LMFDB - Embedded newform 6023.2.a.d.1.10

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [6023,2,Mod(1,6023)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(6023, 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("6023.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 6023 = 19 \cdot 317 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	6023.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:	$48.0938971374$
Analytic rank:	$0$
Dimension:	$140$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.10
Character	$\chi$	$=$	6023.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-2.56765 q^{2} +0.729440 q^{3} +4.59285 q^{4} -3.21691 q^{5} -1.87295 q^{6} +3.04493 q^{7} -6.65754 q^{8} -2.46792 q^{9} +O(q^{10})$	\(q-2.56765 q^{2} +0.729440 q^{3} +4.59285 q^{4} -3.21691 q^{5} -1.87295 q^{6} +3.04493 q^{7} -6.65754 q^{8} -2.46792 q^{9} +8.25992 q^{10} +3.60988 q^{11} +3.35021 q^{12} +5.51328 q^{13} -7.81832 q^{14} -2.34654 q^{15} +7.90858 q^{16} -4.15347 q^{17} +6.33676 q^{18} -1.00000 q^{19} -14.7748 q^{20} +2.22109 q^{21} -9.26893 q^{22} -1.11850 q^{23} -4.85628 q^{24} +5.34852 q^{25} -14.1562 q^{26} -3.98852 q^{27} +13.9849 q^{28} -1.00957 q^{29} +6.02511 q^{30} +5.28241 q^{31} -6.99140 q^{32} +2.63319 q^{33} +10.6647 q^{34} -9.79526 q^{35} -11.3348 q^{36} +0.858796 q^{37} +2.56765 q^{38} +4.02161 q^{39} +21.4167 q^{40} -10.7190 q^{41} -5.70299 q^{42} -8.43024 q^{43} +16.5796 q^{44} +7.93907 q^{45} +2.87193 q^{46} +5.80023 q^{47} +5.76883 q^{48} +2.27157 q^{49} -13.7332 q^{50} -3.02971 q^{51} +25.3217 q^{52} +8.35204 q^{53} +10.2411 q^{54} -11.6127 q^{55} -20.2717 q^{56} -0.729440 q^{57} +2.59222 q^{58} +11.7897 q^{59} -10.7773 q^{60} +13.0890 q^{61} -13.5634 q^{62} -7.51463 q^{63} +2.13435 q^{64} -17.7357 q^{65} -6.76112 q^{66} +13.3772 q^{67} -19.0763 q^{68} -0.815880 q^{69} +25.1508 q^{70} -2.34548 q^{71} +16.4303 q^{72} -7.23535 q^{73} -2.20509 q^{74} +3.90143 q^{75} -4.59285 q^{76} +10.9918 q^{77} -10.3261 q^{78} +7.64037 q^{79} -25.4412 q^{80} +4.49437 q^{81} +27.5227 q^{82} +12.6626 q^{83} +10.2011 q^{84} +13.3613 q^{85} +21.6459 q^{86} -0.736417 q^{87} -24.0329 q^{88} -3.63274 q^{89} -20.3848 q^{90} +16.7875 q^{91} -5.13711 q^{92} +3.85320 q^{93} -14.8930 q^{94} +3.21691 q^{95} -5.09980 q^{96} +3.45561 q^{97} -5.83262 q^{98} -8.90889 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 140 q + 4 q^{2} + 3 q^{3} + 162 q^{4} + 13 q^{5} + 12 q^{6} + 25 q^{7} + 12 q^{8} + 181 q^{9}+O(q^{10}) $ 140 * q + 4 * q^2 + 3 * q^3 + 162 * q^4 + 13 * q^5 + 12 * q^6 + 25 * q^7 + 12 * q^8 + 181 * q^9	\( 140 q + 4 q^{2} + 3 q^{3} + 162 q^{4} + 13 q^{5} + 12 q^{6} + 25 q^{7} + 12 q^{8} + 181 q^{9} + 8 q^{10} + 19 q^{11} + 17 q^{12} + 28 q^{13} + 5 q^{14} + 14 q^{15} + 202 q^{16} + 38 q^{17} + 26 q^{18} - 140 q^{19} + 36 q^{20} + 4 q^{21} + 53 q^{22} + 58 q^{23} + 47 q^{24} + 279 q^{25} + 29 q^{26} + 21 q^{27} + 69 q^{28} + 18 q^{29} + 50 q^{30} + 20 q^{31} + 13 q^{32} + 47 q^{33} + 6 q^{34} + 35 q^{35} + 230 q^{36} + 88 q^{37} - 4 q^{38} + 32 q^{39} + 32 q^{40} + 24 q^{41} + 75 q^{42} + 100 q^{43} + 63 q^{44} + 87 q^{45} + 23 q^{46} + 35 q^{47} + 46 q^{48} + 255 q^{49} + 11 q^{50} - 6 q^{51} + 47 q^{52} + 77 q^{53} + 16 q^{54} + 63 q^{55} + 21 q^{56} - 3 q^{57} + 165 q^{58} + 18 q^{59} + 28 q^{60} + 99 q^{61} + 34 q^{62} + 89 q^{63} + 298 q^{64} + 78 q^{65} - 3 q^{66} + 28 q^{67} + 93 q^{68} + 19 q^{69} + 16 q^{70} + q^{71} + 43 q^{72} + 201 q^{73} + 32 q^{74} + 22 q^{75} - 162 q^{76} + 86 q^{77} + 122 q^{78} + 58 q^{79} + 92 q^{80} + 288 q^{81} + 143 q^{82} + 57 q^{83} + q^{84} + 136 q^{85} - 6 q^{86} + 43 q^{87} + 198 q^{88} + 46 q^{89} + 30 q^{90} + 26 q^{91} + 129 q^{92} + 111 q^{93} + 44 q^{94} - 13 q^{95} + 32 q^{96} + 110 q^{97} - 34 q^{98} + 62 q^{99}+O(q^{100}) \) 140 * q + 4 * q^2 + 3 * q^3 + 162 * q^4 + 13 * q^5 + 12 * q^6 + 25 * q^7 + 12 * q^8 + 181 * q^9 + 8 * q^10 + 19 * q^11 + 17 * q^12 + 28 * q^13 + 5 * q^14 + 14 * q^15 + 202 * q^16 + 38 * q^17 + 26 * q^18 - 140 * q^19 + 36 * q^20 + 4 * q^21 + 53 * q^22 + 58 * q^23 + 47 * q^24 + 279 * q^25 + 29 * q^26 + 21 * q^27 + 69 * q^28 + 18 * q^29 + 50 * q^30 + 20 * q^31 + 13 * q^32 + 47 * q^33 + 6 * q^34 + 35 * q^35 + 230 * q^36 + 88 * q^37 - 4 * q^38 + 32 * q^39 + 32 * q^40 + 24 * q^41 + 75 * q^42 + 100 * q^43 + 63 * q^44 + 87 * q^45 + 23 * q^46 + 35 * q^47 + 46 * q^48 + 255 * q^49 + 11 * q^50 - 6 * q^51 + 47 * q^52 + 77 * q^53 + 16 * q^54 + 63 * q^55 + 21 * q^56 - 3 * q^57 + 165 * q^58 + 18 * q^59 + 28 * q^60 + 99 * q^61 + 34 * q^62 + 89 * q^63 + 298 * q^64 + 78 * q^65 - 3 * q^66 + 28 * q^67 + 93 * q^68 + 19 * q^69 + 16 * q^70 + q^71 + 43 * q^72 + 201 * q^73 + 32 * q^74 + 22 * q^75 - 162 * q^76 + 86 * q^77 + 122 * q^78 + 58 * q^79 + 92 * q^80 + 288 * q^81 + 143 * q^82 + 57 * q^83 + q^84 + 136 * q^85 - 6 * q^86 + 43 * q^87 + 198 * q^88 + 46 * q^89 + 30 * q^90 + 26 * q^91 + 129 * q^92 + 111 * q^93 + 44 * q^94 - 13 * q^95 + 32 * q^96 + 110 * q^97 - 34 * q^98 + 62 * 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 $

$2$	−2.56765	−1.81561	−0.907803	−	0.419397i	$-0.862242\pi$
$2$	−2.56765	−1.81561	−0.907803	+	0.419397i	$0.862242\pi$
$3$	0.729440	0.421142	0.210571	−	0.977579i	$-0.432468\pi$
$3$	0.729440	0.421142	0.210571	+	0.977579i	$0.432468\pi$
$4$	4.59285	2.29643
$5$	−3.21691	−1.43865	−0.719323	−	0.694675i	$-0.755548\pi$
$5$	−3.21691	−1.43865	−0.719323	+	0.694675i	$0.755548\pi$
$6$	−1.87295	−0.764628
$7$	3.04493	1.15087	0.575437	−	0.817846i	$-0.304832\pi$
$7$	3.04493	1.15087	0.575437	+	0.817846i	$0.304832\pi$
$8$	−6.65754	−2.35380
$9$	−2.46792	−0.822639
$10$	8.25992	2.61202
$11$	3.60988	1.08842	0.544210	−	0.838949i	$-0.316829\pi$
$11$	3.60988	1.08842	0.544210	+	0.838949i	$0.316829\pi$
$12$	3.35021	0.967122
$13$	5.51328	1.52911	0.764554	−	0.644559i	$-0.222959\pi$
$13$	5.51328	1.52911	0.764554	+	0.644559i	$0.222959\pi$
$14$	−7.81832	−2.08953
$15$	−2.34654	−0.605875
$16$	7.90858	1.97714
$17$	−4.15347	−1.00736	−0.503682	−	0.863889i	$-0.668022\pi$
$17$	−4.15347	−1.00736	−0.503682	+	0.863889i	$0.668022\pi$
$18$	6.33676	1.49359
$19$	−1.00000	−0.229416
$19$	−1.00000	−0.229416
$20$	−14.7748	−3.30374
$21$	2.22109	0.484682
$22$	−9.26893	−1.97614
