LMFDB - Embedded newform 186.2.a.d.1.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [186,2,Mod(1,186)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(186, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([0, 0]))

N = Newforms(chi, 2, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("186.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 186 = 2 \cdot 3 \cdot 31 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	186.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:	$1.48521747760$
Analytic rank:	$0$
Dimension:	$2$
Coefficient field:	$\Q(\sqrt{17}) $
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{2} - x - 4 $ x^2 - x - 4
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.1
Root			$-1.56155$ of defining polynomial
Character	$\chi$	$=$	186.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.00000 q^{2} -1.00000 q^{3} +1.00000 q^{4} -0.561553 q^{5} -1.00000 q^{6} +5.12311 q^{7} +1.00000 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q+1.00000 q^{2} -1.00000 q^{3} +1.00000 q^{4} -0.561553 q^{5} -1.00000 q^{6} +5.12311 q^{7} +1.00000 q^{8} +1.00000 q^{9} -0.561553 q^{10} -2.56155 q^{11} -1.00000 q^{12} -0.561553 q^{13} +5.12311 q^{14} +0.561553 q^{15} +1.00000 q^{16} +5.68466 q^{17} +1.00000 q^{18} -2.56155 q^{19} -0.561553 q^{20} -5.12311 q^{21} -2.56155 q^{22} -8.00000 q^{23} -1.00000 q^{24} -4.68466 q^{25} -0.561553 q^{26} -1.00000 q^{27} +5.12311 q^{28} -7.12311 q^{29} +0.561553 q^{30} -1.00000 q^{31} +1.00000 q^{32} +2.56155 q^{33} +5.68466 q^{34} -2.87689 q^{35} +1.00000 q^{36} +8.24621 q^{37} -2.56155 q^{38} +0.561553 q^{39} -0.561553 q^{40} +4.24621 q^{41} -5.12311 q^{42} -9.12311 q^{43} -2.56155 q^{44} -0.561553 q^{45} -8.00000 q^{46} -3.68466 q^{47} -1.00000 q^{48} +19.2462 q^{49} -4.68466 q^{50} -5.68466 q^{51} -0.561553 q^{52} -2.00000 q^{53} -1.00000 q^{54} +1.43845 q^{55} +5.12311 q^{56} +2.56155 q^{57} -7.12311 q^{58} -1.12311 q^{59} +0.561553 q^{60} -0.561553 q^{61} -1.00000 q^{62} +5.12311 q^{63} +1.00000 q^{64} +0.315342 q^{65} +2.56155 q^{66} +0.315342 q^{67} +5.68466 q^{68} +8.00000 q^{69} -2.87689 q^{70} -1.43845 q^{71} +1.00000 q^{72} +10.0000 q^{73} +8.24621 q^{74} +4.68466 q^{75} -2.56155 q^{76} -13.1231 q^{77} +0.561553 q^{78} -3.68466 q^{79} -0.561553 q^{80} +1.00000 q^{81} +4.24621 q^{82} +12.8078 q^{83} -5.12311 q^{84} -3.19224 q^{85} -9.12311 q^{86} +7.12311 q^{87} -2.56155 q^{88} -0.246211 q^{89} -0.561553 q^{90} -2.87689 q^{91} -8.00000 q^{92} +1.00000 q^{93} -3.68466 q^{94} +1.43845 q^{95} -1.00000 q^{96} -14.8078 q^{97} +19.2462 q^{98} -2.56155 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 2 q + 2 q^{2} - 2 q^{3} + 2 q^{4} + 3 q^{5} - 2 q^{6} + 2 q^{7} + 2 q^{8} + 2 q^{9}+O(q^{10}) $ 2 * q + 2 * q^2 - 2 * q^3 + 2 * q^4 + 3 * q^5 - 2 * q^6 + 2 * q^7 + 2 * q^8 + 2 * q^9	\( 2 q + 2 q^{2} - 2 q^{3} + 2 q^{4} + 3 q^{5} - 2 q^{6} + 2 q^{7} + 2 q^{8} + 2 q^{9} + 3 q^{10} - q^{11} - 2 q^{12} + 3 q^{13} + 2 q^{14} - 3 q^{15} + 2 q^{16} - q^{17} + 2 q^{18} - q^{19} + 3 q^{20} - 2 q^{21} - q^{22} - 16 q^{23} - 2 q^{24} + 3 q^{25} + 3 q^{26} - 2 q^{27} + 2 q^{28} - 6 q^{29} - 3 q^{30} - 2 q^{31} + 2 q^{32} + q^{33} - q^{34} - 14 q^{35} + 2 q^{36} - q^{38} - 3 q^{39} + 3 q^{40} - 8 q^{41} - 2 q^{42} - 10 q^{43} - q^{44} + 3 q^{45} - 16 q^{46} + 5 q^{47} - 2 q^{48} + 22 q^{49} + 3 q^{50} + q^{51} + 3 q^{52} - 4 q^{53} - 2 q^{54} + 7 q^{55} + 2 q^{56} + q^{57} - 6 q^{58} + 6 q^{59} - 3 q^{60} + 3 q^{61} - 2 q^{62} + 2 q^{63} + 2 q^{64} + 13 q^{65} + q^{66} + 13 q^{67} - q^{68} + 16 q^{69} - 14 q^{70} - 7 q^{71} + 2 q^{72} + 20 q^{73} - 3 q^{75} - q^{76} - 18 q^{77} - 3 q^{78} + 5 q^{79} + 3 q^{80} + 2 q^{81} - 8 q^{82} + 5 q^{83} - 2 q^{84} - 27 q^{85} - 10 q^{86} + 6 q^{87} - q^{88} + 16 q^{89} + 3 q^{90} - 14 q^{91} - 16 q^{92} + 2 q^{93} + 5 q^{94} + 7 q^{95} - 2 q^{96} - 9 q^{97} + 22 q^{98} - q^{99}+O(q^{100}) \) 2 * q + 2 * q^2 - 2 * q^3 + 2 * q^4 + 3 * q^5 - 2 * q^6 + 2 * q^7 + 2 * q^8 + 2 * q^9 + 3 * q^10 - q^11 - 2 * q^12 + 3 * q^13 + 2 * q^14 - 3 * q^15 + 2 * q^16 - q^17 + 2 * q^18 - q^19 + 3 * q^20 - 2 * q^21 - q^22 - 16 * q^23 - 2 * q^24 + 3 * q^25 + 3 * q^26 - 2 * q^27 + 2 * q^28 - 6 * q^29 - 3 * q^30 - 2 * q^31 + 2 * q^32 + q^33 - q^34 - 14 * q^35 + 2 * q^36 - q^38 - 3 * q^39 + 3 * q^40 - 8 * q^41 - 2 * q^42 - 10 * q^43 - q^44 + 3 * q^45 - 16 * q^46 + 5 * q^47 - 2 * q^48 + 22 * q^49 + 3 * q^50 + q^51 + 3 * q^52 - 4 * q^53 - 2 * q^54 + 7 * q^55 + 2 * q^56 + q^57 - 6 * q^58 + 6 * q^59 - 3 * q^60 + 3 * q^61 - 2 * q^62 + 2 * q^63 + 2 * q^64 + 13 * q^65 + q^66 + 13 * q^67 - q^68 + 16 * q^69 - 14 * q^70 - 7 * q^71 + 2 * q^72 + 20 * q^73 - 3 * q^75 - q^76 - 18 * q^77 - 3 * q^78 + 5 * q^79 + 3 * q^80 + 2 * q^81 - 8 * q^82 + 5 * q^83 - 2 * q^84 - 27 * q^85 - 10 * q^86 + 6 * q^87 - q^88 + 16 * q^89 + 3 * q^90 - 14 * q^91 - 16 * q^92 + 2 * q^93 + 5 * q^94 + 7 * q^95 - 2 * q^96 - 9 * q^97 + 22 * q^98 - 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
$5$	−0.561553	−0.251134	−0.125567	−	0.992085i	$-0.540075\pi$
$5$	−0.561553	−0.251134	−0.125567	+	0.992085i	$0.540075\pi$
$6$	−1.00000	−0.408248
$7$	5.12311	1.93635	0.968176	−	0.250270i	$-0.0805195\pi$
$7$	5.12311	1.93635	0.968176	+	0.250270i	$0.0805195\pi$
$8$	1.00000	0.353553
$9$	1.00000	0.333333
$10$	−0.561553	−0.177579
$11$	−2.56155	−0.772337	−0.386169	−	0.922428i	$-0.626202\pi$
$11$	−2.56155	−0.772337	−0.386169	+	0.922428i	$0.626202\pi$
$12$	−1.00000	−0.288675
$13$	−0.561553	−0.155747	−0.0778734	−	0.996963i	$-0.524813\pi$
$13$	−0.561553	−0.155747	−0.0778734	+	0.996963i	$0.524813\pi$
$14$	5.12311	1.36921
$15$	0.561553	0.144992
$16$	1.00000	0.250000
$17$	5.68466	1.37873	0.689366	−	0.724413i	$-0.257889\pi$
$17$	5.68466	1.37873	0.689366	+	0.724413i	$0.257889\pi$
$18$	1.00000	0.235702
$19$	−2.56155	−0.587661	−0.293830	−	0.955858i	$-0.594930\pi$
$19$	−2.56155	−0.587661	−0.293830	+	0.955858i	$0.594930\pi$
$20$	−0.561553	−0.125567
$21$	−5.12311	−1.11795
$22$	−2.56155	−0.546125
$23$	−8.00000	−1.66812	−0.834058	−	0.551677i	$-0.813988\pi$
$23$	−8.00000	−1.66812	−0.834058	+	0.551677i	$0.813988\pi$
$24$	−1.00000	−0.204124
$25$	−4.68466	−0.936932
$26$	−0.561553	−0.110130
$27$	−1.00000	−0.192450
$28$	5.12311	0.968176
$29$	−7.12311	−1.32273	−0.661364	−	0.750065i	$-0.730022\pi$
