LMFDB - Embedded newform 6026.2.a.h.1.15

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			1.15
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)

$f(q)$	$=$	$q-1.00000 q^{2} +0.977360 q^{3} +1.00000 q^{4} +1.34259 q^{5} -0.977360 q^{6} -1.08765 q^{7} -1.00000 q^{8} -2.04477 q^{9} +O(q^{10})$	\(q-1.00000 q^{2} +0.977360 q^{3} +1.00000 q^{4} +1.34259 q^{5} -0.977360 q^{6} -1.08765 q^{7} -1.00000 q^{8} -2.04477 q^{9} -1.34259 q^{10} +3.05583 q^{11} +0.977360 q^{12} +1.13909 q^{13} +1.08765 q^{14} +1.31220 q^{15} +1.00000 q^{16} -3.38956 q^{17} +2.04477 q^{18} +2.02326 q^{19} +1.34259 q^{20} -1.06303 q^{21} -3.05583 q^{22} -1.00000 q^{23} -0.977360 q^{24} -3.19745 q^{25} -1.13909 q^{26} -4.93056 q^{27} -1.08765 q^{28} +1.84426 q^{29} -1.31220 q^{30} +1.02560 q^{31} -1.00000 q^{32} +2.98665 q^{33} +3.38956 q^{34} -1.46027 q^{35} -2.04477 q^{36} -2.61798 q^{37} -2.02326 q^{38} +1.11331 q^{39} -1.34259 q^{40} -7.20544 q^{41} +1.06303 q^{42} -5.50653 q^{43} +3.05583 q^{44} -2.74529 q^{45} +1.00000 q^{46} +5.56770 q^{47} +0.977360 q^{48} -5.81701 q^{49} +3.19745 q^{50} -3.31282 q^{51} +1.13909 q^{52} -13.2665 q^{53} +4.93056 q^{54} +4.10273 q^{55} +1.08765 q^{56} +1.97745 q^{57} -1.84426 q^{58} +5.29844 q^{59} +1.31220 q^{60} +4.01137 q^{61} -1.02560 q^{62} +2.22400 q^{63} +1.00000 q^{64} +1.52934 q^{65} -2.98665 q^{66} -9.80250 q^{67} -3.38956 q^{68} -0.977360 q^{69} +1.46027 q^{70} -7.93317 q^{71} +2.04477 q^{72} +3.80586 q^{73} +2.61798 q^{74} -3.12506 q^{75} +2.02326 q^{76} -3.32369 q^{77} -1.11331 q^{78} +2.61951 q^{79} +1.34259 q^{80} +1.31537 q^{81} +7.20544 q^{82} +9.13497 q^{83} -1.06303 q^{84} -4.55079 q^{85} +5.50653 q^{86} +1.80251 q^{87} -3.05583 q^{88} -8.47498 q^{89} +2.74529 q^{90} -1.23894 q^{91} -1.00000 q^{92} +1.00239 q^{93} -5.56770 q^{94} +2.71641 q^{95} -0.977360 q^{96} +1.60299 q^{97} +5.81701 q^{98} -6.24846 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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
$3$	0.977360	0.564279	0.282140	−	0.959373i	$-0.408956\pi$
$3$	0.977360	0.564279	0.282140	+	0.959373i	$0.408956\pi$
$4$	1.00000	0.500000
$5$	1.34259	0.600425	0.300213	−	0.953872i	$-0.402942\pi$
$5$	1.34259	0.600425	0.300213	+	0.953872i	$0.402942\pi$
$6$	−0.977360	−0.399006
$7$	−1.08765	−0.411094	−0.205547	−	0.978647i	$-0.565897\pi$
$7$	−1.08765	−0.411094	−0.205547	+	0.978647i	$0.565897\pi$
$8$	−1.00000	−0.353553
$9$	−2.04477	−0.681589
$10$	−1.34259	−0.424565
$11$	3.05583	0.921368	0.460684	−	0.887564i	$-0.347604\pi$
$11$	3.05583	0.921368	0.460684	+	0.887564i	$0.347604\pi$
$12$	0.977360	0.282140
$13$	1.13909	0.315928	0.157964	−	0.987445i	$-0.449507\pi$
$13$	1.13909	0.315928	0.157964	+	0.987445i	$0.449507\pi$
$14$	1.08765	0.290688
$15$	1.31220	0.338807
$16$	1.00000	0.250000
$17$	−3.38956	−0.822089	−0.411044	−	0.911615i	$-0.634836\pi$
$17$	−3.38956	−0.822089	−0.411044	+	0.911615i	$0.634836\pi$
$18$	2.04477	0.481956
$19$	2.02326	0.464167	0.232083	−	0.972696i	$-0.425446\pi$
$19$	2.02326	0.464167	0.232083	+	0.972696i	$0.425446\pi$
$20$	1.34259	0.300213
$21$	−1.06303	−0.231972
$22$	−3.05583	−0.651506
$23$	−1.00000	−0.208514
$23$	−1.00000	−0.208514
$24$	−0.977360	−0.199503
$25$	−3.19745	−0.639490
$26$	−1.13909	−0.223395
$27$	−4.93056	−0.948886
$28$	−1.08765	−0.205547
$29$	1.84426	0.342470	0.171235	−	0.985230i	$-0.445224\pi$
$29$	1.84426	0.342470	0.171235	+	0.985230i	$0.445224\pi$
$30$	−1.31220	−0.239573
$31$	1.02560	0.184204	0.0921020	−	0.995750i	$-0.470641\pi$
$31$	1.02560	0.184204	0.0921020	+	0.995750i	$0.470641\pi$
$32$	−1.00000	−0.176777
$33$	2.98665	0.519909
$34$	3.38956	0.581305
$35$	−1.46027	−0.246831
$36$	−2.04477	−0.340794
$37$	−2.61798	−0.430393	−0.215196	−	0.976571i	$-0.569039\pi$
$37$	−2.61798	−0.430393	−0.215196	+	0.976571i	$0.569039\pi$
$38$	−2.02326	−0.328215
$39$	1.11331	0.178272
$40$	−1.34259	−0.212282
$41$	−7.20544	−1.12530	−0.562650	−	0.826695i	$-0.690218\pi$
$41$	−7.20544	−1.12530	−0.562650	+	0.826695i	$0.690218\pi$
$42$	1.06303	0.164029
$43$	−5.50653	−0.839737	−0.419869	−	0.907585i	$-0.637924\pi$
$43$	−5.50653	−0.839737	−0.419869	+	0.907585i	$0.637924\pi$
$44$	3.05583	0.460684
$45$	−2.74529	−0.409243
$46$	1.00000	0.147442
$47$	5.56770	0.812133	0.406066	−	0.913844i	$-0.366900\pi$
$47$	5.56770	0.812133	0.406066	+	0.913844i	$0.366900\pi$
$48$	0.977360	0.141070
$49$	−5.81701	−0.831001
$50$	3.19745	0.452187
$51$	−3.31282	−0.463888
$52$	1.13909	0.157964
$53$	−13.2665	−1.82229	−0.911144	−	0.412089i	$-0.864799\pi$
$53$	−13.2665	−1.82229	−0.911144	+	0.412089i	$0.864799\pi$
$54$	4.93056	0.670964
$55$	4.10273	0.553213
$56$	1.08765	0.145344
$57$	1.97745	0.261920
$58$	−1.84426	−0.242163
$59$	5.29844	0.689799	0.344899	−	0.938640i	$-0.387913\pi$
$59$	5.29844	0.689799	0.344899	+	0.938640i	$0.387913\pi$
$60$	1.31220	0.169404
$61$	4.01137	0.513604	0.256802	−	0.966464i	$-0.417331\pi$
$61$	4.01137	0.513604	0.256802	+	0.966464i	$0.417331\pi$
$62$	−1.02560	−0.130252
$63$	2.22400	0.280197
$64$	1.00000	0.125000
$65$	1.52934	0.189691
$66$	−2.98665	−0.367631
$67$	−9.80250	−1.19757	−0.598783	−	0.800911i	$-0.704349\pi$
$67$	−9.80250	−1.19757	−0.598783	+	0.800911i	$0.704349\pi$
$68$	−3.38956	−0.411044
$69$	−0.977360	−0.117660
$70$	1.46027	0.174536
$71$	−7.93317	−0.941494	−0.470747	−	0.882268i	$-0.656015\pi$
$71$	−7.93317	−0.941494	−0.470747	+	0.882268i	$0.656015\pi$
$72$	2.04477	0.240978
$73$	3.80586	0.445442	0.222721	−	0.974882i	$-0.428506\pi$
$73$	3.80586	0.445442	0.222721	+	0.974882i	$0.428506\pi$
$74$	2.61798	0.304333
$75$	−3.12506	−0.360851
$76$	2.02326	0.232083
