LMFDB - Embedded newform 324.3.k.a.17.5

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [324,3,Mod(17,324)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(324, base_ring=CyclotomicField(18))

chi = DirichletCharacter(H, H._module([0, 11]))

N = Newforms(chi, 3, names="a")

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

chi := DirichletCharacter("324.17");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 324 = 2^{2} \cdot 3^{4} $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	324.k (of order $18$, degree $6$, 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:	$8.82836056527$
Analytic rank:	$0$
Dimension:	$36$
Relative dimension:	$6$ over $\Q(\zeta_{18})$
Twist minimal:	no (minimal twist has level 108)
Sato-Tate group:	$\mathrm{SU}(2)[C_{18}]$

Embedding invariants

Embedding label			17.5
Character	$\chi$	$=$	324.17
Dual form			324.3.k.a.305.5

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(5.13754 + 0.905886i) q^{5} +(-8.93347 + 7.49607i) q^{7} +O(q^{10})$	$q+(5.13754 + 0.905886i) q^{5} +(-8.93347 + 7.49607i) q^{7} +(-16.7592 + 2.95510i) q^{11} +(-12.2141 + 4.44559i) q^{13} +(24.5630 + 14.1815i) q^{17} +(-13.9412 - 24.1469i) q^{19} +(-6.09173 + 7.25984i) q^{23} +(2.08134 + 0.757544i) q^{25} +(-4.43920 + 12.1966i) q^{29} +(11.4748 + 9.62853i) q^{31} +(-52.6866 + 30.4186i) q^{35} +(-19.3390 + 33.4961i) q^{37} +(0.663254 + 1.82228i) q^{41} +(9.15032 + 51.8940i) q^{43} +(-1.66892 - 1.98894i) q^{47} +(15.1070 - 85.6762i) q^{49} +14.7096i q^{53} -88.7782 q^{55} +(16.7995 + 2.96221i) q^{59} +(-17.6298 + 14.7932i) q^{61} +(-66.7778 + 11.7747i) q^{65} +(50.8610 - 18.5119i) q^{67} +(73.9041 + 42.6686i) q^{71} +(-1.73700 - 3.00857i) q^{73} +(127.566 - 152.028i) q^{77} +(-15.2280 - 5.54254i) q^{79} +(31.4813 - 86.4941i) q^{83} +(113.347 + 95.1090i) q^{85} +(55.7558 - 32.1906i) q^{89} +(75.7903 - 131.273i) q^{91} +(-49.7492 - 136.685i) q^{95} +(7.70330 + 43.6876i) q^{97} +O(q^{100})$
$\operatorname{Tr}(f)(q)$	$=$	$ 36 q + 9 q^{5}+O(q^{10}) $ 36 * q + 9 * q^5	$ 36 q + 9 q^{5} - 36 q^{11} + 18 q^{23} - 9 q^{25} + 18 q^{29} + 45 q^{31} + 243 q^{35} + 198 q^{41} + 90 q^{43} + 243 q^{47} + 72 q^{49} - 252 q^{59} - 144 q^{61} - 747 q^{65} + 108 q^{67} - 324 q^{71} - 63 q^{73} - 495 q^{77} + 36 q^{79} + 27 q^{83} - 180 q^{85} + 567 q^{89} + 99 q^{91} + 1044 q^{95} - 216 q^{97}+O(q^{100}) $ 36 * q + 9 * q^5 - 36 * q^11 + 18 * q^23 - 9 * q^25 + 18 * q^29 + 45 * q^31 + 243 * q^35 + 198 * q^41 + 90 * q^43 + 243 * q^47 + 72 * q^49 - 252 * q^59 - 144 * q^61 - 747 * q^65 + 108 * q^67 - 324 * q^71 - 63 * q^73 - 495 * q^77 + 36 * q^79 + 27 * q^83 - 180 * q^85 + 567 * q^89 + 99 * q^91 + 1044 * q^95 - 216 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/324\mathbb{Z}\right)^\times$.

$n$	$163$	$245$
$\chi(n)$	$1$	$e\left(\frac{11}{18}\right)$

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
$5$	5.13754	+	0.905886i	1.02751	+	0.181177i	0.661900	−	0.749592i	$-0.269750\pi$
$5$	5.13754	+	0.905886i	1.02751	+	0.181177i	0.365607	+	0.930769i	$0.380861\pi$
$6$		0			0
$7$	−8.93347	+	7.49607i	−1.27621	+	1.07087i	−0.282455	+	0.959281i	$0.591149\pi$
$7$	−8.93347	+	7.49607i	−1.27621	+	1.07087i	−0.993755	+	0.111586i	$0.964407\pi$
$8$		0			0
$9$		0			0
$10$		0			0
$11$	−16.7592	+	2.95510i	−1.52357	+	0.268646i	−0.871833	−	0.489803i	$-0.837069\pi$
$11$	−16.7592	+	2.95510i	−1.52357	+	0.268646i	−0.651733	+	0.758448i	$0.725958\pi$
$12$		0			0
$13$	−12.2141	+	4.44559i	−0.939550	+	0.341968i	−0.765988	−	0.642855i	$-0.777750\pi$
$13$	−12.2141	+	4.44559i	−0.939550	+	0.341968i	−0.173562	+	0.984823i	$0.555528\pi$
$14$		0			0
$15$		0			0
$16$		0			0
$17$	24.5630	+	14.1815i	1.44488	+	0.834203i	0.998170	−	0.0604744i	$-0.0192613\pi$
$17$	24.5630	+	14.1815i	1.44488	+	0.834203i	0.446713	+	0.894678i	$0.352595\pi$
$18$		0			0
$19$	−13.9412	−	24.1469i	−0.733749	−	1.27089i	−0.955270	−	0.295735i	$-0.904435\pi$
$19$	−13.9412	−	24.1469i	−0.733749	−	1.27089i	0.221521	−	0.975156i	$-0.428898\pi$
$20$		0			0
$21$		0			0
$22$		0			0
$23$	−6.09173	+	7.25984i	−0.264858	+	0.315645i	−0.882040	−	0.471175i	$-0.843830\pi$
$23$	−6.09173	+	7.25984i	−0.264858	+	0.315645i	0.617182	+	0.786821i	$0.288274\pi$
$24$		0			0
$25$	2.08134	+	0.757544i	0.0832534	+	0.0303018i
$26$		0			0
$27$		0			0
$28$		0			0
$29$	−4.43920	+	12.1966i	−0.153076	+	0.420573i	−0.992399	−	0.123060i	$-0.960729\pi$
$29$	−4.43920	+	12.1966i	−0.153076	+	0.420573i	0.839323	+	0.543633i	$0.182951\pi$
$30$		0			0
$31$	11.4748	+	9.62853i	0.370156	+	0.310598i	0.808823	−	0.588052i	$-0.200105\pi$
$31$	11.4748	+	9.62853i	0.370156	+	0.310598i	−0.438667	+	0.898650i	$0.644549\pi$
$32$		0			0
$33$		0			0
$34$		0			0
$35$	−52.6866	+	30.4186i	−1.50533	+	0.869103i
$36$		0			0
$37$	−19.3390	+	33.4961i	−0.522676	+	0.905301i	0.476976	+	0.878916i	$0.341733\pi$
$37$	−19.3390	+	33.4961i	−0.522676	+	0.905301i	−0.999652	+	0.0263844i	$0.991601\pi$
$38$		0			0
$39$		0			0
$40$		0			0
$41$	0.663254	+	1.82228i	0.0161769	+	0.0444458i	0.947518	−	0.319702i	$-0.103583\pi$
$41$	0.663254	+	1.82228i	0.0161769	+	0.0444458i	−0.931341	+	0.364147i	$0.881360\pi$
$42$		0			0
$43$	9.15032	+	51.8940i	0.212798	+	1.20684i	0.884687	+	0.466186i	$0.154372\pi$
$43$	9.15032	+	51.8940i	0.212798	+	1.20684i	−0.671889	+	0.740652i	$0.734517\pi$
$44$		0			0
$45$		0			0
$46$		0			0
$47$	−1.66892	−	1.98894i	−0.0355088	−	0.0423178i	0.747998	−	0.663701i	$-0.231015\pi$
