LMFDB - Embedded newform 1620.2.i.n.541.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1620,2,Mod(541,1620)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1620, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 4, 0]))

N = Newforms(chi, 2, names="a")

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

chi := DirichletCharacter("1620.541");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1620 = 2^{2} \cdot 3^{4} \cdot 5 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1620.i (of order $3$, degree $2$, not minimal)

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:	no
Analytic conductor:	$12.9357651274$
Analytic rank:	$0$
Dimension:	$4$
Relative dimension:	$2$ over $\Q(\zeta_{3})$
Coefficient field:	$\Q(\zeta_{12})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} - x^{2} + 1 $ x^4 - x^2 + 1
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 3 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			541.1
Root			$0.866025 - 0.500000i$ of defining polynomial
Character	$\chi$	$=$	1620.541
Dual form			1620.2.i.n.1081.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.500000 + 0.866025i) q^{5} +(-0.366025 + 0.633975i) q^{7} +O(q^{10})$	$q+(0.500000 + 0.866025i) q^{5} +(-0.366025 + 0.633975i) q^{7} +(0.866025 - 1.50000i) q^{11} +(0.732051 + 1.26795i) q^{13} -1.26795 q^{17} +2.46410 q^{19} +(1.73205 + 3.00000i) q^{23} +(-0.500000 + 0.866025i) q^{25} +(2.13397 - 3.69615i) q^{29} +(3.96410 + 6.86603i) q^{31} -0.732051 q^{35} +4.19615 q^{37} +(0.401924 + 0.696152i) q^{41} +(-3.36603 + 5.83013i) q^{43} +(2.36603 - 4.09808i) q^{47} +(3.23205 + 5.59808i) q^{49} -10.7321 q^{53} +1.73205 q^{55} +(2.13397 + 3.69615i) q^{59} +(2.00000 - 3.46410i) q^{61} +(-0.732051 + 1.26795i) q^{65} +(7.19615 + 12.4641i) q^{67} -0.803848 q^{71} +10.1962 q^{73} +(0.633975 + 1.09808i) q^{77} +(-3.19615 + 5.53590i) q^{79} +(-4.56218 + 7.90192i) q^{83} +(-0.633975 - 1.09808i) q^{85} -5.19615 q^{89} -1.07180 q^{91} +(1.23205 + 2.13397i) q^{95} +(1.36603 - 2.36603i) q^{97} +O(q^{100})$
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q + 2 q^{5} + 2 q^{7}+O(q^{10}) $ 4 * q + 2 * q^5 + 2 * q^7	$ 4 q + 2 q^{5} + 2 q^{7} - 4 q^{13} - 12 q^{17} - 4 q^{19} - 2 q^{25} + 12 q^{29} + 2 q^{31} + 4 q^{35} - 4 q^{37} + 12 q^{41} - 10 q^{43} + 6 q^{47} + 6 q^{49} - 36 q^{53} + 12 q^{59} + 8 q^{61} + 4 q^{65} + 8 q^{67} - 24 q^{71} + 20 q^{73} + 6 q^{77} + 8 q^{79} + 6 q^{83} - 6 q^{85} - 32 q^{91} - 2 q^{95} + 2 q^{97}+O(q^{100}) $ 4 * q + 2 * q^5 + 2 * q^7 - 4 * q^13 - 12 * q^17 - 4 * q^19 - 2 * q^25 + 12 * q^29 + 2 * q^31 + 4 * q^35 - 4 * q^37 + 12 * q^41 - 10 * q^43 + 6 * q^47 + 6 * q^49 - 36 * q^53 + 12 * q^59 + 8 * q^61 + 4 * q^65 + 8 * q^67 - 24 * q^71 + 20 * q^73 + 6 * q^77 + 8 * q^79 + 6 * q^83 - 6 * q^85 - 32 * q^91 - 2 * q^95 + 2 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1620\mathbb{Z}\right)^\times$.

$n$	$811$	$1297$	$1541$
$\chi(n)$	$1$	$1$	$e\left(\frac{2}{3}\right)$

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 $

$2$		0			0
$2$		0			0
$3$		0			0
$3$		0			0
$4$		0			0
$5$	0.500000	+	0.866025i	0.223607	+	0.387298i
$5$	0.500000	+	0.866025i	0.223607	+	0.387298i
$6$		0			0
$7$	−0.366025	+	0.633975i	−0.138345	+	0.239620i	−0.926870	−	0.375382i	$-0.877511\pi$
$7$	−0.366025	+	0.633975i	−0.138345	+	0.239620i	0.788526	+	0.615002i	$0.210845\pi$
$8$		0			0
$9$		0			0
$10$		0			0
$11$	0.866025	−	1.50000i	0.261116	−	0.452267i	−0.705422	−	0.708787i	$-0.749243\pi$
$11$	0.866025	−	1.50000i	0.261116	−	0.452267i	0.966539	+	0.256520i	$0.0825760\pi$
$12$		0			0
$13$	0.732051	+	1.26795i	0.203034	+	0.351666i	0.949505	−	0.313753i	$-0.101586\pi$
$13$	0.732051	+	1.26795i	0.203034	+	0.351666i	−0.746470	+	0.665419i	$0.768253\pi$
$14$		0			0
$15$		0			0
$16$		0			0
$17$	−1.26795			−0.307523			−0.153761	−	0.988108i	$-0.549139\pi$
$17$	−1.26795			−0.307523			−0.153761	+	0.988108i	$0.549139\pi$
$18$		0			0
$19$	2.46410			0.565304			0.282652	−	0.959223i	$-0.408786\pi$
$19$	2.46410			0.565304			0.282652	+	0.959223i	$0.408786\pi$
$20$		0			0
$21$		0			0
$22$		0			0
$23$	1.73205	+	3.00000i	0.361158	+	0.625543i	0.988152	−	0.153481i	$-0.0490483\pi$
$23$	1.73205	+	3.00000i	0.361158	+	0.625543i	−0.626994	+	0.779024i	$0.715715\pi$
$24$		0			0
$25$	−0.500000	+	0.866025i	−0.100000	+	0.173205i
$26$		0			0
$27$		0			0
$28$		0			0
$29$	2.13397	−	3.69615i	0.396269	−	0.686358i	−0.596993	−	0.802246i	$-0.703638\pi$
$29$	2.13397	−	3.69615i	0.396269	−	0.686358i	0.993262	+	0.115888i	$0.0369714\pi$
$30$		0			0
$31$	3.96410	+	6.86603i	0.711974	+	1.23317i	0.964115	+	0.265484i	$0.0855318\pi$
$31$	3.96410	+	6.86603i	0.711974	+	1.23317i	−0.252142	+	0.967690i	$0.581135\pi$
$32$		0			0
$33$		0			0
$34$		0			0
$35$	−0.732051			−0.123739
$36$		0			0
$37$	4.19615			0.689843			0.344922	−	0.938631i	$-0.387905\pi$
$37$	4.19615			0.689843			0.344922	+	0.938631i	$0.387905\pi$
$38$		0			0
$39$		0			0
$40$		0			0
$41$	0.401924	+	0.696152i	0.0627700	+	0.108721i	0.895703	−	0.444654i	$-0.146673\pi$
$41$	0.401924	+	0.696152i	0.0627700	+	0.108721i	−0.832933	+	0.553374i	$0.813340\pi$
$42$		0			0
$43$	−3.36603	+	5.83013i	−0.513314	+	0.889086i	0.486567	+	0.873643i	$0.338249\pi$
$43$	−3.36603	+	5.83013i	−0.513314	+	0.889086i	−0.999881	+	0.0154426i	$0.995084\pi$
$44$		0			0
$45$		0			0
$46$		0			0
$47$	2.36603	−	4.09808i	0.345120	−	0.597766i	−0.640255	−	0.768162i	$-0.721171\pi$
$47$	2.36603	−	4.09808i	0.345120	−	0.597766i	0.985376	+	0.170396i	$0.0545048\pi$
$48$		0			0
$49$	3.23205	+	5.59808i	0.461722	+	0.799725i
$50$		0			0
$51$		0			0
$52$		0			0
$53$	−10.7321			−1.47416			−0.737080	−	0.675805i	$-0.763796\pi$
$53$	−10.7321			−1.47416			−0.737080	+	0.675805i	$0.763796\pi$
$54$		0			0
$55$	1.73205			0.233550
$56$		0			0
$57$		0			0
$58$		0			0
$59$	2.13397	+	3.69615i	0.277820	+	0.481198i	0.970843	−	0.239718i	$-0.0770548\pi$
