.660433\pi$
$727$	−26.0433	−0.965892	−0.482946	+	0.875650i	$0.660433\pi$
$728$	8.14193	0.301760
$729$	1.00000	0.0370370
$730$	63.6965	2.35751
$731$	3.96524	0.146660
$732$	−10.1507	−0.375182
$733$	40.2967	1.48839	0.744196	−	0.667961i	$-0.232833\pi$
$733$	40.2967	1.48839	0.744196	+	0.667961i	$0.232833\pi$
$734$	52.1268	1.92404
$735$	3.82317	0.141020
$736$	4.43822	0.163595
$737$	−6.53957	−0.240888
$738$	−2.34419	−0.0862908
$739$	49.6899	1.82787	0.913937	−	0.405856i	$-0.133027\pi$
$739$	49.6899	1.82787	0.913937	+	0.405856i	$0.133027\pi$
$740$	−28.1879	−1.03621
$741$	−17.5885	−0.646130
$742$	−11.2896	−0.414455
$743$	−23.6452	−0.867457	−0.433728	−	0.901044i	$-0.642802\pi$
$743$	−23.6452	−0.867457	−0.433728	+	0.901044i	$0.642802\pi$
$744$	−2.70385	−0.0991281
$745$	9.54170	0.349581
$746$	15.6879	0.574376
$747$	−6.95751	−0.254562
$748$	−6.29306	−0.230097
$749$	−12.5051	−0.456928
$750$	−31.8219	−1.16197
$751$	19.1363	0.698294	0.349147	−	0.937068i	$-0.386471\pi$
$751$	19.1363	0.698294	0.349147	+	0.937068i	$0.386471\pi$
$752$	12.0220	0.438398
$753$	−12.8620	−0.468717
$754$	−79.3785	−2.89079
$755$	29.8555	1.08655
$756$	−1.25060	−0.0454838
$757$	35.8011	1.30121	0.650606	−	0.759415i	$-0.274515\pi$
$757$	35.8011	1.30121	0.650606	+	0.759415i	$0.274515\pi$
$758$	45.4551	1.65100
$759$	1.02678	0.0372699
$760$	−15.0771	−0.546905
$761$	−41.9161	−1.51946	−0.759729	−	0.650240i	$-0.774669\pi$
$761$	−41.9161	−1.51946	−0.759729	+	0.650240i	$0.774669\pi$
$762$	−1.01703	−0.0368432
$763$	−8.78451	−0.318021
$764$	−1.25060	−0.0452450
$765$	−13.4141	−0.484986
$766$	−25.4467	−0.919428
$767$	−54.4242	−1.96514
$768$	−20.7249	−0.747844
$769$	−40.2864	−1.45277	−0.726383	−	0.687290i	$-0.758800\pi$
$769$	−40.2864	−1.45277	−0.726383	+	0.687290i	$0.758800\pi$
$770$	−9.88580	−0.356260
$771$	20.4966	0.738166
$772$	−15.3529	−0.552562
$773$	11.5712	0.416187	0.208093	−	0.978109i	$-0.433274\pi$
$773$	11.5712	0.416187	0.208093	+	0.978109i	$0.433274\pi$
$774$	−2.03758	−0.0732392
$775$	19.2445	0.691284
$776$	12.8948	0.462897
$777$	−5.89552	−0.211501
$778$	8.09883	0.290357
$779$	3.79498	0.135969
$780$	28.8118	1.03163
$781$	3.62855	0.129840
$782$	−4.52887	−0.161952
$783$	−7.30619	−0.261102
$784$	−4.93720	−0.176329
$785$	−30.5096	−1.08894
$786$	12.6087	0.449737
$787$	−38.6652	−1.37826	−0.689132	−	0.724636i	$-0.742008\pi$
$787$	−38.6652	−1.37826	−0.689132	+	0.724636i	$0.742008\pi$
$788$	19.8458	0.706976
$789$	26.5195	0.944119
$790$	−116.798	−4.15550
$791$	0.732957	0.0260610
$792$	−1.93778	−0.0688560