$23$	−1.11850	−0.233224	−0.116612	−	0.993178i	$-0.537203\pi$
$23$	−1.11850	−0.233224	−0.116612	+	0.993178i	$0.537203\pi$
$24$	−4.85628	−0.991284
$25$	5.34852	1.06970
$26$	−14.1562	−2.77626
$27$	−3.98852	−0.767590
$28$	13.9849	2.64290
$29$	−1.00957	−0.187472	−0.0937358	−	0.995597i	$-0.529881\pi$
$29$	−1.00957	−0.187472	−0.0937358	+	0.995597i	$0.529881\pi$
$30$	6.02511	1.10003
$31$	5.28241	0.948749	0.474375	−	0.880323i	$-0.342674\pi$
$31$	5.28241	0.948749	0.474375	+	0.880323i	$0.342674\pi$
$32$	−6.99140	−1.23592
$33$	2.63319	0.458380
$34$	10.6647	1.82898
$35$	−9.79526	−1.65570
$36$	−11.3348	−1.88913
$37$	0.858796	0.141185	0.0705926	−	0.997505i	$-0.477511\pi$
$37$	0.858796	0.141185	0.0705926	+	0.997505i	$0.477511\pi$
$38$	2.56765	0.416529
$39$	4.02161	0.643972
$40$	21.4167	3.38628
$41$	−10.7190	−1.67403	−0.837015	−	0.547181i	$-0.815701\pi$
$41$	−10.7190	−1.67403	−0.837015	+	0.547181i	$0.815701\pi$
$42$	−5.70299	−0.879991
$43$	−8.43024	−1.28560	−0.642800	−	0.766034i	$-0.722227\pi$
$43$	−8.43024	−1.28560	−0.642800	+	0.766034i	$0.722227\pi$
$44$	16.5796	2.49948
$45$	7.93907	1.18349
$46$	2.87193	0.423442
$47$	5.80023	0.846050	0.423025	−	0.906118i	$-0.360968\pi$
$47$	5.80023	0.846050	0.423025	+	0.906118i	$0.360968\pi$
$48$	5.76883	0.832659
$49$	2.27157	0.324511
$50$	−13.7332	−1.94216
$51$	−3.02971	−0.424244
$52$	25.3217	3.51148
$53$	8.35204	1.14724	0.573620	−	0.819121i	$-0.305539\pi$
$53$	8.35204	1.14724	0.573620	+	0.819121i	$0.305539\pi$
$54$	10.2411	1.39364
$55$	−11.6127	−1.56585
$56$	−20.2717	−2.70892
$57$	−0.729440	−0.0966167
$58$	2.59222	0.340375
$59$	11.7897	1.53488	0.767441	−	0.641120i	$-0.221530\pi$
$59$	11.7897	1.53488	0.767441	+	0.641120i	$0.221530\pi$
$60$	−10.7773	−1.39135
$61$	13.0890	1.67588	0.837939	−	0.545764i	$-0.183761\pi$
$61$	13.0890	1.67588	0.837939	+	0.545764i	$0.183761\pi$
$62$	−13.5634	−1.72256
$63$	−7.51463	−0.946754
$64$	2.13435	0.266794
$65$	−17.7357	−2.19985
$66$	−6.76112	−0.832237
$67$	13.3772	1.63428	0.817140	−	0.576440i	$-0.195558\pi$
$67$	13.3772	1.63428	0.817140	+	0.576440i	$0.195558\pi$
$68$	−19.0763	−2.31334
$69$	−0.815880	−0.0982204
$70$	25.1508	3.00610
$71$	−2.34548	−0.278358	−0.139179	−	0.990267i	$-0.544446\pi$
$71$	−2.34548	−0.278358	−0.139179	+	0.990267i	$0.544446\pi$
$72$	16.4303	1.93633
$73$	−7.23535	−0.846834	−0.423417	−	0.905935i	$-0.639169\pi$
$73$	−7.23535	−0.846834	−0.423417	+	0.905935i	$0.639169\pi$
$74$	−2.20509	−0.256337
$75$	3.90143	0.450498
$76$	−4.59285	−0.526836
$77$	10.9918	1.25263
$78$	−10.3261	−1.16920
$79$	7.64037	0.859609	0.429804	−	0.902922i	$-0.358583\pi$
$79$	7.64037	0.859609	0.429804	+	0.902922i	$0.358583\pi$
$80$	−25.4412	−2.84441
$81$	4.49437	0.499375
$82$	27.5227	3.03938
$83$	12.6626	1.38990	0.694948	−	0.719060i	$-0.255427\pi$
$83$	12.6626	1.38990	0.694948	+	0.719060i	$0.255427\pi$
$84$	10.2011	1.11304
$85$	13.3613	1.44924
$86$	21.6459	2.33414
$87$	−0.736417	−0.0789522
$88$	−24.0329	−2.56192
$89$	−3.63274	−0.385070	−0.192535	−	0.981290i	$-0.561671\pi$
$89$	−3.63274	−0.385070	−0.192535	+	0.981290i	$0.561671\pi$
$90$	−20.3848	−2.14875
$91$	16.7875	1.75981
$92$	−5.13711	−0.535581
$93$	3.85320	0.399558
$94$	−14.8930	−1.53609
$95$	3.21691	0.330048
$96$	−5.09980	−0.520497
$97$	3.45561	0.350864	0.175432	−	0.984492i	$-0.443868\pi$
$97$	3.45561	0.350864	0.175432	+	0.984492i	$0.443868\pi$
$98$	−5.83262	−0.589183
$99$	−8.90889	−0.895377
$100$	24.5650	2.45650
$101$	1.04750	0.104230	0.0521151	−	0.998641i	$-0.483404\pi$
$101$	1.04750	0.104230	0.0521151	+	0.998641i	$0.483404\pi$
$102$	7.77924	0.770259
$103$	−12.8129	−1.26249	−0.631247	−	0.775582i	$-0.717456\pi$
$103$	−12.8129	−1.26249	−0.631247	+	0.775582i	$0.717456\pi$
$104$	−36.7049	−3.59921
$105$	−7.14505	−0.697286
$106$	−21.4451	−2.08294
$107$	−12.3010	−1.18918	−0.594589	−	0.804029i	$-0.702685\pi$
$107$	−12.3010	−1.18918	−0.594589	+	0.804029i	$0.702685\pi$
$108$	−18.3187	−1.76271
$109$	−3.90240	−0.373782	−0.186891	−	0.982381i	$-0.559841\pi$
$109$	−3.90240	−0.373782	−0.186891	+	0.982381i	$0.559841\pi$
$110$	29.8173	2.84297
$111$	0.626440	0.0594590
$112$	24.0810	2.27544
$113$	−4.18515	−0.393706	−0.196853	−	0.980433i	$-0.563072\pi$
$113$	−4.18515	−0.393706	−0.196853	+	0.980433i	$0.563072\pi$
$114$	1.87295	0.175418
$115$	3.59812	0.335527
$116$	−4.63679	−0.430515
$117$	−13.6063	−1.25790
$118$	−30.2718	−2.78674
$119$	−12.6470	−1.15935
$120$	15.6222	1.42611
$121$	2.03124	0.184658
$122$	−33.6081	−3.04273
$123$	−7.81888	−0.705004
$124$	24.2613	2.17873
$125$	−1.12117	−0.100280
$126$	19.2950	1.71893
$127$	−15.8218	−1.40396	−0.701980	−	0.712197i	$-0.747700\pi$
$127$	−15.8218	−1.40396	−0.701980	+	0.712197i	$0.747700\pi$
$128$	8.50252	0.751524
$129$	−6.14935	−0.541420
$130$	45.5392	3.99406
$131$	3.48777	0.304728	0.152364	−	0.988324i	$-0.451311\pi$
$131$	3.48777	0.304728	0.152364	+	0.988324i	$0.451311\pi$
$132$	12.0939	1.05263
$133$	−3.04493	−0.264029
$134$	−34.3479	−2.96721
$135$	12.8307	1.10429
$136$	27.6519	2.37113
$137$	−7.28345	−0.622267	−0.311134	−	0.950366i	$-0.600709\pi$
$137$	−7.28345	−0.622267	−0.311134	+	0.950366i	$0.600709\pi$
$138$	2.09490	0.178330
$139$	−16.6923	−1.41582	−0.707912	−	0.706301i	$-0.750363\pi$
$139$	−16.6923	−1.41582	−0.707912	+	0.706301i	$0.750363\pi$
$140$	−44.9882	−3.80219
$141$	4.23091	0.356307
$142$	6.02239	0.505388
$143$	19.9023	1.66431
$144$	−19.5177	−1.62648
$145$	3.24768	0.269706
$146$	18.5779	1.53752
$147$	1.65698	0.136665
$148$	3.94432	0.324221
$149$	−13.5137	−1.10708	−0.553542	−	0.832821i	$-0.686724\pi$
$149$	−13.5137	−1.10708	−0.553542	+	0.832821i	$0.686724\pi$
$150$	−10.0175	−0.817927
$151$	4.27544	0.347931	0.173965	−	0.984752i	$-0.444342\pi$
$151$	4.27544	0.347931	0.173965	+	0.984752i	$0.444342\pi$
$152$	6.65754	0.539998
$153$	10.2504	0.828697
$154$	−28.2232	−2.27429
$155$	−16.9931	−1.36492
$156$	18.4706	1.47883
$157$	1.57835	0.125966	0.0629829	−	0.998015i	$-0.479939\pi$
$157$	1.57835	0.125966	0.0629829	+	0.998015i	$0.479939\pi$
$158$	−19.6178	−1.56071
$159$	6.09231	0.483151
$160$	22.4907	1.77805
$161$	−3.40576	−0.268411
$162$	−11.5400	−0.906667
$163$	−9.46467	−0.741330	−0.370665	−	0.928767i	$-0.620870\pi$
$163$	−9.46467	−0.741330	−0.370665	+	0.928767i	$0.620870\pi$
$164$	−49.2308	−3.84428
$165$	−8.47074	−0.659446