$59$	2.13397	+	3.69615i	0.277820	+	0.481198i	−0.693023	+	0.720916i	$0.743722\pi$
$60$		0			0
$61$	2.00000	−	3.46410i	0.256074	−	0.443533i	−0.709113	−	0.705095i	$-0.750904\pi$
$61$	2.00000	−	3.46410i	0.256074	−	0.443533i	0.965187	+	0.261562i	$0.0842377\pi$
$62$		0			0
$63$		0			0
$64$		0			0
$65$	−0.732051	+	1.26795i	−0.0907997	+	0.157270i
$66$		0			0
$67$	7.19615	+	12.4641i	0.879150	+	1.52273i	0.852275	+	0.523094i	$0.175222\pi$
$67$	7.19615	+	12.4641i	0.879150	+	1.52273i	0.0268747	+	0.999639i	$0.491444\pi$
$68$		0			0
$69$		0			0
$70$		0			0
$71$	−0.803848			−0.0953992			−0.0476996	−	0.998862i	$-0.515189\pi$
$71$	−0.803848			−0.0953992			−0.0476996	+	0.998862i	$0.515189\pi$
$72$		0			0
$73$	10.1962			1.19337			0.596685	−	0.802476i	$-0.296484\pi$
$73$	10.1962			1.19337			0.596685	+	0.802476i	$0.296484\pi$
$74$		0			0
$75$		0			0
$76$		0			0
$77$	0.633975	+	1.09808i	0.0722481	+	0.125137i
$78$		0			0
$79$	−3.19615	+	5.53590i	−0.359595	+	0.622837i	−0.987893	−	0.155136i	$-0.950419\pi$
$79$	−3.19615	+	5.53590i	−0.359595	+	0.622837i	0.628298	+	0.777973i	$0.283752\pi$
$80$		0			0
$81$		0			0
$82$		0			0
$83$	−4.56218	+	7.90192i	−0.500764	+	0.867349i	0.499236	+	0.866466i	$0.333614\pi$
$83$	−4.56218	+	7.90192i	−0.500764	+	0.867349i	−1.00000		0.000882500i	$0.999719\pi$
$84$		0			0
$85$	−0.633975	−	1.09808i	−0.0687642	−	0.119103i
$86$		0			0
$87$		0			0
$88$		0			0
$89$	−5.19615			−0.550791			−0.275396	−	0.961331i	$-0.588809\pi$
$89$	−5.19615			−0.550791			−0.275396	+	0.961331i	$0.588809\pi$
$90$		0			0
$91$	−1.07180			−0.112355
$92$		0			0
$93$		0			0
$94$		0			0
$95$	1.23205	+	2.13397i	0.126406	+	0.218941i
$96$		0			0
$97$	1.36603	−	2.36603i	0.138699	−	0.240233i	−0.788305	−	0.615284i	$-0.789041\pi$
$97$	1.36603	−	2.36603i	0.138699	−	0.240233i	0.927004	+	0.375051i	$0.122375\pi$
$98$		0			0
$99$		0			0
$100$		0			0
$101$	9.06218	−	15.6962i	0.901720	−	1.56183i	0.0764604	−	0.997073i	$-0.475638\pi$
$101$	9.06218	−	15.6962i	0.901720	−	1.56183i	0.825260	−	0.564753i	$-0.191029\pi$
$102$		0			0
$103$	1.19615	+	2.07180i	0.117860	+	0.204140i	0.918920	−	0.394445i	$-0.129063\pi$
$103$	1.19615	+	2.07180i	0.117860	+	0.204140i	−0.801059	+	0.598585i	$0.795730\pi$
$104$		0			0
$105$		0			0
$106$		0			0
$107$	−3.46410			−0.334887			−0.167444	−	0.985882i	$-0.553551\pi$
$107$	−3.46410			−0.334887			−0.167444	+	0.985882i	$0.553551\pi$
$108$		0			0
$109$	5.92820			0.567819			0.283909	−	0.958851i	$-0.408368\pi$
$109$	5.92820			0.567819			0.283909	+	0.958851i	$0.408368\pi$
$110$		0			0
$111$		0			0
$112$		0			0
$113$	8.83013	+	15.2942i	0.830668	+	1.43876i	0.897509	+	0.440996i	$0.145375\pi$
$113$	8.83013	+	15.2942i	0.830668	+	1.43876i	−0.0668404	+	0.997764i	$0.521292\pi$
$114$		0			0
$115$	−1.73205	+	3.00000i	−0.161515	+	0.279751i
$116$		0			0
$117$		0			0
$118$		0			0
$119$	0.464102	−	0.803848i	0.0425441	−	0.0736886i
$120$		0			0
$121$	4.00000	+	6.92820i	0.363636	+	0.629837i
$122$		0			0
$123$		0			0
$124$		0			0
$125$	−1.00000			−0.0894427
$126$		0			0
$127$	−6.19615			−0.549820			−0.274910	−	0.961470i	$-0.588648\pi$
$127$	−6.19615			−0.549820			−0.274910	+	0.961470i	$0.588648\pi$
$128$		0			0
$129$		0			0
$130$		0			0
$131$	−6.86603	−	11.8923i	−0.599887	−	1.03904i	−0.992837	−	0.119476i	$-0.961879\pi$
$131$	−6.86603	−	11.8923i	−0.599887	−	1.03904i	0.392950	−	0.919560i	$-0.371455\pi$
$132$		0			0
$133$	−0.901924	+	1.56218i	−0.0782067	+	0.135458i
$134$		0			0
$135$		0			0
$136$		0			0
$137$	8.19615	−	14.1962i	0.700245	−	1.21286i	−0.268136	−	0.963381i	$-0.586408\pi$
$137$	8.19615	−	14.1962i	0.700245	−	1.21286i	0.968380	−	0.249478i	$-0.0802590\pi$
$138$		0			0
$139$	2.69615	+	4.66987i	0.228685	+	0.396093i	0.957419	−	0.288704i	$-0.0932242\pi$
$139$	2.69615	+	4.66987i	0.228685	+	0.396093i	−0.728734	+	0.684797i	$0.759891\pi$
$140$		0			0
$141$		0			0
$142$		0			0
$143$	2.53590			0.212062
$144$		0			0
$145$	4.26795			0.354434
$146$		0			0
$147$		0			0
$148$		0			0
$149$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$149$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$150$		0			0
$151$	−1.69615	+	2.93782i	−0.138031	+	0.239077i	−0.926751	−	0.375676i	$-0.877411\pi$
$151$	−1.69615	+	2.93782i	−0.138031	+	0.239077i	0.788720	+	0.614752i	$0.210744\pi$
$152$		0			0
$153$		0			0
$154$		0			0
$155$	−3.96410	+	6.86603i	−0.318404	+	0.551492i
$156$		0			0
$157$	−3.36603	−	5.83013i	−0.268638	−	0.465295i	0.699872	−	0.714268i	$-0.253240\pi$
$157$	−3.36603	−	5.83013i	−0.268638	−	0.465295i	−0.968510	+	0.248973i	$0.919907\pi$
$158$		0			0
$159$		0			0
$160$		0			0
$161$	−2.53590			−0.199857
$162$		0			0
$163$	15.2679			1.19588			0.597939	−	0.801542i	$-0.295986\pi$
$163$	15.2679			1.19588			0.597939	+	0.801542i	$0.295986\pi$
$164$		0			0
$165$		0			0
$166$		0			0
$167$	−1.56218	−	2.70577i	−0.120885	−	0.209379i	0.799232	−	0.601023i	$-0.205240\pi$
$167$	−1.56218	−	2.70577i	−0.120885	−	0.209379i	−0.920117	+	0.391644i	$0.871907\pi$
$168$		0			0
$169$	5.42820	−	9.40192i	0.417554	−	0.723225i
$170$		0			0
$171$		0			0
$172$		0			0
$173$	−12.1244	+	21.0000i	−0.921798	+	1.59660i	−0.125166	+	0.992136i	$0.539946\pi$
$173$	−12.1244	+	21.0000i	−0.921798	+	1.59660i	−0.796632	+	0.604465i	$0.793387\pi$
$174$		0			0
$175$	−0.366025	−	0.633975i	−0.0276689	−	0.0479240i
$176$		0			0
$177$		0			0
$178$		0			0
$179$	12.1244			0.906217			0.453108	−	0.891455i	$-0.350315\pi$
$179$	12.1244			0.906217			0.453108	+	0.891455i	$0.350315\pi$
$180$		0			0
$181$	−9.53590			−0.708798			−0.354399	−	0.935094i	$-0.615314\pi$
$181$	−9.53590			−0.708798			−0.354399	+	0.935094i	$0.615314\pi$
$182$		0			0
$183$		0			0
$184$		0			0
$185$	2.09808	+	3.63397i	0.154254	+	0.267175i
$186$		0			0
$187$	−1.09808	+	1.90192i	−0.0802993	+	0.139082i
$188$		0			0
$189$		0			0
$190$		0			0
$191$	9.52628	−	16.5000i	0.689297	−	1.19390i	−0.282768	−	0.959188i	$-0.591253\pi$
$191$	9.52628	−	16.5000i	0.689297	−	1.19390i	0.972065	−	0.234710i	$-0.0754140\pi$
