LMFDB - Embedded newform 5610.2.a.bz.1.2

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:	$1$
Dimension:	$3$
Coefficient field:	3.3.148.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{3} - x^{2} - 3x + 1 $ x^3 - x^2 - 3*x + 1
Coefficient ring:	$\Z[a_1, \ldots, a_{19}]$
Coefficient ring index:	$ 2^{2} $
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.2
Root			$0.311108$ 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)

$f(q)$	$=$	$q-1.00000 q^{2} +1.00000 q^{3} +1.00000 q^{4} +1.00000 q^{5} -1.00000 q^{6} -1.37778 q^{7} -1.00000 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q-1.00000 q^{2} +1.00000 q^{3} +1.00000 q^{4} +1.00000 q^{5} -1.00000 q^{6} -1.37778 q^{7} -1.00000 q^{8} +1.00000 q^{9} -1.00000 q^{10} -1.00000 q^{11} +1.00000 q^{12} -0.622216 q^{13} +1.37778 q^{14} +1.00000 q^{15} +1.00000 q^{16} -1.00000 q^{17} -1.00000 q^{18} -4.42864 q^{19} +1.00000 q^{20} -1.37778 q^{21} +1.00000 q^{22} -4.42864 q^{23} -1.00000 q^{24} +1.00000 q^{25} +0.622216 q^{26} +1.00000 q^{27} -1.37778 q^{28} +9.61285 q^{29} -1.00000 q^{30} +4.85728 q^{31} -1.00000 q^{32} -1.00000 q^{33} +1.00000 q^{34} -1.37778 q^{35} +1.00000 q^{36} -3.24443 q^{37} +4.42864 q^{38} -0.622216 q^{39} -1.00000 q^{40} -11.8064 q^{41} +1.37778 q^{42} +6.23506 q^{43} -1.00000 q^{44} +1.00000 q^{45} +4.42864 q^{46} +4.00000 q^{47} +1.00000 q^{48} -5.10171 q^{49} -1.00000 q^{50} -1.00000 q^{51} -0.622216 q^{52} +6.42864 q^{53} -1.00000 q^{54} -1.00000 q^{55} +1.37778 q^{56} -4.42864 q^{57} -9.61285 q^{58} -4.13335 q^{59} +1.00000 q^{60} -10.0000 q^{61} -4.85728 q^{62} -1.37778 q^{63} +1.00000 q^{64} -0.622216 q^{65} +1.00000 q^{66} +14.6637 q^{67} -1.00000 q^{68} -4.42864 q^{69} +1.37778 q^{70} -6.23506 q^{71} -1.00000 q^{72} -4.23506 q^{73} +3.24443 q^{74} +1.00000 q^{75} -4.42864 q^{76} +1.37778 q^{77} +0.622216 q^{78} -17.2859 q^{79} +1.00000 q^{80} +1.00000 q^{81} +11.8064 q^{82} +10.1017 q^{83} -1.37778 q^{84} -1.00000 q^{85} -6.23506 q^{86} +9.61285 q^{87} +1.00000 q^{88} -3.24443 q^{89} -1.00000 q^{90} +0.857279 q^{91} -4.42864 q^{92} +4.85728 q^{93} -4.00000 q^{94} -4.42864 q^{95} -1.00000 q^{96} -2.29529 q^{97} +5.10171 q^{98} -1.00000 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 3 q - 3 q^{2} + 3 q^{3} + 3 q^{4} + 3 q^{5} - 3 q^{6} - 4 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 - 4 * 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} - 4 q^{7} - 3 q^{8} + 3 q^{9} - 3 q^{10} - 3 q^{11} + 3 q^{12} - 2 q^{13} + 4 q^{14} + 3 q^{15} + 3 q^{16} - 3 q^{17} - 3 q^{18} + 3 q^{20} - 4 q^{21} + 3 q^{22} - 3 q^{24} + 3 q^{25} + 2 q^{26} + 3 q^{27} - 4 q^{28} + 2 q^{29} - 3 q^{30} - 12 q^{31} - 3 q^{32} - 3 q^{33} + 3 q^{34} - 4 q^{35} + 3 q^{36} - 10 q^{37} - 2 q^{39} - 3 q^{40} - 22 q^{41} + 4 q^{42} - 8 q^{43} - 3 q^{44} + 3 q^{45} + 12 q^{47} + 3 q^{48} + 11 q^{49} - 3 q^{50} - 3 q^{51} - 2 q^{52} + 6 q^{53} - 3 q^{54} - 3 q^{55} + 4 q^{56} - 2 q^{58} - 12 q^{59} + 3 q^{60} - 30 q^{61} + 12 q^{62} - 4 q^{63} + 3 q^{64} - 2 q^{65} + 3 q^{66} + 4 q^{67} - 3 q^{68} + 4 q^{70} + 8 q^{71} - 3 q^{72} + 14 q^{73} + 10 q^{74} + 3 q^{75} + 4 q^{77} + 2 q^{78} - 12 q^{79} + 3 q^{80} + 3 q^{81} + 22 q^{82} + 4 q^{83} - 4 q^{84} - 3 q^{85} + 8 q^{86} + 2 q^{87} + 3 q^{88} - 10 q^{89} - 3 q^{90} - 24 q^{91} - 12 q^{93} - 12 q^{94} - 3 q^{96} + 6 q^{97} - 11 q^{98} - 3 q^{99}+O(q^{100}) $ 3 * q - 3 * q^2 + 3 * q^3 + 3 * q^4 + 3 * q^5 - 3 * q^6 - 4 * q^7 - 3 * q^8 + 3 * q^9 - 3 * q^10 - 3 * q^11 + 3 * q^12 - 2 * q^13 + 4 * q^14 + 3 * q^15 + 3 * q^16 - 3 * q^17 - 3 * q^18 + 3 * q^20 - 4 * q^21 + 3 * q^22 - 3 * q^24 + 3 * q^25 + 2 * q^26 + 3 * q^27 - 4 * q^28 + 2 * q^29 - 3 * q^30 - 12 * q^31 - 3 * q^32 - 3 * q^33 + 3 * q^34 - 4 * q^35 + 3 * q^36 - 10 * q^37 - 2 * q^39 - 3 * q^40 - 22 * q^41 + 4 * q^42 - 8 * q^43 - 3 * q^44 + 3 * q^45 + 12 * q^47 + 3 * q^48 + 11 * q^49 - 3 * q^50 - 3 * q^51 - 2 * q^52 + 6 * q^53 - 3 * q^54 - 3 * q^55 + 4 * q^56 - 2 * q^58 - 12 * q^59 + 3 * q^60 - 30 * q^61 + 12 * q^62 - 4 * q^63 + 3 * q^64 - 2 * q^65 + 3 * q^66 + 4 * q^67 - 3 * q^68 + 4 * q^70 + 8 * q^71 - 3 * q^72 + 14 * q^73 + 10 * q^74 + 3 * q^75 + 4 * q^77 + 2 * q^78 - 12 * q^79 + 3 * q^80 + 3 * q^81 + 22 * q^82 + 4 * q^83 - 4 * q^84 - 3 * q^85 + 8 * q^86 + 2 * q^87 + 3 * q^88 - 10 * q^89 - 3 * q^90 - 24 * q^91 - 12 * q^93 - 12 * q^94 - 3 * q^96 + 6 * q^97 - 11 * q^98 - 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
$7$	−1.37778	−0.520754	−0.260377	−	0.965507i	$-0.583847\pi$
$7$	−1.37778	−0.520754	−0.260377	+	0.965507i	$0.583847\pi$
$8$	−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
$13$	−0.622216	−0.172572	−0.0862858	−	0.996270i	$-0.527500\pi$
$13$	−0.622216	−0.172572	−0.0862858	+	0.996270i	$0.527500\pi$
$14$	1.37778	0.368228
$15$	1.00000	0.258199
$16$	1.00000	0.250000
$17$	−1.00000	−0.242536
$17$	−1.00000	−0.242536
$18$	−1.00000	−0.235702
$19$	−4.42864	−1.01600	−0.508000	−	0.861357i	$-0.669615\pi$
$19$	−4.42864	−1.01600	−0.508000	+	0.861357i	$0.669615\pi$
$20$	1.00000	0.223607
$21$	−1.37778	−0.300657
$22$	1.00000	0.213201
$23$	−4.42864	−0.923435	−0.461718	−	0.887027i	$-0.652767\pi$
$23$	−4.42864	−0.923435	−0.461718	+	0.887027i	$0.652767\pi$
$24$	−1.00000	−0.204124
$25$	1.00000	0.200000
$26$	0.622216	0.122027
$27$	1.00000	0.192450
$28$	−1.37778	−0.260377
$29$	9.61285	1.78506	0.892531	−	0.450987i	$-0.148928\pi$
$29$	9.61285	1.78506	0.892531	+	0.450987i	$0.148928\pi$
$30$	−1.00000	−0.182574
$31$	4.85728	0.872393	0.436197	−	0.899851i	$-0.356325\pi$
$31$	4.85728	0.872393	0.436197	+	0.899851i	$0.356325\pi$
$32$	−1.00000	−0.176777
$33$	−1.00000	−0.174078
$34$	1.00000	0.171499
$35$	−1.37778	−0.232888
$36$	1.00000	0.166667
$37$	−3.24443	−0.533381	−0.266691	−	0.963782i	$-0.585930\pi$
$37$	−3.24443	−0.533381	−0.266691	+	0.963782i	$0.585930\pi$
$38$	4.42864	0.718420
$39$	−0.622216	−0.0996342
$40$	−1.00000	−0.158114
$41$	−11.8064	−1.84385	−0.921927	−	0.387364i	$-0.873386\pi$
$41$	−11.8064	−1.84385	−0.921927	+	0.387364i	$0.873386\pi$
$42$	1.37778	0.212597
$43$	6.23506	0.950838	0.475419	−	0.879759i	$-0.342296\pi$