$29$	−7.12311	−1.32273	−0.661364	+	0.750065i	$0.730022\pi$
$30$	0.561553	0.102525
$31$	−1.00000	−0.179605
$31$	−1.00000	−0.179605
$32$	1.00000	0.176777
$33$	2.56155	0.445909
$34$	5.68466	0.974911
$35$	−2.87689	−0.486284
$36$	1.00000	0.166667
$37$	8.24621	1.35567	0.677834	−	0.735215i	$-0.262919\pi$
$37$	8.24621	1.35567	0.677834	+	0.735215i	$0.262919\pi$
$38$	−2.56155	−0.415539
$39$	0.561553	0.0899204
$40$	−0.561553	−0.0887893
$41$	4.24621	0.663147	0.331573	−	0.943429i	$-0.392421\pi$
$41$	4.24621	0.663147	0.331573	+	0.943429i	$0.392421\pi$
$42$	−5.12311	−0.790512
$43$	−9.12311	−1.39126	−0.695630	−	0.718400i	$-0.744875\pi$
$43$	−9.12311	−1.39126	−0.695630	+	0.718400i	$0.744875\pi$
$44$	−2.56155	−0.386169
$45$	−0.561553	−0.0837114
$46$	−8.00000	−1.17954
$47$	−3.68466	−0.537463	−0.268731	−	0.963215i	$-0.586604\pi$
$47$	−3.68466	−0.537463	−0.268731	+	0.963215i	$0.586604\pi$
$48$	−1.00000	−0.144338
$49$	19.2462	2.74946
$50$	−4.68466	−0.662511
$51$	−5.68466	−0.796011
$52$	−0.561553	−0.0778734
$53$	−2.00000	−0.274721	−0.137361	−	0.990521i	$-0.543862\pi$
$53$	−2.00000	−0.274721	−0.137361	+	0.990521i	$0.543862\pi$
$54$	−1.00000	−0.136083
$55$	1.43845	0.193960
$56$	5.12311	0.684604
$57$	2.56155	0.339286
$58$	−7.12311	−0.935310
$59$	−1.12311	−0.146216	−0.0731079	−	0.997324i	$-0.523292\pi$
$59$	−1.12311	−0.146216	−0.0731079	+	0.997324i	$0.523292\pi$
$60$	0.561553	0.0724962
$61$	−0.561553	−0.0718995	−0.0359497	−	0.999354i	$-0.511446\pi$
$61$	−0.561553	−0.0718995	−0.0359497	+	0.999354i	$0.511446\pi$
$62$	−1.00000	−0.127000
$63$	5.12311	0.645451
$64$	1.00000	0.125000
$65$	0.315342	0.0391133
$66$	2.56155	0.315305
$67$	0.315342	0.0385251	0.0192626	−	0.999814i	$-0.493868\pi$
$67$	0.315342	0.0385251	0.0192626	+	0.999814i	$0.493868\pi$
$68$	5.68466	0.689366
$69$	8.00000	0.963087
$70$	−2.87689	−0.343855
$71$	−1.43845	−0.170712	−0.0853561	−	0.996351i	$-0.527203\pi$
$71$	−1.43845	−0.170712	−0.0853561	+	0.996351i	$0.527203\pi$
$72$	1.00000	0.117851
$73$	10.0000	1.17041	0.585206	−	0.810885i	$-0.301014\pi$
$73$	10.0000	1.17041	0.585206	+	0.810885i	$0.301014\pi$
$74$	8.24621	0.958603
$75$	4.68466	0.540938
$76$	−2.56155	−0.293830
$77$	−13.1231	−1.49552
$78$	0.561553	0.0635833
$79$	−3.68466	−0.414556	−0.207278	−	0.978282i	$-0.566461\pi$
$79$	−3.68466	−0.414556	−0.207278	+	0.978282i	$0.566461\pi$
$80$	−0.561553	−0.0627835
$81$	1.00000	0.111111
$82$	4.24621	0.468916
$83$	12.8078	1.40583	0.702917	−	0.711272i	$-0.251880\pi$
$83$	12.8078	1.40583	0.702917	+	0.711272i	$0.251880\pi$
$84$	−5.12311	−0.558977
$85$	−3.19224	−0.346247
$86$	−9.12311	−0.983770
$87$	7.12311	0.763677
$88$	−2.56155	−0.273062
$89$	−0.246211	−0.0260983	−0.0130492	−	0.999915i	$-0.504154\pi$
$89$	−0.246211	−0.0260983	−0.0130492	+	0.999915i	$0.504154\pi$
$90$	−0.561553	−0.0591929
$91$	−2.87689	−0.301580
$92$	−8.00000	−0.834058
$93$	1.00000	0.103695
$94$	−3.68466	−0.380043
$95$	1.43845	0.147582
$96$	−1.00000	−0.102062
$97$	−14.8078	−1.50350	−0.751750	−	0.659448i	$-0.770790\pi$
$97$	−14.8078	−1.50350	−0.751750	+	0.659448i	$0.770790\pi$
$98$	19.2462	1.94416
$99$	−2.56155	−0.257446
$100$	−4.68466	−0.468466
$101$	16.2462	1.61656	0.808279	−	0.588799i	$-0.200399\pi$
$101$	16.2462	1.61656	0.808279	+	0.588799i	$0.200399\pi$
$102$	−5.68466	−0.562865
$103$	−5.12311	−0.504795	−0.252397	−	0.967624i	$-0.581219\pi$
$103$	−5.12311	−0.504795	−0.252397	+	0.967624i	$0.581219\pi$
$104$	−0.561553	−0.0550648
$105$	2.87689	0.280756
$106$	−2.00000	−0.194257
$107$	−4.00000	−0.386695	−0.193347	−	0.981130i	$-0.561934\pi$
$107$	−4.00000	−0.386695	−0.193347	+	0.981130i	$0.561934\pi$
$108$	−1.00000	−0.0962250
$109$	14.0000	1.34096	0.670478	−	0.741929i	$-0.266089\pi$
$109$	14.0000	1.34096	0.670478	+	0.741929i	$0.266089\pi$
$110$	1.43845	0.137151
$111$	−8.24621	−0.782696
$112$	5.12311	0.484088
$113$	−14.0000	−1.31701	−0.658505	−	0.752577i	$-0.728811\pi$
$113$	−14.0000	−1.31701	−0.658505	+	0.752577i	$0.728811\pi$
$114$	2.56155	0.239911
$115$	4.49242	0.418921
$116$	−7.12311	−0.661364
$117$	−0.561553	−0.0519156
$118$	−1.12311	−0.103390
$119$	29.1231	2.66971
$120$	0.561553	0.0512625
$121$	−4.43845	−0.403495
$122$	−0.561553	−0.0508406
$123$	−4.24621	−0.382868
$124$	−1.00000	−0.0898027
$125$	5.43845	0.486430
$126$	5.12311	0.456403
$127$	10.2462	0.909204	0.454602	−	0.890695i	$-0.349781\pi$
$127$	10.2462	0.909204	0.454602	+	0.890695i	$0.349781\pi$
$128$	1.00000	0.0883883
$129$	9.12311	0.803245
$130$	0.315342	0.0276573
$131$	17.1231	1.49605	0.748026	−	0.663669i	$-0.231002\pi$
$131$	17.1231	1.49605	0.748026	+	0.663669i	$0.231002\pi$
$132$	2.56155	0.222955
$133$	−13.1231	−1.13792
$134$	0.315342	0.0272414
$135$	0.561553	0.0483308
$136$	5.68466	0.487455
$137$	−6.00000	−0.512615	−0.256307	−	0.966595i	$-0.582506\pi$
$137$	−6.00000	−0.512615	−0.256307	+	0.966595i	$0.582506\pi$
$138$	8.00000	0.681005
$139$	−12.0000	−1.01783	−0.508913	−	0.860818i	$-0.669953\pi$
$139$	−12.0000	−1.01783	−0.508913	+	0.860818i	$0.669953\pi$
$140$	−2.87689	−0.243142
$141$	3.68466	0.310304
$142$	−1.43845	−0.120712
$143$	1.43845	0.120289
$144$	1.00000	0.0833333
$145$	4.00000	0.332182
$146$	10.0000	0.827606
$147$	−19.2462	−1.58740
$148$	8.24621	0.677834
$149$	9.68466	0.793398	0.396699	−	0.917949i	$-0.370156\pi$
$149$	9.68466	0.793398	0.396699	+	0.917949i	$0.370156\pi$
$150$	4.68466	0.382501
$151$	5.93087	0.482647	0.241324	−	0.970445i	$-0.422418\pi$
$151$	5.93087	0.482647	0.241324	+	0.970445i	$0.422418\pi$
$152$	−2.56155	−0.207769
$153$	5.68466	0.459577
$154$	−13.1231	−1.05749
$155$	0.561553	0.0451050
$156$	0.561553	0.0449602
$157$	−9.36932	−0.747753	−0.373876	−	0.927479i	$-0.621972\pi$
$157$	−9.36932	−0.747753	−0.373876	+	0.927479i	$0.621972\pi$
$158$	−3.68466	−0.293136
$159$	2.00000	0.158610
$160$	−0.561553	−0.0443946
$161$	−40.9848	−3.23006
$162$	1.00000	0.0785674
$163$	−23.0540	−1.80573	−0.902863	−	0.429928i	$-0.858539\pi$
$163$	−23.0540	−1.80573	−0.902863	+	0.429928i	$0.858539\pi$
$164$	4.24621	0.331573
$165$	−1.43845	−0.111983
$166$	12.8078	0.994075
$167$	−5.12311	−0.396438	−0.198219	−	0.980158i	$-0.563516\pi$
$167$	−5.12311	−0.396438	−0.198219	+	0.980158i	$0.563516\pi$
$168$	−5.12311	−0.395256
$169$	−12.6847	−0.975743
$170$	−3.19224	−0.244833
$171$	−2.56155	−0.195887
$172$	−9.12311	−0.695630
$173$	4.56155	0.346808	0.173404	−	0.984851i	$-0.444523\pi$
