LMFDB - Embedded newform 6026.2.a.h.1.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [6026,2,Mod(1,6026)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(6026, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("6026.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 6026 = 2 \cdot 23 \cdot 131 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	6026.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:	$48.1178522580$
Analytic rank:	$1$
Dimension:	$24$
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.3
Character	$\chi$	$=$	6026.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.00000 q^{2} -2.99000 q^{3} +1.00000 q^{4} -3.60098 q^{5} +2.99000 q^{6} +0.0770196 q^{7} -1.00000 q^{8} +5.94012 q^{9} +O(q^{10})$	\(q-1.00000 q^{2} -2.99000 q^{3} +1.00000 q^{4} -3.60098 q^{5} +2.99000 q^{6} +0.0770196 q^{7} -1.00000 q^{8} +5.94012 q^{9} +3.60098 q^{10} -3.44726 q^{11} -2.99000 q^{12} -1.64024 q^{13} -0.0770196 q^{14} +10.7669 q^{15} +1.00000 q^{16} +1.47240 q^{17} -5.94012 q^{18} -4.21923 q^{19} -3.60098 q^{20} -0.230289 q^{21} +3.44726 q^{22} -1.00000 q^{23} +2.99000 q^{24} +7.96704 q^{25} +1.64024 q^{26} -8.79097 q^{27} +0.0770196 q^{28} +1.09731 q^{29} -10.7669 q^{30} -7.91422 q^{31} -1.00000 q^{32} +10.3073 q^{33} -1.47240 q^{34} -0.277346 q^{35} +5.94012 q^{36} -5.70246 q^{37} +4.21923 q^{38} +4.90432 q^{39} +3.60098 q^{40} +4.71846 q^{41} +0.230289 q^{42} -7.51355 q^{43} -3.44726 q^{44} -21.3902 q^{45} +1.00000 q^{46} +12.4554 q^{47} -2.99000 q^{48} -6.99407 q^{49} -7.96704 q^{50} -4.40248 q^{51} -1.64024 q^{52} +3.15448 q^{53} +8.79097 q^{54} +12.4135 q^{55} -0.0770196 q^{56} +12.6155 q^{57} -1.09731 q^{58} +6.93982 q^{59} +10.7669 q^{60} +1.16148 q^{61} +7.91422 q^{62} +0.457506 q^{63} +1.00000 q^{64} +5.90646 q^{65} -10.3073 q^{66} -7.07056 q^{67} +1.47240 q^{68} +2.99000 q^{69} +0.277346 q^{70} -11.7341 q^{71} -5.94012 q^{72} +11.7419 q^{73} +5.70246 q^{74} -23.8215 q^{75} -4.21923 q^{76} -0.265506 q^{77} -4.90432 q^{78} +9.37314 q^{79} -3.60098 q^{80} +8.46468 q^{81} -4.71846 q^{82} -1.82659 q^{83} -0.230289 q^{84} -5.30207 q^{85} +7.51355 q^{86} -3.28097 q^{87} +3.44726 q^{88} -5.14553 q^{89} +21.3902 q^{90} -0.126330 q^{91} -1.00000 q^{92} +23.6635 q^{93} -12.4554 q^{94} +15.1933 q^{95} +2.99000 q^{96} +9.78642 q^{97} +6.99407 q^{98} -20.4771 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 24 q - 24 q^{2} - q^{3} + 24 q^{4} - q^{5} + q^{6} - 7 q^{7} - 24 q^{8} + 27 q^{9}+O(q^{10}) $ 24 * q - 24 * q^2 - q^3 + 24 * q^4 - q^5 + q^6 - 7 * q^7 - 24 * q^8 + 27 * q^9	\( 24 q - 24 q^{2} - q^{3} + 24 q^{4} - q^{5} + q^{6} - 7 q^{7} - 24 q^{8} + 27 q^{9} + q^{10} - 4 q^{11} - q^{12} - 5 q^{13} + 7 q^{14} - 6 q^{15} + 24 q^{16} + 5 q^{17} - 27 q^{18} - 20 q^{19} - q^{20} + 4 q^{22} - 24 q^{23} + q^{24} + q^{25} + 5 q^{26} - q^{27} - 7 q^{28} - 6 q^{29} + 6 q^{30} - 23 q^{31} - 24 q^{32} - 6 q^{33} - 5 q^{34} + 5 q^{35} + 27 q^{36} - 6 q^{37} + 20 q^{38} - 39 q^{39} + q^{40} - q^{41} - 44 q^{43} - 4 q^{44} - 13 q^{45} + 24 q^{46} + 32 q^{47} - q^{48} - 13 q^{49} - q^{50} - 44 q^{51} - 5 q^{52} + 21 q^{53} + q^{54} - 13 q^{55} + 7 q^{56} + 10 q^{57} + 6 q^{58} - 24 q^{59} - 6 q^{60} - 40 q^{61} + 23 q^{62} - 54 q^{63} + 24 q^{64} - 29 q^{65} + 6 q^{66} - 17 q^{67} + 5 q^{68} + q^{69} - 5 q^{70} + 4 q^{71} - 27 q^{72} - 16 q^{73} + 6 q^{74} - 36 q^{75} - 20 q^{76} + 24 q^{77} + 39 q^{78} - 53 q^{79} - q^{80} + 24 q^{81} + q^{82} - 9 q^{83} - 37 q^{85} + 44 q^{86} + 7 q^{87} + 4 q^{88} - 46 q^{89} + 13 q^{90} - 44 q^{91} - 24 q^{92} + 23 q^{93} - 32 q^{94} + 28 q^{95} + q^{96} - 20 q^{97} + 13 q^{98} - 78 q^{99}+O(q^{100}) \) 24 * q - 24 * q^2 - q^3 + 24 * q^4 - q^5 + q^6 - 7 * q^7 - 24 * q^8 + 27 * q^9 + q^10 - 4 * q^11 - q^12 - 5 * q^13 + 7 * q^14 - 6 * q^15 + 24 * q^16 + 5 * q^17 - 27 * q^18 - 20 * q^19 - q^20 + 4 * q^22 - 24 * q^23 + q^24 + q^25 + 5 * q^26 - q^27 - 7 * q^28 - 6 * q^29 + 6 * q^30 - 23 * q^31 - 24 * q^32 - 6 * q^33 - 5 * q^34 + 5 * q^35 + 27 * q^36 - 6 * q^37 + 20 * q^38 - 39 * q^39 + q^40 - q^41 - 44 * q^43 - 4 * q^44 - 13 * q^45 + 24 * q^46 + 32 * q^47 - q^48 - 13 * q^49 - q^50 - 44 * q^51 - 5 * q^52 + 21 * q^53 + q^54 - 13 * q^55 + 7 * q^56 + 10 * q^57 + 6 * q^58 - 24 * q^59 - 6 * q^60 - 40 * q^61 + 23 * q^62 - 54 * q^63 + 24 * q^64 - 29 * q^65 + 6 * q^66 - 17 * q^67 + 5 * q^68 + q^69 - 5 * q^70 + 4 * q^71 - 27 * q^72 - 16 * q^73 + 6 * q^74 - 36 * q^75 - 20 * q^76 + 24 * q^77 + 39 * q^78 - 53 * q^79 - q^80 + 24 * q^81 + q^82 - 9 * q^83 - 37 * q^85 + 44 * q^86 + 7 * q^87 + 4 * q^88 - 46 * q^89 + 13 * q^90 - 44 * q^91 - 24 * q^92 + 23 * q^93 - 32 * q^94 + 28 * q^95 + q^96 - 20 * q^97 + 13 * q^98 - 78 * q^99

Display 100 coefficients 10 coefficients

Coefficient data

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

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

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

$2$	−1.00000	−0.707107
$2$	−1.00000	−0.707107
$3$	−2.99000	−1.72628	−0.863140	−	0.504965i	$-0.831505\pi$
$3$	−2.99000	−1.72628	−0.863140	+	0.504965i	$0.831505\pi$
$4$	1.00000	0.500000
$5$	−3.60098	−1.61041	−0.805203	−	0.592999i	$-0.797944\pi$
$5$	−3.60098	−1.61041	−0.805203	+	0.592999i	$0.797944\pi$
$6$	2.99000	1.22066
$7$	0.0770196	0.0291107	0.0145553	−	0.999894i	$-0.495367\pi$
$7$	0.0770196	0.0291107	0.0145553	+	0.999894i	$0.495367\pi$
$8$	−1.00000	−0.353553
$9$	5.94012	1.98004
$10$	3.60098	1.13873
$11$	−3.44726	−1.03939	−0.519693	−	0.854353i	$-0.673954\pi$
$11$	−3.44726	−1.03939	−0.519693	+	0.854353i	$0.673954\pi$
$12$	−2.99000	−0.863140
$13$	−1.64024	−0.454920	−0.227460	−	0.973787i	$-0.573042\pi$
$13$	−1.64024	−0.454920	−0.227460	+	0.973787i	$0.573042\pi$
$14$	−0.0770196	−0.0205844
$15$	10.7669	2.78001
$16$	1.00000	0.250000
$17$	1.47240	0.357109	0.178554	−	0.983930i	$-0.442858\pi$
$17$	1.47240	0.357109	0.178554	+	0.983930i	$0.442858\pi$
$18$	−5.94012	−1.40010
$19$	−4.21923	−0.967957	−0.483978	−	0.875080i	$-0.660809\pi$
$19$	−4.21923	−0.967957	−0.483978	+	0.875080i	$0.660809\pi$
$20$	−3.60098	−0.805203
$21$	−0.230289	−0.0502531
$22$	3.44726	0.734958
$23$	−1.00000	−0.208514
$23$	−1.00000	−0.208514
$24$	2.99000	0.610332
$25$	7.96704	1.59341
$26$	1.64024	0.321677
