LMFDB - Embedded newform 8041.2.a.d.1.5

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [8041,2,Mod(1,8041)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(8041, 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("8041.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 8041 = 11 \cdot 17 \cdot 43 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	8041.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:	$64.2077082653$
Analytic rank:	$1$
Dimension:	$62$
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.5
Character	$\chi$	$=$	8041.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-2.41829 q^{2} -2.95622 q^{3} +3.84815 q^{4} +1.73328 q^{5} +7.14900 q^{6} +3.91504 q^{7} -4.46936 q^{8} +5.73922 q^{9} +O(q^{10})$	\(q-2.41829 q^{2} -2.95622 q^{3} +3.84815 q^{4} +1.73328 q^{5} +7.14900 q^{6} +3.91504 q^{7} -4.46936 q^{8} +5.73922 q^{9} -4.19159 q^{10} +1.00000 q^{11} -11.3760 q^{12} -4.30297 q^{13} -9.46772 q^{14} -5.12396 q^{15} +3.11194 q^{16} -1.00000 q^{17} -13.8791 q^{18} -4.70651 q^{19} +6.66993 q^{20} -11.5737 q^{21} -2.41829 q^{22} +2.91407 q^{23} +13.2124 q^{24} -1.99573 q^{25} +10.4058 q^{26} -8.09772 q^{27} +15.0656 q^{28} +0.120660 q^{29} +12.3912 q^{30} +3.92880 q^{31} +1.41314 q^{32} -2.95622 q^{33} +2.41829 q^{34} +6.78587 q^{35} +22.0854 q^{36} -3.92597 q^{37} +11.3817 q^{38} +12.7205 q^{39} -7.74667 q^{40} -7.98994 q^{41} +27.9886 q^{42} +1.00000 q^{43} +3.84815 q^{44} +9.94769 q^{45} -7.04708 q^{46} -0.691641 q^{47} -9.19957 q^{48} +8.32754 q^{49} +4.82627 q^{50} +2.95622 q^{51} -16.5585 q^{52} +6.01950 q^{53} +19.5827 q^{54} +1.73328 q^{55} -17.4977 q^{56} +13.9135 q^{57} -0.291792 q^{58} -1.61610 q^{59} -19.7177 q^{60} +11.8440 q^{61} -9.50099 q^{62} +22.4693 q^{63} -9.64126 q^{64} -7.45826 q^{65} +7.14900 q^{66} +8.61193 q^{67} -3.84815 q^{68} -8.61463 q^{69} -16.4102 q^{70} -9.85561 q^{71} -25.6506 q^{72} +13.8809 q^{73} +9.49414 q^{74} +5.89982 q^{75} -18.1113 q^{76} +3.91504 q^{77} -30.7619 q^{78} -4.80268 q^{79} +5.39387 q^{80} +6.72097 q^{81} +19.3220 q^{82} +2.58465 q^{83} -44.5373 q^{84} -1.73328 q^{85} -2.41829 q^{86} -0.356698 q^{87} -4.46936 q^{88} -17.8813 q^{89} -24.0564 q^{90} -16.8463 q^{91} +11.2138 q^{92} -11.6144 q^{93} +1.67259 q^{94} -8.15771 q^{95} -4.17754 q^{96} +9.87351 q^{97} -20.1384 q^{98} +5.73922 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 62 q - 7 q^{2} - 8 q^{3} + 49 q^{4} - 13 q^{5} - 2 q^{6} - 11 q^{7} - 9 q^{8} + 40 q^{9}+O(q^{10}) $ 62 * q - 7 * q^2 - 8 * q^3 + 49 * q^4 - 13 * q^5 - 2 * q^6 - 11 * q^7 - 9 * q^8 + 40 * q^9	\( 62 q - 7 q^{2} - 8 q^{3} + 49 q^{4} - 13 q^{5} - 2 q^{6} - 11 q^{7} - 9 q^{8} + 40 q^{9} - 7 q^{10} + 62 q^{11} - 17 q^{12} - 31 q^{14} - 20 q^{15} + 27 q^{16} - 62 q^{17} + 3 q^{18} - 29 q^{20} - 18 q^{21} - 7 q^{22} - 50 q^{23} - 31 q^{24} + 35 q^{25} - 32 q^{26} - 14 q^{27} - 13 q^{28} - 26 q^{29} - 10 q^{30} - 58 q^{31} - 5 q^{32} - 8 q^{33} + 7 q^{34} - 32 q^{35} - 29 q^{36} - 41 q^{37} - 10 q^{38} - 53 q^{39} - 31 q^{40} - 55 q^{41} - 7 q^{42} + 62 q^{43} + 49 q^{44} - 34 q^{45} - 39 q^{46} - 31 q^{47} - 30 q^{48} + 35 q^{49} - 40 q^{50} + 8 q^{51} + 13 q^{52} - 74 q^{53} + 48 q^{54} - 13 q^{55} - 75 q^{56} - 43 q^{57} - 46 q^{58} - 65 q^{59} - 8 q^{60} - 14 q^{61} - 29 q^{62} - 23 q^{63} - 15 q^{64} - 9 q^{65} - 2 q^{66} - q^{67} - 49 q^{68} - 59 q^{69} - 31 q^{70} - 141 q^{71} + 9 q^{72} - 4 q^{73} - 94 q^{74} - 43 q^{75} + 34 q^{76} - 11 q^{77} - 11 q^{78} - 63 q^{79} - 41 q^{80} - 30 q^{81} + 38 q^{82} - 44 q^{83} - 16 q^{84} + 13 q^{85} - 7 q^{86} - 8 q^{87} - 9 q^{88} - 58 q^{89} - 55 q^{90} - 78 q^{91} - 104 q^{92} - 5 q^{94} - 99 q^{95} - 148 q^{96} - 26 q^{97} + 16 q^{98} + 40 q^{99}+O(q^{100}) \) 62 * q - 7 * q^2 - 8 * q^3 + 49 * q^4 - 13 * q^5 - 2 * q^6 - 11 * q^7 - 9 * q^8 + 40 * q^9 - 7 * q^10 + 62 * q^11 - 17 * q^12 - 31 * q^14 - 20 * q^15 + 27 * q^16 - 62 * q^17 + 3 * q^18 - 29 * q^20 - 18 * q^21 - 7 * q^22 - 50 * q^23 - 31 * q^24 + 35 * q^25 - 32 * q^26 - 14 * q^27 - 13 * q^28 - 26 * q^29 - 10 * q^30 - 58 * q^31 - 5 * q^32 - 8 * q^33 + 7 * q^34 - 32 * q^35 - 29 * q^36 - 41 * q^37 - 10 * q^38 - 53 * q^39 - 31 * q^40 - 55 * q^41 - 7 * q^42 + 62 * q^43 + 49 * q^44 - 34 * q^45 - 39 * q^46 - 31 * q^47 - 30 * q^48 + 35 * q^49 - 40 * q^50 + 8 * q^51 + 13 * q^52 - 74 * q^53 + 48 * q^54 - 13 * q^55 - 75 * q^56 - 43 * q^57 - 46 * q^58 - 65 * q^59 - 8 * q^60 - 14 * q^61 - 29 * q^62 - 23 * q^63 - 15 * q^64 - 9 * q^65 - 2 * q^66 - q^67 - 49 * q^68 - 59 * q^69 - 31 * q^70 - 141 * q^71 + 9 * q^72 - 4 * q^73 - 94 * q^74 - 43 * q^75 + 34 * q^76 - 11 * q^77 - 11 * q^78 - 63 * q^79 - 41 * q^80 - 30 * q^81 + 38 * q^82 - 44 * q^83 - 16 * q^84 + 13 * q^85 - 7 * q^86 - 8 * q^87 - 9 * q^88 - 58 * q^89 - 55 * q^90 - 78 * q^91 - 104 * q^92 - 5 * q^94 - 99 * q^95 - 148 * q^96 - 26 * q^97 + 16 * q^98 + 40 * 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 $

$2$	−2.41829	−1.70999	−0.854996	−	0.518634i	$-0.826441\pi$
$2$	−2.41829	−1.70999	−0.854996	+	0.518634i	$0.826441\pi$
$3$	−2.95622	−1.70677	−0.853386	−	0.521279i	$-0.825455\pi$
$3$	−2.95622	−1.70677	−0.853386	+	0.521279i	$0.825455\pi$
$4$	3.84815	1.92407
$5$	1.73328	0.775147	0.387574	−	0.921839i	$-0.373313\pi$
$5$	1.73328	0.775147	0.387574	+	0.921839i	$0.373313\pi$
$6$	7.14900	2.91857
$7$	3.91504	1.47975	0.739873	−	0.672747i	$-0.234886\pi$
$7$	3.91504	1.47975	0.739873	+	0.672747i	$0.234886\pi$
$8$	−4.46936	−1.58016
$9$	5.73922	1.91307
$10$	−4.19159	−1.32550
$11$	1.00000	0.301511
$11$	1.00000	0.301511
$12$	−11.3760	−3.28396
$13$	−4.30297	−1.19343	−0.596715	−	0.802454i	$-0.703528\pi$
$13$	−4.30297	−1.19343	−0.596715	+	0.802454i	$0.703528\pi$
$14$	−9.46772	−2.53035
$15$	−5.12396	−1.32300
$16$	3.11194	0.777985
$17$	−1.00000	−0.242536
$17$	−1.00000	−0.242536
$18$	−13.8791	−3.27134
$19$	−4.70651	−1.07975	−0.539874	−	0.841746i	$-0.681528\pi$
$19$	−4.70651	−1.07975	−0.539874	+	0.841746i	$0.681528\pi$
$20$	6.66993	1.49144
$21$	−11.5737	−2.52559
$22$	−2.41829	−0.515582
$23$	2.91407	0.607626	0.303813	−	0.952732i	$-0.401740\pi$
$23$	2.91407	0.607626	0.303813	+	0.952732i	$0.401740\pi$
$24$	13.2124	2.69697
$25$	−1.99573	−0.399146
$26$	10.4058	2.04075