$173$	4.56155	0.346808	0.173404	+	0.984851i	$0.444523\pi$
$174$	7.12311	0.540001
$175$	−24.0000	−1.81423
$176$	−2.56155	−0.193084
$177$	1.12311	0.0844178
$178$	−0.246211	−0.0184543
$179$	23.0540	1.72314	0.861568	−	0.507643i	$-0.169483\pi$
$179$	23.0540	1.72314	0.861568	+	0.507643i	$0.169483\pi$
$180$	−0.561553	−0.0418557
$181$	−12.2462	−0.910254	−0.455127	−	0.890427i	$-0.650406\pi$
$181$	−12.2462	−0.910254	−0.455127	+	0.890427i	$0.650406\pi$
$182$	−2.87689	−0.213250
$183$	0.561553	0.0415112
$184$	−8.00000	−0.589768
$185$	−4.63068	−0.340455
$186$	1.00000	0.0733236
$187$	−14.5616	−1.06485
$188$	−3.68466	−0.268731
$189$	−5.12311	−0.372651
$190$	1.43845	0.104356
$191$	16.0000	1.15772	0.578860	−	0.815427i	$-0.303498\pi$
$191$	16.0000	1.15772	0.578860	+	0.815427i	$0.303498\pi$
$192$	−1.00000	−0.0721688
$193$	24.5616	1.76798	0.883990	−	0.467507i	$-0.154848\pi$
$193$	24.5616	1.76798	0.883990	+	0.467507i	$0.154848\pi$
$194$	−14.8078	−1.06314
$195$	−0.315342	−0.0225821
$196$	19.2462	1.37473
$197$	8.24621	0.587518	0.293759	−	0.955879i	$-0.405094\pi$
$197$	8.24621	0.587518	0.293759	+	0.955879i	$0.405094\pi$
$198$	−2.56155	−0.182042
$199$	4.31534	0.305906	0.152953	−	0.988233i	$-0.451122\pi$
$199$	4.31534	0.305906	0.152953	+	0.988233i	$0.451122\pi$
$200$	−4.68466	−0.331255
$201$	−0.315342	−0.0222425
$202$	16.2462	1.14308
$203$	−36.4924	−2.56127
$204$	−5.68466	−0.398006
$205$	−2.38447	−0.166539
$206$	−5.12311	−0.356944
$207$	−8.00000	−0.556038
$208$	−0.561553	−0.0389367
$209$	6.56155	0.453872
$210$	2.87689	0.198525
$211$	−1.75379	−0.120736	−0.0603679	−	0.998176i	$-0.519227\pi$
$211$	−1.75379	−0.120736	−0.0603679	+	0.998176i	$0.519227\pi$
$212$	−2.00000	−0.137361
$213$	1.43845	0.0985608
$214$	−4.00000	−0.273434
$215$	5.12311	0.349393
$216$	−1.00000	−0.0680414
$217$	−5.12311	−0.347779
$218$	14.0000	0.948200
$219$	−10.0000	−0.675737
$220$	1.43845	0.0969801
$221$	−3.19224	−0.214733
$222$	−8.24621	−0.553449
$223$	19.6847	1.31818	0.659091	−	0.752063i	$-0.270941\pi$
$223$	19.6847	1.31818	0.659091	+	0.752063i	$0.270941\pi$
$224$	5.12311	0.342302
$225$	−4.68466	−0.312311
$226$	−14.0000	−0.931266
$227$	−19.3693	−1.28559	−0.642793	−	0.766040i	$-0.722225\pi$
$227$	−19.3693	−1.28559	−0.642793	+	0.766040i	$0.722225\pi$
$228$	2.56155	0.169643
$229$	17.6847	1.16864	0.584318	−	0.811525i	$-0.301362\pi$
$229$	17.6847	1.16864	0.584318	+	0.811525i	$0.301362\pi$
$230$	4.49242	0.296222
$231$	13.1231	0.863437
$232$	−7.12311	−0.467655
$233$	11.6155	0.760959	0.380479	−	0.924789i	$-0.375759\pi$
$233$	11.6155	0.760959	0.380479	+	0.924789i	$0.375759\pi$
$234$	−0.561553	−0.0367099
$235$	2.06913	0.134975
$236$	−1.12311	−0.0731079
$237$	3.68466	0.239344
$238$	29.1231	1.88777
$239$	−20.4924	−1.32554	−0.662772	−	0.748821i	$-0.730620\pi$
$239$	−20.4924	−1.32554	−0.662772	+	0.748821i	$0.730620\pi$
$240$	0.561553	0.0362481
$241$	7.75379	0.499465	0.249733	−	0.968315i	$-0.419657\pi$
$241$	7.75379	0.499465	0.249733	+	0.968315i	$0.419657\pi$
$242$	−4.43845	−0.285314
$243$	−1.00000	−0.0641500
$244$	−0.561553	−0.0359497
$245$	−10.8078	−0.690483
$246$	−4.24621	−0.270729
$247$	1.43845	0.0915262
$248$	−1.00000	−0.0635001
$249$	−12.8078	−0.811659
$250$	5.43845	0.343958
$251$	20.0000	1.26239	0.631194	−	0.775625i	$-0.282565\pi$
$251$	20.0000	1.26239	0.631194	+	0.775625i	$0.282565\pi$
$252$	5.12311	0.322725
$253$	20.4924	1.28835
$254$	10.2462	0.642904
$255$	3.19224	0.199906
$256$	1.00000	0.0625000
$257$	−16.8769	−1.05275	−0.526376	−	0.850252i	$-0.676450\pi$
$257$	−16.8769	−1.05275	−0.526376	+	0.850252i	$0.676450\pi$
$258$	9.12311	0.567980
$259$	42.2462	2.62505
$260$	0.315342	0.0195567
$261$	−7.12311	−0.440909
$262$	17.1231	1.05787
$263$	−2.24621	−0.138507	−0.0692537	−	0.997599i	$-0.522062\pi$
$263$	−2.24621	−0.138507	−0.0692537	+	0.997599i	$0.522062\pi$
$264$	2.56155	0.157653
$265$	1.12311	0.0689918
$266$	−13.1231	−0.804629
$267$	0.246211	0.0150679
$268$	0.315342	0.0192626
$269$	−14.4924	−0.883619	−0.441809	−	0.897109i	$-0.645663\pi$
$269$	−14.4924	−0.883619	−0.441809	+	0.897109i	$0.645663\pi$
$270$	0.561553	0.0341750
$271$	−3.68466	−0.223827	−0.111914	−	0.993718i	$-0.535698\pi$
$271$	−3.68466	−0.223827	−0.111914	+	0.993718i	$0.535698\pi$
$272$	5.68466	0.344683
$273$	2.87689	0.174118
$274$	−6.00000	−0.362473
$275$	12.0000	0.723627
$276$	8.00000	0.481543
$277$	7.43845	0.446933	0.223466	−	0.974712i	$-0.428263\pi$
$277$	7.43845	0.446933	0.223466	+	0.974712i	$0.428263\pi$
$278$	−12.0000	−0.719712
$279$	−1.00000	−0.0598684
$280$	−2.87689	−0.171927
$281$	14.4924	0.864545	0.432273	−	0.901743i	$-0.357712\pi$
$281$	14.4924	0.864545	0.432273	+	0.901743i	$0.357712\pi$
$282$	3.68466	0.219418
$283$	−3.19224	−0.189759	−0.0948794	−	0.995489i	$-0.530247\pi$
$283$	−3.19224	−0.189759	−0.0948794	+	0.995489i	$0.530247\pi$
$284$	−1.43845	−0.0853561
$285$	−1.43845	−0.0852063
$286$	1.43845	0.0850572
$287$	21.7538	1.28409
$288$	1.00000	0.0589256
$289$	15.3153	0.900902
$290$	4.00000	0.234888
$291$	14.8078	0.868047
$292$	10.0000	0.585206
$293$	6.00000	0.350524	0.175262	−	0.984522i	$-0.443923\pi$
$293$	6.00000	0.350524	0.175262	+	0.984522i	$0.443923\pi$
$294$	−19.2462	−1.12246
$295$	0.630683	0.0367198
$296$	8.24621	0.479301
$297$	2.56155	0.148636
$298$	9.68466	0.561017
$299$	4.49242	0.259804
$300$	4.68466	0.270469
$301$	−46.7386	−2.69397
$302$	5.93087	0.341283
$303$	−16.2462	−0.933320
$304$	−2.56155	−0.146915
$305$	0.315342	0.0180564
$306$	5.68466	0.324970
$307$	−1.75379	−0.100094	−0.0500470	−	0.998747i	$-0.515937\pi$
$307$	−1.75379	−0.100094	−0.0500470	+	0.998747i	$0.515937\pi$
$308$	−13.1231	−0.747758
$309$	5.12311	0.291443
$310$	0.561553	0.0318941
$311$	21.9309	1.24359	0.621793	−	0.783182i	$-0.286405\pi$
$311$	21.9309	1.24359	0.621793	+	0.783182i	$0.286405\pi$
$312$	0.561553	0.0317917
$313$	−16.2462	−0.918290	−0.459145	−	0.888361i	$-0.651844\pi$
$313$	−16.2462	−0.918290	−0.459145	+	0.888361i	$0.651844\pi$
$314$	−9.36932	−0.528741
$315$	−2.87689	−0.162095
$316$	−3.68466	−0.207278
$317$	10.3153	0.579367	0.289684	−	0.957122i	$-0.406450\pi$
$317$	10.3153	0.579367	0.289684	+	0.957122i	$0.406450\pi$
$318$	2.00000	0.112154
$319$	18.2462	1.02159
$320$	−0.561553	−0.0313918
$321$	4.00000	0.223258
$322$	−40.9848	−2.28400
$323$	−14.5616	−0.810226
$324$	1.00000	0.0555556
$325$	2.63068	0.145924
$326$	−23.0540	−1.27684
