LMFDB - Embedded newform 5290.2.a.p.1.3

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:	$1$
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			1.3
Root			$-2.47735$ 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)

$f(q)$	$=$	$q+1.00000 q^{2} +2.47735 q^{3} +1.00000 q^{4} -1.00000 q^{5} +2.47735 q^{6} -2.13727 q^{7} +1.00000 q^{8} +3.13727 q^{9} +O(q^{10})$	\(q+1.00000 q^{2} +2.47735 q^{3} +1.00000 q^{4} -1.00000 q^{5} +2.47735 q^{6} -2.13727 q^{7} +1.00000 q^{8} +3.13727 q^{9} -1.00000 q^{10} -4.47735 q^{11} +2.47735 q^{12} +0.137275 q^{13} -2.13727 q^{14} -2.47735 q^{15} +1.00000 q^{16} -1.52265 q^{17} +3.13727 q^{18} -5.09198 q^{19} -1.00000 q^{20} -5.29478 q^{21} -4.47735 q^{22} +2.47735 q^{24} +1.00000 q^{25} +0.137275 q^{26} +0.340078 q^{27} -2.13727 q^{28} -7.22925 q^{29} -2.47735 q^{30} -2.81743 q^{31} +1.00000 q^{32} -11.0920 q^{33} -1.52265 q^{34} +2.13727 q^{35} +3.13727 q^{36} +11.9094 q^{37} -5.09198 q^{38} +0.340078 q^{39} -1.00000 q^{40} +4.47735 q^{41} -5.29478 q^{42} +7.22925 q^{43} -4.47735 q^{44} -3.13727 q^{45} -4.68016 q^{47} +2.47735 q^{48} -2.43206 q^{49} +1.00000 q^{50} -3.77213 q^{51} +0.137275 q^{52} -1.72545 q^{53} +0.340078 q^{54} +4.47735 q^{55} -2.13727 q^{56} -12.6146 q^{57} -7.22925 q^{58} -13.2293 q^{59} -2.47735 q^{60} -9.15751 q^{61} -2.81743 q^{62} -6.70522 q^{63} +1.00000 q^{64} -0.137275 q^{65} -11.0920 q^{66} -2.95470 q^{67} -1.52265 q^{68} +2.13727 q^{70} -1.52265 q^{71} +3.13727 q^{72} -15.2293 q^{73} +11.9094 q^{74} +2.47735 q^{75} -5.09198 q^{76} +9.56933 q^{77} +0.340078 q^{78} -4.68016 q^{79} -1.00000 q^{80} -8.56933 q^{81} +4.47735 q^{82} +16.1840 q^{83} -5.29478 q^{84} +1.52265 q^{85} +7.22925 q^{86} -17.9094 q^{87} -4.47735 q^{88} -4.27455 q^{89} -3.13727 q^{90} -0.293394 q^{91} -6.97977 q^{93} -4.68016 q^{94} +5.09198 q^{95} +2.47735 q^{96} +19.4321 q^{97} -2.43206 q^{98} -14.0467 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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
$3$	2.47735	1.43030	0.715150	−	0.698971i	$-0.246358\pi$
$3$	2.47735	1.43030	0.715150	+	0.698971i	$0.246358\pi$
$4$	1.00000	0.500000
$5$	−1.00000	−0.447214
$5$	−1.00000	−0.447214
$6$	2.47735	1.01137
$7$	−2.13727	−0.807814	−0.403907	−	0.914800i	$-0.632348\pi$
$7$	−2.13727	−0.807814	−0.403907	+	0.914800i	$0.632348\pi$
$8$	1.00000	0.353553
$9$	3.13727	1.04576
$10$	−1.00000	−0.316228
$11$	−4.47735	−1.34997	−0.674986	−	0.737830i	$-0.735850\pi$
$11$	−4.47735	−1.34997	−0.674986	+	0.737830i	$0.735850\pi$
$12$	2.47735	0.715150
$13$	0.137275	0.0380731	0.0190366	−	0.999819i	$-0.493940\pi$
$13$	0.137275	0.0380731	0.0190366	+	0.999819i	$0.493940\pi$
$14$	−2.13727	−0.571211
$15$	−2.47735	−0.639650
$16$	1.00000	0.250000
$17$	−1.52265	−0.369296	−0.184648	−	0.982805i	$-0.559115\pi$
$17$	−1.52265	−0.369296	−0.184648	+	0.982805i	$0.559115\pi$
$18$	3.13727	0.739463
$19$	−5.09198	−1.16818	−0.584090	−	0.811689i	$-0.698549\pi$
$19$	−5.09198	−1.16818	−0.584090	+	0.811689i	$0.698549\pi$
$20$	−1.00000	−0.223607
$21$	−5.29478	−1.15542
$22$	−4.47735	−0.954575
$23$	0	0
$23$	0	0
$24$	2.47735	0.505687
$25$	1.00000	0.200000
$26$	0.137275	0.0269218
$27$	0.340078	0.0654480
$28$	−2.13727	−0.403907
$29$	−7.22925	−1.34244	−0.671219	−	0.741259i	$-0.734229\pi$
$29$	−7.22925	−1.34244	−0.671219	+	0.741259i	$0.734229\pi$
$30$	−2.47735	−0.452301
$31$	−2.81743	−0.506025	−0.253013	−	0.967463i	$-0.581421\pi$
$31$	−2.81743	−0.506025	−0.253013	+	0.967463i	$0.581421\pi$
$32$	1.00000	0.176777
$33$	−11.0920	−1.93087
$34$	−1.52265	−0.261132
$35$	2.13727	0.361265
$36$	3.13727	0.522879
$37$	11.9094	1.95789	0.978947	−	0.204113i	$-0.0654309\pi$
$37$	11.9094	1.95789	0.978947	+	0.204113i	$0.0654309\pi$
$38$	−5.09198	−0.826028
$39$	0.340078	0.0544560
$40$	−1.00000	−0.158114
$41$	4.47735	0.699245	0.349622	−	0.936891i	$-0.386310\pi$
$41$	4.47735	0.699245	0.349622	+	0.936891i	$0.386310\pi$
$42$	−5.29478	−0.817003
$43$	7.22925	1.10245	0.551225	−	0.834356i	$-0.314160\pi$
$43$	7.22925	1.10245	0.551225	+	0.834356i	$0.314160\pi$
$44$	−4.47735	−0.674986
$45$	−3.13727	−0.467677
$46$	0	0
$47$	−4.68016	−0.682671	−0.341335	−	0.939942i	$-0.610879\pi$
$47$	−4.68016	−0.682671	−0.341335	+	0.939942i	$0.610879\pi$
$48$	2.47735	0.357575
$49$	−2.43206	−0.347437
$50$	1.00000	0.141421
$51$	−3.77213	−0.528205
$52$	0.137275	0.0190366
$53$	−1.72545	−0.237009	−0.118504	−	0.992954i	$-0.537810\pi$
$53$	−1.72545	−0.237009	−0.118504	+	0.992954i	$0.537810\pi$
$54$	0.340078	0.0462787
$55$	4.47735	0.603726
$56$	−2.13727	−0.285605
$57$	−12.6146	−1.67085
$58$	−7.22925	−0.949248
$59$	−13.2293	−1.72230	−0.861151	−	0.508349i	$-0.830256\pi$
$59$	−13.2293	−1.72230	−0.861151	+	0.508349i	$0.830256\pi$
$60$	−2.47735	−0.319825
$61$	−9.15751	−1.17250	−0.586249	−	0.810131i	$-0.699396\pi$
$61$	−9.15751	−1.17250	−0.586249	+	0.810131i	$0.699396\pi$
$62$	−2.81743	−0.357814
$63$	−6.70522	−0.844778
$64$	1.00000	0.125000
$65$	−0.137275	−0.0170268
$66$	−11.0920	−1.36533
$67$	−2.95470	−0.360975	−0.180487	−	0.983577i	$-0.557767\pi$
$67$	−2.95470	−0.360975	−0.180487	+	0.983577i	$0.557767\pi$
$68$	−1.52265	−0.184648
$69$	0	0
$70$	2.13727	0.255453
$71$	−1.52265	−0.180705	−0.0903525	−	0.995910i	$-0.528799\pi$
$71$	−1.52265	−0.180705	−0.0903525	+	0.995910i	$0.528799\pi$
$72$	3.13727	0.369731
$73$	−15.2293	−1.78245	−0.891225	−	0.453562i	$-0.850153\pi$
$73$	−15.2293	−1.78245	−0.891225	+	0.453562i	$0.850153\pi$
$74$	11.9094	1.38444
$75$	2.47735	0.286060
$76$	−5.09198	−0.584090
$77$	9.56933	1.09053
