LMFDB - Embedded newform 722.4.a.k.1.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [722,4,Mod(1,722)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(722, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([0]))

N = Newforms(chi, 4, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("722.1");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 722 = 2 \cdot 19^{2} $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	722.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:	$42.5993790241$
Analytic rank:	$0$
Dimension:	$3$
Coefficient field:	3.3.253788.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{3} - x^{2} - 63x + 15 $ x^3 - x^2 - 63*x + 15
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 38)
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.2
Root			$0.237413$ of defining polynomial
Character	$\chi$	$=$	722.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+2.00000 q^{2} -1.76259 q^{3} +4.00000 q^{4} -20.7092 q^{5} -3.52517 q^{6} +8.76259 q^{7} +8.00000 q^{8} -23.8933 q^{9} +O(q^{10})$	\(q+2.00000 q^{2} -1.76259 q^{3} +4.00000 q^{4} -20.7092 q^{5} -3.52517 q^{6} +8.76259 q^{7} +8.00000 q^{8} -23.8933 q^{9} -41.4185 q^{10} -62.1780 q^{11} -7.05035 q^{12} +64.5222 q^{13} +17.5252 q^{14} +36.5018 q^{15} +16.0000 q^{16} -46.4155 q^{17} -47.7866 q^{18} -82.8369 q^{20} -15.4448 q^{21} -124.356 q^{22} -37.2848 q^{23} -14.1007 q^{24} +303.872 q^{25} +129.044 q^{26} +89.7038 q^{27} +35.0503 q^{28} +66.4238 q^{29} +73.0036 q^{30} -112.370 q^{31} +32.0000 q^{32} +109.594 q^{33} -92.8309 q^{34} -181.466 q^{35} -95.5731 q^{36} +189.018 q^{37} -113.726 q^{39} -165.674 q^{40} +240.010 q^{41} -30.8896 q^{42} +168.274 q^{43} -248.712 q^{44} +494.812 q^{45} -74.5695 q^{46} +187.848 q^{47} -28.2014 q^{48} -266.217 q^{49} +607.744 q^{50} +81.8113 q^{51} +258.089 q^{52} +113.057 q^{53} +179.408 q^{54} +1287.66 q^{55} +70.1007 q^{56} +132.848 q^{58} -185.988 q^{59} +146.007 q^{60} +308.643 q^{61} -224.741 q^{62} -209.367 q^{63} +64.0000 q^{64} -1336.20 q^{65} +219.188 q^{66} -39.4557 q^{67} -185.662 q^{68} +65.7176 q^{69} -362.933 q^{70} +350.202 q^{71} -191.146 q^{72} -9.60561 q^{73} +378.036 q^{74} -535.601 q^{75} -544.840 q^{77} -227.452 q^{78} +1176.54 q^{79} -331.348 q^{80} +487.008 q^{81} +480.019 q^{82} -257.980 q^{83} -61.7793 q^{84} +961.228 q^{85} +336.548 q^{86} -117.078 q^{87} -497.424 q^{88} +133.749 q^{89} +989.623 q^{90} +565.381 q^{91} -149.139 q^{92} +198.063 q^{93} +375.696 q^{94} -56.4028 q^{96} -1196.77 q^{97} -532.434 q^{98} +1485.64 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 3 q + 6 q^{2} - 5 q^{3} + 12 q^{4} + q^{5} - 10 q^{6} + 26 q^{7} + 24 q^{8} + 54 q^{9}+O(q^{10}) $ 3 * q + 6 * q^2 - 5 * q^3 + 12 * q^4 + q^5 - 10 * q^6 + 26 * q^7 + 24 * q^8 + 54 * q^9	\( 3 q + 6 q^{2} - 5 q^{3} + 12 q^{4} + q^{5} - 10 q^{6} + 26 q^{7} + 24 q^{8} + 54 q^{9} + 2 q^{10} + 4 q^{11} - 20 q^{12} + 129 q^{13} + 52 q^{14} - 77 q^{15} + 48 q^{16} + 51 q^{17} + 108 q^{18} + 4 q^{20} - 170 q^{21} + 8 q^{22} - 47 q^{23} - 40 q^{24} + 338 q^{25} + 258 q^{26} - 359 q^{27} + 104 q^{28} - 125 q^{29} - 154 q^{30} + 50 q^{31} + 96 q^{32} + 274 q^{33} + 102 q^{34} + 84 q^{35} + 216 q^{36} + 188 q^{37} - 773 q^{39} + 8 q^{40} + 475 q^{41} - 340 q^{42} + 73 q^{43} + 16 q^{44} + 1594 q^{45} - 94 q^{46} + 241 q^{47} - 80 q^{48} - 677 q^{49} + 676 q^{50} + 69 q^{51} + 516 q^{52} + 29 q^{53} - 718 q^{54} + 1838 q^{55} + 208 q^{56} - 250 q^{58} - 1065 q^{59} - 308 q^{60} + 981 q^{61} + 100 q^{62} + 872 q^{63} + 192 q^{64} - 293 q^{65} + 548 q^{66} + 877 q^{67} + 204 q^{68} + 763 q^{69} + 168 q^{70} + 2135 q^{71} + 432 q^{72} - 667 q^{73} + 376 q^{74} - 2292 q^{75} - 246 q^{77} - 1546 q^{78} + 1671 q^{79} + 16 q^{80} + 1287 q^{81} + 950 q^{82} + 588 q^{83} - 680 q^{84} + 1929 q^{85} + 146 q^{86} - 3215 q^{87} + 32 q^{88} + 693 q^{89} + 3188 q^{90} + 1676 q^{91} - 188 q^{92} + 3138 q^{93} + 482 q^{94} - 160 q^{96} - 985 q^{97} - 1354 q^{98} + 3184 q^{99}+O(q^{100}) \) 3 * q + 6 * q^2 - 5 * q^3 + 12 * q^4 + q^5 - 10 * q^6 + 26 * q^7 + 24 * q^8 + 54 * q^9 + 2 * q^10 + 4 * q^11 - 20 * q^12 + 129 * q^13 + 52 * q^14 - 77 * q^15 + 48 * q^16 + 51 * q^17 + 108 * q^18 + 4 * q^20 - 170 * q^21 + 8 * q^22 - 47 * q^23 - 40 * q^24 + 338 * q^25 + 258 * q^26 - 359 * q^27 + 104 * q^28 - 125 * q^29 - 154 * q^30 + 50 * q^31 + 96 * q^32 + 274 * q^33 + 102 * q^34 + 84 * q^35 + 216 * q^36 + 188 * q^37 - 773 * q^39 + 8 * q^40 + 475 * q^41 - 340 * q^42 + 73 * q^43 + 16 * q^44 + 1594 * q^45 - 94 * q^46 + 241 * q^47 - 80 * q^48 - 677 * q^49 + 676 * q^50 + 69 * q^51 + 516 * q^52 + 29 * q^53 - 718 * q^54 + 1838 * q^55 + 208 * q^56 - 250 * q^58 - 1065 * q^59 - 308 * q^60 + 981 * q^61 + 100 * q^62 + 872 * q^63 + 192 * q^64 - 293 * q^65 + 548 * q^66 + 877 * q^67 + 204 * q^68 + 763 * q^69 + 168 * q^70 + 2135 * q^71 + 432 * q^72 - 667 * q^73 + 376 * q^74 - 2292 * q^75 - 246 * q^77 - 1546 * q^78 + 1671 * q^79 + 16 * q^80 + 1287 * q^81 + 950 * q^82 + 588 * q^83 - 680 * q^84 + 1929 * q^85 + 146 * q^86 - 3215 * q^87 + 32 * q^88 + 693 * q^89 + 3188 * q^90 + 1676 * q^91 - 188 * q^92 + 3138 * q^93 + 482 * q^94 - 160 * q^96 - 985 * q^97 - 1354 * q^98 + 3184 * 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 $

$2$	2.00000	0.707107
$2$	2.00000	0.707107
$3$	−1.76259	−0.339210	−0.169605	−	0.985512i	$-0.554249\pi$
$3$	−1.76259	−0.339210	−0.169605	+	0.985512i	$0.554249\pi$
$4$	4.00000	0.500000
$5$	−20.7092	−1.85229	−0.926145	−	0.377168i	$-0.876898\pi$
$5$	−20.7092	−1.85229	−0.926145	+	0.377168i	$0.876898\pi$
$6$	−3.52517	−0.239858
$7$	8.76259	0.473135	0.236568	−	0.971615i	$-0.423978\pi$
$7$	8.76259	0.473135	0.236568	+	0.971615i	$0.423978\pi$
$8$	8.00000	0.353553
$9$	−23.8933	−0.884937
$10$	−41.4185	−1.30977
$11$	−62.1780	−1.70431	−0.852154	−	0.523291i	$-0.824704\pi$
$11$	−62.1780	−1.70431	−0.852154	+	0.523291i	$0.824704\pi$
$12$	−7.05035	−0.169605
$13$	64.5222	1.37656	0.688278	−	0.725447i	$-0.258367\pi$
$13$	64.5222	1.37656	0.688278	+	0.725447i	$0.258367\pi$
$14$	17.5252	0.334557
$15$	36.5018	0.628315
$16$	16.0000	0.250000
$17$	−46.4155	−0.662200	−0.331100	−	0.943596i	$-0.607420\pi$
$17$	−46.4155	−0.662200	−0.331100	+	0.943596i	$0.607420\pi$
$18$	−47.7866	−0.625745
