LMFDB - Embedded newform 5610.2.a.ca.1.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [5610,2,Mod(1,5610)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(5610, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([0, 0, 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("5610.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 5610 = 2 \cdot 3 \cdot 5 \cdot 11 \cdot 17 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	5610.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:	$44.7960755339$
Analytic rank:	$0$
Dimension:	$3$
Coefficient field:	3.3.961.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{3} - x^{2} - 10x + 8 $ x^3 - x^2 - 10*x + 8
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 2 $
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.3
Root			$3.29707$ of defining polynomial
Character	$\chi$	$=$	5610.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.00000 q^{2} +1.00000 q^{3} +1.00000 q^{4} +1.00000 q^{5} -1.00000 q^{6} +3.29707 q^{7} -1.00000 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q-1.00000 q^{2} +1.00000 q^{3} +1.00000 q^{4} +1.00000 q^{5} -1.00000 q^{6} +3.29707 q^{7} -1.00000 q^{8} +1.00000 q^{9} -1.00000 q^{10} +1.00000 q^{11} +1.00000 q^{12} -1.57360 q^{13} -3.29707 q^{14} +1.00000 q^{15} +1.00000 q^{16} -1.00000 q^{17} -1.00000 q^{18} -6.16774 q^{19} +1.00000 q^{20} +3.29707 q^{21} -1.00000 q^{22} +7.29707 q^{23} -1.00000 q^{24} +1.00000 q^{25} +1.57360 q^{26} +1.00000 q^{27} +3.29707 q^{28} +4.87067 q^{29} -1.00000 q^{30} -2.87067 q^{31} -1.00000 q^{32} +1.00000 q^{33} +1.00000 q^{34} +3.29707 q^{35} +1.00000 q^{36} +6.00000 q^{37} +6.16774 q^{38} -1.57360 q^{39} -1.00000 q^{40} -8.59414 q^{41} -3.29707 q^{42} +3.29707 q^{43} +1.00000 q^{44} +1.00000 q^{45} -7.29707 q^{46} -4.00000 q^{47} +1.00000 q^{48} +3.87067 q^{49} -1.00000 q^{50} -1.00000 q^{51} -1.57360 q^{52} +2.42640 q^{53} -1.00000 q^{54} +1.00000 q^{55} -3.29707 q^{56} -6.16774 q^{57} -4.87067 q^{58} -0.426396 q^{59} +1.00000 q^{60} +2.00000 q^{61} +2.87067 q^{62} +3.29707 q^{63} +1.00000 q^{64} -1.57360 q^{65} -1.00000 q^{66} +12.3355 q^{67} -1.00000 q^{68} +7.29707 q^{69} -3.29707 q^{70} +7.57360 q^{71} -1.00000 q^{72} +4.16774 q^{73} -6.00000 q^{74} +1.00000 q^{75} -6.16774 q^{76} +3.29707 q^{77} +1.57360 q^{78} +10.1677 q^{79} +1.00000 q^{80} +1.00000 q^{81} +8.59414 q^{82} -9.18828 q^{83} +3.29707 q^{84} -1.00000 q^{85} -3.29707 q^{86} +4.87067 q^{87} -1.00000 q^{88} +8.59414 q^{89} -1.00000 q^{90} -5.18828 q^{91} +7.29707 q^{92} -2.87067 q^{93} +4.00000 q^{94} -6.16774 q^{95} -1.00000 q^{96} +11.4648 q^{97} -3.87067 q^{98} +1.00000 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 3 q - 3 q^{2} + 3 q^{3} + 3 q^{4} + 3 q^{5} - 3 q^{6} + q^{7} - 3 q^{8} + 3 q^{9}+O(q^{10}) $ 3 * q - 3 * q^2 + 3 * q^3 + 3 * q^4 + 3 * q^5 - 3 * q^6 + q^7 - 3 * q^8 + 3 * q^9	\( 3 q - 3 q^{2} + 3 q^{3} + 3 q^{4} + 3 q^{5} - 3 q^{6} + q^{7} - 3 q^{8} + 3 q^{9} - 3 q^{10} + 3 q^{11} + 3 q^{12} - 2 q^{13} - q^{14} + 3 q^{15} + 3 q^{16} - 3 q^{17} - 3 q^{18} + 2 q^{19} + 3 q^{20} + q^{21} - 3 q^{22} + 13 q^{23} - 3 q^{24} + 3 q^{25} + 2 q^{26} + 3 q^{27} + q^{28} + 3 q^{29} - 3 q^{30} + 3 q^{31} - 3 q^{32} + 3 q^{33} + 3 q^{34} + q^{35} + 3 q^{36} + 18 q^{37} - 2 q^{38} - 2 q^{39} - 3 q^{40} - 8 q^{41} - q^{42} + q^{43} + 3 q^{44} + 3 q^{45} - 13 q^{46} - 12 q^{47} + 3 q^{48} - 3 q^{50} - 3 q^{51} - 2 q^{52} + 10 q^{53} - 3 q^{54} + 3 q^{55} - q^{56} + 2 q^{57} - 3 q^{58} - 4 q^{59} + 3 q^{60} + 6 q^{61} - 3 q^{62} + q^{63} + 3 q^{64} - 2 q^{65} - 3 q^{66} - 4 q^{67} - 3 q^{68} + 13 q^{69} - q^{70} + 20 q^{71} - 3 q^{72} - 8 q^{73} - 18 q^{74} + 3 q^{75} + 2 q^{76} + q^{77} + 2 q^{78} + 10 q^{79} + 3 q^{80} + 3 q^{81} + 8 q^{82} + 8 q^{83} + q^{84} - 3 q^{85} - q^{86} + 3 q^{87} - 3 q^{88} + 8 q^{89} - 3 q^{90} + 20 q^{91} + 13 q^{92} + 3 q^{93} + 12 q^{94} + 2 q^{95} - 3 q^{96} + 5 q^{97} + 3 q^{99}+O(q^{100}) \) 3 * q - 3 * q^2 + 3 * q^3 + 3 * q^4 + 3 * q^5 - 3 * q^6 + q^7 - 3 * q^8 + 3 * q^9 - 3 * q^10 + 3 * q^11 + 3 * q^12 - 2 * q^13 - q^14 + 3 * q^15 + 3 * q^16 - 3 * q^17 - 3 * q^18 + 2 * q^19 + 3 * q^20 + q^21 - 3 * q^22 + 13 * q^23 - 3 * q^24 + 3 * q^25 + 2 * q^26 + 3 * q^27 + q^28 + 3 * q^29 - 3 * q^30 + 3 * q^31 - 3 * q^32 + 3 * q^33 + 3 * q^34 + q^35 + 3 * q^36 + 18 * q^37 - 2 * q^38 - 2 * q^39 - 3 * q^40 - 8 * q^41 - q^42 + q^43 + 3 * q^44 + 3 * q^45 - 13 * q^46 - 12 * q^47 + 3 * q^48 - 3 * q^50 - 3 * q^51 - 2 * q^52 + 10 * q^53 - 3 * q^54 + 3 * q^55 - q^56 + 2 * q^57 - 3 * q^58 - 4 * q^59 + 3 * q^60 + 6 * q^61 - 3 * q^62 + q^63 + 3 * q^64 - 2 * q^65 - 3 * q^66 - 4 * q^67 - 3 * q^68 + 13 * q^69 - q^70 + 20 * q^71 - 3 * q^72 - 8 * q^73 - 18 * q^74 + 3 * q^75 + 2 * q^76 + q^77 + 2 * q^78 + 10 * q^79 + 3 * q^80 + 3 * q^81 + 8 * q^82 + 8 * q^83 + q^84 - 3 * q^85 - q^86 + 3 * q^87 - 3 * q^88 + 8 * q^89 - 3 * q^90 + 20 * q^91 + 13 * q^92 + 3 * q^93 + 12 * q^94 + 2 * q^95 - 3 * q^96 + 5 * q^97 + 3 * 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
$3$	1.00000	0.577350
$3$	1.00000	0.577350
$4$	1.00000	0.500000
$5$	1.00000	0.447214
$5$	1.00000	0.447214
$6$	−1.00000	−0.408248
$7$	3.29707	1.24618	0.623088	−	0.782152i	$-0.285878\pi$
$7$	3.29707	1.24618	0.623088	+	0.782152i	$0.285878\pi$
$8$	−1.00000	−0.353553
$9$	1.00000	0.333333
$10$	−1.00000	−0.316228
$11$	1.00000	0.301511
$11$	1.00000	0.301511
$12$	1.00000	0.288675
$13$	−1.57360	−0.436439	−0.218220	−	0.975900i	$-0.570025\pi$
$13$	−1.57360	−0.436439	−0.218220	+	0.975900i	$0.570025\pi$
$14$	−3.29707	−0.881179
$15$	1.00000	0.258199
$16$	1.00000	0.250000
$17$	−1.00000	−0.242536
$17$	−1.00000	−0.242536
$18$	−1.00000	−0.235702
$19$	−6.16774	−1.41498	−0.707489	−	0.706725i	$-0.750172\pi$
$19$	−6.16774	−1.41498	−0.707489	+	0.706725i	$0.750172\pi$
$20$	1.00000	0.223607
$21$	3.29707	0.719480
$22$	−1.00000	−0.213201
$23$	7.29707	1.52154	0.760772	−	0.649019i	$-0.224820\pi$
$23$	7.29707	1.52154	0.760772	+	0.649019i	$0.224820\pi$
$24$	−1.00000	−0.204124
$25$	1.00000	0.200000
$26$	1.57360	0.308609
$27$	1.00000	0.192450
$28$	3.29707	0.623088
$29$	4.87067	0.904461	0.452231	−	0.891901i	$-0.350628\pi$
$29$	4.87067	0.904461	0.452231	+	0.891901i	$0.350628\pi$