$327$	−14.0000	−0.774202
$328$	4.24621	0.234458
$329$	−18.8769	−1.04072
$330$	−1.43845	−0.0791839
$331$	−12.0000	−0.659580	−0.329790	−	0.944054i	$-0.606978\pi$
$331$	−12.0000	−0.659580	−0.329790	+	0.944054i	$0.606978\pi$
$332$	12.8078	0.702917
$333$	8.24621	0.451890
$334$	−5.12311	−0.280324
$335$	−0.177081	−0.00967497
$336$	−5.12311	−0.279488
$337$	−27.1231	−1.47749	−0.738745	−	0.673985i	$-0.764581\pi$
$337$	−27.1231	−1.47749	−0.738745	+	0.673985i	$0.764581\pi$
$338$	−12.6847	−0.689954
$339$	14.0000	0.760376
$340$	−3.19224	−0.173123
$341$	2.56155	0.138716
$342$	−2.56155	−0.138513
$343$	62.7386	3.38757
$344$	−9.12311	−0.491885
$345$	−4.49242	−0.241864
$346$	4.56155	0.245231
$347$	12.1771	0.653700	0.326850	−	0.945076i	$-0.394013\pi$
$347$	12.1771	0.653700	0.326850	+	0.945076i	$0.394013\pi$
$348$	7.12311	0.381839
$349$	15.6155	0.835880	0.417940	−	0.908475i	$-0.362752\pi$
$349$	15.6155	0.835880	0.417940	+	0.908475i	$0.362752\pi$
$350$	−24.0000	−1.28285
$351$	0.561553	0.0299735
$352$	−2.56155	−0.136531
$353$	18.8078	1.00104	0.500518	−	0.865726i	$-0.333143\pi$
$353$	18.8078	1.00104	0.500518	+	0.865726i	$0.333143\pi$
$354$	1.12311	0.0596924
$355$	0.807764	0.0428717
$356$	−0.246211	−0.0130492
$357$	−29.1231	−1.54136
$358$	23.0540	1.21844
$359$	29.3002	1.54640	0.773202	−	0.634159i	$-0.218654\pi$
$359$	29.3002	1.54640	0.773202	+	0.634159i	$0.218654\pi$
$360$	−0.561553	−0.0295964
$361$	−12.4384	−0.654655
$362$	−12.2462	−0.643647
$363$	4.43845	0.232958
$364$	−2.87689	−0.150790
$365$	−5.61553	−0.293930
$366$	0.561553	0.0293528
$367$	32.8078	1.71255	0.856276	−	0.516519i	$-0.172772\pi$
$367$	32.8078	1.71255	0.856276	+	0.516519i	$0.172772\pi$
$368$	−8.00000	−0.417029
$369$	4.24621	0.221049
$370$	−4.63068	−0.240738
$371$	−10.2462	−0.531957
$372$	1.00000	0.0518476
$373$	3.12311	0.161708	0.0808541	−	0.996726i	$-0.474235\pi$
$373$	3.12311	0.161708	0.0808541	+	0.996726i	$0.474235\pi$
$374$	−14.5616	−0.752960
$375$	−5.43845	−0.280840
$376$	−3.68466	−0.190022
$377$	4.00000	0.206010
$378$	−5.12311	−0.263504
$379$	−17.9309	−0.921047	−0.460523	−	0.887648i	$-0.652338\pi$
$379$	−17.9309	−0.921047	−0.460523	+	0.887648i	$0.652338\pi$
$380$	1.43845	0.0737908
$381$	−10.2462	−0.524929
$382$	16.0000	0.818631
$383$	−17.6155	−0.900111	−0.450056	−	0.893000i	$-0.648596\pi$
$383$	−17.6155	−0.900111	−0.450056	+	0.893000i	$0.648596\pi$
$384$	−1.00000	−0.0510310
$385$	7.36932	0.375575
$386$	24.5616	1.25015
$387$	−9.12311	−0.463754
$388$	−14.8078	−0.751750
$389$	−12.2462	−0.620908	−0.310454	−	0.950588i	$-0.600481\pi$
$389$	−12.2462	−0.620908	−0.310454	+	0.950588i	$0.600481\pi$
$390$	−0.315342	−0.0159679
$391$	−45.4773	−2.29988
$392$	19.2462	0.972080
$393$	−17.1231	−0.863746
$394$	8.24621	0.415438
$395$	2.06913	0.104109
$396$	−2.56155	−0.128723
$397$	12.7386	0.639334	0.319667	−	0.947530i	$-0.396429\pi$
$397$	12.7386	0.639334	0.319667	+	0.947530i	$0.396429\pi$
$398$	4.31534	0.216309
$399$	13.1231	0.656977
$400$	−4.68466	−0.234233
$401$	−27.9309	−1.39480	−0.697401	−	0.716682i	$-0.745660\pi$
$401$	−27.9309	−1.39480	−0.697401	+	0.716682i	$0.745660\pi$
$402$	−0.315342	−0.0157278
$403$	0.561553	0.0279729
$404$	16.2462	0.808279
$405$	−0.561553	−0.0279038
$406$	−36.4924	−1.81109
$407$	−21.1231	−1.04703
$408$	−5.68466	−0.281433
$409$	4.24621	0.209962	0.104981	−	0.994474i	$-0.466522\pi$
$409$	4.24621	0.209962	0.104981	+	0.994474i	$0.466522\pi$
$410$	−2.38447	−0.117761
$411$	6.00000	0.295958
$412$	−5.12311	−0.252397
$413$	−5.75379	−0.283125
$414$	−8.00000	−0.393179
$415$	−7.19224	−0.353053
$416$	−0.561553	−0.0275324
$417$	12.0000	0.587643
$418$	6.56155	0.320936
$419$	−6.24621	−0.305147	−0.152574	−	0.988292i	$-0.548756\pi$
$419$	−6.24621	−0.305147	−0.152574	+	0.988292i	$0.548756\pi$
$420$	2.87689	0.140378
$421$	−24.7386	−1.20569	−0.602844	−	0.797859i	$-0.705966\pi$
$421$	−24.7386	−1.20569	−0.602844	+	0.797859i	$0.705966\pi$
$422$	−1.75379	−0.0853731
$423$	−3.68466	−0.179154
$424$	−2.00000	−0.0971286
$425$	−26.6307	−1.29178
$426$	1.43845	0.0696930
$427$	−2.87689	−0.139223
$428$	−4.00000	−0.193347
$429$	−1.43845	−0.0694489
$430$	5.12311	0.247058
$431$	40.9848	1.97417	0.987085	−	0.160196i	$-0.0512126\pi$
$431$	40.9848	1.97417	0.987085	+	0.160196i	$0.0512126\pi$
$432$	−1.00000	−0.0481125
$433$	35.6155	1.71157	0.855787	−	0.517329i	$-0.173074\pi$
$433$	35.6155	1.71157	0.855787	+	0.517329i	$0.173074\pi$
$434$	−5.12311	−0.245917
$435$	−4.00000	−0.191785
$436$	14.0000	0.670478
$437$	20.4924	0.980286
$438$	−10.0000	−0.477818
$439$	−38.7386	−1.84889	−0.924447	−	0.381310i	$-0.875473\pi$
$439$	−38.7386	−1.84889	−0.924447	+	0.381310i	$0.875473\pi$
$440$	1.43845	0.0685753
$441$	19.2462	0.916486
$442$	−3.19224	−0.151839
$443$	−11.3693	−0.540173	−0.270086	−	0.962836i	$-0.587052\pi$
$443$	−11.3693	−0.540173	−0.270086	+	0.962836i	$0.587052\pi$
$444$	−8.24621	−0.391348
$445$	0.138261	0.00655418
$446$	19.6847	0.932096
$447$	−9.68466	−0.458069
$448$	5.12311	0.242044
$449$	2.80776	0.132507	0.0662533	−	0.997803i	$-0.478895\pi$
$449$	2.80776	0.132507	0.0662533	+	0.997803i	$0.478895\pi$
$450$	−4.68466	−0.220837
$451$	−10.8769	−0.512173
$452$	−14.0000	−0.658505
$453$	−5.93087	−0.278657
$454$	−19.3693	−0.909047
$455$	1.61553	0.0757371
$456$	2.56155	0.119956
$457$	−0.246211	−0.0115173	−0.00575864	−	0.999983i	$-0.501833\pi$
$457$	−0.246211	−0.0115173	−0.00575864	+	0.999983i	$0.501833\pi$
$458$	17.6847	0.826350
$459$	−5.68466	−0.265337
$460$	4.49242	0.209460
$461$	32.2462	1.50186	0.750928	−	0.660384i	$-0.229607\pi$
$461$	32.2462	1.50186	0.750928	+	0.660384i	$0.229607\pi$
$462$	13.1231	0.610542
$463$	−13.9309	−0.647422	−0.323711	−	0.946156i	$-0.604931\pi$
$463$	−13.9309	−0.647422	−0.323711	+	0.946156i	$0.604931\pi$
$464$	−7.12311	−0.330682
$465$	−0.561553	−0.0260414
$466$	11.6155	0.538079
$467$	−22.2462	−1.02943	−0.514716	−	0.857361i	$-0.672103\pi$
$467$	−22.2462	−1.02943	−0.514716	+	0.857361i	$0.672103\pi$
$468$	−0.561553	−0.0259578
$469$	1.61553	0.0745982
$470$	2.06913	0.0954419
$471$	9.36932	0.431715
$472$	−1.12311	−0.0516951
$473$	23.3693	1.07452
$474$	3.68466	0.169242
$475$	12.0000	0.550598
$476$	29.1231	1.33486
$477$	−2.00000	−0.0915737
$478$	−20.4924	−0.937302
$479$	29.9309	1.36758	0.683788	−	0.729681i	$-0.260331\pi$
$479$	29.9309	1.36758	0.683788	+	0.729681i	$0.260331\pi$
$480$	0.561553	0.0256313