$43$	6.23506	0.950838	0.475419	+	0.879759i	$0.342296\pi$
$44$	−1.00000	−0.150756
$45$	1.00000	0.149071
$46$	4.42864	0.652967
$47$	4.00000	0.583460	0.291730	−	0.956501i	$-0.405769\pi$
$47$	4.00000	0.583460	0.291730	+	0.956501i	$0.405769\pi$
$48$	1.00000	0.144338
$49$	−5.10171	−0.728816
$50$	−1.00000	−0.141421
$51$	−1.00000	−0.140028
$52$	−0.622216	−0.0862858
$53$	6.42864	0.883042	0.441521	−	0.897251i	$-0.354439\pi$
$53$	6.42864	0.883042	0.441521	+	0.897251i	$0.354439\pi$
$54$	−1.00000	−0.136083
$55$	−1.00000	−0.134840
$56$	1.37778	0.184114
$57$	−4.42864	−0.586588
$58$	−9.61285	−1.26223
$59$	−4.13335	−0.538117	−0.269058	−	0.963124i	$-0.586712\pi$
$59$	−4.13335	−0.538117	−0.269058	+	0.963124i	$0.586712\pi$
$60$	1.00000	0.129099
$61$	−10.0000	−1.28037	−0.640184	−	0.768221i	$-0.721142\pi$
$61$	−10.0000	−1.28037	−0.640184	+	0.768221i	$0.721142\pi$
$62$	−4.85728	−0.616875
$63$	−1.37778	−0.173585
$64$	1.00000	0.125000
$65$	−0.622216	−0.0771764
$66$	1.00000	0.123091
$67$	14.6637	1.79146	0.895728	−	0.444602i	$-0.146655\pi$
$67$	14.6637	1.79146	0.895728	+	0.444602i	$0.146655\pi$
$68$	−1.00000	−0.121268
$69$	−4.42864	−0.533146
$70$	1.37778	0.164677
$71$	−6.23506	−0.739966	−0.369983	−	0.929039i	$-0.620636\pi$
$71$	−6.23506	−0.739966	−0.369983	+	0.929039i	$0.620636\pi$
$72$	−1.00000	−0.117851
$73$	−4.23506	−0.495677	−0.247838	−	0.968801i	$-0.579720\pi$
$73$	−4.23506	−0.495677	−0.247838	+	0.968801i	$0.579720\pi$
$74$	3.24443	0.377157
$75$	1.00000	0.115470
$76$	−4.42864	−0.508000
$77$	1.37778	0.157013
$78$	0.622216	0.0704520
$79$	−17.2859	−1.94482	−0.972409	−	0.233283i	$-0.925053\pi$
$79$	−17.2859	−1.94482	−0.972409	+	0.233283i	$0.925053\pi$
$80$	1.00000	0.111803
$81$	1.00000	0.111111
$82$	11.8064	1.30380
$83$	10.1017	1.10881	0.554403	−	0.832248i	$-0.312946\pi$
$83$	10.1017	1.10881	0.554403	+	0.832248i	$0.312946\pi$
$84$	−1.37778	−0.150329
$85$	−1.00000	−0.108465
$86$	−6.23506	−0.672344
$87$	9.61285	1.03061
$88$	1.00000	0.106600
$89$	−3.24443	−0.343909	−0.171955	−	0.985105i	$-0.555008\pi$
$89$	−3.24443	−0.343909	−0.171955	+	0.985105i	$0.555008\pi$
$90$	−1.00000	−0.105409
$91$	0.857279	0.0898673
$92$	−4.42864	−0.461718
$93$	4.85728	0.503676
$94$	−4.00000	−0.412568
$95$	−4.42864	−0.454369
$96$	−1.00000	−0.102062
$97$	−2.29529	−0.233051	−0.116526	−	0.993188i	$-0.537176\pi$
$97$	−2.29529	−0.233051	−0.116526	+	0.993188i	$0.537176\pi$
$98$	5.10171	0.515351
$99$	−1.00000	−0.100504
$100$	1.00000	0.100000
$101$	−5.05086	−0.502579	−0.251289	−	0.967912i	$-0.580855\pi$
$101$	−5.05086	−0.502579	−0.251289	+	0.967912i	$0.580855\pi$
$102$	1.00000	0.0990148
$103$	−17.7146	−1.74547	−0.872734	−	0.488197i	$-0.837655\pi$
$103$	−17.7146	−1.74547	−0.872734	+	0.488197i	$0.837655\pi$
$104$	0.622216	0.0610133
$105$	−1.37778	−0.134458
$106$	−6.42864	−0.624405
$107$	−15.3461	−1.48357	−0.741784	−	0.670639i	$-0.766020\pi$
$107$	−15.3461	−1.48357	−0.741784	+	0.670639i	$0.766020\pi$
$108$	1.00000	0.0962250
$109$	−1.14272	−0.109453	−0.0547264	−	0.998501i	$-0.517429\pi$
$109$	−1.14272	−0.109453	−0.0547264	+	0.998501i	$0.517429\pi$
$110$	1.00000	0.0953463
$111$	−3.24443	−0.307948
$112$	−1.37778	−0.130188
$113$	−7.67307	−0.721822	−0.360911	−	0.932600i	$-0.617534\pi$
$113$	−7.67307	−0.721822	−0.360911	+	0.932600i	$0.617534\pi$
$114$	4.42864	0.414780
$115$	−4.42864	−0.412973
$116$	9.61285	0.892531
$117$	−0.622216	−0.0575239
$118$	4.13335	0.380506
$119$	1.37778	0.126301
$120$	−1.00000	−0.0912871
$121$	1.00000	0.0909091
$122$	10.0000	0.905357
$123$	−11.8064	−1.06455
$124$	4.85728	0.436197
$125$	1.00000	0.0894427
$126$	1.37778	0.122743
$127$	−16.8573	−1.49584	−0.747921	−	0.663788i	$-0.768948\pi$
$127$	−16.8573	−1.49584	−0.747921	+	0.663788i	$0.768948\pi$
$128$	−1.00000	−0.0883883
$129$	6.23506	0.548967
$130$	0.622216	0.0545719
$131$	−15.6128	−1.36410	−0.682050	−	0.731305i	$-0.738912\pi$
$131$	−15.6128	−1.36410	−0.682050	+	0.731305i	$0.738912\pi$
$132$	−1.00000	−0.0870388
$133$	6.10171	0.529085
$134$	−14.6637	−1.26675
$135$	1.00000	0.0860663
$136$	1.00000	0.0857493
$137$	16.9590	1.44890	0.724452	−	0.689325i	$-0.242093\pi$
$137$	16.9590	1.44890	0.724452	+	0.689325i	$0.242093\pi$
$138$	4.42864	0.376991
$139$	9.71456	0.823978	0.411989	−	0.911189i	$-0.364834\pi$
$139$	9.71456	0.823978	0.411989	+	0.911189i	$0.364834\pi$
$140$	−1.37778	−0.116444
$141$	4.00000	0.336861
$142$	6.23506	0.523235
$143$	0.622216	0.0520323
$144$	1.00000	0.0833333
$145$	9.61285	0.798304
$146$	4.23506	0.350496
$147$	−5.10171	−0.420782
$148$	−3.24443	−0.266691
$149$	6.29529	0.515730	0.257865	−	0.966181i	$-0.416981\pi$
$149$	6.29529	0.515730	0.257865	+	0.966181i	$0.416981\pi$
$150$	−1.00000	−0.0816497
$151$	6.10171	0.496550	0.248275	−	0.968690i	$-0.420136\pi$
$151$	6.10171	0.496550	0.248275	+	0.968690i	$0.420136\pi$
$152$	4.42864	0.359210
$153$	−1.00000	−0.0808452
$154$	−1.37778	−0.111025
$155$	4.85728	0.390146
$156$	−0.622216	−0.0498171
$157$	10.2953	0.821653	0.410827	−	0.911713i	$-0.365240\pi$
$157$	10.2953	0.821653	0.410827	+	0.911713i	$0.365240\pi$
$158$	17.2859	1.37519
$159$	6.42864	0.509824
$160$	−1.00000	−0.0790569
$161$	6.10171	0.480882
$162$	−1.00000	−0.0785674
$163$	−10.3684	−0.812117	−0.406059	−	0.913847i	$-0.633097\pi$
$163$	−10.3684	−0.812117	−0.406059	+	0.913847i	$0.633097\pi$
$164$	−11.8064	−0.921927
$165$	−1.00000	−0.0778499
$166$	−10.1017	−0.784045
$167$	−16.4701	−1.27450	−0.637248	−	0.770659i	$-0.719927\pi$
$167$	−16.4701	−1.27450	−0.637248	+	0.770659i	$0.719927\pi$
$168$	1.37778	0.106298
$169$	−12.6128	−0.970219
$170$	1.00000	0.0766965
$171$	−4.42864	−0.338667
$172$	6.23506	0.475419
$173$	21.2257	1.61376	0.806880	−	0.590716i	$-0.201154\pi$
$173$	21.2257	1.61376	0.806880	+	0.590716i	$0.201154\pi$
$174$	−9.61285	−0.728748
$175$	−1.37778	−0.104151
$176$	−1.00000	−0.0753778
$177$	−4.13335	−0.310682
$178$	3.24443	0.243180
$179$	4.13335	0.308941	0.154471	−	0.987997i	$-0.450633\pi$
$179$	4.13335	0.308941	0.154471	+	0.987997i	$0.450633\pi$
$180$	1.00000	0.0745356
$181$	−17.6128	−1.30915	−0.654576	−	0.755996i	$-0.727153\pi$
$181$	−17.6128	−1.30915	−0.654576	+	0.755996i	$0.727153\pi$
$182$	−0.857279	−0.0635457
