LMFDB - Embedded newform 5290.2.a.q.1.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [5290,2,Mod(1,5290)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(5290, 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("5290.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 5290 = 2 \cdot 5 \cdot 23^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	5290.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:	$42.2408626693$
Analytic rank:	$0$
Dimension:	$3$
Coefficient field:	3.3.1509.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{3} - x^{2} - 7x + 4 $ x^3 - x^2 - 7*x + 4
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.2
Root			$0.551929$ of defining polynomial
Character	$\chi$	$=$	5290.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.00000 q^{2} -0.551929 q^{3} +1.00000 q^{4} +1.00000 q^{5} -0.551929 q^{6} -3.69537 q^{7} +1.00000 q^{8} -2.69537 q^{9} +O(q^{10})$	\(q+1.00000 q^{2} -0.551929 q^{3} +1.00000 q^{4} +1.00000 q^{5} -0.551929 q^{6} -3.69537 q^{7} +1.00000 q^{8} -2.69537 q^{9} +1.00000 q^{10} +1.44807 q^{11} -0.551929 q^{12} -5.69537 q^{13} -3.69537 q^{14} -0.551929 q^{15} +1.00000 q^{16} +4.55193 q^{17} -2.69537 q^{18} -6.79923 q^{19} +1.00000 q^{20} +2.03959 q^{21} +1.44807 q^{22} -0.551929 q^{24} +1.00000 q^{25} -5.69537 q^{26} +3.14344 q^{27} -3.69537 q^{28} +10.4946 q^{29} -0.551929 q^{30} -2.59152 q^{31} +1.00000 q^{32} -0.799233 q^{33} +4.55193 q^{34} -3.69537 q^{35} -2.69537 q^{36} +0.207718 q^{37} -6.79923 q^{38} +3.14344 q^{39} +1.00000 q^{40} +1.44807 q^{41} +2.03959 q^{42} +10.4946 q^{43} +1.44807 q^{44} -2.69537 q^{45} -10.2869 q^{47} -0.551929 q^{48} +6.65579 q^{49} +1.00000 q^{50} -2.51234 q^{51} -5.69537 q^{52} +13.3907 q^{53} +3.14344 q^{54} +1.44807 q^{55} -3.69537 q^{56} +3.75270 q^{57} +10.4946 q^{58} +4.49461 q^{59} -0.551929 q^{60} +11.7350 q^{61} -2.59152 q^{62} +9.96041 q^{63} +1.00000 q^{64} -5.69537 q^{65} -0.799233 q^{66} -3.10386 q^{67} +4.55193 q^{68} -3.69537 q^{70} -4.55193 q^{71} -2.69537 q^{72} +2.49461 q^{73} +0.207718 q^{74} -0.551929 q^{75} -6.79923 q^{76} -5.35116 q^{77} +3.14344 q^{78} +10.2869 q^{79} +1.00000 q^{80} +6.35116 q^{81} +1.44807 q^{82} +7.59847 q^{83} +2.03959 q^{84} +4.55193 q^{85} +10.4946 q^{86} -5.79228 q^{87} +1.44807 q^{88} -7.39075 q^{89} -2.69537 q^{90} +21.0465 q^{91} +1.43033 q^{93} -10.2869 q^{94} -6.79923 q^{95} -0.551929 q^{96} -10.3442 q^{97} +6.65579 q^{98} -3.90309 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 3 q + 3 q^{2} - q^{3} + 3 q^{4} + 3 q^{5} - q^{6} + 3 q^{7} + 3 q^{8} + 6 q^{9}+O(q^{10}) $ 3 * q + 3 * q^2 - q^3 + 3 * q^4 + 3 * q^5 - q^6 + 3 * q^7 + 3 * q^8 + 6 * q^9	\( 3 q + 3 q^{2} - q^{3} + 3 q^{4} + 3 q^{5} - q^{6} + 3 q^{7} + 3 q^{8} + 6 q^{9} + 3 q^{10} + 5 q^{11} - q^{12} - 3 q^{13} + 3 q^{14} - q^{15} + 3 q^{16} + 13 q^{17} + 6 q^{18} - 5 q^{19} + 3 q^{20} - 6 q^{21} + 5 q^{22} - q^{24} + 3 q^{25} - 3 q^{26} - 4 q^{27} + 3 q^{28} + 2 q^{29} - q^{30} + 5 q^{31} + 3 q^{32} + 13 q^{33} + 13 q^{34} + 3 q^{35} + 6 q^{36} - 2 q^{37} - 5 q^{38} - 4 q^{39} + 3 q^{40} + 5 q^{41} - 6 q^{42} + 2 q^{43} + 5 q^{44} + 6 q^{45} - 4 q^{47} - q^{48} + 18 q^{49} + 3 q^{50} - 19 q^{51} - 3 q^{52} + 12 q^{53} - 4 q^{54} + 5 q^{55} + 3 q^{56} + 26 q^{57} + 2 q^{58} - 16 q^{59} - q^{60} + 9 q^{61} + 5 q^{62} + 42 q^{63} + 3 q^{64} - 3 q^{65} + 13 q^{66} - 8 q^{67} + 13 q^{68} + 3 q^{70} - 13 q^{71} + 6 q^{72} - 22 q^{73} - 2 q^{74} - q^{75} - 5 q^{76} - 4 q^{78} + 4 q^{79} + 3 q^{80} + 3 q^{81} + 5 q^{82} - 8 q^{83} - 6 q^{84} + 13 q^{85} + 2 q^{86} - 20 q^{87} + 5 q^{88} + 6 q^{89} + 6 q^{90} + 33 q^{91} - 36 q^{93} - 4 q^{94} - 5 q^{95} - q^{96} - 33 q^{97} + 18 q^{98} + 5 q^{99}+O(q^{100}) \) 3 * q + 3 * q^2 - q^3 + 3 * q^4 + 3 * q^5 - q^6 + 3 * q^7 + 3 * q^8 + 6 * q^9 + 3 * q^10 + 5 * q^11 - q^12 - 3 * q^13 + 3 * q^14 - q^15 + 3 * q^16 + 13 * q^17 + 6 * q^18 - 5 * q^19 + 3 * q^20 - 6 * q^21 + 5 * q^22 - q^24 + 3 * q^25 - 3 * q^26 - 4 * q^27 + 3 * q^28 + 2 * q^29 - q^30 + 5 * q^31 + 3 * q^32 + 13 * q^33 + 13 * q^34 + 3 * q^35 + 6 * q^36 - 2 * q^37 - 5 * q^38 - 4 * q^39 + 3 * q^40 + 5 * q^41 - 6 * q^42 + 2 * q^43 + 5 * q^44 + 6 * q^45 - 4 * q^47 - q^48 + 18 * q^49 + 3 * q^50 - 19 * q^51 - 3 * q^52 + 12 * q^53 - 4 * q^54 + 5 * q^55 + 3 * q^56 + 26 * q^57 + 2 * q^58 - 16 * q^59 - q^60 + 9 * q^61 + 5 * q^62 + 42 * q^63 + 3 * q^64 - 3 * q^65 + 13 * q^66 - 8 * q^67 + 13 * q^68 + 3 * q^70 - 13 * q^71 + 6 * q^72 - 22 * q^73 - 2 * q^74 - q^75 - 5 * q^76 - 4 * q^78 + 4 * q^79 + 3 * q^80 + 3 * q^81 + 5 * q^82 - 8 * q^83 - 6 * q^84 + 13 * q^85 + 2 * q^86 - 20 * q^87 + 5 * q^88 + 6 * q^89 + 6 * q^90 + 33 * q^91 - 36 * q^93 - 4 * q^94 - 5 * q^95 - q^96 - 33 * q^97 + 18 * q^98 + 5 * 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
$3$	−0.551929	−0.318657	−0.159328	−	0.987226i	$-0.550933\pi$
$3$	−0.551929	−0.318657	−0.159328	+	0.987226i	$0.550933\pi$
$4$	1.00000	0.500000
$5$	1.00000	0.447214
$5$	1.00000	0.447214
$6$	−0.551929	−0.225324
$7$	−3.69537	−1.39672	−0.698360	−	0.715747i	$-0.746087\pi$
$7$	−3.69537	−1.39672	−0.698360	+	0.715747i	$0.746087\pi$
$8$	1.00000	0.353553
$9$	−2.69537	−0.898458
$10$	1.00000	0.316228
$11$	1.44807	0.436610	0.218305	−	0.975881i	$-0.429947\pi$
$11$	1.44807	0.436610	0.218305	+	0.975881i	$0.429947\pi$
$12$	−0.551929	−0.159328
$13$	−5.69537	−1.57961	−0.789806	−	0.613356i	$-0.789819\pi$
$13$	−5.69537	−1.57961	−0.789806	+	0.613356i	$0.789819\pi$
$14$	−3.69537	−0.987630
$15$	−0.551929	−0.142508
$16$	1.00000	0.250000
$17$	4.55193	1.10401	0.552003	−	0.833842i	$-0.313864\pi$
$17$	4.55193	1.10401	0.552003	+	0.833842i	$0.313864\pi$
$18$	−2.69537	−0.635306
$19$	−6.79923	−1.55985	−0.779925	−	0.625872i	$-0.784743\pi$
$19$	−6.79923	−1.55985	−0.779925	+	0.625872i	$0.784743\pi$
$20$	1.00000	0.223607
$21$	2.03959	0.445074
$22$	1.44807	0.308730
$23$	0	0
$23$	0	0
$24$	−0.551929	−0.112662
$25$	1.00000	0.200000
$26$	−5.69537	−1.11695
$27$	3.14344	0.604956
$28$	−3.69537	−0.698360
$29$	10.4946	1.94880	0.974400	−	0.224822i	$-0.0721802\pi$
$29$	10.4946	1.94880	0.974400	+	0.224822i	$0.0721802\pi$