$19$	0	0
$19$	0	0
$20$	−82.8369	−0.926145
$21$	−15.4448	−0.160492
$22$	−124.356	−1.20513
$23$	−37.2848	−0.338018	−0.169009	−	0.985615i	$-0.554057\pi$
$23$	−37.2848	−0.338018	−0.169009	+	0.985615i	$0.554057\pi$
$24$	−14.1007	−0.119929
$25$	303.872	2.43098
$26$	129.044	0.973372
$27$	89.7038	0.639389
$28$	35.0503	0.236568
$29$	66.4238	0.425330	0.212665	−	0.977125i	$-0.431786\pi$
$29$	66.4238	0.425330	0.212665	+	0.977125i	$0.431786\pi$
$30$	73.0036	0.444286
$31$	−112.370	−0.651043	−0.325521	−	0.945535i	$-0.605540\pi$
$31$	−112.370	−0.651043	−0.325521	+	0.945535i	$0.605540\pi$
$32$	32.0000	0.176777
$33$	109.594	0.578118
$34$	−92.8309	−0.468246
$35$	−181.466	−0.876384
$36$	−95.5731	−0.442468
$37$	189.018	0.839848	0.419924	−	0.907559i	$-0.362057\pi$
$37$	189.018	0.839848	0.419924	+	0.907559i	$0.362057\pi$
$38$	0	0
$39$	−113.726	−0.466942
$40$	−165.674	−0.654883
$41$	240.010	0.914225	0.457112	−	0.889409i	$-0.348884\pi$
$41$	240.010	0.914225	0.457112	+	0.889409i	$0.348884\pi$
$42$	−30.8896	−0.113485
$43$	168.274	0.596780	0.298390	−	0.954444i	$-0.403550\pi$
$43$	168.274	0.596780	0.298390	+	0.954444i	$0.403550\pi$
$44$	−248.712	−0.852154
$45$	494.812	1.63916
$46$	−74.5695	−0.239015
$47$	187.848	0.582989	0.291494	−	0.956573i	$-0.405847\pi$
$47$	187.848	0.582989	0.291494	+	0.956573i	$0.405847\pi$
$48$	−28.2014	−0.0848025
$49$	−266.217	−0.776143
$50$	607.744	1.71896
$51$	81.8113	0.224625
$52$	258.089	0.688278
$53$	113.057	0.293011	0.146505	−	0.989210i	$-0.453197\pi$
$53$	113.057	0.293011	0.146505	+	0.989210i	$0.453197\pi$
$54$	179.408	0.452117
$55$	1287.66	3.15687
$56$	70.1007	0.167279
$57$	0	0
$58$	132.848	0.300754
$59$	−185.988	−0.410400	−0.205200	−	0.978720i	$-0.565784\pi$
$59$	−185.988	−0.410400	−0.205200	+	0.978720i	$0.565784\pi$
$60$	146.007	0.314158
$61$	308.643	0.647831	0.323916	−	0.946086i	$-0.395001\pi$
$61$	308.643	0.647831	0.323916	+	0.946086i	$0.395001\pi$
$62$	−224.741	−0.460357
$63$	−209.367	−0.418695
$64$	64.0000	0.125000
$65$	−1336.20	−2.54978
$66$	219.188	0.408791
$67$	−39.4557	−0.0719446	−0.0359723	−	0.999353i	$-0.511453\pi$
$67$	−39.4557	−0.0719446	−0.0359723	+	0.999353i	$0.511453\pi$
$68$	−185.662	−0.331100
$69$	65.7176	0.114659
$70$	−362.933	−0.619697
$71$	350.202	0.585371	0.292686	−	0.956209i	$-0.405451\pi$
$71$	350.202	0.585371	0.292686	+	0.956209i	$0.405451\pi$
$72$	−191.146	−0.312872
$73$	−9.60561	−0.0154007	−0.00770035	−	0.999970i	$-0.502451\pi$
$73$	−9.60561	−0.0154007	−0.00770035	+	0.999970i	$0.502451\pi$
$74$	378.036	0.593862
$75$	−535.601	−0.824612
$76$	0	0
$77$	−544.840	−0.806368
$78$	−227.452	−0.330178
$79$	1176.54	1.67558	0.837791	−	0.545991i	$-0.183847\pi$
$79$	1176.54	1.67558	0.837791	+	0.545991i	$0.183847\pi$
$80$	−331.348	−0.463072
$81$	487.008	0.668049
$82$	480.019	0.646454
$83$	−257.980	−0.341168	−0.170584	−	0.985343i	$-0.554565\pi$
$83$	−257.980	−0.341168	−0.170584	+	0.985343i	$0.554565\pi$
$84$	−61.7793	−0.0802461
$85$	961.228	1.22659
$86$	336.548	0.421987
$87$	−117.078	−0.144276
$88$	−497.424	−0.602564
$89$	133.749	0.159296	0.0796479	−	0.996823i	$-0.474620\pi$
$89$	133.749	0.159296	0.0796479	+	0.996823i	$0.474620\pi$
$90$	989.623	1.15906
$91$	565.381	0.651297
$92$	−149.139	−0.169009
$93$	198.063	0.220840
$94$	375.696	0.412235
$95$	0	0
$96$	−56.4028	−0.0599644
$97$	−1196.77	−1.25272	−0.626361	−	0.779533i	$-0.715456\pi$
$97$	−1196.77	−1.25272	−0.626361	+	0.779533i	$0.715456\pi$
$98$	−532.434	−0.548816
$99$	1485.64	1.50820
$100$	1215.49	1.21549
$101$	868.943	0.856070	0.428035	−	0.903762i	$-0.359206\pi$
$101$	868.943	0.856070	0.428035	+	0.903762i	$0.359206\pi$
$102$	163.623	0.158834
$103$	1491.56	1.42687	0.713437	−	0.700720i	$-0.247138\pi$
$103$	1491.56	1.42687	0.713437	+	0.700720i	$0.247138\pi$
$104$	516.177	0.486686
$105$	319.850	0.297278
$106$	226.114	0.207190
$107$	1610.18	1.45478	0.727392	−	0.686222i	$-0.240732\pi$
$107$	1610.18	1.45478	0.727392	+	0.686222i	$0.240732\pi$
$108$	358.815	0.319695
$109$	51.0222	0.0448352	0.0224176	−	0.999749i	$-0.492864\pi$
$109$	51.0222	0.0448352	0.0224176	+	0.999749i	$0.492864\pi$
$110$	2575.32	2.23225
$111$	−333.161	−0.284885
$112$	140.201	0.118284
$113$	−1789.55	−1.48979	−0.744895	−	0.667181i	$-0.767501\pi$
$113$	−1789.55	−1.48979	−0.744895	+	0.667181i	$0.767501\pi$
$114$	0	0
$115$	772.139	0.626107
$116$	265.695	0.212665
$117$	−1541.65	−1.21816
$118$	−371.976	−0.290196
$119$	−406.719	−0.313310
$120$	292.015	0.222143
$121$	2535.11	1.90466
$122$	617.286	0.458086
$123$	−423.038	−0.310114
$124$	−449.482	−0.325521
$125$	−3704.31	−2.65059
$126$	−418.734	−0.296062
$127$	−277.775	−0.194083	−0.0970416	−	0.995280i	$-0.530938\pi$
$127$	−277.775	−0.194083	−0.0970416	+	0.995280i	$0.530938\pi$
$128$	128.000	0.0883883
$129$	−296.598	−0.202434
$130$	−2672.41	−1.80297
$131$	−1822.68	−1.21564	−0.607819	−	0.794076i	$-0.707955\pi$
$131$	−1822.68	−1.21564	−0.607819	+	0.794076i	$0.707955\pi$
$132$	438.377	0.289059
$133$	0	0
$134$	−78.9115	−0.0508725
$135$	−1857.70	−1.18433
$136$	−371.324	−0.234123
$137$	660.963	0.412189	0.206094	−	0.978532i	$-0.433925\pi$
$137$	660.963	0.412189	0.206094	+	0.978532i	$0.433925\pi$
$138$	131.435	0.0810762
$139$	−1245.95	−0.760289	−0.380144	−	0.924927i	$-0.624126\pi$
$139$	−1245.95	−0.760289	−0.380144	+	0.924927i	$0.624126\pi$
$140$	−725.866	−0.438192
$141$	−331.099	−0.197756
$142$	700.404	0.413920
$143$	−4011.86	−2.34608
$144$	−382.293	−0.221234
$145$	−1375.59	−0.787835
$146$	−19.2112	−0.0108899
$147$	469.231	0.263276
$148$	756.072	0.419924
$149$	2272.01	1.24920	0.624599	−	0.780945i	$-0.285262\pi$
$149$	2272.01	1.24920	0.624599	+	0.780945i	$0.285262\pi$
$150$	−1071.20	−0.583089
$151$	−3637.77	−1.96051	−0.980256	−	0.197734i	$-0.936642\pi$
$151$	−3637.77	−1.96051	−0.980256	+	0.197734i	$0.936642\pi$
$152$	0	0
$153$	1109.02	0.586005
$154$	−1089.68	−0.570188
$155$	2327.10	1.20592
$156$	−454.904	−0.233471
$157$	−451.770	−0.229651	−0.114825	−	0.993386i	$-0.536631\pi$
$157$	−451.770	−0.229651	−0.114825	+	0.993386i	$0.536631\pi$
$158$	2353.08	1.18482
$159$	−199.273	−0.0993922
$160$	−662.695	−0.327442
$161$	−326.711	−0.159928
$162$	974.016	0.472382
$163$	215.631	0.103617	0.0518084	−	0.998657i	$-0.483502\pi$
$163$	215.631	0.103617	0.0518084	+	0.998657i	$0.483502\pi$