$183$	−10.0000	−0.739221
$184$	4.42864	0.326484
$185$	−3.24443	−0.238535
$186$	−4.85728	−0.356153
$187$	1.00000	0.0731272
$188$	4.00000	0.291730
$189$	−1.37778	−0.100219
$190$	4.42864	0.321287
$191$	0.387152	0.0280134	0.0140067	−	0.999902i	$-0.495541\pi$
$191$	0.387152	0.0280134	0.0140067	+	0.999902i	$0.495541\pi$
$192$	1.00000	0.0721688
$193$	−14.9906	−1.07905	−0.539525	−	0.841970i	$-0.681396\pi$
$193$	−14.9906	−1.07905	−0.539525	+	0.841970i	$0.681396\pi$
$194$	2.29529	0.164792
$195$	−0.622216	−0.0445578
$196$	−5.10171	−0.364408
$197$	−11.1240	−0.792551	−0.396276	−	0.918132i	$-0.629698\pi$
$197$	−11.1240	−0.792551	−0.396276	+	0.918132i	$0.629698\pi$
$198$	1.00000	0.0710669
$199$	−26.3684	−1.86921	−0.934604	−	0.355691i	$-0.884246\pi$
$199$	−26.3684	−1.86921	−0.934604	+	0.355691i	$0.884246\pi$
$200$	−1.00000	−0.0707107
$201$	14.6637	1.03430
$202$	5.05086	0.355377
$203$	−13.2444	−0.929577
$204$	−1.00000	−0.0700140
$205$	−11.8064	−0.824596
$206$	17.7146	1.23423
$207$	−4.42864	−0.307812
$208$	−0.622216	−0.0431429
$209$	4.42864	0.306335
$210$	1.37778	0.0950762
$211$	3.61285	0.248719	0.124359	−	0.992237i	$-0.460312\pi$
$211$	3.61285	0.248719	0.124359	+	0.992237i	$0.460312\pi$
$212$	6.42864	0.441521
$213$	−6.23506	−0.427220
$214$	15.3461	1.04904
$215$	6.23506	0.425228
$216$	−1.00000	−0.0680414
$217$	−6.69228	−0.454302
$218$	1.14272	0.0773948
$219$	−4.23506	−0.286179
$220$	−1.00000	−0.0674200
$221$	0.622216	0.0418548
$222$	3.24443	0.217752
$223$	−25.9813	−1.73983	−0.869917	−	0.493198i	$-0.835828\pi$
$223$	−25.9813	−1.73983	−0.869917	+	0.493198i	$0.835828\pi$
$224$	1.37778	0.0920571
$225$	1.00000	0.0666667
$226$	7.67307	0.510405
$227$	2.10171	0.139495	0.0697477	−	0.997565i	$-0.477781\pi$
$227$	2.10171	0.139495	0.0697477	+	0.997565i	$0.477781\pi$
$228$	−4.42864	−0.293294
$229$	6.85728	0.453142	0.226571	−	0.973995i	$-0.427249\pi$
$229$	6.85728	0.453142	0.226571	+	0.973995i	$0.427249\pi$
$230$	4.42864	0.292016
$231$	1.37778	0.0906516
$232$	−9.61285	−0.631114
$233$	4.36842	0.286184	0.143092	−	0.989709i	$-0.454295\pi$
$233$	4.36842	0.286184	0.143092	+	0.989709i	$0.454295\pi$
$234$	0.622216	0.0406755
$235$	4.00000	0.260931
$236$	−4.13335	−0.269058
$237$	−17.2859	−1.12284
$238$	−1.37778	−0.0893085
$239$	−17.9813	−1.16311	−0.581556	−	0.813507i	$-0.697556\pi$
$239$	−17.9813	−1.16311	−0.581556	+	0.813507i	$0.697556\pi$
$240$	1.00000	0.0645497
$241$	2.04149	0.131504	0.0657519	−	0.997836i	$-0.479055\pi$
$241$	2.04149	0.131504	0.0657519	+	0.997836i	$0.479055\pi$
$242$	−1.00000	−0.0642824
$243$	1.00000	0.0641500
$244$	−10.0000	−0.640184
$245$	−5.10171	−0.325936
$246$	11.8064	0.752750
$247$	2.75557	0.175333
$248$	−4.85728	−0.308438
$249$	10.1017	0.640170
$250$	−1.00000	−0.0632456
$251$	10.2351	0.646031	0.323016	−	0.946394i	$-0.395303\pi$
$251$	10.2351	0.646031	0.323016	+	0.946394i	$0.395303\pi$
$252$	−1.37778	−0.0867923
$253$	4.42864	0.278426
$254$	16.8573	1.05772
$255$	−1.00000	−0.0626224
$256$	1.00000	0.0625000
$257$	15.2444	0.950921	0.475461	−	0.879737i	$-0.342281\pi$
$257$	15.2444	0.950921	0.475461	+	0.879737i	$0.342281\pi$
$258$	−6.23506	−0.388178
$259$	4.47013	0.277760
$260$	−0.622216	−0.0385882
$261$	9.61285	0.595020
$262$	15.6128	0.964565
$263$	−17.9813	−1.10877	−0.554386	−	0.832260i	$-0.687047\pi$
$263$	−17.9813	−1.10877	−0.554386	+	0.832260i	$0.687047\pi$
$264$	1.00000	0.0615457
$265$	6.42864	0.394908
$266$	−6.10171	−0.374120
$267$	−3.24443	−0.198556
$268$	14.6637	0.895728
$269$	14.0000	0.853595	0.426798	−	0.904347i	$-0.359642\pi$
$269$	14.0000	0.853595	0.426798	+	0.904347i	$0.359642\pi$
$270$	−1.00000	−0.0608581
$271$	−0.266706	−0.0162012	−0.00810062	−	0.999967i	$-0.502579\pi$
$271$	−0.266706	−0.0162012	−0.00810062	+	0.999967i	$0.502579\pi$
$272$	−1.00000	−0.0606339
$273$	0.857279	0.0518849
$274$	−16.9590	−1.02453
$275$	−1.00000	−0.0603023
$276$	−4.42864	−0.266573
$277$	2.38715	0.143430	0.0717150	−	0.997425i	$-0.477153\pi$
$277$	2.38715	0.143430	0.0717150	+	0.997425i	$0.477153\pi$
$278$	−9.71456	−0.582640
$279$	4.85728	0.290798
$280$	1.37778	0.0823384
$281$	−14.4701	−0.863215	−0.431608	−	0.902061i	$-0.642054\pi$
$281$	−14.4701	−0.863215	−0.431608	+	0.902061i	$0.642054\pi$
$282$	−4.00000	−0.238197
$283$	−27.3461	−1.62556	−0.812780	−	0.582571i	$-0.802047\pi$
$283$	−27.3461	−1.62556	−0.812780	+	0.582571i	$0.802047\pi$
$284$	−6.23506	−0.369983
$285$	−4.42864	−0.262330
$286$	−0.622216	−0.0367924
$287$	16.2667	0.960193
$288$	−1.00000	−0.0589256
$289$	1.00000	0.0588235
$290$	−9.61285	−0.564486
$291$	−2.29529	−0.134552
$292$	−4.23506	−0.247838
$293$	10.0000	0.584206	0.292103	−	0.956387i	$-0.405645\pi$
$293$	10.0000	0.584206	0.292103	+	0.956387i	$0.405645\pi$
$294$	5.10171	0.297538
$295$	−4.13335	−0.240653
$296$	3.24443	0.188579
$297$	−1.00000	−0.0580259
$298$	−6.29529	−0.364676
$299$	2.75557	0.159359
$300$	1.00000	0.0577350
$301$	−8.59057	−0.495152
$302$	−6.10171	−0.351114
$303$	−5.05086	−0.290164
$304$	−4.42864	−0.254000
$305$	−10.0000	−0.572598
$306$	1.00000	0.0571662
$307$	23.0923	1.31795	0.658975	−	0.752165i	$-0.270990\pi$
$307$	23.0923	1.31795	0.658975	+	0.752165i	$0.270990\pi$
$308$	1.37778	0.0785066
$309$	−17.7146	−1.00775
$310$	−4.85728	−0.275875
$311$	32.8069	1.86031	0.930154	−	0.367169i	$-0.119673\pi$
$311$	32.8069	1.86031	0.930154	+	0.367169i	$0.119673\pi$
$312$	0.622216	0.0352260
$313$	0.193576	0.0109416	0.00547079	−	0.999985i	$-0.498259\pi$
$313$	0.193576	0.0109416	0.00547079	+	0.999985i	$0.498259\pi$
$314$	−10.2953	−0.580997
$315$	−1.37778	−0.0776294
$316$	−17.2859	−0.972409
$317$	22.0830	1.24030	0.620152	−	0.784482i	$-0.287071\pi$
$317$	22.0830	1.24030	0.620152	+	0.784482i	$0.287071\pi$
$318$	−6.42864	−0.360500
$319$	−9.61285	−0.538216
$320$	1.00000	0.0559017
$321$	−15.3461	−0.856538
$322$	−6.10171	−0.340035
$323$	4.42864	0.246416
$324$	1.00000	0.0555556
$325$	−0.622216	−0.0345143
$326$	10.3684	0.574253
$327$	−1.14272	−0.0631926
$328$	11.8064	0.651901
$329$	−5.51114	−0.303839
$330$	1.00000	0.0550482
$331$	−5.12399	−0.281640	−0.140820	−	0.990035i	$-0.544974\pi$
$331$	−5.12399	−0.281640	−0.140820	+	0.990035i	$0.544974\pi$
