LMFDB - Embedded newform 1944.2.i.r.1297.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1944,2,Mod(649,1944)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1944, base_ring=CyclotomicField(6))

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

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

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

chi := DirichletCharacter("1944.649");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1944 = 2^{3} \cdot 3^{5} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1944.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:	$15.5229181529$
Analytic rank:	$0$
Dimension:	$12$
Relative dimension:	$6$ over $\Q(\zeta_{3})$
Coefficient field:	$\mathbb{Q}[x]/(x^{12} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{12} - 18x^{10} + 153x^{8} - 647x^{6} + 1512x^{4} - 1989x^{2} + 1369 $ x^12 - 18x^10 + 153x^8 - 647x^6 + 1512x^4 - 1989*x^2 + 1369
Coefficient ring:	$\Z[a_1, \ldots, a_{11}]$
Coefficient ring index:	$ 3^{6} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			1297.1
Root			$2.53804 + 0.984808i$ of defining polynomial
Character	$\chi$	$=$	1944.1297
Dual form			1944.2.i.r.649.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-2.09277 + 3.62478i) q^{5} +(-0.0737368 - 0.127716i) q^{7} +O(q^{10})$	$q+(-2.09277 + 3.62478i) q^{5} +(-0.0737368 - 0.127716i) q^{7} +(0.900655 + 1.55998i) q^{11} +(-1.05316 + 1.82413i) q^{13} +5.26400 q^{17} -7.39831 q^{19} +(-2.06716 + 3.58042i) q^{23} +(-6.25934 - 10.8415i) q^{25} +(2.85831 + 4.95074i) q^{29} +(-3.03229 + 5.25207i) q^{31} +0.617256 q^{35} +7.57611 q^{37} +(-0.946838 + 1.63997i) q^{41} +(-1.15952 - 2.00836i) q^{43} +(-3.97826 - 6.89055i) q^{47} +(3.48913 - 6.04334i) q^{49} -2.04263 q^{53} -7.53944 q^{55} +(7.29421 - 12.6339i) q^{59} +(-1.69906 - 2.94286i) q^{61} +(-4.40804 - 7.63495i) q^{65} +(-5.86995 + 10.1671i) q^{67} -7.41399 q^{71} -11.3921 q^{73} +(0.132823 - 0.230056i) q^{77} +(-7.69953 - 13.3360i) q^{79} +(0.707584 + 1.22557i) q^{83} +(-11.0163 + 19.0808i) q^{85} -11.8200 q^{89} +0.310627 q^{91} +(15.4829 - 26.8172i) q^{95} +(-5.33270 - 9.23651i) q^{97} +O(q^{100})$
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q - 3 q^{7}+O(q^{10}) $ 12 * q - 3 * q^7	$ 12 q - 3 q^{7} + 3 q^{11} - 3 q^{13} + 18 q^{17} + 18 q^{19} + 6 q^{23} - 18 q^{25} + 3 q^{29} - 24 q^{31} - 30 q^{35} + 30 q^{37} - 21 q^{41} - 18 q^{43} + 6 q^{47} - 21 q^{49} + 24 q^{53} + 36 q^{55} + 12 q^{59} - 18 q^{61} - 33 q^{65} - 24 q^{67} - 30 q^{71} + 12 q^{73} - 3 q^{77} - 21 q^{79} + 18 q^{83} - 24 q^{85} + 36 q^{89} + 60 q^{91} + 39 q^{95} - 27 q^{97}+O(q^{100}) $ 12 * q - 3 * q^7 + 3 * q^11 - 3 * q^13 + 18 * q^17 + 18 * q^19 + 6 * q^23 - 18 * q^25 + 3 * q^29 - 24 * q^31 - 30 * q^35 + 30 * q^37 - 21 * q^41 - 18 * q^43 + 6 * q^47 - 21 * q^49 + 24 * q^53 + 36 * q^55 + 12 * q^59 - 18 * q^61 - 33 * q^65 - 24 * q^67 - 30 * q^71 + 12 * q^73 - 3 * q^77 - 21 * q^79 + 18 * q^83 - 24 * q^85 + 36 * q^89 + 60 * q^91 + 39 * q^95 - 27 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1944\mathbb{Z}\right)^\times$.

$n$	$487$	$973$	$1217$
$\chi(n)$	$1$	$1$	$e\left(\frac{1}{3}\right)$

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
$5$	−2.09277	+	3.62478i	−0.935913	+	1.62105i	−0.162916	+	0.986640i	$0.552090\pi$
$5$	−2.09277	+	3.62478i	−0.935913	+	1.62105i	−0.772997	+	0.634409i	$0.781243\pi$
$6$		0			0
$7$	−0.0737368	−	0.127716i	−0.0278699	−	0.0482721i	0.851754	−	0.523942i	$-0.175539\pi$
$7$	−0.0737368	−	0.127716i	−0.0278699	−	0.0482721i	−0.879624	+	0.475670i	$0.842206\pi$
$8$		0			0
$9$		0			0
$10$		0			0
$11$	0.900655	+	1.55998i	0.271558	+	0.470352i	0.969261	−	0.246035i	$-0.0791279\pi$
$11$	0.900655	+	1.55998i	0.271558	+	0.470352i	−0.697703	+	0.716387i	$0.745795\pi$
$12$		0			0
$13$	−1.05316	+	1.82413i	−0.292095	+	0.505923i	−0.974305	−	0.225233i	$-0.927686\pi$
$13$	−1.05316	+	1.82413i	−0.292095	+	0.505923i	0.682210	+	0.731156i	$0.261019\pi$
$14$		0			0
$15$		0			0
$16$		0			0
$17$	5.26400			1.27671			0.638354	−	0.769743i	$-0.279616\pi$
$17$	5.26400			1.27671			0.638354	+	0.769743i	$0.279616\pi$
$18$		0			0
$19$	−7.39831			−1.69729			−0.848645	−	0.528963i	$-0.822581\pi$
$19$	−7.39831			−1.69729			−0.848645	+	0.528963i	$0.822581\pi$
$20$		0			0
$21$		0			0
$22$		0			0
$23$	−2.06716	+	3.58042i	−0.431032	+	0.746569i	−0.996962	−	0.0778836i	$-0.975184\pi$
$23$	−2.06716	+	3.58042i	−0.431032	+	0.746569i	0.565930	+	0.824453i	$0.308517\pi$
$24$		0			0
$25$	−6.25934	−	10.8415i	−1.25187	−	2.16830i
$26$		0			0
$27$		0			0
$28$		0			0
$29$	2.85831	+	4.95074i	0.530775	+	0.919330i	0.999355	+	0.0359086i	$0.0114325\pi$
$29$	2.85831	+	4.95074i	0.530775	+	0.919330i	−0.468580	+	0.883421i	$0.655234\pi$
$30$		0			0
$31$	−3.03229	+	5.25207i	−0.544615	+	0.943300i	0.454017	+	0.890993i	$0.349991\pi$
$31$	−3.03229	+	5.25207i	−0.544615	+	0.943300i	−0.998631	+	0.0523068i	$0.983343\pi$
$32$		0			0
$33$		0			0
$34$		0			0
$35$	0.617256			0.104335
$36$		0			0
$37$	7.57611			1.24550			0.622752	−	0.782419i	$-0.286015\pi$
$37$	7.57611			1.24550			0.622752	+	0.782419i	$0.286015\pi$
$38$		0			0
$39$		0			0
$40$		0			0
$41$	−0.946838	+	1.63997i	−0.147871	+	0.256121i	−0.930440	−	0.366443i	$-0.880575\pi$
$41$	−0.946838	+	1.63997i	−0.147871	+	0.256121i	0.782569	+	0.622564i	$0.213909\pi$
$42$		0			0
$43$	−1.15952	−	2.00836i	−0.176826	−	0.306271i	0.763966	−	0.645257i	$-0.223250\pi$
$43$	−1.15952	−	2.00836i	−0.176826	−	0.306271i	−0.940792	+	0.338985i	$0.889916\pi$
$44$		0			0
$45$		0			0
$46$		0			0
$47$	−3.97826	−	6.89055i	−0.580289	−	1.00509i	−0.995445	−	0.0953399i	$-0.969606\pi$
$47$	−3.97826	−	6.89055i	−0.580289	−	1.00509i	0.415156	−	0.909750i	$-0.363727\pi$
$48$		0			0
$49$	3.48913	−	6.04334i	0.498447	−	0.863335i
$50$		0			0
$51$		0			0
$52$		0			0
$53$	−2.04263			−0.280577			−0.140288	−	0.990111i	$-0.544803\pi$
$53$	−2.04263			−0.280577			−0.140288	+	0.990111i	$0.544803\pi$
