LMFDB - Embedded newform 6026.2.a.i.1.2

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:	$25$
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.2
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)

$f(q)$	$=$	$q-1.00000 q^{2} -2.94469 q^{3} +1.00000 q^{4} -3.10338 q^{5} +2.94469 q^{6} +2.18728 q^{7} -1.00000 q^{8} +5.67118 q^{9} +O(q^{10})$	\(q-1.00000 q^{2} -2.94469 q^{3} +1.00000 q^{4} -3.10338 q^{5} +2.94469 q^{6} +2.18728 q^{7} -1.00000 q^{8} +5.67118 q^{9} +3.10338 q^{10} +3.62591 q^{11} -2.94469 q^{12} +2.36826 q^{13} -2.18728 q^{14} +9.13847 q^{15} +1.00000 q^{16} +2.10389 q^{17} -5.67118 q^{18} -7.83273 q^{19} -3.10338 q^{20} -6.44085 q^{21} -3.62591 q^{22} +1.00000 q^{23} +2.94469 q^{24} +4.63094 q^{25} -2.36826 q^{26} -7.86580 q^{27} +2.18728 q^{28} -6.98856 q^{29} -9.13847 q^{30} +8.62487 q^{31} -1.00000 q^{32} -10.6772 q^{33} -2.10389 q^{34} -6.78794 q^{35} +5.67118 q^{36} -3.55379 q^{37} +7.83273 q^{38} -6.97379 q^{39} +3.10338 q^{40} +8.94001 q^{41} +6.44085 q^{42} -6.48678 q^{43} +3.62591 q^{44} -17.5998 q^{45} -1.00000 q^{46} -5.16620 q^{47} -2.94469 q^{48} -2.21582 q^{49} -4.63094 q^{50} -6.19531 q^{51} +2.36826 q^{52} -0.484015 q^{53} +7.86580 q^{54} -11.2526 q^{55} -2.18728 q^{56} +23.0649 q^{57} +6.98856 q^{58} -2.97827 q^{59} +9.13847 q^{60} -12.4970 q^{61} -8.62487 q^{62} +12.4045 q^{63} +1.00000 q^{64} -7.34961 q^{65} +10.6772 q^{66} +2.65610 q^{67} +2.10389 q^{68} -2.94469 q^{69} +6.78794 q^{70} +11.1030 q^{71} -5.67118 q^{72} +3.40502 q^{73} +3.55379 q^{74} -13.6367 q^{75} -7.83273 q^{76} +7.93088 q^{77} +6.97379 q^{78} -17.7107 q^{79} -3.10338 q^{80} +6.14878 q^{81} -8.94001 q^{82} +12.1133 q^{83} -6.44085 q^{84} -6.52917 q^{85} +6.48678 q^{86} +20.5791 q^{87} -3.62591 q^{88} +10.4427 q^{89} +17.5998 q^{90} +5.18005 q^{91} +1.00000 q^{92} -25.3976 q^{93} +5.16620 q^{94} +24.3079 q^{95} +2.94469 q^{96} -10.9363 q^{97} +2.21582 q^{98} +20.5632 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 25 q - 25 q^{2} - 4 q^{3} + 25 q^{4} - 3 q^{5} + 4 q^{6} - 11 q^{7} - 25 q^{8} + 19 q^{9}+O(q^{10}) $ 25 * q - 25 * q^2 - 4 * q^3 + 25 * q^4 - 3 * q^5 + 4 * q^6 - 11 * q^7 - 25 * q^8 + 19 * q^9	\( 25 q - 25 q^{2} - 4 q^{3} + 25 q^{4} - 3 q^{5} + 4 q^{6} - 11 q^{7} - 25 q^{8} + 19 q^{9} + 3 q^{10} - 12 q^{11} - 4 q^{12} - 6 q^{13} + 11 q^{14} + 25 q^{16} + 8 q^{17} - 19 q^{18} - 23 q^{19} - 3 q^{20} - 16 q^{21} + 12 q^{22} + 25 q^{23} + 4 q^{24} + 4 q^{25} + 6 q^{26} - 13 q^{27} - 11 q^{28} - 7 q^{29} - 7 q^{31} - 25 q^{32} + 3 q^{33} - 8 q^{34} - 18 q^{35} + 19 q^{36} - 7 q^{37} + 23 q^{38} - 2 q^{39} + 3 q^{40} - 10 q^{41} + 16 q^{42} - 26 q^{43} - 12 q^{44} + 20 q^{45} - 25 q^{46} - 2 q^{47} - 4 q^{48} + 2 q^{49} - 4 q^{50} - 28 q^{51} - 6 q^{52} + 47 q^{53} + 13 q^{54} - 38 q^{55} + 11 q^{56} - 4 q^{57} + 7 q^{58} - 19 q^{59} - 26 q^{61} + 7 q^{62} - 15 q^{63} + 25 q^{64} + 13 q^{65} - 3 q^{66} - 34 q^{67} + 8 q^{68} - 4 q^{69} + 18 q^{70} - 10 q^{71} - 19 q^{72} - 22 q^{73} + 7 q^{74} - 8 q^{75} - 23 q^{76} + 28 q^{77} + 2 q^{78} - 21 q^{79} - 3 q^{80} - 27 q^{81} + 10 q^{82} - 16 q^{83} - 16 q^{84} - 42 q^{85} + 26 q^{86} - 17 q^{87} + 12 q^{88} + 27 q^{89} - 20 q^{90} - 26 q^{91} + 25 q^{92} - 27 q^{93} + 2 q^{94} + 4 q^{96} + 4 q^{97} - 2 q^{98} - 2 q^{99}+O(q^{100}) \) 25 * q - 25 * q^2 - 4 * q^3 + 25 * q^4 - 3 * q^5 + 4 * q^6 - 11 * q^7 - 25 * q^8 + 19 * q^9 + 3 * q^10 - 12 * q^11 - 4 * q^12 - 6 * q^13 + 11 * q^14 + 25 * q^16 + 8 * q^17 - 19 * q^18 - 23 * q^19 - 3 * q^20 - 16 * q^21 + 12 * q^22 + 25 * q^23 + 4 * q^24 + 4 * q^25 + 6 * q^26 - 13 * q^27 - 11 * q^28 - 7 * q^29 - 7 * q^31 - 25 * q^32 + 3 * q^33 - 8 * q^34 - 18 * q^35 + 19 * q^36 - 7 * q^37 + 23 * q^38 - 2 * q^39 + 3 * q^40 - 10 * q^41 + 16 * q^42 - 26 * q^43 - 12 * q^44 + 20 * q^45 - 25 * q^46 - 2 * q^47 - 4 * q^48 + 2 * q^49 - 4 * q^50 - 28 * q^51 - 6 * q^52 + 47 * q^53 + 13 * q^54 - 38 * q^55 + 11 * q^56 - 4 * q^57 + 7 * q^58 - 19 * q^59 - 26 * q^61 + 7 * q^62 - 15 * q^63 + 25 * q^64 + 13 * q^65 - 3 * q^66 - 34 * q^67 + 8 * q^68 - 4 * q^69 + 18 * q^70 - 10 * q^71 - 19 * q^72 - 22 * q^73 + 7 * q^74 - 8 * q^75 - 23 * q^76 + 28 * q^77 + 2 * q^78 - 21 * q^79 - 3 * q^80 - 27 * q^81 + 10 * q^82 - 16 * q^83 - 16 * q^84 - 42 * q^85 + 26 * q^86 - 17 * q^87 + 12 * q^88 + 27 * q^89 - 20 * q^90 - 26 * q^91 + 25 * q^92 - 27 * q^93 + 2 * q^94 + 4 * q^96 + 4 * q^97 - 2 * q^98 - 2 * 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
$3$	−2.94469	−1.70012	−0.850058	−	0.526689i	$-0.823433\pi$
$3$	−2.94469	−1.70012	−0.850058	+	0.526689i	$0.823433\pi$
$4$	1.00000	0.500000
$5$	−3.10338	−1.38787	−0.693936	−	0.720037i	$-0.744125\pi$
$5$	−3.10338	−1.38787	−0.693936	+	0.720037i	$0.744125\pi$
$6$	2.94469	1.20216
$7$	2.18728	0.826713	0.413357	−	0.910569i	$-0.364356\pi$
$7$	2.18728	0.826713	0.413357	+	0.910569i	$0.364356\pi$
$8$	−1.00000	−0.353553
$9$	5.67118	1.89039
$10$	3.10338	0.981373
$11$	3.62591	1.09325	0.546627	−	0.837376i	$-0.315912\pi$
$11$	3.62591	1.09325	0.546627	+	0.837376i	$0.315912\pi$
$12$	−2.94469	−0.850058
$13$	2.36826	0.656838	0.328419	−	0.944532i	$-0.393484\pi$
$13$	2.36826	0.656838	0.328419	+	0.944532i	$0.393484\pi$
$14$	−2.18728	−0.584575
$15$	9.13847	2.35954
$16$	1.00000	0.250000
$17$	2.10389	0.510269	0.255135	−	0.966906i	$-0.417880\pi$
$17$	2.10389	0.510269	0.255135	+	0.966906i	$0.417880\pi$
$18$	−5.67118	−1.33671
$19$	−7.83273	−1.79695	−0.898475	−	0.439024i	$-0.855324\pi$
$19$	−7.83273	−1.79695	−0.898475	+	0.439024i	$0.855324\pi$
$20$	−3.10338	−0.693936
$21$	−6.44085	−1.40551
$22$	−3.62591	−0.773047
$23$	1.00000	0.208514
$23$	1.00000	0.208514
$24$	2.94469	0.601082
$25$	4.63094	0.926188
$26$	−2.36826	−0.464454
$27$	−7.86580	−1.51377
$28$	2.18728	0.413357
$29$	−6.98856	−1.29774	−0.648871	−	0.760898i	$-0.724759\pi$
$29$	−6.98856	−1.29774	−0.648871	+	0.760898i	$0.724759\pi$
$30$	−9.13847	−1.66845
$31$	8.62487	1.54907	0.774537	−	0.632529i	$-0.217983\pi$
$31$	8.62487	1.54907	0.774537	+	0.632529i	$0.217983\pi$
$32$	−1.00000	−0.176777
$33$	−10.6772	−1.85866
$34$	−2.10389	−0.360815
$35$	−6.78794	−1.14737
$36$	5.67118	0.945197
