LMFDB - Embedded newform 6031.2.a.e.1.20

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [6031,2,Mod(1,6031)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(6031, 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("6031.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 6031 = 37 \cdot 163 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	6031.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:	$48.1577774590$
Analytic rank:	$0$
Dimension:	$134$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.20
Character	$\chi$	$=$	6031.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-2.07881 q^{2} +1.94163 q^{3} +2.32147 q^{4} -0.214355 q^{5} -4.03630 q^{6} -5.01421 q^{7} -0.668275 q^{8} +0.769946 q^{9} +O(q^{10})$	\(q-2.07881 q^{2} +1.94163 q^{3} +2.32147 q^{4} -0.214355 q^{5} -4.03630 q^{6} -5.01421 q^{7} -0.668275 q^{8} +0.769946 q^{9} +0.445604 q^{10} -5.86836 q^{11} +4.50745 q^{12} -0.535154 q^{13} +10.4236 q^{14} -0.416198 q^{15} -3.25372 q^{16} +1.58341 q^{17} -1.60057 q^{18} -3.37117 q^{19} -0.497618 q^{20} -9.73577 q^{21} +12.1992 q^{22} -5.32004 q^{23} -1.29755 q^{24} -4.95405 q^{25} +1.11249 q^{26} -4.32995 q^{27} -11.6403 q^{28} -10.5945 q^{29} +0.865199 q^{30} -8.88257 q^{31} +8.10043 q^{32} -11.3942 q^{33} -3.29162 q^{34} +1.07482 q^{35} +1.78740 q^{36} +1.00000 q^{37} +7.00804 q^{38} -1.03907 q^{39} +0.143248 q^{40} +0.616315 q^{41} +20.2389 q^{42} +8.31253 q^{43} -13.6232 q^{44} -0.165041 q^{45} +11.0594 q^{46} -9.25723 q^{47} -6.31753 q^{48} +18.1423 q^{49} +10.2986 q^{50} +3.07441 q^{51} -1.24234 q^{52} +11.5898 q^{53} +9.00116 q^{54} +1.25791 q^{55} +3.35087 q^{56} -6.54559 q^{57} +22.0240 q^{58} +12.2264 q^{59} -0.966192 q^{60} -4.97536 q^{61} +18.4652 q^{62} -3.86067 q^{63} -10.3318 q^{64} +0.114713 q^{65} +23.6865 q^{66} +0.693082 q^{67} +3.67584 q^{68} -10.3296 q^{69} -2.23435 q^{70} -16.5701 q^{71} -0.514535 q^{72} -9.07592 q^{73} -2.07881 q^{74} -9.61896 q^{75} -7.82608 q^{76} +29.4252 q^{77} +2.16004 q^{78} +13.8492 q^{79} +0.697450 q^{80} -10.7170 q^{81} -1.28120 q^{82} +7.17977 q^{83} -22.6013 q^{84} -0.339412 q^{85} -17.2802 q^{86} -20.5707 q^{87} +3.92168 q^{88} +3.07571 q^{89} +0.343091 q^{90} +2.68338 q^{91} -12.3503 q^{92} -17.2467 q^{93} +19.2441 q^{94} +0.722627 q^{95} +15.7281 q^{96} +8.65701 q^{97} -37.7146 q^{98} -4.51832 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 134 q + 9 q^{2} + 7 q^{3} + 149 q^{4} + 22 q^{5} + 20 q^{6} + 11 q^{7} + 27 q^{8} + 181 q^{9}+O(q^{10}) $ 134 * q + 9 * q^2 + 7 * q^3 + 149 * q^4 + 22 * q^5 + 20 * q^6 + 11 * q^7 + 27 * q^8 + 181 * q^9	\( 134 q + 9 q^{2} + 7 q^{3} + 149 q^{4} + 22 q^{5} + 20 q^{6} + 11 q^{7} + 27 q^{8} + 181 q^{9} + 15 q^{10} + 20 q^{11} + 28 q^{12} + 11 q^{13} + 17 q^{14} - 13 q^{15} + 143 q^{16} + 76 q^{17} + 23 q^{18} + 15 q^{19} + 67 q^{20} + 63 q^{21} + 2 q^{22} + 22 q^{23} + 33 q^{24} + 160 q^{25} + 65 q^{26} + 31 q^{27} + 10 q^{28} + 73 q^{29} + 20 q^{30} + 10 q^{31} + 53 q^{32} + 72 q^{33} - 7 q^{34} + 52 q^{35} + 201 q^{36} + 134 q^{37} + 70 q^{38} + 6 q^{39} + 11 q^{40} + 182 q^{41} - 15 q^{42} + 12 q^{43} + 33 q^{44} + 29 q^{45} + 24 q^{46} + 80 q^{47} + 21 q^{48} + 229 q^{49} + 37 q^{50} + 57 q^{51} - 15 q^{52} + 75 q^{53} + 95 q^{54} - 9 q^{55} + 39 q^{56} + 19 q^{57} - 21 q^{58} + 91 q^{59} + 62 q^{60} + 58 q^{61} + 108 q^{62} + 9 q^{63} + 167 q^{64} + 76 q^{65} + 105 q^{66} - 17 q^{67} + 109 q^{68} + 48 q^{69} - 55 q^{70} + 56 q^{71} + 48 q^{72} + 54 q^{73} + 9 q^{74} + 28 q^{75} + 82 q^{76} + 156 q^{77} + 16 q^{78} - 2 q^{79} + 98 q^{80} + 270 q^{81} - 42 q^{82} + 130 q^{83} + 229 q^{84} + 22 q^{85} + 72 q^{86} + 22 q^{87} + 61 q^{88} + 157 q^{89} + 176 q^{90} + 31 q^{91} - 18 q^{92} + 36 q^{93} + 83 q^{94} + 98 q^{95} + 111 q^{96} + 35 q^{97} + 53 q^{98} + 55 q^{99}+O(q^{100}) \) 134 * q + 9 * q^2 + 7 * q^3 + 149 * q^4 + 22 * q^5 + 20 * q^6 + 11 * q^7 + 27 * q^8 + 181 * q^9 + 15 * q^10 + 20 * q^11 + 28 * q^12 + 11 * q^13 + 17 * q^14 - 13 * q^15 + 143 * q^16 + 76 * q^17 + 23 * q^18 + 15 * q^19 + 67 * q^20 + 63 * q^21 + 2 * q^22 + 22 * q^23 + 33 * q^24 + 160 * q^25 + 65 * q^26 + 31 * q^27 + 10 * q^28 + 73 * q^29 + 20 * q^30 + 10 * q^31 + 53 * q^32 + 72 * q^33 - 7 * q^34 + 52 * q^35 + 201 * q^36 + 134 * q^37 + 70 * q^38 + 6 * q^39 + 11 * q^40 + 182 * q^41 - 15 * q^42 + 12 * q^43 + 33 * q^44 + 29 * q^45 + 24 * q^46 + 80 * q^47 + 21 * q^48 + 229 * q^49 + 37 * q^50 + 57 * q^51 - 15 * q^52 + 75 * q^53 + 95 * q^54 - 9 * q^55 + 39 * q^56 + 19 * q^57 - 21 * q^58 + 91 * q^59 + 62 * q^60 + 58 * q^61 + 108 * q^62 + 9 * q^63 + 167 * q^64 + 76 * q^65 + 105 * q^66 - 17 * q^67 + 109 * q^68 + 48 * q^69 - 55 * q^70 + 56 * q^71 + 48 * q^72 + 54 * q^73 + 9 * q^74 + 28 * q^75 + 82 * q^76 + 156 * q^77 + 16 * q^78 - 2 * q^79 + 98 * q^80 + 270 * q^81 - 42 * q^82 + 130 * q^83 + 229 * q^84 + 22 * q^85 + 72 * q^86 + 22 * q^87 + 61 * q^88 + 157 * q^89 + 176 * q^90 + 31 * q^91 - 18 * q^92 + 36 * q^93 + 83 * q^94 + 98 * q^95 + 111 * q^96 + 35 * q^97 + 53 * q^98 + 55 * 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 $

$2$	−2.07881	−1.46994	−0.734972	−	0.678098i	$-0.762805\pi$
$2$	−2.07881	−1.46994	−0.734972	+	0.678098i	$0.762805\pi$
$3$	1.94163	1.12100	0.560502	−	0.828153i	$-0.310608\pi$
$3$	1.94163	1.12100	0.560502	+	0.828153i	$0.310608\pi$
$4$	2.32147	1.16073
$5$	−0.214355	−0.0958623	−0.0479312	−	0.998851i	$-0.515263\pi$
$5$	−0.214355	−0.0958623	−0.0479312	+	0.998851i	$0.515263\pi$
$6$	−4.03630	−1.64781
$7$	−5.01421	−1.89519	−0.947597	−	0.319467i	$-0.896496\pi$
$7$	−5.01421	−1.89519	−0.947597	+	0.319467i	$0.896496\pi$
$8$	−0.668275	−0.236271
$9$	0.769946	0.256649
$10$	0.445604	0.140912
$11$	−5.86836	−1.76938	−0.884689	−	0.466181i	$-0.845629\pi$
$11$	−5.86836	−1.76938	−0.884689	+	0.466181i	$0.845629\pi$
$12$	4.50745	1.30119
$13$	−0.535154	−0.148425	−0.0742126	−	0.997242i	$-0.523644\pi$
$13$	−0.535154	−0.148425	−0.0742126	+	0.997242i	$0.523644\pi$
$14$	10.4236	2.78583
$15$	−0.416198	−0.107462
$16$	−3.25372	−0.813430
$17$	1.58341	0.384034	0.192017	−	0.981392i	$-0.438497\pi$
$17$	1.58341	0.384034	0.192017	+	0.981392i	$0.438497\pi$
$18$	−1.60057	−0.377259
$19$	−3.37117	−0.773400	−0.386700	−	0.922206i	$-0.626385\pi$
$19$	−3.37117	−0.773400	−0.386700	+	0.922206i	$0.626385\pi$