$27$	−8.79097	−1.69182
$28$	0.0770196	0.0145553
$29$	1.09731	0.203766	0.101883	−	0.994796i	$-0.467513\pi$
$29$	1.09731	0.203766	0.101883	+	0.994796i	$0.467513\pi$
$30$	−10.7669	−1.96576
$31$	−7.91422	−1.42144	−0.710718	−	0.703477i	$-0.751630\pi$
$31$	−7.91422	−1.42144	−0.710718	+	0.703477i	$0.751630\pi$
$32$	−1.00000	−0.176777
$33$	10.3073	1.79427
$34$	−1.47240	−0.252514
$35$	−0.277346	−0.0468800
$36$	5.94012	0.990020
$37$	−5.70246	−0.937479	−0.468740	−	0.883336i	$-0.655292\pi$
$37$	−5.70246	−0.937479	−0.468740	+	0.883336i	$0.655292\pi$
$38$	4.21923	0.684449
$39$	4.90432	0.785319
$40$	3.60098	0.569364
$41$	4.71846	0.736900	0.368450	−	0.929648i	$-0.379889\pi$
$41$	4.71846	0.736900	0.368450	+	0.929648i	$0.379889\pi$
$42$	0.230289	0.0355343
$43$	−7.51355	−1.14581	−0.572903	−	0.819623i	$-0.694183\pi$
$43$	−7.51355	−1.14581	−0.572903	+	0.819623i	$0.694183\pi$
$44$	−3.44726	−0.519693
$45$	−21.3902	−3.18867
$46$	1.00000	0.147442
$47$	12.4554	1.81680	0.908401	−	0.418099i	$-0.137304\pi$
$47$	12.4554	1.81680	0.908401	+	0.418099i	$0.137304\pi$
$48$	−2.99000	−0.431570
$49$	−6.99407	−0.999153
$50$	−7.96704	−1.12671
$51$	−4.40248	−0.616470
$52$	−1.64024	−0.227460
$53$	3.15448	0.433301	0.216650	−	0.976249i	$-0.430487\pi$
$53$	3.15448	0.433301	0.216650	+	0.976249i	$0.430487\pi$
$54$	8.79097	1.19630
$55$	12.4135	1.67383
$56$	−0.0770196	−0.0102922
$57$	12.6155	1.67096
$58$	−1.09731	−0.144084
$59$	6.93982	0.903488	0.451744	−	0.892148i	$-0.350802\pi$
$59$	6.93982	0.903488	0.451744	+	0.892148i	$0.350802\pi$
$60$	10.7669	1.39001
$61$	1.16148	0.148712	0.0743562	−	0.997232i	$-0.476310\pi$
$61$	1.16148	0.148712	0.0743562	+	0.997232i	$0.476310\pi$
$62$	7.91422	1.00511
$63$	0.457506	0.0576403
$64$	1.00000	0.125000
$65$	5.90646	0.732606
$66$	−10.3073	−1.26874
$67$	−7.07056	−0.863807	−0.431903	−	0.901920i	$-0.642158\pi$
$67$	−7.07056	−0.863807	−0.431903	+	0.901920i	$0.642158\pi$
$68$	1.47240	0.178554
$69$	2.99000	0.359954
$70$	0.277346	0.0331492
$71$	−11.7341	−1.39258	−0.696288	−	0.717762i	$-0.745166\pi$
$71$	−11.7341	−1.39258	−0.696288	+	0.717762i	$0.745166\pi$
$72$	−5.94012	−0.700050
$73$	11.7419	1.37428	0.687142	−	0.726523i	$-0.258865\pi$
$73$	11.7419	1.37428	0.687142	+	0.726523i	$0.258865\pi$
$74$	5.70246	0.662898
$75$	−23.8215	−2.75067
$76$	−4.21923	−0.483978
$77$	−0.265506	−0.0302573
$78$	−4.90432	−0.555304
$79$	9.37314	1.05456	0.527280	−	0.849691i	$-0.323212\pi$
$79$	9.37314	1.05456	0.527280	+	0.849691i	$0.323212\pi$
$80$	−3.60098	−0.402601
$81$	8.46468	0.940520
$82$	−4.71846	−0.521067
$83$	−1.82659	−0.200494	−0.100247	−	0.994963i	$-0.531963\pi$
$83$	−1.82659	−0.200494	−0.100247	+	0.994963i	$0.531963\pi$
$84$	−0.230289	−0.0251266
$85$	−5.30207	−0.575090
$86$	7.51355	0.810207
$87$	−3.28097	−0.351757
$88$	3.44726	0.367479
$89$	−5.14553	−0.545425	−0.272712	−	0.962096i	$-0.587921\pi$
$89$	−5.14553	−0.545425	−0.272712	+	0.962096i	$0.587921\pi$
$90$	21.3902	2.25473
$91$	−0.126330	−0.0132430
$92$	−1.00000	−0.104257
$93$	23.6635	2.45379
$94$	−12.4554	−1.28467
$95$	15.1933	1.55880
$96$	2.99000	0.305166
$97$	9.78642	0.993660	0.496830	−	0.867848i	$-0.334497\pi$
$97$	9.78642	0.993660	0.496830	+	0.867848i	$0.334497\pi$
$98$	6.99407	0.706508
$99$	−20.4771	−2.05803
$100$	7.96704	0.796704
$101$	16.9790	1.68947	0.844734	−	0.535186i	$-0.179758\pi$
$101$	16.9790	1.68947	0.844734	+	0.535186i	$0.179758\pi$
$102$	4.40248	0.435910
$103$	4.64990	0.458169	0.229084	−	0.973407i	$-0.426427\pi$
$103$	4.64990	0.458169	0.229084	+	0.973407i	$0.426427\pi$
$104$	1.64024	0.160838
$105$	0.829265	0.0809280
$106$	−3.15448	−0.306390
$107$	3.22063	0.311350	0.155675	−	0.987808i	$-0.450245\pi$
$107$	3.22063	0.311350	0.155675	+	0.987808i	$0.450245\pi$
$108$	−8.79097	−0.845912
$109$	13.7492	1.31693	0.658465	−	0.752611i	$-0.271206\pi$
$109$	13.7492	1.31693	0.658465	+	0.752611i	$0.271206\pi$
$110$	−12.4135	−1.18358
$111$	17.0504	1.61835
$112$	0.0770196	0.00727767
$113$	12.9767	1.22074	0.610371	−	0.792116i	$-0.291020\pi$
$113$	12.9767	1.22074	0.610371	+	0.792116i	$0.291020\pi$
$114$	−12.6155	−1.18155
$115$	3.60098	0.335793
$116$	1.09731	0.101883
$117$	−9.74321	−0.900760
$118$	−6.93982	−0.638862
$119$	0.113403	0.0103957
$120$	−10.7669	−0.982882
$121$	0.883578	0.0803253
$122$	−1.16148	−0.105155
$123$	−14.1082	−1.27209
$124$	−7.91422	−0.710718
$125$	−10.6842	−0.955626
$126$	−0.457506	−0.0407578
$127$	−9.74780	−0.864977	−0.432489	−	0.901639i	$-0.642364\pi$
$127$	−9.74780	−0.864977	−0.432489	+	0.901639i	$0.642364\pi$
$128$	−1.00000	−0.0883883
$129$	22.4656	1.97798
$130$	−5.90646	−0.518031
$131$	−1.00000	−0.0873704
$131$	−1.00000	−0.0873704
$132$	10.3073	0.897136
$133$	−0.324963	−0.0281779
$134$	7.07056	0.610804
$135$	31.6561	2.72452
$136$	−1.47240	−0.126257
$137$	−1.83693	−0.156939	−0.0784696	−	0.996917i	$-0.525003\pi$
$137$	−1.83693	−0.156939	−0.0784696	+	0.996917i	$0.525003\pi$
$138$	−2.99000	−0.254526
$139$	13.1562	1.11590	0.557948	−	0.829876i	$-0.311589\pi$
$139$	13.1562	1.11590	0.557948	+	0.829876i	$0.311589\pi$
$140$	−0.277346	−0.0234400
$141$	−37.2416	−3.13631
$142$	11.7341	0.984700
$143$	5.65432	0.472838
$144$	5.94012	0.495010
$145$	−3.95140	−0.328146
$146$	−11.7419	−0.971766
$147$	20.9123	1.72482
$148$	−5.70246	−0.468740
$149$	−9.49063	−0.777503	−0.388751	−	0.921343i	$-0.627094\pi$
$149$	−9.49063	−0.777503	−0.388751	+	0.921343i	$0.627094\pi$
$150$	23.8215	1.94501
$151$	9.18991	0.747864	0.373932	−	0.927456i	$-0.378009\pi$
$151$	9.18991	0.747864	0.373932	+	0.927456i	$0.378009\pi$
$152$	4.21923	0.342224
$153$	8.74622	0.707090
$154$	0.265506	0.0213951
$155$	28.4989	2.28909
$156$	4.90432	0.392659
$157$	−4.04858	−0.323112	−0.161556	−	0.986864i	$-0.551651\pi$
$157$	−4.04858	−0.323112	−0.161556	+	0.986864i	$0.551651\pi$
$158$	−9.37314	−0.745687
$159$	−9.43190	−0.747998
$160$	3.60098	0.284682
$161$	−0.0770196	−0.00606999
$162$	−8.46468	−0.665048
$163$	10.8577	0.850439	0.425219	−	0.905090i	$-0.360197\pi$
$163$	10.8577	0.850439	0.425219	+	0.905090i	$0.360197\pi$
$164$	4.71846	0.368450
$165$	−37.1164	−2.88951
$166$	1.82659	0.141771
$167$	8.96759	0.693933	0.346966	−	0.937878i	$-0.387212\pi$
$167$	8.96759	0.693933	0.346966	+	0.937878i	$0.387212\pi$
$168$	0.230289	0.0177672
$169$	−10.3096	−0.793048
