LMFDB - Embedded newform 187.2.a.e.1.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [187,2,Mod(1,187)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(187, 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("187.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 187 = 11 \cdot 17 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	187.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:	$1.49320251780$
Analytic rank:	$1$
Dimension:	$3$
Coefficient field:	3.3.148.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{3} - x^{2} - 3x + 1 $ x^3 - x^2 - 3*x + 1
Coefficient ring:	$\Z[a_1, a_2]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.1
Root			$-1.48119$ of defining polynomial
Character	$\chi$	$=$	187.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-2.48119 q^{2} -2.67513 q^{3} +4.15633 q^{4} -0.518806 q^{5} +6.63752 q^{6} +3.35026 q^{7} -5.35026 q^{8} +4.15633 q^{9} +O(q^{10})$	\(q-2.48119 q^{2} -2.67513 q^{3} +4.15633 q^{4} -0.518806 q^{5} +6.63752 q^{6} +3.35026 q^{7} -5.35026 q^{8} +4.15633 q^{9} +1.28726 q^{10} -1.00000 q^{11} -11.1187 q^{12} -5.44358 q^{13} -8.31265 q^{14} +1.38787 q^{15} +4.96239 q^{16} -1.00000 q^{17} -10.3127 q^{18} +4.09332 q^{19} -2.15633 q^{20} -8.96239 q^{21} +2.48119 q^{22} -6.67513 q^{23} +14.3127 q^{24} -4.73084 q^{25} +13.5066 q^{26} -3.09332 q^{27} +13.9248 q^{28} -2.71274 q^{29} -3.44358 q^{30} -5.09332 q^{31} -1.61213 q^{32} +2.67513 q^{33} +2.48119 q^{34} -1.73813 q^{35} +17.2750 q^{36} -8.41327 q^{37} -10.1563 q^{38} +14.5623 q^{39} +2.77575 q^{40} +3.35026 q^{41} +22.2374 q^{42} +3.22425 q^{43} -4.15633 q^{44} -2.15633 q^{45} +16.5623 q^{46} +8.54420 q^{47} -13.2750 q^{48} +4.22425 q^{49} +11.7381 q^{50} +2.67513 q^{51} -22.6253 q^{52} -13.7685 q^{53} +7.67513 q^{54} +0.518806 q^{55} -17.9248 q^{56} -10.9502 q^{57} +6.73084 q^{58} -11.0811 q^{59} +5.76845 q^{60} -5.35026 q^{61} +12.6375 q^{62} +13.9248 q^{63} -5.92478 q^{64} +2.82416 q^{65} -6.63752 q^{66} -1.26187 q^{67} -4.15633 q^{68} +17.8568 q^{69} +4.31265 q^{70} -6.44358 q^{71} -22.2374 q^{72} -5.67513 q^{73} +20.8749 q^{74} +12.6556 q^{75} +17.0132 q^{76} -3.35026 q^{77} -36.1319 q^{78} -0.637519 q^{79} -2.57452 q^{80} -4.19394 q^{81} -8.31265 q^{82} +9.92478 q^{83} -37.2506 q^{84} +0.518806 q^{85} -8.00000 q^{86} +7.25694 q^{87} +5.35026 q^{88} +10.6629 q^{89} +5.35026 q^{90} -18.2374 q^{91} -27.7440 q^{92} +13.6253 q^{93} -21.1998 q^{94} -2.12364 q^{95} +4.31265 q^{96} -0.362481 q^{97} -10.4812 q^{98} -4.15633 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 3 q - 2 q^{2} - 3 q^{3} + 2 q^{4} - 7 q^{5} + 4 q^{6} - 6 q^{8} + 2 q^{9}+O(q^{10}) $ 3 * q - 2 * q^2 - 3 * q^3 + 2 * q^4 - 7 * q^5 + 4 * q^6 - 6 * q^8 + 2 * q^9	\( 3 q - 2 q^{2} - 3 q^{3} + 2 q^{4} - 7 q^{5} + 4 q^{6} - 6 q^{8} + 2 q^{9} - 2 q^{10} - 3 q^{11} - 12 q^{12} - 4 q^{14} + 5 q^{15} + 4 q^{16} - 3 q^{17} - 10 q^{18} + 6 q^{19} + 4 q^{20} - 16 q^{21} + 2 q^{22} - 15 q^{23} + 22 q^{24} + 8 q^{25} + 20 q^{26} - 3 q^{27} + 20 q^{28} - 14 q^{29} + 6 q^{30} - 9 q^{31} - 4 q^{32} + 3 q^{33} + 2 q^{34} + 4 q^{35} + 20 q^{36} - 11 q^{37} - 20 q^{38} + 6 q^{39} + 10 q^{40} + 24 q^{42} + 8 q^{43} - 2 q^{44} + 4 q^{45} + 12 q^{46} + 16 q^{47} - 8 q^{48} + 11 q^{49} + 26 q^{50} + 3 q^{51} - 26 q^{52} - 30 q^{53} + 18 q^{54} + 7 q^{55} - 32 q^{56} + 4 q^{57} - 2 q^{58} - q^{59} + 6 q^{60} - 6 q^{61} + 22 q^{62} + 20 q^{63} + 4 q^{64} - 20 q^{65} - 4 q^{66} - 13 q^{67} - 2 q^{68} + 23 q^{69} - 8 q^{70} - 3 q^{71} - 24 q^{72} - 12 q^{73} + 4 q^{74} - 6 q^{75} + 10 q^{76} - 46 q^{78} + 14 q^{79} + 4 q^{80} - 13 q^{81} - 4 q^{82} + 8 q^{83} - 28 q^{84} + 7 q^{85} - 24 q^{86} + 18 q^{87} + 6 q^{88} + q^{89} + 6 q^{90} - 12 q^{91} - 20 q^{92} - q^{93} - 10 q^{94} + 2 q^{95} - 8 q^{96} - 17 q^{97} - 26 q^{98} - 2 q^{99}+O(q^{100}) \) 3 * q - 2 * q^2 - 3 * q^3 + 2 * q^4 - 7 * q^5 + 4 * q^6 - 6 * q^8 + 2 * q^9 - 2 * q^10 - 3 * q^11 - 12 * q^12 - 4 * q^14 + 5 * q^15 + 4 * q^16 - 3 * q^17 - 10 * q^18 + 6 * q^19 + 4 * q^20 - 16 * q^21 + 2 * q^22 - 15 * q^23 + 22 * q^24 + 8 * q^25 + 20 * q^26 - 3 * q^27 + 20 * q^28 - 14 * q^29 + 6 * q^30 - 9 * q^31 - 4 * q^32 + 3 * q^33 + 2 * q^34 + 4 * q^35 + 20 * q^36 - 11 * q^37 - 20 * q^38 + 6 * q^39 + 10 * q^40 + 24 * q^42 + 8 * q^43 - 2 * q^44 + 4 * q^45 + 12 * q^46 + 16 * q^47 - 8 * q^48 + 11 * q^49 + 26 * q^50 + 3 * q^51 - 26 * q^52 - 30 * q^53 + 18 * q^54 + 7 * q^55 - 32 * q^56 + 4 * q^57 - 2 * q^58 - q^59 + 6 * q^60 - 6 * q^61 + 22 * q^62 + 20 * q^63 + 4 * q^64 - 20 * q^65 - 4 * q^66 - 13 * q^67 - 2 * q^68 + 23 * q^69 - 8 * q^70 - 3 * q^71 - 24 * q^72 - 12 * q^73 + 4 * q^74 - 6 * q^75 + 10 * q^76 - 46 * q^78 + 14 * q^79 + 4 * q^80 - 13 * q^81 - 4 * q^82 + 8 * q^83 - 28 * q^84 + 7 * q^85 - 24 * q^86 + 18 * q^87 + 6 * q^88 + q^89 + 6 * q^90 - 12 * q^91 - 20 * q^92 - q^93 - 10 * q^94 + 2 * q^95 - 8 * q^96 - 17 * q^97 - 26 * q^98 - 2 * 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 $

$2$	−2.48119	−1.75447	−0.877235	−	0.480062i	$-0.840614\pi$
$2$	−2.48119	−1.75447	−0.877235	+	0.480062i	$0.840614\pi$
$3$	−2.67513	−1.54449	−0.772244	−	0.635326i	$-0.780866\pi$
$3$	−2.67513	−1.54449	−0.772244	+	0.635326i	$0.780866\pi$
$4$	4.15633	2.07816
$5$	−0.518806	−0.232017	−0.116008	−	0.993248i	$-0.537010\pi$
$5$	−0.518806	−0.232017	−0.116008	+	0.993248i	$0.537010\pi$
$6$	6.63752	2.70976
$7$	3.35026	1.26628	0.633140	−	0.774037i	$-0.281766\pi$
$7$	3.35026	1.26628	0.633140	+	0.774037i	$0.281766\pi$
$8$	−5.35026	−1.89160
$9$	4.15633	1.38544
$10$	1.28726	0.407067
$11$	−1.00000	−0.301511
$11$	−1.00000	−0.301511
$12$	−11.1187	−3.20970
$13$	−5.44358	−1.50978	−0.754889	−	0.655852i	$-0.772309\pi$
$13$	−5.44358	−1.50978	−0.754889	+	0.655852i	$0.772309\pi$
$14$	−8.31265	−2.22165
$15$	1.38787	0.358347
$16$	4.96239	1.24060
$17$	−1.00000	−0.242536
$17$	−1.00000	−0.242536
$18$	−10.3127	−2.43071
$19$	4.09332	0.939072	0.469536	−	0.882913i	$-0.344421\pi$
$19$	4.09332	0.939072	0.469536	+	0.882913i	$0.344421\pi$
$20$	−2.15633	−0.482169
$21$	−8.96239	−1.95575
$22$	2.48119	0.528992
$23$	−6.67513	−1.39186	−0.695931	−	0.718109i	$-0.745008\pi$
$23$	−6.67513	−1.39186	−0.695931	+	0.718109i	$0.745008\pi$
$24$	14.3127	2.92156
$25$	−4.73084	−0.946168