$77$	−3.32369	−0.378769
$78$	−1.11331	−0.126057
$79$	2.61951	0.294718	0.147359	−	0.989083i	$-0.452923\pi$
$79$	2.61951	0.294718	0.147359	+	0.989083i	$0.452923\pi$
$80$	1.34259	0.150106
$81$	1.31537	0.146152
$82$	7.20544	0.795707
$83$	9.13497	1.00269	0.501346	−	0.865247i	$-0.332838\pi$
$83$	9.13497	1.00269	0.501346	+	0.865247i	$0.332838\pi$
$84$	−1.06303	−0.115986
$85$	−4.55079	−0.493603
$86$	5.50653	0.593784
$87$	1.80251	0.193249
$88$	−3.05583	−0.325753
$89$	−8.47498	−0.898346	−0.449173	−	0.893445i	$-0.648281\pi$
$89$	−8.47498	−0.898346	−0.449173	+	0.893445i	$0.648281\pi$
$90$	2.74529	0.289379
$91$	−1.23894	−0.129876
$92$	−1.00000	−0.104257
$93$	1.00239	0.103942
$94$	−5.56770	−0.574265
$95$	2.71641	0.278697
$96$	−0.977360	−0.0997514
$97$	1.60299	0.162759	0.0813793	−	0.996683i	$-0.474067\pi$
$97$	1.60299	0.162759	0.0813793	+	0.996683i	$0.474067\pi$
$98$	5.81701	0.587607
$99$	−6.24846	−0.627994
$100$	−3.19745	−0.319745
$101$	−12.4278	−1.23662	−0.618308	−	0.785936i	$-0.712182\pi$
$101$	−12.4278	−1.23662	−0.618308	+	0.785936i	$0.712182\pi$
$102$	3.31282	0.328018
$103$	6.16490	0.607446	0.303723	−	0.952760i	$-0.401770\pi$
$103$	6.16490	0.607446	0.303723	+	0.952760i	$0.401770\pi$
$104$	−1.13909	−0.111697
$105$	−1.42721	−0.139282
$106$	13.2665	1.28855
$107$	11.9928	1.15939	0.579695	−	0.814833i	$-0.303172\pi$
$107$	11.9928	1.15939	0.579695	+	0.814833i	$0.303172\pi$
$108$	−4.93056	−0.474443
$109$	2.28864	0.219212	0.109606	−	0.993975i	$-0.465041\pi$
$109$	2.28864	0.219212	0.109606	+	0.993975i	$0.465041\pi$
$110$	−4.10273	−0.391180
$111$	−2.55871	−0.242862
$112$	−1.08765	−0.102774
$113$	4.66948	0.439268	0.219634	−	0.975582i	$-0.429514\pi$
$113$	4.66948	0.439268	0.219634	+	0.975582i	$0.429514\pi$
$114$	−1.97745	−0.185205
$115$	−1.34259	−0.125197
$116$	1.84426	0.171235
$117$	−2.32918	−0.215333
$118$	−5.29844	−0.487761
$119$	3.68667	0.337956
$120$	−1.31220	−0.119787
$121$	−1.66189	−0.151081
$122$	−4.01137	−0.363173
$123$	−7.04231	−0.634984
$124$	1.02560	0.0921020
$125$	−11.0058	−0.984391
$126$	−2.22400	−0.198130
$127$	−4.36870	−0.387659	−0.193830	−	0.981035i	$-0.562091\pi$
$127$	−4.36870	−0.387659	−0.193830	+	0.981035i	$0.562091\pi$
$128$	−1.00000	−0.0883883
$129$	−5.38186	−0.473846
$130$	−1.52934	−0.134132
$131$	−1.00000	−0.0873704
$131$	−1.00000	−0.0873704
$132$	2.98665	0.259954
$133$	−2.20060	−0.190816
$134$	9.80250	0.846807
$135$	−6.61972	−0.569735
$136$	3.38956	0.290652
$137$	13.1951	1.12733	0.563667	−	0.826002i	$-0.309390\pi$
$137$	13.1951	1.12733	0.563667	+	0.826002i	$0.309390\pi$
$138$	0.977360	0.0831984
$139$	−12.7683	−1.08299	−0.541497	−	0.840703i	$-0.682142\pi$
$139$	−12.7683	−1.08299	−0.541497	+	0.840703i	$0.682142\pi$
$140$	−1.46027	−0.123416
$141$	5.44165	0.458270
$142$	7.93317	0.665737
$143$	3.48088	0.291086
$144$	−2.04477	−0.170397
$145$	2.47609	0.205628
$146$	−3.80586	−0.314975
$147$	−5.68531	−0.468917
$148$	−2.61798	−0.215196
$149$	−0.816955	−0.0669276	−0.0334638	−	0.999440i	$-0.510654\pi$
$149$	−0.816955	−0.0669276	−0.0334638	+	0.999440i	$0.510654\pi$
$150$	3.12506	0.255160
$151$	−9.22880	−0.751029	−0.375514	−	0.926817i	$-0.622534\pi$
$151$	−9.22880	−0.751029	−0.375514	+	0.926817i	$0.622534\pi$
$152$	−2.02326	−0.164108
$153$	6.93086	0.560327
$154$	3.32369	0.267830
$155$	1.37697	0.110601
$156$	1.11331	0.0891358
$157$	5.69698	0.454669	0.227334	−	0.973817i	$-0.426999\pi$
$157$	5.69698	0.454669	0.227334	+	0.973817i	$0.426999\pi$
$158$	−2.61951	−0.208397
$159$	−12.9661	−1.02828
$160$	−1.34259	−0.106141
$161$	1.08765	0.0857191
$162$	−1.31537	−0.103345
$163$	17.8122	1.39516	0.697581	−	0.716505i	$-0.254260\pi$
$163$	17.8122	1.39516	0.697581	+	0.716505i	$0.254260\pi$
$164$	−7.20544	−0.562650
$165$	4.00985	0.312166
$166$	−9.13497	−0.709011
$167$	−21.9424	−1.69796	−0.848979	−	0.528427i	$-0.822782\pi$
$167$	−21.9424	−1.69796	−0.848979	+	0.528427i	$0.822782\pi$
$168$	1.06303	0.0820145
$169$	−11.7025	−0.900189
$170$	4.55079	0.349030
$171$	−4.13709	−0.316371
$172$	−5.50653	−0.419869
$173$	10.8450	0.824533	0.412266	−	0.911063i	$-0.364737\pi$
$173$	10.8450	0.824533	0.412266	+	0.911063i	$0.364737\pi$
$174$	−1.80251	−0.136648
$175$	3.47772	0.262891
$176$	3.05583	0.230342
$177$	5.17849	0.389239
$178$	8.47498	0.635227
$179$	−12.3874	−0.925881	−0.462941	−	0.886389i	$-0.653206\pi$
$179$	−12.3874	−0.925881	−0.462941	+	0.886389i	$0.653206\pi$
$180$	−2.74529	−0.204622
$181$	−18.3079	−1.36082	−0.680409	−	0.732833i	$-0.738198\pi$
$181$	−18.3079	−1.36082	−0.680409	+	0.732833i	$0.738198\pi$
$182$	1.23894	0.0918364
$183$	3.92056	0.289816
$184$	1.00000	0.0737210
$185$	−3.51487	−0.258419
$186$	−1.00239	−0.0734984
$187$	−10.3579	−0.757446
$188$	5.56770	0.406066
$189$	5.36274	0.390082
$190$	−2.71641	−0.197069
$191$	−20.2664	−1.46643	−0.733214	−	0.679998i	$-0.761981\pi$
$191$	−20.2664	−1.46643	−0.733214	+	0.679998i	$0.761981\pi$
$192$	0.977360	0.0705349
$193$	5.17560	0.372548	0.186274	−	0.982498i	$-0.440359\pi$
$193$	5.17560	0.372548	0.186274	+	0.982498i	$0.440359\pi$
$194$	−1.60299	−0.115088
$195$	1.49472	0.107039
$196$	−5.81701	−0.415501
$197$	−13.4412	−0.957648	−0.478824	−	0.877911i	$-0.658937\pi$
$197$	−13.4412	−0.957648	−0.478824	+	0.877911i	$0.658937\pi$
$198$	6.24846	0.444059
$199$	8.30474	0.588707	0.294354	−	0.955697i	$-0.404896\pi$
$199$	8.30474	0.588707	0.294354	+	0.955697i	$0.404896\pi$
$200$	3.19745	0.226094
$201$	−9.58057	−0.675762
$202$	12.4278	0.874420
$203$	−2.00592	−0.140788
$204$	−3.31282	−0.231944
$205$	−9.67396	−0.675659
$206$	−6.16490	−0.429529
$207$	2.04477	0.142121
$208$	1.13909	0.0789820
$209$	6.18273	0.427668