$170$	5.30207	0.406650
$171$	−25.0627	−1.91659
$172$	−7.51355	−0.572903
$173$	1.81878	0.138279	0.0691395	−	0.997607i	$-0.477975\pi$
$173$	1.81878	0.138279	0.0691395	+	0.997607i	$0.477975\pi$
$174$	3.28097	0.248730
$175$	0.613618	0.0463851
$176$	−3.44726	−0.259847
$177$	−20.7501	−1.55967
$178$	5.14553	0.385674
$179$	8.29213	0.619783	0.309892	−	0.950772i	$-0.399707\pi$
$179$	8.29213	0.619783	0.309892	+	0.950772i	$0.399707\pi$
$180$	−21.3902	−1.59433
$181$	0.918978	0.0683071	0.0341536	−	0.999417i	$-0.489126\pi$
$181$	0.918978	0.0683071	0.0341536	+	0.999417i	$0.489126\pi$
$182$	0.126330	0.00936423
$183$	−3.47283	−0.256719
$184$	1.00000	0.0737210
$185$	20.5344	1.50972
$186$	−23.6635	−1.73509
$187$	−5.07573	−0.371174
$188$	12.4554	0.908401
$189$	−0.677077	−0.0492501
$190$	−15.1933	−1.10224
$191$	0.947662	0.0685704	0.0342852	−	0.999412i	$-0.489085\pi$
$191$	0.947662	0.0685704	0.0342852	+	0.999412i	$0.489085\pi$
$192$	−2.99000	−0.215785
$193$	8.03115	0.578095	0.289047	−	0.957315i	$-0.406661\pi$
$193$	8.03115	0.578095	0.289047	+	0.957315i	$0.406661\pi$
$194$	−9.78642	−0.702624
$195$	−17.6603	−1.26468
$196$	−6.99407	−0.499576
$197$	19.3318	1.37733	0.688666	−	0.725079i	$-0.258197\pi$
$197$	19.3318	1.37733	0.688666	+	0.725079i	$0.258197\pi$
$198$	20.4771	1.45525
$199$	−8.17427	−0.579459	−0.289729	−	0.957109i	$-0.593565\pi$
$199$	−8.17427	−0.579459	−0.289729	+	0.957109i	$0.593565\pi$
$200$	−7.96704	−0.563355
$201$	21.1410	1.49117
$202$	−16.9790	−1.19463
$203$	0.0845147	0.00593177
$204$	−4.40248	−0.308235
$205$	−16.9911	−1.18671
$206$	−4.64990	−0.323974
$207$	−5.94012	−0.412867
$208$	−1.64024	−0.113730
$209$	14.5448	1.00608
$210$	−0.829265	−0.0572247
$211$	1.06067	0.0730193	0.0365096	−	0.999333i	$-0.488376\pi$
$211$	1.06067	0.0730193	0.0365096	+	0.999333i	$0.488376\pi$
$212$	3.15448	0.216650
$213$	35.0849	2.40398
$214$	−3.22063	−0.220158
$215$	27.0561	1.84521
$216$	8.79097	0.598150
$217$	−0.609550	−0.0413789
$218$	−13.7492	−0.931210
$219$	−35.1083	−2.37240
$220$	12.4135	0.836917
$221$	−2.41508	−0.162456
$222$	−17.0504	−1.14435
$223$	0.663109	0.0444051	0.0222025	−	0.999753i	$-0.492932\pi$
$223$	0.663109	0.0444051	0.0222025	+	0.999753i	$0.492932\pi$
$224$	−0.0770196	−0.00514609
$225$	47.3252	3.15501
$226$	−12.9767	−0.863195
$227$	14.0558	0.932915	0.466457	−	0.884544i	$-0.345530\pi$
$227$	14.0558	0.932915	0.466457	+	0.884544i	$0.345530\pi$
$228$	12.6155	0.835482
$229$	−24.7782	−1.63739	−0.818696	−	0.574227i	$-0.805303\pi$
$229$	−24.7782	−1.63739	−0.818696	+	0.574227i	$0.805303\pi$
$230$	−3.60098	−0.237441
$231$	0.793865	0.0522325
$232$	−1.09731	−0.0720422
$233$	30.1574	1.97568	0.987838	−	0.155488i	$-0.0496950\pi$
$233$	30.1574	1.97568	0.987838	+	0.155488i	$0.0496950\pi$
$234$	9.74321	0.636933
$235$	−44.8515	−2.92579
$236$	6.93982	0.451744
$237$	−28.0257	−1.82047
$238$	−0.113403	−0.00735086
$239$	−19.4110	−1.25560	−0.627798	−	0.778376i	$-0.716044\pi$
$239$	−19.4110	−1.25560	−0.627798	+	0.778376i	$0.716044\pi$
$240$	10.7669	0.695003
$241$	−18.3537	−1.18227	−0.591133	−	0.806574i	$-0.701319\pi$
$241$	−18.3537	−1.18227	−0.591133	+	0.806574i	$0.701319\pi$
$242$	−0.883578	−0.0567986
$243$	1.06351	0.0682239
$244$	1.16148	0.0743562
$245$	25.1855	1.60904
$246$	14.1082	0.899507
$247$	6.92053	0.440343
$248$	7.91422	0.502553
$249$	5.46151	0.346109
$250$	10.6842	0.675730
$251$	12.4385	0.785114	0.392557	−	0.919728i	$-0.371591\pi$
$251$	12.4385	0.785114	0.392557	+	0.919728i	$0.371591\pi$
$252$	0.457506	0.0288202
$253$	3.44726	0.216727
$254$	9.74780	0.611631
$255$	15.8532	0.992767
$256$	1.00000	0.0625000
$257$	−2.45137	−0.152913	−0.0764563	−	0.997073i	$-0.524361\pi$
$257$	−2.45137	−0.152913	−0.0764563	+	0.997073i	$0.524361\pi$
$258$	−22.4656	−1.39864
$259$	−0.439201	−0.0272906
$260$	5.90646	0.366303
$261$	6.51818	0.403465
$262$	1.00000	0.0617802
$263$	0.617517	0.0380778	0.0190389	−	0.999819i	$-0.493939\pi$
$263$	0.617517	0.0380778	0.0190389	+	0.999819i	$0.493939\pi$
$264$	−10.3073	−0.634371
$265$	−11.3592	−0.697790
$266$	0.324963	0.0199248
$267$	15.3851	0.941556
$268$	−7.07056	−0.431903
$269$	1.11424	0.0679365	0.0339683	−	0.999423i	$-0.489185\pi$
$269$	1.11424	0.0679365	0.0339683	+	0.999423i	$0.489185\pi$
$270$	−31.6561	−1.92653
$271$	26.6667	1.61989	0.809944	−	0.586507i	$-0.199497\pi$
$271$	26.6667	1.61989	0.809944	+	0.586507i	$0.199497\pi$
$272$	1.47240	0.0892772
$273$	0.377728	0.0228612
$274$	1.83693	0.110973
$275$	−27.4644	−1.65617
$276$	2.99000	0.179977
$277$	−11.1258	−0.668482	−0.334241	−	0.942488i	$-0.608480\pi$
$277$	−11.1258	−0.668482	−0.334241	+	0.942488i	$0.608480\pi$
$278$	−13.1562	−0.789058
$279$	−47.0114	−2.81450
$280$	0.277346	0.0165746
$281$	16.7834	1.00121	0.500606	−	0.865675i	$-0.333111\pi$
$281$	16.7834	1.00121	0.500606	+	0.865675i	$0.333111\pi$
$282$	37.2416	2.21771
$283$	−14.3100	−0.850641	−0.425321	−	0.905043i	$-0.639839\pi$
$283$	−14.3100	−0.850641	−0.425321	+	0.905043i	$0.639839\pi$
$284$	−11.7341	−0.696288
$285$	−45.4281	−2.69093
$286$	−5.65432	−0.334347
$287$	0.363414	0.0214516
$288$	−5.94012	−0.350025
$289$	−14.8320	−0.872473
$290$	3.95140	0.232034
$291$	−29.2614	−1.71534
$292$	11.7419	0.687142
$293$	0.942375	0.0550542	0.0275271	−	0.999621i	$-0.491237\pi$
$293$	0.942375	0.0550542	0.0275271	+	0.999621i	$0.491237\pi$
$294$	−20.9123	−1.21963
$295$	−24.9901	−1.45498
$296$	5.70246	0.331449
$297$	30.3047	1.75846
$298$	9.49063	0.549778
$299$	1.64024	0.0948574
$300$	−23.8215	−1.37533
$301$	−0.578691	−0.0333552
$302$	−9.18991	−0.528820
$303$	−50.7671	−2.91649
$304$	−4.21923	−0.241989
$305$	−4.18246	−0.239487
$306$	−8.74622	−0.499988
$307$	−8.75562	−0.499710	−0.249855	−	0.968283i	$-0.580383\pi$
$307$	−8.75562	−0.499710	−0.249855	+	0.968283i	$0.580383\pi$
$308$	−0.265506	−0.0151286
$309$	−13.9032	−0.790927
$310$	−28.4989	−1.61863
$311$	−9.14464	−0.518545	−0.259272	−	0.965804i	$-0.583483\pi$
$311$	−9.14464	−0.518545	−0.259272	+	0.965804i	$0.583483\pi$
$312$	−4.90432	−0.277652
$313$	−12.0482	−0.681004	−0.340502	−	0.940244i	$-0.610597\pi$
$313$	−12.0482	−0.681004	−0.340502	+	0.940244i	$0.610597\pi$
$314$	4.04858	0.228475
$315$	−1.64747	−0.0928243
$316$	9.37314	0.527280
$317$	−12.7793	−0.717756	−0.358878	−	0.933384i	$-0.616841\pi$