$30$	−1.00000	−0.182574
$31$	−2.87067	−0.515588	−0.257794	−	0.966200i	$-0.582996\pi$
$31$	−2.87067	−0.515588	−0.257794	+	0.966200i	$0.582996\pi$
$32$	−1.00000	−0.176777
$33$	1.00000	0.174078
$34$	1.00000	0.171499
$35$	3.29707	0.557307
$36$	1.00000	0.166667
$37$	6.00000	0.986394	0.493197	−	0.869918i	$-0.335828\pi$
$37$	6.00000	0.986394	0.493197	+	0.869918i	$0.335828\pi$
$38$	6.16774	1.00054
$39$	−1.57360	−0.251978
$40$	−1.00000	−0.158114
$41$	−8.59414	−1.34218	−0.671090	−	0.741376i	$-0.734173\pi$
$41$	−8.59414	−1.34218	−0.671090	+	0.741376i	$0.734173\pi$
$42$	−3.29707	−0.508749
$43$	3.29707	0.502799	0.251399	−	0.967883i	$-0.419109\pi$
$43$	3.29707	0.502799	0.251399	+	0.967883i	$0.419109\pi$
$44$	1.00000	0.150756
$45$	1.00000	0.149071
$46$	−7.29707	−1.07589
$47$	−4.00000	−0.583460	−0.291730	−	0.956501i	$-0.594231\pi$
$47$	−4.00000	−0.583460	−0.291730	+	0.956501i	$0.594231\pi$
$48$	1.00000	0.144338
$49$	3.87067	0.552953
$50$	−1.00000	−0.141421
$51$	−1.00000	−0.140028
$52$	−1.57360	−0.218220
$53$	2.42640	0.333291	0.166646	−	0.986017i	$-0.446706\pi$
$53$	2.42640	0.333291	0.166646	+	0.986017i	$0.446706\pi$
$54$	−1.00000	−0.136083
$55$	1.00000	0.134840
$56$	−3.29707	−0.440590
$57$	−6.16774	−0.816938
$58$	−4.87067	−0.639551
$59$	−0.426396	−0.0555121	−0.0277560	−	0.999615i	$-0.508836\pi$
$59$	−0.426396	−0.0555121	−0.0277560	+	0.999615i	$0.508836\pi$
$60$	1.00000	0.129099
$61$	2.00000	0.256074	0.128037	−	0.991769i	$-0.459132\pi$
$61$	2.00000	0.256074	0.128037	+	0.991769i	$0.459132\pi$
$62$	2.87067	0.364576
$63$	3.29707	0.415392
$64$	1.00000	0.125000
$65$	−1.57360	−0.195182
$66$	−1.00000	−0.123091
$67$	12.3355	1.50702	0.753510	−	0.657437i	$-0.228359\pi$
$67$	12.3355	1.50702	0.753510	+	0.657437i	$0.228359\pi$
$68$	−1.00000	−0.121268
$69$	7.29707	0.878464
$70$	−3.29707	−0.394075
$71$	7.57360	0.898821	0.449411	−	0.893325i	$-0.351634\pi$
$71$	7.57360	0.898821	0.449411	+	0.893325i	$0.351634\pi$
$72$	−1.00000	−0.117851
$73$	4.16774	0.487798	0.243899	−	0.969801i	$-0.421574\pi$
$73$	4.16774	0.487798	0.243899	+	0.969801i	$0.421574\pi$
$74$	−6.00000	−0.697486
$75$	1.00000	0.115470
$76$	−6.16774	−0.707489
$77$	3.29707	0.375736
$78$	1.57360	0.178176
$79$	10.1677	1.14396	0.571980	−	0.820267i	$-0.306175\pi$
$79$	10.1677	1.14396	0.571980	+	0.820267i	$0.306175\pi$
$80$	1.00000	0.111803
$81$	1.00000	0.111111
$82$	8.59414	0.949064
$83$	−9.18828	−1.00854	−0.504272	−	0.863545i	$-0.668239\pi$
$83$	−9.18828	−1.00854	−0.504272	+	0.863545i	$0.668239\pi$
$84$	3.29707	0.359740
$85$	−1.00000	−0.108465
$86$	−3.29707	−0.355532
$87$	4.87067	0.522191
$88$	−1.00000	−0.106600
$89$	8.59414	0.910977	0.455489	−	0.890242i	$-0.349465\pi$
$89$	8.59414	0.910977	0.455489	+	0.890242i	$0.349465\pi$
$90$	−1.00000	−0.105409
$91$	−5.18828	−0.543880
$92$	7.29707	0.760772
$93$	−2.87067	−0.297675
$94$	4.00000	0.412568
$95$	−6.16774	−0.632797
$96$	−1.00000	−0.102062
$97$	11.4648	1.16408	0.582038	−	0.813162i	$-0.302256\pi$
$97$	11.4648	1.16408	0.582038	+	0.813162i	$0.302256\pi$
$98$	−3.87067	−0.390997
$99$	1.00000	0.100504
$100$	1.00000	0.100000
$101$	6.00000	0.597022	0.298511	−	0.954406i	$-0.403510\pi$
$101$	6.00000	0.597022	0.298511	+	0.954406i	$0.403510\pi$
$102$	1.00000	0.0990148
$103$	17.4648	1.72086	0.860430	−	0.509569i	$-0.170195\pi$
$103$	17.4648	1.72086	0.860430	+	0.509569i	$0.170195\pi$
$104$	1.57360	0.154305
$105$	3.29707	0.321761
$106$	−2.42640	−0.235672
$107$	−5.12933	−0.495871	−0.247935	−	0.968777i	$-0.579752\pi$
$107$	−5.12933	−0.495871	−0.247935	+	0.968777i	$0.579752\pi$
$108$	1.00000	0.0962250
$109$	16.5941	1.58943	0.794715	−	0.606982i	$-0.207620\pi$
$109$	16.5941	1.58943	0.794715	+	0.606982i	$0.207620\pi$
$110$	−1.00000	−0.0953463
$111$	6.00000	0.569495
$112$	3.29707	0.311544
$113$	−9.02054	−0.848581	−0.424290	−	0.905526i	$-0.639476\pi$
$113$	−9.02054	−0.848581	−0.424290	+	0.905526i	$0.639476\pi$
$114$	6.16774	0.577662
$115$	7.29707	0.680455
$116$	4.87067	0.452231
$117$	−1.57360	−0.145480
$118$	0.426396	0.0392530
$119$	−3.29707	−0.302242
$120$	−1.00000	−0.0912871
$121$	1.00000	0.0909091
$122$	−2.00000	−0.181071
$123$	−8.59414	−0.774908
$124$	−2.87067	−0.257794
$125$	1.00000	0.0894427
$126$	−3.29707	−0.293726
$127$	−7.44693	−0.660809	−0.330404	−	0.943840i	$-0.607185\pi$
$127$	−7.44693	−0.660809	−0.330404	+	0.943840i	$0.607185\pi$
$128$	−1.00000	−0.0883883
$129$	3.29707	0.290291
$130$	1.57360	0.138014
$131$	9.18828	0.802784	0.401392	−	0.915906i	$-0.368527\pi$
$131$	9.18828	0.802784	0.401392	+	0.915906i	$0.368527\pi$
$132$	1.00000	0.0870388
$133$	−20.3355	−1.76331
$134$	−12.3355	−1.06562
$135$	1.00000	0.0860663
$136$	1.00000	0.0857493
$137$	−10.0590	−0.859395	−0.429697	−	0.902973i	$-0.641380\pi$
$137$	−10.0590	−0.859395	−0.429697	+	0.902973i	$0.641380\pi$
$138$	−7.29707	−0.621168
$139$	19.2062	1.62905	0.814523	−	0.580132i	$-0.196999\pi$
$139$	19.2062	1.62905	0.814523	+	0.580132i	$0.196999\pi$
$140$	3.29707	0.278653
$141$	−4.00000	−0.336861
$142$	−7.57360	−0.635563
$143$	−1.57360	−0.131591
$144$	1.00000	0.0833333
$145$	4.87067	0.404487
$146$	−4.16774	−0.344925
$147$	3.87067	0.319248
$148$	6.00000	0.493197
$149$	−8.59414	−0.704059	−0.352030	−	0.935989i	$-0.614508\pi$
$149$	−8.59414	−0.704059	−0.352030	+	0.935989i	$0.614508\pi$
$150$	−1.00000	−0.0816497
$151$	4.00000	0.325515	0.162758	−	0.986666i	$-0.447961\pi$
$151$	4.00000	0.325515	0.162758	+	0.986666i	$0.447961\pi$
$152$	6.16774	0.500270
$153$	−1.00000	−0.0808452
$154$	−3.29707	−0.265686
$155$	−2.87067	−0.230578
$156$	−1.57360	−0.125989
$157$	10.0000	0.798087	0.399043	−	0.916932i	$-0.369342\pi$
$157$	10.0000	0.798087	0.399043	+	0.916932i	$0.369342\pi$
$158$	−10.1677	−0.808902
$159$	2.42640	0.192426
$160$	−1.00000	−0.0790569
$161$	24.0590	1.89611
$162$	−1.00000	−0.0785674
$163$	0.276533	0.0216597	0.0108299	−	0.999941i	$-0.496553\pi$
$163$	0.276533	0.0216597	0.0108299	+	0.999941i	$0.496553\pi$
$164$	−8.59414	−0.671090
$165$	1.00000	0.0778499
$166$	9.18828	0.713149
$167$	−12.8886	−0.997346	−0.498673	−	0.866790i	$-0.666179\pi$
$167$	−12.8886	−0.997346	−0.498673	+	0.866790i	$0.666179\pi$
$168$	−3.29707	−0.254375
$169$	−10.5238	−0.809521
$170$	1.00000	0.0766965
$171$	−6.16774	−0.471659
$172$	3.29707	0.251399