$27$	−8.09772	−1.55841
$28$	15.0656	2.84714
$29$	0.120660	0.0224060	0.0112030	−	0.999937i	$-0.496434\pi$
$29$	0.120660	0.0224060	0.0112030	+	0.999937i	$0.496434\pi$
$30$	12.3912	2.26232
$31$	3.92880	0.705633	0.352816	−	0.935693i	$-0.385224\pi$
$31$	3.92880	0.705633	0.352816	+	0.935693i	$0.385224\pi$
$32$	1.41314	0.249810
$33$	−2.95622	−0.514611
$34$	2.41829	0.414734
$35$	6.78587	1.14702
$36$	22.0854	3.68089
$37$	−3.92597	−0.645425	−0.322712	−	0.946497i	$-0.604595\pi$
$37$	−3.92597	−0.645425	−0.322712	+	0.946497i	$0.604595\pi$
$38$	11.3817	1.84636
$39$	12.7205	2.03691
$40$	−7.74667	−1.22486
$41$	−7.98994	−1.24782	−0.623910	−	0.781496i	$-0.714457\pi$
$41$	−7.98994	−1.24782	−0.623910	+	0.781496i	$0.714457\pi$
$42$	27.9886	4.31874
$43$	1.00000	0.152499
$43$	1.00000	0.152499
$44$	3.84815	0.580130
$45$	9.94769	1.48291
$46$	−7.04708	−1.03904
$47$	−0.691641	−0.100886	−0.0504431	−	0.998727i	$-0.516063\pi$
$47$	−0.691641	−0.100886	−0.0504431	+	0.998727i	$0.516063\pi$
$48$	−9.19957	−1.32784
$49$	8.32754	1.18965
$50$	4.82627	0.682537
$51$	2.95622	0.413953
$52$	−16.5585	−2.29625
$53$	6.01950	0.826842	0.413421	−	0.910540i	$-0.364334\pi$
$53$	6.01950	0.826842	0.413421	+	0.910540i	$0.364334\pi$
$54$	19.5827	2.66486
$55$	1.73328	0.233716
$56$	−17.4977	−2.33823
$57$	13.9135	1.84288
$58$	−0.291792	−0.0383141
$59$	−1.61610	−0.210398	−0.105199	−	0.994451i	$-0.533548\pi$
$59$	−1.61610	−0.210398	−0.105199	+	0.994451i	$0.533548\pi$
$60$	−19.7177	−2.54555
$61$	11.8440	1.51647	0.758236	−	0.651980i	$-0.226061\pi$
$61$	11.8440	1.51647	0.758236	+	0.651980i	$0.226061\pi$
$62$	−9.50099	−1.20663
$63$	22.4693	2.83086
$64$	−9.64126	−1.20516
$65$	−7.45826	−0.925084
$66$	7.14900	0.879981
$67$	8.61193	1.05211	0.526057	−	0.850449i	$-0.323670\pi$
$67$	8.61193	1.05211	0.526057	+	0.850449i	$0.323670\pi$
$68$	−3.84815	−0.466656
$69$	−8.61463	−1.03708
$70$	−16.4102	−1.96140
$71$	−9.85561	−1.16965	−0.584823	−	0.811161i	$-0.698836\pi$
$71$	−9.85561	−1.16965	−0.584823	+	0.811161i	$0.698836\pi$
$72$	−25.6506	−3.02296
$73$	13.8809	1.62463	0.812317	−	0.583216i	$-0.198206\pi$
$73$	13.8809	1.62463	0.812317	+	0.583216i	$0.198206\pi$
$74$	9.49414	1.10367
$75$	5.89982	0.681252
$76$	−18.1113	−2.07751
$77$	3.91504	0.446160
$78$	−30.7619	−3.48310
$79$	−4.80268	−0.540344	−0.270172	−	0.962812i	$-0.587081\pi$
$79$	−4.80268	−0.540344	−0.270172	+	0.962812i	$0.587081\pi$
$80$	5.39387	0.603053
$81$	6.72097	0.746774
$82$	19.3220	2.13376
$83$	2.58465	0.283703	0.141851	−	0.989888i	$-0.454695\pi$
$83$	2.58465	0.283703	0.141851	+	0.989888i	$0.454695\pi$
$84$	−44.5373	−4.85942
$85$	−1.73328	−0.188001
$86$	−2.41829	−0.260771
$87$	−0.356698	−0.0382420
$88$	−4.46936	−0.476436
$89$	−17.8813	−1.89541	−0.947704	−	0.319149i	$-0.896603\pi$
$89$	−17.8813	−1.89541	−0.947704	+	0.319149i	$0.896603\pi$
$90$	−24.0564	−2.53577
$91$	−16.8463	−1.76597
$92$	11.2138	1.16912
$93$	−11.6144	−1.20435
$94$	1.67259	0.172515
$95$	−8.15771	−0.836964
$96$	−4.17754	−0.426369
$97$	9.87351	1.00250	0.501252	−	0.865302i	$-0.332873\pi$
$97$	9.87351	1.00250	0.501252	+	0.865302i	$0.332873\pi$
$98$	−20.1384	−2.03429
$99$	5.73922	0.576813
$100$	−7.67987	−0.767987
$101$	3.96931	0.394961	0.197481	−	0.980307i	$-0.436724\pi$
$101$	3.96931	0.394961	0.197481	+	0.980307i	$0.436724\pi$
$102$	−7.14900	−0.707857
$103$	−7.08661	−0.698264	−0.349132	−	0.937074i	$-0.613524\pi$
$103$	−7.08661	−0.698264	−0.349132	+	0.937074i	$0.613524\pi$
$104$	19.2315	1.88581
$105$	−20.0605	−1.95770
$106$	−14.5569	−1.41389
$107$	18.0224	1.74229	0.871147	−	0.491023i	$-0.163377\pi$
$107$	18.0224	1.74229	0.871147	+	0.491023i	$0.163377\pi$
$108$	−31.1612	−2.99849
$109$	−4.83528	−0.463136	−0.231568	−	0.972819i	$-0.574386\pi$
$109$	−4.83528	−0.463136	−0.231568	+	0.972819i	$0.574386\pi$
$110$	−4.19159	−0.399652
$111$	11.6060	1.10159
$112$	12.1834	1.15122
$113$	−18.5447	−1.74454	−0.872268	−	0.489028i	$-0.837352\pi$
$113$	−18.5447	−1.74454	−0.872268	+	0.489028i	$0.837352\pi$
$114$	−33.6468	−3.15132
$115$	5.05091	0.471000
$116$	0.464318	0.0431108
$117$	−24.6957	−2.28312
$118$	3.90820	0.359779
$119$	−3.91504	−0.358891
$120$	22.9008	2.09055
$121$	1.00000	0.0909091
$122$	−28.6424	−2.59316
$123$	23.6200	2.12974
$124$	15.1186	1.35769
$125$	−12.1256	−1.08454
$126$	−54.3373	−4.84075
$127$	−15.1521	−1.34453	−0.672265	−	0.740310i	$-0.734679\pi$
$127$	−15.1521	−1.34453	−0.672265	+	0.740310i	$0.734679\pi$
$128$	20.4891	1.81100
$129$	−2.95622	−0.260280
$130$	18.0363	1.58189
$131$	11.2123	0.979627	0.489814	−	0.871827i	$-0.337065\pi$
$131$	11.2123	0.979627	0.489814	+	0.871827i	$0.337065\pi$
$132$	−11.3760	−0.990150
$133$	−18.4262	−1.59775
$134$	−20.8262	−1.79911
$135$	−14.0356	−1.20800
$136$	4.46936	0.383245
$137$	−5.32727	−0.455140	−0.227570	−	0.973762i	$-0.573078\pi$
$137$	−5.32727	−0.455140	−0.227570	+	0.973762i	$0.573078\pi$
$138$	20.8327	1.77340
$139$	−5.22807	−0.443439	−0.221720	−	0.975110i	$-0.571167\pi$
$139$	−5.22807	−0.443439	−0.221720	+	0.975110i	$0.571167\pi$
$140$	26.1130	2.20695
$141$	2.04464	0.172190
$142$	23.8338	2.00009
$143$	−4.30297	−0.359832
$144$	17.8601	1.48834
$145$	0.209138	0.0173680
$146$	−33.5680	−2.77811
$147$	−24.6180	−2.03046
$148$	−15.1077	−1.24184
$149$	6.43533	0.527203	0.263602	−	0.964632i	$-0.415090\pi$
$149$	6.43533	0.527203	0.263602	+	0.964632i	$0.415090\pi$
$150$	−14.2675	−1.16494
$151$	−15.1733	−1.23478	−0.617392	−	0.786656i	$-0.711811\pi$
$151$	−15.1733	−1.23478	−0.617392	+	0.786656i	$0.711811\pi$
$152$	21.0351	1.70617
$153$	−5.73922	−0.463988
$154$	−9.46772	−0.762930
$155$	6.80971	0.546969
$156$	48.9504	3.91917
$157$	−15.6954	−1.25263	−0.626314	−	0.779571i	$-0.715437\pi$
$157$	−15.6954	−1.25263	−0.626314	+	0.779571i	$0.715437\pi$
$158$	11.6143	0.923985
$159$	−17.7950	−1.41123
$160$	2.44937	0.193640
$161$	11.4087	0.899132
$162$	−16.2533	−1.27698
$163$	15.1145	1.18386	0.591929	−	0.805990i	$-0.298367\pi$
$163$	15.1145	1.18386	0.591929	+	0.805990i	$0.298367\pi$
$164$	−30.7465	−2.40090
$165$	−5.12396	−0.398900
$166$	−6.25045	−0.485129
$167$	0.218240	0.0168879	0.00844395	−	0.999964i	$-0.497312\pi$
$167$	0.218240	0.0168879	0.00844395	+	0.999964i	$0.497312\pi$
$168$	51.7271	3.99083
$169$	5.51555	0.424273