$30$	−0.551929	−0.100768
$31$	−2.59152	−0.465450	−0.232725	−	0.972543i	$-0.574764\pi$
$31$	−2.59152	−0.465450	−0.232725	+	0.972543i	$0.574764\pi$
$32$	1.00000	0.176777
$33$	−0.799233	−0.139129
$34$	4.55193	0.780649
$35$	−3.69537	−0.624632
$36$	−2.69537	−0.449229
$37$	0.207718	0.0341486	0.0170743	−	0.999854i	$-0.494565\pi$
$37$	0.207718	0.0341486	0.0170743	+	0.999854i	$0.494565\pi$
$38$	−6.79923	−1.10298
$39$	3.14344	0.503354
$40$	1.00000	0.158114
$41$	1.44807	0.226151	0.113075	−	0.993586i	$-0.463930\pi$
$41$	1.44807	0.226151	0.113075	+	0.993586i	$0.463930\pi$
$42$	2.03959	0.314715
$43$	10.4946	1.60041	0.800206	−	0.599725i	$-0.204723\pi$
$43$	10.4946	1.60041	0.800206	+	0.599725i	$0.204723\pi$
$44$	1.44807	0.218305
$45$	−2.69537	−0.401803
$46$	0	0
$47$	−10.2869	−1.50050	−0.750248	−	0.661156i	$-0.770066\pi$
$47$	−10.2869	−1.50050	−0.750248	+	0.661156i	$0.770066\pi$
$48$	−0.551929	−0.0796642
$49$	6.65579	0.950827
$50$	1.00000	0.141421
$51$	−2.51234	−0.351799
$52$	−5.69537	−0.789806
$53$	13.3907	1.83936	0.919680	−	0.392668i	$-0.128448\pi$
$53$	13.3907	1.83936	0.919680	+	0.392668i	$0.128448\pi$
$54$	3.14344	0.427769
$55$	1.44807	0.195258
$56$	−3.69537	−0.493815
$57$	3.75270	0.497057
$58$	10.4946	1.37801
$59$	4.49461	0.585148	0.292574	−	0.956243i	$-0.405488\pi$
$59$	4.49461	0.585148	0.292574	+	0.956243i	$0.405488\pi$
$60$	−0.551929	−0.0712538
$61$	11.7350	1.50251	0.751254	−	0.660013i	$-0.229449\pi$
$61$	11.7350	1.50251	0.751254	+	0.660013i	$0.229449\pi$
$62$	−2.59152	−0.329123
$63$	9.96041	1.25489
$64$	1.00000	0.125000
$65$	−5.69537	−0.706424
$66$	−0.799233	−0.0983788
$67$	−3.10386	−0.379197	−0.189598	−	0.981862i	$-0.560719\pi$
$67$	−3.10386	−0.379197	−0.189598	+	0.981862i	$0.560719\pi$
$68$	4.55193	0.552003
$69$	0	0
$70$	−3.69537	−0.441682
$71$	−4.55193	−0.540215	−0.270107	−	0.962830i	$-0.587059\pi$
$71$	−4.55193	−0.540215	−0.270107	+	0.962830i	$0.587059\pi$
$72$	−2.69537	−0.317653
$73$	2.49461	0.291972	0.145986	−	0.989287i	$-0.453365\pi$
$73$	2.49461	0.291972	0.145986	+	0.989287i	$0.453365\pi$
$74$	0.207718	0.0241467
$75$	−0.551929	−0.0637313
$76$	−6.79923	−0.779925
$77$	−5.35116	−0.609822
$78$	3.14344	0.355925
$79$	10.2869	1.15737	0.578683	−	0.815553i	$-0.303567\pi$
$79$	10.2869	1.15737	0.578683	+	0.815553i	$0.303567\pi$
$80$	1.00000	0.111803
$81$	6.35116	0.705685
$82$	1.44807	0.159913
$83$	7.59847	0.834040	0.417020	−	0.908897i	$-0.363075\pi$
$83$	7.59847	0.834040	0.417020	+	0.908897i	$0.363075\pi$
$84$	2.03959	0.222537
$85$	4.55193	0.493726
$86$	10.4946	1.13166
$87$	−5.79228	−0.620998
$88$	1.44807	0.154365
$89$	−7.39075	−0.783418	−0.391709	−	0.920089i	$-0.628116\pi$
$89$	−7.39075	−0.783418	−0.391709	+	0.920089i	$0.628116\pi$
$90$	−2.69537	−0.284117
$91$	21.0465	2.20628
$92$	0	0
$93$	1.43033	0.148319
$94$	−10.2869	−1.06101
$95$	−6.79923	−0.697587
$96$	−0.551929	−0.0563311
$97$	−10.3442	−1.05030	−0.525148	−	0.851011i	$-0.675990\pi$
$97$	−10.3442	−1.05030	−0.525148	+	0.851011i	$0.675990\pi$
$98$	6.65579	0.672336
$99$	−3.90309	−0.392275
$100$	1.00000	0.100000
$101$	0.207718	0.0206687	0.0103343	−	0.999947i	$-0.496710\pi$
$101$	0.207718	0.0206687	0.0103343	+	0.999947i	$0.496710\pi$
$102$	−2.51234	−0.248759
$103$	8.63110	0.850448	0.425224	−	0.905088i	$-0.360195\pi$
$103$	8.63110	0.850448	0.425224	+	0.905088i	$0.360195\pi$
$104$	−5.69537	−0.558477
$105$	2.03959	0.199043
$106$	13.3907	1.30062
$107$	6.00000	0.580042	0.290021	−	0.957020i	$-0.406338\pi$
$107$	6.00000	0.580042	0.290021	+	0.957020i	$0.406338\pi$
$108$	3.14344	0.302478
$109$	18.7992	1.80064	0.900320	−	0.435229i	$-0.143332\pi$
$109$	18.7992	1.80064	0.900320	+	0.435229i	$0.143332\pi$
$110$	1.44807	0.138068
$111$	−0.114646	−0.0108817
$112$	−3.69537	−0.349180
$113$	−4.49461	−0.422817	−0.211409	−	0.977398i	$-0.567805\pi$
$113$	−4.49461	−0.422817	−0.211409	+	0.977398i	$0.567805\pi$
$114$	3.75270	0.351472
$115$	0	0
$116$	10.4946	0.974400
$117$	15.3512	1.41922
$118$	4.49461	0.413762
$119$	−16.8211	−1.54199
$120$	−0.551929	−0.0503840
$121$	−8.90309	−0.809372
$122$	11.7350	1.06243
$123$	−0.799233	−0.0720644
$124$	−2.59152	−0.232725
$125$	1.00000	0.0894427
$126$	9.96041	0.887344
$127$	−15.8062	−1.40257	−0.701286	−	0.712880i	$-0.747390\pi$
$127$	−15.8062	−1.40257	−0.701286	+	0.712880i	$0.747390\pi$
$128$	1.00000	0.0883883
$129$	−5.79228	−0.509982
$130$	−5.69537	−0.499517
$131$	−6.20772	−0.542371	−0.271185	−	0.962527i	$-0.587416\pi$
$131$	−6.20772	−0.542371	−0.271185	+	0.962527i	$0.587416\pi$
$132$	−0.799233	−0.0695643
$133$	25.1257	2.17868
$134$	−3.10386	−0.268133
$135$	3.14344	0.270545
$136$	4.55193	0.390325
$137$	17.2938	1.47751	0.738756	−	0.673973i	$-0.235413\pi$
$137$	17.2938	1.47751	0.738756	+	0.673973i	$0.235413\pi$
$138$	0	0
$139$	10.8961	0.924199	0.462099	−	0.886828i	$-0.347096\pi$
$139$	10.8961	0.924199	0.462099	+	0.886828i	$0.347096\pi$
$140$	−3.69537	−0.312316
$141$	5.67764	0.478143
$142$	−4.55193	−0.381989
$143$	−8.24730	−0.689674
$144$	−2.69537	−0.224614
$145$	10.4946	0.871530
$146$	2.49461	0.206455
$147$	−3.67353	−0.302987
$148$	0.207718	0.0170743
$149$	5.20077	0.426063	0.213032	−	0.977045i	$-0.431666\pi$
$149$	5.20077	0.426063	0.213032	+	0.977045i	$0.431666\pi$
$150$	−0.551929	−0.0450648
$151$	15.4481	1.25715	0.628573	−	0.777751i	$-0.283639\pi$
$151$	15.4481	1.25715	0.628573	+	0.777751i	$0.283639\pi$
$152$	−6.79923	−0.551491
$153$	−12.2692	−0.991902
$154$	−5.35116	−0.431209
$155$	−2.59152	−0.208155
$156$	3.14344	0.251677
$157$	−8.89614	−0.709989	−0.354995	−	0.934868i	$-0.615517\pi$
$157$	−8.89614	−0.709989	−0.354995	+	0.934868i	$0.615517\pi$
$158$	10.2869	0.818381
$159$	−7.39075	−0.586124
$160$	1.00000	0.0790569
$161$	0	0
$162$	6.35116	0.498994
$163$	12.1900	0.954793	0.477396	−	0.878688i	$-0.341581\pi$
$163$	12.1900	0.954793	0.477396	+	0.878688i	$0.341581\pi$
$164$	1.44807	0.113075
$165$	−0.799233	−0.0622202
$166$	7.59847	0.589755
$167$	−13.5985	−1.05228	−0.526140	−	0.850398i	$-0.676361\pi$
$167$	−13.5985	−1.05228	−0.526140	+	0.850398i	$0.676361\pi$
$168$	2.03959	0.157357
$169$	19.4373	1.49518
$170$	4.55193	0.349117
$171$	18.3265	1.40146
$172$	10.4946	0.800206