$166$	−32.5131	−2.52350
$167$	5.14766	0.398338	0.199169	−	0.979965i	$-0.436176\pi$
$167$	5.14766	0.398338	0.199169	+	0.979965i	$0.436176\pi$
$168$	−14.7870	−1.14084
$169$	17.3963	1.33817
$170$	−34.3073	−2.63125
$171$	2.46792	0.188726
$172$	−38.7188	−2.95228
$173$	13.1699	1.00129	0.500645	−	0.865653i	$-0.333096\pi$
$173$	13.1699	1.00129	0.500645	+	0.865653i	$0.333096\pi$
$174$	1.89087	0.143346
$175$	16.2859	1.23110
$176$	28.5490	2.15196
$177$	8.59984	0.646404
$178$	9.32763	0.699136
$179$	25.9029	1.93607	0.968035	−	0.250815i	$-0.0806986\pi$
$179$	25.9029	1.93607	0.968035	+	0.250815i	$0.0806986\pi$
$180$	36.4630	2.71779
$181$	20.1907	1.50077	0.750383	−	0.661004i	$-0.229869\pi$
$181$	20.1907	1.50077	0.750383	+	0.661004i	$0.229869\pi$
$182$	−43.1046	−3.19512
$183$	9.54765	0.705783
$184$	7.44648	0.548962
$185$	−2.76267	−0.203116
$186$	−9.89369	−0.725441
$187$	−14.9935	−1.09644
$188$	26.6396	1.94289
$189$	−12.1447	−0.883400
$190$	−8.25992	−0.599238
$191$	1.67948	0.121523	0.0607614	−	0.998152i	$-0.480647\pi$
$191$	1.67948	0.121523	0.0607614	+	0.998152i	$0.480647\pi$
$192$	1.55688	0.112358
$193$	−6.48099	−0.466512	−0.233256	−	0.972415i	$-0.574938\pi$
$193$	−6.48099	−0.466512	−0.233256	+	0.972415i	$0.574938\pi$
$194$	−8.87281	−0.637031
$195$	−12.9372	−0.926449
$196$	10.4330	0.745214
$197$	22.5024	1.60323	0.801615	−	0.597841i	$-0.203975\pi$
$197$	22.5024	1.60323	0.801615	+	0.597841i	$0.203975\pi$
$198$	22.8750	1.62565
$199$	2.49539	0.176893	0.0884466	−	0.996081i	$-0.471810\pi$
$199$	2.49539	0.176893	0.0884466	+	0.996081i	$0.471810\pi$
$200$	−35.6080	−2.51787
$201$	9.75783	0.688264
$202$	−2.68962	−0.189241
$203$	−3.07405	−0.215756
$204$	−13.9150	−0.974244
$205$	34.4821	2.40834
$206$	32.8991	2.29219
$207$	2.76037	0.191859
$208$	43.6022	3.02327
$209$	−3.60988	−0.249701
$210$	18.3460	1.26600
$211$	−18.9941	−1.30761	−0.653804	−	0.756664i	$-0.726828\pi$
$211$	−18.9941	−1.30761	−0.653804	+	0.756664i	$0.726828\pi$
$212$	38.3597	2.63455
$213$	−1.71089	−0.117228
$214$	31.5846	2.15908
$215$	27.1193	1.84952
$216$	26.5537	1.80675
$217$	16.0846	1.09189
$218$	10.0200	0.678641
$219$	−5.27775	−0.356637
$220$	−53.3353	−3.59586
$221$	−22.8992	−1.54037
$222$	−1.60848	−0.107954
$223$	24.5096	1.64129	0.820643	−	0.571441i	$-0.193616\pi$
$223$	24.5096	1.64129	0.820643	+	0.571441i	$0.193616\pi$
$224$	−21.2883	−1.42238
$225$	−13.1997	−0.879981
$226$	10.7460	0.714815
$227$	−7.26483	−0.482184	−0.241092	−	0.970502i	$-0.577505\pi$
$227$	−7.26483	−0.482184	−0.241092	+	0.970502i	$0.577505\pi$
$228$	−3.35021	−0.221873
$229$	15.6381	1.03340	0.516698	−	0.856167i	$-0.327161\pi$
$229$	15.6381	1.03340	0.516698	+	0.856167i	$0.327161\pi$
$230$	−9.23874	−0.609184
$231$	8.01787	0.527537
$232$	6.72123	0.441270
$233$	−5.52486	−0.361945	−0.180973	−	0.983488i	$-0.557925\pi$
$233$	−5.52486	−0.361945	−0.180973	+	0.983488i	$0.557925\pi$
$234$	34.9363	2.28386
$235$	−18.6588	−1.21717
$236$	54.1481	3.52474
$237$	5.57319	0.362017
$238$	32.4731	2.10492
$239$	21.9207	1.41793	0.708965	−	0.705244i	$-0.249163\pi$
$239$	21.9207	1.41793	0.708965	+	0.705244i	$0.249163\pi$
$240$	−18.5578	−1.19790
$241$	−12.4217	−0.800150	−0.400075	−	0.916482i	$-0.631016\pi$
$241$	−12.4217	−0.800150	−0.400075	+	0.916482i	$0.631016\pi$
$242$	−5.21553	−0.335267
$243$	15.2439	0.977898
$244$	60.1159	3.84853
$245$	−7.30745	−0.466856
$246$	20.0762	1.28001
$247$	−5.51328	−0.350802
$248$	−35.1679	−2.23316
$249$	9.23657	0.585344
$250$	2.87877	0.182070
$251$	−15.6049	−0.984975	−0.492487	−	0.870320i	$-0.663912\pi$
$251$	−15.6049	−0.984975	−0.492487	+	0.870320i	$0.663912\pi$
$252$	−34.5136	−2.17415
$253$	−4.03766	−0.253845
$254$	40.6250	2.54904
$255$	9.74630	0.610337
$256$	−26.1002	−1.63127
$257$	−10.6937	−0.667055	−0.333528	−	0.942740i	$-0.608239\pi$
$257$	−10.6937	−0.667055	−0.333528	+	0.942740i	$0.608239\pi$
$258$	15.7894	0.983006
$259$	2.61497	0.162486
$260$	−81.4576	−5.05179
$261$	2.49153	0.154222
$262$	−8.95539	−0.553266
$263$	18.6542	1.15027	0.575134	−	0.818060i	$-0.304950\pi$
$263$	18.6542	1.15027	0.575134	+	0.818060i	$0.304950\pi$
$264$	−17.5306	−1.07893
$265$	−26.8678	−1.65047
$266$	7.81832	0.479372
$267$	−2.64987	−0.162169
$268$	61.4393	3.75300
$269$	−30.5635	−1.86349	−0.931745	−	0.363113i	$-0.881714\pi$
$269$	−30.5635	−1.86349	−0.931745	+	0.363113i	$0.881714\pi$
$270$	−32.9448	−2.00496
$271$	18.1653	1.10346	0.551732	−	0.834021i	$-0.313967\pi$
$271$	18.1653	1.10346	0.551732	+	0.834021i	$0.313967\pi$
$272$	−32.8480	−1.99170
$273$	12.2455	0.741131
$274$	18.7014	1.12979
$275$	19.3075	1.16429
$276$	−3.74721	−0.225556
$277$	−7.08238	−0.425539	−0.212769	−	0.977102i	$-0.568248\pi$
$277$	−7.08238	−0.425539	−0.212769	+	0.977102i	$0.568248\pi$
$278$	42.8601	2.57058
$279$	−13.0366	−0.780478
$280$	65.2124	3.89718
$281$	−0.891232	−0.0531664	−0.0265832	−	0.999647i	$-0.508463\pi$
$281$	−0.891232	−0.0531664	−0.0265832	+	0.999647i	$0.508463\pi$
$282$	−10.8635	−0.646914
$283$	14.1783	0.842814	0.421407	−	0.906872i	$-0.361536\pi$
$283$	14.1783	0.842814	0.421407	+	0.906872i	$0.361536\pi$
$284$	−10.7725	−0.639228
$285$	2.34654	0.138997
$286$	−51.1022	−3.02174
$287$	−32.6386	−1.92660
$288$	17.2542	1.01671
$289$	0.251304	0.0147826
$290$	−8.33893	−0.489679
$291$	2.52066	0.147764
$292$	−33.2309	−1.94469
$293$	−4.59938	−0.268699	−0.134349	−	0.990934i	$-0.542894\pi$
$293$	−4.59938	−0.268699	−0.134349	+	0.990934i	$0.542894\pi$
$294$	−4.25454	−0.248130
$295$	−37.9263	−2.20815
$296$	−5.71747	−0.332321
$297$	−14.3981	−0.835461
$298$	34.6985	2.01003
$299$	−6.16661	−0.356624
$300$	17.9187	1.03453
$301$	−25.6695	−1.47956
$302$	−10.9779	−0.631705
$303$	0.764089	0.0438957
$304$	−7.90858	−0.453588
$305$	−42.1062	−2.41100
$306$	−26.3195	−1.50459
$307$	−17.4579	−0.996374	−0.498187	−	0.867070i	$-0.666001\pi$
$307$	−17.4579	−0.996374	−0.498187	+	0.867070i	$0.666001\pi$
$308$	50.4838	2.87658
$309$	−9.34624	−0.531689
$310$	43.6323	2.47815
$311$	−14.5504	−0.825079	−0.412540	−	0.910940i	$-0.635358\pi$
$311$	−14.5504	−0.825079	−0.412540	+	0.910940i	$0.635358\pi$
$312$	−26.7740	−1.51578
$313$	−5.13690	−0.290355	−0.145177	−	0.989406i	$-0.546375\pi$
$313$	−5.13690	−0.290355	−0.145177	+	0.989406i	$0.546375\pi$
$314$	−4.05265	−0.228704
$315$	24.1739	1.36204