$481$	−4.63068	−0.211141
$482$	7.75379	0.353175
$483$	40.9848	1.86488
$484$	−4.43845	−0.201748
$485$	8.31534	0.377580
$486$	−1.00000	−0.0453609
$487$	−11.6847	−0.529482	−0.264741	−	0.964319i	$-0.585287\pi$
$487$	−11.6847	−0.529482	−0.264741	+	0.964319i	$0.585287\pi$
$488$	−0.561553	−0.0254203
$489$	23.0540	1.04254
$490$	−10.8078	−0.488245
$491$	20.0000	0.902587	0.451294	−	0.892375i	$-0.350963\pi$
$491$	20.0000	0.902587	0.451294	+	0.892375i	$0.350963\pi$
$492$	−4.24621	−0.191434
$493$	−40.4924	−1.82369
$494$	1.43845	0.0647188
$495$	1.43845	0.0646534
$496$	−1.00000	−0.0449013
$497$	−7.36932	−0.330559
$498$	−12.8078	−0.573930
$499$	1.75379	0.0785104	0.0392552	−	0.999229i	$-0.487501\pi$
$499$	1.75379	0.0785104	0.0392552	+	0.999229i	$0.487501\pi$
$500$	5.43845	0.243215
$501$	5.12311	0.228883
$502$	20.0000	0.892644
$503$	−32.1771	−1.43471	−0.717353	−	0.696710i	$-0.754646\pi$
$503$	−32.1771	−1.43471	−0.717353	+	0.696710i	$0.754646\pi$
$504$	5.12311	0.228201
$505$	−9.12311	−0.405973
$506$	20.4924	0.910999
$507$	12.6847	0.563345
$508$	10.2462	0.454602
$509$	−37.8617	−1.67819	−0.839096	−	0.543983i	$-0.816915\pi$
$509$	−37.8617	−1.67819	−0.839096	+	0.543983i	$0.816915\pi$
$510$	3.19224	0.141355
$511$	51.2311	2.26633
$512$	1.00000	0.0441942
$513$	2.56155	0.113095
$514$	−16.8769	−0.744408
$515$	2.87689	0.126771
$516$	9.12311	0.401622
$517$	9.43845	0.415102
$518$	42.2462	1.85619
$519$	−4.56155	−0.200230
$520$	0.315342	0.0138286
$521$	−23.6155	−1.03462	−0.517308	−	0.855800i	$-0.673066\pi$
$521$	−23.6155	−1.03462	−0.517308	+	0.855800i	$0.673066\pi$
$522$	−7.12311	−0.311770
$523$	−25.1231	−1.09856	−0.549278	−	0.835639i	$-0.685097\pi$
$523$	−25.1231	−1.09856	−0.549278	+	0.835639i	$0.685097\pi$
$524$	17.1231	0.748026
$525$	24.0000	1.04745
$526$	−2.24621	−0.0979395
$527$	−5.68466	−0.247628
$528$	2.56155	0.111477
$529$	41.0000	1.78261
$530$	1.12311	0.0487846
$531$	−1.12311	−0.0487386
$532$	−13.1231	−0.568959
$533$	−2.38447	−0.103283
$534$	0.246211	0.0106546
$535$	2.24621	0.0971122
$536$	0.315342	0.0136207
$537$	−23.0540	−0.994852
$538$	−14.4924	−0.624813
$539$	−49.3002	−2.12351
$540$	0.561553	0.0241654
$541$	−41.3693	−1.77861	−0.889303	−	0.457319i	$-0.848810\pi$
$541$	−41.3693	−1.77861	−0.889303	+	0.457319i	$0.848810\pi$
$542$	−3.68466	−0.158270
$543$	12.2462	0.525535
$544$	5.68466	0.243728
$545$	−7.86174	−0.336760
$546$	2.87689	0.123120
$547$	−26.7386	−1.14326	−0.571631	−	0.820511i	$-0.693689\pi$
$547$	−26.7386	−1.14326	−0.571631	+	0.820511i	$0.693689\pi$
$548$	−6.00000	−0.256307
$549$	−0.561553	−0.0239665
$550$	12.0000	0.511682
$551$	18.2462	0.777315
$552$	8.00000	0.340503
$553$	−18.8769	−0.802727
$554$	7.43845	0.316029
$555$	4.63068	0.196562
$556$	−12.0000	−0.508913
$557$	−17.3693	−0.735962	−0.367981	−	0.929833i	$-0.619951\pi$
$557$	−17.3693	−0.735962	−0.367981	+	0.929833i	$0.619951\pi$
$558$	−1.00000	−0.0423334
$559$	5.12311	0.216684
$560$	−2.87689	−0.121571
$561$	14.5616	0.614789
$562$	14.4924	0.611326
$563$	−12.0000	−0.505740	−0.252870	−	0.967500i	$-0.581374\pi$
$563$	−12.0000	−0.505740	−0.252870	+	0.967500i	$0.581374\pi$
$564$	3.68466	0.155152
$565$	7.86174	0.330746
$566$	−3.19224	−0.134180
$567$	5.12311	0.215150
$568$	−1.43845	−0.0603559
$569$	4.24621	0.178010	0.0890052	−	0.996031i	$-0.471631\pi$
$569$	4.24621	0.178010	0.0890052	+	0.996031i	$0.471631\pi$
$570$	−1.43845	−0.0602499
$571$	28.9848	1.21298	0.606489	−	0.795092i	$-0.292577\pi$
$571$	28.9848	1.21298	0.606489	+	0.795092i	$0.292577\pi$
$572$	1.43845	0.0601445
$573$	−16.0000	−0.668410
$574$	21.7538	0.907986
$575$	37.4773	1.56291
$576$	1.00000	0.0416667
$577$	−7.43845	−0.309667	−0.154833	−	0.987941i	$-0.549484\pi$
$577$	−7.43845	−0.309667	−0.154833	+	0.987941i	$0.549484\pi$
$578$	15.3153	0.637034
$579$	−24.5616	−1.02074
$580$	4.00000	0.166091
$581$	65.6155	2.72219
$582$	14.8078	0.613802
$583$	5.12311	0.212177
$584$	10.0000	0.413803
$585$	0.315342	0.0130378
$586$	6.00000	0.247858
$587$	25.3002	1.04425	0.522125	−	0.852869i	$-0.325139\pi$
$587$	25.3002	1.04425	0.522125	+	0.852869i	$0.325139\pi$
$588$	−19.2462	−0.793700
$589$	2.56155	0.105547
$590$	0.630683	0.0259648
$591$	−8.24621	−0.339204
$592$	8.24621	0.338917
$593$	−34.4924	−1.41643	−0.708217	−	0.705995i	$-0.750500\pi$
$593$	−34.4924	−1.41643	−0.708217	+	0.705995i	$0.750500\pi$
$594$	2.56155	0.105102
$595$	−16.3542	−0.670455
$596$	9.68466	0.396699
$597$	−4.31534	−0.176615
$598$	4.49242	0.183709
$599$	−20.3153	−0.830062	−0.415031	−	0.909807i	$-0.636229\pi$
$599$	−20.3153	−0.830062	−0.415031	+	0.909807i	$0.636229\pi$
$600$	4.68466	0.191250
$601$	−11.7538	−0.479447	−0.239724	−	0.970841i	$-0.577057\pi$
$601$	−11.7538	−0.479447	−0.239724	+	0.970841i	$0.577057\pi$
$602$	−46.7386	−1.90492
$603$	0.315342	0.0128417
$604$	5.93087	0.241324
$605$	2.49242	0.101331
$606$	−16.2462	−0.659957
$607$	7.36932	0.299111	0.149556	−	0.988753i	$-0.452216\pi$
$607$	7.36932	0.299111	0.149556	+	0.988753i	$0.452216\pi$
$608$	−2.56155	−0.103885
$609$	36.4924	1.47875
$610$	0.315342	0.0127678
$611$	2.06913	0.0837081
$612$	5.68466	0.229789
$613$	13.1922	0.532829	0.266415	−	0.963859i	$-0.414161\pi$
$613$	13.1922	0.532829	0.266415	+	0.963859i	$0.414161\pi$
$614$	−1.75379	−0.0707772
$615$	2.38447	0.0961512
$616$	−13.1231	−0.528745
$617$	−22.0000	−0.885687	−0.442843	−	0.896599i	$-0.646030\pi$
$617$	−22.0000	−0.885687	−0.442843	+	0.896599i	$0.646030\pi$
$618$	5.12311	0.206082
$619$	9.75379	0.392038	0.196019	−	0.980600i	$-0.437199\pi$
$619$	9.75379	0.392038	0.196019	+	0.980600i	$0.437199\pi$
$620$	0.561553	0.0225525
$621$	8.00000	0.321029
$622$	21.9309	0.879348
$623$	−1.26137	−0.0505356
$624$	0.561553	0.0224801
$625$	20.3693	0.814773
$626$	−16.2462	−0.649329
$627$	−6.56155	−0.262043
$628$	−9.36932	−0.373876
$629$	46.8769	1.86910
$630$	−2.87689	−0.114618
$631$	8.00000	0.318475	0.159237	−	0.987240i	$-0.449096\pi$
$631$	8.00000	0.318475	0.159237	+	0.987240i	$0.449096\pi$
$632$	−3.68466	−0.146568
$633$	1.75379	0.0697068
$634$	10.3153	0.409675
$635$	−5.75379	−0.228332
$636$	2.00000	0.0793052
$637$	−10.8078	−0.428219
$638$	18.2462	0.722374
$639$	−1.43845	−0.0569041
$640$	−0.561553	−0.0221973
$641$	−10.3153	−0.407431	−0.203716	−	0.979030i	$-0.565302\pi$
$641$	−10.3153	−0.407431	−0.203716	+	0.979030i	$0.565302\pi$
$642$	4.00000	0.157867