$332$	10.1017	0.554403
$333$	−3.24443	−0.177794
$334$	16.4701	0.901205
$335$	14.6637	0.801164
$336$	−1.37778	−0.0751643
$337$	−1.74620	−0.0951216	−0.0475608	−	0.998868i	$-0.515145\pi$
$337$	−1.74620	−0.0951216	−0.0475608	+	0.998868i	$0.515145\pi$
$338$	12.6128	0.686048
$339$	−7.67307	−0.416744
$340$	−1.00000	−0.0542326
$341$	−4.85728	−0.263036
$342$	4.42864	0.239473
$343$	16.6735	0.900287
$344$	−6.23506	−0.336172
$345$	−4.42864	−0.238430
$346$	−21.2257	−1.14110
$347$	35.8163	1.92272	0.961359	−	0.275298i	$-0.0887764\pi$
$347$	35.8163	1.92272	0.961359	+	0.275298i	$0.0887764\pi$
$348$	9.61285	0.515303
$349$	−18.1619	−0.972186	−0.486093	−	0.873907i	$-0.661578\pi$
$349$	−18.1619	−0.972186	−0.486093	+	0.873907i	$0.661578\pi$
$350$	1.37778	0.0736457
$351$	−0.622216	−0.0332114
$352$	1.00000	0.0533002
$353$	6.47013	0.344370	0.172185	−	0.985065i	$-0.444917\pi$
$353$	6.47013	0.344370	0.172185	+	0.985065i	$0.444917\pi$
$354$	4.13335	0.219685
$355$	−6.23506	−0.330923
$356$	−3.24443	−0.171955
$357$	1.37778	0.0729201
$358$	−4.13335	−0.218454
$359$	−34.5718	−1.82463	−0.912316	−	0.409487i	$-0.865708\pi$
$359$	−34.5718	−1.82463	−0.912316	+	0.409487i	$0.865708\pi$
$360$	−1.00000	−0.0527046
$361$	0.612848	0.0322551
$362$	17.6128	0.925711
$363$	1.00000	0.0524864
$364$	0.857279	0.0449336
$365$	−4.23506	−0.221673
$366$	10.0000	0.522708
$367$	26.2766	1.37162	0.685812	−	0.727778i	$-0.259447\pi$
$367$	26.2766	1.37162	0.685812	+	0.727778i	$0.259447\pi$
$368$	−4.42864	−0.230859
$369$	−11.8064	−0.614618
$370$	3.24443	0.168670
$371$	−8.85728	−0.459847
$372$	4.85728	0.251838
$373$	−13.0094	−0.673600	−0.336800	−	0.941576i	$-0.609345\pi$
$373$	−13.0094	−0.673600	−0.336800	+	0.941576i	$0.609345\pi$
$374$	−1.00000	−0.0517088
$375$	1.00000	0.0516398
$376$	−4.00000	−0.206284
$377$	−5.98126	−0.308051
$378$	1.37778	0.0708656
$379$	4.85728	0.249502	0.124751	−	0.992188i	$-0.460187\pi$
$379$	4.85728	0.249502	0.124751	+	0.992188i	$0.460187\pi$
$380$	−4.42864	−0.227184
$381$	−16.8573	−0.863625
$382$	−0.387152	−0.0198084
$383$	−10.9590	−0.559978	−0.279989	−	0.960003i	$-0.590331\pi$
$383$	−10.9590	−0.559978	−0.279989	+	0.960003i	$0.590331\pi$
$384$	−1.00000	−0.0510310
$385$	1.37778	0.0702184
$386$	14.9906	0.763003
$387$	6.23506	0.316946
$388$	−2.29529	−0.116526
$389$	13.4795	0.683438	0.341719	−	0.939802i	$-0.388991\pi$
$389$	13.4795	0.683438	0.341719	+	0.939802i	$0.388991\pi$
$390$	0.622216	0.0315071
$391$	4.42864	0.223966
$392$	5.10171	0.257675
$393$	−15.6128	−0.787564
$394$	11.1240	0.560418
$395$	−17.2859	−0.869749
$396$	−1.00000	−0.0502519
$397$	13.8796	0.696595	0.348297	−	0.937384i	$-0.386760\pi$
$397$	13.8796	0.696595	0.348297	+	0.937384i	$0.386760\pi$
$398$	26.3684	1.32173
$399$	6.10171	0.305468
$400$	1.00000	0.0500000
$401$	1.86665	0.0932159	0.0466079	−	0.998913i	$-0.485159\pi$
$401$	1.86665	0.0932159	0.0466079	+	0.998913i	$0.485159\pi$
$402$	−14.6637	−0.731359
$403$	−3.02227	−0.150550
$404$	−5.05086	−0.251289
$405$	1.00000	0.0496904
$406$	13.2444	0.657310
$407$	3.24443	0.160820
$408$	1.00000	0.0495074
$409$	5.87955	0.290725	0.145363	−	0.989378i	$-0.453565\pi$
$409$	5.87955	0.290725	0.145363	+	0.989378i	$0.453565\pi$
$410$	11.8064	0.583078
$411$	16.9590	0.836525
$412$	−17.7146	−0.872734
$413$	5.69487	0.280226
$414$	4.42864	0.217656
$415$	10.1017	0.495873
$416$	0.622216	0.0305066
$417$	9.71456	0.475724
$418$	−4.42864	−0.216612
$419$	10.1017	0.493501	0.246750	−	0.969079i	$-0.420637\pi$
$419$	10.1017	0.493501	0.246750	+	0.969079i	$0.420637\pi$
$420$	−1.37778	−0.0672290
$421$	−9.22570	−0.449633	−0.224816	−	0.974401i	$-0.572178\pi$
$421$	−9.22570	−0.449633	−0.224816	+	0.974401i	$0.572178\pi$
$422$	−3.61285	−0.175871
$423$	4.00000	0.194487
$424$	−6.42864	−0.312202
$425$	−1.00000	−0.0485071
$426$	6.23506	0.302090
$427$	13.7778	0.666757
$428$	−15.3461	−0.741784
$429$	0.622216	0.0300409
$430$	−6.23506	−0.300681
$431$	35.4005	1.70518	0.852592	−	0.522577i	$-0.175029\pi$
$431$	35.4005	1.70518	0.852592	+	0.522577i	$0.175029\pi$
$432$	1.00000	0.0481125
$433$	38.2034	1.83594	0.917970	−	0.396651i	$-0.129828\pi$
$433$	38.2034	1.83594	0.917970	+	0.396651i	$0.129828\pi$
$434$	6.69228	0.321240
$435$	9.61285	0.460901
$436$	−1.14272	−0.0547264
$437$	19.6128	0.938210
$438$	4.23506	0.202359
$439$	−19.7748	−0.943799	−0.471899	−	0.881652i	$-0.656431\pi$
$439$	−19.7748	−0.943799	−0.471899	+	0.881652i	$0.656431\pi$
$440$	1.00000	0.0476731
$441$	−5.10171	−0.242939
$442$	−0.622216	−0.0295958
$443$	−16.4286	−0.780548	−0.390274	−	0.920699i	$-0.627620\pi$
$443$	−16.4286	−0.780548	−0.390274	+	0.920699i	$0.627620\pi$
$444$	−3.24443	−0.153974
$445$	−3.24443	−0.153801
$446$	25.9813	1.23025
$447$	6.29529	0.297757
$448$	−1.37778	−0.0650942
$449$	−9.47949	−0.447365	−0.223683	−	0.974662i	$-0.571808\pi$
$449$	−9.47949	−0.447365	−0.223683	+	0.974662i	$0.571808\pi$
$450$	−1.00000	−0.0471405
$451$	11.8064	0.555943
$452$	−7.67307	−0.360911
$453$	6.10171	0.286683
$454$	−2.10171	−0.0986381
$455$	0.857279	0.0401899
$456$	4.42864	0.207390
$457$	19.4479	0.909732	0.454866	−	0.890560i	$-0.349687\pi$
$457$	19.4479	0.909732	0.454866	+	0.890560i	$0.349687\pi$
$458$	−6.85728	−0.320420
$459$	−1.00000	−0.0466760
$460$	−4.42864	−0.206486
$461$	−25.5210	−1.18863	−0.594315	−	0.804232i	$-0.702577\pi$
$461$	−25.5210	−1.18863	−0.594315	+	0.804232i	$0.702577\pi$
$462$	−1.37778	−0.0641003
$463$	−33.4479	−1.55445	−0.777227	−	0.629221i	$-0.783374\pi$
$463$	−33.4479	−1.55445	−0.777227	+	0.629221i	$0.783374\pi$
$464$	9.61285	0.446265
$465$	4.85728	0.225251
$466$	−4.36842	−0.202363
$467$	1.46965	0.0680073	0.0340037	−	0.999422i	$-0.489174\pi$
$467$	1.46965	0.0680073	0.0340037	+	0.999422i	$0.489174\pi$
$468$	−0.622216	−0.0287619
$469$	−20.2034	−0.932907
$470$	−4.00000	−0.184506
$471$	10.2953	0.474382
$472$	4.13335	0.190253
$473$	−6.23506	−0.286689
$474$	17.2859	0.793969
$475$	−4.42864	−0.203200
$476$	1.37778	0.0631506
$477$	6.42864	0.294347
$478$	17.9813	0.822444
$479$	−8.29529	−0.379021	−0.189511	−	0.981879i	$-0.560690\pi$
$479$	−8.29529	−0.379021	−0.189511	+	0.981879i	$0.560690\pi$
$480$	−1.00000	−0.0456435