$317$	−12.7793	−0.717756	−0.358878	+	0.933384i	$0.616841\pi$
$318$	9.43190	0.528915
$319$	−3.78272	−0.211792
$320$	−3.60098	−0.201301
$321$	−9.62970	−0.537478
$322$	0.0770196	0.00429213
$323$	−6.21238	−0.345666
$324$	8.46468	0.470260
$325$	−13.0678	−0.724873
$326$	−10.8577	−0.601351
$327$	−41.1100	−2.27339
$328$	−4.71846	−0.260533
$329$	0.959308	0.0528883
$330$	37.1164	2.04319
$331$	−34.6205	−1.90291	−0.951456	−	0.307784i	$-0.900412\pi$
$331$	−34.6205	−1.90291	−0.951456	+	0.307784i	$0.900412\pi$
$332$	−1.82659	−0.100247
$333$	−33.8733	−1.85625
$334$	−8.96759	−0.490685
$335$	25.4609	1.39108
$336$	−0.230289	−0.0125633
$337$	15.6335	0.851614	0.425807	−	0.904814i	$-0.359990\pi$
$337$	15.6335	0.851614	0.425807	+	0.904814i	$0.359990\pi$
$338$	10.3096	0.560770
$339$	−38.8003	−2.10734
$340$	−5.30207	−0.287545
$341$	27.2823	1.47742
$342$	25.0627	1.35524
$343$	−1.07782	−0.0581967
$344$	7.51355	0.405104
$345$	−10.7669	−0.579672
$346$	−1.81878	−0.0977780
$347$	−7.02646	−0.377200	−0.188600	−	0.982054i	$-0.560395\pi$
$347$	−7.02646	−0.377200	−0.188600	+	0.982054i	$0.560395\pi$
$348$	−3.28097	−0.175879
$349$	12.5396	0.671232	0.335616	−	0.941999i	$-0.391056\pi$
$349$	12.5396	0.671232	0.335616	+	0.941999i	$0.391056\pi$
$350$	−0.613618	−0.0327993
$351$	14.4193	0.769644
$352$	3.44726	0.183739
$353$	10.6415	0.566392	0.283196	−	0.959062i	$-0.408605\pi$
$353$	10.6415	0.566392	0.283196	+	0.959062i	$0.408605\pi$
$354$	20.7501	1.10285
$355$	42.2541	2.24261
$356$	−5.14553	−0.272712
$357$	−0.339077	−0.0179459
$358$	−8.29213	−0.438253
$359$	7.40017	0.390566	0.195283	−	0.980747i	$-0.437437\pi$
$359$	7.40017	0.390566	0.195283	+	0.980747i	$0.437437\pi$
$360$	21.3902	1.12736
$361$	−1.19813	−0.0630596
$362$	−0.918978	−0.0483004
$363$	−2.64190	−0.138664
$364$	−0.126330	−0.00662151
$365$	−42.2823	−2.21316
$366$	3.47283	0.181528
$367$	22.4962	1.17429	0.587146	−	0.809481i	$-0.300252\pi$
$367$	22.4962	1.17429	0.587146	+	0.809481i	$0.300252\pi$
$368$	−1.00000	−0.0521286
$369$	28.0282	1.45909
$370$	−20.5344	−1.06753
$371$	0.242957	0.0126137
$372$	23.6635	1.22690
$373$	26.6507	1.37992	0.689960	−	0.723847i	$-0.257628\pi$
$373$	26.6507	1.37992	0.689960	+	0.723847i	$0.257628\pi$
$374$	5.07573	0.262460
$375$	31.9459	1.64968
$376$	−12.4554	−0.642337
$377$	−1.79986	−0.0926973
$378$	0.677077	0.0348251
$379$	−28.1563	−1.44629	−0.723145	−	0.690696i	$-0.757304\pi$
$379$	−28.1563	−1.44629	−0.723145	+	0.690696i	$0.757304\pi$
$380$	15.1933	0.779402
$381$	29.1460	1.49319
$382$	−0.947662	−0.0484866
$383$	−27.0559	−1.38249	−0.691245	−	0.722621i	$-0.742937\pi$
$383$	−27.0559	−1.38249	−0.691245	+	0.722621i	$0.742937\pi$
$384$	2.99000	0.152583
$385$	0.956082	0.0487265
$386$	−8.03115	−0.408775
$387$	−44.6314	−2.26874
$388$	9.78642	0.496830
$389$	19.6655	0.997081	0.498540	−	0.866867i	$-0.333870\pi$
$389$	19.6655	0.997081	0.498540	+	0.866867i	$0.333870\pi$
$390$	17.6603	0.894265
$391$	−1.47240	−0.0744624
$392$	6.99407	0.353254
$393$	2.99000	0.150826
$394$	−19.3318	−0.973920
$395$	−33.7525	−1.69827
$396$	−20.4771	−1.02901
$397$	22.1898	1.11367	0.556836	−	0.830622i	$-0.312015\pi$
$397$	22.1898	1.11367	0.556836	+	0.830622i	$0.312015\pi$
$398$	8.17427	0.409739
$399$	0.971641	0.0486429
$400$	7.96704	0.398352
$401$	−9.10238	−0.454551	−0.227276	−	0.973830i	$-0.572982\pi$
$401$	−9.10238	−0.454551	−0.227276	+	0.973830i	$0.572982\pi$
$402$	−21.1410	−1.05442
$403$	12.9812	0.646639
$404$	16.9790	0.844734
$405$	−30.4811	−1.51462
$406$	−0.0845147	−0.00419439
$407$	19.6579	0.974404
$408$	4.40248	0.217955
$409$	6.54110	0.323437	0.161718	−	0.986837i	$-0.448296\pi$
$409$	6.54110	0.323437	0.161718	+	0.986837i	$0.448296\pi$
$410$	16.9911	0.839129
$411$	5.49242	0.270921
$412$	4.64990	0.229084
$413$	0.534502	0.0263011
$414$	5.94012	0.291941
$415$	6.57751	0.322877
$416$	1.64024	0.0804192
$417$	−39.3371	−1.92635
$418$	−14.5448	−0.711407
$419$	−28.3613	−1.38554	−0.692770	−	0.721158i	$-0.743610\pi$
$419$	−28.3613	−1.38554	−0.692770	+	0.721158i	$0.743610\pi$
$420$	0.829265	0.0404640
$421$	−36.7888	−1.79298	−0.896489	−	0.443066i	$-0.853891\pi$
$421$	−36.7888	−1.79298	−0.896489	+	0.443066i	$0.853891\pi$
$422$	−1.06067	−0.0516324
$423$	73.9864	3.59734
$424$	−3.15448	−0.153195
$425$	11.7306	0.569020
$426$	−35.0849	−1.69987
$427$	0.0894567	0.00432912
$428$	3.22063	0.155675
$429$	−16.9064	−0.816250
$430$	−27.0561	−1.30476
$431$	−14.3946	−0.693363	−0.346681	−	0.937983i	$-0.612691\pi$
$431$	−14.3946	−0.693363	−0.346681	+	0.937983i	$0.612691\pi$
$432$	−8.79097	−0.422956
$433$	−28.1237	−1.35154	−0.675770	−	0.737113i	$-0.736189\pi$
$433$	−28.1237	−1.35154	−0.675770	+	0.737113i	$0.736189\pi$
$434$	0.609550	0.0292593
$435$	11.8147	0.566472
$436$	13.7492	0.658465
$437$	4.21923	0.201833
$438$	35.1083	1.67754
$439$	10.9517	0.522698	0.261349	−	0.965244i	$-0.415833\pi$
$439$	10.9517	0.522698	0.261349	+	0.965244i	$0.415833\pi$
$440$	−12.4135	−0.591790
$441$	−41.5456	−1.97836
$442$	2.41508	0.114874
$443$	−31.2553	−1.48498	−0.742492	−	0.669855i	$-0.766356\pi$
$443$	−31.2553	−1.48498	−0.742492	+	0.669855i	$0.766356\pi$
$444$	17.0504	0.809175
$445$	18.5289	0.878355
$446$	−0.663109	−0.0313991
$447$	28.3770	1.34219
$448$	0.0770196	0.00363883
$449$	−1.86012	−0.0877846	−0.0438923	−	0.999036i	$-0.513976\pi$
$449$	−1.86012	−0.0877846	−0.0438923	+	0.999036i	$0.513976\pi$
$450$	−47.3252	−2.23093
$451$	−16.2657	−0.765924
$452$	12.9767	0.610371
$453$	−27.4779	−1.29102
$454$	−14.0558	−0.659670
$455$	0.454913	0.0213266
$456$	−12.6155	−0.590775
$457$	−23.3474	−1.09214	−0.546072	−	0.837738i	$-0.683878\pi$
$457$	−23.3474	−1.09214	−0.546072	+	0.837738i	$0.683878\pi$
$458$	24.7782	1.15781
$459$	−12.9438	−0.604165
$460$	3.60098	0.167896
$461$	−34.9380	−1.62722	−0.813612	−	0.581408i	$-0.802502\pi$
$461$	−34.9380	−1.62722	−0.813612	+	0.581408i	$0.802502\pi$
$462$	−0.793865	−0.0369339
$463$	−14.4155	−0.669947	−0.334973	−	0.942228i	$-0.608727\pi$
$463$	−14.4155	−0.669947	−0.334973	+	0.942228i	$0.608727\pi$
$464$	1.09731	0.0509415
$465$	−85.2119	−3.95161
$466$	−30.1574	−1.39701
$467$	−4.75470	−0.220021	−0.110011	−	0.993930i	$-0.535088\pi$
$467$	−4.75470	−0.220021	−0.110011	+	0.993930i	$0.535088\pi$
$468$	−9.74321	−0.450380
$469$	−0.544572	−0.0251460
$470$	44.8515	2.06885