$643$	−20.0000	−0.788723	−0.394362	−	0.918955i	$-0.629034\pi$
$643$	−20.0000	−0.788723	−0.394362	+	0.918955i	$0.629034\pi$
$644$	−40.9848	−1.61503
$645$	−5.12311	−0.201722
$646$	−14.5616	−0.572917
$647$	−35.8617	−1.40987	−0.704935	−	0.709272i	$-0.749024\pi$
$647$	−35.8617	−1.40987	−0.704935	+	0.709272i	$0.749024\pi$
$648$	1.00000	0.0392837
$649$	2.87689	0.112928
$650$	2.63068	0.103184
$651$	5.12311	0.200790
$652$	−23.0540	−0.902863
$653$	−33.5464	−1.31277	−0.656386	−	0.754425i	$-0.727916\pi$
$653$	−33.5464	−1.31277	−0.656386	+	0.754425i	$0.727916\pi$
$654$	−14.0000	−0.547443
$655$	−9.61553	−0.375710
$656$	4.24621	0.165787
$657$	10.0000	0.390137
$658$	−18.8769	−0.735898
$659$	−19.3693	−0.754521	−0.377261	−	0.926107i	$-0.623134\pi$
$659$	−19.3693	−0.754521	−0.377261	+	0.926107i	$0.623134\pi$
$660$	−1.43845	−0.0559915
$661$	44.1080	1.71560	0.857800	−	0.513983i	$-0.171831\pi$
$661$	44.1080	1.71560	0.857800	+	0.513983i	$0.171831\pi$
$662$	−12.0000	−0.466393
$663$	3.19224	0.123976
$664$	12.8078	0.497038
$665$	7.36932	0.285770
$666$	8.24621	0.319534
$667$	56.9848	2.20646
$668$	−5.12311	−0.198219
$669$	−19.6847	−0.761053
$670$	−0.177081	−0.00684123
$671$	1.43845	0.0555306
$672$	−5.12311	−0.197628
$673$	−0.876894	−0.0338018	−0.0169009	−	0.999857i	$-0.505380\pi$
$673$	−0.876894	−0.0338018	−0.0169009	+	0.999857i	$0.505380\pi$
$674$	−27.1231	−1.04474
$675$	4.68466	0.180313
$676$	−12.6847	−0.487871
$677$	0.876894	0.0337018	0.0168509	−	0.999858i	$-0.494636\pi$
$677$	0.876894	0.0337018	0.0168509	+	0.999858i	$0.494636\pi$
$678$	14.0000	0.537667
$679$	−75.8617	−2.91131
$680$	−3.19224	−0.122417
$681$	19.3693	0.742234
$682$	2.56155	0.0980869
$683$	−50.7386	−1.94146	−0.970730	−	0.240174i	$-0.922796\pi$
$683$	−50.7386	−1.94146	−0.970730	+	0.240174i	$0.922796\pi$
$684$	−2.56155	−0.0979434
$685$	3.36932	0.128735
$686$	62.7386	2.39537
$687$	−17.6847	−0.674712
$688$	−9.12311	−0.347815
$689$	1.12311	0.0427869
$690$	−4.49242	−0.171024
$691$	−4.17708	−0.158904	−0.0794518	−	0.996839i	$-0.525317\pi$
$691$	−4.17708	−0.158904	−0.0794518	+	0.996839i	$0.525317\pi$
$692$	4.56155	0.173404
$693$	−13.1231	−0.498506
$694$	12.1771	0.462236
$695$	6.73863	0.255611
$696$	7.12311	0.270001
$697$	24.1383	0.914302
$698$	15.6155	0.591056
$699$	−11.6155	−0.439340
$700$	−24.0000	−0.907115
$701$	−4.06913	−0.153689	−0.0768445	−	0.997043i	$-0.524484\pi$
$701$	−4.06913	−0.153689	−0.0768445	+	0.997043i	$0.524484\pi$
$702$	0.561553	0.0211944
$703$	−21.1231	−0.796673
$704$	−2.56155	−0.0965422
$705$	−2.06913	−0.0779280
$706$	18.8078	0.707840
$707$	83.2311	3.13023
$708$	1.12311	0.0422089
$709$	−20.4233	−0.767013	−0.383506	−	0.923538i	$-0.625284\pi$
$709$	−20.4233	−0.767013	−0.383506	+	0.923538i	$0.625284\pi$
$710$	0.807764	0.0303148
$711$	−3.68466	−0.138185
$712$	−0.246211	−0.00922716
$713$	8.00000	0.299602
$714$	−29.1231	−1.08990
$715$	−0.807764	−0.0302087
$716$	23.0540	0.861568
$717$	20.4924	0.765304
$718$	29.3002	1.09347
$719$	4.49242	0.167539	0.0837695	−	0.996485i	$-0.473304\pi$
$719$	4.49242	0.167539	0.0837695	+	0.996485i	$0.473304\pi$
$720$	−0.561553	−0.0209278
$721$	−26.2462	−0.977460
$722$	−12.4384	−0.462911
$723$	−7.75379	−0.288367
$724$	−12.2462	−0.455127
$725$	33.3693	1.23931
$726$	4.43845	0.164726
$727$	−13.7538	−0.510100	−0.255050	−	0.966928i	$-0.582092\pi$
$727$	−13.7538	−0.510100	−0.255050	+	0.966928i	$0.582092\pi$
$728$	−2.87689	−0.106625
$729$	1.00000	0.0370370
$730$	−5.61553	−0.207840
$731$	−51.8617	−1.91818
$732$	0.561553	0.0207556
$733$	8.24621	0.304581	0.152290	−	0.988336i	$-0.451335\pi$
$733$	8.24621	0.304581	0.152290	+	0.988336i	$0.451335\pi$
$734$	32.8078	1.21096
$735$	10.8078	0.398650
$736$	−8.00000	−0.294884
$737$	−0.807764	−0.0297544
$738$	4.24621	0.156305
$739$	12.0000	0.441427	0.220714	−	0.975339i	$-0.429161\pi$
$739$	12.0000	0.441427	0.220714	+	0.975339i	$0.429161\pi$
$740$	−4.63068	−0.170227
$741$	−1.43845	−0.0528427
$742$	−10.2462	−0.376150
$743$	−8.00000	−0.293492	−0.146746	−	0.989174i	$-0.546880\pi$
$743$	−8.00000	−0.293492	−0.146746	+	0.989174i	$0.546880\pi$
$744$	1.00000	0.0366618
$745$	−5.43845	−0.199249
$746$	3.12311	0.114345
$747$	12.8078	0.468612
$748$	−14.5616	−0.532423
$749$	−20.4924	−0.748777
$750$	−5.43845	−0.198584
$751$	−18.8769	−0.688828	−0.344414	−	0.938818i	$-0.611922\pi$
$751$	−18.8769	−0.688828	−0.344414	+	0.938818i	$0.611922\pi$
$752$	−3.68466	−0.134366
$753$	−20.0000	−0.728841
$754$	4.00000	0.145671
$755$	−3.33050	−0.121209
$756$	−5.12311	−0.186326
$757$	40.2462	1.46277	0.731387	−	0.681963i	$-0.238873\pi$
$757$	40.2462	1.46277	0.731387	+	0.681963i	$0.238873\pi$
$758$	−17.9309	−0.651279
$759$	−20.4924	−0.743828
$760$	1.43845	0.0521780
$761$	−40.4233	−1.46534	−0.732672	−	0.680582i	$-0.761727\pi$
$761$	−40.4233	−1.46534	−0.732672	+	0.680582i	$0.761727\pi$
$762$	−10.2462	−0.371181
$763$	71.7235	2.59656
$764$	16.0000	0.578860
$765$	−3.19224	−0.115416
$766$	−17.6155	−0.636475
$767$	0.630683	0.0227726
$768$	−1.00000	−0.0360844
$769$	7.75379	0.279609	0.139804	−	0.990179i	$-0.455353\pi$
$769$	7.75379	0.279609	0.139804	+	0.990179i	$0.455353\pi$
$770$	7.36932	0.265572
$771$	16.8769	0.607807
$772$	24.5616	0.883990
$773$	31.6155	1.13713	0.568566	−	0.822638i	$-0.307498\pi$
$773$	31.6155	1.13713	0.568566	+	0.822638i	$0.307498\pi$
$774$	−9.12311	−0.327923
$775$	4.68466	0.168278
$776$	−14.8078	−0.531568
$777$	−42.2462	−1.51557
$778$	−12.2462	−0.439048
$779$	−10.8769	−0.389705
$780$	−0.315342	−0.0112910
$781$	3.68466	0.131847
$782$	−45.4773	−1.62626
$783$	7.12311	0.254559
$784$	19.2462	0.687365
$785$	5.26137	0.187786
$786$	−17.1231	−0.610761
$787$	−15.5076	−0.552785	−0.276393	−	0.961045i	$-0.589139\pi$
$787$	−15.5076	−0.552785	−0.276393	+	0.961045i	$0.589139\pi$
$788$	8.24621	0.293759
$789$	2.24621	0.0799672
$790$	2.06913	0.0736164
$791$	−71.7235	−2.55019
$792$	−2.56155	−0.0910208
$793$	0.315342	0.0111981
$794$	12.7386	0.452077
$795$	−1.12311	−0.0398325
$796$	4.31534	0.152953
$797$	54.3542	1.92532	0.962662	−	0.270708i	$-0.0872577\pi$
$797$	54.3542	1.92532	0.962662	+	0.270708i	$0.0872577\pi$
$798$	13.1231	0.464553
$799$	−20.9460	−0.741017
$800$	−4.68466	−0.165628
$801$	−0.246211	−0.00869945
$802$	−27.9309	−0.986273
$803$	−25.6155	−0.903952
$804$	−0.315342	−0.0111212
$805$	23.0152	0.811178
$806$	0.561553	0.0197799
$807$	14.4924	0.510157
$808$	16.2462	0.571540