$78$	0.340078	0.0385062
$79$	−4.68016	−0.526559	−0.263279	−	0.964720i	$-0.584804\pi$
$79$	−4.68016	−0.526559	−0.263279	+	0.964720i	$0.584804\pi$
$80$	−1.00000	−0.111803
$81$	−8.56933	−0.952148
$82$	4.47735	0.494441
$83$	16.1840	1.77642	0.888210	−	0.459437i	$-0.151949\pi$
$83$	16.1840	1.77642	0.888210	+	0.459437i	$0.151949\pi$
$84$	−5.29478	−0.577708
$85$	1.52265	0.165154
$86$	7.22925	0.779551
$87$	−17.9094	−1.92009
$88$	−4.47735	−0.477287
$89$	−4.27455	−0.453101	−0.226551	−	0.973999i	$-0.572745\pi$
$89$	−4.27455	−0.453101	−0.226551	+	0.973999i	$0.572745\pi$
$90$	−3.13727	−0.330698
$91$	−0.293394	−0.0307560
$92$	0	0
$93$	−6.97977	−0.723768
$94$	−4.68016	−0.482721
$95$	5.09198	0.522426
$96$	2.47735	0.252844
$97$	19.4321	1.97303	0.986513	−	0.163682i	$-0.0523370\pi$
$97$	19.4321	1.97303	0.986513	+	0.163682i	$0.0523370\pi$
$98$	−2.43206	−0.245675
$99$	−14.0467	−1.41174
$100$	1.00000	0.100000
$101$	−11.9094	−1.18503	−0.592515	−	0.805559i	$-0.701865\pi$
$101$	−11.9094	−1.18503	−0.592515	+	0.805559i	$0.701865\pi$
$102$	−3.77213	−0.373497
$103$	−12.1122	−1.19345	−0.596726	−	0.802445i	$-0.703532\pi$
$103$	−12.1122	−1.19345	−0.596726	+	0.802445i	$0.703532\pi$
$104$	0.137275	0.0134609
$105$	5.29478	0.516718
$106$	−1.72545	−0.167591
$107$	−6.00000	−0.580042	−0.290021	−	0.957020i	$-0.593662\pi$
$107$	−6.00000	−0.580042	−0.290021	+	0.957020i	$0.593662\pi$
$108$	0.340078	0.0327240
$109$	−6.90802	−0.661668	−0.330834	−	0.943689i	$-0.607330\pi$
$109$	−6.90802	−0.661668	−0.330834	+	0.943689i	$0.607330\pi$
$110$	4.47735	0.426899
$111$	29.5038	2.80038
$112$	−2.13727	−0.201953
$113$	−13.2293	−1.24450	−0.622252	−	0.782817i	$-0.713782\pi$
$113$	−13.2293	−1.24450	−0.622252	+	0.782817i	$0.713782\pi$
$114$	−12.6146	−1.18147
$115$	0	0
$116$	−7.22925	−0.671219
$117$	0.430668	0.0398153
$118$	−13.2293	−1.21785
$119$	3.25432	0.298323
$120$	−2.47735	−0.226150
$121$	9.04668	0.822426
$122$	−9.15751	−0.829082
$123$	11.0920	1.00013
$124$	−2.81743	−0.253013
$125$	−1.00000	−0.0894427
$126$	−6.70522	−0.597348
$127$	20.0934	1.78300	0.891499	−	0.453023i	$-0.149654\pi$
$127$	20.0934	1.78300	0.891499	+	0.453023i	$0.149654\pi$
$128$	1.00000	0.0883883
$129$	17.9094	1.57684
$130$	−0.137275	−0.0120398
$131$	5.90941	0.516307	0.258154	−	0.966104i	$-0.416886\pi$
$131$	5.90941	0.516307	0.258154	+	0.966104i	$0.416886\pi$
$132$	−11.0920	−0.965433
$133$	10.8830	0.943672
$134$	−2.95470	−0.255248
$135$	−0.340078	−0.0292692
$136$	−1.52265	−0.130566
$137$	12.3212	1.05267	0.526337	−	0.850276i	$-0.323565\pi$
$137$	12.3212	1.05267	0.526337	+	0.850276i	$0.323565\pi$
$138$	0	0
$139$	16.9547	1.43808	0.719040	−	0.694969i	$-0.244582\pi$
$139$	16.9547	1.43808	0.719040	+	0.694969i	$0.244582\pi$
$140$	2.13727	0.180633
$141$	−11.5944	−0.976424
$142$	−1.52265	−0.127778
$143$	−0.614627	−0.0513977
$144$	3.13727	0.261440
$145$	7.22925	0.600357
$146$	−15.2293	−1.26038
$147$	−6.02506	−0.496939
$148$	11.9094	0.978947
$149$	−17.0920	−1.40023	−0.700115	−	0.714030i	$-0.746868\pi$
$149$	−17.0920	−1.40023	−0.700115	+	0.714030i	$0.746868\pi$
$150$	2.47735	0.202275
$151$	18.4774	1.50367	0.751833	−	0.659354i	$-0.229170\pi$
$151$	18.4774	1.50367	0.751833	+	0.659354i	$0.229170\pi$
$152$	−5.09198	−0.413014
$153$	−4.77696	−0.386195
$154$	9.56933	0.771119
$155$	2.81743	0.226301
$156$	0.340078	0.0272280
$157$	14.9547	1.19352	0.596758	−	0.802422i	$-0.296455\pi$
$157$	14.9547	1.19352	0.596758	+	0.802422i	$0.296455\pi$
$158$	−4.68016	−0.372333
$159$	−4.27455	−0.338994
$160$	−1.00000	−0.0790569
$161$	0	0
$162$	−8.56933	−0.673270
$163$	−11.3665	−0.890295	−0.445148	−	0.895457i	$-0.646849\pi$
$163$	−11.3665	−0.890295	−0.445148	+	0.895457i	$0.646849\pi$
$164$	4.47735	0.349622
$165$	11.0920	0.863509
$166$	16.1840	1.25612
$167$	10.1840	0.788058	0.394029	−	0.919098i	$-0.371081\pi$
$167$	10.1840	0.788058	0.394029	+	0.919098i	$0.371081\pi$
$168$	−5.29478	−0.408501
$169$	−12.9812	−0.998550
$170$	1.52265	0.116782
$171$	−15.9749	−1.22163
$172$	7.22925	0.551225
$173$	4.47735	0.340407	0.170203	−	0.985409i	$-0.445558\pi$
$173$	4.47735	0.340407	0.170203	+	0.985409i	$0.445558\pi$
$174$	−17.9094	−1.35771
$175$	−2.13727	−0.161563
$176$	−4.47735	−0.337493
$177$	−32.7735	−2.46341
$178$	−4.27455	−0.320391
$179$	−7.72545	−0.577427	−0.288714	−	0.957415i	$-0.593228\pi$
$179$	−7.72545	−0.577427	−0.288714	+	0.957415i	$0.593228\pi$
$180$	−3.13727	−0.233839
$181$	−9.36653	−0.696209	−0.348104	−	0.937456i	$-0.613174\pi$
$181$	−9.36653	−0.696209	−0.348104	+	0.937456i	$0.613174\pi$
$182$	−0.293394	−0.0217478
$183$	−22.6864	−1.67702
$184$	0	0
$185$	−11.9094	−0.875597
$186$	−6.97977	−0.511781
$187$	6.81743	0.498540
$188$	−4.68016	−0.341335
$189$	−0.726839	−0.0528698
$190$	5.09198	0.369411
$191$	−16.2745	−1.17759	−0.588793	−	0.808284i	$-0.700396\pi$
$191$	−16.2745	−1.17759	−0.588793	+	0.808284i	$0.700396\pi$
$192$	2.47735	0.178788
$193$	−6.95470	−0.500611	−0.250305	−	0.968167i	$-0.580531\pi$
$193$	−6.95470	−0.500611	−0.250305	+	0.968167i	$0.580531\pi$
$194$	19.4321	1.39514
$195$	−0.340078	−0.0243535
$196$	−2.43206	−0.173718
$197$	1.43206	0.102030	0.0510149	−	0.998698i	$-0.483754\pi$
$197$	1.43206	0.102030	0.0510149	+	0.998698i	$0.483754\pi$
$198$	−14.0467	−0.998254
$199$	5.90941	0.418907	0.209453	−	0.977819i	$-0.432832\pi$
$199$	5.90941	0.418907	0.209453	+	0.977819i	$0.432832\pi$
$200$	1.00000	0.0707107
$201$	−7.31984	−0.516302
$202$	−11.9094	−0.837943
$203$	15.4509	1.08444
$204$	−3.77213	−0.264102
$205$	−4.47735	−0.312712
$206$	−12.1122	−0.843898