$26$	13.5066	2.64886
$27$	−3.09332	−0.595310
$28$	13.9248	2.63154
$29$	−2.71274	−0.503744	−0.251872	−	0.967761i	$-0.581046\pi$
$29$	−2.71274	−0.503744	−0.251872	+	0.967761i	$0.581046\pi$
$30$	−3.44358	−0.628709
$31$	−5.09332	−0.914787	−0.457394	−	0.889264i	$-0.651217\pi$
$31$	−5.09332	−0.914787	−0.457394	+	0.889264i	$0.651217\pi$
$32$	−1.61213	−0.284986
$33$	2.67513	0.465681
$34$	2.48119	0.425521
$35$	−1.73813	−0.293798
$36$	17.2750	2.87917
$37$	−8.41327	−1.38313	−0.691566	−	0.722313i	$-0.743079\pi$
$37$	−8.41327	−1.38313	−0.691566	+	0.722313i	$0.743079\pi$
$38$	−10.1563	−1.64757
$39$	14.5623	2.33183
$40$	2.77575	0.438884
$41$	3.35026	0.523223	0.261611	−	0.965173i	$-0.415746\pi$
$41$	3.35026	0.523223	0.261611	+	0.965173i	$0.415746\pi$
$42$	22.2374	3.43131
$43$	3.22425	0.491694	0.245847	−	0.969309i	$-0.420934\pi$
$43$	3.22425	0.491694	0.245847	+	0.969309i	$0.420934\pi$
$44$	−4.15633	−0.626590
$45$	−2.15633	−0.321446
$46$	16.5623	2.44198
$47$	8.54420	1.24630	0.623150	−	0.782103i	$-0.285853\pi$
$47$	8.54420	1.24630	0.623150	+	0.782103i	$0.285853\pi$
$48$	−13.2750	−1.91609
$49$	4.22425	0.603465
$50$	11.7381	1.66002
$51$	2.67513	0.374593
$52$	−22.6253	−3.13756
$53$	−13.7685	−1.89124	−0.945621	−	0.325270i	$-0.894545\pi$
$53$	−13.7685	−1.89124	−0.945621	+	0.325270i	$0.894545\pi$
$54$	7.67513	1.04445
$55$	0.518806	0.0699557
$56$	−17.9248	−2.39530
$57$	−10.9502	−1.45039
$58$	6.73084	0.883803
$59$	−11.0811	−1.44264	−0.721318	−	0.692604i	$-0.756464\pi$
$59$	−11.0811	−1.44264	−0.721318	+	0.692604i	$0.756464\pi$
$60$	5.76845	0.744704
$61$	−5.35026	−0.685031	−0.342515	−	0.939512i	$-0.611279\pi$
$61$	−5.35026	−0.685031	−0.342515	+	0.939512i	$0.611279\pi$
$62$	12.6375	1.60497
$63$	13.9248	1.75436
$64$	−5.92478	−0.740597
$65$	2.82416	0.350294
$66$	−6.63752	−0.817022
$67$	−1.26187	−0.154161	−0.0770807	−	0.997025i	$-0.524560\pi$
$67$	−1.26187	−0.154161	−0.0770807	+	0.997025i	$0.524560\pi$
$68$	−4.15633	−0.504028
$69$	17.8568	2.14971
$70$	4.31265	0.515460
$71$	−6.44358	−0.764713	−0.382356	−	0.924015i	$-0.624887\pi$
$71$	−6.44358	−0.764713	−0.382356	+	0.924015i	$0.624887\pi$
$72$	−22.2374	−2.62071
$73$	−5.67513	−0.664224	−0.332112	−	0.943240i	$-0.607761\pi$
$73$	−5.67513	−0.664224	−0.332112	+	0.943240i	$0.607761\pi$
$74$	20.8749	2.42666
$75$	12.6556	1.46134
$76$	17.0132	1.95154
$77$	−3.35026	−0.381798
$78$	−36.1319	−4.09113
$79$	−0.637519	−0.0717265	−0.0358633	−	0.999357i	$-0.511418\pi$
$79$	−0.637519	−0.0717265	−0.0358633	+	0.999357i	$0.511418\pi$
$80$	−2.57452	−0.287840
$81$	−4.19394	−0.465993
$82$	−8.31265	−0.917979
$83$	9.92478	1.08939	0.544693	−	0.838636i	$-0.316646\pi$
$83$	9.92478	1.08939	0.544693	+	0.838636i	$0.316646\pi$
$84$	−37.2506	−4.06437
$85$	0.518806	0.0562724
$86$	−8.00000	−0.862662
$87$	7.25694	0.778026
$88$	5.35026	0.570340
$89$	10.6629	1.13027	0.565133	−	0.825000i	$-0.308825\pi$
$89$	10.6629	1.13027	0.565133	+	0.825000i	$0.308825\pi$
$90$	5.35026	0.563967
$91$	−18.2374	−1.91180
$92$	−27.7440	−2.89251
$93$	13.6253	1.41288
$94$	−21.1998	−2.18659
$95$	−2.12364	−0.217881
$96$	4.31265	0.440158
$97$	−0.362481	−0.0368043	−0.0184022	−	0.999831i	$-0.505858\pi$
$97$	−0.362481	−0.0368043	−0.0184022	+	0.999831i	$0.505858\pi$
$98$	−10.4812	−1.05876
$99$	−4.15633	−0.417726
$100$	−19.6629	−1.96629
$101$	8.79384	0.875020	0.437510	−	0.899213i	$-0.355860\pi$
$101$	8.79384	0.875020	0.437510	+	0.899213i	$0.355860\pi$
$102$	−6.63752	−0.657212
$103$	19.7440	1.94544	0.972718	−	0.231992i	$-0.0745242\pi$
$103$	19.7440	1.94544	0.972718	+	0.231992i	$0.0745242\pi$
$104$	29.1246	2.85590
$105$	4.64974	0.453768
$106$	34.1622	3.31813
$107$	−3.93700	−0.380604	−0.190302	−	0.981726i	$-0.560947\pi$
$107$	−3.93700	−0.380604	−0.190302	+	0.981726i	$0.560947\pi$
$108$	−12.8568	−1.23715
$109$	−16.8242	−1.61146	−0.805731	−	0.592281i	$-0.798227\pi$
$109$	−16.8242	−1.61146	−0.805731	+	0.592281i	$0.798227\pi$
$110$	−1.28726	−0.122735
$111$	22.5066	2.13623
$112$	16.6253	1.57094
$113$	13.4060	1.26113	0.630564	−	0.776137i	$-0.282824\pi$
$113$	13.4060	1.26113	0.630564	+	0.776137i	$0.282824\pi$
$114$	27.1695	2.54466
$115$	3.46310	0.322935
$116$	−11.2750	−1.04686
$117$	−22.6253	−2.09171
$118$	27.4944	2.53106
$119$	−3.35026	−0.307118
$120$	−7.42548	−0.677851
$121$	1.00000	0.0909091
$122$	13.2750	1.20187
$123$	−8.96239	−0.808111
$124$	−21.1695	−1.90108
$125$	5.04842	0.451544
$126$	−34.5501	−3.07797
$127$	5.22425	0.463578	0.231789	−	0.972766i	$-0.425542\pi$
$127$	5.22425	0.463578	0.231789	+	0.972766i	$0.425542\pi$
$128$	17.9248	1.58434
$129$	−8.62530	−0.759415
$130$	−7.00729	−0.614580
$131$	−17.3258	−1.51376	−0.756882	−	0.653551i	$-0.773278\pi$
$131$	−17.3258	−1.51376	−0.756882	+	0.653551i	$0.773278\pi$
$132$	11.1187	0.967760
$133$	13.7137	1.18913
$134$	3.13093	0.270471
$135$	1.60483	0.138122
$136$	5.35026	0.458781
$137$	−5.26187	−0.449551	−0.224776	−	0.974411i	$-0.572165\pi$
$137$	−5.26187	−0.449551	−0.224776	+	0.974411i	$0.572165\pi$
$138$	−44.3063	−3.77160
$139$	10.2496	0.869364	0.434682	−	0.900584i	$-0.356861\pi$
$139$	10.2496	0.869364	0.434682	+	0.900584i	$0.356861\pi$
$140$	−7.22425	−0.610561
$141$	−22.8568	−1.92489
$142$	15.9878	1.34166
$143$	5.44358	0.455215
$144$	20.6253	1.71878
$145$	1.40739	0.116877
$146$	14.0811	1.16536
$147$	−11.3004	−0.932044
$148$	−34.9683	−2.87437
$149$	0.793845	0.0650343	0.0325171	−	0.999471i	$-0.489648\pi$
$149$	0.793845	0.0650343	0.0325171	+	0.999471i	$0.489648\pi$
$150$	−31.4010	−2.56388
$151$	12.0933	0.984141	0.492070	−	0.870555i	$-0.336240\pi$
$151$	12.0933	0.984141	0.492070	+	0.870555i	$0.336240\pi$
$152$	−21.9003	−1.77635
$153$	−4.15633	−0.336019
$154$	8.31265	0.669852
$155$	2.64244	0.212246
$156$	60.5256	4.84593
$157$	−9.05079	−0.722331	−0.361166	−	0.932502i	$-0.617621\pi$
$157$	−9.05079	−0.722331	−0.361166	+	0.932502i	$0.617621\pi$
$158$	1.58181	0.125842
$159$	36.8324	2.92100
$160$	0.836381	0.0661217
$161$	−22.3634	−1.76249
$162$	10.4060	0.817570
$163$	−10.2374	−0.801857	−0.400929	−	0.916109i	$-0.631312\pi$
$163$	−10.2374	−0.801857	−0.400929	+	0.916109i	$0.631312\pi$
$164$	13.9248	1.08734
$165$	−1.38787	−0.108046
$166$	−24.6253	−1.91129
$167$	−2.51151	−0.194347	−0.0971733	−	0.995267i	$-0.530980\pi$
$167$	−2.51151	−0.194347	−0.0971733	+	0.995267i	$0.530980\pi$
