LMFDB - Embedded newform 187.2.a.e.1.3

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			1.3
Root			$2.17009$ 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)

$f(q)$	$=$	$q+1.17009 q^{2} -1.53919 q^{3} -0.630898 q^{4} -4.17009 q^{5} -1.80098 q^{6} +1.07838 q^{7} -3.07838 q^{8} -0.630898 q^{9} +O(q^{10})$	\(q+1.17009 q^{2} -1.53919 q^{3} -0.630898 q^{4} -4.17009 q^{5} -1.80098 q^{6} +1.07838 q^{7} -3.07838 q^{8} -0.630898 q^{9} -4.87936 q^{10} -1.00000 q^{11} +0.971071 q^{12} +5.51026 q^{13} +1.26180 q^{14} +6.41855 q^{15} -2.34017 q^{16} -1.00000 q^{17} -0.738205 q^{18} -4.58864 q^{19} +2.63090 q^{20} -1.65983 q^{21} -1.17009 q^{22} -5.53919 q^{23} +4.73820 q^{24} +12.3896 q^{25} +6.44748 q^{26} +5.58864 q^{27} -0.680346 q^{28} -8.87936 q^{29} +7.51026 q^{30} +3.58864 q^{31} +3.41855 q^{32} +1.53919 q^{33} -1.17009 q^{34} -4.49693 q^{35} +0.398032 q^{36} -10.0361 q^{37} -5.36910 q^{38} -8.48133 q^{39} +12.8371 q^{40} +1.07838 q^{41} -1.94214 q^{42} -6.83710 q^{43} +0.630898 q^{44} +2.63090 q^{45} -6.48133 q^{46} +8.78765 q^{47} +3.60197 q^{48} -5.83710 q^{49} +14.4969 q^{50} +1.53919 q^{51} -3.47641 q^{52} -3.95055 q^{53} +6.53919 q^{54} +4.17009 q^{55} -3.31965 q^{56} +7.06278 q^{57} -10.3896 q^{58} +8.31124 q^{59} -4.04945 q^{60} -3.07838 q^{61} +4.19902 q^{62} -0.680346 q^{63} +8.68035 q^{64} -22.9783 q^{65} +1.80098 q^{66} +1.49693 q^{67} +0.630898 q^{68} +8.52586 q^{69} -5.26180 q^{70} +4.51026 q^{71} +1.94214 q^{72} -4.53919 q^{73} -11.7431 q^{74} -19.0700 q^{75} +2.89496 q^{76} -1.07838 q^{77} -9.92389 q^{78} +7.80098 q^{79} +9.75872 q^{80} -6.70928 q^{81} +1.26180 q^{82} -4.68035 q^{83} +1.04718 q^{84} +4.17009 q^{85} -8.00000 q^{86} +13.6670 q^{87} +3.07838 q^{88} -1.18342 q^{89} +3.07838 q^{90} +5.94214 q^{91} +3.49466 q^{92} -5.52359 q^{93} +10.2823 q^{94} +19.1350 q^{95} -5.26180 q^{96} -8.80098 q^{97} -6.82991 q^{98} +0.630898 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	1.17009	0.827376	0.413688	−	0.910419i	$-0.364240\pi$
$2$	1.17009	0.827376	0.413688	+	0.910419i	$0.364240\pi$
$3$	−1.53919	−0.888651	−0.444326	−	0.895865i	$-0.646557\pi$
$3$	−1.53919	−0.888651	−0.444326	+	0.895865i	$0.646557\pi$
$4$	−0.630898	−0.315449
$5$	−4.17009	−1.86492	−0.932460	−	0.361274i	$-0.882342\pi$
$5$	−4.17009	−1.86492	−0.932460	+	0.361274i	$0.882342\pi$
$6$	−1.80098	−0.735249
$7$	1.07838	0.407588	0.203794	−	0.979014i	$-0.434673\pi$
$7$	1.07838	0.407588	0.203794	+	0.979014i	$0.434673\pi$
$8$	−3.07838	−1.08837
$9$	−0.630898	−0.210299
$10$	−4.87936	−1.54299
$11$	−1.00000	−0.301511
$11$	−1.00000	−0.301511
$12$	0.971071	0.280324
$13$	5.51026	1.52827	0.764136	−	0.645056i	$-0.223166\pi$
$13$	5.51026	1.52827	0.764136	+	0.645056i	$0.223166\pi$
$14$	1.26180	0.337229
$15$	6.41855	1.65726
$16$	−2.34017	−0.585043
$17$	−1.00000	−0.242536
$17$	−1.00000	−0.242536
$18$	−0.738205	−0.173997
$19$	−4.58864	−1.05271	−0.526353	−	0.850266i	$-0.676441\pi$
$19$	−4.58864	−1.05271	−0.526353	+	0.850266i	$0.676441\pi$
$20$	2.63090	0.588287
$21$	−1.65983	−0.362204
$22$	−1.17009	−0.249463
$23$	−5.53919	−1.15500	−0.577500	−	0.816390i	$-0.695972\pi$
$23$	−5.53919	−1.15500	−0.577500	+	0.816390i	$0.695972\pi$
$24$	4.73820	0.967182
$25$	12.3896	2.47792
$26$	6.44748	1.26445
$27$	5.58864	1.07553
$28$	−0.680346	−0.128573
$29$	−8.87936	−1.64886	−0.824428	−	0.565967i	$-0.808503\pi$
$29$	−8.87936	−1.64886	−0.824428	+	0.565967i	$0.808503\pi$
$30$	7.51026	1.37118
$31$	3.58864	0.644538	0.322269	−	0.946648i	$-0.395554\pi$
$31$	3.58864	0.644538	0.322269	+	0.946648i	$0.395554\pi$
$32$	3.41855	0.604320
$33$	1.53919	0.267938
$34$	−1.17009	−0.200668
$35$	−4.49693	−0.760120
$36$	0.398032	0.0663386
$37$	−10.0361	−1.64993	−0.824964	−	0.565186i	$-0.808805\pi$
$37$	−10.0361	−1.64993	−0.824964	+	0.565186i	$0.808805\pi$
$38$	−5.36910	−0.870983
$39$	−8.48133	−1.35810
$40$	12.8371	2.02972
$41$	1.07838	0.168414	0.0842072	−	0.996448i	$-0.473164\pi$
$41$	1.07838	0.168414	0.0842072	+	0.996448i	$0.473164\pi$
$42$	−1.94214	−0.299679
$43$	−6.83710	−1.04265	−0.521324	−	0.853359i	$-0.674562\pi$
$43$	−6.83710	−1.04265	−0.521324	+	0.853359i	$0.674562\pi$
$44$	0.630898	0.0951114
$45$	2.63090	0.392191
$46$	−6.48133	−0.955620
$47$	8.78765	1.28181	0.640905	−	0.767620i	$-0.278559\pi$
$47$	8.78765	1.28181	0.640905	+	0.767620i	$0.278559\pi$
$48$	3.60197	0.519899
$49$	−5.83710	−0.833872
$50$	14.4969	2.05018
$51$	1.53919	0.215530
$52$	−3.47641	−0.482091
$53$	−3.95055	−0.542650	−0.271325	−	0.962488i	$-0.587462\pi$
$53$	−3.95055	−0.542650	−0.271325	+	0.962488i	$0.587462\pi$
$54$	6.53919	0.889871
$55$	4.17009	0.562294
$56$	−3.31965	−0.443607
$57$	7.06278	0.935488
$58$	−10.3896	−1.36422
$59$	8.31124	1.08203	0.541016	−	0.841012i	$-0.318040\pi$
$59$	8.31124	1.08203	0.541016	+	0.841012i	$0.318040\pi$
$60$	−4.04945	−0.522782
$61$	−3.07838	−0.394146	−0.197073	−	0.980389i	$-0.563144\pi$
$61$	−3.07838	−0.394146	−0.197073	+	0.980389i	$0.563144\pi$
$62$	4.19902	0.533276
$63$	−0.680346	−0.0857155
$64$	8.68035	1.08504
$65$	−22.9783	−2.85010
$66$	1.80098	0.221686
$67$	1.49693	0.182879	0.0914395	−	0.995811i	$-0.470853\pi$
$67$	1.49693	0.182879	0.0914395	+	0.995811i	$0.470853\pi$
$68$	0.630898	0.0765076
$69$	8.52586	1.02639
$70$	−5.26180	−0.628905
$71$	4.51026	0.535269	0.267635	−	0.963520i	$-0.413758\pi$
$71$	4.51026	0.535269	0.267635	+	0.963520i	$0.413758\pi$
$72$	1.94214	0.228884
$73$	−4.53919	−0.531272	−0.265636	−	0.964073i	$-0.585582\pi$
$73$	−4.53919	−0.531272	−0.265636	+	0.964073i	$0.585582\pi$
$74$	−11.7431	−1.36511
$75$	−19.0700	−2.20201
$76$	2.89496	0.332075
$77$	−1.07838	−0.122893
$78$	−9.92389	−1.12366