$192$		0			0
$193$	−10.2942	−	17.8301i	−0.740995	−	1.28344i	−0.952043	−	0.305965i	$-0.901021\pi$
$193$	−10.2942	−	17.8301i	−0.740995	−	1.28344i	0.211048	−	0.977476i	$-0.432312\pi$
$194$		0			0
$195$		0			0
$196$		0			0
$197$	13.8564			0.987228			0.493614	−	0.869681i	$-0.335676\pi$
$197$	13.8564			0.987228			0.493614	+	0.869681i	$0.335676\pi$
$198$		0			0
$199$	−11.8564			−0.840478			−0.420239	−	0.907413i	$-0.638054\pi$
$199$	−11.8564			−0.840478			−0.420239	+	0.907413i	$0.638054\pi$
$200$		0			0
$201$		0			0
$202$		0			0
$203$	1.56218	+	2.70577i	0.109643	+	0.189908i
$204$		0			0
$205$	−0.401924	+	0.696152i	−0.0280716	+	0.0486214i
$206$		0			0
$207$		0			0
$208$		0			0
$209$	2.13397	−	3.69615i	0.147610	−	0.255668i
$210$		0			0
$211$	3.03590	+	5.25833i	0.209000	+	0.361998i	0.951400	−	0.307959i	$-0.0996458\pi$
$211$	3.03590	+	5.25833i	0.209000	+	0.361998i	−0.742400	+	0.669957i	$0.766313\pi$
$212$		0			0
$213$		0			0
$214$		0			0
$215$	−6.73205			−0.459122
$216$		0			0
$217$	−5.80385			−0.393991
$218$		0			0
$219$		0			0
$220$		0			0
$221$	−0.928203	−	1.60770i	−0.0624377	−	0.108145i
$222$		0			0
$223$	−10.9282	+	18.9282i	−0.731807	+	1.26753i	0.224304	+	0.974519i	$0.427989\pi$
$223$	−10.9282	+	18.9282i	−0.731807	+	1.26753i	−0.956110	+	0.293007i	$0.905344\pi$
$224$		0			0
$225$		0			0
$226$		0			0
$227$	−7.90192	+	13.6865i	−0.524469	+	0.908407i	0.475125	+	0.879918i	$0.342403\pi$
$227$	−7.90192	+	13.6865i	−0.524469	+	0.908407i	−0.999594	+	0.0284888i	$0.990930\pi$
$228$		0			0
$229$	−4.92820	−	8.53590i	−0.325665	−	0.564068i	0.655982	−	0.754777i	$-0.272255\pi$
$229$	−4.92820	−	8.53590i	−0.325665	−	0.564068i	−0.981647	+	0.190709i	$0.938921\pi$
$230$		0			0
$231$		0			0
$232$		0			0
$233$	−6.58846			−0.431624			−0.215812	−	0.976435i	$-0.569240\pi$
$233$	−6.58846			−0.431624			−0.215812	+	0.976435i	$0.569240\pi$
$234$		0			0
$235$	4.73205			0.308685
$236$		0			0
$237$		0			0
$238$		0			0
$239$	−7.73205	−	13.3923i	−0.500145	−	0.866276i	−1.00000		0.000167197i	$-0.999947\pi$
$239$	−7.73205	−	13.3923i	−0.500145	−	0.866276i	0.499855	−	0.866109i	$-0.333387\pi$
$240$		0			0
$241$	12.1603	−	21.0622i	0.783311	−	1.35673i	−0.146692	−	0.989182i	$-0.546863\pi$
$241$	12.1603	−	21.0622i	0.783311	−	1.35673i	0.930003	−	0.367552i	$-0.119804\pi$
$242$		0			0
$243$		0			0
$244$		0			0
$245$	−3.23205	+	5.59808i	−0.206488	+	0.357648i
$246$		0			0
$247$	1.80385	+	3.12436i	0.114776	+	0.198798i
$248$		0			0
$249$		0			0
$250$		0			0
$251$	27.4641			1.73352			0.866759	−	0.498727i	$-0.166199\pi$
$251$	27.4641			1.73352			0.866759	+	0.498727i	$0.166199\pi$
$252$		0			0
$253$	6.00000			0.377217
$254$		0			0
$255$		0			0
$256$		0			0
$257$	−4.26795	−	7.39230i	−0.266227	−	0.461119i	0.701657	−	0.712515i	$-0.252444\pi$
$257$	−4.26795	−	7.39230i	−0.266227	−	0.461119i	−0.967884	+	0.251395i	$0.919111\pi$
$258$		0			0
$259$	−1.53590	+	2.66025i	−0.0954361	+	0.165300i
$260$		0			0
$261$		0			0
$262$		0			0
$263$	−12.1244	+	21.0000i	−0.747620	+	1.29492i	0.201341	+	0.979521i	$0.435470\pi$
$263$	−12.1244	+	21.0000i	−0.747620	+	1.29492i	−0.948961	+	0.315394i	$0.897863\pi$
$264$		0			0
$265$	−5.36603	−	9.29423i	−0.329632	−	0.570940i
$266$		0			0
$267$		0			0
$268$		0			0
$269$	−19.7321			−1.20308			−0.601542	−	0.798841i	$-0.705447\pi$
$269$	−19.7321			−1.20308			−0.601542	+	0.798841i	$0.705447\pi$
$270$		0			0
$271$	−24.7846			−1.50556			−0.752779	−	0.658273i	$-0.771287\pi$
$271$	−24.7846			−1.50556			−0.752779	+	0.658273i	$0.771287\pi$
$272$		0			0
$273$		0			0
$274$		0			0
$275$	0.866025	+	1.50000i	0.0522233	+	0.0904534i
$276$		0			0
$277$	9.56218	−	16.5622i	0.574536	−	0.995125i	−0.421556	−	0.906802i	$-0.638516\pi$
$277$	9.56218	−	16.5622i	0.574536	−	0.995125i	0.996092	−	0.0883226i	$-0.0281506\pi$
$278$		0			0
$279$		0			0
$280$		0			0
$281$	2.66025	−	4.60770i	0.158697	−	0.274872i	−0.775702	−	0.631100i	$-0.782604\pi$
$281$	2.66025	−	4.60770i	0.158697	−	0.274872i	0.934399	+	0.356228i	$0.115937\pi$
$282$		0			0
$283$	−11.7321	−	20.3205i	−0.697398	−	1.20793i	−0.969366	−	0.245622i	$-0.921008\pi$
$283$	−11.7321	−	20.3205i	−0.697398	−	1.20793i	0.271968	−	0.962306i	$-0.412326\pi$
$284$		0			0
$285$		0			0
$286$		0			0
$287$	−0.588457			−0.0347355
$288$		0			0
$289$	−15.3923			−0.905430
$290$		0			0
$291$		0			0
$292$		0			0
$293$	3.29423	+	5.70577i	0.192451	+	0.333335i	0.946062	−	0.323986i	$-0.105023\pi$
$293$	3.29423	+	5.70577i	0.192451	+	0.333335i	−0.753611	+	0.657321i	$0.771690\pi$
$294$		0			0
$295$	−2.13397	+	3.69615i	−0.124245	+	0.215198i
$296$		0			0
$297$		0			0
$298$		0			0
$299$	−2.53590	+	4.39230i	−0.146655	+	0.254014i
$300$		0			0
$301$	−2.46410	−	4.26795i	−0.142028	−	0.246001i
$302$		0			0
$303$		0			0
$304$		0			0
$305$	4.00000			0.229039
$306$		0			0
$307$	−12.1962			−0.696071			−0.348036	−	0.937481i	$-0.613151\pi$
$307$	−12.1962			−0.696071			−0.348036	+	0.937481i	$0.613151\pi$
$308$		0			0
$309$		0			0
$310$		0			0
$311$	−14.2583	−	24.6962i	−0.808516	−	1.40039i	−0.913892	−	0.405958i	$-0.866938\pi$
$311$	−14.2583	−	24.6962i	−0.808516	−	1.40039i	0.105376	−	0.994432i	$-0.466395\pi$
$312$		0			0
$313$	−0.535898	+	0.928203i	−0.0302908	+	0.0524651i	−0.880773	−	0.473538i	$-0.842977\pi$
$313$	−0.535898	+	0.928203i	−0.0302908	+	0.0524651i	0.850483	+	0.526003i	$0.176310\pi$
$314$		0			0
$315$		0			0
$316$		0			0
$317$	10.5622	−	18.2942i	0.593231	−	1.02751i	−0.400563	−	0.916269i	$-0.631185\pi$
$317$	10.5622	−	18.2942i	0.593231	−	1.02751i	0.993794	−	0.111237i	$-0.0354813\pi$
$318$		0			0
$319$	−3.69615	−	6.40192i	−0.206945	−	0.358439i
$320$		0			0
$321$		0			0
$322$		0			0
$323$	−3.12436			−0.173844
$324$		0			0
$325$	−1.46410			−0.0812137
$326$		0			0
$327$		0			0
$328$		0			0
$329$	1.73205	+	3.00000i	0.0954911	+	0.165395i
$330$		0			0
$331$	4.30385	−	7.45448i	0.236561	−	0.409735i	−0.723164	−	0.690676i	$-0.757313\pi$
$331$	4.30385	−	7.45448i	0.236561	−	0.409735i	0.959725	+	0.280941i	$0.0906464\pi$