$47$	−1.66892	−	1.98894i	−0.0355088	−	0.0423178i	−0.783507	+	0.621383i	$0.786571\pi$
$48$		0			0
$49$	15.1070	−	85.6762i	0.308306	−	1.74849i
$50$		0			0
$51$		0			0
$52$		0			0
$53$			14.7096i			0.277539i	0.990325	+	0.138770i	$0.0443147\pi$
$53$			14.7096i			0.277539i	−0.990325	+	0.138770i	$0.955685\pi$
$54$		0			0
$55$	−88.7782			−1.61415
$56$		0			0
$57$		0			0
$58$		0			0
$59$	16.7995	+	2.96221i	0.284738	+	0.0502070i	0.314193	−	0.949359i	$-0.398266\pi$
$59$	16.7995	+	2.96221i	0.284738	+	0.0502070i	−0.0294551	+	0.999566i	$0.509377\pi$
$60$		0			0
$61$	−17.6298	+	14.7932i	−0.289013	+	0.242511i	−0.775754	−	0.631036i	$-0.782630\pi$
$61$	−17.6298	+	14.7932i	−0.289013	+	0.242511i	0.486741	+	0.873547i	$0.338186\pi$
$62$		0			0
$63$		0			0
$64$		0			0
$65$	−66.7778	+	11.7747i	−1.02735	+	0.181150i
$66$		0			0
$67$	50.8610	−	18.5119i	0.759119	−	0.276297i	0.0666813	−	0.997774i	$-0.478759\pi$
$67$	50.8610	−	18.5119i	0.759119	−	0.276297i	0.692438	+	0.721478i	$0.256537\pi$
$68$		0			0
$69$		0			0
$70$		0			0
$71$	73.9041	+	42.6686i	1.04090	+	0.600966i	0.920089	−	0.391710i	$-0.128116\pi$
$71$	73.9041	+	42.6686i	1.04090	+	0.600966i	0.120814	+	0.992675i	$0.461450\pi$
$72$		0			0
$73$	−1.73700	−	3.00857i	−0.0237945	−	0.0412132i	0.853883	−	0.520465i	$-0.174241\pi$
$73$	−1.73700	−	3.00857i	−0.0237945	−	0.0412132i	−0.877677	+	0.479252i	$0.840908\pi$
$74$		0			0
$75$		0			0
$76$		0			0
$77$	127.566	−	152.028i	1.65671	−	1.97439i
$78$		0			0
$79$	−15.2280	−	5.54254i	−0.192759	−	0.0701587i	0.243837	−	0.969816i	$-0.421594\pi$
$79$	−15.2280	−	5.54254i	−0.192759	−	0.0701587i	−0.436596	+	0.899658i	$0.643816\pi$
$80$		0			0
$81$		0			0
$82$		0			0
$83$	31.4813	−	86.4941i	0.379292	−	1.04210i	−0.592358	−	0.805675i	$-0.701803\pi$
$83$	31.4813	−	86.4941i	0.379292	−	1.04210i	0.971650	−	0.236422i	$-0.0759749\pi$
$84$		0			0
$85$	113.347	+	95.1090i	1.33349	+	1.11893i
$86$		0			0
$87$		0			0
$88$		0			0
$89$	55.7558	−	32.1906i	0.626469	−	0.361692i	−0.152914	−	0.988239i	$-0.548866\pi$
$89$	55.7558	−	32.1906i	0.626469	−	0.361692i	0.779383	+	0.626547i	$0.215532\pi$
$90$		0			0
$91$	75.7903	−	131.273i	0.832860	−	1.44256i
$92$		0			0
$93$		0			0
$94$		0			0
$95$	−49.7492	−	136.685i	−0.523676	−	1.43879i
$96$		0			0
$97$	7.70330	+	43.6876i	0.0794154	+	0.450387i	0.998423	+	0.0561463i	$0.0178813\pi$
$97$	7.70330	+	43.6876i	0.0794154	+	0.450387i	−0.919007	+	0.394241i	$0.871008\pi$
$98$		0			0
$99$		0			0
$100$		0			0
$101$	−4.15348	−	4.94993i	−0.0411236	−	0.0490092i	0.745091	−	0.666963i	$-0.232406\pi$
$101$	−4.15348	−	4.94993i	−0.0411236	−	0.0490092i	−0.786214	+	0.617954i	$0.787962\pi$
$102$		0			0
$103$	3.14264	−	17.8228i	0.0305111	−	0.173037i	−0.965744	−	0.259495i	$-0.916444\pi$
$103$	3.14264	−	17.8228i	0.0305111	−	0.173037i	0.996255	+	0.0864583i	$0.0275549\pi$
$104$		0			0
$105$		0			0
$106$		0			0
$107$			184.373i			1.72311i	0.507661	+	0.861557i	$0.330510\pi$
$107$			184.373i			1.72311i	−0.507661	+	0.861557i	$0.669490\pi$
$108$		0			0
$109$	−13.0774			−0.119976			−0.0599882	−	0.998199i	$-0.519106\pi$
$109$	−13.0774			−0.119976			−0.0599882	+	0.998199i	$0.519106\pi$
$110$		0			0
$111$		0			0
$112$		0			0
$113$	30.9310	+	5.45397i	0.273726	+	0.0482652i	0.308826	−	0.951119i	$-0.400064\pi$
$113$	30.9310	+	5.45397i	0.273726	+	0.0482652i	−0.0351002	+	0.999384i	$0.511175\pi$
$114$		0			0
$115$	−37.8731	+	31.7793i	−0.329331	+	0.276342i
$116$		0			0
$117$		0			0
$118$		0			0
$119$	−325.738	+	57.4364i	−2.73729	+	0.482659i
$120$		0			0
$121$	158.436	−	57.6661i	1.30939	−	0.476580i
$122$		0			0
$123$		0			0
$124$		0			0
$125$	−102.940	−	59.4325i	−0.823521	−	0.475460i
$126$		0			0
$127$	−52.0434	−	90.1418i	−0.409790	−	0.709778i	0.585076	−	0.810979i	$-0.301065\pi$
$127$	−52.0434	−	90.1418i	−0.409790	−	0.709778i	−0.994866	+	0.101201i	$0.967731\pi$
$128$		0			0
$129$		0			0
$130$		0			0
$131$	−29.7988	+	35.5129i	−0.227472	+	0.271091i	−0.867693	−	0.497100i	$-0.834398\pi$
$131$	−29.7988	+	35.5129i	−0.227472	+	0.271091i	0.640221	+	0.768191i	$0.278843\pi$
$132$		0			0
$133$	305.551	+	111.211i	2.29737	+	0.836175i
$134$		0			0
$135$		0			0
$136$		0			0
$137$	75.3084	−	206.908i	0.549697	−	1.51028i	−0.284425	−	0.958698i	$-0.591803\pi$
$137$	75.3084	−	206.908i	0.549697	−	1.51028i	0.834121	−	0.551581i	$-0.185975\pi$
$138$		0			0
$139$	−137.198	−	115.123i	−0.987037	−	0.828222i	−0.00190072	−	0.999998i	$-0.500605\pi$
$139$	−137.198	−	115.123i	−0.987037	−	0.828222i	−0.985136	+	0.171776i	$0.945049\pi$
$140$		0			0
$141$		0			0
$142$		0			0
$143$	191.563	−	110.599i	1.33960	−	0.773417i
$144$		0			0
$145$	−33.8553	+	58.6391i	−0.233485	+	0.404408i
$146$		0			0
$147$		0			0
$148$		0			0
$149$	48.9623	+	134.523i	0.328606	+	0.902837i	0.988465	+	0.151448i	$0.0483936\pi$
$149$	48.9623	+	134.523i	0.328606	+	0.902837i	−0.659859	+	0.751389i	$0.729384\pi$
$150$		0			0
$151$	12.9241	+	73.2964i	0.0855903	+	0.485407i	0.997228	+	0.0744111i	$0.0237077\pi$
$151$	12.9241	+	73.2964i	0.0855903	+	0.485407i	−0.911637	+	0.410995i	$0.865181\pi$
$152$		0			0
$153$		0			0
$154$		0			0
$155$	50.2300	+	59.8618i	0.324065	+	0.386205i
$156$		0			0
$157$	5.61396	−	31.8383i	0.0357577	−	0.202792i	−0.961695	−	0.274121i	$-0.911613\pi$
$157$	5.61396	−	31.8383i	0.0357577	−	0.202792i	0.997453	+	0.0713294i	$0.0227241\pi$
$158$		0			0
$159$		0			0
$160$		0			0
$161$		−	110.520i		−	0.686457i