$173$	−14.3355	−1.08991	−0.544954	−	0.838466i	$-0.683453\pi$
$173$	−14.3355	−1.08991	−0.544954	+	0.838466i	$0.683453\pi$
$174$	−4.87067	−0.369245
$175$	3.29707	0.249235
$176$	1.00000	0.0753778
$177$	−0.426396	−0.0320499
$178$	−8.59414	−0.644158
$179$	−25.9502	−1.93961	−0.969803	−	0.243888i	$-0.921577\pi$
$179$	−25.9502	−1.93961	−0.969803	+	0.243888i	$0.921577\pi$
$180$	1.00000	0.0745356
$181$	4.87067	0.362034	0.181017	−	0.983480i	$-0.442061\pi$
$181$	4.87067	0.362034	0.181017	+	0.983480i	$0.442061\pi$
$182$	5.18828	0.384581
$183$	2.00000	0.147844
$184$	−7.29707	−0.537947
$185$	6.00000	0.441129
$186$	2.87067	0.210488
$187$	−1.00000	−0.0731272
$188$	−4.00000	−0.291730
$189$	3.29707	0.239827
$190$	6.16774	0.447455
$191$	−22.6531	−1.63912	−0.819560	−	0.572993i	$-0.805782\pi$
$191$	−22.6531	−1.63912	−0.819560	+	0.572993i	$0.805782\pi$
$192$	1.00000	0.0721688
$193$	−0.167745	−0.0120745	−0.00603726	−	0.999982i	$-0.501922\pi$
$193$	−0.167745	−0.0120745	−0.00603726	+	0.999982i	$0.501922\pi$
$194$	−11.4648	−0.823126
$195$	−1.57360	−0.112688
$196$	3.87067	0.276477
$197$	8.92963	0.636210	0.318105	−	0.948056i	$-0.396954\pi$
$197$	8.92963	0.636210	0.318105	+	0.948056i	$0.396954\pi$
$198$	−1.00000	−0.0710669
$199$	−4.33549	−0.307335	−0.153667	−	0.988123i	$-0.549108\pi$
$199$	−4.33549	−0.307335	−0.153667	+	0.988123i	$0.549108\pi$
$200$	−1.00000	−0.0707107
$201$	12.3355	0.870078
$202$	−6.00000	−0.422159
$203$	16.0590	1.12712
$204$	−1.00000	−0.0700140
$205$	−8.59414	−0.600241
$206$	−17.4648	−1.21683
$207$	7.29707	0.507181
$208$	−1.57360	−0.109110
$209$	−6.16774	−0.426632
$210$	−3.29707	−0.227519
$211$	−11.2062	−0.771464	−0.385732	−	0.922611i	$-0.626051\pi$
$211$	−11.2062	−0.771464	−0.385732	+	0.922611i	$0.626051\pi$
$212$	2.42640	0.166646
$213$	7.57360	0.518935
$214$	5.12933	0.350633
$215$	3.29707	0.224858
$216$	−1.00000	−0.0680414
$217$	−9.46482	−0.642514
$218$	−16.5941	−1.12390
$219$	4.16774	0.281630
$220$	1.00000	0.0674200
$221$	1.57360	0.105852
$222$	−6.00000	−0.402694
$223$	17.4648	1.16953	0.584765	−	0.811203i	$-0.301187\pi$
$223$	17.4648	1.16953	0.584765	+	0.811203i	$0.301187\pi$
$224$	−3.29707	−0.220295
$225$	1.00000	0.0666667
$226$	9.02054	0.600037
$227$	−5.12933	−0.340445	−0.170223	−	0.985406i	$-0.554449\pi$
$227$	−5.12933	−0.340445	−0.170223	+	0.985406i	$0.554449\pi$
$228$	−6.16774	−0.408469
$229$	10.8886	0.719536	0.359768	−	0.933042i	$-0.382856\pi$
$229$	10.8886	0.719536	0.359768	+	0.933042i	$0.382856\pi$
$230$	−7.29707	−0.481155
$231$	3.29707	0.216931
$232$	−4.87067	−0.319775
$233$	0.870674	0.0570398	0.0285199	−	0.999593i	$-0.490921\pi$
$233$	0.870674	0.0570398	0.0285199	+	0.999593i	$0.490921\pi$
$234$	1.57360	0.102870
$235$	−4.00000	−0.260931
$236$	−0.426396	−0.0277560
$237$	10.1677	0.660466
$238$	3.29707	0.213717
$239$	10.9296	0.706979	0.353490	−	0.935438i	$-0.384995\pi$
$239$	10.9296	0.706979	0.353490	+	0.935438i	$0.384995\pi$
$240$	1.00000	0.0645497
$241$	−14.4854	−0.933084	−0.466542	−	0.884499i	$-0.654500\pi$
$241$	−14.4854	−0.933084	−0.466542	+	0.884499i	$0.654500\pi$
$242$	−1.00000	−0.0642824
$243$	1.00000	0.0641500
$244$	2.00000	0.128037
$245$	3.87067	0.247288
$246$	8.59414	0.547942
$247$	9.70559	0.617552
$248$	2.87067	0.182288
$249$	−9.18828	−0.582284
$250$	−1.00000	−0.0632456
$251$	−26.5032	−1.67287	−0.836435	−	0.548067i	$-0.815364\pi$
$251$	−26.5032	−1.67287	−0.836435	+	0.548067i	$0.815364\pi$
$252$	3.29707	0.207696
$253$	7.29707	0.458763
$254$	7.44693	0.467262
$255$	−1.00000	−0.0626224
$256$	1.00000	0.0625000
$257$	0.870674	0.0543112	0.0271556	−	0.999631i	$-0.491355\pi$
$257$	0.870674	0.0543112	0.0271556	+	0.999631i	$0.491355\pi$
$258$	−3.29707	−0.205267
$259$	19.7824	1.22922
$260$	−1.57360	−0.0975908
$261$	4.87067	0.301487
$262$	−9.18828	−0.567654
$263$	17.4648	1.07693	0.538463	−	0.842649i	$-0.319005\pi$
$263$	17.4648	1.07693	0.538463	+	0.842649i	$0.319005\pi$
$264$	−1.00000	−0.0615457
$265$	2.42640	0.149052
$266$	20.3355	1.24685
$267$	8.59414	0.525953
$268$	12.3355	0.753510
$269$	11.1883	0.682162	0.341081	−	0.940034i	$-0.389207\pi$
$269$	11.1883	0.682162	0.341081	+	0.940034i	$0.389207\pi$
$270$	−1.00000	−0.0608581
$271$	9.12933	0.554567	0.277284	−	0.960788i	$-0.410566\pi$
$271$	9.12933	0.554567	0.277284	+	0.960788i	$0.410566\pi$
$272$	−1.00000	−0.0606339
$273$	−5.18828	−0.314009
$274$	10.0590	0.607684
$275$	1.00000	0.0603023
$276$	7.29707	0.439232
$277$	14.3355	0.861336	0.430668	−	0.902510i	$-0.358278\pi$
$277$	14.3355	0.861336	0.430668	+	0.902510i	$0.358278\pi$
$278$	−19.2062	−1.15191
$279$	−2.87067	−0.171863
$280$	−3.29707	−0.197038
$281$	19.8003	1.18119	0.590594	−	0.806969i	$-0.298894\pi$
$281$	19.8003	1.18119	0.590594	+	0.806969i	$0.298894\pi$
$282$	4.00000	0.238197
$283$	−16.6352	−0.988861	−0.494430	−	0.869217i	$-0.664623\pi$
$283$	−16.6352	−0.988861	−0.494430	+	0.869217i	$0.664623\pi$
$284$	7.57360	0.449411
$285$	−6.16774	−0.365346
$286$	1.57360	0.0930491
$287$	−28.3355	−1.67259
$288$	−1.00000	−0.0589256
$289$	1.00000	0.0588235
$290$	−4.87067	−0.286016
$291$	11.4648	0.672079
$292$	4.16774	0.243899
$293$	−8.01788	−0.468410	−0.234205	−	0.972187i	$-0.575249\pi$
$293$	−8.01788	−0.468410	−0.234205	+	0.972187i	$0.575249\pi$
$294$	−3.87067	−0.225742
$295$	−0.426396	−0.0248258
$296$	−6.00000	−0.348743
$297$	1.00000	0.0580259
$298$	8.59414	0.497845
$299$	−11.4827	−0.664061
$300$	1.00000	0.0577350
$301$	10.8707	0.626575
$302$	−4.00000	−0.230174
$303$	6.00000	0.344691
$304$	−6.16774	−0.353744
$305$	2.00000	0.114520
$306$	1.00000	0.0571662
$307$	−7.02054	−0.400683	−0.200342	−	0.979726i	$-0.564205\pi$
$307$	−7.02054	−0.400683	−0.200342	+	0.979726i	$0.564205\pi$
$308$	3.29707	0.187868
$309$	17.4648	0.993539
$310$	2.87067	0.163043
$311$	23.6915	1.34342	0.671711	−	0.740813i	$-0.265560\pi$
$311$	23.6915	1.34342	0.671711	+	0.740813i	$0.265560\pi$
$312$	1.57360	0.0890878
$313$	−26.9475	−1.52316	−0.761582	−	0.648069i	$-0.775577\pi$
$313$	−26.9475	−1.52316	−0.761582	+	0.648069i	$0.775577\pi$
$314$	−10.0000	−0.564333
$315$	3.29707	0.185769
$316$	10.1677	0.571980
$317$	−10.0590	−0.564967	−0.282484	−	0.959272i	$-0.591158\pi$
$317$	−10.0590	−0.564967	−0.282484	+	0.959272i	$0.591158\pi$
$318$	−2.42640	−0.136066