$20$	−0.497618	−0.111271
$21$	−9.73577	−2.12452
$22$	12.1992	2.60089
$23$	−5.32004	−1.10931	−0.554653	−	0.832082i	$-0.687149\pi$
$23$	−5.32004	−1.10931	−0.554653	+	0.832082i	$0.687149\pi$
$24$	−1.29755	−0.264860
$25$	−4.95405	−0.990810
$26$	1.11249	0.218177
$27$	−4.32995	−0.833300
$28$	−11.6403	−2.19982
$29$	−10.5945	−1.96735	−0.983677	−	0.179945i	$-0.942408\pi$
$29$	−10.5945	−1.96735	−0.983677	+	0.179945i	$0.942408\pi$
$30$	0.865199	0.157963
$31$	−8.88257	−1.59536	−0.797678	−	0.603084i	$-0.793938\pi$
$31$	−8.88257	−1.59536	−0.797678	+	0.603084i	$0.793938\pi$
$32$	8.10043	1.43197
$33$	−11.3942	−1.98348
$34$	−3.29162	−0.564508
$35$	1.07482	0.181678
$36$	1.78740	0.297901
$37$	1.00000	0.164399
$37$	1.00000	0.164399
$38$	7.00804	1.13685
$39$	−1.03907	−0.166385
$40$	0.143248	0.0226495
$41$	0.616315	0.0962522	0.0481261	−	0.998841i	$-0.484675\pi$
$41$	0.616315	0.0962522	0.0481261	+	0.998841i	$0.484675\pi$
$42$	20.2389	3.12292
$43$	8.31253	1.26765	0.633824	−	0.773477i	$-0.281484\pi$
$43$	8.31253	1.26765	0.633824	+	0.773477i	$0.281484\pi$
$44$	−13.6232	−2.05378
$45$	−0.165041	−0.0246029
$46$	11.0594	1.63062
$47$	−9.25723	−1.35031	−0.675153	−	0.737678i	$-0.735922\pi$
$47$	−9.25723	−1.35031	−0.675153	+	0.737678i	$0.735922\pi$
$48$	−6.31753	−0.911857
$49$	18.1423	2.59176
$50$	10.2986	1.45644
$51$	3.07441	0.430503
$52$	−1.24234	−0.172282
$53$	11.5898	1.59198	0.795992	−	0.605307i	$-0.206950\pi$
$53$	11.5898	1.59198	0.795992	+	0.605307i	$0.206950\pi$
$54$	9.00116	1.22490
$55$	1.25791	0.169617
$56$	3.35087	0.447779
$57$	−6.54559	−0.866984
$58$	22.0240	2.89190
$59$	12.2264	1.59175	0.795874	−	0.605463i	$-0.207012\pi$
$59$	12.2264	1.59175	0.795874	+	0.605463i	$0.207012\pi$
$60$	−0.966192	−0.124735
$61$	−4.97536	−0.637029	−0.318515	−	0.947918i	$-0.603184\pi$
$61$	−4.97536	−0.637029	−0.318515	+	0.947918i	$0.603184\pi$
$62$	18.4652	2.34508
$63$	−3.86067	−0.486399
$64$	−10.3318	−1.29148
$65$	0.114713	0.0142284
$66$	23.6865	2.91560
$67$	0.693082	0.0846735	0.0423367	−	0.999103i	$-0.486520\pi$
$67$	0.693082	0.0846735	0.0423367	+	0.999103i	$0.486520\pi$
$68$	3.67584	0.445761
$69$	−10.3296	−1.24354
$70$	−2.23435	−0.267056
$71$	−16.5701	−1.96651	−0.983255	−	0.182234i	$-0.941667\pi$
$71$	−16.5701	−1.96651	−0.983255	+	0.182234i	$0.941667\pi$
$72$	−0.514535	−0.0606386
$73$	−9.07592	−1.06226	−0.531128	−	0.847291i	$-0.678232\pi$
$73$	−9.07592	−1.06226	−0.531128	+	0.847291i	$0.678232\pi$
$74$	−2.07881	−0.241657
$75$	−9.61896	−1.11070
$76$	−7.82608	−0.897712
$77$	29.4252	3.35332
$78$	2.16004	0.244577
$79$	13.8492	1.55815	0.779076	−	0.626929i	$-0.215689\pi$
$79$	13.8492	1.55815	0.779076	+	0.626929i	$0.215689\pi$
$80$	0.697450	0.0779773
$81$	−10.7170	−1.19078
$82$	−1.28120	−0.141485
$83$	7.17977	0.788082	0.394041	−	0.919093i	$-0.371077\pi$
$83$	7.17977	0.788082	0.394041	+	0.919093i	$0.371077\pi$
$84$	−22.6013	−2.46600
$85$	−0.339412	−0.0368144
$86$	−17.2802	−1.86337
$87$	−20.5707	−2.20541
$88$	3.92168	0.418053
$89$	3.07571	0.326025	0.163012	−	0.986624i	$-0.447879\pi$
$89$	3.07571	0.326025	0.163012	+	0.986624i	$0.447879\pi$
$90$	0.343091	0.0361649
$91$	2.68338	0.281295
$92$	−12.3503	−1.28761
$93$	−17.2467	−1.78840
$94$	19.2441	1.98487
$95$	0.722627	0.0741399
$96$	15.7281	1.60524
$97$	8.65701	0.878986	0.439493	−	0.898246i	$-0.355158\pi$
$97$	8.65701	0.878986	0.439493	+	0.898246i	$0.355158\pi$
$98$	−37.7146	−3.80975
$99$	−4.51832	−0.454108
$100$	−11.5007	−1.15007
$101$	−17.4864	−1.73996	−0.869981	−	0.493085i	$-0.835869\pi$
$101$	−17.4864	−1.73996	−0.869981	+	0.493085i	$0.835869\pi$
$102$	−6.39112	−0.632816
$103$	16.8941	1.66462	0.832312	−	0.554307i	$-0.187017\pi$
$103$	16.8941	1.66462	0.832312	+	0.554307i	$0.187017\pi$
$104$	0.357630	0.0350685
$105$	2.08691	0.203661
$106$	−24.0931	−2.34013
$107$	−4.11697	−0.398002	−0.199001	−	0.979999i	$-0.563770\pi$
$107$	−4.11697	−0.398002	−0.199001	+	0.979999i	$0.563770\pi$
$108$	−10.0518	−0.967240
$109$	−4.66340	−0.446672	−0.223336	−	0.974741i	$-0.571695\pi$
$109$	−4.66340	−0.446672	−0.223336	+	0.974741i	$0.571695\pi$
$110$	−2.61496	−0.249327
$111$	1.94163	0.184292
$112$	16.3148	1.54161
$113$	2.04084	0.191986	0.0959929	−	0.995382i	$-0.469397\pi$
$113$	2.04084	0.191986	0.0959929	+	0.995382i	$0.469397\pi$
$114$	13.6071	1.27442
$115$	1.14038	0.106341
$116$	−24.5949	−2.28358
$117$	−0.412040	−0.0380931
$118$	−25.4165	−2.33978
$119$	−7.93957	−0.727819
$120$	0.278135	0.0253901
$121$	23.4377	2.13070
$122$	10.3428	0.936397
$123$	1.19666	0.107899
$124$	−20.6206	−1.85178
$125$	2.13370	0.190844
$126$	8.02562	0.714979
$127$	−10.0742	−0.893943	−0.446972	−	0.894548i	$-0.647497\pi$
$127$	−10.0742	−0.893943	−0.446972	+	0.894548i	$0.647497\pi$
$128$	5.27714	0.466438
$129$	16.1399	1.42104
$130$	−0.238467	−0.0209149
$131$	4.73602	0.413788	0.206894	−	0.978363i	$-0.433664\pi$
$131$	4.73602	0.413788	0.206894	+	0.978363i	$0.433664\pi$
$132$	−26.4513	−2.30229
$133$	16.9038	1.46574
$134$	−1.44079	−0.124465
$135$	0.928145	0.0798820
$136$	−1.05815	−0.0907360
$137$	−10.3990	−0.888443	−0.444221	−	0.895917i	$-0.646520\pi$
$137$	−10.3990	−0.888443	−0.444221	+	0.895917i	$0.646520\pi$
$138$	21.4733	1.82793
$139$	6.79753	0.576559	0.288279	−	0.957546i	$-0.406917\pi$
$139$	6.79753	0.576559	0.288279	+	0.957546i	$0.406917\pi$
$140$	2.49516	0.210880
$141$	−17.9742	−1.51370
$142$	34.4462	2.89066
$143$	3.14048	0.262620
$144$	−2.50519	−0.208766
$145$	2.27099	0.188595
$146$	18.8672	1.56146
$147$	35.2258	2.90538
$148$	2.32147	0.190824
$149$	13.9595	1.14361	0.571805	−	0.820390i	$-0.306243\pi$
$149$	13.9595	1.14361	0.571805	+	0.820390i	$0.306243\pi$
$150$	19.9960	1.63267
$151$	−17.5222	−1.42594	−0.712968	−	0.701197i	$-0.752650\pi$
$151$	−17.5222	−1.42594	−0.712968	+	0.701197i	$0.752650\pi$
$152$	2.25287	0.182732
$153$	1.21914	0.0985617
$154$	−61.1696	−4.92919
$155$	1.90402	0.152935
$156$	−2.41218	−0.193129
$157$	−0.607351	−0.0484719	−0.0242359	−	0.999706i	$-0.507715\pi$
$157$	−0.607351	−0.0484719	−0.0242359	+	0.999706i	$0.507715\pi$
$158$	−28.7898	−2.29040
$159$	22.5032	1.78462
$160$	−1.73636	−0.137272
$161$	26.6758	2.10235
$162$	22.2787	1.75038
$163$	−1.00000	−0.0783260
$163$	−1.00000	−0.0783260
$164$	1.43076	0.111723
$165$	2.44240	0.190141
$166$	−14.9254	−1.15844
$167$	−13.7612	−1.06487	−0.532437	−	0.846470i	$-0.678724\pi$
