LMFDB - Embedded newform 190.2.a.d.1.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [190,2,Mod(1,190)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(190, 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("190.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 190 = 2 \cdot 5 \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	190.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:	$1.51715763840$
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:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.1
Root			$2.56155$ of defining polynomial
Character	$\chi$	$=$	190.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.00000 q^{2} -2.56155 q^{3} +1.00000 q^{4} +1.00000 q^{5} +2.56155 q^{6} -2.56155 q^{7} -1.00000 q^{8} +3.56155 q^{9} +O(q^{10})$	\(q-1.00000 q^{2} -2.56155 q^{3} +1.00000 q^{4} +1.00000 q^{5} +2.56155 q^{6} -2.56155 q^{7} -1.00000 q^{8} +3.56155 q^{9} -1.00000 q^{10} +4.00000 q^{11} -2.56155 q^{12} +5.68466 q^{13} +2.56155 q^{14} -2.56155 q^{15} +1.00000 q^{16} +3.43845 q^{17} -3.56155 q^{18} -1.00000 q^{19} +1.00000 q^{20} +6.56155 q^{21} -4.00000 q^{22} +7.68466 q^{23} +2.56155 q^{24} +1.00000 q^{25} -5.68466 q^{26} -1.43845 q^{27} -2.56155 q^{28} -5.68466 q^{29} +2.56155 q^{30} -5.12311 q^{31} -1.00000 q^{32} -10.2462 q^{33} -3.43845 q^{34} -2.56155 q^{35} +3.56155 q^{36} -6.00000 q^{37} +1.00000 q^{38} -14.5616 q^{39} -1.00000 q^{40} +12.2462 q^{41} -6.56155 q^{42} -2.87689 q^{43} +4.00000 q^{44} +3.56155 q^{45} -7.68466 q^{46} +6.24621 q^{47} -2.56155 q^{48} -0.438447 q^{49} -1.00000 q^{50} -8.80776 q^{51} +5.68466 q^{52} -4.56155 q^{53} +1.43845 q^{54} +4.00000 q^{55} +2.56155 q^{56} +2.56155 q^{57} +5.68466 q^{58} +2.56155 q^{59} -2.56155 q^{60} +11.1231 q^{61} +5.12311 q^{62} -9.12311 q^{63} +1.00000 q^{64} +5.68466 q^{65} +10.2462 q^{66} -2.56155 q^{67} +3.43845 q^{68} -19.6847 q^{69} +2.56155 q^{70} +10.2462 q^{71} -3.56155 q^{72} -1.68466 q^{73} +6.00000 q^{74} -2.56155 q^{75} -1.00000 q^{76} -10.2462 q^{77} +14.5616 q^{78} -5.12311 q^{79} +1.00000 q^{80} -7.00000 q^{81} -12.2462 q^{82} +2.87689 q^{83} +6.56155 q^{84} +3.43845 q^{85} +2.87689 q^{86} +14.5616 q^{87} -4.00000 q^{88} +2.00000 q^{89} -3.56155 q^{90} -14.5616 q^{91} +7.68466 q^{92} +13.1231 q^{93} -6.24621 q^{94} -1.00000 q^{95} +2.56155 q^{96} +6.00000 q^{97} +0.438447 q^{98} +14.2462 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 2 q - 2 q^{2} - q^{3} + 2 q^{4} + 2 q^{5} + q^{6} - q^{7} - 2 q^{8} + 3 q^{9}+O(q^{10}) $ 2 * q - 2 * q^2 - q^3 + 2 * q^4 + 2 * q^5 + q^6 - q^7 - 2 * q^8 + 3 * q^9	\( 2 q - 2 q^{2} - q^{3} + 2 q^{4} + 2 q^{5} + q^{6} - q^{7} - 2 q^{8} + 3 q^{9} - 2 q^{10} + 8 q^{11} - q^{12} - q^{13} + q^{14} - q^{15} + 2 q^{16} + 11 q^{17} - 3 q^{18} - 2 q^{19} + 2 q^{20} + 9 q^{21} - 8 q^{22} + 3 q^{23} + q^{24} + 2 q^{25} + q^{26} - 7 q^{27} - q^{28} + q^{29} + q^{30} - 2 q^{31} - 2 q^{32} - 4 q^{33} - 11 q^{34} - q^{35} + 3 q^{36} - 12 q^{37} + 2 q^{38} - 25 q^{39} - 2 q^{40} + 8 q^{41} - 9 q^{42} - 14 q^{43} + 8 q^{44} + 3 q^{45} - 3 q^{46} - 4 q^{47} - q^{48} - 5 q^{49} - 2 q^{50} + 3 q^{51} - q^{52} - 5 q^{53} + 7 q^{54} + 8 q^{55} + q^{56} + q^{57} - q^{58} + q^{59} - q^{60} + 14 q^{61} + 2 q^{62} - 10 q^{63} + 2 q^{64} - q^{65} + 4 q^{66} - q^{67} + 11 q^{68} - 27 q^{69} + q^{70} + 4 q^{71} - 3 q^{72} + 9 q^{73} + 12 q^{74} - q^{75} - 2 q^{76} - 4 q^{77} + 25 q^{78} - 2 q^{79} + 2 q^{80} - 14 q^{81} - 8 q^{82} + 14 q^{83} + 9 q^{84} + 11 q^{85} + 14 q^{86} + 25 q^{87} - 8 q^{88} + 4 q^{89} - 3 q^{90} - 25 q^{91} + 3 q^{92} + 18 q^{93} + 4 q^{94} - 2 q^{95} + q^{96} + 12 q^{97} + 5 q^{98} + 12 q^{99}+O(q^{100}) \) 2 * q - 2 * q^2 - q^3 + 2 * q^4 + 2 * q^5 + q^6 - q^7 - 2 * q^8 + 3 * q^9 - 2 * q^10 + 8 * q^11 - q^12 - q^13 + q^14 - q^15 + 2 * q^16 + 11 * q^17 - 3 * q^18 - 2 * q^19 + 2 * q^20 + 9 * q^21 - 8 * q^22 + 3 * q^23 + q^24 + 2 * q^25 + q^26 - 7 * q^27 - q^28 + q^29 + q^30 - 2 * q^31 - 2 * q^32 - 4 * q^33 - 11 * q^34 - q^35 + 3 * q^36 - 12 * q^37 + 2 * q^38 - 25 * q^39 - 2 * q^40 + 8 * q^41 - 9 * q^42 - 14 * q^43 + 8 * q^44 + 3 * q^45 - 3 * q^46 - 4 * q^47 - q^48 - 5 * q^49 - 2 * q^50 + 3 * q^51 - q^52 - 5 * q^53 + 7 * q^54 + 8 * q^55 + q^56 + q^57 - q^58 + q^59 - q^60 + 14 * q^61 + 2 * q^62 - 10 * q^63 + 2 * q^64 - q^65 + 4 * q^66 - q^67 + 11 * q^68 - 27 * q^69 + q^70 + 4 * q^71 - 3 * q^72 + 9 * q^73 + 12 * q^74 - q^75 - 2 * q^76 - 4 * q^77 + 25 * q^78 - 2 * q^79 + 2 * q^80 - 14 * q^81 - 8 * q^82 + 14 * q^83 + 9 * q^84 + 11 * q^85 + 14 * q^86 + 25 * q^87 - 8 * q^88 + 4 * q^89 - 3 * q^90 - 25 * q^91 + 3 * q^92 + 18 * q^93 + 4 * q^94 - 2 * q^95 + q^96 + 12 * q^97 + 5 * q^98 + 12 * q^99

Display 100 coefficients 10 coefficients

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$	$a_n / n^{(k-1)/2}$	$ \alpha_n $			$ \theta_n $
$p$	$a_p$	$a_p / p^{(k-1)/2}$	$ \alpha_p$			$ \theta_p $

$2$	−1.00000	−0.707107
$2$	−1.00000	−0.707107
$3$	−2.56155	−1.47891	−0.739457	−	0.673204i	$-0.764917\pi$
$3$	−2.56155	−1.47891	−0.739457	+	0.673204i	$0.764917\pi$
$4$	1.00000	0.500000
$5$	1.00000	0.447214
$5$	1.00000	0.447214
$6$	2.56155	1.04575
$7$	−2.56155	−0.968176	−0.484088	−	0.875019i	$-0.660849\pi$
$7$	−2.56155	−0.968176	−0.484088	+	0.875019i	$0.660849\pi$
$8$	−1.00000	−0.353553
$9$	3.56155	1.18718
$10$	−1.00000	−0.316228
$11$	4.00000	1.20605	0.603023	−	0.797724i	$-0.293963\pi$
$11$	4.00000	1.20605	0.603023	+	0.797724i	$0.293963\pi$
$12$	−2.56155	−0.739457
$13$	5.68466	1.57664	0.788320	−	0.615265i	$-0.210951\pi$
$13$	5.68466	1.57664	0.788320	+	0.615265i	$0.210951\pi$
$14$	2.56155	0.684604
$15$	−2.56155	−0.661390
$16$	1.00000	0.250000
$17$	3.43845	0.833946	0.416973	−	0.908919i	$-0.363091\pi$
$17$	3.43845	0.833946	0.416973	+	0.908919i	$0.363091\pi$
$18$	−3.56155	−0.839466
$19$	−1.00000	−0.229416
$19$	−1.00000	−0.229416
$20$	1.00000	0.223607
$21$	6.56155	1.43185
$22$	−4.00000	−0.852803
$23$	7.68466	1.60236	0.801181	−	0.598422i	$-0.204205\pi$
$23$	7.68466	1.60236	0.801181	+	0.598422i	$0.204205\pi$
$24$	2.56155	0.522875
$25$	1.00000	0.200000
$26$	−5.68466	−1.11485
$27$	−1.43845	−0.276829
$28$	−2.56155	−0.484088
$29$	−5.68466	−1.05561	−0.527807	−	0.849364i	$-0.676986\pi$
$29$	−5.68466	−1.05561	−0.527807	+	0.849364i	$0.676986\pi$