$79$	7.80098	0.877679	0.438840	−	0.898565i	$-0.355390\pi$
$79$	7.80098	0.877679	0.438840	+	0.898565i	$0.355390\pi$
$80$	9.75872	1.09106
$81$	−6.70928	−0.745475
$82$	1.26180	0.139342
$83$	−4.68035	−0.513735	−0.256867	−	0.966447i	$-0.582690\pi$
$83$	−4.68035	−0.513735	−0.256867	+	0.966447i	$0.582690\pi$
$84$	1.04718	0.114257
$85$	4.17009	0.452309
$86$	−8.00000	−0.862662
$87$	13.6670	1.46526
$88$	3.07838	0.328156
$89$	−1.18342	−0.125442	−0.0627210	−	0.998031i	$-0.519978\pi$
$89$	−1.18342	−0.125442	−0.0627210	+	0.998031i	$0.519978\pi$
$90$	3.07838	0.324490
$91$	5.94214	0.622906
$92$	3.49466	0.364344
$93$	−5.52359	−0.572770
$94$	10.2823	1.06054
$95$	19.1350	1.96321
$96$	−5.26180	−0.537030
$97$	−8.80098	−0.893605	−0.446802	−	0.894633i	$-0.647437\pi$
$97$	−8.80098	−0.893605	−0.446802	+	0.894633i	$0.647437\pi$
$98$	−6.82991	−0.689925
$99$	0.630898	0.0634076
$100$	−7.81658	−0.781658
$101$	−4.43188	−0.440989	−0.220494	−	0.975388i	$-0.570767\pi$
$101$	−4.43188	−0.440989	−0.220494	+	0.975388i	$0.570767\pi$
$102$	1.80098	0.178324
$103$	−11.4947	−1.13260	−0.566301	−	0.824198i	$-0.691626\pi$
$103$	−11.4947	−1.13260	−0.566301	+	0.824198i	$0.691626\pi$
$104$	−16.9627	−1.66333
$105$	6.92162	0.675481
$106$	−4.62249	−0.448976
$107$	−0.0422604	−0.00408547	−0.00204273	−	0.999998i	$-0.500650\pi$
$107$	−0.0422604	−0.00408547	−0.00204273	+	0.999998i	$0.500650\pi$
$108$	−3.52586	−0.339276
$109$	8.97826	0.859961	0.429981	−	0.902838i	$-0.358520\pi$
$109$	8.97826	0.859961	0.429981	+	0.902838i	$0.358520\pi$
$110$	4.87936	0.465229
$111$	15.4475	1.46621
$112$	−2.52359	−0.238457
$113$	−4.85043	−0.456290	−0.228145	−	0.973627i	$-0.573266\pi$
$113$	−4.85043	−0.456290	−0.228145	+	0.973627i	$0.573266\pi$
$114$	8.26406	0.774000
$115$	23.0989	2.15398
$116$	5.60197	0.520130
$117$	−3.47641	−0.321394
$118$	9.72487	0.895247
$119$	−1.07838	−0.0988547
$120$	−19.7587	−1.80372
$121$	1.00000	0.0909091
$122$	−3.60197	−0.326107
$123$	−1.65983	−0.149662
$124$	−2.26406	−0.203319
$125$	−30.8154	−2.75621
$126$	−0.796064	−0.0709190
$127$	−4.83710	−0.429223	−0.214612	−	0.976699i	$-0.568849\pi$
$127$	−4.83710	−0.429223	−0.214612	+	0.976699i	$0.568849\pi$
$128$	3.31965	0.293419
$129$	10.5236	0.926550
$130$	−26.8865	−2.35811
$131$	6.36683	0.556273	0.278136	−	0.960542i	$-0.410283\pi$
$131$	6.36683	0.556273	0.278136	+	0.960542i	$0.410283\pi$
$132$	−0.971071	−0.0845208
$133$	−4.94828	−0.429071
$134$	1.75154	0.151310
$135$	−23.3051	−2.00578
$136$	3.07838	0.263969
$137$	−2.50307	−0.213852	−0.106926	−	0.994267i	$-0.534101\pi$
$137$	−2.50307	−0.213852	−0.106926	+	0.994267i	$0.534101\pi$
$138$	9.97599	0.849213
$139$	−3.21953	−0.273077	−0.136539	−	0.990635i	$-0.543598\pi$
$139$	−3.21953	−0.273077	−0.136539	+	0.990635i	$0.543598\pi$
$140$	2.83710	0.239779
$141$	−13.5259	−1.13908
$142$	5.27739	0.442869
$143$	−5.51026	−0.460791
$144$	1.47641	0.123034
$145$	37.0277	3.07498
$146$	−5.31124	−0.439562
$147$	8.98440	0.741021
$148$	6.33176	0.520468
$149$	−12.4319	−1.01846	−0.509230	−	0.860631i	$-0.670070\pi$
$149$	−12.4319	−1.01846	−0.509230	+	0.860631i	$0.670070\pi$
$150$	−22.3135	−1.82189
$151$	3.41136	0.277613	0.138806	−	0.990320i	$-0.455673\pi$
$151$	3.41136	0.277613	0.138806	+	0.990320i	$0.455673\pi$
$152$	14.1256	1.14573
$153$	0.630898	0.0510050
$154$	−1.26180	−0.101678
$155$	−14.9649	−1.20201
$156$	5.35085	0.428411
$157$	−2.23513	−0.178383	−0.0891915	−	0.996014i	$-0.528428\pi$
$157$	−2.23513	−0.178383	−0.0891915	+	0.996014i	$0.528428\pi$
$158$	9.12783	0.726171
$159$	6.08065	0.482227
$160$	−14.2557	−1.12701
$161$	−5.97334	−0.470765
$162$	−7.85043	−0.616788
$163$	13.9421	1.09203	0.546016	−	0.837774i	$-0.316144\pi$
$163$	13.9421	1.09203	0.546016	+	0.837774i	$0.316144\pi$
$164$	−0.680346	−0.0531261
$165$	−6.41855	−0.499683
$166$	−5.47641	−0.425052
$167$	13.7165	1.06141	0.530706	−	0.847556i	$-0.321927\pi$
$167$	13.7165	1.06141	0.530706	+	0.847556i	$0.321927\pi$
$168$	5.10957	0.394212
$169$	17.3630	1.33561
$170$	4.87936	0.374230
$171$	2.89496	0.221383
$172$	4.31351	0.328902
$173$	6.65368	0.505870	0.252935	−	0.967483i	$-0.418604\pi$
$173$	6.65368	0.505870	0.252935	+	0.967483i	$0.418604\pi$
$174$	15.9916	1.21232
$175$	13.3607	1.00997
$176$	2.34017	0.176397
$177$	−12.7926	−0.961549
$178$	−1.38470	−0.103788
$179$	3.42469	0.255974	0.127987	−	0.991776i	$-0.459148\pi$
$179$	3.42469	0.255974	0.127987	+	0.991776i	$0.459148\pi$
$180$	−1.65983	−0.123716
$181$	−0.460811	−0.0342518	−0.0171259	−	0.999853i	$-0.505452\pi$
$181$	−0.460811	−0.0342518	−0.0171259	+	0.999853i	$0.505452\pi$
$182$	6.95282	0.515377
$183$	4.73820	0.350258
$184$	17.0517	1.25707
$185$	41.8515	3.07698
$186$	−6.46308	−0.473896
$187$	1.00000	0.0731272
$188$	−5.54411	−0.404346
$189$	6.02666	0.438375
$190$	22.3896	1.62431
$191$	−5.83710	−0.422358	−0.211179	−	0.977447i	$-0.567730\pi$
$191$	−5.83710	−0.422358	−0.211179	+	0.977447i	$0.567730\pi$
$192$	−13.3607	−0.964225
$193$	15.2195	1.09553	0.547763	−	0.836634i	$-0.315480\pi$
$193$	15.2195	1.09553	0.547763	+	0.836634i	$0.315480\pi$
$194$	−10.2979	−0.739347
$195$	35.3679	2.53275
$196$	3.68261	0.263044
$197$	−21.0628	−1.50066	−0.750330	−	0.661063i	$-0.770106\pi$
$197$	−21.0628	−1.50066	−0.750330	+	0.661063i	$0.770106\pi$
$198$	0.738205	0.0524619
$199$	14.1256	1.00133	0.500667	−	0.865640i	$-0.333088\pi$
$199$	14.1256	1.00133	0.500667	+	0.865640i	$0.333088\pi$
$200$	−38.1399	−2.69690
$201$	−2.30406	−0.162516
$202$	−5.18568	−0.364864
$203$	−9.57531	−0.672055
$204$	−0.971071	−0.0679885
$205$	−4.49693	−0.314079
$206$	−13.4497	−0.937088
$207$	3.49466	0.242896
$208$	−12.8950	−0.894105
$209$	4.58864	0.317403