$54$		0			0
$55$	−7.53944			−1.01662
$56$		0			0
$57$		0			0
$58$		0			0
$59$	7.29421	−	12.6339i	0.949625	−	1.64480i	0.203410	−	0.979094i	$-0.434798\pi$
$59$	7.29421	−	12.6339i	0.949625	−	1.64480i	0.746215	−	0.665705i	$-0.231869\pi$
$60$		0			0
$61$	−1.69906	−	2.94286i	−0.217542	−	0.376794i	0.736514	−	0.676423i	$-0.236471\pi$
$61$	−1.69906	−	2.94286i	−0.217542	−	0.376794i	−0.954056	+	0.299628i	$0.903137\pi$
$62$		0			0
$63$		0			0
$64$		0			0
$65$	−4.40804	−	7.63495i	−0.546750	−	0.946999i
$66$		0			0
$67$	−5.86995	+	10.1671i	−0.717129	+	1.24210i	0.245004	+	0.969522i	$0.421211\pi$
$67$	−5.86995	+	10.1671i	−0.717129	+	1.24210i	−0.962133	+	0.272582i	$0.912122\pi$
$68$		0			0
$69$		0			0
$70$		0			0
$71$	−7.41399			−0.879879			−0.439940	−	0.898027i	$-0.645000\pi$
$71$	−7.41399			−0.879879			−0.439940	+	0.898027i	$0.645000\pi$
$72$		0			0
$73$	−11.3921			−1.33334			−0.666672	−	0.745351i	$-0.732282\pi$
$73$	−11.3921			−1.33334			−0.666672	+	0.745351i	$0.732282\pi$
$74$		0			0
$75$		0			0
$76$		0			0
$77$	0.132823	−	0.230056i	0.0151366	−	0.0262173i
$78$		0			0
$79$	−7.69953	−	13.3360i	−0.866264	−	1.50041i	−0.865786	−	0.500414i	$-0.833181\pi$
$79$	−7.69953	−	13.3360i	−0.866264	−	1.50041i	−0.000478285	−	1.00000i	$-0.500152\pi$
$80$		0			0
$81$		0			0
$82$		0			0
$83$	0.707584	+	1.22557i	0.0776675	+	0.134524i	0.902243	−	0.431228i	$-0.141919\pi$
$83$	0.707584	+	1.22557i	0.0776675	+	0.134524i	−0.824576	+	0.565752i	$0.808586\pi$
$84$		0			0
$85$	−11.0163	+	19.0808i	−1.19489	+	2.06961i
$86$		0			0
$87$		0			0
$88$		0			0
$89$	−11.8200			−1.25292			−0.626458	−	0.779455i	$-0.715496\pi$
$89$	−11.8200			−1.25292			−0.626458	+	0.779455i	$0.715496\pi$
$90$		0			0
$91$	0.310627			0.0325626
$92$		0			0
$93$		0			0
$94$		0			0
$95$	15.4829	−	26.8172i	1.58852	−	2.75139i
$96$		0			0
$97$	−5.33270	−	9.23651i	−0.541454	−	0.937826i	−0.998821	−	0.0485478i	$-0.984541\pi$
$97$	−5.33270	−	9.23651i	−0.541454	−	0.937826i	0.457367	−	0.889278i	$-0.348793\pi$
$98$		0			0
$99$		0			0
$100$		0			0
$101$	3.68087	+	6.37545i	0.366260	+	0.634381i	0.988978	−	0.148066i	$-0.0473047\pi$
$101$	3.68087	+	6.37545i	0.366260	+	0.634381i	−0.622718	+	0.782447i	$0.713971\pi$
$102$		0			0
$103$	1.57921	−	2.73527i	0.155604	−	0.269514i	−0.777675	−	0.628667i	$-0.783601\pi$
$103$	1.57921	−	2.73527i	0.155604	−	0.269514i	0.933279	+	0.359153i	$0.116934\pi$
$104$		0			0
$105$		0			0
$106$		0			0
$107$	−14.9022			−1.44065			−0.720323	−	0.693639i	$-0.756006\pi$
$107$	−14.9022			−1.44065			−0.720323	+	0.693639i	$0.756006\pi$
$108$		0			0
$109$	3.02336			0.289586			0.144793	−	0.989462i	$-0.453748\pi$
$109$	3.02336			0.289586			0.144793	+	0.989462i	$0.453748\pi$
$110$		0			0
$111$		0			0
$112$		0			0
$113$	−6.53105	+	11.3121i	−0.614390	+	1.06415i	0.376101	+	0.926579i	$0.377264\pi$
$113$	−6.53105	+	11.3121i	−0.614390	+	1.06415i	−0.990491	+	0.137576i	$0.956069\pi$
$114$		0			0
$115$	−8.65215	−	14.9860i	−0.806817	−	1.39745i
$116$		0			0
$117$		0			0
$118$		0			0
$119$	−0.388151	−	0.672297i	−0.0355817	−	0.0616293i
$120$		0			0
$121$	3.87764	−	6.71627i	0.352513	−	0.610570i
$122$		0			0
$123$		0			0
$124$		0			0
$125$	31.4696			2.81473
$126$		0			0
$127$	11.6116			1.03037			0.515183	−	0.857080i	$-0.327724\pi$
$127$	11.6116			1.03037			0.515183	+	0.857080i	$0.327724\pi$
$128$		0			0
$129$		0			0
$130$		0			0
$131$	−3.25044	+	5.62993i	−0.283992	+	0.491889i	−0.972364	−	0.233469i	$-0.924992\pi$
$131$	−3.25044	+	5.62993i	−0.283992	+	0.491889i	0.688372	+	0.725358i	$0.258326\pi$
$132$		0			0
$133$	0.545528	+	0.944883i	0.0473033	+	0.0819317i
$134$		0			0
$135$		0			0
$136$		0			0
$137$	4.68947	+	8.12240i	0.400648	+	0.693943i	0.993804	−	0.111144i	$-0.0354515\pi$
$137$	4.68947	+	8.12240i	0.400648	+	0.693943i	−0.593156	+	0.805088i	$0.702118\pi$
$138$		0			0
$139$	6.38630	−	11.0614i	0.541679	−	0.938216i	−0.457129	−	0.889401i	$-0.651122\pi$
$139$	6.38630	−	11.0614i	0.541679	−	0.938216i	0.998808	−	0.0488153i	$-0.0155446\pi$
$140$		0			0
$141$		0			0
$142$		0			0
$143$	−3.79414			−0.317282
$144$		0			0
$145$	−23.9271			−1.98704
$146$		0			0
$147$		0			0
$148$		0			0
$149$	−1.00583	+	1.74215i	−0.0824008	+	0.142722i	−0.904281	−	0.426938i	$-0.859592\pi$
$149$	−1.00583	+	1.74215i	−0.0824008	+	0.142722i	0.821880	+	0.569661i	$0.192925\pi$
$150$		0			0
$151$	0.551246	+	0.954786i	0.0448598	+	0.0776994i	0.887583	−	0.460647i	$-0.152383\pi$
$151$	0.551246	+	0.954786i	0.0448598	+	0.0776994i	−0.842724	+	0.538346i	$0.819049\pi$
$152$		0			0
$153$		0			0
$154$		0			0
$155$	−12.6917	−	21.9827i	−1.01942	−	1.76569i
$156$		0			0
$157$	−11.2920	+	19.5582i	−0.901196	+	1.56092i	−0.0752521	+	0.997165i	$0.523976\pi$
$157$	−11.2920	+	19.5582i	−0.901196	+	1.56092i	−0.825944	+	0.563753i	$0.809357\pi$
$158$		0			0
$159$		0			0
$160$		0			0
$161$	0.609702			0.0480513
$162$		0			0
$163$	1.81655			0.142283			0.0711415	−	0.997466i	$-0.477336\pi$
$163$	1.81655			0.142283			0.0711415	+	0.997466i	$0.477336\pi$
$164$		0			0
$165$		0			0
$166$		0			0
$167$	−4.07658	+	7.06085i	−0.315455	+	0.546385i	−0.979534	−	0.201278i	$-0.935491\pi$
$167$	−4.07658	+	7.06085i	−0.315455	+	0.546385i	0.664079	+	0.747663i	$0.268824\pi$
$168$		0			0
$169$	4.28170	+	7.41612i	0.329362	+	0.570471i
$170$		0			0
$171$		0			0
$172$		0			0
$173$	1.68132	+	2.91212i	0.127828	+	0.221405i	0.922835	−	0.385196i	$-0.125866\pi$
$173$	1.68132	+	2.91212i	0.127828	+	0.221405i	−0.795007	+	0.606601i	$0.792533\pi$
$174$		0			0
$175$	−0.923087	+	1.59883i	−0.0697788	+	0.120860i
$176$		0			0
$177$		0			0
$178$		0			0
$179$	8.70434			0.650593			0.325296	−	0.945612i	$-0.394536\pi$
$179$	8.70434			0.650593			0.325296	+	0.945612i	$0.394536\pi$
$180$		0			0
$181$	−8.09212			−0.601483			−0.300741	−	0.953706i	$-0.597234\pi$
$181$	−8.09212			−0.601483			−0.300741	+	0.953706i	$0.597234\pi$
$182$		0			0
$183$		0			0
$184$		0			0
$185$	−15.8550	+	27.4617i	−1.16568	+	2.01902i