$30$	2.56155	0.467673
$31$	−5.12311	−0.920137	−0.460068	−	0.887883i	$-0.652175\pi$
$31$	−5.12311	−0.920137	−0.460068	+	0.887883i	$0.652175\pi$
$32$	−1.00000	−0.176777
$33$	−10.2462	−1.78364
$34$	−3.43845	−0.589689
$35$	−2.56155	−0.432981
$36$	3.56155	0.593592
$37$	−6.00000	−0.986394	−0.493197	−	0.869918i	$-0.664172\pi$
$37$	−6.00000	−0.986394	−0.493197	+	0.869918i	$0.664172\pi$
$38$	1.00000	0.162221
$39$	−14.5616	−2.33171
$40$	−1.00000	−0.158114
$41$	12.2462	1.91254	0.956268	−	0.292490i	$-0.0944840\pi$
$41$	12.2462	1.91254	0.956268	+	0.292490i	$0.0944840\pi$
$42$	−6.56155	−1.01247
$43$	−2.87689	−0.438722	−0.219361	−	0.975644i	$-0.570397\pi$
$43$	−2.87689	−0.438722	−0.219361	+	0.975644i	$0.570397\pi$
$44$	4.00000	0.603023
$45$	3.56155	0.530925
$46$	−7.68466	−1.13304
$47$	6.24621	0.911104	0.455552	−	0.890209i	$-0.349442\pi$
$47$	6.24621	0.911104	0.455552	+	0.890209i	$0.349442\pi$
$48$	−2.56155	−0.369728
$49$	−0.438447	−0.0626353
$50$	−1.00000	−0.141421
$51$	−8.80776	−1.23333
$52$	5.68466	0.788320
$53$	−4.56155	−0.626577	−0.313289	−	0.949658i	$-0.601431\pi$
$53$	−4.56155	−0.626577	−0.313289	+	0.949658i	$0.601431\pi$
$54$	1.43845	0.195748
$55$	4.00000	0.539360
$56$	2.56155	0.342302
$57$	2.56155	0.339286
$58$	5.68466	0.746432
$59$	2.56155	0.333486	0.166743	−	0.986000i	$-0.446675\pi$
$59$	2.56155	0.333486	0.166743	+	0.986000i	$0.446675\pi$
$60$	−2.56155	−0.330695
$61$	11.1231	1.42417	0.712084	−	0.702094i	$-0.247752\pi$
$61$	11.1231	1.42417	0.712084	+	0.702094i	$0.247752\pi$
$62$	5.12311	0.650635
$63$	−9.12311	−1.14940
$64$	1.00000	0.125000
$65$	5.68466	0.705095
$66$	10.2462	1.26122
$67$	−2.56155	−0.312943	−0.156472	−	0.987682i	$-0.550012\pi$
$67$	−2.56155	−0.312943	−0.156472	+	0.987682i	$0.550012\pi$
$68$	3.43845	0.416973
$69$	−19.6847	−2.36975
$70$	2.56155	0.306164
$71$	10.2462	1.21600	0.608001	−	0.793936i	$-0.291972\pi$
$71$	10.2462	1.21600	0.608001	+	0.793936i	$0.291972\pi$
$72$	−3.56155	−0.419733
$73$	−1.68466	−0.197174	−0.0985872	−	0.995128i	$-0.531432\pi$
$73$	−1.68466	−0.197174	−0.0985872	+	0.995128i	$0.531432\pi$
$74$	6.00000	0.697486
$75$	−2.56155	−0.295783
$76$	−1.00000	−0.114708
$77$	−10.2462	−1.16766
$78$	14.5616	1.64877
$79$	−5.12311	−0.576394	−0.288197	−	0.957571i	$-0.593056\pi$
$79$	−5.12311	−0.576394	−0.288197	+	0.957571i	$0.593056\pi$
$80$	1.00000	0.111803
$81$	−7.00000	−0.777778
$82$	−12.2462	−1.35237
$83$	2.87689	0.315780	0.157890	−	0.987457i	$-0.449531\pi$
$83$	2.87689	0.315780	0.157890	+	0.987457i	$0.449531\pi$
$84$	6.56155	0.715924
$85$	3.43845	0.372952
$86$	2.87689	0.310223
$87$	14.5616	1.56116
$88$	−4.00000	−0.426401
$89$	2.00000	0.212000	0.106000	−	0.994366i	$-0.466196\pi$
$89$	2.00000	0.212000	0.106000	+	0.994366i	$0.466196\pi$
$90$	−3.56155	−0.375421
$91$	−14.5616	−1.52647
$92$	7.68466	0.801181
$93$	13.1231	1.36080
$94$	−6.24621	−0.644247
$95$	−1.00000	−0.102598
$96$	2.56155	0.261437
$97$	6.00000	0.609208	0.304604	−	0.952479i	$-0.401476\pi$
$97$	6.00000	0.609208	0.304604	+	0.952479i	$0.401476\pi$
$98$	0.438447	0.0442899
$99$	14.2462	1.43180
$100$	1.00000	0.100000
$101$	−17.3693	−1.72831	−0.864156	−	0.503224i	$-0.832147\pi$
$101$	−17.3693	−1.72831	−0.864156	+	0.503224i	$0.832147\pi$
$102$	8.80776	0.872099
$103$	2.24621	0.221326	0.110663	−	0.993858i	$-0.464703\pi$
$103$	2.24621	0.221326	0.110663	+	0.993858i	$0.464703\pi$
$104$	−5.68466	−0.557427
$105$	6.56155	0.640342
$106$	4.56155	0.443057
$107$	−5.43845	−0.525755	−0.262877	−	0.964829i	$-0.584671\pi$
$107$	−5.43845	−0.525755	−0.262877	+	0.964829i	$0.584671\pi$
$108$	−1.43845	−0.138415
$109$	−0.561553	−0.0537870	−0.0268935	−	0.999638i	$-0.508561\pi$
$109$	−0.561553	−0.0537870	−0.0268935	+	0.999638i	$0.508561\pi$
$110$	−4.00000	−0.381385
$111$	15.3693	1.45879
$112$	−2.56155	−0.242044
$113$	8.87689	0.835068	0.417534	−	0.908661i	$-0.362894\pi$
$113$	8.87689	0.835068	0.417534	+	0.908661i	$0.362894\pi$
$114$	−2.56155	−0.239911
$115$	7.68466	0.716598
$116$	−5.68466	−0.527807
$117$	20.2462	1.87176
$118$	−2.56155	−0.235810
$119$	−8.80776	−0.807406
$120$	2.56155	0.233837
$121$	5.00000	0.454545
$122$	−11.1231	−1.00704
$123$	−31.3693	−2.82848
$124$	−5.12311	−0.460068
$125$	1.00000	0.0894427
$126$	9.12311	0.812751
$127$	13.1231	1.16449	0.582244	−	0.813014i	$-0.302175\pi$
$127$	13.1231	1.16449	0.582244	+	0.813014i	$0.302175\pi$
$128$	−1.00000	−0.0883883
$129$	7.36932	0.648832
$130$	−5.68466	−0.498578
$131$	−16.4924	−1.44095	−0.720475	−	0.693481i	$-0.756076\pi$
$131$	−16.4924	−1.44095	−0.720475	+	0.693481i	$0.756076\pi$
$132$	−10.2462	−0.891818
$133$	2.56155	0.222115
$134$	2.56155	0.221284
$135$	−1.43845	−0.123802
$136$	−3.43845	−0.294844
$137$	−14.8078	−1.26511	−0.632556	−	0.774514i	$-0.717994\pi$
$137$	−14.8078	−1.26511	−0.632556	+	0.774514i	$0.717994\pi$
$138$	19.6847	1.67567
$139$	16.4924	1.39887	0.699435	−	0.714697i	$-0.253435\pi$
$139$	16.4924	1.39887	0.699435	+	0.714697i	$0.253435\pi$
$140$	−2.56155	−0.216491
$141$	−16.0000	−1.34744
$142$	−10.2462	−0.859843
$143$	22.7386	1.90150
$144$	3.56155	0.296796
$145$	−5.68466	−0.472085
$146$	1.68466	0.139423
$147$	1.12311	0.0926322
$148$	−6.00000	−0.493197
$149$	13.3693	1.09526	0.547629	−	0.836722i	$-0.315531\pi$
$149$	13.3693	1.09526	0.547629	+	0.836722i	$0.315531\pi$
$150$	2.56155	0.209150
$151$	5.12311	0.416912	0.208456	−	0.978032i	$-0.433156\pi$
$151$	5.12311	0.416912	0.208456	+	0.978032i	$0.433156\pi$
$152$	1.00000	0.0811107
$153$	12.2462	0.990048
$154$	10.2462	0.825663
$155$	−5.12311	−0.411498
$156$	−14.5616	−1.16586
$157$	−20.2462	−1.61582	−0.807912	−	0.589303i	$-0.799402\pi$
$157$	−20.2462	−1.61582	−0.807912	+	0.589303i	$0.799402\pi$
$158$	5.12311	0.407572
$159$	11.6847	0.926654
$160$	−1.00000	−0.0790569
$161$	−19.6847	−1.55137
$162$	7.00000	0.549972
$163$	−15.3693	−1.20382	−0.601909	−	0.798565i	$-0.705593\pi$
$163$	−15.3693	−1.20382	−0.601909	+	0.798565i	$0.705593\pi$
$164$	12.2462	0.956268
$165$	−10.2462	−0.797666
$166$	−2.87689	−0.223290
$167$	−7.36932	−0.570255	−0.285127	−	0.958490i	$-0.592036\pi$
$167$	−7.36932	−0.570255	−0.285127	+	0.958490i	$0.592036\pi$
$168$	−6.56155	−0.506235
$169$	19.3153	1.48580
$170$	−3.43845	−0.263717
$171$	−3.56155	−0.272359
$172$	−2.87689	−0.219361
$173$	20.2462	1.53929	0.769645	−	0.638471i	$-0.220433\pi$
