LMFDB - Embedded newform 5610.2.a.ca.1.1

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			1.1
Root			$-3.08387$ 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)

$f(q)$	$=$	$q-1.00000 q^{2} +1.00000 q^{3} +1.00000 q^{4} +1.00000 q^{5} -1.00000 q^{6} -3.08387 q^{7} -1.00000 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q-1.00000 q^{2} +1.00000 q^{3} +1.00000 q^{4} +1.00000 q^{5} -1.00000 q^{6} -3.08387 q^{7} -1.00000 q^{8} +1.00000 q^{9} -1.00000 q^{10} +1.00000 q^{11} +1.00000 q^{12} -6.59414 q^{13} +3.08387 q^{14} +1.00000 q^{15} +1.00000 q^{16} -1.00000 q^{17} -1.00000 q^{18} +1.57360 q^{19} +1.00000 q^{20} -3.08387 q^{21} -1.00000 q^{22} +0.916128 q^{23} -1.00000 q^{24} +1.00000 q^{25} +6.59414 q^{26} +1.00000 q^{27} -3.08387 q^{28} +3.51027 q^{29} -1.00000 q^{30} -1.51027 q^{31} -1.00000 q^{32} +1.00000 q^{33} +1.00000 q^{34} -3.08387 q^{35} +1.00000 q^{36} +6.00000 q^{37} -1.57360 q^{38} -6.59414 q^{39} -1.00000 q^{40} +4.16774 q^{41} +3.08387 q^{42} -3.08387 q^{43} +1.00000 q^{44} +1.00000 q^{45} -0.916128 q^{46} -4.00000 q^{47} +1.00000 q^{48} +2.51027 q^{49} -1.00000 q^{50} -1.00000 q^{51} -6.59414 q^{52} -2.59414 q^{53} -1.00000 q^{54} +1.00000 q^{55} +3.08387 q^{56} +1.57360 q^{57} -3.51027 q^{58} +4.59414 q^{59} +1.00000 q^{60} +2.00000 q^{61} +1.51027 q^{62} -3.08387 q^{63} +1.00000 q^{64} -6.59414 q^{65} -1.00000 q^{66} -3.14721 q^{67} -1.00000 q^{68} +0.916128 q^{69} +3.08387 q^{70} +12.5941 q^{71} -1.00000 q^{72} -3.57360 q^{73} -6.00000 q^{74} +1.00000 q^{75} +1.57360 q^{76} -3.08387 q^{77} +6.59414 q^{78} +2.42640 q^{79} +1.00000 q^{80} +1.00000 q^{81} -4.16774 q^{82} +16.3355 q^{83} -3.08387 q^{84} -1.00000 q^{85} +3.08387 q^{86} +3.51027 q^{87} -1.00000 q^{88} -4.16774 q^{89} -1.00000 q^{90} +20.3355 q^{91} +0.916128 q^{92} -1.51027 q^{93} +4.00000 q^{94} +1.57360 q^{95} -1.00000 q^{96} -2.65748 q^{97} -2.51027 q^{98} +1.00000 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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
$7$	−3.08387	−1.16559	−0.582797	−	0.812618i	$-0.698042\pi$
$7$	−3.08387	−1.16559	−0.582797	+	0.812618i	$0.698042\pi$
$8$	−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
$13$	−6.59414	−1.82889	−0.914443	−	0.404715i	$-0.867371\pi$
$13$	−6.59414	−1.82889	−0.914443	+	0.404715i	$0.867371\pi$
$14$	3.08387	0.824200
$15$	1.00000	0.258199
$16$	1.00000	0.250000
$17$	−1.00000	−0.242536
$17$	−1.00000	−0.242536
$18$	−1.00000	−0.235702
$19$	1.57360	0.361009	0.180505	−	0.983574i	$-0.442227\pi$
$19$	1.57360	0.361009	0.180505	+	0.983574i	$0.442227\pi$
$20$	1.00000	0.223607
$21$	−3.08387	−0.672956
$22$	−1.00000	−0.213201
$23$	0.916128	0.191026	0.0955129	−	0.995428i	$-0.469551\pi$
$23$	0.916128	0.191026	0.0955129	+	0.995428i	$0.469551\pi$
$24$	−1.00000	−0.204124
$25$	1.00000	0.200000
$26$	6.59414	1.29322
$27$	1.00000	0.192450
$28$	−3.08387	−0.582797
$29$	3.51027	0.651841	0.325920	−	0.945397i	$-0.394326\pi$
$29$	3.51027	0.651841	0.325920	+	0.945397i	$0.394326\pi$
$30$	−1.00000	−0.182574
$31$	−1.51027	−0.271252	−0.135626	−	0.990760i	$-0.543305\pi$
$31$	−1.51027	−0.271252	−0.135626	+	0.990760i	$0.543305\pi$
$32$	−1.00000	−0.176777
$33$	1.00000	0.174078
$34$	1.00000	0.171499
$35$	−3.08387	−0.521270
$36$	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	$0.335828\pi$
$38$	−1.57360	−0.255272
$39$	−6.59414	−1.05591
$40$	−1.00000	−0.158114
$41$	4.16774	0.650892	0.325446	−	0.945561i	$-0.394486\pi$
$41$	4.16774	0.650892	0.325446	+	0.945561i	$0.394486\pi$
$42$	3.08387	0.475852
$43$	−3.08387	−0.470286	−0.235143	−	0.971961i	$-0.575556\pi$
$43$	−3.08387	−0.470286	−0.235143	+	0.971961i	$0.575556\pi$
$44$	1.00000	0.150756
$45$	1.00000	0.149071
$46$	−0.916128	−0.135076
$47$	−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
$49$	2.51027	0.358610
$50$	−1.00000	−0.141421
$51$	−1.00000	−0.140028
$52$	−6.59414	−0.914443
$53$	−2.59414	−0.356333	−0.178166	−	0.984000i	$-0.557017\pi$
$53$	−2.59414	−0.356333	−0.178166	+	0.984000i	$0.557017\pi$
$54$	−1.00000	−0.136083
$55$	1.00000	0.134840
$56$	3.08387	0.412100
$57$	1.57360	0.208429
$58$	−3.51027	−0.460921
$59$	4.59414	0.598106	0.299053	−	0.954236i	$-0.403329\pi$
$59$	4.59414	0.598106	0.299053	+	0.954236i	$0.403329\pi$
$60$	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	$0.459132\pi$
$62$	1.51027	0.191804
$63$	−3.08387	−0.388531
$64$	1.00000	0.125000
$65$	−6.59414	−0.817903
$66$	−1.00000	−0.123091
$67$	−3.14721	−0.384493	−0.192246	−	0.981347i	$-0.561577\pi$
$67$	−3.14721	−0.384493	−0.192246	+	0.981347i	$0.561577\pi$
$68$	−1.00000	−0.121268
$69$	0.916128	0.110289
$70$	3.08387	0.368593
$71$	12.5941	1.49465	0.747325	−	0.664459i	$-0.231338\pi$
$71$	12.5941	1.49465	0.747325	+	0.664459i	$0.231338\pi$
$72$	−1.00000	−0.117851
$73$	−3.57360	−0.418259	−0.209129	−	0.977888i	$-0.567063\pi$
$73$	−3.57360	−0.418259	−0.209129	+	0.977888i	$0.567063\pi$
$74$	−6.00000	−0.697486
$75$	1.00000	0.115470
$76$	1.57360	0.180505
$77$	−3.08387	−0.351440
$78$	6.59414	0.746639
$79$	2.42640	0.272991	0.136495	−	0.990641i	$-0.456416\pi$
$79$	2.42640	0.272991	0.136495	+	0.990641i	$0.456416\pi$
$80$	1.00000	0.111803
$81$	1.00000	0.111111
$82$	−4.16774	−0.460250
$83$	16.3355	1.79305	0.896526	−	0.442990i	$-0.146082\pi$
$83$	16.3355	1.79305	0.896526	+	0.442990i	$0.146082\pi$
$84$	−3.08387	−0.336478
$85$	−1.00000	−0.108465
$86$	3.08387	0.332543
$87$	3.51027	0.376340
$88$	−1.00000	−0.106600
$89$	−4.16774	−0.441780	−0.220890	−	0.975299i	$-0.570896\pi$