$316$	35.0911	1.97403
$317$	1.00000	0.0561656
$317$	1.00000	0.0561656
$318$	−15.6429	−0.877213
$319$	−3.64441	−0.204048
$320$	−6.86602	−0.383822
$321$	−8.97281	−0.500813
$322$	8.74480	0.487329
$323$	4.15347	0.231105
$324$	20.6420	1.14678
$325$	29.4879	1.63569
$326$	24.3020	1.34596
$327$	−2.84657	−0.157416
$328$	71.3623	3.94033
$329$	17.6613	0.973697
$330$	21.7499	1.19729
$331$	14.2564	0.783605	0.391803	−	0.920049i	$-0.371852\pi$
$331$	14.2564	0.783605	0.391803	+	0.920049i	$0.371852\pi$
$332$	58.1572	3.19179
$333$	−2.11944	−0.116144
$334$	−13.2174	−0.723224
$335$	−43.0331	−2.35115
$336$	17.5657	0.958285
$337$	−0.795787	−0.0433493	−0.0216746	−	0.999765i	$-0.506900\pi$
$337$	−0.795787	−0.0433493	−0.0216746	+	0.999765i	$0.506900\pi$
$338$	−44.6676	−2.42960
$339$	−3.05282	−0.165806
$340$	61.3667	3.32807
$341$	19.0689	1.03264
$342$	−6.33676	−0.342653
$343$	−14.3977	−0.777403
$344$	56.1247	3.02604
$345$	2.62461	0.141304
$346$	−33.8158	−1.81795
$347$	28.3495	1.52188	0.760941	−	0.648821i	$-0.224738\pi$
$347$	28.3495	1.52188	0.760941	+	0.648821i	$0.224738\pi$
$348$	−3.38226	−0.181308
$349$	9.28858	0.497206	0.248603	−	0.968605i	$-0.420028\pi$
$349$	9.28858	0.497206	0.248603	+	0.968605i	$0.420028\pi$
$350$	−41.8165	−2.23518
$351$	−21.9898	−1.17373
$352$	−25.2381	−1.34520
$353$	13.6653	0.727329	0.363665	−	0.931530i	$-0.381525\pi$
$353$	13.6653	0.727329	0.363665	+	0.931530i	$0.381525\pi$
$354$	−22.0814	−1.17361
$355$	7.54522	0.400459
$356$	−16.6847	−0.884285
$357$	−9.22523	−0.488251
$358$	−66.5096	−3.51514
$359$	−13.6122	−0.718423	−0.359211	−	0.933256i	$-0.616954\pi$
$359$	−13.6122	−0.718423	−0.359211	+	0.933256i	$0.616954\pi$
$360$	−52.8547	−2.78569
$361$	1.00000	0.0526316
$362$	−51.8428	−2.72480
$363$	1.48167	0.0777674
$364$	77.1026	4.04128
$365$	23.2755	1.21829
$366$	−24.5151	−1.28142
$367$	0.887382	0.0463210	0.0231605	−	0.999732i	$-0.492627\pi$
$367$	0.887382	0.0463210	0.0231605	+	0.999732i	$0.492627\pi$
$368$	−8.84576	−0.461117
$369$	26.4537	1.37712
$370$	7.09358	0.368778
$371$	25.4313	1.32033
$372$	17.6972	0.917556
$373$	22.3374	1.15658	0.578292	−	0.815830i	$-0.303719\pi$
$373$	22.3374	1.15658	0.578292	+	0.815830i	$0.303719\pi$
$374$	38.4982	1.99069
$375$	−0.817825	−0.0422323
$376$	−38.6153	−1.99143
$377$	−5.56602	−0.286665
$378$	31.1835	1.60391
$379$	−8.49192	−0.436200	−0.218100	−	0.975926i	$-0.569986\pi$
$379$	−8.49192	−0.436200	−0.218100	+	0.975926i	$0.569986\pi$
$380$	14.7748	0.757931
$381$	−11.5411	−0.591267
$382$	−4.31232	−0.220638
$383$	1.65533	0.0845832	0.0422916	−	0.999105i	$-0.486534\pi$
$383$	1.65533	0.0845832	0.0422916	+	0.999105i	$0.486534\pi$
$384$	6.20208	0.316499
$385$	−35.3597	−1.80210
$386$	16.6409	0.847001
$387$	20.8051	1.05758
$388$	15.8711	0.805733
$389$	5.94452	0.301399	0.150700	−	0.988580i	$-0.451847\pi$
$389$	5.94452	0.301399	0.150700	+	0.988580i	$0.451847\pi$
$390$	33.2181	1.68207
$391$	4.64566	0.234941
$392$	−15.1231	−0.763832
$393$	2.54412	0.128334
$394$	−57.7784	−2.91083
$395$	−24.5784	−1.23667
$396$	−40.9172	−2.05617
$397$	1.81413	0.0910488	0.0455244	−	0.998963i	$-0.485504\pi$
$397$	1.81413	0.0910488	0.0455244	+	0.998963i	$0.485504\pi$
$398$	−6.40729	−0.321168
$399$	−2.22109	−0.111194
$400$	42.2992	2.11496
$401$	−0.475862	−0.0237634	−0.0118817	−	0.999929i	$-0.503782\pi$
$401$	−0.475862	−0.0237634	−0.0118817	+	0.999929i	$0.503782\pi$
$402$	−25.0547	−1.24962
$403$	29.1234	1.45074
$404$	4.81101	0.239357
$405$	−14.4580	−0.718424
$406$	7.89311	0.391728
$407$	3.10015	0.153669
$408$	20.1704	0.998584
$409$	−1.93945	−0.0958998	−0.0479499	−	0.998850i	$-0.515269\pi$
$409$	−1.93945	−0.0958998	−0.0479499	+	0.998850i	$0.515269\pi$
$410$	−88.5382	−4.37259
$411$	−5.31284	−0.262063
$412$	−58.8478	−2.89922
$413$	35.8986	1.76646
$414$	−7.08768	−0.348340
$415$	−40.7343	−1.99957
$416$	−38.5455	−1.88985
$417$	−12.1760	−0.596263
$418$	9.26893	0.453358
$419$	35.8437	1.75108	0.875539	−	0.483148i	$-0.160507\pi$
$419$	35.8437	1.75108	0.875539	+	0.483148i	$0.160507\pi$
$420$	−32.8162	−1.60126
$421$	23.7554	1.15777	0.578883	−	0.815410i	$-0.303489\pi$
$421$	23.7554	1.15777	0.578883	+	0.815410i	$0.303489\pi$
$422$	48.7703	2.37410
$423$	−14.3145	−0.695994
$424$	−55.6041	−2.70037
$425$	−22.2149	−1.07758
$426$	4.39297	0.212840
$427$	39.8551	1.92872
$428$	−56.4965	−2.73086
$429$	14.5175	0.700912
$430$	−69.6331	−3.35801
$431$	35.4842	1.70921	0.854606	−	0.519277i	$-0.173799\pi$
$431$	35.4842	1.70921	0.854606	+	0.519277i	$0.173799\pi$
$432$	−31.5435	−1.51764
$433$	−23.5633	−1.13238	−0.566189	−	0.824275i	$-0.691583\pi$
$433$	−23.5633	−1.13238	−0.566189	+	0.824275i	$0.691583\pi$
$434$	−41.2996	−1.98244
$435$	2.36899	0.113584
$436$	−17.9231	−0.858363
$437$	1.11850	0.0535052
$438$	13.5514	0.647513
$439$	37.9962	1.81346	0.906729	−	0.421714i	$-0.138571\pi$
$439$	37.9962	1.81346	0.906729	+	0.421714i	$0.138571\pi$
$440$	77.3119	3.68570
$441$	−5.60606	−0.266955
$442$	58.7973	2.79670
$443$	38.8279	1.84477	0.922384	−	0.386274i	$-0.126238\pi$
$443$	38.8279	1.84477	0.922384	+	0.386274i	$0.126238\pi$
$444$	2.87714	0.136543
$445$	11.6862	0.553980
$446$	−62.9323	−2.97993
$447$	−9.85742	−0.466240
$448$	6.49894	0.307046
$449$	−33.8255	−1.59632	−0.798161	−	0.602444i	$-0.794194\pi$
$449$	−33.8255	−1.59632	−0.798161	+	0.602444i	$0.794194\pi$
$450$	33.8923	1.59770
$451$	−38.6944	−1.82205
$452$	−19.2218	−0.904116
$453$	3.11868	0.146528
$454$	18.6536	0.875455
$455$	−54.0040	−2.53175
$456$	4.85628	0.227416
$457$	−0.899688	−0.0420856	−0.0210428	−	0.999779i	$-0.506699\pi$
$457$	−0.899688	−0.0420856	−0.0210428	+	0.999779i	$0.506699\pi$
$458$	−40.1533	−1.87624
$459$	16.5662	0.773243
$460$	16.5256	0.770512
$461$	28.2956	1.31786	0.658928	−	0.752206i	$-0.271010\pi$
$461$	28.2956	1.31786	0.658928	+	0.752206i	$0.271010\pi$
$462$	−20.5871	−0.957800
$463$	16.1044	0.748436	0.374218	−	0.927341i	$-0.377911\pi$
$463$	16.1044	0.748436	0.374218	+	0.927341i	$0.377911\pi$
$464$	−7.98423	−0.370658
$465$	−12.3954	−0.574823
$466$	14.1859	0.657150
$467$	27.5092	1.27297	0.636487	−	0.771287i	$-0.280387\pi$
$467$	27.5092	1.27297	0.636487	+	0.771287i	$0.280387\pi$
$468$	−62.4918	−2.88868
$469$	40.7324	1.88085
$470$	47.9094	2.20990
$471$	1.15131	0.0530495
$472$	−78.4901	−3.61280