$173$	20.2462	1.53929	0.769645	+	0.638471i	$0.220433\pi$
$174$	−14.5616	−1.10391
$175$	−2.56155	−0.193635
$176$	4.00000	0.301511
$177$	−6.56155	−0.493197
$178$	−2.00000	−0.149906
$179$	−22.2462	−1.66276	−0.831380	−	0.555704i	$-0.812449\pi$
$179$	−22.2462	−1.66276	−0.831380	+	0.555704i	$0.812449\pi$
$180$	3.56155	0.265462
$181$	−18.0000	−1.33793	−0.668965	−	0.743294i	$-0.733262\pi$
$181$	−18.0000	−1.33793	−0.668965	+	0.743294i	$0.733262\pi$
$182$	14.5616	1.07937
$183$	−28.4924	−2.10622
$184$	−7.68466	−0.566521
$185$	−6.00000	−0.441129
$186$	−13.1231	−0.962233
$187$	13.7538	1.00578
$188$	6.24621	0.455552
$189$	3.68466	0.268019
$190$	1.00000	0.0725476
$191$	−3.68466	−0.266613	−0.133306	−	0.991075i	$-0.542559\pi$
$191$	−3.68466	−0.266613	−0.133306	+	0.991075i	$0.542559\pi$
$192$	−2.56155	−0.184864
$193$	−14.4924	−1.04319	−0.521594	−	0.853194i	$-0.674662\pi$
$193$	−14.4924	−1.04319	−0.521594	+	0.853194i	$0.674662\pi$
$194$	−6.00000	−0.430775
$195$	−14.5616	−1.04277
$196$	−0.438447	−0.0313177
$197$	−20.2462	−1.44248	−0.721241	−	0.692684i	$-0.756428\pi$
$197$	−20.2462	−1.44248	−0.721241	+	0.692684i	$0.756428\pi$
$198$	−14.2462	−1.01243
$199$	16.8078	1.19147	0.595735	−	0.803181i	$-0.296861\pi$
$199$	16.8078	1.19147	0.595735	+	0.803181i	$0.296861\pi$
$200$	−1.00000	−0.0707107
$201$	6.56155	0.462816
$202$	17.3693	1.22210
$203$	14.5616	1.02202
$204$	−8.80776	−0.616667
$205$	12.2462	0.855312
$206$	−2.24621	−0.156501
$207$	27.3693	1.90230
$208$	5.68466	0.394160
$209$	−4.00000	−0.276686
$210$	−6.56155	−0.452790
$211$	8.31534	0.572452	0.286226	−	0.958162i	$-0.407599\pi$
$211$	8.31534	0.572452	0.286226	+	0.958162i	$0.407599\pi$
$212$	−4.56155	−0.313289
$213$	−26.2462	−1.79836
$214$	5.43845	0.371765
$215$	−2.87689	−0.196203
$216$	1.43845	0.0978739
$217$	13.1231	0.890854
$218$	0.561553	0.0380332
$219$	4.31534	0.291604
$220$	4.00000	0.269680
$221$	19.5464	1.31483
$222$	−15.3693	−1.03152
$223$	−23.3693	−1.56493	−0.782463	−	0.622698i	$-0.786037\pi$
$223$	−23.3693	−1.56493	−0.782463	+	0.622698i	$0.786037\pi$
$224$	2.56155	0.171151
$225$	3.56155	0.237437
$226$	−8.87689	−0.590482
$227$	25.9309	1.72109	0.860546	−	0.509373i	$-0.170122\pi$
$227$	25.9309	1.72109	0.860546	+	0.509373i	$0.170122\pi$
$228$	2.56155	0.169643
$229$	−14.4924	−0.957686	−0.478843	−	0.877900i	$-0.658944\pi$
$229$	−14.4924	−0.957686	−0.478843	+	0.877900i	$0.658944\pi$
$230$	−7.68466	−0.506711
$231$	26.2462	1.72687
$232$	5.68466	0.373216
$233$	10.0000	0.655122	0.327561	−	0.944830i	$-0.393773\pi$
$233$	10.0000	0.655122	0.327561	+	0.944830i	$0.393773\pi$
$234$	−20.2462	−1.32354
$235$	6.24621	0.407458
$236$	2.56155	0.166743
$237$	13.1231	0.852437
$238$	8.80776	0.570923
$239$	−1.43845	−0.0930454	−0.0465227	−	0.998917i	$-0.514814\pi$
$239$	−1.43845	−0.0930454	−0.0465227	+	0.998917i	$0.514814\pi$
$240$	−2.56155	−0.165348
$241$	23.1231	1.48949	0.744745	−	0.667349i	$-0.232571\pi$
$241$	23.1231	1.48949	0.744745	+	0.667349i	$0.232571\pi$
$242$	−5.00000	−0.321412
$243$	22.2462	1.42710
$244$	11.1231	0.712084
$245$	−0.438447	−0.0280114
$246$	31.3693	2.00003
$247$	−5.68466	−0.361706
$248$	5.12311	0.325318
$249$	−7.36932	−0.467011
$250$	−1.00000	−0.0632456
$251$	6.24621	0.394257	0.197129	−	0.980378i	$-0.436838\pi$
$251$	6.24621	0.394257	0.197129	+	0.980378i	$0.436838\pi$
$252$	−9.12311	−0.574702
$253$	30.7386	1.93252
$254$	−13.1231	−0.823417
$255$	−8.80776	−0.551564
$256$	1.00000	0.0625000
$257$	14.0000	0.873296	0.436648	−	0.899632i	$-0.356166\pi$
$257$	14.0000	0.873296	0.436648	+	0.899632i	$0.356166\pi$
$258$	−7.36932	−0.458794
$259$	15.3693	0.955003
$260$	5.68466	0.352548
$261$	−20.2462	−1.25321
$262$	16.4924	1.01891
$263$	−22.2462	−1.37176	−0.685880	−	0.727715i	$-0.740583\pi$
$263$	−22.2462	−1.37176	−0.685880	+	0.727715i	$0.740583\pi$
$264$	10.2462	0.630611
$265$	−4.56155	−0.280214
$266$	−2.56155	−0.157059
$267$	−5.12311	−0.313529
$268$	−2.56155	−0.156472
$269$	−26.0000	−1.58525	−0.792624	−	0.609711i	$-0.791286\pi$
$269$	−26.0000	−1.58525	−0.792624	+	0.609711i	$0.791286\pi$
$270$	1.43845	0.0875411
$271$	−21.9309	−1.33221	−0.666103	−	0.745860i	$-0.732039\pi$
$271$	−21.9309	−1.33221	−0.666103	+	0.745860i	$0.732039\pi$
$272$	3.43845	0.208486
$273$	37.3002	2.25751
$274$	14.8078	0.894570
$275$	4.00000	0.241209
$276$	−19.6847	−1.18488
$277$	0.876894	0.0526875	0.0263437	−	0.999653i	$-0.491614\pi$
$277$	0.876894	0.0526875	0.0263437	+	0.999653i	$0.491614\pi$
$278$	−16.4924	−0.989150
$279$	−18.2462	−1.09237
$280$	2.56155	0.153082
$281$	2.00000	0.119310	0.0596550	−	0.998219i	$-0.481000\pi$
$281$	2.00000	0.119310	0.0596550	+	0.998219i	$0.481000\pi$
$282$	16.0000	0.952786
$283$	−21.1231	−1.25564	−0.627819	−	0.778359i	$-0.716052\pi$
$283$	−21.1231	−1.25564	−0.627819	+	0.778359i	$0.716052\pi$
$284$	10.2462	0.608001
$285$	2.56155	0.151733
$286$	−22.7386	−1.34456
$287$	−31.3693	−1.85167
$288$	−3.56155	−0.209867
$289$	−5.17708	−0.304534
$290$	5.68466	0.333815
$291$	−15.3693	−0.900965
$292$	−1.68466	−0.0985872
$293$	−22.1771	−1.29560	−0.647799	−	0.761811i	$-0.724311\pi$
$293$	−22.1771	−1.29560	−0.647799	+	0.761811i	$0.724311\pi$
$294$	−1.12311	−0.0655009
$295$	2.56155	0.149139
$296$	6.00000	0.348743
$297$	−5.75379	−0.333869
$298$	−13.3693	−0.774464
$299$	43.6847	2.52635
$300$	−2.56155	−0.147891
$301$	7.36932	0.424760
$302$	−5.12311	−0.294802
$303$	44.4924	2.55602
$304$	−1.00000	−0.0573539
$305$	11.1231	0.636907
$306$	−12.2462	−0.700069
$307$	32.4924	1.85444	0.927220	−	0.374516i	$-0.122191\pi$
$307$	32.4924	1.85444	0.927220	+	0.374516i	$0.122191\pi$
$308$	−10.2462	−0.583832
$309$	−5.75379	−0.327322
$310$	5.12311	0.290973
$311$	−3.68466	−0.208938	−0.104469	−	0.994528i	$-0.533314\pi$
$311$	−3.68466	−0.208938	−0.104469	+	0.994528i	$0.533314\pi$
$312$	14.5616	0.824386
$313$	5.05398	0.285668	0.142834	−	0.989747i	$-0.454379\pi$
$313$	5.05398	0.285668	0.142834	+	0.989747i	$0.454379\pi$
$314$	20.2462	1.14256
$315$	−9.12311	−0.514029
$316$	−5.12311	−0.288197
$317$	13.0540	0.733184	0.366592	−	0.930382i	$-0.380524\pi$
$317$	13.0540	0.733184	0.366592	+	0.930382i	$0.380524\pi$
$318$	−11.6847	−0.655243
$319$	−22.7386	−1.27312
$320$	1.00000	0.0559017
$321$	13.9309	0.777545
$322$	19.6847	1.09698
$323$	−3.43845	−0.191320
$324$	−7.00000	−0.388889
$325$	5.68466	0.315328
$326$	15.3693	0.851228