$164$	960.039	0.457112
$165$	−2269.61	−1.07084
$166$	−515.960	−0.241242
$167$	3321.48	1.53907	0.769533	−	0.638607i	$-0.220489\pi$
$167$	3321.48	1.53907	0.769533	+	0.638607i	$0.220489\pi$
$168$	−123.559	−0.0567426
$169$	1966.11	0.894907
$170$	1922.46	0.867328
$171$	0	0
$172$	673.096	0.298390
$173$	−1472.46	−0.647103	−0.323552	−	0.946211i	$-0.604877\pi$
$173$	−1472.46	−0.647103	−0.323552	+	0.946211i	$0.604877\pi$
$174$	−234.155	−0.102019
$175$	2662.71	1.15018
$176$	−994.849	−0.426077
$177$	327.820	0.139212
$178$	267.497	0.112639
$179$	−3573.98	−1.49236	−0.746179	−	0.665745i	$-0.768114\pi$
$179$	−3573.98	−1.49236	−0.746179	+	0.665745i	$0.768114\pi$
$180$	1979.25	0.819580
$181$	2943.73	1.20887	0.604436	−	0.796654i	$-0.293399\pi$
$181$	2943.73	1.20887	0.604436	+	0.796654i	$0.293399\pi$
$182$	1130.76	0.460537
$183$	−544.011	−0.219751
$184$	−298.278	−0.119507
$185$	−3914.42	−1.55564
$186$	396.125	0.156158
$187$	2886.02	1.12859
$188$	751.393	0.291494
$189$	786.038	0.302518
$190$	0	0
$191$	−700.359	−0.265321	−0.132660	−	0.991162i	$-0.542352\pi$
$191$	−700.359	−0.265321	−0.132660	+	0.991162i	$0.542352\pi$
$192$	−112.806	−0.0424013
$193$	59.9015	0.0223410	0.0111705	−	0.999938i	$-0.496444\pi$
$193$	59.9015	0.0223410	0.0111705	+	0.999938i	$0.496444\pi$
$194$	−2393.55	−0.885808
$195$	2355.18	0.864911
$196$	−1064.87	−0.388072
$197$	−374.382	−0.135399	−0.0676994	−	0.997706i	$-0.521566\pi$
$197$	−374.382	−0.135399	−0.0676994	+	0.997706i	$0.521566\pi$
$198$	2971.28	1.06646
$199$	4603.77	1.63996	0.819981	−	0.572391i	$-0.193984\pi$
$199$	4603.77	1.63996	0.819981	+	0.572391i	$0.193984\pi$
$200$	2430.98	0.859480
$201$	69.5442	0.0244043
$202$	1737.89	0.605333
$203$	582.044	0.201239
$204$	327.245	0.112312
$205$	−4970.42	−1.69341
$206$	2983.12	1.00895
$207$	890.855	0.299124
$208$	1032.35	0.344139
$209$	0	0
$210$	639.701	0.210207
$211$	2956.72	0.964688	0.482344	−	0.875982i	$-0.339786\pi$
$211$	2956.72	0.964688	0.482344	+	0.875982i	$0.339786\pi$
$212$	452.228	0.146505
$213$	−617.262	−0.198564
$214$	3220.36	1.02869
$215$	−3484.83	−1.10541
$216$	717.631	0.226058
$217$	−984.655	−0.308031
$218$	102.044	0.0317033
$219$	16.9307	0.00522407
$220$	5150.64	1.57844
$221$	−2994.83	−0.911555
$222$	−666.321	−0.201444
$223$	−530.640	−0.159347	−0.0796733	−	0.996821i	$-0.525388\pi$
$223$	−530.640	−0.159347	−0.0796733	+	0.996821i	$0.525388\pi$
$224$	280.403	0.0836393
$225$	−7260.51	−2.15126
$226$	−3579.09	−1.05344
$227$	3479.72	1.01743	0.508716	−	0.860934i	$-0.330120\pi$
$227$	3479.72	1.01743	0.508716	+	0.860934i	$0.330120\pi$
$228$	0	0
$229$	3566.48	1.02917	0.514584	−	0.857440i	$-0.327946\pi$
$229$	3566.48	1.02917	0.514584	+	0.857440i	$0.327946\pi$
$230$	1544.28	0.442724
$231$	960.329	0.273528
$232$	531.390	0.150377
$233$	−5991.20	−1.68453	−0.842267	−	0.539061i	$-0.818779\pi$
$233$	−5991.20	−1.68453	−0.842267	+	0.539061i	$0.818779\pi$
$234$	−3083.29	−0.861373
$235$	−3890.19	−1.07986
$236$	−743.952	−0.205200
$237$	−2073.75	−0.568374
$238$	−813.439	−0.221544
$239$	−606.478	−0.164141	−0.0820707	−	0.996627i	$-0.526153\pi$
$239$	−606.478	−0.164141	−0.0820707	+	0.996627i	$0.526153\pi$
$240$	584.029	0.157079
$241$	3445.17	0.920842	0.460421	−	0.887701i	$-0.347699\pi$
$241$	3445.17	0.920842	0.460421	+	0.887701i	$0.347699\pi$
$242$	5070.22	1.34680
$243$	−3280.40	−0.865998
$244$	1234.57	0.323916
$245$	5513.15	1.43764
$246$	−846.076	−0.219284
$247$	0	0
$248$	−898.963	−0.230178
$249$	454.712	0.115728
$250$	−7408.61	−1.87425
$251$	1805.37	0.454001	0.227000	−	0.973895i	$-0.427108\pi$
$251$	1805.37	0.454001	0.227000	+	0.973895i	$0.427108\pi$
$252$	−837.468	−0.209347
$253$	2318.29	0.576086
$254$	−555.551	−0.137238
$255$	−1694.25	−0.416070
$256$	256.000	0.0625000
$257$	−2236.97	−0.542950	−0.271475	−	0.962446i	$-0.587511\pi$
$257$	−2236.97	−0.542950	−0.271475	+	0.962446i	$0.587511\pi$
$258$	−593.195	−0.143142
$259$	1656.29	0.397362
$260$	−5344.82	−1.27489
$261$	−1587.08	−0.376390
$262$	−3645.37	−0.859586
$263$	832.258	0.195130	0.0975651	−	0.995229i	$-0.468895\pi$
$263$	832.258	0.195130	0.0975651	+	0.995229i	$0.468895\pi$
$264$	876.754	0.204396
$265$	−2341.32	−0.542741
$266$	0	0
$267$	−235.743	−0.0540347
$268$	−157.823	−0.0359723
$269$	3483.89	0.789651	0.394826	−	0.918756i	$-0.370805\pi$
$269$	3483.89	0.789651	0.394826	+	0.918756i	$0.370805\pi$
$270$	−3715.40	−0.837451
$271$	1789.11	0.401035	0.200518	−	0.979690i	$-0.435738\pi$
$271$	1789.11	0.401035	0.200518	+	0.979690i	$0.435738\pi$
$272$	−742.647	−0.165550
$273$	−996.533	−0.220927
$274$	1321.93	0.291462
$275$	−18894.2	−4.14313
$276$	262.870	0.0573295
$277$	−5548.66	−1.20356	−0.601781	−	0.798661i	$-0.705542\pi$
$277$	−5548.66	−1.20356	−0.601781	+	0.798661i	$0.705542\pi$
$278$	−2491.90	−0.537605
$279$	2684.90	0.576131
$280$	−1451.73	−0.309848
$281$	45.7896	0.00972091	0.00486046	−	0.999988i	$-0.498453\pi$
$281$	45.7896	0.00972091	0.00486046	+	0.999988i	$0.498453\pi$
$282$	−662.198	−0.139834
$283$	−6120.74	−1.28565	−0.642827	−	0.766011i	$-0.722239\pi$
$283$	−6120.74	−1.28565	−0.642827	+	0.766011i	$0.722239\pi$
$284$	1400.81	0.292686
$285$	0	0
$286$	−8023.72	−1.65893
$287$	2103.11	0.432552
$288$	−764.585	−0.156436
$289$	−2758.61	−0.561491
$290$	−2751.17	−0.557084
$291$	2109.42	0.424936
$292$	−38.4224	−0.00770035
$293$	7395.39	1.47455	0.737276	−	0.675592i	$-0.236112\pi$
$293$	7395.39	1.47455	0.737276	+	0.675592i	$0.236112\pi$
$294$	938.462	0.186164
$295$	3851.67	0.760179
$296$	1512.14	0.296931
$297$	−5577.61	−1.08972
$298$	4544.03	0.883317
$299$	−2405.69	−0.465300
$300$	−2142.40	−0.412306
$301$	1474.52	0.282358
$302$	−7275.53	−1.38629
$303$	−1531.59	−0.290388
$304$	0	0
$305$	−6391.76	−1.19997
$306$	2218.04	0.414368
$307$	575.069	0.106908	0.0534542	−	0.998570i	$-0.482977\pi$
$307$	575.069	0.106908	0.0534542	+	0.998570i	$0.482977\pi$
$308$	−2179.36	−0.403184
$309$	−2629.01	−0.484010
$310$	4654.21	0.852714
$311$	−36.6434	−0.00668120	−0.00334060	−	0.999994i	$-0.501063\pi$
$311$	−36.6434	−0.00668120	−0.00334060	+	0.999994i	$0.501063\pi$
$312$	−909.807	−0.165089
$313$	−4883.73	−0.881932	−0.440966	−	0.897524i	$-0.645364\pi$
$313$	−4883.73	−0.881932	−0.440966	+	0.897524i	$0.645364\pi$
$314$	−903.540	−0.162388
$315$	4335.83	0.775544
$316$	4706.15	0.837791