$173$	1.44807	0.110095	0.0550474	−	0.998484i	$-0.482469\pi$
$173$	1.44807	0.110095	0.0550474	+	0.998484i	$0.482469\pi$
$174$	−5.79228	−0.439112
$175$	−3.69537	−0.279344
$176$	1.44807	0.109152
$177$	−2.48071	−0.186461
$178$	−7.39075	−0.553960
$179$	−19.3907	−1.44933	−0.724666	−	0.689100i	$-0.758006\pi$
$179$	−19.3907	−1.44933	−0.724666	+	0.689100i	$0.758006\pi$
$180$	−2.69537	−0.200901
$181$	−14.1900	−1.05473	−0.527366	−	0.849638i	$-0.676821\pi$
$181$	−14.1900	−1.05473	−0.527366	+	0.849638i	$0.676821\pi$
$182$	21.0465	1.56007
$183$	−6.47687	−0.478784
$184$	0	0
$185$	0.207718	0.0152717
$186$	1.43033	0.104877
$187$	6.59152	0.482019
$188$	−10.2869	−0.750248
$189$	−11.6162	−0.844954
$190$	−6.79923	−0.493268
$191$	4.60925	0.333514	0.166757	−	0.985998i	$-0.446670\pi$
$191$	4.60925	0.333514	0.166757	+	0.985998i	$0.446670\pi$
$192$	−0.551929	−0.0398321
$193$	−0.896141	−0.0645057	−0.0322528	−	0.999480i	$-0.510268\pi$
$193$	−0.896141	−0.0645057	−0.0322528	+	0.999480i	$0.510268\pi$
$194$	−10.3442	−0.742671
$195$	3.14344	0.225107
$196$	6.65579	0.475413
$197$	−7.65579	−0.545452	−0.272726	−	0.962092i	$-0.587925\pi$
$197$	−7.65579	−0.545452	−0.272726	+	0.962092i	$0.587925\pi$
$198$	−3.90309	−0.277381
$199$	6.20772	0.440053	0.220027	−	0.975494i	$-0.429386\pi$
$199$	6.20772	0.440053	0.220027	+	0.975494i	$0.429386\pi$
$200$	1.00000	0.0707107
$201$	1.71311	0.120834
$202$	0.207718	0.0146150
$203$	−38.7815	−2.72193
$204$	−2.51234	−0.175899
$205$	1.44807	0.101138
$206$	8.63110	0.601357
$207$	0	0
$208$	−5.69537	−0.394903
$209$	−9.84577	−0.681046
$210$	2.03959	0.140745
$211$	17.1830	1.18293	0.591464	−	0.806331i	$-0.298550\pi$
$211$	17.1830	1.18293	0.591464	+	0.806331i	$0.298550\pi$
$212$	13.3907	0.919680
$213$	2.51234	0.172143
$214$	6.00000	0.410152
$215$	10.4946	0.715726
$216$	3.14344	0.213884
$217$	9.57662	0.650103
$218$	18.7992	1.27324
$219$	−1.37685	−0.0930387
$220$	1.44807	0.0976289
$221$	−25.9249	−1.74390
$222$	−0.114646	−0.00769450
$223$	−15.8854	−1.06376	−0.531881	−	0.846819i	$-0.678515\pi$
$223$	−15.8854	−1.06376	−0.531881	+	0.846819i	$0.678515\pi$
$224$	−3.69537	−0.246908
$225$	−2.69537	−0.179692
$226$	−4.49461	−0.298977
$227$	−19.1830	−1.27322	−0.636611	−	0.771185i	$-0.719664\pi$
$227$	−19.1830	−1.27322	−0.636611	+	0.771185i	$0.719664\pi$
$228$	3.75270	0.248528
$229$	12.2077	0.806709	0.403354	−	0.915044i	$-0.367844\pi$
$229$	12.2077	0.806709	0.403354	+	0.915044i	$0.367844\pi$
$230$	0	0
$231$	2.95346	0.194324
$232$	10.4946	0.689005
$233$	3.10386	0.203341	0.101670	−	0.994818i	$-0.467581\pi$
$233$	3.10386	0.203341	0.101670	+	0.994818i	$0.467581\pi$
$234$	15.3512	1.00354
$235$	−10.2869	−0.671043
$236$	4.49461	0.292574
$237$	−5.67764	−0.368802
$238$	−16.8211	−1.09035
$239$	12.0000	0.776215	0.388108	−	0.921614i	$-0.373129\pi$
$239$	12.0000	0.776215	0.388108	+	0.921614i	$0.373129\pi$
$240$	−0.551929	−0.0356269
$241$	−6.20772	−0.399874	−0.199937	−	0.979809i	$-0.564074\pi$
$241$	−6.20772	−0.399874	−0.199937	+	0.979809i	$0.564074\pi$
$242$	−8.90309	−0.572312
$243$	−12.9357	−0.829827
$244$	11.7350	0.751254
$245$	6.65579	0.425223
$246$	−0.799233	−0.0509572
$247$	38.7242	2.46396
$248$	−2.59152	−0.164561
$249$	−4.19382	−0.265772
$250$	1.00000	0.0632456
$251$	27.7884	1.75399	0.876996	−	0.480498i	$-0.159544\pi$
$251$	27.7884	1.75399	0.876996	+	0.480498i	$0.159544\pi$
$252$	9.96041	0.627447
$253$	0	0
$254$	−15.8062	−0.991768
$255$	−2.51234	−0.157329
$256$	1.00000	0.0625000
$257$	−12.0931	−0.754345	−0.377173	−	0.926143i	$-0.623104\pi$
$257$	−12.0931	−0.754345	−0.377173	+	0.926143i	$0.623104\pi$
$258$	−5.79228	−0.360612
$259$	−0.767595	−0.0476960
$260$	−5.69537	−0.353212
$261$	−28.2869	−1.75091
$262$	−6.20772	−0.383514
$263$	−2.83882	−0.175049	−0.0875245	−	0.996162i	$-0.527896\pi$
$263$	−2.83882	−0.175049	−0.0875245	+	0.996162i	$0.527896\pi$
$264$	−0.799233	−0.0491894
$265$	13.3907	0.822587
$266$	25.1257	1.54056
$267$	4.07917	0.249641
$268$	−3.10386	−0.189598
$269$	−9.31158	−0.567737	−0.283868	−	0.958863i	$-0.591618\pi$
$269$	−9.31158	−0.567737	−0.283868	+	0.958863i	$0.591618\pi$
$270$	3.14344	0.191304
$271$	−3.00695	−0.182659	−0.0913296	−	0.995821i	$-0.529112\pi$
$271$	−3.00695	−0.182659	−0.0913296	+	0.995821i	$0.529112\pi$
$272$	4.55193	0.276001
$273$	−11.6162	−0.703045
$274$	17.2938	1.04476
$275$	1.44807	0.0873219
$276$	0	0
$277$	25.1969	1.51394	0.756968	−	0.653451i	$-0.226680\pi$
$277$	25.1969	1.51394	0.756968	+	0.653451i	$0.226680\pi$
$278$	10.8961	0.653507
$279$	6.98510	0.418187
$280$	−3.69537	−0.220841
$281$	−4.07917	−0.243343	−0.121671	−	0.992570i	$-0.538825\pi$
$281$	−4.07917	−0.243343	−0.121671	+	0.992570i	$0.538825\pi$
$282$	5.67764	0.338098
$283$	10.4946	0.623840	0.311920	−	0.950108i	$-0.399028\pi$
$283$	10.4946	0.623840	0.311920	+	0.950108i	$0.399028\pi$
$284$	−4.55193	−0.270107
$285$	3.75270	0.222291
$286$	−8.24730	−0.487673
$287$	−5.35116	−0.315869
$288$	−2.69537	−0.158826
$289$	3.72006	0.218827
$290$	10.4946	0.616265
$291$	5.70927	0.334684
$292$	2.49461	0.145986
$293$	−6.41544	−0.374794	−0.187397	−	0.982284i	$-0.560005\pi$
$293$	−6.41544	−0.374794	−0.187397	+	0.982284i	$0.560005\pi$
$294$	−3.67353	−0.214244
$295$	4.49461	0.261686
$296$	0.207718	0.0120733
$297$	4.55193	0.264130
$298$	5.20077	0.301272
$299$	0	0
$300$	−0.551929	−0.0318657
$301$	−38.7815	−2.23533
$302$	15.4481	0.888937
$303$	−0.114646	−0.00658621
$304$	−6.79923	−0.389963
$305$	11.7350	0.671942
$306$	−12.2692	−0.701381
$307$	−3.86351	−0.220502	−0.110251	−	0.993904i	$-0.535165\pi$
$307$	−3.86351	−0.220502	−0.110251	+	0.993904i	$0.535165\pi$
$308$	−5.35116	−0.304911
$309$	−4.76376	−0.271001
$310$	−2.59152	−0.147188
$311$	12.0000	0.680458	0.340229	−	0.940343i	$-0.389495\pi$
$311$	12.0000	0.680458	0.340229	+	0.940343i	$0.389495\pi$
$312$	3.14344	0.177962
$313$	−17.2938	−0.977506	−0.488753	−	0.872422i	$-0.662548\pi$
$313$	−17.2938	−0.977506	−0.488753	+	0.872422i	$0.662548\pi$
$314$	−8.89614	−0.502038
$315$	9.96041	0.561206
$316$	10.2869	0.578683
$317$	−15.4877	−0.869873	−0.434937	−	0.900461i	$-0.643229\pi$
$317$	−15.4877	−0.869873	−0.434937	+	0.900461i	$0.643229\pi$