$473$	−30.4322	−1.39927
$474$	−14.3100	−0.657281
$475$	−5.34852	−0.245407
$476$	−58.0858	−2.66236
$477$	−20.6121	−0.943765
$478$	−56.2847	−2.57440
$479$	6.63082	0.302970	0.151485	−	0.988460i	$-0.451594\pi$
$479$	6.63082	0.302970	0.151485	+	0.988460i	$0.451594\pi$
$480$	16.4056	0.748811
$481$	4.73478	0.215887
$482$	31.8946	1.45276
$483$	−2.48429	−0.113039
$484$	9.32919	0.424054
$485$	−11.1164	−0.504769
$486$	−39.1411	−1.77548
$487$	28.1514	1.27566	0.637831	−	0.770176i	$-0.279832\pi$
$487$	28.1514	1.27566	0.637831	+	0.770176i	$0.279832\pi$
$488$	−87.1407	−3.94468
$489$	−6.90391	−0.312205
$490$	18.7630	0.847627
$491$	−9.96284	−0.449616	−0.224808	−	0.974403i	$-0.572176\pi$
$491$	−9.96284	−0.449616	−0.224808	+	0.974403i	$0.572176\pi$
$492$	−35.9109	−1.61899
$493$	4.19320	0.188852
$494$	14.1562	0.636918
$495$	28.6591	1.28813
$496$	41.7764	1.87581
$497$	−7.14183	−0.320355
$498$	−23.7163	−1.06275
$499$	−17.3002	−0.774463	−0.387231	−	0.921983i	$-0.626569\pi$
$499$	−17.3002	−0.774463	−0.387231	+	0.921983i	$0.626569\pi$
$500$	−5.14936	−0.230286
$501$	3.75490	0.167757
$502$	40.0681	1.78833
$503$	38.3211	1.70865	0.854326	−	0.519738i	$-0.173970\pi$
$503$	38.3211	1.70865	0.854326	+	0.519738i	$0.173970\pi$
$504$	50.0290	2.22847
$505$	−3.36972	−0.149950
$506$	10.3673	0.460883
$507$	12.6895	0.563561
$508$	−72.6672	−3.22409
$509$	−12.9294	−0.573086	−0.286543	−	0.958067i	$-0.592506\pi$
$509$	−12.9294	−0.573086	−0.286543	+	0.958067i	$0.592506\pi$
$510$	−25.0251	−1.10813
$511$	−22.0311	−0.974599
$512$	50.0114	2.21021
$513$	3.98852	0.176097
$514$	27.4578	1.21111
$515$	41.2180	1.81628
$516$	−28.2431	−1.24333
$517$	20.9381	0.920858
$518$	−6.71434	−0.295011
$519$	9.60666	0.421686
$520$	118.076	5.17800
$521$	6.99064	0.306266	0.153133	−	0.988206i	$-0.451064\pi$
$521$	6.99064	0.306266	0.153133	+	0.988206i	$0.451064\pi$
$522$	−6.39738	−0.280006
$523$	32.5563	1.42359	0.711794	−	0.702388i	$-0.247883\pi$
$523$	32.5563	1.42359	0.711794	+	0.702388i	$0.247883\pi$
$524$	16.0188	0.699785
$525$	11.8796	0.518466
$526$	−47.8975	−2.08843
$527$	−21.9403	−0.955736
$528$	20.8248	0.906283
$529$	−21.7490	−0.945607
$530$	68.9872	2.99661
$531$	−29.0959	−1.26265
$532$	−13.9849	−0.606322
$533$	−59.0969	−2.55977
$534$	6.80395	0.294436
$535$	39.5711	1.71081
$536$	−89.0590	−3.84676
$537$	18.8946	0.815361
$538$	78.4765	3.38336
$539$	8.20011	0.353204
$540$	58.9295	2.53592
$541$	−44.7327	−1.92321	−0.961605	−	0.274439i	$-0.911508\pi$
$541$	−44.7327	−1.92321	−0.961605	+	0.274439i	$0.911508\pi$
$542$	−46.6423	−2.00346
$543$	14.7279	0.632036
$544$	29.0386	1.24502
$545$	12.5537	0.537741
$546$	−31.4422	−1.34560
$547$	4.58921	0.196220	0.0981102	−	0.995176i	$-0.468720\pi$
$547$	4.58921	0.196220	0.0981102	+	0.995176i	$0.468720\pi$
$548$	−33.4518	−1.42899
$549$	−32.3026	−1.37864
$550$	−49.5751	−2.11389
$551$	1.00957	0.0430090
$552$	5.43176	0.231191
$553$	23.2644	0.989301
$554$	18.1851	0.772611
$555$	−2.01520	−0.0855406
$556$	−76.6653	−3.25133
$557$	−11.9204	−0.505084	−0.252542	−	0.967586i	$-0.581267\pi$
$557$	−11.9204	−0.505084	−0.252542	+	0.967586i	$0.581267\pi$
$558$	33.4734	1.41704
$559$	−46.4783	−1.96582
$560$	−77.4665	−3.27356
$561$	−10.9369	−0.461755
$562$	2.28838	0.0965293
$563$	−10.1395	−0.427329	−0.213664	−	0.976907i	$-0.568540\pi$
$563$	−10.1395	−0.427329	−0.213664	+	0.976907i	$0.568540\pi$
$564$	19.4320	0.818233
$565$	13.4633	0.566404
$566$	−36.4051	−1.53022
$567$	13.6850	0.574717
$568$	15.6152	0.655198
$569$	−19.2549	−0.807208	−0.403604	−	0.914934i	$-0.632243\pi$
$569$	−19.2549	−0.807208	−0.403604	+	0.914934i	$0.632243\pi$
$570$	−6.02511	−0.252364
$571$	11.5584	0.483702	0.241851	−	0.970313i	$-0.422245\pi$
$571$	11.5584	0.483702	0.241851	+	0.970313i	$0.422245\pi$
$572$	91.4082	3.82197
$573$	1.22508	0.0511784
$574$	83.8047	3.49794
$575$	−5.98233	−0.249481
$576$	−5.26740	−0.219475
$577$	−41.3326	−1.72070	−0.860349	−	0.509705i	$-0.829754\pi$
$577$	−41.3326	−1.72070	−0.860349	+	0.509705i	$0.829754\pi$
$578$	−0.645261	−0.0268393
$579$	−4.72749	−0.196468
$580$	14.9161	0.619359
$581$	38.5566	1.59960
$582$	−6.47218	−0.268281
$583$	30.1499	1.24868
$584$	48.1697	1.99328
$585$	43.7703	1.80968
$586$	11.8096	0.487851
$587$	24.2332	1.00021	0.500107	−	0.865964i	$-0.333294\pi$
$587$	24.2332	1.00021	0.500107	+	0.865964i	$0.333294\pi$
$588$	7.61025	0.313841
$589$	−5.28241	−0.217658
$590$	97.3816	4.00914
$591$	16.4141	0.675188
$592$	6.79185	0.279143
$593$	−44.2880	−1.81869	−0.909345	−	0.416042i	$-0.863417\pi$
$593$	−44.2880	−1.81869	−0.909345	+	0.416042i	$0.863417\pi$
$594$	36.9693	1.51687
$595$	40.6843	1.66789
$596$	−62.0664	−2.54234
$597$	1.82023	0.0744972
$598$	15.8337	0.647490
$599$	−17.9413	−0.733063	−0.366531	−	0.930406i	$-0.619455\pi$
$599$	−17.9413	−0.733063	−0.366531	+	0.930406i	$0.619455\pi$
$600$	−25.9739	−1.06038
$601$	−2.47653	−0.101020	−0.0505099	−	0.998724i	$-0.516085\pi$
$601$	−2.47653	−0.101020	−0.0505099	+	0.998724i	$0.516085\pi$
$602$	65.9103	2.68630
$603$	−33.0137	−1.34442
$604$	19.6365	0.798997
$605$	−6.53433	−0.265658
$606$	−1.96192	−0.0796974
$607$	11.9524	0.485131	0.242566	−	0.970135i	$-0.422011\pi$
$607$	11.9524	0.485131	0.242566	+	0.970135i	$0.422011\pi$
$608$	6.99140	0.283539
$609$	−2.24234	−0.0908641
$610$	108.114	4.37742
$611$	31.9783	1.29370
$612$	47.0786	1.90304
$613$	26.5253	1.07135	0.535673	−	0.844426i	$-0.320058\pi$
$613$	26.5253	1.07135	0.535673	+	0.844426i	$0.320058\pi$
$614$	44.8258	1.80902
$615$	25.1526	1.01425
$616$	−73.1785	−2.94845
$617$	17.4175	0.701200	0.350600	−	0.936525i	$-0.385978\pi$
$617$	17.4175	0.701200	0.350600	+	0.936525i	$0.385978\pi$
$618$	23.9979	0.965338
$619$	37.1266	1.49224	0.746122	−	0.665809i	$-0.231913\pi$
$619$	37.1266	1.49224	0.746122	+	0.665809i	$0.231913\pi$
$620$	−78.0466	−3.13443
$621$	4.46116	0.179020
$622$	37.3605	1.49802
$623$	−11.0614	−0.443167
$624$	31.8052	1.27323
$625$	−23.1359	−0.925437
$626$	13.1898	0.527170
$627$	−2.63319	−0.105160
$628$	7.24911	0.289271
$629$	−3.56698	−0.142225
$630$	−62.0702	−2.47294
$631$	−13.0868	−0.520977	−0.260489	−	0.965477i	$-0.583884\pi$
$631$	−13.0868	−0.520977	−0.260489	+	0.965477i	$0.583884\pi$
$632$	−50.8661	−2.02334
$633$	−13.8550	−0.550689
$634$	−2.56765	−0.101975
$635$	50.8974	2.01980