$210$	1.42721	0.0984872
$211$	0.899204	0.0619038	0.0309519	−	0.999521i	$-0.490146\pi$
$211$	0.899204	0.0619038	0.0309519	+	0.999521i	$0.490146\pi$
$212$	−13.2665	−0.911144
$213$	−7.75356	−0.531265
$214$	−11.9928	−0.819813
$215$	−7.39302	−0.504200
$216$	4.93056	0.335482
$217$	−1.11550	−0.0757252
$218$	−2.28864	−0.155006
$219$	3.71970	0.251354
$220$	4.10273	0.276606
$221$	−3.86103	−0.259721
$222$	2.55871	0.171729
$223$	−0.869638	−0.0582353	−0.0291176	−	0.999576i	$-0.509270\pi$
$223$	−0.869638	−0.0582353	−0.0291176	+	0.999576i	$0.509270\pi$
$224$	1.08765	0.0726719
$225$	6.53804	0.435869
$226$	−4.66948	−0.310609
$227$	17.7853	1.18045	0.590227	−	0.807237i	$-0.299038\pi$
$227$	17.7853	1.18045	0.590227	+	0.807237i	$0.299038\pi$
$228$	1.97745	0.130960
$229$	−22.8703	−1.51131	−0.755657	−	0.654968i	$-0.772682\pi$
$229$	−22.8703	−1.51131	−0.755657	+	0.654968i	$0.772682\pi$
$230$	1.34259	0.0885279
$231$	−3.24844	−0.213732
$232$	−1.84426	−0.121082
$233$	13.2246	0.866375	0.433187	−	0.901304i	$-0.357389\pi$
$233$	13.2246	0.866375	0.433187	+	0.901304i	$0.357389\pi$
$234$	2.32918	0.152263
$235$	7.47515	0.487625
$236$	5.29844	0.344899
$237$	2.56021	0.166303
$238$	−3.68667	−0.238971
$239$	−11.0212	−0.712902	−0.356451	−	0.934314i	$-0.616013\pi$
$239$	−11.0212	−0.712902	−0.356451	+	0.934314i	$0.616013\pi$
$240$	1.31220	0.0847019
$241$	−23.1444	−1.49086	−0.745431	−	0.666582i	$-0.767756\pi$
$241$	−23.1444	−1.49086	−0.745431	+	0.666582i	$0.767756\pi$
$242$	1.66189	0.106830
$243$	16.0773	1.03136
$244$	4.01137	0.256802
$245$	−7.80987	−0.498954
$246$	7.04231	0.449001
$247$	2.30468	0.146643
$248$	−1.02560	−0.0651259
$249$	8.92815	0.565799
$250$	11.0058	0.696069
$251$	−17.8805	−1.12861	−0.564303	−	0.825568i	$-0.690855\pi$
$251$	−17.8805	−1.12861	−0.564303	+	0.825568i	$0.690855\pi$
$252$	2.22400	0.140099
$253$	−3.05583	−0.192119
$254$	4.36870	0.274116
$255$	−4.44776	−0.278530
$256$	1.00000	0.0625000
$257$	10.8135	0.674530	0.337265	−	0.941410i	$-0.390498\pi$
$257$	10.8135	0.674530	0.337265	+	0.941410i	$0.390498\pi$
$258$	5.38186	0.335060
$259$	2.84745	0.176932
$260$	1.52934	0.0948456
$261$	−3.77108	−0.233424
$262$	1.00000	0.0617802
$263$	−24.8936	−1.53500	−0.767502	−	0.641046i	$-0.778501\pi$
$263$	−24.8936	−1.53500	−0.767502	+	0.641046i	$0.778501\pi$
$264$	−2.98665	−0.183816
$265$	−17.8114	−1.09415
$266$	2.20060	0.134928
$267$	−8.28311	−0.506918
$268$	−9.80250	−0.598783
$269$	17.4400	1.06334	0.531668	−	0.846953i	$-0.321566\pi$
$269$	17.4400	1.06334	0.531668	+	0.846953i	$0.321566\pi$
$270$	6.61972	0.402863
$271$	9.07271	0.551128	0.275564	−	0.961283i	$-0.411135\pi$
$271$	9.07271	0.551128	0.275564	+	0.961283i	$0.411135\pi$
$272$	−3.38956	−0.205522
$273$	−1.21089	−0.0732865
$274$	−13.1951	−0.797146
$275$	−9.77086	−0.589205
$276$	−0.977360	−0.0588302
$277$	−1.94904	−0.117106	−0.0585532	−	0.998284i	$-0.518649\pi$
$277$	−1.94904	−0.117106	−0.0585532	+	0.998284i	$0.518649\pi$
$278$	12.7683	0.765793
$279$	−2.09712	−0.125551
$280$	1.46027	0.0872681
$281$	4.47670	0.267058	0.133529	−	0.991045i	$-0.457369\pi$
$281$	4.47670	0.267058	0.133529	+	0.991045i	$0.457369\pi$
$282$	−5.44165	−0.324046
$283$	27.1025	1.61108	0.805538	−	0.592545i	$-0.201877\pi$
$283$	27.1025	1.61108	0.805538	+	0.592545i	$0.201877\pi$
$284$	−7.93317	−0.470747
$285$	2.65491	0.157263
$286$	−3.48088	−0.205829
$287$	7.83702	0.462605
$288$	2.04477	0.120489
$289$	−5.51089	−0.324170
$290$	−2.47609	−0.145401
$291$	1.56669	0.0918413
$292$	3.80586	0.222721
$293$	−33.4634	−1.95495	−0.977477	−	0.211041i	$-0.932315\pi$
$293$	−33.4634	−1.95495	−0.977477	+	0.211041i	$0.932315\pi$
$294$	5.68531	0.331574
$295$	7.11364	0.414172
$296$	2.61798	0.152167
$297$	−15.0669	−0.874273
$298$	0.816955	0.0473250
$299$	−1.13909	−0.0658756
$300$	−3.12506	−0.180425
$301$	5.98919	0.345211
$302$	9.22880	0.531058
$303$	−12.1465	−0.697797
$304$	2.02326	0.116042
$305$	5.38564	0.308381
$306$	−6.93086	−0.396211
$307$	13.4270	0.766317	0.383158	−	0.923683i	$-0.374836\pi$
$307$	13.4270	0.766317	0.383158	+	0.923683i	$0.374836\pi$
$308$	−3.32369	−0.189385
$309$	6.02533	0.342769
$310$	−1.37697	−0.0782065
$311$	7.13048	0.404333	0.202166	−	0.979351i	$-0.435202\pi$
$311$	7.13048	0.404333	0.202166	+	0.979351i	$0.435202\pi$
$312$	−1.11331	−0.0630286
$313$	−28.0091	−1.58317	−0.791585	−	0.611059i	$-0.790744\pi$
$313$	−28.0091	−1.58317	−0.791585	+	0.611059i	$0.790744\pi$
$314$	−5.69698	−0.321499
$315$	2.98592	0.168238
$316$	2.61951	0.147359
$317$	28.0041	1.57287	0.786433	−	0.617675i	$-0.211925\pi$
$317$	28.0041	1.57287	0.786433	+	0.617675i	$0.211925\pi$
$318$	12.9661	0.727103
$319$	5.63575	0.315541
$320$	1.34259	0.0750531
$321$	11.7213	0.654220
$322$	−1.08765	−0.0606126
$323$	−6.85794	−0.381586
$324$	1.31537	0.0730762
$325$	−3.64220	−0.202033
$326$	−17.8122	−0.986529
$327$	2.23683	0.123697
$328$	7.20544	0.397854
$329$	−6.05573	−0.333863
$330$	−4.00985	−0.220735
$331$	−10.3894	−0.571056	−0.285528	−	0.958370i	$-0.592169\pi$
$331$	−10.3894	−0.571056	−0.285528	+	0.958370i	$0.592169\pi$
$332$	9.13497	0.501346
$333$	5.35315	0.293351
$334$	21.9424	1.20064
$335$	−13.1608	−0.719049
$336$	−1.06303	−0.0579930
$337$	−7.84056	−0.427103	−0.213551	−	0.976932i	$-0.568503\pi$
$337$	−7.84056	−0.427103	−0.213551	+	0.976932i	$0.568503\pi$
$338$	11.7025	0.636530
$339$	4.56376	0.247870
$340$	−4.55079	−0.246801
$341$	3.13407	0.169720
$342$	4.13709	0.223708
$343$	13.9405	0.752715
$344$	5.50653	0.296892
$345$	−1.31220	−0.0706462
$346$	−10.8450	−0.583033
$347$	−9.70702	−0.521100	−0.260550	−	0.965460i	$-0.583904\pi$
