LMFDB - Embedded newform 1815.4.a.r.1.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1815,4,Mod(1,1815)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1815, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("1815.1");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 1815 = 3 \cdot 5 \cdot 11^{2} $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	1815.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:	$107.088466660$
Analytic rank:	$0$
Dimension:	$3$
Coefficient field:	3.3.47528.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{3} - x^{2} - 26x - 22 $ x^3 - x^2 - 26*x - 22
Coefficient ring:	$\Z[a_1, a_2]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 165)
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.3
Root			$-4.06484$ of defining polynomial
Character	$\chi$	$=$	1815.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+5.06484 q^{2} +3.00000 q^{3} +17.6526 q^{4} -5.00000 q^{5} +15.1945 q^{6} -27.4348 q^{7} +48.8887 q^{8} +9.00000 q^{9} +O(q^{10})$	\(q+5.06484 q^{2} +3.00000 q^{3} +17.6526 q^{4} -5.00000 q^{5} +15.1945 q^{6} -27.4348 q^{7} +48.8887 q^{8} +9.00000 q^{9} -25.3242 q^{10} +52.9577 q^{12} -22.6949 q^{13} -138.953 q^{14} -15.0000 q^{15} +106.392 q^{16} +41.1755 q^{17} +45.5835 q^{18} +142.128 q^{19} -88.2628 q^{20} -82.3044 q^{21} +176.166 q^{23} +146.666 q^{24} +25.0000 q^{25} -114.946 q^{26} +27.0000 q^{27} -484.295 q^{28} -76.2044 q^{29} -75.9725 q^{30} +197.373 q^{31} +147.751 q^{32} +208.547 q^{34} +137.174 q^{35} +158.873 q^{36} +367.297 q^{37} +719.856 q^{38} -68.0846 q^{39} -244.443 q^{40} +238.279 q^{41} -416.858 q^{42} -30.2905 q^{43} -45.0000 q^{45} +892.254 q^{46} +137.390 q^{47} +319.177 q^{48} +409.668 q^{49} +126.621 q^{50} +123.526 q^{51} -400.623 q^{52} +638.665 q^{53} +136.751 q^{54} -1341.25 q^{56} +426.385 q^{57} -385.963 q^{58} +103.146 q^{59} -264.788 q^{60} -605.596 q^{61} +999.662 q^{62} -246.913 q^{63} -102.804 q^{64} +113.474 q^{65} -704.925 q^{67} +726.852 q^{68} +528.499 q^{69} +694.764 q^{70} -782.162 q^{71} +439.998 q^{72} +243.132 q^{73} +1860.30 q^{74} +75.0000 q^{75} +2508.93 q^{76} -344.837 q^{78} +532.874 q^{79} -531.962 q^{80} +81.0000 q^{81} +1206.84 q^{82} -1204.91 q^{83} -1452.88 q^{84} -205.877 q^{85} -153.416 q^{86} -228.613 q^{87} +1058.49 q^{89} -227.918 q^{90} +622.629 q^{91} +3109.79 q^{92} +592.119 q^{93} +695.857 q^{94} -710.641 q^{95} +443.254 q^{96} -85.1964 q^{97} +2074.90 q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 3 q + 2 q^{2} + 9 q^{3} + 30 q^{4} - 15 q^{5} + 6 q^{6} - 10 q^{7} - 18 q^{8} + 27 q^{9}+O(q^{10}) $ 3 * q + 2 * q^2 + 9 * q^3 + 30 * q^4 - 15 * q^5 + 6 * q^6 - 10 * q^7 - 18 * q^8 + 27 * q^9	\( 3 q + 2 q^{2} + 9 q^{3} + 30 q^{4} - 15 q^{5} + 6 q^{6} - 10 q^{7} - 18 q^{8} + 27 q^{9} - 10 q^{10} + 90 q^{12} - 114 q^{13} - 68 q^{14} - 45 q^{15} + 178 q^{16} + 104 q^{17} + 18 q^{18} + 58 q^{19} - 150 q^{20} - 30 q^{21} + 120 q^{23} - 54 q^{24} + 75 q^{25} - 120 q^{26} + 81 q^{27} - 676 q^{28} + 220 q^{29} - 30 q^{30} + 248 q^{31} + 258 q^{32} - 80 q^{34} + 50 q^{35} + 270 q^{36} + 838 q^{37} + 600 q^{38} - 342 q^{39} + 90 q^{40} - 156 q^{41} - 204 q^{42} - 122 q^{43} - 135 q^{45} + 1256 q^{46} + 504 q^{47} + 534 q^{48} + 279 q^{49} + 50 q^{50} + 312 q^{51} - 520 q^{52} + 282 q^{53} + 54 q^{54} - 1644 q^{56} + 174 q^{57} - 1644 q^{58} + 548 q^{59} - 450 q^{60} - 414 q^{61} + 2448 q^{62} - 90 q^{63} - 58 q^{64} + 570 q^{65} - 428 q^{67} + 1704 q^{68} + 360 q^{69} + 340 q^{70} - 912 q^{71} - 162 q^{72} - 618 q^{73} + 1612 q^{74} + 225 q^{75} + 2752 q^{76} - 360 q^{78} + 542 q^{79} - 890 q^{80} + 243 q^{81} + 3372 q^{82} - 2028 q^{84} - 520 q^{85} - 1548 q^{86} + 660 q^{87} + 790 q^{89} - 90 q^{90} - 772 q^{91} + 1912 q^{92} + 744 q^{93} + 424 q^{94} - 290 q^{95} + 774 q^{96} + 2074 q^{97} + 3978 q^{98}+O(q^{100}) \) 3 * q + 2 * q^2 + 9 * q^3 + 30 * q^4 - 15 * q^5 + 6 * q^6 - 10 * q^7 - 18 * q^8 + 27 * q^9 - 10 * q^10 + 90 * q^12 - 114 * q^13 - 68 * q^14 - 45 * q^15 + 178 * q^16 + 104 * q^17 + 18 * q^18 + 58 * q^19 - 150 * q^20 - 30 * q^21 + 120 * q^23 - 54 * q^24 + 75 * q^25 - 120 * q^26 + 81 * q^27 - 676 * q^28 + 220 * q^29 - 30 * q^30 + 248 * q^31 + 258 * q^32 - 80 * q^34 + 50 * q^35 + 270 * q^36 + 838 * q^37 + 600 * q^38 - 342 * q^39 + 90 * q^40 - 156 * q^41 - 204 * q^42 - 122 * q^43 - 135 * q^45 + 1256 * q^46 + 504 * q^47 + 534 * q^48 + 279 * q^49 + 50 * q^50 + 312 * q^51 - 520 * q^52 + 282 * q^53 + 54 * q^54 - 1644 * q^56 + 174 * q^57 - 1644 * q^58 + 548 * q^59 - 450 * q^60 - 414 * q^61 + 2448 * q^62 - 90 * q^63 - 58 * q^64 + 570 * q^65 - 428 * q^67 + 1704 * q^68 + 360 * q^69 + 340 * q^70 - 912 * q^71 - 162 * q^72 - 618 * q^73 + 1612 * q^74 + 225 * q^75 + 2752 * q^76 - 360 * q^78 + 542 * q^79 - 890 * q^80 + 243 * q^81 + 3372 * q^82 - 2028 * q^84 - 520 * q^85 - 1548 * q^86 + 660 * q^87 + 790 * q^89 - 90 * q^90 - 772 * q^91 + 1912 * q^92 + 744 * q^93 + 424 * q^94 - 290 * q^95 + 774 * q^96 + 2074 * q^97 + 3978 * q^98

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 $

$2$	5.06484	1.79069	0.895345	−	0.445373i	$-0.146929\pi$
$2$	5.06484	1.79069	0.895345	+	0.445373i	$0.146929\pi$
$3$	3.00000	0.577350
$3$	3.00000	0.577350
$4$	17.6526	2.20657
$5$	−5.00000	−0.447214
$5$	−5.00000	−0.447214
$6$	15.1945	1.03386
$7$	−27.4348	−1.48134	−0.740670	−	0.671869i	$-0.765492\pi$
$7$	−27.4348	−1.48134	−0.740670	+	0.671869i	$0.765492\pi$
$8$	48.8887	2.16059
$9$	9.00000	0.333333
$10$	−25.3242	−0.800821
$11$	0	0
$11$	0	0
$12$	52.9577	1.27396
$13$	−22.6949	−0.484187	−0.242093	−	0.970253i	$-0.577834\pi$
$13$	−22.6949	−0.484187	−0.242093	+	0.970253i	$0.577834\pi$
$14$	−138.953	−2.65262
$15$	−15.0000	−0.258199
$16$	106.392	1.66238
$17$	41.1755	0.587442	0.293721	−	0.955891i	$-0.405106\pi$
$17$	41.1755	0.587442	0.293721	+	0.955891i	$0.405106\pi$
$18$	45.5835	0.596897
$19$	142.128	1.71613	0.858064	−	0.513542i	$-0.171667\pi$
$19$	142.128	1.71613	0.858064	+	0.513542i	$0.171667\pi$
$20$	−88.2628	−0.986808
$21$	−82.3044	−0.855252
$22$	0	0
$23$	176.166	1.59710	0.798548	−	0.601931i	$-0.205602\pi$