$89$	−4.16774	−0.441780	−0.220890	+	0.975299i	$0.570896\pi$
$90$	−1.00000	−0.105409
$91$	20.3355	2.13174
$92$	0.916128	0.0955129
$93$	−1.51027	−0.156608
$94$	4.00000	0.412568
$95$	1.57360	0.161448
$96$	−1.00000	−0.102062
$97$	−2.65748	−0.269826	−0.134913	−	0.990857i	$-0.543075\pi$
$97$	−2.65748	−0.269826	−0.134913	+	0.990857i	$0.543075\pi$
$98$	−2.51027	−0.253575
$99$	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
$103$	3.34252	0.329349	0.164674	−	0.986348i	$-0.447343\pi$
$103$	3.34252	0.329349	0.164674	+	0.986348i	$0.447343\pi$
$104$	6.59414	0.646609
$105$	−3.08387	−0.300955
$106$	2.59414	0.251965
$107$	−6.48973	−0.627386	−0.313693	−	0.949524i	$-0.601566\pi$
$107$	−6.48973	−0.627386	−0.313693	+	0.949524i	$0.601566\pi$
$108$	1.00000	0.0962250
$109$	3.83226	0.367063	0.183532	−	0.983014i	$-0.441247\pi$
$109$	3.83226	0.367063	0.183532	+	0.983014i	$0.441247\pi$
$110$	−1.00000	−0.0953463
$111$	6.00000	0.569495
$112$	−3.08387	−0.291399
$113$	8.76189	0.824249	0.412124	−	0.911128i	$-0.364787\pi$
$113$	8.76189	0.824249	0.412124	+	0.911128i	$0.364787\pi$
$114$	−1.57360	−0.147381
$115$	0.916128	0.0854293
$116$	3.51027	0.325920
$117$	−6.59414	−0.609629
$118$	−4.59414	−0.422925
$119$	3.08387	0.282698
$120$	−1.00000	−0.0912871
$121$	1.00000	0.0909091
$122$	−2.00000	−0.181071
$123$	4.16774	0.375793
$124$	−1.51027	−0.135626
$125$	1.00000	0.0894427
$126$	3.08387	0.274733
$127$	15.3560	1.36263	0.681314	−	0.731992i	$-0.261409\pi$
$127$	15.3560	1.36263	0.681314	+	0.731992i	$0.261409\pi$
$128$	−1.00000	−0.0883883
$129$	−3.08387	−0.271520
$130$	6.59414	0.578344
$131$	−16.3355	−1.42724	−0.713619	−	0.700534i	$-0.752945\pi$
$131$	−16.3355	−1.42724	−0.713619	+	0.700534i	$0.752945\pi$
$132$	1.00000	0.0870388
$133$	−4.85279	−0.420790
$134$	3.14721	0.271877
$135$	1.00000	0.0860663
$136$	1.00000	0.0857493
$137$	16.8252	1.43748	0.718738	−	0.695281i	$-0.244720\pi$
$137$	16.8252	1.43748	0.718738	+	0.695281i	$0.244720\pi$
$138$	−0.916128	−0.0779860
$139$	2.36306	0.200432	0.100216	−	0.994966i	$-0.468047\pi$
$139$	2.36306	0.200432	0.100216	+	0.994966i	$0.468047\pi$
$140$	−3.08387	−0.260635
$141$	−4.00000	−0.336861
$142$	−12.5941	−1.05688
$143$	−6.59414	−0.551430
$144$	1.00000	0.0833333
$145$	3.51027	0.291512
$146$	3.57360	0.295754
$147$	2.51027	0.207043
$148$	6.00000	0.493197
$149$	4.16774	0.341435	0.170717	−	0.985320i	$-0.445391\pi$
$149$	4.16774	0.341435	0.170717	+	0.985320i	$0.445391\pi$
$150$	−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	$0.447961\pi$
$152$	−1.57360	−0.127636
$153$	−1.00000	−0.0808452
$154$	3.08387	0.248506
$155$	−1.51027	−0.121308
$156$	−6.59414	−0.527954
$157$	10.0000	0.798087	0.399043	−	0.916932i	$-0.369342\pi$
$157$	10.0000	0.798087	0.399043	+	0.916932i	$0.369342\pi$
$158$	−2.42640	−0.193034
$159$	−2.59414	−0.205729
$160$	−1.00000	−0.0790569
$161$	−2.82522	−0.222659
$162$	−1.00000	−0.0785674
$163$	11.6780	0.914693	0.457346	−	0.889289i	$-0.348800\pi$
$163$	11.6780	0.914693	0.457346	+	0.889289i	$0.348800\pi$
$164$	4.16774	0.325446
$165$	1.00000	0.0778499
$166$	−16.3355	−1.26788
$167$	−20.2088	−1.56381	−0.781903	−	0.623400i	$-0.785751\pi$
$167$	−20.2088	−1.56381	−0.781903	+	0.623400i	$0.785751\pi$
$168$	3.08387	0.237926
$169$	30.4827	2.34482
$170$	1.00000	0.0766965
$171$	1.57360	0.120336
$172$	−3.08387	−0.235143
$173$	1.14721	0.0872206	0.0436103	−	0.999049i	$-0.486114\pi$
$173$	1.14721	0.0872206	0.0436103	+	0.999049i	$0.486114\pi$
$174$	−3.51027	−0.266113
$175$	−3.08387	−0.233119
$176$	1.00000	0.0753778
$177$	4.59414	0.345317
$178$	4.16774	0.312386
$179$	20.0768	1.50061	0.750307	−	0.661090i	$-0.229906\pi$
$179$	20.0768	1.50061	0.750307	+	0.661090i	$0.229906\pi$
$180$	1.00000	0.0745356
$181$	3.51027	0.260916	0.130458	−	0.991454i	$-0.458355\pi$
$181$	3.51027	0.260916	0.130458	+	0.991454i	$0.458355\pi$
$182$	−20.3355	−1.50737
$183$	2.00000	0.147844
$184$	−0.916128	−0.0675378
$185$	6.00000	0.441129
$186$	1.51027	0.110738
$187$	−1.00000	−0.0731272
$188$	−4.00000	−0.291730
$189$	−3.08387	−0.224319
$190$	−1.57360	−0.114161
$191$	16.9930	1.22957	0.614784	−	0.788696i	$-0.289243\pi$
$191$	16.9930	1.22957	0.614784	+	0.788696i	$0.289243\pi$
$192$	1.00000	0.0721688
$193$	7.57360	0.545160	0.272580	−	0.962133i	$-0.412123\pi$
$193$	7.57360	0.545160	0.272580	+	0.962133i	$0.412123\pi$
$194$	2.65748	0.190796
$195$	−6.59414	−0.472216
$196$	2.51027	0.179305
$197$	−19.3150	−1.37613	−0.688067	−	0.725647i	$-0.741540\pi$
$197$	−19.3150	−1.37613	−0.688067	+	0.725647i	$0.741540\pi$
$198$	−1.00000	−0.0710669
$199$	11.1472	0.790205	0.395102	−	0.918637i	$-0.370709\pi$
$199$	11.1472	0.790205	0.395102	+	0.918637i	$0.370709\pi$
$200$	−1.00000	−0.0707107
$201$	−3.14721	−0.221987
$202$	−6.00000	−0.422159
$203$	−10.8252	−0.759782
$204$	−1.00000	−0.0700140
$205$	4.16774	0.291088
$206$	−3.34252	−0.232885
$207$	0.916128	0.0636753
$208$	−6.59414	−0.457221
$209$	1.57360	0.108848
$210$	3.08387	0.212807
$211$	5.63694	0.388063	0.194031	−	0.980995i	$-0.437844\pi$
$211$	5.63694	0.388063	0.194031	+	0.980995i	$0.437844\pi$
$212$	−2.59414	−0.178166
$213$	12.5941	0.862936
$214$	6.48973	0.443629
$215$	−3.08387	−0.210318
$216$	−1.00000	−0.0680414
$217$	4.65748	0.316170
$218$	−3.83226	−0.259553
$219$	−3.57360	−0.241482
$220$	1.00000	0.0674200
$221$	6.59414	0.443570
$222$	−6.00000	−0.402694
$223$	3.34252	0.223832	0.111916	−	0.993718i	$-0.464301\pi$
$223$	3.34252	0.223832	0.111916	+	0.993718i	$0.464301\pi$