$471$	12.1053	0.557782
$472$	−6.93982	−0.319431
$473$	25.9012	1.19094
$474$	28.0257	1.28726
$475$	−33.6147	−1.54235
$476$	0.113403	0.00519784
$477$	18.7380	0.857953
$478$	19.4110	0.887841
$479$	26.2639	1.20003	0.600015	−	0.799989i	$-0.295161\pi$
$479$	26.2639	1.20003	0.600015	+	0.799989i	$0.295161\pi$
$480$	−10.7669	−0.491441
$481$	9.35339	0.426478
$482$	18.3537	0.835988
$483$	0.230289	0.0104785
$484$	0.883578	0.0401627
$485$	−35.2407	−1.60020
$486$	−1.06351	−0.0482416
$487$	5.11045	0.231576	0.115788	−	0.993274i	$-0.463061\pi$
$487$	5.11045	0.231576	0.115788	+	0.993274i	$0.463061\pi$
$488$	−1.16148	−0.0525777
$489$	−32.4645	−1.46809
$490$	−25.1855	−1.13776
$491$	−9.56913	−0.431849	−0.215924	−	0.976410i	$-0.569276\pi$
$491$	−9.56913	−0.431849	−0.215924	+	0.976410i	$0.569276\pi$
$492$	−14.1082	−0.636047
$493$	1.61568	0.0727667
$494$	−6.92053	−0.311369
$495$	73.7376	3.31426
$496$	−7.91422	−0.355359
$497$	−0.903752	−0.0405388
$498$	−5.46151	−0.244736
$499$	−32.1300	−1.43834	−0.719169	−	0.694835i	$-0.755477\pi$
$499$	−32.1300	−1.43834	−0.719169	+	0.694835i	$0.755477\pi$
$500$	−10.6842	−0.477813
$501$	−26.8131	−1.19792
$502$	−12.4385	−0.555160
$503$	−11.6372	−0.518878	−0.259439	−	0.965759i	$-0.583538\pi$
$503$	−11.6372	−0.518878	−0.259439	+	0.965759i	$0.583538\pi$
$504$	−0.457506	−0.0203789
$505$	−61.1408	−2.72073
$506$	−3.44726	−0.153249
$507$	30.8258	1.36902
$508$	−9.74780	−0.432489
$509$	12.6193	0.559339	0.279670	−	0.960096i	$-0.409775\pi$
$509$	12.6193	0.559339	0.279670	+	0.960096i	$0.409775\pi$
$510$	−15.8532	−0.701992
$511$	0.904355	0.0400063
$512$	−1.00000	−0.0441942
$513$	37.0911	1.63761
$514$	2.45137	0.108126
$515$	−16.7442	−0.737837
$516$	22.4656	0.988991
$517$	−42.9369	−1.88836
$518$	0.439201	0.0192974
$519$	−5.43815	−0.238708
$520$	−5.90646	−0.259015
$521$	−18.3199	−0.802611	−0.401306	−	0.915944i	$-0.631443\pi$
$521$	−18.3199	−0.802611	−0.401306	+	0.915944i	$0.631443\pi$
$522$	−6.51818	−0.285293
$523$	35.4819	1.55151	0.775757	−	0.631032i	$-0.217368\pi$
$523$	35.4819	1.55151	0.775757	+	0.631032i	$0.217368\pi$
$524$	−1.00000	−0.0436852
$525$	−1.83472	−0.0800737
$526$	−0.617517	−0.0269250
$527$	−11.6529	−0.507607
$528$	10.3073	0.448568
$529$	1.00000	0.0434783
$530$	11.3592	0.493412
$531$	41.2234	1.78894
$532$	−0.324963	−0.0140889
$533$	−7.73939	−0.335230
$534$	−15.3851	−0.665780
$535$	−11.5974	−0.501400
$536$	7.07056	0.305402
$537$	−24.7935	−1.06992
$538$	−1.11424	−0.0480384
$539$	24.1103	1.03851
$540$	31.6561	1.36226
$541$	−6.96693	−0.299532	−0.149766	−	0.988722i	$-0.547852\pi$
$541$	−6.96693	−0.299532	−0.149766	+	0.988722i	$0.547852\pi$
$542$	−26.6667	−1.14543
$543$	−2.74775	−0.117917
$544$	−1.47240	−0.0631285
$545$	−49.5104	−2.12079
$546$	−0.377728	−0.0161653
$547$	3.85875	0.164988	0.0824941	−	0.996592i	$-0.473711\pi$
$547$	3.85875	0.164988	0.0824941	+	0.996592i	$0.473711\pi$
$548$	−1.83693	−0.0784696
$549$	6.89933	0.294456
$550$	27.4644	1.17109
$551$	−4.62982	−0.197237
$552$	−2.99000	−0.127263
$553$	0.721915	0.0306990
$554$	11.1258	0.472688
$555$	−61.3980	−2.60620
$556$	13.1562	0.557948
$557$	−38.1197	−1.61518	−0.807592	−	0.589742i	$-0.799230\pi$
$557$	−38.1197	−1.61518	−0.807592	+	0.589742i	$0.799230\pi$
$558$	47.0114	1.99015
$559$	12.3240	0.521250
$560$	−0.277346	−0.0117200
$561$	15.1765	0.640751
$562$	−16.7834	−0.707963
$563$	28.4896	1.20069	0.600346	−	0.799740i	$-0.295029\pi$
$563$	28.4896	1.20069	0.600346	+	0.799740i	$0.295029\pi$
$564$	−37.2416	−1.56815
$565$	−46.7287	−1.96589
$566$	14.3100	0.601494
$567$	0.651946	0.0273792
$568$	11.7341	0.492350
$569$	7.59471	0.318387	0.159193	−	0.987247i	$-0.449111\pi$
$569$	7.59471	0.318387	0.159193	+	0.987247i	$0.449111\pi$
$570$	45.4281	1.90277
$571$	30.2555	1.26615	0.633076	−	0.774090i	$-0.281792\pi$
$571$	30.2555	1.26615	0.633076	+	0.774090i	$0.281792\pi$
$572$	5.65432	0.236419
$573$	−2.83351	−0.118372
$574$	−0.363414	−0.0151686
$575$	−7.96704	−0.332248
$576$	5.94012	0.247505
$577$	11.3262	0.471514	0.235757	−	0.971812i	$-0.424243\pi$
$577$	11.3262	0.471514	0.235757	+	0.971812i	$0.424243\pi$
$578$	14.8320	0.616932
$579$	−24.0132	−0.997953
$580$	−3.95140	−0.164073
$581$	−0.140683	−0.00583652
$582$	29.2614	1.21293
$583$	−10.8743	−0.450367
$584$	−11.7419	−0.485883
$585$	35.0851	1.45059
$586$	−0.942375	−0.0389292
$587$	11.5012	0.474705	0.237353	−	0.971424i	$-0.423720\pi$
$587$	11.5012	0.474705	0.237353	+	0.971424i	$0.423720\pi$
$588$	20.9123	0.862408
$589$	33.3919	1.37589
$590$	24.9901	1.02883
$591$	−57.8020	−2.37766
$592$	−5.70246	−0.234370
$593$	16.7957	0.689715	0.344858	−	0.938655i	$-0.387927\pi$
$593$	16.7957	0.689715	0.344858	+	0.938655i	$0.387927\pi$
$594$	−30.3047	−1.24342
$595$	−0.408363	−0.0167413
$596$	−9.49063	−0.388751
$597$	24.4411	1.00031
$598$	−1.64024	−0.0670743
$599$	−8.67551	−0.354472	−0.177236	−	0.984168i	$-0.556716\pi$
$599$	−8.67551	−0.354472	−0.177236	+	0.984168i	$0.556716\pi$
$600$	23.8215	0.972507
$601$	43.6184	1.77923	0.889616	−	0.456710i	$-0.150972\pi$
$601$	43.6184	1.77923	0.889616	+	0.456710i	$0.150972\pi$
$602$	0.578691	0.0235857
$603$	−42.0000	−1.71037
$604$	9.18991	0.373932
$605$	−3.18175	−0.129356
$606$	50.7671	2.06227
$607$	−28.0310	−1.13774	−0.568872	−	0.822426i	$-0.692620\pi$
$607$	−28.0310	−1.13774	−0.568872	+	0.822426i	$0.692620\pi$
$608$	4.21923	0.171112
$609$	−0.252699	−0.0102399
$610$	4.18246	0.169343
$611$	−20.4298	−0.826500
$612$	8.74622	0.353545
$613$	40.9667	1.65463	0.827315	−	0.561738i	$-0.189867\pi$
$613$	40.9667	1.65463	0.827315	+	0.561738i	$0.189867\pi$
$614$	8.75562	0.353348
$615$	50.8033	2.04859
$616$	0.265506	0.0106976
$617$	5.54719	0.223321	0.111661	−	0.993746i	$-0.464383\pi$
$617$	5.54719	0.223321	0.111661	+	0.993746i	$0.464383\pi$
$618$	13.9032	0.559270
$619$	23.8468	0.958485	0.479243	−	0.877682i	$-0.340911\pi$
$619$	23.8468	0.958485	0.479243	+	0.877682i	$0.340911\pi$
$620$	28.4989	1.14454
$621$	8.79097	0.352770
$622$	9.14464	0.366667
$623$	−0.396306	−0.0158777
$624$	4.90432	0.196330
$625$	−1.36152	−0.0544607
$626$	12.0482	0.481543
$627$	−43.4889	−1.73678
$628$	−4.04858	−0.161556
$629$	−8.39630	−0.334782
$630$	1.64747	0.0656367
$631$	−24.8882	−0.990783	−0.495392	−	0.868670i	$-0.664975\pi$
$631$	−24.8882	−0.990783	−0.495392	+	0.868670i	$0.664975\pi$
