LMFDB - Embedded newform 6023.2.a.d.1.6

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			1.6
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)

$f(q)$	$=$	$q-2.67904 q^{2} -0.649743 q^{3} +5.17727 q^{4} -3.70919 q^{5} +1.74069 q^{6} -4.64503 q^{7} -8.51205 q^{8} -2.57783 q^{9} +O(q^{10})$	\(q-2.67904 q^{2} -0.649743 q^{3} +5.17727 q^{4} -3.70919 q^{5} +1.74069 q^{6} -4.64503 q^{7} -8.51205 q^{8} -2.57783 q^{9} +9.93707 q^{10} +5.55022 q^{11} -3.36390 q^{12} +3.68913 q^{13} +12.4442 q^{14} +2.41002 q^{15} +12.4496 q^{16} +6.65447 q^{17} +6.90613 q^{18} -1.00000 q^{19} -19.2035 q^{20} +3.01808 q^{21} -14.8693 q^{22} +1.40715 q^{23} +5.53065 q^{24} +8.75807 q^{25} -9.88333 q^{26} +3.62416 q^{27} -24.0486 q^{28} -9.03434 q^{29} -6.45655 q^{30} +1.41822 q^{31} -16.3289 q^{32} -3.60622 q^{33} -17.8276 q^{34} +17.2293 q^{35} -13.3461 q^{36} +9.39984 q^{37} +2.67904 q^{38} -2.39699 q^{39} +31.5728 q^{40} +3.79229 q^{41} -8.08556 q^{42} +2.91101 q^{43} +28.7350 q^{44} +9.56167 q^{45} -3.76982 q^{46} -0.144828 q^{47} -8.08904 q^{48} +14.5763 q^{49} -23.4632 q^{50} -4.32370 q^{51} +19.0996 q^{52} +10.4115 q^{53} -9.70928 q^{54} -20.5868 q^{55} +39.5387 q^{56} +0.649743 q^{57} +24.2034 q^{58} -12.4343 q^{59} +12.4773 q^{60} +0.894834 q^{61} -3.79948 q^{62} +11.9741 q^{63} +18.8467 q^{64} -13.6837 q^{65} +9.66121 q^{66} -2.81839 q^{67} +34.4520 q^{68} -0.914286 q^{69} -46.1580 q^{70} +3.31995 q^{71} +21.9426 q^{72} +14.2178 q^{73} -25.1826 q^{74} -5.69050 q^{75} -5.17727 q^{76} -25.7809 q^{77} +6.42163 q^{78} -3.61496 q^{79} -46.1779 q^{80} +5.37873 q^{81} -10.1597 q^{82} -10.7456 q^{83} +15.6254 q^{84} -24.6827 q^{85} -7.79873 q^{86} +5.87000 q^{87} -47.2437 q^{88} -0.927022 q^{89} -25.6161 q^{90} -17.1361 q^{91} +7.28520 q^{92} -0.921480 q^{93} +0.388000 q^{94} +3.70919 q^{95} +10.6096 q^{96} -8.98110 q^{97} -39.0506 q^{98} -14.3075 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	−2.67904	−1.89437	−0.947185	−	0.320688i	$-0.896086\pi$
$2$	−2.67904	−1.89437	−0.947185	+	0.320688i	$0.896086\pi$
$3$	−0.649743	−0.375129	−0.187565	−	0.982252i	$-0.560059\pi$
$3$	−0.649743	−0.375129	−0.187565	+	0.982252i	$0.560059\pi$
$4$	5.17727	2.58864
$5$	−3.70919	−1.65880	−0.829399	−	0.558656i	$-0.811317\pi$
$5$	−3.70919	−1.65880	−0.829399	+	0.558656i	$0.811317\pi$
$6$	1.74069	0.710634
$7$	−4.64503	−1.75566	−0.877829	−	0.478975i	$-0.841008\pi$
$7$	−4.64503	−1.75566	−0.877829	+	0.478975i	$0.841008\pi$
$8$	−8.51205	−3.00946
$9$	−2.57783	−0.859278
$10$	9.93707	3.14238
$11$	5.55022	1.67345	0.836726	−	0.547621i	$-0.184466\pi$
$11$	5.55022	1.67345	0.836726	+	0.547621i	$0.184466\pi$
$12$	−3.36390	−0.971074
$13$	3.68913	1.02318	0.511590	−	0.859230i	$-0.329057\pi$
$13$	3.68913	1.02318	0.511590	+	0.859230i	$0.329057\pi$
$14$	12.4442	3.32586
$15$	2.41002	0.622264
$16$	12.4496	3.11240
$17$	6.65447	1.61395	0.806973	−	0.590588i	$-0.201104\pi$
$17$	6.65447	1.61395	0.806973	+	0.590588i	$0.201104\pi$
$18$	6.90613	1.62779
$19$	−1.00000	−0.229416
$19$	−1.00000	−0.229416
$20$	−19.2035	−4.29403
$21$	3.01808	0.658599
$22$	−14.8693	−3.17014
$23$	1.40715	0.293411	0.146706	−	0.989180i	$-0.453133\pi$
$23$	1.40715	0.293411	0.146706	+	0.989180i	$0.453133\pi$
$24$	5.53065	1.12894
$25$	8.75807	1.75161
$26$	−9.88333	−1.93828
$27$	3.62416	0.697470
$28$	−24.0486	−4.54476
$29$	−9.03434	−1.67763	−0.838817	−	0.544413i	$-0.816752\pi$
$29$	−9.03434	−1.67763	−0.838817	+	0.544413i	$0.816752\pi$
$30$	−6.45655	−1.17880
$31$	1.41822	0.254720	0.127360	−	0.991857i	$-0.459350\pi$
$31$	1.41822	0.254720	0.127360	+	0.991857i	$0.459350\pi$
$32$	−16.3289	−2.88657
$33$	−3.60622	−0.627761
$34$	−17.8276	−3.05741
$35$	17.2293	2.91228
$36$	−13.3461	−2.22436
$37$	9.39984	1.54532	0.772662	−	0.634818i	$-0.218925\pi$
$37$	9.39984	1.54532	0.772662	+	0.634818i	$0.218925\pi$
$38$	2.67904	0.434598
$39$	−2.39699	−0.383825
$40$	31.5728	4.99209
$41$	3.79229	0.592257	0.296128	−	0.955148i	$-0.404304\pi$
$41$	3.79229	0.592257	0.296128	+	0.955148i	$0.404304\pi$
$42$	−8.08556	−1.24763
$43$	2.91101	0.443925	0.221963	−	0.975055i	$-0.428754\pi$
$43$	2.91101	0.443925	0.221963	+	0.975055i	$0.428754\pi$
$44$	28.7350	4.33196
$45$	9.56167	1.42537
$46$	−3.76982	−0.555829
$47$	−0.144828	−0.0211253	−0.0105627	−	0.999944i	$-0.503362\pi$
$47$	−0.144828	−0.0211253	−0.0105627	+	0.999944i	$0.503362\pi$
$48$	−8.08904	−1.16755
$49$	14.5763	2.08233
$50$	−23.4632	−3.31820
$51$	−4.32370	−0.605439
$52$	19.0996	2.64864
$53$	10.4115	1.43013	0.715065	−	0.699057i	$-0.246397\pi$
$53$	10.4115	1.43013	0.715065	+	0.699057i	$0.246397\pi$
$54$	−9.70928	−1.32127
$55$	−20.5868	−2.77592
$56$	39.5387	5.28359
$57$	0.649743	0.0860606
$58$	24.2034	3.17806
$59$	−12.4343	−1.61881	−0.809406	−	0.587250i	$-0.800211\pi$
$59$	−12.4343	−1.61881	−0.809406	+	0.587250i	$0.800211\pi$
$60$	12.4773	1.61082
$61$	0.894834	0.114572	0.0572859	−	0.998358i	$-0.481755\pi$
$61$	0.894834	0.114572	0.0572859	+	0.998358i	$0.481755\pi$
$62$	−3.79948	−0.482534
$63$	11.9741	1.50860
$64$	18.8467	2.35583
$65$	−13.6837	−1.69725
$66$	9.66121	1.18921
$67$	−2.81839	−0.344322	−0.172161	−	0.985069i	$-0.555075\pi$
$67$	−2.81839	−0.344322	−0.172161	+	0.985069i	$0.555075\pi$
$68$	34.4520	4.17792
$69$	−0.914286	−0.110067
$70$	−46.1580	−5.51694
$71$	3.31995	0.394006	0.197003	−	0.980403i	$-0.436879\pi$
$71$	3.31995	0.394006	0.197003	+	0.980403i	$0.436879\pi$
$72$	21.9426	2.58597
$73$	14.2178	1.66407	0.832035	−	0.554723i	$-0.187176\pi$
$73$	14.2178	1.66407	0.832035	+	0.554723i	$0.187176\pi$