$37$	−3.55379	−0.584240	−0.292120	−	0.956382i	$-0.594361\pi$
$37$	−3.55379	−0.584240	−0.292120	+	0.956382i	$0.594361\pi$
$38$	7.83273	1.27064
$39$	−6.97379	−1.11670
$40$	3.10338	0.490687
$41$	8.94001	1.39620	0.698098	−	0.716003i	$-0.254030\pi$
$41$	8.94001	1.39620	0.698098	+	0.716003i	$0.254030\pi$
$42$	6.44085	0.993845
$43$	−6.48678	−0.989225	−0.494612	−	0.869114i	$-0.664690\pi$
$43$	−6.48678	−0.989225	−0.494612	+	0.869114i	$0.664690\pi$
$44$	3.62591	0.546627
$45$	−17.5998	−2.62363
$46$	−1.00000	−0.147442
$47$	−5.16620	−0.753567	−0.376784	−	0.926301i	$-0.622970\pi$
$47$	−5.16620	−0.753567	−0.376784	+	0.926301i	$0.622970\pi$
$48$	−2.94469	−0.425029
$49$	−2.21582	−0.316545
$50$	−4.63094	−0.654913
$51$	−6.19531	−0.867517
$52$	2.36826	0.328419
$53$	−0.484015	−0.0664845	−0.0332423	−	0.999447i	$-0.510583\pi$
$53$	−0.484015	−0.0664845	−0.0332423	+	0.999447i	$0.510583\pi$
$54$	7.86580	1.07040
$55$	−11.2526	−1.51730
$56$	−2.18728	−0.292287
$57$	23.0649	3.05502
$58$	6.98856	0.917643
$59$	−2.97827	−0.387737	−0.193869	−	0.981027i	$-0.562104\pi$
$59$	−2.97827	−0.387737	−0.193869	+	0.981027i	$0.562104\pi$
$60$	9.13847	1.17977
$61$	−12.4970	−1.60008	−0.800042	−	0.599945i	$-0.795189\pi$
$61$	−12.4970	−1.60008	−0.800042	+	0.599945i	$0.795189\pi$
$62$	−8.62487	−1.09536
$63$	12.4045	1.56281
$64$	1.00000	0.125000
$65$	−7.34961	−0.911607
$66$	10.6772	1.31427
$67$	2.65610	0.324494	0.162247	−	0.986750i	$-0.448126\pi$
$67$	2.65610	0.324494	0.162247	+	0.986750i	$0.448126\pi$
$68$	2.10389	0.255135
$69$	−2.94469	−0.354499
$70$	6.78794	0.811314
$71$	11.1030	1.31769	0.658845	−	0.752279i	$-0.271045\pi$
$71$	11.1030	1.31769	0.658845	+	0.752279i	$0.271045\pi$
$72$	−5.67118	−0.668356
$73$	3.40502	0.398527	0.199264	−	0.979946i	$-0.436145\pi$
$73$	3.40502	0.398527	0.199264	+	0.979946i	$0.436145\pi$
$74$	3.55379	0.413120
$75$	−13.6367	−1.57463
$76$	−7.83273	−0.898475
$77$	7.93088	0.903808
$78$	6.97379	0.789627
$79$	−17.7107	−1.99261	−0.996303	−	0.0859104i	$-0.972620\pi$
$79$	−17.7107	−1.99261	−0.996303	+	0.0859104i	$0.972620\pi$
$80$	−3.10338	−0.346968
$81$	6.14878	0.683198
$82$	−8.94001	−0.987259
$83$	12.1133	1.32961	0.664805	−	0.747017i	$-0.268515\pi$
$83$	12.1133	1.32961	0.664805	+	0.747017i	$0.268515\pi$
$84$	−6.44085	−0.702754
$85$	−6.52917	−0.708188
$86$	6.48678	0.699487
$87$	20.5791	2.20631
$88$	−3.62591	−0.386524
$89$	10.4427	1.10692	0.553461	−	0.832875i	$-0.313307\pi$
$89$	10.4427	1.10692	0.553461	+	0.832875i	$0.313307\pi$
$90$	17.5998	1.85518
$91$	5.18005	0.543017
$92$	1.00000	0.104257
$93$	−25.3976	−2.63360
$94$	5.16620	0.532853
$95$	24.3079	2.49394
$96$	2.94469	0.300541
$97$	−10.9363	−1.11042	−0.555208	−	0.831712i	$-0.687361\pi$
$97$	−10.9363	−1.11042	−0.555208	+	0.831712i	$0.687361\pi$
$98$	2.21582	0.223831
$99$	20.5632	2.06668
$100$	4.63094	0.463094
$101$	2.37124	0.235947	0.117973	−	0.993017i	$-0.462360\pi$
$101$	2.37124	0.235947	0.117973	+	0.993017i	$0.462360\pi$
$102$	6.19531	0.613427
$103$	5.46826	0.538803	0.269402	−	0.963028i	$-0.413174\pi$
$103$	5.46826	0.538803	0.269402	+	0.963028i	$0.413174\pi$
$104$	−2.36826	−0.232227
$105$	19.9884	1.95067
$106$	0.484015	0.0470117
$107$	−10.6025	−1.02498	−0.512490	−	0.858693i	$-0.671277\pi$
$107$	−10.6025	−1.02498	−0.512490	+	0.858693i	$0.671277\pi$
$108$	−7.86580	−0.756887
$109$	−8.89287	−0.851783	−0.425891	−	0.904774i	$-0.640039\pi$
$109$	−8.89287	−0.851783	−0.425891	+	0.904774i	$0.640039\pi$
$110$	11.2526	1.07289
$111$	10.4648	0.993276
$112$	2.18728	0.206678
$113$	17.5993	1.65560	0.827800	−	0.561024i	$-0.189592\pi$
$113$	17.5993	1.65560	0.827800	+	0.561024i	$0.189592\pi$
$114$	−23.0649	−2.16023
$115$	−3.10338	−0.289391
$116$	−6.98856	−0.648871
$117$	13.4309	1.24168
$118$	2.97827	0.274172
$119$	4.60180	0.421846
$120$	−9.13847	−0.834224
$121$	2.14725	0.195204
$122$	12.4970	1.13143
$123$	−26.3255	−2.37369
$124$	8.62487	0.774537
$125$	1.14534	0.102442
$126$	−12.4045	−1.10508
$127$	6.05866	0.537619	0.268809	−	0.963193i	$-0.413370\pi$
$127$	6.05866	0.537619	0.268809	+	0.963193i	$0.413370\pi$
$128$	−1.00000	−0.0883883
$129$	19.1015	1.68180
$130$	7.34961	0.644603
$131$	1.00000	0.0873704
$131$	1.00000	0.0873704
$132$	−10.6772	−0.929329
$133$	−17.1323	−1.48556
$134$	−2.65610	−0.229452
$135$	24.4105	2.10092
$136$	−2.10389	−0.180407
$137$	4.99231	0.426522	0.213261	−	0.976995i	$-0.431592\pi$
$137$	4.99231	0.426522	0.213261	+	0.976995i	$0.431592\pi$
$138$	2.94469	0.250668
$139$	17.5415	1.48785	0.743925	−	0.668263i	$-0.232962\pi$
$139$	17.5415	1.48785	0.743925	+	0.668263i	$0.232962\pi$
$140$	−6.78794	−0.573686
$141$	15.2128	1.28115
$142$	−11.1030	−0.931747
$143$	8.58711	0.718091
$144$	5.67118	0.472599
$145$	21.6881	1.80110
$146$	−3.40502	−0.281801
$147$	6.52489	0.538164
$148$	−3.55379	−0.292120
$149$	15.8629	1.29954	0.649768	−	0.760132i	$-0.274866\pi$
$149$	15.8629	1.29954	0.649768	+	0.760132i	$0.274866\pi$
$150$	13.6367	1.11343
$151$	−14.8429	−1.20790	−0.603949	−	0.797023i	$-0.706407\pi$
$151$	−14.8429	−1.20790	−0.603949	+	0.797023i	$0.706407\pi$
$152$	7.83273	0.635318
$153$	11.9316	0.964610
$154$	−7.93088	−0.639088
$155$	−26.7662	−2.14991
$156$	−6.97379	−0.558350
$157$	20.9546	1.67236	0.836179	−	0.548457i	$-0.184785\pi$
$157$	20.9546	1.67236	0.836179	+	0.548457i	$0.184785\pi$
$158$	17.7107	1.40899
$159$	1.42527	0.113031
$160$	3.10338	0.245343
$161$	2.18728	0.172382
$162$	−6.14878	−0.483094
$163$	−15.9931	−1.25268	−0.626339	−	0.779551i	$-0.715447\pi$
$163$	−15.9931	−1.25268	−0.626339	+	0.779551i	$0.715447\pi$
$164$	8.94001	0.698098
$165$	33.1353	2.57958
$166$	−12.1133	−0.940176
$167$	17.4060	1.34692	0.673460	−	0.739224i	$-0.264807\pi$
$167$	17.4060	1.34692	0.673460	+	0.739224i	$0.264807\pi$
$168$	6.44085	0.496922
$169$	−7.39133	−0.568564
$170$	6.52917	0.500765
$171$	−44.4208	−3.39695
$172$	−6.48678	−0.494612
$173$	−6.34656	−0.482520	−0.241260	−	0.970461i	$-0.577561\pi$
$173$	−6.34656	−0.482520	−0.241260	+	0.970461i	$0.577561\pi$
$174$	−20.5791	−1.56010
$175$	10.1291	0.765692
$176$	3.62591	0.273313
$177$	8.77007	0.659199
$178$	−10.4427	−0.782711
$179$	−19.4219	−1.45166	−0.725832	−	0.687872i	$-0.758545\pi$