$317$	5867.29	1.03956	0.519779	−	0.854301i	$-0.326014\pi$
$317$	5867.29	1.03956	0.519779	+	0.854301i	$0.326014\pi$
$318$	−398.546	−0.0702809
$319$	−4130.10	−0.724894
$320$	−1325.39	−0.231536
$321$	−2838.08	−0.493478
$322$	−653.422	−0.113086
$323$	0	0
$324$	1948.03	0.334025
$325$	19606.5	3.34638
$326$	431.262	0.0732681
$327$	−89.9310	−0.0152086
$328$	1920.08	0.323227
$329$	1646.04	0.275833
$330$	−4539.22	−0.757200
$331$	8866.06	1.47227	0.736137	−	0.676833i	$-0.236648\pi$
$331$	8866.06	1.47227	0.736137	+	0.676833i	$0.236648\pi$
$332$	−1031.92	−0.170584
$333$	−4516.26	−0.743212
$334$	6642.96	1.08828
$335$	817.098	0.133262
$336$	−247.117	−0.0401231
$337$	−3027.20	−0.489324	−0.244662	−	0.969608i	$-0.578677\pi$
$337$	−3027.20	−0.489324	−0.244662	+	0.969608i	$0.578677\pi$
$338$	3932.22	0.632795
$339$	3154.23	0.505352
$340$	3844.91	0.613293
$341$	6986.97	1.10958
$342$	0	0
$343$	−5338.32	−0.840356
$344$	1346.19	0.210994
$345$	−1360.96	−0.212382
$346$	−2944.91	−0.457571
$347$	−8875.76	−1.37313	−0.686564	−	0.727069i	$-0.740882\pi$
$347$	−8875.76	−1.37313	−0.686564	+	0.727069i	$0.740882\pi$
$348$	−468.311	−0.0721382
$349$	2808.70	0.430791	0.215395	−	0.976527i	$-0.430896\pi$
$349$	2808.70	0.430791	0.215395	+	0.976527i	$0.430896\pi$
$350$	5325.41	0.813301
$351$	5787.89	0.880155
$352$	−1989.70	−0.301282
$353$	11702.4	1.76446	0.882230	−	0.470819i	$-0.156041\pi$
$353$	11702.4	1.76446	0.882230	+	0.470819i	$0.156041\pi$
$354$	655.640	0.0984375
$355$	−7252.42	−1.08428
$356$	534.994	0.0796479
$357$	716.878	0.106278
$358$	−7147.97	−1.05526
$359$	−1686.03	−0.247869	−0.123935	−	0.992290i	$-0.539551\pi$
$359$	−1686.03	−0.247869	−0.123935	+	0.992290i	$0.539551\pi$
$360$	3958.49	0.579530
$361$	0	0
$362$	5887.46	0.854801
$363$	−4468.35	−0.646081
$364$	2261.52	0.325649
$365$	198.925	0.0285266
$366$	−1088.02	−0.155387
$367$	−8436.03	−1.19988	−0.599941	−	0.800044i	$-0.704809\pi$
$367$	−8436.03	−1.19988	−0.599941	+	0.800044i	$0.704809\pi$
$368$	−596.556	−0.0845044
$369$	−5734.62	−0.809031
$370$	−7828.83	−1.10000
$371$	990.672	0.138634
$372$	792.250	0.110420
$373$	1743.67	0.242048	0.121024	−	0.992650i	$-0.461382\pi$
$373$	1743.67	0.242048	0.121024	+	0.992650i	$0.461382\pi$
$374$	5772.04	0.798035
$375$	6529.16	0.899105
$376$	1502.79	0.206118
$377$	4285.81	0.585491
$378$	1572.08	0.213912
$379$	1591.45	0.215693	0.107846	−	0.994168i	$-0.465605\pi$
$379$	1591.45	0.215693	0.107846	+	0.994168i	$0.465605\pi$
$380$	0	0
$381$	489.603	0.0658350
$382$	−1400.72	−0.187610
$383$	−9004.90	−1.20138	−0.600691	−	0.799481i	$-0.705108\pi$
$383$	−9004.90	−1.20138	−0.600691	+	0.799481i	$0.705108\pi$
$384$	−225.611	−0.0299822
$385$	11283.2	1.49363
$386$	119.803	0.0157975
$387$	−4020.62	−0.528113
$388$	−4787.10	−0.626361
$389$	4069.93	0.530472	0.265236	−	0.964183i	$-0.414550\pi$
$389$	4069.93	0.530472	0.265236	+	0.964183i	$0.414550\pi$
$390$	4710.35	0.611585
$391$	1730.59	0.223835
$392$	−2129.74	−0.274408
$393$	3212.64	0.412357
$394$	−748.763	−0.0957415
$395$	−24365.2	−3.10366
$396$	5942.55	0.754102
$397$	329.570	0.0416641	0.0208321	−	0.999783i	$-0.493368\pi$
$397$	329.570	0.0416641	0.0208321	+	0.999783i	$0.493368\pi$
$398$	9207.53	1.15963
$399$	0	0
$400$	4861.96	0.607744
$401$	−8187.06	−1.01956	−0.509778	−	0.860306i	$-0.670273\pi$
$401$	−8187.06	−1.01956	−0.509778	+	0.860306i	$0.670273\pi$
$402$	139.088	0.0172565
$403$	−7250.38	−0.896197
$404$	3475.77	0.428035
$405$	−10085.6	−1.23742
$406$	1164.09	0.142297
$407$	−11752.8	−1.43136
$408$	654.490	0.0794169
$409$	−4998.50	−0.604303	−0.302152	−	0.953260i	$-0.597705\pi$
$409$	−4998.50	−0.604303	−0.302152	+	0.953260i	$0.597705\pi$
$410$	−9940.83	−1.19742
$411$	−1165.00	−0.139819
$412$	5966.25	0.713437
$413$	−1629.74	−0.194175
$414$	1781.71	0.211513
$415$	5342.56	0.631942
$416$	2064.71	0.243343
$417$	2196.10	0.257898
$418$	0	0
$419$	11941.1	1.39227	0.696134	−	0.717912i	$-0.254902\pi$
$419$	11941.1	1.39227	0.696134	+	0.717912i	$0.254902\pi$
$420$	1279.40	0.148639
$421$	11982.8	1.38719	0.693594	−	0.720367i	$-0.256026\pi$
$421$	11982.8	1.38719	0.693594	+	0.720367i	$0.256026\pi$
$422$	5913.45	0.682138
$423$	−4488.31	−0.515908
$424$	904.456	0.103595
$425$	−14104.4	−1.60979
$426$	−1234.52	−0.140406
$427$	2704.51	0.306512
$428$	6440.72	0.727392
$429$	7071.26	0.795812
$430$	−6969.65	−0.781643
$431$	−7082.98	−0.791590	−0.395795	−	0.918339i	$-0.629531\pi$
$431$	−7082.98	−0.791590	−0.395795	+	0.918339i	$0.629531\pi$
$432$	1435.26	0.159847
$433$	7403.00	0.821629	0.410815	−	0.911719i	$-0.365244\pi$
$433$	7403.00	0.821629	0.410815	+	0.911719i	$0.365244\pi$
$434$	−1969.31	−0.217811
$435$	2424.59	0.267242
$436$	204.089	0.0224176
$437$	0	0
$438$	33.8614	0.00369398
$439$	7675.43	0.834461	0.417231	−	0.908801i	$-0.363001\pi$
$439$	7675.43	0.834461	0.417231	+	0.908801i	$0.363001\pi$
$440$	10301.3	1.11612
$441$	6360.80	0.686837
$442$	−5989.65	−0.644567
$443$	−2683.89	−0.287845	−0.143923	−	0.989589i	$-0.545972\pi$
$443$	−2683.89	−0.287845	−0.143923	+	0.989589i	$0.545972\pi$
$444$	−1332.64	−0.142442
$445$	−2769.83	−0.295062
$446$	−1061.28	−0.112675
$447$	−4004.62	−0.423741
$448$	560.806	0.0591419
$449$	14097.6	1.48175	0.740874	−	0.671644i	$-0.234411\pi$
$449$	14097.6	1.48175	0.740874	+	0.671644i	$0.234411\pi$
$450$	−14521.0	−1.52117
$451$	−14923.3	−1.55812
$452$	−7158.18	−0.744895
$453$	6411.88	0.665025
$454$	6959.44	0.719434
$455$	−11708.6	−1.20639
$456$	0	0
$457$	7040.20	0.720627	0.360314	−	0.932831i	$-0.382670\pi$
$457$	7040.20	0.720627	0.360314	+	0.932831i	$0.382670\pi$
$458$	7132.95	0.727732
$459$	−4163.64	−0.423404
$460$	3088.55	0.313053
$461$	7353.08	0.742879	0.371440	−	0.928457i	$-0.378864\pi$
$461$	7353.08	0.742879	0.371440	+	0.928457i	$0.378864\pi$
$462$	1920.66	0.193414
$463$	14054.7	1.41075	0.705377	−	0.708832i	$-0.250778\pi$
$463$	14054.7	1.41075	0.705377	+	0.708832i	$0.250778\pi$
$464$	1062.78	0.106333
$465$	−4101.72	−0.409060
$466$	−11982.4	−1.19115
$467$	5875.16	0.582163	0.291081	−	0.956698i	$-0.405985\pi$
$467$	5875.16	0.582163	0.291081	+	0.956698i	$0.405985\pi$
$468$	−6166.59	−0.609082
$469$	−345.734	−0.0340395
$470$	−7780.39	−0.763580
$471$	796.284	0.0778999
$472$	−1487.90	−0.145098
$473$	−10463.0	−1.01710
$474$	−4147.50	−0.401901
$475$	0	0
$476$	−1626.88	−0.156655