$809$	−17.0540	−0.599586	−0.299793	−	0.954004i	$-0.596918\pi$
$809$	−17.0540	−0.599586	−0.299793	+	0.954004i	$0.596918\pi$
$810$	−0.561553	−0.0197310
$811$	16.4924	0.579127	0.289564	−	0.957159i	$-0.406490\pi$
$811$	16.4924	0.579127	0.289564	+	0.957159i	$0.406490\pi$
$812$	−36.4924	−1.28063
$813$	3.68466	0.129227
$814$	−21.1231	−0.740364
$815$	12.9460	0.453479
$816$	−5.68466	−0.199003
$817$	23.3693	0.817589
$818$	4.24621	0.148465
$819$	−2.87689	−0.100527
$820$	−2.38447	−0.0832694
$821$	−2.00000	−0.0698005	−0.0349002	−	0.999391i	$-0.511111\pi$
$821$	−2.00000	−0.0698005	−0.0349002	+	0.999391i	$0.511111\pi$
$822$	6.00000	0.209274
$823$	11.6847	0.407302	0.203651	−	0.979044i	$-0.434719\pi$
$823$	11.6847	0.407302	0.203651	+	0.979044i	$0.434719\pi$
$824$	−5.12311	−0.178472
$825$	−12.0000	−0.417786
$826$	−5.75379	−0.200200
$827$	−30.4233	−1.05792	−0.528961	−	0.848646i	$-0.677418\pi$
$827$	−30.4233	−1.05792	−0.528961	+	0.848646i	$0.677418\pi$
$828$	−8.00000	−0.278019
$829$	−4.24621	−0.147477	−0.0737385	−	0.997278i	$-0.523493\pi$
$829$	−4.24621	−0.147477	−0.0737385	+	0.997278i	$0.523493\pi$
$830$	−7.19224	−0.249646
$831$	−7.43845	−0.258037
$832$	−0.561553	−0.0194683
$833$	109.408	3.79077
$834$	12.0000	0.415526
$835$	2.87689	0.0995590
$836$	6.56155	0.226936
$837$	1.00000	0.0345651
$838$	−6.24621	−0.215772
$839$	−13.7538	−0.474834	−0.237417	−	0.971408i	$-0.576301\pi$
$839$	−13.7538	−0.474834	−0.237417	+	0.971408i	$0.576301\pi$
$840$	2.87689	0.0992623
$841$	21.7386	0.749608
$842$	−24.7386	−0.852550
$843$	−14.4924	−0.499146
$844$	−1.75379	−0.0603679
$845$	7.12311	0.245042
$846$	−3.68466	−0.126681
$847$	−22.7386	−0.781309
$848$	−2.00000	−0.0686803
$849$	3.19224	0.109557
$850$	−26.6307	−0.913425
$851$	−65.9697	−2.26141
$852$	1.43845	0.0492804
$853$	−29.2311	−1.00085	−0.500426	−	0.865779i	$-0.666823\pi$
$853$	−29.2311	−1.00085	−0.500426	+	0.865779i	$0.666823\pi$
$854$	−2.87689	−0.0984453
$855$	1.43845	0.0491939
$856$	−4.00000	−0.136717
$857$	−28.1080	−0.960149	−0.480075	−	0.877228i	$-0.659390\pi$
$857$	−28.1080	−0.960149	−0.480075	+	0.877228i	$0.659390\pi$
$858$	−1.43845	−0.0491078
$859$	58.1080	1.98262	0.991309	−	0.131555i	$-0.0419971\pi$
$859$	58.1080	1.98262	0.991309	+	0.131555i	$0.0419971\pi$
$860$	5.12311	0.174696
$861$	−21.7538	−0.741367
$862$	40.9848	1.39595
$863$	17.6155	0.599640	0.299820	−	0.953996i	$-0.403073\pi$
$863$	17.6155	0.599640	0.299820	+	0.953996i	$0.403073\pi$
$864$	−1.00000	−0.0340207
$865$	−2.56155	−0.0870954
$866$	35.6155	1.21026
$867$	−15.3153	−0.520136
$868$	−5.12311	−0.173890
$869$	9.43845	0.320177
$870$	−4.00000	−0.135613
$871$	−0.177081	−0.00600016
$872$	14.0000	0.474100
$873$	−14.8078	−0.501167
$874$	20.4924	0.693167
$875$	27.8617	0.941899
$876$	−10.0000	−0.337869
$877$	31.6155	1.06758	0.533790	−	0.845617i	$-0.320767\pi$
$877$	31.6155	1.06758	0.533790	+	0.845617i	$0.320767\pi$
$878$	−38.7386	−1.30737
$879$	−6.00000	−0.202375
$880$	1.43845	0.0484900
$881$	47.9309	1.61483	0.807416	−	0.589983i	$-0.200865\pi$
$881$	47.9309	1.61483	0.807416	+	0.589983i	$0.200865\pi$
$882$	19.2462	0.648054
$883$	14.8769	0.500647	0.250324	−	0.968162i	$-0.419463\pi$
$883$	14.8769	0.500647	0.250324	+	0.968162i	$0.419463\pi$
$884$	−3.19224	−0.107367
$885$	−0.630683	−0.0212002
$886$	−11.3693	−0.381960
$887$	28.4924	0.956682	0.478341	−	0.878174i	$-0.341238\pi$
$887$	28.4924	0.956682	0.478341	+	0.878174i	$0.341238\pi$
$888$	−8.24621	−0.276725
$889$	52.4924	1.76054
$890$	0.138261	0.00463451
$891$	−2.56155	−0.0858152
$892$	19.6847	0.659091
$893$	9.43845	0.315846
$894$	−9.68466	−0.323903
$895$	−12.9460	−0.432738
$896$	5.12311	0.171151
$897$	−4.49242	−0.149998
$898$	2.80776	0.0936963
$899$	7.12311	0.237569
$900$	−4.68466	−0.156155
$901$	−11.3693	−0.378767
$902$	−10.8769	−0.362161
$903$	46.7386	1.55536
$904$	−14.0000	−0.465633
$905$	6.87689	0.228596
$906$	−5.93087	−0.197040
$907$	5.43845	0.180581	0.0902903	−	0.995915i	$-0.471220\pi$
$907$	5.43845	0.180581	0.0902903	+	0.995915i	$0.471220\pi$
$908$	−19.3693	−0.642793
$909$	16.2462	0.538853
$910$	1.61553	0.0535542
$911$	−16.0000	−0.530104	−0.265052	−	0.964234i	$-0.585389\pi$
$911$	−16.0000	−0.530104	−0.265052	+	0.964234i	$0.585389\pi$
$912$	2.56155	0.0848215
$913$	−32.8078	−1.08578
$914$	−0.246211	−0.00814394
$915$	−0.315342	−0.0104249
$916$	17.6847	0.584318
$917$	87.7235	2.89688
$918$	−5.68466	−0.187622
$919$	44.4924	1.46767	0.733835	−	0.679328i	$-0.237729\pi$
$919$	44.4924	1.46767	0.733835	+	0.679328i	$0.237729\pi$
$920$	4.49242	0.148111
$921$	1.75379	0.0577893
$922$	32.2462	1.06197
$923$	0.807764	0.0265879
$924$	13.1231	0.431718
$925$	−38.6307	−1.27017
$926$	−13.9309	−0.457797
$927$	−5.12311	−0.168265
$928$	−7.12311	−0.233827
$929$	6.49242	0.213009	0.106505	−	0.994312i	$-0.466034\pi$
$929$	6.49242	0.213009	0.106505	+	0.994312i	$0.466034\pi$
$930$	−0.561553	−0.0184140
$931$	−49.3002	−1.61575
$932$	11.6155	0.380479
$933$	−21.9309	−0.717984
$934$	−22.2462	−0.727918
$935$	8.17708	0.267419
$936$	−0.561553	−0.0183549
$937$	−1.05398	−0.0344319	−0.0172159	−	0.999852i	$-0.505480\pi$
$937$	−1.05398	−0.0344319	−0.0172159	+	0.999852i	$0.505480\pi$
$938$	1.61553	0.0527489
$939$	16.2462	0.530175
$940$	2.06913	0.0674876
$941$	−2.63068	−0.0857578	−0.0428789	−	0.999080i	$-0.513653\pi$
$941$	−2.63068	−0.0857578	−0.0428789	+	0.999080i	$0.513653\pi$
$942$	9.36932	0.305269
$943$	−33.9697	−1.10621
$944$	−1.12311	−0.0365540
$945$	2.87689	0.0935854
$946$	23.3693	0.759802
$947$	34.5616	1.12310	0.561550	−	0.827443i	$-0.310205\pi$
$947$	34.5616	1.12310	0.561550	+	0.827443i	$0.310205\pi$
$948$	3.68466	0.119672
$949$	−5.61553	−0.182288
$950$	12.0000	0.389331
$951$	−10.3153	−0.334498
$952$	29.1231	0.943885
$953$	−21.5464	−0.697956	−0.348978	−	0.937131i	$-0.613471\pi$
$953$	−21.5464	−0.697956	−0.348978	+	0.937131i	$0.613471\pi$
$954$	−2.00000	−0.0647524
$955$	−8.98485	−0.290743
$956$	−20.4924	−0.662772
$957$	−18.2462	−0.589816
$958$	29.9309	0.967023
$959$	−30.7386	−0.992602
$960$	0.561553	0.0181240
$961$	1.00000	0.0322581
$962$	−4.63068	−0.149299
$963$	−4.00000	−0.128898
$964$	7.75379	0.249733
$965$	−13.7926	−0.444000
$966$	40.9848	1.31867
$967$	46.5616	1.49732	0.748659	−	0.662955i	$-0.230698\pi$
$967$	46.5616	1.49732	0.748659	+	0.662955i	$0.230698\pi$
$968$	−4.43845	−0.142657
$969$	14.5616	0.467784