$179$	−19.4219	−1.45166	−0.725832	+	0.687872i	$0.758545\pi$
$180$	−17.5998	−1.31181
$181$	1.49109	0.110832	0.0554160	−	0.998463i	$-0.482351\pi$
$181$	1.49109	0.110832	0.0554160	+	0.998463i	$0.482351\pi$
$182$	−5.18005	−0.383971
$183$	36.7999	2.72033
$184$	−1.00000	−0.0737210
$185$	11.0288	0.810850
$186$	25.3976	1.86224
$187$	7.62854	0.557854
$188$	−5.16620	−0.376784
$189$	−17.2047	−1.25146
$190$	−24.3079	−1.76348
$191$	10.1041	0.731110	0.365555	−	0.930790i	$-0.380879\pi$
$191$	10.1041	0.731110	0.365555	+	0.930790i	$0.380879\pi$
$192$	−2.94469	−0.212515
$193$	5.66583	0.407835	0.203918	−	0.978988i	$-0.434632\pi$
$193$	5.66583	0.407835	0.203918	+	0.978988i	$0.434632\pi$
$194$	10.9363	0.785182
$195$	21.6423	1.54984
$196$	−2.21582	−0.158273
$197$	16.5679	1.18042	0.590208	−	0.807251i	$-0.299046\pi$
$197$	16.5679	1.18042	0.590208	+	0.807251i	$0.299046\pi$
$198$	−20.5632	−1.46136
$199$	−18.5510	−1.31505	−0.657523	−	0.753435i	$-0.728396\pi$
$199$	−18.5510	−1.31505	−0.657523	+	0.753435i	$0.728396\pi$
$200$	−4.63094	−0.327457
$201$	−7.82137	−0.551677
$202$	−2.37124	−0.166840
$203$	−15.2859	−1.07286
$204$	−6.19531	−0.433759
$205$	−27.7442	−1.93774
$206$	−5.46826	−0.380992
$207$	5.67118	0.394175
$208$	2.36826	0.164209
$209$	−28.4008	−1.96452
$210$	−19.9884	−1.37933
$211$	−11.4540	−0.788527	−0.394264	−	0.918997i	$-0.629000\pi$
$211$	−11.4540	−0.788527	−0.394264	+	0.918997i	$0.629000\pi$
$212$	−0.484015	−0.0332423
$213$	−32.6950	−2.24023
$214$	10.6025	0.724770
$215$	20.1309	1.37292
$216$	7.86580	0.535200
$217$	18.8650	1.28064
$218$	8.89287	0.602301
$219$	−10.0267	−0.677543
$220$	−11.2526	−0.758648
$221$	4.98257	0.335164
$222$	−10.4648	−0.702352
$223$	12.2575	0.820825	0.410412	−	0.911900i	$-0.365385\pi$
$223$	12.2575	0.820825	0.410412	+	0.911900i	$0.365385\pi$
$224$	−2.18728	−0.146144
$225$	26.2629	1.75086
$226$	−17.5993	−1.17069
$227$	19.0016	1.26118	0.630589	−	0.776117i	$-0.282813\pi$
$227$	19.0016	1.26118	0.630589	+	0.776117i	$0.282813\pi$
$228$	23.0649	1.52751
$229$	11.8474	0.782895	0.391448	−	0.920200i	$-0.371974\pi$
$229$	11.8474	0.782895	0.391448	+	0.920200i	$0.371974\pi$
$230$	3.10338	0.204631
$231$	−23.3540	−1.53658
$232$	6.98856	0.458821
$233$	−16.5439	−1.08383	−0.541914	−	0.840434i	$-0.682300\pi$
$233$	−16.5439	−1.08383	−0.541914	+	0.840434i	$0.682300\pi$
$234$	−13.4309	−0.878002
$235$	16.0326	1.04585
$236$	−2.97827	−0.193869
$237$	52.1524	3.38766
$238$	−4.60180	−0.298290
$239$	4.23998	0.274261	0.137131	−	0.990553i	$-0.456212\pi$
$239$	4.23998	0.274261	0.137131	+	0.990553i	$0.456212\pi$
$240$	9.13847	0.589886
$241$	−12.1426	−0.782176	−0.391088	−	0.920353i	$-0.627901\pi$
$241$	−12.1426	−0.782176	−0.391088	+	0.920353i	$0.627901\pi$
$242$	−2.14725	−0.138030
$243$	5.49117	0.352259
$244$	−12.4970	−0.800042
$245$	6.87651	0.439324
$246$	26.3255	1.67846
$247$	−18.5500	−1.18031
$248$	−8.62487	−0.547680
$249$	−35.6700	−2.26049
$250$	−1.14534	−0.0724376
$251$	−16.9133	−1.06756	−0.533778	−	0.845625i	$-0.679228\pi$
$251$	−16.9133	−1.06756	−0.533778	+	0.845625i	$0.679228\pi$
$252$	12.4045	0.781407
$253$	3.62591	0.227959
$254$	−6.05866	−0.380154
$255$	19.2264	1.20400
$256$	1.00000	0.0625000
$257$	−24.8346	−1.54914	−0.774569	−	0.632489i	$-0.782033\pi$
$257$	−24.8346	−1.54914	−0.774569	+	0.632489i	$0.782033\pi$
$258$	−19.1015	−1.18921
$259$	−7.77313	−0.482999
$260$	−7.34961	−0.455803
$261$	−39.6334	−2.45325
$262$	−1.00000	−0.0617802
$263$	−27.7018	−1.70817	−0.854084	−	0.520135i	$-0.825882\pi$
$263$	−27.7018	−1.70817	−0.854084	+	0.520135i	$0.825882\pi$
$264$	10.6772	0.657135
$265$	1.50208	0.0922720
$266$	17.1323	1.05045
$267$	−30.7504	−1.88189
$268$	2.65610	0.162247
$269$	−8.55168	−0.521405	−0.260703	−	0.965419i	$-0.583954\pi$
$269$	−8.55168	−0.521405	−0.260703	+	0.965419i	$0.583954\pi$
$270$	−24.4105	−1.48558
$271$	5.58610	0.339331	0.169666	−	0.985502i	$-0.445731\pi$
$271$	5.58610	0.339331	0.169666	+	0.985502i	$0.445731\pi$
$272$	2.10389	0.127567
$273$	−15.2536	−0.923191
$274$	−4.99231	−0.301596
$275$	16.7914	1.01256
$276$	−2.94469	−0.177249
$277$	−24.9240	−1.49754	−0.748768	−	0.662832i	$-0.769354\pi$
$277$	−24.9240	−1.49754	−0.748768	+	0.662832i	$0.769354\pi$
$278$	−17.5415	−1.05207
$279$	48.9133	2.92836
$280$	6.78794	0.405657
$281$	−30.8789	−1.84208	−0.921041	−	0.389466i	$-0.872660\pi$
$281$	−30.8789	−1.84208	−0.921041	+	0.389466i	$0.872660\pi$
$282$	−15.2128	−0.905911
$283$	11.5982	0.689442	0.344721	−	0.938705i	$-0.387974\pi$
$283$	11.5982	0.689442	0.344721	+	0.938705i	$0.387974\pi$
$284$	11.1030	0.658845
$285$	−71.5791	−4.23998
$286$	−8.58711	−0.507767
$287$	19.5543	1.15425
$288$	−5.67118	−0.334178
$289$	−12.5736	−0.739625
$290$	−21.6881	−1.27357
$291$	32.2040	1.88783
$292$	3.40502	0.199264
$293$	27.0359	1.57945	0.789726	−	0.613460i	$-0.210223\pi$
$293$	27.0359	1.57945	0.789726	+	0.613460i	$0.210223\pi$
$294$	−6.52489	−0.380539
$295$	9.24268	0.538130
$296$	3.55379	0.206560
$297$	−28.5207	−1.65494
$298$	−15.8629	−0.918911
$299$	2.36826	0.136960
$300$	−13.6367	−0.787313
$301$	−14.1884	−0.817805
$302$	14.8429	0.854113
$303$	−6.98255	−0.401137
$304$	−7.83273	−0.449238
$305$	38.7830	2.22071
$306$	−11.9316	−0.682083
$307$	−8.64534	−0.493416	−0.246708	−	0.969090i	$-0.579349\pi$
$307$	−8.64534	−0.493416	−0.246708	+	0.969090i	$0.579349\pi$
$308$	7.93088	0.451904
$309$	−16.1023	−0.916028
$310$	26.7662	1.52022
$311$	−20.8347	−1.18142	−0.590712	−	0.806882i	$-0.701153\pi$
$311$	−20.8347	−1.18142	−0.590712	+	0.806882i	$0.701153\pi$
$312$	6.97379	0.394813
$313$	−26.6602	−1.50692	−0.753461	−	0.657493i	$-0.771617\pi$
$313$	−26.6602	−1.50692	−0.753461	+	0.657493i	$0.771617\pi$
$314$	−20.9546	−1.18254
$315$	−38.4957	−2.16899
$316$	−17.7107	−0.996303
$317$	−28.7093	−1.61248	−0.806238	−	0.591592i	$-0.798500\pi$
$317$	−28.7093	−1.61248	−0.806238	+	0.591592i	$0.798500\pi$
$318$	−1.42527	−0.0799253
$319$	−25.3399	−1.41876
$320$	−3.10338	−0.173484
$321$	31.2210	1.74258
$322$	−2.18728	−0.121892
$323$	−16.4792	−0.916929
$324$	6.14878	0.341599
$325$	10.9673	0.608355
$326$	15.9931	0.885777
$327$	26.1867	1.44813
$328$	−8.94001	−0.493630