$477$	−2701.30	−0.259296
$478$	−1212.96	−0.116066
$479$	−177.781	−0.0169583	−0.00847914	−	0.999964i	$-0.502699\pi$
$479$	−177.781	−0.0169583	−0.00847914	+	0.999964i	$0.502699\pi$
$480$	1168.06	0.111072
$481$	12195.8	1.15610
$482$	6890.34	0.651133
$483$	575.856	0.0542492
$484$	10140.4	0.952332
$485$	24784.3	2.32040
$486$	−6560.80	−0.612353
$487$	−12319.9	−1.14634	−0.573172	−	0.819435i	$-0.694287\pi$
$487$	−12319.9	−1.14634	−0.573172	+	0.819435i	$0.694287\pi$
$488$	2469.15	0.229043
$489$	−380.068	−0.0351478
$490$	11026.3	1.01657
$491$	−8441.83	−0.775916	−0.387958	−	0.921677i	$-0.626819\pi$
$491$	−8441.83	−0.775916	−0.387958	+	0.921677i	$0.626819\pi$
$492$	−1692.15	−0.155057
$493$	−3083.09	−0.281654
$494$	0	0
$495$	−30766.4	−2.79363
$496$	−1797.93	−0.162761
$497$	3068.68	0.276960
$498$	909.424	0.0818318
$499$	−6211.24	−0.557221	−0.278610	−	0.960404i	$-0.589874\pi$
$499$	−6211.24	−0.557221	−0.278610	+	0.960404i	$0.589874\pi$
$500$	−14817.2	−1.32529
$501$	−5854.40	−0.522067
$502$	3610.75	0.321027
$503$	15673.4	1.38935	0.694675	−	0.719324i	$-0.255548\pi$
$503$	15673.4	1.38935	0.694675	+	0.719324i	$0.255548\pi$
$504$	−1674.94	−0.148031
$505$	−17995.1	−1.58569
$506$	4636.59	0.407354
$507$	−3465.44	−0.303561
$508$	−1111.10	−0.0970416
$509$	19795.4	1.72381	0.861903	−	0.507073i	$-0.169273\pi$
$509$	19795.4	1.72381	0.861903	+	0.507073i	$0.169273\pi$
$510$	−3388.50	−0.294206
$511$	−84.1700	−0.00728661
$512$	512.000	0.0441942
$513$	0	0
$514$	−4473.93	−0.383923
$515$	−30889.1	−2.64298
$516$	−1186.39	−0.101217
$517$	−11680.0	−0.993593
$518$	3312.57	0.280977
$519$	2595.33	0.219504
$520$	−10689.6	−0.901484
$521$	21391.1	1.79877	0.899385	−	0.437157i	$-0.144014\pi$
$521$	21391.1	1.79877	0.899385	+	0.437157i	$0.144014\pi$
$522$	−3174.16	−0.266148
$523$	−3202.13	−0.267724	−0.133862	−	0.991000i	$-0.542738\pi$
$523$	−3202.13	−0.267724	−0.133862	+	0.991000i	$0.542738\pi$
$524$	−7290.73	−0.607819
$525$	−4693.25	−0.390153
$526$	1664.52	0.137978
$527$	5215.72	0.431120
$528$	1753.51	0.144530
$529$	−10776.8	−0.885744
$530$	−4682.65	−0.383776
$531$	4443.87	0.363178
$532$	0	0
$533$	15485.9	1.25848
$534$	−471.487	−0.0382083
$535$	−33345.6	−2.69468
$536$	−315.646	−0.0254363
$537$	6299.46	0.506223
$538$	6967.77	0.558368
$539$	16552.9	1.32279
$540$	−7430.79	−0.592167
$541$	−7363.00	−0.585139	−0.292569	−	0.956244i	$-0.594510\pi$
$541$	−7363.00	−0.585139	−0.292569	+	0.956244i	$0.594510\pi$
$542$	3578.21	0.283575
$543$	−5188.58	−0.410061
$544$	−1485.29	−0.117062
$545$	−1056.63	−0.0830478
$546$	−1993.07	−0.156219
$547$	12969.3	1.01376	0.506880	−	0.862016i	$-0.330799\pi$
$547$	12969.3	1.01376	0.506880	+	0.862016i	$0.330799\pi$
$548$	2643.85	0.206094
$549$	−7374.50	−0.573290
$550$	−37788.4	−2.92964
$551$	0	0
$552$	525.741	0.0405381
$553$	10309.5	0.792777
$554$	−11097.3	−0.851047
$555$	6899.50	0.527689
$556$	−4983.80	−0.380144
$557$	19994.5	1.52100	0.760499	−	0.649339i	$-0.224954\pi$
$557$	19994.5	1.52100	0.760499	+	0.649339i	$0.224954\pi$
$558$	5369.80	0.407386
$559$	10857.4	0.821502
$560$	−2903.46	−0.219096
$561$	−5086.86	−0.382830
$562$	91.5792	0.00687372
$563$	15654.6	1.17187	0.585936	−	0.810358i	$-0.300727\pi$
$563$	15654.6	1.17187	0.585936	+	0.810358i	$0.300727\pi$
$564$	−1324.40	−0.0988779
$565$	37060.1	2.75952
$566$	−12241.5	−0.909095
$567$	4267.45	0.316078
$568$	2801.62	0.206960
$569$	6450.45	0.475249	0.237625	−	0.971357i	$-0.423631\pi$
$569$	6450.45	0.475249	0.237625	+	0.971357i	$0.423631\pi$
$570$	0	0
$571$	18704.6	1.37086	0.685431	−	0.728138i	$-0.259614\pi$
$571$	18704.6	1.37086	0.685431	+	0.728138i	$0.259614\pi$
$572$	−16047.4	−1.17304
$573$	1234.44	0.0899994
$574$	4206.21	0.305860
$575$	−11329.8	−0.821714
$576$	−1529.17	−0.110617
$577$	−12394.4	−0.894257	−0.447128	−	0.894470i	$-0.647553\pi$
$577$	−12394.4	−0.894257	−0.447128	+	0.894470i	$0.647553\pi$
$578$	−5517.21	−0.397034
$579$	−105.582	−0.00757828
$580$	−5502.34	−0.393918
$581$	−2260.57	−0.161419
$582$	4218.84	0.300475
$583$	−7029.66	−0.499381
$584$	−76.8448	−0.00544497
$585$	31926.3	2.25639
$586$	14790.8	1.04267
$587$	−6424.61	−0.451741	−0.225871	−	0.974157i	$-0.572523\pi$
$587$	−6424.61	−0.451741	−0.225871	+	0.974157i	$0.572523\pi$
$588$	1876.92	0.131638
$589$	0	0
$590$	7703.34	0.537528
$591$	659.880	0.0459287
$592$	3024.29	0.209962
$593$	18100.1	1.25343	0.626714	−	0.779250i	$-0.284400\pi$
$593$	18100.1	1.25343	0.626714	+	0.779250i	$0.284400\pi$
$594$	−11155.2	−0.770546
$595$	8422.85	0.580341
$596$	9088.05	0.624599
$597$	−8114.54	−0.556291
$598$	−4811.39	−0.329017
$599$	2847.19	0.194212	0.0971061	−	0.995274i	$-0.469041\pi$
$599$	2847.19	0.194212	0.0971061	+	0.995274i	$0.469041\pi$
$600$	−4284.81	−0.291544
$601$	−6934.19	−0.470635	−0.235317	−	0.971919i	$-0.575613\pi$
$601$	−6934.19	−0.470635	−0.235317	+	0.971919i	$0.575613\pi$
$602$	2949.03	0.199657
$603$	942.728	0.0636664
$604$	−14551.1	−0.980256
$605$	−52500.1	−3.52799
$606$	−3063.18	−0.205335
$607$	−9089.78	−0.607813	−0.303907	−	0.952702i	$-0.598291\pi$
$607$	−9089.78	−0.607813	−0.303907	+	0.952702i	$0.598291\pi$
$608$	0	0
$609$	−1025.90	−0.0682622
$610$	−12783.5	−0.848508
$611$	12120.4	0.802517
$612$	4436.07	0.293003
$613$	25637.2	1.68920	0.844598	−	0.535400i	$-0.179839\pi$
$613$	25637.2	1.68920	0.844598	+	0.535400i	$0.179839\pi$
$614$	1150.14	0.0755957
$615$	8760.79	0.574421
$616$	−4358.72	−0.285094
$617$	21782.2	1.42126	0.710630	−	0.703566i	$-0.248410\pi$
$617$	21782.2	1.42126	0.710630	+	0.703566i	$0.248410\pi$
$618$	−5258.02	−0.342247
$619$	−23717.7	−1.54006	−0.770029	−	0.638008i	$-0.779758\pi$
$619$	−23717.7	−1.54006	−0.770029	+	0.638008i	$0.779758\pi$
$620$	9308.42	0.602960
$621$	−3344.59	−0.216125
$622$	−73.2867	−0.00472432
$623$	1171.98	0.0753684
$624$	−1819.61	−0.116735
$625$	38729.3	2.47868
$626$	−9767.46	−0.623620
$627$	0	0
$628$	−1807.08	−0.114825
$629$	−8773.35	−0.556147
$630$	8671.66	0.548392
$631$	−26203.2	−1.65314	−0.826571	−	0.562832i	$-0.809712\pi$
$631$	−26203.2	−1.65314	−0.826571	+	0.562832i	$0.809712\pi$
$632$	9412.31	0.592408
$633$	−5211.48	−0.327232
$634$	11734.6	0.735079
$635$	5752.51	0.359498
$636$	−797.091	−0.0496961
$637$	−17176.9	−1.06840
$638$	−8260.20	−0.512577
$639$	−8367.48	−0.518016
$640$	−2650.78	−0.163721