$168$	47.9511	3.69951
$169$	16.6326	1.27943
$170$	−1.28726	−0.0987282
$171$	17.0132	1.30103
$172$	13.4010	1.02182
$173$	8.43866	0.641579	0.320790	−	0.947150i	$-0.396052\pi$
$173$	8.43866	0.641579	0.320790	+	0.947150i	$0.396052\pi$
$174$	−18.0059	−1.36502
$175$	−15.8496	−1.19811
$176$	−4.96239	−0.374054
$177$	29.6434	2.22813
$178$	−26.4568	−1.98302
$179$	3.91160	0.292367	0.146183	−	0.989257i	$-0.453301\pi$
$179$	3.91160	0.292367	0.146183	+	0.989257i	$0.453301\pi$
$180$	−8.96239	−0.668017
$181$	0.675131	0.0501821	0.0250910	−	0.999685i	$-0.492012\pi$
$181$	0.675131	0.0501821	0.0250910	+	0.999685i	$0.492012\pi$
$182$	45.2506	3.35420
$183$	14.3127	1.05802
$184$	35.7137	2.63285
$185$	4.36485	0.320910
$186$	−33.8070	−2.47885
$187$	1.00000	0.0731272
$188$	35.5125	2.59001
$189$	−10.3634	−0.753829
$190$	5.26916	0.382265
$191$	4.22425	0.305656	0.152828	−	0.988253i	$-0.451162\pi$
$191$	4.22425	0.305656	0.152828	+	0.988253i	$0.451162\pi$
$192$	15.8496	1.14384
$193$	1.75035	0.125993	0.0629966	−	0.998014i	$-0.479934\pi$
$193$	1.75035	0.125993	0.0629966	+	0.998014i	$0.479934\pi$
$194$	0.899385	0.0645721
$195$	−7.55500	−0.541025
$196$	17.5574	1.25410
$197$	−3.04983	−0.217291	−0.108646	−	0.994081i	$-0.534651\pi$
$197$	−3.04983	−0.217291	−0.108646	+	0.994081i	$0.534651\pi$
$198$	10.3127	0.732888
$199$	−21.9003	−1.55247	−0.776237	−	0.630441i	$-0.782874\pi$
$199$	−21.9003	−1.55247	−0.776237	+	0.630441i	$0.782874\pi$
$200$	25.3112	1.78977
$201$	3.37565	0.238100
$202$	−21.8192	−1.53520
$203$	−9.08840	−0.637880
$204$	11.1187	0.778466
$205$	−1.73813	−0.121397
$206$	−48.9887	−3.41321
$207$	−27.7440	−1.92834
$208$	−27.0132	−1.87303
$209$	−4.09332	−0.283141
$210$	−11.5369	−0.796122
$211$	−21.8496	−1.50419	−0.752093	−	0.659057i	$-0.770955\pi$
$211$	−21.8496	−1.50419	−0.752093	+	0.659057i	$0.770955\pi$
$212$	−57.2262	−3.93031
$213$	17.2374	1.18109
$214$	9.76845	0.667758
$215$	−1.67276	−0.114081
$216$	16.5501	1.12609
$217$	−17.0640	−1.15838
$218$	41.7440	2.82726
$219$	15.1817	1.02589
$220$	2.15633	0.145379
$221$	5.44358	0.366175
$222$	−55.8432	−3.74795
$223$	−9.88129	−0.661700	−0.330850	−	0.943683i	$-0.607335\pi$
$223$	−9.88129	−0.661700	−0.330850	+	0.943683i	$0.607335\pi$
$224$	−5.40105	−0.360873
$225$	−19.6629	−1.31086
$226$	−33.2628	−2.21261
$227$	10.8749	0.721796	0.360898	−	0.932605i	$-0.382470\pi$
$227$	10.8749	0.721796	0.360898	+	0.932605i	$0.382470\pi$
$228$	−45.5125	−3.01414
$229$	18.6180	1.23031	0.615156	−	0.788405i	$-0.289093\pi$
$229$	18.6180	1.23031	0.615156	+	0.788405i	$0.289093\pi$
$230$	−8.59261	−0.566580
$231$	8.96239	0.589682
$232$	14.5139	0.952883
$233$	19.2750	1.26275	0.631375	−	0.775478i	$-0.282491\pi$
$233$	19.2750	1.26275	0.631375	+	0.775478i	$0.282491\pi$
$234$	56.1378	3.66984
$235$	−4.43278	−0.289163
$236$	−46.0567	−2.99803
$237$	1.70545	0.110781
$238$	8.31265	0.538829
$239$	−9.56959	−0.619005	−0.309503	−	0.950899i	$-0.600163\pi$
$239$	−9.56959	−0.619005	−0.309503	+	0.950899i	$0.600163\pi$
$240$	6.88717	0.444565
$241$	−17.4617	−1.12481	−0.562403	−	0.826863i	$-0.690123\pi$
$241$	−17.4617	−1.12481	−0.562403	+	0.826863i	$0.690123\pi$
$242$	−2.48119	−0.159497
$243$	20.4993	1.31503
$244$	−22.2374	−1.42361
$245$	−2.19157	−0.140014
$246$	22.2374	1.41781
$247$	−22.2823	−1.41779
$248$	27.2506	1.73041
$249$	−26.5501	−1.68254
$250$	−12.5261	−0.792220
$251$	7.72496	0.487595	0.243798	−	0.969826i	$-0.421607\pi$
$251$	7.72496	0.487595	0.243798	+	0.969826i	$0.421607\pi$
$252$	57.8759	3.64584
$253$	6.67513	0.419662
$254$	−12.9624	−0.813333
$255$	−1.38787	−0.0869120
$256$	−32.6253	−2.03908
$257$	−14.2677	−0.889997	−0.444999	−	0.895531i	$-0.646796\pi$
$257$	−14.2677	−0.889997	−0.444999	+	0.895531i	$0.646796\pi$
$258$	21.4010	1.33237
$259$	−28.1866	−1.75143
$260$	11.7381	0.727968
$261$	−11.2750	−0.697907
$262$	42.9887	2.65585
$263$	−15.9575	−0.983979	−0.491990	−	0.870601i	$-0.663730\pi$
$263$	−15.9575	−0.983979	−0.491990	+	0.870601i	$0.663730\pi$
$264$	−14.3127	−0.880883
$265$	7.14315	0.438800
$266$	−34.0263	−2.08629
$267$	−28.5247	−1.74568
$268$	−5.24472	−0.320372
$269$	21.3503	1.30175	0.650874	−	0.759186i	$-0.274403\pi$
$269$	21.3503	1.30175	0.650874	+	0.759186i	$0.274403\pi$
$270$	−3.98190	−0.242331
$271$	−5.16362	−0.313668	−0.156834	−	0.987625i	$-0.550129\pi$
$271$	−5.16362	−0.313668	−0.156834	+	0.987625i	$0.550129\pi$
$272$	−4.96239	−0.300889
$273$	48.7875	2.95275
$274$	13.0557	0.788724
$275$	4.73084	0.285280
$276$	74.2189	4.46745
$277$	28.2130	1.69515	0.847577	−	0.530672i	$-0.178060\pi$
$277$	28.2130	1.69515	0.847577	+	0.530672i	$0.178060\pi$
$278$	−25.4314	−1.52527
$279$	−21.1695	−1.26738
$280$	9.29948	0.555750
$281$	−2.21933	−0.132394	−0.0661970	−	0.997807i	$-0.521087\pi$
$281$	−2.21933	−0.132394	−0.0661970	+	0.997807i	$0.521087\pi$
$282$	56.7123	3.37717
$283$	−0.661957	−0.0393493	−0.0196746	−	0.999806i	$-0.506263\pi$
$283$	−0.661957	−0.0393493	−0.0196746	+	0.999806i	$0.506263\pi$
$284$	−26.7816	−1.58920
$285$	5.68101	0.336514
$286$	−13.5066	−0.798661
$287$	11.2243	0.662547
$288$	−6.70052	−0.394832
$289$	1.00000	0.0588235
$290$	−3.49200	−0.205057
$291$	0.969683	0.0568438
$292$	−23.5877	−1.38037
$293$	−16.3127	−0.952995	−0.476498	−	0.879176i	$-0.658094\pi$
$293$	−16.3127	−0.952995	−0.476498	+	0.879176i	$0.658094\pi$
$294$	28.0386	1.63524
$295$	5.74894	0.334716
$296$	45.0132	2.61634
$297$	3.09332	0.179493
$298$	−1.96968	−0.114101
$299$	36.3366	2.10140
$300$	52.6009	3.03691
$301$	10.8021	0.622622
$302$	−30.0059	−1.72664
$303$	−23.5247	−1.35146
$304$	20.3127	1.16501
$305$	2.77575	0.158939
$306$	10.3127	0.589535
$307$	20.2193	1.15398	0.576989	−	0.816752i	$-0.304228\pi$
$307$	20.2193	1.15398	0.576989	+	0.816752i	$0.304228\pi$
$308$	−13.9248	−0.793438
$309$	−52.8178	−3.00470
$310$	−6.55642	−0.372379
$311$	−3.16362	−0.179392	−0.0896962	−	0.995969i	$-0.528590\pi$
$311$	−3.16362	−0.179392	−0.0896962	+	0.995969i	$0.528590\pi$
$312$	−77.9121	−4.41090
$313$	−10.9575	−0.619352	−0.309676	−	0.950842i	$-0.600221\pi$
$313$	−10.9575	−0.619352	−0.309676	+	0.950842i	$0.600221\pi$
$314$	22.4568	1.26731
$315$	−7.22425	−0.407041
$316$	−2.64974	−0.149059
$317$	−19.8691	−1.11596	−0.557979	−	0.829855i	$-0.688423\pi$
$317$	−19.8691	−1.11596	−0.557979	+	0.829855i	$0.688423\pi$