$186$		0			0
$187$	4.74105	+	8.21173i	0.346700	+	0.600501i
$188$		0			0
$189$		0			0
$190$		0			0
$191$	11.2396	+	19.4675i	0.813267	+	1.40862i	0.910566	+	0.413364i	$0.135646\pi$
$191$	11.2396	+	19.4675i	0.813267	+	1.40862i	−0.0972993	+	0.995255i	$0.531020\pi$
$192$		0			0
$193$	8.13082	−	14.0830i	0.585269	−	1.01372i	−0.409572	−	0.912278i	$-0.634322\pi$
$193$	8.13082	−	14.0830i	0.585269	−	1.01372i	0.994842	−	0.101439i	$-0.0323446\pi$
$194$		0			0
$195$		0			0
$196$		0			0
$197$	1.48679			0.105930			0.0529648	−	0.998596i	$-0.483133\pi$
$197$	1.48679			0.105930			0.0529648	+	0.998596i	$0.483133\pi$
$198$		0			0
$199$	8.77723			0.622201			0.311101	−	0.950377i	$-0.399302\pi$
$199$	8.77723			0.622201			0.311101	+	0.950377i	$0.399302\pi$
$200$		0			0
$201$		0			0
$202$		0			0
$203$	0.421526	−	0.730104i	0.0295853	−	0.0512433i
$204$		0			0
$205$	−3.96302	−	6.86415i	−0.276789	−	0.479413i
$206$		0			0
$207$		0			0
$208$		0			0
$209$	−6.66333	−	11.5412i	−0.460912	−	0.798323i
$210$		0			0
$211$	−9.54657	+	16.5351i	−0.657213	+	1.13833i	0.324121	+	0.946015i	$0.394931\pi$
$211$	−9.54657	+	16.5351i	−0.657213	+	1.13833i	−0.981334	+	0.192310i	$0.938402\pi$
$212$		0			0
$213$		0			0
$214$		0			0
$215$	9.70645			0.661975
$216$		0			0
$217$	0.894364			0.0607134
$218$		0			0
$219$		0			0
$220$		0			0
$221$	−5.54384	+	9.60222i	−0.372919	+	0.645915i
$222$		0			0
$223$	−10.9790	−	19.0162i	−0.735209	−	1.27342i	−0.954632	−	0.297789i	$-0.903751\pi$
$223$	−10.9790	−	19.0162i	−0.735209	−	1.27342i	0.219423	−	0.975630i	$-0.429583\pi$
$224$		0			0
$225$		0			0
$226$		0			0
$227$	6.17910	+	10.7025i	0.410122	+	0.710351i	0.994903	−	0.100840i	$-0.0321530\pi$
$227$	6.17910	+	10.7025i	0.410122	+	0.710351i	−0.584781	+	0.811191i	$0.698820\pi$
$228$		0			0
$229$	−2.52100	+	4.36650i	−0.166592	+	0.288546i	−0.937220	−	0.348740i	$-0.886610\pi$
$229$	−2.52100	+	4.36650i	−0.166592	+	0.288546i	0.770627	+	0.637286i	$0.219943\pi$
$230$		0			0
$231$		0			0
$232$		0			0
$233$	14.6127			0.957311			0.478655	−	0.878003i	$-0.341124\pi$
$233$	14.6127			0.957311			0.478655	+	0.878003i	$0.341124\pi$
$234$		0			0
$235$	33.3023			2.17240
$236$		0			0
$237$		0			0
$238$		0			0
$239$	−3.55969	+	6.16556i	−0.230257	+	0.398817i	−0.957884	−	0.287157i	$-0.907290\pi$
$239$	−3.55969	+	6.16556i	−0.230257	+	0.398817i	0.727627	+	0.685973i	$0.240623\pi$
$240$		0			0
$241$	4.14720	+	7.18316i	0.267145	+	0.462708i	0.968123	−	0.250474i	$-0.0805865\pi$
$241$	4.14720	+	7.18316i	0.267145	+	0.462708i	−0.700979	+	0.713182i	$0.747253\pi$
$242$		0			0
$243$		0			0
$244$		0			0
$245$	14.6038	+	25.2946i	0.933005	+	1.61601i
$246$		0			0
$247$	7.79162	−	13.4955i	0.495769	−	0.858697i
$248$		0			0
$249$		0			0
$250$		0			0
$251$	−6.17579			−0.389812			−0.194906	−	0.980822i	$-0.562440\pi$
$251$	−6.17579			−0.389812			−0.194906	+	0.980822i	$0.562440\pi$
$252$		0			0
$253$	−7.44718			−0.468200
$254$		0			0
$255$		0			0
$256$		0			0
$257$	−4.49311	+	7.78229i	−0.280272	+	0.485446i	−0.971452	−	0.237237i	$-0.923758\pi$
$257$	−4.49311	+	7.78229i	−0.280272	+	0.485446i	0.691179	+	0.722683i	$0.257091\pi$
$258$		0			0
$259$	−0.558638	−	0.967589i	−0.0347121	−	0.0601231i
$260$		0			0
$261$		0			0
$262$		0			0
$263$	−1.82026	−	3.15279i	−0.112242	−	0.194409i	0.804432	−	0.594045i	$-0.202470\pi$
$263$	−1.82026	−	3.15279i	−0.112242	−	0.194409i	−0.916674	+	0.399636i	$0.869137\pi$
$264$		0			0
$265$	4.27474	−	7.40407i	0.262595	−	0.454828i
$266$		0			0
$267$		0			0
$268$		0			0
$269$	−12.1017			−0.737852			−0.368926	−	0.929459i	$-0.620274\pi$
$269$	−12.1017			−0.737852			−0.368926	+	0.929459i	$0.620274\pi$
$270$		0			0
$271$	−19.9404			−1.21129			−0.605645	−	0.795735i	$-0.707085\pi$
$271$	−19.9404			−1.21129			−0.605645	+	0.795735i	$0.707085\pi$
$272$		0			0
$273$		0			0
$274$		0			0
$275$	11.2750	−	19.5289i	0.679908	−	1.17764i
$276$		0			0
$277$	11.2510	+	19.4873i	0.676007	+	1.17088i	0.976173	+	0.216992i	$0.0696246\pi$
$277$	11.2510	+	19.4873i	0.676007	+	1.17088i	−0.300166	+	0.953887i	$0.597042\pi$
$278$		0			0
$279$		0			0
$280$		0			0
$281$	−6.41678	−	11.1142i	−0.382793	−	0.663017i	0.608667	−	0.793426i	$-0.291704\pi$
$281$	−6.41678	−	11.1142i	−0.382793	−	0.663017i	−0.991460	+	0.130408i	$0.958371\pi$
$282$		0			0
$283$	8.10586	−	14.0398i	0.481843	−	0.834577i	−0.517940	−	0.855417i	$-0.673301\pi$
$283$	8.10586	−	14.0398i	0.481843	−	0.834577i	0.999783	+	0.0208403i	$0.00663416\pi$
$284$		0			0
$285$		0			0
$286$		0			0
$287$	0.279267			0.0164846
$288$		0			0
$289$	10.7097			0.629982
$290$		0			0
$291$		0			0
$292$		0			0
$293$	−2.08193	+	3.60601i	−0.121628	+	0.210665i	−0.920410	−	0.390955i	$-0.872145\pi$
$293$	−2.08193	+	3.60601i	−0.121628	+	0.210665i	0.798782	+	0.601621i	$0.205478\pi$
$294$		0			0
$295$	30.5301	+	52.8797i	1.77753	+	3.07878i
$296$		0			0
$297$		0			0
$298$		0			0
$299$	−4.35410	−	7.54153i	−0.251804	−	0.436138i
$300$		0			0
$301$	−0.170999	+	0.296179i	−0.00985624	+	0.0170715i
$302$		0			0
$303$		0			0
$304$		0			0
$305$	14.2229			0.814403
$306$		0			0
$307$	−22.9278			−1.30856			−0.654279	−	0.756254i	$-0.727028\pi$
$307$	−22.9278			−1.30856			−0.654279	+	0.756254i	$0.727028\pi$
$308$		0			0
$309$		0			0
$310$		0			0
$311$	15.7694	−	27.3134i	0.894199	−	1.54880i	0.0594070	−	0.998234i	$-0.481079\pi$
$311$	15.7694	−	27.3134i	0.894199	−	1.54880i	0.834792	−	0.550565i	$-0.185588\pi$
$312$		0			0
$313$	2.45334	+	4.24931i	0.138671	+	0.240185i	0.926994	−	0.375077i	$-0.122384\pi$
$313$	2.45334	+	4.24931i	0.138671	+	0.240185i	−0.788323	+	0.615262i	$0.789050\pi$
$314$		0			0
$315$		0			0
$316$		0			0
$317$	6.93306	+	12.0084i	0.389399	+	0.674460i	0.992369	−	0.123305i	$-0.0393492\pi$
$317$	6.93306	+	12.0084i	0.389399	+	0.674460i	−0.602969	+	0.797764i	$0.706016\pi$
$318$		0			0
$319$	−5.14870	+	8.91782i	−0.288272	+	0.499302i
$320$		0			0
$321$		0			0
$322$		0			0
$323$	−38.9447			−2.16694
$324$		0			0