$23$	176.166	1.59710	0.798548	+	0.601931i	$0.205602\pi$
$24$	146.666	1.24742
$25$	25.0000	0.200000
$26$	−114.946	−0.867028
$27$	27.0000	0.192450
$28$	−484.295	−3.26868
$29$	−76.2044	−0.487959	−0.243979	−	0.969780i	$-0.578453\pi$
$29$	−76.2044	−0.487959	−0.243979	+	0.969780i	$0.578453\pi$
$30$	−75.9725	−0.462354
$31$	197.373	1.14352	0.571762	−	0.820420i	$-0.306260\pi$
$31$	197.373	1.14352	0.571762	+	0.820420i	$0.306260\pi$
$32$	147.751	0.816218
$33$	0	0
$34$	208.547	1.05193
$35$	137.174	0.662475
$36$	158.873	0.735523
$37$	367.297	1.63198	0.815989	−	0.578067i	$-0.196193\pi$
$37$	367.297	1.63198	0.815989	+	0.578067i	$0.196193\pi$
$38$	719.856	3.07305
$39$	−68.0846	−0.279545
$40$	−244.443	−0.966247
$41$	238.279	0.907633	0.453817	−	0.891095i	$-0.350062\pi$
$41$	238.279	0.907633	0.453817	+	0.891095i	$0.350062\pi$
$42$	−416.858	−1.53149
$43$	−30.2905	−0.107425	−0.0537123	−	0.998556i	$-0.517105\pi$
$43$	−30.2905	−0.107425	−0.0537123	+	0.998556i	$0.517105\pi$
$44$	0	0
$45$	−45.0000	−0.149071
$46$	892.254	2.85990
$47$	137.390	0.426391	0.213195	−	0.977010i	$-0.431613\pi$
$47$	137.390	0.426391	0.213195	+	0.977010i	$0.431613\pi$
$48$	319.177	0.959777
$49$	409.668	1.19437
$50$	126.621	0.358138
$51$	123.526	0.339160
$52$	−400.623	−1.06839
$53$	638.665	1.65523	0.827617	−	0.561293i	$-0.189696\pi$
$53$	638.665	1.65523	0.827617	+	0.561293i	$0.189696\pi$
$54$	136.751	0.344618
$55$	0	0
$56$	−1341.25	−3.20057
$57$	426.385	0.990807
$58$	−385.963	−0.873783
$59$	103.146	0.227601	0.113800	−	0.993504i	$-0.463698\pi$
$59$	103.146	0.227601	0.113800	+	0.993504i	$0.463698\pi$
$60$	−264.788	−0.569734
$61$	−605.596	−1.27113	−0.635563	−	0.772049i	$-0.719232\pi$
$61$	−605.596	−1.27113	−0.635563	+	0.772049i	$0.719232\pi$
$62$	999.662	2.04770
$63$	−246.913	−0.493780
$64$	−102.804	−0.200789
$65$	113.474	0.216535
$66$	0	0
$67$	−704.925	−1.28538	−0.642688	−	0.766128i	$-0.722181\pi$
$67$	−704.925	−1.28538	−0.642688	+	0.766128i	$0.722181\pi$
$68$	726.852	1.29623
$69$	528.499	0.922084
$70$	694.764	1.18629
$71$	−782.162	−1.30740	−0.653701	−	0.756753i	$-0.726785\pi$
$71$	−782.162	−1.30740	−0.653701	+	0.756753i	$0.726785\pi$
$72$	439.998	0.720198
$73$	243.132	0.389814	0.194907	−	0.980822i	$-0.437560\pi$
$73$	243.132	0.389814	0.194907	+	0.980822i	$0.437560\pi$
$74$	1860.30	2.92237
$75$	75.0000	0.115470
$76$	2508.93	3.78676
$77$	0	0
$78$	−344.837	−0.500579
$79$	532.874	0.758899	0.379449	−	0.925212i	$-0.376113\pi$
$79$	532.874	0.758899	0.379449	+	0.925212i	$0.376113\pi$
$80$	−531.962	−0.743440
$81$	81.0000	0.111111
$82$	1206.84	1.62529
$83$	−1204.91	−1.59344	−0.796722	−	0.604345i	$-0.793435\pi$
$83$	−1204.91	−1.59344	−0.796722	+	0.604345i	$0.793435\pi$
$84$	−1452.88	−1.88717
$85$	−205.877	−0.262712
$86$	−153.416	−0.192364
$87$	−228.613	−0.281723
$88$	0	0
$89$	1058.49	1.26067	0.630337	−	0.776322i	$-0.282917\pi$
$89$	1058.49	1.26067	0.630337	+	0.776322i	$0.282917\pi$
$90$	−227.918	−0.266940
$91$	622.629	0.717245
$92$	3109.79	3.52411
$93$	592.119	0.660214
$94$	695.857	0.763533
$95$	−710.641	−0.767476
$96$	443.254	0.471244
$97$	−85.1964	−0.0891792	−0.0445896	−	0.999005i	$-0.514198\pi$
$97$	−85.1964	−0.0891792	−0.0445896	+	0.999005i	$0.514198\pi$
$98$	2074.90	2.13874
$99$	0	0
$100$	441.314	0.441314
$101$	7.81823	0.00770241	0.00385120	−	0.999993i	$-0.498774\pi$
$101$	7.81823	0.00770241	0.00385120	+	0.999993i	$0.498774\pi$
$102$	625.641	0.607330
$103$	12.4770	0.0119359	0.00596794	−	0.999982i	$-0.498100\pi$
$103$	12.4770	0.0119359	0.00596794	+	0.999982i	$0.498100\pi$
$104$	−1109.52	−1.04613
$105$	411.522	0.382480
$106$	3234.73	2.96401
$107$	1376.81	1.24393	0.621967	−	0.783043i	$-0.286334\pi$
$107$	1376.81	1.24393	0.621967	+	0.783043i	$0.286334\pi$
$108$	476.619	0.424655
$109$	−610.189	−0.536197	−0.268099	−	0.963391i	$-0.586395\pi$
$109$	−610.189	−0.536197	−0.268099	+	0.963391i	$0.586395\pi$
$110$	0	0
$111$	1101.89	0.942223
$112$	−2918.86	−2.46255
$113$	−36.7727	−0.0306132	−0.0153066	−	0.999883i	$-0.504872\pi$
$113$	−36.7727	−0.0306132	−0.0153066	+	0.999883i	$0.504872\pi$
$114$	2159.57	1.77423
$115$	−880.832	−0.714243
$116$	−1345.20	−1.07672
$117$	−204.254	−0.161396
$118$	522.416	0.407562
$119$	−1129.64	−0.870201
$120$	−733.330	−0.557863
$121$	0	0
$122$	−3067.25	−2.27619
$123$	714.838	0.524022
$124$	3484.14	2.52326
$125$	−125.000	−0.0894427
$126$	−1250.57	−0.884207
$127$	54.5310	0.0381011	0.0190506	−	0.999819i	$-0.493936\pi$
$127$	54.5310	0.0381011	0.0190506	+	0.999819i	$0.493936\pi$
$128$	−1702.69	−1.17577
$129$	−90.8715	−0.0620216
$130$	574.729	0.387747
$131$	−2377.83	−1.58589	−0.792947	−	0.609290i	$-0.791454\pi$
$131$	−2377.83	−1.58589	−0.792947	+	0.609290i	$0.791454\pi$
$132$	0	0
$133$	−3899.26	−2.54217
$134$	−3570.33	−2.30171
$135$	−135.000	−0.0860663
$136$	2013.01	1.26922
$137$	−3078.41	−1.91976	−0.959878	−	0.280417i	$-0.909527\pi$
$137$	−3078.41	−1.91976	−0.959878	+	0.280417i	$0.909527\pi$
$138$	2676.76	1.65117
$139$	1197.18	0.730530	0.365265	−	0.930904i	$-0.380978\pi$
$139$	1197.18	0.730530	0.365265	+	0.930904i	$0.380978\pi$
$140$	2421.47	1.46180
$141$	412.169	0.246177
$142$	−3961.52	−2.34115
$143$	0	0
$144$	957.532	0.554128
$145$	381.022	0.218222
$146$	1231.42	0.698035
$147$	1229.00	0.689569
$148$	6483.73	3.60108
$149$	749.456	0.412066	0.206033	−	0.978545i	$-0.433945\pi$
$149$	749.456	0.412066	0.206033	+	0.978545i	$0.433945\pi$
$150$	379.863	0.206771
$151$	2645.72	1.42586	0.712931	−	0.701234i	$-0.247367\pi$
$151$	2645.72	1.42586	0.712931	+	0.701234i	$0.247367\pi$
$152$	6948.46	3.70786
$153$	370.579	0.195814
$154$	0	0
$155$	−986.865	−0.511399
$156$	−1201.87	−0.616836
$157$	−3475.74	−1.76684	−0.883422	−	0.468578i	$-0.844767\pi$
$157$	−3475.74	−1.76684	−0.883422	+	0.468578i	$0.844767\pi$
$158$	2698.92	1.35895
$159$	1916.00	0.955650
$160$	−738.757	−0.365024
$161$	−4833.09	−2.36584
$162$	410.252	0.198966
$163$	3518.89	1.69092	0.845462	−	0.534035i	$-0.179325\pi$
$163$	3518.89	1.69092	0.845462	+	0.534035i	$0.179325\pi$
$164$	4206.24	2.00276
$165$	0	0
$166$	−6102.67	−2.85337
$167$	−250.304	−0.115983	−0.0579914	−	0.998317i	$-0.518470\pi$