$318$	−91.3884	−5.12481
$319$	2.71274	0.151884
$320$	3.07381	0.171831
$321$	10.5320	0.587838
$322$	55.4880	3.09223
$323$	−4.09332	−0.227758
$324$	−17.4314	−0.968409
$325$	25.7527	1.42850
$326$	25.4010	1.40683
$327$	45.0068	2.48888
$328$	−17.9248	−0.989730
$329$	28.6253	1.57816
$330$	3.44358	0.189563
$331$	15.2882	0.840316	0.420158	−	0.907451i	$-0.361975\pi$
$331$	15.2882	0.840316	0.420158	+	0.907451i	$0.361975\pi$
$332$	41.2506	2.26392
$333$	−34.9683	−1.91625
$334$	6.23155	0.340975
$335$	0.654663	0.0357681
$336$	−44.4749	−2.42630
$337$	9.08840	0.495077	0.247538	−	0.968878i	$-0.420378\pi$
$337$	9.08840	0.495077	0.247538	+	0.968878i	$0.420378\pi$
$338$	−41.2687	−2.24472
$339$	−35.8627	−1.94780
$340$	2.15633	0.116943
$341$	5.09332	0.275819
$342$	−42.2130	−2.28262
$343$	−9.29948	−0.502125
$344$	−17.2506	−0.930090
$345$	−9.26423	−0.498770
$346$	−20.9380	−1.12563
$347$	6.06063	0.325352	0.162676	−	0.986680i	$-0.447987\pi$
$347$	6.06063	0.325352	0.162676	+	0.986680i	$0.447987\pi$
$348$	30.1622	1.61686
$349$	−6.20123	−0.331944	−0.165972	−	0.986130i	$-0.553076\pi$
$349$	−6.20123	−0.331944	−0.165972	+	0.986130i	$0.553076\pi$
$350$	39.3258	2.10205
$351$	16.8388	0.898786
$352$	1.61213	0.0859267
$353$	7.60483	0.404764	0.202382	−	0.979307i	$-0.435132\pi$
$353$	7.60483	0.404764	0.202382	+	0.979307i	$0.435132\pi$
$354$	−73.5510	−3.90919
$355$	3.34297	0.177426
$356$	44.3185	2.34888
$357$	8.96239	0.474340
$358$	−9.70545	−0.512949
$359$	11.6956	0.617270	0.308635	−	0.951181i	$-0.400128\pi$
$359$	11.6956	0.617270	0.308635	+	0.951181i	$0.400128\pi$
$360$	11.5369	0.608048
$361$	−2.24472	−0.118143
$362$	−1.67513	−0.0880429
$363$	−2.67513	−0.140408
$364$	−75.8007	−3.97304
$365$	2.94429	0.154111
$366$	−35.5125	−1.85627
$367$	19.8446	1.03588	0.517941	−	0.855417i	$-0.326699\pi$
$367$	19.8446	1.03588	0.517941	+	0.855417i	$0.326699\pi$
$368$	−33.1246	−1.72674
$369$	13.9248	0.724895
$370$	−10.8300	−0.563027
$371$	−46.1279	−2.39484
$372$	56.6312	2.93619
$373$	29.6810	1.53682	0.768412	−	0.639955i	$-0.221047\pi$
$373$	29.6810	1.53682	0.768412	+	0.639955i	$0.221047\pi$
$374$	−2.48119	−0.128300
$375$	−13.5052	−0.697404
$376$	−45.7137	−2.35750
$377$	14.7670	0.760541
$378$	25.7137	1.32257
$379$	16.3077	0.837672	0.418836	−	0.908062i	$-0.362438\pi$
$379$	16.3077	0.837672	0.418836	+	0.908062i	$0.362438\pi$
$380$	−8.82653	−0.452792
$381$	−13.9756	−0.715990
$382$	−10.4812	−0.536265
$383$	−16.7235	−0.854533	−0.427267	−	0.904126i	$-0.640523\pi$
$383$	−16.7235	−0.854533	−0.427267	+	0.904126i	$0.640523\pi$
$384$	−47.9511	−2.44700
$385$	1.73813	0.0885836
$386$	−4.34297	−0.221051
$387$	13.4010	0.681214
$388$	−1.50659	−0.0764854
$389$	10.6932	0.542168	0.271084	−	0.962556i	$-0.412618\pi$
$389$	10.6932	0.542168	0.271084	+	0.962556i	$0.412618\pi$
$390$	18.7454	0.949212
$391$	6.67513	0.337576
$392$	−22.6009	−1.14152
$393$	46.3488	2.33799
$394$	7.56722	0.381231
$395$	0.330749	0.0166418
$396$	−17.2750	−0.868103
$397$	2.86670	0.143875	0.0719377	−	0.997409i	$-0.477082\pi$
$397$	2.86670	0.143875	0.0719377	+	0.997409i	$0.477082\pi$
$398$	54.3390	2.72377
$399$	−36.6859	−1.83659
$400$	−23.4763	−1.17381
$401$	−29.3561	−1.46598	−0.732988	−	0.680242i	$-0.761875\pi$
$401$	−29.3561	−1.46598	−0.732988	+	0.680242i	$0.761875\pi$
$402$	−8.37565	−0.417740
$403$	27.7259	1.38113
$404$	36.5501	1.81843
$405$	2.17584	0.108118
$406$	22.5501	1.11914
$407$	8.41327	0.417030
$408$	−14.3127	−0.708582
$409$	16.5926	0.820452	0.410226	−	0.911984i	$-0.365450\pi$
$409$	16.5926	0.820452	0.410226	+	0.911984i	$0.365450\pi$
$410$	4.31265	0.212987
$411$	14.0762	0.694327
$412$	82.0625	4.04293
$413$	−37.1246	−1.82678
$414$	68.8383	3.38322
$415$	−5.14903	−0.252756
$416$	8.77575	0.430266
$417$	−27.4191	−1.34272
$418$	10.1563	0.496762
$419$	13.1128	0.640604	0.320302	−	0.947316i	$-0.396216\pi$
$419$	13.1128	0.640604	0.320302	+	0.947316i	$0.396216\pi$
$420$	19.3258	0.943004
$421$	27.5428	1.34235	0.671177	−	0.741298i	$-0.265789\pi$
$421$	27.5428	1.34235	0.671177	+	0.741298i	$0.265789\pi$
$422$	54.2130	2.63905
$423$	35.5125	1.72668
$424$	73.6648	3.57748
$425$	4.73084	0.229479
$426$	−42.7694	−2.07218
$427$	−17.9248	−0.867441
$428$	−16.3634	−0.790957
$429$	−14.5623	−0.703074
$430$	4.15045	0.200152
$431$	2.68830	0.129491	0.0647455	−	0.997902i	$-0.479376\pi$
$431$	2.68830	0.129491	0.0647455	+	0.997902i	$0.479376\pi$
$432$	−15.3503	−0.738540
$433$	−15.1417	−0.727665	−0.363833	−	0.931464i	$-0.618532\pi$
$433$	−15.1417	−0.727665	−0.363833	+	0.931464i	$0.618532\pi$
$434$	42.3390	2.03234
$435$	−3.76494	−0.180515
$436$	−69.9267	−3.34888
$437$	−27.3235	−1.30706
$438$	−37.6688	−1.79988
$439$	−26.4626	−1.26299	−0.631496	−	0.775379i	$-0.717559\pi$
$439$	−26.4626	−1.26299	−0.631496	+	0.775379i	$0.717559\pi$
$440$	−2.77575	−0.132329
$441$	17.5574	0.836065
$442$	−13.5066	−0.642443
$443$	24.0336	1.14187	0.570936	−	0.820994i	$-0.306580\pi$
$443$	24.0336	1.14187	0.570936	+	0.820994i	$0.306580\pi$
$444$	93.5447	4.43943
$445$	−5.53198	−0.262241
$446$	24.5174	1.16093
$447$	−2.12364	−0.100445
$448$	−19.8496	−0.937803
$449$	−27.8242	−1.31310	−0.656552	−	0.754281i	$-0.727986\pi$
$449$	−27.8242	−1.31310	−0.656552	+	0.754281i	$0.727986\pi$
$450$	48.7875	2.29987
$451$	−3.35026	−0.157758
$452$	55.7196	2.62083
$453$	−32.3512	−1.51999
$454$	−26.9829	−1.26637
$455$	9.46168	0.443570
$456$	58.5863	2.74355
$457$	−27.8070	−1.30076	−0.650379	−	0.759610i	$-0.725390\pi$
$457$	−27.8070	−1.30076	−0.650379	+	0.759610i	$0.725390\pi$
$458$	−46.1949	−2.15855
$459$	3.09332	0.144384
$460$	14.3938	0.671112
$461$	3.37470	0.157175	0.0785877	−	0.996907i	$-0.474959\pi$
$461$	3.37470	0.157175	0.0785877	+	0.996907i	$0.474959\pi$
$462$	−22.2374	−1.03458
$463$	−12.1695	−0.565565	−0.282782	−	0.959184i	$-0.591257\pi$
$463$	−12.1695	−0.565565	−0.282782	+	0.959184i	$0.591257\pi$
$464$	−13.4617	−0.624943
$465$	−7.06888	−0.327812
$466$	−47.8251	−2.21546
$467$	18.6082	0.861083	0.430541	−	0.902571i	$-0.358323\pi$
$467$	18.6082	0.861083	0.430541	+	0.902571i	$0.358323\pi$
$468$	−94.0381	−4.34691
$469$	−4.22758	−0.195211
$470$	10.9986	0.507327
$471$	24.2120	1.11563
$472$	59.2868	2.72890
$473$	−3.22425	−0.148251
$474$	−4.23155	−0.194361
$475$	−19.3649	−0.888520
$476$	−13.9248	−0.638241