$329$	−11.2999	−0.622984
$330$	−33.1353	−1.82404
$331$	27.2290	1.49664	0.748322	−	0.663336i	$-0.230860\pi$
$331$	27.2290	1.49664	0.748322	+	0.663336i	$0.230860\pi$
$332$	12.1133	0.664805
$333$	−20.1542	−1.10444
$334$	−17.4060	−0.952416
$335$	−8.24286	−0.450356
$336$	−6.44085	−0.351377
$337$	32.8194	1.78779	0.893893	−	0.448280i	$-0.147963\pi$
$337$	32.8194	1.78779	0.893893	+	0.448280i	$0.147963\pi$
$338$	7.39133	0.402035
$339$	−51.8243	−2.81471
$340$	−6.52917	−0.354094
$341$	31.2730	1.69353
$342$	44.4208	2.40200
$343$	−20.1575	−1.08841
$344$	6.48678	0.349744
$345$	9.13847	0.491999
$346$	6.34656	0.341193
$347$	−8.08355	−0.433948	−0.216974	−	0.976177i	$-0.569619\pi$
$347$	−8.08355	−0.433948	−0.216974	+	0.976177i	$0.569619\pi$
$348$	20.5791	1.10316
$349$	11.8759	0.635703	0.317852	−	0.948140i	$-0.397039\pi$
$349$	11.8759	0.635703	0.317852	+	0.948140i	$0.397039\pi$
$350$	−10.1291	−0.541426
$351$	−18.6283	−0.994304
$352$	−3.62591	−0.193262
$353$	8.38985	0.446547	0.223273	−	0.974756i	$-0.428326\pi$
$353$	8.38985	0.446547	0.223273	+	0.974756i	$0.428326\pi$
$354$	−8.77007	−0.466124
$355$	−34.4569	−1.82878
$356$	10.4427	0.553461
$357$	−13.5509	−0.717188
$358$	19.4219	1.02648
$359$	−35.4681	−1.87193	−0.935967	−	0.352087i	$-0.885472\pi$
$359$	−35.4681	−1.87193	−0.935967	+	0.352087i	$0.885472\pi$
$360$	17.5998	0.927592
$361$	42.3516	2.22903
$362$	−1.49109	−0.0783701
$363$	−6.32297	−0.331870
$364$	5.18005	0.271508
$365$	−10.5671	−0.553105
$366$	−36.7999	−1.92356
$367$	0.676424	0.0353091	0.0176545	−	0.999844i	$-0.494380\pi$
$367$	0.676424	0.0353091	0.0176545	+	0.999844i	$0.494380\pi$
$368$	1.00000	0.0521286
$369$	50.7005	2.63936
$370$	−11.0288	−0.573357
$371$	−1.05867	−0.0549637
$372$	−25.3976	−1.31680
$373$	6.07299	0.314447	0.157224	−	0.987563i	$-0.449746\pi$
$373$	6.07299	0.314447	0.157224	+	0.987563i	$0.449746\pi$
$374$	−7.62854	−0.394462
$375$	−3.37266	−0.174164
$376$	5.16620	0.266426
$377$	−16.5507	−0.852406
$378$	17.2047	0.884914
$379$	36.2852	1.86384	0.931922	−	0.362659i	$-0.118131\pi$
$379$	36.2852	1.86384	0.931922	+	0.362659i	$0.118131\pi$
$380$	24.3079	1.24697
$381$	−17.8409	−0.914015
$382$	−10.1041	−0.516973
$383$	0.322645	0.0164864	0.00824320	−	0.999966i	$-0.497376\pi$
$383$	0.322645	0.0164864	0.00824320	+	0.999966i	$0.497376\pi$
$384$	2.94469	0.150270
$385$	−24.6125	−1.25437
$386$	−5.66583	−0.288383
$387$	−36.7877	−1.87003
$388$	−10.9363	−0.555208
$389$	26.8223	1.35995	0.679973	−	0.733237i	$-0.261992\pi$
$389$	26.8223	1.35995	0.679973	+	0.733237i	$0.261992\pi$
$390$	−21.6423	−1.09590
$391$	2.10389	0.106399
$392$	2.21582	0.111916
$393$	−2.94469	−0.148540
$394$	−16.5679	−0.834680
$395$	54.9628	2.76548
$396$	20.5632	1.03334
$397$	9.55849	0.479727	0.239863	−	0.970807i	$-0.422897\pi$
$397$	9.55849	0.479727	0.239863	+	0.970807i	$0.422897\pi$
$398$	18.5510	0.929877
$399$	50.4494	2.52563
$400$	4.63094	0.231547
$401$	−5.91647	−0.295455	−0.147727	−	0.989028i	$-0.547196\pi$
$401$	−5.91647	−0.295455	−0.147727	+	0.989028i	$0.547196\pi$
$402$	7.82137	0.390095
$403$	20.4260	1.01749
$404$	2.37124	0.117973
$405$	−19.0820	−0.948191
$406$	15.2859	0.758627
$407$	−12.8857	−0.638722
$408$	6.19531	0.306714
$409$	−32.3124	−1.59775	−0.798873	−	0.601499i	$-0.794570\pi$
$409$	−32.3124	−1.59775	−0.798873	+	0.601499i	$0.794570\pi$
$410$	27.7442	1.37019
$411$	−14.7008	−0.725136
$412$	5.46826	0.269402
$413$	−6.51430	−0.320548
$414$	−5.67118	−0.278724
$415$	−37.5922	−1.84533
$416$	−2.36826	−0.116114
$417$	−51.6542	−2.52952
$418$	28.4008	1.38913
$419$	21.7720	1.06363	0.531817	−	0.846859i	$-0.321510\pi$
$419$	21.7720	1.06363	0.531817	+	0.846859i	$0.321510\pi$
$420$	19.9884	0.975333
$421$	36.4888	1.77836	0.889179	−	0.457560i	$-0.151276\pi$
$421$	36.4888	1.77836	0.889179	+	0.457560i	$0.151276\pi$
$422$	11.4540	0.557573
$423$	−29.2985	−1.42454
$424$	0.484015	0.0235058
$425$	9.74300	0.472605
$426$	32.6950	1.58408
$427$	−27.3345	−1.32281
$428$	−10.6025	−0.512490
$429$	−25.2864	−1.22084
$430$	−20.1309	−0.970799
$431$	4.27848	0.206087	0.103044	−	0.994677i	$-0.467142\pi$
$431$	4.27848	0.206087	0.103044	+	0.994677i	$0.467142\pi$
$432$	−7.86580	−0.378444
$433$	33.7058	1.61980	0.809900	−	0.586569i	$-0.199522\pi$
$433$	33.7058	1.61980	0.809900	+	0.586569i	$0.199522\pi$
$434$	−18.8650	−0.905549
$435$	−63.8647	−3.06208
$436$	−8.89287	−0.425891
$437$	−7.83273	−0.374690
$438$	10.0267	0.479095
$439$	−20.8215	−0.993757	−0.496879	−	0.867820i	$-0.665521\pi$
$439$	−20.8215	−0.993757	−0.496879	+	0.867820i	$0.665521\pi$
$440$	11.2526	0.536445
$441$	−12.5663	−0.598395
$442$	−4.98257	−0.236997
$443$	−14.9194	−0.708842	−0.354421	−	0.935086i	$-0.615322\pi$
$443$	−14.9194	−0.708842	−0.354421	+	0.935086i	$0.615322\pi$
$444$	10.4648	0.496638
$445$	−32.4075	−1.53626
$446$	−12.2575	−0.580411
$447$	−46.7112	−2.20936
$448$	2.18728	0.103339
$449$	−26.4598	−1.24871	−0.624357	−	0.781139i	$-0.714639\pi$
$449$	−26.4598	−1.24871	−0.624357	+	0.781139i	$0.714639\pi$
$450$	−26.2629	−1.23805
$451$	32.4157	1.52640
$452$	17.5993	0.827800
$453$	43.7077	2.05357
$454$	−19.0016	−0.891788
$455$	−16.0756	−0.753637
$456$	−23.0649	−1.08011
$457$	7.95332	0.372041	0.186020	−	0.982546i	$-0.440441\pi$
$457$	7.95332	0.372041	0.186020	+	0.982546i	$0.440441\pi$
$458$	−11.8474	−0.553591
$459$	−16.5488	−0.772433
$460$	−3.10338	−0.144696
$461$	−2.10206	−0.0979027	−0.0489514	−	0.998801i	$-0.515588\pi$
$461$	−2.10206	−0.0979027	−0.0489514	+	0.998801i	$0.515588\pi$
$462$	23.3540	1.08652
$463$	−16.4349	−0.763796	−0.381898	−	0.924204i	$-0.624729\pi$
$463$	−16.4349	−0.763796	−0.381898	+	0.924204i	$0.624729\pi$
$464$	−6.98856	−0.324436
$465$	78.8182	3.65510
$466$	16.5439	0.766382
$467$	1.76742	0.0817864	0.0408932	−	0.999164i	$-0.486980\pi$
$467$	1.76742	0.0817864	0.0408932	+	0.999164i	$0.486980\pi$
$468$	13.4309	0.620841
$469$	5.80962	0.268263
$470$	−16.0326	−0.739531
$471$	−61.7047	−2.84320
$472$	2.97827	0.137086
$473$	−23.5205	−1.08147
$474$	−52.1524	−2.39544
$475$	−36.2729	−1.66431
$476$	4.60180	0.210923
$477$	−2.74494	−0.125682
$478$	−4.23998	−0.193932
$479$	0.341661	0.0156109	0.00780544	−	0.999970i	$-0.497515\pi$