$167$	−250.304	−0.115983	−0.0579914	+	0.998317i	$0.518470\pi$
$168$	−4023.75	−1.84785
$169$	−1681.94	−0.765563
$170$	−1042.73	−0.470436
$171$	1279.15	0.572043
$172$	−534.705	−0.237040
$173$	−941.985	−0.413976	−0.206988	−	0.978344i	$-0.566366\pi$
$173$	−941.985	−0.413976	−0.206988	+	0.978344i	$0.566366\pi$
$174$	−1157.89	−0.504479
$175$	−685.870	−0.296268
$176$	0	0
$177$	309.437	0.131405
$178$	5361.09	2.25748
$179$	336.037	0.140316	0.0701582	−	0.997536i	$-0.477650\pi$
$179$	336.037	0.140316	0.0701582	+	0.997536i	$0.477650\pi$
$180$	−794.365	−0.328936
$181$	1107.45	0.454784	0.227392	−	0.973803i	$-0.426980\pi$
$181$	1107.45	0.454784	0.227392	+	0.973803i	$0.426980\pi$
$182$	3153.52	1.28436
$183$	−1816.79	−0.733885
$184$	8612.53	3.45068
$185$	−1836.48	−0.729843
$186$	2998.98	1.18224
$187$	0	0
$188$	2425.28	0.940861
$189$	−740.740	−0.285084
$190$	−3599.28	−1.37431
$191$	−4243.01	−1.60740	−0.803700	−	0.595035i	$-0.797138\pi$
$191$	−4243.01	−1.60740	−0.803700	+	0.595035i	$0.797138\pi$
$192$	−308.411	−0.115925
$193$	3324.23	1.23981	0.619905	−	0.784677i	$-0.287171\pi$
$193$	3324.23	1.23981	0.619905	+	0.784677i	$0.287171\pi$
$194$	−431.506	−0.159692
$195$	340.423	0.125016
$196$	7231.69	2.63546
$197$	−2677.14	−0.968213	−0.484107	−	0.875009i	$-0.660855\pi$
$197$	−2677.14	−0.968213	−0.484107	+	0.875009i	$0.660855\pi$
$198$	0	0
$199$	2779.90	0.990261	0.495131	−	0.868819i	$-0.335120\pi$
$199$	2779.90	0.990261	0.495131	+	0.868819i	$0.335120\pi$
$200$	1222.22	0.432119
$201$	−2114.77	−0.742113
$202$	39.5981	0.0137926
$203$	2090.65	0.722833
$204$	2180.56	0.748380
$205$	−1191.40	−0.405906
$206$	63.1940	0.0213735
$207$	1585.50	0.532365
$208$	−2414.56	−0.804903
$209$	0	0
$210$	2084.29	0.684904
$211$	−3056.15	−0.997129	−0.498564	−	0.866853i	$-0.666139\pi$
$211$	−3056.15	−0.997129	−0.498564	+	0.866853i	$0.666139\pi$
$212$	11274.1	3.65239
$213$	−2346.49	−0.754829
$214$	6973.30	2.22750
$215$	151.453	0.0480417
$216$	1319.99	0.415806
$217$	−5414.89	−1.69395
$218$	−3090.51	−0.960163
$219$	729.395	0.225059
$220$	0	0
$221$	−934.472	−0.284432
$222$	5580.89	1.68723
$223$	571.375	0.171579	0.0857895	−	0.996313i	$-0.472659\pi$
$223$	571.375	0.171579	0.0857895	+	0.996313i	$0.472659\pi$
$224$	−4053.53	−1.20910
$225$	225.000	0.0666667
$226$	−186.248	−0.0548187
$227$	1094.40	0.319989	0.159995	−	0.987118i	$-0.448852\pi$
$227$	1094.40	0.319989	0.159995	+	0.987118i	$0.448852\pi$
$228$	7526.78	2.18629
$229$	−645.240	−0.186195	−0.0930975	−	0.995657i	$-0.529677\pi$
$229$	−645.240	−0.186195	−0.0930975	+	0.995657i	$0.529677\pi$
$230$	−4461.27	−1.27899
$231$	0	0
$232$	−3725.53	−1.05428
$233$	2337.39	0.657201	0.328600	−	0.944469i	$-0.393423\pi$
$233$	2337.39	0.657201	0.328600	+	0.944469i	$0.393423\pi$
$234$	−1034.51	−0.289009
$235$	−686.949	−0.190688
$236$	1820.79	0.502217
$237$	1598.62	0.438151
$238$	−5721.44	−1.55826
$239$	3656.91	0.989733	0.494866	−	0.868969i	$-0.335217\pi$
$239$	3656.91	0.989733	0.494866	+	0.868969i	$0.335217\pi$
$240$	−1595.89	−0.429225
$241$	389.034	0.103983	0.0519914	−	0.998648i	$-0.483443\pi$
$241$	389.034	0.103983	0.0519914	+	0.998648i	$0.483443\pi$
$242$	0	0
$243$	243.000	0.0641500
$244$	−10690.3	−2.80483
$245$	−2048.34	−0.534138
$246$	3620.53	0.938361
$247$	−3225.58	−0.830927
$248$	9649.30	2.47069
$249$	−3614.73	−0.919976
$250$	−633.104	−0.160164
$251$	2299.55	0.578271	0.289135	−	0.957288i	$-0.406632\pi$
$251$	2299.55	0.578271	0.289135	+	0.957288i	$0.406632\pi$
$252$	−4358.65	−1.08956
$253$	0	0
$254$	276.191	0.0682273
$255$	−617.632	−0.151677
$256$	−7801.44	−1.90465
$257$	4921.61	1.19456	0.597279	−	0.802033i	$-0.296248\pi$
$257$	4921.61	1.19456	0.597279	+	0.802033i	$0.296248\pi$
$258$	−460.249	−0.111062
$259$	−10076.7	−2.41752
$260$	2003.11	0.477799
$261$	−685.840	−0.162653
$262$	−12043.3	−2.83985
$263$	2575.61	0.603875	0.301938	−	0.953328i	$-0.402367\pi$
$263$	2575.61	0.603875	0.301938	+	0.953328i	$0.402367\pi$
$264$	0	0
$265$	−3193.33	−0.740243
$266$	−19749.1	−4.55224
$267$	3175.48	0.727850
$268$	−12443.7	−2.83627
$269$	−4794.97	−1.08682	−0.543410	−	0.839468i	$-0.682867\pi$
$269$	−4794.97	−1.08682	−0.543410	+	0.839468i	$0.682867\pi$
$270$	−683.753	−0.154118
$271$	−2729.47	−0.611821	−0.305910	−	0.952060i	$-0.598961\pi$
$271$	−2729.47	−0.611821	−0.305910	+	0.952060i	$0.598961\pi$
$272$	4380.76	0.976553
$273$	1867.89	0.414102
$274$	−15591.7	−3.43769
$275$	0	0
$276$	9329.36	2.03464
$277$	3761.45	0.815898	0.407949	−	0.913005i	$-0.366244\pi$
$277$	3761.45	0.815898	0.407949	+	0.913005i	$0.366244\pi$
$278$	6063.53	1.30815
$279$	1776.36	0.381174
$280$	6706.25	1.43134
$281$	6434.87	1.36609	0.683046	−	0.730375i	$-0.260655\pi$
$281$	6434.87	1.36609	0.683046	+	0.730375i	$0.260655\pi$
$282$	2087.57	0.440826
$283$	−3335.65	−0.700649	−0.350325	−	0.936628i	$-0.613929\pi$
$283$	−3335.65	−0.700649	−0.350325	+	0.936628i	$0.613929\pi$
$284$	−13807.2	−2.88487
$285$	−2131.92	−0.443103
$286$	0	0
$287$	−6537.14	−1.34451
$288$	1329.76	0.272073
$289$	−3217.58	−0.654912
$290$	1929.81	0.390768
$291$	−255.589	−0.0514876
$292$	4291.89	0.860151
$293$	2878.93	0.574023	0.287012	−	0.957927i	$-0.407338\pi$
$293$	2878.93	0.574023	0.287012	+	0.957927i	$0.407338\pi$
$294$	6224.71	1.23480
$295$	−515.729	−0.101786
$296$	17956.6	3.52604
$297$	0	0
$298$	3795.87	0.737883
$299$	−3998.07	−0.773293
$300$	1323.94	0.254793
$301$	831.014	0.159132
$302$	13400.1	2.55328
$303$	23.4547	0.00444699
$304$	15121.4	2.85286
$305$	3027.98	0.568465
$306$	1876.92	0.350642
$307$	8154.28	1.51593	0.757963	−	0.652297i	$-0.226195\pi$
$307$	8154.28	1.51593	0.757963	+	0.652297i	$0.226195\pi$
$308$	0	0
$309$	37.4310	0.00689119
$310$	−4998.31	−0.915757
$311$	3818.24	0.696182	0.348091	−	0.937461i	$-0.386830\pi$
$311$	3818.24	0.696182	0.348091	+	0.937461i	$0.386830\pi$
$312$	−3328.57	−0.603984
$313$	2527.23	0.456381	0.228191	−	0.973616i	$-0.426719\pi$
$313$	2527.23	0.456381	0.228191	+	0.973616i	$0.426719\pi$
$314$	−17604.1	−3.16387
$315$	1234.57	0.220825
$316$	9406.59	1.67456
$317$	−11084.7	−1.96398	−0.981989	−	0.188937i	$-0.939496\pi$
$317$	−11084.7	−1.96398	−0.981989	+	0.188937i	$0.939496\pi$