$318$	−7.39075	−0.414453
$319$	15.1969	0.850865
$320$	1.00000	0.0559017
$321$	−3.31158	−0.184834
$322$	0	0
$323$	−30.9496	−1.72208
$324$	6.35116	0.352842
$325$	−5.69537	−0.315923
$326$	12.1900	0.675141
$327$	−10.3758	−0.573786
$328$	1.44807	0.0799563
$329$	38.0139	2.09577
$330$	−0.799233	−0.0439963
$331$	11.3907	0.626092	0.313046	−	0.949738i	$-0.398651\pi$
$331$	11.3907	0.626092	0.313046	+	0.949738i	$0.398651\pi$
$332$	7.59847	0.417020
$333$	−0.559877	−0.0306811
$334$	−13.5985	−0.744075
$335$	−3.10386	−0.169582
$336$	2.03959	0.111269
$337$	2.09691	0.114226	0.0571129	−	0.998368i	$-0.481810\pi$
$337$	2.09691	0.114226	0.0571129	+	0.998368i	$0.481810\pi$
$338$	19.4373	1.05725
$339$	2.48071	0.134733
$340$	4.55193	0.246863
$341$	−3.75270	−0.203220
$342$	18.3265	0.990982
$343$	1.27199	0.0686811
$344$	10.4946	0.565831
$345$	0	0
$346$	1.44807	0.0778488
$347$	−13.1257	−0.704625	−0.352312	−	0.935882i	$-0.614605\pi$
$347$	−13.1257	−0.704625	−0.352312	+	0.935882i	$0.614605\pi$
$348$	−5.79228	−0.310499
$349$	18.3800	0.983857	0.491928	−	0.870636i	$-0.336292\pi$
$349$	18.3800	0.983857	0.491928	+	0.870636i	$0.336292\pi$
$350$	−3.69537	−0.197526
$351$	−17.9031	−0.955596
$352$	1.44807	0.0771824
$353$	28.1722	1.49946	0.749729	−	0.661745i	$-0.230184\pi$
$353$	28.1722	1.49946	0.749729	+	0.661745i	$0.230184\pi$
$354$	−2.48071	−0.131848
$355$	−4.55193	−0.241591
$356$	−7.39075	−0.391709
$357$	9.28405	0.491364
$358$	−19.3907	−1.02483
$359$	16.0792	0.848626	0.424313	−	0.905516i	$-0.360516\pi$
$359$	16.0792	0.848626	0.424313	+	0.905516i	$0.360516\pi$
$360$	−2.69537	−0.142059
$361$	27.2296	1.43314
$362$	−14.1900	−0.745809
$363$	4.91388	0.257912
$364$	21.0465	1.10314
$365$	2.49461	0.130574
$366$	−6.47687	−0.338551
$367$	−15.1969	−0.793273	−0.396637	−	0.917976i	$-0.629823\pi$
$367$	−15.1969	−0.793273	−0.396637	+	0.917976i	$0.629823\pi$
$368$	0	0
$369$	−3.90309	−0.203187
$370$	0.207718	0.0107987
$371$	−49.4838	−2.56907
$372$	1.43033	0.0741593
$373$	−25.3907	−1.31468	−0.657342	−	0.753593i	$-0.728319\pi$
$373$	−25.3907	−1.31468	−0.657342	+	0.753593i	$0.728319\pi$
$374$	6.59152	0.340839
$375$	−0.551929	−0.0285015
$376$	−10.2869	−0.530506
$377$	−59.7707	−3.07835
$378$	−11.6162	−0.597473
$379$	−25.4481	−1.30718	−0.653590	−	0.756849i	$-0.726738\pi$
$379$	−25.4481	−1.30718	−0.653590	+	0.756849i	$0.726738\pi$
$380$	−6.79923	−0.348793
$381$	8.72390	0.446939
$382$	4.60925	0.235830
$383$	20.5738	1.05127	0.525635	−	0.850710i	$-0.323828\pi$
$383$	20.5738	1.05127	0.525635	+	0.850710i	$0.323828\pi$
$384$	−0.551929	−0.0281655
$385$	−5.35116	−0.272720
$386$	−0.896141	−0.0456124
$387$	−28.2869	−1.43790
$388$	−10.3442	−0.525148
$389$	26.6311	1.35025	0.675125	−	0.737703i	$-0.264090\pi$
$389$	26.6311	1.35025	0.675125	+	0.737703i	$0.264090\pi$
$390$	3.14344	0.159174
$391$	0	0
$392$	6.65579	0.336168
$393$	3.42622	0.172830
$394$	−7.65579	−0.385693
$395$	10.2869	0.517590
$396$	−3.90309	−0.196138
$397$	27.1257	1.36140	0.680700	−	0.732562i	$-0.261676\pi$
$397$	27.1257	1.36140	0.680700	+	0.732562i	$0.261676\pi$
$398$	6.20772	0.311165
$399$	−13.8676	−0.694249
$400$	1.00000	0.0500000
$401$	26.0139	1.29907	0.649536	−	0.760331i	$-0.274963\pi$
$401$	26.0139	1.29907	0.649536	+	0.760331i	$0.274963\pi$
$402$	1.71311	0.0854422
$403$	14.7596	0.735230
$404$	0.207718	0.0103343
$405$	6.35116	0.315592
$406$	−38.7815	−1.92469
$407$	0.300790	0.0149096
$408$	−2.51234	−0.124380
$409$	−7.48766	−0.370241	−0.185120	−	0.982716i	$-0.559268\pi$
$409$	−7.48766	−0.370241	−0.185120	+	0.982716i	$0.559268\pi$
$410$	1.44807	0.0715151
$411$	−9.54498	−0.470819
$412$	8.63110	0.425224
$413$	−16.6093	−0.817288
$414$	0	0
$415$	7.59847	0.372994
$416$	−5.69537	−0.279239
$417$	−6.01390	−0.294502
$418$	−9.84577	−0.481572
$419$	−4.28689	−0.209428	−0.104714	−	0.994502i	$-0.533393\pi$
$419$	−4.28689	−0.209428	−0.104714	+	0.994502i	$0.533393\pi$
$420$	2.03959	0.0995216
$421$	33.9962	1.65687	0.828436	−	0.560084i	$-0.189231\pi$
$421$	33.9962	1.65687	0.828436	+	0.560084i	$0.189231\pi$
$422$	17.1830	0.836457
$423$	27.7270	1.34813
$424$	13.3907	0.650312
$425$	4.55193	0.220801
$426$	2.51234	0.121723
$427$	−43.3651	−2.09858
$428$	6.00000	0.290021
$429$	4.55193	0.219769
$430$	10.4946	0.506095
$431$	17.7923	0.857024	0.428512	−	0.903536i	$-0.359038\pi$
$431$	17.7923	0.857024	0.428512	+	0.903536i	$0.359038\pi$
$432$	3.14344	0.151239
$433$	2.51234	0.120736	0.0603678	−	0.998176i	$-0.480773\pi$
$433$	2.51234	0.120736	0.0603678	+	0.998176i	$0.480773\pi$
$434$	9.57662	0.459692
$435$	−5.79228	−0.277719
$436$	18.7992	0.900320
$437$	0	0
$438$	−1.37685	−0.0657883
$439$	36.7638	1.75464	0.877319	−	0.479907i	$-0.159330\pi$
$439$	36.7638	1.75464	0.877319	+	0.479907i	$0.159330\pi$
$440$	1.44807	0.0690341
$441$	−17.9398	−0.854278
$442$	−25.9249	−1.23312
$443$	0.383797	0.0182348	0.00911738	−	0.999958i	$-0.497098\pi$
$443$	0.383797	0.0182348	0.00911738	+	0.999958i	$0.497098\pi$
$444$	−0.114646	−0.00544084
$445$	−7.39075	−0.350355
$446$	−15.8854	−0.752193
$447$	−2.87046	−0.135768
$448$	−3.69537	−0.174590
$449$	−28.6707	−1.35305	−0.676527	−	0.736418i	$-0.736516\pi$
$449$	−28.6707	−1.35305	−0.676527	+	0.736418i	$0.736516\pi$
$450$	−2.69537	−0.127061
$451$	2.09691	0.0987396
$452$	−4.49461	−0.211409
$453$	−8.52624	−0.400598
$454$	−19.1830	−0.900304
$455$	21.0465	0.986677
$456$	3.75270	0.175736
$457$	1.71311	0.0801360	0.0400680	−	0.999197i	$-0.487243\pi$
$457$	1.71311	0.0801360	0.0400680	+	0.999197i	$0.487243\pi$
$458$	12.2077	0.570429
$459$	14.3087	0.667875
$460$	0	0
$461$	10.6093	0.494122	0.247061	−	0.969000i	$-0.420535\pi$
$461$	10.6093	0.494122	0.247061	+	0.969000i	$0.420535\pi$
$462$	2.95346	0.137408
$463$	−26.1722	−1.21633	−0.608164	−	0.793812i	$-0.708094\pi$
$463$	−26.1722	−1.21633	−0.608164	+	0.793812i	$0.708094\pi$
$464$	10.4946	0.487200
$465$	1.43033	0.0663301
$466$	3.10386	0.143783
$467$	7.59847	0.351615	0.175808	−	0.984425i	$-0.443746\pi$
$467$	7.59847	0.351615	0.175808	+	0.984425i	$0.443746\pi$
$468$	15.3512	0.709608
$469$	11.4699	0.529632
$470$	−10.2869	−0.474499
$471$	4.91004	0.226243
$472$	4.49461	0.206881
$473$	15.1969	0.698756