$162$		0			0
$163$	99.7820			0.612160			0.306080	−	0.952006i	$-0.400983\pi$
$163$	99.7820			0.612160			0.306080	+	0.952006i	$0.400983\pi$
$164$		0			0
$165$		0			0
$166$		0			0
$167$	165.964	+	29.2639i	0.993795	+	0.175233i	0.646821	−	0.762642i	$-0.276098\pi$
$167$	165.964	+	29.2639i	0.993795	+	0.175233i	0.346974	+	0.937875i	$0.387209\pi$
$168$		0			0
$169$	−0.0393605	+	0.0330274i	−0.000232903	+	0.000195428i
$170$		0			0
$171$		0			0
$172$		0			0
$173$	134.040	−	23.6349i	0.774800	−	0.136618i	0.227752	−	0.973719i	$-0.426863\pi$
$173$	134.040	−	23.6349i	0.774800	−	0.136618i	0.547048	+	0.837101i	$0.315751\pi$
$174$		0			0
$175$	−24.2721	+	8.83434i	−0.138698	+	0.0504819i
$176$		0			0
$177$		0			0
$178$		0			0
$179$	−81.1087	−	46.8281i	−0.453121	−	0.261610i	0.256026	−	0.966670i	$-0.417587\pi$
$179$	−81.1087	−	46.8281i	−0.453121	−	0.261610i	−0.709147	+	0.705060i	$0.750920\pi$
$180$		0			0
$181$	−8.38226	−	14.5185i	−0.0463108	−	0.0802127i	0.841941	−	0.539570i	$-0.181413\pi$
$181$	−8.38226	−	14.5185i	−0.0463108	−	0.0802127i	−0.888252	+	0.459357i	$0.848080\pi$
$182$		0			0
$183$		0			0
$184$		0			0
$185$	−129.698	+	154.569i	−0.701073	+	0.835506i
$186$		0			0
$187$	−453.565	−	165.084i	−2.42548	−	0.882802i
$188$		0			0
$189$		0			0
$190$		0			0
$191$	−35.4147	+	97.3010i	−0.185417	+	0.509430i	−0.997221	−	0.0745008i	$-0.976264\pi$
$191$	−35.4147	+	97.3010i	−0.185417	+	0.509430i	0.811804	+	0.583930i	$0.198486\pi$
$192$		0			0
$193$	−179.148	−	150.323i	−0.928228	−	0.778876i	0.0472702	−	0.998882i	$-0.484948\pi$
$193$	−179.148	−	150.323i	−0.928228	−	0.778876i	−0.975498	+	0.220006i	$0.929392\pi$
$194$		0			0
$195$		0			0
$196$		0			0
$197$	−193.515	+	111.726i	−0.982309	+	0.567136i	−0.902966	−	0.429711i	$-0.858615\pi$
$197$	−193.515	+	111.726i	−0.982309	+	0.567136i	−0.0793425	+	0.996847i	$0.525282\pi$
$198$		0			0
$199$	−167.619	+	290.325i	−0.842306	+	1.45892i	0.0456336	+	0.998958i	$0.485469\pi$
$199$	−167.619	+	290.325i	−0.842306	+	1.45892i	−0.887940	+	0.459959i	$0.847864\pi$
$200$		0			0
$201$		0			0
$202$		0			0
$203$	−51.7691	−	142.235i	−0.255020	−	0.700663i
$204$		0			0
$205$	1.75672	+	9.96284i	0.00856936	+	0.0485992i
$206$		0			0
$207$		0			0
$208$		0			0
$209$	305.001	+	363.486i	1.45934	+	1.73917i
$210$		0			0
$211$	−70.9699	+	402.490i	−0.336350	+	1.90754i	0.0771240	+	0.997022i	$0.475426\pi$
$211$	−70.9699	+	402.490i	−0.336350	+	1.90754i	−0.413474	+	0.910516i	$0.635685\pi$
$212$		0			0
$213$		0			0
$214$		0			0
$215$			274.897i			1.27859i
$216$		0			0
$217$	−174.686			−0.805005
$218$		0			0
$219$		0			0
$220$		0			0
$221$	−363.061	−	64.0174i	−1.64281	−	0.289672i
$222$		0			0
$223$	120.793	−	101.358i	0.541674	−	0.454518i	−0.330436	−	0.943828i	$-0.607196\pi$
$223$	120.793	−	101.358i	0.541674	−	0.454518i	0.872110	+	0.489310i	$0.162751\pi$
$224$		0			0
$225$		0			0
$226$		0			0
$227$	−277.370	+	48.9078i	−1.22189	+	0.215453i	−0.747141	−	0.664666i	$-0.768574\pi$
$227$	−277.370	+	48.9078i	−1.22189	+	0.215453i	−0.474753	+	0.880119i	$0.657463\pi$
$228$		0			0
$229$	−108.465	+	39.4779i	−0.473645	+	0.172393i	−0.567803	−	0.823165i	$-0.692206\pi$
$229$	−108.465	+	39.4779i	−0.473645	+	0.172393i	0.0941577	+	0.995557i	$0.469984\pi$
$230$		0			0
$231$		0			0
$232$		0			0
$233$	195.583	+	112.920i	0.839414	+	0.484636i	0.857065	−	0.515208i	$-0.172285\pi$
$233$	195.583	+	112.920i	0.839414	+	0.484636i	−0.0176510	+	0.999844i	$0.505619\pi$
$234$		0			0
$235$	−6.77236	−	11.7301i	−0.0288186	−	0.0499152i
$236$		0			0
$237$		0			0
$238$		0			0
$239$	113.450	−	135.204i	0.474685	−	0.565707i	−0.474569	−	0.880218i	$-0.657396\pi$
$239$	113.450	−	135.204i	0.474685	−	0.565707i	0.949254	+	0.314511i	$0.101841\pi$
$240$		0			0
$241$	−66.1775	−	24.0866i	−0.274596	−	0.0999446i	0.201052	−	0.979581i	$-0.435564\pi$
$241$	−66.1775	−	24.0866i	−0.274596	−	0.0999446i	−0.475647	+	0.879636i	$0.657786\pi$
$242$		0			0
$243$		0			0
$244$		0			0
$245$	155.226	−	426.479i	0.633574	−	1.74073i
$246$		0			0
$247$	277.628	+	232.957i	1.12400	+	0.943146i
$248$		0			0
$249$		0			0
$250$		0			0
$251$	−239.695	+	138.388i	−0.954959	+	0.551346i	−0.894618	−	0.446832i	$-0.852552\pi$
$251$	−239.695	+	138.388i	−0.954959	+	0.551346i	−0.0603413	+	0.998178i	$0.519219\pi$
$252$		0			0
$253$	80.6391	−	139.671i	0.318732	−	0.552060i
$254$		0			0
$255$		0			0
$256$		0			0
$257$	125.873	+	345.834i	0.489780	+	1.34566i	0.900880	+	0.434069i	$0.142923\pi$
$257$	125.873	+	345.834i	0.489780	+	1.34566i	−0.411100	+	0.911590i	$0.634855\pi$
$258$		0			0
$259$	−78.3250	−	444.203i	−0.302413	−	1.71507i
$260$		0			0
$261$		0			0
$262$		0			0
$263$	237.412	+	282.937i	0.902709	+	1.07581i	0.996776	+	0.0802408i	$0.0255689\pi$
$263$	237.412	+	282.937i	0.902709	+	1.07581i	−0.0940665	+	0.995566i	$0.529987\pi$
$264$		0			0
$265$	−13.3252	+	75.5710i	−0.0502838	+	0.285173i
$266$		0			0
$267$		0			0
$268$		0			0
$269$		−	484.753i		−	1.80205i	−0.433762	−	0.901027i	$-0.642814\pi$
$269$		−	484.753i		−	1.80205i	0.433762	−	0.901027i	$-0.357186\pi$
$270$		0			0
$271$	361.878			1.33534			0.667672	−	0.744455i	$-0.267291\pi$
$271$	361.878			1.33534			0.667672	+	0.744455i	$0.267291\pi$
$272$		0			0
$273$		0			0
$274$		0			0
$275$	−37.1202	−	6.54529i	−0.134983	−	0.0238011i
$276$		0			0
$277$	−158.794	+	133.244i	−0.573263	+	0.481024i	−0.882727	−	0.469887i	$-0.844295\pi$
$277$	−158.794	+	133.244i	−0.573263	+	0.481024i	0.309464	+	0.950911i	$0.399850\pi$