$477$	−57.2262	−2.62021
$478$	23.7440	1.08603
$479$	16.6859	0.762400	0.381200	−	0.924493i	$-0.375511\pi$
$479$	16.6859	0.762400	0.381200	+	0.924493i	$0.375511\pi$
$480$	−2.23743	−0.102124
$481$	45.7983	2.08822
$482$	43.3258	1.97344
$483$	59.8251	2.72214
$484$	4.15633	0.188924
$485$	0.188057	0.00853923
$486$	−50.8627	−2.30718
$487$	2.44946	0.110996	0.0554979	−	0.998459i	$-0.482325\pi$
$487$	2.44946	0.110996	0.0554979	+	0.998459i	$0.482325\pi$
$488$	28.6253	1.29581
$489$	27.3865	1.23846
$490$	5.43770	0.245650
$491$	−34.0543	−1.53685	−0.768424	−	0.639941i	$-0.778959\pi$
$491$	−34.0543	−1.53685	−0.768424	+	0.639941i	$0.778959\pi$
$492$	−37.2506	−1.67939
$493$	2.71274	0.122176
$494$	55.2868	2.48747
$495$	2.15633	0.0969196
$496$	−25.2750	−1.13488
$497$	−21.5877	−0.968340
$498$	65.8759	2.95197
$499$	23.1695	1.03721	0.518605	−	0.855014i	$-0.326452\pi$
$499$	23.1695	1.03721	0.518605	+	0.855014i	$0.326452\pi$
$500$	20.9829	0.938382
$501$	6.71862	0.300166
$502$	−19.1671	−0.855471
$503$	−18.7997	−0.838238	−0.419119	−	0.907931i	$-0.637661\pi$
$503$	−18.7997	−0.838238	−0.419119	+	0.907931i	$0.637661\pi$
$504$	−74.5012	−3.31855
$505$	−4.56230	−0.203020
$506$	−16.5623	−0.736284
$507$	−44.4944	−1.97606
$508$	21.7137	0.963390
$509$	−35.7974	−1.58669	−0.793345	−	0.608772i	$-0.791662\pi$
$509$	−35.7974	−1.58669	−0.793345	+	0.608772i	$0.791662\pi$
$510$	3.44358	0.152484
$511$	−19.0132	−0.841093
$512$	45.1002	1.99316
$513$	−12.6620	−0.559039
$514$	35.4010	1.56147
$515$	−10.2433	−0.451374
$516$	−35.8496	−1.57819
$517$	−8.54420	−0.375773
$518$	69.9365	3.07283
$519$	−22.5745	−0.990911
$520$	−15.1100	−0.662618
$521$	0.569591	0.0249542	0.0124771	−	0.999922i	$-0.496028\pi$
$521$	0.569591	0.0249542	0.0124771	+	0.999922i	$0.496028\pi$
$522$	27.9756	1.22446
$523$	15.1998	0.664642	0.332321	−	0.943166i	$-0.392168\pi$
$523$	15.1998	0.664642	0.332321	+	0.943166i	$0.392168\pi$
$524$	−72.0118	−3.14585
$525$	42.3996	1.85047
$526$	39.5936	1.72636
$527$	5.09332	0.221869
$528$	13.2750	0.577722
$529$	21.5574	0.937277
$530$	−17.7235	−0.769862
$531$	−46.0567	−1.99869
$532$	56.9986	2.47120
$533$	−18.2374	−0.789951
$534$	70.7753	3.06275
$535$	2.04254	0.0883065
$536$	6.75131	0.291612
$537$	−10.4641	−0.451557
$538$	−52.9741	−2.28388
$539$	−4.22425	−0.181951
$540$	6.67021	0.287040
$541$	−9.91256	−0.426174	−0.213087	−	0.977033i	$-0.568352\pi$
$541$	−9.91256	−0.426174	−0.213087	+	0.977033i	$0.568352\pi$
$542$	12.8119	0.550320
$543$	−1.80606	−0.0775056
$544$	1.61213	0.0691194
$545$	8.72847	0.373887
$546$	−121.051	−5.18052
$547$	34.4264	1.47197	0.735984	−	0.676999i	$-0.236720\pi$
$547$	34.4264	1.47197	0.735984	+	0.676999i	$0.236720\pi$
$548$	−21.8700	−0.934241
$549$	−22.2374	−0.949070
$550$	−11.7381	−0.500516
$551$	−11.1041	−0.473052
$552$	−95.5388	−4.06640
$553$	−2.13586	−0.0908259
$554$	−70.0019	−2.97410
$555$	−11.6765	−0.495642
$556$	42.6009	1.80668
$557$	−42.7005	−1.80928	−0.904640	−	0.426177i	$-0.859860\pi$
$557$	−42.7005	−1.80928	−0.904640	+	0.426177i	$0.859860\pi$
$558$	52.5256	2.22359
$559$	−17.5515	−0.742349
$560$	−8.62530	−0.364485
$561$	−2.67513	−0.112944
$562$	5.50659	0.232281
$563$	−29.9184	−1.26091	−0.630456	−	0.776225i	$-0.717132\pi$
$563$	−29.9184	−1.26091	−0.630456	+	0.776225i	$0.717132\pi$
$564$	−95.0005	−4.00024
$565$	−6.95509	−0.292603
$566$	1.64244	0.0690371
$567$	−14.0508	−0.590078
$568$	34.4749	1.44653
$569$	−18.7005	−0.783967	−0.391983	−	0.919972i	$-0.628211\pi$
$569$	−18.7005	−0.783967	−0.391983	+	0.919972i	$0.628211\pi$
$570$	−14.0957	−0.590404
$571$	12.8895	0.539410	0.269705	−	0.962943i	$-0.413074\pi$
$571$	12.8895	0.539410	0.269705	+	0.962943i	$0.413074\pi$
$572$	22.6253	0.946011
$573$	−11.3004	−0.472082
$574$	−27.8496	−1.16242
$575$	31.5790	1.31693
$576$	−24.6253	−1.02605
$577$	−26.9511	−1.12199	−0.560995	−	0.827819i	$-0.689581\pi$
$577$	−26.9511	−1.12199	−0.560995	+	0.827819i	$0.689581\pi$
$578$	−2.48119	−0.103204
$579$	−4.68243	−0.194595
$580$	5.84955	0.242890
$581$	33.2506	1.37947
$582$	−2.40597	−0.0997307
$583$	13.7685	0.570231
$584$	30.3634	1.25645
$585$	11.7381	0.485312
$586$	40.4749	1.67200
$587$	−17.9452	−0.740680	−0.370340	−	0.928896i	$-0.620759\pi$
$587$	−17.9452	−0.740680	−0.370340	+	0.928896i	$0.620759\pi$
$588$	−46.9683	−1.93694
$589$	−20.8486	−0.859052
$590$	−14.2642	−0.587249
$591$	8.15869	0.335604
$592$	−41.7499	−1.71591
$593$	−16.3698	−0.672226	−0.336113	−	0.941822i	$-0.609112\pi$
$593$	−16.3698	−0.672226	−0.336113	+	0.941822i	$0.609112\pi$
$594$	−7.67513	−0.314914
$595$	1.73813	0.0712566
$596$	3.29948	0.135152
$597$	58.5863	2.39778
$598$	−90.1582	−3.68684
$599$	12.3331	0.503918	0.251959	−	0.967738i	$-0.418925\pi$
$599$	12.3331	0.503918	0.251959	+	0.967738i	$0.418925\pi$
$600$	−67.7109	−2.76428
$601$	29.1392	1.18861	0.594306	−	0.804239i	$-0.297427\pi$
$601$	29.1392	1.18861	0.594306	+	0.804239i	$0.297427\pi$
$602$	−26.8021	−1.09237
$603$	−5.24472	−0.213582
$604$	50.2638	2.04520
$605$	−0.518806	−0.0210925
$606$	58.3693	2.37109
$607$	−8.17679	−0.331886	−0.165943	−	0.986135i	$-0.553067\pi$
$607$	−8.17679	−0.331886	−0.165943	+	0.986135i	$0.553067\pi$
$608$	−6.59895	−0.267623
$609$	24.3127	0.985198
$610$	−6.88717	−0.278853
$611$	−46.5111	−1.88164
$612$	−17.2750	−0.698302
$613$	27.1900	1.09819	0.549096	−	0.835759i	$-0.314972\pi$
$613$	27.1900	1.09819	0.549096	+	0.835759i	$0.314972\pi$
$614$	−50.1681	−2.02462
$615$	4.64974	0.187496
$616$	17.9248	0.722210
$617$	−4.76116	−0.191677	−0.0958385	−	0.995397i	$-0.530553\pi$
$617$	−4.76116	−0.191677	−0.0958385	+	0.995397i	$0.530553\pi$
$618$	131.051	5.27166
$619$	−15.8545	−0.637245	−0.318623	−	0.947882i	$-0.603220\pi$
$619$	−15.8545	−0.637245	−0.318623	+	0.947882i	$0.603220\pi$
$620$	10.9829	0.441082
$621$	20.6483	0.828589
$622$	7.84955	0.314738
$623$	35.7235	1.43123
$624$	72.2638	2.89287
$625$	21.0351	0.841402
$626$	27.1876	1.08663
$627$	10.9502	0.437308
$628$	−37.6180	−1.50112
$629$	8.41327	0.335459
$630$	17.9248	0.714140
$631$	6.28489	0.250197	0.125099	−	0.992144i	$-0.460075\pi$
$631$	6.28489	0.250197	0.125099	+	0.992144i	$0.460075\pi$
$632$	3.41090	0.135678
$633$	58.4504	2.32320
$634$	49.2990	1.95791
$635$	−2.71037	−0.107558
$636$	153.087	6.07031
$637$	−22.9951	−0.911098
$638$	−6.73084	−0.266477
$639$	−26.7816	−1.05946