$210$	8.09890	0.558877
$211$	7.36069	0.506731	0.253365	−	0.967371i	$-0.418462\pi$
$211$	7.36069	0.506731	0.253365	+	0.967371i	$0.418462\pi$
$212$	2.49239	0.171178
$213$	−6.94214	−0.475668
$214$	−0.0494483	−0.00338022
$215$	28.5113	1.94445
$216$	−17.2039	−1.17058
$217$	3.86991	0.262706
$218$	10.5053	0.711511
$219$	6.98667	0.472115
$220$	−2.63090	−0.177375
$221$	−5.51026	−0.370660
$222$	18.0749	1.21311
$223$	−21.9711	−1.47129	−0.735646	−	0.677366i	$-0.763121\pi$
$223$	−21.9711	−1.47129	−0.735646	+	0.677366i	$0.763121\pi$
$224$	3.68649	0.246314
$225$	−7.81658	−0.521106
$226$	−5.67543	−0.377524
$227$	−21.7431	−1.44314	−0.721571	−	0.692340i	$-0.756580\pi$
$227$	−21.7431	−1.44314	−0.721571	+	0.692340i	$0.756580\pi$
$228$	−4.45589	−0.295099
$229$	−20.4101	−1.34874	−0.674370	−	0.738394i	$-0.735585\pi$
$229$	−20.4101	−1.34874	−0.674370	+	0.738394i	$0.735585\pi$
$230$	27.0277	1.78215
$231$	1.65983	0.109209
$232$	27.3340	1.79457
$233$	2.39803	0.157100	0.0785501	−	0.996910i	$-0.474971\pi$
$233$	2.39803	0.157100	0.0785501	+	0.996910i	$0.474971\pi$
$234$	−4.06770	−0.265914
$235$	−36.6453	−2.39047
$236$	−5.24354	−0.341326
$237$	−12.0072	−0.779951
$238$	−1.26180	−0.0817900
$239$	−6.40522	−0.414319	−0.207160	−	0.978307i	$-0.566422\pi$
$239$	−6.40522	−0.414319	−0.207160	+	0.978307i	$0.566422\pi$
$240$	−15.0205	−0.969570
$241$	16.7792	1.08085	0.540423	−	0.841393i	$-0.318264\pi$
$241$	16.7792	1.08085	0.540423	+	0.841393i	$0.318264\pi$
$242$	1.17009	0.0752160
$243$	−6.43907	−0.413067
$244$	1.94214	0.124333
$245$	24.3412	1.55510
$246$	−1.94214	−0.123826
$247$	−25.2846	−1.60882
$248$	−11.0472	−0.701497
$249$	7.20394	0.456531
$250$	−36.0566	−2.28042
$251$	24.6020	1.55286	0.776431	−	0.630202i	$-0.217028\pi$
$251$	24.6020	1.55286	0.776431	+	0.630202i	$0.217028\pi$
$252$	0.429229	0.0270389
$253$	5.53919	0.348246
$254$	−5.65983	−0.355129
$255$	−6.41855	−0.401945
$256$	−13.4764	−0.842276
$257$	22.4885	1.40280	0.701398	−	0.712770i	$-0.252560\pi$
$257$	22.4885	1.40280	0.701398	+	0.712770i	$0.252560\pi$
$258$	12.3135	0.766606
$259$	−10.8227	−0.672491
$260$	14.4969	0.899061
$261$	5.60197	0.346753
$262$	7.44975	0.460247
$263$	−17.8238	−1.09906	−0.549530	−	0.835474i	$-0.685193\pi$
$263$	−17.8238	−1.09906	−0.549530	+	0.835474i	$0.685193\pi$
$264$	−4.73820	−0.291616
$265$	16.4741	1.01200
$266$	−5.78992	−0.355003
$267$	1.82150	0.111474
$268$	−0.944409	−0.0576889
$269$	19.0784	1.16323	0.581615	−	0.813464i	$-0.302421\pi$
$269$	19.0784	1.16323	0.581615	+	0.813464i	$0.302421\pi$
$270$	−27.2690	−1.65954
$271$	−20.2557	−1.23044	−0.615222	−	0.788354i	$-0.710933\pi$
$271$	−20.2557	−1.23044	−0.615222	+	0.788354i	$0.710933\pi$
$272$	2.34017	0.141894
$273$	−9.14608	−0.553546
$274$	−2.92881	−0.176936
$275$	−12.3896	−0.747122
$276$	−5.37894	−0.323774
$277$	−17.3874	−1.04470	−0.522352	−	0.852730i	$-0.674945\pi$
$277$	−17.3874	−1.04470	−0.522352	+	0.852730i	$0.674945\pi$
$278$	−3.76713	−0.225938
$279$	−2.26406	−0.135546
$280$	13.8432	0.827292
$281$	−1.32684	−0.0791528	−0.0395764	−	0.999217i	$-0.512601\pi$
$281$	−1.32684	−0.0791528	−0.0395764	+	0.999217i	$0.512601\pi$
$282$	−15.8264	−0.942450
$283$	−13.6442	−0.811065	−0.405533	−	0.914081i	$-0.632914\pi$
$283$	−13.6442	−0.811065	−0.405533	+	0.914081i	$0.632914\pi$
$284$	−2.84551	−0.168850
$285$	−29.4524	−1.74461
$286$	−6.44748	−0.381247
$287$	1.16290	0.0686437
$288$	−2.15676	−0.127088
$289$	1.00000	0.0588235
$290$	43.3256	2.54417
$291$	13.5464	0.794103
$292$	2.86376	0.167589
$293$	−6.73820	−0.393650	−0.196825	−	0.980439i	$-0.563063\pi$
$293$	−6.73820	−0.393650	−0.196825	+	0.980439i	$0.563063\pi$
$294$	10.5125	0.613103
$295$	−34.6586	−2.01790
$296$	30.8950	1.79573
$297$	−5.58864	−0.324286
$298$	−14.5464	−0.842649
$299$	−30.5224	−1.76515
$300$	12.0312	0.694621
$301$	−7.37298	−0.424971
$302$	3.99159	0.229690
$303$	6.82150	0.391885
$304$	10.7382	0.615878
$305$	12.8371	0.735050
$306$	0.738205	0.0422004
$307$	19.3268	1.10304	0.551521	−	0.834161i	$-0.314048\pi$
$307$	19.3268	1.10304	0.551521	+	0.834161i	$0.314048\pi$
$308$	0.680346	0.0387663
$309$	17.6925	1.00649
$310$	−17.5103	−0.994516
$311$	−18.2557	−1.03518	−0.517592	−	0.855628i	$-0.673171\pi$
$311$	−18.2557	−1.03518	−0.517592	+	0.855628i	$0.673171\pi$
$312$	26.1087	1.47812
$313$	−12.8238	−0.724842	−0.362421	−	0.932014i	$-0.618050\pi$
$313$	−12.8238	−0.724842	−0.362421	+	0.932014i	$0.618050\pi$
$314$	−2.61530	−0.147590
$315$	2.83710	0.159853
$316$	−4.92162	−0.276863
$317$	−21.2485	−1.19343	−0.596716	−	0.802452i	$-0.703528\pi$
$317$	−21.2485	−1.19343	−0.596716	+	0.802452i	$0.703528\pi$
$318$	7.11488	0.398983
$319$	8.87936	0.497149
$320$	−36.1978	−2.02352
$321$	0.0650468	0.00363056
$322$	−6.98932	−0.389500
$323$	4.58864	0.255319
$324$	4.23287	0.235159
$325$	68.2700	3.78694
$326$	16.3135	0.903522
$327$	−13.8192	−0.764205
$328$	−3.31965	−0.183297
$329$	9.47641	0.522451
$330$	−7.51026	−0.413426
$331$	−15.7070	−0.863335	−0.431668	−	0.902033i	$-0.642075\pi$
$331$	−15.7070	−0.863335	−0.431668	+	0.902033i	$0.642075\pi$
$332$	2.95282	0.162057
$333$	6.33176	0.346978
$334$	16.0494	0.878187
$335$	−6.24232	−0.341054
$336$	3.88428	0.211905
$337$	9.57531	0.521600	0.260800	−	0.965393i	$-0.416014\pi$
$337$	9.57531	0.521600	0.260800	+	0.965393i	$0.416014\pi$
$338$	20.3162	1.10505
$339$	7.46573	0.405483
$340$	−2.63090	−0.142680
$341$	−3.58864	−0.194336
$342$	3.38735	0.183167
$343$	−13.8432	−0.747465
$344$	21.0472	1.13479
$345$	−35.5536	−1.91414
$346$	7.78539	0.418545
$347$	−19.0928	−1.02495	−0.512476	−	0.858701i	$-0.671272\pi$
$347$	−19.0928	−1.02495	−0.512476	+	0.858701i	$0.671272\pi$