$325$	26.3684			1.46265
$326$		0			0
$327$		0			0
$328$		0			0
$329$	−0.586689	+	1.01617i	−0.0323452	+	0.0560235i
$330$		0			0
$331$	6.73906	+	11.6724i	0.370412	+	0.641573i	0.989629	−	0.143647i	$-0.0458830\pi$
$331$	6.73906	+	11.6724i	0.370412	+	0.641573i	−0.619217	+	0.785220i	$0.712550\pi$
$332$		0			0
$333$		0			0
$334$		0			0
$335$	−24.5689	−	42.5545i	−1.34234	−	2.32500i
$336$		0			0
$337$	9.48769	−	16.4332i	0.516827	−	0.895171i	−0.482982	−	0.875630i	$-0.660446\pi$
$337$	9.48769	−	16.4332i	0.516827	−	0.895171i	0.999809	−	0.0195407i	$-0.00622038\pi$
$338$		0			0
$339$		0			0
$340$		0			0
$341$	−10.9242			−0.591577
$342$		0			0
$343$	−2.06142			−0.111306
$344$		0			0
$345$		0			0
$346$		0			0
$347$	7.25618	−	12.5681i	0.389532	−	0.674689i	−0.602855	−	0.797851i	$-0.705970\pi$
$347$	7.25618	−	12.5681i	0.389532	−	0.674689i	0.992387	+	0.123162i	$0.0393035\pi$
$348$		0			0
$349$	4.38348	+	7.59242i	0.234642	+	0.406413i	0.959169	−	0.282835i	$-0.0912747\pi$
$349$	4.38348	+	7.59242i	0.234642	+	0.406413i	−0.724526	+	0.689247i	$0.757941\pi$
$350$		0			0
$351$		0			0
$352$		0			0
$353$	−7.31567	−	12.6711i	−0.389374	−	0.674416i	0.602991	−	0.797748i	$-0.293975\pi$
$353$	−7.31567	−	12.6711i	−0.389374	−	0.674416i	−0.992365	+	0.123332i	$0.960642\pi$
$354$		0			0
$355$	15.5158	−	26.8741i	0.823491	−	1.42633i
$356$		0			0
$357$		0			0
$358$		0			0
$359$	−30.6776			−1.61910			−0.809551	−	0.587050i	$-0.800289\pi$
$359$	−30.6776			−1.61910			−0.809551	+	0.587050i	$0.800289\pi$
$360$		0			0
$361$	35.7351			1.88079
$362$		0			0
$363$		0			0
$364$		0			0
$365$	23.8410	−	41.2938i	1.24789	−	2.16142i
$366$		0			0
$367$	−3.29769	−	5.71176i	−0.172138	−	0.298151i	0.767029	−	0.641612i	$-0.221734\pi$
$367$	−3.29769	−	5.71176i	−0.172138	−	0.298151i	−0.939167	+	0.343461i	$0.888401\pi$
$368$		0			0
$369$		0			0
$370$		0			0
$371$	0.150617	+	0.260876i	0.00781964	+	0.0135440i
$372$		0			0
$373$	14.9002	−	25.8079i	0.771504	−	1.33628i	−0.165235	−	0.986254i	$-0.552838\pi$
$373$	14.9002	−	25.8079i	0.771504	−	1.33628i	0.936739	−	0.350029i	$-0.113828\pi$
$374$		0			0
$375$		0			0
$376$		0			0
$377$	−12.0411			−0.620146
$378$		0			0
$379$	−14.8452			−0.762547			−0.381273	−	0.924462i	$-0.624514\pi$
$379$	−14.8452			−0.762547			−0.381273	+	0.924462i	$0.624514\pi$
$380$		0			0
$381$		0			0
$382$		0			0
$383$	−4.09846	+	7.09874i	−0.209421	+	0.362728i	−0.951532	−	0.307549i	$-0.900491\pi$
$383$	−4.09846	+	7.09874i	−0.209421	+	0.362728i	0.742111	+	0.670277i	$0.233825\pi$
$384$		0			0
$385$	0.555934	+	0.962906i	0.0283330	+	0.0490742i
$386$		0			0
$387$		0			0
$388$		0			0
$389$	12.5721	+	21.7756i	0.637433	+	1.10407i	0.985994	+	0.166780i	$0.0533369\pi$
$389$	12.5721	+	21.7756i	0.637433	+	1.10407i	−0.348562	+	0.937286i	$0.613330\pi$
$390$		0			0
$391$	−10.8815	+	18.8473i	−0.550302	+	0.953151i
$392$		0			0
$393$		0			0
$394$		0			0
$395$	64.4532			3.24299
$396$		0			0
$397$	14.6412			0.734820			0.367410	−	0.930059i	$-0.380245\pi$
$397$	14.6412			0.734820			0.367410	+	0.930059i	$0.380245\pi$
$398$		0			0
$399$		0			0
$400$		0			0
$401$	−1.16083	+	2.01061i	−0.0579690	+	0.100405i	−0.893554	−	0.448957i	$-0.851796\pi$
$401$	−1.16083	+	2.01061i	−0.0579690	+	0.100405i	0.835585	+	0.549362i	$0.185129\pi$
$402$		0			0
$403$	−6.38697	−	11.0626i	−0.318158	−	0.551066i
$404$		0			0
$405$		0			0
$406$		0			0
$407$	6.82345	+	11.8186i	0.338226	+	0.585825i
$408$		0			0
$409$	−14.8974	+	25.8030i	−0.736627	+	1.27588i	0.217379	+	0.976087i	$0.430249\pi$
$409$	−14.8974	+	25.8030i	−0.736627	+	1.27588i	−0.954006	+	0.299788i	$0.903084\pi$
$410$		0			0
$411$		0			0
$412$		0			0
$413$	−2.15141			−0.105864
$414$		0			0
$415$	−5.92323			−0.290760
$416$		0			0
$417$		0			0
$418$		0			0
$419$	−0.906194	+	1.56957i	−0.0442705	+	0.0766787i	−0.887312	−	0.461170i	$-0.847430\pi$
$419$	−0.906194	+	1.56957i	−0.0442705	+	0.0766787i	0.843041	+	0.537849i	$0.180763\pi$
$420$		0			0
$421$	2.80811	+	4.86378i	0.136859	+	0.237046i	0.926306	−	0.376772i	$-0.122966\pi$
$421$	2.80811	+	4.86378i	0.136859	+	0.237046i	−0.789447	+	0.613818i	$0.789633\pi$
$422$		0			0
$423$		0			0
$424$		0			0
$425$	−32.9492	−	57.0696i	−1.59827	−	2.76828i
$426$		0			0
$427$	−0.250567	+	0.433994i	−0.0121258	+	0.0210024i
$428$		0			0
$429$		0			0
$430$		0			0
$431$	10.3737			0.499686			0.249843	−	0.968286i	$-0.419621\pi$
$431$	10.3737			0.499686			0.249843	+	0.968286i	$0.419621\pi$
$432$		0			0
$433$	19.1514			0.920358			0.460179	−	0.887826i	$-0.347785\pi$
$433$	19.1514			0.920358			0.460179	+	0.887826i	$0.347785\pi$
$434$		0			0
$435$		0			0
$436$		0			0
$437$	15.2935	−	26.4891i	0.731586	−	1.26714i
$438$		0			0
$439$	14.6339	+	25.3467i	0.698439	+	1.20973i	0.969008	+	0.247031i	$0.0794549\pi$
$439$	14.6339	+	25.3467i	0.698439	+	1.20973i	−0.270569	+	0.962701i	$0.587212\pi$
$440$		0			0
$441$		0			0
$442$		0			0
$443$	14.9759	+	25.9390i	0.711527	+	1.23240i	0.964284	+	0.264871i	$0.0853293\pi$
$443$	14.9759	+	25.9390i	0.711527	+	1.23240i	−0.252757	+	0.967530i	$0.581337\pi$
$444$		0			0
$445$	24.7365	−	42.8448i	1.17262	−	2.03104i
$446$		0			0
$447$		0			0
$448$		0			0
$449$	−24.4886			−1.15569			−0.577844	−	0.816147i	$-0.696106\pi$
$449$	−24.4886			−1.15569			−0.577844	+	0.816147i	$0.696106\pi$
$450$		0			0
$451$	−3.41110			−0.160622
$452$		0			0
$453$		0			0
$454$		0			0
$455$	−0.650070	+	1.12595i	−0.0304758	+	0.0527855i
$456$		0			0
$457$	1.22440	+	2.12072i	0.0572749	+	0.0992030i	0.893241	−	0.449578i	$-0.148426\pi$
$457$	1.22440	+	2.12072i	0.0572749	+	0.0992030i	−0.835966	+	0.548781i	$0.815092\pi$
$458$		0			0
$459$		0			0
$460$		0			0
$461$	9.63859	+	16.6945i	0.448914	+	0.777542i	0.998316	−	0.0580165i	$-0.0184776\pi$
$461$	9.63859	+	16.6945i	0.448914	+	0.777542i	−0.549402	+	0.835558i	$0.685144\pi$
$462$		0			0
$463$	0.965715	−	1.67267i	0.0448806	−	0.0777355i	−0.842712	−	0.538364i	$-0.819043\pi$
$463$	0.965715	−	1.67267i	0.0448806	−	0.0777355i	0.887593	+	0.460628i	$0.152376\pi$