$474$	−5.67764	−0.260782
$475$	−6.79923	−0.311970
$476$	−16.8211	−0.770993
$477$	−36.0931	−1.65259
$478$	12.0000	0.548867
$479$	−10.8170	−0.494240	−0.247120	−	0.968985i	$-0.579484\pi$
$479$	−10.8170	−0.494240	−0.247120	+	0.968985i	$0.579484\pi$
$480$	−0.551929	−0.0251920
$481$	−1.18303	−0.0539415
$482$	−6.20772	−0.282754
$483$	0	0
$484$	−8.90309	−0.404686
$485$	−10.3442	−0.469706
$486$	−12.9357	−0.586776
$487$	3.39075	0.153649	0.0768247	−	0.997045i	$-0.475522\pi$
$487$	3.39075	0.153649	0.0768247	+	0.997045i	$0.475522\pi$
$488$	11.7350	0.531217
$489$	−6.72801	−0.304251
$490$	6.65579	0.300678
$491$	−4.60925	−0.208013	−0.104006	−	0.994577i	$-0.533166\pi$
$491$	−4.60925	−0.208013	−0.104006	+	0.994577i	$0.533166\pi$
$492$	−0.799233	−0.0360322
$493$	47.7707	2.15148
$494$	38.7242	1.74228
$495$	−3.90309	−0.175431
$496$	−2.59152	−0.116362
$497$	16.8211	0.754529
$498$	−4.19382	−0.187929
$499$	−6.70232	−0.300037	−0.150019	−	0.988683i	$-0.547933\pi$
$499$	−6.70232	−0.300037	−0.150019	+	0.988683i	$0.547933\pi$
$500$	1.00000	0.0447214
$501$	7.50539	0.335316
$502$	27.7884	1.24026
$503$	−30.0614	−1.34037	−0.670187	−	0.742193i	$-0.733786\pi$
$503$	−30.0614	−1.34037	−0.670187	+	0.742193i	$0.733786\pi$
$504$	9.96041	0.443672
$505$	0.207718	0.00924332
$506$	0	0
$507$	−10.7280	−0.476448
$508$	−15.8062	−0.701286
$509$	30.3008	1.34306	0.671529	−	0.740978i	$-0.265638\pi$
$509$	30.3008	1.34306	0.671529	+	0.740978i	$0.265638\pi$
$510$	−2.51234	−0.111248
$511$	−9.21850	−0.407803
$512$	1.00000	0.0441942
$513$	−21.3730	−0.943641
$514$	−12.0931	−0.533403
$515$	8.63110	0.380332
$516$	−5.79228	−0.254991
$517$	−14.8961	−0.655132
$518$	−0.767595	−0.0337262
$519$	−0.799233	−0.0350824
$520$	−5.69537	−0.249759
$521$	21.8715	0.958206	0.479103	−	0.877759i	$-0.340962\pi$
$521$	21.8715	0.958206	0.479103	+	0.877759i	$0.340962\pi$
$522$	−28.2869	−1.23808
$523$	13.3907	0.585537	0.292768	−	0.956183i	$-0.405424\pi$
$523$	13.3907	0.585537	0.292768	+	0.956183i	$0.405424\pi$
$524$	−6.20772	−0.271185
$525$	2.03959	0.0890148
$526$	−2.83882	−0.123778
$527$	−11.7964	−0.513859
$528$	−0.799233	−0.0347821
$529$	0	0
$530$	13.3907	0.581657
$531$	−12.1146	−0.525731
$532$	25.1257	1.08934
$533$	−8.24730	−0.357230
$534$	4.07917	0.176523
$535$	6.00000	0.259403
$536$	−3.10386	−0.134066
$537$	10.7023	0.461839
$538$	−9.31158	−0.401451
$539$	9.63805	0.415140
$540$	3.14344	0.135272
$541$	3.71311	0.159639	0.0798196	−	0.996809i	$-0.474566\pi$
$541$	3.71311	0.159639	0.0798196	+	0.996809i	$0.474566\pi$
$542$	−3.00695	−0.129160
$543$	7.83187	0.336098
$544$	4.55193	0.195162
$545$	18.7992	0.805271
$546$	−11.6162	−0.497128
$547$	−33.9823	−1.45298	−0.726488	−	0.687179i	$-0.758849\pi$
$547$	−33.9823	−1.45298	−0.726488	+	0.687179i	$0.758849\pi$
$548$	17.2938	0.738756
$549$	−31.6301	−1.34994
$550$	1.44807	0.0617459
$551$	−71.3553	−3.03984
$552$	0	0
$553$	−38.0139	−1.61652
$554$	25.1969	1.07052
$555$	−0.114646	−0.00486643
$556$	10.8961	0.462099
$557$	39.4046	1.66963	0.834814	−	0.550532i	$-0.185575\pi$
$557$	39.4046	1.66963	0.834814	+	0.550532i	$0.185575\pi$
$558$	6.98510	0.295703
$559$	−59.7707	−2.52803
$560$	−3.69537	−0.156158
$561$	−3.63805	−0.153599
$562$	−4.07917	−0.172069
$563$	−12.6232	−0.532002	−0.266001	−	0.963973i	$-0.585703\pi$
$563$	−12.6232	−0.532002	−0.266001	+	0.963973i	$0.585703\pi$
$564$	5.67764	0.239072
$565$	−4.49461	−0.189090
$566$	10.4946	0.441121
$567$	−23.4699	−0.985644
$568$	−4.55193	−0.190995
$569$	6.09307	0.255435	0.127717	−	0.991811i	$-0.459235\pi$
$569$	6.09307	0.255435	0.127717	+	0.991811i	$0.459235\pi$
$570$	3.75270	0.157183
$571$	−13.7489	−0.575372	−0.287686	−	0.957725i	$-0.592886\pi$
$571$	−13.7489	−0.575372	−0.287686	+	0.957725i	$0.592886\pi$
$572$	−8.24730	−0.344837
$573$	−2.54398	−0.106276
$574$	−5.35116	−0.223353
$575$	0	0
$576$	−2.69537	−0.112307
$577$	15.1830	0.632078	0.316039	−	0.948746i	$-0.397647\pi$
$577$	15.1830	0.632078	0.316039	+	0.948746i	$0.397647\pi$
$578$	3.72006	0.154734
$579$	0.494607	0.0205552
$580$	10.4946	0.435765
$581$	−28.0792	−1.16492
$582$	5.70927	0.236657
$583$	19.3907	0.803083
$584$	2.49461	0.103228
$585$	15.3512	0.634692
$586$	−6.41544	−0.265019
$587$	−7.33343	−0.302683	−0.151341	−	0.988482i	$-0.548359\pi$
$587$	−7.33343	−0.302683	−0.151341	+	0.988482i	$0.548359\pi$
$588$	−3.67353	−0.151494
$589$	17.6203	0.726032
$590$	4.49461	0.185040
$591$	4.22545	0.173812
$592$	0.207718	0.00853715
$593$	−2.98921	−0.122752	−0.0613761	−	0.998115i	$-0.519549\pi$
$593$	−2.98921	−0.122752	−0.0613761	+	0.998115i	$0.519549\pi$
$594$	4.55193	0.186768
$595$	−16.8211	−0.689597
$596$	5.20077	0.213032
$597$	−3.42622	−0.140226
$598$	0	0
$599$	−13.2404	−0.540986	−0.270493	−	0.962722i	$-0.587187\pi$
$599$	−13.2404	−0.540986	−0.270493	+	0.962722i	$0.587187\pi$
$600$	−0.551929	−0.0225324
$601$	1.08612	0.0443038	0.0221519	−	0.999755i	$-0.492948\pi$
$601$	1.08612	0.0443038	0.0221519	+	0.999755i	$0.492948\pi$
$602$	−38.7815	−1.58062
$603$	8.36606	0.340692
$604$	15.4481	0.628573
$605$	−8.90309	−0.361962
$606$	−0.114646	−0.00465716
$607$	−14.4015	−0.584540	−0.292270	−	0.956336i	$-0.594411\pi$
$607$	−14.4015	−0.584540	−0.292270	+	0.956336i	$0.594411\pi$
$608$	−6.79923	−0.275745
$609$	21.4046	0.867360
$610$	11.7350	0.475135
$611$	58.5877	2.37020
$612$	−12.2692	−0.495951
$613$	10.4946	0.423873	0.211937	−	0.977283i	$-0.432023\pi$
$613$	10.4946	0.423873	0.211937	+	0.977283i	$0.432023\pi$
$614$	−3.86351	−0.155918
$615$	−0.799233	−0.0322282
$616$	−5.35116	−0.215604
$617$	−16.4373	−0.661740	−0.330870	−	0.943676i	$-0.607342\pi$
$617$	−16.4373	−0.661740	−0.330870	+	0.943676i	$0.607342\pi$
$618$	−4.76376	−0.191626
$619$	−22.9930	−0.924169	−0.462084	−	0.886836i	$-0.652898\pi$
$619$	−22.9930	−0.924169	−0.462084	+	0.886836i	$0.652898\pi$
$620$	−2.59152	−0.104078
$621$	0	0
$622$	12.0000	0.481156
$623$	27.3116	1.09422
$624$	3.14344	0.125838
$625$	1.00000	0.0400000
$626$	−17.2938	−0.691201
$627$	5.43417	0.217020
$628$	−8.89614	−0.354995
$629$	0.945516	0.0377002
$630$	9.96041	0.396832
$631$	−23.8854	−0.950861	−0.475430	−	0.879753i	$-0.657708\pi$
$631$	−23.8854	−0.950861	−0.475430	+	0.879753i	$0.657708\pi$