$170$	4.19159	0.321480
$171$	−27.0117	−2.06564
$172$	3.84815	0.293418
$173$	4.80299	0.365165	0.182582	−	0.983191i	$-0.441554\pi$
$173$	4.80299	0.365165	0.182582	+	0.983191i	$0.441554\pi$
$174$	0.862600	0.0653935
$175$	−7.81337	−0.590635
$176$	3.11194	0.234571
$177$	4.77754	0.359102
$178$	43.2421	3.24113
$179$	3.02281	0.225935	0.112968	−	0.993599i	$-0.463964\pi$
$179$	3.02281	0.225935	0.112968	+	0.993599i	$0.463964\pi$
$180$	38.2802	2.85323
$181$	−7.24714	−0.538675	−0.269338	−	0.963046i	$-0.586805\pi$
$181$	−7.24714	−0.538675	−0.269338	+	0.963046i	$0.586805\pi$
$182$	40.7393	3.01980
$183$	−35.0135	−2.58827
$184$	−13.0240	−0.960145
$185$	−6.80481	−0.500299
$186$	28.0870	2.05944
$187$	−1.00000	−0.0731272
$188$	−2.66153	−0.194112
$189$	−31.7029	−2.30605
$190$	19.7277	1.43120
$191$	−7.08917	−0.512955	−0.256477	−	0.966550i	$-0.582562\pi$
$191$	−7.08917	−0.512955	−0.256477	+	0.966550i	$0.582562\pi$
$192$	28.5017	2.05693
$193$	17.0055	1.22408	0.612041	−	0.790826i	$-0.290349\pi$
$193$	17.0055	1.22408	0.612041	+	0.790826i	$0.290349\pi$
$194$	−23.8771	−1.71427
$195$	22.0482	1.57891
$196$	32.0456	2.28897
$197$	−8.09229	−0.576552	−0.288276	−	0.957547i	$-0.593082\pi$
$197$	−8.09229	−0.576552	−0.288276	+	0.957547i	$0.593082\pi$
$198$	−13.8791	−0.986346
$199$	8.71172	0.617558	0.308779	−	0.951134i	$-0.400080\pi$
$199$	8.71172	0.617558	0.308779	+	0.951134i	$0.400080\pi$
$200$	8.91965	0.630714
$201$	−25.4587	−1.79572
$202$	−9.59897	−0.675381
$203$	0.472389	0.0331552
$204$	11.3760	0.796476
$205$	−13.8488	−0.967244
$206$	17.1375	1.19403
$207$	16.7245	1.16243
$208$	−13.3906	−0.928470
$209$	−4.70651	−0.325556
$210$	48.5122	3.34766
$211$	13.1306	0.903948	0.451974	−	0.892031i	$-0.350720\pi$
$211$	13.1306	0.903948	0.451974	+	0.892031i	$0.350720\pi$
$212$	23.1639	1.59091
$213$	29.1353	1.99632
$214$	−43.5835	−2.97931
$215$	1.73328	0.118209
$216$	36.1917	2.46253
$217$	15.3814	1.04416
$218$	11.6931	0.791959
$219$	−41.0349	−2.77288
$220$	6.66993	0.449686
$221$	4.30297	0.289449
$222$	−28.0667	−1.88372
$223$	7.45784	0.499414	0.249707	−	0.968321i	$-0.419666\pi$
$223$	7.45784	0.499414	0.249707	+	0.968321i	$0.419666\pi$
$224$	5.53249	0.369655
$225$	−11.4539	−0.763596
$226$	44.8465	2.98314
$227$	−17.0200	−1.12966	−0.564830	−	0.825207i	$-0.691058\pi$
$227$	−17.0200	−1.12966	−0.564830	+	0.825207i	$0.691058\pi$
$228$	53.5411	3.54584
$229$	0.568249	0.0375509	0.0187755	−	0.999824i	$-0.494023\pi$
$229$	0.568249	0.0375509	0.0187755	+	0.999824i	$0.494023\pi$
$230$	−12.2146	−0.805406
$231$	−11.5737	−0.761494
$232$	−0.539274	−0.0354051
$233$	13.5441	0.887301	0.443651	−	0.896200i	$-0.353683\pi$
$233$	13.5441	0.887301	0.443651	+	0.896200i	$0.353683\pi$
$234$	59.7214	3.90411
$235$	−1.19881	−0.0782016
$236$	−6.21899	−0.404822
$237$	14.1978	0.922245
$238$	9.46772	0.613701
$239$	−19.7601	−1.27817	−0.639087	−	0.769134i	$-0.720688\pi$
$239$	−19.7601	−1.27817	−0.639087	+	0.769134i	$0.720688\pi$
$240$	−15.9455	−1.02927
$241$	13.2027	0.850459	0.425230	−	0.905085i	$-0.360193\pi$
$241$	13.2027	0.850459	0.425230	+	0.905085i	$0.360193\pi$
$242$	−2.41829	−0.155454
$243$	4.42452	0.283833
$244$	45.5776	2.91781
$245$	14.4340	0.922153
$246$	−57.1201	−3.64185
$247$	20.2520	1.28860
$248$	−17.5592	−1.11501
$249$	−7.64080	−0.484216
$250$	29.3232	1.85456
$251$	−19.8554	−1.25326	−0.626630	−	0.779317i	$-0.715566\pi$
$251$	−19.8554	−1.25326	−0.626630	+	0.779317i	$0.715566\pi$
$252$	86.4650	5.44679
$253$	2.91407	0.183206
$254$	36.6422	2.29914
$255$	5.12396	0.320875
$256$	−30.2662	−1.89164
$257$	19.9962	1.24733	0.623663	−	0.781693i	$-0.285644\pi$
$257$	19.9962	1.24733	0.623663	+	0.781693i	$0.285644\pi$
$258$	7.14900	0.445077
$259$	−15.3703	−0.955065
$260$	−28.7005	−1.77993
$261$	0.692495	0.0428644
$262$	−27.1148	−1.67516
$263$	−22.4950	−1.38710	−0.693551	−	0.720407i	$-0.743955\pi$
$263$	−22.4950	−1.38710	−0.693551	+	0.720407i	$0.743955\pi$
$264$	13.2124	0.813167
$265$	10.4335	0.640925
$266$	44.5599	2.73214
$267$	52.8609	3.23503
$268$	33.1400	2.02435
$269$	18.4176	1.12294	0.561471	−	0.827497i	$-0.310236\pi$
$269$	18.4176	1.12294	0.561471	+	0.827497i	$0.310236\pi$
$270$	33.9423	2.06566
$271$	−17.0139	−1.03352	−0.516761	−	0.856130i	$-0.672862\pi$
$271$	−17.0139	−1.03352	−0.516761	+	0.856130i	$0.672862\pi$
$272$	−3.11194	−0.188689
$273$	49.8013	3.01411
$274$	12.8829	0.778285
$275$	−1.99573	−0.120347
$276$	−33.1504	−1.99542
$277$	−2.12017	−0.127389	−0.0636944	−	0.997969i	$-0.520288\pi$
$277$	−2.12017	−0.127389	−0.0636944	+	0.997969i	$0.520288\pi$
$278$	12.6430	0.758278
$279$	22.5482	1.34993
$280$	−30.3285	−1.81248
$281$	0.611735	0.0364931	0.0182465	−	0.999834i	$-0.494192\pi$
$281$	0.611735	0.0364931	0.0182465	+	0.999834i	$0.494192\pi$
$282$	−4.94454	−0.294443
$283$	20.6822	1.22943	0.614713	−	0.788751i	$-0.289272\pi$
$283$	20.6822	1.22943	0.614713	+	0.788751i	$0.289272\pi$
$284$	−37.9258	−2.25048
$285$	24.1160	1.42851
$286$	10.4058	0.615311
$287$	−31.2809	−1.84646
$288$	8.11031	0.477905
$289$	1.00000	0.0588235
$290$	−0.505758	−0.0296991
$291$	−29.1882	−1.71105
$292$	53.4156	3.12591
$293$	−16.6401	−0.972127	−0.486063	−	0.873924i	$-0.661568\pi$
$293$	−16.6401	−0.972127	−0.486063	+	0.873924i	$0.661568\pi$
$294$	59.5336	3.47207
$295$	−2.80116	−0.163090
$296$	17.5466	1.01987
$297$	−8.09772	−0.469878
$298$	−15.5625	−0.901513
$299$	−12.5392	−0.725159
$300$	22.7034	1.31078
$301$	3.91504	0.225659
$302$	36.6934	2.11147
$303$	−11.7342	−0.674109
$304$	−14.6464	−0.840027
$305$	20.5291	1.17549
$306$	13.8791	0.793416
$307$	2.19559	0.125309	0.0626545	−	0.998035i	$-0.480043\pi$
$307$	2.19559	0.125309	0.0626545	+	0.998035i	$0.480043\pi$
$308$	15.0656	0.858445
$309$	20.9496	1.19178
$310$	−16.4679	−0.935314
$311$	−23.5360	−1.33460	−0.667301	−	0.744788i	$-0.732551\pi$
$311$	−23.5360	−1.33460	−0.667301	+	0.744788i	$0.732551\pi$
$312$	−56.8526	−3.21864
$313$	21.6726	1.22501	0.612503	−	0.790468i	$-0.290163\pi$
$313$	21.6726	1.22501	0.612503	+	0.790468i	$0.290163\pi$
$314$	37.9561	2.14199
$315$	38.9456	2.19434
$316$	−18.4814	−1.03966
$317$	−27.9121	−1.56770	−0.783850	−	0.620950i	$-0.786747\pi$
$317$	−27.9121	−1.56770	−0.783850	+	0.620950i	$0.786747\pi$
$318$	43.0334	2.41320
$319$	0.120660	0.00675567