$481$	2.01874	0.0920464
$482$	−2.04149	−0.0929872
$483$	6.10171	0.277637
$484$	1.00000	0.0454545
$485$	−2.29529	−0.104224
$486$	−1.00000	−0.0453609
$487$	−14.0731	−0.637714	−0.318857	−	0.947803i	$-0.603299\pi$
$487$	−14.0731	−0.637714	−0.318857	+	0.947803i	$0.603299\pi$
$488$	10.0000	0.452679
$489$	−10.3684	−0.468876
$490$	5.10171	0.230472
$491$	−18.2766	−0.824809	−0.412405	−	0.911001i	$-0.635311\pi$
$491$	−18.2766	−0.824809	−0.412405	+	0.911001i	$0.635311\pi$
$492$	−11.8064	−0.532275
$493$	−9.61285	−0.432941
$494$	−2.75557	−0.123979
$495$	−1.00000	−0.0449467
$496$	4.85728	0.218098
$497$	8.59057	0.385340
$498$	−10.1017	−0.452668
$499$	−22.4889	−1.00674	−0.503370	−	0.864071i	$-0.667907\pi$
$499$	−22.4889	−1.00674	−0.503370	+	0.864071i	$0.667907\pi$
$500$	1.00000	0.0447214
$501$	−16.4701	−0.735831
$502$	−10.2351	−0.456813
$503$	36.9403	1.64708	0.823542	−	0.567255i	$-0.191995\pi$
$503$	36.9403	1.64708	0.823542	+	0.567255i	$0.191995\pi$
$504$	1.37778	0.0613714
$505$	−5.05086	−0.224760
$506$	−4.42864	−0.196877
$507$	−12.6128	−0.560156
$508$	−16.8573	−0.747921
$509$	18.9906	0.841745	0.420872	−	0.907120i	$-0.361724\pi$
$509$	18.9906	0.841745	0.420872	+	0.907120i	$0.361724\pi$
$510$	1.00000	0.0442807
$511$	5.83500	0.258125
$512$	−1.00000	−0.0441942
$513$	−4.42864	−0.195529
$514$	−15.2444	−0.672403
$515$	−17.7146	−0.780597
$516$	6.23506	0.274483
$517$	−4.00000	−0.175920
$518$	−4.47013	−0.196406
$519$	21.2257	0.931705
$520$	0.622216	0.0272860
$521$	4.88892	0.214188	0.107094	−	0.994249i	$-0.465845\pi$
$521$	4.88892	0.214188	0.107094	+	0.994249i	$0.465845\pi$
$522$	−9.61285	−0.420743
$523$	−7.00937	−0.306498	−0.153249	−	0.988188i	$-0.548974\pi$
$523$	−7.00937	−0.306498	−0.153249	+	0.988188i	$0.548974\pi$
$524$	−15.6128	−0.682050
$525$	−1.37778	−0.0601314
$526$	17.9813	0.784020
$527$	−4.85728	−0.211586
$528$	−1.00000	−0.0435194
$529$	−3.38715	−0.147267
$530$	−6.42864	−0.279242
$531$	−4.13335	−0.179372
$532$	6.10171	0.264543
$533$	7.34614	0.318197
$534$	3.24443	0.140400
$535$	−15.3461	−0.663472
$536$	−14.6637	−0.633375
$537$	4.13335	0.178367
$538$	−14.0000	−0.603583
$539$	5.10171	0.219746
$540$	1.00000	0.0430331
$541$	7.71456	0.331675	0.165837	−	0.986153i	$-0.446967\pi$
$541$	7.71456	0.331675	0.165837	+	0.986153i	$0.446967\pi$
$542$	0.266706	0.0114560
$543$	−17.6128	−0.755840
$544$	1.00000	0.0428746
$545$	−1.14272	−0.0489488
$546$	−0.857279	−0.0366882
$547$	−28.7368	−1.22870	−0.614349	−	0.789034i	$-0.710581\pi$
$547$	−28.7368	−1.22870	−0.614349	+	0.789034i	$0.710581\pi$
$548$	16.9590	0.724452
$549$	−10.0000	−0.426790
$550$	1.00000	0.0426401
$551$	−42.5718	−1.81362
$552$	4.42864	0.188495
$553$	23.8163	1.01277
$554$	−2.38715	−0.101420
$555$	−3.24443	−0.137718
$556$	9.71456	0.411989
$557$	11.8983	0.504147	0.252073	−	0.967708i	$-0.418888\pi$
$557$	11.8983	0.504147	0.252073	+	0.967708i	$0.418888\pi$
$558$	−4.85728	−0.205625
$559$	−3.87955	−0.164088
$560$	−1.37778	−0.0582220
$561$	1.00000	0.0422200
$562$	14.4701	0.610385
$563$	−7.61285	−0.320843	−0.160422	−	0.987049i	$-0.551285\pi$
$563$	−7.61285	−0.320843	−0.160422	+	0.987049i	$0.551285\pi$
$564$	4.00000	0.168430
$565$	−7.67307	−0.322809
$566$	27.3461	1.14944
$567$	−1.37778	−0.0578615
$568$	6.23506	0.261617
$569$	−17.7333	−0.743418	−0.371709	−	0.928349i	$-0.621228\pi$
$569$	−17.7333	−0.743418	−0.371709	+	0.928349i	$0.621228\pi$
$570$	4.42864	0.185495
$571$	−26.2480	−1.09844	−0.549222	−	0.835677i	$-0.685076\pi$
$571$	−26.2480	−1.09844	−0.549222	+	0.835677i	$0.685076\pi$
$572$	0.622216	0.0260161
$573$	0.387152	0.0161735
$574$	−16.2667	−0.678959
$575$	−4.42864	−0.184687
$576$	1.00000	0.0416667
$577$	−34.7368	−1.44611	−0.723057	−	0.690789i	$-0.757263\pi$
$577$	−34.7368	−1.44611	−0.723057	+	0.690789i	$0.757263\pi$
$578$	−1.00000	−0.0415945
$579$	−14.9906	−0.622989
$580$	9.61285	0.399152
$581$	−13.9180	−0.577415
$582$	2.29529	0.0951427
$583$	−6.42864	−0.266247
$584$	4.23506	0.175248
$585$	−0.622216	−0.0257255
$586$	−10.0000	−0.413096
$587$	17.8193	0.735482	0.367741	−	0.929928i	$-0.380131\pi$
$587$	17.8193	0.735482	0.367741	+	0.929928i	$0.380131\pi$
$588$	−5.10171	−0.210391
$589$	−21.5111	−0.886351
$590$	4.13335	0.170167
$591$	−11.1240	−0.457580
$592$	−3.24443	−0.133345
$593$	−8.10171	−0.332697	−0.166349	−	0.986067i	$-0.553198\pi$
$593$	−8.10171	−0.332697	−0.166349	+	0.986067i	$0.553198\pi$
$594$	1.00000	0.0410305
$595$	1.37778	0.0564837
$596$	6.29529	0.257865
$597$	−26.3684	−1.07919
$598$	−2.75557	−0.112684
$599$	18.6351	0.761410	0.380705	−	0.924696i	$-0.375681\pi$
$599$	18.6351	0.761410	0.380705	+	0.924696i	$0.375681\pi$
$600$	−1.00000	−0.0408248
$601$	12.7971	0.522003	0.261001	−	0.965338i	$-0.415947\pi$
$601$	12.7971	0.522003	0.261001	+	0.965338i	$0.415947\pi$
$602$	8.59057	0.350126
$603$	14.6637	0.597152
$604$	6.10171	0.248275
$605$	1.00000	0.0406558
$606$	5.05086	0.205177
$607$	−32.6035	−1.32333	−0.661667	−	0.749798i	$-0.730151\pi$
$607$	−32.6035	−1.32333	−0.661667	+	0.749798i	$0.730151\pi$
$608$	4.42864	0.179605
$609$	−13.2444	−0.536691
$610$	10.0000	0.404888
$611$	−2.48886	−0.100689
$612$	−1.00000	−0.0404226
$613$	−20.2351	−0.817287	−0.408643	−	0.912694i	$-0.633998\pi$
$613$	−20.2351	−0.817287	−0.408643	+	0.912694i	$0.633998\pi$
$614$	−23.0923	−0.931931
$615$	−11.8064	−0.476081
$616$	−1.37778	−0.0555125
$617$	−35.3689	−1.42390	−0.711949	−	0.702231i	$-0.752187\pi$
$617$	−35.3689	−1.42390	−0.711949	+	0.702231i	$0.752187\pi$
$618$	17.7146	0.712584
$619$	−24.7368	−0.994257	−0.497129	−	0.867677i	$-0.665612\pi$
$619$	−24.7368	−0.994257	−0.497129	+	0.867677i	$0.665612\pi$
$620$	4.85728	0.195073
$621$	−4.42864	−0.177715
$622$	−32.8069	−1.31544
$623$	4.47013	0.179092
$624$	−0.622216	−0.0249086
$625$	1.00000	0.0400000
$626$	−0.193576	−0.00773686
$627$	4.42864	0.176863
$628$	10.2953	0.410827
$629$	3.24443	0.129364
$630$	1.37778	0.0548922
$631$	−4.47013	−0.177953	−0.0889765	−	0.996034i	$-0.528360\pi$
$631$	−4.47013	−0.177953	−0.0889765	+	0.996034i	$0.528360\pi$
$632$	17.2859	0.687597
$633$	3.61285	0.143598
$634$	−22.0830	−0.877027
$635$	−16.8573	−0.668961
$636$	6.42864	0.254912