$348$	−8.62249	−0.462214
$349$	−28.5958	−1.53070	−0.765350	−	0.643615i	$-0.777434\pi$
$349$	−28.5958	−1.53070	−0.765350	+	0.643615i	$0.777434\pi$
$350$	15.6332	0.835628
$351$	30.7948	1.64371
$352$	−3.41855	−0.182209
$353$	−17.3051	−0.921058	−0.460529	−	0.887645i	$-0.652340\pi$
$353$	−17.3051	−0.921058	−0.460529	+	0.887645i	$0.652340\pi$
$354$	−14.9684	−0.795562
$355$	−18.8082	−0.998234
$356$	0.746615	0.0395705
$357$	1.65983	0.0878474
$358$	4.00719	0.211786
$359$	16.3207	0.861374	0.430687	−	0.902501i	$-0.358271\pi$
$359$	16.3207	0.861374	0.430687	+	0.902501i	$0.358271\pi$
$360$	−8.09890	−0.426849
$361$	2.05559	0.108189
$362$	−0.539189	−0.0283391
$363$	−1.53919	−0.0807865
$364$	−3.74888	−0.196495
$365$	18.9288	0.990779
$366$	5.54411	0.289795
$367$	−0.196748	−0.0102702	−0.00513509	−	0.999987i	$-0.501635\pi$
$367$	−0.196748	−0.0102702	−0.00513509	+	0.999987i	$0.501635\pi$
$368$	12.9627	0.675725
$369$	−0.680346	−0.0354174
$370$	48.9698	2.54582
$371$	−4.26019	−0.221178
$372$	3.48482	0.180680
$373$	−5.45240	−0.282315	−0.141157	−	0.989987i	$-0.545082\pi$
$373$	−5.45240	−0.282315	−0.141157	+	0.989987i	$0.545082\pi$
$374$	1.17009	0.0605037
$375$	47.4307	2.44931
$376$	−27.0517	−1.39509
$377$	−48.9276	−2.51990
$378$	7.05172	0.362701
$379$	15.9021	0.816838	0.408419	−	0.912794i	$-0.366080\pi$
$379$	15.9021	0.816838	0.408419	+	0.912794i	$0.366080\pi$
$380$	−12.0722	−0.619293
$381$	7.44521	0.381430
$382$	−6.82991	−0.349449
$383$	20.2762	1.03606	0.518032	−	0.855361i	$-0.326665\pi$
$383$	20.2762	1.03606	0.518032	+	0.855361i	$0.326665\pi$
$384$	−5.10957	−0.260747
$385$	4.49693	0.229185
$386$	17.8082	0.906412
$387$	4.31351	0.219268
$388$	5.55252	0.281886
$389$	−13.7298	−0.696128	−0.348064	−	0.937471i	$-0.613161\pi$
$389$	−13.7298	−0.696128	−0.348064	+	0.937471i	$0.613161\pi$
$390$	41.3835	2.09553
$391$	5.53919	0.280129
$392$	17.9688	0.907562
$393$	−9.79976	−0.494333
$394$	−24.6453	−1.24161
$395$	−32.5308	−1.63680
$396$	−0.398032	−0.0200019
$397$	−24.8020	−1.24478	−0.622389	−	0.782708i	$-0.713838\pi$
$397$	−24.8020	−1.24478	−0.622389	+	0.782708i	$0.713838\pi$
$398$	16.5281	0.828480
$399$	7.61634	0.381294
$400$	−28.9939	−1.44969
$401$	6.91321	0.345229	0.172615	−	0.984989i	$-0.444778\pi$
$401$	6.91321	0.345229	0.172615	+	0.984989i	$0.444778\pi$
$402$	−2.69594	−0.134461
$403$	19.7743	0.985029
$404$	2.79606	0.139109
$405$	27.9783	1.39025
$406$	−11.2039	−0.556042
$407$	10.0361	0.497472
$408$	−4.73820	−0.234576
$409$	−19.0277	−0.940860	−0.470430	−	0.882437i	$-0.655901\pi$
$409$	−19.0277	−0.940860	−0.470430	+	0.882437i	$0.655901\pi$
$410$	−5.26180	−0.259862
$411$	3.85270	0.190040
$412$	7.25195	0.357278
$413$	8.96266	0.441024
$414$	4.08906	0.200966
$415$	19.5174	0.958074
$416$	18.8371	0.923565
$417$	4.95547	0.242671
$418$	5.36910	0.262611
$419$	35.0205	1.71086	0.855432	−	0.517915i	$-0.173292\pi$
$419$	35.0205	1.71086	0.855432	+	0.517915i	$0.173292\pi$
$420$	−4.36683	−0.213080
$421$	−26.0905	−1.27157	−0.635786	−	0.771865i	$-0.719324\pi$
$421$	−26.0905	−1.27157	−0.635786	+	0.771865i	$0.719324\pi$
$422$	8.61265	0.419257
$423$	−5.54411	−0.269564
$424$	12.1613	0.590604
$425$	−12.3896	−0.600985
$426$	−8.12291	−0.393556
$427$	−3.31965	−0.160649
$428$	0.0266620	0.00128876
$429$	8.48133	0.409482
$430$	33.3607	1.60880
$431$	−12.5659	−0.605276	−0.302638	−	0.953106i	$-0.597867\pi$
$431$	−12.5659	−0.605276	−0.302638	+	0.953106i	$0.597867\pi$
$432$	−13.0784	−0.629234
$433$	29.4040	1.41307	0.706533	−	0.707680i	$-0.250258\pi$
$433$	29.4040	1.41307	0.706533	+	0.707680i	$0.250258\pi$
$434$	4.52813	0.217357
$435$	−56.9926	−2.73259
$436$	−5.66436	−0.271274
$437$	25.4173	1.21588
$438$	8.17501	0.390617
$439$	32.6069	1.55624	0.778121	−	0.628114i	$-0.216173\pi$
$439$	32.6069	1.55624	0.778121	+	0.628114i	$0.216173\pi$
$440$	−12.8371	−0.611985
$441$	3.68261	0.175363
$442$	−6.44748	−0.306675
$443$	15.6765	0.744812	0.372406	−	0.928070i	$-0.378533\pi$
$443$	15.6765	0.744812	0.372406	+	0.928070i	$0.378533\pi$
$444$	−9.74578	−0.462514
$445$	4.93495	0.233939
$446$	−25.7081	−1.21731
$447$	19.1350	0.905055
$448$	9.36069	0.442251
$449$	−2.02174	−0.0954119	−0.0477059	−	0.998861i	$-0.515191\pi$
$449$	−2.02174	−0.0954119	−0.0477059	+	0.998861i	$0.515191\pi$
$450$	−9.14608	−0.431150
$451$	−1.07838	−0.0507788
$452$	3.06013	0.143936
$453$	−5.25073	−0.246701
$454$	−25.4413	−1.19402
$455$	−24.7792	−1.16167
$456$	−21.7419	−1.01816
$457$	−0.463079	−0.0216619	−0.0108310	−	0.999941i	$-0.503448\pi$
$457$	−0.463079	−0.0216619	−0.0108310	+	0.999941i	$0.503448\pi$
$458$	−23.8816	−1.11592
$459$	−5.58864	−0.260855
$460$	−14.5730	−0.679471
$461$	22.5236	1.04903	0.524514	−	0.851402i	$-0.324247\pi$
$461$	22.5236	1.04903	0.524514	+	0.851402i	$0.324247\pi$
$462$	1.94214	0.0903566
$463$	6.73594	0.313046	0.156523	−	0.987674i	$-0.449972\pi$
$463$	6.73594	0.313046	0.156523	+	0.987674i	$0.449972\pi$
$464$	20.7792	0.964652
$465$	23.0338	1.06817
$466$	2.80590	0.129981
$467$	−2.08225	−0.0963552	−0.0481776	−	0.998839i	$-0.515341\pi$
$467$	−2.08225	−0.0963552	−0.0481776	+	0.998839i	$0.515341\pi$
$468$	2.19326	0.101383
$469$	1.61425	0.0745393
$470$	−42.8781	−1.97782
$471$	3.44029	0.158520
$472$	−25.5851	−1.17765
$473$	6.83710	0.314370
$474$	−14.0494	−0.645313
$475$	−56.8515	−2.60852
$476$	0.680346	0.0311836
$477$	2.49239	0.114119
$478$	−7.49466	−0.342798
$479$	−27.6163	−1.26182	−0.630911	−	0.775855i	$-0.717319\pi$
$479$	−27.6163	−1.26182	−0.630911	+	0.775855i	$0.717319\pi$
$480$	21.9421	1.00152
$481$	−55.3016	−2.52154
$482$	19.6332	0.894266
$483$	9.19410	0.418346
$484$	−0.630898	−0.0286772
$485$	36.7009	1.66650