$318$	9704.20	1.71127
$319$	0	0
$320$	514.019	0.0897954
$321$	4130.42	0.718186
$322$	−24478.8	−4.23649
$323$	5852.19	1.00813
$324$	1429.86	0.245174
$325$	−567.372	−0.0968373
$326$	17822.6	3.02792
$327$	−1830.57	−0.309574
$328$	11649.1	1.96103
$329$	−3769.26	−0.631629
$330$	0	0
$331$	−9417.70	−1.56388	−0.781939	−	0.623355i	$-0.785769\pi$
$331$	−9417.70	−1.56388	−0.781939	+	0.623355i	$0.785769\pi$
$332$	−21269.7	−3.51605
$333$	3305.67	0.543993
$334$	−1267.75	−0.207689
$335$	3524.62	0.574838
$336$	−8756.57	−1.42176
$337$	11263.2	1.82061	0.910305	−	0.413938i	$-0.135847\pi$
$337$	11263.2	1.82061	0.910305	+	0.413938i	$0.135847\pi$
$338$	−8518.76	−1.37089
$339$	−110.318	−0.0176745
$340$	−3634.26	−0.579693
$341$	0	0
$342$	6478.70	1.02435
$343$	−1829.03	−0.287925
$344$	−1480.86	−0.232101
$345$	−2642.49	−0.412369
$346$	−4771.00	−0.741302
$347$	4213.25	0.651814	0.325907	−	0.945402i	$-0.394330\pi$
$347$	4213.25	0.651814	0.325907	+	0.945402i	$0.394330\pi$
$348$	−4035.61	−0.621642
$349$	−4987.07	−0.764905	−0.382452	−	0.923975i	$-0.624920\pi$
$349$	−4987.07	−0.764905	−0.382452	+	0.923975i	$0.624920\pi$
$350$	−3473.82	−0.530524
$351$	−612.762	−0.0931817
$352$	0	0
$353$	−7633.47	−1.15096	−0.575480	−	0.817816i	$-0.695185\pi$
$353$	−7633.47	−1.15096	−0.575480	+	0.817816i	$0.695185\pi$
$354$	1567.25	0.235306
$355$	3910.81	0.584688
$356$	18685.1	2.78177
$357$	−3388.92	−0.502411
$358$	1701.97	0.251263
$359$	3114.76	0.457913	0.228957	−	0.973437i	$-0.426469\pi$
$359$	3114.76	0.457913	0.228957	+	0.973437i	$0.426469\pi$
$360$	−2199.99	−0.322082
$361$	13341.4	1.94510
$362$	5609.04	0.814378
$363$	0	0
$364$	10991.0	1.58265
$365$	−1215.66	−0.174330
$366$	−9201.74	−1.31416
$367$	5931.48	0.843653	0.421827	−	0.906677i	$-0.361389\pi$
$367$	5931.48	0.843653	0.421827	+	0.906677i	$0.361389\pi$
$368$	18742.8	2.65499
$369$	2144.51	0.302544
$370$	−9301.49	−1.30692
$371$	−17521.7	−2.45196
$372$	10452.4	1.45681
$373$	−13918.9	−1.93215	−0.966073	−	0.258267i	$-0.916848\pi$
$373$	−13918.9	−1.93215	−0.966073	+	0.258267i	$0.916848\pi$
$374$	0	0
$375$	−375.000	−0.0516398
$376$	6716.80	0.921257
$377$	1729.45	0.236263
$378$	−3751.72	−0.510497
$379$	−12267.3	−1.66261	−0.831303	−	0.555820i	$-0.812404\pi$
$379$	−12267.3	−1.66261	−0.831303	+	0.555820i	$0.812404\pi$
$380$	−12544.6	−1.69349
$381$	163.593	0.0219977
$382$	−21490.1	−2.87835
$383$	−6935.04	−0.925233	−0.462616	−	0.886559i	$-0.653089\pi$
$383$	−6935.04	−0.925233	−0.462616	+	0.886559i	$0.653089\pi$
$384$	−5108.08	−0.678830
$385$	0	0
$386$	16836.7	2.22012
$387$	−272.615	−0.0358082
$388$	−1503.93	−0.196780
$389$	2775.18	0.361715	0.180858	−	0.983509i	$-0.442113\pi$
$389$	2775.18	0.361715	0.180858	+	0.983509i	$0.442113\pi$
$390$	1724.19	0.223866
$391$	7253.73	0.938202
$392$	20028.1	2.58054
$393$	−7133.50	−0.915617
$394$	−13559.3	−1.73377
$395$	−2664.37	−0.339390
$396$	0	0
$397$	10539.5	1.33240	0.666198	−	0.745775i	$-0.267921\pi$
$397$	10539.5	1.33240	0.666198	+	0.745775i	$0.267921\pi$
$398$	14079.7	1.77325
$399$	−11697.8	−1.46772
$400$	2659.81	0.332477
$401$	−12295.3	−1.53117	−0.765585	−	0.643334i	$-0.777550\pi$
$401$	−12295.3	−1.53117	−0.765585	+	0.643334i	$0.777550\pi$
$402$	−10711.0	−1.32889
$403$	−4479.35	−0.553679
$404$	138.012	0.0169959
$405$	−405.000	−0.0496904
$406$	10588.8	1.29437
$407$	0	0
$408$	6039.04	0.732787
$409$	11545.7	1.39584	0.697918	−	0.716178i	$-0.254110\pi$
$409$	11545.7	1.39584	0.697918	+	0.716178i	$0.254110\pi$
$410$	−6034.22	−0.726852
$411$	−9235.24	−1.10837
$412$	220.251	0.0263374
$413$	−2829.78	−0.337154
$414$	8030.28	0.953301
$415$	6024.54	0.712610
$416$	−3353.20	−0.395202
$417$	3591.55	0.421772
$418$	0	0
$419$	1851.51	0.215876	0.107938	−	0.994158i	$-0.465575\pi$
$419$	1851.51	0.215876	0.107938	+	0.994158i	$0.465575\pi$
$420$	7264.42	0.843970
$421$	−1303.60	−0.150911	−0.0754557	−	0.997149i	$-0.524041\pi$
$421$	−1303.60	−0.150911	−0.0754557	+	0.997149i	$0.524041\pi$
$422$	−15478.9	−1.78555
$423$	1236.51	0.142130
$424$	31223.5	3.57629
$425$	1029.39	0.117488
$426$	−11884.6	−1.35166
$427$	16614.4	1.88297
$428$	24304.2	2.74483
$429$	0	0
$430$	767.082	0.0860279
$431$	−8228.85	−0.919652	−0.459826	−	0.888009i	$-0.652088\pi$
$431$	−8228.85	−0.919652	−0.459826	+	0.888009i	$0.652088\pi$
$432$	2872.60	0.319926
$433$	5830.21	0.647072	0.323536	−	0.946216i	$-0.395128\pi$
$433$	5830.21	0.647072	0.323536	+	0.946216i	$0.395128\pi$
$434$	−27425.5	−3.03333
$435$	1143.07	0.125990
$436$	−10771.4	−1.18316
$437$	25038.2	2.74082
$438$	3694.26	0.403011
$439$	−14261.0	−1.55044	−0.775218	−	0.631694i	$-0.782360\pi$
$439$	−14261.0	−1.55044	−0.775218	+	0.631694i	$0.782360\pi$
$440$	0	0
$441$	3687.01	0.398123
$442$	−4732.95	−0.509329
$443$	12025.7	1.28975	0.644875	−	0.764288i	$-0.276910\pi$
$443$	12025.7	1.28975	0.644875	+	0.764288i	$0.276910\pi$
$444$	19451.2	2.07908
$445$	−5292.46	−0.563790
$446$	2893.92	0.307245
$447$	2248.37	0.237907
$448$	2820.40	0.297436
$449$	−7073.28	−0.743449	−0.371725	−	0.928343i	$-0.621233\pi$
$449$	−7073.28	−0.743449	−0.371725	+	0.928343i	$0.621233\pi$
$450$	1139.59	0.119379
$451$	0	0
$452$	−649.133	−0.0675501
$453$	7937.15	0.823222
$454$	5542.93	0.573001
$455$	−3113.15	−0.320762
$456$	20845.4	2.14073
$457$	−2732.31	−0.279677	−0.139838	−	0.990174i	$-0.544658\pi$
$457$	−2732.31	−0.279677	−0.139838	+	0.990174i	$0.544658\pi$
$458$	−3268.04	−0.333418
$459$	1111.74	0.113053
$460$	−15548.9	−1.57603
$461$	332.708	0.0336134	0.0168067	−	0.999859i	$-0.494650\pi$
$461$	332.708	0.0336134	0.0168067	+	0.999859i	$0.494650\pi$
$462$	0	0
$463$	8248.39	0.827937	0.413969	−	0.910291i	$-0.364142\pi$
$463$	8248.39	0.827937	0.413969	+	0.910291i	$0.364142\pi$
$464$	−8107.58	−0.811174
$465$	−2960.59	−0.295256
$466$	11838.5	1.17684
$467$	7359.35	0.729229	0.364615	−	0.931158i	$-0.381201\pi$
$467$	7359.35	0.729229	0.364615	+	0.931158i	$0.381201\pi$
$468$	−3605.60	−0.356131
$469$	19339.5	1.90408
$470$	−3479.28	−0.341462
$471$	−10427.2	−1.02009
$472$	5042.66	0.491752
$473$	0	0
$474$	8096.76	0.784592
$475$	3553.21	0.343226
$476$	−19941.0	−1.92016
$477$	5747.99	0.551745
$478$	18521.7	1.77230