$278$		0			0
$279$		0			0
$280$		0			0
$281$	−323.449	+	57.0328i	−1.15106	+	0.202964i	−0.716440	−	0.697648i	$-0.754230\pi$
$281$	−323.449	+	57.0328i	−1.15106	+	0.202964i	−0.434624	+	0.900612i	$0.643119\pi$
$282$		0			0
$283$	−88.6536	+	32.2673i	−0.313264	+	0.114019i	−0.493867	−	0.869537i	$-0.664417\pi$
$283$	−88.6536	+	32.2673i	−0.313264	+	0.114019i	0.180604	+	0.983556i	$0.442195\pi$
$284$		0			0
$285$		0			0
$286$		0			0
$287$	−19.5851	−	11.3074i	−0.0682407	−	0.0393988i
$288$		0			0
$289$	257.727	+	446.397i	0.891790	+	1.54463i
$290$		0			0
$291$		0			0
$292$		0			0
$293$	−267.257	+	318.504i	−0.912139	+	1.08704i	0.0837526	+	0.996487i	$0.473309\pi$
$293$	−267.257	+	318.504i	−0.912139	+	1.08704i	−0.995891	+	0.0905579i	$0.971135\pi$
$294$		0			0
$295$	83.6248	+	30.4369i	0.283474	+	0.103176i
$296$		0			0
$297$		0			0
$298$		0			0
$299$	42.1310	−	115.754i	0.140907	−	0.387137i
$300$		0			0
$301$	−470.745	−	395.002i	−1.56394	−	1.31230i
$302$		0			0
$303$		0			0
$304$		0			0
$305$	−103.975	+	60.0298i	−0.340900	+	0.196819i
$306$		0			0
$307$	259.704	−	449.820i	0.845941	−	1.46521i	−0.0388611	−	0.999245i	$-0.512373\pi$
$307$	259.704	−	449.820i	0.845941	−	1.46521i	0.884802	−	0.465968i	$-0.154294\pi$
$308$		0			0
$309$		0			0
$310$		0			0
$311$	23.9377	+	65.7684i	0.0769702	+	0.211474i	0.972210	−	0.234111i	$-0.0752179\pi$
$311$	23.9377	+	65.7684i	0.0769702	+	0.211474i	−0.895240	+	0.445585i	$0.852996\pi$
$312$		0			0
$313$	−52.1791	−	295.923i	−0.166706	−	0.945439i	−0.947287	−	0.320385i	$-0.896188\pi$
$313$	−52.1791	−	295.923i	−0.166706	−	0.945439i	0.780581	−	0.625055i	$-0.214923\pi$
$314$		0			0
$315$		0			0
$316$		0			0
$317$	281.650	+	335.657i	0.888485	+	1.05886i	0.997894	+	0.0648589i	$0.0206597\pi$
$317$	281.650	+	335.657i	0.888485	+	1.05886i	−0.109409	+	0.993997i	$0.534896\pi$
$318$		0			0
$319$	38.3554	−	217.524i	0.120236	−	0.681894i
$320$		0			0
$321$		0			0
$322$		0			0
$323$		−	790.828i		−	2.44838i
$324$		0			0
$325$	−28.7895			−0.0885830
$326$		0			0
$327$		0			0
$328$		0			0
$329$	29.8184	+	5.25779i	0.0906334	+	0.0159811i
$330$		0			0
$331$	83.1781	−	69.7947i	0.251293	−	0.210860i	−0.508436	−	0.861100i	$-0.669776\pi$
$331$	83.1781	−	69.7947i	0.251293	−	0.210860i	0.759729	+	0.650240i	$0.225332\pi$
$332$		0			0
$333$		0			0
$334$		0			0
$335$	278.070	−	49.0312i	0.830059	−	0.146362i
$336$		0			0
$337$	−515.109	+	187.484i	−1.52851	+	0.556334i	−0.963257	−	0.268581i	$-0.913445\pi$
$337$	−515.109	+	187.484i	−1.52851	+	0.556334i	−0.565257	+	0.824915i	$0.691223\pi$
$338$		0			0
$339$		0			0
$340$		0			0
$341$	−220.763	−	127.457i	−0.647398	−	0.373775i
$342$		0			0
$343$	221.562	+	383.756i	0.645953	+	1.11882i
$344$		0			0
$345$		0			0
$346$		0			0
$347$	−153.713	+	183.189i	−0.442978	+	0.527921i	−0.940620	−	0.339462i	$-0.889755\pi$
$347$	−153.713	+	183.189i	−0.442978	+	0.527921i	0.497642	+	0.867383i	$0.334199\pi$
$348$		0			0
$349$	431.921	+	157.206i	1.23760	+	0.450448i	0.876192	−	0.481962i	$-0.160076\pi$
$349$	431.921	+	157.206i	1.23760	+	0.450448i	0.361403	+	0.932410i	$0.382298\pi$
$350$		0			0
$351$		0			0
$352$		0			0
$353$	144.709	−	397.585i	0.409940	−	1.12630i	−0.547282	−	0.836948i	$-0.684337\pi$
$353$	144.709	−	397.585i	0.409940	−	1.12630i	0.957222	−	0.289354i	$-0.0934404\pi$
$354$		0			0
$355$	341.032	+	286.160i	0.960654	+	0.806084i
$356$		0			0
$357$		0			0
$358$		0			0
$359$	585.472	−	338.023i	1.63084	−	0.941567i	0.647008	−	0.762483i	$-0.276020\pi$
$359$	585.472	−	338.023i	1.63084	−	0.941567i	0.983834	−	0.179084i	$-0.0573134\pi$
$360$		0			0
$361$	−208.216	+	360.641i	−0.576776	+	0.999005i
$362$		0			0
$363$		0			0
$364$		0			0
$365$	−6.19846	−	17.0301i	−0.0169821	−	0.0466579i
$366$		0			0
$367$	80.7428	+	457.915i	0.220008	+	1.24772i	0.872002	+	0.489501i	$0.162821\pi$
$367$	80.7428	+	457.915i	0.220008	+	1.24772i	−0.651995	+	0.758223i	$0.726068\pi$
$368$		0			0
$369$		0			0
$370$		0			0
$371$	−110.264	−	131.407i	−0.297207	−	0.354198i
$372$		0			0
$373$	−13.5537	+	76.8670i	−0.0363371	+	0.206078i	−0.997571	−	0.0696562i	$-0.977810\pi$
$373$	−13.5537	+	76.8670i	−0.0363371	+	0.206078i	0.961234	+	0.275734i	$0.0889209\pi$
$374$		0			0
$375$		0			0
$376$		0			0
$377$		−	168.706i		−	0.447496i
$378$		0			0
$379$	66.6563			0.175874			0.0879371	−	0.996126i	$-0.471973\pi$
$379$	66.6563			0.175874			0.0879371	+	0.996126i	$0.471973\pi$
$380$		0			0
$381$		0			0
$382$		0			0
$383$	−82.5111	−	14.5489i	−0.215434	−	0.0379868i	0.0648895	−	0.997892i	$-0.479331\pi$
$383$	−82.5111	−	14.5489i	−0.215434	−	0.0379868i	−0.280323	+	0.959906i	$0.590442\pi$
$384$		0			0
$385$	793.097	−	665.487i	2.05999	−	1.72854i
$386$		0			0
$387$		0			0
$388$		0			0
$389$	523.234	−	92.2603i	1.34507	−	0.237173i	0.545687	−	0.837989i	$-0.316269\pi$
$389$	523.234	−	92.2603i	1.34507	−	0.237173i	0.799387	+	0.600816i	$0.205158\pi$
$390$		0			0
$391$	−252.586	+	91.9339i	−0.646001	+	0.235125i
$392$		0			0
$393$		0			0
$394$		0			0
$395$	−73.2135	−	42.2698i	−0.185351	−	0.107012i
$396$		0			0
$397$	−230.531	−	399.291i	−0.580682	−	1.00577i	−0.995399	−	0.0958197i	$-0.969453\pi$
$397$	−230.531	−	399.291i	−0.580682	−	1.00577i	0.414717	−	0.909950i	$-0.363881\pi$
$398$		0			0
$399$		0			0
$400$		0			0
$401$	−127.933	+	152.465i	−0.319036	+	0.380212i	−0.901599	−	0.432574i	$-0.857606\pi$
$401$	−127.933	+	152.465i	−0.319036	+	0.380212i	0.582563	+	0.812786i	$0.302050\pi$