$793$	48.9114	1.73690
$794$	−3.66274	−0.129986
$795$	23.9398	0.849057
$796$	27.1623	0.962744
$797$	−26.8450	−0.950898	−0.475449	−	0.879743i	$-0.657714\pi$
$797$	−26.8450	−0.950898	−0.475449	+	0.879743i	$0.657714\pi$
$798$	5.26236	0.186285
$799$	−8.54346	−0.302246
$800$	59.6154	2.10772
$801$	−1.56197	−0.0551894
$802$	43.7265	1.54404
$803$	−13.2531	−0.467692
$804$	−5.70242	−0.201109
$805$	−2.73712	−0.0964710
$806$	−21.7419	−0.765826
$807$	17.9988	0.633589
$808$	−6.07175	−0.213604
$809$	4.69816	0.165178	0.0825892	−	0.996584i	$-0.473681\pi$
$809$	4.69816	0.165178	0.0825892	+	0.996584i	$0.473681\pi$
$810$	6.89294	0.242193
$811$	−1.01681	−0.0357051	−0.0178526	−	0.999841i	$-0.505683\pi$
$811$	−1.01681	−0.0357051	−0.0178526	+	0.999841i	$0.505683\pi$
$812$	9.13710	0.320649
$813$	−12.9460	−0.454037
$814$	15.2444	0.534317
$815$	3.46909	0.121517
$816$	17.3228	0.606419
$817$	3.29861	0.115404
$818$	−46.7347	−1.63404
$819$	6.02601	0.210566
$820$	−6.21658	−0.217092
$821$	42.3769	1.47896	0.739482	−	0.673176i	$-0.235070\pi$
$821$	42.3769	1.47896	0.739482	+	0.673176i	$0.235070\pi$
$822$	26.6503	0.929537
$823$	3.25796	0.113565	0.0567827	−	0.998387i	$-0.481916\pi$
$823$	3.25796	0.113565	0.0567827	+	0.998387i	$0.481916\pi$
$824$	0.382603	0.0133286
$825$	13.7920	0.480177
$826$	16.2833	0.566570
$827$	−23.5635	−0.819384	−0.409692	−	0.912224i	$-0.634364\pi$
$827$	−23.5635	−0.819384	−0.409692	+	0.912224i	$0.634364\pi$
$828$	0.895342	0.0311153
$829$	23.5315	0.817283	0.408641	−	0.912695i	$-0.366003\pi$
$829$	23.5315	0.817283	0.408641	+	0.912695i	$0.366003\pi$
$830$	−47.9577	−1.66464
$831$	19.0936	0.662349
$832$	−7.84848	−0.272097
$833$	3.50863	0.121567
$834$	2.40894	0.0834149
$835$	−28.3885	−0.982426
$836$	−5.23508	−0.181059
$837$	−2.00118	−0.0691709
$838$	24.6972	0.853152
$839$	−0.731602	−0.0252577	−0.0126289	−	0.999920i	$-0.504020\pi$
$839$	−0.731602	−0.0252577	−0.0126289	+	0.999920i	$0.504020\pi$
$840$	5.16559	0.178230
$841$	24.3804	0.840704
$842$	−4.69920	−0.161945
$843$	−14.1429	−0.487107
$844$	−15.3332	−0.527792
$845$	−89.1289	−3.06613
$846$	4.39014	0.150936
$847$	−8.94309	−0.307288
$848$	−30.9156	−1.06165
$849$	−14.0331	−0.481616
$850$	−60.8331	−2.08656
$851$	4.22079	0.144687
$852$	3.16405	0.108399
$853$	−0.516774	−0.0176940	−0.00884701	−	0.999961i	$-0.502816\pi$
$853$	−0.516774	−0.0176940	−0.00884701	+	0.999961i	$0.502816\pi$
$854$	−14.6340	−0.500764
$855$	−11.1589	−0.381627
$856$	−16.8961	−0.577496
$857$	11.4271	0.390343	0.195171	−	0.980769i	$-0.437474\pi$