$641$	−4185.32	−0.257894	−0.128947	−	0.991651i	$-0.541160\pi$
$641$	−4185.32	−0.257894	−0.128947	+	0.991651i	$0.541160\pi$
$642$	−5676.16	−0.348941
$643$	32198.2	1.97477	0.987383	−	0.158350i	$-0.0506175\pi$
$643$	32198.2	1.97477	0.987383	+	0.158350i	$0.0506175\pi$
$644$	−1306.84	−0.0799641
$645$	6142.31	0.374966
$646$	0	0
$647$	371.159	0.0225530	0.0112765	−	0.999936i	$-0.496411\pi$
$647$	371.159	0.0225530	0.0112765	+	0.999936i	$0.496411\pi$
$648$	3896.06	0.236191
$649$	11564.4	0.699447
$650$	39213.0	2.36625
$651$	1735.54	0.104487
$652$	862.524	0.0518084
$653$	1659.89	0.0994741	0.0497370	−	0.998762i	$-0.484162\pi$
$653$	1659.89	0.0994741	0.0497370	+	0.998762i	$0.484162\pi$
$654$	−179.862	−0.0107541
$655$	37746.4	2.25171
$656$	3840.15	0.228556
$657$	229.510	0.0136286
$658$	3292.07	0.195043
$659$	24730.0	1.46183	0.730914	−	0.682469i	$-0.239094\pi$
$659$	24730.0	1.46183	0.730914	+	0.682469i	$0.239094\pi$
$660$	−9078.45	−0.535421
$661$	8399.85	0.494276	0.247138	−	0.968980i	$-0.420510\pi$
$661$	8399.85	0.494276	0.247138	+	0.968980i	$0.420510\pi$
$662$	17732.1	1.04105
$663$	5278.64	0.309209
$664$	−2063.84	−0.120621
$665$	0	0
$666$	−9032.52	−0.525530
$667$	−2476.59	−0.143769
$668$	13285.9	0.769533
$669$	935.299	0.0540519
$670$	1634.20	0.0942306
$671$	−19190.8	−1.10410
$672$	−494.234	−0.0283713
$673$	−27850.0	−1.59516	−0.797578	−	0.603216i	$-0.793886\pi$
$673$	−27850.0	−1.59516	−0.797578	+	0.603216i	$0.793886\pi$
$674$	−6054.40	−0.346004
$675$	27258.5	1.55434
$676$	7864.44	0.447453
$677$	−20343.1	−1.15487	−0.577437	−	0.816435i	$-0.695947\pi$
$677$	−20343.1	−1.15487	−0.577437	+	0.816435i	$0.695947\pi$
$678$	6308.46	0.357338
$679$	−10486.8	−0.592707
$680$	7689.83	0.433664
$681$	−6133.31	−0.345123
$682$	13973.9	0.784589
$683$	26794.4	1.50111	0.750556	−	0.660807i	$-0.229786\pi$
$683$	26794.4	1.50111	0.750556	+	0.660807i	$0.229786\pi$
$684$	0	0
$685$	−13688.0	−0.763493
$686$	−10676.6	−0.594221
$687$	−6286.23	−0.349104
$688$	2692.39	0.149195
$689$	7294.68	0.403346
$690$	−2721.92	−0.150177
$691$	29092.3	1.60162	0.800812	−	0.598916i	$-0.204402\pi$
$691$	29092.3	1.60162	0.800812	+	0.598916i	$0.204402\pi$
$692$	−5889.83	−0.323552
$693$	13018.0	0.713585
$694$	−17751.5	−0.970948
$695$	25802.7	1.40827
$696$	−936.621	−0.0510094
$697$	−11140.2	−0.605400
$698$	5617.39	0.304615
$699$	10560.0	0.571411
$700$	10650.8	0.575091
$701$	21523.0	1.15965	0.579824	−	0.814742i	$-0.303121\pi$
$701$	21523.0	1.15965	0.579824	+	0.814742i	$0.303121\pi$
$702$	11575.8	0.622364
$703$	0	0
$704$	−3979.39	−0.213038
$705$	6856.80	0.366301
$706$	23404.7	1.24766
$707$	7614.19	0.405037
$708$	1311.28	0.0696058
$709$	14965.8	0.792741	0.396370	−	0.918091i	$-0.370270\pi$
$709$	14965.8	0.792741	0.396370	+	0.918091i	$0.370270\pi$
$710$	−14504.8	−0.766700
$711$	−28111.4	−1.48278
$712$	1069.99	0.0563195
$713$	4189.70	0.220064
$714$	1433.76	0.0751499
$715$	83082.6	4.34561
$716$	−14295.9	−0.746179
$717$	1068.97	0.0556784
$718$	−3372.06	−0.175270
$719$	7357.79	0.381640	0.190820	−	0.981625i	$-0.438885\pi$
$719$	7357.79	0.381640	0.190820	+	0.981625i	$0.438885\pi$
$720$	7916.99	0.409790
$721$	13069.9	0.675104
$722$	0	0
$723$	−6072.41	−0.312359
$724$	11774.9	0.604436
$725$	20184.3	1.03397
$726$	−8936.70	−0.456849
$727$	29148.4	1.48701	0.743503	−	0.668732i	$-0.233163\pi$
$727$	29148.4	1.48701	0.743503	+	0.668732i	$0.233163\pi$
$728$	4523.05	0.230268
$729$	−7367.23	−0.374294
$730$	397.849	0.0201713
$731$	−7810.52	−0.395188
$732$	−2176.04	−0.109875
$733$	21514.5	1.08412	0.542059	−	0.840341i	$-0.317645\pi$
$733$	21514.5	1.08412	0.542059	+	0.840341i	$0.317645\pi$
$734$	−16872.1	−0.848445
$735$	−9717.41	−0.487663
$736$	−1193.11	−0.0597537
$737$	2453.28	0.122616
$738$	−11469.2	−0.572071
$739$	−23115.9	−1.15065	−0.575326	−	0.817924i	$-0.695125\pi$
$739$	−23115.9	−1.15065	−0.575326	+	0.817924i	$0.695125\pi$
$740$	−15657.7	−0.777821
$741$	0	0
$742$	1981.34	0.0980289
$743$	−15102.9	−0.745725	−0.372862	−	0.927887i	$-0.621624\pi$
$743$	−15102.9	−0.745725	−0.372862	+	0.927887i	$0.621624\pi$
$744$	1584.50	0.0780788
$745$	−47051.7	−2.31388
$746$	3487.35	0.171154
$747$	6163.99	0.301912
$748$	11544.1	0.564296
$749$	14109.3	0.688310
$750$	13058.3	0.635763
$751$	−28595.9	−1.38945	−0.694726	−	0.719275i	$-0.744474\pi$
$751$	−28595.9	−1.38945	−0.694726	+	0.719275i	$0.744474\pi$
$752$	3005.57	0.145747
$753$	−3182.13	−0.154002
$754$	8571.61	0.414005
$755$	75335.3	3.63144
$756$	3144.15	0.151259
$757$	−7645.65	−0.367088	−0.183544	−	0.983011i	$-0.558757\pi$
$757$	−7645.65	−0.367088	−0.183544	+	0.983011i	$0.558757\pi$
$758$	3182.91	0.152518
$759$	−4086.19	−0.195414
$760$	0	0
$761$	10724.9	0.510876	0.255438	−	0.966825i	$-0.417780\pi$
$761$	10724.9	0.510876	0.255438	+	0.966825i	$0.417780\pi$
$762$	979.206	0.0465524
$763$	447.086	0.0212131
$764$	−2801.44	−0.132660
$765$	−22966.9	−1.08545
$766$	−18009.8	−0.849505
$767$	−12000.4	−0.564938
$768$	−451.222	−0.0212006
$769$	−3963.53	−0.185863	−0.0929315	−	0.995673i	$-0.529624\pi$
$769$	−3963.53	−0.185863	−0.0929315	+	0.995673i	$0.529624\pi$
$770$	22566.5	1.05615
$771$	3942.85	0.184174
$772$	239.606	0.0111705
$773$	4445.30	0.206839	0.103419	−	0.994638i	$-0.467022\pi$
$773$	4445.30	0.206839	0.103419	+	0.994638i	$0.467022\pi$
$774$	−8041.24	−0.373432
$775$	−34146.2	−1.58267
$776$	−9574.19	−0.442904
$777$	−2919.35	−0.134789
$778$	8139.86	0.375100
$779$	0	0
$780$	9420.71	0.432456
$781$	−21774.9	−0.997653
$782$	3461.18	0.158276
$783$	5958.47	0.271952
$784$	−4259.47	−0.194036
$785$	9355.81	0.425380
$786$	6425.28	0.291580
$787$	−3452.08	−0.156357	−0.0781787	−	0.996939i	$-0.524910\pi$
$787$	−3452.08	−0.156357	−0.0781787	+	0.996939i	$0.524910\pi$
$788$	−1497.53	−0.0676994
$789$	−1466.93	−0.0661901
$790$	−48730.4	−2.19462
$791$	−15681.1	−0.704872
$792$	11885.1	0.533231
$793$	19914.3	0.891776
$794$	659.140	0.0294610
$795$	4126.79	0.184103
$796$	18415.1	0.819981
$797$	25298.0	1.12434	0.562171	−	0.827021i	$-0.309966\pi$
$797$	25298.0	1.12434	0.562171	+	0.827021i	$0.309966\pi$
$798$	0	0
$799$	−8719.06	−0.386055
$800$	9723.91	0.429740
$801$	−3195.69	−0.140967
$802$	−16374.1	−0.720935
$803$	597.258	0.0262475
$804$	278.177	0.0122022
$805$	6765.93	0.296233
$806$	−14500.8	−0.633707
$807$	−6140.65	−0.267858
$808$	6951.54	0.302666