$632$	10.2869	0.409190
$633$	−9.48382	−0.376948
$634$	−15.4877	−0.615093
$635$	−15.8062	−0.627249
$636$	−7.39075	−0.293062
$637$	−37.9072	−1.50194
$638$	15.1969	0.601652
$639$	12.2692	0.485360
$640$	1.00000	0.0395285
$641$	26.6669	1.05328	0.526639	−	0.850089i	$-0.323452\pi$
$641$	26.6669	1.05328	0.526639	+	0.850089i	$0.323452\pi$
$642$	−3.31158	−0.130698
$643$	38.4591	1.51668	0.758340	−	0.651859i	$-0.226011\pi$
$643$	38.4591	1.51668	0.758340	+	0.651859i	$0.226011\pi$
$644$	0	0
$645$	−5.79228	−0.228071
$646$	−30.9496	−1.21770
$647$	44.4591	1.74787	0.873934	−	0.486044i	$-0.161560\pi$
$647$	44.4591	1.74787	0.873934	+	0.486044i	$0.161560\pi$
$648$	6.35116	0.249497
$649$	6.50851	0.255481
$650$	−5.69537	−0.223391
$651$	−5.28562	−0.207160
$652$	12.1900	0.477396
$653$	35.2938	1.38115	0.690577	−	0.723259i	$-0.257357\pi$
$653$	35.2938	1.38115	0.690577	+	0.723259i	$0.257357\pi$
$654$	−10.3758	−0.405728
$655$	−6.20772	−0.242556
$656$	1.44807	0.0565377
$657$	−6.72390	−0.262324
$658$	38.0139	1.48194
$659$	−46.2653	−1.80224	−0.901120	−	0.433569i	$-0.857254\pi$
$659$	−46.2653	−1.80224	−0.901120	+	0.433569i	$0.857254\pi$
$660$	−0.799233	−0.0311101
$661$	−36.0357	−1.40163	−0.700814	−	0.713344i	$-0.747180\pi$
$661$	−36.0357	−1.40163	−0.700814	+	0.713344i	$0.747180\pi$
$662$	11.3907	0.442714
$663$	14.3087	0.555705
$664$	7.59847	0.294878
$665$	25.1257	0.974333
$666$	−0.559877	−0.0216948
$667$	0	0
$668$	−13.5985	−0.526140
$669$	8.76759	0.338975
$670$	−3.10386	−0.119913
$671$	16.9930	0.656009
$672$	2.03959	0.0786787
$673$	15.2622	0.588315	0.294157	−	0.955757i	$-0.404961\pi$
$673$	15.2622	0.588315	0.294157	+	0.955757i	$0.404961\pi$
$674$	2.09691	0.0807699
$675$	3.14344	0.120991
$676$	19.4373	0.747588
$677$	24.8607	0.955473	0.477737	−	0.878503i	$-0.341457\pi$
$677$	24.8607	0.955473	0.477737	+	0.878503i	$0.341457\pi$
$678$	2.48071	0.0952709
$679$	38.2257	1.46697
$680$	4.55193	0.174559
$681$	10.5877	0.405721
$682$	−3.75270	−0.143698
$683$	38.3977	1.46925	0.734624	−	0.678475i	$-0.237359\pi$
$683$	38.3977	1.46925	0.734624	+	0.678475i	$0.237359\pi$
$684$	18.3265	0.700730
$685$	17.2938	0.660764
$686$	1.27199	0.0485648
$687$	−6.73780	−0.257063
$688$	10.4946	0.400103
$689$	−76.2653	−2.90548
$690$	0	0
$691$	37.7568	1.43634	0.718168	−	0.695869i	$-0.244981\pi$
$691$	37.7568	1.43634	0.718168	+	0.695869i	$0.244981\pi$
$692$	1.44807	0.0550474
$693$	14.4234	0.547899
$694$	−13.1257	−0.498245
$695$	10.8961	0.413314
$696$	−5.79228	−0.219556
$697$	6.59152	0.249671
$698$	18.3800	0.695692
$699$	−1.71311	−0.0647958
$700$	−3.69537	−0.139672
$701$	26.1900	0.989182	0.494591	−	0.869126i	$-0.335318\pi$
$701$	26.1900	0.989182	0.494591	+	0.869126i	$0.335318\pi$
$702$	−17.9031	−0.675709
$703$	−1.41232	−0.0532667
$704$	1.44807	0.0545762
$705$	5.67764	0.213832
$706$	28.1722	1.06028
$707$	−0.767595	−0.0288684
$708$	−2.48071	−0.0932306
$709$	−29.7134	−1.11591	−0.557955	−	0.829871i	$-0.688414\pi$
$709$	−29.7134	−1.11591	−0.557955	+	0.829871i	$0.688414\pi$
$710$	−4.55193	−0.170831
$711$	−27.7270	−1.03984
$712$	−7.39075	−0.276980
$713$	0	0
$714$	9.28405	0.347447
$715$	−8.24730	−0.308432
$716$	−19.3907	−0.724666
$717$	−6.62315	−0.247346
$718$	16.0792	0.600069
$719$	−31.7745	−1.18499	−0.592495	−	0.805574i	$-0.701857\pi$
$719$	−31.7745	−1.18499	−0.592495	+	0.805574i	$0.701857\pi$
$720$	−2.69537	−0.100451
$721$	−31.8951	−1.18784
$722$	27.2296	1.01338
$723$	3.42622	0.127423
$724$	−14.1900	−0.527366
$725$	10.4946	0.389760
$726$	4.91388	0.182371
$727$	−8.93189	−0.331265	−0.165633	−	0.986188i	$-0.552967\pi$
$727$	−8.93189	−0.331265	−0.165633	+	0.986188i	$0.552967\pi$
$728$	21.0465	0.780037
$729$	−11.9139	−0.441255
$730$	2.49461	0.0923295
$731$	47.7707	1.76686
$732$	−6.47687	−0.239392
$733$	24.9753	0.922484	0.461242	−	0.887274i	$-0.347404\pi$
$733$	24.9753	0.922484	0.461242	+	0.887274i	$0.347404\pi$
$734$	−15.1969	−0.560929
$735$	−3.67353	−0.135500
$736$	0	0
$737$	−4.49461	−0.165561
$738$	−3.90309	−0.143675
$739$	43.8854	1.61435	0.807174	−	0.590313i	$-0.200996\pi$
$739$	43.8854	1.61435	0.807174	+	0.590313i	$0.200996\pi$
$740$	0.207718	0.00763586
$741$	−21.3730	−0.785157
$742$	−49.4838	−1.81661
$743$	−18.8923	−0.693091	−0.346546	−	0.938033i	$-0.612645\pi$
$743$	−18.8923	−0.693091	−0.346546	+	0.938033i	$0.612645\pi$
$744$	1.43033	0.0524386
$745$	5.20077	0.190541
$746$	−25.3907	−0.929621
$747$	−20.4807	−0.749350
$748$	6.59152	0.241010
$749$	−22.1722	−0.810156
$750$	−0.551929	−0.0201536
$751$	−1.59847	−0.0583288	−0.0291644	−	0.999575i	$-0.509285\pi$
$751$	−1.59847	−0.0583288	−0.0291644	+	0.999575i	$0.509285\pi$
$752$	−10.2869	−0.375124
$753$	−15.3373	−0.558921
$754$	−59.7707	−2.17672
$755$	15.4481	0.562213
$756$	−11.6162	−0.422477
$757$	−13.3907	−0.486695	−0.243348	−	0.969939i	$-0.578246\pi$
$757$	−13.3907	−0.486695	−0.243348	+	0.969939i	$0.578246\pi$
$758$	−25.4481	−0.924316
$759$	0	0
$760$	−6.79923	−0.246634
$761$	−21.2799	−0.771397	−0.385699	−	0.922625i	$-0.626040\pi$
$761$	−21.2799	−0.771397	−0.385699	+	0.922625i	$0.626040\pi$
$762$	8.72390	0.316033
$763$	−69.4702	−2.51499
$764$	4.60925	0.166757
$765$	−12.2692	−0.443592
$766$	20.5738	0.743361
$767$	−25.5985	−0.924307
$768$	−0.551929	−0.0199160
$769$	6.20772	0.223856	0.111928	−	0.993716i	$-0.464297\pi$
$769$	6.20772	0.223856	0.111928	+	0.993716i	$0.464297\pi$
$770$	−5.35116	−0.192842
$771$	6.67452	0.240377
$772$	−0.896141	−0.0322528
$773$	−17.4699	−0.628349	−0.314175	−	0.949365i	$-0.601728\pi$
$773$	−17.4699	−0.628349	−0.314175	+	0.949365i	$0.601728\pi$
$774$	−28.2869	−1.01675
$775$	−2.59152	−0.0930900
$776$	−10.3442	−0.371336
$777$	0.423658	0.0151986
$778$	26.6311	0.954771
$779$	−9.84577	−0.352761
$780$	3.14344	0.112553
$781$	−6.59152	−0.235863
$782$	0	0
$783$	32.9892	1.17894
$784$	6.65579	0.237707
$785$	−8.89614	−0.317517
$786$	3.42622	0.122209
$787$	−50.4591	−1.79867	−0.899337	−	0.437256i	$-0.855950\pi$
$787$	−50.4591	−1.79867	−0.899337	+	0.437256i	$0.855950\pi$
$788$	−7.65579	−0.272726
$789$	1.56683	0.0557805
$790$	10.2869	0.365991
$791$	16.6093	0.590557
$792$	−3.90309	−0.138690
$793$	−66.8350	−2.37338