$857$	11.4271	0.390343	0.195171	+	0.980769i	$0.437474\pi$
$858$	−15.5819	−0.531956
$859$	−8.05822	−0.274943	−0.137471	−	0.990506i	$-0.543898\pi$
$859$	−8.05822	−0.274943	−0.137471	+	0.990506i	$0.543898\pi$
$860$	−5.40347	−0.184257
$861$	−1.30020	−0.0443108
$862$	−27.1292	−0.924024
$863$	−23.0992	−0.786306	−0.393153	−	0.919473i	$-0.628616\pi$
$863$	−23.0992	−0.786306	−0.393153	+	0.919473i	$0.628616\pi$
$864$	−6.19922	−0.210902
$865$	−15.6256	−0.531287
$866$	5.54712	0.188499
$867$	4.68954	0.159265
$868$	2.50267	0.0849461
$869$	24.3019	0.824385
$870$	−50.3612	−1.70740
$871$	27.4772	0.931028
$872$	−11.8690	−0.401936
$873$	9.54373	0.323006
$874$	−3.76749	−0.127437
$875$	−17.6500	−0.596680
$876$	−11.5565	−0.390459
$877$	28.5887	0.965371	0.482685	−	0.875794i	$-0.339661\pi$
$877$	28.5887	0.965371	0.482685	+	0.875794i	$0.339661\pi$
$878$	−35.1221	−1.18531
$879$	3.42960	0.115678
$880$	−27.0714	−0.912578
$881$	−10.8838	−0.366685	−0.183342	−	0.983049i	$-0.558692\pi$
$881$	−10.8838	−0.366685	−0.183342	+	0.983049i	$0.558692\pi$
$882$	−1.80294	−0.0607082
$883$	29.9458	1.00776	0.503879	−	0.863774i	$-0.331906\pi$
$883$	29.9458	1.00776	0.503879	+	0.863774i	$0.331906\pi$
$884$	26.4414	0.889321
$885$	−34.5291	−1.16068
$886$	28.0920	0.943771
$887$	34.7389	1.16642	0.583210	−	0.812322i	$-0.301797\pi$
$887$	34.7389	1.16642	0.583210	+	0.812322i	$0.301797\pi$
$888$	−7.96561	−0.267309
$889$	−0.564097	−0.0189192
$890$	−10.7665	−0.360896
$891$	−1.43419	−0.0480472
$892$	−22.7196	−0.760708
$893$	−7.10715	−0.237832
$894$	−4.49971	−0.150493
$895$	−54.8519	−1.83350
$896$	−10.0502	−0.335755
$897$	−4.31421	−0.144047
$898$	−18.1915	−0.607059
$899$	14.6210	0.487638
$900$	12.0265	0.400883
$901$	21.9702	0.731934
$902$	3.36202	0.111943
$903$	−1.13014	−0.0376087
$904$	0.990320	0.0329376
$905$	8.03209	0.266996
$906$	−14.0793	−0.467755
$907$	−43.1064	−1.43132	−0.715662	−	0.698447i	$-0.753875\pi$
$907$	−43.1064	−1.43132	−0.715662	+	0.698447i	$0.753875\pi$
$908$	11.3076	0.375256
$909$	−4.49383	−0.149051
$910$	41.5370	1.37694
$911$	−48.6401	−1.61152	−0.805759	−	0.592244i	$-0.798242\pi$
$911$	−48.6401	−1.61152	−0.805759	+	0.592244i	$0.798242\pi$
$912$	14.4105	0.477180
$913$	9.97841	0.330237
$914$	23.3931	0.773774
$915$	31.0315	1.02587
$916$	11.7329	0.387665
$917$	6.99339	0.230942
$918$	6.32585	0.208784
$919$	−27.7962	−0.916913	−0.458456	−	0.888717i	$-0.651597\pi$
$919$	−27.7962	−0.916913	−0.458456	+	0.888717i	$0.651597\pi$
$920$	−3.69821	−0.121926
$921$	−17.8012	−0.586569