$632$	−9.37314	−0.372844
$633$	−3.17140	−0.126052
$634$	12.7793	0.507530
$635$	35.1016	1.39296
$636$	−9.43190	−0.373999
$637$	11.4719	0.454534
$638$	3.78272	0.149759
$639$	−69.7017	−2.75736
$640$	3.60098	0.142341
$641$	33.3289	1.31641	0.658206	−	0.752838i	$-0.271316\pi$
$641$	33.3289	1.31641	0.658206	+	0.752838i	$0.271316\pi$
$642$	9.62970	0.380054
$643$	−5.29873	−0.208961	−0.104481	−	0.994527i	$-0.533318\pi$
$643$	−5.29873	−0.208961	−0.104481	+	0.994527i	$0.533318\pi$
$644$	−0.0770196	−0.00303500
$645$	−80.8979	−3.18535
$646$	6.21238	0.244423
$647$	24.4003	0.959276	0.479638	−	0.877466i	$-0.340768\pi$
$647$	24.4003	0.959276	0.479638	+	0.877466i	$0.340768\pi$
$648$	−8.46468	−0.332524
$649$	−23.9233	−0.939073
$650$	13.0678	0.512562
$651$	1.82256	0.0714316
$652$	10.8577	0.425219
$653$	−1.86903	−0.0731407	−0.0365703	−	0.999331i	$-0.511643\pi$
$653$	−1.86903	−0.0731407	−0.0365703	+	0.999331i	$0.511643\pi$
$654$	41.1100	1.60753
$655$	3.60098	0.140702
$656$	4.71846	0.184225
$657$	69.7482	2.72114
$658$	−0.959308	−0.0373977
$659$	−16.4831	−0.642089	−0.321044	−	0.947064i	$-0.604034\pi$
$659$	−16.4831	−0.642089	−0.321044	+	0.947064i	$0.604034\pi$
$660$	−37.1164	−1.44475
$661$	−10.2400	−0.398291	−0.199145	−	0.979970i	$-0.563817\pi$
$661$	−10.2400	−0.398291	−0.199145	+	0.979970i	$0.563817\pi$
$662$	34.6205	1.34556
$663$	7.22110	0.280444
$664$	1.82659	0.0708854
$665$	1.17018	0.0453778
$666$	33.8733	1.31256
$667$	−1.09731	−0.0424882
$668$	8.96759	0.346966
$669$	−1.98270	−0.0766555
$670$	−25.4609	−0.983642
$671$	−4.00392	−0.154570
$672$	0.230289	0.00888359
$673$	34.9902	1.34877	0.674387	−	0.738378i	$-0.264408\pi$
$673$	34.9902	1.34877	0.674387	+	0.738378i	$0.264408\pi$
$674$	−15.6335	−0.602182
$675$	−70.0380	−2.69576
$676$	−10.3096	−0.396524
$677$	15.8005	0.607263	0.303632	−	0.952789i	$-0.401801\pi$
$677$	15.8005	0.607263	0.303632	+	0.952789i	$0.401801\pi$
$678$	38.8003	1.49012
$679$	0.753746	0.0289261
$680$	5.30207	0.203325
$681$	−42.0268	−1.61047
$682$	−27.2823	−1.04469
$683$	23.6768	0.905968	0.452984	−	0.891519i	$-0.350360\pi$
$683$	23.6768	0.905968	0.452984	+	0.891519i	$0.350360\pi$
$684$	−25.0627	−0.958297
$685$	6.61473	0.252736
$686$	1.07782	0.0411513
$687$	74.0870	2.82660
$688$	−7.51355	−0.286452
$689$	−5.17409	−0.197117
$690$	10.7669	0.409890
$691$	23.0648	0.877426	0.438713	−	0.898627i	$-0.355435\pi$
$691$	23.0648	0.877426	0.438713	+	0.898627i	$0.355435\pi$
$692$	1.81878	0.0691395
$693$	−1.57714	−0.0599106
$694$	7.02646	0.266721
$695$	−47.3752	−1.79705
$696$	3.28097	0.124365
$697$	6.94745	0.263153
$698$	−12.5396	−0.474633
$699$	−90.1707	−3.41057
$700$	0.613618	0.0231926
$701$	39.0006	1.47303	0.736516	−	0.676420i	$-0.236469\pi$
$701$	39.0006	1.47303	0.736516	+	0.676420i	$0.236469\pi$
$702$	−14.4193	−0.544221
$703$	24.0600	0.907439
$704$	−3.44726	−0.129923
$705$	134.106	5.05073
$706$	−10.6415	−0.400500
$707$	1.30771	0.0491816
$708$	−20.7501	−0.779836
$709$	−33.5908	−1.26153	−0.630764	−	0.775975i	$-0.717258\pi$
$709$	−33.5908	−1.26153	−0.630764	+	0.775975i	$0.717258\pi$
$710$	−42.2541	−1.58577
$711$	55.6776	2.08807
$712$	5.14553	0.192837
$713$	7.91422	0.296390
$714$	0.339077	0.0126896
$715$	−20.3611	−0.761461
$716$	8.29213	0.309892
$717$	58.0391	2.16751
$718$	−7.40017	−0.276172
$719$	−21.0588	−0.785361	−0.392681	−	0.919675i	$-0.628452\pi$
$719$	−21.0588	−0.785361	−0.392681	+	0.919675i	$0.628452\pi$
$720$	−21.3902	−0.797167
$721$	0.358134	0.0133376
$722$	1.19813	0.0445899
$723$	54.8776	2.04092
$724$	0.918978	0.0341536
$725$	8.74234	0.324682
$726$	2.64190	0.0980502
$727$	−27.3263	−1.01348	−0.506738	−	0.862100i	$-0.669149\pi$
$727$	−27.3263	−1.01348	−0.506738	+	0.862100i	$0.669149\pi$
$728$	0.126330	0.00468212
$729$	−28.5739	−1.05829
$730$	42.2823	1.56494
$731$	−11.0629	−0.409178
$732$	−3.47283	−0.128360
$733$	19.9590	0.737202	0.368601	−	0.929588i	$-0.379837\pi$
$733$	19.9590	0.737202	0.368601	+	0.929588i	$0.379837\pi$
$734$	−22.4962	−0.830349
$735$	−75.3047	−2.77765
$736$	1.00000	0.0368605
$737$	24.3740	0.897829
$738$	−28.0282	−1.03173
$739$	−13.4618	−0.495200	−0.247600	−	0.968862i	$-0.579642\pi$
$739$	−13.4618	−0.495200	−0.247600	+	0.968862i	$0.579642\pi$
$740$	20.5344	0.754861
$741$	−20.6924	−0.760155
$742$	−0.242957	−0.00891921
$743$	−6.99538	−0.256635	−0.128318	−	0.991733i	$-0.540958\pi$
$743$	−6.99538	−0.256635	−0.128318	+	0.991733i	$0.540958\pi$
$744$	−23.6635	−0.867547
$745$	34.1755	1.25210
$746$	−26.6507	−0.975751
$747$	−10.8502	−0.396987
$748$	−5.07573	−0.185587
$749$	0.248052	0.00906361
$750$	−31.9459	−1.16650
$751$	−35.7870	−1.30589	−0.652943	−	0.757407i	$-0.726466\pi$
$751$	−35.7870	−1.30589	−0.652943	+	0.757407i	$0.726466\pi$
$752$	12.4554	0.454201
$753$	−37.1913	−1.35533
$754$	1.79986	0.0655469
$755$	−33.0927	−1.20437
$756$	−0.677077	−0.0246251
$757$	−9.06855	−0.329602	−0.164801	−	0.986327i	$-0.552698\pi$
$757$	−9.06855	−0.329602	−0.164801	+	0.986327i	$0.552698\pi$
$758$	28.1563	1.02268
$759$	−10.3073	−0.374132
$760$	−15.1933	−0.551120
$761$	−4.50028	−0.163135	−0.0815675	−	0.996668i	$-0.525993\pi$
$761$	−4.50028	−0.163135	−0.0815675	+	0.996668i	$0.525993\pi$
$762$	−29.1460	−1.05585
$763$	1.05895	0.0383367
$764$	0.947662	0.0342852
$765$	−31.4949	−1.13870
$766$	27.0559	0.977568
$767$	−11.3830	−0.411015
$768$	−2.99000	−0.107892
$769$	−12.6478	−0.456090	−0.228045	−	0.973651i	$-0.573233\pi$
$769$	−12.6478	−0.456090	−0.228045	+	0.973651i	$0.573233\pi$
$770$	−0.956082	−0.0344548
$771$	7.32962	0.263970
$772$	8.03115	0.289047
$773$	−2.83952	−0.102131	−0.0510653	−	0.998695i	$-0.516262\pi$
$773$	−2.83952	−0.102131	−0.0510653	+	0.998695i	$0.516262\pi$
$774$	44.6314	1.60424
$775$	−63.0529	−2.26493
$776$	−9.78642	−0.351312
$777$	1.31321	0.0471113
$778$	−19.6655	−0.705042
$779$	−19.9082	−0.713287
$780$	−17.6603	−0.632341
$781$	40.4503	1.44743
$782$	1.47240	0.0526528
$783$	−9.64646	−0.344736
$784$	−6.99407	−0.249788
$785$	14.5789	0.520342
$786$	−2.99000	−0.106650
$787$	48.6368	1.73371	0.866857	−	0.498558i	$-0.166137\pi$
$787$	48.6368	1.73371	0.866857	+	0.498558i	$0.166137\pi$
$788$	19.3318	0.688666
$789$	−1.84638	−0.0657328
$790$	33.7525	1.20086
$791$	0.999457	0.0355366
$792$	20.4771	0.727623
$793$	−1.90510	−0.0676522