$320$	−16.7110	−0.934175
$321$	−53.2782	−2.97370
$322$	−27.5896	−1.53751
$323$	4.70651	0.261877
$324$	25.8633	1.43685
$325$	8.58757	0.476353
$326$	−36.5513	−2.02439
$327$	14.2941	0.790468
$328$	35.7100	1.97175
$329$	−2.70780	−0.149286
$330$	12.3912	0.682115
$331$	−15.9380	−0.876033	−0.438016	−	0.898967i	$-0.644319\pi$
$331$	−15.9380	−0.876033	−0.438016	+	0.898967i	$0.644319\pi$
$332$	9.94613	0.545865
$333$	−22.5320	−1.23474
$334$	−0.527768	−0.0288782
$335$	14.9269	0.815544
$336$	−36.0167	−1.96487
$337$	4.29169	0.233783	0.116892	−	0.993145i	$-0.462707\pi$
$337$	4.29169	0.233783	0.116892	+	0.993145i	$0.462707\pi$
$338$	−13.3382	−0.725504
$339$	54.8221	2.97753
$340$	−6.66993	−0.361727
$341$	3.92880	0.212756
$342$	65.3222	3.53222
$343$	5.19735	0.280631
$344$	−4.46936	−0.240972
$345$	−14.9316	−0.803890
$346$	−11.6150	−0.624429
$347$	−13.7645	−0.738914	−0.369457	−	0.929248i	$-0.620456\pi$
$347$	−13.7645	−0.738914	−0.369457	+	0.929248i	$0.620456\pi$
$348$	−1.37262	−0.0735804
$349$	33.4161	1.78872	0.894362	−	0.447344i	$-0.147630\pi$
$349$	33.4161	1.78872	0.894362	+	0.447344i	$0.147630\pi$
$350$	18.8950	1.00998
$351$	34.8443	1.85985
$352$	1.41314	0.0753205
$353$	11.0236	0.586725	0.293363	−	0.956001i	$-0.405226\pi$
$353$	11.0236	0.586725	0.293363	+	0.956001i	$0.405226\pi$
$354$	−11.5535	−0.614061
$355$	−17.0826	−0.906648
$356$	−68.8097	−3.64691
$357$	11.5737	0.612545
$358$	−7.31004	−0.386348
$359$	−35.1169	−1.85340	−0.926699	−	0.375804i	$-0.877367\pi$
$359$	−35.1169	−1.85340	−0.926699	+	0.375804i	$0.877367\pi$
$360$	−44.4598	−2.34324
$361$	3.15124	0.165855
$362$	17.5257	0.921131
$363$	−2.95622	−0.155161
$364$	−64.8270	−3.39786
$365$	24.0595	1.25933
$366$	84.6730	4.42593
$367$	−2.52848	−0.131985	−0.0659927	−	0.997820i	$-0.521021\pi$
$367$	−2.52848	−0.131985	−0.0659927	+	0.997820i	$0.521021\pi$
$368$	9.06842	0.472724
$369$	−45.8560	−2.38717
$370$	16.4560	0.855508
$371$	23.5666	1.22352
$372$	−44.6938	−2.31727
$373$	−38.2095	−1.97842	−0.989208	−	0.146521i	$-0.953192\pi$
$373$	−38.2095	−1.97842	−0.989208	+	0.146521i	$0.953192\pi$
$374$	2.41829	0.125047
$375$	35.8458	1.85107
$376$	3.09119	0.159416
$377$	−0.519197	−0.0267400
$378$	76.6670	3.94332
$379$	−5.08056	−0.260971	−0.130486	−	0.991450i	$-0.541654\pi$
$379$	−5.08056	−0.260971	−0.130486	+	0.991450i	$0.541654\pi$
$380$	−31.3921	−1.61038
$381$	44.7929	2.29481
$382$	17.1437	0.877148
$383$	−15.9929	−0.817198	−0.408599	−	0.912714i	$-0.633983\pi$
$383$	−15.9929	−0.817198	−0.408599	+	0.912714i	$0.633983\pi$
$384$	−60.5703	−3.09097
$385$	6.78587	0.345840
$386$	−41.1243	−2.09317
$387$	5.73922	0.291741
$388$	37.9947	1.92889
$389$	−19.0707	−0.966922	−0.483461	−	0.875366i	$-0.660621\pi$
$389$	−19.0707	−0.966922	−0.483461	+	0.875366i	$0.660621\pi$
$390$	−53.3191	−2.69992
$391$	−2.91407	−0.147371
$392$	−37.2188	−1.87983
$393$	−33.1461	−1.67200
$394$	19.5695	0.985899
$395$	−8.32441	−0.418847
$396$	22.0854	1.10983
$397$	22.6555	1.13705	0.568525	−	0.822666i	$-0.307514\pi$
$397$	22.6555	1.13705	0.568525	+	0.822666i	$0.307514\pi$
$398$	−21.0675	−1.05602
$399$	54.4718	2.72700
$400$	−6.21060	−0.310530
$401$	−8.94613	−0.446748	−0.223374	−	0.974733i	$-0.571707\pi$
$401$	−8.94613	−0.446748	−0.223374	+	0.974733i	$0.571707\pi$
$402$	61.5667	3.07067
$403$	−16.9055	−0.842123
$404$	15.2745	0.759935
$405$	11.6493	0.578860
$406$	−1.14238	−0.0566952
$407$	−3.92597	−0.194603
$408$	−13.2124	−0.654112
$409$	4.55186	0.225075	0.112538	−	0.993647i	$-0.464102\pi$
$409$	4.55186	0.225075	0.112538	+	0.993647i	$0.464102\pi$
$410$	33.4905	1.65398
$411$	15.7486	0.776820
$412$	−27.2703	−1.34351
$413$	−6.32709	−0.311336
$414$	−40.4448	−1.98775
$415$	4.47994	0.219911
$416$	−6.08069	−0.298130
$417$	15.4553	0.756850
$418$	11.3817	0.556698
$419$	−30.7228	−1.50091	−0.750453	−	0.660924i	$-0.770164\pi$
$419$	−30.7228	−1.50091	−0.750453	+	0.660924i	$0.770164\pi$
$420$	−77.1958	−3.76677
$421$	14.7378	0.718275	0.359138	−	0.933285i	$-0.383071\pi$
$421$	14.7378	0.718275	0.359138	+	0.933285i	$0.383071\pi$
$422$	−31.7536	−1.54574
$423$	−3.96948	−0.193003
$424$	−26.9033	−1.30654
$425$	1.99573	0.0968072
$426$	−70.4578	−3.41369
$427$	46.3699	2.24399
$428$	69.3529	3.35230
$429$	12.7205	0.614152
$430$	−4.19159	−0.202136
$431$	−25.8551	−1.24540	−0.622699	−	0.782461i	$-0.713964\pi$
$431$	−25.8551	−1.24540	−0.622699	+	0.782461i	$0.713964\pi$
$432$	−25.1996	−1.21242
$433$	−28.6199	−1.37538	−0.687692	−	0.726003i	$-0.741376\pi$
$433$	−28.6199	−1.37538	−0.687692	+	0.726003i	$0.741376\pi$
$434$	−37.1967	−1.78550
$435$	−0.618258	−0.0296432
$436$	−18.6069	−0.891107
$437$	−13.7151	−0.656083
$438$	99.2344	4.74160
$439$	20.9962	1.00210	0.501048	−	0.865420i	$-0.332948\pi$
$439$	20.9962	1.00210	0.501048	+	0.865420i	$0.332948\pi$
$440$	−7.74667	−0.369308
$441$	47.7935	2.27588
$442$	−10.4058	−0.494956
$443$	−27.1113	−1.28810	−0.644048	−	0.764985i	$-0.722746\pi$
$443$	−27.1113	−1.28810	−0.644048	+	0.764985i	$0.722746\pi$
$444$	44.6616	2.11955
$445$	−30.9933	−1.46922
$446$	−18.0352	−0.853993
$447$	−19.0242	−0.899816
$448$	−37.7459	−1.78333
$449$	3.04639	0.143768	0.0718840	−	0.997413i	$-0.477099\pi$
$449$	3.04639	0.143768	0.0718840	+	0.997413i	$0.477099\pi$
$450$	27.6990	1.30574
$451$	−7.98994	−0.376232
$452$	−71.3626	−3.35662
$453$	44.8555	2.10750
$454$	41.1595	1.93171
$455$	−29.1994	−1.36889
$456$	−62.1843	−2.91205
$457$	−3.79899	−0.177709	−0.0888547	−	0.996045i	$-0.528321\pi$
$457$	−3.79899	−0.177709	−0.0888547	+	0.996045i	$0.528321\pi$
$458$	−1.37419	−0.0642118
$459$	8.09772	0.377969
$460$	19.4366	0.906238
$461$	−0.195709	−0.00911506	−0.00455753	−	0.999990i	$-0.501451\pi$
$461$	−0.195709	−0.00911506	−0.00455753	+	0.999990i	$0.501451\pi$
$462$	27.9886	1.30215
$463$	13.4755	0.626259	0.313130	−	0.949710i	$-0.398623\pi$
$463$	13.4755	0.626259	0.313130	+	0.949710i	$0.398623\pi$
$464$	0.375487	0.0174316
$465$	−20.1310	−0.933552
$466$	−32.7535	−1.51728
$467$	14.0552	0.650397	0.325198	−	0.945646i	$-0.394569\pi$
$467$	14.0552	0.650397	0.325198	+	0.945646i	$0.394569\pi$
$468$	−95.0326	−4.39288
$469$	33.7161	1.55686
$470$	2.89907	0.133724
$471$	46.3990	2.13795
$472$	7.22293	0.332462
$473$	1.00000	0.0459800
$474$	−34.3344	−1.57703
$475$	9.39293	0.430977