$479$	0.341661	0.0156109	0.00780544	+	0.999970i	$0.497515\pi$
$480$	−9.13847	−0.417112
$481$	−8.41631	−0.383751
$482$	12.1426	0.553082
$483$	−6.44085	−0.293069
$484$	2.14725	0.0976021
$485$	33.9395	1.54111
$486$	−5.49117	−0.249085
$487$	3.60667	0.163434	0.0817169	−	0.996656i	$-0.473960\pi$
$487$	3.60667	0.163434	0.0817169	+	0.996656i	$0.473960\pi$
$488$	12.4970	0.565715
$489$	47.0947	2.12970
$490$	−6.87651	−0.310649
$491$	−37.2123	−1.67937	−0.839684	−	0.543075i	$-0.817260\pi$
$491$	−37.2123	−1.67937	−0.839684	+	0.543075i	$0.817260\pi$
$492$	−26.3255	−1.18685
$493$	−14.7032	−0.662198
$494$	18.5500	0.834602
$495$	−63.8154	−2.86829
$496$	8.62487	0.387268
$497$	24.2855	1.08935
$498$	35.6700	1.59841
$499$	19.3933	0.868163	0.434082	−	0.900874i	$-0.357073\pi$
$499$	19.3933	0.868163	0.434082	+	0.900874i	$0.357073\pi$
$500$	1.14534	0.0512211
$501$	−51.2554	−2.28992
$502$	16.9133	0.754876
$503$	1.57219	0.0701003	0.0350502	−	0.999386i	$-0.488841\pi$
$503$	1.57219	0.0701003	0.0350502	+	0.999386i	$0.488841\pi$
$504$	−12.4045	−0.552538
$505$	−7.35883	−0.327464
$506$	−3.62591	−0.161191
$507$	21.7652	0.966625
$508$	6.05866	0.268809
$509$	−1.78489	−0.0791139	−0.0395569	−	0.999217i	$-0.512595\pi$
$509$	−1.78489	−0.0791139	−0.0395569	+	0.999217i	$0.512595\pi$
$510$	−19.2264	−0.851358
$511$	7.44772	0.329468
$512$	−1.00000	−0.0441942
$513$	61.6107	2.72018
$514$	24.8346	1.09541
$515$	−16.9701	−0.747790
$516$	19.1015	0.840898
$517$	−18.7322	−0.823840
$518$	7.77313	0.341532
$519$	18.6886	0.820340
$520$	7.34961	0.322302
$521$	−8.37462	−0.366899	−0.183449	−	0.983029i	$-0.558726\pi$
$521$	−8.37462	−0.366899	−0.183449	+	0.983029i	$0.558726\pi$
$522$	39.6334	1.73471
$523$	−9.43547	−0.412584	−0.206292	−	0.978490i	$-0.566140\pi$
$523$	−9.43547	−0.412584	−0.206292	+	0.978490i	$0.566140\pi$
$524$	1.00000	0.0436852
$525$	−29.8272	−1.30176
$526$	27.7018	1.20786
$527$	18.1458	0.790444
$528$	−10.6772	−0.464665
$529$	1.00000	0.0434783
$530$	−1.50208	−0.0652462
$531$	−16.8903	−0.732977
$532$	−17.1323	−0.742781
$533$	21.1723	0.917074
$534$	30.7504	1.33070
$535$	32.9035	1.42254
$536$	−2.65610	−0.114726
$537$	57.1915	2.46800
$538$	8.55168	0.368689
$539$	−8.03436	−0.346064
$540$	24.4105	1.05046
$541$	−26.4989	−1.13927	−0.569637	−	0.821896i	$-0.692916\pi$
$541$	−26.4989	−1.13927	−0.569637	+	0.821896i	$0.692916\pi$
$542$	−5.58610	−0.239944
$543$	−4.39080	−0.188427
$544$	−2.10389	−0.0902037
$545$	27.5979	1.18217
$546$	15.2536	0.652795
$547$	−19.0525	−0.814627	−0.407314	−	0.913288i	$-0.633534\pi$
$547$	−19.0525	−0.814627	−0.407314	+	0.913288i	$0.633534\pi$
$548$	4.99231	0.213261
$549$	−70.8731	−3.02479
$550$	−16.7914	−0.715987
$551$	54.7395	2.33198
$552$	2.94469	0.125334
$553$	−38.7381	−1.64731
$554$	24.9240	1.05892
$555$	−32.4762	−1.37854
$556$	17.5415	0.743925
$557$	31.4974	1.33459	0.667294	−	0.744794i	$-0.267452\pi$
$557$	31.4974	1.33459	0.667294	+	0.744794i	$0.267452\pi$
$558$	−48.9133	−2.07066
$559$	−15.3624	−0.649760
$560$	−6.78794	−0.286843
$561$	−22.4637	−0.948416
$562$	30.8789	1.30255
$563$	38.8046	1.63542	0.817710	−	0.575630i	$-0.195243\pi$
$563$	38.8046	1.63542	0.817710	+	0.575630i	$0.195243\pi$
$564$	15.2128	0.640576
$565$	−54.6171	−2.29776
$566$	−11.5982	−0.487509
$567$	13.4491	0.564809
$568$	−11.1030	−0.465874
$569$	−5.13364	−0.215213	−0.107607	−	0.994194i	$-0.534319\pi$
$569$	−5.13364	−0.215213	−0.107607	+	0.994194i	$0.534319\pi$
$570$	71.5791	2.99812
$571$	−43.9866	−1.84078	−0.920390	−	0.391001i	$-0.872129\pi$
$571$	−43.9866	−1.84078	−0.920390	+	0.391001i	$0.872129\pi$
$572$	8.58711	0.359045
$573$	−29.7535	−1.24297
$574$	−19.5543	−0.816180
$575$	4.63094	0.193123
$576$	5.67118	0.236299
$577$	28.4783	1.18557	0.592783	−	0.805362i	$-0.298029\pi$
$577$	28.4783	1.18557	0.592783	+	0.805362i	$0.298029\pi$
$578$	12.5736	0.522994
$579$	−16.6841	−0.693368
$580$	21.6881	0.900550
$581$	26.4952	1.09921
$582$	−32.2040	−1.33490
$583$	−1.75500	−0.0726845
$584$	−3.40502	−0.140901
$585$	−41.6810	−1.72330
$586$	−27.0359	−1.11684
$587$	−39.5940	−1.63422	−0.817110	−	0.576482i	$-0.804425\pi$
$587$	−39.5940	−1.63422	−0.817110	+	0.576482i	$0.804425\pi$
$588$	6.52489	0.269082
$589$	−67.5563	−2.78361
$590$	−9.24268	−0.380515
$591$	−48.7874	−2.00684
$592$	−3.55379	−0.146060
$593$	−20.2218	−0.830411	−0.415205	−	0.909728i	$-0.636290\pi$
$593$	−20.2218	−0.830411	−0.415205	+	0.909728i	$0.636290\pi$
$594$	28.5207	1.17022
$595$	−14.2811	−0.585469
$596$	15.8629	0.649768
$597$	54.6269	2.23573
$598$	−2.36826	−0.0968455
$599$	−17.6542	−0.721331	−0.360665	−	0.932695i	$-0.617450\pi$
$599$	−17.6542	−0.721331	−0.360665	+	0.932695i	$0.617450\pi$
$600$	13.6367	0.556714
$601$	36.2954	1.48052	0.740259	−	0.672321i	$-0.234703\pi$
$601$	36.2954	1.48052	0.740259	+	0.672321i	$0.234703\pi$
$602$	14.1884	0.578276
$603$	15.0632	0.613422
$604$	−14.8429	−0.603949
$605$	−6.66371	−0.270918
$606$	6.98255	0.283647
$607$	−8.46238	−0.343478	−0.171739	−	0.985143i	$-0.554938\pi$
$607$	−8.46238	−0.343478	−0.171739	+	0.985143i	$0.554938\pi$
$608$	7.83273	0.317659
$609$	45.0122	1.82399
$610$	−38.7830	−1.57028
$611$	−12.2349	−0.494972
$612$	11.9316	0.482305
$613$	−3.71525	−0.150057	−0.0750287	−	0.997181i	$-0.523905\pi$
$613$	−3.71525	−0.150057	−0.0750287	+	0.997181i	$0.523905\pi$
$614$	8.64534	0.348898
$615$	81.6980	3.29438
$616$	−7.93088	−0.319544
$617$	−17.5091	−0.704890	−0.352445	−	0.935832i	$-0.614650\pi$
$617$	−17.5091	−0.704890	−0.352445	+	0.935832i	$0.614650\pi$
$618$	16.1023	0.647730
$619$	19.0680	0.766408	0.383204	−	0.923664i	$-0.374821\pi$
$619$	19.0680	0.766408	0.383204	+	0.923664i	$0.374821\pi$
$620$	−26.7662	−1.07496
$621$	−7.86580	−0.315644
$622$	20.8347	0.835393
$623$	22.8410	0.915106
$624$	−6.97379	−0.279175
$625$	−26.7091	−1.06836
$626$	26.6602	1.06555
$627$	83.6314	3.33992
$628$	20.9546	0.836179
$629$	−7.47680	−0.298120
$630$	38.4957	1.53370
$631$	−11.5181	−0.458529	−0.229264	−	0.973364i	$-0.573632\pi$
$631$	−11.5181	−0.458529	−0.229264	+	0.973364i	$0.573632\pi$
$632$	17.7107	0.704493
$633$	33.7285	1.34059
$634$	28.7093	1.14019
$635$	−18.8023	−0.746146
$636$	1.42527	0.0565157
$637$	−5.24763	−0.207919