$224$	3.08387	0.206050
$225$	1.00000	0.0666667
$226$	−8.76189	−0.582832
$227$	−6.48973	−0.430739	−0.215369	−	0.976533i	$-0.569096\pi$
$227$	−6.48973	−0.430739	−0.215369	+	0.976533i	$0.569096\pi$
$228$	1.57360	0.104214
$229$	18.2088	1.20327	0.601636	−	0.798770i	$-0.294516\pi$
$229$	18.2088	1.20327	0.601636	+	0.798770i	$0.294516\pi$
$230$	−0.916128	−0.0604077
$231$	−3.08387	−0.202904
$232$	−3.51027	−0.230460
$233$	−0.489731	−0.0320834	−0.0160417	−	0.999871i	$-0.505106\pi$
$233$	−0.489731	−0.0320834	−0.0160417	+	0.999871i	$0.505106\pi$
$234$	6.59414	0.431072
$235$	−4.00000	−0.260931
$236$	4.59414	0.299053
$237$	2.42640	0.157611
$238$	−3.08387	−0.199898
$239$	−17.3150	−1.12001	−0.560006	−	0.828489i	$-0.689201\pi$
$239$	−17.3150	−1.12001	−0.560006	+	0.828489i	$0.689201\pi$
$240$	1.00000	0.0645497
$241$	17.4194	1.12208	0.561040	−	0.827789i	$-0.310401\pi$
$241$	17.4194	1.12208	0.561040	+	0.827789i	$0.310401\pi$
$242$	−1.00000	−0.0642824
$243$	1.00000	0.0641500
$244$	2.00000	0.128037
$245$	2.51027	0.160375
$246$	−4.16774	−0.265726
$247$	−10.3766	−0.660245
$248$	1.51027	0.0959022
$249$	16.3355	1.03522
$250$	−1.00000	−0.0632456
$251$	−3.27919	−0.206981	−0.103490	−	0.994630i	$-0.533001\pi$
$251$	−3.27919	−0.206981	−0.103490	+	0.994630i	$0.533001\pi$
$252$	−3.08387	−0.194266
$253$	0.916128	0.0575965
$254$	−15.3560	−0.963523
$255$	−1.00000	−0.0626224
$256$	1.00000	0.0625000
$257$	−0.489731	−0.0305486	−0.0152743	−	0.999883i	$-0.504862\pi$
$257$	−0.489731	−0.0305486	−0.0152743	+	0.999883i	$0.504862\pi$
$258$	3.08387	0.191994
$259$	−18.5032	−1.14974
$260$	−6.59414	−0.408951
$261$	3.51027	0.217280
$262$	16.3355	1.00921
$263$	3.34252	0.206109	0.103054	−	0.994676i	$-0.467138\pi$
$263$	3.34252	0.206109	0.103054	+	0.994676i	$0.467138\pi$
$264$	−1.00000	−0.0615457
$265$	−2.59414	−0.159357
$266$	4.85279	0.297544
$267$	−4.16774	−0.255062
$268$	−3.14721	−0.192246
$269$	−14.3355	−0.874050	−0.437025	−	0.899449i	$-0.643968\pi$
$269$	−14.3355	−0.874050	−0.437025	+	0.899449i	$0.643968\pi$
$270$	−1.00000	−0.0608581
$271$	10.4897	0.637206	0.318603	−	0.947888i	$-0.396786\pi$
$271$	10.4897	0.637206	0.318603	+	0.947888i	$0.396786\pi$
$272$	−1.00000	−0.0606339
$273$	20.3355	1.23076
$274$	−16.8252	−1.01645
$275$	1.00000	0.0603023
$276$	0.916128	0.0551444
$277$	−1.14721	−0.0689290	−0.0344645	−	0.999406i	$-0.510973\pi$
$277$	−1.14721	−0.0689290	−0.0344645	+	0.999406i	$0.510973\pi$
$278$	−2.36306	−0.141727
$279$	−1.51027	−0.0904174
$280$	3.08387	0.184297
$281$	−9.80468	−0.584898	−0.292449	−	0.956281i	$-0.594470\pi$
$281$	−9.80468	−0.584898	−0.292449	+	0.956281i	$0.594470\pi$
$282$	4.00000	0.238197
$283$	31.6915	1.88387	0.941933	−	0.335802i	$-0.109007\pi$
$283$	31.6915	1.88387	0.941933	+	0.335802i	$0.109007\pi$
$284$	12.5941	0.747325
$285$	1.57360	0.0932122
$286$	6.59414	0.389920
$287$	−12.8528	−0.758676
$288$	−1.00000	−0.0589256
$289$	1.00000	0.0588235
$290$	−3.51027	−0.206130
$291$	−2.65748	−0.155784
$292$	−3.57360	−0.209129
$293$	−16.6986	−0.975540	−0.487770	−	0.872972i	$-0.662189\pi$
$293$	−16.6986	−0.975540	−0.487770	+	0.872972i	$0.662189\pi$
$294$	−2.51027	−0.146402
$295$	4.59414	0.267481
$296$	−6.00000	−0.348743
$297$	1.00000	0.0580259
$298$	−4.16774	−0.241431
$299$	−6.04107	−0.349364
$300$	1.00000	0.0577350
$301$	9.51027	0.548163
$302$	−4.00000	−0.230174
$303$	6.00000	0.344691
$304$	1.57360	0.0902524
$305$	2.00000	0.114520
$306$	1.00000	0.0571662
$307$	10.7619	0.614213	0.307107	−	0.951675i	$-0.400639\pi$
$307$	10.7619	0.614213	0.307107	+	0.951675i	$0.400639\pi$
$308$	−3.08387	−0.175720
$309$	3.34252	0.190150
$310$	1.51027	0.0857775
$311$	−25.0563	−1.42081	−0.710406	−	0.703792i	$-0.751489\pi$
$311$	−25.0563	−1.42081	−0.710406	+	0.703792i	$0.751489\pi$
$312$	6.59414	0.373320
$313$	−7.38360	−0.417346	−0.208673	−	0.977986i	$-0.566914\pi$
$313$	−7.38360	−0.417346	−0.208673	+	0.977986i	$0.566914\pi$
$314$	−10.0000	−0.564333
$315$	−3.08387	−0.173757
$316$	2.42640	0.136495
$317$	16.8252	0.944999	0.472499	−	0.881331i	$-0.343352\pi$
$317$	16.8252	0.944999	0.472499	+	0.881331i	$0.343352\pi$
$318$	2.59414	0.145472
$319$	3.51027	0.196537
$320$	1.00000	0.0559017
$321$	−6.48973	−0.362221
$322$	2.82522	0.157443
$323$	−1.57360	−0.0875576
$324$	1.00000	0.0555556
$325$	−6.59414	−0.365777
$326$	−11.6780	−0.646785
$327$	3.83226	0.211924
$328$	−4.16774	−0.230125
$329$	12.3355	0.680078
$330$	−1.00000	−0.0550482
$331$	−13.3836	−0.735629	−0.367815	−	0.929899i	$-0.619894\pi$
$331$	−13.3836	−0.735629	−0.367815	+	0.929899i	$0.619894\pi$
$332$	16.3355	0.896526
$333$	6.00000	0.328798
$334$	20.2088	1.10578
$335$	−3.14721	−0.171950
$336$	−3.08387	−0.168239
$337$	−5.27919	−0.287576	−0.143788	−	0.989609i	$-0.545928\pi$
$337$	−5.27919	−0.287576	−0.143788	+	0.989609i	$0.545928\pi$
$338$	−30.4827	−1.65804
$339$	8.76189	0.475880
$340$	−1.00000	−0.0542326
$341$	−1.51027	−0.0817856
$342$	−1.57360	−0.0850907
$343$	13.8458	0.747601
$344$	3.08387	0.166271
$345$	0.916128	0.0493227
$346$	−1.14721	−0.0616742
$347$	7.48270	0.401692	0.200846	−	0.979623i	$-0.435631\pi$
$347$	7.48270	0.401692	0.200846	+	0.979623i	$0.435631\pi$
$348$	3.51027	0.188170
$349$	0.761886	0.0407828	0.0203914	−	0.999792i	$-0.493509\pi$
$349$	0.761886	0.0407828	0.0203914	+	0.999792i	$0.493509\pi$
$350$	3.08387	0.164840
$351$	−6.59414	−0.351969
$352$	−1.00000	−0.0533002
$353$	26.5308	1.41209	0.706046	−	0.708166i	$-0.250477\pi$
$353$	26.5308	1.41209	0.706046	+	0.708166i	$0.250477\pi$