$479$	10327.6	0.985140	0.492570	−	0.870273i	$-0.336058\pi$
$479$	10327.6	0.985140	0.492570	+	0.870273i	$0.336058\pi$
$480$	−2216.27	−0.210747
$481$	−8335.75	−0.790182
$482$	1970.39	0.186201
$483$	−14499.3	−1.36592
$484$	0	0
$485$	425.982	0.0398822
$486$	1230.76	0.114873
$487$	9622.57	0.895360	0.447680	−	0.894194i	$-0.352250\pi$
$487$	9622.57	0.895360	0.447680	+	0.894194i	$0.352250\pi$
$488$	−29606.8	−2.74639
$489$	10556.7	0.976256
$490$	−10374.5	−0.956475
$491$	8993.59	0.826629	0.413315	−	0.910588i	$-0.364371\pi$
$491$	8993.59	0.826629	0.413315	+	0.910588i	$0.364371\pi$
$492$	12618.7	1.15629
$493$	−3137.75	−0.286648
$494$	−16337.0	−1.48793
$495$	0	0
$496$	20999.0	1.90097
$497$	21458.5	1.93671
$498$	−18308.0	−1.64739
$499$	2623.70	0.235377	0.117688	−	0.993051i	$-0.462452\pi$
$499$	2623.70	0.235377	0.117688	+	0.993051i	$0.462452\pi$
$500$	−2206.57	−0.197362
$501$	−750.912	−0.0669627
$502$	11646.8	1.03550
$503$	−13234.5	−1.17316	−0.586579	−	0.809892i	$-0.699526\pi$
$503$	−13234.5	−1.17316	−0.586579	+	0.809892i	$0.699526\pi$
$504$	−12071.3	−1.06686
$505$	−39.0912	−0.00344462
$506$	0	0
$507$	−5045.83	−0.441998
$508$	962.612	0.0840728
$509$	−12810.3	−1.11553	−0.557765	−	0.829999i	$-0.688341\pi$
$509$	−12810.3	−1.11553	−0.557765	+	0.829999i	$0.688341\pi$
$510$	−3128.20	−0.271606
$511$	−6670.26	−0.577446
$512$	−25891.5	−2.23487
$513$	3837.46	0.330269
$514$	24927.1	2.13908
$515$	−62.3850	−0.00533789
$516$	−1604.12	−0.136855
$517$	0	0
$518$	−51036.9	−4.32902
$519$	−2825.95	−0.239009
$520$	5547.61	0.467844
$521$	1151.47	0.0968268	0.0484134	−	0.998827i	$-0.484584\pi$
$521$	1151.47	0.0968268	0.0484134	+	0.998827i	$0.484584\pi$
$522$	−3473.67	−0.291261
$523$	17319.1	1.44801	0.724005	−	0.689794i	$-0.242299\pi$
$523$	17319.1	1.44801	0.724005	+	0.689794i	$0.242299\pi$
$524$	−41974.8	−3.49939
$525$	−2057.61	−0.171050
$526$	13045.1	1.08135
$527$	8126.92	0.671754
$528$	0	0
$529$	18867.6	1.55072
$530$	−16173.7	−1.32555
$531$	928.312	0.0758669
$532$	−68831.9	−5.60948
$533$	−5407.72	−0.439464
$534$	16083.3	1.30335
$535$	−6884.03	−0.556304
$536$	−34462.8	−2.77718
$537$	1008.11	0.0810117
$538$	−24285.7	−1.94616
$539$	0	0
$540$	−2383.10	−0.189911
$541$	7190.73	0.571449	0.285724	−	0.958312i	$-0.407766\pi$
$541$	7190.73	0.571449	0.285724	+	0.958312i	$0.407766\pi$
$542$	−13824.3	−1.09558
$543$	3322.34	0.262570
$544$	6083.73	0.479481
$545$	3050.94	0.239795
$546$	9460.55	0.741527
$547$	−18670.5	−1.45940	−0.729701	−	0.683766i	$-0.760341\pi$
$547$	−18670.5	−1.45940	−0.729701	+	0.683766i	$0.760341\pi$
$548$	−54341.9	−4.23608
$549$	−5450.37	−0.423709
$550$	0	0
$551$	−10830.8	−0.837400
$552$	25837.6	1.99225
$553$	−14619.3	−1.12419
$554$	19051.1	1.46102
$555$	−5509.45	−0.421375
$556$	21133.3	1.61197
$557$	5510.44	0.419183	0.209591	−	0.977789i	$-0.432787\pi$
$557$	5510.44	0.419183	0.209591	+	0.977789i	$0.432787\pi$
$558$	8996.95	0.682565
$559$	687.439	0.0520136
$560$	14594.3	1.10129
$561$	0	0
$562$	32591.5	2.44625
$563$	−3576.57	−0.267734	−0.133867	−	0.990999i	$-0.542740\pi$
$563$	−3576.57	−0.267734	−0.133867	+	0.990999i	$0.542740\pi$
$564$	7275.84	0.543206
$565$	183.864	0.0136906
$566$	−16894.5	−1.25465
$567$	−2222.22	−0.164593
$568$	−38238.8	−2.82476
$569$	−12285.2	−0.905138	−0.452569	−	0.891729i	$-0.649492\pi$
$569$	−12285.2	−0.905138	−0.452569	+	0.891729i	$0.649492\pi$
$570$	−10797.8	−0.793459
$571$	−13889.5	−1.01797	−0.508983	−	0.860777i	$-0.669978\pi$
$571$	−13889.5	−1.01797	−0.508983	+	0.860777i	$0.669978\pi$
$572$	0	0
$573$	−12729.0	−0.928032
$574$	−33109.5	−2.40761
$575$	4404.16	0.319419
$576$	−925.234	−0.0669296
$577$	11579.4	0.835457	0.417728	−	0.908572i	$-0.362826\pi$
$577$	11579.4	0.835457	0.417728	+	0.908572i	$0.362826\pi$
$578$	−16296.5	−1.17274
$579$	9972.69	0.715805
$580$	6726.02	0.481522
$581$	33056.4	2.36043
$582$	−1294.52	−0.0921984
$583$	0	0
$584$	11886.4	0.842229
$585$	1021.27	0.0721783
$586$	14581.3	1.02790
$587$	26468.0	1.86107	0.930537	−	0.366199i	$-0.119341\pi$
$587$	26468.0	1.86107	0.930537	+	0.366199i	$0.119341\pi$
$588$	21695.1	1.52158
$589$	28052.3	1.96243
$590$	−2612.08	−0.182267
$591$	−8031.41	−0.558998
$592$	39077.6	2.71297
$593$	−1059.52	−0.0733716	−0.0366858	−	0.999327i	$-0.511680\pi$
$593$	−1059.52	−0.0733716	−0.0366858	+	0.999327i	$0.511680\pi$
$594$	0	0
$595$	5648.20	0.389166
$596$	13229.8	0.909253
$597$	8339.70	0.571728
$598$	−20249.6	−1.38473
$599$	−17858.7	−1.21817	−0.609086	−	0.793104i	$-0.708464\pi$
$599$	−17858.7	−1.21817	−0.609086	+	0.793104i	$0.708464\pi$
$600$	3666.65	0.249484
$601$	9650.91	0.655023	0.327511	−	0.944847i	$-0.393790\pi$
$601$	9650.91	0.655023	0.327511	+	0.944847i	$0.393790\pi$
$602$	4208.95	0.284957
$603$	−6344.32	−0.428459
$604$	46703.7	3.14627
$605$	0	0
$606$	118.794	0.00796318
$607$	−22754.9	−1.52157	−0.760786	−	0.649002i	$-0.775187\pi$
$607$	−22754.9	−1.52157	−0.760786	+	0.649002i	$0.775187\pi$
$608$	20999.6	1.40074
$609$	6271.96	0.417328
$610$	15336.2	1.01794
$611$	−3118.04	−0.206453
$612$	6541.67	0.432077
$613$	−13074.5	−0.861459	−0.430729	−	0.902481i	$-0.641744\pi$
$613$	−13074.5	−0.861459	−0.430729	+	0.902481i	$0.641744\pi$
$614$	41300.1	2.71455
$615$	−3574.19	−0.234350
$616$	0	0
$617$	−13393.0	−0.873878	−0.436939	−	0.899491i	$-0.643937\pi$
$617$	−13393.0	−0.873878	−0.436939	+	0.899491i	$0.643937\pi$
$618$	189.582	0.0123400
$619$	−15965.3	−1.03667	−0.518336	−	0.855177i	$-0.673448\pi$
$619$	−15965.3	−1.03667	−0.518336	+	0.855177i	$0.673448\pi$
$620$	−17420.7	−1.12844
$621$	4756.49	0.307361
$622$	19338.8	1.24665
$623$	−29039.5	−1.86749
$624$	−7243.69	−0.464711
$625$	625.000	0.0400000
$626$	12800.0	0.817237
$627$	0	0
$628$	−61355.8	−3.89867
$629$	15123.6	0.958693
$630$	6252.87	0.395429
$631$	17698.3	1.11657	0.558287	−	0.829648i	$-0.311459\pi$
$631$	17698.3	1.11657	0.558287	+	0.829648i	$0.311459\pi$
$632$	26051.5	1.63967
$633$	−9168.45	−0.575693
$634$	−56142.4	−3.51688
$635$	−272.655	−0.0170393
$636$	33822.2	2.10871
$637$	−9297.37	−0.578297
$638$	0	0
$639$	−7039.46	−0.435801
$640$	8513.47	0.525820
$641$	18264.8	1.12546	0.562728	−	0.826642i	$-0.309752\pi$