$638$	25.3399	1.00322
$639$	62.9674	2.49095
$640$	3.10338	0.122672
$641$	32.2720	1.27467	0.637334	−	0.770588i	$-0.280037\pi$
$641$	32.2720	1.27467	0.637334	+	0.770588i	$0.280037\pi$
$642$	−31.2210	−1.23219
$643$	−21.8448	−0.861477	−0.430738	−	0.902477i	$-0.641747\pi$
$643$	−21.8448	−0.861477	−0.430738	+	0.902477i	$0.641747\pi$
$644$	2.18728	0.0861908
$645$	−59.2792	−2.33412
$646$	16.4792	0.648367
$647$	−5.56417	−0.218750	−0.109375	−	0.994001i	$-0.534885\pi$
$647$	−5.56417	−0.218750	−0.109375	+	0.994001i	$0.534885\pi$
$648$	−6.14878	−0.241547
$649$	−10.7989	−0.423895
$650$	−10.9673	−0.430172
$651$	−55.5515	−2.17724
$652$	−15.9931	−0.626339
$653$	26.7343	1.04619	0.523097	−	0.852273i	$-0.324777\pi$
$653$	26.7343	1.04619	0.523097	+	0.852273i	$0.324777\pi$
$654$	−26.1867	−1.02398
$655$	−3.10338	−0.121259
$656$	8.94001	0.349049
$657$	19.3105	0.753374
$658$	11.2999	0.440516
$659$	−29.7182	−1.15766	−0.578828	−	0.815449i	$-0.696490\pi$
$659$	−29.7182	−1.15766	−0.578828	+	0.815449i	$0.696490\pi$
$660$	33.1353	1.28979
$661$	−32.1926	−1.25215	−0.626074	−	0.779764i	$-0.715339\pi$
$661$	−32.1926	−1.25215	−0.626074	+	0.779764i	$0.715339\pi$
$662$	−27.2290	−1.05829
$663$	−14.6721	−0.569818
$664$	−12.1133	−0.470088
$665$	53.1681	2.06177
$666$	20.1542	0.780960
$667$	−6.98856	−0.270598
$668$	17.4060	0.673460
$669$	−36.0946	−1.39550
$670$	8.24286	0.318450
$671$	−45.3132	−1.74930
$672$	6.44085	0.248461
$673$	−24.7289	−0.953229	−0.476614	−	0.879112i	$-0.658136\pi$
$673$	−24.7289	−0.953229	−0.476614	+	0.879112i	$0.658136\pi$
$674$	−32.8194	−1.26416
$675$	−36.4260	−1.40204
$676$	−7.39133	−0.284282
$677$	19.8487	0.762846	0.381423	−	0.924401i	$-0.375434\pi$
$677$	19.8487	0.762846	0.381423	+	0.924401i	$0.375434\pi$
$678$	51.8243	1.99030
$679$	−23.9208	−0.917995
$680$	6.52917	0.250382
$681$	−55.9537	−2.14415
$682$	−31.2730	−1.19751
$683$	49.5924	1.89760	0.948801	−	0.315875i	$-0.102298\pi$
$683$	49.5924	1.89760	0.948801	+	0.315875i	$0.102298\pi$
$684$	−44.4208	−1.69847
$685$	−15.4930	−0.591957
$686$	20.1575	0.769619
$687$	−34.8868	−1.33101
$688$	−6.48678	−0.247306
$689$	−1.14627	−0.0436696
$690$	−9.13847	−0.347896
$691$	4.18250	0.159110	0.0795550	−	0.996830i	$-0.474650\pi$
$691$	4.18250	0.159110	0.0795550	+	0.996830i	$0.474650\pi$
$692$	−6.34656	−0.241260
$693$	44.9775	1.70855
$694$	8.08355	0.306847
$695$	−54.4378	−2.06494
$696$	−20.5791	−0.780049
$697$	18.8088	0.712436
$698$	−11.8759	−0.449510
$699$	48.7166	1.84263
$700$	10.1291	0.382846
$701$	20.5458	0.776004	0.388002	−	0.921659i	$-0.373165\pi$
$701$	20.5458	0.776004	0.388002	+	0.921659i	$0.373165\pi$
$702$	18.6283	0.703079
$703$	27.8359	1.04985
$704$	3.62591	0.136657
$705$	−47.2111	−1.77807
$706$	−8.38985	−0.315756
$707$	5.18655	0.195060
$708$	8.77007	0.329599
$709$	7.59865	0.285373	0.142687	−	0.989768i	$-0.454426\pi$
$709$	7.59865	0.285373	0.142687	+	0.989768i	$0.454426\pi$
$710$	34.4569	1.29315
$711$	−100.440	−3.76681
$712$	−10.4427	−0.391356
$713$	8.62487	0.323004
$714$	13.5509	0.507128
$715$	−26.6490	−0.996617
$716$	−19.4219	−0.725832
$717$	−12.4854	−0.466276
$718$	35.4681	1.32366
$719$	−33.4537	−1.24761	−0.623806	−	0.781579i	$-0.714415\pi$
$719$	−33.4537	−1.24761	−0.623806	+	0.781579i	$0.714415\pi$
$720$	−17.5998	−0.655906
$721$	11.9606	0.445436
$722$	−42.3516	−1.57616
$723$	35.7563	1.32979
$724$	1.49109	0.0554160
$725$	−32.3636	−1.20195
$726$	6.32297	0.234667
$727$	5.83441	0.216386	0.108193	−	0.994130i	$-0.465494\pi$
$727$	5.83441	0.216386	0.108193	+	0.994130i	$0.465494\pi$
$728$	−5.18005	−0.191985
$729$	−34.6161	−1.28208
$730$	10.5671	0.391104
$731$	−13.6475	−0.504771
$732$	36.7999	1.36016
$733$	−29.1527	−1.07678	−0.538389	−	0.842696i	$-0.680967\pi$
$733$	−29.1527	−1.07678	−0.538389	+	0.842696i	$0.680967\pi$
$734$	−0.676424	−0.0249673
$735$	−20.2492	−0.746902
$736$	−1.00000	−0.0368605
$737$	9.63078	0.354754
$738$	−50.7005	−1.86631
$739$	−27.7366	−1.02031	−0.510153	−	0.860084i	$-0.670411\pi$
$739$	−27.7366	−1.02031	−0.510153	+	0.860084i	$0.670411\pi$
$740$	11.0288	0.405425
$741$	54.6238	2.00666
$742$	1.05867	0.0388652
$743$	−27.0473	−0.992271	−0.496135	−	0.868245i	$-0.665248\pi$
$743$	−27.0473	−0.992271	−0.496135	+	0.868245i	$0.665248\pi$
$744$	25.3976	0.931120
$745$	−49.2284	−1.80359
$746$	−6.07299	−0.222348
$747$	68.6969	2.51349
$748$	7.62854	0.278927
$749$	−23.1906	−0.847365
$750$	3.37266	0.123152
$751$	−12.9927	−0.474112	−0.237056	−	0.971496i	$-0.576182\pi$
$751$	−12.9927	−0.474112	−0.237056	+	0.971496i	$0.576182\pi$
$752$	−5.16620	−0.188392
$753$	49.8043	1.81497
$754$	16.5507	0.602742
$755$	46.0631	1.67641
$756$	−17.2047	−0.625729
$757$	−6.19153	−0.225035	−0.112517	−	0.993650i	$-0.535891\pi$
$757$	−6.19153	−0.225035	−0.112517	+	0.993650i	$0.535891\pi$
$758$	−36.2852	−1.31794
$759$	−10.6772	−0.387557
$760$	−24.3079	−0.881740
$761$	44.2892	1.60548	0.802741	−	0.596327i	$-0.203374\pi$
$761$	44.2892	1.60548	0.802741	+	0.596327i	$0.203374\pi$
$762$	17.8409	0.646306
$763$	−19.4512	−0.704180
$764$	10.1041	0.365555
$765$	−37.0281	−1.33876
$766$	−0.322645	−0.0116576
$767$	−7.05332	−0.254681
$768$	−2.94469	−0.106257
$769$	−12.2490	−0.441711	−0.220855	−	0.975307i	$-0.570885\pi$
$769$	−12.2490	−0.441711	−0.220855	+	0.975307i	$0.570885\pi$
$770$	24.6125	0.886973
$771$	73.1301	2.63372
$772$	5.66583	0.203918
$773$	9.67856	0.348114	0.174057	−	0.984736i	$-0.444312\pi$
$773$	9.67856	0.348114	0.174057	+	0.984736i	$0.444312\pi$
$774$	36.7877	1.32231
$775$	39.9413	1.43473
$776$	10.9363	0.392591
$777$	22.8894	0.821154
$778$	−26.8223	−0.961627
$779$	−70.0247	−2.50889
$780$	21.6423	0.774919
$781$	40.2587	1.44057
$782$	−2.10389	−0.0752351
$783$	54.9706	1.96449
$784$	−2.21582	−0.0791363
$785$	−65.0299	−2.32102
$786$	2.94469	0.105034
$787$	−36.5828	−1.30404	−0.652018	−	0.758203i	$-0.726077\pi$
$787$	−36.5828	−1.30404	−0.652018	+	0.758203i	$0.726077\pi$
$788$	16.5679	0.590208
$789$	81.5732	2.90408
$790$	−54.9628	−1.95549
$791$	38.4945	1.36871
$792$	−20.5632	−0.730682
$793$	−29.5963	−1.05100
$794$	−9.55849	−0.339218
$795$	−4.42315	−0.156873
$796$	−18.5510	−0.657523
$797$	14.2359	0.504262	0.252131	−	0.967693i	$-0.418869\pi$