$476$	−15.0656	−0.690533
$477$	34.5472	1.58181
$478$	47.7857	2.18567
$479$	−29.3815	−1.34248	−0.671238	−	0.741242i	$-0.734237\pi$
$479$	−29.3815	−1.34248	−0.671238	+	0.741242i	$0.734237\pi$
$480$	−7.24086	−0.330499
$481$	16.8933	0.770269
$482$	−31.9280	−1.45428
$483$	−33.7266	−1.53461
$484$	3.84815	0.174916
$485$	17.1136	0.777088
$486$	−10.6998	−0.485353
$487$	−11.4251	−0.517723	−0.258861	−	0.965914i	$-0.583347\pi$
$487$	−11.4251	−0.517723	−0.258861	+	0.965914i	$0.583347\pi$
$488$	−52.9353	−2.39627
$489$	−44.6817	−2.02057
$490$	−34.9056	−1.57687
$491$	22.8391	1.03071	0.515357	−	0.856976i	$-0.327659\pi$
$491$	22.8391	1.03071	0.515357	+	0.856976i	$0.327659\pi$
$492$	90.8932	4.09778
$493$	−0.120660	−0.00543426
$494$	−48.9752	−2.20350
$495$	9.94769	0.447115
$496$	12.2262	0.548972
$497$	−38.5851	−1.73078
$498$	18.4777	0.828006
$499$	9.53084	0.426659	0.213329	−	0.976980i	$-0.431569\pi$
$499$	9.53084	0.426659	0.213329	+	0.976980i	$0.431569\pi$
$500$	−46.6610	−2.08674
$501$	−0.645164	−0.0288238
$502$	48.0161	2.14306
$503$	1.52836	0.0681460	0.0340730	−	0.999419i	$-0.489152\pi$
$503$	1.52836	0.0681460	0.0340730	+	0.999419i	$0.489152\pi$
$504$	−100.423	−4.47321
$505$	6.87994	0.306153
$506$	−7.04708	−0.313281
$507$	−16.3052	−0.724138
$508$	−58.3075	−2.58698
$509$	7.59421	0.336607	0.168304	−	0.985735i	$-0.446171\pi$
$509$	7.59421	0.336607	0.168304	+	0.985735i	$0.446171\pi$
$510$	−12.3912	−0.548693
$511$	54.3442	2.40404
$512$	32.2144	1.42369
$513$	38.1120	1.68269
$514$	−48.3566	−2.13292
$515$	−12.2831	−0.541258
$516$	−11.3760	−0.500799
$517$	−0.691641	−0.0304183
$518$	37.1699	1.63315
$519$	−14.1987	−0.623253
$520$	33.3337	1.46178
$521$	40.8638	1.79027	0.895137	−	0.445791i	$-0.147078\pi$
$521$	40.8638	1.79027	0.895137	+	0.445791i	$0.147078\pi$
$522$	−1.67466	−0.0732977
$523$	−4.86422	−0.212698	−0.106349	−	0.994329i	$-0.533916\pi$
$523$	−4.86422	−0.212698	−0.106349	+	0.994329i	$0.533916\pi$
$524$	43.1468	1.88487
$525$	23.0980	1.00808
$526$	54.3996	2.37194
$527$	−3.92880	−0.171141
$528$	−9.19957	−0.400360
$529$	−14.5082	−0.630791
$530$	−25.2313	−1.09598
$531$	−9.27514	−0.402507
$532$	−70.9066	−3.07419
$533$	34.3805	1.48918
$534$	−127.833	−5.53188
$535$	31.2380	1.35053
$536$	−38.4898	−1.66251
$537$	−8.93608	−0.385620
$538$	−44.5392	−1.92022
$539$	8.32754	0.358692
$540$	−54.0112	−2.32427
$541$	−33.9337	−1.45892	−0.729461	−	0.684022i	$-0.760229\pi$
$541$	−33.9337	−1.45892	−0.729461	+	0.684022i	$0.760229\pi$
$542$	41.1446	1.76731
$543$	21.4241	0.919396
$544$	−1.41314	−0.0605878
$545$	−8.38091	−0.358999
$546$	−120.434	−5.15411
$547$	35.3406	1.51106	0.755528	−	0.655117i	$-0.227381\pi$
$547$	35.3406	1.51106	0.755528	+	0.655117i	$0.227381\pi$
$548$	−20.5001	−0.875722
$549$	67.9755	2.90112
$550$	4.82627	0.205793
$551$	−0.567888	−0.0241929
$552$	38.5019	1.63875
$553$	−18.8027	−0.799572
$554$	5.12720	0.217834
$555$	20.1165	0.853897
$556$	−20.1184	−0.853210
$557$	−16.7108	−0.708059	−0.354029	−	0.935234i	$-0.615189\pi$
$557$	−16.7108	−0.708059	−0.354029	+	0.935234i	$0.615189\pi$
$558$	−54.5282	−2.30836
$559$	−4.30297	−0.181996
$560$	21.1172	0.892365
$561$	2.95622	0.124812
$562$	−1.47936	−0.0624029
$563$	4.72754	0.199242	0.0996210	−	0.995025i	$-0.468237\pi$
$563$	4.72754	0.199242	0.0996210	+	0.995025i	$0.468237\pi$
$564$	7.86807	0.331306
$565$	−32.1432	−1.35227
$566$	−50.0155	−2.10231
$567$	26.3129	1.10504
$568$	44.0483	1.84823
$569$	−36.5301	−1.53142	−0.765712	−	0.643184i	$-0.777613\pi$
$569$	−36.5301	−1.53142	−0.765712	+	0.643184i	$0.777613\pi$
$570$	−58.3195	−2.44273
$571$	29.9909	1.25508	0.627540	−	0.778584i	$-0.284062\pi$
$571$	29.9909	1.25508	0.627540	+	0.778584i	$0.284062\pi$
$572$	−16.5585	−0.692344
$573$	20.9571	0.875497
$574$	75.6465	3.15742
$575$	−5.81571	−0.242532
$576$	−55.3333	−2.30556
$577$	−19.2118	−0.799798	−0.399899	−	0.916559i	$-0.630955\pi$
$577$	−19.2118	−0.799798	−0.399899	+	0.916559i	$0.630955\pi$
$578$	−2.41829	−0.100588
$579$	−50.2719	−2.08923
$580$	0.804794	0.0334173
$581$	10.1190	0.419808
$582$	70.5858	2.92587
$583$	6.01950	0.249302
$584$	−62.0387	−2.56718
$585$	−42.8046	−1.76975
$586$	40.2407	1.66233
$587$	42.5731	1.75718	0.878590	−	0.477578i	$-0.158485\pi$
$587$	42.5731	1.75718	0.878590	+	0.477578i	$0.158485\pi$
$588$	−94.7337	−3.90675
$589$	−18.4909	−0.761905
$590$	6.77402	0.278882
$591$	23.9226	0.984042
$592$	−12.2174	−0.502131
$593$	8.96426	0.368118	0.184059	−	0.982915i	$-0.441076\pi$
$593$	8.96426	0.368118	0.184059	+	0.982915i	$0.441076\pi$
$594$	19.5827	0.803487
$595$	−6.78587	−0.278194
$596$	24.7641	1.01438
$597$	−25.7537	−1.05403
$598$	30.3234	1.24002
$599$	−19.7777	−0.808096	−0.404048	−	0.914738i	$-0.632397\pi$
$599$	−19.7777	−0.808096	−0.404048	+	0.914738i	$0.632397\pi$
$600$	−26.3684	−1.07649
$601$	34.1469	1.39288	0.696441	−	0.717614i	$-0.254766\pi$
$601$	34.1469	1.39288	0.696441	+	0.717614i	$0.254766\pi$
$602$	−9.46772	−0.385875
$603$	49.4257	2.01277
$604$	−58.3890	−2.37581
$605$	1.73328	0.0704680
$606$	28.3766	1.15272
$607$	1.97248	0.0800605	0.0400303	−	0.999198i	$-0.487255\pi$
$607$	1.97248	0.0800605	0.0400303	+	0.999198i	$0.487255\pi$
$608$	−6.65095	−0.269732
$609$	−1.39649	−0.0565884
$610$	−49.6453	−2.01008
$611$	2.97611	0.120400
$612$	−22.0854	−0.892748
$613$	13.9078	0.561732	0.280866	−	0.959747i	$-0.409378\pi$
$613$	13.9078	0.561732	0.280866	+	0.959747i	$0.409378\pi$
$614$	−5.30958	−0.214277
$615$	40.9401	1.65087
$616$	−17.4977	−0.705004
$617$	−48.7129	−1.96111	−0.980555	−	0.196246i	$-0.937125\pi$
$617$	−48.7129	−1.96111	−0.980555	+	0.196246i	$0.937125\pi$
$618$	−50.6622	−2.03793
$619$	−13.2443	−0.532332	−0.266166	−	0.963927i	$-0.585757\pi$
$619$	−13.2443	−0.532332	−0.266166	+	0.963927i	$0.585757\pi$
$620$	26.2048	1.05241
$621$	−23.5973	−0.946929
$622$	56.9169	2.28216
$623$	−70.0058	−2.80472
$624$	39.5855	1.58469
$625$	−11.0384	−0.441536
$626$	−52.4106	−2.09475
$627$	13.9135	0.555650
$628$	−60.3982	−2.41015
$629$	3.92597	0.156539
$630$	−94.1819	−3.75230
$631$	−44.3942	−1.76731	−0.883653	−	0.468142i	$-0.844923\pi$
$631$	−44.3942	−1.76731	−0.883653	+	0.468142i	$0.844923\pi$
$632$	21.4649	0.853829
$633$	−38.8169	−1.54283
$634$	67.4997	2.68076
$635$	−26.2629	−1.04221