$347$	−9.70702	−0.521100	−0.260550	+	0.965460i	$0.583904\pi$
$348$	1.80251	0.0966245
$349$	0.644751	0.0345128	0.0172564	−	0.999851i	$-0.494507\pi$
$349$	0.644751	0.0345128	0.0172564	+	0.999851i	$0.494507\pi$
$350$	−3.47772	−0.185892
$351$	−5.61637	−0.299780
$352$	−3.05583	−0.162876
$353$	21.2459	1.13081	0.565403	−	0.824815i	$-0.308721\pi$
$353$	21.2459	1.13081	0.565403	+	0.824815i	$0.308721\pi$
$354$	−5.17849	−0.275234
$355$	−10.6510	−0.565296
$356$	−8.47498	−0.449173
$357$	3.60320	0.190702
$358$	12.3874	0.654697
$359$	28.1546	1.48594	0.742970	−	0.669324i	$-0.233416\pi$
$359$	28.1546	1.48594	0.742970	+	0.669324i	$0.233416\pi$
$360$	2.74529	0.144689
$361$	−14.9064	−0.784549
$362$	18.3079	0.962243
$363$	−1.62427	−0.0852519
$364$	−1.23894	−0.0649381
$365$	5.10972	0.267455
$366$	−3.92056	−0.204931
$367$	−30.4735	−1.59071	−0.795353	−	0.606147i	$-0.792715\pi$
$367$	−30.4735	−1.59071	−0.795353	+	0.606147i	$0.792715\pi$
$368$	−1.00000	−0.0521286
$369$	14.7334	0.766992
$370$	3.51487	0.182729
$371$	14.4293	0.749132
$372$	1.00239	0.0519712
$373$	11.0261	0.570908	0.285454	−	0.958392i	$-0.407856\pi$
$373$	11.0261	0.570908	0.285454	+	0.958392i	$0.407856\pi$
$374$	10.3579	0.535595
$375$	−10.7567	−0.555471
$376$	−5.56770	−0.287132
$377$	2.10079	0.108196
$378$	−5.36274	−0.275829
$379$	33.8550	1.73902	0.869508	−	0.493918i	$-0.164436\pi$
$379$	33.8550	1.73902	0.869508	+	0.493918i	$0.164436\pi$
$380$	2.71641	0.139349
$381$	−4.26979	−0.218748
$382$	20.2664	1.03692
$383$	−11.8256	−0.604260	−0.302130	−	0.953267i	$-0.597698\pi$
$383$	−11.8256	−0.604260	−0.302130	+	0.953267i	$0.597698\pi$
$384$	−0.977360	−0.0498757
$385$	−4.46235	−0.227423
$386$	−5.17560	−0.263431
$387$	11.2596	0.572356
$388$	1.60299	0.0813793
$389$	24.4588	1.24011	0.620055	−	0.784558i	$-0.287110\pi$
$389$	24.4588	1.24011	0.620055	+	0.784558i	$0.287110\pi$
$390$	−1.49472	−0.0756879
$391$	3.38956	0.171417
$392$	5.81701	0.293803
$393$	−0.977360	−0.0493013
$394$	13.4412	0.677159
$395$	3.51694	0.176956
$396$	−6.24846	−0.313997
$397$	−15.7383	−0.789883	−0.394941	−	0.918706i	$-0.629235\pi$
$397$	−15.7383	−0.789883	−0.394941	+	0.918706i	$0.629235\pi$
$398$	−8.30474	−0.416279
$399$	−2.15078	−0.107674
$400$	−3.19745	−0.159872
$401$	14.1335	0.705792	0.352896	−	0.935663i	$-0.385197\pi$
$401$	14.1335	0.705792	0.352896	+	0.935663i	$0.385197\pi$
$402$	9.58057	0.477836
$403$	1.16826	0.0581952
$404$	−12.4278	−0.618308
$405$	1.76601	0.0877535
$406$	2.00592	0.0995519
$407$	−8.00009	−0.396550
$408$	3.31282	0.164009
$409$	9.11375	0.450646	0.225323	−	0.974284i	$-0.427656\pi$
$409$	9.11375	0.450646	0.225323	+	0.974284i	$0.427656\pi$
$410$	9.67396	0.477763
$411$	12.8964	0.636131
$412$	6.16490	0.303723
$413$	−5.76287	−0.283572
$414$	−2.04477	−0.100495
$415$	12.2645	0.602042
$416$	−1.13909	−0.0558487
$417$	−12.4792	−0.611111
$418$	−6.18273	−0.302407
$419$	−16.6027	−0.811093	−0.405547	−	0.914074i	$-0.632919\pi$
$419$	−16.6027	−0.811093	−0.405547	+	0.914074i	$0.632919\pi$
$420$	−1.42721	−0.0696409
$421$	26.7918	1.30575	0.652877	−	0.757464i	$-0.273562\pi$
$421$	26.7918	1.30575	0.652877	+	0.757464i	$0.273562\pi$
$422$	−0.899204	−0.0437726
$423$	−11.3847	−0.553541
$424$	13.2665	0.644276
$425$	10.8379	0.525717
$426$	7.75356	0.375661
$427$	−4.36299	−0.211140
$428$	11.9928	0.579695
$429$	3.40208	0.164254
$430$	7.39302	0.356523
$431$	−2.77242	−0.133543	−0.0667713	−	0.997768i	$-0.521270\pi$
$431$	−2.77242	−0.133543	−0.0667713	+	0.997768i	$0.521270\pi$
$432$	−4.93056	−0.237221
$433$	−25.1108	−1.20675	−0.603375	−	0.797458i	$-0.706178\pi$
$433$	−25.1108	−1.20675	−0.603375	+	0.797458i	$0.706178\pi$
$434$	1.11550	0.0535458
$435$	2.42003	0.116032
$436$	2.28864	0.109606
$437$	−2.02326	−0.0967855
$438$	−3.71970	−0.177734
$439$	−24.2836	−1.15899	−0.579495	−	0.814975i	$-0.696750\pi$
$439$	−24.2836	−1.15899	−0.579495	+	0.814975i	$0.696750\pi$
$440$	−4.10273	−0.195590
$441$	11.8944	0.566401
$442$	3.86103	0.183650
$443$	−5.83354	−0.277160	−0.138580	−	0.990351i	$-0.544254\pi$
$443$	−5.83354	−0.277160	−0.138580	+	0.990351i	$0.544254\pi$
$444$	−2.55871	−0.121431
$445$	−11.3784	−0.539390
$446$	0.869638	0.0411786
$447$	−0.798460	−0.0377658
$448$	−1.08765	−0.0513868
$449$	8.73062	0.412024	0.206012	−	0.978550i	$-0.433951\pi$
$449$	8.73062	0.412024	0.206012	+	0.978550i	$0.433951\pi$
$450$	−6.53804	−0.308206
$451$	−22.0186	−1.03682
$452$	4.66948	0.219634
$453$	−9.01986	−0.423790
$454$	−17.7853	−0.834707
$455$	−1.66339	−0.0779810
$456$	−1.97745	−0.0926026
$457$	6.33039	0.296123	0.148062	−	0.988978i	$-0.452697\pi$
$457$	6.33039	0.296123	0.148062	+	0.988978i	$0.452697\pi$
$458$	22.8703	1.06866
$459$	16.7124	0.780068
$460$	−1.34259	−0.0625987
$461$	25.3714	1.18166	0.590831	−	0.806795i	$-0.298800\pi$
$461$	25.3714	1.18166	0.590831	+	0.806795i	$0.298800\pi$
$462$	3.24844	0.151131
$463$	16.1769	0.751805	0.375903	−	0.926659i	$-0.377333\pi$
$463$	16.1769	0.751805	0.375903	+	0.926659i	$0.377333\pi$
$464$	1.84426	0.0856176
$465$	1.34579	0.0624097
$466$	−13.2246	−0.612620
$467$	17.8833	0.827541	0.413771	−	0.910381i	$-0.364212\pi$
$467$	17.8833	0.827541	0.413771	+	0.910381i	$0.364212\pi$
$468$	−2.32918	−0.107667
$469$	10.6617	0.492313
$470$	−7.47515	−0.344803
$471$	5.56801	0.256560
$472$	−5.29844	−0.243881
$473$	−16.8270	−0.773707
$474$	−2.56021	−0.117594
$475$	−6.46926	−0.296830
$476$	3.68667	0.168978
$477$	27.1268	1.24205
$478$	11.0212	0.504098
$479$	−4.95166	−0.226247	−0.113124	−	0.993581i	$-0.536086\pi$
$479$	−4.95166	−0.226247	−0.113124	+	0.993581i	$0.536086\pi$
$480$	−1.31220	−0.0598933
$481$	−2.98212	−0.135973
$482$	23.1444	1.05420