$167$	−13.7612	−1.06487	−0.532437	+	0.846470i	$0.678724\pi$
$168$	6.50617	0.501962
$169$	−12.7136	−0.977970
$170$	0.705574	0.0541151
$171$	−2.59562	−0.198492
$172$	19.2973	1.47140
$173$	20.7185	1.57519	0.787597	−	0.616190i	$-0.211325\pi$
$173$	20.7185	1.57519	0.787597	+	0.616190i	$0.211325\pi$
$174$	42.7627	3.24183
$175$	24.8407	1.87778
$176$	19.0940	1.43927
$177$	23.7393	1.78435
$178$	−6.39383	−0.479238
$179$	8.79599	0.657443	0.328722	−	0.944427i	$-0.393382\pi$
$179$	8.79599	0.657443	0.328722	+	0.944427i	$0.393382\pi$
$180$	−0.383139	−0.0285575
$181$	−20.7838	−1.54485	−0.772423	−	0.635108i	$-0.780956\pi$
$181$	−20.7838	−1.54485	−0.772423	+	0.635108i	$0.780956\pi$
$182$	−5.57825	−0.413487
$183$	−9.66033	−0.714112
$184$	3.55525	0.262097
$185$	−0.214355	−0.0157597
$186$	35.8527	2.62885
$187$	−9.29204	−0.679501
$188$	−21.4904	−1.56735
$189$	21.7113	1.57926
$190$	−1.50221	−0.108982
$191$	−9.64412	−0.697824	−0.348912	−	0.937155i	$-0.613449\pi$
$191$	−9.64412	−0.697824	−0.348912	+	0.937155i	$0.613449\pi$
$192$	−20.0607	−1.44775
$193$	0.761303	0.0547998	0.0273999	−	0.999625i	$-0.491277\pi$
$193$	0.761303	0.0547998	0.0273999	+	0.999625i	$0.491277\pi$
$194$	−17.9963	−1.29206
$195$	0.222730	0.0159501
$196$	42.1169	3.00835
$197$	5.14022	0.366226	0.183113	−	0.983092i	$-0.441383\pi$
$197$	5.14022	0.366226	0.183113	+	0.983092i	$0.441383\pi$
$198$	9.39275	0.667514
$199$	−24.3254	−1.72438	−0.862190	−	0.506585i	$-0.830908\pi$
$199$	−24.3254	−1.72438	−0.862190	+	0.506585i	$0.830908\pi$
$200$	3.31067	0.234100
$201$	1.34571	0.0949192
$202$	36.3510	2.55765
$203$	53.1232	3.72852
$204$	7.13715	0.499700
$205$	−0.132110	−0.00922696
$206$	−35.1197	−2.44690
$207$	−4.09614	−0.284702
$208$	1.74124	0.120733
$209$	19.7833	1.36844
$210$	−4.33830	−0.299371
$211$	5.10634	0.351535	0.175768	−	0.984432i	$-0.443759\pi$
$211$	5.10634	0.351535	0.175768	+	0.984432i	$0.443759\pi$
$212$	26.9054	1.84787
$213$	−32.1731	−2.20446
$214$	8.55841	0.585041
$215$	−1.78183	−0.121520
$216$	2.89360	0.196884
$217$	44.5391	3.02351
$218$	9.69433	0.656583
$219$	−17.6221	−1.19079
$220$	2.92020	0.196880
$221$	−0.847370	−0.0570003
$222$	−4.03630	−0.270899
$223$	−16.4421	−1.10104	−0.550521	−	0.834821i	$-0.685571\pi$
$223$	−16.4421	−1.10104	−0.550521	+	0.834821i	$0.685571\pi$
$224$	−40.6173	−2.71386
$225$	−3.81435	−0.254290
$226$	−4.24252	−0.282208
$227$	5.86403	0.389209	0.194605	−	0.980882i	$-0.437658\pi$
$227$	5.86403	0.389209	0.194605	+	0.980882i	$0.437658\pi$
$228$	−15.1954	−1.00634
$229$	−3.54618	−0.234338	−0.117169	−	0.993112i	$-0.537382\pi$
$229$	−3.54618	−0.234338	−0.117169	+	0.993112i	$0.537382\pi$
$230$	−2.37063	−0.156315
$231$	57.1331	3.75908
$232$	7.08005	0.464828
$233$	−21.0714	−1.38043	−0.690217	−	0.723603i	$-0.742485\pi$
$233$	−21.0714	−1.38043	−0.690217	+	0.723603i	$0.742485\pi$
$234$	0.856554	0.0559947
$235$	1.98433	0.129443
$236$	28.3833	1.84760
$237$	26.8900	1.74669
$238$	16.5049	1.06985
$239$	2.21596	0.143339	0.0716693	−	0.997428i	$-0.477167\pi$
$239$	2.21596	0.143339	0.0716693	+	0.997428i	$0.477167\pi$
$240$	1.35419	0.0874128
$241$	−13.5136	−0.870487	−0.435244	−	0.900313i	$-0.643338\pi$
$241$	−13.5136	−0.870487	−0.435244	+	0.900313i	$0.643338\pi$
$242$	−48.7226	−3.13201
$243$	−7.81869	−0.501569
$244$	−11.5501	−0.739422
$245$	−3.88890	−0.248452
$246$	−2.48763	−0.158606
$247$	1.80410	0.114792
$248$	5.93600	0.376936
$249$	13.9405	0.883443
$250$	−4.43556	−0.280530
$251$	26.0652	1.64522	0.822611	−	0.568605i	$-0.192517\pi$
$251$	26.0652	1.64522	0.822611	+	0.568605i	$0.192517\pi$
$252$	−8.96243	−0.564580
$253$	31.2200	1.96278
$254$	20.9424	1.31405
$255$	−0.659014	−0.0412690
$256$	9.69350	0.605844
$257$	−8.59092	−0.535887	−0.267943	−	0.963435i	$-0.586344\pi$
$257$	−8.59092	−0.535887	−0.267943	+	0.963435i	$0.586344\pi$
$258$	−33.5518	−2.08885
$259$	−5.01421	−0.311568
$260$	0.266302	0.0165154
$261$	−8.15721	−0.504918
$262$	−9.84531	−0.608245
$263$	22.4544	1.38459	0.692297	−	0.721612i	$-0.256599\pi$
$263$	22.4544	1.38459	0.692297	+	0.721612i	$0.256599\pi$
$264$	7.61447	0.468638
$265$	−2.48433	−0.152611
$266$	−35.1398	−2.15456
$267$	5.97190	0.365475
$268$	1.60897	0.0982834
$269$	3.93197	0.239737	0.119868	−	0.992790i	$-0.461753\pi$
$269$	3.93197	0.239737	0.119868	+	0.992790i	$0.461753\pi$
$270$	−1.92944	−0.117422
$271$	−23.0858	−1.40236	−0.701181	−	0.712983i	$-0.747344\pi$
$271$	−23.0858	−1.40236	−0.701181	+	0.712983i	$0.747344\pi$
$272$	−5.15198	−0.312385
$273$	5.21014	0.315332
$274$	21.6175	1.30596
$275$	29.0722	1.75312
$276$	−23.9798	−1.44341
$277$	16.1344	0.969424	0.484712	−	0.874674i	$-0.338924\pi$
$277$	16.1344	0.969424	0.484712	+	0.874674i	$0.338924\pi$
$278$	−14.1308	−0.847509
$279$	−6.83909	−0.409446
$280$	−0.718276	−0.0429252
$281$	−15.2607	−0.910378	−0.455189	−	0.890395i	$-0.650428\pi$
$281$	−15.2607	−0.910378	−0.455189	+	0.890395i	$0.650428\pi$
$282$	37.3649	2.22505
$283$	−1.16520	−0.0692639	−0.0346320	−	0.999400i	$-0.511026\pi$
$283$	−1.16520	−0.0692639	−0.0346320	+	0.999400i	$0.511026\pi$
$284$	−38.4670	−2.28260
$285$	1.40308	0.0831111
$286$	−6.52848	−0.386037
$287$	−3.09034	−0.182417
$288$	6.23689	0.367512
$289$	−14.4928	−0.852518
$290$	−4.72096	−0.277224
$291$	16.8088	0.985347
$292$	−21.0695	−1.23300
$293$	−7.05497	−0.412156	−0.206078	−	0.978536i	$-0.566070\pi$
$293$	−7.05497	−0.412156	−0.206078	+	0.978536i	$0.566070\pi$
$294$	−73.2279	−4.27074
$295$	−2.62080	−0.152589
$296$	−0.668275	−0.0388427
$297$	25.4097	1.47442
$298$	−29.0193	−1.68104
$299$	2.84705	0.164649
$300$	−22.3301	−1.28923
$301$	−41.6808	−2.40244
$302$	36.4254	2.09605
$303$	−33.9522	−1.95050
$304$	10.9689	0.629107
$305$	1.06649	0.0610671
$306$	−2.53437	−0.144880
$307$	−15.7524	−0.899038	−0.449519	−	0.893271i	$-0.648405\pi$
$307$	−15.7524	−0.899038	−0.449519	+	0.893271i	$0.648405\pi$
$308$	68.3098	3.89231
$309$	32.8022	1.86605
$310$	−3.95810	−0.224805
$311$	−3.49731	−0.198314	−0.0991571	−	0.995072i	$-0.531615\pi$
$311$	−3.49731	−0.198314	−0.0991571	+	0.995072i	$0.531615\pi$
$312$	0.694388	0.0393120
$313$	−12.4907	−0.706018	−0.353009	−	0.935620i	$-0.614841\pi$
$313$	−12.4907	−0.706018	−0.353009	+	0.935620i	$0.614841\pi$
$314$	1.26257	0.0712509
$315$	0.827553	0.0466273
$316$	32.1504	1.80860
$317$	8.87220	0.498313	0.249156	−	0.968463i	$-0.419847\pi$