$332$		0			0
$333$		0			0
$334$		0			0
$335$	−7.19615	+	12.4641i	−0.393168	+	0.680987i
$336$		0			0
$337$	−7.12436	−	12.3397i	−0.388088	−	0.672189i	0.604104	−	0.796905i	$-0.293531\pi$
$337$	−7.12436	−	12.3397i	−0.388088	−	0.672189i	−0.992192	+	0.124717i	$0.960198\pi$
$338$		0			0
$339$		0			0
$340$		0			0
$341$	13.7321			0.743632
$342$		0			0
$343$	−9.85641			−0.532196
$344$		0			0
$345$		0			0
$346$		0			0
$347$	−16.0981	−	27.8827i	−0.864190	−	1.49682i	−0.867849	−	0.496828i	$-0.834498\pi$
$347$	−16.0981	−	27.8827i	−0.864190	−	1.49682i	0.00365919	−	0.999993i	$-0.498835\pi$
$348$		0			0
$349$	12.5000	−	21.6506i	0.669110	−	1.15893i	−0.309044	−	0.951048i	$-0.600009\pi$
$349$	12.5000	−	21.6506i	0.669110	−	1.15893i	0.978153	−	0.207884i	$-0.0666577\pi$
$350$		0			0
$351$		0			0
$352$		0			0
$353$	−11.4904	+	19.9019i	−0.611571	+	1.05927i	0.379404	+	0.925231i	$0.376129\pi$
$353$	−11.4904	+	19.9019i	−0.611571	+	1.05927i	−0.990976	+	0.134042i	$0.957204\pi$
$354$		0			0
$355$	−0.401924	−	0.696152i	−0.0213319	−	0.0369479i
$356$		0			0
$357$		0			0
$358$		0			0
$359$	26.6603			1.40707			0.703537	−	0.710658i	$-0.251603\pi$
$359$	26.6603			1.40707			0.703537	+	0.710658i	$0.251603\pi$
$360$		0			0
$361$	−12.9282			−0.680432
$362$		0			0
$363$		0			0
$364$		0			0
$365$	5.09808	+	8.83013i	0.266846	+	0.462190i
$366$		0			0
$367$	2.80385	−	4.85641i	0.146360	−	0.253502i	−0.783520	−	0.621367i	$-0.786578\pi$
$367$	2.80385	−	4.85641i	0.146360	−	0.253502i	0.929879	+	0.367865i	$0.119911\pi$
$368$		0			0
$369$		0			0
$370$		0			0
$371$	3.92820	−	6.80385i	0.203942	−	0.353238i
$372$		0			0
$373$	−12.0263	−	20.8301i	−0.622697	−	1.07854i	−0.988981	−	0.148040i	$-0.952704\pi$
$373$	−12.0263	−	20.8301i	−0.622697	−	1.07854i	0.366284	−	0.930503i	$-0.380630\pi$
$374$		0			0
$375$		0			0
$376$		0			0
$377$	6.24871			0.321825
$378$		0			0
$379$	11.4641			0.588871			0.294436	−	0.955671i	$-0.404868\pi$
$379$	11.4641			0.588871			0.294436	+	0.955671i	$0.404868\pi$
$380$		0			0
$381$		0			0
$382$		0			0
$383$	15.1244	+	26.1962i	0.772818	+	1.33856i	0.936012	+	0.351967i	$0.114487\pi$
$383$	15.1244	+	26.1962i	0.772818	+	1.33856i	−0.163194	+	0.986594i	$0.552180\pi$
$384$		0			0
$385$	−0.633975	+	1.09808i	−0.0323103	+	0.0559631i
$386$		0			0
$387$		0			0
$388$		0			0
$389$	−10.2679	+	17.7846i	−0.520606	+	0.901716i	0.479107	+	0.877756i	$0.340960\pi$
$389$	−10.2679	+	17.7846i	−0.520606	+	0.901716i	−0.999713	+	0.0239591i	$0.992373\pi$
$390$		0			0
$391$	−2.19615	−	3.80385i	−0.111064	−	0.192369i
$392$		0			0
$393$		0			0
$394$		0			0
$395$	−6.39230			−0.321632
$396$		0			0
$397$	2.67949			0.134480			0.0672399	−	0.997737i	$-0.478581\pi$
$397$	2.67949			0.134480			0.0672399	+	0.997737i	$0.478581\pi$
$398$		0			0
$399$		0			0
$400$		0			0
$401$	−13.3923	−	23.1962i	−0.668780	−	1.15836i	−0.978246	−	0.207450i	$-0.933484\pi$
$401$	−13.3923	−	23.1962i	−0.668780	−	1.15836i	0.309466	−	0.950911i	$-0.399850\pi$
$402$		0			0
$403$	−5.80385	+	10.0526i	−0.289110	+	0.500754i
$404$		0			0
$405$		0			0
$406$		0			0
$407$	3.63397	−	6.29423i	0.180129	−	0.311993i
$408$		0			0
$409$	−4.92820	−	8.53590i	−0.243684	−	0.422073i	0.718077	−	0.695964i	$-0.245023\pi$
$409$	−4.92820	−	8.53590i	−0.243684	−	0.422073i	−0.961761	+	0.273891i	$0.911689\pi$
$410$		0			0
$411$		0			0
$412$		0			0
$413$	−3.12436			−0.153739
$414$		0			0
$415$	−9.12436			−0.447897
$416$		0			0
$417$		0			0
$418$		0			0
$419$	−7.26795	−	12.5885i	−0.355063	−	0.614986i	0.632066	−	0.774914i	$-0.282207\pi$
$419$	−7.26795	−	12.5885i	−0.355063	−	0.614986i	−0.987129	+	0.159928i	$0.948874\pi$
$420$		0			0
$421$	13.8923	−	24.0622i	0.677070	−	1.17272i	−0.298790	−	0.954319i	$-0.596583\pi$
$421$	13.8923	−	24.0622i	0.677070	−	1.17272i	0.975859	−	0.218400i	$-0.0700837\pi$
$422$		0			0
$423$		0			0
$424$		0			0
$425$	0.633975	−	1.09808i	0.0307523	−	0.0532645i
$426$		0			0
$427$	1.46410	+	2.53590i	0.0708528	+	0.122721i
$428$		0			0
$429$		0			0
$430$		0			0
$431$	−2.41154			−0.116160			−0.0580800	−	0.998312i	$-0.518498\pi$
$431$	−2.41154			−0.116160			−0.0580800	+	0.998312i	$0.518498\pi$
$432$		0			0
$433$	4.53590			0.217981			0.108991	−	0.994043i	$-0.465238\pi$
$433$	4.53590			0.217981			0.108991	+	0.994043i	$0.465238\pi$
$434$		0			0
$435$		0			0
$436$		0			0
$437$	4.26795	+	7.39230i	0.204164	+	0.353622i
$438$		0			0
$439$	−13.6962	+	23.7224i	−0.653682	+	1.13221i	0.328541	+	0.944490i	$0.393443\pi$
$439$	−13.6962	+	23.7224i	−0.653682	+	1.13221i	−0.982223	+	0.187720i	$0.939890\pi$
$440$		0			0
$441$		0			0
$442$		0			0
$443$	−20.3660	+	35.2750i	−0.967619	+	1.67597i	−0.265212	+	0.964190i	$0.585442\pi$
$443$	−20.3660	+	35.2750i	−0.967619	+	1.67597i	−0.702407	+	0.711775i	$0.747891\pi$
$444$		0			0
$445$	−2.59808	−	4.50000i	−0.123161	−	0.213320i
$446$		0			0
$447$		0			0
$448$		0			0
$449$	−0.124356			−0.00586871			−0.00293435	−	0.999996i	$-0.500934\pi$
$449$	−0.124356			−0.00586871			−0.00293435	+	0.999996i	$0.500934\pi$
$450$		0			0
$451$	1.39230			0.0655611
$452$		0			0
$453$		0			0
$454$		0			0
$455$	−0.535898	−	0.928203i	−0.0251233	−	0.0435148i
$456$		0			0
$457$	−5.90192	+	10.2224i	−0.276080	+	0.478185i	−0.970407	−	0.241475i	$-0.922369\pi$
$457$	−5.90192	+	10.2224i	−0.276080	+	0.478185i	0.694327	+	0.719660i	$0.255702\pi$
$458$		0			0
$459$		0			0
$460$		0			0
$461$	10.7942	−	18.6962i	0.502737	−	0.870767i	−0.497258	−	0.867603i	$-0.665660\pi$
$461$	10.7942	−	18.6962i	0.502737	−	0.870767i	0.999995	−	0.00316371i	$-0.00100704\pi$
$462$		0			0
$463$	−9.19615	−	15.9282i	−0.427381	−	0.740246i	0.569258	−	0.822159i	$-0.307231\pi$
$463$	−9.19615	−	15.9282i	−0.427381	−	0.740246i	−0.996640	+	0.0819125i	$0.973897\pi$
$464$		0			0
$465$		0			0
$466$		0			0
$467$	15.8038			0.731315			0.365657	−	0.930750i	$-0.380844\pi$
$467$	15.8038			0.731315			0.365657	+	0.930750i	$0.380844\pi$
$468$		0			0
$469$	−10.5359			−0.486503