$636$	−68.4776	−2.71531
$637$	−35.8331	−1.41976
$638$	−0.291792	−0.0115521
$639$	−56.5635	−2.23762
$640$	35.5135	1.40379
$641$	23.5914	0.931806	0.465903	−	0.884836i	$-0.345730\pi$
$641$	23.5914	0.931806	0.465903	+	0.884836i	$0.345730\pi$
$642$	128.842	5.08500
$643$	−34.5986	−1.36444	−0.682219	−	0.731148i	$-0.738985\pi$
$643$	−34.5986	−1.36444	−0.682219	+	0.731148i	$0.738985\pi$
$644$	43.9024	1.73000
$645$	−5.12396	−0.201756
$646$	−11.3817	−0.447808
$647$	−3.00287	−0.118055	−0.0590274	−	0.998256i	$-0.518800\pi$
$647$	−3.00287	−0.118055	−0.0590274	+	0.998256i	$0.518800\pi$
$648$	−30.0385	−1.18002
$649$	−1.61610	−0.0634374
$650$	−20.7673	−0.814560
$651$	−45.4707	−1.78214
$652$	58.1627	2.27783
$653$	−14.5388	−0.568948	−0.284474	−	0.958684i	$-0.591819\pi$
$653$	−14.5388	−0.568948	−0.284474	+	0.958684i	$0.591819\pi$
$654$	−34.5674	−1.35169
$655$	19.4342	0.759356
$656$	−24.8642	−0.970785
$657$	79.6654	3.10804
$658$	6.54826	0.255278
$659$	25.4343	0.990780	0.495390	−	0.868671i	$-0.335025\pi$
$659$	25.4343	0.990780	0.495390	+	0.868671i	$0.335025\pi$
$660$	−19.7177	−0.767512
$661$	−22.4058	−0.871484	−0.435742	−	0.900072i	$-0.643514\pi$
$661$	−22.4058	−0.871484	−0.435742	+	0.900072i	$0.643514\pi$
$662$	38.5428	1.49801
$663$	−12.7205	−0.494024
$664$	−11.5518	−0.448295
$665$	−31.9378	−1.23849
$666$	54.4889	2.11140
$667$	0.351612	0.0136145
$668$	0.839819	0.0324936
$669$	−22.0470	−0.852385
$670$	−36.0977	−1.39457
$671$	11.8440	0.457234
$672$	−16.3552	−0.630917
$673$	26.6122	1.02583	0.512913	−	0.858440i	$-0.328566\pi$
$673$	26.6122	1.02583	0.512913	+	0.858440i	$0.328566\pi$
$674$	−10.3786	−0.399768
$675$	16.1609	0.622033
$676$	21.2247	0.816333
$677$	34.5764	1.32888	0.664439	−	0.747343i	$-0.268671\pi$
$677$	34.5764	1.32888	0.664439	+	0.747343i	$0.268671\pi$
$678$	−132.576	−5.09155
$679$	38.6552	1.48345
$680$	7.74667	0.297071
$681$	50.3149	1.92807
$682$	−9.50099	−0.363812
$683$	−1.33035	−0.0509046	−0.0254523	−	0.999676i	$-0.508103\pi$
$683$	−1.33035	−0.0509046	−0.0254523	+	0.999676i	$0.508103\pi$
$684$	−103.945	−3.97443
$685$	−9.23367	−0.352800
$686$	−12.5687	−0.479876
$687$	−1.67987	−0.0640909
$688$	3.11194	0.118642
$689$	−25.9017	−0.986778
$690$	36.1090	1.37464
$691$	−10.5569	−0.401602	−0.200801	−	0.979632i	$-0.564354\pi$
$691$	−10.5569	−0.401602	−0.200801	+	0.979632i	$0.564354\pi$
$692$	18.4826	0.702604
$693$	22.4693	0.853537
$694$	33.2865	1.26354
$695$	−9.06172	−0.343731
$696$	1.59421	0.0604284
$697$	7.98994	0.302641
$698$	−80.8100	−3.05870
$699$	−40.0392	−1.51442
$700$	−30.0670	−1.13643
$701$	28.7505	1.08589	0.542946	−	0.839768i	$-0.317309\pi$
$701$	28.7505	1.08589	0.542946	+	0.839768i	$0.317309\pi$
$702$	−84.2637	−3.18033
$703$	18.4776	0.696896
$704$	−9.64126	−0.363369
$705$	3.54394	0.133472
$706$	−26.6582	−1.00330
$707$	15.5400	0.584443
$708$	18.3847	0.690938
$709$	−3.21546	−0.120759	−0.0603796	−	0.998175i	$-0.519231\pi$
$709$	−3.21546	−0.120759	−0.0603796	+	0.998175i	$0.519231\pi$
$710$	41.3106	1.55036
$711$	−27.5637	−1.03372
$712$	79.9178	2.99505
$713$	11.4488	0.428761
$714$	−27.9886	−1.04745
$715$	−7.45826	−0.278923
$716$	11.6322	0.434716
$717$	58.4151	2.18155
$718$	84.9230	3.16930
$719$	−28.1358	−1.04929	−0.524644	−	0.851322i	$-0.675801\pi$
$719$	−28.1358	−1.04929	−0.524644	+	0.851322i	$0.675801\pi$
$720$	30.9566	1.15368
$721$	−27.7444	−1.03325
$722$	−7.62062	−0.283610
$723$	−39.0300	−1.45154
$724$	−27.8880	−1.03645
$725$	−0.240805	−0.00894329
$726$	7.14900	0.265324
$727$	17.6632	0.655092	0.327546	−	0.944835i	$-0.393778\pi$
$727$	17.6632	0.655092	0.327546	+	0.944835i	$0.393778\pi$
$728$	75.2922	2.79052
$729$	−33.2428	−1.23121
$730$	−58.1829	−2.15345
$731$	−1.00000	−0.0369863
$732$	−134.737	−4.98003
$733$	−14.8822	−0.549686	−0.274843	−	0.961489i	$-0.588626\pi$
$733$	−14.8822	−0.549686	−0.274843	+	0.961489i	$0.588626\pi$
$734$	6.11460	0.225694
$735$	−42.6699	−1.57390
$736$	4.11799	0.151791
$737$	8.61193	0.317225
$738$	110.893	4.08204
$739$	7.47593	0.275006	0.137503	−	0.990501i	$-0.456092\pi$
$739$	7.47593	0.275006	0.137503	+	0.990501i	$0.456092\pi$
$740$	−26.1859	−0.962613
$741$	−59.8692	−2.19935
$742$	−56.9910	−2.09220
$743$	21.8406	0.801255	0.400627	−	0.916241i	$-0.368792\pi$
$743$	21.8406	0.801255	0.400627	+	0.916241i	$0.368792\pi$
$744$	51.9089	1.90307
$745$	11.1543	0.408660
$746$	92.4019	3.38307
$747$	14.8339	0.542744
$748$	−3.84815	−0.140702
$749$	70.5585	2.57815
$750$	−86.6858	−3.16532
$751$	18.2066	0.664369	0.332185	−	0.943214i	$-0.392214\pi$
$751$	18.2066	0.664369	0.332185	+	0.943214i	$0.392214\pi$
$752$	−2.15234	−0.0784879
$753$	58.6968	2.13903
$754$	1.25557	0.0457252
$755$	−26.2996	−0.957140
$756$	−121.997	−4.43700
$757$	41.7237	1.51647	0.758237	−	0.651979i	$-0.226061\pi$
$757$	41.7237	1.51647	0.758237	+	0.651979i	$0.226061\pi$
$758$	12.2863	0.446258
$759$	−8.61463	−0.312691
$760$	36.4598	1.32253
$761$	−42.6301	−1.54534	−0.772670	−	0.634808i	$-0.781079\pi$
$761$	−42.6301	−1.54534	−0.772670	+	0.634808i	$0.781079\pi$
$762$	−108.322	−3.92410
$763$	−18.9303	−0.685323
$764$	−27.2802	−0.986962
$765$	−9.94769	−0.359659
$766$	38.6755	1.39740
$767$	6.95403	0.251095
$768$	89.4735	3.22860
$769$	−10.9951	−0.396492	−0.198246	−	0.980152i	$-0.563524\pi$
$769$	−10.9951	−0.396492	−0.198246	+	0.980152i	$0.563524\pi$
$770$	−16.4102	−0.591384
$771$	−59.1130	−2.12890
$772$	65.4396	2.35522
$773$	−46.2123	−1.66214	−0.831071	−	0.556167i	$-0.812272\pi$
$773$	−46.2123	−1.66214	−0.831071	+	0.556167i	$0.812272\pi$
$774$	−13.8791	−0.498875
$775$	−7.84083	−0.281651
$776$	−44.1283	−1.58411
$777$	45.4380	1.63008
$778$	46.1185	1.65343
$779$	37.6047	1.34733
$780$	84.8449	3.03793
$781$	−9.85561	−0.352661
$782$	7.04708	0.252003
$783$	−0.977073	−0.0349177
$784$	25.9148	0.925528
$785$	−27.2046	−0.970972
$786$	80.1571	2.85911
$787$	2.57268	0.0917062	0.0458531	−	0.998948i	$-0.485399\pi$
$787$	2.57268	0.0917062	0.0458531	+	0.998948i	$0.485399\pi$
$788$	−31.1403	−1.10933
$789$	66.5002	2.36747
$790$	20.1309	0.716224
$791$	−72.6031	−2.58147
$792$	−25.6506	−0.911456
$793$	−50.9645	−1.80980
$794$	−54.7878	−1.94435
$795$	−30.8437	−1.09391
$796$	33.5240	1.18823
$797$	−12.4170	−0.439834	−0.219917	−	0.975519i	$-0.570579\pi$