$74$	−25.1826	−2.92742
$75$	−5.69050	−0.657082
$76$	−5.17727	−0.593874
$77$	−25.7809	−2.93801
$78$	6.42163	0.727106
$79$	−3.61496	−0.406714	−0.203357	−	0.979105i	$-0.565185\pi$
$79$	−3.61496	−0.406714	−0.203357	+	0.979105i	$0.565185\pi$
$80$	−46.1779	−5.16284
$81$	5.37873	0.597636
$82$	−10.1597	−1.12195
$83$	−10.7456	−1.17948	−0.589741	−	0.807592i	$-0.700770\pi$
$83$	−10.7456	−1.17948	−0.589741	+	0.807592i	$0.700770\pi$
$84$	15.6254	1.70487
$85$	−24.6827	−2.67721
$86$	−7.79873	−0.840959
$87$	5.87000	0.629330
$88$	−47.2437	−5.03619
$89$	−0.927022	−0.0982641	−0.0491321	−	0.998792i	$-0.515646\pi$
$89$	−0.927022	−0.0982641	−0.0491321	+	0.998792i	$0.515646\pi$
$90$	−25.6161	−2.70018
$91$	−17.1361	−1.79635
$92$	7.28520	0.759535
$93$	−0.921480	−0.0955530
$94$	0.388000	0.0400191
$95$	3.70919	0.380555
$96$	10.6096	1.08284
$97$	−8.98110	−0.911892	−0.455946	−	0.890007i	$-0.650699\pi$
$97$	−8.98110	−0.911892	−0.455946	+	0.890007i	$0.650699\pi$
$98$	−39.0506	−3.94471
$99$	−14.3075	−1.43796
$100$	45.3429	4.53429
$101$	−17.8474	−1.77588	−0.887941	−	0.459957i	$-0.847865\pi$
$101$	−17.8474	−1.77588	−0.887941	+	0.459957i	$0.847865\pi$
$102$	11.5834	1.14692
$103$	13.8719	1.36684	0.683419	−	0.730026i	$-0.260492\pi$
$103$	13.8719	1.36684	0.683419	+	0.730026i	$0.260492\pi$
$104$	−31.4020	−3.07922
$105$	−11.1946	−1.09248
$106$	−27.8929	−2.70920
$107$	5.87027	0.567501	0.283750	−	0.958898i	$-0.408421\pi$
$107$	5.87027	0.567501	0.283750	+	0.958898i	$0.408421\pi$
$108$	18.7633	1.80550
$109$	5.43009	0.520108	0.260054	−	0.965594i	$-0.416260\pi$
$109$	5.43009	0.520108	0.260054	+	0.965594i	$0.416260\pi$
$110$	55.1529	5.25862
$111$	−6.10748	−0.579697
$112$	−57.8288	−5.46431
$113$	3.62763	0.341259	0.170630	−	0.985335i	$-0.445420\pi$
$113$	3.62763	0.341259	0.170630	+	0.985335i	$0.445420\pi$
$114$	−1.74069	−0.163031
$115$	−5.21938	−0.486710
$116$	−46.7732	−4.34278
$117$	−9.50996	−0.879196
$118$	33.3121	3.06663
$119$	−30.9102	−2.83354
$120$	−20.5142	−1.87268
$121$	19.8049	1.80044
$122$	−2.39730	−0.217041
$123$	−2.46402	−0.222173
$124$	7.34252	0.659378
$125$	−13.9394	−1.24678
$126$	−32.0792	−2.85784
$127$	2.18933	0.194272	0.0971360	−	0.995271i	$-0.469032\pi$
$127$	2.18933	0.194272	0.0971360	+	0.995271i	$0.469032\pi$
$128$	−17.8332	−1.57625
$129$	−1.89141	−0.166529
$130$	36.6591	3.21522
$131$	−12.1928	−1.06529	−0.532647	−	0.846338i	$-0.678803\pi$
$131$	−12.1928	−1.06529	−0.532647	+	0.846338i	$0.678803\pi$
$132$	−18.6704	−1.62505
$133$	4.64503	0.402775
$134$	7.55060	0.652272
$135$	−13.4427	−1.15696
$136$	−56.6432	−4.85711
$137$	14.3531	1.22627	0.613136	−	0.789978i	$-0.289908\pi$
$137$	14.3531	1.22627	0.613136	+	0.789978i	$0.289908\pi$
$138$	2.44941	0.208508
$139$	6.78629	0.575606	0.287803	−	0.957690i	$-0.407075\pi$
$139$	6.78629	0.575606	0.287803	+	0.957690i	$0.407075\pi$
$140$	89.2007	7.53884
$141$	0.0941009	0.00792472
$142$	−8.89430	−0.746393
$143$	20.4755	1.71224
$144$	−32.0930	−2.67442
$145$	33.5100	2.78286
$146$	−38.0902	−3.15236
$147$	−9.47087	−0.781144
$148$	48.6655	4.00028
$149$	−21.5630	−1.76651	−0.883255	−	0.468892i	$-0.844653\pi$
$149$	−21.5630	−1.76651	−0.883255	+	0.468892i	$0.844653\pi$
$150$	15.2451	1.24476
$151$	−11.6634	−0.949155	−0.474578	−	0.880214i	$-0.657399\pi$
$151$	−11.6634	−0.949155	−0.474578	+	0.880214i	$0.657399\pi$
$152$	8.51205	0.690418
$153$	−17.1541	−1.38683
$154$	69.0682	5.56568
$155$	−5.26045	−0.422529
$156$	−12.4098	−0.993583
$157$	5.47271	0.436770	0.218385	−	0.975863i	$-0.429921\pi$
$157$	5.47271	0.436770	0.218385	+	0.975863i	$0.429921\pi$
$158$	9.68463	0.770468
$159$	−6.76481	−0.536484
$160$	60.5670	4.78824
$161$	−6.53626	−0.515129
$162$	−14.4098	−1.13214
$163$	−6.11324	−0.478826	−0.239413	−	0.970918i	$-0.576955\pi$
$163$	−6.11324	−0.478826	−0.239413	+	0.970918i	$0.576955\pi$
$164$	19.6337	1.53314
$165$	13.3761	1.04133
$166$	28.7879	2.23438
$167$	−17.3337	−1.34133	−0.670663	−	0.741762i	$-0.733990\pi$
$167$	−17.3337	−1.34133	−0.670663	+	0.741762i	$0.733990\pi$
$168$	−25.6900	−1.98203
$169$	0.609662	0.0468971
$170$	66.1260	5.07163
$171$	2.57783	0.197132
$172$	15.0711	1.14916
$173$	4.16141	0.316386	0.158193	−	0.987408i	$-0.449433\pi$
$173$	4.16141	0.316386	0.158193	+	0.987408i	$0.449433\pi$
$174$	−15.7260	−1.19218
$175$	−40.6815	−3.07523
$176$	69.0979	5.20845
$177$	8.07912	0.607264
$178$	2.48353	0.186149
$179$	24.3189	1.81768	0.908840	−	0.417144i	$-0.136969\pi$
$179$	24.3189	1.81768	0.908840	+	0.417144i	$0.136969\pi$
$180$	49.5033	3.68976
$181$	−1.40274	−0.104265	−0.0521323	−	0.998640i	$-0.516602\pi$
$181$	−1.40274	−0.104265	−0.0521323	+	0.998640i	$0.516602\pi$
$182$	45.9084	3.40296
$183$	−0.581413	−0.0429793
$184$	−11.9777	−0.883010
$185$	−34.8658	−2.56338
$186$	2.46868	0.181013
$187$	36.9337	2.70086
$188$	−0.749813	−0.0546857
$189$	−16.8343	−1.22452
$190$	−9.93707	−0.720911
$191$	−16.5784	−1.19957	−0.599784	−	0.800162i	$-0.704747\pi$
$191$	−16.5784	−1.19957	−0.599784	+	0.800162i	$0.704747\pi$
$192$	−12.2455	−0.883743
$193$	4.97196	0.357889	0.178945	−	0.983859i	$-0.442732\pi$
$193$	4.97196	0.357889	0.178945	+	0.983859i	$0.442732\pi$
$194$	24.0608	1.72746
$195$	8.89087	0.636688
$196$	75.4656	5.39040
$197$	−9.45279	−0.673483	−0.336742	−	0.941597i	$-0.609325\pi$
$197$	−9.45279	−0.673483	−0.336742	+	0.941597i	$0.609325\pi$
$198$	38.3305	2.72403
$199$	6.20071	0.439557	0.219778	−	0.975550i	$-0.429467\pi$
$199$	6.20071	0.439557	0.219778	+	0.975550i	$0.429467\pi$
$200$	−74.5491	−5.27142
$201$	1.83123	0.129165
$202$	47.8139	3.36418
$203$	41.9648	2.94535