$636$	27.9811	1.10952
$637$	12.5238	0.496212
$638$	9.35759	0.370471
$639$	5.78846	0.228988
$640$	−27.3519	−1.08118
$641$	1.69668	0.0670148	0.0335074	−	0.999438i	$-0.489332\pi$
$641$	1.69668	0.0670148	0.0335074	+	0.999438i	$0.489332\pi$
$642$	23.0391	0.909280
$643$	35.7132	1.40839	0.704196	−	0.710006i	$-0.251308\pi$
$643$	35.7132	1.40839	0.704196	+	0.710006i	$0.251308\pi$
$644$	−15.6421	−0.616386
$645$	19.7819	0.778913
$646$	−10.6647	−0.419596
$647$	32.7420	1.28722	0.643610	−	0.765354i	$-0.277436\pi$
$647$	32.7420	1.28722	0.643610	+	0.765354i	$0.277436\pi$
$648$	−29.9215	−1.17543
$649$	42.5592	1.67060
$650$	−75.7148	−2.96978
$651$	11.7327	0.459841
$652$	−43.4698	−1.70241
$653$	−2.73121	−0.106881	−0.0534403	−	0.998571i	$-0.517019\pi$
$653$	−2.73121	−0.106881	−0.0534403	+	0.998571i	$0.517019\pi$
$654$	7.30900	0.285805
$655$	−11.2199	−0.438396
$656$	−84.7721	−3.30980
$657$	17.8562	0.696639
$658$	−45.3480	−1.76785
$659$	−21.1247	−0.822901	−0.411450	−	0.911432i	$-0.634978\pi$
$659$	−21.1247	−0.822901	−0.411450	+	0.911432i	$0.634978\pi$
$660$	−38.9049	−1.51437
$661$	0.457676	0.0178015	0.00890077	−	0.999960i	$-0.497167\pi$
$661$	0.457676	0.0178015	0.00890077	+	0.999960i	$0.497167\pi$
$662$	−36.6056	−1.42272
$663$	−16.7036	−0.648715
$664$	−84.3015	−3.27153
$665$	9.79526	0.379844
$666$	5.44198	0.210873
$667$	1.12920	0.0437229
$668$	23.6424	0.914752
$669$	17.8783	0.691215
$670$	110.494	4.26876
$671$	47.2498	1.82406
$672$	−15.5285	−0.599026
$673$	−0.256852	−0.00990091	−0.00495046	−	0.999988i	$-0.501576\pi$
$673$	−0.256852	−0.00990091	−0.00495046	+	0.999988i	$0.501576\pi$
$674$	2.04331	0.0787052
$675$	−21.3327	−0.821095
$676$	79.8984	3.07302
$677$	−14.1890	−0.545326	−0.272663	−	0.962110i	$-0.587904\pi$
$677$	−14.1890	−0.545326	−0.272663	+	0.962110i	$0.587904\pi$
$678$	7.83858	0.301039
$679$	10.5221	0.403800
$680$	−88.9537	−3.41122
$681$	−5.29925	−0.203068
$682$	−48.9623	−1.87486
$683$	38.2484	1.46353	0.731767	−	0.681555i	$-0.238696\pi$
$683$	38.2484	1.46353	0.731767	+	0.681555i	$0.238696\pi$
$684$	11.3348	0.433396
$685$	23.4302	0.895223
$686$	36.9683	1.41146
$687$	11.4071	0.435207
$688$	−66.6712	−2.54182
$689$	46.0471	1.75426
$690$	−6.73910	−0.256553
$691$	47.1035	1.79190	0.895951	−	0.444152i	$-0.146495\pi$
$691$	47.1035	1.79190	0.895951	+	0.444152i	$0.146495\pi$
$692$	60.4875	2.29939
$693$	−27.1269	−1.03047
$694$	−72.7918	−2.76314
$695$	53.6977	2.03687
$696$	4.90273	0.185838
$697$	44.5211	1.68636
$698$	−23.8499	−0.902731
$699$	−4.03005	−0.152431
$700$	74.7985	2.82712
$701$	39.5507	1.49381	0.746905	−	0.664931i	$-0.231539\pi$
$701$	39.5507	1.49381	0.746905	+	0.664931i	$0.231539\pi$
$702$	56.4622	2.13103
$703$	−0.858796	−0.0323901
$704$	7.70475	0.290384
$705$	−13.6105	−0.512600
$706$	−35.0877	−1.32054
$707$	3.18956	0.119956
$708$	39.4978	1.48442
$709$	−5.43694	−0.204188	−0.102094	−	0.994775i	$-0.532554\pi$
$709$	−5.43694	−0.204188	−0.102094	+	0.994775i	$0.532554\pi$
$710$	−19.3735	−0.727075
$711$	−18.8558	−0.707148
$712$	24.1852	0.906377
$713$	−5.90839	−0.221271
$714$	23.6872	0.886471
$715$	−64.0239	−2.39436
$716$	118.968	4.44604
$717$	15.9898	0.597150
$718$	34.9513	1.30437
$719$	−5.86134	−0.218591	−0.109296	−	0.994009i	$-0.534860\pi$
$719$	−5.86134	−0.218591	−0.109296	+	0.994009i	$0.534860\pi$
$720$	62.7868	2.33992
$721$	−39.0143	−1.45297
$722$	−2.56765	−0.0955582
$723$	−9.06086	−0.336977
$724$	92.7330	3.44640
$725$	−5.39969	−0.200539
$726$	−3.80441	−0.141195
$727$	46.3824	1.72023	0.860114	−	0.510103i	$-0.170393\pi$
$727$	46.3824	1.72023	0.860114	+	0.510103i	$0.170393\pi$
$728$	−111.764	−4.14224
$729$	−2.36359	−0.0875404
$730$	−59.7634	−2.21194
$731$	35.0147	1.29507
$732$	43.8509	1.62078
$733$	18.7011	0.690740	0.345370	−	0.938467i	$-0.387753\pi$
$733$	18.7011	0.690740	0.345370	+	0.938467i	$0.387753\pi$
$734$	−2.27849	−0.0841007
$735$	−5.33035	−0.196613
$736$	7.81989	0.288245
$737$	48.2899	1.77878
$738$	−67.9238	−2.50031
$739$	23.4166	0.861394	0.430697	−	0.902497i	$-0.358268\pi$
$739$	23.4166	0.861394	0.430697	+	0.902497i	$0.358268\pi$
$740$	−12.6885	−0.466440
$741$	−4.02161	−0.147737
$742$	−65.2989	−2.39720
$743$	40.7457	1.49482	0.747408	−	0.664365i	$-0.231298\pi$
$743$	40.7457	1.49482	0.747408	+	0.664365i	$0.231298\pi$
$744$	−25.6529	−0.940480
$745$	43.4724	1.59270
$746$	−57.3546	−2.09990
$747$	−31.2502	−1.14338
$748$	−68.8630	−2.51788
$749$	−37.4555	−1.36859
$750$	2.09989	0.0766772
$751$	−3.14066	−0.114604	−0.0573021	−	0.998357i	$-0.518250\pi$
$751$	−3.14066	−0.114604	−0.0573021	+	0.998357i	$0.518250\pi$
$752$	45.8715	1.67276
$753$	−11.3829	−0.414814
$754$	14.2916	0.520470
$755$	−13.7537	−0.500549
$756$	−55.7790	−2.02866
$757$	−34.2151	−1.24357	−0.621784	−	0.783188i	$-0.713592\pi$
$757$	−34.2151	−1.24357	−0.621784	+	0.783188i	$0.713592\pi$
$758$	21.8043	0.791968
$759$	−2.94523	−0.106905
$760$	−21.4167	−0.776867
$761$	−40.7749	−1.47809	−0.739044	−	0.673657i	$-0.764722\pi$
$761$	−40.7749	−1.47809	−0.739044	+	0.673657i	$0.764722\pi$
$762$	29.6335	1.07351
$763$	−11.8825	−0.430176
$764$	7.71359	0.279068
$765$	−32.9747	−1.19220
$766$	−4.25031	−0.153570
$767$	64.9997	2.34700
$768$	−19.0386	−0.686995
$769$	8.01713	0.289105	0.144553	−	0.989497i	$-0.453826\pi$
$769$	8.01713	0.289105	0.144553	+	0.989497i	$0.453826\pi$
$770$	90.7916	3.27190
$771$	−7.80042	−0.280925
$772$	−29.7662	−1.07131
$773$	−19.2916	−0.693870	−0.346935	−	0.937889i	$-0.612778\pi$
$773$	−19.2916	−0.693870	−0.346935	+	0.937889i	$0.612778\pi$
$774$	−53.4204	−1.92016
$775$	28.2531	1.01488
$776$	−23.0059	−0.825863
$777$	1.90746	0.0684299
$778$	−15.2635	−0.547223
$779$	10.7190	0.384049
$780$	−59.4184	−2.12752
$781$	−8.46692	−0.302970
$782$	−11.9285	−0.426561
$783$	4.02667	0.143901
$784$	17.9649	0.641604
$785$	−5.07740	−0.181220
$786$	−6.53242	−0.233004
$787$	−37.0231	−1.31973	−0.659865	−	0.751384i	$-0.729386\pi$
$787$	−37.0231	−1.31973	−0.659865	+	0.751384i	$0.729386\pi$
$788$	103.350	3.68170
$789$	13.6071	0.484426
$790$	63.1088	2.24531
$791$	−12.7435	−0.453106
$792$	59.3113	2.10754
$793$	72.1634	2.56260
$794$	−4.65807	−0.165309
$795$	−19.5984	−0.695084
$796$	11.4609	0.406222
$797$	26.6233	0.943045	0.471522	−	0.881854i	$-0.343705\pi$
$797$	26.6233	0.943045	0.471522	+	0.881854i	$0.343705\pi$