$797$	−12.4170	−0.439834	−0.219917	+	0.975519i	$0.570579\pi$
$798$	−131.729	−4.66315
$799$	0.691641	0.0244685
$800$	−2.82025	−0.0997107
$801$	−102.624	−3.62606
$802$	21.6344	0.763936
$803$	13.8809	0.489845
$804$	−97.9689	−3.45510
$805$	19.7745	0.696960
$806$	40.8825	1.44002
$807$	−54.4465	−1.91661
$808$	−17.7403	−0.624102
$809$	−3.60736	−0.126828	−0.0634140	−	0.997987i	$-0.520199\pi$
$809$	−3.60736	−0.126828	−0.0634140	+	0.997987i	$0.520199\pi$
$810$	−28.1715	−0.989847
$811$	−0.909532	−0.0319380	−0.0159690	−	0.999872i	$-0.505083\pi$
$811$	−0.909532	−0.0319380	−0.0159690	+	0.999872i	$0.505083\pi$
$812$	1.81782	0.0637931
$813$	50.2968	1.76399
$814$	9.49414	0.332769
$815$	26.1977	0.917664
$816$	9.19957	0.322049
$817$	−4.70651	−0.164660
$818$	−11.0077	−0.384877
$819$	−96.6846	−3.37843
$820$	−53.2923	−1.86105
$821$	50.4550	1.76089	0.880446	−	0.474147i	$-0.157243\pi$
$821$	50.4550	1.76089	0.880446	+	0.474147i	$0.157243\pi$
$822$	−38.0847	−1.32836
$823$	1.46113	0.0509318	0.0254659	−	0.999676i	$-0.491893\pi$
$823$	1.46113	0.0509318	0.0254659	+	0.999676i	$0.491893\pi$
$824$	31.6726	1.10337
$825$	5.89982	0.205405
$826$	15.3008	0.532382
$827$	−18.9354	−0.658448	−0.329224	−	0.944252i	$-0.606787\pi$
$827$	−18.9354	−0.658448	−0.329224	+	0.944252i	$0.606787\pi$
$828$	64.3583	2.23661
$829$	45.9865	1.59718	0.798589	−	0.601877i	$-0.205580\pi$
$829$	45.9865	1.59718	0.798589	+	0.601877i	$0.205580\pi$
$830$	−10.8338	−0.376047
$831$	6.26769	0.217424
$832$	41.4861	1.43827
$833$	−8.32754	−0.288532
$834$	−37.3755	−1.29421
$835$	0.378271	0.0130906
$836$	−18.1113	−0.626394
$837$	−31.8143	−1.09966
$838$	74.2967	2.56654
$839$	−38.1174	−1.31596	−0.657980	−	0.753035i	$-0.728589\pi$
$839$	−38.1174	−1.31596	−0.657980	+	0.753035i	$0.728589\pi$
$840$	89.6577	3.09348
$841$	−28.9854	−0.999498
$842$	−35.6403	−1.22825
$843$	−1.80842	−0.0622854
$844$	50.5285	1.73926
$845$	9.56001	0.328874
$846$	9.59936	0.330033
$847$	3.91504	0.134522
$848$	18.7323	0.643271
$849$	−61.1409	−2.09835
$850$	−4.82627	−0.165540
$851$	−11.4405	−0.392177
$852$	112.117	3.84107
$853$	−5.71128	−0.195550	−0.0977752	−	0.995209i	$-0.531173\pi$
$853$	−5.71128	−0.195550	−0.0977752	+	0.995209i	$0.531173\pi$
$854$	−112.136	−3.83721
$855$	−46.8189	−1.60117
$856$	−80.5488	−2.75310
$857$	39.2816	1.34183	0.670916	−	0.741533i	$-0.265901\pi$
$857$	39.2816	1.34183	0.670916	+	0.741533i	$0.265901\pi$
$858$	−30.7619	−1.05020
$859$	−54.6872	−1.86590	−0.932952	−	0.360001i	$-0.882776\pi$
$859$	−54.6872	−1.86590	−0.932952	+	0.360001i	$0.882776\pi$
$860$	6.66993	0.227443
$861$	92.4733	3.15148
$862$	62.5253	2.12962
$863$	23.3557	0.795039	0.397519	−	0.917594i	$-0.369871\pi$
$863$	23.3557	0.795039	0.397519	+	0.917594i	$0.369871\pi$
$864$	−11.4432	−0.389306
$865$	8.32494	0.283057
$866$	69.2113	2.35189
$867$	−2.95622	−0.100398
$868$	59.1899	2.00904
$869$	−4.80268	−0.162920
$870$	1.49513	0.0506896
$871$	−37.0569	−1.25562
$872$	21.6106	0.731828
$873$	56.6662	1.91786
$874$	33.1672	1.12190
$875$	−47.4721	−1.60485
$876$	−157.908	−5.33522
$877$	−24.3245	−0.821381	−0.410691	−	0.911775i	$-0.634712\pi$
$877$	−24.3245	−0.821381	−0.410691	+	0.911775i	$0.634712\pi$
$878$	−50.7751	−1.71358
$879$	49.1918	1.65920
$880$	5.39387	0.181827
$881$	50.1474	1.68951	0.844754	−	0.535155i	$-0.179747\pi$
$881$	50.1474	1.68951	0.844754	+	0.535155i	$0.179747\pi$
$882$	−115.579	−3.89174
$883$	−33.6266	−1.13163	−0.565813	−	0.824534i	$-0.691438\pi$
$883$	−33.6266	−1.13163	−0.565813	+	0.824534i	$0.691438\pi$
$884$	16.5585	0.556921
$885$	8.28082	0.278357
$886$	65.5631	2.20263
$887$	−25.1075	−0.843027	−0.421513	−	0.906822i	$-0.638501\pi$
$887$	−25.1075	−0.843027	−0.421513	+	0.906822i	$0.638501\pi$
$888$	−51.8715	−1.74069
$889$	−59.3210	−1.98956
$890$	74.9508	2.51236
$891$	6.72097	0.225161
$892$	28.6988	0.960908
$893$	3.25521	0.108932
$894$	46.0062	1.53868
$895$	5.23938	0.175133
$896$	80.2158	2.67982
$897$	37.0685	1.23768
$898$	−7.36706	−0.245842
$899$	0.474049	0.0158104
$900$	−44.0764	−1.46921
$901$	−6.01950	−0.200539
$902$	19.3220	0.643353
$903$	−11.5737	−0.385149
$904$	82.8829	2.75664
$905$	−12.5613	−0.417553
$906$	−108.474	−3.60380
$907$	39.2824	1.30435	0.652176	−	0.758068i	$-0.273856\pi$
$907$	39.2824	1.30435	0.652176	+	0.758068i	$0.273856\pi$
$908$	−65.4956	−2.17355
$909$	22.7808	0.755590
$910$	70.6127	2.34079
$911$	−2.55695	−0.0847154	−0.0423577	−	0.999103i	$-0.513487\pi$
$911$	−2.55695	−0.0847154	−0.0423577	+	0.999103i	$0.513487\pi$
$912$	43.2979	1.43374
$913$	2.58465	0.0855396
$914$	9.18708	0.303882
$915$	−60.6883	−2.00629
$916$	2.18670	0.0722508
$917$	43.8968	1.44960
$918$	−19.5827	−0.646325
$919$	−50.1492	−1.65427	−0.827135	−	0.562003i	$-0.810031\pi$
$919$	−50.1492	−1.65427	−0.827135	+	0.562003i	$0.810031\pi$
$920$	−22.5743	−0.744254
$921$	−6.49064	−0.213874
$922$	0.473281	0.0155867
$923$	42.4084	1.39589
$924$	−44.5373	−1.46517
$925$	7.83518	0.257619
$926$	−32.5877	−1.07090
$927$	−40.6716	−1.33583
$928$	0.170510	0.00559725
$929$	13.3469	0.437897	0.218949	−	0.975736i	$-0.429737\pi$
$929$	13.3469	0.437897	0.218949	+	0.975736i	$0.429737\pi$
$930$	48.6827	1.59637
$931$	−39.1936	−1.28452
$932$	52.1196	1.70723
$933$	69.5774	2.27786
$934$	−33.9896	−1.11217
$935$	−1.73328	−0.0566844
$936$	110.374	3.60769
$937$	15.2077	0.496814	0.248407	−	0.968656i	$-0.420093\pi$
$937$	15.2077	0.496814	0.248407	+	0.968656i	$0.420093\pi$
$938$	−81.5353	−2.66222
$939$	−64.0688	−2.09081
$940$	−4.61319	−0.150466
$941$	−30.2302	−0.985476	−0.492738	−	0.870178i	$-0.664004\pi$
$941$	−30.2302	−0.985476	−0.492738	+	0.870178i	$0.664004\pi$
$942$	−112.206	−3.65588
$943$	−23.2833	−0.758208
$944$	−5.02920	−0.163687
$945$	−54.9501	−1.78753
$946$	−2.41829	−0.0786255
$947$	31.5618	1.02562	0.512810	−	0.858502i	$-0.328604\pi$
$947$	31.5618	1.02562	0.512810	+	0.858502i	$0.328604\pi$
$948$	54.6351	1.77447
$949$	−59.7290	−1.93889
$950$	−22.7149	−0.736968
$951$	82.5143	2.67571
$952$	17.4977	0.567105
$953$	−17.1145	−0.554394	−0.277197	−	0.960813i	$-0.589406\pi$
$953$	−17.1145	−0.554394	−0.277197	+	0.960813i	$0.589406\pi$
$954$	−83.5454	−2.70488
$955$	−12.2875	−0.397615
$956$	−76.0398	−2.45930
$957$	−0.356698	−0.0115304
$958$	71.0531	2.29562
$959$	−20.8565	−0.673491