$204$	−22.3850	−1.56726
$205$	−14.0663	−0.982435
$206$	−37.1634	−2.58930
$207$	−3.62740	−0.252122
$208$	45.9282	3.18454
$209$	−5.55022	−0.383916
$210$	29.9909	2.06957
$211$	5.32008	0.366249	0.183125	−	0.983090i	$-0.441379\pi$
$211$	5.32008	0.366249	0.183125	+	0.983090i	$0.441379\pi$
$212$	53.9032	3.70209
$213$	−2.15712	−0.147803
$214$	−15.7267	−1.07506
$215$	−10.7975	−0.736383
$216$	−30.8490	−2.09901
$217$	−6.58769	−0.447201
$218$	−14.5474	−0.985277
$219$	−9.23794	−0.624242
$220$	−106.583	−7.18585
$221$	24.5492	1.65136
$222$	16.3622	1.09816
$223$	−26.2448	−1.75748	−0.878740	−	0.477301i	$-0.841615\pi$
$223$	−26.2448	−1.75748	−0.878740	+	0.477301i	$0.841615\pi$
$224$	75.8483	5.06783
$225$	−22.5768	−1.50512
$226$	−9.71859	−0.646471
$227$	1.47217	0.0977116	0.0488558	−	0.998806i	$-0.484443\pi$
$227$	1.47217	0.0977116	0.0488558	+	0.998806i	$0.484443\pi$
$228$	3.36390	0.222780
$229$	−1.29396	−0.0855071	−0.0427536	−	0.999086i	$-0.513613\pi$
$229$	−1.29396	−0.0855071	−0.0427536	+	0.999086i	$0.513613\pi$
$230$	13.9830	0.922009
$231$	16.7510	1.10213
$232$	76.9007	5.04878
$233$	−19.4627	−1.27505	−0.637523	−	0.770431i	$-0.720041\pi$
$233$	−19.4627	−1.27505	−0.637523	+	0.770431i	$0.720041\pi$
$234$	25.4776	1.66552
$235$	0.537193	0.0350426
$236$	−64.3759	−4.19051
$237$	2.34879	0.152571
$238$	82.8098	5.36776
$239$	−12.4075	−0.802573	−0.401287	−	0.915952i	$-0.631437\pi$
$239$	−12.4075	−0.802573	−0.401287	+	0.915952i	$0.631437\pi$
$240$	30.0038	1.93674
$241$	9.89873	0.637633	0.318817	−	0.947816i	$-0.396715\pi$
$241$	9.89873	0.637633	0.318817	+	0.947816i	$0.396715\pi$
$242$	−53.0582	−3.41071
$243$	−14.3673	−0.921661
$244$	4.63280	0.296585
$245$	−54.0663	−3.45417
$246$	6.60121	0.420878
$247$	−3.68913	−0.234734
$248$	−12.0720	−0.766571
$249$	6.98188	0.442459
$250$	37.3442	2.36185
$251$	30.8267	1.94576	0.972882	−	0.231302i	$-0.0742985\pi$
$251$	30.8267	1.94576	0.972882	+	0.231302i	$0.0742985\pi$
$252$	61.9933	3.90521
$253$	7.80999	0.491010
$254$	−5.86532	−0.368023
$255$	16.0374	1.00430
$256$	10.0826	0.630162
$257$	−9.07628	−0.566163	−0.283082	−	0.959096i	$-0.591357\pi$
$257$	−9.07628	−0.566163	−0.283082	+	0.959096i	$0.591357\pi$
$258$	5.06717	0.315468
$259$	−43.6626	−2.71306
$260$	−70.8440	−4.39356
$261$	23.2890	1.44155
$262$	32.6652	2.01806
$263$	10.4361	0.643520	0.321760	−	0.946821i	$-0.395725\pi$
$263$	10.4361	0.643520	0.321760	+	0.946821i	$0.395725\pi$
$264$	30.6963	1.88923
$265$	−38.6182	−2.37230
$266$	−12.4442	−0.763005
$267$	0.602326	0.0368618
$268$	−14.5916	−0.891323
$269$	−24.5275	−1.49547	−0.747734	−	0.663999i	$-0.768858\pi$
$269$	−24.5275	−1.49547	−0.747734	+	0.663999i	$0.768858\pi$
$270$	36.0135	2.19171
$271$	28.2437	1.71568	0.857841	−	0.513915i	$-0.171805\pi$
$271$	28.2437	1.71568	0.857841	+	0.513915i	$0.171805\pi$
$272$	82.8455	5.02325
$273$	11.1341	0.673865
$274$	−38.4527	−2.32301
$275$	48.6092	2.93124
$276$	−4.73351	−0.284924
$277$	22.3703	1.34410	0.672050	−	0.740506i	$-0.265414\pi$
$277$	22.3703	1.34410	0.672050	+	0.740506i	$0.265414\pi$
$278$	−18.1808	−1.09041
$279$	−3.65594	−0.218875
$280$	−146.657	−8.76441
$281$	13.9099	0.829795	0.414898	−	0.909868i	$-0.363817\pi$
$281$	13.9099	0.829795	0.414898	+	0.909868i	$0.363817\pi$
$282$	−0.252100	−0.0150124
$283$	15.8337	0.941217	0.470609	−	0.882342i	$-0.344034\pi$
$283$	15.8337	0.941217	0.470609	+	0.882342i	$0.344034\pi$
$284$	17.1883	1.01994
$285$	−2.41002	−0.142757
$286$	−54.8546	−3.24362
$287$	−17.6153	−1.03980
$288$	42.0932	2.48037
$289$	27.2820	1.60482
$290$	−89.7749	−5.27176
$291$	5.83541	0.342078
$292$	73.6095	4.30767
$293$	15.1567	0.885464	0.442732	−	0.896654i	$-0.354009\pi$
$293$	15.1567	0.885464	0.442732	+	0.896654i	$0.354009\pi$
$294$	25.3729	1.47978
$295$	46.1212	2.68528
$296$	−80.0119	−4.65060
$297$	20.1149	1.16718
$298$	57.7682	3.34642
$299$	5.19116	0.300212
$300$	−29.4612	−1.70095
$301$	−13.5217	−0.779381
$302$	31.2468	1.79805
$303$	11.5962	0.666186
$304$	−12.4496	−0.714033
$305$	−3.31911	−0.190052
$306$	45.9566	2.62717
$307$	−14.3770	−0.820540	−0.410270	−	0.911964i	$-0.634565\pi$
$307$	−14.3770	−0.820540	−0.410270	+	0.911964i	$0.634565\pi$
$308$	−133.475	−7.60544
$309$	−9.01317	−0.512741
$310$	14.0930	0.800427
$311$	−7.42616	−0.421099	−0.210549	−	0.977583i	$-0.567525\pi$
$311$	−7.42616	−0.421099	−0.210549	+	0.977583i	$0.567525\pi$
$312$	20.4033	1.15511
$313$	27.2016	1.53753	0.768763	−	0.639534i	$-0.220872\pi$
$313$	27.2016	1.53753	0.768763	+	0.639534i	$0.220872\pi$
$314$	−14.6616	−0.827403
$315$	−44.4143	−2.50246
$316$	−18.7156	−1.05284
$317$	1.00000	0.0561656
$317$	1.00000	0.0561656
$318$	18.1232	1.01630
$319$	−50.1425	−2.80744
$320$	−69.9058	−3.90785
$321$	−3.81417	−0.212886
$322$	17.5109	0.975845
$323$	−6.65447	−0.370265
$324$	27.8471	1.54706
$325$	32.3096	1.79222
$326$	16.3776	0.907073
$327$	−3.52816	−0.195108
$328$	−32.2802	−1.78237
$329$	0.672730	0.0370888
$330$	−35.8352	−1.97266
$331$	−3.05716	−0.168037	−0.0840184	−	0.996464i	$-0.526775\pi$
$331$	−3.05716	−0.168037	−0.0840184	+	0.996464i	$0.526775\pi$
$332$	−55.6329	−3.05325
$333$	−24.2312	−1.32786
$334$	46.4379	2.54097
$335$	10.4540	0.571160
$336$	37.5739	2.04982
$337$	−7.61681	−0.414914	−0.207457	−	0.978244i	$-0.566519\pi$
$337$	−7.61681	−0.414914	−0.207457	+	0.978244i	$0.566519\pi$
$338$	−1.63331	−0.0888404
$339$	−2.35703	−0.128016
$340$	−127.789	−6.93033
$341$	7.87144	0.426262
$342$	−6.90613	−0.373441
$343$	−35.1923	−1.90020
$344$	−24.7787	−1.33598
$345$	3.39126	0.182579
$346$	−11.1486	−0.599352