$317$	8.87220	0.498313	0.249156	+	0.968463i	$0.419847\pi$
$318$	−46.7800	−2.62329
$319$	62.1725	3.48099
$320$	2.21468	0.123804
$321$	−7.99364	−0.446162
$322$	−55.4541	−3.09034
$323$	−5.33796	−0.297012
$324$	−24.8792	−1.38218
$325$	2.65118	0.147061
$326$	2.07881	0.115135
$327$	−9.05461	−0.500721
$328$	−0.411868	−0.0227416
$329$	46.4177	2.55909
$330$	−5.07731	−0.279496
$331$	−9.53028	−0.523832	−0.261916	−	0.965091i	$-0.584354\pi$
$331$	−9.53028	−0.523832	−0.261916	+	0.965091i	$0.584354\pi$
$332$	16.6676	0.914754
$333$	0.769946	0.0421928
$334$	28.6070	1.56530
$335$	−0.148565	−0.00811700
$336$	31.6775	1.72815
$337$	9.17184	0.499622	0.249811	−	0.968295i	$-0.419632\pi$
$337$	9.17184	0.499622	0.249811	+	0.968295i	$0.419632\pi$
$338$	26.4292	1.43756
$339$	3.96256	0.215217
$340$	−0.787934	−0.0427317
$341$	52.1261	2.82279
$342$	5.39581	0.291772
$343$	−55.8701	−3.01670
$344$	−5.55506	−0.299509
$345$	2.21419	0.119208
$346$	−43.0698	−2.31545
$347$	−21.8294	−1.17186	−0.585932	−	0.810360i	$-0.699271\pi$
$347$	−21.8294	−1.17186	−0.585932	+	0.810360i	$0.699271\pi$
$348$	−47.7542	−2.55990
$349$	16.5931	0.888210	0.444105	−	0.895975i	$-0.353522\pi$
$349$	16.5931	0.888210	0.444105	+	0.895975i	$0.353522\pi$
$350$	−51.6392	−2.76023
$351$	2.31719	0.123683
$352$	−47.5363	−2.53369
$353$	13.5446	0.720909	0.360454	−	0.932777i	$-0.382622\pi$
$353$	13.5446	0.720909	0.360454	+	0.932777i	$0.382622\pi$
$354$	−49.3496	−2.62290
$355$	3.55188	0.188514
$356$	7.14017	0.378428
$357$	−15.4157	−0.815888
$358$	−18.2852	−0.966404
$359$	16.0132	0.845142	0.422571	−	0.906330i	$-0.361128\pi$
$359$	16.0132	0.845142	0.422571	+	0.906330i	$0.361128\pi$
$360$	0.110293	0.00581296
$361$	−7.63519	−0.401852
$362$	43.2056	2.27084
$363$	45.5075	2.38852
$364$	6.22938	0.326508
$365$	1.94547	0.101830
$366$	20.0820	1.04970
$367$	−34.5520	−1.80360	−0.901801	−	0.432153i	$-0.857754\pi$
$367$	−34.5520	−1.80360	−0.901801	+	0.432153i	$0.857754\pi$
$368$	17.3099	0.902342
$369$	0.474529	0.0247030
$370$	0.445604	0.0231658
$371$	−58.1138	−3.01712
$372$	−40.0377	−2.07586
$373$	3.43302	0.177755	0.0888776	−	0.996043i	$-0.471672\pi$
$373$	3.43302	0.177755	0.0888776	+	0.996043i	$0.471672\pi$
$374$	19.3164	0.998829
$375$	4.14286	0.213936
$376$	6.18637	0.319038
$377$	5.66971	0.292005
$378$	−45.1338	−2.32143
$379$	−5.08042	−0.260964	−0.130482	−	0.991451i	$-0.541652\pi$
$379$	−5.08042	−0.260964	−0.130482	+	0.991451i	$0.541652\pi$
$380$	1.67756	0.0860568
$381$	−19.5605	−1.00211
$382$	20.0483	1.02576
$383$	−13.8947	−0.709984	−0.354992	−	0.934869i	$-0.615516\pi$
$383$	−13.8947	−0.709984	−0.354992	+	0.934869i	$0.615516\pi$
$384$	10.2463	0.522878
$385$	−6.30744	−0.321457
$386$	−1.58261	−0.0805527
$387$	6.40020	0.325340
$388$	20.0970	1.02027
$389$	4.89836	0.248357	0.124178	−	0.992260i	$-0.460370\pi$
$389$	4.89836	0.248357	0.124178	+	0.992260i	$0.460370\pi$
$390$	−0.463015	−0.0234457
$391$	−8.42382	−0.426011
$392$	−12.1241	−0.612358
$393$	9.19563	0.463858
$394$	−10.6856	−0.538331
$395$	−2.96863	−0.149368
$396$	−10.4891	−0.527099
$397$	20.7112	1.03947	0.519733	−	0.854329i	$-0.326031\pi$
$397$	20.7112	1.03947	0.519733	+	0.854329i	$0.326031\pi$
$398$	50.5680	2.53474
$399$	32.8210	1.64310
$400$	16.1191	0.805955
$401$	−36.2532	−1.81040	−0.905200	−	0.424986i	$-0.860279\pi$
$401$	−36.2532	−1.81040	−0.905200	+	0.424986i	$0.860279\pi$
$402$	−2.79749	−0.139526
$403$	4.75354	0.236791
$404$	−40.5942	−2.01964
$405$	2.29724	0.114151
$406$	−110.433	−5.48071
$407$	−5.86836	−0.290884
$408$	−2.05455	−0.101715
$409$	21.7676	1.07634	0.538169	−	0.842837i	$-0.319116\pi$
$409$	21.7676	1.07634	0.538169	+	0.842837i	$0.319116\pi$
$410$	0.274632	0.0135631
$411$	−20.1910	−0.995947
$412$	39.2191	1.93219
$413$	−61.3060	−3.01667
$414$	8.51512	0.418495
$415$	−1.53902	−0.0755474
$416$	−4.33498	−0.212540
$417$	13.1983	0.646324
$418$	−41.1258	−2.01153
$419$	−7.71485	−0.376895	−0.188447	−	0.982083i	$-0.560346\pi$
$419$	−7.71485	−0.376895	−0.188447	+	0.982083i	$0.560346\pi$
$420$	4.84469	0.236397
$421$	3.71400	0.181009	0.0905046	−	0.995896i	$-0.471152\pi$
$421$	3.71400	0.181009	0.0905046	+	0.995896i	$0.471152\pi$
$422$	−10.6151	−0.516737
$423$	−7.12756	−0.346554
$424$	−7.74519	−0.376139
$425$	−7.84431	−0.380505
$426$	66.8819	3.24044
$427$	24.9475	1.20729
$428$	−9.55741	−0.461975
$429$	6.09767	0.294398
$430$	3.70409	0.178627
$431$	21.8668	1.05329	0.526644	−	0.850086i	$-0.323450\pi$
$431$	21.8668	1.05329	0.526644	+	0.850086i	$0.323450\pi$
$432$	14.0884	0.677831
$433$	18.2577	0.877409	0.438704	−	0.898631i	$-0.355438\pi$
$433$	18.2577	0.877409	0.438704	+	0.898631i	$0.355438\pi$
$434$	−92.5885	−4.44439
$435$	4.40942	0.211416
$436$	−10.8259	−0.518468
$437$	17.9348	0.857937
$438$	36.6331	1.75040
$439$	−21.7135	−1.03633	−0.518164	−	0.855281i	$-0.673384\pi$
$439$	−21.7135	−1.03633	−0.518164	+	0.855281i	$0.673384\pi$
$440$	−0.840631	−0.0400755
$441$	13.9686	0.665172
$442$	1.76153	0.0837872
$443$	3.25425	0.154614	0.0773069	−	0.997007i	$-0.475368\pi$
$443$	3.25425	0.154614	0.0773069	+	0.997007i	$0.475368\pi$
$444$	4.50745	0.213914
$445$	−0.659293	−0.0312535
$446$	34.1800	1.61847
$447$	27.1043	1.28199
$448$	51.8061	2.44761
$449$	−6.91673	−0.326421	−0.163210	−	0.986591i	$-0.552185\pi$
$449$	−6.91673	−0.326421	−0.163210	+	0.986591i	$0.552185\pi$
$450$	7.92933	0.373792
$451$	−3.61676	−0.170307
$452$	4.73774	0.222845
$453$	−34.0217	−1.59848
$454$	−12.1902	−0.572116
$455$	−0.575195	−0.0269656
$456$	4.37425	0.204843
$457$	−4.01980	−0.188038	−0.0940191	−	0.995570i	$-0.529971\pi$
$457$	−4.01980	−0.188038	−0.0940191	+	0.995570i	$0.529971\pi$
$458$	7.37185	0.344464
$459$	−6.85610	−0.320015
$460$	2.64735	0.123433
$461$	−3.07767	−0.143341	−0.0716707	−	0.997428i	$-0.522833\pi$
$461$	−3.07767	−0.143341	−0.0716707	+	0.997428i	$0.522833\pi$
$462$	−118.769	−5.52564
$463$	−16.7560	−0.778717	−0.389359	−	0.921086i	$-0.627303\pi$
$463$	−16.7560	−0.778717	−0.389359	+	0.921086i	$0.627303\pi$
$464$	34.4716	1.60030
$465$	3.69691	0.171440
$466$	43.8035	2.02916
$467$	9.50960	0.440052	0.220026	−	0.975494i	$-0.429386\pi$
$467$	9.50960	0.440052	0.220026	+	0.975494i	$0.429386\pi$
$468$	−0.956538	−0.0442160
$469$	−3.47526	−0.160473
$470$	−4.12505	−0.190275
$471$	−1.17925	−0.0543371
$472$	−8.17063	−0.376084