$402$		0			0
$403$	−182.960	−	66.5919i	−0.453994	−	0.165240i
$404$		0			0
$405$		0			0
$406$		0			0
$407$	225.122	−	618.518i	0.553126	−	1.51970i
$408$		0			0
$409$	95.6855	+	80.2897i	0.233950	+	0.196307i	0.752224	−	0.658907i	$-0.228981\pi$
$409$	95.6855	+	80.2897i	0.233950	+	0.196307i	−0.518274	+	0.855214i	$0.673425\pi$
$410$		0			0
$411$		0			0
$412$		0			0
$413$	−172.283	+	99.4676i	−0.417150	+	0.240842i
$414$		0			0
$415$	240.090	−	415.848i	0.578530	−	1.00204i
$416$		0			0
$417$		0			0
$418$		0			0
$419$	2.14955	+	5.90584i	0.00513019	+	0.0140951i	0.942231	−	0.334963i	$-0.108724\pi$
$419$	2.14955	+	5.90584i	0.00513019	+	0.0140951i	−0.937101	+	0.349058i	$0.886502\pi$
$420$		0			0
$421$	−70.5491	−	400.104i	−0.167575	−	0.950365i	−0.946370	−	0.323086i	$-0.895280\pi$
$421$	−70.5491	−	400.104i	−0.167575	−	0.950365i	0.778795	−	0.627279i	$-0.215831\pi$
$422$		0			0
$423$		0			0
$424$		0			0
$425$	40.3808	+	48.1239i	0.0950136	+	0.113233i
$426$		0			0
$427$	46.6047	−	264.308i	0.109144	−	0.618989i
$428$		0			0
$429$		0			0
$430$		0			0
$431$			605.028i			1.40378i	0.712287	+	0.701889i	$0.247660\pi$
$431$			605.028i			1.40378i	−0.712287	+	0.701889i	$0.752340\pi$
$432$		0			0
$433$	535.568			1.23688			0.618439	−	0.785833i	$-0.287766\pi$
$433$	535.568			1.23688			0.618439	+	0.785833i	$0.287766\pi$
$434$		0			0
$435$		0			0
$436$		0			0
$437$	260.229	+	45.8854i	0.595490	+	0.105001i
$438$		0			0
$439$	−367.682	+	308.522i	−0.837545	+	0.702784i	−0.957010	−	0.290055i	$-0.906326\pi$
$439$	−367.682	+	308.522i	−0.837545	+	0.702784i	0.119465	+	0.992838i	$0.461882\pi$
$440$		0			0
$441$		0			0
$442$		0			0
$443$	−478.290	+	84.3355i	−1.07966	+	0.190373i	−0.685066	−	0.728481i	$-0.740227\pi$
$443$	−478.290	+	84.3355i	−1.07966	+	0.190373i	−0.394596	+	0.918855i	$0.629115\pi$
$444$		0			0
$445$	315.608	−	114.872i	0.709232	−	0.258139i
$446$		0			0
$447$		0			0
$448$		0			0
$449$	−423.011	−	244.226i	−0.942118	−	0.543932i	−0.0514944	−	0.998673i	$-0.516398\pi$
$449$	−423.011	−	244.226i	−0.942118	−	0.543932i	−0.890624	+	0.454741i	$0.849732\pi$
$450$		0			0
$451$	−16.5007	−	28.5800i	−0.0365868	−	0.0633702i
$452$		0			0
$453$		0			0
$454$		0			0
$455$	508.293	−	605.760i	1.11713	−	1.33134i
$456$		0			0
$457$	−561.056	−	204.208i	−1.22769	−	0.446844i	−0.354887	−	0.934909i	$-0.615481\pi$
$457$	−561.056	−	204.208i	−1.22769	−	0.446844i	−0.872807	+	0.488065i	$0.837703\pi$
$458$		0			0
$459$		0			0
$460$		0			0
$461$	−289.819	+	796.271i	−0.628675	+	1.72727i	0.0560100	+	0.998430i	$0.482162\pi$
$461$	−289.819	+	796.271i	−0.628675	+	1.72727i	−0.684685	+	0.728839i	$0.740060\pi$
$462$		0			0
$463$	433.712	+	363.927i	0.936743	+	0.786020i	0.977015	−	0.213168i	$-0.0683783\pi$
$463$	433.712	+	363.927i	0.936743	+	0.786020i	−0.0402729	+	0.999189i	$0.512823\pi$
$464$		0			0
$465$		0			0
$466$		0			0
$467$	265.877	−	153.504i	0.569330	−	0.328703i	−0.187551	−	0.982255i	$-0.560055\pi$
$467$	265.877	−	153.504i	0.569330	−	0.328703i	0.756882	+	0.653552i	$0.226722\pi$
$468$		0			0
$469$	−315.599	+	546.633i	−0.672918	+	1.16553i
$470$		0			0
$471$		0			0
$472$		0			0
$473$	−306.705	−	842.664i	−0.648424	−	1.78153i
$474$		0			0
$475$	−10.7240	−	60.8190i	−0.0225769	−	0.128040i
$476$		0			0
$477$		0			0
$478$		0			0
$479$	239.776	+	285.754i	0.500576	+	0.596564i	0.955875	−	0.293775i	$-0.0949117\pi$
$479$	239.776	+	285.754i	0.500576	+	0.596564i	−0.455298	+	0.890339i	$0.650467\pi$
$480$		0			0
$481$	87.2994	−	495.100i	0.181496	−	1.02931i
$482$		0			0
$483$		0			0
$484$		0			0
$485$			231.425i			0.477164i
$486$		0			0
$487$	596.051			1.22392			0.611962	−	0.790887i	$-0.290381\pi$
$487$	596.051			1.22392			0.611962	+	0.790887i	$0.290381\pi$
$488$		0			0
$489$		0			0
$490$		0			0
$491$	−172.551	−	30.4253i	−0.351427	−	0.0619660i	−0.00485164	−	0.999988i	$-0.501544\pi$
$491$	−172.551	−	30.4253i	−0.351427	−	0.0619660i	−0.346575	+	0.938022i	$0.612655\pi$
$492$		0			0
$493$	−282.006	+	236.631i	−0.572020	+	0.479982i
$494$		0			0
$495$		0			0
$496$		0			0
$497$	−980.066	+	172.812i	−1.97196	+	0.347711i
$498$		0			0
$499$	88.9017	−	32.3576i	0.178160	−	0.0648448i	−0.251400	−	0.967883i	$-0.580891\pi$
$499$	88.9017	−	32.3576i	0.178160	−	0.0648448i	0.429560	+	0.903038i	$0.358669\pi$
$500$		0			0
$501$		0			0
$502$		0			0
$503$	161.807	+	93.4192i	0.321683	+	0.185724i	0.652143	−	0.758096i	$-0.273870\pi$
$503$	161.807	+	93.4192i	0.321683	+	0.185724i	−0.330459	+	0.943820i	$0.607204\pi$
$504$		0			0
$505$	−16.8546	−	29.1930i	−0.0333754	−	0.0578080i
$506$		0			0
$507$		0			0
$508$		0			0
$509$	−289.843	+	345.421i	−0.569435	+	0.678627i	−0.971515	−	0.236978i	$-0.923843\pi$
$509$	−289.843	+	345.421i	−0.569435	+	0.678627i	0.402080	+	0.915605i	$0.368288\pi$
$510$		0			0
$511$	38.0698	+	13.8563i	0.0745006	+	0.0271160i
$512$		0			0
$513$		0			0
$514$		0			0
$515$	32.2909	−	88.7185i	0.0627007	−	0.172269i
$516$		0			0
$517$	33.8473	+	28.4012i	0.0654686	+	0.0549347i
$518$		0			0
$519$		0			0
$520$		0			0
$521$	96.0094	−	55.4311i	0.184279	−	0.106394i	−0.405022	−	0.914307i	$-0.632736\pi$
$521$	96.0094	−	55.4311i	0.184279	−	0.106394i	0.589302	+	0.807913i	$0.299403\pi$
$522$		0			0
$523$	−59.5704	+	103.179i	−0.113901	+	0.197283i	−0.917340	−	0.398104i	$-0.869668\pi$
$523$	−59.5704	+	103.179i	−0.113901	+	0.197283i	0.803439	+	0.595388i	$0.203001\pi$
$524$		0			0
$525$		0			0
$526$		0			0