$797$	14.2359	0.504262	0.252131	+	0.967693i	$0.418869\pi$
$798$	−50.4494	−1.78589
$799$	−10.8691	−0.384522
$800$	−4.63094	−0.163728
$801$	59.2223	2.09252
$802$	5.91647	0.208918
$803$	12.3463	0.435692
$804$	−7.82137	−0.275839
$805$	−6.78794	−0.239244
$806$	−20.4260	−0.719474
$807$	25.1820	0.886449
$808$	−2.37124	−0.0834198
$809$	−28.0023	−0.984508	−0.492254	−	0.870452i	$-0.663827\pi$
$809$	−28.0023	−0.984508	−0.492254	+	0.870452i	$0.663827\pi$
$810$	19.0820	0.670472
$811$	−36.6956	−1.28856	−0.644278	−	0.764791i	$-0.722842\pi$
$811$	−36.6956	−1.28856	−0.644278	+	0.764791i	$0.722842\pi$
$812$	−15.2859	−0.536431
$813$	−16.4493	−0.576903
$814$	12.8857	0.451645
$815$	49.6326	1.73856
$816$	−6.19531	−0.216879
$817$	50.8092	1.77759
$818$	32.3124	1.12978
$819$	29.3770	1.02652
$820$	−27.7442	−0.968870
$821$	45.2201	1.57819	0.789096	−	0.614270i	$-0.210550\pi$
$821$	45.2201	1.57819	0.789096	+	0.614270i	$0.210550\pi$
$822$	14.7008	0.512749
$823$	35.2499	1.22873	0.614367	−	0.789020i	$-0.289411\pi$
$823$	35.2499	1.22873	0.614367	+	0.789020i	$0.289411\pi$
$824$	−5.46826	−0.190496
$825$	−49.4454	−1.72147
$826$	6.51430	0.226661
$827$	−32.6500	−1.13535	−0.567676	−	0.823252i	$-0.692157\pi$
$827$	−32.6500	−1.13535	−0.567676	+	0.823252i	$0.692157\pi$
$828$	5.67118	0.197087
$829$	−44.1424	−1.53313	−0.766565	−	0.642166i	$-0.778036\pi$
$829$	−44.1424	−1.53313	−0.766565	+	0.642166i	$0.778036\pi$
$830$	37.5922	1.30484
$831$	73.3933	2.54599
$832$	2.36826	0.0821047
$833$	−4.66184	−0.161523
$834$	51.6542	1.78864
$835$	−54.0175	−1.86935
$836$	−28.4008	−0.982262
$837$	−67.8416	−2.34495
$838$	−21.7720	−0.752102
$839$	−3.42614	−0.118283	−0.0591417	−	0.998250i	$-0.518836\pi$
$839$	−3.42614	−0.118283	−0.0591417	+	0.998250i	$0.518836\pi$
$840$	−19.9884	−0.689664
$841$	19.8399	0.684136
$842$	−36.4888	−1.25749
$843$	90.9288	3.13175
$844$	−11.4540	−0.394264
$845$	22.9381	0.789094
$846$	29.2985	1.00730
$847$	4.69662	0.161378
$848$	−0.484015	−0.0166211
$849$	−34.1531	−1.17213
$850$	−9.74300	−0.334182
$851$	−3.55379	−0.121822
$852$	−32.6950	−1.12011
$853$	30.7936	1.05435	0.527176	−	0.849756i	$-0.323251\pi$
$853$	30.7936	1.05435	0.527176	+	0.849756i	$0.323251\pi$
$854$	27.3345	0.935368
$855$	137.855	4.71453
$856$	10.6025	0.362385
$857$	−5.53233	−0.188981	−0.0944904	−	0.995526i	$-0.530122\pi$
$857$	−5.53233	−0.188981	−0.0944904	+	0.995526i	$0.530122\pi$
$858$	25.2864	0.863262
$859$	23.4669	0.800680	0.400340	−	0.916367i	$-0.368892\pi$
$859$	23.4669	0.800680	0.400340	+	0.916367i	$0.368892\pi$
$860$	20.1309	0.686458
$861$	−57.5813	−1.96236
$862$	−4.27848	−0.145726
$863$	−20.3034	−0.691136	−0.345568	−	0.938394i	$-0.612314\pi$
$863$	−20.3034	−0.691136	−0.345568	+	0.938394i	$0.612314\pi$
$864$	7.86580	0.267600
$865$	19.6957	0.669675
$866$	−33.7058	−1.14537
$867$	37.0254	1.25745
$868$	18.8650	0.640320
$869$	−64.2173	−2.17842
$870$	63.8647	2.16522
$871$	6.29033	0.213140
$872$	8.89287	0.301151
$873$	−62.0219	−2.09912
$874$	7.83273	0.264946
$875$	2.50517	0.0846903
$876$	−10.0267	−0.338772
$877$	18.6966	0.631340	0.315670	−	0.948869i	$-0.397771\pi$
$877$	18.6966	0.631340	0.315670	+	0.948869i	$0.397771\pi$
$878$	20.8215	0.702692
$879$	−79.6121	−2.68525
$880$	−11.2526	−0.379324
$881$	22.7740	0.767276	0.383638	−	0.923484i	$-0.374671\pi$
$881$	22.7740	0.767276	0.383638	+	0.923484i	$0.374671\pi$
$882$	12.5663	0.423129
$883$	−38.1457	−1.28371	−0.641853	−	0.766828i	$-0.721834\pi$
$883$	−38.1457	−1.28371	−0.641853	+	0.766828i	$0.721834\pi$
$884$	4.98257	0.167582
$885$	−27.2168	−0.914883
$886$	14.9194	0.501227
$887$	−8.21436	−0.275811	−0.137906	−	0.990445i	$-0.544037\pi$
$887$	−8.21436	−0.275811	−0.137906	+	0.990445i	$0.544037\pi$
$888$	−10.4648	−0.351176
$889$	13.2520	0.444457
$890$	32.4075	1.08630
$891$	22.2949	0.746909
$892$	12.2575	0.410412
$893$	40.4654	1.35412
$894$	46.7112	1.56226
$895$	60.2735	2.01472
$896$	−2.18728	−0.0730718
$897$	−6.97379	−0.232848
$898$	26.4598	0.882975
$899$	−60.2754	−2.01030
$900$	26.2629	0.875430
$901$	−1.01832	−0.0339250
$902$	−32.4157	−1.07932
$903$	41.7804	1.39036
$904$	−17.5993	−0.585343
$905$	−4.62742	−0.153821
$906$	−43.7077	−1.45209
$907$	24.1789	0.802847	0.401423	−	0.915893i	$-0.368516\pi$
$907$	24.1789	0.802847	0.401423	+	0.915893i	$0.368516\pi$
$908$	19.0016	0.630589
$909$	13.4477	0.446032
$910$	16.0756	0.532902
$911$	−16.7466	−0.554840	−0.277420	−	0.960749i	$-0.589479\pi$
$911$	−16.7466	−0.554840	−0.277420	+	0.960749i	$0.589479\pi$
$912$	23.0649	0.763756
$913$	43.9219	1.45360
$914$	−7.95332	−0.263072
$915$	−114.204	−3.77546
$916$	11.8474	0.391448
$917$	2.18728	0.0722303
$918$	16.5488	0.546192
$919$	−36.3207	−1.19811	−0.599054	−	0.800708i	$-0.704457\pi$
$919$	−36.3207	−1.19811	−0.599054	+	0.800708i	$0.704457\pi$
$920$	3.10338	0.102315
$921$	25.4578	0.838864
$922$	2.10206	0.0692277
$923$	26.2949	0.865508
$924$	−23.3540	−0.768289
$925$	−16.4574	−0.541116
$926$	16.4349	0.540086
$927$	31.0115	1.01855
$928$	6.98856	0.229411
$929$	49.7041	1.63074	0.815369	−	0.578941i	$-0.196534\pi$
$929$	49.7041	1.63074	0.815369	+	0.578941i	$0.196534\pi$
$930$	−78.8182	−2.58455
$931$	17.3559	0.568816
$932$	−16.5439	−0.541914
$933$	61.3515	2.00856
$934$	−1.76742	−0.0578317
$935$	−23.6742	−0.774230
$936$	−13.4309	−0.439001
$937$	−5.30193	−0.173207	−0.0866033	−	0.996243i	$-0.527601\pi$
$937$	−5.30193	−0.173207	−0.0866033	+	0.996243i	$0.527601\pi$
$938$	−5.80962	−0.189691
$939$	78.5058	2.56194
$940$	16.0326	0.522927
$941$	−11.9137	−0.388375	−0.194188	−	0.980964i	$-0.562207\pi$
$941$	−11.9137	−0.388375	−0.194188	+	0.980964i	$0.562207\pi$
$942$	61.7047	2.01045
$943$	8.94001	0.291127
$944$	−2.97827	−0.0969344
$945$	53.3926	1.73686
$946$	23.5205	0.764717
$947$	−22.9230	−0.744897	−0.372449	−	0.928053i	$-0.621482\pi$
$947$	−22.9230	−0.744897	−0.372449	+	0.928053i	$0.621482\pi$
$948$	52.1524	1.69383
$949$	8.06398	0.261768
$950$	36.2729	1.17685
$951$	84.5399	2.74140
$952$	−4.60180	−0.149145
$953$	36.4016	1.17916	0.589582	−	0.807708i	$-0.299292\pi$
$953$	36.4016	1.17916	0.589582	+	0.807708i	$0.299292\pi$
$954$	2.74494	0.0888706
$955$	−31.3569	−1.01469