$483$	1.06303	0.0483695
$484$	−1.66189	−0.0755405
$485$	2.15215	0.0977243
$486$	−16.0773	−0.729279
$487$	11.5578	0.523734	0.261867	−	0.965104i	$-0.415662\pi$
$487$	11.5578	0.523734	0.261867	+	0.965104i	$0.415662\pi$
$488$	−4.01137	−0.181586
$489$	17.4090	0.787262
$490$	7.80987	0.352814
$491$	−28.3671	−1.28019	−0.640096	−	0.768295i	$-0.721105\pi$
$491$	−28.3671	−1.28019	−0.640096	+	0.768295i	$0.721105\pi$
$492$	−7.04231	−0.317492
$493$	−6.25122	−0.281541
$494$	−2.30468	−0.103692
$495$	−8.38913	−0.377064
$496$	1.02560	0.0460510
$497$	8.62854	0.387043
$498$	−8.92815	−0.400080
$499$	−4.72561	−0.211547	−0.105774	−	0.994390i	$-0.533732\pi$
$499$	−4.72561	−0.211547	−0.105774	+	0.994390i	$0.533732\pi$
$500$	−11.0058	−0.492195
$501$	−21.4457	−0.958122
$502$	17.8805	0.798045
$503$	−39.8092	−1.77501	−0.887503	−	0.460802i	$-0.847562\pi$
$503$	−39.8092	−1.77501	−0.887503	+	0.460802i	$0.847562\pi$
$504$	−2.22400	−0.0990648
$505$	−16.6855	−0.742496
$506$	3.05583	0.135848
$507$	−11.4375	−0.507958
$508$	−4.36870	−0.193830
$509$	5.86870	0.260126	0.130063	−	0.991506i	$-0.458482\pi$
$509$	5.86870	0.260126	0.130063	+	0.991506i	$0.458482\pi$
$510$	4.44776	0.196950
$511$	−4.13946	−0.183119
$512$	−1.00000	−0.0441942
$513$	−9.97577	−0.440441
$514$	−10.8135	−0.476965
$515$	8.27694	0.364726
$516$	−5.38186	−0.236923
$517$	17.0140	0.748273
$518$	−2.84745	−0.125110
$519$	10.5995	0.465267
$520$	−1.52934	−0.0670660
$521$	−2.89066	−0.126642	−0.0633211	−	0.997993i	$-0.520169\pi$
$521$	−2.89066	−0.126642	−0.0633211	+	0.997993i	$0.520169\pi$
$522$	3.77108	0.165056
$523$	−17.9706	−0.785800	−0.392900	−	0.919581i	$-0.628528\pi$
$523$	−17.9706	−0.785800	−0.392900	+	0.919581i	$0.628528\pi$
$524$	−1.00000	−0.0436852
$525$	3.39898	0.148344
$526$	24.8936	1.08541
$527$	−3.47635	−0.151432
$528$	2.98665	0.129977
$529$	1.00000	0.0434783
$530$	17.8114	0.773679
$531$	−10.8341	−0.470159
$532$	−2.20060	−0.0954082
$533$	−8.20768	−0.355514
$534$	8.28311	0.358445
$535$	16.1015	0.696127
$536$	9.80250	0.423403
$537$	−12.1070	−0.522456
$538$	−17.4400	−0.751892
$539$	−17.7758	−0.765658
$540$	−6.61972	−0.284867
$541$	−29.9398	−1.28721	−0.643606	−	0.765357i	$-0.722563\pi$
$541$	−29.9398	−1.28721	−0.643606	+	0.765357i	$0.722563\pi$
$542$	−9.07271	−0.389706
$543$	−17.8934	−0.767881
$544$	3.38956	0.145326
$545$	3.07271	0.131620
$546$	1.21089	0.0518214
$547$	−16.4989	−0.705440	−0.352720	−	0.935729i	$-0.614743\pi$
$547$	−16.4989	−0.705440	−0.352720	+	0.935729i	$0.614743\pi$
$548$	13.1951	0.563667
$549$	−8.20232	−0.350067
$550$	9.77086	0.416631
$551$	3.73141	0.158963
$552$	0.977360	0.0415992
$553$	−2.84912	−0.121157
$554$	1.94904	0.0828068
$555$	−3.43530	−0.145820
$556$	−12.7683	−0.541497
$557$	17.3769	0.736284	0.368142	−	0.929770i	$-0.379994\pi$
$557$	17.3769	0.736284	0.368142	+	0.929770i	$0.379994\pi$
$558$	2.09712	0.0887782
$559$	−6.27246	−0.265297
$560$	−1.46027	−0.0617079
$561$	−10.1234	−0.427411
$562$	−4.47670	−0.188838
$563$	9.87953	0.416372	0.208186	−	0.978089i	$-0.433244\pi$
$563$	9.87953	0.416372	0.208186	+	0.978089i	$0.433244\pi$
$564$	5.44165	0.229135
$565$	6.26920	0.263747
$566$	−27.1025	−1.13920
$567$	−1.43067	−0.0600824
$568$	7.93317	0.332868
$569$	−31.8109	−1.33358	−0.666790	−	0.745245i	$-0.732332\pi$
$569$	−31.8109	−1.33358	−0.666790	+	0.745245i	$0.732332\pi$
$570$	−2.65491	−0.111202
$571$	−37.0210	−1.54928	−0.774639	−	0.632403i	$-0.782069\pi$
$571$	−37.0210	−1.54928	−0.774639	+	0.632403i	$0.782069\pi$
$572$	3.48088	0.145543
$573$	−19.8076	−0.827475
$574$	−7.83702	−0.327111
$575$	3.19745	0.133343
$576$	−2.04477	−0.0851986
$577$	−40.0244	−1.66624	−0.833118	−	0.553095i	$-0.813447\pi$
$577$	−40.0244	−1.66624	−0.833118	+	0.553095i	$0.813447\pi$
$578$	5.51089	0.229223
$579$	5.05843	0.210221
$580$	2.47609	0.102814
$581$	−9.93568	−0.412201
$582$	−1.56669	−0.0649416
$583$	−40.5400	−1.67900
$584$	−3.80586	−0.157488
$585$	−3.12714	−0.129291
$586$	33.4634	1.38236
$587$	14.2726	0.589093	0.294546	−	0.955637i	$-0.404831\pi$
$587$	14.2726	0.589093	0.294546	+	0.955637i	$0.404831\pi$
$588$	−5.68531	−0.234458
$589$	2.07506	0.0855014
$590$	−7.11364	−0.292864
$591$	−13.1369	−0.540381
$592$	−2.61798	−0.107598
$593$	−23.4674	−0.963691	−0.481846	−	0.876256i	$-0.660033\pi$
$593$	−23.4674	−0.963691	−0.481846	+	0.876256i	$0.660033\pi$
$594$	15.0669	0.618204
$595$	4.94969	0.202917
$596$	−0.816955	−0.0334638
$597$	8.11672	0.332195
$598$	1.13909	0.0465811
$599$	−34.7621	−1.42034	−0.710170	−	0.704030i	$-0.751382\pi$
$599$	−34.7621	−1.42034	−0.710170	+	0.704030i	$0.751382\pi$
$600$	3.12506	0.127580
$601$	−30.2985	−1.23590	−0.617952	−	0.786216i	$-0.712037\pi$
$601$	−30.2985	−1.23590	−0.617952	+	0.786216i	$0.712037\pi$
$602$	−5.98919	−0.244101
$603$	20.0438	0.816248
$604$	−9.22880	−0.375514
$605$	−2.23124	−0.0907129
$606$	12.1465	0.493417
$607$	−29.5440	−1.19915	−0.599576	−	0.800318i	$-0.704664\pi$
$607$	−29.5440	−1.19915	−0.599576	+	0.800318i	$0.704664\pi$
$608$	−2.02326	−0.0820539
$609$	−1.96050	−0.0794436
$610$	−5.38564	−0.218058
$611$	6.34214	0.256576
$612$	6.93086	0.280163
$613$	46.0877	1.86146	0.930732	−	0.365701i	$-0.119171\pi$
$613$	46.0877	1.86146	0.930732	+	0.365701i	$0.119171\pi$
$614$	−13.4270	−0.541868
$615$	−9.45494	−0.381260
$616$	3.32369	0.133915
$617$	27.7635	1.11772	0.558859	−	0.829263i	$-0.311239\pi$
$617$	27.7635	1.11772	0.558859	+	0.829263i	$0.311239\pi$
$618$	−6.02533	−0.242374
$619$	19.0086	0.764019	0.382009	−	0.924158i	$-0.375232\pi$
$619$	19.0086	0.764019	0.382009	+	0.924158i	$0.375232\pi$
$620$	1.37697	0.0553004
$621$	4.93056	0.197856