$809$	−23140.8	−1.00567	−0.502834	−	0.864383i	$-0.667709\pi$
$809$	−23140.8	−1.00567	−0.502834	+	0.864383i	$0.667709\pi$
$810$	−20171.1	−0.874989
$811$	11108.8	0.480988	0.240494	−	0.970651i	$-0.422691\pi$
$811$	11108.8	0.480988	0.240494	+	0.970651i	$0.422691\pi$
$812$	2328.18	0.100619
$813$	−3153.46	−0.136035
$814$	−23505.5	−1.01212
$815$	−4465.55	−0.191928
$816$	1308.98	0.0561562
$817$	0	0
$818$	−9997.00	−0.427307
$819$	−13508.8	−0.576357
$820$	−19881.7	−0.846705
$821$	12409.0	0.527500	0.263750	−	0.964591i	$-0.415041\pi$
$821$	12409.0	0.527500	0.263750	+	0.964591i	$0.415041\pi$
$822$	−2330.01	−0.0988667
$823$	−19072.1	−0.807791	−0.403895	−	0.914805i	$-0.632344\pi$
$823$	−19072.1	−0.807791	−0.403895	+	0.914805i	$0.632344\pi$
$824$	11932.5	0.504476
$825$	33302.6	1.40539
$826$	−3259.47	−0.137302
$827$	−4287.12	−0.180263	−0.0901317	−	0.995930i	$-0.528729\pi$
$827$	−4287.12	−0.180263	−0.0901317	+	0.995930i	$0.528729\pi$
$828$	3563.42	0.149562
$829$	22544.9	0.944533	0.472266	−	0.881456i	$-0.343436\pi$
$829$	22544.9	0.944533	0.472266	+	0.881456i	$0.343436\pi$
$830$	10685.1	0.446851
$831$	9779.99	0.408260
$832$	4129.42	0.172070
$833$	12356.6	0.513962
$834$	4392.19	0.182361
$835$	−68785.3	−2.85080
$836$	0	0
$837$	−10080.1	−0.416270
$838$	23882.2	0.984482
$839$	−38597.8	−1.58825	−0.794127	−	0.607752i	$-0.792071\pi$
$839$	−38597.8	−1.58825	−0.794127	+	0.607752i	$0.792071\pi$
$840$	2558.80	0.105104
$841$	−19976.9	−0.819094
$842$	23965.6	0.980889
$843$	−80.7081	−0.00329743
$844$	11826.9	0.482344
$845$	−40716.6	−1.65763
$846$	−8976.62	−0.364802
$847$	22214.1	0.901164
$848$	1808.91	0.0732527
$849$	10788.3	0.436107
$850$	−28208.7	−1.13830
$851$	−7047.49	−0.283883
$852$	−2469.05	−0.0992819
$853$	3609.89	0.144900	0.0724502	−	0.997372i	$-0.476918\pi$
$853$	3609.89	0.144900	0.0724502	+	0.997372i	$0.476918\pi$
$854$	5409.03	0.216737
$855$	0	0
$856$	12881.4	0.514344
$857$	2418.11	0.0963841	0.0481921	−	0.998838i	$-0.484654\pi$
$857$	2418.11	0.0963841	0.0481921	+	0.998838i	$0.484654\pi$
$858$	14142.5	0.562724
$859$	34852.3	1.38434	0.692168	−	0.721736i	$-0.256656\pi$
$859$	34852.3	1.38434	0.692168	+	0.721736i	$0.256656\pi$
$860$	−13939.3	−0.552705
$861$	−3706.91	−0.146726
$862$	−14166.0	−0.559739
$863$	32080.0	1.26537	0.632685	−	0.774409i	$-0.281953\pi$
$863$	32080.0	1.26537	0.632685	+	0.774409i	$0.281953\pi$
$864$	2870.52	0.113029
$865$	30493.5	1.19862
$866$	14806.0	0.580980
$867$	4862.28	0.190463
$868$	−3938.62	−0.154016
$869$	−73154.9	−2.85571
$870$	4849.18	0.188968
$871$	−2545.77	−0.0990358
$872$	408.177	0.0158516
$873$	28594.9	1.10858
$874$	0	0
$875$	−32459.3	−1.25409
$876$	67.7229	0.00261204
$877$	−43014.6	−1.65621	−0.828107	−	0.560570i	$-0.810582\pi$
$877$	−43014.6	−1.65621	−0.828107	+	0.560570i	$0.810582\pi$
$878$	15350.9	0.590053
$879$	−13035.0	−0.500182
$880$	20602.5	0.789218
$881$	20270.3	0.775170	0.387585	−	0.921834i	$-0.373309\pi$
$881$	20270.3	0.775170	0.387585	+	0.921834i	$0.373309\pi$
$882$	12721.6	0.485667
$883$	−19658.3	−0.749214	−0.374607	−	0.927184i	$-0.622222\pi$
$883$	−19658.3	−0.749214	−0.374607	+	0.927184i	$0.622222\pi$
$884$	−11979.3	−0.455778
$885$	−6788.90	−0.257860
$886$	−5367.78	−0.203537
$887$	−44845.4	−1.69759	−0.848795	−	0.528722i	$-0.822671\pi$
$887$	−44845.4	−1.69759	−0.848795	+	0.528722i	$0.822671\pi$
$888$	−2665.28	−0.100722
$889$	−2434.03	−0.0918276
$890$	−5539.66	−0.208640
$891$	−30281.2	−1.13856
$892$	−2122.56	−0.0796733
$893$	0	0
$894$	−8009.24	−0.299630
$895$	74014.5	2.76428
$896$	1121.61	0.0418196
$897$	4240.24	0.157835
$898$	28195.1	1.04775
$899$	−7464.07	−0.276908
$900$	−29042.0	−1.07563
$901$	−5247.59	−0.194032
$902$	−29846.7	−1.10176
$903$	−2598.96	−0.0957786
$904$	−14316.4	−0.526720
$905$	−60962.4	−2.23918
$906$	12823.8	0.470244
$907$	−7211.31	−0.264000	−0.132000	−	0.991250i	$-0.542140\pi$
$907$	−7211.31	−0.264000	−0.132000	+	0.991250i	$0.542140\pi$
$908$	13918.9	0.508716
$909$	−20761.9	−0.757568
$910$	−23417.2	−0.853047
$911$	−29098.8	−1.05827	−0.529136	−	0.848537i	$-0.677484\pi$
$911$	−29098.8	−1.05827	−0.529136	+	0.848537i	$0.677484\pi$
$912$	0	0
$913$	16040.7	0.581456
$914$	14080.4	0.509561
$915$	11266.0	0.407042
$916$	14265.9	0.514584
$917$	−15971.4	−0.575161
$918$	−8327.29	−0.299392
$919$	−15321.9	−0.549972	−0.274986	−	0.961448i	$-0.588673\pi$
$919$	−15321.9	−0.549972	−0.274986	+	0.961448i	$0.588673\pi$
$920$	6177.11	0.221362
$921$	−1013.61	−0.0362644
$922$	14706.2	0.525295
$923$	22595.8	0.805796
$924$	3841.32	0.136764
$925$	57437.3	2.04165
$926$	28109.5	0.997554
$927$	−35638.3	−1.26269
$928$	2125.56	0.0751885
$929$	−20544.9	−0.725573	−0.362787	−	0.931872i	$-0.618175\pi$
$929$	−20544.9	−0.725573	−0.362787	+	0.931872i	$0.618175\pi$
$930$	−8203.45	−0.289249
$931$	0	0
$932$	−23964.8	−0.842267
$933$	64.5871	0.00226633
$934$	11750.3	0.411651
$935$	−59767.3	−2.09048
$936$	−12333.2	−0.430686
$937$	47835.3	1.66778	0.833891	−	0.551930i	$-0.186108\pi$
$937$	47835.3	1.66778	0.833891	+	0.551930i	$0.186108\pi$
$938$	−691.469	−0.0240696
$939$	8608.00	0.299160
$940$	−15560.8	−0.539932
$941$	445.310	0.0154269	0.00771344	−	0.999970i	$-0.497545\pi$
$941$	445.310	0.0154269	0.00771344	+	0.999970i	$0.497545\pi$
$942$	1592.57	0.0550835
$943$	−8948.70	−0.309024
$944$	−2975.81	−0.102600
$945$	−16278.2	−0.560350
$946$	−20925.9	−0.719196
$947$	44046.1	1.51141	0.755705	−	0.654912i	$-0.227294\pi$
$947$	44046.1	1.51141	0.755705	+	0.654912i	$0.227294\pi$
$948$	−8295.01	−0.284187
$949$	−619.775	−0.0211999
$950$	0	0
$951$	−10341.6	−0.352629
$952$	−3253.76	−0.110772
$953$	−3517.33	−0.119557	−0.0597783	−	0.998212i	$-0.519039\pi$
$953$	−3517.33	−0.119557	−0.0597783	+	0.998212i	$0.519039\pi$
$954$	−5402.61	−0.183350
$955$	14503.9	0.491451
$956$	−2425.91	−0.0820707
$957$	7279.66	0.245891
$958$	−355.562	−0.0119913
$959$	5791.75	0.195021
$960$	2336.12	0.0785394
$961$	−17163.9	−0.576144
$962$	24391.7	0.817484
$963$	−38472.5	−1.28739
$964$	13780.7	0.460421
$965$	−1240.51	−0.0413820
$966$	1151.71	0.0383600
$967$	−15243.5	−0.506928	−0.253464	−	0.967345i	$-0.581570\pi$
$967$	−15243.5	−0.506928	−0.253464	+	0.967345i	$0.581570\pi$
$968$	20280.9	0.673401
$969$	0	0
$970$	49568.5	1.64077
$971$	−3267.03	−0.107975	−0.0539876	−	0.998542i	$-0.517193\pi$