$640$	−9.29948	−0.367594
$641$	19.1236	0.755338	0.377669	−	0.925941i	$-0.376726\pi$
$641$	19.1236	0.755338	0.377669	+	0.925941i	$0.376726\pi$
$642$	−26.1319	−1.03134
$643$	−0.987781	−0.0389543	−0.0194771	−	0.999810i	$-0.506200\pi$
$643$	−0.987781	−0.0389543	−0.0194771	+	0.999810i	$0.506200\pi$
$644$	−92.9497	−3.66273
$645$	4.47486	0.176197
$646$	10.1563	0.399595
$647$	−13.8714	−0.545342	−0.272671	−	0.962107i	$-0.587907\pi$
$647$	−13.8714	−0.545342	−0.272671	+	0.962107i	$0.587907\pi$
$648$	22.4387	0.881474
$649$	11.0811	0.434971
$650$	−63.8975	−2.50627
$651$	45.6483	1.78910
$652$	−42.5501	−1.66639
$653$	−47.5828	−1.86206	−0.931029	−	0.364946i	$-0.881087\pi$
$653$	−47.5828	−1.86206	−0.931029	+	0.364946i	$0.881087\pi$
$654$	−111.671	−4.36667
$655$	8.98874	0.351219
$656$	16.6253	0.649109
$657$	−23.5877	−0.920243
$658$	−71.0249	−2.76884
$659$	35.3585	1.37737	0.688686	−	0.725060i	$-0.258188\pi$
$659$	35.3585	1.37737	0.688686	+	0.725060i	$0.258188\pi$
$660$	−5.76845	−0.224537
$661$	38.8192	1.50989	0.754947	−	0.655786i	$-0.227663\pi$
$661$	38.8192	1.50989	0.754947	+	0.655786i	$0.227663\pi$
$662$	−37.9330	−1.47431
$663$	−14.5623	−0.565553
$664$	−53.1002	−2.06069
$665$	−7.11474	−0.275898
$666$	86.7631	3.36200
$667$	18.1079	0.701141
$668$	−10.4387	−0.403884
$669$	26.4337	1.02199
$670$	−1.62435	−0.0627539
$671$	5.35026	0.206545
$672$	14.4485	0.557363
$673$	19.9271	0.768135	0.384068	−	0.923305i	$-0.374523\pi$
$673$	19.9271	0.768135	0.384068	+	0.923305i	$0.374523\pi$
$674$	−22.5501	−0.868597
$675$	14.6340	0.563263
$676$	69.1305	2.65886
$677$	4.21345	0.161936	0.0809680	−	0.996717i	$-0.474199\pi$
$677$	4.21345	0.161936	0.0809680	+	0.996717i	$0.474199\pi$
$678$	88.9824	3.41735
$679$	−1.21440	−0.0466046
$680$	−2.77575	−0.106445
$681$	−29.0919	−1.11480
$682$	−12.6375	−0.483916
$683$	−35.9149	−1.37425	−0.687123	−	0.726541i	$-0.741127\pi$
$683$	−35.9149	−1.37425	−0.687123	+	0.726541i	$0.741127\pi$
$684$	70.7123	2.70375
$685$	2.72989	0.104304
$686$	23.0738	0.880962
$687$	−49.8056	−1.90020
$688$	16.0000	0.609994
$689$	74.9497	2.85536
$690$	22.9864	0.875076
$691$	40.3947	1.53669	0.768344	−	0.640038i	$-0.221081\pi$
$691$	40.3947	1.53669	0.768344	+	0.640038i	$0.221081\pi$
$692$	35.0738	1.33331
$693$	−13.9248	−0.528959
$694$	−15.0376	−0.570820
$695$	−5.31757	−0.201707
$696$	−38.8265	−1.47172
$697$	−3.35026	−0.126900
$698$	15.3865	0.582386
$699$	−51.5633	−1.95030
$700$	−65.8759	−2.48988
$701$	2.07522	0.0783801	0.0391900	−	0.999232i	$-0.487522\pi$
$701$	2.07522	0.0783801	0.0391900	+	0.999232i	$0.487522\pi$
$702$	−41.7802	−1.57689
$703$	−34.4382	−1.29886
$704$	5.92478	0.223298
$705$	11.8583	0.446608
$706$	−18.8691	−0.710147
$707$	29.4617	1.10802
$708$	123.208	4.63043
$709$	−9.12364	−0.342645	−0.171323	−	0.985215i	$-0.554804\pi$
$709$	−9.12364	−0.342645	−0.171323	+	0.985215i	$0.554804\pi$
$710$	−8.29455	−0.311289
$711$	−2.64974	−0.0993729
$712$	−57.0494	−2.13802
$713$	33.9986	1.27326
$714$	−22.2374	−0.832215
$715$	−2.82416	−0.105618
$716$	16.2579	0.607586
$717$	25.5999	0.956046
$718$	−29.0191	−1.08298
$719$	−40.2628	−1.50155	−0.750775	−	0.660558i	$-0.770320\pi$
$719$	−40.2628	−1.50155	−0.750775	+	0.660558i	$0.770320\pi$
$720$	−10.7005	−0.398785
$721$	66.1476	2.46347
$722$	5.56959	0.207279
$723$	46.7123	1.73725
$724$	2.80606	0.104287
$725$	12.8336	0.476626
$726$	6.63752	0.246341
$727$	−48.9511	−1.81550	−0.907748	−	0.419515i	$-0.862200\pi$
$727$	−48.9511	−1.81550	−0.907748	+	0.419515i	$0.862200\pi$
$728$	97.5750	3.61637
$729$	−42.2565	−1.56505
$730$	−7.30536	−0.270383
$731$	−3.22425	−0.119253
$732$	59.4880	2.19874
$733$	−39.3766	−1.45441	−0.727204	−	0.686421i	$-0.759181\pi$
$733$	−39.3766	−1.45441	−0.727204	+	0.686421i	$0.759181\pi$
$734$	−49.2384	−1.81742
$735$	5.86273	0.216250
$736$	10.7612	0.396662
$737$	1.26187	0.0464814
$738$	−34.5501	−1.27181
$739$	3.89209	0.143173	0.0715864	−	0.997434i	$-0.477194\pi$
$739$	3.89209	0.143173	0.0715864	+	0.997434i	$0.477194\pi$
$740$	18.1417	0.666904
$741$	59.6082	2.18976
$742$	114.452	4.20168
$743$	−19.3014	−0.708099	−0.354050	−	0.935227i	$-0.615196\pi$
$743$	−19.3014	−0.708099	−0.354050	+	0.935227i	$0.615196\pi$
$744$	−72.8989	−2.67260
$745$	−0.411851	−0.0150891
$746$	−73.6444	−2.69631
$747$	41.2506	1.50928
$748$	4.15633	0.151970
$749$	−13.1900	−0.481951
$750$	33.5090	1.22357
$751$	−9.87892	−0.360487	−0.180243	−	0.983622i	$-0.557689\pi$
$751$	−9.87892	−0.360487	−0.180243	+	0.983622i	$0.557689\pi$
$752$	42.3996	1.54616
$753$	−20.6653	−0.753085
$754$	−36.6399	−1.33435
$755$	−6.27408	−0.228337
$756$	−43.0738	−1.56658
$757$	−20.5745	−0.747793	−0.373897	−	0.927470i	$-0.621979\pi$
$757$	−20.5745	−0.747793	−0.373897	+	0.927470i	$0.621979\pi$
$758$	−40.4626	−1.46967
$759$	−17.8568	−0.648163
$760$	11.3620	0.412144
$761$	−16.0689	−0.582497	−0.291248	−	0.956647i	$-0.594071\pi$
$761$	−16.0689	−0.582497	−0.291248	+	0.956647i	$0.594071\pi$
$762$	34.6761	1.25618
$763$	−56.3653	−2.04056
$764$	17.5574	0.635203
$765$	2.15633	0.0779621
$766$	41.4944	1.49925
$767$	60.3209	2.17806
$768$	87.2769	3.14934
$769$	−19.3404	−0.697433	−0.348717	−	0.937228i	$-0.613382\pi$
$769$	−19.3404	−0.697433	−0.348717	+	0.937228i	$0.613382\pi$
$770$	−4.31265	−0.155417
$771$	38.1681	1.37459
$772$	7.27504	0.261834
$773$	23.0435	0.828817	0.414408	−	0.910091i	$-0.363989\pi$
$773$	23.0435	0.828817	0.414408	+	0.910091i	$0.363989\pi$
$774$	−33.2506	−1.19517
$775$	24.0957	0.865543
$776$	1.93937	0.0696192
$777$	75.4030	2.70507
$778$	−26.5320	−0.951218
$779$	13.7137	0.491344
$780$	−31.4010	−1.12434
$781$	6.44358	0.230570
$782$	−16.5623	−0.592267
$783$	8.39138	0.299884
$784$	20.9624	0.748657
$785$	4.69560	0.167593
$786$	−115.000	−4.10193
$787$	−1.92241	−0.0685264	−0.0342632	−	0.999413i	$-0.510908\pi$
$787$	−1.92241	−0.0685264	−0.0342632	+	0.999413i	$0.510908\pi$
$788$	−12.6761	−0.451567
$789$	42.6883	1.51974
$790$	−0.820652	−0.0291975
$791$	44.9135	1.59694
$792$	22.2374	0.790173
$793$	29.1246	1.03424
$794$	−7.11283	−0.252425
$795$	−19.1089	−0.677722
$796$	−91.0249	−3.22629
$797$	−13.1721	−0.466578	−0.233289	−	0.972407i	$-0.574949\pi$
$797$	−13.1721	−0.466578	−0.233289	+	0.972407i	$0.574949\pi$
$798$	91.0249	3.22225
$799$	−8.54420	−0.302272
$800$	7.62672	0.269645