$319$	4.87067	0.272705
$320$	1.00000	0.0559017
$321$	−5.12933	−0.286291
$322$	−24.0590	−1.34075
$323$	6.16774	0.343182
$324$	1.00000	0.0555556
$325$	−1.57360	−0.0872878
$326$	−0.276533	−0.0153158
$327$	16.5941	0.917658
$328$	8.59414	0.474532
$329$	−13.1883	−0.727094
$330$	−1.00000	−0.0550482
$331$	−32.9475	−1.81096	−0.905480	−	0.424390i	$-0.860489\pi$
$331$	−32.9475	−1.81096	−0.905480	+	0.424390i	$0.860489\pi$
$332$	−9.18828	−0.504272
$333$	6.00000	0.328798
$334$	12.8886	0.705230
$335$	12.3355	0.673960
$336$	3.29707	0.179870
$337$	−28.5032	−1.55267	−0.776335	−	0.630320i	$-0.782924\pi$
$337$	−28.5032	−1.55267	−0.776335	+	0.630320i	$0.782924\pi$
$338$	10.5238	0.572418
$339$	−9.02054	−0.489928
$340$	−1.00000	−0.0542326
$341$	−2.87067	−0.155456
$342$	6.16774	0.333513
$343$	−10.3176	−0.557098
$344$	−3.29707	−0.177766
$345$	7.29707	0.392861
$346$	14.3355	0.770681
$347$	−33.5238	−1.79965	−0.899825	−	0.436251i	$-0.856306\pi$
$347$	−33.5238	−1.79965	−0.899825	+	0.436251i	$0.856306\pi$
$348$	4.87067	0.261096
$349$	−17.0205	−0.911088	−0.455544	−	0.890213i	$-0.650555\pi$
$349$	−17.0205	−0.911088	−0.455544	+	0.890213i	$0.650555\pi$
$350$	−3.29707	−0.176236
$351$	−1.57360	−0.0839927
$352$	−1.00000	−0.0533002
$353$	30.6120	1.62931	0.814657	−	0.579943i	$-0.196925\pi$
$353$	30.6120	1.62931	0.814657	+	0.579943i	$0.196925\pi$
$354$	0.426396	0.0226627
$355$	7.57360	0.401965
$356$	8.59414	0.455489
$357$	−3.29707	−0.174499
$358$	25.9502	1.37151
$359$	18.9296	0.999068	0.499534	−	0.866294i	$-0.333505\pi$
$359$	18.9296	0.999068	0.499534	+	0.866294i	$0.333505\pi$
$360$	−1.00000	−0.0527046
$361$	19.0411	1.00216
$362$	−4.87067	−0.255997
$363$	1.00000	0.0524864
$364$	−5.18828	−0.271940
$365$	4.16774	0.218150
$366$	−2.00000	−0.104542
$367$	−12.8886	−0.672777	−0.336389	−	0.941723i	$-0.609206\pi$
$367$	−12.8886	−0.672777	−0.336389	+	0.941723i	$0.609206\pi$
$368$	7.29707	0.380386
$369$	−8.59414	−0.447393
$370$	−6.00000	−0.311925
$371$	8.00000	0.415339
$372$	−2.87067	−0.148838
$373$	36.8387	1.90744	0.953718	−	0.300701i	$-0.0972207\pi$
$373$	36.8387	1.90744	0.953718	+	0.300701i	$0.0972207\pi$
$374$	1.00000	0.0517088
$375$	1.00000	0.0516398
$376$	4.00000	0.206284
$377$	−7.66451	−0.394742
$378$	−3.29707	−0.169583
$379$	8.85279	0.454737	0.227369	−	0.973809i	$-0.426988\pi$
$379$	8.85279	0.454737	0.227369	+	0.973809i	$0.426988\pi$
$380$	−6.16774	−0.316399
$381$	−7.44693	−0.381518
$382$	22.6531	1.15903
$383$	22.6299	1.15633	0.578167	−	0.815918i	$-0.303768\pi$
$383$	22.6299	1.15633	0.578167	+	0.815918i	$0.303768\pi$
$384$	−1.00000	−0.0510310
$385$	3.29707	0.168034
$386$	0.167745	0.00853798
$387$	3.29707	0.167600
$388$	11.4648	0.582038
$389$	14.2088	0.720416	0.360208	−	0.932872i	$-0.382706\pi$
$389$	14.2088	0.720416	0.360208	+	0.932872i	$0.382706\pi$
$390$	1.57360	0.0796825
$391$	−7.29707	−0.369029
$392$	−3.87067	−0.195499
$393$	9.18828	0.463488
$394$	−8.92963	−0.449868
$395$	10.1677	0.511595
$396$	1.00000	0.0502519
$397$	−5.66451	−0.284294	−0.142147	−	0.989846i	$-0.545401\pi$
$397$	−5.66451	−0.284294	−0.142147	+	0.989846i	$0.545401\pi$
$398$	4.33549	0.217318
$399$	−20.3355	−1.01805
$400$	1.00000	0.0500000
$401$	10.4854	0.523614	0.261807	−	0.965120i	$-0.415682\pi$
$401$	10.4854	0.523614	0.261807	+	0.965120i	$0.415682\pi$
$402$	−12.3355	−0.615238
$403$	4.51730	0.225023
$404$	6.00000	0.298511
$405$	1.00000	0.0496904
$406$	−16.0590	−0.796993
$407$	6.00000	0.297409
$408$	1.00000	0.0495074
$409$	−6.29973	−0.311501	−0.155751	−	0.987796i	$-0.549780\pi$
$409$	−6.29973	−0.311501	−0.155751	+	0.987796i	$0.549780\pi$
$410$	8.59414	0.424434
$411$	−10.0590	−0.496172
$412$	17.4648	0.860430
$413$	−1.40586	−0.0691778
$414$	−7.29707	−0.358631
$415$	−9.18828	−0.451035
$416$	1.57360	0.0771523
$417$	19.2062	0.940530
$418$	6.16774	0.301674
$419$	15.1704	0.741123	0.370561	−	0.928808i	$-0.379165\pi$
$419$	15.1704	0.741123	0.370561	+	0.928808i	$0.379165\pi$
$420$	3.29707	0.160881
$421$	16.9296	0.825100	0.412550	−	0.910935i	$-0.364638\pi$
$421$	16.9296	0.825100	0.412550	+	0.910935i	$0.364638\pi$
$422$	11.2062	0.545508
$423$	−4.00000	−0.194487
$424$	−2.42640	−0.117836
$425$	−1.00000	−0.0485071
$426$	−7.57360	−0.366942
$427$	6.59414	0.319113
$428$	−5.12933	−0.247935
$429$	−1.57360	−0.0759743
$430$	−3.29707	−0.158999
$431$	8.91175	0.429264	0.214632	−	0.976695i	$-0.431145\pi$
$431$	8.91175	0.429264	0.214632	+	0.976695i	$0.431145\pi$
$432$	1.00000	0.0481125
$433$	−38.9707	−1.87281	−0.936406	−	0.350918i	$-0.885870\pi$
$433$	−38.9707	−1.87281	−0.936406	+	0.350918i	$0.885870\pi$
$434$	9.46482	0.454326
$435$	4.87067	0.233531
$436$	16.5941	0.794715
$437$	−45.0065	−2.15295
$438$	−4.16774	−0.199143
$439$	−20.2446	−0.966221	−0.483111	−	0.875559i	$-0.660493\pi$
$439$	−20.2446	−0.966221	−0.483111	+	0.875559i	$0.660493\pi$
$440$	−1.00000	−0.0476731
$441$	3.87067	0.184318
$442$	−1.57360	−0.0748487
$443$	8.36744	0.397549	0.198775	−	0.980045i	$-0.436304\pi$
$443$	8.36744	0.397549	0.198775	+	0.980045i	$0.436304\pi$
$444$	6.00000	0.284747
$445$	8.59414	0.407401
$446$	−17.4648	−0.826983
$447$	−8.59414	−0.406489
$448$	3.29707	0.155772
$449$	10.1856	0.480689	0.240345	−	0.970688i	$-0.422740\pi$
$449$	10.1856	0.480689	0.240345	+	0.970688i	$0.422740\pi$
$450$	−1.00000	−0.0471405
$451$	−8.59414	−0.404682
$452$	−9.02054	−0.424290
$453$	4.00000	0.187936
$454$	5.12933	0.240731
$455$	−5.18828	−0.243230
$456$	6.16774	0.288831
$457$	−10.0000	−0.467780	−0.233890	−	0.972263i	$-0.575146\pi$
$457$	−10.0000	−0.467780	−0.233890	+	0.972263i	$0.575146\pi$
$458$	−10.8886	−0.508789
$459$	−1.00000	−0.0466760
$460$	7.29707	0.340228
$461$	−28.6299	−1.33343	−0.666714	−	0.745314i	$-0.732300\pi$
$461$	−28.6299	−1.33343	−0.666714	+	0.745314i	$0.732300\pi$
$462$	−3.29707	−0.153394
$463$	8.00000	0.371792	0.185896	−	0.982569i	$-0.440481\pi$
$463$	8.00000	0.371792	0.185896	+	0.982569i	$0.440481\pi$
$464$	4.87067	0.226115
$465$	−2.87067	−0.133124
$466$	−0.870674	−0.0403332
$467$	−21.0616	−0.974615	−0.487308	−	0.873230i	$-0.662021\pi$
$467$	−21.0616	−0.974615	−0.487308	+	0.873230i	$0.662021\pi$
$468$	−1.57360	−0.0727399
$469$	40.6710	1.87801
$470$	4.00000	0.184506
$471$	10.0000	0.460776
$472$	0.426396	0.0196265