$354$	−4.59414	−0.244176
$355$	12.5941	0.668428
$356$	−4.16774	−0.220890
$357$	3.08387	0.163216
$358$	−20.0768	−1.06109
$359$	−9.31495	−0.491624	−0.245812	−	0.969317i	$-0.579055\pi$
$359$	−9.31495	−0.491624	−0.245812	+	0.969317i	$0.579055\pi$
$360$	−1.00000	−0.0527046
$361$	−16.5238	−0.869672
$362$	−3.51027	−0.184496
$363$	1.00000	0.0524864
$364$	20.3355	1.06587
$365$	−3.57360	−0.187051
$366$	−2.00000	−0.104542
$367$	−20.2088	−1.05489	−0.527446	−	0.849589i	$-0.676850\pi$
$367$	−20.2088	−1.05489	−0.527446	+	0.849589i	$0.676850\pi$
$368$	0.916128	0.0477565
$369$	4.16774	0.216964
$370$	−6.00000	−0.311925
$371$	8.00000	0.415339
$372$	−1.51027	−0.0783038
$373$	−1.86802	−0.0967223	−0.0483612	−	0.998830i	$-0.515400\pi$
$373$	−1.86802	−0.0967223	−0.0483612	+	0.998830i	$0.515400\pi$
$374$	1.00000	0.0517088
$375$	1.00000	0.0516398
$376$	4.00000	0.206284
$377$	−23.1472	−1.19214
$378$	3.08387	0.158617
$379$	−1.18828	−0.0610380	−0.0305190	−	0.999534i	$-0.509716\pi$
$379$	−1.18828	−0.0610380	−0.0305190	+	0.999534i	$0.509716\pi$
$380$	1.57360	0.0807242
$381$	15.3560	0.786713
$382$	−16.9930	−0.869436
$383$	27.2294	1.39136	0.695678	−	0.718354i	$-0.255104\pi$
$383$	27.2294	1.39136	0.695678	+	0.718354i	$0.255104\pi$
$384$	−1.00000	−0.0510310
$385$	−3.08387	−0.157169
$386$	−7.57360	−0.385486
$387$	−3.08387	−0.156762
$388$	−2.65748	−0.134913
$389$	−29.0974	−1.47530	−0.737648	−	0.675186i	$-0.764063\pi$
$389$	−29.0974	−1.47530	−0.737648	+	0.675186i	$0.764063\pi$
$390$	6.59414	0.333907
$391$	−0.916128	−0.0463306
$392$	−2.51027	−0.126788
$393$	−16.3355	−0.824016
$394$	19.3150	0.973073
$395$	2.42640	0.122085
$396$	1.00000	0.0502519
$397$	−21.1472	−1.06135	−0.530674	−	0.847576i	$-0.678061\pi$
$397$	−21.1472	−1.06135	−0.530674	+	0.847576i	$0.678061\pi$
$398$	−11.1472	−0.558759
$399$	−4.85279	−0.242944
$400$	1.00000	0.0500000
$401$	−21.4194	−1.06963	−0.534816	−	0.844969i	$-0.679619\pi$
$401$	−21.4194	−1.06963	−0.534816	+	0.844969i	$0.679619\pi$
$402$	3.14721	0.156968
$403$	9.95893	0.496089
$404$	6.00000	0.298511
$405$	1.00000	0.0496904
$406$	10.8252	0.537247
$407$	6.00000	0.297409
$408$	1.00000	0.0495074
$409$	26.5443	1.31253	0.656266	−	0.754530i	$-0.272135\pi$
$409$	26.5443	1.31253	0.656266	+	0.754530i	$0.272135\pi$
$410$	−4.16774	−0.205830
$411$	16.8252	0.829927
$412$	3.34252	0.164674
$413$	−14.1677	−0.697149
$414$	−0.916128	−0.0450252
$415$	16.3355	0.801878
$416$	6.59414	0.323304
$417$	2.36306	0.115720
$418$	−1.57360	−0.0769675
$419$	−19.0340	−0.929874	−0.464937	−	0.885344i	$-0.653923\pi$
$419$	−19.0340	−0.929874	−0.464937	+	0.885344i	$0.653923\pi$
$420$	−3.08387	−0.150478
$421$	−11.3150	−0.551457	−0.275729	−	0.961236i	$-0.588919\pi$
$421$	−11.3150	−0.551457	−0.275729	+	0.961236i	$0.588919\pi$
$422$	−5.63694	−0.274402
$423$	−4.00000	−0.194487
$424$	2.59414	0.125983
$425$	−1.00000	−0.0485071
$426$	−12.5941	−0.610188
$427$	−6.16774	−0.298478
$428$	−6.48973	−0.313693
$429$	−6.59414	−0.318368
$430$	3.08387	0.148718
$431$	−28.0135	−1.34936	−0.674681	−	0.738109i	$-0.735719\pi$
$431$	−28.0135	−1.34936	−0.674681	+	0.738109i	$0.735719\pi$
$432$	1.00000	0.0481125
$433$	24.8387	1.19367	0.596836	−	0.802363i	$-0.296424\pi$
$433$	24.8387	1.19367	0.596836	+	0.802363i	$0.296424\pi$
$434$	−4.65748	−0.223566
$435$	3.51027	0.168305
$436$	3.83226	0.183532
$437$	1.44162	0.0689621
$438$	3.57360	0.170753
$439$	5.70027	0.272059	0.136030	−	0.990705i	$-0.456566\pi$
$439$	5.70027	0.272059	0.136030	+	0.990705i	$0.456566\pi$
$440$	−1.00000	−0.0476731
$441$	2.51027	0.119537
$442$	−6.59414	−0.313651
$443$	30.2311	1.43632	0.718161	−	0.695877i	$-0.244984\pi$
$443$	30.2311	1.43632	0.718161	+	0.695877i	$0.244984\pi$
$444$	6.00000	0.284747
$445$	−4.16774	−0.197570
$446$	−3.34252	−0.158273
$447$	4.16774	0.197128
$448$	−3.08387	−0.145699
$449$	11.1249	0.525019	0.262509	−	0.964929i	$-0.415450\pi$
$449$	11.1249	0.525019	0.262509	+	0.964929i	$0.415450\pi$
$450$	−1.00000	−0.0471405
$451$	4.16774	0.196251
$452$	8.76189	0.412124
$453$	4.00000	0.187936
$454$	6.48973	0.304578
$455$	20.3355	0.953342
$456$	−1.57360	−0.0736907
$457$	−10.0000	−0.467780	−0.233890	−	0.972263i	$-0.575146\pi$
$457$	−10.0000	−0.467780	−0.233890	+	0.972263i	$0.575146\pi$
$458$	−18.2088	−0.850842
$459$	−1.00000	−0.0466760
$460$	0.916128	0.0427147
$461$	−33.2294	−1.54765	−0.773823	−	0.633402i	$-0.781658\pi$
$461$	−33.2294	−1.54765	−0.773823	+	0.633402i	$0.781658\pi$
$462$	3.08387	0.143475
$463$	8.00000	0.371792	0.185896	−	0.982569i	$-0.440481\pi$
$463$	8.00000	0.371792	0.185896	+	0.982569i	$0.440481\pi$
$464$	3.51027	0.162960
$465$	−1.51027	−0.0700370
$466$	0.489731	0.0226864
$467$	32.2857	1.49400	0.747001	−	0.664823i	$-0.231493\pi$
$467$	32.2857	1.49400	0.747001	+	0.664823i	$0.231493\pi$
$468$	−6.59414	−0.304814
$469$	9.70559	0.448162
$470$	4.00000	0.184506
$471$	10.0000	0.460776
$472$	−4.59414	−0.211462
$473$	−3.08387	−0.141797
$474$	−2.42640	−0.111448
$475$	1.57360	0.0722019
$476$	3.08387	0.141349
$477$	−2.59414	−0.118778
$478$	17.3150	0.791967
$479$	4.78415	0.218593	0.109297	−	0.994009i	$-0.465140\pi$
$479$	4.78415	0.218593	0.109297	+	0.994009i	$0.465140\pi$
$480$	−1.00000	−0.0456435
$481$	−39.5648	−1.80400
$482$	−17.4194	−0.793430
$483$	−2.82522	−0.128552
$484$	1.00000	0.0454545
$485$	−2.65748	−0.120670
$486$	−1.00000	−0.0453609
$487$	−30.8387	−1.39744	−0.698718	−	0.715397i	$-0.746246\pi$
$487$	−30.8387	−1.39744	−0.698718	+	0.715397i	$0.746246\pi$
$488$	−2.00000	−0.0905357