$527$	145.310	+	399.235i	0.275730	+	0.757562i
$528$		0			0
$529$	76.2638	+	432.513i	0.144166	+	0.817605i
$530$		0			0
$531$		0			0
$532$		0			0
$533$	−16.2022	−	19.3090i	−0.0303981	−	0.0362270i
$534$		0			0
$535$	−167.021	+	947.224i	−0.312189	+	1.77051i
$536$		0			0
$537$		0			0
$538$		0			0
$539$			1480.51i			2.74677i
$540$		0			0
$541$	−967.717			−1.78876			−0.894378	−	0.447312i	$-0.852381\pi$
$541$	−967.717			−1.78876			−0.894378	+	0.447312i	$0.852381\pi$
$542$		0			0
$543$		0			0
$544$		0			0
$545$	−67.1857	−	11.8467i	−0.123277	−	0.0217370i
$546$		0			0
$547$	−53.4636	+	44.8613i	−0.0977397	+	0.0820133i	−0.690348	−	0.723477i	$-0.742543\pi$
$547$	−53.4636	+	44.8613i	−0.0977397	+	0.0820133i	0.592608	+	0.805491i	$0.298098\pi$
$548$		0			0
$549$		0			0
$550$		0			0
$551$	356.399	−	62.8427i	0.646821	−	0.114052i
$552$		0			0
$553$	177.586	−	64.6360i	0.321132	−	0.116882i
$554$		0			0
$555$		0			0
$556$		0			0
$557$	−67.9974	−	39.2583i	−0.122078	−	0.0704818i	0.437718	−	0.899113i	$-0.355787\pi$
$557$	−67.9974	−	39.2583i	−0.122078	−	0.0704818i	−0.559796	+	0.828631i	$0.689120\pi$
$558$		0			0
$559$	−342.463	−	593.163i	−0.612635	−	1.06111i
$560$		0			0
$561$		0			0
$562$		0			0
$563$	406.246	−	484.146i	0.721575	−	0.859939i	−0.273208	−	0.961955i	$-0.588085\pi$
$563$	406.246	−	484.146i	0.721575	−	0.859939i	0.994783	+	0.102016i	$0.0325293\pi$
$564$		0			0
$565$	153.969	+	56.0400i	0.272511	+	0.0991858i
$566$		0			0
$567$		0			0
$568$		0			0
$569$	50.9515	−	139.988i	0.0895457	−	0.246025i	−0.886833	−	0.462089i	$-0.847100\pi$
$569$	50.9515	−	139.988i	0.0895457	−	0.246025i	0.976379	+	0.216065i	$0.0693222\pi$
$570$		0			0
$571$	−504.945	−	423.699i	−0.884317	−	0.742030i	0.0827453	−	0.996571i	$-0.473631\pi$
$571$	−504.945	−	423.699i	−0.884317	−	0.742030i	−0.967062	+	0.254541i	$0.918076\pi$
$572$		0			0
$573$		0			0
$574$		0			0
$575$	−18.1786	+	10.4954i	−0.0316149	+	0.0182529i
$576$		0			0
$577$	−125.956	+	218.162i	−0.218295	+	0.378098i	−0.954287	−	0.298893i	$-0.903383\pi$
$577$	−125.956	+	218.162i	−0.218295	+	0.378098i	0.735992	+	0.676990i	$0.236716\pi$
$578$		0			0
$579$		0			0
$580$		0			0
$581$	367.129	+	1008.68i	0.631891	+	1.73611i
$582$		0			0
$583$	−43.4683	−	246.521i	−0.0745597	−	0.422849i
$584$		0			0
$585$		0			0
$586$		0			0
$587$	−309.575	−	368.937i	−0.527385	−	0.628513i	0.434925	−	0.900467i	$-0.356775\pi$
$587$	−309.575	−	368.937i	−0.527385	−	0.628513i	−0.962310	+	0.271953i	$0.912330\pi$
$588$		0			0
$589$	72.5260	−	411.315i	0.123134	−	0.698328i
$590$		0			0
$591$		0			0
$592$		0			0
$593$		−	458.703i		−	0.773529i	−0.922178	−	0.386765i	$-0.873593\pi$
$593$		−	458.703i		−	0.773529i	0.922178	−	0.386765i	$-0.126407\pi$
$594$		0			0
$595$	−1725.52			−2.90004
$596$		0			0
$597$		0			0
$598$		0			0
$599$	−264.076	−	46.5637i	−0.440861	−	0.0777357i	−0.0511881	−	0.998689i	$-0.516301\pi$
$599$	−264.076	−	46.5637i	−0.440861	−	0.0777357i	−0.389673	+	0.920953i	$0.627412\pi$
$600$		0			0
$601$	−596.139	+	500.220i	−0.991913	+	0.832314i	−0.985844	−	0.167668i	$-0.946376\pi$
$601$	−596.139	+	500.220i	−0.991913	+	0.832314i	−0.00606910	+	0.999982i	$0.501932\pi$
$602$		0			0
$603$		0			0
$604$		0			0
$605$	866.212	−	152.736i	1.43175	−	0.252457i
$606$		0			0
$607$	−60.1810	+	21.9041i	−0.0991449	+	0.0360858i	−0.391116	−	0.920341i	$-0.627911\pi$
$607$	−60.1810	+	21.9041i	−0.0991449	+	0.0360858i	0.291971	+	0.956427i	$0.405689\pi$
$608$		0			0
$609$		0			0
$610$		0			0
$611$	29.2264	+	16.8738i	0.0478337	+	0.0276168i
$612$		0			0
$613$	6.41301	+	11.1077i	0.0104617	+	0.0181202i	0.871209	−	0.490913i	$-0.163337\pi$
$613$	6.41301	+	11.1077i	0.0104617	+	0.0181202i	−0.860747	+	0.509033i	$0.830003\pi$
$614$		0			0
$615$		0			0
$616$		0			0
$617$	−109.778	+	130.829i	−0.177923	+	0.212040i	−0.847634	−	0.530582i	$-0.821974\pi$
$617$	−109.778	+	130.829i	−0.177923	+	0.212040i	0.669711	+	0.742622i	$0.266418\pi$
$618$		0			0
$619$	678.707	+	247.029i	1.09646	+	0.399078i	0.826009	−	0.563657i	$-0.190606\pi$
$619$	678.707	+	247.029i	1.09646	+	0.399078i	0.270448	+	0.962734i	$0.412828\pi$
$620$		0			0
$621$		0			0
$622$		0			0
$623$	−256.789	+	705.523i	−0.412182	+	1.13246i
$624$		0			0
$625$	−517.438	−	434.182i	−0.827900	−	0.694691i
$626$		0			0
$627$		0			0
$628$		0			0
$629$	−950.047	+	548.510i	−1.51041	+	0.872035i
$630$		0			0
$631$	−88.4036	+	153.120i	−0.140101	+	0.242662i	−0.927534	−	0.373738i	$-0.878076\pi$
$631$	−88.4036	+	153.120i	−0.140101	+	0.242662i	0.787434	+	0.616399i	$0.211409\pi$
$632$		0			0
$633$		0			0
$634$		0			0
$635$	−185.717	−	510.252i	−0.292467	−	0.803546i
$636$		0			0
$637$	196.361	+	1113.62i	0.308260	+	1.74823i
$638$		0			0
$639$		0			0
$640$		0			0
$641$	−335.280	−	399.571i	−0.523057	−	0.623355i	0.438244	−	0.898856i	$-0.355601\pi$
$641$	−335.280	−	399.571i	−0.523057	−	0.623355i	−0.961301	+	0.275501i	$0.911156\pi$
$642$		0			0
$643$	70.9572	−	402.418i	0.110353	−	0.625844i	−0.878593	−	0.477571i	$-0.841517\pi$
$643$	70.9572	−	402.418i	0.110353	−	0.625844i	0.988946	−	0.148273i	$-0.0473716\pi$
$644$		0			0
$645$		0			0
$646$		0			0
$647$			310.156i			0.479376i	0.970850	+	0.239688i	$0.0770451\pi$
$647$			310.156i			0.479376i	−0.970850	+	0.239688i	$0.922955\pi$
$648$		0			0
$649$	−290.301			−0.447305
$650$		0			0
$651$		0			0
$652$		0			0
$653$	1016.19	+	179.182i	1.55619	+	0.274398i	0.884537	−	0.466471i	$-0.154475\pi$