$464$		0			0
$465$		0			0
$466$		0			0
$467$	−28.0112			−1.29620			−0.648101	−	0.761554i	$-0.724437\pi$
$467$	−28.0112			−1.29620			−0.648101	+	0.761554i	$0.724437\pi$
$468$		0			0
$469$	1.73133			0.0799453
$470$		0			0
$471$		0			0
$472$		0			0
$473$	2.08866	−	3.61767i	0.0960368	−	0.166341i
$474$		0			0
$475$	46.3085	+	80.2087i	2.12478	+	3.68023i
$476$		0			0
$477$		0			0
$478$		0			0
$479$	16.2216	+	28.0967i	0.741185	+	1.28377i	0.951956	+	0.306234i	$0.0990691\pi$
$479$	16.2216	+	28.0967i	0.741185	+	1.28377i	−0.210771	+	0.977535i	$0.567598\pi$
$480$		0			0
$481$	−7.97886	+	13.8198i	−0.363805	+	0.630129i
$482$		0			0
$483$		0			0
$484$		0			0
$485$	44.6404			2.02702
$486$		0			0
$487$	6.19820			0.280867			0.140434	−	0.990090i	$-0.455150\pi$
$487$	6.19820			0.280867			0.140434	+	0.990090i	$0.455150\pi$
$488$		0			0
$489$		0			0
$490$		0			0
$491$	−13.0201	+	22.5514i	−0.587587	+	1.01773i	0.406960	+	0.913446i	$0.366589\pi$
$491$	−13.0201	+	22.5514i	−0.587587	+	1.01773i	−0.994547	+	0.104285i	$0.966744\pi$
$492$		0			0
$493$	15.0462	+	26.0607i	0.677645	+	1.17372i
$494$		0			0
$495$		0			0
$496$		0			0
$497$	0.546684	+	0.946885i	0.0245221	+	0.0424736i
$498$		0			0
$499$	−13.4772	+	23.3431i	−0.603321	+	1.04498i	0.388994	+	0.921240i	$0.372823\pi$
$499$	−13.4772	+	23.3431i	−0.603321	+	1.04498i	−0.992314	+	0.123742i	$0.960511\pi$
$500$		0			0
$501$		0			0
$502$		0			0
$503$	−18.9664			−0.845670			−0.422835	−	0.906207i	$-0.638965\pi$
$503$	−18.9664			−0.845670			−0.422835	+	0.906207i	$0.638965\pi$
$504$		0			0
$505$	−30.8128			−1.37115
$506$		0			0
$507$		0			0
$508$		0			0
$509$	−19.5411	+	33.8462i	−0.866145	+	1.50021i	−0.000239444		1.00000i	$0.500076\pi$
$509$	−19.5411	+	33.8462i	−0.866145	+	1.50021i	−0.865906	+	0.500207i	$0.833257\pi$
$510$		0			0
$511$	0.840017	+	1.45495i	0.0371602	+	0.0643633i
$512$		0			0
$513$		0			0
$514$		0			0
$515$	6.60982	+	11.4486i	0.291264	+	0.504483i
$516$		0			0
$517$	7.16608	−	12.4120i	0.315164	−	0.545880i
$518$		0			0
$519$		0			0
$520$		0			0
$521$	−19.6528			−0.861003			−0.430502	−	0.902590i	$-0.641663\pi$
$521$	−19.6528			−0.861003			−0.430502	+	0.902590i	$0.641663\pi$
$522$		0			0
$523$	24.9339			1.09028			0.545142	−	0.838344i	$-0.316476\pi$
$523$	24.9339			1.09028			0.545142	+	0.838344i	$0.316476\pi$
$524$		0			0
$525$		0			0
$526$		0			0
$527$	−15.9620	+	27.6469i	−0.695314	+	1.20432i
$528$		0			0
$529$	2.95372	+	5.11600i	0.128423	+	0.222435i
$530$		0			0
$531$		0			0
$532$		0			0
$533$	−1.99435	−	3.45431i	−0.0863848	−	0.149623i
$534$		0			0
$535$	31.1867	−	54.0170i	1.34832	−	2.33536i
$536$		0			0
$537$		0			0
$538$		0			0
$539$	12.5700			0.541428
$540$		0			0
$541$	11.8293			0.508583			0.254292	−	0.967128i	$-0.418158\pi$
$541$	11.8293			0.508583			0.254292	+	0.967128i	$0.418158\pi$
$542$		0			0
$543$		0			0
$544$		0			0
$545$	−6.32719	+	10.9590i	−0.271027	+	0.469433i
$546$		0			0
$547$	−17.5615	−	30.4175i	−0.750877	−	1.30056i	−0.947398	−	0.320058i	$-0.896298\pi$
$547$	−17.5615	−	30.4175i	−0.750877	−	1.30056i	0.196521	−	0.980500i	$-0.437036\pi$
$548$		0			0
$549$		0			0
$550$		0			0
$551$	−21.1467	−	36.6272i	−0.900879	−	1.56037i
$552$		0			0
$553$	−1.13548	+	1.96670i	−0.0482854	+	0.0836328i
$554$		0			0
$555$		0			0
$556$		0			0
$557$	10.4916			0.444543			0.222271	−	0.974985i	$-0.428653\pi$
$557$	10.4916			0.444543			0.222271	+	0.974985i	$0.428653\pi$
$558$		0			0
$559$	4.88467			0.206599
$560$		0			0
$561$		0			0
$562$		0			0
$563$	−1.07865	+	1.86827i	−0.0454596	+	0.0787383i	−0.887860	−	0.460114i	$-0.847809\pi$
$563$	−1.07865	+	1.86827i	−0.0454596	+	0.0787383i	0.842400	+	0.538852i	$0.181142\pi$
$564$		0			0
$565$	−27.3359	−	47.3472i	−1.15003	−	1.99191i
$566$		0			0
$567$		0			0
$568$		0			0
$569$	1.96322	+	3.40039i	0.0823024	+	0.142552i	0.904239	−	0.427028i	$-0.140439\pi$
$569$	1.96322	+	3.40039i	0.0823024	+	0.142552i	−0.821936	+	0.569580i	$0.807106\pi$
$570$		0			0
$571$	1.64085	−	2.84203i	0.0686674	−	0.118935i	−0.829648	−	0.558288i	$-0.811459\pi$
$571$	1.64085	−	2.84203i	0.0686674	−	0.118935i	0.898315	+	0.439352i	$0.144792\pi$
$572$		0			0
$573$		0			0
$574$		0			0
$575$	51.7561			2.15838
$576$		0			0
$577$	10.4941			0.436874			0.218437	−	0.975851i	$-0.429904\pi$
$577$	10.4941			0.436874			0.218437	+	0.975851i	$0.429904\pi$
$578$		0			0
$579$		0			0
$580$		0			0
$581$	0.104350	−	0.180740i	0.00432917	−	0.00749834i
$582$		0			0
$583$	−1.83970	−	3.18646i	−0.0761927	−	0.131970i
$584$		0			0
$585$		0			0
$586$		0			0
$587$	−5.15058	−	8.92107i	−0.212587	−	0.368212i	0.739936	−	0.672677i	$-0.234856\pi$
$587$	−5.15058	−	8.92107i	−0.212587	−	0.368212i	−0.952523	+	0.304465i	$0.901522\pi$
$588$		0			0
$589$	22.4338	−	38.8565i	0.924369	−	1.60105i
$590$		0			0
$591$		0			0
$592$		0			0
$593$	−30.7706			−1.26360			−0.631799	−	0.775133i	$-0.717683\pi$
$593$	−30.7706			−1.26360			−0.631799	+	0.775133i	$0.717683\pi$
$594$		0			0
$595$	3.24923			0.133206
$596$		0			0
$597$		0			0
$598$		0			0
$599$	−16.6606	+	28.8571i	−0.680735	+	1.17907i	0.294022	+	0.955799i	$0.405006\pi$
$599$	−16.6606	+	28.8571i	−0.680735	+	1.17907i	−0.974757	+	0.223269i	$0.928327\pi$
$600$		0			0
$601$	20.3126	+	35.1824i	0.828567	+	1.43512i	0.899163	+	0.437615i	$0.144177\pi$
$601$	20.3126	+	35.1824i	0.828567	+	1.43512i	−0.0705958	+	0.997505i	$0.522490\pi$
$602$		0			0
$603$		0			0
$604$		0			0
$605$	16.2300	+	28.1112i	0.659843	+	1.14288i
$606$		0			0
$607$	−5.34630	+	9.26006i	−0.217000	+	0.375854i	−0.953889	−	0.300159i	$-0.902960\pi$
$607$	−5.34630	+	9.26006i	−0.217000	+	0.375854i	0.736890	+	0.676013i	$0.236294\pi$
$608$		0			0
$609$		0			0
$610$		0			0
$611$	16.7590			0.677997
$612$		0			0
$613$	−46.1159			−1.86260			−0.931302	−	0.364249i	$-0.881326\pi$
$613$	−46.1159			−1.86260			−0.931302	+	0.364249i	$0.881326\pi$
$614$		0			0
$615$		0			0
$616$		0			0