$473$	−48.7810	−2.24295
$474$	−55.8993	−2.56754
$475$	16.7010	0.766293
$476$	−18.4315	−0.844805
$477$	8.92353	0.408580
$478$	−4.60657	−0.210700
$479$	−14.2272	−0.650059	−0.325029	−	0.945704i	$-0.605374\pi$
$479$	−14.2272	−0.650059	−0.325029	+	0.945704i	$0.605374\pi$
$480$	−3.37139	−0.153882
$481$	−0.535154	−0.0244009
$482$	28.0923	1.27957
$483$	51.7947	2.35674
$484$	54.4099	2.47318
$485$	−1.85567	−0.0842617
$486$	16.2536	0.737278
$487$	−26.3090	−1.19217	−0.596087	−	0.802920i	$-0.703279\pi$
$487$	−26.3090	−1.19217	−0.596087	+	0.802920i	$0.703279\pi$
$488$	3.32491	0.150511
$489$	−1.94163	−0.0878038
$490$	8.08429	0.365211
$491$	−26.7571	−1.20753	−0.603765	−	0.797163i	$-0.706333\pi$
$491$	−26.7571	−1.20753	−0.603765	+	0.797163i	$0.706333\pi$
$492$	2.77801	0.125242
$493$	−16.7755	−0.755530
$494$	−3.75039	−0.168738
$495$	0.968523	0.0435319
$496$	28.9014	1.29771
$497$	83.0861	3.72692
$498$	−28.9797	−1.29861
$499$	−36.2426	−1.62244	−0.811221	−	0.584740i	$-0.801197\pi$
$499$	−36.2426	−1.62244	−0.811221	+	0.584740i	$0.801197\pi$
$500$	4.95331	0.221519
$501$	−26.7192	−1.19373
$502$	−54.1847	−2.41838
$503$	25.8016	1.15044	0.575218	−	0.818000i	$-0.304917\pi$
$503$	25.8016	1.15044	0.575218	+	0.818000i	$0.304917\pi$
$504$	2.57999	0.114922
$505$	3.74829	0.166797
$506$	−64.9005	−2.88518
$507$	−24.6852	−1.09631
$508$	−23.3870	−1.03763
$509$	18.2191	0.807547	0.403774	−	0.914859i	$-0.367698\pi$
$509$	18.2191	0.807547	0.403774	+	0.914859i	$0.367698\pi$
$510$	1.36997	0.0606632
$511$	45.5086	2.01318
$512$	−30.7053	−1.35699
$513$	14.5970	0.644474
$514$	17.8589	0.787723
$515$	−3.62133	−0.159575
$516$	37.4683	1.64945
$517$	54.3248	2.38920
$518$	10.4236	0.457988
$519$	40.2277	1.76580
$520$	−0.0766597	−0.00336175
$521$	−12.4585	−0.545818	−0.272909	−	0.962040i	$-0.587986\pi$
$521$	−12.4585	−0.545818	−0.272909	+	0.962040i	$0.587986\pi$
$522$	16.9573	0.742202
$523$	43.6020	1.90658	0.953291	−	0.302054i	$-0.0976724\pi$
$523$	43.6020	1.90658	0.953291	+	0.302054i	$0.0976724\pi$
$524$	10.9945	0.480298
$525$	48.2315	2.10500
$526$	−46.6784	−2.03528
$527$	−14.0648	−0.612671
$528$	37.0736	1.61342
$529$	5.30286	0.230559
$530$	5.16446	0.224330
$531$	9.41370	0.408520
$532$	39.2416	1.70134
$533$	−0.329824	−0.0142862
$534$	−12.4145	−0.537227
$535$	0.882491	0.0381534
$536$	−0.463170	−0.0200059
$537$	17.0786	0.736996
$538$	−8.17384	−0.352399
$539$	−106.466	−4.58581
$540$	2.15466	0.0927218
$541$	14.9289	0.641842	0.320921	−	0.947106i	$-0.396008\pi$
$541$	14.9289	0.641842	0.320921	+	0.947106i	$0.396008\pi$
$542$	47.9911	2.06139
$543$	−40.3545	−1.73178
$544$	12.8263	0.549924
$545$	0.999621	0.0428190
$546$	−10.8309	−0.463521
$547$	−34.0960	−1.45784	−0.728919	−	0.684600i	$-0.759977\pi$
$547$	−34.0960	−1.45784	−0.728919	+	0.684600i	$0.759977\pi$
$548$	−24.1409	−1.03125
$549$	−3.83075	−0.163493
$550$	−60.4357	−2.57699
$551$	35.7160	1.52155
$552$	6.90300	0.293811
$553$	−69.4427	−2.95300
$554$	−33.5405	−1.42500
$555$	−0.416198	−0.0176666
$556$	15.7803	0.669232
$557$	5.57082	0.236043	0.118022	−	0.993011i	$-0.462345\pi$
$557$	5.57082	0.236043	0.118022	+	0.993011i	$0.462345\pi$
$558$	14.2172	0.601862
$559$	−4.44849	−0.188151
$560$	−3.49716	−0.147782
$561$	−18.0418	−0.761723
$562$	31.7242	1.33820
$563$	−32.5404	−1.37142	−0.685708	−	0.727877i	$-0.740507\pi$
$563$	−32.5404	−1.37142	−0.685708	+	0.727877i	$0.740507\pi$
$564$	−41.7264	−1.75700
$565$	−0.437463	−0.0184042
$566$	2.42223	0.101814
$567$	53.7374	2.25676
$568$	11.0734	0.464629
$569$	−2.28137	−0.0956402	−0.0478201	−	0.998856i	$-0.515227\pi$
$569$	−2.28137	−0.0956402	−0.0478201	+	0.998856i	$0.515227\pi$
$570$	−2.91674	−0.122169
$571$	−30.0121	−1.25597	−0.627984	−	0.778226i	$-0.716120\pi$
$571$	−30.0121	−1.25597	−0.627984	+	0.778226i	$0.716120\pi$
$572$	7.29053	0.304832
$573$	−18.7254	−0.782263
$574$	6.42423	0.268142
$575$	26.3558	1.09911
$576$	−7.95496	−0.331457
$577$	−18.2072	−0.757977	−0.378989	−	0.925401i	$-0.623728\pi$
$577$	−18.2072	−0.757977	−0.378989	+	0.925401i	$0.623728\pi$
$578$	30.1279	1.25315
$579$	1.47817	0.0614308
$580$	5.27202	0.218909
$581$	−36.0009	−1.49357
$582$	−34.9423	−1.44840
$583$	−68.0133	−2.81682
$584$	6.06521	0.250980
$585$	0.0883227	0.00365169
$586$	14.6660	0.605845
$587$	29.7734	1.22888	0.614441	−	0.788963i	$-0.289382\pi$
$587$	29.7734	1.22888	0.614441	+	0.788963i	$0.289382\pi$
$588$	81.7756	3.37237
$589$	29.9447	1.23385
$590$	5.44815	0.224297
$591$	9.98043	0.410540
$592$	−3.25372	−0.133727
$593$	16.1934	0.664984	0.332492	−	0.943106i	$-0.392111\pi$
$593$	16.1934	0.664984	0.332492	+	0.943106i	$0.392111\pi$
$594$	−52.8221	−2.16732
$595$	1.70188	0.0697704
$596$	32.4066	1.32743
$597$	−47.2310	−1.93304
$598$	−5.91848	−0.242025
$599$	−13.3343	−0.544823	−0.272412	−	0.962181i	$-0.587821\pi$
$599$	−13.3343	−0.544823	−0.272412	+	0.962181i	$0.587821\pi$
$600$	6.42811	0.262427
$601$	17.2080	0.701927	0.350964	−	0.936389i	$-0.385854\pi$
$601$	17.2080	0.701927	0.350964	+	0.936389i	$0.385854\pi$
$602$	86.6467	3.53145
$603$	0.533636	0.0217313
$604$	−40.6772	−1.65513
$605$	−5.02398	−0.204254
$606$	70.5804	2.86713
$607$	−5.96903	−0.242276	−0.121138	−	0.992636i	$-0.538654\pi$
$607$	−5.96903	−0.242276	−0.121138	+	0.992636i	$0.538654\pi$
$608$	−27.3079	−1.10748
$609$	103.146	4.17968
$610$	−2.21704	−0.0897652
$611$	4.95405	0.200419
$612$	2.83020	0.114404
$613$	31.1632	1.25867	0.629335	−	0.777134i	$-0.283327\pi$
$613$	31.1632	1.25867	0.629335	+	0.777134i	$0.283327\pi$
$614$	32.7464	1.32154
$615$	−0.256509	−0.0103435
$616$	−19.6642	−0.792291
$617$	−47.2000	−1.90020	−0.950101	−	0.311943i	$-0.899020\pi$
$617$	−47.2000	−1.90020	−0.950101	+	0.311943i	$0.899020\pi$
$618$	−68.1896	−2.74299
$619$	−25.0066	−1.00510	−0.502550	−	0.864548i	$-0.667605\pi$
$619$	−25.0066	−1.00510	−0.502550	+	0.864548i	$0.667605\pi$
$620$	4.42012	0.177516
$621$	23.0355	0.924384
$622$	7.27026	0.291511
$623$	−15.4223	−0.617880
$624$	3.38086	0.135343
$625$	24.3129	0.972516
$626$	25.9659	1.03781
$627$	38.4119	1.53402
$628$	−1.40995	−0.0562630
$629$	1.58341	0.0631348
$630$	−1.72033	−0.0685396
$631$	10.7729	0.428863	0.214431	−	0.976739i	$-0.431210\pi$
$631$	10.7729	0.428863	0.214431	+	0.976739i	$0.431210\pi$
$632$	−9.25505	−0.368146
$633$	9.91465	0.394072
$634$	−18.4437	−0.732492
$635$	2.15946	0.0856955