$327$	1.43845	0.0795463
$328$	−12.2462	−0.676184
$329$	−16.0000	−0.882109
$330$	10.2462	0.564035
$331$	−2.56155	−0.140796	−0.0703978	−	0.997519i	$-0.522427\pi$
$331$	−2.56155	−0.140796	−0.0703978	+	0.997519i	$0.522427\pi$
$332$	2.87689	0.157890
$333$	−21.3693	−1.17103
$334$	7.36932	0.403231
$335$	−2.56155	−0.139953
$336$	6.56155	0.357962
$337$	−26.0000	−1.41631	−0.708155	−	0.706057i	$-0.750472\pi$
$337$	−26.0000	−1.41631	−0.708155	+	0.706057i	$0.750472\pi$
$338$	−19.3153	−1.05062
$339$	−22.7386	−1.23499
$340$	3.43845	0.186476
$341$	−20.4924	−1.10973
$342$	3.56155	0.192587
$343$	19.0540	1.02882
$344$	2.87689	0.155112
$345$	−19.6847	−1.05979
$346$	−20.2462	−1.08844
$347$	−8.63068	−0.463319	−0.231660	−	0.972797i	$-0.574416\pi$
$347$	−8.63068	−0.463319	−0.231660	+	0.972797i	$0.574416\pi$
$348$	14.5616	0.780581
$349$	3.75379	0.200936	0.100468	−	0.994940i	$-0.467966\pi$
$349$	3.75379	0.200936	0.100468	+	0.994940i	$0.467966\pi$
$350$	2.56155	0.136921
$351$	−8.17708	−0.436460
$352$	−4.00000	−0.213201
$353$	−3.93087	−0.209219	−0.104610	−	0.994513i	$-0.533359\pi$
$353$	−3.93087	−0.209219	−0.104610	+	0.994513i	$0.533359\pi$
$354$	6.56155	0.348743
$355$	10.2462	0.543812
$356$	2.00000	0.106000
$357$	22.5616	1.19408
$358$	22.2462	1.17575
$359$	1.43845	0.0759183	0.0379592	−	0.999279i	$-0.487914\pi$
$359$	1.43845	0.0759183	0.0379592	+	0.999279i	$0.487914\pi$
$360$	−3.56155	−0.187710
$361$	1.00000	0.0526316
$362$	18.0000	0.946059
$363$	−12.8078	−0.672233
$364$	−14.5616	−0.763233
$365$	−1.68466	−0.0881791
$366$	28.4924	1.48932
$367$	6.24621	0.326050	0.163025	−	0.986622i	$-0.447875\pi$
$367$	6.24621	0.326050	0.163025	+	0.986622i	$0.447875\pi$
$368$	7.68466	0.400591
$369$	43.6155	2.27053
$370$	6.00000	0.311925
$371$	11.6847	0.606637
$372$	13.1231	0.680401
$373$	−23.4384	−1.21360	−0.606798	−	0.794856i	$-0.707546\pi$
$373$	−23.4384	−1.21360	−0.606798	+	0.794856i	$0.707546\pi$
$374$	−13.7538	−0.711191
$375$	−2.56155	−0.132278
$376$	−6.24621	−0.322124
$377$	−32.3153	−1.66432
$378$	−3.68466	−0.189518
$379$	10.5616	0.542511	0.271255	−	0.962507i	$-0.412561\pi$
$379$	10.5616	0.542511	0.271255	+	0.962507i	$0.412561\pi$
$380$	−1.00000	−0.0512989
$381$	−33.6155	−1.72218
$382$	3.68466	0.188524
$383$	13.7538	0.702786	0.351393	−	0.936228i	$-0.385708\pi$
$383$	13.7538	0.702786	0.351393	+	0.936228i	$0.385708\pi$
$384$	2.56155	0.130719
$385$	−10.2462	−0.522195
$386$	14.4924	0.737645
$387$	−10.2462	−0.520844
$388$	6.00000	0.304604
$389$	−7.12311	−0.361156	−0.180578	−	0.983561i	$-0.557797\pi$
$389$	−7.12311	−0.361156	−0.180578	+	0.983561i	$0.557797\pi$
$390$	14.5616	0.737353
$391$	26.4233	1.33628
$392$	0.438447	0.0221449
$393$	42.2462	2.13104
$394$	20.2462	1.01999
$395$	−5.12311	−0.257771
$396$	14.2462	0.715899
$397$	−7.12311	−0.357498	−0.178749	−	0.983895i	$-0.557205\pi$
$397$	−7.12311	−0.357498	−0.178749	+	0.983895i	$0.557205\pi$
$398$	−16.8078	−0.842497
$399$	−6.56155	−0.328489
$400$	1.00000	0.0500000
$401$	−3.75379	−0.187455	−0.0937276	−	0.995598i	$-0.529878\pi$
$401$	−3.75379	−0.187455	−0.0937276	+	0.995598i	$0.529878\pi$
$402$	−6.56155	−0.327261
$403$	−29.1231	−1.45073
$404$	−17.3693	−0.864156
$405$	−7.00000	−0.347833
$406$	−14.5616	−0.722678
$407$	−24.0000	−1.18964
$408$	8.80776	0.436049
$409$	24.7386	1.22325	0.611623	−	0.791149i	$-0.290517\pi$
$409$	24.7386	1.22325	0.611623	+	0.791149i	$0.290517\pi$
$410$	−12.2462	−0.604797
$411$	37.9309	1.87099
$412$	2.24621	0.110663
$413$	−6.56155	−0.322873
$414$	−27.3693	−1.34513
$415$	2.87689	0.141221
$416$	−5.68466	−0.278713
$417$	−42.2462	−2.06881
$418$	4.00000	0.195646
$419$	23.8617	1.16572	0.582861	−	0.812572i	$-0.301933\pi$
$419$	23.8617	1.16572	0.582861	+	0.812572i	$0.301933\pi$
$420$	6.56155	0.320171
$421$	−23.9309	−1.16632	−0.583160	−	0.812358i	$-0.698184\pi$
$421$	−23.9309	−1.16632	−0.583160	+	0.812358i	$0.698184\pi$
$422$	−8.31534	−0.404784
$423$	22.2462	1.08165
$424$	4.56155	0.221529
$425$	3.43845	0.166789
$426$	26.2462	1.27163
$427$	−28.4924	−1.37884
$428$	−5.43845	−0.262877
$429$	−58.2462	−2.81215
$430$	2.87689	0.138736
$431$	−16.0000	−0.770693	−0.385346	−	0.922772i	$-0.625918\pi$
$431$	−16.0000	−0.770693	−0.385346	+	0.922772i	$0.625918\pi$
$432$	−1.43845	−0.0692073
$433$	14.6307	0.703106	0.351553	−	0.936168i	$-0.385654\pi$
$433$	14.6307	0.703106	0.351553	+	0.936168i	$0.385654\pi$
$434$	−13.1231	−0.629929
$435$	14.5616	0.698173
$436$	−0.561553	−0.0268935
$437$	−7.68466	−0.367607
$438$	−4.31534	−0.206195
$439$	−13.1231	−0.626332	−0.313166	−	0.949698i	$-0.601390\pi$
$439$	−13.1231	−0.626332	−0.313166	+	0.949698i	$0.601390\pi$
$440$	−4.00000	−0.190693
$441$	−1.56155	−0.0743597
$442$	−19.5464	−0.929727
$443$	2.24621	0.106721	0.0533604	−	0.998575i	$-0.483007\pi$
$443$	2.24621	0.106721	0.0533604	+	0.998575i	$0.483007\pi$
$444$	15.3693	0.729396
$445$	2.00000	0.0948091
$446$	23.3693	1.10657
$447$	−34.2462	−1.61979
$448$	−2.56155	−0.121022
$449$	−28.7386	−1.35626	−0.678130	−	0.734942i	$-0.737209\pi$
$449$	−28.7386	−1.35626	−0.678130	+	0.734942i	$0.737209\pi$
$450$	−3.56155	−0.167893
$451$	48.9848	2.30661
$452$	8.87689	0.417534
$453$	−13.1231	−0.616577
$454$	−25.9309	−1.21700
$455$	−14.5616	−0.682656
$456$	−2.56155	−0.119956
$457$	6.31534	0.295419	0.147710	−	0.989031i	$-0.452810\pi$
$457$	6.31534	0.295419	0.147710	+	0.989031i	$0.452810\pi$
$458$	14.4924	0.677186
$459$	−4.94602	−0.230861
$460$	7.68466	0.358299
$461$	3.75379	0.174831	0.0874157	−	0.996172i	$-0.472139\pi$
$461$	3.75379	0.174831	0.0874157	+	0.996172i	$0.472139\pi$
$462$	−26.2462	−1.22108
$463$	−30.2462	−1.40566	−0.702830	−	0.711358i	$-0.748081\pi$
$463$	−30.2462	−1.40566	−0.702830	+	0.711358i	$0.748081\pi$
$464$	−5.68466	−0.263904
$465$	13.1231	0.608569
$466$	−10.0000	−0.463241
$467$	18.2462	0.844334	0.422167	−	0.906518i	$-0.361270\pi$
$467$	18.2462	0.844334	0.422167	+	0.906518i	$0.361270\pi$
$468$	20.2462	0.935881
$469$	6.56155	0.302984
$470$	−6.24621	−0.288116
$471$	51.8617	2.38966
$472$	−2.56155	−0.117905
$473$	−11.5076	−0.529119
$474$	−13.1231	−0.602764
$475$	−1.00000	−0.0458831
$476$	−8.80776	−0.403703
$477$	−16.2462	−0.743863
$478$	1.43845	0.0657930
$479$	32.0000	1.46212	0.731059	−	0.682315i	$-0.239027\pi$
$479$	32.0000	1.46212	0.731059	+	0.682315i	$0.239027\pi$
$480$	2.56155	0.116918