$617$	−10.8481	+	18.7894i	−0.436726	+	0.756432i	−0.997435	−	0.0715813i	$-0.977195\pi$
$617$	−10.8481	+	18.7894i	−0.436726	+	0.756432i	0.560709	+	0.828013i	$0.310529\pi$
$618$		0			0
$619$	−3.98046	−	6.89436i	−0.159988	−	0.277108i	0.774876	−	0.632113i	$-0.217812\pi$
$619$	−3.98046	−	6.89436i	−0.159988	−	0.277108i	−0.934864	+	0.355006i	$0.884479\pi$
$620$		0			0
$621$		0			0
$622$		0			0
$623$	0.871569	+	1.50960i	0.0349187	+	0.0604809i
$624$		0			0
$625$	−34.5619	+	59.8630i	−1.38248	+	2.39452i
$626$		0			0
$627$		0			0
$628$		0			0
$629$	39.8806			1.59014
$630$		0			0
$631$	39.0517			1.55463			0.777313	−	0.629114i	$-0.216582\pi$
$631$	39.0517			1.55463			0.777313	+	0.629114i	$0.216582\pi$
$632$		0			0
$633$		0			0
$634$		0			0
$635$	−24.3004	+	42.0896i	−0.964334	+	1.67028i
$636$		0			0
$637$	7.34923	+	12.7292i	0.291187	+	0.504351i
$638$		0			0
$639$		0			0
$640$		0			0
$641$	11.1933	+	19.3874i	0.442110	+	0.765757i	0.997846	−	0.0656019i	$-0.0208967\pi$
$641$	11.1933	+	19.3874i	0.442110	+	0.765757i	−0.555736	+	0.831359i	$0.687563\pi$
$642$		0			0
$643$	−1.13534	+	1.96646i	−0.0447733	+	0.0775496i	−0.887544	−	0.460724i	$-0.847590\pi$
$643$	−1.13534	+	1.96646i	−0.0447733	+	0.0775496i	0.842770	+	0.538273i	$0.180923\pi$
$644$		0			0
$645$		0			0
$646$		0			0
$647$	−5.57106			−0.219021			−0.109511	−	0.993986i	$-0.534928\pi$
$647$	−5.57106			−0.219021			−0.109511	+	0.993986i	$0.534928\pi$
$648$		0			0
$649$	26.2782			1.03151
$650$		0			0
$651$		0			0
$652$		0			0
$653$	13.3144	−	23.0612i	0.521033	−	0.902456i	−0.478668	−	0.877996i	$-0.658880\pi$
$653$	13.3144	−	23.0612i	0.521033	−	0.902456i	0.999701	−	0.0244599i	$-0.00778659\pi$
$654$		0			0
$655$	−13.6048	−	23.5643i	−0.531585	−	0.920732i
$656$		0			0
$657$		0			0
$658$		0			0
$659$	−1.65251	−	2.86224i	−0.0643727	−	0.111497i	0.832043	−	0.554711i	$-0.187171\pi$
$659$	−1.65251	−	2.86224i	−0.0643727	−	0.111497i	−0.896416	+	0.443215i	$0.853838\pi$
$660$		0			0
$661$	−6.32294	+	10.9517i	−0.245934	+	0.425970i	−0.962394	−	0.271658i	$-0.912428\pi$
$661$	−6.32294	+	10.9517i	−0.245934	+	0.425970i	0.716460	+	0.697628i	$0.245761\pi$
$662$		0			0
$663$		0			0
$664$		0			0
$665$	−4.56665			−0.177087
$666$		0			0
$667$	−23.6343			−0.915125
$668$		0			0
$669$		0			0
$670$		0			0
$671$	3.06053	−	5.30100i	0.118151	−	0.204643i
$672$		0			0
$673$	2.22963	+	3.86183i	0.0859458	+	0.148862i	0.905794	−	0.423719i	$-0.139275\pi$
$673$	2.22963	+	3.86183i	0.0859458	+	0.148862i	−0.819848	+	0.572581i	$0.805942\pi$
$674$		0			0
$675$		0			0
$676$		0			0
$677$	−7.79354	−	13.4988i	−0.299530	−	0.518801i	0.676498	−	0.736444i	$-0.263497\pi$
$677$	−7.79354	−	13.4988i	−0.299530	−	0.518801i	−0.976028	+	0.217643i	$0.930163\pi$
$678$		0			0
$679$	−0.786433	+	1.36214i	−0.0301805	+	0.0522742i
$680$		0			0
$681$		0			0
$682$		0			0
$683$	16.1187			0.616763			0.308382	−	0.951263i	$-0.400213\pi$
$683$	16.1187			0.616763			0.308382	+	0.951263i	$0.400213\pi$
$684$		0			0
$685$	−39.2558			−1.49989
$686$		0			0
$687$		0			0
$688$		0			0
$689$	2.15122	−	3.72602i	0.0819549	−	0.141950i
$690$		0			0
$691$	−11.9640	−	20.7222i	−0.455132	−	0.788311i	0.543564	−	0.839368i	$-0.317075\pi$
$691$	−11.9640	−	20.7222i	−0.455132	−	0.788311i	−0.998696	+	0.0510563i	$0.983741\pi$
$692$		0			0
$693$		0			0
$694$		0			0
$695$	26.7301	+	46.2978i	1.01393	+	1.75618i
$696$		0			0
$697$	−4.98416	+	8.63281i	−0.188788	+	0.326991i
$698$		0			0
$699$		0			0
$700$		0			0
$701$	−22.2229			−0.839348			−0.419674	−	0.907675i	$-0.637856\pi$
$701$	−22.2229			−0.839348			−0.419674	+	0.907675i	$0.637856\pi$
$702$		0			0
$703$	−56.0504			−2.11398
$704$		0			0
$705$		0			0
$706$		0			0
$707$	0.542831	−	0.940211i	0.0204153	−	0.0353603i
$708$		0			0
$709$	11.1216	+	19.2631i	0.417679	+	0.723442i	0.995706	−	0.0925762i	$-0.0295102\pi$
$709$	11.1216	+	19.2631i	0.417679	+	0.723442i	−0.578026	+	0.816018i	$0.696177\pi$
$710$		0			0
$711$		0			0
$712$		0			0
$713$	−12.5364	−	21.7137i	−0.469493	−	0.813185i
$714$		0			0
$715$	7.94025	−	13.7529i	0.296948	−	0.514330i
$716$		0			0
$717$		0			0
$718$		0			0
$719$	10.5788			0.394522			0.197261	−	0.980351i	$-0.436795\pi$
$719$	10.5788			0.394522			0.197261	+	0.980351i	$0.436795\pi$
$720$		0			0
$721$	−0.465783			−0.0173467
$722$		0			0
$723$		0			0
$724$		0			0
$725$	35.7823	−	61.9767i	1.32892	−	2.30176i
$726$		0			0
$727$	1.61997	+	2.80588i	0.0600815	+	0.104064i	0.894502	−	0.447065i	$-0.147531\pi$
$727$	1.61997	+	2.80588i	0.0600815	+	0.104064i	−0.834420	+	0.551129i	$0.814197\pi$
$728$		0			0
$729$		0			0
$730$		0			0
$731$	−6.10374	−	10.5720i	−0.225755	−	0.391019i
$732$		0			0
$733$	1.74289	−	3.01878i	0.0643753	−	0.111501i	−0.832041	−	0.554713i	$-0.812828\pi$
$733$	1.74289	−	3.01878i	0.0643753	−	0.111501i	0.896417	+	0.443212i	$0.146161\pi$
$734$		0			0
$735$		0			0
$736$		0			0
$737$	−21.1472			−0.778967
$738$		0			0
$739$	32.8561			1.20863			0.604316	−	0.796745i	$-0.293447\pi$
$739$	32.8561			1.20863			0.604316	+	0.796745i	$0.293447\pi$
$740$		0			0
$741$		0			0
$742$		0			0
$743$	8.46349	−	14.6592i	0.310495	−	0.537794i	−0.667974	−	0.744184i	$-0.732838\pi$
$743$	8.46349	−	14.6592i	0.310495	−	0.537794i	0.978470	+	0.206391i	$0.0661718\pi$
$744$		0			0
$745$	−4.20994	−	7.29182i	−0.154240	−	0.267152i
$746$		0			0
$747$		0			0
$748$		0			0
$749$	1.09884	+	1.90324i	0.0401507	+	0.0695430i
$750$		0			0
$751$	−7.45729	+	12.9164i	−0.272121	+	0.471327i	−0.969405	−	0.245468i	$-0.921058\pi$
$751$	−7.45729	+	12.9164i	−0.272121	+	0.471327i	0.697284	+	0.716795i	$0.254392\pi$
$752$		0			0
$753$		0			0
$754$		0			0
$755$	−4.61452			−0.167939
$756$		0			0
$757$	−27.4936			−0.999271			−0.499636	−	0.866236i	$-0.666533\pi$
$757$	−27.4936			−0.999271			−0.499636	+	0.866236i	$0.666533\pi$
$758$		0			0
$759$		0			0
$760$		0			0
$761$	11.9676	−	20.7285i	0.433825	−	0.751407i	−0.563374	−	0.826202i	$-0.690497\pi$
$761$	11.9676	−	20.7285i	0.433825	−	0.751407i	0.997199	+	0.0747953i	$0.0238303\pi$