$486$	−7.53427	−0.341761
$487$	−42.5018	−1.92594	−0.962971	−	0.269604i	$-0.913107\pi$
$487$	−42.5018	−1.92594	−0.962971	+	0.269604i	$0.913107\pi$
$488$	9.47641	0.428977
$489$	−21.4596	−0.970436
$490$	28.4813	1.28666
$491$	35.8069	1.61595	0.807973	−	0.589220i	$-0.200565\pi$
$491$	35.8069	1.61595	0.807973	+	0.589220i	$0.200565\pi$
$492$	1.04718	0.0472106
$493$	8.87936	0.399906
$494$	−29.5851	−1.33110
$495$	−2.63090	−0.118250
$496$	−8.39803	−0.377083
$497$	4.86376	0.218170
$498$	8.42923	0.377723
$499$	4.26406	0.190886	0.0954428	−	0.995435i	$-0.469573\pi$
$499$	4.26406	0.190886	0.0954428	+	0.995435i	$0.469573\pi$
$500$	19.4413	0.869443
$501$	−21.1122	−0.943225
$502$	28.7864	1.28480
$503$	28.4235	1.26734	0.633670	−	0.773603i	$-0.281548\pi$
$503$	28.4235	1.26734	0.633670	+	0.773603i	$0.281548\pi$
$504$	2.09436	0.0932903
$505$	18.4813	0.822408
$506$	6.48133	0.288130
$507$	−26.7249	−1.18689
$508$	3.05172	0.135398
$509$	40.4740	1.79398	0.896988	−	0.442054i	$-0.145750\pi$
$509$	40.4740	1.79398	0.896988	+	0.442054i	$0.145750\pi$
$510$	−7.51026	−0.332560
$511$	−4.89496	−0.216540
$512$	−22.4079	−0.990297
$513$	−25.6442	−1.13222
$514$	26.3135	1.16064
$515$	47.9337	2.11221
$516$	−6.63931	−0.292279
$517$	−8.78765	−0.386481
$518$	−12.6635	−0.556403
$519$	−10.2413	−0.449542
$520$	70.7358	3.10197
$521$	−2.59478	−0.113679	−0.0568397	−	0.998383i	$-0.518102\pi$
$521$	−2.59478	−0.113679	−0.0568397	+	0.998383i	$0.518102\pi$
$522$	6.55479	0.286895
$523$	−16.2823	−0.711976	−0.355988	−	0.934491i	$-0.615856\pi$
$523$	−16.2823	−0.711976	−0.355988	+	0.934491i	$0.615856\pi$
$524$	−4.01682	−0.175476
$525$	−20.5646	−0.897514
$526$	−20.8554	−0.909337
$527$	−3.58864	−0.156323
$528$	−3.60197	−0.156756
$529$	7.68261	0.334027
$530$	19.2762	0.837303
$531$	−5.24354	−0.227550
$532$	3.12186	0.135350
$533$	5.94214	0.257383
$534$	2.13132	0.0922311
$535$	0.176230	0.00761907
$536$	−4.60811	−0.199040
$537$	−5.27125	−0.227471
$538$	22.3234	0.962428
$539$	5.83710	0.251422
$540$	14.7031	0.632722
$541$	15.4030	0.662225	0.331112	−	0.943591i	$-0.392576\pi$
$541$	15.4030	0.662225	0.331112	+	0.943591i	$0.392576\pi$
$542$	−23.7009	−1.01804
$543$	0.709275	0.0304379
$544$	−3.41855	−0.146569
$545$	−37.4401	−1.60376
$546$	−10.7017	−0.457991
$547$	21.9311	0.937705	0.468853	−	0.883276i	$-0.344668\pi$
$547$	21.9311	0.937705	0.468853	+	0.883276i	$0.344668\pi$
$548$	1.57918	0.0674593
$549$	1.94214	0.0828886
$550$	−14.4969	−0.618151
$551$	40.7442	1.73576
$552$	−26.2458	−1.11710
$553$	8.41241	0.357732
$554$	−20.3447	−0.864364
$555$	−64.4173	−2.73436
$556$	2.03120	0.0861419
$557$	−38.1568	−1.61675	−0.808377	−	0.588665i	$-0.799654\pi$
$557$	−38.1568	−1.61675	−0.808377	+	0.588665i	$0.799654\pi$
$558$	−2.64915	−0.112147
$559$	−37.6742	−1.59345
$560$	10.5236	0.444703
$561$	−1.53919	−0.0649846
$562$	−1.55252	−0.0654891
$563$	29.3945	1.23883	0.619416	−	0.785063i	$-0.287369\pi$
$563$	29.3945	1.23883	0.619416	+	0.785063i	$0.287369\pi$
$564$	8.53343	0.359322
$565$	20.2267	0.850945
$566$	−15.9649	−0.671056
$567$	−7.23513	−0.303847
$568$	−13.8843	−0.582572
$569$	−14.1568	−0.593482	−0.296741	−	0.954958i	$-0.595900\pi$
$569$	−14.1568	−0.593482	−0.296741	+	0.954958i	$0.595900\pi$
$570$	−34.4619	−1.44345
$571$	20.0300	0.838228	0.419114	−	0.907934i	$-0.362341\pi$
$571$	20.0300	0.838228	0.419114	+	0.907934i	$0.362341\pi$
$572$	3.47641	0.145356
$573$	8.98440	0.375329
$574$	1.36069	0.0567942
$575$	−68.6285	−2.86200
$576$	−5.47641	−0.228184
$577$	15.8904	0.661527	0.330764	−	0.943714i	$-0.392694\pi$
$577$	15.8904	0.661527	0.330764	+	0.943714i	$0.392694\pi$
$578$	1.17009	0.0486692
$579$	−23.4257	−0.973540
$580$	−23.3607	−0.970000
$581$	−5.04718	−0.209392
$582$	15.8504	0.657022
$583$	3.95055	0.163615
$584$	13.9733	0.578221
$585$	14.4969	0.599374
$586$	−7.88428	−0.325697
$587$	−9.10116	−0.375645	−0.187823	−	0.982203i	$-0.560143\pi$
$587$	−9.10116	−0.375645	−0.187823	+	0.982203i	$0.560143\pi$
$588$	−5.66824	−0.233754
$589$	−16.4670	−0.678509
$590$	−40.5536	−1.66956
$591$	32.4196	1.33356
$592$	23.4863	0.965279
$593$	−44.6875	−1.83510	−0.917549	−	0.397624i	$-0.869835\pi$
$593$	−44.6875	−1.83510	−0.917549	+	0.397624i	$0.869835\pi$
$594$	−6.53919	−0.268306
$595$	4.49693	0.184356
$596$	7.84324	0.321272
$597$	−21.7419	−0.889837
$598$	−35.7138	−1.46045
$599$	8.51971	0.348106	0.174053	−	0.984736i	$-0.444314\pi$
$599$	8.51971	0.348106	0.174053	+	0.984736i	$0.444314\pi$
$600$	58.7046	2.39660
$601$	22.8104	0.930457	0.465229	−	0.885191i	$-0.345972\pi$
$601$	22.8104	0.930457	0.465229	+	0.885191i	$0.345972\pi$
$602$	−8.62702	−0.351611
$603$	−0.944409	−0.0384593
$604$	−2.15222	−0.0875726
$605$	−4.17009	−0.169538
$606$	7.98175	0.324236
$607$	−9.15061	−0.371412	−0.185706	−	0.982605i	$-0.559457\pi$
$607$	−9.15061	−0.371412	−0.185706	+	0.982605i	$0.559457\pi$
$608$	−15.6865	−0.636171
$609$	14.7382	0.597222
$610$	15.0205	0.608163
$611$	48.4222	1.95895
$612$	−0.398032	−0.0160895
$613$	14.0456	0.567295	0.283648	−	0.958929i	$-0.408455\pi$
$613$	14.0456	0.567295	0.283648	+	0.958929i	$0.408455\pi$
$614$	22.6141	0.912630
$615$	6.92162	0.279107
$616$	3.31965	0.133753
$617$	24.9360	1.00389	0.501943	−	0.864901i	$-0.332619\pi$
$617$	24.9360	1.00389	0.501943	+	0.864901i	$0.332619\pi$
$618$	20.7017	0.832745
$619$	22.5246	0.905342	0.452671	−	0.891678i	$-0.350471\pi$
$619$	22.5246	0.905342	0.452671	+	0.891678i	$0.350471\pi$
$620$	9.44134	0.379173
$621$	−30.9565	−1.24224
$622$	−21.3607	−0.856486
$623$	−1.27617	−0.0511287
$624$	19.8478	0.794547
$625$	66.5546	2.66218
$626$	−15.0049	−0.599717
$627$	−7.06278	−0.282060
$628$	1.41014	0.0562707
$629$	10.0361	0.400166