$636$	52.2405	2.07147
$637$	−9.70896	−0.384683
$638$	−129.245	−5.11686
$639$	−12.7581	−0.504702
$640$	−1.13118	−0.0447138
$641$	35.8792	1.41714	0.708572	−	0.705638i	$-0.249340\pi$
$641$	35.8792	1.41714	0.708572	+	0.705638i	$0.249340\pi$
$642$	16.6173	0.655833
$643$	−16.8844	−0.665854	−0.332927	−	0.942953i	$-0.608036\pi$
$643$	−16.8844	−0.665854	−0.332927	+	0.942953i	$0.608036\pi$
$644$	61.9271	2.44027
$645$	−3.45966	−0.136224
$646$	11.0966	0.436591
$647$	−6.65066	−0.261465	−0.130732	−	0.991418i	$-0.541733\pi$
$647$	−6.65066	−0.261465	−0.130732	+	0.991418i	$0.541733\pi$
$648$	7.16192	0.281347
$649$	−71.7492	−2.81640
$650$	−5.51132	−0.216172
$651$	86.4786	3.38937
$652$	−2.32147	−0.0909158
$653$	−7.40135	−0.289637	−0.144819	−	0.989458i	$-0.546260\pi$
$653$	−7.40135	−0.289637	−0.144819	+	0.989458i	$0.546260\pi$
$654$	18.8229	0.736032
$655$	−1.01519	−0.0396667
$656$	−2.00532	−0.0782944
$657$	−6.98797	−0.272627
$658$	−96.4938	−3.76172
$659$	28.2404	1.10009	0.550045	−	0.835135i	$-0.314610\pi$
$659$	28.2404	1.10009	0.550045	+	0.835135i	$0.314610\pi$
$660$	5.66997	0.220703
$661$	−25.9347	−1.00874	−0.504372	−	0.863487i	$-0.668276\pi$
$661$	−25.9347	−1.00874	−0.504372	+	0.863487i	$0.668276\pi$
$662$	19.8117	0.770003
$663$	−1.64528	−0.0638975
$664$	−4.79806	−0.186201
$665$	−3.62341	−0.140510
$666$	−1.60057	−0.0620210
$667$	56.3633	2.18240
$668$	−31.9462	−1.23604
$669$	−31.9245	−1.23427
$670$	0.308840	0.0119315
$671$	29.1972	1.12715
$672$	−78.8639	−3.04224
$673$	13.3740	0.515530	0.257765	−	0.966208i	$-0.417014\pi$
$673$	13.3740	0.515530	0.257765	+	0.966208i	$0.417014\pi$
$674$	−19.0665	−0.734416
$675$	21.4508	0.825642
$676$	−29.5143	−1.13516
$677$	0.774107	0.0297514	0.0148757	−	0.999889i	$-0.495265\pi$
$677$	0.774107	0.0297514	0.0148757	+	0.999889i	$0.495265\pi$
$678$	−8.23743	−0.316356
$679$	−43.4081	−1.66585
$680$	0.226820	0.00869817
$681$	11.3858	0.436305
$682$	−108.361	−4.14934
$683$	0.293898	0.0112457	0.00562284	−	0.999984i	$-0.498210\pi$
$683$	0.293898	0.0112457	0.00562284	+	0.999984i	$0.498210\pi$
$684$	−6.02565	−0.230397
$685$	2.22906	0.0851682
$686$	116.144	4.43438
$687$	−6.88539	−0.262694
$688$	−27.0466	−1.03114
$689$	−6.20234	−0.236290
$690$	−4.60290	−0.175229
$691$	47.1710	1.79447	0.897234	−	0.441554i	$-0.145573\pi$
$691$	47.1710	1.79447	0.897234	+	0.441554i	$0.145573\pi$
$692$	48.0973	1.82838
$693$	22.6558	0.860624
$694$	45.3793	1.72257
$695$	−1.45708	−0.0552703
$696$	13.7469	0.521074
$697$	0.975881	0.0369641
$698$	−34.4941	−1.30562
$699$	−40.9130	−1.54747
$700$	57.6669	2.17960
$701$	38.4753	1.45319	0.726596	−	0.687065i	$-0.241101\pi$
$701$	38.4753	1.45319	0.726596	+	0.687065i	$0.241101\pi$
$702$	−4.81701	−0.181806
$703$	−3.37117	−0.127146
$704$	60.6311	2.28512
$705$	3.85284	0.145106
$706$	−28.1568	−1.05970
$707$	87.6806	3.29757
$708$	55.1100	2.07116
$709$	20.2877	0.761919	0.380960	−	0.924592i	$-0.375594\pi$
$709$	20.2877	0.761919	0.380960	+	0.924592i	$0.375594\pi$
$710$	−7.38370	−0.277105
$711$	10.6631	0.399897
$712$	−2.05542	−0.0770301
$713$	47.2556	1.76974
$714$	32.0465	1.19931
$715$	−0.673177	−0.0251754
$716$	20.4196	0.763117
$717$	4.30259	0.160683
$718$	−33.2884	−1.24231
$719$	−3.54633	−0.132256	−0.0661279	−	0.997811i	$-0.521065\pi$
$719$	−3.54633	−0.132256	−0.0661279	+	0.997811i	$0.521065\pi$
$720$	0.536998	0.0200127
$721$	−84.7106	−3.15479
$722$	15.8721	0.590700
$723$	−26.2385	−0.975819
$724$	−48.2489	−1.79316
$725$	52.4858	1.94927
$726$	−94.6016	−3.51099
$727$	−19.3496	−0.717637	−0.358818	−	0.933407i	$-0.616820\pi$
$727$	−19.3496	−0.717637	−0.358818	+	0.933407i	$0.616820\pi$
$728$	−1.79324	−0.0664617
$729$	16.9700	0.628520
$730$	−4.04426	−0.149685
$731$	13.1622	0.486820
$732$	−22.4262	−0.828894
$733$	49.9501	1.84495	0.922475	−	0.386056i	$-0.126163\pi$
$733$	49.9501	1.84495	0.922475	+	0.386056i	$0.126163\pi$
$734$	71.8272	2.65119
$735$	−7.55082	−0.278516
$736$	−43.0946	−1.58849
$737$	−4.06726	−0.149819
$738$	−0.986458	−0.0363120
$739$	37.8290	1.39156	0.695781	−	0.718254i	$-0.255058\pi$
$739$	37.8290	1.39156	0.695781	+	0.718254i	$0.255058\pi$
$740$	−0.497618	−0.0182928
$741$	3.50290	0.128682
$742$	120.808	4.43500
$743$	−32.6742	−1.19870	−0.599351	−	0.800486i	$-0.704575\pi$
$743$	−32.6742	−1.19870	−0.599351	+	0.800486i	$0.704575\pi$
$744$	11.5255	0.422547
$745$	−2.99229	−0.109629
$746$	−7.13662	−0.261290
$747$	5.52803	0.202260
$748$	−21.5712	−0.788721
$749$	20.6434	0.754292
$750$	−8.61224	−0.314475
$751$	−3.08110	−0.112431	−0.0562155	−	0.998419i	$-0.517903\pi$
$751$	−3.08110	−0.112431	−0.0562155	+	0.998419i	$0.517903\pi$
$752$	30.1204	1.09838
$753$	50.6091	1.84430
$754$	−11.7863	−0.429230
$755$	3.75596	0.136694
$756$	50.4021	1.83311
$757$	−7.17170	−0.260660	−0.130330	−	0.991471i	$-0.541604\pi$
$757$	−7.17170	−0.260660	−0.130330	+	0.991471i	$0.541604\pi$
$758$	10.5613	0.383602
$759$	60.6178	2.20028
$760$	−0.482913	−0.0175171
$761$	18.8893	0.684736	0.342368	−	0.939566i	$-0.388771\pi$
$761$	18.8893	0.684736	0.342368	+	0.939566i	$0.388771\pi$
$762$	40.6626	1.47305
$763$	23.3833	0.846531
$764$	−22.3885	−0.809989
$765$	−0.261329	−0.00944836
$766$	28.8844	1.04364
$767$	−6.54304	−0.236255
$768$	18.8212	0.679153
$769$	17.0318	0.614184	0.307092	−	0.951680i	$-0.400644\pi$
$769$	17.0318	0.614184	0.307092	+	0.951680i	$0.400644\pi$
$770$	13.1120	0.472523
$771$	−16.6804	−0.600731
$772$	1.76734	0.0636081
$773$	27.6576	0.994776	0.497388	−	0.867528i	$-0.334292\pi$
$773$	27.6576	0.994776	0.497388	+	0.867528i	$0.334292\pi$
$774$	−13.3048	−0.478232
$775$	44.0047	1.58070
$776$	−5.78526	−0.207679
$777$	−9.73577	−0.349269
$778$	−10.1828	−0.365071
$779$	−2.07770	−0.0744415
$780$	0.517062	0.0185138
$781$	97.2395	3.47950
$782$	17.5116	0.626212
$783$	45.8738	1.63939
$784$	−59.0301	−2.10822
$785$	0.130188	0.00464663
$786$	−19.1160	−0.681845
$787$	−41.8634	−1.49227	−0.746135	−	0.665794i	$-0.768093\pi$
$787$	−41.8634	−1.49227	−0.746135	+	0.665794i	$0.768093\pi$
$788$	11.9329	0.425091
$789$	43.5982	1.55214
$790$	6.17124	0.219563
$791$	−10.2332	−0.363850
$792$	3.01948	0.107293
$793$	2.66258	0.0945511
$794$	−43.0548	−1.52796
$795$	−4.82366	−0.171078
$796$	−56.4706	−2.00155
$797$	12.2399	0.433559	0.216780	−	0.976221i	$-0.430445\pi$
$797$	12.2399	0.433559	0.216780	+	0.976221i	$0.430445\pi$