$762$		0			0
$763$	−0.222933	−	0.386132i	−0.00807072	−	0.0139789i
$764$		0			0
$765$		0			0
$766$		0			0
$767$	15.3640	+	26.6112i	0.554761	+	0.960873i
$768$		0			0
$769$	−7.69496	+	13.3281i	−0.277487	+	0.480622i	−0.970760	−	0.240054i	$-0.922835\pi$
$769$	−7.69496	+	13.3281i	−0.277487	+	0.480622i	0.693272	+	0.720676i	$0.256168\pi$
$770$		0			0
$771$		0			0
$772$		0			0
$773$	−31.5535			−1.13490			−0.567450	−	0.823408i	$-0.692070\pi$
$773$	−31.5535			−1.13490			−0.567450	+	0.823408i	$0.692070\pi$
$774$		0			0
$775$	75.9204			2.72714
$776$		0			0
$777$		0			0
$778$		0			0
$779$	7.00501	−	12.1330i	0.250980	−	0.434711i
$780$		0			0
$781$	−6.67745	−	11.5657i	−0.238938	−	0.413853i
$782$		0			0
$783$		0			0
$784$		0			0
$785$	−47.2628	−	81.8616i	−1.68688	−	2.92177i
$786$		0			0
$787$	3.90400	−	6.76193i	0.139163	−	0.241037i	−0.788017	−	0.615653i	$-0.788892\pi$
$787$	3.90400	−	6.76193i	0.139163	−	0.241037i	0.927180	+	0.374616i	$0.122226\pi$
$788$		0			0
$789$		0			0
$790$		0			0
$791$	1.92632			0.0684919
$792$		0			0
$793$	7.15754			0.254172
$794$		0			0
$795$		0			0
$796$		0			0
$797$	7.03965	−	12.1930i	0.249357	−	0.431899i	−0.713991	−	0.700155i	$-0.753114\pi$
$797$	7.03965	−	12.1930i	0.249357	−	0.431899i	0.963348	+	0.268256i	$0.0864474\pi$
$798$		0			0
$799$	−20.9416	−	36.2719i	−0.740860	−	1.28321i
$800$		0			0
$801$		0			0
$802$		0			0
$803$	−10.2603	−	17.7714i	−0.362080	−	0.627141i
$804$		0			0
$805$	−1.27596	+	2.21004i	−0.0449718	+	0.0778935i
$806$		0			0
$807$		0			0
$808$		0			0
$809$	10.9542			0.385128			0.192564	−	0.981284i	$-0.438320\pi$
$809$	10.9542			0.385128			0.192564	+	0.981284i	$0.438320\pi$
$810$		0			0
$811$	44.2693			1.55451			0.777253	−	0.629188i	$-0.216613\pi$
$811$	44.2693			1.55451			0.777253	+	0.629188i	$0.216613\pi$
$812$		0			0
$813$		0			0
$814$		0			0
$815$	−3.80161	+	6.58458i	−0.133165	+	0.230648i
$816$		0			0
$817$	8.57853	+	14.8584i	0.300125	+	0.519831i
$818$		0			0
$819$		0			0
$820$		0			0
$821$	7.28650	+	12.6206i	0.254301	+	0.440462i	0.964705	−	0.263332i	$-0.0848214\pi$
$821$	7.28650	+	12.6206i	0.254301	+	0.440462i	−0.710405	+	0.703793i	$0.751488\pi$
$822$		0			0
$823$	11.3194	−	19.6058i	0.394569	−	0.683414i	−0.598477	−	0.801140i	$-0.704227\pi$
$823$	11.3194	−	19.6058i	0.394569	−	0.683414i	0.993046	+	0.117726i	$0.0375606\pi$
$824$		0			0
$825$		0			0
$826$		0			0
$827$	−28.3220			−0.984853			−0.492427	−	0.870354i	$-0.663890\pi$
$827$	−28.3220			−0.984853			−0.492427	+	0.870354i	$0.663890\pi$
$828$		0			0
$829$	−41.4532			−1.43973			−0.719864	−	0.694115i	$-0.755796\pi$
$829$	−41.4532			−1.43973			−0.719864	+	0.694115i	$0.755796\pi$
$830$		0			0
$831$		0			0
$832$		0			0
$833$	18.3668	−	31.8122i	0.636371	−	1.10223i
$834$		0			0
$835$	−17.0627	−	29.5534i	−0.590478	−	1.02274i
$836$		0			0
$837$		0			0
$838$		0			0
$839$	8.44919	+	14.6344i	0.291699	+	0.505237i	0.974211	−	0.225637i	$-0.0724463\pi$
$839$	8.44919	+	14.6344i	0.291699	+	0.505237i	−0.682513	+	0.730873i	$0.739113\pi$
$840$		0			0
$841$	−1.83990	+	3.18680i	−0.0634448	+	0.109890i
$842$		0			0
$843$		0			0
$844$		0			0
$845$	−35.8424			−1.23302
$846$		0			0
$847$	−1.14370			−0.0392980
$848$		0			0
$849$		0			0
$850$		0			0
$851$	−15.6610	+	27.1256i	−0.536852	+	0.929855i
$852$		0			0
$853$	−23.0470	−	39.9186i	−0.789115	−	1.36679i	−0.926509	−	0.376271i	$-0.877206\pi$
$853$	−23.0470	−	39.9186i	−0.789115	−	1.36679i	0.137394	−	0.990516i	$-0.456127\pi$
$854$		0			0
$855$		0			0
$856$		0			0
$857$	−17.2590	−	29.8934i	−0.589556	−	1.02114i	−0.994291	−	0.106706i	$-0.965970\pi$
$857$	−17.2590	−	29.8934i	−0.589556	−	1.02114i	0.404735	−	0.914434i	$-0.367364\pi$
$858$		0			0
$859$	−14.9317	+	25.8625i	−0.509463	+	0.882417i	0.490476	+	0.871454i	$0.336823\pi$
$859$	−14.9317	+	25.8625i	−0.509463	+	0.882417i	−0.999940	+	0.0109621i	$0.996511\pi$
$860$		0			0
$861$		0			0
$862$		0			0
$863$	41.7589			1.42149			0.710744	−	0.703451i	$-0.248358\pi$
$863$	41.7589			1.42149			0.710744	+	0.703451i	$0.248358\pi$
$864$		0			0
$865$	−14.0744			−0.478544
$866$		0			0
$867$		0			0
$868$		0			0
$869$	13.8692	−	24.0222i	0.470481	−	0.814898i
$870$		0			0
$871$	−12.3640	−	21.4151i	−0.418939	−	0.725624i
$872$		0			0
$873$		0			0
$874$		0			0
$875$	−2.32047	−	4.01917i	−0.0784463	−	0.135873i
$876$		0			0
$877$	−8.04714	+	13.9381i	−0.271733	+	0.470655i	−0.969306	−	0.245859i	$-0.920930\pi$
$877$	−8.04714	+	13.9381i	−0.271733	+	0.470655i	0.697573	+	0.716514i	$0.254263\pi$
$878$		0			0
$879$		0			0
$880$		0			0
$881$	−50.1211			−1.68862			−0.844312	−	0.535852i	$-0.819991\pi$
$881$	−50.1211			−1.68862			−0.844312	+	0.535852i	$0.819991\pi$
$882$		0			0
$883$	−39.0282			−1.31340			−0.656701	−	0.754151i	$-0.728049\pi$
$883$	−39.0282			−1.31340			−0.656701	+	0.754151i	$0.728049\pi$
$884$		0			0
$885$		0			0
$886$		0			0
$887$	−15.8948	+	27.5306i	−0.533695	+	0.924387i	0.465530	+	0.885032i	$0.345864\pi$
$887$	−15.8948	+	27.5306i	−0.533695	+	0.924387i	−0.999225	+	0.0393548i	$0.987470\pi$
$888$		0			0
$889$	−0.856206	−	1.48299i	−0.0287162	−	0.0497379i
$890$		0			0
$891$		0			0
$892$		0			0
$893$	29.4324	+	50.9785i	0.984919	+	1.70593i
$894$		0			0
$895$	−18.2161	+	31.5513i	−0.608899	+	1.05464i
$896$		0			0
$897$		0			0
$898$		0			0
$899$	−34.6689			−1.15627
$900$		0			0
$901$	−10.7524			−0.358214
$902$		0			0
$903$		0			0
$904$		0			0
$905$	16.9349	−	29.3321i	0.562936	−	0.975033i
$906$		0			0
$907$	−2.49153	−	4.31546i	−0.0827299	−	0.143292i	0.821692	−	0.569932i	$-0.193031\pi$
$907$	−2.49153	−	4.31546i	−0.0827299	−	0.143292i	−0.904422	+	0.426640i	$0.859697\pi$
$908$		0			0
$909$		0			0
$910$		0			0
$911$	−21.1409	−	36.6171i	−0.700430	−	1.21318i	−0.968316	−	0.249729i	$-0.919658\pi$
$911$	−21.1409	−	36.6171i	−0.700430	−	1.21318i	0.267886	−	0.963451i	$-0.413675\pi$
$912$		0			0
$913$	−1.27458	+	2.20763i	−0.0421824	+	0.0730620i
$914$		0			0
$915$		0			0
$916$		0			0