$347$	−11.2340	−0.603075	−0.301538	−	0.953454i	$-0.597500\pi$
$347$	−11.2340	−0.603075	−0.301538	+	0.953454i	$0.597500\pi$
$348$	30.3906	1.62911
$349$	11.2441	0.601885	0.300943	−	0.953642i	$-0.402699\pi$
$349$	11.2441	0.601885	0.300943	+	0.953642i	$0.402699\pi$
$350$	108.988	5.82563
$351$	13.3700	0.713637
$352$	−90.6290	−4.83054
$353$	−1.83868	−0.0978628	−0.0489314	−	0.998802i	$-0.515582\pi$
$353$	−1.83868	−0.0978628	−0.0489314	+	0.998802i	$0.515582\pi$
$354$	−21.6443	−1.15038
$355$	−12.3143	−0.653577
$356$	−4.79944	−0.254370
$357$	20.0837	1.06294
$358$	−65.1514	−3.44336
$359$	14.5887	0.769962	0.384981	−	0.922924i	$-0.374208\pi$
$359$	14.5887	0.769962	0.384981	+	0.922924i	$0.374208\pi$
$360$	−81.3894	−4.28960
$361$	1.00000	0.0526316
$362$	3.75800	0.197516
$363$	−12.8681	−0.675400
$364$	−88.7183	−4.65010
$365$	−52.7366	−2.76036
$366$	1.55763	0.0814186
$367$	13.5479	0.707195	0.353597	−	0.935398i	$-0.384958\pi$
$367$	13.5479	0.707195	0.353597	+	0.935398i	$0.384958\pi$
$368$	17.5185	0.913213
$369$	−9.77590	−0.508913
$370$	93.4069	4.85599
$371$	−48.3618	−2.51082
$372$	−4.77075	−0.247352
$373$	−19.9149	−1.03115	−0.515577	−	0.856843i	$-0.672422\pi$
$373$	−19.9149	−1.03115	−0.515577	+	0.856843i	$0.672422\pi$
$374$	−98.9471	−5.11643
$375$	9.05702	0.467702
$376$	1.23278	0.0635758
$377$	−33.3288	−1.71652
$378$	45.0999	2.31969
$379$	9.93524	0.510339	0.255170	−	0.966896i	$-0.417869\pi$
$379$	9.93524	0.510339	0.255170	+	0.966896i	$0.417869\pi$
$380$	19.2035	0.985117
$381$	−1.42250	−0.0728771
$382$	44.4142	2.27243
$383$	13.5542	0.692586	0.346293	−	0.938126i	$-0.387440\pi$
$383$	13.5542	0.692586	0.346293	+	0.938126i	$0.387440\pi$
$384$	11.5870	0.591297
$385$	95.6263	4.87357
$386$	−13.3201	−0.677974
$387$	−7.50411	−0.381455
$388$	−46.4976	−2.36056
$389$	30.2527	1.53388	0.766938	−	0.641722i	$-0.221780\pi$
$389$	30.2527	1.53388	0.766938	+	0.641722i	$0.221780\pi$
$390$	−23.8190	−1.20612
$391$	9.36384	0.473550
$392$	−124.074	−6.26670
$393$	7.92222	0.399623
$394$	25.3244	1.27583
$395$	13.4086	0.674658
$396$	−74.0740	−3.72236
$397$	−15.2064	−0.763188	−0.381594	−	0.924330i	$-0.624625\pi$
$397$	−15.2064	−0.763188	−0.381594	+	0.924330i	$0.624625\pi$
$398$	−16.6120	−0.832683
$399$	−3.01808	−0.151093
$400$	109.034	5.45172
$401$	−29.1722	−1.45679	−0.728395	−	0.685158i	$-0.759733\pi$
$401$	−29.1722	−1.45679	−0.728395	+	0.685158i	$0.759733\pi$
$402$	−4.90595	−0.244687
$403$	5.23200	0.260625
$404$	−92.4008	−4.59711
$405$	−19.9507	−0.991359
$406$	−112.425	−5.57958
$407$	52.1711	2.58603
$408$	36.8035	1.82205
$409$	−9.00371	−0.445205	−0.222602	−	0.974909i	$-0.571455\pi$
$409$	−9.00371	−0.445205	−0.222602	+	0.974909i	$0.571455\pi$
$410$	37.6843	1.86109
$411$	−9.32585	−0.460010
$412$	71.8185	3.53825
$413$	57.7578	2.84208
$414$	9.71796	0.477612
$415$	39.8574	1.95652
$416$	−60.2394	−2.95348
$417$	−4.40935	−0.215927
$418$	14.8693	0.727280
$419$	33.9755	1.65981	0.829907	−	0.557902i	$-0.188394\pi$
$419$	33.9755	1.65981	0.829907	+	0.557902i	$0.188394\pi$
$420$	−57.9576	−2.82804
$421$	8.31715	0.405353	0.202677	−	0.979246i	$-0.435036\pi$
$421$	8.31715	0.405353	0.202677	+	0.979246i	$0.435036\pi$
$422$	−14.2527	−0.693812
$423$	0.373342	0.0181525
$424$	−88.6233	−4.30393
$425$	58.2803	2.82701
$426$	5.77901	0.279994
$427$	−4.15654	−0.201149
$428$	30.3920	1.46905
$429$	−13.3038	−0.642313
$430$	28.9269	1.39498
$431$	30.5462	1.47136	0.735679	−	0.677331i	$-0.236863\pi$
$431$	30.5462	1.47136	0.735679	+	0.677331i	$0.236863\pi$
$432$	45.1193	2.17081
$433$	15.4326	0.741644	0.370822	−	0.928704i	$-0.379076\pi$
$433$	15.4326	0.741644	0.370822	+	0.928704i	$0.379076\pi$
$434$	17.6487	0.847164
$435$	−21.7729	−1.04393
$436$	28.1131	1.34637
$437$	−1.40715	−0.0673131
$438$	24.7488	1.18254
$439$	22.1036	1.05495	0.527475	−	0.849571i	$-0.323139\pi$
$439$	22.1036	1.05495	0.527475	+	0.849571i	$0.323139\pi$
$440$	175.236	8.35403
$441$	−37.5753	−1.78930
$442$	−65.7683	−3.12828
$443$	−22.0478	−1.04752	−0.523762	−	0.851865i	$-0.675472\pi$
$443$	−22.0478	−1.04752	−0.523762	+	0.851865i	$0.675472\pi$
$444$	−31.6201	−1.50062
$445$	3.43850	0.163000
$446$	70.3108	3.32932
$447$	14.0104	0.662670
$448$	−87.5434	−4.13604
$449$	22.4377	1.05890	0.529449	−	0.848341i	$-0.322399\pi$
$449$	22.4377	1.05890	0.529449	+	0.848341i	$0.322399\pi$
$450$	60.4843	2.85126
$451$	21.0480	0.991114
$452$	18.7812	0.883396
$453$	7.57823	0.356056
$454$	−3.94402	−0.185102
$455$	63.5611	2.97979
$456$	−5.53065	−0.258996
$457$	27.0692	1.26624	0.633122	−	0.774052i	$-0.281773\pi$
$457$	27.0692	1.26624	0.633122	+	0.774052i	$0.281773\pi$
$458$	3.46657	0.161982
$459$	24.1169	1.12568
$460$	−27.0222	−1.25991
$461$	−9.44060	−0.439692	−0.219846	−	0.975535i	$-0.570556\pi$
$461$	−9.44060	−0.439692	−0.219846	+	0.975535i	$0.570556\pi$
$462$	−44.8766	−2.08785
$463$	−10.2764	−0.477584	−0.238792	−	0.971071i	$-0.576751\pi$
$463$	−10.2764	−0.477584	−0.238792	+	0.971071i	$0.576751\pi$
$464$	−112.474	−5.22147
$465$	3.41794	0.158503
$466$	52.1415	2.41541
$467$	1.34172	0.0620875	0.0310438	−	0.999518i	$-0.490117\pi$
$467$	1.34172	0.0620875	0.0310438	+	0.999518i	$0.490117\pi$
$468$	−49.2356	−2.27592
$469$	13.0915	0.604511
$470$	−1.43916	−0.0663837
$471$	−3.55586	−0.163845
$472$	105.842	4.87175
$473$	16.1567	0.742888
$474$	−6.29252	−0.289025
$475$	−8.75807	−0.401848
$476$	−160.031	−7.33499
$477$	−26.8391	−1.22888
$478$	33.2402	1.52037
$479$	−5.29499	−0.241934	−0.120967	−	0.992657i	$-0.538600\pi$
$479$	−5.29499	−0.241934	−0.120967	+	0.992657i	$0.538600\pi$
$480$	−39.3530	−1.79621