$622$	−7.13048	−0.285906
$623$	9.21785	0.369305
$624$	1.11331	0.0445679
$625$	1.21091	0.0484365
$626$	28.0091	1.11947
$627$	6.04276	0.241324
$628$	5.69698	0.227334
$629$	8.87378	0.353821
$630$	−2.98592	−0.118962
$631$	23.3994	0.931517	0.465759	−	0.884912i	$-0.345782\pi$
$631$	23.3994	0.931517	0.465759	+	0.884912i	$0.345782\pi$
$632$	−2.61951	−0.104199
$633$	0.878847	0.0349310
$634$	−28.0041	−1.11218
$635$	−5.86538	−0.232760
$636$	−12.9661	−0.514139
$637$	−6.62613	−0.262537
$638$	−5.63575	−0.223121
$639$	16.2215	0.641712
$640$	−1.34259	−0.0530706
$641$	−21.0647	−0.832007	−0.416003	−	0.909363i	$-0.636570\pi$
$641$	−21.0647	−0.832007	−0.416003	+	0.909363i	$0.636570\pi$
$642$	−11.7213	−0.462603
$643$	2.19744	0.0866585	0.0433293	−	0.999061i	$-0.486204\pi$
$643$	2.19744	0.0866585	0.0433293	+	0.999061i	$0.486204\pi$
$644$	1.08765	0.0428596
$645$	−7.22564	−0.284509
$646$	6.85794	0.269822
$647$	43.5428	1.71185	0.855923	−	0.517104i	$-0.172990\pi$
$647$	43.5428	1.71185	0.855923	+	0.517104i	$0.172990\pi$
$648$	−1.31537	−0.0516727
$649$	16.1912	0.635558
$650$	3.64220	0.142859
$651$	−1.09025	−0.0427302
$652$	17.8122	0.697581
$653$	−29.4533	−1.15260	−0.576299	−	0.817239i	$-0.695504\pi$
$653$	−29.4533	−1.15260	−0.576299	+	0.817239i	$0.695504\pi$
$654$	−2.23683	−0.0874668
$655$	−1.34259	−0.0524594
$656$	−7.20544	−0.281325
$657$	−7.78210	−0.303608
$658$	6.05573	0.236077
$659$	−6.60498	−0.257294	−0.128647	−	0.991690i	$-0.541063\pi$
$659$	−6.60498	−0.257294	−0.128647	+	0.991690i	$0.541063\pi$
$660$	4.00985	0.156083
$661$	−13.4755	−0.524135	−0.262068	−	0.965050i	$-0.584404\pi$
$661$	−13.4755	−0.524135	−0.262068	+	0.965050i	$0.584404\pi$
$662$	10.3894	0.403797
$663$	−3.77362	−0.146555
$664$	−9.13497	−0.354505
$665$	−2.95451	−0.114571
$666$	−5.35315	−0.207430
$667$	−1.84426	−0.0714100
$668$	−21.9424	−0.848979
$669$	−0.849950	−0.0328610
$670$	13.1608	0.508444
$671$	12.2581	0.473218
$672$	1.06303	0.0410073
$673$	17.3540	0.668947	0.334473	−	0.942405i	$-0.391442\pi$
$673$	17.3540	0.668947	0.334473	+	0.942405i	$0.391442\pi$
$674$	7.84056	0.302007
$675$	15.7652	0.606803
$676$	−11.7025	−0.450095
$677$	−23.7168	−0.911512	−0.455756	−	0.890105i	$-0.650631\pi$
$677$	−23.7168	−0.911512	−0.455756	+	0.890105i	$0.650631\pi$
$678$	−4.56376	−0.175270
$679$	−1.74349	−0.0669091
$680$	4.55079	0.174515
$681$	17.3827	0.666106
$682$	−3.13407	−0.120010
$683$	29.4933	1.12853	0.564265	−	0.825594i	$-0.309160\pi$
$683$	29.4933	1.12853	0.564265	+	0.825594i	$0.309160\pi$
$684$	−4.13709	−0.158185
$685$	17.7156	0.676880
$686$	−13.9405	−0.532250
$687$	−22.3525	−0.852803
$688$	−5.50653	−0.209934
$689$	−15.1117	−0.575712
$690$	1.31220	0.0499544
$691$	−28.8651	−1.09808	−0.549040	−	0.835796i	$-0.685007\pi$
$691$	−28.8651	−1.09808	−0.549040	+	0.835796i	$0.685007\pi$
$692$	10.8450	0.412266
$693$	6.79616	0.258165
$694$	9.70702	0.368474
$695$	−17.1426	−0.650257
$696$	−1.80251	−0.0683238
$697$	24.4233	0.925097
$698$	−0.644751	−0.0244042
$699$	12.9252	0.488877
$700$	3.47772	0.131445
$701$	31.4782	1.18891	0.594457	−	0.804128i	$-0.297367\pi$
$701$	31.4782	1.18891	0.594457	+	0.804128i	$0.297367\pi$
$702$	5.61637	0.211976
$703$	−5.29683	−0.199774
$704$	3.05583	0.115171
$705$	7.30591	0.275157
$706$	−21.2459	−0.799600
$707$	13.5172	0.508366
$708$	5.17849	0.194620
$709$	36.2435	1.36115	0.680577	−	0.732676i	$-0.261729\pi$
$709$	36.2435	1.36115	0.680577	+	0.732676i	$0.261729\pi$
$710$	10.6510	0.399725
$711$	−5.35629	−0.200877
$712$	8.47498	0.317613
$713$	−1.02560	−0.0384092
$714$	−3.60320	−0.134846
$715$	4.67340	0.174775
$716$	−12.3874	−0.462941
$717$	−10.7717	−0.402276
$718$	−28.1546	−1.05072
$719$	−44.1278	−1.64569	−0.822845	−	0.568266i	$-0.807615\pi$
$719$	−44.1278	−1.64569	−0.822845	+	0.568266i	$0.807615\pi$
$720$	−2.74529	−0.102311
$721$	−6.70528	−0.249717
$722$	14.9064	0.554760
$723$	−22.6204	−0.841263
$724$	−18.3079	−0.680409
$725$	−5.89692	−0.219006
$726$	1.62427	0.0602822
$727$	3.23433	0.119954	0.0599772	−	0.998200i	$-0.480897\pi$
$727$	3.23433	0.119954	0.0599772	+	0.998200i	$0.480897\pi$
$728$	1.23894	0.0459182
$729$	11.7672	0.435821
$730$	−5.10972	−0.189119
$731$	18.6647	0.690339
$732$	3.92056	0.144908
$733$	−27.7708	−1.02574	−0.512869	−	0.858467i	$-0.671417\pi$
$733$	−27.7708	−1.02574	−0.512869	+	0.858467i	$0.671417\pi$
$734$	30.4735	1.12480
$735$	−7.63305	−0.281549
$736$	1.00000	0.0368605
$737$	−29.9548	−1.10340
$738$	−14.7334	−0.542345
$739$	0.113971	0.00419249	0.00209625	−	0.999998i	$-0.499333\pi$
$739$	0.113971	0.00419249	0.00209625	+	0.999998i	$0.499333\pi$
$740$	−3.51487	−0.129209
$741$	2.25250	0.0827478
$742$	−14.4293	−0.529717
$743$	10.6334	0.390100	0.195050	−	0.980793i	$-0.437513\pi$
$743$	10.6334	0.390100	0.195050	+	0.980793i	$0.437513\pi$
$744$	−1.00239	−0.0367492
$745$	−1.09684	−0.0401850
$746$	−11.0261	−0.403693
$747$	−18.6789	−0.683424
$748$	−10.3579	−0.378723
$749$	−13.0440	−0.476619
$750$	10.7567	0.392778
$751$	4.01884	0.146650	0.0733248	−	0.997308i	$-0.476639\pi$
$751$	4.01884	0.146650	0.0733248	+	0.997308i	$0.476639\pi$
$752$	5.56770	0.203033
$753$	−17.4757	−0.636849
$754$	−2.10079	−0.0765061
$755$	−12.3905	−0.450937
$756$	5.36274	0.195041
$757$	33.1181	1.20370	0.601849	−	0.798610i	$-0.294431\pi$
$757$	33.1181	1.20370	0.601849	+	0.798610i	$0.294431\pi$
$758$	−33.8550	−1.22967
$759$	−2.98665	−0.108408
$760$	−2.71641	−0.0985344
$761$	−5.72492	−0.207528	−0.103764	−	0.994602i	$-0.533089\pi$
$761$	−5.72492	−0.207528	−0.103764	+	0.994602i	$0.533089\pi$
$762$	4.26979	0.154678
$763$	−2.48925	−0.0901168
$764$	−20.2664	−0.733214
$765$	9.30531	0.336434