$207$	0	0
$208$	0.137275	0.00951828
$209$	22.7986	1.57701
$210$	5.29478	0.365375
$211$	17.6349	1.21403	0.607017	−	0.794689i	$-0.292366\pi$
$211$	17.6349	1.21403	0.607017	+	0.794689i	$0.292366\pi$
$212$	−1.72545	−0.118504
$213$	−3.77213	−0.258462
$214$	−6.00000	−0.410152
$215$	−7.22925	−0.493031
$216$	0.340078	0.0231394
$217$	6.02162	0.408774
$218$	−6.90802	−0.467870
$219$	−37.7282	−2.54944
$220$	4.47735	0.301863
$221$	−0.209021	−0.0140603
$222$	29.5038	1.98017
$223$	13.5038	0.904282	0.452141	−	0.891947i	$-0.350660\pi$
$223$	13.5038	0.904282	0.452141	+	0.891947i	$0.350660\pi$
$224$	−2.13727	−0.142803
$225$	3.13727	0.209152
$226$	−13.2293	−0.879997
$227$	19.6349	1.30321	0.651606	−	0.758558i	$-0.274096\pi$
$227$	19.6349	1.30321	0.651606	+	0.758558i	$0.274096\pi$
$228$	−12.6146	−0.835424
$229$	−0.0905906	−0.00598640	−0.00299320	−	0.999996i	$-0.500953\pi$
$229$	−0.0905906	−0.00598640	−0.00299320	+	0.999996i	$0.500953\pi$
$230$	0	0
$231$	23.7066	1.55978
$232$	−7.22925	−0.474624
$233$	−2.95470	−0.193569	−0.0967846	−	0.995305i	$-0.530856\pi$
$233$	−2.95470	−0.193569	−0.0967846	+	0.995305i	$0.530856\pi$
$234$	0.430668	0.0281537
$235$	4.68016	0.305300
$236$	−13.2293	−0.861151
$237$	−11.5944	−0.753137
$238$	3.25432	0.210946
$239$	12.0000	0.776215	0.388108	−	0.921614i	$-0.373129\pi$
$239$	12.0000	0.776215	0.388108	+	0.921614i	$0.373129\pi$
$240$	−2.47735	−0.159912
$241$	−5.90941	−0.380659	−0.190329	−	0.981720i	$-0.560956\pi$
$241$	−5.90941	−0.380659	−0.190329	+	0.981720i	$0.560956\pi$
$242$	9.04668	0.581543
$243$	−22.2495	−1.42731
$244$	−9.15751	−0.586249
$245$	2.43206	0.155378
$246$	11.0920	0.707199
$247$	−0.699000	−0.0444763
$248$	−2.81743	−0.178907
$249$	40.0934	2.54081
$250$	−1.00000	−0.0632456
$251$	19.5505	1.23402	0.617008	−	0.786957i	$-0.288345\pi$
$251$	19.5505	1.23402	0.617008	+	0.786957i	$0.288345\pi$
$252$	−6.70522	−0.422389
$253$	0	0
$254$	20.0934	1.26077
$255$	3.77213	0.236220
$256$	1.00000	0.0625000
$257$	29.4132	1.83475	0.917373	−	0.398029i	$-0.130306\pi$
$257$	29.4132	1.83475	0.917373	+	0.398029i	$0.130306\pi$
$258$	17.9094	1.11499
$259$	−25.4537	−1.58161
$260$	−0.137275	−0.00851341
$261$	−22.6802	−1.40387
$262$	5.90941	0.365085
$263$	−5.79720	−0.357470	−0.178735	−	0.983897i	$-0.557201\pi$
$263$	−5.79720	−0.357470	−0.178735	+	0.983897i	$0.557201\pi$
$264$	−11.0920	−0.682664
$265$	1.72545	0.105994
$266$	10.8830	0.667277
$267$	−10.5896	−0.648071
$268$	−2.95470	−0.180487
$269$	8.86411	0.540455	0.270227	−	0.962797i	$-0.412901\pi$
$269$	8.86411	0.540455	0.270227	+	0.962797i	$0.412901\pi$
$270$	−0.340078	−0.0206965
$271$	21.0014	1.27574	0.637872	−	0.770143i	$-0.279815\pi$
$271$	21.0014	1.27574	0.637872	+	0.770143i	$0.279815\pi$
$272$	−1.52265	−0.0923241
$273$	−0.726839	−0.0439903
$274$	12.3212	0.744353
$275$	−4.47735	−0.269995
$276$	0	0
$277$	−22.3679	−1.34396	−0.671979	−	0.740570i	$-0.734555\pi$
$277$	−22.3679	−1.34396	−0.671979	+	0.740570i	$0.734555\pi$
$278$	16.9547	1.01688
$279$	−8.83905	−0.529180
$280$	2.13727	0.127727
$281$	10.5896	0.631720	0.315860	−	0.948806i	$-0.397707\pi$
$281$	10.5896	0.631720	0.315860	+	0.948806i	$0.397707\pi$
$282$	−11.5944	−0.690436
$283$	7.22925	0.429735	0.214867	−	0.976643i	$-0.431068\pi$
$283$	7.22925	0.429735	0.214867	+	0.976643i	$0.431068\pi$
$284$	−1.52265	−0.0903525
$285$	12.6146	0.747226
$286$	−0.614627	−0.0363437
$287$	−9.56933	−0.564860
$288$	3.13727	0.184866
$289$	−14.6815	−0.863620
$290$	7.22925	0.424516
$291$	48.1401	2.82202
$292$	−15.2293	−0.891225
$293$	−17.8188	−1.04099	−0.520493	−	0.853866i	$-0.674252\pi$
$293$	−17.8188	−1.04099	−0.520493	+	0.853866i	$0.674252\pi$
$294$	−6.02506	−0.351389
$295$	13.2293	0.770237
$296$	11.9094	0.692220
$297$	−1.52265	−0.0883530
$298$	−17.0920	−0.990112
$299$	0	0
$300$	2.47735	0.143030
$301$	−15.4509	−0.890575
$302$	18.4774	1.06325
$303$	−29.5038	−1.69495
$304$	−5.09198	−0.292045
$305$	9.15751	0.524357
$306$	−4.77696	−0.273081
$307$	17.3415	0.989730	0.494865	−	0.868970i	$-0.335218\pi$
$307$	17.3415	0.989730	0.494865	+	0.868970i	$0.335218\pi$
$308$	9.56933	0.545263
$309$	−30.0062	−1.70699
$310$	2.81743	0.160019
$311$	12.0000	0.680458	0.340229	−	0.940343i	$-0.389495\pi$
$311$	12.0000	0.680458	0.340229	+	0.940343i	$0.389495\pi$
$312$	0.340078	0.0192531
$313$	−12.3212	−0.696437	−0.348219	−	0.937413i	$-0.613213\pi$
$313$	−12.3212	−0.696437	−0.348219	+	0.937413i	$0.613213\pi$
$314$	14.9547	0.843943
$315$	6.70522	0.377796
$316$	−4.68016	−0.263279
$317$	−21.7721	−1.22284	−0.611422	−	0.791304i	$-0.709402\pi$
$317$	−21.7721	−1.22284	−0.611422	+	0.791304i	$0.709402\pi$
$318$	−4.27455	−0.239705
$319$	32.3679	1.81226
$320$	−1.00000	−0.0559017
$321$	−14.8641	−0.829634
$322$	0	0
$323$	7.75329	0.431405
$324$	−8.56933	−0.476074
$325$	0.137275	0.00761463
$326$	−11.3665	−0.629534
$327$	−17.1136	−0.946384
$328$	4.47735	0.247220
$329$	10.0028	0.551471
$330$	11.0920	0.610593
$331$	−0.274549	−0.0150906	−0.00754530	−	0.999972i	$-0.502402\pi$
$331$	−0.274549	−0.0150906	−0.00754530	+	0.999972i	$0.502402\pi$
$332$	16.1840	0.888210
$333$	37.3631	2.04748
$334$	10.1840	0.557241
$335$	2.95470	0.161433
$336$	−5.29478	−0.288854
$337$	−20.0467	−1.09201	−0.546006	−	0.837781i	$-0.683853\pi$
$337$	−20.0467	−1.09201	−0.546006	+	0.837781i	$0.683853\pi$
$338$	−12.9812	−0.706082
$339$	−32.7735	−1.78001
$340$	1.52265	0.0825772
$341$	12.6146	0.683120
$342$	−15.9749	−0.863826
$343$	20.1589	1.08848
$344$	7.22925	0.389775
$345$	0	0
$346$	4.47735	0.240704
$347$	1.11704	0.0599659	0.0299830	−	0.999550i	$-0.490455\pi$