$630$	3.31965	0.132258
$631$	−28.9299	−1.15168	−0.575840	−	0.817563i	$-0.695325\pi$
$631$	−28.9299	−1.15168	−0.575840	+	0.817563i	$0.695325\pi$
$632$	−24.0144	−0.955241
$633$	−11.3295	−0.450307
$634$	−24.8625	−0.987418
$635$	20.1711	0.800467
$636$	−3.83626	−0.152118
$637$	−32.1639	−1.27438
$638$	10.3896	0.411329
$639$	−2.84551	−0.112567
$640$	−13.8432	−0.547202
$641$	−2.13501	−0.0843280	−0.0421640	−	0.999111i	$-0.513425\pi$
$641$	−2.13501	−0.0843280	−0.0421640	+	0.999111i	$0.513425\pi$
$642$	0.0761103	0.00300383
$643$	9.72261	0.383422	0.191711	−	0.981451i	$-0.438596\pi$
$643$	9.72261	0.383422	0.191711	+	0.981451i	$0.438596\pi$
$644$	3.76856	0.148502
$645$	−43.8843	−1.72794
$646$	5.36910	0.211245
$647$	−44.2990	−1.74157	−0.870786	−	0.491662i	$-0.836389\pi$
$647$	−44.2990	−1.74157	−0.870786	+	0.491662i	$0.836389\pi$
$648$	20.6537	0.811353
$649$	−8.31124	−0.326245
$650$	79.8818	3.13322
$651$	−5.95652	−0.233454
$652$	−8.79606	−0.344480
$653$	−30.3002	−1.18574	−0.592869	−	0.805299i	$-0.702005\pi$
$653$	−30.3002	−1.18574	−0.592869	+	0.805299i	$0.702005\pi$
$654$	−16.1697	−0.632285
$655$	−26.5503	−1.03740
$656$	−2.52359	−0.0985297
$657$	2.86376	0.111726
$658$	11.0882	0.432264
$659$	28.1373	1.09607	0.548036	−	0.836454i	$-0.315376\pi$
$659$	28.1373	1.09607	0.548036	+	0.836454i	$0.315376\pi$
$660$	4.04945	0.157625
$661$	22.1857	0.862923	0.431462	−	0.902131i	$-0.357998\pi$
$661$	22.1857	0.862923	0.431462	+	0.902131i	$0.357998\pi$
$662$	−18.3786	−0.714303
$663$	8.48133	0.329388
$664$	14.4079	0.559134
$665$	20.6348	0.800182
$666$	7.40871	0.287082
$667$	49.1845	1.90443
$668$	−8.65368	−0.334821
$669$	33.8176	1.30747
$670$	−7.30406	−0.282180
$671$	3.07838	0.118839
$672$	−5.67420	−0.218887
$673$	34.3701	1.32487	0.662436	−	0.749119i	$-0.269523\pi$
$673$	34.3701	1.32487	0.662436	+	0.749119i	$0.269523\pi$
$674$	11.2039	0.431560
$675$	69.2411	2.66509
$676$	−10.9542	−0.421317
$677$	37.3184	1.43426	0.717132	−	0.696937i	$-0.245454\pi$
$677$	37.3184	1.43426	0.717132	+	0.696937i	$0.245454\pi$
$678$	8.73555	0.335487
$679$	−9.49079	−0.364223
$680$	−12.8371	−0.492280
$681$	33.4668	1.28245
$682$	−4.19902	−0.160789
$683$	−39.6475	−1.51707	−0.758535	−	0.651632i	$-0.774085\pi$
$683$	−39.6475	−1.51707	−0.758535	+	0.651632i	$0.774085\pi$
$684$	−1.82642	−0.0698350
$685$	10.4380	0.398816
$686$	−16.1978	−0.618435
$687$	31.4151	1.19856
$688$	16.0000	0.609994
$689$	−21.7686	−0.829316
$690$	−41.6007	−1.58371
$691$	−13.4007	−0.509786	−0.254893	−	0.966969i	$-0.582040\pi$
$691$	−13.4007	−0.509786	−0.254893	+	0.966969i	$0.582040\pi$
$692$	−4.19779	−0.159576
$693$	0.680346	0.0258442
$694$	−22.3402	−0.848021
$695$	13.4257	0.509267
$696$	−42.0722	−1.59474
$697$	−1.07838	−0.0408465
$698$	−33.4596	−1.26646
$699$	−3.69102	−0.139607
$700$	−8.42923	−0.318595
$701$	16.6803	0.630008	0.315004	−	0.949090i	$-0.397994\pi$
$701$	16.6803	0.630008	0.315004	+	0.949090i	$0.397994\pi$
$702$	36.0326	1.35996
$703$	46.0521	1.73689
$704$	−8.68035	−0.327153
$705$	56.4040	2.12430
$706$	−20.2485	−0.762061
$707$	−4.77924	−0.179742
$708$	8.07080	0.303319
$709$	12.1350	0.455740	0.227870	−	0.973692i	$-0.426824\pi$
$709$	12.1350	0.455740	0.227870	+	0.973692i	$0.426824\pi$
$710$	−22.0072	−0.825915
$711$	−4.92162	−0.184575
$712$	3.64301	0.136527
$713$	−19.8781	−0.744442
$714$	1.94214	0.0726828
$715$	22.9783	0.859338
$716$	−2.16063	−0.0807466
$717$	9.85884	0.368185
$718$	19.0966	0.712680
$719$	−12.6754	−0.472714	−0.236357	−	0.971666i	$-0.575953\pi$
$719$	−12.6754	−0.472714	−0.236357	+	0.971666i	$0.575953\pi$
$720$	−6.15676	−0.229449
$721$	−12.3956	−0.461636
$722$	2.40522	0.0895130
$723$	−25.8264	−0.960495
$724$	0.290725	0.0108047
$725$	−110.012	−4.08574
$726$	−1.80098	−0.0668408
$727$	−6.10957	−0.226592	−0.113296	−	0.993561i	$-0.536141\pi$
$727$	−6.10957	−0.226592	−0.113296	+	0.993561i	$0.536141\pi$
$728$	−18.2922	−0.677952
$729$	30.0388	1.11255
$730$	22.1483	0.819747
$731$	6.83710	0.252879
$732$	−2.98932	−0.110489
$733$	−8.86830	−0.327558	−0.163779	−	0.986497i	$-0.552368\pi$
$733$	−8.86830	−0.327558	−0.163779	+	0.986497i	$0.552368\pi$
$734$	−0.230213	−0.00849731
$735$	−37.4657	−1.38194
$736$	−18.9360	−0.697990
$737$	−1.49693	−0.0551401
$738$	−0.796064	−0.0293035
$739$	−27.1845	−0.999997	−0.499998	−	0.866026i	$-0.666666\pi$
$739$	−27.1845	−0.999997	−0.499998	+	0.866026i	$0.666666\pi$
$740$	−26.4040	−0.970630
$741$	38.9177	1.42968
$742$	−4.98479	−0.182997
$743$	25.8120	0.946952	0.473476	−	0.880807i	$-0.342999\pi$
$743$	25.8120	0.946952	0.473476	+	0.880807i	$0.342999\pi$
$744$	17.0037	0.623386
$745$	51.8420	1.89934
$746$	−6.37978	−0.233580
$747$	2.95282	0.108038
$748$	−0.630898	−0.0230679
$749$	−0.0455727	−0.00166519
$750$	55.4980	2.02650
$751$	7.07942	0.258332	0.129166	−	0.991623i	$-0.458770\pi$
$751$	7.07942	0.258332	0.129166	+	0.991623i	$0.458770\pi$
$752$	−20.5646	−0.749915
$753$	−37.8671	−1.37995
$754$	−57.2495	−2.08490
$755$	−14.2257	−0.517725
$756$	−3.80221	−0.138285
$757$	−8.24128	−0.299534	−0.149767	−	0.988721i	$-0.547852\pi$
$757$	−8.24128	−0.299534	−0.149767	+	0.988721i	$0.547852\pi$
$758$	18.6069	0.675833
$759$	−8.52586	−0.309469
$760$	−58.9048	−2.13670
$761$	14.0338	0.508727	0.254363	−	0.967109i	$-0.418134\pi$
$761$	14.0338	0.508727	0.254363	+	0.967109i	$0.418134\pi$
$762$	8.71154	0.315586
$763$	9.68195	0.350510
$764$	3.68261	0.133232
$765$	−2.63090	−0.0951203
$766$	23.7249	0.857215
$767$	45.7971	1.65364
$768$	20.7427	0.748489
$769$	−35.4063	−1.27678	−0.638391	−	0.769712i	$-0.720400\pi$
$769$	−35.4063	−1.27678	−0.638391	+	0.769712i	$0.720400\pi$
$770$	5.26180	0.189622
$771$	−34.6141	−1.24660