$766$	11.8256	0.427276
$767$	6.03543	0.217927
$768$	0.977360	0.0352675
$769$	−22.9595	−0.827940	−0.413970	−	0.910291i	$-0.635858\pi$
$769$	−22.9595	−0.827940	−0.413970	+	0.910291i	$0.635858\pi$
$770$	4.46235	0.160812
$771$	10.5687	0.380624
$772$	5.17560	0.186274
$773$	16.9375	0.609201	0.304600	−	0.952480i	$-0.401477\pi$
$773$	16.9375	0.609201	0.304600	+	0.952480i	$0.401477\pi$
$774$	−11.2596	−0.404717
$775$	−3.27932	−0.117797
$776$	−1.60299	−0.0575438
$777$	2.78299	0.0998391
$778$	−24.4588	−0.876890
$779$	−14.5784	−0.522327
$780$	1.49472	0.0535194
$781$	−24.2424	−0.867462
$782$	−3.38956	−0.121210
$783$	−9.09322	−0.324965
$784$	−5.81701	−0.207750
$785$	7.64872	0.272995
$786$	0.977360	0.0348613
$787$	11.3264	0.403744	0.201872	−	0.979412i	$-0.435298\pi$
$787$	11.3264	0.403744	0.201872	+	0.979412i	$0.435298\pi$
$788$	−13.4412	−0.478824
$789$	−24.3300	−0.866171
$790$	−3.51694	−0.125127
$791$	−5.07877	−0.180580
$792$	6.24846	0.222029
$793$	4.56934	0.162262
$794$	15.7383	0.558532
$795$	−17.4082	−0.617405
$796$	8.30474	0.294354
$797$	17.3872	0.615887	0.307944	−	0.951405i	$-0.400359\pi$
$797$	17.3872	0.615887	0.307944	+	0.951405i	$0.400359\pi$
$798$	2.15078	0.0761368
$799$	−18.8721	−0.667645
$800$	3.19745	0.113047
$801$	17.3294	0.612303
$802$	−14.1335	−0.499070
$803$	11.6301	0.410416
$804$	−9.58057	−0.337881
$805$	1.46027	0.0514679
$806$	−1.16826	−0.0411502
$807$	17.0452	0.600018
$808$	12.4278	0.437210
$809$	−26.4030	−0.928279	−0.464140	−	0.885762i	$-0.653636\pi$
$809$	−26.4030	−0.928279	−0.464140	+	0.885762i	$0.653636\pi$
$810$	−1.76601	−0.0620511
$811$	−9.18322	−0.322467	−0.161233	−	0.986916i	$-0.551547\pi$
$811$	−9.18322	−0.322467	−0.161233	+	0.986916i	$0.551547\pi$
$812$	−2.00592	−0.0703938
$813$	8.86731	0.310990
$814$	8.00009	0.280403
$815$	23.9146	0.837691
$816$	−3.31282	−0.115972
$817$	−11.1411	−0.389778
$818$	−9.11375	−0.318655
$819$	2.53335	0.0885222
$820$	−9.67396	−0.337829
$821$	56.1117	1.95831	0.979157	−	0.203106i	$-0.0651036\pi$
$821$	56.1117	1.95831	0.979157	+	0.203106i	$0.0651036\pi$
$822$	−12.8964	−0.449813
$823$	−37.7029	−1.31424	−0.657121	−	0.753785i	$-0.728226\pi$
$823$	−37.7029	−1.31424	−0.657121	+	0.753785i	$0.728226\pi$
$824$	−6.16490	−0.214764
$825$	−9.54965	−0.332476
$826$	5.76287	0.200516
$827$	−4.73970	−0.164815	−0.0824077	−	0.996599i	$-0.526261\pi$
$827$	−4.73970	−0.164815	−0.0824077	+	0.996599i	$0.526261\pi$
$828$	2.04477	0.0710606
$829$	14.1949	0.493009	0.246505	−	0.969142i	$-0.420718\pi$
$829$	14.1949	0.493009	0.246505	+	0.969142i	$0.420718\pi$
$830$	−12.2645	−0.425708
$831$	−1.90491	−0.0660808
$832$	1.13909	0.0394910
$833$	19.7171	0.683157
$834$	12.4792	0.432121
$835$	−29.4597	−1.01950
$836$	6.18273	0.213834
$837$	−5.05680	−0.174789
$838$	16.6027	0.573529
$839$	28.7673	0.993158	0.496579	−	0.867991i	$-0.334589\pi$
$839$	28.7673	0.993158	0.496579	+	0.867991i	$0.334589\pi$
$840$	1.42721	0.0492436
$841$	−25.5987	−0.882714
$842$	−26.7918	−0.923308
$843$	4.37535	0.150695
$844$	0.899204	0.0309519
$845$	−15.7116	−0.540496
$846$	11.3847	0.391412
$847$	1.80756	0.0621086
$848$	−13.2665	−0.455572
$849$	26.4889	0.909096
$850$	−10.8379	−0.371738
$851$	2.61798	0.0897430
$852$	−7.75356	−0.265633
$853$	−19.0966	−0.653855	−0.326927	−	0.945049i	$-0.606013\pi$
$853$	−19.0966	−0.653855	−0.326927	+	0.945049i	$0.606013\pi$
$854$	4.36299	0.149298
$855$	−5.55442	−0.189957
$856$	−11.9928	−0.409906
$857$	12.3672	0.422456	0.211228	−	0.977437i	$-0.432254\pi$
$857$	12.3672	0.422456	0.211228	+	0.977437i	$0.432254\pi$
$858$	−3.40208	−0.116145
$859$	−1.71691	−0.0585801	−0.0292900	−	0.999571i	$-0.509325\pi$
$859$	−1.71691	−0.0585801	−0.0292900	+	0.999571i	$0.509325\pi$
$860$	−7.39302	−0.252100
$861$	7.65959	0.261038
$862$	2.77242	0.0944289
$863$	−11.7362	−0.399503	−0.199752	−	0.979847i	$-0.564014\pi$
$863$	−11.7362	−0.399503	−0.199752	+	0.979847i	$0.564014\pi$
$864$	4.93056	0.167741
$865$	14.5605	0.495070
$866$	25.1108	0.853301
$867$	−5.38613	−0.182922
$868$	−1.11550	−0.0378626
$869$	8.00479	0.271544
$870$	−2.42003	−0.0820467
$871$	−11.1660	−0.378345
$872$	−2.28864	−0.0775031
$873$	−3.27773	−0.110934
$874$	2.02326	0.0684377
$875$	11.9705	0.404678
$876$	3.71970	0.125677
$877$	30.4781	1.02917	0.514586	−	0.857439i	$-0.327946\pi$
$877$	30.4781	1.02917	0.514586	+	0.857439i	$0.327946\pi$
$878$	24.2836	0.819530
$879$	−32.7058	−1.10314
$880$	4.10273	0.138303
$881$	−11.7812	−0.396919	−0.198460	−	0.980109i	$-0.563594\pi$
$881$	−11.7812	−0.396919	−0.198460	+	0.980109i	$0.563594\pi$
$882$	−11.8944	−0.400506
$883$	10.2471	0.344841	0.172421	−	0.985023i	$-0.444841\pi$
$883$	10.2471	0.344841	0.172421	+	0.985023i	$0.444841\pi$
$884$	−3.86103	−0.129860
$885$	6.95259	0.233709
$886$	5.83354	0.195982
$887$	22.6551	0.760683	0.380342	−	0.924846i	$-0.375806\pi$
$887$	22.6551	0.760683	0.380342	+	0.924846i	$0.375806\pi$
$888$	2.55871	0.0858645
$889$	4.75163	0.159365
$890$	11.3784	0.381406
$891$	4.01955	0.134660
$892$	−0.869638	−0.0291176
$893$	11.2649	0.376965
$894$	0.798460	0.0267045
$895$	−16.6313	−0.555922
$896$	1.08765	0.0363360
$897$	−1.11331	−0.0371722
$898$	−8.73062	−0.291345
$899$	1.89148	0.0630844
$900$	6.53804	0.217935
$901$	44.9674	1.49808
$902$	22.0186	0.733139
$903$	5.85360	0.194796
$904$	−4.66948	−0.155305
$905$	−24.5801	−0.817069
$906$	9.01986	0.299665
$907$	12.5588	0.417007	0.208503	−	0.978022i	$-0.433141\pi$
$907$	12.5588	0.417007	0.208503	+	0.978022i	$0.433141\pi$
$908$	17.7853	0.590227
$909$	25.4120	0.842864
$910$	1.66339	0.0551409
$911$	−16.1396	−0.534729	−0.267365	−	0.963595i	$-0.586153\pi$