$922$	−14.6682	−0.483070
$923$	−15.2460	−0.501828
$924$	1.79360	0.0590050
$925$	56.6949	1.86412
$926$	22.6668	0.744878
$927$	0.283173	0.00930061
$928$	45.2927	1.48681
$929$	0.649154	0.0212980	0.0106490	−	0.999943i	$-0.496610\pi$
$929$	0.649154	0.0212980	0.0106490	+	0.999943i	$0.496610\pi$
$930$	−13.7940	−0.452324
$931$	2.91876	0.0956586
$932$	20.8082	0.681595
$933$	26.5219	0.868289
$934$	−71.4456	−2.33777
$935$	19.2383	0.629161
$936$	8.14193	0.266127
$937$	−46.9066	−1.53237	−0.766185	−	0.642620i	$-0.777848\pi$
$937$	−46.9066	−1.53237	−0.766185	+	0.642620i	$0.777848\pi$
$938$	−8.22098	−0.268424
$939$	34.1314	1.11384
$940$	11.6422	0.379728
$941$	−4.89460	−0.159560	−0.0797798	−	0.996813i	$-0.525422\pi$
$941$	−4.89460	−0.159560	−0.0797798	+	0.996813i	$0.525422\pi$
$942$	14.3878	0.468781
$943$	0.930856	0.0303129
$944$	44.5906	1.45130
$945$	3.82317	0.124368
$946$	2.92228	0.0950114
$947$	−41.5003	−1.34858	−0.674289	−	0.738467i	$-0.735550\pi$
$947$	−41.5003	−1.34858	−0.674289	+	0.738467i	$0.735550\pi$
$948$	21.1909	0.688249
$949$	55.6853	1.80762
$950$	−50.6060	−1.64187
$951$	−15.6255	−0.506692
$952$	4.74061	0.153644
$953$	1.81207	0.0586986	0.0293493	−	0.999569i	$-0.490656\pi$
$953$	1.81207	0.0586986	0.0293493	+	0.999569i	$0.490656\pi$
$954$	−11.2896	−0.365515
$955$	3.82317	0.123715
$956$	−2.23467	−0.0722744
$957$	10.4785	0.338721
$958$	67.3801	2.17695
$959$	14.7816	0.477323
$960$	−4.97942	−0.160710
$961$	−26.9953	−0.870815
$962$	−64.0522	−2.06513
$963$	−12.5051	−0.402973
$964$	29.3557	0.945482
$965$	46.9348	1.51089
$966$	1.29078	0.0415302
$967$	−29.1145	−0.936260	−0.468130	−	0.883660i	$-0.655072\pi$
$967$	−29.1145	−0.936260	−0.468130	+	0.883660i	$0.655072\pi$
$968$	−12.0833	−0.388371
$969$	−10.2408	−0.328983
$970$	65.7844	2.11221
$971$	55.2343	1.77255	0.886277	−	0.463156i	$-0.153283\pi$
$971$	55.2343	1.77255	0.886277	+	0.463156i	$0.153283\pi$
$972$	−1.25060	−0.0401129
$973$	1.33612	0.0428340
$974$	−15.4953	−0.496501
$975$	−57.9498	−1.85588
$976$	−40.0738	−1.28273
$977$	3.86913	0.123784	0.0618922	−	0.998083i	$-0.480287\pi$
$977$	3.86913	0.123784	0.0618922	+	0.998083i	$0.480287\pi$
$978$	−1.63596	−0.0523123
$979$	2.24016	0.0715958
$980$	−4.78124	−0.152731
$981$	−8.78451	−0.280468
$982$	−52.0485	−1.66094
$983$	19.5531	0.623648	0.311824	−	0.950140i	$-0.399060\pi$
$983$	19.5531	0.623648	0.311824	+	0.950140i	$0.399060\pi$
$984$	−1.75674	−0.0560029
$985$	−60.6700	−1.93311
$986$	−46.2178	−1.47188
$987$	2.43499	0.0775065
$988$	21.9961	0.699790