$481$	−34.1080	−1.55519
$482$	−23.1231	−1.05323
$483$	50.4233	2.29434
$484$	5.00000	0.227273
$485$	6.00000	0.272446
$486$	−22.2462	−1.00911
$487$	−17.6155	−0.798236	−0.399118	−	0.916900i	$-0.630684\pi$
$487$	−17.6155	−0.798236	−0.399118	+	0.916900i	$0.630684\pi$
$488$	−11.1231	−0.503519
$489$	39.3693	1.78034
$490$	0.438447	0.0198070
$491$	−1.12311	−0.0506850	−0.0253425	−	0.999679i	$-0.508068\pi$
$491$	−1.12311	−0.0506850	−0.0253425	+	0.999679i	$0.508068\pi$
$492$	−31.3693	−1.41424
$493$	−19.5464	−0.880325
$494$	5.68466	0.255765
$495$	14.2462	0.640320
$496$	−5.12311	−0.230034
$497$	−26.2462	−1.17730
$498$	7.36932	0.330227
$499$	42.1080	1.88501	0.942505	−	0.334191i	$-0.108463\pi$
$499$	42.1080	1.88501	0.942505	+	0.334191i	$0.108463\pi$
$500$	1.00000	0.0447214
$501$	18.8769	0.843357
$502$	−6.24621	−0.278782
$503$	−7.05398	−0.314521	−0.157261	−	0.987557i	$-0.550266\pi$
$503$	−7.05398	−0.314521	−0.157261	+	0.987557i	$0.550266\pi$
$504$	9.12311	0.406375
$505$	−17.3693	−0.772924
$506$	−30.7386	−1.36650
$507$	−49.4773	−2.19736
$508$	13.1231	0.582244
$509$	2.49242	0.110475	0.0552373	−	0.998473i	$-0.482408\pi$
$509$	2.49242	0.110475	0.0552373	+	0.998473i	$0.482408\pi$
$510$	8.80776	0.390014
$511$	4.31534	0.190899
$512$	−1.00000	−0.0441942
$513$	1.43845	0.0635090
$514$	−14.0000	−0.617514
$515$	2.24621	0.0989799
$516$	7.36932	0.324416
$517$	24.9848	1.09883
$518$	−15.3693	−0.675289
$519$	−51.8617	−2.27648
$520$	−5.68466	−0.249289
$521$	−3.12311	−0.136826	−0.0684129	−	0.997657i	$-0.521794\pi$
$521$	−3.12311	−0.136826	−0.0684129	+	0.997657i	$0.521794\pi$
$522$	20.2462	0.886153
$523$	−31.6847	−1.38547	−0.692737	−	0.721191i	$-0.743595\pi$
$523$	−31.6847	−1.38547	−0.692737	+	0.721191i	$0.743595\pi$
$524$	−16.4924	−0.720475
$525$	6.56155	0.286370
$526$	22.2462	0.969981
$527$	−17.6155	−0.767344
$528$	−10.2462	−0.445909
$529$	36.0540	1.56756
$530$	4.56155	0.198141
$531$	9.12311	0.395909
$532$	2.56155	0.111057
$533$	69.6155	3.01538
$534$	5.12311	0.221698
$535$	−5.43845	−0.235125
$536$	2.56155	0.110642
$537$	56.9848	2.45908
$538$	26.0000	1.12094
$539$	−1.75379	−0.0755410
$540$	−1.43845	−0.0619009
$541$	−0.384472	−0.0165297	−0.00826487	−	0.999966i	$-0.502631\pi$
$541$	−0.384472	−0.0165297	−0.00826487	+	0.999966i	$0.502631\pi$
$542$	21.9309	0.942012
$543$	46.1080	1.97868
$544$	−3.43845	−0.147422
$545$	−0.561553	−0.0240543
$546$	−37.3002	−1.59630
$547$	16.4924	0.705165	0.352583	−	0.935781i	$-0.385304\pi$
$547$	16.4924	0.705165	0.352583	+	0.935781i	$0.385304\pi$
$548$	−14.8078	−0.632556
$549$	39.6155	1.69075
$550$	−4.00000	−0.170561
$551$	5.68466	0.242175
$552$	19.6847	0.837835
$553$	13.1231	0.558051
$554$	−0.876894	−0.0372557
$555$	15.3693	0.652391
$556$	16.4924	0.699435
$557$	39.6155	1.67856	0.839282	−	0.543697i	$-0.182976\pi$
$557$	39.6155	1.67856	0.839282	+	0.543697i	$0.182976\pi$
$558$	18.2462	0.772424
$559$	−16.3542	−0.691707
$560$	−2.56155	−0.108245
$561$	−35.2311	−1.48746
$562$	−2.00000	−0.0843649
$563$	−8.49242	−0.357913	−0.178956	−	0.983857i	$-0.557272\pi$
$563$	−8.49242	−0.357913	−0.178956	+	0.983857i	$0.557272\pi$
$564$	−16.0000	−0.673722
$565$	8.87689	0.373454
$566$	21.1231	0.887870
$567$	17.9309	0.753026
$568$	−10.2462	−0.429921
$569$	−3.12311	−0.130927	−0.0654637	−	0.997855i	$-0.520853\pi$
$569$	−3.12311	−0.130927	−0.0654637	+	0.997855i	$0.520853\pi$
$570$	−2.56155	−0.107292
$571$	21.6155	0.904582	0.452291	−	0.891870i	$-0.350607\pi$
$571$	21.6155	0.904582	0.452291	+	0.891870i	$0.350607\pi$
$572$	22.7386	0.950750
$573$	9.43845	0.394297
$574$	31.3693	1.30933
$575$	7.68466	0.320472
$576$	3.56155	0.148398
$577$	−10.3153	−0.429433	−0.214717	−	0.976676i	$-0.568883\pi$
$577$	−10.3153	−0.429433	−0.214717	+	0.976676i	$0.568883\pi$
$578$	5.17708	0.215338
$579$	37.1231	1.54278
$580$	−5.68466	−0.236043
$581$	−7.36932	−0.305731
$582$	15.3693	0.637079
$583$	−18.2462	−0.755681
$584$	1.68466	0.0697117
$585$	20.2462	0.837078
$586$	22.1771	0.916127
$587$	−7.36932	−0.304164	−0.152082	−	0.988368i	$-0.548598\pi$
$587$	−7.36932	−0.304164	−0.152082	+	0.988368i	$0.548598\pi$
$588$	1.12311	0.0463161
$589$	5.12311	0.211094
$590$	−2.56155	−0.105457
$591$	51.8617	2.13331
$592$	−6.00000	−0.246598
$593$	7.75379	0.318410	0.159205	−	0.987246i	$-0.449107\pi$
$593$	7.75379	0.318410	0.159205	+	0.987246i	$0.449107\pi$
$594$	5.75379	0.236081
$595$	−8.80776	−0.361083
$596$	13.3693	0.547629
$597$	−43.0540	−1.76208
$598$	−43.6847	−1.78640
$599$	−11.8617	−0.484658	−0.242329	−	0.970194i	$-0.577911\pi$
$599$	−11.8617	−0.484658	−0.242329	+	0.970194i	$0.577911\pi$
$600$	2.56155	0.104575
$601$	18.0000	0.734235	0.367118	−	0.930175i	$-0.380345\pi$
$601$	18.0000	0.734235	0.367118	+	0.930175i	$0.380345\pi$
$602$	−7.36932	−0.300351
$603$	−9.12311	−0.371522
$604$	5.12311	0.208456
$605$	5.00000	0.203279
$606$	−44.4924	−1.80738
$607$	−21.1231	−0.857360	−0.428680	−	0.903456i	$-0.641021\pi$
$607$	−21.1231	−0.857360	−0.428680	+	0.903456i	$0.641021\pi$
$608$	1.00000	0.0405554
$609$	−37.3002	−1.51148
$610$	−11.1231	−0.450361
$611$	35.5076	1.43648
$612$	12.2462	0.495024
$613$	5.36932	0.216865	0.108432	−	0.994104i	$-0.465417\pi$
$613$	5.36932	0.216865	0.108432	+	0.994104i	$0.465417\pi$
$614$	−32.4924	−1.31129
$615$	−31.3693	−1.26493
$616$	10.2462	0.412832
$617$	12.2462	0.493014	0.246507	−	0.969141i	$-0.420717\pi$
$617$	12.2462	0.493014	0.246507	+	0.969141i	$0.420717\pi$
$618$	5.75379	0.231451
$619$	−36.0000	−1.44696	−0.723481	−	0.690344i	$-0.757459\pi$
$619$	−36.0000	−1.44696	−0.723481	+	0.690344i	$0.757459\pi$
$620$	−5.12311	−0.205749
$621$	−11.0540	−0.443581
$622$	3.68466	0.147741
$623$	−5.12311	−0.205253
$624$	−14.5616	−0.582929
$625$	1.00000	0.0400000
$626$	−5.05398	−0.201997
$627$	10.2462	0.409194
$628$	−20.2462	−0.807912
$629$	−20.6307	−0.822599
$630$	9.12311	0.363473
$631$	−20.4924	−0.815790	−0.407895	−	0.913029i	$-0.633737\pi$
$631$	−20.4924	−0.815790	−0.407895	+	0.913029i	$0.633737\pi$
$632$	5.12311	0.203786
$633$	−21.3002	−0.846606
$634$	−13.0540	−0.518440
$635$	13.1231	0.520775
$636$	11.6847	0.463327
$637$	−2.49242	−0.0987534
$638$	22.7386	0.900231
$639$	36.4924	1.44362
$640$	−1.00000	−0.0395285
$641$	21.8617	0.863487	0.431743	−	0.901996i	$-0.357899\pi$
$641$	21.8617	0.863487	0.431743	+	0.901996i	$0.357899\pi$
$642$	−13.9309	−0.549808