$347$	1.11704	0.0599659	0.0299830	+	0.999550i	$0.490455\pi$
$348$	−17.9094	−0.960045
$349$	−28.7331	−1.53805	−0.769023	−	0.639222i	$-0.779257\pi$
$349$	−28.7331	−1.53805	−0.769023	+	0.639222i	$0.779257\pi$
$350$	−2.13727	−0.114242
$351$	0.0466840	0.00249181
$352$	−4.47735	−0.238644
$353$	−6.82365	−0.363186	−0.181593	−	0.983374i	$-0.558125\pi$
$353$	−6.82365	−0.363186	−0.181593	+	0.983374i	$0.558125\pi$
$354$	−32.7735	−1.74189
$355$	1.52265	0.0808137
$356$	−4.27455	−0.226551
$357$	8.06209	0.426691
$358$	−7.72545	−0.408303
$359$	−22.5896	−1.19223	−0.596116	−	0.802898i	$-0.703290\pi$
$359$	−22.5896	−1.19223	−0.596116	+	0.802898i	$0.703290\pi$
$360$	−3.13727	−0.165349
$361$	6.92825	0.364645
$362$	−9.36653	−0.492294
$363$	22.4118	1.17632
$364$	−0.293394	−0.0153780
$365$	15.2293	0.797136
$366$	−22.6864	−1.18584
$367$	−32.3679	−1.68959	−0.844796	−	0.535089i	$-0.820278\pi$
$367$	−32.3679	−1.68959	−0.844796	+	0.535089i	$0.820278\pi$
$368$	0	0
$369$	14.0467	0.731241
$370$	−11.9094	−0.619141
$371$	3.68776	0.191459
$372$	−6.97977	−0.361884
$373$	13.7255	0.710677	0.355338	−	0.934738i	$-0.384366\pi$
$373$	13.7255	0.710677	0.355338	+	0.934738i	$0.384366\pi$
$374$	6.81743	0.352521
$375$	−2.47735	−0.127930
$376$	−4.68016	−0.241361
$377$	−0.992393	−0.0511109
$378$	−0.726839	−0.0373846
$379$	28.4774	1.46278	0.731392	−	0.681958i	$-0.238871\pi$
$379$	28.4774	1.46278	0.731392	+	0.681958i	$0.238871\pi$
$380$	5.09198	0.261213
$381$	49.7784	2.55022
$382$	−16.2745	−0.832678
$383$	−9.36031	−0.478290	−0.239145	−	0.970984i	$-0.576867\pi$
$383$	−9.36031	−0.478290	−0.239145	+	0.970984i	$0.576867\pi$
$384$	2.47735	0.126422
$385$	−9.56933	−0.487698
$386$	−6.95470	−0.353985
$387$	22.6802	1.15290
$388$	19.4321	0.986513
$389$	−30.1122	−1.52675	−0.763375	−	0.645956i	$-0.776459\pi$
$389$	−30.1122	−1.52675	−0.763375	+	0.645956i	$0.776459\pi$
$390$	−0.340078	−0.0172205
$391$	0	0
$392$	−2.43206	−0.122837
$393$	14.6397	0.738475
$394$	1.43206	0.0721460
$395$	4.68016	0.235484
$396$	−14.0467	−0.705872
$397$	12.8830	0.646577	0.323289	−	0.946300i	$-0.395212\pi$
$397$	12.8830	0.646577	0.323289	+	0.946300i	$0.395212\pi$
$398$	5.90941	0.296212
$399$	26.9609	1.34973
$400$	1.00000	0.0500000
$401$	22.0028	1.09877	0.549383	−	0.835571i	$-0.314863\pi$
$401$	22.0028	1.09877	0.549383	+	0.835571i	$0.314863\pi$
$402$	−7.31984	−0.365081
$403$	−0.386762	−0.0192660
$404$	−11.9094	−0.592515
$405$	8.56933	0.425814
$406$	15.4509	0.766815
$407$	−53.3226	−2.64310
$408$	−3.77213	−0.186748
$409$	−13.7721	−0.680988	−0.340494	−	0.940247i	$-0.610594\pi$
$409$	−13.7721	−0.680988	−0.340494	+	0.940247i	$0.610594\pi$
$410$	−4.47735	−0.221121
$411$	30.5240	1.50564
$412$	−12.1122	−0.596726
$413$	28.2745	1.39130
$414$	0	0
$415$	−16.1840	−0.794439
$416$	0.137275	0.00673044
$417$	42.0028	2.05688
$418$	22.7986	1.11512
$419$	−1.31984	−0.0644786	−0.0322393	−	0.999480i	$-0.510264\pi$
$419$	−1.31984	−0.0644786	−0.0322393	+	0.999480i	$0.510264\pi$
$420$	5.29478	0.258359
$421$	25.4599	1.24084	0.620420	−	0.784270i	$-0.286962\pi$
$421$	25.4599	1.24084	0.620420	+	0.784270i	$0.286962\pi$
$422$	17.6349	0.858452
$423$	−14.6829	−0.713909
$424$	−1.72545	−0.0837953
$425$	−1.52265	−0.0738593
$426$	−3.77213	−0.182761
$427$	19.5721	0.947161
$428$	−6.00000	−0.290021
$429$	−1.52265	−0.0735141
$430$	−7.22925	−0.348626
$431$	−29.9094	−1.44069	−0.720343	−	0.693618i	$-0.756015\pi$
$431$	−29.9094	−1.44069	−0.720343	+	0.693618i	$0.756015\pi$
$432$	0.340078	0.0163620
$433$	3.77213	0.181277	0.0906386	−	0.995884i	$-0.471109\pi$
$433$	3.77213	0.181277	0.0906386	+	0.995884i	$0.471109\pi$
$434$	6.02162	0.289047
$435$	17.9094	0.858690
$436$	−6.90802	−0.330834
$437$	0	0
$438$	−37.7282	−1.80272
$439$	1.99378	0.0951580	0.0475790	−	0.998867i	$-0.484849\pi$
$439$	1.99378	0.0951580	0.0475790	+	0.998867i	$0.484849\pi$
$440$	4.47735	0.213449
$441$	−7.63003	−0.363335
$442$	−0.209021	−0.00994211
$443$	12.7268	0.604670	0.302335	−	0.953202i	$-0.402234\pi$
$443$	12.7268	0.604670	0.302335	+	0.953202i	$0.402234\pi$
$444$	29.5038	1.40019
$445$	4.27455	0.202633
$446$	13.5038	0.639424
$447$	−42.3429	−2.00275
$448$	−2.13727	−0.100977
$449$	−35.4070	−1.67096	−0.835480	−	0.549521i	$-0.814810\pi$
$449$	−35.4070	−1.67096	−0.835480	+	0.549521i	$0.814810\pi$
$450$	3.13727	0.147893
$451$	−20.0467	−0.943961
$452$	−13.2293	−0.622252
$453$	45.7749	2.15069
$454$	19.6349	0.921510
$455$	0.293394	0.0137545
$456$	−12.6146	−0.590734
$457$	−7.31984	−0.342408	−0.171204	−	0.985236i	$-0.554766\pi$
$457$	−7.31984	−0.342408	−0.171204	+	0.985236i	$0.554766\pi$
$458$	−0.0905906	−0.00423302
$459$	−0.517818	−0.0241697
$460$	0	0
$461$	22.2745	1.03743	0.518715	−	0.854947i	$-0.326411\pi$
$461$	22.2745	1.03743	0.518715	+	0.854947i	$0.326411\pi$
$462$	23.7066	1.10293
$463$	8.82365	0.410070	0.205035	−	0.978755i	$-0.434269\pi$
$463$	8.82365	0.410070	0.205035	+	0.978755i	$0.434269\pi$
$464$	−7.22925	−0.335610
$465$	6.97977	0.323679
$466$	−2.95470	−0.136874
$467$	16.1840	0.748904	0.374452	−	0.927246i	$-0.377831\pi$
$467$	16.1840	0.748904	0.374452	+	0.927246i	$0.377831\pi$
$468$	0.430668	0.0199076
$469$	6.31502	0.291600
$470$	4.68016	0.215879
$471$	37.0481	1.70709
$472$	−13.2293	−0.608926
$473$	−32.3679	−1.48828
$474$	−11.5944	−0.532548
$475$	−5.09198	−0.233636
$476$	3.25432	0.149161
$477$	−5.41321	−0.247854
$478$	12.0000	0.548867
$479$	10.3651	0.473595	0.236798	−	0.971559i	$-0.423902\pi$
$479$	10.3651	0.473595	0.236798	+	0.971559i	$0.423902\pi$
$480$	−2.47735	−0.113075