$641$	18264.8	1.12546	0.562728	+	0.826642i	$0.309752\pi$
$642$	20919.9	1.28605
$643$	−15730.5	−0.964778	−0.482389	−	0.875957i	$-0.660231\pi$
$643$	−15730.5	−0.964778	−0.482389	+	0.875957i	$0.660231\pi$
$644$	−85316.4	−5.22040
$645$	454.358	0.0277369
$646$	29640.4	1.80524
$647$	21176.6	1.28676	0.643382	−	0.765545i	$-0.277531\pi$
$647$	21176.6	1.28676	0.643382	+	0.765545i	$0.277531\pi$
$648$	3959.98	0.240066
$649$	0	0
$650$	−2873.65	−0.173406
$651$	−16244.7	−0.978001
$652$	62117.4	3.73114
$653$	−28293.6	−1.69558	−0.847791	−	0.530331i	$-0.822068\pi$
$653$	−28293.6	−1.69558	−0.847791	+	0.530331i	$0.822068\pi$
$654$	−9271.52	−0.554350
$655$	11889.2	0.709234
$656$	25351.1	1.50883
$657$	2188.18	0.129938
$658$	−19090.7	−1.13105
$659$	3894.19	0.230191	0.115096	−	0.993354i	$-0.463283\pi$
$659$	3894.19	0.230191	0.115096	+	0.993354i	$0.463283\pi$
$660$	0	0
$661$	−6063.63	−0.356805	−0.178402	−	0.983958i	$-0.557093\pi$
$661$	−6063.63	−0.356805	−0.178402	+	0.983958i	$0.557093\pi$
$662$	−47699.1	−2.80042
$663$	−2803.42	−0.164217
$664$	−58906.4	−3.44279
$665$	19496.3	1.13689
$666$	16742.7	0.974123
$667$	−13424.7	−0.779317
$668$	−4418.51	−0.255924
$669$	1714.13	0.0990612
$670$	17851.6	1.02936
$671$	0	0
$672$	−12160.6	−0.698072
$673$	−17297.1	−0.990719	−0.495360	−	0.868688i	$-0.664964\pi$
$673$	−17297.1	−0.990719	−0.495360	+	0.868688i	$0.664964\pi$
$674$	57046.3	3.26015
$675$	675.000	0.0384900
$676$	−29690.6	−1.68927
$677$	4640.36	0.263432	0.131716	−	0.991287i	$-0.457951\pi$
$677$	4640.36	0.263432	0.131716	+	0.991287i	$0.457951\pi$
$678$	−558.744	−0.0316496
$679$	2337.35	0.132105
$680$	−10065.1	−0.567614
$681$	3283.19	0.184746
$682$	0	0
$683$	−14694.9	−0.823256	−0.411628	−	0.911352i	$-0.635040\pi$
$683$	−14694.9	−0.823256	−0.411628	+	0.911352i	$0.635040\pi$
$684$	22580.3	1.26225
$685$	15392.1	0.858541
$686$	−9263.73	−0.515584
$687$	−1935.72	−0.107500
$688$	−3222.68	−0.178581
$689$	−14494.4	−0.801442
$690$	−13383.8	−0.738424
$691$	−9905.09	−0.545307	−0.272654	−	0.962112i	$-0.587901\pi$
$691$	−9905.09	−0.545307	−0.272654	+	0.962112i	$0.587901\pi$
$692$	−16628.4	−0.913466
$693$	0	0
$694$	21339.4	1.16720
$695$	−5985.91	−0.326703
$696$	−11176.6	−0.608689
$697$	9811.25	0.533182
$698$	−25258.7	−1.36971
$699$	7012.18	0.379435
$700$	−12107.4	−0.653736
$701$	947.946	0.0510748	0.0255374	−	0.999674i	$-0.491870\pi$
$701$	947.946	0.0510748	0.0255374	+	0.999674i	$0.491870\pi$
$702$	−3103.54	−0.166860
$703$	52203.2	2.80069
$704$	0	0
$705$	−2060.85	−0.110094
$706$	−38662.3	−2.06101
$707$	−214.492	−0.0114099
$708$	5462.36	0.289955
$709$	−3310.76	−0.175371	−0.0876855	−	0.996148i	$-0.527947\pi$
$709$	−3310.76	−0.175371	−0.0876855	+	0.996148i	$0.527947\pi$
$710$	19807.6	1.04699
$711$	4795.87	0.252966
$712$	51748.3	2.72380
$713$	34770.5	1.82632
$714$	−17164.3	−0.899662
$715$	0	0
$716$	5931.92	0.309618
$717$	10970.7	0.571423
$718$	15775.8	0.819981
$719$	3061.15	0.158778	0.0793892	−	0.996844i	$-0.474703\pi$
$719$	3061.15	0.158778	0.0793892	+	0.996844i	$0.474703\pi$
$720$	−4787.66	−0.247813
$721$	−342.304	−0.0176811
$722$	67572.1	3.48307
$723$	1167.10	0.0600345
$724$	19549.3	1.00351
$725$	−1905.11	−0.0975918
$726$	0	0
$727$	−7405.09	−0.377771	−0.188886	−	0.981999i	$-0.560488\pi$
$727$	−7405.09	−0.377771	−0.188886	+	0.981999i	$0.560488\pi$
$728$	30439.5	1.54967
$729$	729.000	0.0370370
$730$	−6157.11	−0.312171
$731$	−1247.23	−0.0631057
$732$	−32071.0	−1.61937
$733$	−29791.4	−1.50119	−0.750593	−	0.660765i	$-0.770232\pi$
$733$	−29791.4	−1.50119	−0.750593	+	0.660765i	$0.770232\pi$
$734$	30042.0	1.51072
$735$	−6145.02	−0.308384
$736$	26028.8	1.30358
$737$	0	0
$738$	10861.6	0.541763
$739$	7150.93	0.355955	0.177978	−	0.984035i	$-0.443045\pi$
$739$	7150.93	0.355955	0.177978	+	0.984035i	$0.443045\pi$
$740$	−32418.6	−1.61045
$741$	−9676.75	−0.479736
$742$	−88744.3	−4.39071
$743$	1940.69	0.0958239	0.0479120	−	0.998852i	$-0.484743\pi$
$743$	1940.69	0.0958239	0.0479120	+	0.998852i	$0.484743\pi$
$744$	28947.9	1.42645
$745$	−3747.28	−0.184282
$746$	−70496.7	−3.45988
$747$	−10844.2	−0.531148
$748$	0	0
$749$	−37772.4	−1.84269
$750$	−1899.31	−0.0924708
$751$	−29491.2	−1.43295	−0.716476	−	0.697611i	$-0.754246\pi$
$751$	−29491.2	−1.43295	−0.716476	+	0.697611i	$0.754246\pi$
$752$	14617.2	0.708824
$753$	6898.64	0.333865
$754$	8759.38	0.423074
$755$	−13228.6	−0.637665
$756$	−13076.0	−0.629058
$757$	3542.54	0.170087	0.0850436	−	0.996377i	$-0.472897\pi$
$757$	3542.54	0.170087	0.0850436	+	0.996377i	$0.472897\pi$
$758$	−62131.7	−2.97721
$759$	0	0
$760$	−34742.3	−1.65820
$761$	−8552.86	−0.407412	−0.203706	−	0.979032i	$-0.565299\pi$
$761$	−8552.86	−0.407412	−0.203706	+	0.979032i	$0.565299\pi$
$762$	828.572	0.0393911
$763$	16740.4	0.794290
$764$	−74900.0	−3.54684
$765$	−1852.90	−0.0875707
$766$	−35124.9	−1.65680
$767$	−2340.88	−0.110201
$768$	−23404.3	−1.09965
$769$	3128.73	0.146716	0.0733582	−	0.997306i	$-0.476628\pi$
$769$	3128.73	0.146716	0.0733582	+	0.997306i	$0.476628\pi$
$770$	0	0
$771$	14764.8	0.689679
$772$	58681.2	2.73573
$773$	−5364.51	−0.249609	−0.124805	−	0.992181i	$-0.539830\pi$
$773$	−5364.51	−0.249609	−0.124805	+	0.992181i	$0.539830\pi$
$774$	−1380.75	−0.0641214
$775$	4934.32	0.228705
$776$	−4165.14	−0.192680
$777$	−30230.1	−1.39575
$778$	14055.8	0.647719
$779$	33866.2	1.55762
$780$	6009.34	0.275858
$781$	0	0
$782$	36738.9	1.68003
$783$	−2057.52	−0.0939077
$784$	43585.6	1.98550
$785$	17378.7	0.790157
$786$	−36130.0	−1.63959
$787$	−12160.9	−0.550813	−0.275406	−	0.961328i	$-0.588812\pi$
$787$	−12160.9	−0.550813	−0.275406	+	0.961328i	$0.588812\pi$
$788$	−47258.3	−2.13643
$789$	7726.84	0.348648
$790$	−13494.6	−0.607742
$791$	1008.85	0.0453485
$792$	0	0
$793$	13743.9	0.615462
$794$	53380.7	2.38591
$795$	−9579.98	−0.427380
$796$	49072.4	2.18508
$797$	−581.179	−0.0258299	−0.0129149	−	0.999917i	$-0.504111\pi$
$797$	−581.179	−0.0258299	−0.0129149	+	0.999917i	$0.504111\pi$
$798$	−59247.3	−2.62824
$799$	5657.09	0.250480
$800$	3693.78	0.163244
$801$	9526.43	0.420225
$802$	−62273.8	−2.74185
$803$	0	0
$804$	−37331.2	−1.63752
$805$	24165.4	1.05804