$489$	11.6780	0.528098
$490$	−2.51027	−0.113402
$491$	0	0		−	1.00000i	$-0.5\pi$
$491$	0	0			1.00000i	$0.5\pi$
$492$	4.16774	0.187896
$493$	−3.51027	−0.158095
$494$	10.3766	0.466864
$495$	1.00000	0.0449467
$496$	−1.51027	−0.0678131
$497$	−38.8387	−1.74215
$498$	−16.3355	−0.732011
$499$	39.4827	1.76749	0.883744	−	0.467970i	$-0.155015\pi$
$499$	39.4827	1.76749	0.883744	+	0.467970i	$0.155015\pi$
$500$	1.00000	0.0447214
$501$	−20.2088	−0.902863
$502$	3.27919	0.146357
$503$	8.67098	0.386620	0.193310	−	0.981138i	$-0.438078\pi$
$503$	8.67098	0.386620	0.193310	+	0.981138i	$0.438078\pi$
$504$	3.08387	0.137367
$505$	6.00000	0.266996
$506$	−0.916128	−0.0407268
$507$	30.4827	1.35378
$508$	15.3560	0.681314
$509$	−5.09738	−0.225937	−0.112969	−	0.993599i	$-0.536036\pi$
$509$	−5.09738	−0.225937	−0.112969	+	0.993599i	$0.536036\pi$
$510$	1.00000	0.0442807
$511$	11.0205	0.487520
$512$	−1.00000	−0.0441942
$513$	1.57360	0.0694763
$514$	0.489731	0.0216011
$515$	3.34252	0.147289
$516$	−3.08387	−0.135760
$517$	−4.00000	−0.175920
$518$	18.5032	0.812985
$519$	1.14721	0.0503568
$520$	6.59414	0.289172
$521$	−21.0974	−0.924293	−0.462146	−	0.886804i	$-0.652921\pi$
$521$	−21.0974	−0.924293	−0.462146	+	0.886804i	$0.652921\pi$
$522$	−3.51027	−0.153640
$523$	12.1455	0.531085	0.265542	−	0.964099i	$-0.414449\pi$
$523$	12.1455	0.531085	0.265542	+	0.964099i	$0.414449\pi$
$524$	−16.3355	−0.713619
$525$	−3.08387	−0.134591
$526$	−3.34252	−0.145741
$527$	1.51027	0.0657883
$528$	1.00000	0.0435194
$529$	−22.1607	−0.963509
$530$	2.59414	0.112682
$531$	4.59414	0.199369
$532$	−4.85279	−0.210395
$533$	−27.4827	−1.19041
$534$	4.16774	0.180356
$535$	−6.48973	−0.280576
$536$	3.14721	0.135939
$537$	20.0768	0.866379
$538$	14.3355	0.618047
$539$	2.51027	0.108125
$540$	1.00000	0.0430331
$541$	17.3560	0.746194	0.373097	−	0.927792i	$-0.378296\pi$
$541$	17.3560	0.746194	0.373097	+	0.927792i	$0.378296\pi$
$542$	−10.4897	−0.450573
$543$	3.51027	0.150640
$544$	1.00000	0.0428746
$545$	3.83226	0.164156
$546$	−20.3355	−0.870279
$547$	11.8733	0.507667	0.253833	−	0.967248i	$-0.418308\pi$
$547$	11.8733	0.507667	0.253833	+	0.967248i	$0.418308\pi$
$548$	16.8252	0.718738
$549$	2.00000	0.0853579
$550$	−1.00000	−0.0426401
$551$	5.52377	0.235321
$552$	−0.916128	−0.0389930
$553$	−7.48270	−0.318197
$554$	1.14721	0.0487402
$555$	6.00000	0.254686
$556$	2.36306	0.100216
$557$	0.363061	0.0153834	0.00769170	−	0.999970i	$-0.497552\pi$
$557$	0.363061	0.0153834	0.00769170	+	0.999970i	$0.497552\pi$
$558$	1.51027	0.0639348
$559$	20.3355	0.860100
$560$	−3.08387	−0.130317
$561$	−1.00000	−0.0422200
$562$	9.80468	0.413586
$563$	42.7121	1.80010	0.900049	−	0.435788i	$-0.143530\pi$
$563$	42.7121	1.80010	0.900049	+	0.435788i	$0.143530\pi$
$564$	−4.00000	−0.168430
$565$	8.76189	0.368615
$566$	−31.6915	−1.33209
$567$	−3.08387	−0.129510
$568$	−12.5941	−0.528438
$569$	6.00000	0.251533	0.125767	−	0.992060i	$-0.459861\pi$
$569$	6.00000	0.251533	0.125767	+	0.992060i	$0.459861\pi$
$570$	−1.57360	−0.0659110
$571$	2.29441	0.0960183	0.0480091	−	0.998847i	$-0.484712\pi$
$571$	2.29441	0.0960183	0.0480091	+	0.998847i	$0.484712\pi$
$572$	−6.59414	−0.275715
$573$	16.9930	0.709891
$574$	12.8528	0.536465
$575$	0.916128	0.0382052
$576$	1.00000	0.0416667
$577$	5.14721	0.214281	0.107141	−	0.994244i	$-0.465831\pi$
$577$	5.14721	0.214281	0.107141	+	0.994244i	$0.465831\pi$
$578$	−1.00000	−0.0415945
$579$	7.57360	0.314748
$580$	3.51027	0.145756
$581$	−50.3766	−2.08997
$582$	2.65748	0.110156
$583$	−2.59414	−0.107438
$584$	3.57360	0.147877
$585$	−6.59414	−0.272634
$586$	16.6986	0.689811
$587$	4.91613	0.202910	0.101455	−	0.994840i	$-0.467650\pi$
$587$	4.91613	0.202910	0.101455	+	0.994840i	$0.467650\pi$
$588$	2.51027	0.103522
$589$	−2.37656	−0.0979246
$590$	−4.59414	−0.189138
$591$	−19.3150	−0.794511
$592$	6.00000	0.246598
$593$	−31.5238	−1.29453	−0.647263	−	0.762267i	$-0.724086\pi$
$593$	−31.5238	−1.29453	−0.647263	+	0.762267i	$0.724086\pi$
$594$	−1.00000	−0.0410305
$595$	3.08387	0.126426
$596$	4.16774	0.170717
$597$	11.1472	0.456225
$598$	6.04107	0.247038
$599$	13.3014	0.543482	0.271741	−	0.962370i	$-0.412401\pi$
$599$	13.3014	0.543482	0.271741	+	0.962370i	$0.412401\pi$
$600$	−1.00000	−0.0408248
$601$	29.9502	1.22169	0.610846	−	0.791749i	$-0.290829\pi$
$601$	29.9502	1.22169	0.610846	+	0.791749i	$0.290829\pi$
$602$	−9.51027	−0.387610
$603$	−3.14721	−0.128164
$604$	4.00000	0.162758
$605$	1.00000	0.0406558
$606$	−6.00000	−0.243733
$607$	−6.42640	−0.260839	−0.130420	−	0.991459i	$-0.541632\pi$
$607$	−6.42640	−0.260839	−0.130420	+	0.991459i	$0.541632\pi$
$608$	−1.57360	−0.0638181
$609$	−10.8252	−0.438660
$610$	−2.00000	−0.0809776
$611$	26.3766	1.06708
$612$	−1.00000	−0.0404226
$613$	−29.9502	−1.20968	−0.604838	−	0.796349i	$-0.706762\pi$
$613$	−29.9502	−1.20968	−0.604838	+	0.796349i	$0.706762\pi$
$614$	−10.7619	−0.434314
$615$	4.16774	0.168060
$616$	3.08387	0.124253
$617$	−4.09091	−0.164694	−0.0823469	−	0.996604i	$-0.526242\pi$
$617$	−4.09091	−0.164694	−0.0823469	+	0.996604i	$0.526242\pi$
$618$	−3.34252	−0.134456
$619$	9.83226	0.395192	0.197596	−	0.980284i	$-0.436687\pi$
$619$	9.83226	0.395192	0.197596	+	0.980284i	$0.436687\pi$
$620$	−1.51027	−0.0606539
$621$	0.916128	0.0367629
$622$	25.0563	1.00467
$623$	12.8528	0.514936
$624$	−6.59414	−0.263977
$625$	1.00000	0.0400000
$626$	7.38360	0.295108
$627$	1.57360	0.0628437
$628$	10.0000	0.399043
$629$	−6.00000	−0.239236
$630$	3.08387	0.122864