$481$	1.63486	0.0745432
$482$	−5.90941	−0.269166
$483$	0	0
$484$	9.04668	0.411213
$485$	−19.4321	−0.882364
$486$	−22.2495	−1.00926
$487$	−8.27455	−0.374956	−0.187478	−	0.982269i	$-0.560031\pi$
$487$	−8.27455	−0.374956	−0.187478	+	0.982269i	$0.560031\pi$
$488$	−9.15751	−0.414541
$489$	−28.1589	−1.27339
$490$	2.43206	0.109869
$491$	−16.2745	−0.734460	−0.367230	−	0.930130i	$-0.619694\pi$
$491$	−16.2745	−0.734460	−0.367230	+	0.930130i	$0.619694\pi$
$492$	11.0920	0.500065
$493$	11.0076	0.495758
$494$	−0.699000	−0.0314495
$495$	14.0467	0.631351
$496$	−2.81743	−0.126506
$497$	3.25432	0.145976
$498$	40.0934	1.79663
$499$	23.1387	1.03583	0.517914	−	0.855432i	$-0.326709\pi$
$499$	23.1387	1.03583	0.517914	+	0.855432i	$0.326709\pi$
$500$	−1.00000	−0.0447214
$501$	25.2293	1.12716
$502$	19.5505	0.872581
$503$	25.1324	1.12060	0.560300	−	0.828290i	$-0.310686\pi$
$503$	25.1324	1.12060	0.560300	+	0.828290i	$0.310686\pi$
$504$	−6.70522	−0.298674
$505$	11.9094	0.529962
$506$	0	0
$507$	−32.1589	−1.42823
$508$	20.0934	0.891499
$509$	−23.3226	−1.03376	−0.516879	−	0.856059i	$-0.672906\pi$
$509$	−23.3226	−1.03376	−0.516879	+	0.856059i	$0.672906\pi$
$510$	3.77213	0.167033
$511$	32.5491	1.43989
$512$	1.00000	0.0441942
$513$	−1.73167	−0.0764550
$514$	29.4132	1.29736
$515$	12.1122	0.533728
$516$	17.9094	0.788418
$517$	20.9547	0.921587
$518$	−25.4537	−1.11837
$519$	11.0920	0.486884
$520$	−0.137275	−0.00601989
$521$	−40.4990	−1.77429	−0.887146	−	0.461489i	$-0.847316\pi$
$521$	−40.4990	−1.77429	−0.887146	+	0.461489i	$0.847316\pi$
$522$	−22.6802	−0.992683
$523$	−1.72545	−0.0754487	−0.0377243	−	0.999288i	$-0.512011\pi$
$523$	−1.72545	−0.0754487	−0.0377243	+	0.999288i	$0.512011\pi$
$524$	5.90941	0.258154
$525$	−5.29478	−0.231083
$526$	−5.79720	−0.252770
$527$	4.28995	0.186873
$528$	−11.0920	−0.482716
$529$	0	0
$530$	1.72545	0.0749488
$531$	−41.5038	−1.80111
$532$	10.8830	0.471836
$533$	0.614627	0.0266225
$534$	−10.5896	−0.458255
$535$	6.00000	0.259403
$536$	−2.95470	−0.127624
$537$	−19.1387	−0.825894
$538$	8.86411	0.382159
$539$	10.8892	0.469030
$540$	−0.340078	−0.0146346
$541$	9.31984	0.400691	0.200346	−	0.979725i	$-0.435793\pi$
$541$	9.31984	0.400691	0.200346	+	0.979725i	$0.435793\pi$
$542$	21.0014	0.902087
$543$	−23.2042	−0.995787
$544$	−1.52265	−0.0652830
$545$	6.90802	0.295907
$546$	−0.726839	−0.0311059
$547$	−22.5429	−0.963864	−0.481932	−	0.876209i	$-0.660065\pi$
$547$	−22.5429	−0.963864	−0.481932	+	0.876209i	$0.660065\pi$
$548$	12.3212	0.526337
$549$	−28.7296	−1.22615
$550$	−4.47735	−0.190915
$551$	36.8112	1.56821
$552$	0	0
$553$	10.0028	0.425361
$554$	−22.3679	−0.950322
$555$	−29.5038	−1.25237
$556$	16.9547	0.719040
$557$	20.2773	0.859178	0.429589	−	0.903025i	$-0.358658\pi$
$557$	20.2773	0.859178	0.429589	+	0.903025i	$0.358658\pi$
$558$	−8.83905	−0.374187
$559$	0.992393	0.0419738
$560$	2.13727	0.0903163
$561$	16.8892	0.713062
$562$	10.5896	0.446694
$563$	−23.7282	−1.00003	−0.500013	−	0.866018i	$-0.666671\pi$
$563$	−23.7282	−1.00003	−0.500013	+	0.866018i	$0.666671\pi$
$564$	−11.5944	−0.488212
$565$	13.2293	0.556559
$566$	7.22925	0.303868
$567$	18.3150	0.769158
$568$	−1.52265	−0.0638889
$569$	35.4132	1.48460	0.742300	−	0.670068i	$-0.233735\pi$
$569$	35.4132	1.48460	0.742300	+	0.670068i	$0.233735\pi$
$570$	12.6146	0.528369
$571$	−36.8453	−1.54193	−0.770963	−	0.636880i	$-0.780225\pi$
$571$	−36.8453	−1.54193	−0.770963	+	0.636880i	$0.780225\pi$
$572$	−0.614627	−0.0256988
$573$	−40.3178	−1.68430
$574$	−9.56933	−0.399416
$575$	0	0
$576$	3.13727	0.130720
$577$	15.6349	0.650888	0.325444	−	0.945561i	$-0.394486\pi$
$577$	15.6349	0.650888	0.325444	+	0.945561i	$0.394486\pi$
$578$	−14.6815	−0.610672
$579$	−17.2293	−0.716023
$580$	7.22925	0.300178
$581$	−34.5896	−1.43502
$582$	48.1401	1.99547
$583$	7.72545	0.319955
$584$	−15.2293	−0.630191
$585$	−0.430668	−0.0178059
$586$	−17.8188	−0.736089
$587$	19.0265	0.785306	0.392653	−	0.919687i	$-0.371557\pi$
$587$	19.0265	0.785306	0.392653	+	0.919687i	$0.371557\pi$
$588$	−6.02506	−0.248469
$589$	14.3463	0.591129
$590$	13.2293	0.544640
$591$	3.54771	0.145933
$592$	11.9094	0.489474
$593$	32.4585	1.33291	0.666456	−	0.745545i	$-0.267811\pi$
$593$	32.4585	1.33291	0.666456	+	0.745545i	$0.267811\pi$
$594$	−1.52265	−0.0624750
$595$	−3.25432	−0.133414
$596$	−17.0920	−0.700115
$597$	14.6397	0.599163
$598$	0	0
$599$	−28.3868	−1.15985	−0.579926	−	0.814669i	$-0.696918\pi$
$599$	−28.3868	−1.15985	−0.579926	+	0.814669i	$0.696918\pi$
$600$	2.47735	0.101137
$601$	−16.4118	−0.669452	−0.334726	−	0.942315i	$-0.608644\pi$
$601$	−16.4118	−0.669452	−0.334726	+	0.942315i	$0.608644\pi$
$602$	−15.4509	−0.629732
$603$	−9.26972	−0.377492
$604$	18.4774	0.751833
$605$	−9.04668	−0.367800
$606$	−29.5038	−1.19851
$607$	−38.1840	−1.54984	−0.774920	−	0.632060i	$-0.782210\pi$
$607$	−38.1840	−1.54984	−0.774920	+	0.632060i	$0.782210\pi$
$608$	−5.09198	−0.206507
$609$	38.2773	1.55108
$610$	9.15751	0.370777
$611$	−0.642467	−0.0259914
$612$	−4.77696	−0.193097
$613$	7.22925	0.291987	0.145993	−	0.989286i	$-0.453362\pi$
$613$	7.22925	0.291987	0.145993	+	0.989286i	$0.453362\pi$
$614$	17.3415	0.699845
$615$	−11.0920	−0.447272
$616$	9.56933	0.385559
$617$	−15.9812	−0.643377	−0.321689	−	0.946846i	$-0.604250\pi$
$617$	−15.9812	−0.643377	−0.321689	+	0.946846i	$0.604250\pi$
$618$	−30.0062	−1.20703
$619$	47.0014	1.88915	0.944573	−	0.328302i	$-0.106477\pi$
$619$	47.0014	1.88915	0.944573	+	0.328302i	$0.106477\pi$
$620$	2.81743	0.113151
$621$	0	0
$622$	12.0000	0.481156