$637$	3.17436	0.125773
$638$	9.61285	0.380576
$639$	−6.23506	−0.246655
$640$	−1.00000	−0.0395285
$641$	6.07007	0.239753	0.119877	−	0.992789i	$-0.461750\pi$
$641$	6.07007	0.239753	0.119877	+	0.992789i	$0.461750\pi$
$642$	15.3461	0.605664
$643$	34.1017	1.34484	0.672420	−	0.740170i	$-0.265255\pi$
$643$	34.1017	1.34484	0.672420	+	0.740170i	$0.265255\pi$
$644$	6.10171	0.240441
$645$	6.23506	0.245505
$646$	−4.42864	−0.174242
$647$	35.8163	1.40808	0.704041	−	0.710159i	$-0.251377\pi$
$647$	35.8163	1.40808	0.704041	+	0.710159i	$0.251377\pi$
$648$	−1.00000	−0.0392837
$649$	4.13335	0.162248
$650$	0.622216	0.0244053
$651$	−6.69228	−0.262291
$652$	−10.3684	−0.406059
$653$	−7.51114	−0.293934	−0.146967	−	0.989141i	$-0.546951\pi$
$653$	−7.51114	−0.293934	−0.146967	+	0.989141i	$0.546951\pi$
$654$	1.14272	0.0446839
$655$	−15.6128	−0.610044
$656$	−11.8064	−0.460963
$657$	−4.23506	−0.165226
$658$	5.51114	0.214847
$659$	−17.3363	−0.675326	−0.337663	−	0.941267i	$-0.609636\pi$
$659$	−17.3363	−0.675326	−0.337663	+	0.941267i	$0.609636\pi$
$660$	−1.00000	−0.0389249
$661$	−4.22216	−0.164223	−0.0821114	−	0.996623i	$-0.526166\pi$
$661$	−4.22216	−0.164223	−0.0821114	+	0.996623i	$0.526166\pi$
$662$	5.12399	0.199149
$663$	0.622216	0.0241649
$664$	−10.1017	−0.392022
$665$	6.10171	0.236614
$666$	3.24443	0.125719
$667$	−42.5718	−1.64839
$668$	−16.4701	−0.637248
$669$	−25.9813	−1.00449
$670$	−14.6637	−0.566508
$671$	10.0000	0.386046
$672$	1.37778	0.0531492
$673$	8.23506	0.317438	0.158719	−	0.987324i	$-0.449264\pi$
$673$	8.23506	0.317438	0.158719	+	0.987324i	$0.449264\pi$
$674$	1.74620	0.0672611
$675$	1.00000	0.0384900
$676$	−12.6128	−0.485110
$677$	−11.1240	−0.427529	−0.213765	−	0.976885i	$-0.568573\pi$
$677$	−11.1240	−0.427529	−0.213765	+	0.976885i	$0.568573\pi$
$678$	7.67307	0.294683
$679$	3.16241	0.121362
$680$	1.00000	0.0383482
$681$	2.10171	0.0805377
$682$	4.85728	0.185995
$683$	14.4889	0.554401	0.277200	−	0.960812i	$-0.410593\pi$
$683$	14.4889	0.554401	0.277200	+	0.960812i	$0.410593\pi$
$684$	−4.42864	−0.169333
$685$	16.9590	0.647970
$686$	−16.6735	−0.636599
$687$	6.85728	0.261622
$688$	6.23506	0.237710
$689$	−4.00000	−0.152388
$690$	4.42864	0.168595
$691$	−11.7333	−0.446356	−0.223178	−	0.974778i	$-0.571643\pi$
$691$	−11.7333	−0.446356	−0.223178	+	0.974778i	$0.571643\pi$
$692$	21.2257	0.806880
$693$	1.37778	0.0523377
$694$	−35.8163	−1.35957
$695$	9.71456	0.368494
$696$	−9.61285	−0.364374
$697$	11.8064	0.447200
$698$	18.1619	0.687439
$699$	4.36842	0.165229
$700$	−1.37778	−0.0520754
$701$	−4.00984	−0.151450	−0.0757249	−	0.997129i	$-0.524127\pi$
$701$	−4.00984	−0.151450	−0.0757249	+	0.997129i	$0.524127\pi$
$702$	0.622216	0.0234840
$703$	14.3684	0.541915
$704$	−1.00000	−0.0376889
$705$	4.00000	0.150649
$706$	−6.47013	−0.243506
$707$	6.95899	0.261720
$708$	−4.13335	−0.155341
$709$	−17.0223	−0.639285	−0.319642	−	0.947538i	$-0.603563\pi$
$709$	−17.0223	−0.639285	−0.319642	+	0.947538i	$0.603563\pi$
$710$	6.23506	0.233998
$711$	−17.2859	−0.648273
$712$	3.24443	0.121590
$713$	−21.5111	−0.805598
$714$	−1.37778	−0.0515623
$715$	0.622216	0.0232695
$716$	4.13335	0.154471
$717$	−17.9813	−0.671523
$718$	34.5718	1.29021
$719$	32.1334	1.19837	0.599186	−	0.800610i	$-0.295491\pi$
$719$	32.1334	1.19837	0.599186	+	0.800610i	$0.295491\pi$
$720$	1.00000	0.0372678
$721$	24.4068	0.908958
$722$	−0.612848	−0.0228078
$723$	2.04149	0.0759237
$724$	−17.6128	−0.654576
$725$	9.61285	0.357012
$726$	−1.00000	−0.0371135
$727$	42.6548	1.58198	0.790990	−	0.611829i	$-0.209566\pi$
$727$	42.6548	1.58198	0.790990	+	0.611829i	$0.209566\pi$
$728$	−0.857279	−0.0317729
$729$	1.00000	0.0370370
$730$	4.23506	0.156747
$731$	−6.23506	−0.230612
$732$	−10.0000	−0.369611
$733$	26.2163	0.968322	0.484161	−	0.874979i	$-0.339125\pi$
$733$	26.2163	0.968322	0.484161	+	0.874979i	$0.339125\pi$
$734$	−26.2766	−0.969885
$735$	−5.10171	−0.188179
$736$	4.42864	0.163242
$737$	−14.6637	−0.540144
$738$	11.8064	0.434600
$739$	−18.5303	−0.681650	−0.340825	−	0.940127i	$-0.610706\pi$
$739$	−18.5303	−0.681650	−0.340825	+	0.940127i	$0.610706\pi$
$740$	−3.24443	−0.119268
$741$	2.75557	0.101228
$742$	8.85728	0.325161
$743$	−8.38715	−0.307695	−0.153847	−	0.988095i	$-0.549166\pi$
$743$	−8.38715	−0.307695	−0.153847	+	0.988095i	$0.549166\pi$
$744$	−4.85728	−0.178076
$745$	6.29529	0.230641
$746$	13.0094	0.476307
$747$	10.1017	0.369602
$748$	1.00000	0.0365636
$749$	21.1437	0.772573
$750$	−1.00000	−0.0365148
$751$	−4.59057	−0.167512	−0.0837562	−	0.996486i	$-0.526692\pi$
$751$	−4.59057	−0.167512	−0.0837562	+	0.996486i	$0.526692\pi$
$752$	4.00000	0.145865
$753$	10.2351	0.372986
$754$	5.98126	0.217825
$755$	6.10171	0.222064
$756$	−1.37778	−0.0501095
$757$	5.23459	0.190254	0.0951271	−	0.995465i	$-0.469674\pi$
$757$	5.23459	0.190254	0.0951271	+	0.995465i	$0.469674\pi$
$758$	−4.85728	−0.176424
$759$	4.42864	0.160749
$760$	4.42864	0.160644
$761$	43.5941	1.58029	0.790143	−	0.612923i	$-0.210006\pi$
$761$	43.5941	1.58029	0.790143	+	0.612923i	$0.210006\pi$
$762$	16.8573	0.610675
$763$	1.57442	0.0569979
$764$	0.387152	0.0140067
$765$	−1.00000	−0.0361551
$766$	10.9590	0.395964
$767$	2.57184	0.0928636
$768$	1.00000	0.0360844
$769$	37.9625	1.36896	0.684482	−	0.729030i	$-0.260028\pi$
$769$	37.9625	1.36896	0.684482	+	0.729030i	$0.260028\pi$
$770$	−1.37778	−0.0496519
$771$	15.2444	0.549015
$772$	−14.9906	−0.539525
$773$	−22.6321	−0.814019	−0.407009	−	0.913424i	$-0.633428\pi$
$773$	−22.6321	−0.814019	−0.407009	+	0.913424i	$0.633428\pi$
$774$	−6.23506	−0.224115
$775$	4.85728	0.174479
$776$	2.29529	0.0823960
$777$	4.47013	0.160365
$778$	−13.4795	−0.483263
$779$	52.2864	1.87335
$780$	−0.622216	−0.0222789
$781$	6.23506	0.223108
$782$	−4.42864	−0.158368
$783$	9.61285	0.343535
$784$	−5.10171	−0.182204
$785$	10.2953	0.367455
$786$	15.6128	0.556892
$787$	20.1463	0.718137	0.359068	−	0.933311i	$-0.383095\pi$
$787$	20.1463	0.718137	0.359068	+	0.933311i	$0.383095\pi$
$788$	−11.1240	−0.396276
$789$	−17.9813	−0.640150
$790$	17.2859	0.615005
$791$	10.5718	0.375891
$792$	1.00000	0.0355335
$793$	6.22216	0.220955
$794$	−13.8796	−0.492567
$795$	6.42864	0.228000