$798$	−68.2287	−2.41527
$799$	−14.6580	−0.518563
$800$	−40.1299	−1.41881
$801$	2.36813	0.0836737
$802$	75.3637	2.66119
$803$	53.2608	1.87953
$804$	3.12403	0.110176
$805$	−5.71809	−0.201536
$806$	−9.88174	−0.348069
$807$	7.63445	0.268745
$808$	11.6857	0.411103
$809$	34.4978	1.21288	0.606439	−	0.795130i	$-0.292598\pi$
$809$	34.4978	1.21288	0.606439	+	0.795130i	$0.292598\pi$
$810$	−4.77554	−0.167795
$811$	1.11402	0.0391184	0.0195592	−	0.999809i	$-0.493774\pi$
$811$	1.11402	0.0391184	0.0195592	+	0.999809i	$0.493774\pi$
$812$	123.324	4.32782
$813$	−44.8242	−1.57205
$814$	12.1992	0.427583
$815$	0.214355	0.00750852
$816$	−10.0033	−0.350184
$817$	−28.0230	−0.980400
$818$	−45.2507	−1.58216
$819$	2.06606	0.0721938
$820$	−0.306689	−0.0107101
$821$	30.2147	1.05450	0.527250	−	0.849710i	$-0.323223\pi$
$821$	30.2147	1.05450	0.527250	+	0.849710i	$0.323223\pi$
$822$	41.9733	1.46399
$823$	−24.7455	−0.862572	−0.431286	−	0.902215i	$-0.641940\pi$
$823$	−24.7455	−0.862572	−0.431286	+	0.902215i	$0.641940\pi$
$824$	−11.2899	−0.393302
$825$	56.4476	1.96525
$826$	127.444	4.43434
$827$	24.6380	0.856748	0.428374	−	0.903601i	$-0.359087\pi$
$827$	24.6380	0.856748	0.428374	+	0.903601i	$0.359087\pi$
$828$	−9.50907	−0.330463
$829$	−19.9672	−0.693488	−0.346744	−	0.937960i	$-0.612713\pi$
$829$	−19.9672	−0.693488	−0.346744	+	0.937960i	$0.612713\pi$
$830$	3.19933	0.111050
$831$	31.3272	1.08673
$832$	5.52913	0.191688
$833$	28.7268	0.995325
$834$	−27.4369	−0.950061
$835$	2.94978	0.102081
$836$	45.9263	1.58839
$837$	38.4611	1.32941
$838$	16.0377	0.554014
$839$	−43.1519	−1.48977	−0.744885	−	0.667193i	$-0.767496\pi$
$839$	−43.1519	−1.48977	−0.744885	+	0.667193i	$0.767496\pi$
$840$	−1.39463	−0.0481193
$841$	83.2439	2.87048
$842$	−7.72071	−0.266073
$843$	−29.6307	−1.02054
$844$	11.8542	0.408039
$845$	2.72522	0.0937505
$846$	14.8169	0.509415
$847$	−117.522	−4.03809
$848$	−37.7100	−1.29497
$849$	−2.26239	−0.0776451
$850$	16.3069	0.559321
$851$	−5.32004	−0.182369
$852$	−74.6889	−2.55880
$853$	18.7679	0.642602	0.321301	−	0.946977i	$-0.395880\pi$
$853$	18.7679	0.642602	0.321301	+	0.946977i	$0.395880\pi$
$854$	−51.8612	−1.77465
$855$	0.556383	0.0190279
$856$	2.75127	0.0940363
$857$	15.4993	0.529444	0.264722	−	0.964325i	$-0.414720\pi$
$857$	15.4993	0.529444	0.264722	+	0.964325i	$0.414720\pi$
$858$	−12.6759	−0.432749
$859$	−42.4004	−1.44668	−0.723342	−	0.690490i	$-0.757395\pi$
$859$	−42.4004	−1.44668	−0.723342	+	0.690490i	$0.757395\pi$
$860$	−4.13646	−0.141052
$861$	−6.00030	−0.204490
$862$	−45.4571	−1.54827
$863$	36.1676	1.23116	0.615580	−	0.788074i	$-0.288922\pi$
$863$	36.1676	1.23116	0.615580	+	0.788074i	$0.288922\pi$
$864$	−35.0745	−1.19326
$865$	−4.44110	−0.151002
$866$	−37.9543	−1.28974
$867$	−28.1397	−0.955675
$868$	103.396	3.50949
$869$	−81.2719	−2.75696
$870$	−9.16637	−0.310769
$871$	−0.370906	−0.0125677
$872$	3.11643	0.105536
$873$	6.66543	0.225591
$874$	−37.2831	−1.26112
$875$	−10.6988	−0.361686
$876$	−40.9092	−1.38219
$877$	−15.5681	−0.525698	−0.262849	−	0.964837i	$-0.584662\pi$
$877$	−15.5681	−0.525698	−0.262849	+	0.964837i	$0.584662\pi$
$878$	45.1383	1.52334
$879$	−13.6982	−0.462028
$880$	−4.09289	−0.137971
$881$	34.9763	1.17838	0.589190	−	0.807994i	$-0.299447\pi$
$881$	34.9763	1.17838	0.589190	+	0.807994i	$0.299447\pi$
$882$	−29.0382	−0.977766
$883$	−42.7686	−1.43928	−0.719639	−	0.694349i	$-0.755692\pi$
$883$	−42.7686	−1.43928	−0.719639	+	0.694349i	$0.755692\pi$
$884$	−1.96714	−0.0661622
$885$	−5.08863	−0.171052
$886$	−6.76497	−0.227274
$887$	−8.69128	−0.291824	−0.145912	−	0.989298i	$-0.546612\pi$
$887$	−8.69128	−0.291824	−0.145912	+	0.989298i	$0.546612\pi$
$888$	−1.29755	−0.0435428
$889$	50.5143	1.69420
$890$	1.37055	0.0459408
$891$	62.8914	2.10694
$892$	−38.1698	−1.27802
$893$	31.2077	1.04433
$894$	−56.3449	−1.88445
$895$	−1.88546	−0.0630240
$896$	−26.4607	−0.883990
$897$	5.52792	0.184572
$898$	14.3786	0.479820
$899$	94.1065	3.13863
$900$	−8.85490	−0.295163
$901$	18.3515	0.611376
$902$	7.51857	0.250341
$903$	−80.9289	−2.69315
$904$	−1.36384	−0.0453607
$905$	4.45510	0.148093
$906$	70.7248	2.34967
$907$	−43.0162	−1.42833	−0.714165	−	0.699977i	$-0.753194\pi$
$907$	−43.0162	−1.42833	−0.714165	+	0.699977i	$0.753194\pi$
$908$	13.6132	0.451769
$909$	−13.4636	−0.446559
$910$	1.19572	0.0396378
$911$	12.5844	0.416939	0.208469	−	0.978029i	$-0.433152\pi$
$911$	12.5844	0.416939	0.208469	+	0.978029i	$0.433152\pi$
$912$	21.2975	0.705231
$913$	−42.1335	−1.39442
$914$	8.35642	0.276406
$915$	2.07074	0.0684564
$916$	−8.23235	−0.272004
$917$	−23.7474	−0.784209
$918$	14.2526	0.470404
$919$	−1.01551	−0.0334987	−0.0167494	−	0.999860i	$-0.505332\pi$
$919$	−1.01551	−0.0334987	−0.0167494	+	0.999860i	$0.505332\pi$
$920$	−0.762085	−0.0251252
$921$	−30.5855	−1.00782
$922$	6.39791	0.210704
$923$	8.86757	0.291880
$924$	132.633	4.36329
$925$	−4.95405	−0.162888
$926$	34.8326	1.14467
$927$	13.0075	0.427223
$928$	−85.8202	−2.81718
$929$	−9.90446	−0.324955	−0.162477	−	0.986712i	$-0.551948\pi$
$929$	−9.90446	−0.324955	−0.162477	+	0.986712i	$0.551948\pi$
$930$	−7.68519	−0.252007
$931$	−61.1610	−2.00447
$932$	−48.9166	−1.60232
$933$	−6.79050	−0.222311
$934$	−19.7687	−0.646851
$935$	1.99179	0.0651386
$936$	0.275356	0.00900029
$937$	−29.2349	−0.955064	−0.477532	−	0.878614i	$-0.658468\pi$
$937$	−29.2349	−0.955064	−0.477532	+	0.878614i	$0.658468\pi$
$938$	7.22443	0.235886
$939$	−24.2524	−0.791448
$940$	4.60656	0.150249
$941$	−23.2943	−0.759374	−0.379687	−	0.925115i	$-0.623968\pi$
$941$	−23.2943	−0.759374	−0.379687	+	0.925115i	$0.623968\pi$
$942$	2.45145	0.0798725
$943$	−3.27882	−0.106773
$944$	−39.7814	−1.29477
$945$	−4.65392	−0.151392
$946$	101.407	3.29701
$947$	−19.9939	−0.649716	−0.324858	−	0.945763i	$-0.605316\pi$
$947$	−19.9939	−0.649716	−0.324858	+	0.945763i	$0.605316\pi$
$948$	62.4243	2.02745
$949$	4.85702	0.157666
$950$	−34.7182	−1.12641
$951$	17.2266	0.558610
$952$	5.30582	0.171962
$953$	10.0492	0.325526	0.162763	−	0.986665i	$-0.447959\pi$
$953$	10.0492	0.325526	0.162763	+	0.986665i	$0.447959\pi$
$954$	−18.5504	−0.600590
$955$	2.06726	0.0668951
$956$	5.14429	0.166378
$957$	120.716	3.90220
$958$	29.5758	0.955549
$959$	52.1426	1.68377
$960$	4.30010	0.138785
$961$	47.9000	1.54516
$962$	1.11249	0.0358680
$963$	−3.16984	−0.102147