$481$	34.6772	1.58114
$482$	−26.5191	−1.20791
$483$	4.24689	0.193240
$484$	102.535	4.66070
$485$	33.3126	1.51265
$486$	38.4905	1.74597
$487$	−30.2890	−1.37252	−0.686262	−	0.727355i	$-0.740750\pi$
$487$	−30.2890	−1.37252	−0.686262	+	0.727355i	$0.740750\pi$
$488$	−7.61687	−0.344800
$489$	3.97204	0.179622
$490$	144.846	6.54347
$491$	4.93960	0.222921	0.111461	−	0.993769i	$-0.464447\pi$
$491$	4.93960	0.222921	0.111461	+	0.993769i	$0.464447\pi$
$492$	−12.7569	−0.575125
$493$	−60.1187	−2.70761
$494$	9.88333	0.444672
$495$	53.0693	2.38529
$496$	17.6563	0.792791
$497$	−15.4213	−0.691740
$498$	−18.7048	−0.838180
$499$	−10.4287	−0.466851	−0.233425	−	0.972375i	$-0.574993\pi$
$499$	−10.4287	−0.466851	−0.233425	+	0.972375i	$0.574993\pi$
$500$	−72.1679	−3.22745
$501$	11.2625	0.503171
$502$	−82.5861	−3.68600
$503$	−1.81194	−0.0807904	−0.0403952	−	0.999184i	$-0.512862\pi$
$503$	−1.81194	−0.0807904	−0.0403952	+	0.999184i	$0.512862\pi$
$504$	−101.924	−4.54007
$505$	66.1993	2.94583
$506$	−20.9233	−0.930154
$507$	−0.396124	−0.0175925
$508$	11.3348	0.502899
$509$	−7.28952	−0.323102	−0.161551	−	0.986864i	$-0.551650\pi$
$509$	−7.28952	−0.323102	−0.161551	+	0.986864i	$0.551650\pi$
$510$	−42.9649	−1.90252
$511$	−66.0423	−2.92154
$512$	8.65472	0.382488
$513$	−3.62416	−0.160011
$514$	24.3158	1.07252
$515$	−51.4534	−2.26731
$516$	−9.79235	−0.431084
$517$	−0.803825	−0.0353522
$518$	116.974	5.13954
$519$	−2.70385	−0.118686
$520$	116.476	5.10781
$521$	−19.5112	−0.854799	−0.427400	−	0.904063i	$-0.640570\pi$
$521$	−19.5112	−0.854799	−0.427400	+	0.904063i	$0.640570\pi$
$522$	−62.3923	−2.73084
$523$	−25.7858	−1.12753	−0.563767	−	0.825934i	$-0.690648\pi$
$523$	−25.7858	−1.12753	−0.563767	+	0.825934i	$0.690648\pi$
$524$	−63.1257	−2.75766
$525$	26.4325	1.15361
$526$	−27.9589	−1.21907
$527$	9.43751	0.411105
$528$	−44.8959	−1.95384
$529$	−21.0199	−0.913910
$530$	103.460	4.49401
$531$	32.0536	1.39101
$532$	24.0486	1.04264
$533$	13.9903	0.605985
$534$	−1.61366	−0.0698298
$535$	−21.7739	−0.941369
$536$	23.9903	1.03622
$537$	−15.8010	−0.681866
$538$	65.7102	2.83297
$539$	80.9017	3.48468
$540$	−69.5964	−2.99495
$541$	−35.9000	−1.54346	−0.771731	−	0.635949i	$-0.780609\pi$
$541$	−35.9000	−1.54346	−0.771731	+	0.635949i	$0.780609\pi$
$542$	−75.6661	−3.25014
$543$	0.911420	0.0391128
$544$	−108.660	−4.65877
$545$	−20.1412	−0.862755
$546$	−29.8287	−1.27655
$547$	16.1171	0.689118	0.344559	−	0.938765i	$-0.388028\pi$
$547$	16.1171	0.689118	0.344559	+	0.938765i	$0.388028\pi$
$548$	74.3101	3.17437
$549$	−2.30673	−0.0984490
$550$	−130.226	−5.55286
$551$	9.03434	0.384876
$552$	7.78245	0.331243
$553$	16.7916	0.714051
$554$	−59.9309	−2.54622
$555$	22.6538	0.961600
$556$	35.1345	1.49003
$557$	26.3283	1.11556	0.557782	−	0.829987i	$-0.311652\pi$
$557$	26.3283	1.11556	0.557782	+	0.829987i	$0.311652\pi$
$558$	9.79442	0.414631
$559$	10.7391	0.454215
$560$	214.498	9.06419
$561$	−23.9975	−1.01317
$562$	−37.2652	−1.57194
$563$	−8.25539	−0.347923	−0.173962	−	0.984752i	$-0.555657\pi$
$563$	−8.25539	−0.347923	−0.173962	+	0.984752i	$0.555657\pi$
$564$	0.487186	0.0205142
$565$	−13.4556	−0.566080
$566$	−42.4192	−1.78301
$567$	−24.9844	−1.04924
$568$	−28.2596	−1.18575
$569$	−16.9406	−0.710189	−0.355094	−	0.934830i	$-0.615551\pi$
$569$	−16.9406	−0.710189	−0.355094	+	0.934830i	$0.615551\pi$
$570$	6.45655	0.270435
$571$	−14.0576	−0.588290	−0.294145	−	0.955761i	$-0.595035\pi$
$571$	−14.0576	−0.588290	−0.294145	+	0.955761i	$0.595035\pi$
$572$	106.007	4.43237
$573$	10.7717	0.449993
$574$	47.1922	1.96977
$575$	12.3239	0.513943
$576$	−48.5836	−2.02432
$577$	−0.0193522	−0.000805645 0	−0.000402822	−	1.00000i	$-0.500128\pi$
$577$	−0.0193522	−0.000805645 0	−0.000402822		1.00000i	$0.500128\pi$
$578$	−73.0896	−3.04013
$579$	−3.23049	−0.134255
$580$	173.491	7.20381
$581$	49.9136	2.07077
$582$	−15.6333	−0.648022
$583$	57.7861	2.39326
$584$	−121.023	−5.00796
$585$	35.2742	1.45841
$586$	−40.6055	−1.67740
$587$	−25.6001	−1.05663	−0.528314	−	0.849049i	$-0.677176\pi$
$587$	−25.6001	−1.05663	−0.528314	+	0.849049i	$0.677176\pi$
$588$	−49.0333	−2.02210
$589$	−1.41822	−0.0584368
$590$	−123.561	−5.08692
$591$	6.14188	0.252643
$592$	117.024	4.80967
$593$	44.1778	1.81417	0.907083	−	0.420951i	$-0.138304\pi$
$593$	44.1778	1.81417	0.907083	+	0.420951i	$0.138304\pi$
$594$	−53.8886	−2.21108
$595$	114.652	4.70027
$596$	−111.638	−4.57285
$597$	−4.02887	−0.164891
$598$	−13.9073	−0.568713
$599$	13.7189	0.560538	0.280269	−	0.959922i	$-0.409576\pi$
$599$	13.7189	0.560538	0.280269	+	0.959922i	$0.409576\pi$
$600$	48.4378	1.97746
$601$	−22.1397	−0.903095	−0.451548	−	0.892247i	$-0.649128\pi$
$601$	−22.1397	−0.903095	−0.451548	+	0.892247i	$0.649128\pi$
$602$	36.2253	1.47644
$603$	7.26535	0.295868
$604$	−60.3847	−2.45702
$605$	−73.4600	−2.98658
$606$	−31.0668	−1.26200
$607$	−28.1131	−1.14107	−0.570537	−	0.821272i	$-0.693265\pi$
$607$	−28.1131	−1.14107	−0.570537	+	0.821272i	$0.693265\pi$
$608$	16.3289	0.662225
$609$	−27.2663	−1.10489
$610$	8.89203	0.360028
$611$	−0.534288	−0.0216150
$612$	−88.8115	−3.58999
$613$	41.1613	1.66249	0.831245	−	0.555906i	$-0.187629\pi$
$613$	41.1613	1.66249	0.831245	+	0.555906i	$0.187629\pi$
$614$	38.5166	1.55441
$615$	9.13950	0.368540
$616$	219.448	8.84183
$617$	−17.9458	−0.722470	−0.361235	−	0.932475i	$-0.617645\pi$
$617$	−17.9458	−0.722470	−0.361235	+	0.932475i	$0.617645\pi$
$618$	24.1467	0.971321
$619$	41.9313	1.68536	0.842680	−	0.538415i	$-0.180977\pi$
$619$	41.9313	1.68536	0.842680	+	0.538415i	$0.180977\pi$