$470$		0			0
$471$		0			0
$472$		0			0
$473$	5.83013	+	10.0981i	0.268070	+	0.464310i
$474$		0			0
$475$	−1.23205	+	2.13397i	−0.0565304	+	0.0979135i
$476$		0			0
$477$		0			0
$478$		0			0
$479$	10.3301	−	17.8923i	0.471996	−	0.817520i	−0.527491	−	0.849561i	$-0.676867\pi$
$479$	10.3301	−	17.8923i	0.471996	−	0.817520i	0.999487	+	0.0320403i	$0.0102005\pi$
$480$		0			0
$481$	3.07180	+	5.32051i	0.140062	+	0.242594i
$482$		0			0
$483$		0			0
$484$		0			0
$485$	2.73205			0.124056
$486$		0			0
$487$	−37.4641			−1.69766			−0.848830	−	0.528666i	$-0.822693\pi$
$487$	−37.4641			−1.69766			−0.848830	+	0.528666i	$0.822693\pi$
$488$		0			0
$489$		0			0
$490$		0			0
$491$	3.86603	+	6.69615i	0.174471	+	0.302193i	0.939978	−	0.341235i	$-0.110845\pi$
$491$	3.86603	+	6.69615i	0.174471	+	0.302193i	−0.765507	+	0.643428i	$0.777512\pi$
$492$		0			0
$493$	−2.70577	+	4.68653i	−0.121862	+	0.211071i
$494$		0			0
$495$		0			0
$496$		0			0
$497$	0.294229	−	0.509619i	0.0131980	−	0.0228595i
$498$		0			0
$499$	−3.30385	−	5.72243i	−0.147901	−	0.256171i	0.782551	−	0.622587i	$-0.213918\pi$
$499$	−3.30385	−	5.72243i	−0.147901	−	0.256171i	−0.930451	+	0.366416i	$0.880585\pi$
$500$		0			0
$501$		0			0
$502$		0			0
$503$	−0.679492			−0.0302970			−0.0151485	−	0.999885i	$-0.504822\pi$
$503$	−0.679492			−0.0302970			−0.0151485	+	0.999885i	$0.504822\pi$
$504$		0			0
$505$	18.1244			0.806523
$506$		0			0
$507$		0			0
$508$		0			0
$509$	−7.39230	−	12.8038i	−0.327658	−	0.567521i	0.654389	−	0.756158i	$-0.272926\pi$
$509$	−7.39230	−	12.8038i	−0.327658	−	0.567521i	−0.982047	+	0.188638i	$0.939593\pi$
$510$		0			0
$511$	−3.73205	+	6.46410i	−0.165096	+	0.285955i
$512$		0			0
$513$		0			0
$514$		0			0
$515$	−1.19615	+	2.07180i	−0.0527088	+	0.0912943i
$516$		0			0
$517$	−4.09808	−	7.09808i	−0.180233	−	0.312173i
$518$		0			0
$519$		0			0
$520$		0			0
$521$	10.3923			0.455295			0.227648	−	0.973744i	$-0.426897\pi$
$521$	10.3923			0.455295			0.227648	+	0.973744i	$0.426897\pi$
$522$		0			0
$523$	24.3923			1.06660			0.533301	−	0.845926i	$-0.320952\pi$
$523$	24.3923			1.06660			0.533301	+	0.845926i	$0.320952\pi$
$524$		0			0
$525$		0			0
$526$		0			0
$527$	−5.02628	−	8.70577i	−0.218948	−	0.379229i
$528$		0			0
$529$	5.50000	−	9.52628i	0.239130	−	0.414186i
$530$		0			0
$531$		0			0
$532$		0			0
$533$	−0.588457	+	1.01924i	−0.0254889	+	0.0441481i
$534$		0			0
$535$	−1.73205	−	3.00000i	−0.0748831	−	0.129701i
$536$		0			0
$537$		0			0
$538$		0			0
$539$	11.1962			0.482252
$540$		0			0
$541$	−4.46410			−0.191927			−0.0959634	−	0.995385i	$-0.530593\pi$
$541$	−4.46410			−0.191927			−0.0959634	+	0.995385i	$0.530593\pi$
$542$		0			0
$543$		0			0
$544$		0			0
$545$	2.96410	+	5.13397i	0.126968	+	0.219915i
$546$		0			0
$547$	18.3923	−	31.8564i	0.786398	−	1.36208i	−0.141762	−	0.989901i	$-0.545277\pi$
$547$	18.3923	−	31.8564i	0.786398	−	1.36208i	0.928160	−	0.372181i	$-0.121390\pi$
$548$		0			0
$549$		0			0
$550$		0			0
$551$	5.25833	−	9.10770i	0.224012	−	0.388001i
$552$		0			0
$553$	−2.33975	−	4.05256i	−0.0994961	−	0.172332i
$554$		0			0
$555$		0			0
$556$		0			0
$557$	16.3923			0.694564			0.347282	−	0.937761i	$-0.387105\pi$
$557$	16.3923			0.694564			0.347282	+	0.937761i	$0.387105\pi$
$558$		0			0
$559$	−9.85641			−0.416882
$560$		0			0
$561$		0			0
$562$		0			0
$563$	−9.63397	−	16.6865i	−0.406024	−	0.703254i	0.588416	−	0.808558i	$-0.299752\pi$
$563$	−9.63397	−	16.6865i	−0.406024	−	0.703254i	−0.994440	+	0.105305i	$0.966418\pi$
$564$		0			0
$565$	−8.83013	+	15.2942i	−0.371486	+	0.643433i
$566$		0			0
$567$		0			0
$568$		0			0
$569$	2.47372	−	4.28461i	0.103704	−	0.179620i	−0.809504	−	0.587114i	$-0.800264\pi$
$569$	2.47372	−	4.28461i	0.103704	−	0.179620i	0.913208	+	0.407494i	$0.133597\pi$
$570$		0			0
$571$	13.4282	+	23.2583i	0.561953	+	0.973331i	0.997326	+	0.0730808i	$0.0232831\pi$
$571$	13.4282	+	23.2583i	0.561953	+	0.973331i	−0.435373	+	0.900250i	$0.643384\pi$
$572$		0			0
$573$		0			0
$574$		0			0
$575$	−3.46410			−0.144463
$576$		0			0
$577$	22.1962			0.924038			0.462019	−	0.886870i	$-0.347125\pi$
$577$	22.1962			0.924038			0.462019	+	0.886870i	$0.347125\pi$
$578$		0			0
$579$		0			0
$580$		0			0
$581$	−3.33975	−	5.78461i	−0.138556	−	0.239986i
$582$		0			0
$583$	−9.29423	+	16.0981i	−0.384928	+	0.666714i
$584$		0			0
$585$		0			0
$586$		0			0
$587$	−7.09808	+	12.2942i	−0.292969	+	0.507437i	−0.974510	−	0.224342i	$-0.927977\pi$
$587$	−7.09808	+	12.2942i	−0.292969	+	0.507437i	0.681541	+	0.731780i	$0.261310\pi$
$588$		0			0
$589$	9.76795	+	16.9186i	0.402481	+	0.697118i
$590$		0			0
$591$		0			0
$592$		0			0
$593$	−36.9282			−1.51646			−0.758230	−	0.651987i	$-0.773935\pi$
$593$	−36.9282			−1.51646			−0.758230	+	0.651987i	$0.773935\pi$
$594$		0			0
$595$	0.928203			0.0380526
$596$		0			0
$597$		0			0
$598$		0			0
$599$	22.7942	+	39.4808i	0.931347	+	1.61314i	0.781022	+	0.624504i	$0.214699\pi$
$599$	22.7942	+	39.4808i	0.931347	+	1.61314i	0.150325	+	0.988637i	$0.451968\pi$
$600$		0			0
$601$	−5.16025	+	8.93782i	−0.210491	+	0.364581i	−0.951868	−	0.306507i	$-0.900840\pi$
$601$	−5.16025	+	8.93782i	−0.210491	+	0.364581i	0.741377	+	0.671089i	$0.234173\pi$
$602$		0			0
$603$		0			0
$604$		0			0
$605$	−4.00000	+	6.92820i	−0.162623	+	0.281672i
$606$		0			0
$607$	14.2942	+	24.7583i	0.580185	+	1.00491i	0.995457	+	0.0952124i	$0.0303530\pi$
$607$	14.2942	+	24.7583i	0.580185	+	1.00491i	−0.415272	+	0.909697i	$0.636314\pi$
$608$		0			0
$609$		0			0
$610$		0			0
$611$	6.92820			0.280285
$612$		0			0
$613$	3.60770			0.145713			0.0728567	−	0.997342i	$-0.476788\pi$
$613$	3.60770			0.145713			0.0728567	+	0.997342i	$0.476788\pi$
$614$		0			0
$615$		0			0
$616$		0			0
$617$	6.00000	+	10.3923i	0.241551	+	0.418378i	0.961156	−	0.276005i	$-0.0890106\pi$
$617$	6.00000	+	10.3923i	0.241551	+	0.418378i	−0.719605	+	0.694383i	$0.755677\pi$
$618$		0			0
$619$	5.00000	−	8.66025i	0.200967	−	0.348085i	−0.747873	−	0.663842i	$-0.768925\pi$