$960$	49.4014	1.59442
$961$	−15.5646	−0.502082
$962$	−40.8530	−1.31715
$963$	103.435	3.33313
$964$	50.8059	1.63635
$965$	29.4753	0.948844
$966$	81.5609	2.62418
$967$	−31.9161	−1.02635	−0.513177	−	0.858283i	$-0.671532\pi$
$967$	−31.9161	−1.02635	−0.513177	+	0.858283i	$0.671532\pi$
$968$	−4.46936	−0.143651
$969$	−13.9135	−0.446965
$970$	−41.3857	−1.32881
$971$	23.8477	0.765310	0.382655	−	0.923891i	$-0.375010\pi$
$971$	23.8477	0.765310	0.382655	+	0.923891i	$0.375010\pi$
$972$	17.0262	0.546116
$973$	−20.4681	−0.656177
$974$	27.6294	0.885302
$975$	−25.3867	−0.813026
$976$	36.8579	1.17979
$977$	−10.2877	−0.329132	−0.164566	−	0.986366i	$-0.552622\pi$
$977$	−10.2877	−0.329132	−0.164566	+	0.986366i	$0.552622\pi$
$978$	108.053	3.45517
$979$	−17.8813	−0.571487
$980$	55.5440	1.77429
$981$	−27.7507	−0.886013
$982$	−55.2316	−1.76251
$983$	4.29011	0.136833	0.0684166	−	0.997657i	$-0.478205\pi$
$983$	4.29011	0.136833	0.0684166	+	0.997657i	$0.478205\pi$
$984$	−105.566	−3.36533
$985$	−14.0262	−0.446912
$986$	0.291792	0.00929254
$987$	8.00484	0.254797
$988$	77.9326	2.47937
$989$	2.91407	0.0926621
$990$	−24.0564	−0.764564
$991$	23.4222	0.744030	0.372015	−	0.928227i	$-0.378667\pi$
$991$	23.4222	0.744030	0.372015	+	0.928227i	$0.378667\pi$
$992$	5.55193	0.176274
$993$	47.1163	1.49519
$994$	93.3101	2.95962
$995$	15.0999	0.478698
$996$	−29.4029	−0.931667
$997$	−18.7434	−0.593609	−0.296805	−	0.954938i	$-0.595921\pi$
$997$	−18.7434	−0.593609	−0.296805	+	0.954938i	$0.595921\pi$
$998$	−23.0484	−0.729583
$999$	31.7914	1.00583

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	8041.2.a.d.1.5	✓	62

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
8041.2.a.d.1.5	✓	62	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:	\( N \)	\(=\)	\( 8041 = 11 \cdot 17 \cdot 43 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	8041.a (trivial)

\(f(q)\)	\(=\)	\(q-2.41829 q^{2} -2.95622 q^{3} +3.84815 q^{4} +1.73328 q^{5} +7.14900 q^{6} +3.91504 q^{7} -4.46936 q^{8} +5.73922 q^{9} +O(q^{10})\)	\(q-2.41829 q^{2} -2.95622 q^{3} +3.84815 q^{4} +1.73328 q^{5} +7.14900 q^{6} +3.91504 q^{7} -4.46936 q^{8} +5.73922 q^{9} -4.19159 q^{10} +1.00000 q^{11} -11.3760 q^{12} -4.30297 q^{13} -9.46772 q^{14} -5.12396 q^{15} +3.11194 q^{16} -1.00000 q^{17} -13.8791 q^{18} -4.70651 q^{19} +6.66993 q^{20} -11.5737 q^{21} -2.41829 q^{22} +2.91407 q^{23} +13.2124 q^{24} -1.99573 q^{25} +10.4058 q^{26} -8.09772 q^{27} +15.0656 q^{28} +0.120660 q^{29} +12.3912 q^{30} +3.92880 q^{31} +1.41314 q^{32} -2.95622 q^{33} +2.41829 q^{34} +6.78587 q^{35} +22.0854 q^{36} -3.92597 q^{37} +11.3817 q^{38} +12.7205 q^{39} -7.74667 q^{40} -7.98994 q^{41} +27.9886 q^{42} +1.00000 q^{43} +3.84815 q^{44} +9.94769 q^{45} -7.04708 q^{46} -0.691641 q^{47} -9.19957 q^{48} +8.32754 q^{49} +4.82627 q^{50} +2.95622 q^{51} -16.5585 q^{52} +6.01950 q^{53} +19.5827 q^{54} +1.73328 q^{55} -17.4977 q^{56} +13.9135 q^{57} -0.291792 q^{58} -1.61610 q^{59} -19.7177 q^{60} +11.8440 q^{61} -9.50099 q^{62} +22.4693 q^{63} -9.64126 q^{64} -7.45826 q^{65} +7.14900 q^{66} +8.61193 q^{67} -3.84815 q^{68} -8.61463 q^{69} -16.4102 q^{70} -9.85561 q^{71} -25.6506 q^{72} +13.8809 q^{73} +9.49414 q^{74} +5.89982 q^{75} -18.1113 q^{76} +3.91504 q^{77} -30.7619 q^{78} -4.80268 q^{79} +5.39387 q^{80} +6.72097 q^{81} +19.3220 q^{82} +2.58465 q^{83} -44.5373 q^{84} -1.73328 q^{85} -2.41829 q^{86} -0.356698 q^{87} -4.46936 q^{88} -17.8813 q^{89} -24.0564 q^{90} -16.8463 q^{91} +11.2138 q^{92} -11.6144 q^{93} +1.67259 q^{94} -8.15771 q^{95} -4.17754 q^{96} +9.87351 q^{97} -20.1384 q^{98} +5.73922 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 62 q - 7 q^{2} - 8 q^{3} + 49 q^{4} - 13 q^{5} - 2 q^{6} - 11 q^{7} - 9 q^{8} + 40 q^{9}+O(q^{10}) \) 62 * q - 7 * q^2 - 8 * q^3 + 49 * q^4 - 13 * q^5 - 2 * q^6 - 11 * q^7 - 9 * q^8 + 40 * q^9	\( 62 q - 7 q^{2} - 8 q^{3} + 49 q^{4} - 13 q^{5} - 2 q^{6} - 11 q^{7} - 9 q^{8} + 40 q^{9} - 7 q^{10} + 62 q^{11} - 17 q^{12} - 31 q^{14} - 20 q^{15} + 27 q^{16} - 62 q^{17} + 3 q^{18} - 29 q^{20} - 18 q^{21} - 7 q^{22} - 50 q^{23} - 31 q^{24} + 35 q^{25} - 32 q^{26} - 14 q^{27} - 13 q^{28} - 26 q^{29} - 10 q^{30} - 58 q^{31} - 5 q^{32} - 8 q^{33} + 7 q^{34} - 32 q^{35} - 29 q^{36} - 41 q^{37} - 10 q^{38} - 53 q^{39} - 31 q^{40} - 55 q^{41} - 7 q^{42} + 62 q^{43} + 49 q^{44} - 34 q^{45} - 39 q^{46} - 31 q^{47} - 30 q^{48} + 35 q^{49} - 40 q^{50} + 8 q^{51} + 13 q^{52} - 74 q^{53} + 48 q^{54} - 13 q^{55} - 75 q^{56} - 43 q^{57} - 46 q^{58} - 65 q^{59} - 8 q^{60} - 14 q^{61} - 29 q^{62} - 23 q^{63} - 15 q^{64} - 9 q^{65} - 2 q^{66} - q^{67} - 49 q^{68} - 59 q^{69} - 31 q^{70} - 141 q^{71} + 9 q^{72} - 4 q^{73} - 94 q^{74} - 43 q^{75} + 34 q^{76} - 11 q^{77} - 11 q^{78} - 63 q^{79} - 41 q^{80} - 30 q^{81} + 38 q^{82} - 44 q^{83} - 16 q^{84} + 13 q^{85} - 7 q^{86} - 8 q^{87} - 9 q^{88} - 58 q^{89} - 55 q^{90} - 78 q^{91} - 104 q^{92} - 5 q^{94} - 99 q^{95} - 148 q^{96} - 26 q^{97} + 16 q^{98} + 40 q^{99}+O(q^{100}) \) 62 * q - 7 * q^2 - 8 * q^3 + 49 * q^4 - 13 * q^5 - 2 * q^6 - 11 * q^7 - 9 * q^8 + 40 * q^9 - 7 * q^10 + 62 * q^11 - 17 * q^12 - 31 * q^14 - 20 * q^15 + 27 * q^16 - 62 * q^17 + 3 * q^18 - 29 * q^20 - 18 * q^21 - 7 * q^22 - 50 * q^23 - 31 * q^24 + 35 * q^25 - 32 * q^26 - 14 * q^27 - 13 * q^28 - 26 * q^29 - 10 * q^30 - 58 * q^31 - 5 * q^32 - 8 * q^33 + 7 * q^34 - 32 * q^35 - 29 * q^36 - 41 * q^37 - 10 * q^38 - 53 * q^39 - 31 * q^40 - 55 * q^41 - 7 * q^42 + 62 * q^43 + 49 * q^44 - 34 * q^45 - 39 * q^46 - 31 * q^47 - 30 * q^48 + 35 * q^49 - 40 * q^50 + 8 * q^51 + 13 * q^52 - 74 * q^53 + 48 * q^54 - 13 * q^55 - 75 * q^56 - 43 * q^57 - 46 * q^58 - 65 * q^59 - 8 * q^60 - 14 * q^61 - 29 * q^62 - 23 * q^63 - 15 * q^64 - 9 * q^65 - 2 * q^66 - q^67 - 49 * q^68 - 59 * q^69 - 31 * q^70 - 141 * q^71 + 9 * q^72 - 4 * q^73 - 94 * q^74 - 43 * q^75 + 34 * q^76 - 11 * q^77 - 11 * q^78 - 63 * q^79 - 41 * q^80 - 30 * q^81 + 38 * q^82 - 44 * q^83 - 16 * q^84 + 13 * q^85 - 7 * q^86 - 8 * q^87 - 9 * q^88 - 58 * q^89 - 55 * q^90 - 78 * q^91 - 104 * q^92 - 5 * q^94 - 99 * q^95 - 148 * q^96 - 26 * q^97 + 16 * q^98 + 40 * q^99

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