$801$	44.3185	1.56592
$802$	72.8383	2.57201
$803$	5.67513	0.200271
$804$	14.0303	0.494811
$805$	11.6023	0.408927
$806$	−68.7934	−2.42314
$807$	−57.1147	−2.01053
$808$	−47.0494	−1.65519
$809$	21.3136	0.749346	0.374673	−	0.927157i	$-0.377755\pi$
$809$	21.3136	0.749346	0.374673	+	0.927157i	$0.377755\pi$
$810$	−5.39868	−0.189690
$811$	36.6131	1.28566	0.642830	−	0.766009i	$-0.277760\pi$
$811$	36.6131	1.28566	0.642830	+	0.766009i	$0.277760\pi$
$812$	−37.7743	−1.32562
$813$	13.8134	0.484456
$814$	−20.8749	−0.731667
$815$	5.31124	0.186044
$816$	13.2750	0.464719
$817$	13.1979	0.461736
$818$	−41.1695	−1.43946
$819$	−75.8007	−2.64869
$820$	−7.22425	−0.252282
$821$	−35.4250	−1.23634	−0.618171	−	0.786044i	$-0.712126\pi$
$821$	−35.4250	−1.23634	−0.618171	+	0.786044i	$0.712126\pi$
$822$	−34.9257	−1.21817
$823$	−18.3731	−0.640446	−0.320223	−	0.947342i	$-0.603758\pi$
$823$	−18.3731	−0.640446	−0.320223	+	0.947342i	$0.603758\pi$
$824$	−105.636	−3.67999
$825$	−12.6556	−0.440612
$826$	92.1133	3.20503
$827$	−19.6361	−0.682814	−0.341407	−	0.939916i	$-0.610903\pi$
$827$	−19.6361	−0.682814	−0.341407	+	0.939916i	$0.610903\pi$
$828$	−115.313	−4.00741
$829$	−4.36011	−0.151433	−0.0757165	−	0.997129i	$-0.524124\pi$
$829$	−4.36011	−0.151433	−0.0757165	+	0.997129i	$0.524124\pi$
$830$	12.7757	0.443453
$831$	−75.4734	−2.61814
$832$	32.2520	1.11814
$833$	−4.22425	−0.146362
$834$	68.0322	2.35576
$835$	1.30299	0.0450917
$836$	−17.0132	−0.588413
$837$	15.7553	0.544582
$838$	−32.5355	−1.12392
$839$	9.11379	0.314643	0.157321	−	0.987547i	$-0.449714\pi$
$839$	9.11379	0.314643	0.157321	+	0.987547i	$0.449714\pi$
$840$	−24.8773	−0.858349
$841$	−21.6410	−0.746242
$842$	−68.3390	−2.35512
$843$	5.93700	0.204481
$844$	−90.8139	−3.12594
$845$	−8.62908	−0.296850
$846$	−88.1133	−3.02940
$847$	3.35026	0.115116
$848$	−68.3244	−2.34627
$849$	1.77082	0.0607744
$850$	−11.7381	−0.402615
$851$	56.1596	1.92513
$852$	71.6444	2.45450
$853$	3.34789	0.114630	0.0573148	−	0.998356i	$-0.481746\pi$
$853$	3.34789	0.114630	0.0573148	+	0.998356i	$0.481746\pi$
$854$	44.4749	1.52190
$855$	−8.82653	−0.301861
$856$	21.0640	0.719951
$857$	21.7259	0.742143	0.371072	−	0.928604i	$-0.378990\pi$
$857$	21.7259	0.742143	0.371072	+	0.928604i	$0.378990\pi$
$858$	36.1319	1.23352
$859$	−43.2677	−1.47628	−0.738138	−	0.674650i	$-0.764295\pi$
$859$	−43.2677	−1.47628	−0.738138	+	0.674650i	$0.764295\pi$
$860$	−6.95254	−0.237080
$861$	−30.0263	−1.02330
$862$	−6.67021	−0.227188
$863$	−27.0581	−0.921068	−0.460534	−	0.887642i	$-0.652342\pi$
$863$	−27.0581	−0.921068	−0.460534	+	0.887642i	$0.652342\pi$
$864$	4.98683	0.169655
$865$	−4.37802	−0.148857
$866$	37.5696	1.27667
$867$	−2.67513	−0.0908522
$868$	−70.9234	−2.40730
$869$	0.637519	0.0216264
$870$	9.34155	0.316708
$871$	6.86907	0.232749
$872$	90.0137	3.04825
$873$	−1.50659	−0.0509902
$874$	67.7948	2.29319
$875$	16.9135	0.571781
$876$	63.1002	2.13196
$877$	−58.4725	−1.97448	−0.987238	−	0.159253i	$-0.949091\pi$
$877$	−58.4725	−1.97448	−0.987238	+	0.159253i	$0.949091\pi$
$878$	65.6589	2.21588
$879$	43.6385	1.47189
$880$	2.57452	0.0867869
$881$	−0.392798	−0.0132337	−0.00661685	−	0.999978i	$-0.502106\pi$
$881$	−0.392798	−0.0132337	−0.00661685	+	0.999978i	$0.502106\pi$
$882$	−43.5633	−1.46685
$883$	1.29948	0.0437309	0.0218654	−	0.999761i	$-0.493039\pi$
$883$	1.29948	0.0437309	0.0218654	+	0.999761i	$0.493039\pi$
$884$	22.6253	0.760971
$885$	−15.3792	−0.516965
$886$	−59.6321	−2.00338
$887$	24.9135	0.836514	0.418257	−	0.908329i	$-0.362641\pi$
$887$	24.9135	0.836514	0.418257	+	0.908329i	$0.362641\pi$
$888$	−120.416	−4.04090
$889$	17.5026	0.587019
$890$	13.7259	0.460094
$891$	4.19394	0.140502
$892$	−41.0698	−1.37512
$893$	34.9741	1.17037
$894$	5.26916	0.176227
$895$	−2.02936	−0.0678341
$896$	60.0527	2.00622
$897$	−97.2052	−3.24559
$898$	69.0372	2.30380
$899$	13.8169	0.460818
$900$	−81.7255	−2.72418
$901$	13.7685	0.458694
$902$	8.31265	0.276781
$903$	−28.8970	−0.961632
$904$	−71.7255	−2.38555
$905$	−0.350262	−0.0116431
$906$	80.2697	2.66678
$907$	−38.9525	−1.29340	−0.646699	−	0.762745i	$-0.723851\pi$
$907$	−38.9525	−1.29340	−0.646699	+	0.762745i	$0.723851\pi$
$908$	45.1998	1.50001
$909$	36.5501	1.21229
$910$	−23.4763	−0.778231
$911$	16.1075	0.533664	0.266832	−	0.963743i	$-0.414023\pi$
$911$	16.1075	0.533664	0.266832	+	0.963743i	$0.414023\pi$
$912$	−54.3390	−1.79934
$913$	−9.92478	−0.328462
$914$	68.9946	2.28214
$915$	−7.42548	−0.245479
$916$	77.3825	2.55679
$917$	−58.0460	−1.91685
$918$	−7.67513	−0.253317
$919$	36.7631	1.21270	0.606351	−	0.795197i	$-0.292633\pi$
$919$	36.7631	1.21270	0.606351	+	0.795197i	$0.292633\pi$
$920$	−18.5285	−0.610866
$921$	−54.0894	−1.78230
$922$	−8.37328	−0.275759
$923$	35.0762	1.15455
$924$	37.2506	1.22545
$925$	39.8018	1.30868
$926$	30.1949	0.992266
$927$	82.0625	2.69529
$928$	4.37328	0.143560
$929$	−10.0409	−0.329432	−0.164716	−	0.986341i	$-0.552671\pi$
$929$	−10.0409	−0.329432	−0.164716	+	0.986341i	$0.552671\pi$
$930$	17.5393	0.575135
$931$	17.2912	0.566697
$932$	80.1133	2.62420
$933$	8.46310	0.277069
$934$	−46.1705	−1.51074
$935$	−0.518806	−0.0169668
$936$	121.051	3.95668
$937$	55.1690	1.80229	0.901147	−	0.433514i	$-0.142726\pi$
$937$	55.1690	1.80229	0.901147	+	0.433514i	$0.142726\pi$
$938$	10.4894	0.342492
$939$	29.3127	0.956582
$940$	−18.4241	−0.600927
$941$	1.09825	0.0358018	0.0179009	−	0.999840i	$-0.494302\pi$
$941$	1.09825	0.0358018	0.0179009	+	0.999840i	$0.494302\pi$
$942$	−60.0748	−1.95734
$943$	−22.3634	−0.728254
$944$	−54.9887	−1.78973
$945$	5.37661	0.174901
$946$	8.00000	0.260102
$947$	54.4817	1.77042	0.885209	−	0.465194i	$-0.154016\pi$
$947$	54.4817	1.77042	0.885209	+	0.465194i	$0.154016\pi$
$948$	7.08840	0.230220
$949$	30.8930	1.00283
$950$	48.0480	1.55888
$951$	53.1524	1.72358
$952$	17.9248	0.580945
$953$	7.55149	0.244617	0.122308	−	0.992492i	$-0.460970\pi$
$953$	7.55149	0.244617	0.122308	+	0.992492i	$0.460970\pi$
$954$	141.989	4.59707
$955$	−2.19157	−0.0709174
$956$	−39.7743	−1.28639
$957$	−7.25694	−0.234584
$958$	−41.4010	−1.33761
$959$	−17.6286	−0.569258
$960$	−8.22284	−0.265391
$961$	−5.05808	−0.163164
$962$	−113.635	−3.66372
$963$	−16.3634	−0.527304
$964$	−72.5764	−2.33753
$965$	−0.908093	−0.0292326
$966$	−148.438	−4.77591