$473$	3.29707	0.151599
$474$	−10.1677	−0.467020
$475$	−6.16774	−0.282996
$476$	−3.29707	−0.151121
$477$	2.42640	0.111097
$478$	−10.9296	−0.499910
$479$	−27.5417	−1.25841	−0.629205	−	0.777239i	$-0.716619\pi$
$479$	−27.5417	−1.25841	−0.629205	+	0.777239i	$0.716619\pi$
$480$	−1.00000	−0.0456435
$481$	−9.44162	−0.430501
$482$	14.4854	0.659790
$483$	24.0590	1.09472
$484$	1.00000	0.0454545
$485$	11.4648	0.520590
$486$	−1.00000	−0.0453609
$487$	32.9707	1.49405	0.747023	−	0.664799i	$-0.231483\pi$
$487$	32.9707	1.49405	0.747023	+	0.664799i	$0.231483\pi$
$488$	−2.00000	−0.0905357
$489$	0.276533	0.0125053
$490$	−3.87067	−0.174859
$491$	0	0		−	1.00000i	$-0.5\pi$
$491$	0	0			1.00000i	$0.5\pi$
$492$	−8.59414	−0.387454
$493$	−4.87067	−0.219364
$494$	−9.70559	−0.436675
$495$	1.00000	0.0449467
$496$	−2.87067	−0.128897
$497$	24.9707	1.12009
$498$	9.18828	0.411737
$499$	−1.52377	−0.0682134	−0.0341067	−	0.999418i	$-0.510859\pi$
$499$	−1.52377	−0.0682134	−0.0341067	+	0.999418i	$0.510859\pi$
$500$	1.00000	0.0447214
$501$	−12.8886	−0.575818
$502$	26.5032	1.18290
$503$	−42.3766	−1.88948	−0.944739	−	0.327824i	$-0.893685\pi$
$503$	−42.3766	−1.88948	−0.944739	+	0.327824i	$0.893685\pi$
$504$	−3.29707	−0.146863
$505$	6.00000	0.266996
$506$	−7.29707	−0.324394
$507$	−10.5238	−0.467377
$508$	−7.44693	−0.330404
$509$	38.2088	1.69358	0.846788	−	0.531930i	$-0.178533\pi$
$509$	38.2088	1.69358	0.846788	+	0.531930i	$0.178533\pi$
$510$	1.00000	0.0442807
$511$	13.7413	0.607881
$512$	−1.00000	−0.0441942
$513$	−6.16774	−0.272313
$514$	−0.870674	−0.0384038
$515$	17.4648	0.769592
$516$	3.29707	0.145145
$517$	−4.00000	−0.175920
$518$	−19.7824	−0.869190
$519$	−14.3355	−0.629258
$520$	1.57360	0.0690071
$521$	22.2088	0.972986	0.486493	−	0.873684i	$-0.338276\pi$
$521$	22.2088	0.972986	0.486493	+	0.873684i	$0.338276\pi$
$522$	−4.87067	−0.213184
$523$	13.9270	0.608984	0.304492	−	0.952515i	$-0.401513\pi$
$523$	13.9270	0.608984	0.304492	+	0.952515i	$0.401513\pi$
$524$	9.18828	0.401392
$525$	3.29707	0.143896
$526$	−17.4648	−0.761502
$527$	2.87067	0.125049
$528$	1.00000	0.0435194
$529$	30.2472	1.31510
$530$	−2.42640	−0.105396
$531$	−0.426396	−0.0185040
$532$	−20.3355	−0.881655
$533$	13.5238	0.585780
$534$	−8.59414	−0.371905
$535$	−5.12933	−0.221760
$536$	−12.3355	−0.532812
$537$	−25.9502	−1.11983
$538$	−11.1883	−0.482361
$539$	3.87067	0.166722
$540$	1.00000	0.0430331
$541$	−5.44693	−0.234182	−0.117091	−	0.993121i	$-0.537357\pi$
$541$	−5.44693	−0.234182	−0.117091	+	0.993121i	$0.537357\pi$
$542$	−9.12933	−0.392138
$543$	4.87067	0.209021
$544$	1.00000	0.0428746
$545$	16.5941	0.710815
$546$	5.18828	0.222038
$547$	30.0768	1.28599	0.642996	−	0.765869i	$-0.277691\pi$
$547$	30.0768	1.28599	0.642996	+	0.765869i	$0.277691\pi$
$548$	−10.0590	−0.429697
$549$	2.00000	0.0853579
$550$	−1.00000	−0.0426401
$551$	−30.0411	−1.27979
$552$	−7.29707	−0.310584
$553$	33.5238	1.42558
$554$	−14.3355	−0.609057
$555$	6.00000	0.254686
$556$	19.2062	0.814523
$557$	17.2062	0.729049	0.364524	−	0.931194i	$-0.381232\pi$
$557$	17.2062	0.729049	0.364524	+	0.931194i	$0.381232\pi$
$558$	2.87067	0.121525
$559$	−5.18828	−0.219441
$560$	3.29707	0.139327
$561$	−1.00000	−0.0422200
$562$	−19.8003	−0.835225
$563$	−2.89387	−0.121962	−0.0609810	−	0.998139i	$-0.519423\pi$
$563$	−2.89387	−0.121962	−0.0609810	+	0.998139i	$0.519423\pi$
$564$	−4.00000	−0.168430
$565$	−9.02054	−0.379497
$566$	16.6352	0.699230
$567$	3.29707	0.138464
$568$	−7.57360	−0.317781
$569$	6.00000	0.251533	0.125767	−	0.992060i	$-0.459861\pi$
$569$	6.00000	0.251533	0.125767	+	0.992060i	$0.459861\pi$
$570$	6.16774	0.258338
$571$	−28.6710	−1.19984	−0.599922	−	0.800059i	$-0.704802\pi$
$571$	−28.6710	−1.19984	−0.599922	+	0.800059i	$0.704802\pi$
$572$	−1.57360	−0.0657957
$573$	−22.6531	−0.946347
$574$	28.3355	1.18270
$575$	7.29707	0.304309
$576$	1.00000	0.0416667
$577$	−10.3355	−0.430272	−0.215136	−	0.976584i	$-0.569019\pi$
$577$	−10.3355	−0.430272	−0.215136	+	0.976584i	$0.569019\pi$
$578$	−1.00000	−0.0415945
$579$	−0.167745	−0.00697123
$580$	4.87067	0.202244
$581$	−30.2944	−1.25682
$582$	−11.4648	−0.475232
$583$	2.42640	0.100491
$584$	−4.16774	−0.172463
$585$	−1.57360	−0.0650605
$586$	8.01788	0.331216
$587$	11.2971	0.466280	0.233140	−	0.972443i	$-0.425100\pi$
$587$	11.2971	0.466280	0.233140	+	0.972443i	$0.425100\pi$
$588$	3.87067	0.159624
$589$	17.7056	0.729546
$590$	0.426396	0.0175545
$591$	8.92963	0.367316
$592$	6.00000	0.246598
$593$	4.04107	0.165947	0.0829735	−	0.996552i	$-0.473558\pi$
$593$	4.04107	0.165947	0.0829735	+	0.996552i	$0.473558\pi$
$594$	−1.00000	−0.0410305
$595$	−3.29707	−0.135167
$596$	−8.59414	−0.352030
$597$	−4.33549	−0.177440
$598$	11.4827	0.469562
$599$	21.9821	0.898165	0.449083	−	0.893490i	$-0.351751\pi$
$599$	21.9821	0.898165	0.449083	+	0.893490i	$0.351751\pi$
$600$	−1.00000	−0.0408248
$601$	2.12667	0.0867487	0.0433743	−	0.999059i	$-0.486189\pi$
$601$	2.12667	0.0867487	0.0433743	+	0.999059i	$0.486189\pi$
$602$	−10.8707	−0.443056
$603$	12.3355	0.502340
$604$	4.00000	0.162758
$605$	1.00000	0.0406558
$606$	−6.00000	−0.243733
$607$	−14.1677	−0.575051	−0.287526	−	0.957773i	$-0.592833\pi$
$607$	−14.1677	−0.575051	−0.287526	+	0.957773i	$0.592833\pi$
$608$	6.16774	0.250135
$609$	16.0590	0.650742
$610$	−2.00000	−0.0809776
$611$	6.29441	0.254645
$612$	−1.00000	−0.0404226
$613$	−2.12667	−0.0858954	−0.0429477	−	0.999077i	$-0.513675\pi$
$613$	−2.12667	−0.0858954	−0.0429477	+	0.999077i	$0.513675\pi$
$614$	7.02054	0.283326
$615$	−8.59414	−0.346549
$616$	−3.29707	−0.132843
$617$	−37.3560	−1.50390	−0.751949	−	0.659222i	$-0.770886\pi$
$617$	−37.3560	−1.50390	−0.751949	+	0.659222i	$0.770886\pi$
$618$	−17.4648	−0.702538
$619$	22.5941	0.908135	0.454068	−	0.890967i	$-0.349972\pi$
$619$	22.5941	0.908135	0.454068	+	0.890967i	$0.349972\pi$
$620$	−2.87067	−0.115289
$621$	7.29707	0.292821
$622$	−23.6915	−0.949943
$623$	28.3355	1.13524
$624$	−1.57360	−0.0629946
$625$	1.00000	0.0400000
$626$	26.9475	1.07704
$627$	−6.16774	−0.246316
$628$	10.0000	0.399043
$629$	−6.00000	−0.239236
$630$	−3.29707	−0.131358
$631$	8.55307	0.340492	0.170246	−	0.985402i	$-0.445544\pi$
$631$	8.55307	0.340492	0.170246	+	0.985402i	$0.445544\pi$
$632$	−10.1677	−0.404451
$633$	−11.2062	−0.445405