$619$	5.00000	−	8.66025i	0.200967	−	0.348085i	0.948840	+	0.315757i	$0.102258\pi$
$620$		0			0
$621$		0			0
$622$		0			0
$623$	1.90192	−	3.29423i	0.0761990	−	0.131980i
$624$		0			0
$625$	−0.500000	−	0.866025i	−0.0200000	−	0.0346410i
$626$		0			0
$627$		0			0
$628$		0			0
$629$	−5.32051			−0.212143
$630$		0			0
$631$	−13.9282			−0.554473			−0.277237	−	0.960802i	$-0.589419\pi$
$631$	−13.9282			−0.554473			−0.277237	+	0.960802i	$0.589419\pi$
$632$		0			0
$633$		0			0
$634$		0			0
$635$	−3.09808	−	5.36603i	−0.122943	−	0.212944i
$636$		0			0
$637$	−4.73205	+	8.19615i	−0.187491	+	0.324743i
$638$		0			0
$639$		0			0
$640$		0			0
$641$	11.5981	−	20.0885i	0.458096	−	0.793446i	−0.540764	−	0.841174i	$-0.681865\pi$
$641$	11.5981	−	20.0885i	0.458096	−	0.793446i	0.998860	+	0.0477281i	$0.0151981\pi$
$642$		0			0
$643$	8.29423	+	14.3660i	0.327092	+	0.566541i	0.981934	−	0.189226i	$-0.0605978\pi$
$643$	8.29423	+	14.3660i	0.327092	+	0.566541i	−0.654841	+	0.755767i	$0.727264\pi$
$644$		0			0
$645$		0			0
$646$		0			0
$647$	−48.2487			−1.89685			−0.948426	−	0.316998i	$-0.897325\pi$
$647$	−48.2487			−1.89685			−0.948426	+	0.316998i	$0.897325\pi$
$648$		0			0
$649$	7.39230			0.290173
$650$		0			0
$651$		0			0
$652$		0			0
$653$	4.73205	+	8.19615i	0.185179	+	0.320740i	0.943637	−	0.330982i	$-0.107380\pi$
$653$	4.73205	+	8.19615i	0.185179	+	0.320740i	−0.758458	+	0.651722i	$0.774047\pi$
$654$		0			0
$655$	6.86603	−	11.8923i	0.268278	−	0.464671i
$656$		0			0
$657$		0			0
$658$		0			0
$659$	4.73205	−	8.19615i	0.184335	−	0.319277i	−0.759018	−	0.651070i	$-0.774320\pi$
$659$	4.73205	−	8.19615i	0.184335	−	0.319277i	0.943352	+	0.331793i	$0.107654\pi$
$660$		0			0
$661$	2.69615	+	4.66987i	0.104868	+	0.181637i	0.913684	−	0.406425i	$-0.133225\pi$
$661$	2.69615	+	4.66987i	0.104868	+	0.181637i	−0.808816	+	0.588062i	$0.799891\pi$
$662$		0			0
$663$		0			0
$664$		0			0
$665$	−1.80385			−0.0699502
$666$		0			0
$667$	14.7846			0.572462
$668$		0			0
$669$		0			0
$670$		0			0
$671$	−3.46410	−	6.00000i	−0.133730	−	0.231627i
$672$		0			0
$673$	8.80385	−	15.2487i	0.339363	−	0.587795i	−0.644950	−	0.764225i	$-0.723122\pi$
$673$	8.80385	−	15.2487i	0.339363	−	0.587795i	0.984313	+	0.176430i	$0.0564550\pi$
$674$		0			0
$675$		0			0
$676$		0			0
$677$	14.3205	−	24.8038i	0.550382	−	0.953289i	−0.447865	−	0.894101i	$-0.647815\pi$
$677$	14.3205	−	24.8038i	0.550382	−	0.953289i	0.998247	−	0.0591881i	$-0.0188512\pi$
$678$		0			0
$679$	1.00000	+	1.73205i	0.0383765	+	0.0664700i
$680$		0			0
$681$		0			0
$682$		0			0
$683$	14.5359			0.556201			0.278100	−	0.960552i	$-0.410295\pi$
$683$	14.5359			0.556201			0.278100	+	0.960552i	$0.410295\pi$
$684$		0			0
$685$	16.3923			0.626318
$686$		0			0
$687$		0			0
$688$		0			0
$689$	−7.85641	−	13.6077i	−0.299305	−	0.518412i
$690$		0			0
$691$	5.00000	−	8.66025i	0.190209	−	0.329452i	−0.755110	−	0.655598i	$-0.772417\pi$
$691$	5.00000	−	8.66025i	0.190209	−	0.329452i	0.945319	+	0.326146i	$0.105750\pi$
$692$		0			0
$693$		0			0
$694$		0			0
$695$	−2.69615	+	4.66987i	−0.102271	+	0.177138i
$696$		0			0
$697$	−0.509619	−	0.882686i	−0.0193032	−	0.0334341i
$698$		0			0
$699$		0			0
$700$		0			0
$701$	−42.1244			−1.59101			−0.795507	−	0.605944i	$-0.792796\pi$
$701$	−42.1244			−1.59101			−0.795507	+	0.605944i	$0.792796\pi$
$702$		0			0
$703$	10.3397			0.389971
$704$		0			0
$705$		0			0
$706$		0			0
$707$	6.63397	+	11.4904i	0.249496	+	0.432140i
$708$		0			0
$709$	−8.73205	+	15.1244i	−0.327939	+	0.568007i	−0.982103	−	0.188346i	$-0.939687\pi$
$709$	−8.73205	+	15.1244i	−0.327939	+	0.568007i	0.654164	+	0.756353i	$0.273021\pi$
$710$		0			0
$711$		0			0
$712$		0			0
$713$	−13.7321	+	23.7846i	−0.514269	+	0.890741i
$714$		0			0
$715$	1.26795	+	2.19615i	0.0474186	+	0.0821314i
$716$		0			0
$717$		0			0
$718$		0			0
$719$	−6.80385			−0.253741			−0.126870	−	0.991919i	$-0.540493\pi$
$719$	−6.80385			−0.253741			−0.126870	+	0.991919i	$0.540493\pi$
$720$		0			0
$721$	−1.75129			−0.0652214
$722$		0			0
$723$		0			0
$724$		0			0
$725$	2.13397	+	3.69615i	0.0792538	+	0.137272i
$726$		0			0
$727$	−16.5885	+	28.7321i	−0.615232	+	1.06561i	0.375112	+	0.926980i	$0.377604\pi$
$727$	−16.5885	+	28.7321i	−0.615232	+	1.06561i	−0.990344	+	0.138633i	$0.955729\pi$
$728$		0			0
$729$		0			0
$730$		0			0
$731$	4.26795	−	7.39230i	0.157856	−	0.273414i
$732$		0			0
$733$	19.7846	+	34.2679i	0.730761	+	1.26572i	0.956558	+	0.291541i	$0.0941680\pi$
$733$	19.7846	+	34.2679i	0.730761	+	1.26572i	−0.225797	+	0.974174i	$0.572499\pi$
$734$		0			0
$735$		0			0
$736$		0			0
$737$	24.9282			0.918242
$738$		0			0
$739$	36.1769			1.33079			0.665395	−	0.746492i	$-0.268263\pi$
$739$	36.1769			1.33079			0.665395	+	0.746492i	$0.268263\pi$
$740$		0			0
$741$		0			0
$742$		0			0
$743$	18.2942	+	31.6865i	0.671150	+	1.16247i	0.977578	+	0.210572i	$0.0675328\pi$
$743$	18.2942	+	31.6865i	0.671150	+	1.16247i	−0.306428	+	0.951894i	$0.599134\pi$
$744$		0			0
$745$		0			0
$746$		0			0
$747$		0			0
$748$		0			0
$749$	1.26795	−	2.19615i	0.0463299	−	0.0802457i
$750$		0			0
$751$	0.392305	+	0.679492i	0.0143154	+	0.0247950i	0.873094	−	0.487551i	$-0.162110\pi$
$751$	0.392305	+	0.679492i	0.0143154	+	0.0247950i	−0.858779	+	0.512346i	$0.828776\pi$
$752$		0			0
$753$		0			0
$754$		0			0
$755$	−3.39230			−0.123459
$756$		0			0
$757$	0.392305			0.0142586			0.00712928	−	0.999975i	$-0.497731\pi$
$757$	0.392305			0.0142586			0.00712928	+	0.999975i	$0.497731\pi$
$758$		0			0
$759$		0			0
$760$		0			0
$761$	2.93782	+	5.08846i	0.106496	+	0.184456i	0.914348	−	0.404928i	$-0.132704\pi$
$761$	2.93782	+	5.08846i	0.106496	+	0.184456i	−0.807852	+	0.589385i	$0.799370\pi$
$762$		0			0
$763$	−2.16987	+	3.75833i	−0.0785547	+	0.136061i
$764$		0			0
$765$		0			0
$766$		0			0
$767$	−3.12436	+	5.41154i	−0.112814	+	0.195399i
$768$		0			0
$769$	6.62436	+	11.4737i	0.238880	+	0.413753i	0.960393	−	0.278648i	$-0.0898863\pi$