$794$	27.1257	0.962655
$795$	−7.39075	−0.262123
$796$	6.20772	0.220027
$797$	43.5985	1.54434	0.772168	−	0.635418i	$-0.219172\pi$
$797$	43.5985	1.54434	0.772168	+	0.635418i	$0.219172\pi$
$798$	−13.8676	−0.490908
$799$	−46.8252	−1.65656
$800$	1.00000	0.0353553
$801$	19.9208	0.703868
$802$	26.0139	0.918583
$803$	3.61237	0.127478
$804$	1.71311	0.0604168
$805$	0	0
$806$	14.7596	0.519886
$807$	5.13933	0.180913
$808$	0.207718	0.00730748
$809$	7.12571	0.250527	0.125263	−	0.992124i	$-0.460022\pi$
$809$	7.12571	0.250527	0.125263	+	0.992124i	$0.460022\pi$
$810$	6.35116	0.223157
$811$	41.8993	1.47128	0.735641	−	0.677372i	$-0.236881\pi$
$811$	41.8993	1.47128	0.735641	+	0.677372i	$0.236881\pi$
$812$	−38.7815	−1.36096
$813$	1.65962	0.0582056
$814$	0.300790	0.0105427
$815$	12.1900	0.426996
$816$	−2.51234	−0.0879496
$817$	−71.3553	−2.49641
$818$	−7.48766	−0.261800
$819$	−56.7283	−1.98225
$820$	1.44807	0.0505688
$821$	41.4699	1.44731	0.723655	−	0.690162i	$-0.242461\pi$
$821$	41.4699	1.44731	0.723655	+	0.690162i	$0.242461\pi$
$822$	−9.54498	−0.332919
$823$	34.8607	1.21517	0.607583	−	0.794256i	$-0.292139\pi$
$823$	34.8607	1.21517	0.607583	+	0.794256i	$0.292139\pi$
$824$	8.63110	0.300679
$825$	−0.799233	−0.0278257
$826$	−16.6093	−0.577910
$827$	−3.98610	−0.138610	−0.0693051	−	0.997596i	$-0.522078\pi$
$827$	−3.98610	−0.138610	−0.0693051	+	0.997596i	$0.522078\pi$
$828$	0	0
$829$	49.7707	1.72861	0.864304	−	0.502970i	$-0.167759\pi$
$829$	49.7707	1.72861	0.864304	+	0.502970i	$0.167759\pi$
$830$	7.59847	0.263747
$831$	−13.9069	−0.482426
$832$	−5.69537	−0.197452
$833$	30.2967	1.04972
$834$	−6.01390	−0.208244
$835$	−13.5985	−0.470594
$836$	−9.84577	−0.340523
$837$	−8.14628	−0.281577
$838$	−4.28689	−0.148088
$839$	−27.0823	−0.934984	−0.467492	−	0.883997i	$-0.654842\pi$
$839$	−27.0823	−0.934984	−0.467492	+	0.883997i	$0.654842\pi$
$840$	2.03959	0.0703724
$841$	81.1368	2.79782
$842$	33.9962	1.17159
$843$	2.25141	0.0775428
$844$	17.1830	0.591464
$845$	19.4373	0.668663
$846$	27.7270	0.953274
$847$	32.9003	1.13047
$848$	13.3907	0.459840
$849$	−5.79228	−0.198791
$850$	4.55193	0.156130
$851$	0	0
$852$	2.51234	0.0860715
$853$	26.6846	0.913663	0.456831	−	0.889553i	$-0.348984\pi$
$853$	26.6846	0.913663	0.456831	+	0.889553i	$0.348984\pi$
$854$	−43.3651	−1.48392
$855$	18.3265	0.626752
$856$	6.00000	0.205076
$857$	7.29768	0.249284	0.124642	−	0.992202i	$-0.460222\pi$
$857$	7.29768	0.249284	0.124642	+	0.992202i	$0.460222\pi$
$858$	4.55193	0.155400
$859$	34.0139	1.16054	0.580270	−	0.814424i	$-0.302947\pi$
$859$	34.0139	1.16054	0.580270	+	0.814424i	$0.302947\pi$
$860$	10.4946	0.357863
$861$	2.95346	0.100654
$862$	17.7923	0.606008
$863$	−36.4154	−1.23960	−0.619798	−	0.784761i	$-0.712785\pi$
$863$	−36.4154	−1.23960	−0.619798	+	0.784761i	$0.712785\pi$
$864$	3.14344	0.106942
$865$	1.44807	0.0492359
$866$	2.51234	0.0853729
$867$	−2.05321	−0.0697307
$868$	9.57662	0.325052
$869$	14.8961	0.505317
$870$	−5.79228	−0.196377
$871$	17.6776	0.598984
$872$	18.7992	0.636622
$873$	27.8815	0.943646
$874$	0	0
$875$	−3.69537	−0.124926
$876$	−1.37685	−0.0465193
$877$	−39.4265	−1.33134	−0.665669	−	0.746247i	$-0.731854\pi$
$877$	−39.4265	−1.33134	−0.665669	+	0.746247i	$0.731854\pi$
$878$	36.7638	1.24072
$879$	3.54087	0.119431
$880$	1.44807	0.0488144
$881$	−23.7707	−0.800856	−0.400428	−	0.916328i	$-0.631138\pi$
$881$	−23.7707	−0.800856	−0.400428	+	0.916328i	$0.631138\pi$
$882$	−17.9398	−0.604066
$883$	−57.7530	−1.94354	−0.971771	−	0.235926i	$-0.924188\pi$
$883$	−57.7530	−1.94354	−0.971771	+	0.235926i	$0.924188\pi$
$884$	−25.9249	−0.871950
$885$	−2.48071	−0.0833880
$886$	0.383797	0.0128939
$887$	−40.9100	−1.37362	−0.686812	−	0.726835i	$-0.740991\pi$
$887$	−40.9100	−1.37362	−0.686812	+	0.726835i	$0.740991\pi$
$888$	−0.114646	−0.00384725
$889$	58.4098	1.95900
$890$	−7.39075	−0.247738
$891$	9.19693	0.308109
$892$	−15.8854	−0.531881
$893$	69.9430	2.34055
$894$	−2.87046	−0.0960024
$895$	−19.3907	−0.648161
$896$	−3.69537	−0.123454
$897$	0	0
$898$	−28.6707	−0.956753
$899$	−27.1969	−0.907068
$900$	−2.69537	−0.0898458
$901$	60.9537	2.03066
$902$	2.09691	0.0698194
$903$	21.4046	0.712302
$904$	−4.49461	−0.149488
$905$	−14.1900	−0.471691
$906$	−8.52624	−0.283266
$907$	−47.9784	−1.59310	−0.796549	−	0.604574i	$-0.793343\pi$
$907$	−47.9784	−1.59310	−0.796549	+	0.604574i	$0.793343\pi$
$908$	−19.1830	−0.636611
$909$	−0.559877	−0.0185699
$910$	21.0465	0.697686
$911$	36.0000	1.19273	0.596367	−	0.802712i	$-0.296610\pi$
$911$	36.0000	1.19273	0.596367	+	0.802712i	$0.296610\pi$
$912$	3.75270	0.124264
$913$	11.0031	0.364150
$914$	1.71311	0.0566647
$915$	−6.47687	−0.214119
$916$	12.2077	0.403354
$917$	22.9398	0.757540
$918$	14.3087	0.472259
$919$	18.5085	0.610539	0.305270	−	0.952266i	$-0.401253\pi$
$919$	18.5085	0.610539	0.305270	+	0.952266i	$0.401253\pi$
$920$	0	0
$921$	2.13238	0.0702644
$922$	10.6093	0.349397
$923$	25.9249	0.853330
$924$	2.95346	0.0971618
$925$	0.207718	0.00682972
$926$	−26.1722	−0.860073
$927$	−23.2640	−0.764091
$928$	10.4946	0.344502
$929$	−18.0000	−0.590561	−0.295280	−	0.955411i	$-0.595413\pi$
$929$	−18.0000	−0.590561	−0.295280	+	0.955411i	$0.595413\pi$
$930$	1.43033	0.0469025
$931$	−45.2543	−1.48315
$932$	3.10386	0.101670
$933$	−6.62315	−0.216832
$934$	7.59847	0.248629
$935$	6.59152	0.215566
$936$	15.3512	0.501768
$937$	1.86762	0.0610124	0.0305062	−	0.999535i	$-0.490288\pi$
$937$	1.86762	0.0610124	0.0305062	+	0.999535i	$0.490288\pi$
$938$	11.4699	0.374506
$939$	9.54498	0.311489
$940$	−10.2869	−0.335521
$941$	−35.6203	−1.16119	−0.580595	−	0.814193i	$-0.697180\pi$
$941$	−35.6203	−1.16119	−0.580595	+	0.814193i	$0.697180\pi$
$942$	4.91004	0.159978
$943$	0	0
$944$	4.49461	0.146287
$945$	−11.6162	−0.377875
$946$	15.1969	0.494095
$947$	15.9962	0.519805	0.259903	−	0.965635i	$-0.416309\pi$
$947$	15.9962	0.519805	0.259903	+	0.965635i	$0.416309\pi$
$948$	−5.67764	−0.184401
$949$	−14.2077	−0.461202
$950$	−6.79923	−0.220596
$951$	8.54809	0.277191
$952$	−16.8211	−0.545174
$953$	−16.9674	−0.549627	−0.274813	−	0.961498i	$-0.588616\pi$
$953$	−16.9674	−0.549627	−0.274813	+	0.961498i	$0.588616\pi$