$796$	−26.3684	−0.934604
$797$	31.5526	1.11765	0.558826	−	0.829285i	$-0.311252\pi$
$797$	31.5526	1.11765	0.558826	+	0.829285i	$0.311252\pi$
$798$	−6.10171	−0.215998
$799$	−4.00000	−0.141510
$800$	−1.00000	−0.0353553
$801$	−3.24443	−0.114636
$802$	−1.86665	−0.0659136
$803$	4.23506	0.149452
$804$	14.6637	0.517149
$805$	6.10171	0.215057
$806$	3.02227	0.106455
$807$	14.0000	0.492823
$808$	5.05086	0.177688
$809$	−35.3560	−1.24305	−0.621525	−	0.783394i	$-0.713487\pi$
$809$	−35.3560	−1.24305	−0.621525	+	0.783394i	$0.713487\pi$
$810$	−1.00000	−0.0351364
$811$	−32.8573	−1.15378	−0.576888	−	0.816824i	$-0.695733\pi$
$811$	−32.8573	−1.15378	−0.576888	+	0.816824i	$0.695733\pi$
$812$	−13.2444	−0.464788
$813$	−0.266706	−0.00935379
$814$	−3.24443	−0.113717
$815$	−10.3684	−0.363190
$816$	−1.00000	−0.0350070
$817$	−27.6128	−0.966051
$818$	−5.87955	−0.205574
$819$	0.857279	0.0299558
$820$	−11.8064	−0.412298
$821$	35.3274	1.23293	0.616467	−	0.787380i	$-0.288563\pi$
$821$	35.3274	1.23293	0.616467	+	0.787380i	$0.288563\pi$
$822$	−16.9590	−0.591513
$823$	7.17130	0.249976	0.124988	−	0.992158i	$-0.460111\pi$
$823$	7.17130	0.249976	0.124988	+	0.992158i	$0.460111\pi$
$824$	17.7146	0.617116
$825$	−1.00000	−0.0348155
$826$	−5.69487	−0.198150
$827$	−20.2667	−0.704742	−0.352371	−	0.935860i	$-0.614625\pi$
$827$	−20.2667	−0.704742	−0.352371	+	0.935860i	$0.614625\pi$
$828$	−4.42864	−0.153906
$829$	−26.5906	−0.923529	−0.461764	−	0.887003i	$-0.652783\pi$
$829$	−26.5906	−0.923529	−0.461764	+	0.887003i	$0.652783\pi$
$830$	−10.1017	−0.350635
$831$	2.38715	0.0828094
$832$	−0.622216	−0.0215714
$833$	5.10171	0.176764
$834$	−9.71456	−0.336388
$835$	−16.4701	−0.569972
$836$	4.42864	0.153168
$837$	4.85728	0.167892
$838$	−10.1017	−0.348958
$839$	−55.7659	−1.92525	−0.962626	−	0.270834i	$-0.912701\pi$
$839$	−55.7659	−1.92525	−0.962626	+	0.270834i	$0.912701\pi$
$840$	1.37778	0.0475381
$841$	63.4068	2.18644
$842$	9.22570	0.317938
$843$	−14.4701	−0.498378
$844$	3.61285	0.124359
$845$	−12.6128	−0.433895
$846$	−4.00000	−0.137523
$847$	−1.37778	−0.0473412
$848$	6.42864	0.220760
$849$	−27.3461	−0.938517
$850$	1.00000	0.0342997
$851$	14.3684	0.492543
$852$	−6.23506	−0.213610
$853$	−38.5531	−1.32003	−0.660017	−	0.751251i	$-0.729451\pi$
$853$	−38.5531	−1.32003	−0.660017	+	0.751251i	$0.729451\pi$
$854$	−13.7778	−0.471468
$855$	−4.42864	−0.151456
$856$	15.3461	0.524520
$857$	−45.9625	−1.57005	−0.785025	−	0.619464i	$-0.787350\pi$
$857$	−45.9625	−1.57005	−0.785025	+	0.619464i	$0.787350\pi$
$858$	−0.622216	−0.0212421
$859$	−38.8385	−1.32515	−0.662577	−	0.748994i	$-0.730537\pi$
$859$	−38.8385	−1.32515	−0.662577	+	0.748994i	$0.730537\pi$
$860$	6.23506	0.212614
$861$	16.2667	0.554368
$862$	−35.4005	−1.20575
$863$	−58.0010	−1.97438	−0.987188	−	0.159563i	$-0.948991\pi$
$863$	−58.0010	−1.97438	−0.987188	+	0.159563i	$0.948991\pi$
$864$	−1.00000	−0.0340207
$865$	21.2257	0.721695
$866$	−38.2034	−1.29821
$867$	1.00000	0.0339618
$868$	−6.69228	−0.227151
$869$	17.2859	0.586385
$870$	−9.61285	−0.325906
$871$	−9.12399	−0.309154
$872$	1.14272	0.0386974
$873$	−2.29529	−0.0776837
$874$	−19.6128	−0.663414
$875$	−1.37778	−0.0465776
$876$	−4.23506	−0.143090
$877$	53.8163	1.81725	0.908623	−	0.417617i	$-0.137135\pi$
$877$	53.8163	1.81725	0.908623	+	0.417617i	$0.137135\pi$
$878$	19.7748	0.667367
$879$	10.0000	0.337292
$880$	−1.00000	−0.0337100
$881$	32.2351	1.08603	0.543013	−	0.839724i	$-0.317283\pi$
$881$	32.2351	1.08603	0.543013	+	0.839724i	$0.317283\pi$
$882$	5.10171	0.171784
$883$	−18.7841	−0.632137	−0.316068	−	0.948736i	$-0.602363\pi$
$883$	−18.7841	−0.632137	−0.316068	+	0.948736i	$0.602363\pi$
$884$	0.622216	0.0209274
$885$	−4.13335	−0.138941
$886$	16.4286	0.551931
$887$	20.8573	0.700319	0.350159	−	0.936690i	$-0.386127\pi$
$887$	20.8573	0.700319	0.350159	+	0.936690i	$0.386127\pi$
$888$	3.24443	0.108876
$889$	23.2257	0.778965
$890$	3.24443	0.108754
$891$	−1.00000	−0.0335013
$892$	−25.9813	−0.869917
$893$	−17.7146	−0.592795
$894$	−6.29529	−0.210546
$895$	4.13335	0.138163
$896$	1.37778	0.0460285
$897$	2.75557	0.0920058
$898$	9.47949	0.316335
$899$	46.6923	1.55727
$900$	1.00000	0.0333333
$901$	−6.42864	−0.214169
$902$	−11.8064	−0.393111
$903$	−8.59057	−0.285876
$904$	7.67307	0.255203
$905$	−17.6128	−0.585471
$906$	−6.10171	−0.202716
$907$	−52.7565	−1.75175	−0.875876	−	0.482537i	$-0.839716\pi$
$907$	−52.7565	−1.75175	−0.875876	+	0.482537i	$0.839716\pi$
$908$	2.10171	0.0697477
$909$	−5.05086	−0.167526
$910$	−0.857279	−0.0284185
$911$	21.1941	0.702190	0.351095	−	0.936340i	$-0.385809\pi$
$911$	21.1941	0.702190	0.351095	+	0.936340i	$0.385809\pi$
$912$	−4.42864	−0.146647
$913$	−10.1017	−0.334318
$914$	−19.4479	−0.643278
$915$	−10.0000	−0.330590
$916$	6.85728	0.226571
$917$	21.5111	0.710360
$918$	1.00000	0.0330049
$919$	4.92056	0.162314	0.0811572	−	0.996701i	$-0.474138\pi$
$919$	4.92056	0.162314	0.0811572	+	0.996701i	$0.474138\pi$
$920$	4.42864	0.146008
$921$	23.0923	0.760919
$922$	25.5210	0.840489
$923$	3.87955	0.127697
$924$	1.37778	0.0453258
$925$	−3.24443	−0.106676
$926$	33.4479	1.09916
$927$	−17.7146	−0.581822
$928$	−9.61285	−0.315557
$929$	−26.0701	−0.855331	−0.427666	−	0.903937i	$-0.640664\pi$
$929$	−26.0701	−0.855331	−0.427666	+	0.903937i	$0.640664\pi$
$930$	−4.85728	−0.159276
$931$	22.5936	0.740476
$932$	4.36842	0.143092
$933$	32.8069	1.07405
$934$	−1.46965	−0.0480884
$935$	1.00000	0.0327035
$936$	0.622216	0.0203378
$937$	47.2444	1.54341	0.771704	−	0.635982i	$-0.219405\pi$
$937$	47.2444	1.54341	0.771704	+	0.635982i	$0.219405\pi$
$938$	20.2034	0.659665
$939$	0.193576	0.00631712
$940$	4.00000	0.130466
$941$	48.8385	1.59209	0.796046	−	0.605237i	$-0.206922\pi$
$941$	48.8385	1.59209	0.796046	+	0.605237i	$0.206922\pi$
$942$	−10.2953	−0.335439
$943$	52.2864	1.70268
$944$	−4.13335	−0.134529
$945$	−1.37778	−0.0448193
$946$	6.23506	0.202719
$947$	−53.2070	−1.72899	−0.864497	−	0.502638i	$-0.832363\pi$
$947$	−53.2070	−1.72899	−0.864497	+	0.502638i	$0.832363\pi$
$948$	−17.2859	−0.561421
$949$	2.63512	0.0855397
$950$	4.42864	0.143684
$951$	22.0830	0.716090
$952$	−1.37778	−0.0446542