$967$	37.6956	1.21221	0.606104	−	0.795385i	$-0.292731\pi$
$967$	37.6956	1.21221	0.606104	+	0.795385i	$0.292731\pi$
$968$	−5.35026	−0.171964
$969$	10.9502	0.351770
$970$	−0.466606	−0.0149818
$971$	14.6424	0.469898	0.234949	−	0.972008i	$-0.424508\pi$
$971$	14.6424	0.469898	0.234949	+	0.972008i	$0.424508\pi$
$972$	85.2017	2.73285
$973$	34.3390	1.10086
$974$	−6.07759	−0.194739
$975$	−68.8919	−2.20631
$976$	−26.5501	−0.849847
$977$	−11.0449	−0.353358	−0.176679	−	0.984269i	$-0.556535\pi$
$977$	−11.0449	−0.353358	−0.176679	+	0.984269i	$0.556535\pi$
$978$	−67.9511	−2.17284
$979$	−10.6629	−0.340788
$980$	−9.10886	−0.290972
$981$	−69.9267	−2.23259
$982$	84.4953	2.69635
$983$	−12.4436	−0.396889	−0.198444	−	0.980112i	$-0.563589\pi$
$983$	−12.4436	−0.396889	−0.198444	+	0.980112i	$0.563589\pi$
$984$	47.9511	1.52863
$985$	1.58227	0.0504153
$986$	−6.73084	−0.214354
$987$	−76.5764	−2.43745
$988$	−92.6126	−2.94640
$989$	−21.5223	−0.684370
$990$	−5.35026	−0.170042
$991$	0.499293	0.0158606	0.00793028	−	0.999969i	$-0.497476\pi$
$991$	0.499293	0.0158606	0.00793028	+	0.999969i	$0.497476\pi$
$992$	8.21108	0.260702
$993$	−40.8980	−1.29786
$994$	53.5633	1.69892
$995$	11.3620	0.360200
$996$	−110.351	−3.49660
$997$	−3.65069	−0.115619	−0.0578093	−	0.998328i	$-0.518412\pi$
$997$	−3.65069	−0.115619	−0.0578093	+	0.998328i	$0.518412\pi$
$998$	−57.4880	−1.81975
$999$	26.0249	0.823392

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	187.2.a.e.1.1	✓	3
3.2	odd	2		1683.2.a.v.1.3		3
4.3	odd	2		2992.2.a.r.1.3		3
5.4	even	2		4675.2.a.bc.1.3		3
7.6	odd	2		9163.2.a.j.1.1		3
11.10	odd	2		2057.2.a.p.1.3		3
17.16	even	2		3179.2.a.t.1.1		3

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
187.2.a.e.1.1	✓	3	1.1	even	1	trivial
1683.2.a.v.1.3		3	3.2	odd	2
2057.2.a.p.1.3		3	11.10	odd	2
2992.2.a.r.1.3		3	4.3	odd	2
3179.2.a.t.1.1		3	17.16	even	2
4675.2.a.bc.1.3		3	5.4	even	2
9163.2.a.j.1.1		3	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:	\( N \)	\(=\)	\( 187 = 11 \cdot 17 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	187.a (trivial)

\(f(q)\)	\(=\)	\(q-2.48119 q^{2} -2.67513 q^{3} +4.15633 q^{4} -0.518806 q^{5} +6.63752 q^{6} +3.35026 q^{7} -5.35026 q^{8} +4.15633 q^{9} +O(q^{10})\)	\(q-2.48119 q^{2} -2.67513 q^{3} +4.15633 q^{4} -0.518806 q^{5} +6.63752 q^{6} +3.35026 q^{7} -5.35026 q^{8} +4.15633 q^{9} +1.28726 q^{10} -1.00000 q^{11} -11.1187 q^{12} -5.44358 q^{13} -8.31265 q^{14} +1.38787 q^{15} +4.96239 q^{16} -1.00000 q^{17} -10.3127 q^{18} +4.09332 q^{19} -2.15633 q^{20} -8.96239 q^{21} +2.48119 q^{22} -6.67513 q^{23} +14.3127 q^{24} -4.73084 q^{25} +13.5066 q^{26} -3.09332 q^{27} +13.9248 q^{28} -2.71274 q^{29} -3.44358 q^{30} -5.09332 q^{31} -1.61213 q^{32} +2.67513 q^{33} +2.48119 q^{34} -1.73813 q^{35} +17.2750 q^{36} -8.41327 q^{37} -10.1563 q^{38} +14.5623 q^{39} +2.77575 q^{40} +3.35026 q^{41} +22.2374 q^{42} +3.22425 q^{43} -4.15633 q^{44} -2.15633 q^{45} +16.5623 q^{46} +8.54420 q^{47} -13.2750 q^{48} +4.22425 q^{49} +11.7381 q^{50} +2.67513 q^{51} -22.6253 q^{52} -13.7685 q^{53} +7.67513 q^{54} +0.518806 q^{55} -17.9248 q^{56} -10.9502 q^{57} +6.73084 q^{58} -11.0811 q^{59} +5.76845 q^{60} -5.35026 q^{61} +12.6375 q^{62} +13.9248 q^{63} -5.92478 q^{64} +2.82416 q^{65} -6.63752 q^{66} -1.26187 q^{67} -4.15633 q^{68} +17.8568 q^{69} +4.31265 q^{70} -6.44358 q^{71} -22.2374 q^{72} -5.67513 q^{73} +20.8749 q^{74} +12.6556 q^{75} +17.0132 q^{76} -3.35026 q^{77} -36.1319 q^{78} -0.637519 q^{79} -2.57452 q^{80} -4.19394 q^{81} -8.31265 q^{82} +9.92478 q^{83} -37.2506 q^{84} +0.518806 q^{85} -8.00000 q^{86} +7.25694 q^{87} +5.35026 q^{88} +10.6629 q^{89} +5.35026 q^{90} -18.2374 q^{91} -27.7440 q^{92} +13.6253 q^{93} -21.1998 q^{94} -2.12364 q^{95} +4.31265 q^{96} -0.362481 q^{97} -10.4812 q^{98} -4.15633 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 3 q - 2 q^{2} - 3 q^{3} + 2 q^{4} - 7 q^{5} + 4 q^{6} - 6 q^{8} + 2 q^{9}+O(q^{10}) \) 3 * q - 2 * q^2 - 3 * q^3 + 2 * q^4 - 7 * q^5 + 4 * q^6 - 6 * q^8 + 2 * q^9	\( 3 q - 2 q^{2} - 3 q^{3} + 2 q^{4} - 7 q^{5} + 4 q^{6} - 6 q^{8} + 2 q^{9} - 2 q^{10} - 3 q^{11} - 12 q^{12} - 4 q^{14} + 5 q^{15} + 4 q^{16} - 3 q^{17} - 10 q^{18} + 6 q^{19} + 4 q^{20} - 16 q^{21} + 2 q^{22} - 15 q^{23} + 22 q^{24} + 8 q^{25} + 20 q^{26} - 3 q^{27} + 20 q^{28} - 14 q^{29} + 6 q^{30} - 9 q^{31} - 4 q^{32} + 3 q^{33} + 2 q^{34} + 4 q^{35} + 20 q^{36} - 11 q^{37} - 20 q^{38} + 6 q^{39} + 10 q^{40} + 24 q^{42} + 8 q^{43} - 2 q^{44} + 4 q^{45} + 12 q^{46} + 16 q^{47} - 8 q^{48} + 11 q^{49} + 26 q^{50} + 3 q^{51} - 26 q^{52} - 30 q^{53} + 18 q^{54} + 7 q^{55} - 32 q^{56} + 4 q^{57} - 2 q^{58} - q^{59} + 6 q^{60} - 6 q^{61} + 22 q^{62} + 20 q^{63} + 4 q^{64} - 20 q^{65} - 4 q^{66} - 13 q^{67} - 2 q^{68} + 23 q^{69} - 8 q^{70} - 3 q^{71} - 24 q^{72} - 12 q^{73} + 4 q^{74} - 6 q^{75} + 10 q^{76} - 46 q^{78} + 14 q^{79} + 4 q^{80} - 13 q^{81} - 4 q^{82} + 8 q^{83} - 28 q^{84} + 7 q^{85} - 24 q^{86} + 18 q^{87} + 6 q^{88} + q^{89} + 6 q^{90} - 12 q^{91} - 20 q^{92} - q^{93} - 10 q^{94} + 2 q^{95} - 8 q^{96} - 17 q^{97} - 26 q^{98} - 2 q^{99}+O(q^{100}) \) 3 * q - 2 * q^2 - 3 * q^3 + 2 * q^4 - 7 * q^5 + 4 * q^6 - 6 * q^8 + 2 * q^9 - 2 * q^10 - 3 * q^11 - 12 * q^12 - 4 * q^14 + 5 * q^15 + 4 * q^16 - 3 * q^17 - 10 * q^18 + 6 * q^19 + 4 * q^20 - 16 * q^21 + 2 * q^22 - 15 * q^23 + 22 * q^24 + 8 * q^25 + 20 * q^26 - 3 * q^27 + 20 * q^28 - 14 * q^29 + 6 * q^30 - 9 * q^31 - 4 * q^32 + 3 * q^33 + 2 * q^34 + 4 * q^35 + 20 * q^36 - 11 * q^37 - 20 * q^38 + 6 * q^39 + 10 * q^40 + 24 * q^42 + 8 * q^43 - 2 * q^44 + 4 * q^45 + 12 * q^46 + 16 * q^47 - 8 * q^48 + 11 * q^49 + 26 * q^50 + 3 * q^51 - 26 * q^52 - 30 * q^53 + 18 * q^54 + 7 * q^55 - 32 * q^56 + 4 * q^57 - 2 * q^58 - q^59 + 6 * q^60 - 6 * q^61 + 22 * q^62 + 20 * q^63 + 4 * q^64 - 20 * q^65 - 4 * q^66 - 13 * q^67 - 2 * q^68 + 23 * q^69 - 8 * q^70 - 3 * q^71 - 24 * q^72 - 12 * q^73 + 4 * q^74 - 6 * q^75 + 10 * q^76 - 46 * q^78 + 14 * q^79 + 4 * q^80 - 13 * q^81 - 4 * q^82 + 8 * q^83 - 28 * q^84 + 7 * q^85 - 24 * q^86 + 18 * q^87 + 6 * q^88 + q^89 + 6 * q^90 - 12 * q^91 - 20 * q^92 - q^93 - 10 * q^94 + 2 * q^95 - 8 * q^96 - 17 * q^97 - 26 * q^98 - 2 * q^99

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