$634$	10.0590	0.399492
$635$	−7.44693	−0.295523
$636$	2.42640	0.0962129
$637$	−6.09091	−0.241331
$638$	−4.87067	−0.192832
$639$	7.57360	0.299607
$640$	−1.00000	−0.0395285
$641$	−32.0091	−1.26428	−0.632142	−	0.774852i	$-0.717824\pi$
$641$	−32.0091	−1.26428	−0.632142	+	0.774852i	$0.717824\pi$
$642$	5.12933	0.202438
$643$	34.1000	1.34477	0.672387	−	0.740200i	$-0.265269\pi$
$643$	34.1000	1.34477	0.672387	+	0.740200i	$0.265269\pi$
$644$	24.0590	0.948056
$645$	3.29707	0.129822
$646$	−6.16774	−0.242667
$647$	−30.9296	−1.21597	−0.607985	−	0.793949i	$-0.708022\pi$
$647$	−30.9296	−1.21597	−0.607985	+	0.793949i	$0.708022\pi$
$648$	−1.00000	−0.0392837
$649$	−0.426396	−0.0167375
$650$	1.57360	0.0617218
$651$	−9.46482	−0.370955
$652$	0.276533	0.0108299
$653$	−32.1000	−1.25617	−0.628086	−	0.778144i	$-0.716161\pi$
$653$	−32.1000	−1.25617	−0.628086	+	0.778144i	$0.716161\pi$
$654$	−16.5941	−0.648882
$655$	9.18828	0.359016
$656$	−8.59414	−0.335545
$657$	4.16774	0.162599
$658$	13.1883	0.514133
$659$	28.9475	1.12763	0.563817	−	0.825899i	$-0.309332\pi$
$659$	28.9475	1.12763	0.563817	+	0.825899i	$0.309332\pi$
$660$	1.00000	0.0389249
$661$	−5.11144	−0.198812	−0.0994061	−	0.995047i	$-0.531694\pi$
$661$	−5.11144	−0.198812	−0.0994061	+	0.995047i	$0.531694\pi$
$662$	32.9475	1.28054
$663$	1.57360	0.0611137
$664$	9.18828	0.356575
$665$	−20.3355	−0.788576
$666$	−6.00000	−0.232495
$667$	35.5417	1.37618
$668$	−12.8886	−0.498673
$669$	17.4648	0.675229
$670$	−12.3355	−0.476562
$671$	2.00000	0.0772091
$672$	−3.29707	−0.127187
$673$	−19.0974	−0.736150	−0.368075	−	0.929796i	$-0.619983\pi$
$673$	−19.0974	−0.736150	−0.368075	+	0.929796i	$0.619983\pi$
$674$	28.5032	1.09790
$675$	1.00000	0.0384900
$676$	−10.5238	−0.404760
$677$	−19.7056	−0.757347	−0.378674	−	0.925530i	$-0.623620\pi$
$677$	−19.7056	−0.757347	−0.378674	+	0.925530i	$0.623620\pi$
$678$	9.02054	0.346432
$679$	37.8003	1.45064
$680$	1.00000	0.0383482
$681$	−5.12933	−0.196556
$682$	2.87067	0.109924
$683$	23.4827	0.898540	0.449270	−	0.893396i	$-0.351684\pi$
$683$	23.4827	0.898540	0.449270	+	0.893396i	$0.351684\pi$
$684$	−6.16774	−0.235830
$685$	−10.0590	−0.384333
$686$	10.3176	0.393928
$687$	10.8886	0.415424
$688$	3.29707	0.125700
$689$	−3.81819	−0.145461
$690$	−7.29707	−0.277795
$691$	3.66451	0.139405	0.0697023	−	0.997568i	$-0.477795\pi$
$691$	3.66451	0.139405	0.0697023	+	0.997568i	$0.477795\pi$
$692$	−14.3355	−0.544954
$693$	3.29707	0.125245
$694$	33.5238	1.27254
$695$	19.2062	0.728531
$696$	−4.87067	−0.184622
$697$	8.59414	0.325526
$698$	17.0205	0.644237
$699$	0.870674	0.0329319
$700$	3.29707	0.124618
$701$	23.5238	0.888481	0.444240	−	0.895908i	$-0.353474\pi$
$701$	23.5238	0.888481	0.444240	+	0.895908i	$0.353474\pi$
$702$	1.57360	0.0593918
$703$	−37.0065	−1.39573
$704$	1.00000	0.0376889
$705$	−4.00000	−0.150649
$706$	−30.6120	−1.15210
$707$	19.7824	0.743995
$708$	−0.426396	−0.0160250
$709$	42.0000	1.57734	0.788672	−	0.614815i	$-0.210769\pi$
$709$	42.0000	1.57734	0.788672	+	0.614815i	$0.210769\pi$
$710$	−7.57360	−0.284232
$711$	10.1677	0.381320
$712$	−8.59414	−0.322079
$713$	−20.9475	−0.784490
$714$	3.29707	0.123390
$715$	−1.57360	−0.0588494
$716$	−25.9502	−0.969803
$717$	10.9296	0.408175
$718$	−18.9296	−0.706448
$719$	−7.57360	−0.282448	−0.141224	−	0.989978i	$-0.545104\pi$
$719$	−7.57360	−0.282448	−0.141224	+	0.989978i	$0.545104\pi$
$720$	1.00000	0.0372678
$721$	57.5827	2.14449
$722$	−19.0411	−0.708635
$723$	−14.4854	−0.538716
$724$	4.87067	0.181017
$725$	4.87067	0.180892
$726$	−1.00000	−0.0371135
$727$	−21.5006	−0.797412	−0.398706	−	0.917079i	$-0.630541\pi$
$727$	−21.5006	−0.797412	−0.398706	+	0.917079i	$0.630541\pi$
$728$	5.18828	0.192291
$729$	1.00000	0.0370370
$730$	−4.16774	−0.154255
$731$	−3.29707	−0.121947
$732$	2.00000	0.0739221
$733$	−10.2446	−0.378392	−0.189196	−	0.981939i	$-0.560588\pi$
$733$	−10.2446	−0.378392	−0.189196	+	0.981939i	$0.560588\pi$
$734$	12.8886	0.475725
$735$	3.87067	0.142772
$736$	−7.29707	−0.268974
$737$	12.3355	0.454384
$738$	8.59414	0.316355
$739$	15.5736	0.572884	0.286442	−	0.958098i	$-0.407527\pi$
$739$	15.5736	0.572884	0.286442	+	0.958098i	$0.407527\pi$
$740$	6.00000	0.220564
$741$	9.70559	0.356544
$742$	−8.00000	−0.293689
$743$	−3.48270	−0.127768	−0.0638839	−	0.997957i	$-0.520349\pi$
$743$	−3.48270	−0.127768	−0.0638839	+	0.997957i	$0.520349\pi$
$744$	2.87067	0.105244
$745$	−8.59414	−0.314865
$746$	−36.8387	−1.34876
$747$	−9.18828	−0.336182
$748$	−1.00000	−0.0365636
$749$	−16.9117	−0.617942
$750$	−1.00000	−0.0365148
$751$	−25.4648	−0.929224	−0.464612	−	0.885514i	$-0.653806\pi$
$751$	−25.4648	−0.929224	−0.464612	+	0.885514i	$0.653806\pi$
$752$	−4.00000	−0.145865
$753$	−26.5032	−0.965832
$754$	7.66451	0.279125
$755$	4.00000	0.145575
$756$	3.29707	0.119913
$757$	−14.6120	−0.531083	−0.265541	−	0.964099i	$-0.585551\pi$
$757$	−14.6120	−0.531083	−0.265541	+	0.964099i	$0.585551\pi$
$758$	−8.85279	−0.321548
$759$	7.29707	0.264867
$760$	6.16774	0.223728
$761$	−36.9886	−1.34084	−0.670418	−	0.741984i	$-0.733885\pi$
$761$	−36.9886	−1.34084	−0.670418	+	0.741984i	$0.733885\pi$
$762$	7.44693	0.269774
$763$	54.7121	1.98071
$764$	−22.6531	−0.819560
$765$	−1.00000	−0.0361551
$766$	−22.6299	−0.817652
$767$	0.670979	0.0242276
$768$	1.00000	0.0360844
$769$	39.1883	1.41317	0.706583	−	0.707630i	$-0.250236\pi$
$769$	39.1883	1.41317	0.706583	+	0.707630i	$0.250236\pi$
$770$	−3.29707	−0.118818
$771$	0.870674	0.0313566
$772$	−0.167745	−0.00603726
$773$	3.95017	0.142078	0.0710388	−	0.997474i	$-0.477369\pi$
$773$	3.95017	0.142078	0.0710388	+	0.997474i	$0.477369\pi$
$774$	−3.29707	−0.118511
$775$	−2.87067	−0.103118
$776$	−11.4648	−0.411563
$777$	19.7824	0.709690
$778$	−14.2088	−0.509411
$779$	53.0065	1.89915
$780$	−1.57360	−0.0563440
$781$	7.57360	0.271005
$782$	7.29707	0.260943
$783$	4.87067	0.174064
$784$	3.87067	0.138238
$785$	10.0000	0.356915
$786$	−9.18828	−0.327735
$787$	46.1948	1.64667	0.823333	−	0.567559i	$-0.192112\pi$
$787$	46.1948	1.64667	0.823333	+	0.567559i	$0.192112\pi$
$788$	8.92963	0.318105
$789$	17.4648	0.621764
$790$	−10.1677	−0.361752
$791$	−29.7413	−1.05748
$792$	−1.00000	−0.0355335
$793$	−3.14721	−0.111761
$794$	5.66451	0.201026
$795$	2.42640	0.0860554