$956$	4.23998	0.137131
$957$	74.6181	2.41206
$958$	−0.341661	−0.0110386
$959$	10.9196	0.352611
$960$	9.13847	0.294943
$961$	43.3884	1.39963
$962$	8.41631	0.271353
$963$	−60.1286	−1.93762
$964$	−12.1426	−0.391088
$965$	−17.5832	−0.566023
$966$	6.44085	0.207231
$967$	17.6323	0.567017	0.283508	−	0.958970i	$-0.408502\pi$
$967$	17.6323	0.567017	0.283508	+	0.958970i	$0.408502\pi$
$968$	−2.14725	−0.0690151
$969$	48.5262	1.55889
$970$	−33.9395	−1.08973
$971$	−29.8520	−0.957997	−0.478999	−	0.877816i	$-0.659000\pi$
$971$	−29.8520	−0.957997	−0.478999	+	0.877816i	$0.659000\pi$
$972$	5.49117	0.176129
$973$	38.3681	1.23002
$974$	−3.60667	−0.115565
$975$	−32.2952	−1.03427
$976$	−12.4970	−0.400021
$977$	26.6042	0.851142	0.425571	−	0.904925i	$-0.360073\pi$
$977$	26.6042	0.851142	0.425571	+	0.904925i	$0.360073\pi$
$978$	−47.0947	−1.50592
$979$	37.8642	1.21015
$980$	6.87651	0.219662
$981$	−50.4331	−1.61021
$982$	37.2123	1.18749
$983$	−40.9438	−1.30590	−0.652952	−	0.757399i	$-0.726470\pi$
$983$	−40.9438	−1.30590	−0.652952	+	0.757399i	$0.726470\pi$
$984$	26.3255	0.839228
$985$	−51.4165	−1.63827
$986$	14.7032	0.468245
$987$	33.2747	1.05915
$988$	−18.5500	−0.590153
$989$	−6.48678	−0.206268
$990$	63.8154	2.02819
$991$	−20.5602	−0.653116	−0.326558	−	0.945177i	$-0.605889\pi$
$991$	−20.5602	−0.653116	−0.326558	+	0.945177i	$0.605889\pi$
$992$	−8.62487	−0.273840
$993$	−80.1810	−2.54447
$994$	−24.2855	−0.770288
$995$	57.5707	1.82511
$996$	−35.6700	−1.13025
$997$	7.19606	0.227902	0.113951	−	0.993486i	$-0.463649\pi$
$997$	7.19606	0.227902	0.113951	+	0.993486i	$0.463649\pi$
$998$	−19.3933	−0.613884
$999$	27.9534	0.884407

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	6026.2.a.i.1.2	✓	25

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
6026.2.a.i.1.2	✓	25	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)

\(f(q)\)	\(=\)	\(q-1.00000 q^{2} -2.94469 q^{3} +1.00000 q^{4} -3.10338 q^{5} +2.94469 q^{6} +2.18728 q^{7} -1.00000 q^{8} +5.67118 q^{9} +O(q^{10})\)	\(q-1.00000 q^{2} -2.94469 q^{3} +1.00000 q^{4} -3.10338 q^{5} +2.94469 q^{6} +2.18728 q^{7} -1.00000 q^{8} +5.67118 q^{9} +3.10338 q^{10} +3.62591 q^{11} -2.94469 q^{12} +2.36826 q^{13} -2.18728 q^{14} +9.13847 q^{15} +1.00000 q^{16} +2.10389 q^{17} -5.67118 q^{18} -7.83273 q^{19} -3.10338 q^{20} -6.44085 q^{21} -3.62591 q^{22} +1.00000 q^{23} +2.94469 q^{24} +4.63094 q^{25} -2.36826 q^{26} -7.86580 q^{27} +2.18728 q^{28} -6.98856 q^{29} -9.13847 q^{30} +8.62487 q^{31} -1.00000 q^{32} -10.6772 q^{33} -2.10389 q^{34} -6.78794 q^{35} +5.67118 q^{36} -3.55379 q^{37} +7.83273 q^{38} -6.97379 q^{39} +3.10338 q^{40} +8.94001 q^{41} +6.44085 q^{42} -6.48678 q^{43} +3.62591 q^{44} -17.5998 q^{45} -1.00000 q^{46} -5.16620 q^{47} -2.94469 q^{48} -2.21582 q^{49} -4.63094 q^{50} -6.19531 q^{51} +2.36826 q^{52} -0.484015 q^{53} +7.86580 q^{54} -11.2526 q^{55} -2.18728 q^{56} +23.0649 q^{57} +6.98856 q^{58} -2.97827 q^{59} +9.13847 q^{60} -12.4970 q^{61} -8.62487 q^{62} +12.4045 q^{63} +1.00000 q^{64} -7.34961 q^{65} +10.6772 q^{66} +2.65610 q^{67} +2.10389 q^{68} -2.94469 q^{69} +6.78794 q^{70} +11.1030 q^{71} -5.67118 q^{72} +3.40502 q^{73} +3.55379 q^{74} -13.6367 q^{75} -7.83273 q^{76} +7.93088 q^{77} +6.97379 q^{78} -17.7107 q^{79} -3.10338 q^{80} +6.14878 q^{81} -8.94001 q^{82} +12.1133 q^{83} -6.44085 q^{84} -6.52917 q^{85} +6.48678 q^{86} +20.5791 q^{87} -3.62591 q^{88} +10.4427 q^{89} +17.5998 q^{90} +5.18005 q^{91} +1.00000 q^{92} -25.3976 q^{93} +5.16620 q^{94} +24.3079 q^{95} +2.94469 q^{96} -10.9363 q^{97} +2.21582 q^{98} +20.5632 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 25 q - 25 q^{2} - 4 q^{3} + 25 q^{4} - 3 q^{5} + 4 q^{6} - 11 q^{7} - 25 q^{8} + 19 q^{9}+O(q^{10}) \) 25 * q - 25 * q^2 - 4 * q^3 + 25 * q^4 - 3 * q^5 + 4 * q^6 - 11 * q^7 - 25 * q^8 + 19 * q^9	\( 25 q - 25 q^{2} - 4 q^{3} + 25 q^{4} - 3 q^{5} + 4 q^{6} - 11 q^{7} - 25 q^{8} + 19 q^{9} + 3 q^{10} - 12 q^{11} - 4 q^{12} - 6 q^{13} + 11 q^{14} + 25 q^{16} + 8 q^{17} - 19 q^{18} - 23 q^{19} - 3 q^{20} - 16 q^{21} + 12 q^{22} + 25 q^{23} + 4 q^{24} + 4 q^{25} + 6 q^{26} - 13 q^{27} - 11 q^{28} - 7 q^{29} - 7 q^{31} - 25 q^{32} + 3 q^{33} - 8 q^{34} - 18 q^{35} + 19 q^{36} - 7 q^{37} + 23 q^{38} - 2 q^{39} + 3 q^{40} - 10 q^{41} + 16 q^{42} - 26 q^{43} - 12 q^{44} + 20 q^{45} - 25 q^{46} - 2 q^{47} - 4 q^{48} + 2 q^{49} - 4 q^{50} - 28 q^{51} - 6 q^{52} + 47 q^{53} + 13 q^{54} - 38 q^{55} + 11 q^{56} - 4 q^{57} + 7 q^{58} - 19 q^{59} - 26 q^{61} + 7 q^{62} - 15 q^{63} + 25 q^{64} + 13 q^{65} - 3 q^{66} - 34 q^{67} + 8 q^{68} - 4 q^{69} + 18 q^{70} - 10 q^{71} - 19 q^{72} - 22 q^{73} + 7 q^{74} - 8 q^{75} - 23 q^{76} + 28 q^{77} + 2 q^{78} - 21 q^{79} - 3 q^{80} - 27 q^{81} + 10 q^{82} - 16 q^{83} - 16 q^{84} - 42 q^{85} + 26 q^{86} - 17 q^{87} + 12 q^{88} + 27 q^{89} - 20 q^{90} - 26 q^{91} + 25 q^{92} - 27 q^{93} + 2 q^{94} + 4 q^{96} + 4 q^{97} - 2 q^{98} - 2 q^{99}+O(q^{100}) \) 25 * q - 25 * q^2 - 4 * q^3 + 25 * q^4 - 3 * q^5 + 4 * q^6 - 11 * q^7 - 25 * q^8 + 19 * q^9 + 3 * q^10 - 12 * q^11 - 4 * q^12 - 6 * q^13 + 11 * q^14 + 25 * q^16 + 8 * q^17 - 19 * q^18 - 23 * q^19 - 3 * q^20 - 16 * q^21 + 12 * q^22 + 25 * q^23 + 4 * q^24 + 4 * q^25 + 6 * q^26 - 13 * q^27 - 11 * q^28 - 7 * q^29 - 7 * q^31 - 25 * q^32 + 3 * q^33 - 8 * q^34 - 18 * q^35 + 19 * q^36 - 7 * q^37 + 23 * q^38 - 2 * q^39 + 3 * q^40 - 10 * q^41 + 16 * q^42 - 26 * q^43 - 12 * q^44 + 20 * q^45 - 25 * q^46 - 2 * q^47 - 4 * q^48 + 2 * q^49 - 4 * q^50 - 28 * q^51 - 6 * q^52 + 47 * q^53 + 13 * q^54 - 38 * q^55 + 11 * q^56 - 4 * q^57 + 7 * q^58 - 19 * q^59 - 26 * q^61 + 7 * q^62 - 15 * q^63 + 25 * q^64 + 13 * q^65 - 3 * q^66 - 34 * q^67 + 8 * q^68 - 4 * q^69 + 18 * q^70 - 10 * q^71 - 19 * q^72 - 22 * q^73 + 7 * q^74 - 8 * q^75 - 23 * q^76 + 28 * q^77 + 2 * q^78 - 21 * q^79 - 3 * q^80 - 27 * q^81 + 10 * q^82 - 16 * q^83 - 16 * q^84 - 42 * q^85 + 26 * q^86 - 17 * q^87 + 12 * q^88 + 27 * q^89 - 20 * q^90 - 26 * q^91 + 25 * q^92 - 27 * q^93 + 2 * q^94 + 4 * q^96 + 4 * q^97 - 2 * q^98 - 2 * q^99

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