$794$	−22.1898	−0.787485
$795$	33.9640	1.20458
$796$	−8.17427	−0.289729
$797$	−7.94293	−0.281353	−0.140676	−	0.990056i	$-0.544928\pi$
$797$	−7.94293	−0.281353	−0.140676	+	0.990056i	$0.544928\pi$
$798$	−0.971641	−0.0343957
$799$	18.3393	0.648797
$800$	−7.96704	−0.281677
$801$	−30.5651	−1.07996
$802$	9.10238	0.321416
$803$	−40.4773	−1.42841
$804$	21.1410	0.745586
$805$	0.277346	0.00977515
$806$	−12.9812	−0.457243
$807$	−3.33159	−0.117277
$808$	−16.9790	−0.597317
$809$	34.3262	1.20685	0.603423	−	0.797421i	$-0.293803\pi$
$809$	34.3262	1.20685	0.603423	+	0.797421i	$0.293803\pi$
$810$	30.4811	1.07100
$811$	−30.6912	−1.07771	−0.538856	−	0.842398i	$-0.681143\pi$
$811$	−30.6912	−1.07771	−0.538856	+	0.842398i	$0.681143\pi$
$812$	0.0845147	0.00296588
$813$	−79.7336	−2.79638
$814$	−19.6579	−0.689007
$815$	−39.0982	−1.36955
$816$	−4.40248	−0.154117
$817$	31.7014	1.10909
$818$	−6.54110	−0.228704
$819$	−0.750418	−0.0262217
$820$	−16.9911	−0.593354
$821$	24.8130	0.865978	0.432989	−	0.901399i	$-0.357459\pi$
$821$	24.8130	0.865978	0.432989	+	0.901399i	$0.357459\pi$
$822$	−5.49242	−0.191570
$823$	53.0040	1.84760	0.923802	−	0.382870i	$-0.125064\pi$
$823$	53.0040	1.84760	0.923802	+	0.382870i	$0.125064\pi$
$824$	−4.64990	−0.161987
$825$	82.1187	2.85901
$826$	−0.534502	−0.0185977
$827$	−41.3980	−1.43955	−0.719775	−	0.694207i	$-0.755755\pi$
$827$	−41.3980	−1.43955	−0.719775	+	0.694207i	$0.755755\pi$
$828$	−5.94012	−0.206433
$829$	−3.08786	−0.107246	−0.0536230	−	0.998561i	$-0.517077\pi$
$829$	−3.08786	−0.107246	−0.0536230	+	0.998561i	$0.517077\pi$
$830$	−6.57751	−0.228309
$831$	33.2661	1.15399
$832$	−1.64024	−0.0568650
$833$	−10.2981	−0.356806
$834$	39.3371	1.36213
$835$	−32.2921	−1.11751
$836$	14.5448	0.503041
$837$	69.5737	2.40482
$838$	28.3613	0.979725
$839$	−35.6258	−1.22994	−0.614970	−	0.788551i	$-0.710832\pi$
$839$	−35.6258	−1.22994	−0.614970	+	0.788551i	$0.710832\pi$
$840$	−0.829265	−0.0286124
$841$	−27.7959	−0.958479
$842$	36.7888	1.26783
$843$	−50.1823	−1.72837
$844$	1.06067	0.0365096
$845$	37.1247	1.27713
$846$	−73.9864	−2.54371
$847$	0.0680528	0.00233832
$848$	3.15448	0.108325
$849$	42.7870	1.46844
$850$	−11.7306	−0.402358
$851$	5.70246	0.195478
$852$	35.0849	1.20199
$853$	56.2474	1.92587	0.962937	−	0.269725i	$-0.0869329\pi$
$853$	56.2474	1.92587	0.962937	+	0.269725i	$0.0869329\pi$
$854$	−0.0894567	−0.00306115
$855$	90.2503	3.08649
$856$	−3.22063	−0.110079
$857$	−36.1413	−1.23456	−0.617282	−	0.786742i	$-0.711766\pi$
$857$	−36.1413	−1.23456	−0.617282	+	0.786742i	$0.711766\pi$
$858$	16.9064	0.577176
$859$	−35.3588	−1.20643	−0.603213	−	0.797580i	$-0.706113\pi$
$859$	−35.3588	−1.20643	−0.603213	+	0.797580i	$0.706113\pi$
$860$	27.0561	0.922607
$861$	−1.08661	−0.0370315
$862$	14.3946	0.490281
$863$	26.4199	0.899345	0.449672	−	0.893194i	$-0.351541\pi$
$863$	26.4199	0.899345	0.449672	+	0.893194i	$0.351541\pi$
$864$	8.79097	0.299075
$865$	−6.54937	−0.222685
$866$	28.1237	0.955682
$867$	44.3479	1.50613
$868$	−0.609550	−0.0206895
$869$	−32.3116	−1.09610
$870$	−11.8147	−0.400556
$871$	11.5974	0.392963
$872$	−13.7492	−0.465605
$873$	58.1325	1.96749
$874$	−4.21923	−0.142717
$875$	−0.822895	−0.0278189
$876$	−35.1083	−1.18620
$877$	−26.8776	−0.907592	−0.453796	−	0.891106i	$-0.649930\pi$
$877$	−26.8776	−0.907592	−0.453796	+	0.891106i	$0.649930\pi$
$878$	−10.9517	−0.369603
$879$	−2.81771	−0.0950389
$880$	12.4135	0.418459
$881$	−58.4284	−1.96850	−0.984252	−	0.176771i	$-0.943435\pi$
$881$	−58.4284	−1.96850	−0.984252	+	0.176771i	$0.943435\pi$
$882$	41.5456	1.39891
$883$	−0.132011	−0.00444252	−0.00222126	−	0.999998i	$-0.500707\pi$
$883$	−0.132011	−0.00444252	−0.00222126	+	0.999998i	$0.500707\pi$
$884$	−2.41508	−0.0812280
$885$	74.7206	2.51171
$886$	31.2553	1.05004
$887$	−21.1491	−0.710118	−0.355059	−	0.934844i	$-0.615539\pi$
$887$	−21.1491	−0.710118	−0.355059	+	0.934844i	$0.615539\pi$
$888$	−17.0504	−0.572173
$889$	−0.750772	−0.0251801
$890$	−18.5289	−0.621091
$891$	−29.1799	−0.977564
$892$	0.663109	0.0222025
$893$	−52.5520	−1.75859
$894$	−28.3770	−0.949070
$895$	−29.8598	−0.998102
$896$	−0.0770196	−0.00257304
$897$	−4.90432	−0.163750
$898$	1.86012	0.0620731
$899$	−8.68438	−0.289640
$900$	47.3252	1.57751
$901$	4.64465	0.154736
$902$	16.2657	0.541590
$903$	1.73029	0.0575804
$904$	−12.9767	−0.431597
$905$	−3.30922	−0.110002
$906$	27.4779	0.912891
$907$	25.4662	0.845592	0.422796	−	0.906225i	$-0.361049\pi$
$907$	25.4662	0.845592	0.422796	+	0.906225i	$0.361049\pi$
$908$	14.0558	0.466457
$909$	100.857	3.34522
$910$	−0.454913	−0.0150802
$911$	51.7433	1.71433	0.857167	−	0.515039i	$-0.172223\pi$
$911$	51.7433	1.71433	0.857167	+	0.515039i	$0.172223\pi$
$912$	12.6155	0.417741
$913$	6.29672	0.208391
$914$	23.3474	0.772263
$915$	12.5056	0.413422
$916$	−24.7782	−0.818696
$917$	−0.0770196	−0.00254341
$918$	12.9438	0.427209
$919$	−42.5960	−1.40511	−0.702556	−	0.711629i	$-0.747958\pi$
$919$	−42.5960	−1.40511	−0.702556	+	0.711629i	$0.747958\pi$
$920$	−3.60098	−0.118721
$921$	26.1793	0.862638
$922$	34.9380	1.15062
$923$	19.2466	0.633511
$924$	0.793865	0.0261162
$925$	−45.4317	−1.49379
$926$	14.4155	0.473724
$927$	27.6210	0.907192
$928$	−1.09731	−0.0360211
$929$	−5.47417	−0.179602	−0.0898008	−	0.995960i	$-0.528623\pi$
$929$	−5.47417	−0.179602	−0.0898008	+	0.995960i	$0.528623\pi$
$930$	85.2119	2.79421
$931$	29.5096	0.967137
$932$	30.1574	0.987838
$933$	27.3425	0.895153
$934$	4.75470	0.155578
$935$	18.2776	0.597742
$936$	9.74321	0.318467
$937$	10.3028	0.336578	0.168289	−	0.985738i	$-0.446176\pi$
$937$	10.3028	0.336578	0.168289	+	0.985738i	$0.446176\pi$
$938$	0.544572	0.0177809
$939$	36.0241	1.17560
$940$	−44.8515	−1.46289
$941$	28.0391	0.914048	0.457024	−	0.889454i	$-0.348915\pi$
$941$	28.0391	0.914048	0.457024	+	0.889454i	$0.348915\pi$
$942$	−12.1053	−0.394411
$943$	−4.71846	−0.153654
$944$	6.93982	0.225872
$945$	2.43814	0.0793127
$946$	−25.9012	−0.842119
$947$	0.280483	0.00911446	0.00455723	−	0.999990i	$-0.498549\pi$
$947$	0.280483	0.00911446	0.00455723	+	0.999990i	$0.498549\pi$
$948$	−28.0257	−0.910233
$949$	−19.2595	−0.625189
$950$	33.6147	1.09061
$951$	38.2101	1.23905
$952$	−0.113403	−0.00367543
$953$	16.1361	0.522699	0.261350	−	0.965244i	$-0.415832\pi$