$917$	0.958709			0.0316594
$918$		0			0
$919$	−36.9628			−1.21929			−0.609646	−	0.792674i	$-0.708688\pi$
$919$	−36.9628			−1.21929			−0.609646	+	0.792674i	$0.708688\pi$
$920$		0			0
$921$		0			0
$922$		0			0
$923$	7.80814	−	13.5241i	0.257008	−	0.445151i
$924$		0			0
$925$	−47.4214	−	82.1363i	−1.55921	−	2.70062i
$926$		0			0
$927$		0			0
$928$		0			0
$929$	−22.2322	−	38.5073i	−0.729416	−	1.26338i	−0.957131	−	0.289657i	$-0.906459\pi$
$929$	−22.2322	−	38.5073i	−0.729416	−	1.26338i	0.227715	−	0.973728i	$-0.426875\pi$
$930$		0			0
$931$	−25.8137	+	44.7106i	−0.846008	+	1.46533i
$932$		0			0
$933$		0			0
$934$		0			0
$935$	−39.6876			−1.29792
$936$		0			0
$937$	−4.82797			−0.157723			−0.0788615	−	0.996886i	$-0.525128\pi$
$937$	−4.82797			−0.157723			−0.0788615	+	0.996886i	$0.525128\pi$
$938$		0			0
$939$		0			0
$940$		0			0
$941$	22.2008	−	38.4529i	0.723724	−	1.25353i	−0.235773	−	0.971808i	$-0.575762\pi$
$941$	22.2008	−	38.4529i	0.723724	−	1.25353i	0.959497	−	0.281719i	$-0.0909046\pi$
$942$		0			0
$943$	−3.91453	−	6.78016i	−0.127475	−	0.220792i
$944$		0			0
$945$		0			0
$946$		0			0
$947$	−8.85633	−	15.3396i	−0.287792	−	0.498470i	0.685490	−	0.728082i	$-0.259588\pi$
$947$	−8.85633	−	15.3396i	−0.287792	−	0.498470i	−0.973282	+	0.229611i	$0.926255\pi$
$948$		0			0
$949$	11.9977	−	20.7807i	0.389463	−	0.674569i
$950$		0			0
$951$		0			0
$952$		0			0
$953$	30.2262			0.979121			0.489561	−	0.871969i	$-0.337157\pi$
$953$	30.2262			0.979121			0.489561	+	0.871969i	$0.337157\pi$
$954$		0			0
$955$	−94.0871			−3.04459
$956$		0			0
$957$		0			0
$958$		0			0
$959$	0.691573	−	1.19784i	0.0223321	−	0.0386803i
$960$		0			0
$961$	−2.88951	−	5.00478i	−0.0932100	−	0.161444i
$962$		0			0
$963$		0			0
$964$		0			0
$965$	34.0318	+	58.9448i	1.09552	+	1.89750i
$966$		0			0
$967$	−18.0868	+	31.3272i	−0.581631	+	1.00741i	0.413655	+	0.910434i	$0.364252\pi$
$967$	−18.0868	+	31.3272i	−0.581631	+	1.00741i	−0.995286	+	0.0969808i	$0.969081\pi$
$968$		0			0
$969$		0			0
$970$		0			0
$971$	35.8345			1.14998			0.574991	−	0.818159i	$-0.305005\pi$
$971$	35.8345			1.14998			0.574991	+	0.818159i	$0.305005\pi$
$972$		0			0
$973$	−1.88362			−0.0603862
$974$		0			0
$975$		0			0
$976$		0			0
$977$	−7.71115	+	13.3561i	−0.246702	+	0.427300i	−0.962609	−	0.270896i	$-0.912680\pi$
$977$	−7.71115	+	13.3561i	−0.246702	+	0.427300i	0.715907	+	0.698196i	$0.246013\pi$
$978$		0			0
$979$	−10.6457	−	18.4389i	−0.340239	−	0.589311i
$980$		0			0
$981$		0			0
$982$		0			0
$983$	21.7500	+	37.6721i	0.693717	+	1.20155i	0.970611	+	0.240653i	$0.0773616\pi$
$983$	21.7500	+	37.6721i	0.693717	+	1.20155i	−0.276894	+	0.960901i	$0.589305\pi$
$984$		0			0
$985$	−3.11151	+	5.38929i	−0.0991409	+	0.171717i
$986$		0			0
$987$		0			0
$988$		0			0
$989$	9.58768			0.304870
$990$		0			0
$991$	36.6899			1.16549			0.582747	−	0.812653i	$-0.301978\pi$
$991$	36.6899			1.16549			0.582747	+	0.812653i	$0.301978\pi$
$992$		0			0
$993$		0			0
$994$		0			0
$995$	−18.3687	+	31.8155i	−0.582326	+	1.00862i
$996$		0			0
$997$	14.9584	+	25.9087i	0.473737	+	0.820537i	0.999548	−	0.0300645i	$-0.00957127\pi$
$997$	14.9584	+	25.9087i	0.473737	+	0.820537i	−0.525811	+	0.850602i	$0.676238\pi$
$998$		0			0
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1944.2.i.r.1297.1		12
3.2	odd	2		1944.2.i.q.1297.6		12
9.2	odd	6		1944.2.i.q.649.6		12
9.4	even	3		1944.2.a.q.1.6	✓	6
9.5	odd	6		1944.2.a.r.1.1	yes	6
9.7	even	3	inner	1944.2.i.r.649.1		12
36.23	even	6		3888.2.a.bl.1.1		6
36.31	odd	6		3888.2.a.bm.1.6		6

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1944.2.a.q.1.6	✓	6	9.4	even	3
1944.2.a.r.1.1	yes	6	9.5	odd	6
1944.2.i.q.649.6		12	9.2	odd	6
1944.2.i.q.1297.6		12	3.2	odd	2
1944.2.i.r.649.1		12	9.7	even	3	inner
1944.2.i.r.1297.1		12	1.1	even	1	trivial
3888.2.a.bl.1.1		6	36.23	even	6
3888.2.a.bm.1.6		6	36.31	odd	6

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:	\( N \)	\(=\)	\( 1944 = 2^{3} \cdot 3^{5} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1944.i (of order \(3\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(-2.09277 + 3.62478i) q^{5} +(-0.0737368 - 0.127716i) q^{7} +O(q^{10})\)	\(q+(-2.09277 + 3.62478i) q^{5} +(-0.0737368 - 0.127716i) q^{7} +(0.900655 + 1.55998i) q^{11} +(-1.05316 + 1.82413i) q^{13} +5.26400 q^{17} -7.39831 q^{19} +(-2.06716 + 3.58042i) q^{23} +(-6.25934 - 10.8415i) q^{25} +(2.85831 + 4.95074i) q^{29} +(-3.03229 + 5.25207i) q^{31} +0.617256 q^{35} +7.57611 q^{37} +(-0.946838 + 1.63997i) q^{41} +(-1.15952 - 2.00836i) q^{43} +(-3.97826 - 6.89055i) q^{47} +(3.48913 - 6.04334i) q^{49} -2.04263 q^{53} -7.53944 q^{55} +(7.29421 - 12.6339i) q^{59} +(-1.69906 - 2.94286i) q^{61} +(-4.40804 - 7.63495i) q^{65} +(-5.86995 + 10.1671i) q^{67} -7.41399 q^{71} -11.3921 q^{73} +(0.132823 - 0.230056i) q^{77} +(-7.69953 - 13.3360i) q^{79} +(0.707584 + 1.22557i) q^{83} +(-11.0163 + 19.0808i) q^{85} -11.8200 q^{89} +0.310627 q^{91} +(15.4829 - 26.8172i) q^{95} +(-5.33270 - 9.23651i) q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q - 3 q^{7}+O(q^{10}) \) 12 * q - 3 * q^7	\( 12 q - 3 q^{7} + 3 q^{11} - 3 q^{13} + 18 q^{17} + 18 q^{19} + 6 q^{23} - 18 q^{25} + 3 q^{29} - 24 q^{31} - 30 q^{35} + 30 q^{37} - 21 q^{41} - 18 q^{43} + 6 q^{47} - 21 q^{49} + 24 q^{53} + 36 q^{55} + 12 q^{59} - 18 q^{61} - 33 q^{65} - 24 q^{67} - 30 q^{71} + 12 q^{73} - 3 q^{77} - 21 q^{79} + 18 q^{83} - 24 q^{85} + 36 q^{89} + 60 q^{91} + 39 q^{95} - 27 q^{97}+O(q^{100}) \) 12 * q - 3 * q^7 + 3 * q^11 - 3 * q^13 + 18 * q^17 + 18 * q^19 + 6 * q^23 - 18 * q^25 + 3 * q^29 - 24 * q^31 - 30 * q^35 + 30 * q^37 - 21 * q^41 - 18 * q^43 + 6 * q^47 - 21 * q^49 + 24 * q^53 + 36 * q^55 + 12 * q^59 - 18 * q^61 - 33 * q^65 - 24 * q^67 - 30 * q^71 + 12 * q^73 - 3 * q^77 - 21 * q^79 + 18 * q^83 - 24 * q^85 + 36 * q^89 + 60 * q^91 + 39 * q^95 - 27 * q^97

Introduction

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