$653$	1016.19	+	179.182i	1.55619	+	0.274398i	0.671650	+	0.740869i	$0.265586\pi$
$654$		0			0
$655$	−185.263	+	155.454i	−0.282845	+	0.237335i
$656$		0			0
$657$		0			0
$658$		0			0
$659$	−955.212	+	168.430i	−1.44949	+	0.255584i	−0.842315	−	0.538986i	$-0.818808\pi$
$659$	−955.212	+	168.430i	−1.44949	+	0.255584i	−0.607173	+	0.794570i	$0.707696\pi$
$660$		0			0
$661$	658.521	−	239.682i	0.996250	−	0.362605i	0.208113	−	0.978105i	$-0.433268\pi$
$661$	658.521	−	239.682i	0.996250	−	0.362605i	0.788137	+	0.615500i	$0.211046\pi$
$662$		0			0
$663$		0			0
$664$		0			0
$665$	1469.03	+	848.146i	2.20907	+	1.27541i
$666$		0			0
$667$	−61.5030	−	106.526i	−0.0922084	−	0.159710i
$668$		0			0
$669$		0			0
$670$		0			0
$671$	251.747	−	300.020i	0.375181	−	0.447123i
$672$		0			0
$673$	409.377	+	149.001i	0.608287	+	0.221398i	0.627754	−	0.778412i	$-0.283975\pi$
$673$	409.377	+	149.001i	0.608287	+	0.221398i	−0.0194664	+	0.999811i	$0.506197\pi$
$674$		0			0
$675$		0			0
$676$		0			0
$677$	−138.700	+	381.074i	−0.204874	+	0.562887i	−0.998993	−	0.0448762i	$-0.985711\pi$
$677$	−138.700	+	381.074i	−0.204874	+	0.562887i	0.794119	+	0.607763i	$0.207933\pi$
$678$		0			0
$679$	−396.302	−	332.537i	−0.583656	−	0.489745i
$680$		0			0
$681$		0			0
$682$		0			0
$683$	795.421	−	459.236i	1.16460	−	0.672381i	0.212196	−	0.977227i	$-0.431938\pi$
$683$	795.421	−	459.236i	1.16460	−	0.672381i	0.952402	+	0.304846i	$0.0986050\pi$
$684$		0			0
$685$	574.335	−	994.778i	0.838446	−	1.45223i
$686$		0			0
$687$		0			0
$688$		0			0
$689$	−65.3927	−	179.665i	−0.0949095	−	0.260762i
$690$		0			0
$691$	32.3254	+	183.327i	0.0467806	+	0.265306i	0.999223	−	0.0394126i	$-0.0125487\pi$
$691$	32.3254	+	183.327i	0.0467806	+	0.265306i	−0.952442	+	0.304719i	$0.901438\pi$
$692$		0			0
$693$		0			0
$694$		0			0
$695$	−600.572	−	715.734i	−0.864132	−	1.02983i
$696$		0			0
$697$	−9.55101	+	54.1665i	−0.0137030	+	0.0777138i
$698$		0			0
$699$		0			0
$700$		0			0
$701$		−	1096.71i		−	1.56449i	−0.622970	−	0.782246i	$-0.714074\pi$
$701$		−	1096.71i		−	1.56449i	0.622970	−	0.782246i	$-0.285926\pi$
$702$		0			0
$703$	1078.44			1.53405
$704$		0			0
$705$		0			0
$706$		0			0
$707$	74.2100	+	13.0852i	0.104965	+	0.0185081i
$708$		0			0
$709$	−28.7772	+	24.1469i	−0.0405884	+	0.0340577i	−0.662856	−	0.748747i	$-0.730656\pi$
$709$	−28.7772	+	24.1469i	−0.0405884	+	0.0340577i	0.622268	+	0.782804i	$0.286211\pi$
$710$		0			0
$711$		0			0
$712$		0			0
$713$	−139.803	+	24.6511i	−0.196077	+	0.0345737i
$714$		0			0
$715$	1084.35	−	394.671i	1.51657	−	0.551987i
$716$		0			0
$717$		0			0
$718$		0			0
$719$	−62.6620	−	36.1779i	−0.0871516	−	0.0503170i	0.455791	−	0.890087i	$-0.349357\pi$
$719$	−62.6620	−	36.1779i	−0.0871516	−	0.0503170i	−0.542942	+	0.839770i	$0.682690\pi$
$720$		0			0
$721$	105.526	+	182.777i	0.146361	+	0.253505i
$722$		0			0
$723$		0			0
$724$		0			0
$725$	−18.4789	+	22.0223i	−0.0254882	+	0.0303756i
$726$		0			0
$727$	−351.865	−	128.068i	−0.483995	−	0.176160i	0.0884863	−	0.996077i	$-0.471797\pi$
$727$	−351.865	−	128.068i	−0.483995	−	0.176160i	−0.572482	+	0.819917i	$0.694019\pi$
$728$		0			0
$729$		0			0
$730$		0			0
$731$	−511.174	+	1404.44i	−0.699280	+	1.92126i
$732$		0			0
$733$	1086.12	+	911.363i	1.48175	+	1.24333i	0.904295	+	0.426908i	$0.140397\pi$
$733$	1086.12	+	911.363i	1.48175	+	1.24333i	0.577451	+	0.816425i	$0.304047\pi$
$734$		0			0
$735$		0			0
$736$		0			0
$737$	−797.686	+	460.544i	−1.08234	+	0.624891i
$738$		0			0
$739$	382.758	−	662.956i	0.517940	−	0.897098i	−0.481843	−	0.876258i	$-0.660032\pi$
$739$	382.758	−	662.956i	0.517940	−	0.897098i	0.999783	−	0.0208408i	$-0.00663431\pi$
$740$		0			0
$741$		0			0
$742$		0			0
$743$	−111.257	−	305.675i	−0.149740	−	0.411407i	0.842032	−	0.539428i	$-0.181360\pi$
$743$	−111.257	−	305.675i	−0.149740	−	0.411407i	−0.991771	+	0.128021i	$0.959137\pi$
$744$		0			0
$745$	129.683	+	735.470i	0.174071	+	0.987208i
$746$		0			0
$747$		0			0
$748$		0			0
$749$	−1382.07	−	1647.09i	−1.84523	−	2.19905i
$750$		0			0
$751$	−195.557	+	1109.06i	−0.260396	+	1.47678i	0.521436	+	0.853291i	$0.325397\pi$
$751$	−195.557	+	1109.06i	−0.260396	+	1.47678i	−0.781832	+	0.623489i	$0.785714\pi$
$752$		0			0
$753$		0			0
$754$		0			0
$755$			388.271i			0.514266i
$756$		0			0
$757$	−543.494			−0.717957			−0.358979	−	0.933346i	$-0.616875\pi$
$757$	−543.494			−0.717957			−0.358979	+	0.933346i	$0.616875\pi$
$758$		0			0
$759$		0			0
$760$		0			0
$761$	−109.050	−	19.2284i	−0.143298	−	0.0252673i	0.101539	−	0.994832i	$-0.467623\pi$
$761$	−109.050	−	19.2284i	−0.143298	−	0.0252673i	−0.244837	+	0.969564i	$0.578734\pi$
$762$		0			0
$763$	116.827	−	98.0293i	0.153115	−	0.128479i
$764$		0			0
$765$		0			0
$766$		0			0
$767$	−218.361	+	38.5029i	−0.284695	+	0.0501993i
$768$		0			0
$769$	−291.156	+	105.972i	−0.378617	+	0.137805i	−0.524316	−	0.851524i	$-0.675679\pi$
$769$	−291.156	+	105.972i	−0.378617	+	0.137805i	0.145699	+	0.989329i	$0.453457\pi$
$770$		0			0
$771$		0			0
$772$		0			0
$773$	886.108	+	511.595i	1.14632	+	0.661830i	0.947989	−	0.318304i	$-0.103113\pi$
$773$	886.108	+	511.595i	1.14632	+	0.661830i	0.198335	+	0.980134i	$0.436447\pi$
$774$		0			0
$775$	16.5889	+	28.7329i	0.0214051	+	0.0370747i
$776$		0			0
$777$		0			0
$778$		0			0
$779$	34.7558	−	41.4203i	0.0446159	−	0.0531712i
$780$		0			0
$781$	−1364.67	−	496.698i	−1.74733	−	0.635977i
$782$		0			0
$783$		0			0
$784$		0			0
$785$	57.6838	−	158.485i	0.0734826	−	0.201892i