$953$	16.1361	0.522699	0.261350	+	0.965244i	$0.415832\pi$
$954$	−18.7380	−0.606664
$955$	−3.41251	−0.110426
$956$	−19.4110	−0.627798
$957$	11.3104	0.365612
$958$	−26.2639	−0.848550
$959$	−0.141479	−0.00456861
$960$	10.7669	0.347501
$961$	31.6348	1.02048
$962$	−9.35339	−0.301565
$963$	19.1309	0.616486
$964$	−18.3537	−0.591133
$965$	−28.9200	−0.930968
$966$	−0.230289	−0.00740942
$967$	−48.2859	−1.55277	−0.776384	−	0.630260i	$-0.782948\pi$
$967$	−48.2859	−1.55277	−0.776384	+	0.630260i	$0.782948\pi$
$968$	−0.883578	−0.0283993
$969$	18.5750	0.596716
$970$	35.2407	1.13151
$971$	−16.2830	−0.522547	−0.261274	−	0.965265i	$-0.584143\pi$
$971$	−16.2830	−0.522547	−0.261274	+	0.965265i	$0.584143\pi$
$972$	1.06351	0.0341119
$973$	1.01329	0.0324845
$974$	−5.11045	−0.163749
$975$	39.0729	1.25133
$976$	1.16148	0.0371781
$977$	−47.2643	−1.51212	−0.756060	−	0.654502i	$-0.772878\pi$
$977$	−47.2643	−1.51212	−0.756060	+	0.654502i	$0.772878\pi$
$978$	32.4645	1.03810
$979$	17.7380	0.566908
$980$	25.1855	0.804521
$981$	81.6717	2.60758
$982$	9.56913	0.305363
$983$	5.79810	0.184931	0.0924653	−	0.995716i	$-0.470525\pi$
$983$	5.79810	0.184931	0.0924653	+	0.995716i	$0.470525\pi$
$984$	14.1082	0.449753
$985$	−69.6132	−2.21806
$986$	−1.61568	−0.0514538
$987$	−2.86833	−0.0913001
$988$	6.92053	0.220171
$989$	7.51355	0.238917
$990$	−73.7376	−2.34354
$991$	7.60217	0.241491	0.120745	−	0.992684i	$-0.461472\pi$
$991$	7.60217	0.241491	0.120745	+	0.992684i	$0.461472\pi$
$992$	7.91422	0.251277
$993$	103.515	3.28496
$994$	0.903752	0.0286653
$995$	29.4354	0.933163
$996$	5.46151	0.173055
$997$	−16.5320	−0.523575	−0.261787	−	0.965126i	$-0.584312\pi$
$997$	−16.5320	−0.523575	−0.261787	+	0.965126i	$0.584312\pi$
$998$	32.1300	1.01706
$999$	50.1302	1.58605

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	6026.2.a.h.1.3	✓	24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
6026.2.a.h.1.3	✓	24	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:	\( N \)	\(=\)	\( 6026 = 2 \cdot 23 \cdot 131 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	6026.a (trivial)

\(f(q)\)	\(=\)	\(q-1.00000 q^{2} -2.99000 q^{3} +1.00000 q^{4} -3.60098 q^{5} +2.99000 q^{6} +0.0770196 q^{7} -1.00000 q^{8} +5.94012 q^{9} +O(q^{10})\)	\(q-1.00000 q^{2} -2.99000 q^{3} +1.00000 q^{4} -3.60098 q^{5} +2.99000 q^{6} +0.0770196 q^{7} -1.00000 q^{8} +5.94012 q^{9} +3.60098 q^{10} -3.44726 q^{11} -2.99000 q^{12} -1.64024 q^{13} -0.0770196 q^{14} +10.7669 q^{15} +1.00000 q^{16} +1.47240 q^{17} -5.94012 q^{18} -4.21923 q^{19} -3.60098 q^{20} -0.230289 q^{21} +3.44726 q^{22} -1.00000 q^{23} +2.99000 q^{24} +7.96704 q^{25} +1.64024 q^{26} -8.79097 q^{27} +0.0770196 q^{28} +1.09731 q^{29} -10.7669 q^{30} -7.91422 q^{31} -1.00000 q^{32} +10.3073 q^{33} -1.47240 q^{34} -0.277346 q^{35} +5.94012 q^{36} -5.70246 q^{37} +4.21923 q^{38} +4.90432 q^{39} +3.60098 q^{40} +4.71846 q^{41} +0.230289 q^{42} -7.51355 q^{43} -3.44726 q^{44} -21.3902 q^{45} +1.00000 q^{46} +12.4554 q^{47} -2.99000 q^{48} -6.99407 q^{49} -7.96704 q^{50} -4.40248 q^{51} -1.64024 q^{52} +3.15448 q^{53} +8.79097 q^{54} +12.4135 q^{55} -0.0770196 q^{56} +12.6155 q^{57} -1.09731 q^{58} +6.93982 q^{59} +10.7669 q^{60} +1.16148 q^{61} +7.91422 q^{62} +0.457506 q^{63} +1.00000 q^{64} +5.90646 q^{65} -10.3073 q^{66} -7.07056 q^{67} +1.47240 q^{68} +2.99000 q^{69} +0.277346 q^{70} -11.7341 q^{71} -5.94012 q^{72} +11.7419 q^{73} +5.70246 q^{74} -23.8215 q^{75} -4.21923 q^{76} -0.265506 q^{77} -4.90432 q^{78} +9.37314 q^{79} -3.60098 q^{80} +8.46468 q^{81} -4.71846 q^{82} -1.82659 q^{83} -0.230289 q^{84} -5.30207 q^{85} +7.51355 q^{86} -3.28097 q^{87} +3.44726 q^{88} -5.14553 q^{89} +21.3902 q^{90} -0.126330 q^{91} -1.00000 q^{92} +23.6635 q^{93} -12.4554 q^{94} +15.1933 q^{95} +2.99000 q^{96} +9.78642 q^{97} +6.99407 q^{98} -20.4771 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q - 24 q^{2} - q^{3} + 24 q^{4} - q^{5} + q^{6} - 7 q^{7} - 24 q^{8} + 27 q^{9}+O(q^{10}) \) 24 * q - 24 * q^2 - q^3 + 24 * q^4 - q^5 + q^6 - 7 * q^7 - 24 * q^8 + 27 * q^9	\( 24 q - 24 q^{2} - q^{3} + 24 q^{4} - q^{5} + q^{6} - 7 q^{7} - 24 q^{8} + 27 q^{9} + q^{10} - 4 q^{11} - q^{12} - 5 q^{13} + 7 q^{14} - 6 q^{15} + 24 q^{16} + 5 q^{17} - 27 q^{18} - 20 q^{19} - q^{20} + 4 q^{22} - 24 q^{23} + q^{24} + q^{25} + 5 q^{26} - q^{27} - 7 q^{28} - 6 q^{29} + 6 q^{30} - 23 q^{31} - 24 q^{32} - 6 q^{33} - 5 q^{34} + 5 q^{35} + 27 q^{36} - 6 q^{37} + 20 q^{38} - 39 q^{39} + q^{40} - q^{41} - 44 q^{43} - 4 q^{44} - 13 q^{45} + 24 q^{46} + 32 q^{47} - q^{48} - 13 q^{49} - q^{50} - 44 q^{51} - 5 q^{52} + 21 q^{53} + q^{54} - 13 q^{55} + 7 q^{56} + 10 q^{57} + 6 q^{58} - 24 q^{59} - 6 q^{60} - 40 q^{61} + 23 q^{62} - 54 q^{63} + 24 q^{64} - 29 q^{65} + 6 q^{66} - 17 q^{67} + 5 q^{68} + q^{69} - 5 q^{70} + 4 q^{71} - 27 q^{72} - 16 q^{73} + 6 q^{74} - 36 q^{75} - 20 q^{76} + 24 q^{77} + 39 q^{78} - 53 q^{79} - q^{80} + 24 q^{81} + q^{82} - 9 q^{83} - 37 q^{85} + 44 q^{86} + 7 q^{87} + 4 q^{88} - 46 q^{89} + 13 q^{90} - 44 q^{91} - 24 q^{92} + 23 q^{93} - 32 q^{94} + 28 q^{95} + q^{96} - 20 q^{97} + 13 q^{98} - 78 q^{99}+O(q^{100}) \) 24 * q - 24 * q^2 - q^3 + 24 * q^4 - q^5 + q^6 - 7 * q^7 - 24 * q^8 + 27 * q^9 + q^10 - 4 * q^11 - q^12 - 5 * q^13 + 7 * q^14 - 6 * q^15 + 24 * q^16 + 5 * q^17 - 27 * q^18 - 20 * q^19 - q^20 + 4 * q^22 - 24 * q^23 + q^24 + q^25 + 5 * q^26 - q^27 - 7 * q^28 - 6 * q^29 + 6 * q^30 - 23 * q^31 - 24 * q^32 - 6 * q^33 - 5 * q^34 + 5 * q^35 + 27 * q^36 - 6 * q^37 + 20 * q^38 - 39 * q^39 + q^40 - q^41 - 44 * q^43 - 4 * q^44 - 13 * q^45 + 24 * q^46 + 32 * q^47 - q^48 - 13 * q^49 - q^50 - 44 * q^51 - 5 * q^52 + 21 * q^53 + q^54 - 13 * q^55 + 7 * q^56 + 10 * q^57 + 6 * q^58 - 24 * q^59 - 6 * q^60 - 40 * q^61 + 23 * q^62 - 54 * q^63 + 24 * q^64 - 29 * q^65 + 6 * q^66 - 17 * q^67 + 5 * q^68 + q^69 - 5 * q^70 + 4 * q^71 - 27 * q^72 - 16 * q^73 + 6 * q^74 - 36 * q^75 - 20 * q^76 + 24 * q^77 + 39 * q^78 - 53 * q^79 - q^80 + 24 * q^81 + q^82 - 9 * q^83 - 37 * q^85 + 44 * q^86 + 7 * q^87 + 4 * q^88 - 46 * q^89 + 13 * q^90 - 44 * q^91 - 24 * q^92 + 23 * q^93 - 32 * q^94 + 28 * q^95 + q^96 - 20 * q^97 + 13 * q^98 - 78 * q^99

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