$970$	8.31534	0.266990
$971$	−18.3845	−0.589986	−0.294993	−	0.955499i	$-0.595317\pi$
$971$	−18.3845	−0.589986	−0.294993	+	0.955499i	$0.595317\pi$
$972$	−1.00000	−0.0320750
$973$	−61.4773	−1.97087
$974$	−11.6847	−0.374401
$975$	−2.63068	−0.0842493
$976$	−0.561553	−0.0179749
$977$	44.2462	1.41556	0.707781	−	0.706432i	$-0.249696\pi$
$977$	44.2462	1.41556	0.707781	+	0.706432i	$0.249696\pi$
$978$	23.0540	0.737185
$979$	0.630683	0.0201567
$980$	−10.8078	−0.345241
$981$	14.0000	0.446986
$982$	20.0000	0.638226
$983$	−18.2462	−0.581964	−0.290982	−	0.956729i	$-0.593982\pi$
$983$	−18.2462	−0.581964	−0.290982	+	0.956729i	$0.593982\pi$
$984$	−4.24621	−0.135364
$985$	−4.63068	−0.147546
$986$	−40.4924	−1.28954
$987$	18.8769	0.600858
$988$	1.43845	0.0457631
$989$	72.9848	2.32078
$990$	1.43845	0.0457169
$991$	46.7386	1.48470	0.742351	−	0.670011i	$-0.233711\pi$
$991$	46.7386	1.48470	0.742351	+	0.670011i	$0.233711\pi$
$992$	−1.00000	−0.0317500
$993$	12.0000	0.380808
$994$	−7.36932	−0.233741
$995$	−2.42329	−0.0768235
$996$	−12.8078	−0.405830
$997$	−26.0000	−0.823428	−0.411714	−	0.911313i	$-0.635070\pi$
$997$	−26.0000	−0.823428	−0.411714	+	0.911313i	$0.635070\pi$
$998$	1.75379	0.0555152
$999$	−8.24621	−0.260899

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	186.2.a.d.1.1	✓	2
3.2	odd	2		558.2.a.i.1.2		2
4.3	odd	2		1488.2.a.r.1.1		2
5.2	odd	4		4650.2.d.bc.3349.4		4
5.3	odd	4		4650.2.d.bc.3349.1		4
5.4	even	2		4650.2.a.cd.1.1		2
7.6	odd	2		9114.2.a.be.1.2		2
8.3	odd	2		5952.2.a.bk.1.2		2
8.5	even	2		5952.2.a.bs.1.2		2
12.11	even	2		4464.2.a.bb.1.2		2
31.30	odd	2		5766.2.a.v.1.1		2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
186.2.a.d.1.1	✓	2	1.1	even	1	trivial
558.2.a.i.1.2		2	3.2	odd	2
1488.2.a.r.1.1		2	4.3	odd	2
4464.2.a.bb.1.2		2	12.11	even	2
4650.2.a.cd.1.1		2	5.4	even	2
4650.2.d.bc.3349.1		4	5.3	odd	4
4650.2.d.bc.3349.4		4	5.2	odd	4
5766.2.a.v.1.1		2	31.30	odd	2
5952.2.a.bk.1.2		2	8.3	odd	2
5952.2.a.bs.1.2		2	8.5	even	2
9114.2.a.be.1.2		2	7.6	odd	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 186 = 2 \cdot 3 \cdot 31 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	186.a (trivial)

\(f(q)\)	\(=\)	\(q+1.00000 q^{2} -1.00000 q^{3} +1.00000 q^{4} -0.561553 q^{5} -1.00000 q^{6} +5.12311 q^{7} +1.00000 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q+1.00000 q^{2} -1.00000 q^{3} +1.00000 q^{4} -0.561553 q^{5} -1.00000 q^{6} +5.12311 q^{7} +1.00000 q^{8} +1.00000 q^{9} -0.561553 q^{10} -2.56155 q^{11} -1.00000 q^{12} -0.561553 q^{13} +5.12311 q^{14} +0.561553 q^{15} +1.00000 q^{16} +5.68466 q^{17} +1.00000 q^{18} -2.56155 q^{19} -0.561553 q^{20} -5.12311 q^{21} -2.56155 q^{22} -8.00000 q^{23} -1.00000 q^{24} -4.68466 q^{25} -0.561553 q^{26} -1.00000 q^{27} +5.12311 q^{28} -7.12311 q^{29} +0.561553 q^{30} -1.00000 q^{31} +1.00000 q^{32} +2.56155 q^{33} +5.68466 q^{34} -2.87689 q^{35} +1.00000 q^{36} +8.24621 q^{37} -2.56155 q^{38} +0.561553 q^{39} -0.561553 q^{40} +4.24621 q^{41} -5.12311 q^{42} -9.12311 q^{43} -2.56155 q^{44} -0.561553 q^{45} -8.00000 q^{46} -3.68466 q^{47} -1.00000 q^{48} +19.2462 q^{49} -4.68466 q^{50} -5.68466 q^{51} -0.561553 q^{52} -2.00000 q^{53} -1.00000 q^{54} +1.43845 q^{55} +5.12311 q^{56} +2.56155 q^{57} -7.12311 q^{58} -1.12311 q^{59} +0.561553 q^{60} -0.561553 q^{61} -1.00000 q^{62} +5.12311 q^{63} +1.00000 q^{64} +0.315342 q^{65} +2.56155 q^{66} +0.315342 q^{67} +5.68466 q^{68} +8.00000 q^{69} -2.87689 q^{70} -1.43845 q^{71} +1.00000 q^{72} +10.0000 q^{73} +8.24621 q^{74} +4.68466 q^{75} -2.56155 q^{76} -13.1231 q^{77} +0.561553 q^{78} -3.68466 q^{79} -0.561553 q^{80} +1.00000 q^{81} +4.24621 q^{82} +12.8078 q^{83} -5.12311 q^{84} -3.19224 q^{85} -9.12311 q^{86} +7.12311 q^{87} -2.56155 q^{88} -0.246211 q^{89} -0.561553 q^{90} -2.87689 q^{91} -8.00000 q^{92} +1.00000 q^{93} -3.68466 q^{94} +1.43845 q^{95} -1.00000 q^{96} -14.8078 q^{97} +19.2462 q^{98} -2.56155 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q + 2 q^{2} - 2 q^{3} + 2 q^{4} + 3 q^{5} - 2 q^{6} + 2 q^{7} + 2 q^{8} + 2 q^{9}+O(q^{10}) \) 2 * q + 2 * q^2 - 2 * q^3 + 2 * q^4 + 3 * q^5 - 2 * q^6 + 2 * q^7 + 2 * q^8 + 2 * q^9	\( 2 q + 2 q^{2} - 2 q^{3} + 2 q^{4} + 3 q^{5} - 2 q^{6} + 2 q^{7} + 2 q^{8} + 2 q^{9} + 3 q^{10} - q^{11} - 2 q^{12} + 3 q^{13} + 2 q^{14} - 3 q^{15} + 2 q^{16} - q^{17} + 2 q^{18} - q^{19} + 3 q^{20} - 2 q^{21} - q^{22} - 16 q^{23} - 2 q^{24} + 3 q^{25} + 3 q^{26} - 2 q^{27} + 2 q^{28} - 6 q^{29} - 3 q^{30} - 2 q^{31} + 2 q^{32} + q^{33} - q^{34} - 14 q^{35} + 2 q^{36} - q^{38} - 3 q^{39} + 3 q^{40} - 8 q^{41} - 2 q^{42} - 10 q^{43} - q^{44} + 3 q^{45} - 16 q^{46} + 5 q^{47} - 2 q^{48} + 22 q^{49} + 3 q^{50} + q^{51} + 3 q^{52} - 4 q^{53} - 2 q^{54} + 7 q^{55} + 2 q^{56} + q^{57} - 6 q^{58} + 6 q^{59} - 3 q^{60} + 3 q^{61} - 2 q^{62} + 2 q^{63} + 2 q^{64} + 13 q^{65} + q^{66} + 13 q^{67} - q^{68} + 16 q^{69} - 14 q^{70} - 7 q^{71} + 2 q^{72} + 20 q^{73} - 3 q^{75} - q^{76} - 18 q^{77} - 3 q^{78} + 5 q^{79} + 3 q^{80} + 2 q^{81} - 8 q^{82} + 5 q^{83} - 2 q^{84} - 27 q^{85} - 10 q^{86} + 6 q^{87} - q^{88} + 16 q^{89} + 3 q^{90} - 14 q^{91} - 16 q^{92} + 2 q^{93} + 5 q^{94} + 7 q^{95} - 2 q^{96} - 9 q^{97} + 22 q^{98} - q^{99}+O(q^{100}) \) 2 * q + 2 * q^2 - 2 * q^3 + 2 * q^4 + 3 * q^5 - 2 * q^6 + 2 * q^7 + 2 * q^8 + 2 * q^9 + 3 * q^10 - q^11 - 2 * q^12 + 3 * q^13 + 2 * q^14 - 3 * q^15 + 2 * q^16 - q^17 + 2 * q^18 - q^19 + 3 * q^20 - 2 * q^21 - q^22 - 16 * q^23 - 2 * q^24 + 3 * q^25 + 3 * q^26 - 2 * q^27 + 2 * q^28 - 6 * q^29 - 3 * q^30 - 2 * q^31 + 2 * q^32 + q^33 - q^34 - 14 * q^35 + 2 * q^36 - q^38 - 3 * q^39 + 3 * q^40 - 8 * q^41 - 2 * q^42 - 10 * q^43 - q^44 + 3 * q^45 - 16 * q^46 + 5 * q^47 - 2 * q^48 + 22 * q^49 + 3 * q^50 + q^51 + 3 * q^52 - 4 * q^53 - 2 * q^54 + 7 * q^55 + 2 * q^56 + q^57 - 6 * q^58 + 6 * q^59 - 3 * q^60 + 3 * q^61 - 2 * q^62 + 2 * q^63 + 2 * q^64 + 13 * q^65 + q^66 + 13 * q^67 - q^68 + 16 * q^69 - 14 * q^70 - 7 * q^71 + 2 * q^72 + 20 * q^73 - 3 * q^75 - q^76 - 18 * q^77 - 3 * q^78 + 5 * q^79 + 3 * q^80 + 2 * q^81 - 8 * q^82 + 5 * q^83 - 2 * q^84 - 27 * q^85 - 10 * q^86 + 6 * q^87 - q^88 + 16 * q^89 + 3 * q^90 - 14 * q^91 - 16 * q^92 + 2 * q^93 + 5 * q^94 + 7 * q^95 - 2 * q^96 - 9 * q^97 + 22 * q^98 - q^99

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