$954$	−36.0931	−1.16856
$955$	4.60925	0.149152
$956$	12.0000	0.388108
$957$	−8.38763	−0.271134
$958$	−10.8170	−0.349480
$959$	−63.9072	−2.06367
$960$	−0.551929	−0.0178134
$961$	−24.2840	−0.783356
$962$	−1.18303	−0.0381424
$963$	−16.1722	−0.521143
$964$	−6.20772	−0.199937
$965$	−0.896141	−0.0288478
$966$	0	0
$967$	−30.2869	−0.973961	−0.486980	−	0.873413i	$-0.661902\pi$
$967$	−30.2869	−0.973961	−0.486980	+	0.873413i	$0.661902\pi$
$968$	−8.90309	−0.286156
$969$	17.0820	0.548753
$970$	−10.3442	−0.332133
$971$	25.5627	0.820347	0.410173	−	0.912008i	$-0.365468\pi$
$971$	25.5627	0.820347	0.410173	+	0.912008i	$0.365468\pi$
$972$	−12.9357	−0.414914
$973$	−40.2653	−1.29085
$974$	3.39075	0.108647
$975$	3.14344	0.100671
$976$	11.7350	0.375627
$977$	18.0614	0.577836	0.288918	−	0.957354i	$-0.406704\pi$
$977$	18.0614	0.577836	0.288918	+	0.957354i	$0.406704\pi$
$978$	−6.72801	−0.215138
$979$	−10.7023	−0.342048
$980$	6.65579	0.212611
$981$	−50.6710	−1.61780
$982$	−4.60925	−0.147087
$983$	38.8388	1.23877	0.619383	−	0.785089i	$-0.287383\pi$
$983$	38.8388	1.23877	0.619383	+	0.785089i	$0.287383\pi$
$984$	−0.799233	−0.0254786
$985$	−7.65579	−0.243934
$986$	47.7707	1.52133
$987$	−20.9810	−0.667832
$988$	38.7242	1.23198
$989$	0	0
$990$	−3.90309	−0.124048
$991$	−33.6558	−1.06911	−0.534556	−	0.845133i	$-0.679521\pi$
$991$	−33.6558	−1.06911	−0.534556	+	0.845133i	$0.679521\pi$
$992$	−2.59152	−0.0822807
$993$	−6.28689	−0.199508
$994$	16.8211	0.533532
$995$	6.20772	0.196798
$996$	−4.19382	−0.132886
$997$	2.41544	0.0764976	0.0382488	−	0.999268i	$-0.487822\pi$
$997$	2.41544	0.0764976	0.0382488	+	0.999268i	$0.487822\pi$
$998$	−6.70232	−0.212158
$999$	0.652949	0.0206584

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	5290.2.a.q.1.2	yes	3
23.22	odd	2		5290.2.a.p.1.2	✓	3

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
5290.2.a.p.1.2	✓	3	23.22	odd	2
5290.2.a.q.1.2	yes	3	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:	\( N \)	\(=\)	\( 5290 = 2 \cdot 5 \cdot 23^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	5290.a (trivial)

\(f(q)\)	\(=\)	\(q+1.00000 q^{2} -0.551929 q^{3} +1.00000 q^{4} +1.00000 q^{5} -0.551929 q^{6} -3.69537 q^{7} +1.00000 q^{8} -2.69537 q^{9} +O(q^{10})\)	\(q+1.00000 q^{2} -0.551929 q^{3} +1.00000 q^{4} +1.00000 q^{5} -0.551929 q^{6} -3.69537 q^{7} +1.00000 q^{8} -2.69537 q^{9} +1.00000 q^{10} +1.44807 q^{11} -0.551929 q^{12} -5.69537 q^{13} -3.69537 q^{14} -0.551929 q^{15} +1.00000 q^{16} +4.55193 q^{17} -2.69537 q^{18} -6.79923 q^{19} +1.00000 q^{20} +2.03959 q^{21} +1.44807 q^{22} -0.551929 q^{24} +1.00000 q^{25} -5.69537 q^{26} +3.14344 q^{27} -3.69537 q^{28} +10.4946 q^{29} -0.551929 q^{30} -2.59152 q^{31} +1.00000 q^{32} -0.799233 q^{33} +4.55193 q^{34} -3.69537 q^{35} -2.69537 q^{36} +0.207718 q^{37} -6.79923 q^{38} +3.14344 q^{39} +1.00000 q^{40} +1.44807 q^{41} +2.03959 q^{42} +10.4946 q^{43} +1.44807 q^{44} -2.69537 q^{45} -10.2869 q^{47} -0.551929 q^{48} +6.65579 q^{49} +1.00000 q^{50} -2.51234 q^{51} -5.69537 q^{52} +13.3907 q^{53} +3.14344 q^{54} +1.44807 q^{55} -3.69537 q^{56} +3.75270 q^{57} +10.4946 q^{58} +4.49461 q^{59} -0.551929 q^{60} +11.7350 q^{61} -2.59152 q^{62} +9.96041 q^{63} +1.00000 q^{64} -5.69537 q^{65} -0.799233 q^{66} -3.10386 q^{67} +4.55193 q^{68} -3.69537 q^{70} -4.55193 q^{71} -2.69537 q^{72} +2.49461 q^{73} +0.207718 q^{74} -0.551929 q^{75} -6.79923 q^{76} -5.35116 q^{77} +3.14344 q^{78} +10.2869 q^{79} +1.00000 q^{80} +6.35116 q^{81} +1.44807 q^{82} +7.59847 q^{83} +2.03959 q^{84} +4.55193 q^{85} +10.4946 q^{86} -5.79228 q^{87} +1.44807 q^{88} -7.39075 q^{89} -2.69537 q^{90} +21.0465 q^{91} +1.43033 q^{93} -10.2869 q^{94} -6.79923 q^{95} -0.551929 q^{96} -10.3442 q^{97} +6.65579 q^{98} -3.90309 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 3 q + 3 q^{2} - q^{3} + 3 q^{4} + 3 q^{5} - q^{6} + 3 q^{7} + 3 q^{8} + 6 q^{9}+O(q^{10}) \) 3 * q + 3 * q^2 - q^3 + 3 * q^4 + 3 * q^5 - q^6 + 3 * q^7 + 3 * q^8 + 6 * q^9	\( 3 q + 3 q^{2} - q^{3} + 3 q^{4} + 3 q^{5} - q^{6} + 3 q^{7} + 3 q^{8} + 6 q^{9} + 3 q^{10} + 5 q^{11} - q^{12} - 3 q^{13} + 3 q^{14} - q^{15} + 3 q^{16} + 13 q^{17} + 6 q^{18} - 5 q^{19} + 3 q^{20} - 6 q^{21} + 5 q^{22} - q^{24} + 3 q^{25} - 3 q^{26} - 4 q^{27} + 3 q^{28} + 2 q^{29} - q^{30} + 5 q^{31} + 3 q^{32} + 13 q^{33} + 13 q^{34} + 3 q^{35} + 6 q^{36} - 2 q^{37} - 5 q^{38} - 4 q^{39} + 3 q^{40} + 5 q^{41} - 6 q^{42} + 2 q^{43} + 5 q^{44} + 6 q^{45} - 4 q^{47} - q^{48} + 18 q^{49} + 3 q^{50} - 19 q^{51} - 3 q^{52} + 12 q^{53} - 4 q^{54} + 5 q^{55} + 3 q^{56} + 26 q^{57} + 2 q^{58} - 16 q^{59} - q^{60} + 9 q^{61} + 5 q^{62} + 42 q^{63} + 3 q^{64} - 3 q^{65} + 13 q^{66} - 8 q^{67} + 13 q^{68} + 3 q^{70} - 13 q^{71} + 6 q^{72} - 22 q^{73} - 2 q^{74} - q^{75} - 5 q^{76} - 4 q^{78} + 4 q^{79} + 3 q^{80} + 3 q^{81} + 5 q^{82} - 8 q^{83} - 6 q^{84} + 13 q^{85} + 2 q^{86} - 20 q^{87} + 5 q^{88} + 6 q^{89} + 6 q^{90} + 33 q^{91} - 36 q^{93} - 4 q^{94} - 5 q^{95} - q^{96} - 33 q^{97} + 18 q^{98} + 5 q^{99}+O(q^{100}) \) 3 * q + 3 * q^2 - q^3 + 3 * q^4 + 3 * q^5 - q^6 + 3 * q^7 + 3 * q^8 + 6 * q^9 + 3 * q^10 + 5 * q^11 - q^12 - 3 * q^13 + 3 * q^14 - q^15 + 3 * q^16 + 13 * q^17 + 6 * q^18 - 5 * q^19 + 3 * q^20 - 6 * q^21 + 5 * q^22 - q^24 + 3 * q^25 - 3 * q^26 - 4 * q^27 + 3 * q^28 + 2 * q^29 - q^30 + 5 * q^31 + 3 * q^32 + 13 * q^33 + 13 * q^34 + 3 * q^35 + 6 * q^36 - 2 * q^37 - 5 * q^38 - 4 * q^39 + 3 * q^40 + 5 * q^41 - 6 * q^42 + 2 * q^43 + 5 * q^44 + 6 * q^45 - 4 * q^47 - q^48 + 18 * q^49 + 3 * q^50 - 19 * q^51 - 3 * q^52 + 12 * q^53 - 4 * q^54 + 5 * q^55 + 3 * q^56 + 26 * q^57 + 2 * q^58 - 16 * q^59 - q^60 + 9 * q^61 + 5 * q^62 + 42 * q^63 + 3 * q^64 - 3 * q^65 + 13 * q^66 - 8 * q^67 + 13 * q^68 + 3 * q^70 - 13 * q^71 + 6 * q^72 - 22 * q^73 - 2 * q^74 - q^75 - 5 * q^76 - 4 * q^78 + 4 * q^79 + 3 * q^80 + 3 * q^81 + 5 * q^82 - 8 * q^83 - 6 * q^84 + 13 * q^85 + 2 * q^86 - 20 * q^87 + 5 * q^88 + 6 * q^89 + 6 * q^90 + 33 * q^91 - 36 * q^93 - 4 * q^94 - 5 * q^95 - q^96 - 33 * q^97 + 18 * q^98 + 5 * q^99

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