$964$	−31.3714	−1.01040
$965$	−0.163189	−0.00525324
$966$	−107.672	−3.46428
$967$	−38.7090	−1.24480	−0.622399	−	0.782700i	$-0.713842\pi$
$967$	−38.7090	−1.24480	−0.622399	+	0.782700i	$0.713842\pi$
$968$	−15.6628	−0.503422
$969$	−10.3644	−0.332951
$970$	3.85760	0.123860
$971$	13.3189	0.427424	0.213712	−	0.976897i	$-0.431445\pi$
$971$	13.3189	0.427424	0.213712	+	0.976897i	$0.431445\pi$
$972$	−18.1508	−0.582188
$973$	−34.0843	−1.09269
$974$	54.6915	1.75243
$975$	5.14763	0.164856
$976$	16.1884	0.518178
$977$	15.1840	0.485778	0.242889	−	0.970054i	$-0.421905\pi$
$977$	15.1840	0.485778	0.242889	+	0.970054i	$0.421905\pi$
$978$	4.03630	0.129067
$979$	−18.0494	−0.576861
$980$	−9.02795	−0.288387
$981$	−3.59056	−0.114638
$982$	55.6230	1.77500
$983$	−13.6343	−0.434868	−0.217434	−	0.976075i	$-0.569769\pi$
$983$	−13.6343	−0.434868	−0.217434	+	0.976075i	$0.569769\pi$
$984$	−0.799697	−0.0254934
$985$	−1.10183	−0.0351072
$986$	34.8731	1.11059
$987$	90.1263	2.86875
$988$	4.18816	0.133243
$989$	−44.2230	−1.40621
$990$	−2.01338	−0.0639894
$991$	−42.1843	−1.34003	−0.670015	−	0.742348i	$-0.733712\pi$
$991$	−42.1843	−1.34003	−0.670015	+	0.742348i	$0.733712\pi$
$992$	−71.9526	−2.28450
$993$	−18.5043	−0.587217
$994$	−172.721	−5.47836
$995$	5.21426	0.165303
$996$	32.3624	1.02544
$997$	−52.8771	−1.67464	−0.837318	−	0.546716i	$-0.815878\pi$
$997$	−52.8771	−1.67464	−0.837318	+	0.546716i	$0.815878\pi$
$998$	75.3417	2.38490
$999$	−4.32995	−0.136994

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	6031.2.a.e.1.20	✓	134

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
6031.2.a.e.1.20	✓	134	1.1	even	1	trivial

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 6031 = 37 \cdot 163 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	6031.a (trivial)

\(f(q)\)	\(=\)	\(q-2.07881 q^{2} +1.94163 q^{3} +2.32147 q^{4} -0.214355 q^{5} -4.03630 q^{6} -5.01421 q^{7} -0.668275 q^{8} +0.769946 q^{9} +O(q^{10})\)	\(q-2.07881 q^{2} +1.94163 q^{3} +2.32147 q^{4} -0.214355 q^{5} -4.03630 q^{6} -5.01421 q^{7} -0.668275 q^{8} +0.769946 q^{9} +0.445604 q^{10} -5.86836 q^{11} +4.50745 q^{12} -0.535154 q^{13} +10.4236 q^{14} -0.416198 q^{15} -3.25372 q^{16} +1.58341 q^{17} -1.60057 q^{18} -3.37117 q^{19} -0.497618 q^{20} -9.73577 q^{21} +12.1992 q^{22} -5.32004 q^{23} -1.29755 q^{24} -4.95405 q^{25} +1.11249 q^{26} -4.32995 q^{27} -11.6403 q^{28} -10.5945 q^{29} +0.865199 q^{30} -8.88257 q^{31} +8.10043 q^{32} -11.3942 q^{33} -3.29162 q^{34} +1.07482 q^{35} +1.78740 q^{36} +1.00000 q^{37} +7.00804 q^{38} -1.03907 q^{39} +0.143248 q^{40} +0.616315 q^{41} +20.2389 q^{42} +8.31253 q^{43} -13.6232 q^{44} -0.165041 q^{45} +11.0594 q^{46} -9.25723 q^{47} -6.31753 q^{48} +18.1423 q^{49} +10.2986 q^{50} +3.07441 q^{51} -1.24234 q^{52} +11.5898 q^{53} +9.00116 q^{54} +1.25791 q^{55} +3.35087 q^{56} -6.54559 q^{57} +22.0240 q^{58} +12.2264 q^{59} -0.966192 q^{60} -4.97536 q^{61} +18.4652 q^{62} -3.86067 q^{63} -10.3318 q^{64} +0.114713 q^{65} +23.6865 q^{66} +0.693082 q^{67} +3.67584 q^{68} -10.3296 q^{69} -2.23435 q^{70} -16.5701 q^{71} -0.514535 q^{72} -9.07592 q^{73} -2.07881 q^{74} -9.61896 q^{75} -7.82608 q^{76} +29.4252 q^{77} +2.16004 q^{78} +13.8492 q^{79} +0.697450 q^{80} -10.7170 q^{81} -1.28120 q^{82} +7.17977 q^{83} -22.6013 q^{84} -0.339412 q^{85} -17.2802 q^{86} -20.5707 q^{87} +3.92168 q^{88} +3.07571 q^{89} +0.343091 q^{90} +2.68338 q^{91} -12.3503 q^{92} -17.2467 q^{93} +19.2441 q^{94} +0.722627 q^{95} +15.7281 q^{96} +8.65701 q^{97} -37.7146 q^{98} -4.51832 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 134 q + 9 q^{2} + 7 q^{3} + 149 q^{4} + 22 q^{5} + 20 q^{6} + 11 q^{7} + 27 q^{8} + 181 q^{9}+O(q^{10}) \) 134 * q + 9 * q^2 + 7 * q^3 + 149 * q^4 + 22 * q^5 + 20 * q^6 + 11 * q^7 + 27 * q^8 + 181 * q^9	\( 134 q + 9 q^{2} + 7 q^{3} + 149 q^{4} + 22 q^{5} + 20 q^{6} + 11 q^{7} + 27 q^{8} + 181 q^{9} + 15 q^{10} + 20 q^{11} + 28 q^{12} + 11 q^{13} + 17 q^{14} - 13 q^{15} + 143 q^{16} + 76 q^{17} + 23 q^{18} + 15 q^{19} + 67 q^{20} + 63 q^{21} + 2 q^{22} + 22 q^{23} + 33 q^{24} + 160 q^{25} + 65 q^{26} + 31 q^{27} + 10 q^{28} + 73 q^{29} + 20 q^{30} + 10 q^{31} + 53 q^{32} + 72 q^{33} - 7 q^{34} + 52 q^{35} + 201 q^{36} + 134 q^{37} + 70 q^{38} + 6 q^{39} + 11 q^{40} + 182 q^{41} - 15 q^{42} + 12 q^{43} + 33 q^{44} + 29 q^{45} + 24 q^{46} + 80 q^{47} + 21 q^{48} + 229 q^{49} + 37 q^{50} + 57 q^{51} - 15 q^{52} + 75 q^{53} + 95 q^{54} - 9 q^{55} + 39 q^{56} + 19 q^{57} - 21 q^{58} + 91 q^{59} + 62 q^{60} + 58 q^{61} + 108 q^{62} + 9 q^{63} + 167 q^{64} + 76 q^{65} + 105 q^{66} - 17 q^{67} + 109 q^{68} + 48 q^{69} - 55 q^{70} + 56 q^{71} + 48 q^{72} + 54 q^{73} + 9 q^{74} + 28 q^{75} + 82 q^{76} + 156 q^{77} + 16 q^{78} - 2 q^{79} + 98 q^{80} + 270 q^{81} - 42 q^{82} + 130 q^{83} + 229 q^{84} + 22 q^{85} + 72 q^{86} + 22 q^{87} + 61 q^{88} + 157 q^{89} + 176 q^{90} + 31 q^{91} - 18 q^{92} + 36 q^{93} + 83 q^{94} + 98 q^{95} + 111 q^{96} + 35 q^{97} + 53 q^{98} + 55 q^{99}+O(q^{100}) \) 134 * q + 9 * q^2 + 7 * q^3 + 149 * q^4 + 22 * q^5 + 20 * q^6 + 11 * q^7 + 27 * q^8 + 181 * q^9 + 15 * q^10 + 20 * q^11 + 28 * q^12 + 11 * q^13 + 17 * q^14 - 13 * q^15 + 143 * q^16 + 76 * q^17 + 23 * q^18 + 15 * q^19 + 67 * q^20 + 63 * q^21 + 2 * q^22 + 22 * q^23 + 33 * q^24 + 160 * q^25 + 65 * q^26 + 31 * q^27 + 10 * q^28 + 73 * q^29 + 20 * q^30 + 10 * q^31 + 53 * q^32 + 72 * q^33 - 7 * q^34 + 52 * q^35 + 201 * q^36 + 134 * q^37 + 70 * q^38 + 6 * q^39 + 11 * q^40 + 182 * q^41 - 15 * q^42 + 12 * q^43 + 33 * q^44 + 29 * q^45 + 24 * q^46 + 80 * q^47 + 21 * q^48 + 229 * q^49 + 37 * q^50 + 57 * q^51 - 15 * q^52 + 75 * q^53 + 95 * q^54 - 9 * q^55 + 39 * q^56 + 19 * q^57 - 21 * q^58 + 91 * q^59 + 62 * q^60 + 58 * q^61 + 108 * q^62 + 9 * q^63 + 167 * q^64 + 76 * q^65 + 105 * q^66 - 17 * q^67 + 109 * q^68 + 48 * q^69 - 55 * q^70 + 56 * q^71 + 48 * q^72 + 54 * q^73 + 9 * q^74 + 28 * q^75 + 82 * q^76 + 156 * q^77 + 16 * q^78 - 2 * q^79 + 98 * q^80 + 270 * q^81 - 42 * q^82 + 130 * q^83 + 229 * q^84 + 22 * q^85 + 72 * q^86 + 22 * q^87 + 61 * q^88 + 157 * q^89 + 176 * q^90 + 31 * q^91 - 18 * q^92 + 36 * q^93 + 83 * q^94 + 98 * q^95 + 111 * q^96 + 35 * q^97 + 53 * q^98 + 55 * q^99

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