$769$	6.62436	+	11.4737i	0.238880	+	0.413753i	−0.721513	+	0.692401i	$0.756553\pi$
$770$		0			0
$771$		0			0
$772$		0			0
$773$	0.339746			0.0122198			0.00610991	−	0.999981i	$-0.498055\pi$
$773$	0.339746			0.0122198			0.00610991	+	0.999981i	$0.498055\pi$
$774$		0			0
$775$	−7.92820			−0.284789
$776$		0			0
$777$		0			0
$778$		0			0
$779$	0.990381	+	1.71539i	0.0354841	+	0.0614602i
$780$		0			0
$781$	−0.696152	+	1.20577i	−0.0249103	+	0.0431459i
$782$		0			0
$783$		0			0
$784$		0			0
$785$	3.36603	−	5.83013i	0.120139	−	0.208086i
$786$		0			0
$787$	12.9019	+	22.3468i	0.459904	+	0.796577i	0.998955	−	0.0456959i	$-0.0145505\pi$
$787$	12.9019	+	22.3468i	0.459904	+	0.796577i	−0.539051	+	0.842273i	$0.681217\pi$
$788$		0			0
$789$		0			0
$790$		0			0
$791$	−12.9282			−0.459674
$792$		0			0
$793$	5.85641			0.207967
$794$		0			0
$795$		0			0
$796$		0			0
$797$	5.66025	+	9.80385i	0.200496	+	0.347270i	0.948688	−	0.316212i	$-0.102411\pi$
$797$	5.66025	+	9.80385i	0.200496	+	0.347270i	−0.748192	+	0.663482i	$0.769078\pi$
$798$		0			0
$799$	−3.00000	+	5.19615i	−0.106132	+	0.183827i
$800$		0			0
$801$		0			0
$802$		0			0
$803$	8.83013	−	15.2942i	0.311608	−	0.539722i
$804$		0			0
$805$	−1.26795	−	2.19615i	−0.0446893	−	0.0774042i
$806$		0			0
$807$		0			0
$808$		0			0
$809$	−39.5885			−1.39186			−0.695928	−	0.718112i	$-0.745007\pi$
$809$	−39.5885			−1.39186			−0.695928	+	0.718112i	$0.745007\pi$
$810$		0			0
$811$	23.2487			0.816373			0.408186	−	0.912899i	$-0.366161\pi$
$811$	23.2487			0.816373			0.408186	+	0.912899i	$0.366161\pi$
$812$		0			0
$813$		0			0
$814$		0			0
$815$	7.63397	+	13.2224i	0.267406	+	0.463162i
$816$		0			0
$817$	−8.29423	+	14.3660i	−0.290178	+	0.502604i
$818$		0			0
$819$		0			0
$820$		0			0
$821$	−10.3301	+	17.8923i	−0.360524	+	0.624446i	−0.988047	−	0.154152i	$-0.950735\pi$
$821$	−10.3301	+	17.8923i	−0.360524	+	0.624446i	0.627523	+	0.778598i	$0.284069\pi$
$822$		0			0
$823$	1.53590	+	2.66025i	0.0535381	+	0.0927306i	0.891552	−	0.452918i	$-0.149617\pi$
$823$	1.53590	+	2.66025i	0.0535381	+	0.0927306i	−0.838014	+	0.545648i	$0.816283\pi$
$824$		0			0
$825$		0			0
$826$		0			0
$827$	−38.5359			−1.34002			−0.670012	−	0.742350i	$-0.733711\pi$
$827$	−38.5359			−1.34002			−0.670012	+	0.742350i	$0.733711\pi$
$828$		0			0
$829$	−10.2154			−0.354795			−0.177398	−	0.984139i	$-0.556768\pi$
$829$	−10.2154			−0.354795			−0.177398	+	0.984139i	$0.556768\pi$
$830$		0			0
$831$		0			0
$832$		0			0
$833$	−4.09808	−	7.09808i	−0.141990	−	0.245934i
$834$		0			0
$835$	1.56218	−	2.70577i	0.0540614	−	0.0936371i
$836$		0			0
$837$		0			0
$838$		0			0
$839$	19.7942	−	34.2846i	0.683373	−	1.18364i	−0.290573	−	0.956853i	$-0.593846\pi$
$839$	19.7942	−	34.2846i	0.683373	−	1.18364i	0.973945	−	0.226783i	$-0.0728209\pi$
$840$		0			0
$841$	5.39230	+	9.33975i	0.185942	+	0.322060i
$842$		0			0
$843$		0			0
$844$		0			0
$845$	10.8564			0.373472
$846$		0			0
$847$	−5.85641			−0.201229
$848$		0			0
$849$		0			0
$850$		0			0
$851$	7.26795	+	12.5885i	0.249142	+	0.431527i
$852$		0			0
$853$	−5.09808	+	8.83013i	−0.174555	+	0.302338i	−0.940007	−	0.341155i	$-0.889182\pi$
$853$	−5.09808	+	8.83013i	−0.174555	+	0.302338i	0.765452	+	0.643493i	$0.222515\pi$
$854$		0			0
$855$		0			0
$856$		0			0
$857$	21.4641	−	37.1769i	0.733200	−	1.26994i	−0.222309	−	0.974976i	$-0.571359\pi$
$857$	21.4641	−	37.1769i	0.733200	−	1.26994i	0.955509	−	0.294963i	$-0.0953073\pi$
$858$		0			0
$859$	16.8923	+	29.2583i	0.576358	+	0.998281i	0.995893	+	0.0905420i	$0.0288599\pi$
$859$	16.8923	+	29.2583i	0.576358	+	0.998281i	−0.419535	+	0.907739i	$0.637807\pi$
$860$		0			0
$861$		0			0
$862$		0			0
$863$	−4.48334			−0.152615			−0.0763073	−	0.997084i	$-0.524313\pi$
$863$	−4.48334			−0.152615			−0.0763073	+	0.997084i	$0.524313\pi$
$864$		0			0
$865$	−24.2487			−0.824481
$866$		0			0
$867$		0			0
$868$		0			0
$869$	5.53590	+	9.58846i	0.187792	+	0.325266i
$870$		0			0
$871$	−10.5359	+	18.2487i	−0.356995	+	0.618334i
$872$		0			0
$873$		0			0
$874$		0			0
$875$	0.366025	−	0.633975i	0.0123739	−	0.0214323i
$876$		0			0
$877$	17.1244	+	29.6603i	0.578248	+	1.00156i	0.995680	+	0.0928474i	$0.0295969\pi$
$877$	17.1244	+	29.6603i	0.578248	+	1.00156i	−0.417432	+	0.908708i	$0.637070\pi$
$878$		0			0
$879$		0			0
$880$		0			0
$881$	17.1962			0.579353			0.289677	−	0.957125i	$-0.406452\pi$
$881$	17.1962			0.579353			0.289677	+	0.957125i	$0.406452\pi$
$882$		0			0
$883$	32.8372			1.10506			0.552529	−	0.833493i	$-0.313663\pi$
$883$	32.8372			1.10506			0.552529	+	0.833493i	$0.313663\pi$
$884$		0			0
$885$		0			0
$886$		0			0
$887$	−8.36603	−	14.4904i	−0.280904	−	0.486539i	0.690704	−	0.723138i	$-0.257301\pi$
$887$	−8.36603	−	14.4904i	−0.280904	−	0.486539i	−0.971608	+	0.236598i	$0.923967\pi$
$888$		0			0
$889$	2.26795	−	3.92820i	0.0760646	−	0.131748i
$890$		0			0
$891$		0			0
$892$		0			0
$893$	5.83013	−	10.0981i	0.195098	−	0.337919i
$894$		0			0
$895$	6.06218	+	10.5000i	0.202636	+	0.350976i
$896$		0			0
$897$		0			0
$898$		0			0
$899$	33.8372			1.12853
$900$		0			0
$901$	13.6077			0.453338
$902$		0			0
$903$		0			0
$904$		0			0
$905$	−4.76795	−	8.25833i	−0.158492	−	0.274516i
$906$		0			0
$907$	21.3923	−	37.0526i	0.710320	−	1.23031i	−0.254417	−	0.967095i	$-0.581884\pi$
$907$	21.3923	−	37.0526i	0.710320	−	1.23031i	0.964737	−	0.263215i	$-0.0847830\pi$
$908$		0			0
$909$		0			0
$910$		0			0
$911$	8.59808	−	14.8923i	0.284867	−	0.493404i	−0.687710	−	0.725986i	$-0.741384\pi$
$911$	8.59808	−	14.8923i	0.284867	−	0.493404i	0.972577	+	0.232581i	$0.0747172\pi$
$912$		0			0
$913$	7.90192	+	13.6865i	0.261516	+	0.452958i
$914$		0			0
$915$		0			0
$916$		0			0
$917$	10.0526			0.331965
$918$		0			0
$919$	30.6077			1.00965			0.504827	−	0.863220i	$-0.331556\pi$
$919$	30.6077			1.00965			0.504827	+	0.863220i	$0.331556\pi$
$920$		0			0
$921$		0			0
$922$		0			0
$923$	−0.588457	−	1.01924i	−0.0193693	−	0.0335486i
$924$		0			0