$631$	31.3560	1.24826	0.624132	−	0.781319i	$-0.285453\pi$
$631$	31.3560	1.24826	0.624132	+	0.781319i	$0.285453\pi$
$632$	−2.42640	−0.0965169
$633$	5.63694	0.224048
$634$	−16.8252	−0.668215
$635$	15.3560	0.609385
$636$	−2.59414	−0.102864
$637$	−16.5531	−0.655856
$638$	−3.51027	−0.138973
$639$	12.5941	0.498217
$640$	−1.00000	−0.0395285
$641$	40.9021	1.61553	0.807767	−	0.589502i	$-0.200676\pi$
$641$	40.9021	1.61553	0.807767	+	0.589502i	$0.200676\pi$
$642$	6.48973	0.256129
$643$	−28.3490	−1.11798	−0.558988	−	0.829176i	$-0.688810\pi$
$643$	−28.3490	−1.11798	−0.558988	+	0.829176i	$0.688810\pi$
$644$	−2.82522	−0.111329
$645$	−3.08387	−0.121427
$646$	1.57360	0.0619126
$647$	−2.68505	−0.105560	−0.0527801	−	0.998606i	$-0.516808\pi$
$647$	−2.68505	−0.105560	−0.0527801	+	0.998606i	$0.516808\pi$
$648$	−1.00000	−0.0392837
$649$	4.59414	0.180336
$650$	6.59414	0.258643
$651$	4.65748	0.182541
$652$	11.6780	0.457346
$653$	30.3490	1.18765	0.593824	−	0.804595i	$-0.297618\pi$
$653$	30.3490	1.18765	0.593824	+	0.804595i	$0.297618\pi$
$654$	−3.83226	−0.149853
$655$	−16.3355	−0.638280
$656$	4.16774	0.162723
$657$	−3.57360	−0.139420
$658$	−12.3355	−0.480887
$659$	9.38360	0.365533	0.182767	−	0.983156i	$-0.441495\pi$
$659$	9.38360	0.365533	0.182767	+	0.983156i	$0.441495\pi$
$660$	1.00000	0.0389249
$661$	2.20882	0.0859131	0.0429566	−	0.999077i	$-0.486322\pi$
$661$	2.20882	0.0859131	0.0429566	+	0.999077i	$0.486322\pi$
$662$	13.3836	0.520168
$663$	6.59414	0.256095
$664$	−16.3355	−0.633940
$665$	−4.85279	−0.188183
$666$	−6.00000	−0.232495
$667$	3.21585	0.124518
$668$	−20.2088	−0.781903
$669$	3.34252	0.129229
$670$	3.14721	0.121587
$671$	2.00000	0.0772091
$672$	3.08387	0.118963
$673$	16.8886	0.651006	0.325503	−	0.945541i	$-0.394466\pi$
$673$	16.8886	0.651006	0.325503	+	0.945541i	$0.394466\pi$
$674$	5.27919	0.203347
$675$	1.00000	0.0384900
$676$	30.4827	1.17241
$677$	0.376564	0.0144725	0.00723627	−	0.999974i	$-0.497697\pi$
$677$	0.376564	0.0144725	0.00723627	+	0.999974i	$0.497697\pi$
$678$	−8.76189	−0.336498
$679$	8.19532	0.314507
$680$	1.00000	0.0383482
$681$	−6.48973	−0.248687
$682$	1.51027	0.0578312
$683$	18.0411	0.690323	0.345161	−	0.938543i	$-0.387824\pi$
$683$	18.0411	0.690323	0.345161	+	0.938543i	$0.387824\pi$
$684$	1.57360	0.0601682
$685$	16.8252	0.642859
$686$	−13.8458	−0.528634
$687$	18.2088	0.694710
$688$	−3.08387	−0.117572
$689$	17.1061	0.651692
$690$	−0.916128	−0.0348764
$691$	19.1472	0.728394	0.364197	−	0.931322i	$-0.381343\pi$
$691$	19.1472	0.728394	0.364197	+	0.931322i	$0.381343\pi$
$692$	1.14721	0.0436103
$693$	−3.08387	−0.117147
$694$	−7.48270	−0.284039
$695$	2.36306	0.0896360
$696$	−3.51027	−0.133056
$697$	−4.16774	−0.157865
$698$	−0.761886	−0.0288378
$699$	−0.489731	−0.0185233
$700$	−3.08387	−0.116559
$701$	−17.4827	−0.660312	−0.330156	−	0.943926i	$-0.607101\pi$
$701$	−17.4827	−0.660312	−0.330156	+	0.943926i	$0.607101\pi$
$702$	6.59414	0.248880
$703$	9.44162	0.356098
$704$	1.00000	0.0376889
$705$	−4.00000	−0.150649
$706$	−26.5308	−0.998500
$707$	−18.5032	−0.695886
$708$	4.59414	0.172658
$709$	42.0000	1.57734	0.788672	−	0.614815i	$-0.210769\pi$
$709$	42.0000	1.57734	0.788672	+	0.614815i	$0.210769\pi$
$710$	−12.5941	−0.472650
$711$	2.42640	0.0909970
$712$	4.16774	0.156193
$713$	−1.38360	−0.0518162
$714$	−3.08387	−0.115411
$715$	−6.59414	−0.246607
$716$	20.0768	0.750307
$717$	−17.3150	−0.646639
$718$	9.31495	0.347631
$719$	−12.5941	−0.469682	−0.234841	−	0.972034i	$-0.575457\pi$
$719$	−12.5941	−0.469682	−0.234841	+	0.972034i	$0.575457\pi$
$720$	1.00000	0.0372678
$721$	−10.3079	−0.383887
$722$	16.5238	0.614951
$723$	17.4194	0.647833
$724$	3.51027	0.130458
$725$	3.51027	0.130368
$726$	−1.00000	−0.0371135
$727$	−24.7396	−0.917542	−0.458771	−	0.888555i	$-0.651710\pi$
$727$	−24.7396	−0.917542	−0.458771	+	0.888555i	$0.651710\pi$
$728$	−20.3355	−0.753683
$729$	1.00000	0.0370370
$730$	3.57360	0.132265
$731$	3.08387	0.114061
$732$	2.00000	0.0739221
$733$	15.7003	0.579903	0.289951	−	0.957041i	$-0.406361\pi$
$733$	15.7003	0.579903	0.289951	+	0.957041i	$0.406361\pi$
$734$	20.2088	0.745921
$735$	2.51027	0.0925927
$736$	−0.916128	−0.0337689
$737$	−3.14721	−0.115929
$738$	−4.16774	−0.153417
$739$	20.5941	0.757568	0.378784	−	0.925485i	$-0.376342\pi$
$739$	20.5941	0.757568	0.378784	+	0.925485i	$0.376342\pi$
$740$	6.00000	0.220564
$741$	−10.3766	−0.381193
$742$	−8.00000	−0.293689
$743$	1.95893	0.0718660	0.0359330	−	0.999354i	$-0.488560\pi$
$743$	1.95893	0.0718660	0.0359330	+	0.999354i	$0.488560\pi$
$744$	1.51027	0.0553691
$745$	4.16774	0.152694
$746$	1.86802	0.0683930
$747$	16.3355	0.597684
$748$	−1.00000	−0.0365636
$749$	20.0135	0.731277
$750$	−1.00000	−0.0365148
$751$	−11.3425	−0.413895	−0.206947	−	0.978352i	$-0.566353\pi$
$751$	−11.3425	−0.413895	−0.206947	+	0.978352i	$0.566353\pi$
$752$	−4.00000	−0.145865
$753$	−3.27919	−0.119500
$754$	23.1472	0.842972
$755$	4.00000	0.145575
$756$	−3.08387	−0.112159
$757$	−10.5308	−0.382749	−0.191374	−	0.981517i	$-0.561294\pi$
$757$	−10.5308	−0.382749	−0.191374	+	0.981517i	$0.561294\pi$
$758$	1.18828	0.0431604
$759$	0.916128	0.0332533
$760$	−1.57360	−0.0570806
$761$	18.1402	0.657581	0.328790	−	0.944403i	$-0.393359\pi$
$761$	18.1402	0.657581	0.328790	+	0.944403i	$0.393359\pi$
$762$	−15.3560	−0.556290
$763$	−11.8182	−0.427847
$764$	16.9930	0.614784
$765$	−1.00000	−0.0361551
$766$	−27.2294	−0.983837
$767$	−30.2944	−1.09387
$768$	1.00000	0.0360844
$769$	13.6645	0.492755	0.246377	−	0.969174i	$-0.420760\pi$