$796$	−4.33549	−0.153667
$797$	−46.2446	−1.63807	−0.819034	−	0.573746i	$-0.805490\pi$
$797$	−46.2446	−1.63807	−0.819034	+	0.573746i	$0.805490\pi$
$798$	20.3355	0.719869
$799$	4.00000	0.141510
$800$	−1.00000	−0.0353553
$801$	8.59414	0.303659
$802$	−10.4854	−0.370251
$803$	4.16774	0.147077
$804$	12.3355	0.435039
$805$	24.0590	0.847967
$806$	−4.51730	−0.159115
$807$	11.1883	0.393846
$808$	−6.00000	−0.211079
$809$	−7.18828	−0.252727	−0.126363	−	0.991984i	$-0.540330\pi$
$809$	−7.18828	−0.252727	−0.126363	+	0.991984i	$0.540330\pi$
$810$	−1.00000	−0.0351364
$811$	1.44162	0.0506222	0.0253111	−	0.999680i	$-0.491942\pi$
$811$	1.44162	0.0506222	0.0253111	+	0.999680i	$0.491942\pi$
$812$	16.0590	0.563559
$813$	9.12933	0.320179
$814$	−6.00000	−0.210300
$815$	0.276533	0.00968653
$816$	−1.00000	−0.0350070
$817$	−20.3355	−0.711449
$818$	6.29973	0.220265
$819$	−5.18828	−0.181293
$820$	−8.59414	−0.300120
$821$	−24.6173	−0.859151	−0.429575	−	0.903031i	$-0.641337\pi$
$821$	−24.6173	−0.859151	−0.429575	+	0.903031i	$0.641337\pi$
$822$	10.0590	0.350846
$823$	40.1179	1.39842	0.699211	−	0.714915i	$-0.253535\pi$
$823$	40.1179	1.39842	0.699211	+	0.714915i	$0.253535\pi$
$824$	−17.4648	−0.608416
$825$	1.00000	0.0348155
$826$	1.40586	0.0489161
$827$	−19.5417	−0.679530	−0.339765	−	0.940510i	$-0.610348\pi$
$827$	−19.5417	−0.679530	−0.339765	+	0.940510i	$0.610348\pi$
$828$	7.29707	0.253591
$829$	47.2704	1.64177	0.820885	−	0.571094i	$-0.193481\pi$
$829$	47.2704	1.64177	0.820885	+	0.571094i	$0.193481\pi$
$830$	9.18828	0.318930
$831$	14.3355	0.497293
$832$	−1.57360	−0.0545549
$833$	−3.87067	−0.134111
$834$	−19.2062	−0.665055
$835$	−12.8886	−0.446027
$836$	−6.16774	−0.213316
$837$	−2.87067	−0.0992250
$838$	−15.1704	−0.524053
$839$	17.9502	0.619709	0.309854	−	0.950784i	$-0.399720\pi$
$839$	17.9502	0.619709	0.309854	+	0.950784i	$0.399720\pi$
$840$	−3.29707	−0.113760
$841$	−5.27653	−0.181949
$842$	−16.9296	−0.583434
$843$	19.8003	0.681959
$844$	−11.2062	−0.385732
$845$	−10.5238	−0.362029
$846$	4.00000	0.137523
$847$	3.29707	0.113289
$848$	2.42640	0.0833228
$849$	−16.6352	−0.570919
$850$	1.00000	0.0342997
$851$	43.7824	1.50084
$852$	7.57360	0.259467
$853$	−35.8003	−1.22578	−0.612890	−	0.790169i	$-0.709993\pi$
$853$	−35.8003	−1.22578	−0.612890	+	0.790169i	$0.709993\pi$
$854$	−6.59414	−0.225647
$855$	−6.16774	−0.210932
$856$	5.12933	0.175317
$857$	−48.7710	−1.66599	−0.832993	−	0.553284i	$-0.813375\pi$
$857$	−48.7710	−1.66599	−0.832993	+	0.553284i	$0.813375\pi$
$858$	1.57360	0.0537219
$859$	10.6531	0.363479	0.181739	−	0.983347i	$-0.441827\pi$
$859$	10.6531	0.363479	0.181739	+	0.983347i	$0.441827\pi$
$860$	3.29707	0.112429
$861$	−28.3355	−0.965671
$862$	−8.91175	−0.303535
$863$	−18.7121	−0.636966	−0.318483	−	0.947929i	$-0.603173\pi$
$863$	−18.7121	−0.636966	−0.318483	+	0.947929i	$0.603173\pi$
$864$	−1.00000	−0.0340207
$865$	−14.3355	−0.487421
$866$	38.9707	1.32428
$867$	1.00000	0.0339618
$868$	−9.46482	−0.321257
$869$	10.1677	0.344917
$870$	−4.87067	−0.165131
$871$	−19.4112	−0.657722
$872$	−16.5941	−0.561949
$873$	11.4648	0.388025
$874$	45.0065	1.52237
$875$	3.29707	0.111461
$876$	4.16774	0.140815
$877$	−0.752761	−0.0254189	−0.0127095	−	0.999919i	$-0.504046\pi$
$877$	−0.752761	−0.0254189	−0.0127095	+	0.999919i	$0.504046\pi$
$878$	20.2446	0.683222
$879$	−8.01788	−0.270436
$880$	1.00000	0.0337100
$881$	−52.2267	−1.75956	−0.879781	−	0.475379i	$-0.842311\pi$
$881$	−52.2267	−1.75956	−0.879781	+	0.475379i	$0.842311\pi$
$882$	−3.87067	−0.130332
$883$	−53.8593	−1.81251	−0.906254	−	0.422733i	$-0.861071\pi$
$883$	−53.8593	−1.81251	−0.906254	+	0.422733i	$0.861071\pi$
$884$	1.57360	0.0529260
$885$	−0.426396	−0.0143332
$886$	−8.36744	−0.281110
$887$	−9.95893	−0.334388	−0.167194	−	0.985924i	$-0.553471\pi$
$887$	−9.95893	−0.334388	−0.167194	+	0.985924i	$0.553471\pi$
$888$	−6.00000	−0.201347
$889$	−24.5531	−0.823483
$890$	−8.59414	−0.288076
$891$	1.00000	0.0335013
$892$	17.4648	0.584765
$893$	24.6710	0.825583
$894$	8.59414	0.287431
$895$	−25.9502	−0.867418
$896$	−3.29707	−0.110147
$897$	−11.4827	−0.383396
$898$	−10.1856	−0.339899
$899$	−13.9821	−0.466330
$900$	1.00000	0.0333333
$901$	−2.42640	−0.0808350
$902$	8.59414	0.286154
$903$	10.8707	0.361753
$904$	9.02054	0.300019
$905$	4.87067	0.161907
$906$	−4.00000	−0.132891
$907$	−43.3241	−1.43855	−0.719276	−	0.694724i	$-0.755526\pi$
$907$	−43.3241	−1.43855	−0.719276	+	0.694724i	$0.755526\pi$
$908$	−5.12933	−0.170223
$909$	6.00000	0.199007
$910$	5.18828	0.171990
$911$	47.0205	1.55786	0.778930	−	0.627111i	$-0.215763\pi$
$911$	47.0205	1.55786	0.778930	+	0.627111i	$0.215763\pi$
$912$	−6.16774	−0.204234
$913$	−9.18828	−0.304088
$914$	10.0000	0.330771
$915$	2.00000	0.0661180
$916$	10.8886	0.359768
$917$	30.2944	1.00041
$918$	1.00000	0.0330049
$919$	0.829599	0.0273660	0.0136830	−	0.999906i	$-0.495644\pi$
$919$	0.829599	0.0273660	0.0136830	+	0.999906i	$0.495644\pi$
$920$	−7.29707	−0.240577
$921$	−7.02054	−0.231335
$922$	28.6299	0.942876
$923$	−11.9179	−0.392281
$924$	3.29707	0.108466
$925$	6.00000	0.197279
$926$	−8.00000	−0.262896
$927$	17.4648	0.573620
$928$	−4.87067	−0.159888
$929$	35.8912	1.17755	0.588776	−	0.808296i	$-0.299610\pi$
$929$	35.8912	1.17755	0.588776	+	0.808296i	$0.299610\pi$
$930$	2.87067	0.0941331
$931$	−23.8733	−0.782417
$932$	0.870674	0.0285199
$933$	23.6915	0.775625
$934$	21.0616	0.689157
$935$	−1.00000	−0.0327035
$936$	1.57360	0.0514348
$937$	−18.0000	−0.588034	−0.294017	−	0.955800i	$-0.594992\pi$
$937$	−18.0000	−0.588034	−0.294017	+	0.955800i	$0.594992\pi$
$938$	−40.6710	−1.32795
$939$	−26.9475	−0.879399
$940$	−4.00000	−0.130466
$941$	18.0000	0.586783	0.293392	−	0.955992i	$-0.405216\pi$
$941$	18.0000	0.586783	0.293392	+	0.955992i	$0.405216\pi$
$942$	−10.0000	−0.325818
$943$	−62.7121	−2.04219
$944$	−0.426396	−0.0138780
$945$	3.29707	0.107254
$946$	−3.29707	−0.107197
$947$	28.3713	0.921942	0.460971	−	0.887415i	$-0.347501\pi$
$947$	28.3713	0.921942	0.460971	+	0.887415i	$0.347501\pi$
$948$	10.1677	0.330233
$949$	−6.55838	−0.212894
$950$	6.16774	0.200108
$951$	−10.0590	−0.326184
$952$	3.29707	0.106859
$953$	−2.85279	−0.0924110	−0.0462055	−	0.998932i	$-0.514713\pi$
$953$	−2.85279	−0.0924110	−0.0462055	+	0.998932i	$0.514713\pi$