$623$	9.13589	0.366022
$624$	0.340078	0.0136140
$625$	1.00000	0.0400000
$626$	−12.3212	−0.492456
$627$	56.4801	2.25560
$628$	14.9547	0.596758
$629$	−18.1338	−0.723043
$630$	6.70522	0.267142
$631$	−5.50380	−0.219103	−0.109551	−	0.993981i	$-0.534941\pi$
$631$	−5.50380	−0.219103	−0.109551	+	0.993981i	$0.534941\pi$
$632$	−4.68016	−0.186167
$633$	43.6878	1.73643
$634$	−21.7721	−0.864682
$635$	−20.0934	−0.797381
$636$	−4.27455	−0.169497
$637$	−0.333860	−0.0132280
$638$	32.3679	1.28146
$639$	−4.77696	−0.188974
$640$	−1.00000	−0.0395285
$641$	26.0529	1.02903	0.514514	−	0.857482i	$-0.327972\pi$
$641$	26.0529	1.02903	0.514514	+	0.857482i	$0.327972\pi$
$642$	−14.8641	−0.586640
$643$	2.14349	0.0845311	0.0422655	−	0.999106i	$-0.486542\pi$
$643$	2.14349	0.0845311	0.0422655	+	0.999106i	$0.486542\pi$
$644$	0	0
$645$	−17.9094	−0.705182
$646$	7.75329	0.305049
$647$	3.85651	0.151615	0.0758075	−	0.997122i	$-0.475847\pi$
$647$	3.85651	0.151615	0.0758075	+	0.997122i	$0.475847\pi$
$648$	−8.56933	−0.336635
$649$	59.2320	2.32506
$650$	0.137275	0.00538436
$651$	14.9177	0.584670
$652$	−11.3665	−0.445148
$653$	5.67877	0.222227	0.111114	−	0.993808i	$-0.464558\pi$
$653$	5.67877	0.222227	0.111114	+	0.993808i	$0.464558\pi$
$654$	−17.1136	−0.669195
$655$	−5.90941	−0.230900
$656$	4.47735	0.174811
$657$	−47.7784	−1.86401
$658$	10.0028	0.389949
$659$	−30.2369	−1.17786	−0.588930	−	0.808184i	$-0.700451\pi$
$659$	−30.2369	−1.17786	−0.588930	+	0.808184i	$0.700451\pi$
$660$	11.0920	0.431755
$661$	−20.1651	−0.784332	−0.392166	−	0.919894i	$-0.628274\pi$
$661$	−20.1651	−0.784332	−0.392166	+	0.919894i	$0.628274\pi$
$662$	−0.274549	−0.0106707
$663$	−0.517818	−0.0201104
$664$	16.1840	0.628059
$665$	−10.8830	−0.422023
$666$	37.3631	1.44779
$667$	0	0
$668$	10.1840	0.394029
$669$	33.4537	1.29339
$670$	2.95470	0.114150
$671$	41.0014	1.58284
$672$	−5.29478	−0.204251
$673$	22.2244	0.856689	0.428344	−	0.903616i	$-0.359097\pi$
$673$	22.2244	0.856689	0.428344	+	0.903616i	$0.359097\pi$
$674$	−20.0467	−0.772169
$675$	0.340078	0.0130896
$676$	−12.9812	−0.499275
$677$	−8.04047	−0.309020	−0.154510	−	0.987991i	$-0.549380\pi$
$677$	−8.04047	−0.309020	−0.154510	+	0.987991i	$0.549380\pi$
$678$	−32.7735	−1.25866
$679$	−41.5316	−1.59384
$680$	1.52265	0.0583909
$681$	48.6425	1.86398
$682$	12.6146	0.483039
$683$	2.72406	0.104233	0.0521167	−	0.998641i	$-0.483403\pi$
$683$	2.72406	0.104233	0.0521167	+	0.998641i	$0.483403\pi$
$684$	−15.9749	−0.610817
$685$	−12.3212	−0.470770
$686$	20.1589	0.769670
$687$	−0.224425	−0.00856234
$688$	7.22925	0.275613
$689$	−0.236861	−0.00902367
$690$	0	0
$691$	26.9952	1.02694	0.513472	−	0.858106i	$-0.328359\pi$
$691$	26.9952	1.02694	0.513472	+	0.858106i	$0.328359\pi$
$692$	4.47735	0.170203
$693$	30.0216	1.14043
$694$	1.11704	0.0424023
$695$	−16.9547	−0.643129
$696$	−17.9094	−0.678854
$697$	−6.81743	−0.258229
$698$	−28.7331	−1.08756
$699$	−7.31984	−0.276862
$700$	−2.13727	−0.0807814
$701$	−2.63347	−0.0994648	−0.0497324	−	0.998763i	$-0.515837\pi$
$701$	−2.63347	−0.0994648	−0.0497324	+	0.998763i	$0.515837\pi$
$702$	0.0466840	0.00176198
$703$	−60.6425	−2.28717
$704$	−4.47735	−0.168747
$705$	11.5944	0.436670
$706$	−6.82365	−0.256811
$707$	25.4537	0.957284
$708$	−32.7735	−1.23170
$709$	−43.7595	−1.64342	−0.821711	−	0.569904i	$-0.806980\pi$
$709$	−43.7595	−1.64342	−0.821711	+	0.569904i	$0.806980\pi$
$710$	1.52265	0.0571439
$711$	−14.6829	−0.550653
$712$	−4.27455	−0.160196
$713$	0	0
$714$	8.06209	0.301716
$715$	0.614627	0.0229857
$716$	−7.72545	−0.288714
$717$	29.7282	1.11022
$718$	−22.5896	−0.843035
$719$	−32.4523	−1.21027	−0.605133	−	0.796124i	$-0.706880\pi$
$719$	−32.4523	−1.21027	−0.605133	+	0.796124i	$0.706880\pi$
$720$	−3.13727	−0.116919
$721$	25.8871	0.964087
$722$	6.92825	0.257843
$723$	−14.6397	−0.544456
$724$	−9.36653	−0.348104
$725$	−7.22925	−0.268488
$726$	22.4118	0.831781
$727$	−41.2104	−1.52841	−0.764205	−	0.644974i	$-0.776868\pi$
$727$	−41.2104	−1.52841	−0.764205	+	0.644974i	$0.776868\pi$
$728$	−0.293394	−0.0108739
$729$	−29.4118	−1.08933
$730$	15.2293	0.563660
$731$	−11.0076	−0.407131
$732$	−22.6864	−0.838512
$733$	−37.5443	−1.38673	−0.693365	−	0.720587i	$-0.743872\pi$
$733$	−37.5443	−1.38673	−0.693365	+	0.720587i	$0.743872\pi$
$734$	−32.3679	−1.19472
$735$	6.02506	0.222238
$736$	0	0
$737$	13.2293	0.487306
$738$	14.0467	0.517066
$739$	14.4962	0.533251	0.266626	−	0.963800i	$-0.414091\pi$
$739$	14.4962	0.533251	0.266626	+	0.963800i	$0.414091\pi$
$740$	−11.9094	−0.437799
$741$	−1.73167	−0.0636144
$742$	3.68776	0.135382
$743$	−34.5052	−1.26587	−0.632936	−	0.774204i	$-0.718151\pi$
$743$	−34.5052	−1.26587	−0.632936	+	0.774204i	$0.718151\pi$
$744$	−6.97977	−0.255891
$745$	17.0920	0.626202
$746$	13.7255	0.502524
$747$	50.7735	1.85771
$748$	6.81743	0.249270
$749$	12.8236	0.468566
$750$	−2.47735	−0.0904601
$751$	−22.1840	−0.809504	−0.404752	−	0.914426i	$-0.632642\pi$
$751$	−22.1840	−0.809504	−0.404752	+	0.914426i	$0.632642\pi$
$752$	−4.68016	−0.170668
$753$	48.4334	1.76501
$754$	−0.992393	−0.0361408
$755$	−18.4774	−0.672460
$756$	−0.726839	−0.0264349
$757$	1.72545	0.0627126	0.0313563	−	0.999508i	$-0.490017\pi$
$757$	1.72545	0.0627126	0.0313563	+	0.999508i	$0.490017\pi$
$758$	28.4774	1.03434
$759$	0	0
$760$	5.09198	0.184706
$761$	−39.6815	−1.43845	−0.719227	−	0.694775i	$-0.755504\pi$
$761$	−39.6815	−1.43845	−0.719227	+	0.694775i	$0.755504\pi$
$762$	49.7784	1.80328
$763$	14.7643	0.534505
$764$	−16.2745	−0.588793
$765$	4.77696	0.172711
$766$	−9.36031	−0.338202