$971$	−3267.03	−0.107975	−0.0539876	+	0.998542i	$0.517193\pi$
$972$	−13121.6	−0.432999
$973$	−10917.7	−0.359719
$974$	−24639.8	−0.810587
$975$	−34558.2	−1.13512
$976$	4938.29	0.161958
$977$	−40038.2	−1.31109	−0.655545	−	0.755156i	$-0.727561\pi$
$977$	−40038.2	−1.31109	−0.655545	+	0.755156i	$0.727561\pi$
$978$	−760.137	−0.0248533
$979$	−8316.22	−0.271489
$980$	22052.6	0.718821
$981$	−1219.09	−0.0396763
$982$	−16883.7	−0.548655
$983$	−22254.4	−0.722080	−0.361040	−	0.932550i	$-0.617578\pi$
$983$	−22254.4	−0.722080	−0.361040	+	0.932550i	$0.617578\pi$
$984$	−3384.30	−0.109642
$985$	7753.15	0.250798
$986$	−6166.18	−0.199159
$987$	−2901.28	−0.0935652
$988$	0	0
$989$	−6274.06	−0.201722
$990$	−61532.8	−1.97540
$991$	−14779.5	−0.473750	−0.236875	−	0.971540i	$-0.576123\pi$
$991$	−14779.5	−0.473750	−0.236875	+	0.971540i	$0.576123\pi$
$992$	−3595.85	−0.115089
$993$	−15627.2	−0.499410
$994$	6137.35	0.195840
$995$	−95340.5	−3.03768
$996$	1818.85	0.0578638
$997$	28888.4	0.917659	0.458829	−	0.888524i	$-0.348269\pi$
$997$	28888.4	0.917659	0.458829	+	0.888524i	$0.348269\pi$
$998$	−12422.5	−0.394015
$999$	16955.6	0.536990

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	722.4.a.k.1.2		3
19.8	odd	6		38.4.c.c.7.2	✓	6
19.12	odd	6		38.4.c.c.11.2	yes	6
19.18	odd	2		722.4.a.j.1.2		3
57.8	even	6		342.4.g.f.235.1		6
57.50	even	6		342.4.g.f.163.1		6
76.27	even	6		304.4.i.e.273.2		6
76.31	even	6		304.4.i.e.49.2		6

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
38.4.c.c.7.2	✓	6	19.8	odd	6
38.4.c.c.11.2	yes	6	19.12	odd	6
304.4.i.e.49.2		6	76.31	even	6
304.4.i.e.273.2		6	76.27	even	6
342.4.g.f.163.1		6	57.50	even	6
342.4.g.f.235.1		6	57.8	even	6
722.4.a.j.1.2		3	19.18	odd	2
722.4.a.k.1.2		3	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:	\( N \)	\(=\)	\( 722 = 2 \cdot 19^{2} \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	722.a (trivial)

\(f(q)\)	\(=\)	\(q+2.00000 q^{2} -1.76259 q^{3} +4.00000 q^{4} -20.7092 q^{5} -3.52517 q^{6} +8.76259 q^{7} +8.00000 q^{8} -23.8933 q^{9} +O(q^{10})\)	\(q+2.00000 q^{2} -1.76259 q^{3} +4.00000 q^{4} -20.7092 q^{5} -3.52517 q^{6} +8.76259 q^{7} +8.00000 q^{8} -23.8933 q^{9} -41.4185 q^{10} -62.1780 q^{11} -7.05035 q^{12} +64.5222 q^{13} +17.5252 q^{14} +36.5018 q^{15} +16.0000 q^{16} -46.4155 q^{17} -47.7866 q^{18} -82.8369 q^{20} -15.4448 q^{21} -124.356 q^{22} -37.2848 q^{23} -14.1007 q^{24} +303.872 q^{25} +129.044 q^{26} +89.7038 q^{27} +35.0503 q^{28} +66.4238 q^{29} +73.0036 q^{30} -112.370 q^{31} +32.0000 q^{32} +109.594 q^{33} -92.8309 q^{34} -181.466 q^{35} -95.5731 q^{36} +189.018 q^{37} -113.726 q^{39} -165.674 q^{40} +240.010 q^{41} -30.8896 q^{42} +168.274 q^{43} -248.712 q^{44} +494.812 q^{45} -74.5695 q^{46} +187.848 q^{47} -28.2014 q^{48} -266.217 q^{49} +607.744 q^{50} +81.8113 q^{51} +258.089 q^{52} +113.057 q^{53} +179.408 q^{54} +1287.66 q^{55} +70.1007 q^{56} +132.848 q^{58} -185.988 q^{59} +146.007 q^{60} +308.643 q^{61} -224.741 q^{62} -209.367 q^{63} +64.0000 q^{64} -1336.20 q^{65} +219.188 q^{66} -39.4557 q^{67} -185.662 q^{68} +65.7176 q^{69} -362.933 q^{70} +350.202 q^{71} -191.146 q^{72} -9.60561 q^{73} +378.036 q^{74} -535.601 q^{75} -544.840 q^{77} -227.452 q^{78} +1176.54 q^{79} -331.348 q^{80} +487.008 q^{81} +480.019 q^{82} -257.980 q^{83} -61.7793 q^{84} +961.228 q^{85} +336.548 q^{86} -117.078 q^{87} -497.424 q^{88} +133.749 q^{89} +989.623 q^{90} +565.381 q^{91} -149.139 q^{92} +198.063 q^{93} +375.696 q^{94} -56.4028 q^{96} -1196.77 q^{97} -532.434 q^{98} +1485.64 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 3 q + 6 q^{2} - 5 q^{3} + 12 q^{4} + q^{5} - 10 q^{6} + 26 q^{7} + 24 q^{8} + 54 q^{9}+O(q^{10}) \) 3 * q + 6 * q^2 - 5 * q^3 + 12 * q^4 + q^5 - 10 * q^6 + 26 * q^7 + 24 * q^8 + 54 * q^9	\( 3 q + 6 q^{2} - 5 q^{3} + 12 q^{4} + q^{5} - 10 q^{6} + 26 q^{7} + 24 q^{8} + 54 q^{9} + 2 q^{10} + 4 q^{11} - 20 q^{12} + 129 q^{13} + 52 q^{14} - 77 q^{15} + 48 q^{16} + 51 q^{17} + 108 q^{18} + 4 q^{20} - 170 q^{21} + 8 q^{22} - 47 q^{23} - 40 q^{24} + 338 q^{25} + 258 q^{26} - 359 q^{27} + 104 q^{28} - 125 q^{29} - 154 q^{30} + 50 q^{31} + 96 q^{32} + 274 q^{33} + 102 q^{34} + 84 q^{35} + 216 q^{36} + 188 q^{37} - 773 q^{39} + 8 q^{40} + 475 q^{41} - 340 q^{42} + 73 q^{43} + 16 q^{44} + 1594 q^{45} - 94 q^{46} + 241 q^{47} - 80 q^{48} - 677 q^{49} + 676 q^{50} + 69 q^{51} + 516 q^{52} + 29 q^{53} - 718 q^{54} + 1838 q^{55} + 208 q^{56} - 250 q^{58} - 1065 q^{59} - 308 q^{60} + 981 q^{61} + 100 q^{62} + 872 q^{63} + 192 q^{64} - 293 q^{65} + 548 q^{66} + 877 q^{67} + 204 q^{68} + 763 q^{69} + 168 q^{70} + 2135 q^{71} + 432 q^{72} - 667 q^{73} + 376 q^{74} - 2292 q^{75} - 246 q^{77} - 1546 q^{78} + 1671 q^{79} + 16 q^{80} + 1287 q^{81} + 950 q^{82} + 588 q^{83} - 680 q^{84} + 1929 q^{85} + 146 q^{86} - 3215 q^{87} + 32 q^{88} + 693 q^{89} + 3188 q^{90} + 1676 q^{91} - 188 q^{92} + 3138 q^{93} + 482 q^{94} - 160 q^{96} - 985 q^{97} - 1354 q^{98} + 3184 q^{99}+O(q^{100}) \) 3 * q + 6 * q^2 - 5 * q^3 + 12 * q^4 + q^5 - 10 * q^6 + 26 * q^7 + 24 * q^8 + 54 * q^9 + 2 * q^10 + 4 * q^11 - 20 * q^12 + 129 * q^13 + 52 * q^14 - 77 * q^15 + 48 * q^16 + 51 * q^17 + 108 * q^18 + 4 * q^20 - 170 * q^21 + 8 * q^22 - 47 * q^23 - 40 * q^24 + 338 * q^25 + 258 * q^26 - 359 * q^27 + 104 * q^28 - 125 * q^29 - 154 * q^30 + 50 * q^31 + 96 * q^32 + 274 * q^33 + 102 * q^34 + 84 * q^35 + 216 * q^36 + 188 * q^37 - 773 * q^39 + 8 * q^40 + 475 * q^41 - 340 * q^42 + 73 * q^43 + 16 * q^44 + 1594 * q^45 - 94 * q^46 + 241 * q^47 - 80 * q^48 - 677 * q^49 + 676 * q^50 + 69 * q^51 + 516 * q^52 + 29 * q^53 - 718 * q^54 + 1838 * q^55 + 208 * q^56 - 250 * q^58 - 1065 * q^59 - 308 * q^60 + 981 * q^61 + 100 * q^62 + 872 * q^63 + 192 * q^64 - 293 * q^65 + 548 * q^66 + 877 * q^67 + 204 * q^68 + 763 * q^69 + 168 * q^70 + 2135 * q^71 + 432 * q^72 - 667 * q^73 + 376 * q^74 - 2292 * q^75 - 246 * q^77 - 1546 * q^78 + 1671 * q^79 + 16 * q^80 + 1287 * q^81 + 950 * q^82 + 588 * q^83 - 680 * q^84 + 1929 * q^85 + 146 * q^86 - 3215 * q^87 + 32 * q^88 + 693 * q^89 + 3188 * q^90 + 1676 * q^91 - 188 * q^92 + 3138 * q^93 + 482 * q^94 - 160 * q^96 - 985 * q^97 - 1354 * q^98 + 3184 * q^99

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