$954$	−2.42640	−0.0785575
$955$	−22.6531	−0.733037
$956$	10.9296	0.353490
$957$	4.87067	0.157447
$958$	27.5417	0.889830
$959$	−33.1651	−1.07096
$960$	1.00000	0.0322749
$961$	−22.7592	−0.734169
$962$	9.44162	0.304410
$963$	−5.12933	−0.165290
$964$	−14.4854	−0.466542
$965$	−0.167745	−0.00539989
$966$	−24.0590	−0.774084
$967$	17.2240	0.553888	0.276944	−	0.960886i	$-0.410678\pi$
$967$	17.2240	0.553888	0.276944	+	0.960886i	$0.410678\pi$
$968$	−1.00000	−0.0321412
$969$	6.16774	0.198137
$970$	−11.4648	−0.368113
$971$	9.39710	0.301567	0.150784	−	0.988567i	$-0.451820\pi$
$971$	9.39710	0.301567	0.150784	+	0.988567i	$0.451820\pi$
$972$	1.00000	0.0320750
$973$	63.3241	2.03008
$974$	−32.9707	−1.05645
$975$	−1.57360	−0.0503956
$976$	2.00000	0.0640184
$977$	−37.2294	−1.19107	−0.595536	−	0.803328i	$-0.703060\pi$
$977$	−37.2294	−1.19107	−0.595536	+	0.803328i	$0.703060\pi$
$978$	−0.276533	−0.00884255
$979$	8.59414	0.274670
$980$	3.87067	0.123644
$981$	16.5941	0.529810
$982$	0	0
$983$	−3.07949	−0.0982206	−0.0491103	−	0.998793i	$-0.515639\pi$
$983$	−3.07949	−0.0982206	−0.0491103	+	0.998793i	$0.515639\pi$
$984$	8.59414	0.273971
$985$	8.92963	0.284522
$986$	4.87067	0.155114
$987$	−13.1883	−0.419788
$988$	9.70559	0.308776
$989$	24.0590	0.765030
$990$	−1.00000	−0.0317821
$991$	−44.2765	−1.40649	−0.703245	−	0.710947i	$-0.748266\pi$
$991$	−44.2765	−1.40649	−0.703245	+	0.710947i	$0.748266\pi$
$992$	2.87067	0.0911440
$993$	−32.9475	−1.04556
$994$	−24.9707	−0.792023
$995$	−4.33549	−0.137444
$996$	−9.18828	−0.291142
$997$	−2.82960	−0.0896143	−0.0448072	−	0.998996i	$-0.514267\pi$
$997$	−2.82960	−0.0896143	−0.0448072	+	0.998996i	$0.514267\pi$
$998$	1.52377	0.0482341
$999$	6.00000	0.189832

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	5610.2.a.ca.1.3	✓	3

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
5610.2.a.ca.1.3	✓	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:	\( N \)	\(=\)	\( 5610 = 2 \cdot 3 \cdot 5 \cdot 11 \cdot 17 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	5610.a (trivial)

\(f(q)\)	\(=\)	\(q-1.00000 q^{2} +1.00000 q^{3} +1.00000 q^{4} +1.00000 q^{5} -1.00000 q^{6} +3.29707 q^{7} -1.00000 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q-1.00000 q^{2} +1.00000 q^{3} +1.00000 q^{4} +1.00000 q^{5} -1.00000 q^{6} +3.29707 q^{7} -1.00000 q^{8} +1.00000 q^{9} -1.00000 q^{10} +1.00000 q^{11} +1.00000 q^{12} -1.57360 q^{13} -3.29707 q^{14} +1.00000 q^{15} +1.00000 q^{16} -1.00000 q^{17} -1.00000 q^{18} -6.16774 q^{19} +1.00000 q^{20} +3.29707 q^{21} -1.00000 q^{22} +7.29707 q^{23} -1.00000 q^{24} +1.00000 q^{25} +1.57360 q^{26} +1.00000 q^{27} +3.29707 q^{28} +4.87067 q^{29} -1.00000 q^{30} -2.87067 q^{31} -1.00000 q^{32} +1.00000 q^{33} +1.00000 q^{34} +3.29707 q^{35} +1.00000 q^{36} +6.00000 q^{37} +6.16774 q^{38} -1.57360 q^{39} -1.00000 q^{40} -8.59414 q^{41} -3.29707 q^{42} +3.29707 q^{43} +1.00000 q^{44} +1.00000 q^{45} -7.29707 q^{46} -4.00000 q^{47} +1.00000 q^{48} +3.87067 q^{49} -1.00000 q^{50} -1.00000 q^{51} -1.57360 q^{52} +2.42640 q^{53} -1.00000 q^{54} +1.00000 q^{55} -3.29707 q^{56} -6.16774 q^{57} -4.87067 q^{58} -0.426396 q^{59} +1.00000 q^{60} +2.00000 q^{61} +2.87067 q^{62} +3.29707 q^{63} +1.00000 q^{64} -1.57360 q^{65} -1.00000 q^{66} +12.3355 q^{67} -1.00000 q^{68} +7.29707 q^{69} -3.29707 q^{70} +7.57360 q^{71} -1.00000 q^{72} +4.16774 q^{73} -6.00000 q^{74} +1.00000 q^{75} -6.16774 q^{76} +3.29707 q^{77} +1.57360 q^{78} +10.1677 q^{79} +1.00000 q^{80} +1.00000 q^{81} +8.59414 q^{82} -9.18828 q^{83} +3.29707 q^{84} -1.00000 q^{85} -3.29707 q^{86} +4.87067 q^{87} -1.00000 q^{88} +8.59414 q^{89} -1.00000 q^{90} -5.18828 q^{91} +7.29707 q^{92} -2.87067 q^{93} +4.00000 q^{94} -6.16774 q^{95} -1.00000 q^{96} +11.4648 q^{97} -3.87067 q^{98} +1.00000 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 3 q - 3 q^{2} + 3 q^{3} + 3 q^{4} + 3 q^{5} - 3 q^{6} + q^{7} - 3 q^{8} + 3 q^{9}+O(q^{10}) \) 3 * q - 3 * q^2 + 3 * q^3 + 3 * q^4 + 3 * q^5 - 3 * q^6 + q^7 - 3 * q^8 + 3 * q^9	\( 3 q - 3 q^{2} + 3 q^{3} + 3 q^{4} + 3 q^{5} - 3 q^{6} + q^{7} - 3 q^{8} + 3 q^{9} - 3 q^{10} + 3 q^{11} + 3 q^{12} - 2 q^{13} - q^{14} + 3 q^{15} + 3 q^{16} - 3 q^{17} - 3 q^{18} + 2 q^{19} + 3 q^{20} + q^{21} - 3 q^{22} + 13 q^{23} - 3 q^{24} + 3 q^{25} + 2 q^{26} + 3 q^{27} + q^{28} + 3 q^{29} - 3 q^{30} + 3 q^{31} - 3 q^{32} + 3 q^{33} + 3 q^{34} + q^{35} + 3 q^{36} + 18 q^{37} - 2 q^{38} - 2 q^{39} - 3 q^{40} - 8 q^{41} - q^{42} + q^{43} + 3 q^{44} + 3 q^{45} - 13 q^{46} - 12 q^{47} + 3 q^{48} - 3 q^{50} - 3 q^{51} - 2 q^{52} + 10 q^{53} - 3 q^{54} + 3 q^{55} - q^{56} + 2 q^{57} - 3 q^{58} - 4 q^{59} + 3 q^{60} + 6 q^{61} - 3 q^{62} + q^{63} + 3 q^{64} - 2 q^{65} - 3 q^{66} - 4 q^{67} - 3 q^{68} + 13 q^{69} - q^{70} + 20 q^{71} - 3 q^{72} - 8 q^{73} - 18 q^{74} + 3 q^{75} + 2 q^{76} + q^{77} + 2 q^{78} + 10 q^{79} + 3 q^{80} + 3 q^{81} + 8 q^{82} + 8 q^{83} + q^{84} - 3 q^{85} - q^{86} + 3 q^{87} - 3 q^{88} + 8 q^{89} - 3 q^{90} + 20 q^{91} + 13 q^{92} + 3 q^{93} + 12 q^{94} + 2 q^{95} - 3 q^{96} + 5 q^{97} + 3 q^{99}+O(q^{100}) \) 3 * q - 3 * q^2 + 3 * q^3 + 3 * q^4 + 3 * q^5 - 3 * q^6 + q^7 - 3 * q^8 + 3 * q^9 - 3 * q^10 + 3 * q^11 + 3 * q^12 - 2 * q^13 - q^14 + 3 * q^15 + 3 * q^16 - 3 * q^17 - 3 * q^18 + 2 * q^19 + 3 * q^20 + q^21 - 3 * q^22 + 13 * q^23 - 3 * q^24 + 3 * q^25 + 2 * q^26 + 3 * q^27 + q^28 + 3 * q^29 - 3 * q^30 + 3 * q^31 - 3 * q^32 + 3 * q^33 + 3 * q^34 + q^35 + 3 * q^36 + 18 * q^37 - 2 * q^38 - 2 * q^39 - 3 * q^40 - 8 * q^41 - q^42 + q^43 + 3 * q^44 + 3 * q^45 - 13 * q^46 - 12 * q^47 + 3 * q^48 - 3 * q^50 - 3 * q^51 - 2 * q^52 + 10 * q^53 - 3 * q^54 + 3 * q^55 - q^56 + 2 * q^57 - 3 * q^58 - 4 * q^59 + 3 * q^60 + 6 * q^61 - 3 * q^62 + q^63 + 3 * q^64 - 2 * q^65 - 3 * q^66 - 4 * q^67 - 3 * q^68 + 13 * q^69 - q^70 + 20 * q^71 - 3 * q^72 - 8 * q^73 - 18 * q^74 + 3 * q^75 + 2 * q^76 + q^77 + 2 * q^78 + 10 * q^79 + 3 * q^80 + 3 * q^81 + 8 * q^82 + 8 * q^83 + q^84 - 3 * q^85 - q^86 + 3 * q^87 - 3 * q^88 + 8 * q^89 - 3 * q^90 + 20 * q^91 + 13 * q^92 + 3 * q^93 + 12 * q^94 + 2 * q^95 - 3 * q^96 + 5 * q^97 + 3 * q^99

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