$643$	−33.6155	−1.32567	−0.662834	−	0.748767i	$-0.730646\pi$
$643$	−33.6155	−1.32567	−0.662834	+	0.748767i	$0.730646\pi$
$644$	−19.6847	−0.775684
$645$	7.36932	0.290167
$646$	3.43845	0.135284
$647$	5.43845	0.213807	0.106904	−	0.994269i	$-0.465906\pi$
$647$	5.43845	0.213807	0.106904	+	0.994269i	$0.465906\pi$
$648$	7.00000	0.274986
$649$	10.2462	0.402199
$650$	−5.68466	−0.222971
$651$	−33.6155	−1.31750
$652$	−15.3693	−0.601909
$653$	−7.12311	−0.278749	−0.139374	−	0.990240i	$-0.544509\pi$
$653$	−7.12311	−0.278749	−0.139374	+	0.990240i	$0.544509\pi$
$654$	−1.43845	−0.0562477
$655$	−16.4924	−0.644412
$656$	12.2462	0.478134
$657$	−6.00000	−0.234082
$658$	16.0000	0.623745
$659$	−14.0691	−0.548056	−0.274028	−	0.961722i	$-0.588356\pi$
$659$	−14.0691	−0.548056	−0.274028	+	0.961722i	$0.588356\pi$
$660$	−10.2462	−0.398833
$661$	−10.8078	−0.420373	−0.210187	−	0.977661i	$-0.567407\pi$
$661$	−10.8078	−0.420373	−0.210187	+	0.977661i	$0.567407\pi$
$662$	2.56155	0.0995576
$663$	−50.0691	−1.94452
$664$	−2.87689	−0.111645
$665$	2.56155	0.0993328
$666$	21.3693	0.828044
$667$	−43.6847	−1.69148
$668$	−7.36932	−0.285127
$669$	59.8617	2.31439
$670$	2.56155	0.0989614
$671$	44.4924	1.71761
$672$	−6.56155	−0.253117
$673$	21.3693	0.823727	0.411863	−	0.911246i	$-0.364878\pi$
$673$	21.3693	0.823727	0.411863	+	0.911246i	$0.364878\pi$
$674$	26.0000	1.00148
$675$	−1.43845	−0.0553659
$676$	19.3153	0.742898
$677$	40.5616	1.55891	0.779454	−	0.626460i	$-0.215497\pi$
$677$	40.5616	1.55891	0.779454	+	0.626460i	$0.215497\pi$
$678$	22.7386	0.873272
$679$	−15.3693	−0.589820
$680$	−3.43845	−0.131858
$681$	−66.4233	−2.54535
$682$	20.4924	0.784695
$683$	4.00000	0.153056	0.0765279	−	0.997067i	$-0.475617\pi$
$683$	4.00000	0.153056	0.0765279	+	0.997067i	$0.475617\pi$
$684$	−3.56155	−0.136179
$685$	−14.8078	−0.565776
$686$	−19.0540	−0.727484
$687$	37.1231	1.41633
$688$	−2.87689	−0.109681
$689$	−25.9309	−0.987887
$690$	19.6847	0.749382
$691$	−17.1231	−0.651394	−0.325697	−	0.945474i	$-0.605599\pi$
$691$	−17.1231	−0.651394	−0.325697	+	0.945474i	$0.605599\pi$
$692$	20.2462	0.769645
$693$	−36.4924	−1.38623
$694$	8.63068	0.327616
$695$	16.4924	0.625593
$696$	−14.5616	−0.551954
$697$	42.1080	1.59495
$698$	−3.75379	−0.142083
$699$	−25.6155	−0.968868
$700$	−2.56155	−0.0968176
$701$	−20.8769	−0.788509	−0.394255	−	0.919001i	$-0.628997\pi$
$701$	−20.8769	−0.788509	−0.394255	+	0.919001i	$0.628997\pi$
$702$	8.17708	0.308624
$703$	6.00000	0.226294
$704$	4.00000	0.150756
$705$	−16.0000	−0.602595
$706$	3.93087	0.147940
$707$	44.4924	1.67331
$708$	−6.56155	−0.246598
$709$	38.0000	1.42712	0.713560	−	0.700594i	$-0.247082\pi$
$709$	38.0000	1.42712	0.713560	+	0.700594i	$0.247082\pi$
$710$	−10.2462	−0.384533
$711$	−18.2462	−0.684286
$712$	−2.00000	−0.0749532
$713$	−39.3693	−1.47439
$714$	−22.5616	−0.844345
$715$	22.7386	0.850377
$716$	−22.2462	−0.831380
$717$	3.68466	0.137606
$718$	−1.43845	−0.0536824
$719$	−25.4384	−0.948694	−0.474347	−	0.880338i	$-0.657316\pi$
$719$	−25.4384	−0.948694	−0.474347	+	0.880338i	$0.657316\pi$
$720$	3.56155	0.132731
$721$	−5.75379	−0.214282
$722$	−1.00000	−0.0372161
$723$	−59.2311	−2.20283
$724$	−18.0000	−0.668965
$725$	−5.68466	−0.211123
$726$	12.8078	0.475341
$727$	−24.3153	−0.901806	−0.450903	−	0.892573i	$-0.648898\pi$
$727$	−24.3153	−0.901806	−0.450903	+	0.892573i	$0.648898\pi$
$728$	14.5616	0.539687
$729$	−35.9848	−1.33277
$730$	1.68466	0.0623520
$731$	−9.89205	−0.365871
$732$	−28.4924	−1.05311
$733$	−36.8769	−1.36208	−0.681040	−	0.732247i	$-0.738472\pi$
$733$	−36.8769	−1.36208	−0.681040	+	0.732247i	$0.738472\pi$
$734$	−6.24621	−0.230552
$735$	1.12311	0.0414264
$736$	−7.68466	−0.283260
$737$	−10.2462	−0.377424
$738$	−43.6155	−1.60551
$739$	25.1231	0.924168	0.462084	−	0.886836i	$-0.347102\pi$
$739$	25.1231	0.924168	0.462084	+	0.886836i	$0.347102\pi$
$740$	−6.00000	−0.220564
$741$	14.5616	0.534932
$742$	−11.6847	−0.428957
$743$	18.8769	0.692526	0.346263	−	0.938137i	$-0.387450\pi$
$743$	18.8769	0.692526	0.346263	+	0.938137i	$0.387450\pi$
$744$	−13.1231	−0.481116
$745$	13.3693	0.489814
$746$	23.4384	0.858143
$747$	10.2462	0.374889
$748$	13.7538	0.502888
$749$	13.9309	0.509023
$750$	2.56155	0.0935347
$751$	−34.8769	−1.27268	−0.636338	−	0.771410i	$-0.719552\pi$
$751$	−34.8769	−1.27268	−0.636338	+	0.771410i	$0.719552\pi$
$752$	6.24621	0.227776
$753$	−16.0000	−0.583072
$754$	32.3153	1.17686
$755$	5.12311	0.186449
$756$	3.68466	0.134010
$757$	42.4924	1.54441	0.772207	−	0.635371i	$-0.219153\pi$
$757$	42.4924	1.54441	0.772207	+	0.635371i	$0.219153\pi$
$758$	−10.5616	−0.383613
$759$	−78.7386	−2.85803
$760$	1.00000	0.0362738
$761$	41.5464	1.50606	0.753028	−	0.657989i	$-0.228593\pi$
$761$	41.5464	1.50606	0.753028	+	0.657989i	$0.228593\pi$
$762$	33.6155	1.21776
$763$	1.43845	0.0520753
$764$	−3.68466	−0.133306
$765$	12.2462	0.442763
$766$	−13.7538	−0.496945
$767$	14.5616	0.525787
$768$	−2.56155	−0.0924321
$769$	27.4384	0.989456	0.494728	−	0.869048i	$-0.335268\pi$
$769$	27.4384	0.989456	0.494728	+	0.869048i	$0.335268\pi$
$770$	10.2462	0.369248
$771$	−35.8617	−1.29153
$772$	−14.4924	−0.521594
$773$	10.8078	0.388728	0.194364	−	0.980929i	$-0.437736\pi$
$773$	10.8078	0.388728	0.194364	+	0.980929i	$0.437736\pi$
$774$	10.2462	0.368292
$775$	−5.12311	−0.184027
$776$	−6.00000	−0.215387
$777$	−39.3693	−1.41237
$778$	7.12311	0.255376
$779$	−12.2462	−0.438766
$780$	−14.5616	−0.521387
$781$	40.9848	1.46655
$782$	−26.4233	−0.944895
$783$	8.17708	0.292225
$784$	−0.438447	−0.0156588
$785$	−20.2462	−0.722618
$786$	−42.2462	−1.50687
$787$	11.1922	0.398960	0.199480	−	0.979902i	$-0.436075\pi$
$787$	11.1922	0.398960	0.199480	+	0.979902i	$0.436075\pi$
$788$	−20.2462	−0.721241
$789$	56.9848	2.02871
$790$	5.12311	0.182272
$791$	−22.7386	−0.808493
$792$	−14.2462	−0.506217
$793$	63.2311	2.24540
$794$	7.12311	0.252790
$795$	11.6847	0.414412
$796$	16.8078	0.595735
$797$	−11.3002	−0.400273	−0.200137	−	0.979768i	$-0.564139\pi$
$797$	−11.3002	−0.400273	−0.200137	+	0.979768i	$0.564139\pi$
$798$	6.56155	0.232276
$799$	21.4773	0.759811
$800$	−1.00000	−0.0353553
$801$	7.12311	0.251683
$802$	3.75379	0.132551
$803$	−6.73863	−0.237801
$804$	6.56155	0.231408
$805$	−19.6847	−0.693793
$806$	29.1231	1.02582
$807$	66.6004	2.34444
$808$	17.3693	0.611050