$769$	13.6645	0.492755	0.246377	+	0.969174i	$0.420760\pi$
$770$	3.08387	0.111135
$771$	−0.489731	−0.0176372
$772$	7.57360	0.272580
$773$	−42.0768	−1.51340	−0.756699	−	0.653763i	$-0.773189\pi$
$773$	−42.0768	−1.51340	−0.756699	+	0.653763i	$0.773189\pi$
$774$	3.08387	0.110848
$775$	−1.51027	−0.0542505
$776$	2.65748	0.0953978
$777$	−18.5032	−0.663800
$778$	29.0974	1.04319
$779$	6.55838	0.234978
$780$	−6.59414	−0.236108
$781$	12.5941	0.450654
$782$	0.916128	0.0327607
$783$	3.51027	0.125447
$784$	2.51027	0.0896525
$785$	10.0000	0.356915
$786$	16.3355	0.582668
$787$	−25.7771	−0.918855	−0.459427	−	0.888215i	$-0.651945\pi$
$787$	−25.7771	−0.918855	−0.459427	+	0.888215i	$0.651945\pi$
$788$	−19.3150	−0.688067
$789$	3.34252	0.118997
$790$	−2.42640	−0.0863273
$791$	−27.0205	−0.960740
$792$	−1.00000	−0.0355335
$793$	−13.1883	−0.468330
$794$	21.1472	0.750486
$795$	−2.59414	−0.0920047
$796$	11.1472	0.395102
$797$	−20.2997	−0.719053	−0.359527	−	0.933135i	$-0.617062\pi$
$797$	−20.2997	−0.719053	−0.359527	+	0.933135i	$0.617062\pi$
$798$	4.85279	0.171787
$799$	4.00000	0.141510
$800$	−1.00000	−0.0353553
$801$	−4.16774	−0.147260
$802$	21.4194	0.756344
$803$	−3.57360	−0.126110
$804$	−3.14721	−0.110993
$805$	−2.82522	−0.0995759
$806$	−9.95893	−0.350788
$807$	−14.3355	−0.504633
$808$	−6.00000	−0.211079
$809$	18.3355	0.644641	0.322321	−	0.946631i	$-0.395537\pi$
$809$	18.3355	0.644641	0.322321	+	0.946631i	$0.395537\pi$
$810$	−1.00000	−0.0351364
$811$	31.5648	1.10839	0.554196	−	0.832386i	$-0.313026\pi$
$811$	31.5648	1.10839	0.554196	+	0.832386i	$0.313026\pi$
$812$	−10.8252	−0.379891
$813$	10.4897	0.367891
$814$	−6.00000	−0.210300
$815$	11.6780	0.409063
$816$	−1.00000	−0.0350070
$817$	−4.85279	−0.169778
$818$	−26.5443	−0.928100
$819$	20.3355	0.710580
$820$	4.16774	0.145544
$821$	32.3901	1.13042	0.565211	−	0.824947i	$-0.308795\pi$
$821$	32.3901	1.13042	0.565211	+	0.824947i	$0.308795\pi$
$822$	−16.8252	−0.586847
$823$	−13.6504	−0.475824	−0.237912	−	0.971287i	$-0.576463\pi$
$823$	−13.6504	−0.475824	−0.237912	+	0.971287i	$0.576463\pi$
$824$	−3.34252	−0.116442
$825$	1.00000	0.0348155
$826$	14.1677	0.492959
$827$	12.7841	0.444548	0.222274	−	0.974984i	$-0.428652\pi$
$827$	12.7841	0.444548	0.222274	+	0.974984i	$0.428652\pi$
$828$	0.916128	0.0318376
$829$	−49.3830	−1.71514	−0.857572	−	0.514364i	$-0.828028\pi$
$829$	−49.3830	−1.71514	−0.857572	+	0.514364i	$0.828028\pi$
$830$	−16.3355	−0.567013
$831$	−1.14721	−0.0397962
$832$	−6.59414	−0.228611
$833$	−2.51027	−0.0869757
$834$	−2.36306	−0.0818261
$835$	−20.2088	−0.699355
$836$	1.57360	0.0544242
$837$	−1.51027	−0.0522025
$838$	19.0340	0.657520
$839$	−28.0768	−0.969320	−0.484660	−	0.874703i	$-0.661057\pi$
$839$	−28.0768	−0.969320	−0.484660	+	0.874703i	$0.661057\pi$
$840$	3.08387	0.106404
$841$	−16.6780	−0.575104
$842$	11.3150	0.389939
$843$	−9.80468	−0.337691
$844$	5.63694	0.194031
$845$	30.4827	1.04864
$846$	4.00000	0.137523
$847$	−3.08387	−0.105963
$848$	−2.59414	−0.0890832
$849$	31.6915	1.08765
$850$	1.00000	0.0342997
$851$	5.49677	0.188427
$852$	12.5941	0.431468
$853$	−6.19532	−0.212124	−0.106062	−	0.994360i	$-0.533824\pi$
$853$	−6.19532	−0.212124	−0.106062	+	0.994360i	$0.533824\pi$
$854$	6.16774	0.211056
$855$	1.57360	0.0538161
$856$	6.48973	0.221814
$857$	44.6434	1.52499	0.762495	−	0.646994i	$-0.223974\pi$
$857$	44.6434	1.52499	0.762495	+	0.646994i	$0.223974\pi$
$858$	6.59414	0.225120
$859$	−28.9930	−0.989227	−0.494614	−	0.869113i	$-0.664690\pi$
$859$	−28.9930	−0.989227	−0.494614	+	0.869113i	$0.664690\pi$
$860$	−3.08387	−0.105159
$861$	−12.8528	−0.438022
$862$	28.0135	0.954144
$863$	47.8182	1.62775	0.813875	−	0.581040i	$-0.197354\pi$
$863$	47.8182	1.62775	0.813875	+	0.581040i	$0.197354\pi$
$864$	−1.00000	−0.0340207
$865$	1.14721	0.0390062
$866$	−24.8387	−0.844054
$867$	1.00000	0.0339618
$868$	4.65748	0.158085
$869$	2.42640	0.0823099
$870$	−3.51027	−0.119009
$871$	20.7531	0.703193
$872$	−3.83226	−0.129777
$873$	−2.65748	−0.0899419
$874$	−1.44162	−0.0487636
$875$	−3.08387	−0.104254
$876$	−3.57360	−0.120741
$877$	−53.1607	−1.79511	−0.897555	−	0.440903i	$-0.854658\pi$
$877$	−53.1607	−1.79511	−0.897555	+	0.440903i	$0.854658\pi$
$878$	−5.70027	−0.192375
$879$	−16.6986	−0.563228
$880$	1.00000	0.0337100
$881$	−17.6012	−0.592999	−0.296499	−	0.955033i	$-0.595819\pi$
$881$	−17.6012	−0.592999	−0.296499	+	0.955033i	$0.595819\pi$
$882$	−2.51027	−0.0845251
$883$	2.62990	0.0885033	0.0442517	−	0.999020i	$-0.485910\pi$
$883$	2.62990	0.0885033	0.0442517	+	0.999020i	$0.485910\pi$
$884$	6.59414	0.221785
$885$	4.59414	0.154430
$886$	−30.2311	−1.01563
$887$	−45.5238	−1.52854	−0.764269	−	0.644897i	$-0.776900\pi$
$887$	−45.5238	−1.52854	−0.764269	+	0.644897i	$0.776900\pi$
$888$	−6.00000	−0.201347
$889$	−47.3560	−1.58827
$890$	4.16774	0.139703
$891$	1.00000	0.0335013
$892$	3.34252	0.111916
$893$	−6.29441	−0.210635
$894$	−4.16774	−0.139390
$895$	20.0768	0.671095
$896$	3.08387	0.103025
$897$	−6.04107	−0.201706
$898$	−11.1249	−0.371244
$899$	−5.30145	−0.176813
$900$	1.00000	0.0333333
$901$	2.59414	0.0864234
$902$	−4.16774	−0.138771
$903$	9.51027	0.316482
$904$	−8.76189	−0.291416
$905$	3.51027	0.116685
$906$	−4.00000	−0.132891
$907$	27.2874	0.906063	0.453031	−	0.891495i	$-0.350343\pi$
$907$	27.2874	0.906063	0.453031	+	0.891495i	$0.350343\pi$
$908$	−6.48973	−0.215369
$909$	6.00000	0.199007
$910$	−20.3355	−0.674115
$911$	29.2381	0.968702	0.484351	−	0.874874i	$-0.339056\pi$