$620$	−27.2348	−1.09377
$621$	5.09974	0.204645
$622$	19.8950	0.797717
$623$	4.30605	0.172518
$624$	−29.8415	−1.19462
$625$	7.91342	0.316537
$626$	−72.8743	−2.91264
$627$	3.60622	0.144018
$628$	28.3337	1.13064
$629$	62.5510	2.49407
$630$	118.988	4.74058
$631$	20.7490	0.826006	0.413003	−	0.910730i	$-0.364480\pi$
$631$	20.7490	0.826006	0.413003	+	0.910730i	$0.364480\pi$
$632$	30.7707	1.22399
$633$	−3.45669	−0.137391
$634$	−2.67904	−0.106398
$635$	−8.12065	−0.322258
$636$	−35.0233	−1.38876
$637$	53.7739	2.13060
$638$	134.334	5.31833
$639$	−8.55829	−0.338561
$640$	66.1467	2.61468
$641$	−32.1696	−1.27062	−0.635312	−	0.772256i	$-0.719128\pi$
$641$	−32.1696	−1.27062	−0.635312	+	0.772256i	$0.719128\pi$
$642$	10.2183	0.403285
$643$	−6.54020	−0.257920	−0.128960	−	0.991650i	$-0.541164\pi$
$643$	−6.54020	−0.257920	−0.128960	+	0.991650i	$0.541164\pi$
$644$	−33.8400	−1.33348
$645$	7.01560	0.276239
$646$	17.8276	0.701418
$647$	−13.0126	−0.511578	−0.255789	−	0.966733i	$-0.582335\pi$
$647$	−13.0126	−0.511578	−0.255789	+	0.966733i	$0.582335\pi$
$648$	−45.7840	−1.79856
$649$	−69.0132	−2.70900
$650$	−86.5589	−3.39512
$651$	4.28030	0.167758
$652$	−31.6499	−1.23951
$653$	5.56886	0.217926	0.108963	−	0.994046i	$-0.465247\pi$
$653$	5.56886	0.217926	0.108963	+	0.994046i	$0.465247\pi$
$654$	9.45210	0.369607
$655$	45.2255	1.76711
$656$	47.2125	1.84334
$657$	−36.6512	−1.42990
$658$	−1.80227	−0.0702599
$659$	6.29681	0.245289	0.122644	−	0.992451i	$-0.460863\pi$
$659$	6.29681	0.245289	0.122644	+	0.992451i	$0.460863\pi$
$660$	69.2518	2.69562
$661$	−38.4213	−1.49442	−0.747208	−	0.664591i	$-0.768606\pi$
$661$	−38.4213	−1.49442	−0.747208	+	0.664591i	$0.768606\pi$
$662$	8.19027	0.318324
$663$	−15.9507	−0.619473
$664$	91.4670	3.54961
$665$	−17.2293	−0.668123
$666$	64.9165	2.51546
$667$	−12.7127	−0.492237
$668$	−89.7415	−3.47220
$669$	17.0524	0.659282
$670$	−28.0066	−1.08199
$671$	4.96652	0.191731
$672$	−49.2819	−1.90109
$673$	33.2960	1.28347	0.641734	−	0.766928i	$-0.278215\pi$
$673$	33.2960	1.28347	0.641734	+	0.766928i	$0.278215\pi$
$674$	20.4058	0.786001
$675$	31.7406	1.22170
$676$	3.15639	0.121399
$677$	−8.26653	−0.317709	−0.158854	−	0.987302i	$-0.550780\pi$
$677$	−8.26653	−0.317709	−0.158854	+	0.987302i	$0.550780\pi$
$678$	6.31459	0.242510
$679$	41.7175	1.60097
$680$	210.100	8.05697
$681$	−0.956535	−0.0366545
$682$	−21.0879	−0.807498
$683$	0.217927	0.00833873	0.00416936	−	0.999991i	$-0.498673\pi$
$683$	0.217927	0.00833873	0.00416936	+	0.999991i	$0.498673\pi$
$684$	13.3461	0.510303
$685$	−53.2385	−2.03414
$686$	94.2816	3.59969
$687$	0.840740	0.0320762
$688$	36.2409	1.38167
$689$	38.4094	1.46328
$690$	−9.08533	−0.345873
$691$	37.5532	1.42859	0.714296	−	0.699843i	$-0.246747\pi$
$691$	37.5532	1.42859	0.714296	+	0.699843i	$0.246747\pi$
$692$	21.5447	0.819008
$693$	66.4589	2.52457
$694$	30.0965	1.14245
$695$	−25.1716	−0.954814
$696$	−49.9657	−1.89395
$697$	25.2357	0.955871
$698$	−30.1235	−1.14019
$699$	12.6458	0.478307
$700$	−210.619	−7.96066
$701$	5.43037	0.205102	0.102551	−	0.994728i	$-0.467299\pi$
$701$	5.43037	0.205102	0.102551	+	0.994728i	$0.467299\pi$
$702$	−35.8188	−1.35189
$703$	−9.39984	−0.354522
$704$	104.603	3.94238
$705$	−0.349038	−0.0131455
$706$	4.92589	0.185388
$707$	82.9017	3.11784
$708$	41.8278	1.57198
$709$	−4.78218	−0.179598	−0.0897992	−	0.995960i	$-0.528623\pi$
$709$	−4.78218	−0.179598	−0.0897992	+	0.995960i	$0.528623\pi$
$710$	32.9906	1.23812
$711$	9.31876	0.349481
$712$	7.89085	0.295722
$713$	1.99565	0.0747377
$714$	−53.8051	−2.01361
$715$	−75.9473	−2.84027
$716$	125.906	4.70531
$717$	8.06168	0.301069
$718$	−39.0838	−1.45859
$719$	−42.2214	−1.57459	−0.787296	−	0.616575i	$-0.788520\pi$
$719$	−42.2214	−1.57459	−0.787296	+	0.616575i	$0.788520\pi$
$720$	119.039	4.43632
$721$	−64.4354	−2.39970
$722$	−2.67904	−0.0997037
$723$	−6.43163	−0.239195
$724$	−7.26236	−0.269903
$725$	−79.1233	−2.93857
$726$	34.4742	1.27946
$727$	10.0772	0.373744	0.186872	−	0.982384i	$-0.440165\pi$
$727$	10.0772	0.373744	0.186872	+	0.982384i	$0.440165\pi$
$728$	145.863	5.40606
$729$	−6.80114	−0.251894
$730$	141.284	5.22914
$731$	19.3713	0.716472
$732$	−3.01013	−0.111258
$733$	16.4087	0.606067	0.303034	−	0.952980i	$-0.402001\pi$
$733$	16.4087	0.606067	0.303034	+	0.952980i	$0.402001\pi$
$734$	−36.2954	−1.33969
$735$	35.1292	1.29576
$736$	−22.9772	−0.846952
$737$	−15.6427	−0.576206
$738$	26.1901	0.964070
$739$	−24.8106	−0.912672	−0.456336	−	0.889807i	$-0.650839\pi$
$739$	−24.8106	−0.912672	−0.456336	+	0.889807i	$0.650839\pi$
$740$	−180.510	−6.63566
$741$	2.39699	0.0880555
$742$	129.563	4.75642
$743$	−33.0339	−1.21190	−0.605949	−	0.795504i	$-0.707206\pi$
$743$	−33.0339	−1.21190	−0.605949	+	0.795504i	$0.707206\pi$
$744$	7.84368	0.287563
$745$	79.9812	2.93029
$746$	53.3528	1.95339
$747$	27.7004	1.01350
$748$	191.216	6.99155
$749$	−27.2676	−0.996337
$750$	−24.2641	−0.886001
$751$	12.6510	0.461642	0.230821	−	0.972996i	$-0.425859\pi$
$751$	12.6510	0.461642	0.230821	+	0.972996i	$0.425859\pi$
$752$	−1.80305	−0.0657504
$753$	−20.0294	−0.729913
$754$	89.2894	3.25173
$755$	43.2618	1.57446
$756$	−87.1560	−3.16983
$757$	28.6451	1.04112	0.520562	−	0.853824i	$-0.325723\pi$
$757$	28.6451	1.04112	0.520562	+	0.853824i	$0.325723\pi$
$758$	−26.6169	−0.966771
$759$	−5.07449	−0.184192
$760$	−31.5728	−1.14526
$761$	12.5558	0.455148	0.227574	−	0.973761i	$-0.426921\pi$
$761$	12.5558	0.455148	0.227574	+	0.973761i	$0.426921\pi$
$762$	3.81095	0.138056
$763$	−25.2229	−0.913132
$764$	−85.8307	−3.10525
$765$	63.6278	2.30047