$809$	−12.5616	−0.441641	−0.220820	−	0.975315i	$-0.570873\pi$
$809$	−12.5616	−0.441641	−0.220820	+	0.975315i	$0.570873\pi$
$810$	7.00000	0.245955
$811$	−20.8078	−0.730659	−0.365330	−	0.930878i	$-0.619044\pi$
$811$	−20.8078	−0.730659	−0.365330	+	0.930878i	$0.619044\pi$
$812$	14.5616	0.511010
$813$	56.1771	1.97022
$814$	24.0000	0.841200
$815$	−15.3693	−0.538364
$816$	−8.80776	−0.308333
$817$	2.87689	0.100650
$818$	−24.7386	−0.864966
$819$	−51.8617	−1.81220
$820$	12.2462	0.427656
$821$	−17.3693	−0.606193	−0.303097	−	0.952960i	$-0.598021\pi$
$821$	−17.3693	−0.606193	−0.303097	+	0.952960i	$0.598021\pi$
$822$	−37.9309	−1.32299
$823$	−29.4384	−1.02616	−0.513080	−	0.858341i	$-0.671496\pi$
$823$	−29.4384	−1.02616	−0.513080	+	0.858341i	$0.671496\pi$
$824$	−2.24621	−0.0782505
$825$	−10.2462	−0.356727
$826$	6.56155	0.228306
$827$	−10.5616	−0.367261	−0.183631	−	0.982995i	$-0.558785\pi$
$827$	−10.5616	−0.367261	−0.183631	+	0.982995i	$0.558785\pi$
$828$	27.3693	0.951150
$829$	−21.0540	−0.731235	−0.365617	−	0.930765i	$-0.619142\pi$
$829$	−21.0540	−0.731235	−0.365617	+	0.930765i	$0.619142\pi$
$830$	−2.87689	−0.0998585
$831$	−2.24621	−0.0779202
$832$	5.68466	0.197080
$833$	−1.50758	−0.0522345
$834$	42.2462	1.46287
$835$	−7.36932	−0.255026
$836$	−4.00000	−0.138343
$837$	7.36932	0.254721
$838$	−23.8617	−0.824290
$839$	20.4924	0.707477	0.353738	−	0.935344i	$-0.384910\pi$
$839$	20.4924	0.707477	0.353738	+	0.935344i	$0.384910\pi$
$840$	−6.56155	−0.226395
$841$	3.31534	0.114322
$842$	23.9309	0.824712
$843$	−5.12311	−0.176449
$844$	8.31534	0.286226
$845$	19.3153	0.664468
$846$	−22.2462	−0.764840
$847$	−12.8078	−0.440080
$848$	−4.56155	−0.156644
$849$	54.1080	1.85698
$850$	−3.43845	−0.117938
$851$	−46.1080	−1.58056
$852$	−26.2462	−0.899180
$853$	−24.7386	−0.847035	−0.423517	−	0.905888i	$-0.639205\pi$
$853$	−24.7386	−0.847035	−0.423517	+	0.905888i	$0.639205\pi$
$854$	28.4924	0.974991
$855$	−3.56155	−0.121803
$856$	5.43845	0.185882
$857$	14.6307	0.499775	0.249887	−	0.968275i	$-0.419606\pi$
$857$	14.6307	0.499775	0.249887	+	0.968275i	$0.419606\pi$
$858$	58.2462	1.98849
$859$	−52.9848	−1.80782	−0.903910	−	0.427723i	$-0.859316\pi$
$859$	−52.9848	−1.80782	−0.903910	+	0.427723i	$0.859316\pi$
$860$	−2.87689	−0.0981013
$861$	80.3542	2.73846
$862$	16.0000	0.544962
$863$	2.24621	0.0764619	0.0382310	−	0.999269i	$-0.487828\pi$
$863$	2.24621	0.0764619	0.0382310	+	0.999269i	$0.487828\pi$
$864$	1.43845	0.0489370
$865$	20.2462	0.688392
$866$	−14.6307	−0.497171
$867$	13.2614	0.450380
$868$	13.1231	0.445427
$869$	−20.4924	−0.695158
$870$	−14.5616	−0.493683
$871$	−14.5616	−0.493399
$872$	0.561553	0.0190166
$873$	21.3693	0.723242
$874$	7.68466	0.259937
$875$	−2.56155	−0.0865963
$876$	4.31534	0.145802
$877$	−3.93087	−0.132736	−0.0663680	−	0.997795i	$-0.521141\pi$
$877$	−3.93087	−0.132736	−0.0663680	+	0.997795i	$0.521141\pi$
$878$	13.1231	0.442883
$879$	56.8078	1.91608
$880$	4.00000	0.134840
$881$	42.9848	1.44820	0.724098	−	0.689697i	$-0.242256\pi$
$881$	42.9848	1.44820	0.724098	+	0.689697i	$0.242256\pi$
$882$	1.56155	0.0525802
$883$	−6.38447	−0.214855	−0.107427	−	0.994213i	$-0.534261\pi$
$883$	−6.38447	−0.214855	−0.107427	+	0.994213i	$0.534261\pi$
$884$	19.5464	0.657417
$885$	−6.56155	−0.220564
$886$	−2.24621	−0.0754629
$887$	28.4924	0.956682	0.478341	−	0.878174i	$-0.341238\pi$
$887$	28.4924	0.956682	0.478341	+	0.878174i	$0.341238\pi$
$888$	−15.3693	−0.515761
$889$	−33.6155	−1.12743
$890$	−2.00000	−0.0670402
$891$	−28.0000	−0.938035
$892$	−23.3693	−0.782463
$893$	−6.24621	−0.209021
$894$	34.2462	1.14536
$895$	−22.2462	−0.743609
$896$	2.56155	0.0855755
$897$	−111.901	−3.73625
$898$	28.7386	0.959021
$899$	29.1231	0.971310
$900$	3.56155	0.118718
$901$	−15.6847	−0.522532
$902$	−48.9848	−1.63102
$903$	−18.8769	−0.628184
$904$	−8.87689	−0.295241
$905$	−18.0000	−0.598340
$906$	13.1231	0.435986
$907$	−20.1771	−0.669969	−0.334984	−	0.942224i	$-0.608731\pi$
$907$	−20.1771	−0.669969	−0.334984	+	0.942224i	$0.608731\pi$
$908$	25.9309	0.860546
$909$	−61.8617	−2.05182
$910$	14.5616	0.482711
$911$	4.49242	0.148841	0.0744203	−	0.997227i	$-0.476289\pi$
$911$	4.49242	0.148841	0.0744203	+	0.997227i	$0.476289\pi$
$912$	2.56155	0.0848215
$913$	11.5076	0.380845
$914$	−6.31534	−0.208893
$915$	−28.4924	−0.941930
$916$	−14.4924	−0.478843
$917$	42.2462	1.39509
$918$	4.94602	0.163243
$919$	−2.06913	−0.0682543	−0.0341272	−	0.999417i	$-0.510865\pi$
$919$	−2.06913	−0.0682543	−0.0341272	+	0.999417i	$0.510865\pi$
$920$	−7.68466	−0.253356
$921$	−83.2311	−2.74256
$922$	−3.75379	−0.123624
$923$	58.2462	1.91720
$924$	26.2462	0.863437
$925$	−6.00000	−0.197279
$926$	30.2462	0.993952
$927$	8.00000	0.262754
$928$	5.68466	0.186608
$929$	−19.3002	−0.633219	−0.316609	−	0.948556i	$-0.602544\pi$
$929$	−19.3002	−0.633219	−0.316609	+	0.948556i	$0.602544\pi$
$930$	−13.1231	−0.430324
$931$	0.438447	0.0143695
$932$	10.0000	0.327561
$933$	9.43845	0.309001
$934$	−18.2462	−0.597034
$935$	13.7538	0.449797
$936$	−20.2462	−0.661768
$937$	40.5616	1.32509	0.662544	−	0.749023i	$-0.269477\pi$
$937$	40.5616	1.32509	0.662544	+	0.749023i	$0.269477\pi$
$938$	−6.56155	−0.214242
$939$	−12.9460	−0.422478
$940$	6.24621	0.203729
$941$	54.8078	1.78668	0.893341	−	0.449379i	$-0.148355\pi$
$941$	54.8078	1.78668	0.893341	+	0.449379i	$0.148355\pi$
$942$	−51.8617	−1.68975
$943$	94.1080	3.06458
$944$	2.56155	0.0833714
$945$	3.68466	0.119862
$946$	11.5076	0.374144
$947$	−34.2462	−1.11285	−0.556426	−	0.830897i	$-0.687828\pi$
$947$	−34.2462	−1.11285	−0.556426	+	0.830897i	$0.687828\pi$
$948$	13.1231	0.426219
$949$	−9.57671	−0.310873
$950$	1.00000	0.0324443
$951$	−33.4384	−1.08432
$952$	8.80776	0.285461
$953$	44.1080	1.42880	0.714398	−	0.699739i	$-0.246700\pi$
$953$	44.1080	1.42880	0.714398	+	0.699739i	$0.246700\pi$
$954$	16.2462	0.525991
$955$	−3.68466	−0.119233
$956$	−1.43845	−0.0465227
$957$	58.2462	1.88283
$958$	−32.0000	−1.03387
$959$	37.9309	1.22485
$960$	−2.56155	−0.0826738
$961$	−4.75379	−0.153348
$962$	34.1080	1.09968
$963$	−19.3693	−0.624168
$964$	23.1231	0.744745
$965$	−14.4924	−0.466528
$966$	−50.4233	−1.62234
$967$	−15.5076	−0.498690	−0.249345	−	0.968415i	$-0.580215\pi$
$967$	−15.5076	−0.498690	−0.249345	+	0.968415i	$0.580215\pi$
$968$	−5.00000	−0.160706
$969$	8.80776	0.282946