$911$	29.2381	0.968702	0.484351	+	0.874874i	$0.339056\pi$
$912$	1.57360	0.0521072
$913$	16.3355	0.540626
$914$	10.0000	0.330771
$915$	2.00000	0.0661180
$916$	18.2088	0.601636
$917$	50.3766	1.66358
$918$	1.00000	0.0330049
$919$	35.0340	1.15567	0.577833	−	0.816155i	$-0.303898\pi$
$919$	35.0340	1.15567	0.577833	+	0.816155i	$0.303898\pi$
$920$	−0.916128	−0.0302038
$921$	10.7619	0.354616
$922$	33.2294	1.09435
$923$	−83.0475	−2.73354
$924$	−3.08387	−0.101452
$925$	6.00000	0.197279
$926$	−8.00000	−0.262896
$927$	3.34252	0.109783
$928$	−3.51027	−0.115230
$929$	16.7484	0.549497	0.274748	−	0.961516i	$-0.411405\pi$
$929$	16.7484	0.549497	0.274748	+	0.961516i	$0.411405\pi$
$930$	1.51027	0.0495237
$931$	3.95017	0.129462
$932$	−0.489731	−0.0160417
$933$	−25.0563	−0.820306
$934$	−32.2857	−1.05642
$935$	−1.00000	−0.0327035
$936$	6.59414	0.215536
$937$	−18.0000	−0.588034	−0.294017	−	0.955800i	$-0.594992\pi$
$937$	−18.0000	−0.588034	−0.294017	+	0.955800i	$0.594992\pi$
$938$	−9.70559	−0.316899
$939$	−7.38360	−0.240955
$940$	−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
$943$	3.81819	0.124337
$944$	4.59414	0.149527
$945$	−3.08387	−0.100318
$946$	3.08387	0.100265
$947$	30.2499	0.982989	0.491495	−	0.870881i	$-0.336451\pi$
$947$	30.2499	0.982989	0.491495	+	0.870881i	$0.336451\pi$
$948$	2.42640	0.0788057
$949$	23.5648	0.764947
$950$	−1.57360	−0.0510544
$951$	16.8252	0.545595
$952$	−3.08387	−0.0999489
$953$	7.18828	0.232851	0.116426	−	0.993199i	$-0.462856\pi$
$953$	7.18828	0.232851	0.116426	+	0.993199i	$0.462856\pi$
$954$	2.59414	0.0839884
$955$	16.9930	0.549879
$956$	−17.3150	−0.560006
$957$	3.51027	0.113471
$958$	−4.78415	−0.154569
$959$	−51.8868	−1.67551
$960$	1.00000	0.0322749
$961$	−28.7191	−0.926422
$962$	39.5648	1.27562
$963$	−6.48973	−0.209129
$964$	17.4194	0.561040
$965$	7.57360	0.243803
$966$	2.82522	0.0909000
$967$	9.06161	0.291402	0.145701	−	0.989329i	$-0.453456\pi$
$967$	9.06161	0.291402	0.145701	+	0.989329i	$0.453456\pi$
$968$	−1.00000	−0.0321412
$969$	−1.57360	−0.0505514
$970$	2.65748	0.0853264
$971$	−59.4329	−1.90729	−0.953646	−	0.300932i	$-0.902702\pi$
$971$	−59.4329	−1.90729	−0.953646	+	0.300932i	$0.902702\pi$
$972$	1.00000	0.0320750
$973$	−7.28738	−0.233623
$974$	30.8387	0.988136
$975$	−6.59414	−0.211182
$976$	2.00000	0.0640184
$977$	23.8593	0.763325	0.381663	−	0.924302i	$-0.375352\pi$
$977$	23.8593	0.763325	0.381663	+	0.924302i	$0.375352\pi$
$978$	−11.6780	−0.373422
$979$	−4.16774	−0.133202
$980$	2.51027	0.0801876
$981$	3.83226	0.122354
$982$	0	0
$983$	41.5871	1.32642	0.663211	−	0.748432i	$-0.269193\pi$
$983$	41.5871	1.32642	0.663211	+	0.748432i	$0.269193\pi$
$984$	−4.16774	−0.132863
$985$	−19.3150	−0.615426
$986$	3.51027	0.111790
$987$	12.3355	0.392643
$988$	−10.3766	−0.330122
$989$	−2.82522	−0.0898368
$990$	−1.00000	−0.0317821
$991$	−55.6780	−1.76867	−0.884335	−	0.466853i	$-0.845388\pi$
$991$	−55.6780	−1.76867	−0.884335	+	0.466853i	$0.845388\pi$
$992$	1.51027	0.0479511
$993$	−13.3836	−0.424716
$994$	38.8387	1.23189
$995$	11.1472	0.353390
$996$	16.3355	0.517610
$997$	−37.0340	−1.17288	−0.586440	−	0.809993i	$-0.699471\pi$
$997$	−37.0340	−1.17288	−0.586440	+	0.809993i	$0.699471\pi$
$998$	−39.4827	−1.24980
$999$	6.00000	0.189832

Twists

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

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
5610.2.a.ca.1.1	✓	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)

\(f(q)\)	\(=\)	\(q-1.00000 q^{2} +1.00000 q^{3} +1.00000 q^{4} +1.00000 q^{5} -1.00000 q^{6} -3.08387 q^{7} -1.00000 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q-1.00000 q^{2} +1.00000 q^{3} +1.00000 q^{4} +1.00000 q^{5} -1.00000 q^{6} -3.08387 q^{7} -1.00000 q^{8} +1.00000 q^{9} -1.00000 q^{10} +1.00000 q^{11} +1.00000 q^{12} -6.59414 q^{13} +3.08387 q^{14} +1.00000 q^{15} +1.00000 q^{16} -1.00000 q^{17} -1.00000 q^{18} +1.57360 q^{19} +1.00000 q^{20} -3.08387 q^{21} -1.00000 q^{22} +0.916128 q^{23} -1.00000 q^{24} +1.00000 q^{25} +6.59414 q^{26} +1.00000 q^{27} -3.08387 q^{28} +3.51027 q^{29} -1.00000 q^{30} -1.51027 q^{31} -1.00000 q^{32} +1.00000 q^{33} +1.00000 q^{34} -3.08387 q^{35} +1.00000 q^{36} +6.00000 q^{37} -1.57360 q^{38} -6.59414 q^{39} -1.00000 q^{40} +4.16774 q^{41} +3.08387 q^{42} -3.08387 q^{43} +1.00000 q^{44} +1.00000 q^{45} -0.916128 q^{46} -4.00000 q^{47} +1.00000 q^{48} +2.51027 q^{49} -1.00000 q^{50} -1.00000 q^{51} -6.59414 q^{52} -2.59414 q^{53} -1.00000 q^{54} +1.00000 q^{55} +3.08387 q^{56} +1.57360 q^{57} -3.51027 q^{58} +4.59414 q^{59} +1.00000 q^{60} +2.00000 q^{61} +1.51027 q^{62} -3.08387 q^{63} +1.00000 q^{64} -6.59414 q^{65} -1.00000 q^{66} -3.14721 q^{67} -1.00000 q^{68} +0.916128 q^{69} +3.08387 q^{70} +12.5941 q^{71} -1.00000 q^{72} -3.57360 q^{73} -6.00000 q^{74} +1.00000 q^{75} +1.57360 q^{76} -3.08387 q^{77} +6.59414 q^{78} +2.42640 q^{79} +1.00000 q^{80} +1.00000 q^{81} -4.16774 q^{82} +16.3355 q^{83} -3.08387 q^{84} -1.00000 q^{85} +3.08387 q^{86} +3.51027 q^{87} -1.00000 q^{88} -4.16774 q^{89} -1.00000 q^{90} +20.3355 q^{91} +0.916128 q^{92} -1.51027 q^{93} +4.00000 q^{94} +1.57360 q^{95} -1.00000 q^{96} -2.65748 q^{97} -2.51027 q^{98} +1.00000 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 3 q - 3 q^{2} + 3 q^{3} + 3 q^{4} + 3 q^{5} - 3 q^{6} + q^{7} - 3 q^{8} + 3 q^{9}+O(q^{10}) \) 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

Introduction

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