$911$	−16.1396	−0.534729	−0.267365	+	0.963595i	$0.586153\pi$
$912$	1.97745	0.0654799
$913$	27.9149	0.923849
$914$	−6.33039	−0.209391
$915$	5.26371	0.174013
$916$	−22.8703	−0.755657
$917$	1.08765	0.0359175
$918$	−16.7124	−0.551592
$919$	−22.2275	−0.733218	−0.366609	−	0.930375i	$-0.619481\pi$
$919$	−22.2275	−0.733218	−0.366609	+	0.930375i	$0.619481\pi$
$920$	1.34259	0.0442639
$921$	13.1230	0.432417
$922$	−25.3714	−0.835562
$923$	−9.03663	−0.297444
$924$	−3.24844	−0.106866
$925$	8.37084	0.275232
$926$	−16.1769	−0.531607
$927$	−12.6058	−0.414028
$928$	−1.84426	−0.0605408
$929$	47.1627	1.54736	0.773680	−	0.633577i	$-0.218414\pi$
$929$	47.1627	1.54736	0.773680	+	0.633577i	$0.218414\pi$
$930$	−1.34579	−0.0441303
$931$	−11.7693	−0.385723
$932$	13.2246	0.433187
$933$	6.96905	0.228156
$934$	−17.8833	−0.585160
$935$	−13.9065	−0.454790
$936$	2.32918	0.0761317
$937$	−14.2267	−0.464767	−0.232384	−	0.972624i	$-0.574652\pi$
$937$	−14.2267	−0.464767	−0.232384	+	0.972624i	$0.574652\pi$
$938$	−10.6617	−0.348118
$939$	−27.3750	−0.893350
$940$	7.47515	0.243812
$941$	21.7894	0.710315	0.355157	−	0.934807i	$-0.384427\pi$
$941$	21.7894	0.710315	0.355157	+	0.934807i	$0.384427\pi$
$942$	−5.56801	−0.181415
$943$	7.20544	0.234641
$944$	5.29844	0.172450
$945$	7.19996	0.234215
$946$	16.8270	0.547094
$947$	18.1897	0.591084	0.295542	−	0.955330i	$-0.404500\pi$
$947$	18.1897	0.591084	0.295542	+	0.955330i	$0.404500\pi$
$948$	2.56021	0.0831517
$949$	4.33524	0.140728
$950$	6.46926	0.209890
$951$	27.3701	0.887536
$952$	−3.68667	−0.119486
$953$	25.6055	0.829444	0.414722	−	0.909948i	$-0.363879\pi$
$953$	25.6055	0.829444	0.414722	+	0.909948i	$0.363879\pi$
$954$	−27.1268	−0.878263
$955$	−27.2095	−0.880480
$956$	−11.0212	−0.356451
$957$	5.50815	0.178053
$958$	4.95166	0.159981
$959$	−14.3517	−0.463441
$960$	1.31220	0.0423509
$961$	−29.9481	−0.966069
$962$	2.98212	0.0961475
$963$	−24.5225	−0.790228
$964$	−23.1444	−0.745431
$965$	6.94872	0.223687
$966$	−1.06303	−0.0342024
$967$	−15.9968	−0.514423	−0.257211	−	0.966355i	$-0.582804\pi$
$967$	−15.9968	−0.514423	−0.257211	+	0.966355i	$0.582804\pi$
$968$	1.66189	0.0534152
$969$	−6.70268	−0.215321
$970$	−2.15215	−0.0691015
$971$	−3.87290	−0.124287	−0.0621436	−	0.998067i	$-0.519794\pi$
$971$	−3.87290	−0.124287	−0.0621436	+	0.998067i	$0.519794\pi$
$972$	16.0773	0.515678
$973$	13.8875	0.445213
$974$	−11.5578	−0.370336
$975$	−3.55974	−0.114003
$976$	4.01137	0.128401
$977$	37.6902	1.20582	0.602908	−	0.797811i	$-0.294009\pi$
$977$	37.6902	1.20582	0.602908	+	0.797811i	$0.294009\pi$
$978$	−17.4090	−0.556678
$979$	−25.8981	−0.827707
$980$	−7.80987	−0.249477
$981$	−4.67973	−0.149412
$982$	28.3671	0.905232
$983$	−19.8076	−0.631764	−0.315882	−	0.948798i	$-0.602300\pi$
$983$	−19.8076	−0.631764	−0.315882	+	0.948798i	$0.602300\pi$
$984$	7.04231	0.224501
$985$	−18.0461	−0.574996
$986$	6.25122	0.199080
$987$	−5.91863	−0.188392
$988$	2.30468	0.0733217
$989$	5.50653	0.175097
$990$	8.38913	0.266624
$991$	−59.4399	−1.88817	−0.944086	−	0.329700i	$-0.893052\pi$
$991$	−59.4399	−1.88817	−0.944086	+	0.329700i	$0.893052\pi$
$992$	−1.02560	−0.0325630
$993$	−10.1542	−0.322235
$994$	−8.62854	−0.273681
$995$	11.1499	0.353475
$996$	8.92815	0.282899
$997$	−6.06009	−0.191925	−0.0959625	−	0.995385i	$-0.530593\pi$
$997$	−6.06009	−0.191925	−0.0959625	+	0.995385i	$0.530593\pi$
$998$	4.72561	0.149587
$999$	12.9081	0.408393

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	6026.2.a.h.1.15	✓	24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
6026.2.a.h.1.15	✓	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)

\(f(q)\)	\(=\)	\(q-1.00000 q^{2} +0.977360 q^{3} +1.00000 q^{4} +1.34259 q^{5} -0.977360 q^{6} -1.08765 q^{7} -1.00000 q^{8} -2.04477 q^{9} +O(q^{10})\)	\(q-1.00000 q^{2} +0.977360 q^{3} +1.00000 q^{4} +1.34259 q^{5} -0.977360 q^{6} -1.08765 q^{7} -1.00000 q^{8} -2.04477 q^{9} -1.34259 q^{10} +3.05583 q^{11} +0.977360 q^{12} +1.13909 q^{13} +1.08765 q^{14} +1.31220 q^{15} +1.00000 q^{16} -3.38956 q^{17} +2.04477 q^{18} +2.02326 q^{19} +1.34259 q^{20} -1.06303 q^{21} -3.05583 q^{22} -1.00000 q^{23} -0.977360 q^{24} -3.19745 q^{25} -1.13909 q^{26} -4.93056 q^{27} -1.08765 q^{28} +1.84426 q^{29} -1.31220 q^{30} +1.02560 q^{31} -1.00000 q^{32} +2.98665 q^{33} +3.38956 q^{34} -1.46027 q^{35} -2.04477 q^{36} -2.61798 q^{37} -2.02326 q^{38} +1.11331 q^{39} -1.34259 q^{40} -7.20544 q^{41} +1.06303 q^{42} -5.50653 q^{43} +3.05583 q^{44} -2.74529 q^{45} +1.00000 q^{46} +5.56770 q^{47} +0.977360 q^{48} -5.81701 q^{49} +3.19745 q^{50} -3.31282 q^{51} +1.13909 q^{52} -13.2665 q^{53} +4.93056 q^{54} +4.10273 q^{55} +1.08765 q^{56} +1.97745 q^{57} -1.84426 q^{58} +5.29844 q^{59} +1.31220 q^{60} +4.01137 q^{61} -1.02560 q^{62} +2.22400 q^{63} +1.00000 q^{64} +1.52934 q^{65} -2.98665 q^{66} -9.80250 q^{67} -3.38956 q^{68} -0.977360 q^{69} +1.46027 q^{70} -7.93317 q^{71} +2.04477 q^{72} +3.80586 q^{73} +2.61798 q^{74} -3.12506 q^{75} +2.02326 q^{76} -3.32369 q^{77} -1.11331 q^{78} +2.61951 q^{79} +1.34259 q^{80} +1.31537 q^{81} +7.20544 q^{82} +9.13497 q^{83} -1.06303 q^{84} -4.55079 q^{85} +5.50653 q^{86} +1.80251 q^{87} -3.05583 q^{88} -8.47498 q^{89} +2.74529 q^{90} -1.23894 q^{91} -1.00000 q^{92} +1.00239 q^{93} -5.56770 q^{94} +2.71641 q^{95} -0.977360 q^{96} +1.60299 q^{97} +5.81701 q^{98} -6.24846 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q - 24 q^{2} - q^{3} + 24 q^{4} - q^{5} + q^{6} - 7 q^{7} - 24 q^{8} + 27 q^{9}+O(q^{10}) \) 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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