$806$	−22687.2	−0.991467
$807$	−14384.9	−0.627475
$808$	382.223	0.0166418
$809$	−4763.37	−0.207010	−0.103505	−	0.994629i	$-0.533006\pi$
$809$	−4763.37	−0.207010	−0.103505	+	0.994629i	$0.533006\pi$
$810$	−2051.26	−0.0889801
$811$	18055.4	0.781762	0.390881	−	0.920441i	$-0.372170\pi$
$811$	18055.4	0.781762	0.390881	+	0.920441i	$0.372170\pi$
$812$	36905.4	1.59498
$813$	−8188.40	−0.353235
$814$	0	0
$815$	−17594.4	−0.756205
$816$	13142.3	0.563813
$817$	−4305.14	−0.184354
$818$	58476.9	2.49951
$819$	5603.66	0.239082
$820$	−21031.2	−0.895660
$821$	−1128.04	−0.0479522	−0.0239761	−	0.999713i	$-0.507633\pi$
$821$	−1128.04	−0.0479522	−0.0239761	+	0.999713i	$0.507633\pi$
$822$	−46775.0	−1.98475
$823$	−32124.2	−1.36061	−0.680304	−	0.732930i	$-0.738152\pi$
$823$	−32124.2	−1.36061	−0.680304	+	0.732930i	$0.738152\pi$
$824$	609.984	0.0257886
$825$	0	0
$826$	−14332.4	−0.603738
$827$	−11914.2	−0.500964	−0.250482	−	0.968121i	$-0.580589\pi$
$827$	−11914.2	−0.500964	−0.250482	+	0.968121i	$0.580589\pi$
$828$	27988.1	1.17470
$829$	−37721.6	−1.58037	−0.790185	−	0.612868i	$-0.790016\pi$
$829$	−37721.6	−1.58037	−0.790185	+	0.612868i	$0.790016\pi$
$830$	30513.3	1.27606
$831$	11284.4	0.471059
$832$	2333.12	0.0972192
$833$	16868.3	0.701622
$834$	18190.6	0.755262
$835$	1251.52	0.0518690
$836$	0	0
$837$	5329.07	0.220071
$838$	9377.57	0.386567
$839$	−16550.5	−0.681034	−0.340517	−	0.940238i	$-0.610602\pi$
$839$	−16550.5	−0.681034	−0.340517	+	0.940238i	$0.610602\pi$
$840$	20118.8	0.826384
$841$	−18581.9	−0.761896
$842$	−6602.53	−0.270236
$843$	19304.6	0.788714
$844$	−53948.9	−2.20023
$845$	8409.71	0.342370
$846$	6262.71	0.254511
$847$	0	0
$848$	67949.2	2.75163
$849$	−10006.9	−0.404520
$850$	5213.67	0.210385
$851$	64705.3	2.60643
$852$	−41421.5	−1.66558
$853$	−1045.52	−0.0419672	−0.0209836	−	0.999780i	$-0.506680\pi$
$853$	−1045.52	−0.0419672	−0.0209836	+	0.999780i	$0.506680\pi$
$854$	84149.3	3.37181
$855$	−6395.77	−0.255825
$856$	67310.2	2.68764
$857$	14016.5	0.558688	0.279344	−	0.960191i	$-0.409883\pi$
$857$	14016.5	0.558688	0.279344	+	0.960191i	$0.409883\pi$
$858$	0	0
$859$	−20476.3	−0.813319	−0.406660	−	0.913580i	$-0.633306\pi$
$859$	−20476.3	−0.813319	−0.406660	+	0.913580i	$0.633306\pi$
$860$	2673.53	0.106008
$861$	−19611.4	−0.776255
$862$	−41677.8	−1.64681
$863$	24083.0	0.949936	0.474968	−	0.880003i	$-0.342460\pi$
$863$	24083.0	0.949936	0.474968	+	0.880003i	$0.342460\pi$
$864$	3989.29	0.157081
$865$	4709.92	0.185135
$866$	29529.1	1.15871
$867$	−9652.75	−0.378114
$868$	−95586.6	−3.73781
$869$	0	0
$870$	5789.44	0.225610
$871$	15998.2	0.622362
$872$	−29831.3	−1.15850
$873$	−766.768	−0.0297264
$874$	126814.	4.90796
$875$	3429.35	0.132495
$876$	12875.7	0.496608
$877$	−30432.5	−1.17176	−0.585879	−	0.810399i	$-0.699250\pi$
$877$	−30432.5	−1.17176	−0.585879	+	0.810399i	$0.699250\pi$
$878$	−72229.7	−2.77635
$879$	8636.79	0.331413
$880$	0	0
$881$	24559.2	0.939183	0.469592	−	0.882884i	$-0.344401\pi$
$881$	24559.2	0.939183	0.469592	+	0.882884i	$0.344401\pi$
$882$	18674.1	0.712914
$883$	6013.88	0.229200	0.114600	−	0.993412i	$-0.463441\pi$
$883$	6013.88	0.229200	0.114600	+	0.993412i	$0.463441\pi$
$884$	−16495.8	−0.627618
$885$	−1547.19	−0.0587662
$886$	60908.3	2.30954
$887$	−13395.5	−0.507075	−0.253538	−	0.967325i	$-0.581594\pi$
$887$	−13395.5	−0.507075	−0.253538	+	0.967325i	$0.581594\pi$
$888$	53869.9	2.03576
$889$	−1496.05	−0.0564407
$890$	−26805.4	−1.00957
$891$	0	0
$892$	10086.2	0.378601
$893$	19527.0	0.731741
$894$	11387.6	0.426017
$895$	−1680.19	−0.0627514
$896$	46713.1	1.74171
$897$	−11994.2	−0.446461
$898$	−35825.0	−1.33129
$899$	−15040.7	−0.557992
$900$	3971.83	0.147105
$901$	26297.3	0.972354
$902$	0	0
$903$	2493.04	0.0918751
$904$	−1797.77	−0.0661426
$905$	−5537.24	−0.203386
$906$	40200.3	1.47414
$907$	−32078.9	−1.17438	−0.587189	−	0.809450i	$-0.699766\pi$
$907$	−32078.9	−1.17438	−0.587189	+	0.809450i	$0.699766\pi$
$908$	19318.9	0.706079
$909$	70.3641	0.00256747
$910$	−15767.6	−0.574385
$911$	−15992.0	−0.581600	−0.290800	−	0.956784i	$-0.593921\pi$
$911$	−15992.0	−0.581600	−0.290800	+	0.956784i	$0.593921\pi$
$912$	45364.1	1.64710
$913$	0	0
$914$	−13838.7	−0.500814
$915$	9083.94	0.328203
$916$	−11390.1	−0.410852
$917$	65235.4	2.34925
$918$	5630.77	0.202443
$919$	−33876.1	−1.21596	−0.607980	−	0.793952i	$-0.708020\pi$
$919$	−33876.1	−1.21596	−0.607980	+	0.793952i	$0.708020\pi$
$920$	−43062.7	−1.54319
$921$	24462.8	0.875220
$922$	1685.11	0.0601912
$923$	17751.1	0.633026
$924$	0	0
$925$	9182.42	0.326396
$926$	41776.7	1.48258
$927$	112.293	0.00397863
$928$	−11259.3	−0.398281
$929$	21163.4	0.747416	0.373708	−	0.927546i	$-0.378086\pi$
$929$	21163.4	0.747416	0.373708	+	0.927546i	$0.378086\pi$
$930$	−14994.9	−0.528713
$931$	58225.4	2.04969
$932$	41261.0	1.45016
$933$	11454.7	0.401941
$934$	37273.9	1.30582
$935$	0	0
$936$	−9985.70	−0.348710
$937$	49771.9	1.73530	0.867650	−	0.497175i	$-0.165629\pi$
$937$	49771.9	1.73530	0.867650	+	0.497175i	$0.165629\pi$
$938$	97951.2	3.40962
$939$	7581.68	0.263492
$940$	−12126.4	−0.420766
$941$	−32194.6	−1.11532	−0.557659	−	0.830070i	$-0.688300\pi$
$941$	−32194.6	−1.11532	−0.557659	+	0.830070i	$0.688300\pi$
$942$	−52812.2	−1.82666
$943$	41976.8	1.44958
$944$	10973.9	0.378359
$945$	3703.70	0.127493
$946$	0	0
$947$	−30091.9	−1.03258	−0.516291	−	0.856413i	$-0.672688\pi$
$947$	−30091.9	−1.03258	−0.516291	+	0.856413i	$0.672688\pi$
$948$	28219.8	0.966810
$949$	−5517.84	−0.188742
$950$	17996.4	0.614611
$951$	−33254.2	−1.13390
$952$	−55226.6	−1.88015
$953$	−5710.17	−0.194093	−0.0970465	−	0.995280i	$-0.530940\pi$
$953$	−5710.17	−0.194093	−0.0970465	+	0.995280i	$0.530940\pi$
$954$	29112.6	0.988004
$955$	21215.0	0.718851
$956$	64553.9	2.18392
$957$	0	0
$958$	52307.8	1.76408
$959$	84455.7	2.84381
$960$	1542.06	0.0518434
$961$	9165.07	0.307646
$962$	−42219.2	−1.41497
$963$	12391.3	0.414645
$964$	6867.44	0.229445
$965$	−16621.2	−0.554460
$966$	−73436.4	−2.44594
$967$	−29638.4	−0.985634	−0.492817	−	0.870133i	$-0.664033\pi$
$967$	−29638.4	−0.985634	−0.492817	+	0.870133i	$0.664033\pi$
$968$	0	0
$969$	17556.6	0.582042