$766$	−36.3122	−1.31201
$767$	−45.8718	−1.65633
$768$	−6.55110	−0.236392
$769$	19.0609	0.687355	0.343677	−	0.939088i	$-0.388327\pi$
$769$	19.0609	0.687355	0.343677	+	0.939088i	$0.388327\pi$
$770$	−256.187	−9.23234
$771$	5.89725	0.212384
$772$	25.7412	0.926445
$773$	12.0841	0.434635	0.217318	−	0.976101i	$-0.430269\pi$
$773$	12.0841	0.434635	0.217318	+	0.976101i	$0.430269\pi$
$774$	20.1038	0.722617
$775$	12.4209	0.446171
$776$	76.4475	2.74431
$777$	28.3695	1.01775
$778$	−81.0484	−2.90573
$779$	−3.79229	−0.135873
$780$	46.0304	1.64815
$781$	18.4265	0.659351
$782$	−25.0861	−0.897078
$783$	−32.7419	−1.17010
$784$	181.469	6.48105
$785$	−20.2993	−0.724513
$786$	−21.2240	−0.757034
$787$	−45.3840	−1.61776	−0.808882	−	0.587970i	$-0.799927\pi$
$787$	−45.3840	−1.61776	−0.808882	+	0.587970i	$0.799927\pi$
$788$	−48.9396	−1.74340
$789$	−6.78082	−0.241403
$790$	−35.9221	−1.27805
$791$	−16.8505	−0.599134
$792$	121.786	4.32749
$793$	3.30116	0.117228
$794$	40.7386	1.44576
$795$	25.0919	0.889920
$796$	32.1028	1.13785
$797$	−5.48850	−0.194413	−0.0972063	−	0.995264i	$-0.530991\pi$
$797$	−5.48850	−0.194413	−0.0972063	+	0.995264i	$0.530991\pi$
$798$	8.08556	0.286226
$799$	−0.963752	−0.0340951
$800$	−143.010	−5.05616
$801$	2.38971	0.0844362
$802$	78.1535	2.75970
$803$	78.9120	2.78474
$804$	9.48079	0.334362
$805$	24.2442	0.854496
$806$	−14.0168	−0.493719
$807$	15.9366	0.560994
$808$	151.918	5.34445
$809$	29.6171	1.04128	0.520640	−	0.853776i	$-0.325693\pi$
$809$	29.6171	1.04128	0.520640	+	0.853776i	$0.325693\pi$
$810$	53.4488	1.87800
$811$	−18.5084	−0.649919	−0.324959	−	0.945728i	$-0.605351\pi$
$811$	−18.5084	−0.649919	−0.324959	+	0.945728i	$0.605351\pi$
$812$	217.263	7.62444
$813$	−18.3512	−0.643603
$814$	−139.769	−4.89889
$815$	22.6752	0.794276
$816$	−53.8283	−1.88437
$817$	−2.91101	−0.101843
$818$	24.1213	0.843383
$819$	44.1741	1.54357
$820$	−72.8252	−2.54317
$821$	8.20584	0.286386	0.143193	−	0.989695i	$-0.454263\pi$
$821$	8.20584	0.286386	0.143193	+	0.989695i	$0.454263\pi$
$822$	24.9844	0.871430
$823$	−28.6475	−0.998588	−0.499294	−	0.866433i	$-0.666407\pi$
$823$	−28.6475	−0.998588	−0.499294	+	0.866433i	$0.666407\pi$
$824$	−118.078	−4.11345
$825$	−31.5835	−1.09960
$826$	−154.736	−5.38394
$827$	−21.7434	−0.756094	−0.378047	−	0.925787i	$-0.623404\pi$
$827$	−21.7434	−0.756094	−0.378047	+	0.925787i	$0.623404\pi$
$828$	−18.7800	−0.652651
$829$	8.73737	0.303461	0.151731	−	0.988422i	$-0.451515\pi$
$829$	8.73737	0.303461	0.151731	+	0.988422i	$0.451515\pi$
$830$	−106.780	−3.70638
$831$	−14.5349	−0.504211
$832$	69.5278	2.41044
$833$	96.9977	3.36077
$834$	11.8128	0.409045
$835$	64.2941	2.22499
$836$	−28.7350	−0.993820
$837$	5.13986	0.177660
$838$	−91.0219	−3.14430
$839$	33.3135	1.15011	0.575055	−	0.818115i	$-0.304981\pi$
$839$	33.3135	1.15011	0.575055	+	0.818115i	$0.304981\pi$
$840$	95.2891	3.28779
$841$	52.6193	1.81446
$842$	−22.2820	−0.767889
$843$	−9.03787	−0.311281
$844$	27.5435	0.948086
$845$	−2.26135	−0.0777928
$846$	−1.00020	−0.0343876
$847$	−91.9944	−3.16096
$848$	129.619	4.45114
$849$	−10.2879	−0.353078
$850$	−156.135	−5.35540
$851$	13.2270	0.453415
$852$	−11.1680	−0.382609
$853$	−19.0517	−0.652319	−0.326160	−	0.945315i	$-0.605755\pi$
$853$	−19.0517	−0.652319	−0.326160	+	0.945315i	$0.605755\pi$
$854$	11.1355	0.381050
$855$	−9.56167	−0.327002
$856$	−49.9680	−1.70787
$857$	58.1085	1.98495	0.992474	−	0.122452i	$-0.0390758\pi$
$857$	58.1085	1.98495	0.992474	+	0.122452i	$0.0390758\pi$
$858$	35.6414	1.21678
$859$	10.8560	0.370401	0.185201	−	0.982701i	$-0.440707\pi$
$859$	10.8560	0.370401	0.185201	+	0.982701i	$0.440707\pi$
$860$	−55.9015	−1.90623
$861$	11.4454	0.390060
$862$	−81.8345	−2.78729
$863$	−49.6872	−1.69137	−0.845687	−	0.533680i	$-0.820809\pi$
$863$	−49.6872	−1.69137	−0.845687	+	0.533680i	$0.820809\pi$
$864$	−59.1786	−2.01330
$865$	−15.4354	−0.524821
$866$	−41.3446	−1.40495
$867$	−17.7263	−0.602016
$868$	−34.1062	−1.15764
$869$	−20.0638	−0.680618
$870$	58.3306	1.97759
$871$	−10.3974	−0.352303
$872$	−46.2212	−1.56525
$873$	23.1518	0.783569
$874$	3.76982	0.127516
$875$	64.7489	2.18891
$876$	−47.8273	−1.61593
$877$	7.03560	0.237575	0.118788	−	0.992920i	$-0.462099\pi$
$877$	7.03560	0.237575	0.118788	+	0.992920i	$0.462099\pi$
$878$	−59.2166	−1.99846
$879$	−9.84796	−0.332164
$880$	−256.297	−8.63978
$881$	19.5635	0.659111	0.329556	−	0.944136i	$-0.393101\pi$
$881$	19.5635	0.659111	0.329556	+	0.944136i	$0.393101\pi$
$882$	100.666	3.38960
$883$	56.2578	1.89323	0.946613	−	0.322371i	$-0.104480\pi$
$883$	56.2578	1.89323	0.946613	+	0.322371i	$0.104480\pi$
$884$	127.098	4.27476
$885$	−29.9670	−1.00733
$886$	59.0670	1.98440
$887$	−35.7882	−1.20165	−0.600825	−	0.799381i	$-0.705161\pi$
$887$	−35.7882	−1.20165	−0.600825	+	0.799381i	$0.705161\pi$
$888$	51.9872	1.74458
$889$	−10.1695	−0.341075
$890$	−9.21188	−0.308783
$891$	29.8531	1.00012
$892$	−135.876	−4.54947
$893$	0.144828	0.00484648
$894$	−37.5345	−1.25534
$895$	−90.2034	−3.01517
$896$	82.8358	2.76735
$897$	−3.37292	−0.112618
$898$	−60.1115	−2.00595
$899$	−12.8127	−0.427327
$900$	−116.886	−3.89622
$901$	69.2831	2.30815
$902$	−56.3886	−1.87754
$903$	8.78567	0.292369
$904$	−30.8786	−1.02701
$905$	5.20302	0.172954
$906$	−20.3024	−0.674502
$907$	7.19344	0.238854	0.119427	−	0.992843i	$-0.461894\pi$
$907$	7.19344	0.238854	0.119427	+	0.992843i	$0.461894\pi$
$908$	7.62185	0.252940
$909$	46.0076	1.52598
$910$	−170.283	−5.64482
$911$	39.1437	1.29689	0.648445	−	0.761262i	$-0.275420\pi$
$911$	39.1437	1.29689	0.648445	+	0.761262i	$0.275420\pi$