$925$	−2.09808	+	3.63397i	−0.0689843	+	0.119484i
$926$		0			0
$927$		0			0
$928$		0			0
$929$	−23.2583	+	40.2846i	−0.763081	+	1.32170i	0.178174	+	0.983999i	$0.442981\pi$
$929$	−23.2583	+	40.2846i	−0.763081	+	1.32170i	−0.941255	+	0.337696i	$0.890352\pi$
$930$		0			0
$931$	7.96410	+	13.7942i	0.261013	+	0.452088i
$932$		0			0
$933$		0			0
$934$		0			0
$935$	−2.19615			−0.0718219
$936$		0			0
$937$	32.9282			1.07572			0.537859	−	0.843035i	$-0.319233\pi$
$937$	32.9282			1.07572			0.537859	+	0.843035i	$0.319233\pi$
$938$		0			0
$939$		0			0
$940$		0			0
$941$	7.73205	+	13.3923i	0.252058	+	0.436577i	0.964092	−	0.265568i	$-0.0855594\pi$
$941$	7.73205	+	13.3923i	0.252058	+	0.436577i	−0.712035	+	0.702144i	$0.752226\pi$
$942$		0			0
$943$	−1.39230	+	2.41154i	−0.0453397	+	0.0785306i
$944$		0			0
$945$		0			0
$946$		0			0
$947$	−8.32051	+	14.4115i	−0.270380	+	0.468312i	−0.968959	−	0.247221i	$-0.920483\pi$
$947$	−8.32051	+	14.4115i	−0.270380	+	0.468312i	0.698579	+	0.715533i	$0.253816\pi$
$948$		0			0
$949$	7.46410	+	12.9282i	0.242295	+	0.419667i
$950$		0			0
$951$		0			0
$952$		0			0
$953$	−9.46410			−0.306572			−0.153286	−	0.988182i	$-0.548986\pi$
$953$	−9.46410			−0.306572			−0.153286	+	0.988182i	$0.548986\pi$
$954$		0			0
$955$	19.0526			0.616526
$956$		0			0
$957$		0			0
$958$		0			0
$959$	6.00000	+	10.3923i	0.193750	+	0.335585i
$960$		0			0
$961$	−15.9282	+	27.5885i	−0.513813	+	0.889950i
$962$		0			0
$963$		0			0
$964$		0			0
$965$	10.2942	−	17.8301i	0.331383	−	0.573972i
$966$		0			0
$967$	−19.2942	−	33.4186i	−0.620461	−	1.07467i	−0.989400	−	0.145216i	$-0.953612\pi$
$967$	−19.2942	−	33.4186i	−0.620461	−	1.07467i	0.368939	−	0.929453i	$-0.379721\pi$
$968$		0			0
$969$		0			0
$970$		0			0
$971$	25.7321			0.825781			0.412890	−	0.910781i	$-0.364519\pi$
$971$	25.7321			0.825781			0.412890	+	0.910781i	$0.364519\pi$
$972$		0			0
$973$	−3.94744			−0.126549
$974$		0			0
$975$		0			0
$976$		0			0
$977$	8.19615	+	14.1962i	0.262218	+	0.454175i	0.966831	−	0.255417i	$-0.0822127\pi$
$977$	8.19615	+	14.1962i	0.262218	+	0.454175i	−0.704613	+	0.709592i	$0.748879\pi$
$978$		0			0
$979$	−4.50000	+	7.79423i	−0.143821	+	0.249105i
$980$		0			0
$981$		0			0
$982$		0			0
$983$	24.6340	−	42.6673i	0.785702	−	1.36088i	−0.142877	−	0.989740i	$-0.545635\pi$
$983$	24.6340	−	42.6673i	0.785702	−	1.36088i	0.928579	−	0.371135i	$-0.121031\pi$
$984$		0			0
$985$	6.92820	+	12.0000i	0.220751	+	0.382352i
$986$		0			0
$987$		0			0
$988$		0			0
$989$	−23.3205			−0.741549
$990$		0			0
$991$	14.2154			0.451567			0.225783	−	0.974178i	$-0.427506\pi$
$991$	14.2154			0.451567			0.225783	+	0.974178i	$0.427506\pi$
$992$		0			0
$993$		0			0
$994$		0			0
$995$	−5.92820	−	10.2679i	−0.187937	−	0.325516i
$996$		0			0
$997$	−20.9019	+	36.2032i	−0.661971	+	1.14657i	0.318127	+	0.948048i	$0.396946\pi$
$997$	−20.9019	+	36.2032i	−0.661971	+	1.14657i	−0.980097	+	0.198518i	$0.936387\pi$
$998$		0			0
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1620.2.i.n.541.1		4
3.2	odd	2		1620.2.i.m.541.1		4
9.2	odd	6		1620.2.a.h.1.2	yes	2
9.4	even	3	inner	1620.2.i.n.1081.1		4
9.5	odd	6		1620.2.i.m.1081.1		4
9.7	even	3		1620.2.a.g.1.2	✓	2
36.7	odd	6		6480.2.a.bh.1.1		2
36.11	even	6		6480.2.a.bp.1.1		2
45.2	even	12		8100.2.d.l.649.3		4
45.7	odd	12		8100.2.d.m.649.3		4
45.29	odd	6		8100.2.a.s.1.1		2
45.34	even	6		8100.2.a.t.1.1		2
45.38	even	12		8100.2.d.l.649.2		4
45.43	odd	12		8100.2.d.m.649.2		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1620.2.a.g.1.2	✓	2	9.7	even	3
1620.2.a.h.1.2	yes	2	9.2	odd	6
1620.2.i.m.541.1		4	3.2	odd	2
1620.2.i.m.1081.1		4	9.5	odd	6
1620.2.i.n.541.1		4	1.1	even	1	trivial
1620.2.i.n.1081.1		4	9.4	even	3	inner
6480.2.a.bh.1.1		2	36.7	odd	6
6480.2.a.bp.1.1		2	36.11	even	6
8100.2.a.s.1.1		2	45.29	odd	6
8100.2.a.t.1.1		2	45.34	even	6
8100.2.d.l.649.2		4	45.38	even	12
8100.2.d.l.649.3		4	45.2	even	12
8100.2.d.m.649.2		4	45.43	odd	12
8100.2.d.m.649.3		4	45.7	odd	12

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:	\( N \)	\(=\)	\( 1620 = 2^{2} \cdot 3^{4} \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1620.i (of order \(3\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(0.500000 + 0.866025i) q^{5} +(-0.366025 + 0.633975i) q^{7} +O(q^{10})\)	\(q+(0.500000 + 0.866025i) q^{5} +(-0.366025 + 0.633975i) q^{7} +(0.866025 - 1.50000i) q^{11} +(0.732051 + 1.26795i) q^{13} -1.26795 q^{17} +2.46410 q^{19} +(1.73205 + 3.00000i) q^{23} +(-0.500000 + 0.866025i) q^{25} +(2.13397 - 3.69615i) q^{29} +(3.96410 + 6.86603i) q^{31} -0.732051 q^{35} +4.19615 q^{37} +(0.401924 + 0.696152i) q^{41} +(-3.36603 + 5.83013i) q^{43} +(2.36603 - 4.09808i) q^{47} +(3.23205 + 5.59808i) q^{49} -10.7321 q^{53} +1.73205 q^{55} +(2.13397 + 3.69615i) q^{59} +(2.00000 - 3.46410i) q^{61} +(-0.732051 + 1.26795i) q^{65} +(7.19615 + 12.4641i) q^{67} -0.803848 q^{71} +10.1962 q^{73} +(0.633975 + 1.09808i) q^{77} +(-3.19615 + 5.53590i) q^{79} +(-4.56218 + 7.90192i) q^{83} +(-0.633975 - 1.09808i) q^{85} -5.19615 q^{89} -1.07180 q^{91} +(1.23205 + 2.13397i) q^{95} +(1.36603 - 2.36603i) q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q + 2 q^{5} + 2 q^{7}+O(q^{10}) \) 4 * q + 2 * q^5 + 2 * q^7	\( 4 q + 2 q^{5} + 2 q^{7} - 4 q^{13} - 12 q^{17} - 4 q^{19} - 2 q^{25} + 12 q^{29} + 2 q^{31} + 4 q^{35} - 4 q^{37} + 12 q^{41} - 10 q^{43} + 6 q^{47} + 6 q^{49} - 36 q^{53} + 12 q^{59} + 8 q^{61} + 4 q^{65} + 8 q^{67} - 24 q^{71} + 20 q^{73} + 6 q^{77} + 8 q^{79} + 6 q^{83} - 6 q^{85} - 32 q^{91} - 2 q^{95} + 2 q^{97}+O(q^{100}) \) 4 * q + 2 * q^5 + 2 * q^7 - 4 * q^13 - 12 * q^17 - 4 * q^19 - 2 * q^25 + 12 * q^29 + 2 * q^31 + 4 * q^35 - 4 * q^37 + 12 * q^41 - 10 * q^43 + 6 * q^47 + 6 * q^49 - 36 * q^53 + 12 * q^59 + 8 * q^61 + 4 * q^65 + 8 * q^67 - 24 * q^71 + 20 * q^73 + 6 * q^77 + 8 * q^79 + 6 * q^83 - 6 * q^85 - 32 * q^91 - 2 * q^95 + 2 * q^97

Introduction

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