$989$	0.809103	0.0257280
$990$	−9.88580	−0.314192
$991$	−34.4643	−1.09480	−0.547398	−	0.836873i	$-0.684381\pi$
$991$	−34.4643	−1.09480	−0.547398	+	0.836873i	$0.684381\pi$
$992$	12.4058	0.393883
$993$	−27.4095	−0.869814
$994$	4.56150	0.144682
$995$	−83.0372	−2.63246
$996$	8.70104	0.275703
$997$	−54.9507	−1.74031	−0.870153	−	0.492782i	$-0.835980\pi$
$997$	−54.9507	−1.74031	−0.870153	+	0.492782i	$0.835980\pi$
$998$	37.8964	1.19959
$999$	−5.89552	−0.186526

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	4011.2.a.l.1.8	✓	28

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
4011.2.a.l.1.8	✓	28	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)

\(f(q)\)	\(=\)	\(q-1.80294 q^{2} -1.00000 q^{3} +1.25060 q^{4} -3.82317 q^{5} +1.80294 q^{6} +1.00000 q^{7} +1.35113 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q-1.80294 q^{2} -1.00000 q^{3} +1.25060 q^{4} -3.82317 q^{5} +1.80294 q^{6} +1.00000 q^{7} +1.35113 q^{8} +1.00000 q^{9} +6.89294 q^{10} -1.43419 q^{11} -1.25060 q^{12} +6.02601 q^{13} -1.80294 q^{14} +3.82317 q^{15} -4.93720 q^{16} +3.50863 q^{17} -1.80294 q^{18} +2.91876 q^{19} -4.78124 q^{20} -1.00000 q^{21} +2.58576 q^{22} +0.715931 q^{23} -1.35113 q^{24} +9.61660 q^{25} -10.8645 q^{26} -1.00000 q^{27} +1.25060 q^{28} +7.30619 q^{29} -6.89294 q^{30} +2.00118 q^{31} +6.19922 q^{32} +1.43419 q^{33} -6.32585 q^{34} -3.82317 q^{35} +1.25060 q^{36} +5.89552 q^{37} -5.26236 q^{38} -6.02601 q^{39} -5.16559 q^{40} +1.30020 q^{41} +1.80294 q^{42} +1.13014 q^{43} -1.79360 q^{44} -3.82317 q^{45} -1.29078 q^{46} -2.43499 q^{47} +4.93720 q^{48} +1.00000 q^{49} -17.3382 q^{50} -3.50863 q^{51} +7.53611 q^{52} +6.26177 q^{53} +1.80294 q^{54} +5.48315 q^{55} +1.35113 q^{56} -2.91876 q^{57} -13.1726 q^{58} -9.03155 q^{59} +4.78124 q^{60} +8.11671 q^{61} -3.60801 q^{62} +1.00000 q^{63} -1.30243 q^{64} -23.0385 q^{65} -2.58576 q^{66} +4.55976 q^{67} +4.38788 q^{68} -0.715931 q^{69} +6.89294 q^{70} -2.53003 q^{71} +1.35113 q^{72} +9.24082 q^{73} -10.6293 q^{74} -9.61660 q^{75} +3.65020 q^{76} -1.43419 q^{77} +10.8645 q^{78} -16.9446 q^{79} +18.8757 q^{80} +1.00000 q^{81} -2.34419 q^{82} -6.95751 q^{83} -1.25060 q^{84} -13.4141 q^{85} -2.03758 q^{86} -7.30619 q^{87} -1.93778 q^{88} -1.56197 q^{89} +6.89294 q^{90} +6.02601 q^{91} +0.895342 q^{92} -2.00118 q^{93} +4.39014 q^{94} -11.1589 q^{95} -6.19922 q^{96} +9.54373 q^{97} -1.80294 q^{98} -1.43419 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 28 q - 6 q^{2} - 28 q^{3} + 34 q^{4} + 8 q^{5} + 