$772$	−9.60197	−0.345582
$773$	−3.65142	−0.131332	−0.0656662	−	0.997842i	$-0.520917\pi$
$773$	−3.65142	−0.131332	−0.0656662	+	0.997842i	$0.520917\pi$
$774$	5.04718	0.181417
$775$	44.4619	1.59712
$776$	27.0928	0.972573
$777$	16.6582	0.597610
$778$	−16.0650	−0.575960
$779$	−4.94828	−0.177291
$780$	−22.3135	−0.798952
$781$	−4.51026	−0.161390
$782$	6.48133	0.231772
$783$	−49.6235	−1.77340
$784$	13.6598	0.487851
$785$	9.32070	0.332670
$786$	−11.4666	−0.408999
$787$	41.7308	1.48754	0.743772	−	0.668434i	$-0.233035\pi$
$787$	41.7308	1.48754	0.743772	+	0.668434i	$0.233035\pi$
$788$	13.2885	0.473382
$789$	27.4341	0.976682
$790$	−38.0638	−1.35425
$791$	−5.23060	−0.185979
$792$	−1.94214	−0.0690110
$793$	−16.9627	−0.602362
$794$	−29.0205	−1.02990
$795$	−25.3568	−0.899314
$796$	−8.91178	−0.315870
$797$	43.9504	1.55680	0.778401	−	0.627767i	$-0.216031\pi$
$797$	43.9504	1.55680	0.778401	+	0.627767i	$0.216031\pi$
$798$	8.91178	0.315474
$799$	−8.78765	−0.310885
$800$	42.3545	1.49746
$801$	0.746615	0.0263804
$802$	8.08906	0.285634
$803$	4.53919	0.160184
$804$	1.45362	0.0512653
$805$	24.9093	0.877939
$806$	23.1377	0.814990
$807$	−29.3652	−1.03370
$808$	13.6430	0.479959
$809$	−13.0894	−0.460200	−0.230100	−	0.973167i	$-0.573905\pi$
$809$	−13.0894	−0.460200	−0.230100	+	0.973167i	$0.573905\pi$
$810$	32.7370	1.15026
$811$	6.75380	0.237158	0.118579	−	0.992945i	$-0.462166\pi$
$811$	6.75380	0.237158	0.118579	+	0.992945i	$0.462166\pi$
$812$	6.04104	0.211999
$813$	31.1773	1.09343
$814$	11.7431	0.411596
$815$	−58.1399	−2.03655
$816$	−3.60197	−0.126094
$817$	31.3730	1.09760
$818$	−22.2641	−0.778445
$819$	−3.74888	−0.130997
$820$	2.83710	0.0990759
$821$	30.9471	1.08006	0.540030	−	0.841646i	$-0.318413\pi$
$821$	30.9471	1.08006	0.540030	+	0.841646i	$0.318413\pi$
$822$	4.50799	0.157234
$823$	−50.9104	−1.77462	−0.887312	−	0.461169i	$-0.847430\pi$
$823$	−50.9104	−1.77462	−0.887312	+	0.461169i	$0.847430\pi$
$824$	35.3849	1.23269
$825$	19.0700	0.663931
$826$	10.4871	0.364892
$827$	42.6791	1.48410	0.742049	−	0.670345i	$-0.233854\pi$
$827$	42.6791	1.48410	0.742049	+	0.670345i	$0.233854\pi$
$828$	−2.20477	−0.0766212
$829$	16.2495	0.564369	0.282184	−	0.959360i	$-0.408941\pi$
$829$	16.2495	0.564369	0.282184	+	0.959360i	$0.408941\pi$
$830$	22.8371	0.792687
$831$	26.7624	0.928378
$832$	47.8310	1.65824
$833$	5.83710	0.202244
$834$	5.79833	0.200780
$835$	−57.1988	−1.97945
$836$	−2.89496	−0.100124
$837$	20.0556	0.693223
$838$	40.9770	1.41553
$839$	6.19287	0.213802	0.106901	−	0.994270i	$-0.465907\pi$
$839$	6.19287	0.213802	0.106901	+	0.994270i	$0.465907\pi$
$840$	−21.3074	−0.735174
$841$	49.8431	1.71873
$842$	−30.5281	−1.05207
$843$	2.04226	0.0703392
$844$	−4.64384	−0.159848
$845$	−72.4050	−2.49081
$846$	−6.48709	−0.223031
$847$	1.07838	0.0370535
$848$	9.24497	0.317474
$849$	21.0010	0.720754
$850$	−14.4969	−0.497241
$851$	55.5919	1.90567
$852$	4.37978	0.150049
$853$	−27.9721	−0.957747	−0.478873	−	0.877884i	$-0.658955\pi$
$853$	−27.9721	−0.957747	−0.478873	+	0.877884i	$0.658955\pi$
$854$	−3.88428	−0.132917
$855$	−12.0722	−0.412862
$856$	0.130094	0.00444650
$857$	13.7743	0.470522	0.235261	−	0.971932i	$-0.424406\pi$
$857$	13.7743	0.470522	0.235261	+	0.971932i	$0.424406\pi$
$858$	9.92389	0.338796
$859$	−6.51148	−0.222169	−0.111084	−	0.993811i	$-0.535432\pi$
$859$	−6.51148	−0.222169	−0.111084	+	0.993811i	$0.535432\pi$
$860$	−17.9877	−0.613376
$861$	−1.78992	−0.0610003
$862$	−14.7031	−0.500791
$863$	−40.1217	−1.36576	−0.682879	−	0.730532i	$-0.739272\pi$
$863$	−40.1217	−1.36576	−0.682879	+	0.730532i	$0.739272\pi$
$864$	19.1050	0.649967
$865$	−27.7464	−0.943407
$866$	34.4052	1.16914
$867$	−1.53919	−0.0522736
$868$	−2.44151	−0.0828704
$869$	−7.80098	−0.264630
$870$	−66.6863	−2.26088
$871$	8.24846	0.279489
$872$	−27.6385	−0.935957
$873$	5.55252	0.187924
$874$	29.7405	1.00599
$875$	−33.2306	−1.12340
$876$	−4.40787	−0.148928
$877$	18.9348	0.639382	0.319691	−	0.947522i	$-0.396421\pi$
$877$	18.9348	0.639382	0.319691	+	0.947522i	$0.396421\pi$
$878$	38.1529	1.28760
$879$	10.3714	0.349818
$880$	−9.75872	−0.328967
$881$	3.74539	0.126185	0.0630927	−	0.998008i	$-0.479904\pi$
$881$	3.74539	0.126185	0.0630927	+	0.998008i	$0.479904\pi$
$882$	4.30898	0.145091
$883$	5.84324	0.196641	0.0983204	−	0.995155i	$-0.468653\pi$
$883$	5.84324	0.196641	0.0983204	+	0.995155i	$0.468653\pi$
$884$	3.47641	0.116924
$885$	53.3461	1.79321
$886$	18.3428	0.616239
$887$	−25.2306	−0.847161	−0.423580	−	0.905859i	$-0.639227\pi$
$887$	−25.2306	−0.847161	−0.423580	+	0.905859i	$0.639227\pi$
$888$	−47.5532	−1.59578
$889$	−5.21622	−0.174946
$890$	5.77432	0.193556
$891$	6.70928	0.224769
$892$	13.8615	0.464117
$893$	−40.3234	−1.34937
$894$	22.3896	0.748821
$895$	−14.2813	−0.477370
$896$	3.57984	0.119594
$897$	46.9797	1.56861
$898$	−2.36561	−0.0789415
$899$	−31.8648	−1.06275
$900$	4.93146	0.164382
$901$	3.95055	0.131612
$902$	−1.26180	−0.0420132
$903$	11.3484	0.377651
$904$	14.9315	0.496613
$905$	1.92162	0.0638769
$906$	−6.14381	−0.204114
$907$	−49.9877	−1.65981	−0.829907	−	0.557901i	$-0.811607\pi$
$907$	−49.9877	−1.65981	−0.829907	+	0.557901i	$0.811607\pi$
$908$	13.7177	0.455237
$909$	2.79606	0.0927396
$910$	−28.9939	−0.961137
$911$	−31.5213	−1.04435	−0.522174	−	0.852839i	$-0.674879\pi$
$911$	−31.5213	−1.04435	−0.522174	+	0.852839i	$0.674879\pi$
$912$	−16.5281	−0.547301
$913$	4.68035	0.154897
$914$	−0.541842	−0.0179225
$915$	−19.7587	−0.653203
$916$	12.8767	0.425458
$917$	6.86585	0.226730
$918$	−6.53919	−0.215825
$919$	−42.5913	−1.40496	−0.702479	−	0.711705i	$-0.747923\pi$
$919$	−42.5913	−1.40496	−0.702479	+	0.711705i	$0.747923\pi$