$767$	−1.81604	−0.0655735
$768$	2.47735	0.0893938
$769$	5.90941	0.213099	0.106549	−	0.994307i	$-0.466020\pi$
$769$	5.90941	0.213099	0.106549	+	0.994307i	$0.466020\pi$
$770$	−9.56933	−0.344855
$771$	72.8669	2.62424
$772$	−6.95470	−0.250305
$773$	12.3150	0.442940	0.221470	−	0.975167i	$-0.428914\pi$
$773$	12.3150	0.442940	0.221470	+	0.975167i	$0.428914\pi$
$774$	22.6802	0.815221
$775$	−2.81743	−0.101205
$776$	19.4321	0.697570
$777$	−63.0577	−2.26218
$778$	−30.1122	−1.07958
$779$	−22.7986	−0.816844
$780$	−0.340078	−0.0121767
$781$	6.81743	0.243947
$782$	0	0
$783$	−2.45851	−0.0878599
$784$	−2.43206	−0.0868592
$785$	−14.9547	−0.533756
$786$	14.6397	0.522180
$787$	9.85651	0.351347	0.175673	−	0.984449i	$-0.443790\pi$
$787$	9.85651	0.351347	0.175673	+	0.984449i	$0.443790\pi$
$788$	1.43206	0.0510149
$789$	−14.3617	−0.511290
$790$	4.68016	0.166512
$791$	28.2745	1.00533
$792$	−14.0467	−0.499127
$793$	−1.25709	−0.0446407
$794$	12.8830	0.457199
$795$	4.27455	0.151603
$796$	5.90941	0.209453
$797$	−19.8160	−0.701920	−0.350960	−	0.936390i	$-0.614145\pi$
$797$	−19.8160	−0.701920	−0.350960	+	0.936390i	$0.614145\pi$
$798$	26.9609	0.954406
$799$	7.12623	0.252108
$800$	1.00000	0.0353553
$801$	−13.4104	−0.473834
$802$	22.0028	0.776945
$803$	68.1867	2.40626
$804$	−7.31984	−0.258151
$805$	0	0
$806$	−0.386762	−0.0136231
$807$	21.9595	0.773012
$808$	−11.9094	−0.418972
$809$	−7.11704	−0.250222	−0.125111	−	0.992143i	$-0.539929\pi$
$809$	−7.11704	−0.250222	−0.125111	+	0.992143i	$0.539929\pi$
$810$	8.56933	0.301096
$811$	−35.5066	−1.24680	−0.623402	−	0.781901i	$-0.714250\pi$
$811$	−35.5066	−1.24680	−0.623402	+	0.781901i	$0.714250\pi$
$812$	15.4509	0.542220
$813$	52.0278	1.82470
$814$	−53.3226	−1.86896
$815$	11.3665	0.398152
$816$	−3.77213	−0.132051
$817$	−36.8112	−1.28786
$818$	−13.7721	−0.481531
$819$	−0.920456	−0.0321634
$820$	−4.47735	−0.156356
$821$	36.3150	1.26740	0.633701	−	0.773578i	$-0.281535\pi$
$821$	36.3150	1.26740	0.633701	+	0.773578i	$0.281535\pi$
$822$	30.5240	1.06465
$823$	18.0405	0.628851	0.314426	−	0.949282i	$-0.398188\pi$
$823$	18.0405	0.628851	0.314426	+	0.949282i	$0.398188\pi$
$824$	−12.1122	−0.421949
$825$	−11.0920	−0.386173
$826$	28.2745	0.983797
$827$	52.0028	1.80831	0.904157	−	0.427201i	$-0.140500\pi$
$827$	52.0028	1.80831	0.904157	+	0.427201i	$0.140500\pi$
$828$	0	0
$829$	−9.00761	−0.312847	−0.156424	−	0.987690i	$-0.549996\pi$
$829$	−9.00761	−0.312847	−0.156424	+	0.987690i	$0.549996\pi$
$830$	−16.1840	−0.561753
$831$	−55.4132	−1.92226
$832$	0.137275	0.00475914
$833$	3.70317	0.128307
$834$	42.0028	1.45444
$835$	−10.1840	−0.352430
$836$	22.7986	0.788506
$837$	−0.958145	−0.0331183
$838$	−1.31984	−0.0455933
$839$	−49.8717	−1.72176	−0.860882	−	0.508805i	$-0.830087\pi$
$839$	−49.8717	−1.72176	−0.860882	+	0.508805i	$0.830087\pi$
$840$	5.29478	0.182687
$841$	23.2621	0.802142
$842$	25.4599	0.877406
$843$	26.2341	0.903550
$844$	17.6349	0.607017
$845$	12.9812	0.446565
$846$	−14.6829	−0.504810
$847$	−19.3352	−0.664367
$848$	−1.72545	−0.0592522
$849$	17.9094	0.614649
$850$	−1.52265	−0.0522264
$851$	0	0
$852$	−3.77213	−0.129231
$853$	−14.5958	−0.499750	−0.249875	−	0.968278i	$-0.580390\pi$
$853$	−14.5958	−0.499750	−0.249875	+	0.968278i	$0.580390\pi$
$854$	19.5721	0.669744
$855$	15.9749	0.546331
$856$	−6.00000	−0.205076
$857$	37.1387	1.26863	0.634316	−	0.773074i	$-0.281282\pi$
$857$	37.1387	1.26863	0.634316	+	0.773074i	$0.281282\pi$
$858$	−1.52265	−0.0519823
$859$	−14.0028	−0.477769	−0.238884	−	0.971048i	$-0.576782\pi$
$859$	−14.0028	−0.477769	−0.238884	+	0.971048i	$0.576782\pi$
$860$	−7.22925	−0.246516
$861$	−23.7066	−0.807919
$862$	−29.9094	−1.01872
$863$	−12.1812	−0.414652	−0.207326	−	0.978272i	$-0.566476\pi$
$863$	−12.1812	−0.414652	−0.207326	+	0.978272i	$0.566476\pi$
$864$	0.340078	0.0115697
$865$	−4.47735	−0.152235
$866$	3.77213	0.128182
$867$	−36.3714	−1.23524
$868$	6.02162	0.204387
$869$	20.9547	0.710840
$870$	17.9094	0.607186
$871$	−0.405606	−0.0137434
$872$	−6.90802	−0.233935
$873$	60.9637	2.06331
$874$	0	0
$875$	2.13727	0.0722531
$876$	−37.7282	−1.27472
$877$	28.4397	0.960339	0.480170	−	0.877176i	$-0.340575\pi$
$877$	28.4397	0.960339	0.480170	+	0.877176i	$0.340575\pi$
$878$	1.99378	0.0672869
$879$	−44.1435	−1.48892
$880$	4.47735	0.150932
$881$	−35.0076	−1.17944	−0.589718	−	0.807609i	$-0.700761\pi$
$881$	−35.0076	−1.17944	−0.589718	+	0.807609i	$0.700761\pi$
$882$	−7.63003	−0.256917
$883$	12.4647	0.419471	0.209736	−	0.977758i	$-0.432740\pi$
$883$	12.4647	0.419471	0.209736	+	0.977758i	$0.432740\pi$
$884$	−0.209021	−0.00703013
$885$	32.7735	1.10167
$886$	12.7268	0.427567
$887$	1.04807	0.0351908	0.0175954	−	0.999845i	$-0.494399\pi$
$887$	1.04807	0.0351908	0.0175954	+	0.999845i	$0.494399\pi$
$888$	29.5038	0.990083
$889$	−42.9450	−1.44033
$890$	4.27455	0.143283
$891$	38.3679	1.28537
$892$	13.5038	0.452141
$893$	23.8313	0.797483
$894$	−42.3429	−1.41616
$895$	7.72545	0.258233
$896$	−2.13727	−0.0714013
$897$	0	0
$898$	−35.4070	−1.18155
$899$	20.3679	0.679308
$900$	3.13727	0.104576
$901$	2.62725	0.0875265
$902$	−20.0467	−0.667482
$903$	−38.2773	−1.27379
$904$	−13.2293	−0.439998
$905$	9.36653	0.311354
$906$	45.7749	1.52077
$907$	−22.9170	−0.760947	−0.380474	−	0.924792i	$-0.624239\pi$
$907$	−22.9170	−0.760947	−0.380474	+	0.924792i	$0.624239\pi$
$908$	19.6349	0.651606
$909$	−37.3631	−1.23926
$910$	0.293394	0.00972590
$911$	−36.0000	−1.19273	−0.596367	−	0.802712i	$-0.703390\pi$
$911$	−36.0000	−1.19273	−0.596367	+	0.802712i	$0.703390\pi$
$912$	−12.6146	−0.417712