$953$	13.4094	0.434374	0.217187	−	0.976130i	$-0.430312\pi$
$953$	13.4094	0.434374	0.217187	+	0.976130i	$0.430312\pi$
$954$	−6.42864	−0.208135
$955$	0.387152	0.0125280
$956$	−17.9813	−0.581556
$957$	−9.61285	−0.310739
$958$	8.29529	0.268009
$959$	−23.3658	−0.754522
$960$	1.00000	0.0322749
$961$	−7.40684	−0.238930
$962$	−2.01874	−0.0650867
$963$	−15.3461	−0.494522
$964$	2.04149	0.0657519
$965$	−14.9906	−0.482566
$966$	−6.10171	−0.196319
$967$	42.7556	1.37493	0.687463	−	0.726219i	$-0.258724\pi$
$967$	42.7556	1.37493	0.687463	+	0.726219i	$0.258724\pi$
$968$	−1.00000	−0.0321412
$969$	4.42864	0.142268
$970$	2.29529	0.0736972
$971$	42.1343	1.35215	0.676077	−	0.736831i	$-0.263679\pi$
$971$	42.1343	1.35215	0.676077	+	0.736831i	$0.263679\pi$
$972$	1.00000	0.0320750
$973$	−13.3846	−0.429089
$974$	14.0731	0.450932
$975$	−0.622216	−0.0199268
$976$	−10.0000	−0.320092
$977$	4.75557	0.152144	0.0760721	−	0.997102i	$-0.475762\pi$
$977$	4.75557	0.152144	0.0760721	+	0.997102i	$0.475762\pi$
$978$	10.3684	0.331545
$979$	3.24443	0.103692
$980$	−5.10171	−0.162968
$981$	−1.14272	−0.0364843
$982$	18.2766	0.583228
$983$	−5.55262	−0.177101	−0.0885506	−	0.996072i	$-0.528224\pi$
$983$	−5.55262	−0.177101	−0.0885506	+	0.996072i	$0.528224\pi$
$984$	11.8064	0.376375
$985$	−11.1240	−0.354440
$986$	9.61285	0.306135
$987$	−5.51114	−0.175421
$988$	2.75557	0.0876663
$989$	−27.6128	−0.878037
$990$	1.00000	0.0317821
$991$	−28.0000	−0.889449	−0.444725	−	0.895667i	$-0.646698\pi$
$991$	−28.0000	−0.889449	−0.444725	+	0.895667i	$0.646698\pi$
$992$	−4.85728	−0.154219
$993$	−5.12399	−0.162605
$994$	−8.59057	−0.272476
$995$	−26.3684	−0.835935
$996$	10.1017	0.320085
$997$	60.0010	1.90025	0.950125	−	0.311870i	$-0.100956\pi$
$997$	60.0010	1.90025	0.950125	+	0.311870i	$0.100956\pi$
$998$	22.4889	0.711873
$999$	−3.24443	−0.102649

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	5610.2.a.bz.1.2	✓	3

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
5610.2.a.bz.1.2	✓	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)

\(f(q)\)	\(=\)	\(q-1.00000 q^{2} +1.00000 q^{3} +1.00000 q^{4} +1.00000 q^{5} -1.00000 q^{6} -1.37778 q^{7} -1.00000 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q-1.00000 q^{2} +1.00000 q^{3} +1.00000 q^{4} +1.00000 q^{5} -1.00000 q^{6} -1.37778 q^{7} -1.00000 q^{8} +1.00000 q^{9} -1.00000 q^{10} -1.00000 q^{11} +1.00000 q^{12} -0.622216 q^{13} +1.37778 q^{14} +1.00000 q^{15} +1.00000 q^{16} -1.00000 q^{17} -1.00000 q^{18} -4.42864 q^{19} +1.00000 q^{20} -1.37778 q^{21} +1.00000 q^{22} -4.42864 q^{23} -1.00000 q^{24} +1.00000 q^{25} +0.622216 q^{26} +1.00000 q^{27} -1.37778 q^{28} +9.61285 q^{29} -1.00000 q^{30} +4.85728 q^{31} -1.00000 q^{32} -1.00000 q^{33} +1.00000 q^{34} -1.37778 q^{35} +1.00000 q^{36} -3.24443 q^{37} +4.42864 q^{38} -0.622216 q^{39} -1.00000 q^{40} -11.8064 q^{41} +1.37778 q^{42} +6.23506 q^{43} -1.00000 q^{44} +1.00000 q^{45} +4.42864 q^{46} +4.00000 q^{47} +1.00000 q^{48} -5.10171 q^{49} -1.00000 q^{50} -1.00000 q^{51} -0.622216 q^{52} +6.42864 q^{53} -1.00000 q^{54} -1.00000 q^{55} +1.37778 q^{56} -4.42864 q^{57} -9.61285 q^{58} -4.13335 q^{59} +1.00000 q^{60} -10.0000 q^{61} -4.85728 q^{62} -1.37778 q^{63} +1.00000 q^{64} -0.622216 q^{65} +1.00000 q^{66} +14.6637 q^{67} -1.00000 q^{68} -4.42864 q^{69} +1.37778 q^{70} -6.23506 q^{71} -1.00000 q^{72} -4.23506 q^{73} +3.24443 q^{74} +1.00000 q^{75} -4.42864 q^{76} +1.37778 q^{77} +0.622216 q^{78} -17.2859 q^{79} +1.00000 q^{80} +1.00000 q^{81} +11.8064 q^{82} +10.1017 q^{83} -1.37778 q^{84} -1.00000 q^{85} -6.23506 q^{86} +9.61285 q^{87} +1.00000 q^{88} -3.24443 q^{89} -1.00000 q^{90} +0.857279 q^{91} -4.42864 q^{92} +4.85728 q^{93} -4.00000 q^{94} -4.42864 q^{95} -1.00000 q^{96} -2.29529 q^{97} +5.10171 q^{98} -1.00000 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 3 q - 3 q^{2} + 3 q^{3} + 3 q^{4} + 3 q^{5} - 3 q^{6} - 4 q^{7} - 3 q^{8} + 3 q^{9}+O(q^{10}) \) 3 * q - 3 * q^2 + 3 * q^3 + 3 * q^4 + 3 * q^5 - 3 * q^6 - 4 * q^7 - 3 * q^8 + 3 * q^9	\( 3 q - 3 q^{2} + 3 q^{3} + 3 q^{4} + 3 q^{5} - 3 q^{6} - 4 q^{7} - 3 q^{8} + 3 q^{9} - 3 q^{10} - 3 q^{11} + 3 q^{12} - 2 q^{13} + 4 q^{14} + 3 q^{15} + 3 q^{16} - 3 q^{17} - 3 q^{18} + 3 q^{20} - 4 q^{21} + 3 q^{22} - 3 q^{24} + 3 q^{25} + 2 q^{26} + 3 q^{27} - 4 q^{28} + 2 q^{29} - 3 q^{30} - 12 q^{31} - 3 q^{32} - 3 q^{33} + 3 q^{34} - 4 q^{35} + 3 q^{36} - 10 q^{37} - 2 q^{39} - 3 q^{40} - 22 q^{41} + 4 q^{42} - 8 q^{43} - 3 q^{44} + 3 q^{45} + 12 q^{47} + 3 q^{48} + 11 q^{49} - 3 q^{50} - 3 q^{51} - 2 q^{52} + 6 q^{53} - 3 q^{54} - 3 q^{55} + 4 q^{56} - 2 q^{58} - 12 q^{59} + 3 q^{60} - 30 q^{61} + 12 q^{62} - 4 q^{63} + 3 q^{64} - 2 q^{65} + 3 q^{66} + 4 q^{67} - 3 q^{68} + 4 q^{70} + 8 q^{71} - 3 q^{72} + 14 q^{73} + 10 q^{74} + 3 q^{75} + 4 q^{77} + 2 q^{78} - 12 q^{79} + 3 q^{80} + 3 q^{81} + 22 q^{82} + 4 q^{83} - 4 q^{84} - 3 q^{85} + 8 q^{86} + 2 q^{87} + 3 q^{88} - 10 q^{89} - 3 q^{90} - 24 q^{91} - 12 q^{93} - 12 q^{94} - 3 q^{96} + 6 q^{97} - 11 q^{98} - 3 q^{99}+O(q^{100}) \) 3 * q - 3 * q^2 + 3 * q^3 + 3 * q^4 + 3 * q^5 - 3 * q^6 - 4 * q^7 - 3 * q^8 + 3 * q^9 - 3 * q^10 - 3 * q^11 + 3 * q^12 - 2 * q^13 + 4 * q^14 + 3 * q^15 + 3 * q^16 - 3 * q^17 - 3 * q^18 + 3 * q^20 - 4 * q^21 + 3 * q^22 - 3 * q^24 + 3 * q^25 + 2 * q^26 + 3 * q^27 - 4 * q^28 + 2 * q^29 - 3 * q^30 - 12 * q^31 - 3 * q^32 - 3 * q^33 + 3 * q^34 - 4 * q^35 + 3 * q^36 - 10 * q^37 - 2 * q^39 - 3 * q^40 - 22 * q^41 + 4 * q^42 - 8 * q^43 - 3 * q^44 + 3 * q^45 + 12 * q^47 + 3 * q^48 + 11 * q^49 - 3 * q^50 - 3 * q^51 - 2 * q^52 + 6 * q^53 - 3 * q^54 - 3 * q^55 + 4 * q^56 - 2 * q^58 - 12 * q^59 + 3 * q^60 - 30 * q^61 + 12 * q^62 - 4 * q^63 + 3 * q^64 - 2 * q^65 + 3 * q^66 + 4 * q^67 - 3 * q^68 + 4 * q^70 + 8 * q^71 - 3 * q^72 + 14 * q^73 + 10 * q^74 + 3 * q^75 + 4 * q^77 + 2 * q^78 - 12 * q^79 + 3 * q^80 + 3 * q^81 + 22 * q^82 + 4 * q^83 - 4 * q^84 - 3 * q^85 + 8 * q^86 + 2 * q^87 + 3 * q^88 - 10 * q^89 - 3 * q^90 - 24 * q^91 - 12 * q^93 - 12 * q^94 - 3 * q^96 + 6 * q^97 - 11 * q^98 - 3 * q^99

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