$798$	5.70299	0.201884
$799$	−24.0911	−0.852280
$800$	−37.3937	−1.32207
$801$	8.96531	0.316774
$802$	1.22185	0.0431450
$803$	−26.1188	−0.921711
$804$	44.8162	1.58055
$805$	10.9560	0.386149
$806$	−74.7789	−2.63397
$807$	−22.2942	−0.784794
$808$	−6.97378	−0.245337
$809$	22.8443	0.803162	0.401581	−	0.915823i	$-0.368461\pi$
$809$	22.8443	0.803162	0.401581	+	0.915823i	$0.368461\pi$
$810$	37.1231	1.30437
$811$	−21.6678	−0.760858	−0.380429	−	0.924810i	$-0.624224\pi$
$811$	−21.6678	−0.760858	−0.380429	+	0.924810i	$0.624224\pi$
$812$	−14.1187	−0.495468
$813$	13.2505	0.464716
$814$	−7.96012	−0.279002
$815$	30.4470	1.06651
$816$	−23.9607	−0.838791
$817$	8.43024	0.294937
$818$	4.97985	0.174116
$819$	−41.4302	−1.44769
$820$	158.371	5.53057
$821$	52.2537	1.82367	0.911833	−	0.410562i	$-0.134667\pi$
$821$	52.2537	1.82367	0.911833	+	0.410562i	$0.134667\pi$
$822$	13.6415	0.475803
$823$	49.6981	1.73237	0.866184	−	0.499725i	$-0.166566\pi$
$823$	49.6981	1.73237	0.866184	+	0.499725i	$0.166566\pi$
$824$	85.3025	2.97165
$825$	14.0837	0.490331
$826$	−92.1753	−3.20719
$827$	−53.0444	−1.84454	−0.922268	−	0.386552i	$-0.873666\pi$
$827$	−53.0444	−1.84454	−0.922268	+	0.386552i	$0.873666\pi$
$828$	12.6780	0.440590
$829$	14.8275	0.514980	0.257490	−	0.966281i	$-0.417105\pi$
$829$	14.8275	0.514980	0.257490	+	0.966281i	$0.417105\pi$
$830$	104.592	3.63043
$831$	−5.16617	−0.179212
$832$	11.7673	0.407957
$833$	−9.43491	−0.326900
$834$	31.2639	1.08258
$835$	−16.5596	−0.573067
$836$	−16.5796	−0.573419
$837$	−21.0690	−0.728251
$838$	−92.0341	−3.17927
$839$	−49.7059	−1.71604	−0.858019	−	0.513617i	$-0.828305\pi$
$839$	−49.7059	−1.71604	−0.858019	+	0.513617i	$0.828305\pi$
$840$	47.5685	1.64127
$841$	−27.9808	−0.964854
$842$	−60.9956	−2.10205
$843$	−0.650100	−0.0223906
$844$	−87.2370	−3.00282
$845$	−55.9622	−1.92516
$846$	36.7546	1.26365
$847$	6.18498	0.212518
$848$	66.0527	2.26826
$849$	10.3422	0.354945
$850$	57.0403	1.95646
$851$	−0.960565	−0.0329277
$852$	−7.85786	−0.269206
$853$	15.1944	0.520248	0.260124	−	0.965575i	$-0.416237\pi$
$853$	15.1944	0.520248	0.260124	+	0.965575i	$0.416237\pi$
$854$	−102.334	−3.50180
$855$	−7.93907	−0.271511
$856$	81.8942	2.79909
$857$	−14.7714	−0.504580	−0.252290	−	0.967652i	$-0.581184\pi$
$857$	−14.7714	−0.504580	−0.252290	+	0.967652i	$0.581184\pi$
$858$	−37.2760	−1.27258
$859$	5.44430	0.185757	0.0928786	−	0.995677i	$-0.470393\pi$
$859$	5.44430	0.185757	0.0928786	+	0.995677i	$0.470393\pi$
$860$	124.555	4.24729
$861$	−23.8079	−0.811371
$862$	−91.1111	−3.10326
$863$	−0.224158	−0.00763041	−0.00381521	−	0.999993i	$-0.501214\pi$
$863$	−0.224158	−0.00763041	−0.00381521	+	0.999993i	$0.501214\pi$
$864$	27.8853	0.948678
$865$	−42.3665	−1.44050
$866$	60.5024	2.05595
$867$	0.183311	0.00622556
$868$	73.8740	2.50745
$869$	27.5808	0.935615
$870$	−6.08275	−0.206225
$871$	73.7520	2.49899
$872$	25.9804	0.879808
$873$	−8.52816	−0.288635
$874$	−2.87193	−0.0971444
$875$	−3.41388	−0.115410
$876$	−24.2399	−0.818991
$877$	6.09008	0.205647	0.102824	−	0.994700i	$-0.467212\pi$
$877$	6.09008	0.205647	0.102824	+	0.994700i	$0.467212\pi$
$878$	−97.5610	−3.29253
$879$	−3.35497	−0.113160
$880$	−91.8397	−3.09591
$881$	13.0020	0.438049	0.219025	−	0.975719i	$-0.429713\pi$
$881$	13.0020	0.438049	0.219025	+	0.975719i	$0.429713\pi$
$882$	14.3944	0.484685
$883$	58.6023	1.97212	0.986061	−	0.166382i	$-0.0532084\pi$
$883$	58.6023	1.97212	0.986061	+	0.166382i	$0.0532084\pi$
$884$	−105.173	−3.53734
$885$	−27.6649	−0.929947
$886$	−99.6966	−3.34937
$887$	56.4711	1.89611	0.948057	−	0.318099i	$-0.103044\pi$
$887$	56.4711	1.89611	0.948057	+	0.318099i	$0.103044\pi$
$888$	−4.17055	−0.139955
$889$	−48.1763	−1.61578
$890$	−30.0062	−1.00581
$891$	16.2241	0.543529
$892$	112.569	3.76909
$893$	−5.80023	−0.194097
$894$	25.3105	0.846508
$895$	−83.3272	−2.78532
$896$	25.8896	0.864909
$897$	−4.49817	−0.150190
$898$	86.8521	2.89829
$899$	−5.33294	−0.177864
$900$	−60.6243	−2.02081
$901$	−34.6899	−1.15569
$902$	99.3538	3.30812
$903$	−18.7243	−0.623106
$904$	27.8628	0.926704
$905$	−64.9518	−2.15907
$906$	−8.00769	−0.266038
$907$	12.9866	0.431212	0.215606	−	0.976480i	$-0.430827\pi$
$907$	12.9866	0.431212	0.215606	+	0.976480i	$0.430827\pi$
$908$	−33.3663	−1.10730
$909$	−2.58515	−0.0857439
$910$	138.664	4.59665
$911$	40.2478	1.33347	0.666734	−	0.745295i	$-0.267692\pi$
$911$	40.2478	1.33347	0.666734	+	0.745295i	$0.267692\pi$
$912$	−5.76883	−0.191025
$913$	45.7103	1.51279
$914$	2.31009	0.0764110
$915$	−30.7140	−1.01537
$916$	71.8236	2.37312
$917$	10.6200	0.350703
$918$	−42.5362	−1.40390
$919$	−8.22188	−0.271215	−0.135607	−	0.990763i	$-0.543299\pi$
$919$	−8.22188	−0.271215	−0.135607	+	0.990763i	$0.543299\pi$
$920$	−23.9547	−0.789762
$921$	−12.7345	−0.419615
$922$	−72.6532	−2.39271
$923$	−12.9313	−0.425639
$924$	36.8249	1.21145
$925$	4.59329	0.151026
$926$	−41.3506	−1.35886
$927$	31.6212	1.03858
$928$	7.05828	0.231699
$929$	32.8167	1.07668	0.538340	−	0.842727i	$-0.319051\pi$
$929$	32.8167	1.07668	0.538340	+	0.842727i	$0.319051\pi$
$930$	31.8271	1.04365
$931$	−2.27157	−0.0744478
$932$	−25.3748	−0.831181
$933$	−10.6137	−0.347476
$934$	−70.6341	−2.31122
$935$	48.2329	1.57738
$936$	90.5847	2.96085
$937$	17.7696	0.580507	0.290254	−	0.956950i	$-0.406260\pi$
$937$	17.7696	0.580507	0.290254	+	0.956950i	$0.406260\pi$
$938$	−104.587	−3.41488
$939$	−3.74706	−0.122281
$940$	−85.6971	−2.79513
$941$	28.1136	0.916478	0.458239	−	0.888829i	$-0.348480\pi$
$941$	28.1136	0.916478	0.458239	+	0.888829i	$0.348480\pi$
$942$	−2.95616	−0.0963170
$943$	11.9892	0.390423
$944$	93.2393	3.03468
$945$	39.0686	1.27090
$946$	78.1393	2.54053
$947$	−16.9320	−0.550215	−0.275107	−	0.961414i	$-0.588713\pi$
$947$	−16.9320	−0.550215	−0.275107	+	0.961414i	$0.588713\pi$
$948$	25.5968	0.831346
$949$	−39.8905	−1.29490
$950$	13.7332	0.445563
$951$	0.729440	0.0236537
$952$	84.1980	2.72887
$953$	41.2860	1.33739	0.668693	−	0.743539i	$-0.266854\pi$
$953$	41.2860	1.33739	0.668693	+	0.743539i	$0.266854\pi$
$954$	52.9249	1.71351
$955$	−5.40273	−0.174828
$956$	100.678	3.25617
$957$	−2.65838	−0.0859332
$958$	−17.0257	−0.550074
$959$	−22.1776	−0.716151
$960$	−5.00835	−0.161644
$961$	−3.09611	−0.0998746
$962$	−12.1573	−0.391967