$913$	−72.4613	−2.39812
$914$	−7.31984	−0.242119
$915$	22.6864	0.749988
$916$	−0.0905906	−0.00299320
$917$	−12.6300	−0.417080
$918$	−0.517818	−0.0170906
$919$	47.2320	1.55804	0.779020	−	0.626998i	$-0.215717\pi$
$919$	47.2320	1.55804	0.779020	+	0.626998i	$0.215717\pi$
$920$	0	0
$921$	42.9609	1.41561
$922$	22.2745	0.733573
$923$	−0.209021	−0.00688001
$924$	23.7066	0.779890
$925$	11.9094	0.391579
$926$	8.82365	0.289963
$927$	−37.9993	−1.24806
$928$	−7.22925	−0.237312
$929$	−18.0000	−0.590561	−0.295280	−	0.955411i	$-0.595413\pi$
$929$	−18.0000	−0.590561	−0.295280	+	0.955411i	$0.595413\pi$
$930$	6.97977	0.228876
$931$	12.3840	0.405869
$932$	−2.95470	−0.0967846
$933$	29.7282	0.973258
$934$	16.1840	0.529555
$935$	−6.81743	−0.222954
$936$	0.430668	0.0140768
$937$	38.9609	1.27280	0.636399	−	0.771360i	$-0.280423\pi$
$937$	38.9609	1.27280	0.636399	+	0.771360i	$0.280423\pi$
$938$	6.31502	0.206193
$939$	−30.5240	−0.996114
$940$	4.68016	0.152650
$941$	3.65370	0.119107	0.0595537	−	0.998225i	$-0.481032\pi$
$941$	3.65370	0.119107	0.0595537	+	0.998225i	$0.481032\pi$
$942$	37.0481	1.20709
$943$	0	0
$944$	−13.2293	−0.430576
$945$	0.726839	0.0236441
$946$	−32.3679	−1.05237
$947$	−43.4599	−1.41226	−0.706128	−	0.708084i	$-0.749560\pi$
$947$	−43.4599	−1.41226	−0.706128	+	0.708084i	$0.749560\pi$
$948$	−11.5944	−0.376568
$949$	−2.09059	−0.0678634
$950$	−5.09198	−0.165206
$951$	−53.9372	−1.74904
$952$	3.25432	0.105473
$953$	−10.2962	−0.333526	−0.166763	−	0.985997i	$-0.553331\pi$
$953$	−10.2962	−0.333526	−0.166763	+	0.985997i	$0.553331\pi$
$954$	−5.41321	−0.175259
$955$	16.2745	0.526632
$956$	12.0000	0.388108
$957$	80.1867	2.59207
$958$	10.3651	0.334882
$959$	−26.3339	−0.850365
$960$	−2.47735	−0.0799562
$961$	−23.0621	−0.743938
$962$	1.63486	0.0527100
$963$	−18.8236	−0.606584
$964$	−5.90941	−0.190329
$965$	6.95470	0.223880
$966$	0	0
$967$	−24.6802	−0.793660	−0.396830	−	0.917892i	$-0.629890\pi$
$967$	−24.6802	−0.793660	−0.396830	+	0.917892i	$0.629890\pi$
$968$	9.04668	0.290771
$969$	19.2076	0.617038
$970$	−19.4321	−0.623926
$971$	−57.9812	−1.86070	−0.930352	−	0.366668i	$-0.880499\pi$
$971$	−57.9812	−1.86070	−0.930352	+	0.366668i	$0.880499\pi$
$972$	−22.2495	−0.713653
$973$	−36.2369	−1.16170
$974$	−8.27455	−0.265134
$975$	0.340078	0.0108912
$976$	−9.15751	−0.293125
$977$	−13.1324	−0.420144	−0.210072	−	0.977686i	$-0.567370\pi$
$977$	−13.1324	−0.420144	−0.210072	+	0.977686i	$0.567370\pi$
$978$	−28.1589	−0.900422
$979$	19.1387	0.611674
$980$	2.43206	0.0776892
$981$	−21.6724	−0.691945
$982$	−16.2745	−0.519342
$983$	−30.2028	−0.963320	−0.481660	−	0.876358i	$-0.659966\pi$
$983$	−30.2028	−0.963320	−0.481660	+	0.876358i	$0.659966\pi$
$984$	11.0920	0.353599
$985$	−1.43206	−0.0456291
$986$	11.0076	0.350554
$987$	24.7804	0.788769
$988$	−0.699000	−0.0222381
$989$	0	0
$990$	14.0467	0.446433
$991$	−24.5679	−0.780426	−0.390213	−	0.920725i	$-0.627599\pi$
$991$	−24.5679	−0.780426	−0.390213	+	0.920725i	$0.627599\pi$
$992$	−2.81743	−0.0894535
$993$	−0.680155	−0.0215841
$994$	3.25432	0.103221
$995$	−5.90941	−0.187341
$996$	40.0934	1.27041
$997$	−21.8188	−0.691009	−0.345504	−	0.938417i	$-0.612292\pi$
$997$	−21.8188	−0.691009	−0.345504	+	0.938417i	$0.612292\pi$
$998$	23.1387	0.732442
$999$	4.05012	0.128140

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	5290.2.a.p.1.3	✓	3
23.22	odd	2		5290.2.a.q.1.3	yes	3

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
5290.2.a.p.1.3	✓	3	1.1	even	1	trivial
5290.2.a.q.1.3	yes	3	23.22	odd	2

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)

\(f(q)\)	\(=\)	\(q+1.00000 q^{2} +2.47735 q^{3} +1.00000 q^{4} -1.00000 q^{5} +2.47735 q^{6} -2.13727 q^{7} +1.00000 q^{8} +3.13727 q^{9} +O(q^{10})\)	\(q+1.00000 q^{2} +2.47735 q^{3} +1.00000 q^{4} -1.00000 q^{5} +2.47735 q^{6} -2.13727 q^{7} +1.00000 q^{8} +3.13727 q^{9} -1.00000 q^{10} -4.47735 q^{11} +2.47735 q^{12} +0.137275 q^{13} -2.13727 q^{14} -2.47735 q^{15} +1.00000 q^{16} -1.52265 q^{17} +3.13727 q^{18} -5.09198 q^{19} -1.00000 q^{20} -5.29478 q^{21} -4.47735 q^{22} +2.47735 q^{24} +1.00000 q^{25} +0.137275 q^{26} +0.340078 q^{27} -2.13727 q^{28} -7.22925 q^{29} -2.47735 q^{30} -2.81743 q^{31} +1.00000 q^{32} -11.0920 q^{33} -1.52265 q^{34} +2.13727 q^{35} +3.13727 q^{36} +11.9094 q^{37} -5.09198 q^{38} +0.340078 q^{39} -1.00000 q^{40} +4.47735 q^{41} -5.29478 q^{42} +7.22925 q^{43} -4.47735 q^{44} -3.13727 q^{45} -4.68016 q^{47} +2.47735 q^{48} -2.43206 q^{49} +1.00000 q^{50} -3.77213 q^{51} +0.137275 q^{52} -1.72545 q^{53} +0.340078 q^{54} +4.47735 q^{55} -2.13727 q^{56} -12.6146 q^{57} -7.22925 q^{58} -13.2293 q^{59} -2.47735 q^{60} -9.15751 q^{61} -2.81743 q^{62} -6.70522 q^{63} +1.00000 q^{64} -0.137275 q^{65} -11.0920 q^{66} -2.95470 q^{67} -1.52265 q^{68} +2.13727 q^{70} -1.52265 q^{71} +3.13727 q^{72} -15.2293 q^{73} +11.9094 q^{74} +2.47735 q^{75} -5.09198 q^{76} +9.56933 q^{77} +0.340078 q^{78} -4.68016 q^{79} -1.00000 q^{80} -8.56933 q^{81} +4.47735 q^{82} +16.1840 q^{83} -5.29478 q^{84} +1.52265 q^{85} +7.22925 q^{86} -17.9094 q^{87} -4.47735 q^{88} -4.27455 q^{89} -3.13727 q^{90} -0.293394 q^{91} -6.97977 q^{93} -4.68016 q^{94} +5.09198 q^{95} +2.47735 q^{96} +19.4321 q^{97} -2.43206 q^{98} -14.0467 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 3 q + 3 q^{2} - q^{3} + 3 q^{4} - 3 q^{5} - q^{6} - 3 q^{7} + 3 q^{8} + 6 q^{9}+O(q^{10}) \) 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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