6 q^{6} + 28 q^{7} - 15 q^{8} + 28 q^{9}+O(q^{10}) \) 28 * q - 6 * q^2 - 28 * q^3 + 34 * q^4 + 8 * q^5 + 6 * q^6 + 28 * q^7 - 15 * q^8 + 28 * q^9	\( 28 q - 6 q^{2} - 28 q^{3} + 34 q^{4} + 8 q^{5} + 6 q^{6} + 28 q^{7} - 15 q^{8} + 28 q^{9} + 4 q^{10} - 8 q^{11} - 34 q^{12} + 26 q^{13} - 6 q^{14} - 8 q^{15} + 62 q^{16} + 9 q^{17} - 6 q^{18} + 25 q^{19} + 20 q^{20} - 28 q^{21} + 3 q^{22} - 30 q^{23} + 15 q^{24} + 42 q^{25} + 25 q^{26} - 28 q^{27} + 34 q^{28} - 5 q^{29} - 4 q^{30} + 18 q^{31} - 26 q^{32} + 8 q^{33} + 30 q^{34} + 8 q^{35} + 34 q^{36} + 36 q^{37} - 2 q^{38} - 26 q^{39} + 28 q^{40} + 21 q^{41} + 6 q^{42} + 8 q^{43} - 20 q^{44} + 8 q^{45} + 24 q^{46} + 6 q^{47} - 62 q^{48} + 28 q^{49} - 48 q^{50} - 9 q^{51} + 54 q^{52} - 12 q^{53} + 6 q^{54} + 15 q^{55} - 15 q^{56} - 25 q^{57} + 19 q^{58} + 33 q^{59} - 20 q^{60} + 48 q^{61} + 28 q^{63} + 75 q^{64} + 21 q^{65} - 3 q^{66} + 27 q^{67} + 19 q^{68} + 30 q^{69} + 4 q^{70} - 45 q^{71} - 15 q^{72} + 61 q^{73} - 31 q^{74} - 42 q^{75} + 63 q^{76} - 8 q^{77} - 25 q^{78} + 35 q^{79} + 84 q^{80} + 28 q^{81} + 11 q^{82} + 43 q^{83} - 34 q^{84} + 43 q^{85} - q^{86} + 5 q^{87} - 27 q^{88} + 25 q^{89} + 4 q^{90} + 26 q^{91} - 102 q^{92} - 18 q^{93} + 55 q^{94} - 43 q^{95} + 26 q^{96} + 40 q^{97} - 6 q^{98} - 8 q^{99}+O(q^{100}) \) 28 * q - 6 * q^2 - 28 * q^3 + 34 * q^4 + 8 * q^5 + 6 * q^6 + 28 * q^7 - 15 * q^8 + 28 * q^9 + 4 * q^10 - 8 * q^11 - 34 * q^12 + 26 * q^13 - 6 * q^14 - 8 * q^15 + 62 * q^16 + 9 * q^17 - 6 * q^18 + 25 * q^19 + 20 * q^20 - 28 * q^21 + 3 * q^22 - 30 * q^23 + 15 * q^24 + 42 * q^25 + 25 * q^26 - 28 * q^27 + 34 * q^28 - 5 * q^29 - 4 * q^30 + 18 * q^31 - 26 * q^32 + 8 * q^33 + 30 * q^34 + 8 * q^35 + 34 * q^36 + 36 * q^37 - 2 * q^38 - 26 * q^39 + 28 * q^40 + 21 * q^41 + 6 * q^42 + 8 * q^43 - 20 * q^44 + 8 * q^45 + 24 * q^46 + 6 * q^47 - 62 * q^48 + 28 * q^49 - 48 * q^50 - 9 * q^51 + 54 * q^52 - 12 * q^53 + 6 * q^54 + 15 * q^55 - 15 * q^56 - 25 * q^57 + 19 * q^58 + 33 * q^59 - 20 * q^60 + 48 * q^61 + 28 * q^63 + 75 * q^64 + 21 * q^65 - 3 * q^66 + 27 * q^67 + 19 * q^68 + 30 * q^69 + 4 * q^70 - 45 * q^71 - 15 * q^72 + 61 * q^73 - 31 * q^74 - 42 * q^75 + 63 * q^76 - 8 * q^77 - 25 * q^78 + 35 * q^79 + 84 * q^80 + 28 * q^81 + 11 * q^82 + 43 * q^83 - 34 * q^84 + 43 * q^85 - q^86 + 5 * q^87 - 27 * q^88 + 25 * q^89 + 4 * q^90 + 26 * q^91 - 102 * q^92 - 18 * q^93 + 55 * q^94 - 43 * q^95 + 26 * q^96 + 40 * q^97 - 6 * q^98 - 8 * q^99

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