$963$	30.3578	0.978265
$964$	−57.0509	−1.83749
$965$	20.8488	0.671145
$966$	6.37881	0.205235
$967$	22.2420	0.715255	0.357627	−	0.933864i	$-0.383586\pi$
$967$	22.2420	0.715255	0.357627	+	0.933864i	$0.383586\pi$
$968$	−13.5231	−0.434648
$969$	3.02971	0.0973282
$970$	28.5431	0.916462
$971$	−37.5892	−1.20630	−0.603148	−	0.797629i	$-0.706087\pi$
$971$	−37.5892	−1.20630	−0.603148	+	0.797629i	$0.706087\pi$
$972$	70.0131	2.24567
$973$	−50.8269	−1.62943
$974$	−72.2831	−2.31610
$975$	21.5097	0.688860
$976$	103.516	3.31345
$977$	10.0436	0.321322	0.160661	−	0.987010i	$-0.448637\pi$
$977$	10.0436	0.321322	0.160661	+	0.987010i	$0.448637\pi$
$978$	17.7268	0.566842
$979$	−13.1138	−0.419118
$980$	−33.5620	−1.07210
$981$	9.63081	0.307488
$982$	25.5811	0.816326
$983$	13.9807	0.445916	0.222958	−	0.974828i	$-0.428429\pi$
$983$	13.9807	0.445916	0.222958	+	0.974828i	$0.428429\pi$
$984$	52.0545	1.65944
$985$	−72.3882	−2.30648
$986$	−10.7667	−0.342881
$987$	12.8828	0.410065
$988$	−25.3217	−0.805590
$989$	9.42924	0.299832
$990$	−73.5867	−2.33874
$991$	46.7598	1.48537	0.742687	−	0.669639i	$-0.233551\pi$
$991$	46.7598	1.48537	0.742687	+	0.669639i	$0.233551\pi$
$992$	−36.9315	−1.17258
$993$	10.3992	0.330009
$994$	18.3377	0.581638
$995$	−8.02744	−0.254487
$996$	42.4222	1.34420
$997$	49.6022	1.57092	0.785458	−	0.618915i	$-0.212427\pi$
$997$	49.6022	1.57092	0.785458	+	0.618915i	$0.212427\pi$
$998$	44.4209	1.40612
$999$	−3.42532	−0.108372

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	6023.2.a.d.1.10	✓	140

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
6023.2.a.d.1.10	✓	140	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:	\( N \)	\(=\)	\( 6023 = 19 \cdot 317 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	6023.a (trivial)

\(f(q)\)	\(=\)	\(q-2.56765 q^{2} +0.729440 q^{3} +4.59285 q^{4} -3.21691 q^{5} -1.87295 q^{6} +3.04493 q^{7} -6.65754 q^{8} -2.46792 q^{9} +O(q^{10})\)	\(q-2.56765 q^{2} +0.729440 q^{3} +4.59285 q^{4} -3.21691 q^{5} -1.87295 q^{6} +3.04493 q^{7} -6.65754 q^{8} -2.46792 q^{9} +8.25992 q^{10} +3.60988 q^{11} +3.35021 q^{12} +5.51328 q^{13} -7.81832 q^{14} -2.34654 q^{15} +7.90858 q^{16} -4.15347 q^{17} +6.33676 q^{18} -1.00000 q^{19} -14.7748 q^{20} +2.22109 q^{21} -9.26893 q^{22} -1.11850 q^{23} -4.85628 q^{24} +5.34852 q^{25} -14.1562 q^{26} -3.98852 q^{27} +13.9849 q^{28} -1.00957 q^{29} +6.02511 q^{30} +5.28241 q^{31} -6.99140 q^{32} +2.63319 q^{33} +10.6647 q^{34} -9.79526 q^{35} -11.3348 q^{36} +0.858796 q^{37} +2.56765 q^{38} +4.02161 q^{39} +21.4167 q^{40} -10.7190 q^{41} -5.70299 q^{42} -8.43024 q^{43} +16.5796 q^{44} +7.93907 q^{45} +2.87193 q^{46} +5.80023 q^{47} +5.76883 q^{48} +2.27157 q^{49} -13.7332 q^{50} -3.02971 q^{51} +25.3217 q^{52} +8.35204 q^{53} +10.2411 q^{54} -11.6127 q^{55} -20.2717 q^{56} -0.729440 q^{57} +2.59222 q^{58} +11.7897 q^{59} -10.7773 q^{60} +13.0890 q^{61} -13.5634 q^{62} -7.51463 q^{63} +2.13435 q^{64} -17.7357 q^{65} -6.76112 q^{66} +13.3772 q^{67} -19.0763 q^{68} -0.815880 q^{69} +25.1508 q^{70} -2.34548 q^{71} +16.4303 q^{72} -7.23535 q^{73} -2.20509 q^{74} +3.90143 q^{75} -4.59285 q^{76} +10.9918 q^{77} -10.3261 q^{78} +7.64037 q^{79} -25.4412 q^{80} +4.49437 q^{81} +27.5227 q^{82} +12.6626 q^{83} +10.2011 q^{84} +13.3613 q^{85} +21.6459 q^{86} -0.736417 q^{87} -24.0329 q^{88} -3.63274 q^{89} -20.3848 q^{90} +16.7875 q^{91} -5.13711 q^{92} +3.85320 q^{93} -14.8930 q^{94} +3.21691 q^{95} -5.09980 q^{96} +3.45561 q^{97} -5.83262 q^{98} -8.90889 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 140 q + 4 q^{2} + 3 q^{3} + 162 q^{4} + 13 q^{5} + 12 q^{6} + 25 q^{7} + 12 q^{8} + 181 q^{9}+O(q^{10}) \) 140 * q + 4 * q^2 + 3 * q^3 + 162 * q^4 + 13 * q^5 + 12 * q^6 + 25 * q^7 + 12 * q^8 + 181 * q^9	\( 140 q + 4 q^{2} + 3 q^{3} + 162 q^{4} + 13 q^{5} + 12 q^{6} + 25 q^{7} + 12 q^{8} + 181 q^{9} + 8 q^{10} + 19 q^{11} + 17 q^{12} + 28 q^{13} + 5 q^{14} + 14 q^{15} + 202 q^{16} + 38 q^{17} + 26 q^{18} - 140 q^{19} + 36 q^{20} + 4 q^{21} + 53 q^{22} + 58 q^{23} + 47 q^{24} + 279 q^{25} + 29 q^{26} + 21 q^{27} + 69 q^{28} + 18 q^{29} + 50 q^{30} + 20 q^{31} + 13 q^{32} + 47 q^{33} + 6 q^{34} + 35 q^{35} + 230 q^{36} + 88 q^{37} - 4 q^{38} + 32 q^{39} + 32 q^{40} + 24 q^{41} + 75 q^{42} + 100 q^{43} + 63 q^{44} + 87 q^{45} + 23 q^{46} + 35 q^{47} + 46 q^{48} + 255 q^{49} + 11 q^{50} - 6 q^{51} + 47 q^{52} + 77 q^{53} + 16 q^{54} + 63 q^{55} + 21 q^{56} - 3 q^{57} + 165 q^{58} + 18 q^{59} + 28 q^{60} + 99 q^{61} + 34 q^{62} + 89 q^{63} + 298 q^{64} + 78 q^{65} - 3 q^{66} + 28 q^{67} + 93 q^{68} + 19 q^{69} + 16 q^{70} + q^{71} + 43 q^{72} + 201 q^{73} + 32 q^{74} + 22 q^{75} - 162 q^{76} + 86 q^{77} + 122 q^{78} + 58 q^{79} + 92 q^{80} + 288 q^{81} + 143 q^{82} + 57 q^{83} + q^{84} + 136 q^{85} - 6 q^{86} + 43 q^{87} + 198 q^{88} + 46 q^{89} + 30 q^{90} + 26 q^{91} + 129 q^{92} + 111 q^{93} + 44 q^{94} - 13 q^{95} + 32 q^{96} + 110 q^{97} - 34 q^{98} + 62 q^{99}+O(q^{100}) \) 140 * q + 4 * q^2 + 3 * q^3 + 162 * q^4 + 13 * q^5 + 12 * q^6 + 25 * q^7 + 12 * q^8 + 181 * q^9 + 8 * q^10 + 19 * q^11 + 17 * q^12 + 28 * q^13 + 5 * q^14 + 14 * q^15 + 202 * q^16 + 38 * q^17 + 26 * q^18 - 140 * q^19 + 36 * q^20 + 4 * q^21 + 53 * q^22 + 58 * q^23 + 47 * q^24 + 279 * q^25 + 29 * q^26 + 21 * q^27 + 69 * q^28 + 18 * q^29 + 50 * q^30 + 20 * q^31 + 13 * q^32 + 47 * q^33 + 6 * q^34 + 35 * q^35 + 230 * q^36 + 88 * q^37 - 4 * q^38 + 32 * q^39 + 32 * q^40 + 24 * q^41 + 75 * q^42 + 100 * q^43 + 63 * q^44 + 87 * q^45 + 23 * q^46 + 35 * q^47 + 46 * q^48 + 255 * q^49 + 11 * q^50 - 6 * q^51 + 47 * q^52 + 77 * q^53 + 16 * q^54 + 63 * q^55 + 21 * q^56 - 3 * q^57 + 165 * q^58 + 18 * q^59 + 28 * q^60 + 99 * q^61 + 34 * q^62 + 89 * q^63 + 298 * q^64 + 78 * q^65 - 3 * q^66 + 28 * q^67 + 93 * q^68 + 19 * q^69 + 16 * q^70 + q^71 + 43 * q^72 + 201 * q^73 + 32 * q^74 + 22 * q^75 - 162 * q^76 + 86 * q^77 + 122 * q^78 + 58 * q^79 + 92 * q^80 + 288 * q^81 + 143 * q^82 + 57 * q^83 + q^84 + 136 * q^85 - 6 * q^86 + 43 * q^87 + 198 * q^88 + 46 * q^89 + 30 * q^90 + 26 * q^91 + 129 * q^92 + 111 * q^93 + 44 * q^94 - 13 * q^95 + 32 * q^96 + 110 * q^97 - 34 * q^98 + 62 * q^99

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