$970$	−6.00000	−0.192648
$971$	−56.4924	−1.81293	−0.906464	−	0.422283i	$-0.861229\pi$
$971$	−56.4924	−1.81293	−0.906464	+	0.422283i	$0.861229\pi$
$972$	22.2462	0.713548
$973$	−42.2462	−1.35435
$974$	17.6155	0.564438
$975$	−14.5616	−0.466343
$976$	11.1231	0.356042
$977$	28.7386	0.919430	0.459715	−	0.888066i	$-0.347952\pi$
$977$	28.7386	0.919430	0.459715	+	0.888066i	$0.347952\pi$
$978$	−39.3693	−1.25889
$979$	8.00000	0.255681
$980$	−0.438447	−0.0140057
$981$	−2.00000	−0.0638551
$982$	1.12311	0.0358397
$983$	18.8769	0.602079	0.301040	−	0.953612i	$-0.402666\pi$
$983$	18.8769	0.602079	0.301040	+	0.953612i	$0.402666\pi$
$984$	31.3693	1.00002
$985$	−20.2462	−0.645098
$986$	19.5464	0.622484
$987$	40.9848	1.30456
$988$	−5.68466	−0.180853
$989$	−22.1080	−0.702992
$990$	−14.2462	−0.452774
$991$	2.87689	0.0913876	0.0456938	−	0.998955i	$-0.485450\pi$
$991$	2.87689	0.0913876	0.0456938	+	0.998955i	$0.485450\pi$
$992$	5.12311	0.162659
$993$	6.56155	0.208225
$994$	26.2462	0.832479
$995$	16.8078	0.532842
$996$	−7.36932	−0.233506
$997$	−16.7386	−0.530118	−0.265059	−	0.964232i	$-0.585391\pi$
$997$	−16.7386	−0.530118	−0.265059	+	0.964232i	$0.585391\pi$
$998$	−42.1080	−1.33290
$999$	8.63068	0.273063

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	190.2.a.d.1.1	✓	2
3.2	odd	2		1710.2.a.w.1.1		2
4.3	odd	2		1520.2.a.n.1.2		2
5.2	odd	4		950.2.b.f.799.2		4
5.3	odd	4		950.2.b.f.799.3		4
5.4	even	2		950.2.a.h.1.2		2
7.6	odd	2		9310.2.a.bc.1.2		2
8.3	odd	2		6080.2.a.bb.1.1		2
8.5	even	2		6080.2.a.bh.1.2		2
15.14	odd	2		8550.2.a.br.1.2		2
19.18	odd	2		3610.2.a.t.1.2		2
20.19	odd	2		7600.2.a.y.1.1		2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
190.2.a.d.1.1	✓	2	1.1	even	1	trivial
950.2.a.h.1.2		2	5.4	even	2
950.2.b.f.799.2		4	5.2	odd	4
950.2.b.f.799.3		4	5.3	odd	4
1520.2.a.n.1.2		2	4.3	odd	2
1710.2.a.w.1.1		2	3.2	odd	2
3610.2.a.t.1.2		2	19.18	odd	2
6080.2.a.bb.1.1		2	8.3	odd	2
6080.2.a.bh.1.2		2	8.5	even	2
7600.2.a.y.1.1		2	20.19	odd	2
8550.2.a.br.1.2		2	15.14	odd	2
9310.2.a.bc.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:	\( N \)	\(=\)	\( 190 = 2 \cdot 5 \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	190.a (trivial)

\(f(q)\)	\(=\)	\(q-1.00000 q^{2} -2.56155 q^{3} +1.00000 q^{4} +1.00000 q^{5} +2.56155 q^{6} -2.56155 q^{7} -1.00000 q^{8} +3.56155 q^{9} +O(q^{10})\)	\(q-1.00000 q^{2} -2.56155 q^{3} +1.00000 q^{4} +1.00000 q^{5} +2.56155 q^{6} -2.56155 q^{7} -1.00000 q^{8} +3.56155 q^{9} -1.00000 q^{10} +4.00000 q^{11} -2.56155 q^{12} +5.68466 q^{13} +2.56155 q^{14} -2.56155 q^{15} +1.00000 q^{16} +3.43845 q^{17} -3.56155 q^{18} -1.00000 q^{19} +1.00000 q^{20} +6.56155 q^{21} -4.00000 q^{22} +7.68466 q^{23} +2.56155 q^{24} +1.00000 q^{25} -5.68466 q^{26} -1.43845 q^{27} -2.56155 q^{28} -5.68466 q^{29} +2.56155 q^{30} -5.12311 q^{31} -1.00000 q^{32} -10.2462 q^{33} -3.43845 q^{34} -2.56155 q^{35} +3.56155 q^{36} -6.00000 q^{37} +1.00000 q^{38} -14.5616 q^{39} -1.00000 q^{40} +12.2462 q^{41} -6.56155 q^{42} -2.87689 q^{43} +4.00000 q^{44} +3.56155 q^{45} -7.68466 q^{46} +6.24621 q^{47} -2.56155 q^{48} -0.438447 q^{49} -1.00000 q^{50} -8.80776 q^{51} +5.68466 q^{52} -4.56155 q^{53} +1.43845 q^{54} +4.00000 q^{55} +2.56155 q^{56} +2.56155 q^{57} +5.68466 q^{58} +2.56155 q^{59} -2.56155 q^{60} +11.1231 q^{61} +5.12311 q^{62} -9.12311 q^{63} +1.00000 q^{64} +5.68466 q^{65} +10.2462 q^{66} -2.56155 q^{67} +3.43845 q^{68} -19.6847 q^{69} +2.56155 q^{70} +10.2462 q^{71} -3.56155 q^{72} -1.68466 q^{73} +6.00000 q^{74} -2.56155 q^{75} -1.00000 q^{76} -10.2462 q^{77} +14.5616 q^{78} -5.12311 q^{79} +1.00000 q^{80} -7.00000 q^{81} -12.2462 q^{82} +2.87689 q^{83} +6.56155 q^{84} +3.43845 q^{85} +2.87689 q^{86} +14.5616 q^{87} -4.00000 q^{88} +2.00000 q^{89} -3.56155 q^{90} -14.5616 q^{91} +7.68466 q^{92} +13.1231 q^{93} -6.24621 q^{94} -1.00000 q^{95} +2.56155 q^{96} +6.00000 q^{97} +0.438447 q^{98} +14.2462 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q - 2 q^{2} - q^{3} + 2 q^{4} + 2 q^{5} + q^{6} - q^{7} - 2 q^{8} + 3 q^{9}+O(q^{10}) \) 2 * q - 2 * q^2 - q^3 + 2 * q^4 + 2 * q^5 + q^6 - q^7 - 2 * q^8 + 3 * q^9	\( 2 q - 2 q^{2} - q^{3} + 2 q^{4} + 2 q^{5} + q^{6} - q^{7} - 2 q^{8} + 3 q^{9} - 2 q^{10} + 8 q^{11} - q^{12} - q^{13} + q^{14} - q^{15} + 2 q^{16} + 11 q^{17} - 3 q^{18} - 2 q^{19} + 2 q^{20} + 9 q^{21} - 8 q^{22} + 3 q^{23} + q^{24} + 2 q^{25} + q^{26} - 7 q^{27} - q^{28} + q^{29} + q^{30} - 2 q^{31} - 2 q^{32} - 4 q^{33} - 11 q^{34} - q^{35} + 3 q^{36} - 12 q^{37} + 2 q^{38} - 25 q^{39} - 2 q^{40} + 8 q^{41} - 9 q^{42} - 14 q^{43} + 8 q^{44} + 3 q^{45} - 3 q^{46} - 4 q^{47} - q^{48} - 5 q^{49} - 2 q^{50} + 3 q^{51} - q^{52} - 5 q^{53} + 7 q^{54} + 8 q^{55} + q^{56} + q^{57} - q^{58} + q^{59} - q^{60} + 14 q^{61} + 2 q^{62} - 10 q^{63} + 2 q^{64} - q^{65} + 4 q^{66} - q^{67} + 11 q^{68} - 27 q^{69} + q^{70} + 4 q^{71} - 3 q^{72} + 9 q^{73} + 12 q^{74} - q^{75} - 2 q^{76} - 4 q^{77} + 25 q^{78} - 2 q^{79} + 2 q^{80} - 14 q^{81} - 8 q^{82} + 14 q^{83} + 9 q^{84} + 11 q^{85} + 14 q^{86} + 25 q^{87} - 8 q^{88} + 4 q^{89} - 3 q^{90} - 25 q^{91} + 3 q^{92} + 18 q^{93} + 4 q^{94} - 2 q^{95} + q^{96} + 12 q^{97} + 5 q^{98} + 12 q^{99}+O(q^{100}) \) 2 * q - 2 * q^2 - q^3 + 2 * q^4 + 2 * q^5 + q^6 - q^7 - 2 * q^8 + 3 * q^9 - 2 * q^10 + 8 * q^11 - q^12 - q^13 + q^14 - q^15 + 2 * q^16 + 11 * q^17 - 3 * q^18 - 2 * q^19 + 2 * q^20 + 9 * q^21 - 8 * q^22 + 3 * q^23 + q^24 + 2 * q^25 + q^26 - 7 * q^27 - q^28 + q^29 + q^30 - 2 * q^31 - 2 * q^32 - 4 * q^33 - 11 * q^34 - q^35 + 3 * q^36 - 12 * q^37 + 2 * q^38 - 25 * q^39 - 2 * q^40 + 8 * q^41 - 9 * q^42 - 14 * q^43 + 8 * q^44 + 3 * q^45 - 3 * q^46 - 4 * q^47 - q^48 - 5 * q^49 - 2 * q^50 + 3 * q^51 - q^52 - 5 * q^53 + 7 * q^54 + 8 * q^55 + q^56 + q^57 - q^58 + q^59 - q^60 + 14 * q^61 + 2 * q^62 - 10 * q^63 + 2 * q^64 - q^65 + 4 * q^66 - q^67 + 11 * q^68 - 27 * q^69 + q^70 + 4 * q^71 - 3 * q^72 + 9 * q^73 + 12 * q^74 - q^75 - 2 * q^76 - 4 * q^77 + 25 * q^78 - 2 * q^79 + 2 * q^80 - 14 * q^81 - 8 * q^82 + 14 * q^83 + 9 * q^84 + 11 * q^85 + 14 * q^86 + 25 * q^87 - 8 * q^88 + 4 * q^89 - 3 * q^90 - 25 * q^91 + 3 * q^92 + 18 * q^93 + 4 * q^94 - 2 * q^95 + q^96 + 12 * q^97 + 5 * q^98 + 12 * q^99

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