$912$	8.08904	0.267855
$913$	−59.6404	−1.97381
$914$	−72.5195	−2.39873
$915$	2.15657	0.0712940
$916$	−6.69917	−0.221347
$917$	56.6362	1.87029
$918$	−64.6101	−2.13245
$919$	12.2079	0.402702	0.201351	−	0.979519i	$-0.435467\pi$
$919$	12.2079	0.402702	0.201351	+	0.979519i	$0.435467\pi$
$920$	44.4276	1.46474
$921$	9.34137	0.307809
$922$	25.2918	0.832940
$923$	12.2477	0.403139
$924$	86.7244	2.85302
$925$	82.3244	2.70681
$926$	27.5309	0.904720
$927$	−35.7594	−1.17449
$928$	147.521	4.84261
$929$	−24.6991	−0.810350	−0.405175	−	0.914239i	$-0.632789\pi$
$929$	−24.6991	−0.810350	−0.405175	+	0.914239i	$0.632789\pi$
$930$	−9.15681	−0.300264
$931$	−14.5763	−0.477720
$932$	−100.764	−3.30063
$933$	4.82510	0.157967
$934$	−3.59453	−0.117617
$935$	−136.994	−4.48019
$936$	80.9492	2.64591
$937$	13.5225	0.441761	0.220880	−	0.975301i	$-0.429107\pi$
$937$	13.5225	0.441761	0.220880	+	0.975301i	$0.429107\pi$
$938$	−35.0728	−1.14517
$939$	−17.6741	−0.576771
$940$	2.78120	0.0907126
$941$	25.5637	0.833351	0.416676	−	0.909055i	$-0.363195\pi$
$941$	25.5637	0.833351	0.416676	+	0.909055i	$0.363195\pi$
$942$	9.52629	0.310383
$943$	5.33633	0.173775
$944$	−154.802	−5.03839
$945$	62.4417	2.03123
$946$	−43.2846	−1.40730
$947$	−24.7587	−0.804549	−0.402275	−	0.915519i	$-0.631780\pi$
$947$	−24.7587	−0.804549	−0.402275	+	0.915519i	$0.631780\pi$
$948$	12.1603	0.394950
$949$	52.4514	1.70264
$950$	23.4632	0.761248
$951$	−0.649743	−0.0210694
$952$	263.109	8.52742
$953$	−40.2965	−1.30533	−0.652666	−	0.757645i	$-0.726350\pi$
$953$	−40.2965	−1.30533	−0.652666	+	0.757645i	$0.726350\pi$
$954$	71.9032	2.32795
$955$	61.4923	1.98984
$956$	−64.2369	−2.07757
$957$	32.5798	1.05315
$958$	14.1855	0.458313
$959$	−66.6708	−2.15291
$960$	45.4208	1.46595
$961$	−28.9886	−0.935118
$962$	−92.9017	−2.99527
$963$	−15.1326	−0.487641
$964$	51.2484	1.65060
$965$	−18.4419	−0.593666
$966$	−11.3776	−0.366068
$967$	51.0070	1.64027	0.820137	−	0.572168i	$-0.193897\pi$
$967$	51.0070	1.64027	0.820137	+	0.572168i	$0.193897\pi$
$968$	−168.580	−5.41837
$969$	4.32370	0.138897
$970$	−89.2458	−2.86551
$971$	35.6689	1.14467	0.572334	−	0.820021i	$-0.306038\pi$
$971$	35.6689	1.14467	0.572334	+	0.820021i	$0.306038\pi$
$972$	−74.3833	−2.38584
$973$	−31.5225	−1.01057
$974$	81.1454	2.60007
$975$	−20.9930	−0.672313
$976$	11.1403	0.356593
$977$	1.17141	0.0374767	0.0187383	−	0.999824i	$-0.494035\pi$
$977$	1.17141	0.0374767	0.0187383	+	0.999824i	$0.494035\pi$
$978$	−10.6413	−0.340270
$979$	−5.14517	−0.164440
$980$	−279.916	−8.94159
$981$	−13.9979	−0.446918
$982$	−13.2334	−0.422295
$983$	−32.6406	−1.04107	−0.520537	−	0.853839i	$-0.674268\pi$
$983$	−32.6406	−1.04107	−0.520537	+	0.853839i	$0.674268\pi$
$984$	20.9738	0.668621
$985$	35.0622	1.11717
$986$	161.061	5.12922
$987$	−0.437102	−0.0139131
$988$	−19.0996	−0.607640
$989$	4.09623	0.130253
$990$	−142.175	−4.51862
$991$	−8.27243	−0.262782	−0.131391	−	0.991331i	$-0.541944\pi$
$991$	−8.27243	−0.262782	−0.131391	+	0.991331i	$0.541944\pi$
$992$	−23.1580	−0.735268
$993$	1.98637	0.0630356
$994$	41.3143	1.31041
$995$	−22.9996	−0.729136
$996$	36.1471	1.14536
$997$	33.2676	1.05359	0.526797	−	0.849991i	$-0.323393\pi$
$997$	33.2676	1.05359	0.526797	+	0.849991i	$0.323393\pi$
$998$	27.9388	0.884388
$999$	34.0665	1.07782

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	6023.2.a.d.1.6	✓	140

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
6023.2.a.d.1.6	✓	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)

\(f(q)\)	\(=\)	\(q-2.67904 q^{2} -0.649743 q^{3} +5.17727 q^{4} -3.70919 q^{5} +1.74069 q^{6} -4.64503 q^{7} -8.51205 q^{8} -2.57783 q^{9} +O(q^{10})\)	\(q-2.67904 q^{2} -0.649743 q^{3} +5.17727 q^{4} -3.70919 q^{5} +1.74069 q^{6} -4.64503 q^{7} -8.51205 q^{8} -2.57783 q^{9} +9.93707 q^{10} +5.55022 q^{11} -3.36390 q^{12} +3.68913 q^{13} +12.4442 q^{14} +2.41002 q^{15} +12.4496 q^{16} +6.65447 q^{17} +6.90613 q^{18} -1.00000 q^{19} -19.2035 q^{20} +3.01808 q^{21} -14.8693 q^{22} +1.40715 q^{23} +5.53065 q^{24} +8.75807 q^{25} -9.88333 q^{26} +3.62416 q^{27} -24.0486 q^{28} -9.03434 q^{29} -6.45655 q^{30} +1.41822 q^{31} -16.3289 q^{32} -3.60622 q^{33} -17.8276 q^{34} +17.2293 q^{35} -13.3461 q^{36} +9.39984 q^{37} +2.67904 q^{38} -2.39699 q^{39} +31.5728 q^{40} +3.79229 q^{41} -8.08556 q^{42} +2.91101 q^{43} +28.7350 q^{44} +9.56167 q^{45} -3.76982 q^{46} -0.144828 q^{47} -8.08904 q^{48} +14.5763 q^{49} -23.4632 q^{50} -4.32370 q^{51} +19.0996 q^{52} +10.4115 q^{53} -9.70928 q^{54} -20.5868 q^{55} +39.5387 q^{56} +0.649743 q^{57} +24.2034 q^{58} -12.4343 q^{59} +12.4773 q^{60} +0.894834 q^{61} -3.79948 q^{62} +11.9741 q^{63} +18.8467 q^{64} -13.6837 q^{65} +9.66121 q^{66} -2.81839 q^{67} +34.4520 q^{68} -0.914286 q^{69} -46.1580 q^{70} +3.31995 q^{71} +21.9426 q^{72} +14.2178 q^{73} -25.1826 q^{74} -5.69050 q^{75} -5.17727 q^{76} -25.7809 q^{77} +6.42163 q^{78} -3.61496 q^{79} -46.1779 q^{80} +5.37873 q^{81} -10.1597 q^{82} -10.7456 q^{83} +15.6254 q^{84} -24.6827 q^{85} -7.79873 q^{86} +5.87000 q^{87} -47.2437 q^{88} -0.927022 q^{89} -25.6161 q^{90} -17.1361 q^{91} +7.28520 q^{92} -0.921480 q^{93} +0.388000 q^{94} +3.70919 q^{95} +10.6096 q^{96} -8.98110 q^{97} -39.0506 q^{98} -14.3075 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 140 q + 4 q^{2} + 3 q^{3} + 162 q^{4} + 13 q^{5} + 12 q^{6} + 25 q^{7} + 12 q^{8} + 181 q^{9}+O(q^{10}) \) 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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