$970$	2157.53	0.0714166
$971$	21416.3	0.707808	0.353904	−	0.935282i	$-0.384854\pi$
$971$	21416.3	0.707808	0.353904	+	0.935282i	$0.384854\pi$
$972$	4289.57	0.141552
$973$	−32844.5	−1.08216
$974$	48736.7	1.60331
$975$	−1702.12	−0.0559090
$976$	−64430.9	−2.11310
$977$	1038.84	0.0340177	0.0170088	−	0.999855i	$-0.494586\pi$
$977$	1038.84	0.0340177	0.0170088	+	0.999855i	$0.494586\pi$
$978$	53467.8	1.74817
$979$	0	0
$980$	−36158.5	−1.17861
$981$	−5491.70	−0.178732
$982$	45551.1	1.48024
$983$	−44173.6	−1.43329	−0.716643	−	0.697440i	$-0.754322\pi$
$983$	−44173.6	−1.43329	−0.716643	+	0.697440i	$0.754322\pi$
$984$	34947.4	1.13220
$985$	13385.7	0.432998
$986$	−15892.2	−0.513297
$987$	−11307.8	−0.364671
$988$	−56939.8	−1.83350
$989$	−5336.17	−0.171567
$990$	0	0
$991$	−23940.9	−0.767414	−0.383707	−	0.923455i	$-0.625353\pi$
$991$	−23940.9	−0.767414	−0.383707	+	0.923455i	$0.625353\pi$
$992$	29162.1	0.933365
$993$	−28253.1	−0.902905
$994$	108684.	3.46804
$995$	−13899.5	−0.442858
$996$	−63809.2	−2.02999
$997$	−13557.9	−0.430674	−0.215337	−	0.976540i	$-0.569085\pi$
$997$	−13557.9	−0.430674	−0.215337	+	0.976540i	$0.569085\pi$
$998$	13288.6	0.421487
$999$	9917.01	0.314074

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1815.4.a.r.1.3		3
11.10	odd	2		165.4.a.e.1.1	✓	3
33.32	even	2		495.4.a.k.1.3		3
55.32	even	4		825.4.c.k.199.1		6
55.43	even	4		825.4.c.k.199.6		6
55.54	odd	2		825.4.a.r.1.3		3
165.164	even	2		2475.4.a.t.1.1		3

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
165.4.a.e.1.1	✓	3	11.10	odd	2
495.4.a.k.1.3		3	33.32	even	2
825.4.a.r.1.3		3	55.54	odd	2
825.4.c.k.199.1		6	55.32	even	4
825.4.c.k.199.6		6	55.43	even	4
1815.4.a.r.1.3		3	1.1	even	1	trivial
2475.4.a.t.1.1		3	165.164	even	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 1815 = 3 \cdot 5 \cdot 11^{2} \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	1815.a (trivial)

\(f(q)\)	\(=\)	\(q+5.06484 q^{2} +3.00000 q^{3} +17.6526 q^{4} -5.00000 q^{5} +15.1945 q^{6} -27.4348 q^{7} +48.8887 q^{8} +9.00000 q^{9} +O(q^{10})\)	\(q+5.06484 q^{2} +3.00000 q^{3} +17.6526 q^{4} -5.00000 q^{5} +15.1945 q^{6} -27.4348 q^{7} +48.8887 q^{8} +9.00000 q^{9} -25.3242 q^{10} +52.9577 q^{12} -22.6949 q^{13} -138.953 q^{14} -15.0000 q^{15} +106.392 q^{16} +41.1755 q^{17} +45.5835 q^{18} +142.128 q^{19} -88.2628 q^{20} -82.3044 q^{21} +176.166 q^{23} +146.666 q^{24} +25.0000 q^{25} -114.946 q^{26} +27.0000 q^{27} -484.295 q^{28} -76.2044 q^{29} -75.9725 q^{30} +197.373 q^{31} +147.751 q^{32} +208.547 q^{34} +137.174 q^{35} +158.873 q^{36} +367.297 q^{37} +719.856 q^{38} -68.0846 q^{39} -244.443 q^{40} +238.279 q^{41} -416.858 q^{42} -30.2905 q^{43} -45.0000 q^{45} +892.254 q^{46} +137.390 q^{47} +319.177 q^{48} +409.668 q^{49} +126.621 q^{50} +123.526 q^{51} -400.623 q^{52} +638.665 q^{53} +136.751 q^{54} -1341.25 q^{56} +426.385 q^{57} -385.963 q^{58} +103.146 q^{59} -264.788 q^{60} -605.596 q^{61} +999.662 q^{62} -246.913 q^{63} -102.804 q^{64} +113.474 q^{65} -704.925 q^{67} +726.852 q^{68} +528.499 q^{69} +694.764 q^{70} -782.162 q^{71} +439.998 q^{72} +243.132 q^{73} +1860.30 q^{74} +75.0000 q^{75} +2508.93 q^{76} -344.837 q^{78} +532.874 q^{79} -531.962 q^{80} +81.0000 q^{81} +1206.84 q^{82} -1204.91 q^{83} -1452.88 q^{84} -205.877 q^{85} -153.416 q^{86} -228.613 q^{87} +1058.49 q^{89} -227.918 q^{90} +622.629 q^{91} +3109.79 q^{92} +592.119 q^{93} +695.857 q^{94} -710.641 q^{95} +443.254 q^{96} -85.1964 q^{97} +2074.90 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 3 q + 2 q^{2} + 9 q^{3} + 30 q^{4} - 15 q^{5} + 6 q^{6} - 10 q^{7} - 18 q^{8} + 27 q^{9}+O(q^{10}) \) 3 * q + 2 * q^2 + 9 * q^3 + 30 * q^4 - 15 * q^5 + 6 * q^6 - 10 * q^7 - 18 * q^8 + 27 * q^9	\( 3 q + 2 q^{2} + 9 q^{3} + 30 q^{4} - 15 q^{5} + 6 q^{6} - 10 q^{7} - 18 q^{8} + 27 q^{9} - 10 q^{10} + 90 q^{12} - 114 q^{13} - 68 q^{14} - 45 q^{15} + 178 q^{16} + 104 q^{17} + 18 q^{18} + 58 q^{19} - 150 q^{20} - 30 q^{21} + 120 q^{23} - 54 q^{24} + 75 q^{25} - 120 q^{26} + 81 q^{27} - 676 q^{28} + 220 q^{29} - 30 q^{30} + 248 q^{31} + 258 q^{32} - 80 q^{34} + 50 q^{35} + 270 q^{36} + 838 q^{37} + 600 q^{38} - 342 q^{39} + 90 q^{40} - 156 q^{41} - 204 q^{42} - 122 q^{43} - 135 q^{45} + 1256 q^{46} + 504 q^{47} + 534 q^{48} + 279 q^{49} + 50 q^{50} + 312 q^{51} - 520 q^{52} + 282 q^{53} + 54 q^{54} - 1644 q^{56} + 174 q^{57} - 1644 q^{58} + 548 q^{59} - 450 q^{60} - 414 q^{61} + 2448 q^{62} - 90 q^{63} - 58 q^{64} + 570 q^{65} - 428 q^{67} + 1704 q^{68} + 360 q^{69} + 340 q^{70} - 912 q^{71} - 162 q^{72} - 618 q^{73} + 1612 q^{74} + 225 q^{75} + 2752 q^{76} - 360 q^{78} + 542 q^{79} - 890 q^{80} + 243 q^{81} + 3372 q^{82} - 2028 q^{84} - 520 q^{85} - 1548 q^{86} + 660 q^{87} + 790 q^{89} - 90 q^{90} - 772 q^{91} + 1912 q^{92} + 744 q^{93} + 424 q^{94} - 290 q^{95} + 774 q^{96} + 2074 q^{97} + 3978 q^{98}+O(q^{100}) \) 3 * q + 2 * q^2 + 9 * q^3 + 30 * q^4 - 15 * q^5 + 6 * q^6 - 10 * q^7 - 18 * q^8 + 27 * q^9 - 10 * q^10 + 90 * q^12 - 114 * q^13 - 68 * q^14 - 45 * q^15 + 178 * q^16 + 104 * q^17 + 18 * q^18 + 58 * q^19 - 150 * q^20 - 30 * q^21 + 120 * q^23 - 54 * q^24 + 75 * q^25 - 120 * q^26 + 81 * q^27 - 676 * q^28 + 220 * q^29 - 30 * q^30 + 248 * q^31 + 258 * q^32 - 80 * q^34 + 50 * q^35 + 270 * q^36 + 838 * q^37 + 600 * q^38 - 342 * q^39 + 90 * q^40 - 156 * q^41 - 204 * q^42 - 122 * q^43 - 135 * q^45 + 1256 * q^46 + 504 * q^47 + 534 * q^48 + 279 * q^49 + 50 * q^50 + 312 * q^51 - 520 * q^52 + 282 * q^53 + 54 * q^54 - 1644 * q^56 + 174 * q^57 - 1644 * q^58 + 548 * q^59 - 450 * q^60 - 414 * q^61 + 2448 * q^62 - 90 * q^63 - 58 * q^64 + 570 * q^65 - 428 * q^67 + 1704 * q^68 + 360 * q^69 + 340 * q^70 - 912 * q^71 - 162 * q^72 - 618 * q^73 + 1612 * q^74 + 225 * q^75 + 2752 * q^76 - 360 * q^78 + 542 * q^79 - 890 * q^80 + 243 * q^81 + 3372 * q^82 - 2028 * q^84 - 520 * q^85 - 1548 * q^86 + 660 * q^87 + 790 * q^89 - 90 * q^90 - 772 * q^91 + 1912 * q^92 + 744 * q^93 + 424 * q^94 - 290 * q^95 + 774 * q^96 + 2074 * q^97 + 3978 * q^98

Introduction

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