$920$	−71.1071	−2.34433
$921$	−29.7477	−0.980219
$922$	26.3545	0.867941
$923$	24.8527	0.818037
$924$	−1.04718	−0.0344497
$925$	−124.344	−4.08840
$926$	7.88163	0.259006
$927$	7.25195	0.238185
$928$	−30.3545	−0.996437
$929$	−21.5630	−0.707460	−0.353730	−	0.935348i	$-0.615087\pi$
$929$	−21.5630	−0.707460	−0.353730	+	0.935348i	$0.615087\pi$
$930$	26.9516	0.883778
$931$	26.7843	0.877821
$932$	−1.51291	−0.0495571
$933$	28.0989	0.919917
$934$	−2.43642	−0.0797220
$935$	−4.17009	−0.136376
$936$	10.7017	0.349796
$937$	−42.4417	−1.38651	−0.693255	−	0.720692i	$-0.743824\pi$
$937$	−42.4417	−1.38651	−0.693255	+	0.720692i	$0.743824\pi$
$938$	1.88882	0.0616721
$939$	19.7382	0.644132
$940$	23.1194	0.754072
$941$	−16.7526	−0.546119	−0.273059	−	0.961997i	$-0.588036\pi$
$941$	−16.7526	−0.546119	−0.273059	+	0.961997i	$0.588036\pi$
$942$	4.02544	0.131156
$943$	−5.97334	−0.194519
$944$	−19.4497	−0.633035
$945$	−25.1317	−0.817534
$946$	8.00000	0.260102
$947$	−52.7035	−1.71263	−0.856317	−	0.516450i	$-0.827253\pi$
$947$	−52.7035	−1.71263	−0.856317	+	0.516450i	$0.827253\pi$
$948$	7.57531	0.246035
$949$	−25.0121	−0.811927
$950$	−66.5211	−2.15823
$951$	32.7054	1.06055
$952$	3.31965	0.107591
$953$	27.6742	0.896455	0.448228	−	0.893919i	$-0.352055\pi$
$953$	27.6742	0.896455	0.448228	+	0.893919i	$0.352055\pi$
$954$	2.91632	0.0944192
$955$	24.3412	0.787663
$956$	4.04104	0.130697
$957$	−13.6670	−0.441792
$958$	−32.3135	−1.04400
$959$	−2.69926	−0.0871635
$960$	55.7152	1.79820
$961$	−18.1217	−0.584570
$962$	−64.7077	−2.08626
$963$	0.0266620	0.000859171 0
$964$	−10.5860	−0.340952
$965$	−63.4668	−2.04307
$966$	10.7579	0.346129
$967$	42.3207	1.36094	0.680471	−	0.732775i	$-0.261775\pi$
$967$	42.3207	1.36094	0.680471	+	0.732775i	$0.261775\pi$
$968$	−3.07838	−0.0989428
$969$	−7.06278	−0.226889
$970$	42.9432	1.37882
$971$	−2.96493	−0.0951491	−0.0475745	−	0.998868i	$-0.515149\pi$
$971$	−2.96493	−0.0951491	−0.0475745	+	0.998868i	$0.515149\pi$
$972$	4.06239	0.130301
$973$	−3.47187	−0.111303
$974$	−49.7308	−1.59348
$975$	−105.080	−3.36527
$976$	7.20394	0.230592
$977$	−38.2267	−1.22298	−0.611491	−	0.791252i	$-0.709430\pi$
$977$	−38.2267	−1.22298	−0.611491	+	0.791252i	$0.709430\pi$
$978$	−25.1096	−0.802916
$979$	1.18342	0.0378222
$980$	−15.3568	−0.490556
$981$	−5.66436	−0.180849
$982$	41.8972	1.33699
$983$	−1.48974	−0.0475153	−0.0237577	−	0.999718i	$-0.507563\pi$
$983$	−1.48974	−0.0475153	−0.0237577	+	0.999718i	$0.507563\pi$
$984$	5.10957	0.162887
$985$	87.8336	2.79861
$986$	10.3896	0.330873
$987$	−14.5860	−0.464277
$988$	15.9520	0.507500
$989$	37.8720	1.20426
$990$	−3.07838	−0.0978373
$991$	−26.4391	−0.839865	−0.419932	−	0.907555i	$-0.637946\pi$
$991$	−26.4391	−0.839865	−0.419932	+	0.907555i	$0.637946\pi$
$992$	12.2679	0.389507
$993$	24.1761	0.767204
$994$	5.69102	0.180508
$995$	−58.9048	−1.86741
$996$	−4.54495	−0.144012
$997$	18.9060	0.598760	0.299380	−	0.954134i	$-0.403220\pi$
$997$	18.9060	0.598760	0.299380	+	0.954134i	$0.403220\pi$
$998$	4.98932	0.157934
$999$	−56.0882	−1.77455

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	187.2.a.e.1.3	✓	3
3.2	odd	2		1683.2.a.v.1.1		3
4.3	odd	2		2992.2.a.r.1.2		3
5.4	even	2		4675.2.a.bc.1.1		3
7.6	odd	2		9163.2.a.j.1.3		3
11.10	odd	2		2057.2.a.p.1.1		3
17.16	even	2		3179.2.a.t.1.3		3

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
187.2.a.e.1.3	✓	3	1.1	even	1	trivial
1683.2.a.v.1.1		3	3.2	odd	2
2057.2.a.p.1.1		3	11.10	odd	2
2992.2.a.r.1.2		3	4.3	odd	2
3179.2.a.t.1.3		3	17.16	even	2
4675.2.a.bc.1.1		3	5.4	even	2
9163.2.a.j.1.3		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)

\(f(q)\)	\(=\)	\(q+1.17009 q^{2} -1.53919 q^{3} -0.630898 q^{4} -4.17009 q^{5} -1.80098 q^{6} +1.07838 q^{7} -3.07838 q^{8} -0.630898 q^{9} +O(q^{10})\)	\(q+1.17009 q^{2} -1.53919 q^{3} -0.630898 q^{4} -4.17009 q^{5} -1.80098 q^{6} +1.07838 q^{7} -3.07838 q^{8} -0.630898 q^{9} -4.87936 q^{10} -1.00000 q^{11} +0.971071 q^{12} +5.51026 q^{13} +1.26180 q^{14} +6.41855 q^{15} -2.34017 q^{16} -1.00000 q^{17} -0.738205 q^{18} -4.58864 q^{19} +2.63090 q^{20} -1.65983 q^{21} -1.17009 q^{22} -5.53919 q^{23} +4.73820 q^{24} +12.3896 q^{25} +6.44748 q^{26} +5.58864 q^{27} -0.680346 q^{28} -8.87936 q^{29} +7.51026 q^{30} +3.58864 q^{31} +3.41855 q^{32} +1.53919 q^{33} -1.17009 q^{34} -4.49693 q^{35} +0.398032 q^{36} -10.0361 q^{37} -5.36910 q^{38} -8.48133 q^{39} +12.8371 q^{40} +1.07838 q^{41} -1.94214 q^{42} -6.83710 q^{43} +0.630898 q^{44} +2.63090 q^{45} -6.48133 q^{46} +8.78765 q^{47} +3.60197 q^{48} -5.83710 q^{49} +14.4969 q^{50} +1.53919 q^{51} -3.47641 q^{52} -3.95055 q^{53} +6.53919 q^{54} +4.17009 q^{55} -3.31965 q^{56} +7.06278 q^{57} -10.3896 q^{58} +8.31124 q^{59} -4.04945 q^{60} -3.07838 q^{61} +4.19902 q^{62} -0.680346 q^{63} +8.68035 q^{64} -22.9783 q^{65} +1.80098 q^{66} +1.49693 q^{67} +0.630898 q^{68} +8.52586 q^{69} -5.26180 q^{70} +4.51026 q^{71} +1.94214 q^{72} -4.53919 q^{73} -11.7431 q^{74} -19.0700 q^{75} +2.89496 q^{76} -1.07838 q^{77} -9.92389 q^{78} +7.80098 q^{79} +9.75872 q^{80} -6.70928 q^{81} +1.26180 q^{82} -4.68035 q^{83} +1.04718 q^{84} +4.17009 q^{85} -8.00000 q^{86} +13.6670 q^{87} +3.07838 q^{88} -1.18342 q^{89} +3.07838 q^{90} +5.94214 q^{91} +3.49466 q^{92} -5.52359 q^{93} +10.2823 q^{94} +19.1350 q^{95} -5.26180 q^{96} -8.80098 q^{97} -6.82991 q^{98} +0.630898 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 3 q - 2 q^{2} - 3 q^{3} + 2 q^{4} - 7 q^{5} + 4 q^{6} - 6 q^{8} + 2 q^{9}+O(q^{10}) \) 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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