$786$		0			0
$787$	−197.978	−	166.124i	−0.251561	−	0.211085i	0.508283	−	0.861190i	$-0.330280\pi$
$787$	−197.978	−	166.124i	−0.251561	−	0.211085i	−0.759844	+	0.650105i	$0.774725\pi$
$788$		0			0
$789$		0			0
$790$		0			0
$791$	−317.205	+	183.138i	−0.401017	+	0.231527i
$792$		0			0
$793$	149.569	−	259.061i	0.188611	−	0.326684i
$794$		0			0
$795$		0			0
$796$		0			0
$797$	−517.692	−	1422.35i	−0.649551	−	1.78463i	−0.619393	−	0.785081i	$-0.712621\pi$
$797$	−517.692	−	1422.35i	−0.649551	−	1.78463i	−0.0301573	−	0.999545i	$-0.509601\pi$
$798$		0			0
$799$	−12.7876	−	72.5219i	−0.0160045	−	0.0907658i
$800$		0			0
$801$		0			0
$802$		0			0
$803$	38.0014	+	45.2882i	0.0473242	+	0.0563988i
$804$		0			0
$805$	100.118	−	567.798i	0.124370	−	0.705340i
$806$		0			0
$807$		0			0
$808$		0			0
$809$			434.934i			0.537619i	0.963193	+	0.268810i	$0.0866303\pi$
$809$			434.934i			0.537619i	−0.963193	+	0.268810i	$0.913370\pi$
$810$		0			0
$811$	207.504			0.255862			0.127931	−	0.991783i	$-0.459166\pi$
$811$	207.504			0.255862			0.127931	+	0.991783i	$0.459166\pi$
$812$		0			0
$813$		0			0
$814$		0			0
$815$	512.634	+	90.3912i	0.628998	+	0.110909i
$816$		0			0
$817$	1125.51	−	944.419i	1.37762	−	1.15596i
$818$		0			0
$819$		0			0
$820$		0			0
$821$	1587.42	−	279.904i	1.93351	−	0.340931i	0.933663	−	0.358154i	$-0.116594\pi$
$821$	1587.42	−	279.904i	1.93351	−	0.340931i	0.999852	+	0.0172230i	$0.00548254\pi$
$822$		0			0
$823$	1516.66	−	552.020i	1.84285	−	0.670741i	0.854309	−	0.519766i	$-0.173981\pi$
$823$	1516.66	−	552.020i	1.84285	−	0.670741i	0.988537	−	0.150976i	$-0.0482415\pi$
$824$		0			0
$825$		0			0
$826$		0			0
$827$	−373.443	−	215.608i	−0.451564	−	0.260710i	0.256927	−	0.966431i	$-0.417290\pi$
$827$	−373.443	−	215.608i	−0.451564	−	0.260710i	−0.708490	+	0.705720i	$0.750623\pi$
$828$		0			0
$829$	−731.702	−	1267.35i	−0.882633	−	1.52876i	−0.848403	−	0.529350i	$-0.822436\pi$
$829$	−731.702	−	1267.35i	−0.882633	−	1.52876i	−0.0342292	−	0.999414i	$-0.510898\pi$
$830$		0			0
$831$		0			0
$832$		0			0
$833$	1586.09	−	1890.22i	1.90407	−	2.26918i
$834$		0			0
$835$	826.135	+	300.688i	0.989383	+	0.360106i
$836$		0			0
$837$		0			0
$838$		0			0
$839$	372.500	−	1023.43i	0.443981	−	1.21983i	−0.492872	−	0.870102i	$-0.664053\pi$
$839$	372.500	−	1023.43i	0.443981	−	1.21983i	0.936852	−	0.349725i	$-0.113725\pi$
$840$		0			0
$841$	515.193	+	432.298i	0.612595	+	0.514028i
$842$		0			0
$843$		0			0
$844$		0			0
$845$	−0.232135	+	0.134023i	−0.000274716	+	0.000158608i
$846$		0			0
$847$	−983.117	+	1702.81i	−1.16070	+	2.01040i
$848$		0			0
$849$		0			0
$850$		0			0
$851$	−125.369	−	344.447i	−0.147319	−	0.404756i
$852$		0			0
$853$	−95.8295	−	543.476i	−0.112344	−	0.637135i	−0.988031	−	0.154256i	$-0.950702\pi$
$853$	−95.8295	−	543.476i	−0.112344	−	0.637135i	0.875687	−	0.482879i	$-0.160409\pi$
$854$		0			0
$855$		0			0
$856$		0			0
$857$	1054.84	+	1257.11i	1.23085	+	1.46687i	0.836551	+	0.547889i	$0.184569\pi$
$857$	1054.84	+	1257.11i	1.23085	+	1.46687i	0.394300	+	0.918982i	$0.370987\pi$
$858$		0			0
$859$	259.895	−	1473.94i	0.302555	−	1.71587i	−0.332242	−	0.943194i	$-0.607805\pi$
$859$	259.895	−	1473.94i	0.302555	−	1.71587i	0.634797	−	0.772679i	$-0.281084\pi$
$860$		0			0
$861$		0			0
$862$		0			0
$863$		−	867.837i		−	1.00561i	−0.864401	−	0.502803i	$-0.832302\pi$
$863$		−	867.837i		−	1.00561i	0.864401	−	0.502803i	$-0.167698\pi$
$864$		0			0
$865$	710.048			0.820865
$866$		0			0
$867$		0			0
$868$		0			0
$869$	271.588	+	47.8883i	0.312530	+	0.0551074i
$870$		0			0
$871$	−538.927	+	452.214i	−0.618745	+	0.519189i
$872$		0			0
$873$		0			0
$874$		0			0
$875$	1365.12	−	240.708i	1.56014	−	0.275095i
$876$		0			0
$877$	451.456	−	164.316i	0.514773	−	0.187362i	−0.0715539	−	0.997437i	$-0.522796\pi$
$877$	451.456	−	164.316i	0.514773	−	0.187362i	0.586327	+	0.810075i	$0.300574\pi$
$878$		0			0
$879$		0			0
$880$		0			0
$881$	716.751	+	413.816i	0.813565	+	0.469712i	0.848192	−	0.529688i	$-0.177691\pi$
$881$	716.751	+	413.816i	0.813565	+	0.469712i	−0.0346271	+	0.999400i	$0.511024\pi$
$882$		0			0
$883$	382.739	+	662.923i	0.433453	+	0.750762i	0.997168	−	0.0752071i	$-0.0239618\pi$
$883$	382.739	+	662.923i	0.433453	+	0.750762i	−0.563715	+	0.825969i	$0.690628\pi$
$884$		0			0
$885$		0			0
$886$		0			0
$887$	−674.009	+	803.252i	−0.759874	+	0.905583i	−0.997840	−	0.0656906i	$-0.979075\pi$
$887$	−674.009	+	803.252i	−0.759874	+	0.905583i	0.237966	+	0.971274i	$0.423519\pi$
$888$		0			0
$889$	1140.64	+	415.158i	1.28306	+	0.466994i
$890$		0			0
$891$		0			0
$892$		0			0
$893$	−24.7599	+	68.0274i	−0.0277267	+	0.0761785i
$894$		0			0
$895$	−374.278	−	314.056i	−0.418188	−	0.350901i
$896$		0			0
$897$		0			0
$898$		0			0
$899$	−168.374	+	97.2110i	−0.187291	+	0.108132i
$900$		0			0
$901$	−208.603	+	361.311i	−0.231524	+	0.401011i
$902$		0			0
$903$		0			0
$904$		0			0
$905$	−29.9121	−	82.1827i	−0.0330520	−	0.0908096i
$906$		0			0
$907$	−119.877	−	679.859i	−0.132169	−	0.749569i	−0.976789	−	0.214203i	$-0.931285\pi$
$907$	−119.877	−	679.859i	−0.132169	−	0.749569i	0.844620	−	0.535366i	$-0.179826\pi$
$908$		0			0
$909$		0			0
$910$		0			0
$911$	−583.708	−	695.636i	−0.640733	−	0.763596i	0.343752	−	0.939060i	$-0.388302\pi$
$911$	−583.708	−	695.636i	−0.640733	−	0.763596i	−0.984486	+	0.175464i	$0.943857\pi$
$912$		0			0
$913$	−272.003	+	1542.60i	−0.297922	+	1.68960i
$914$		0			0
$915$		0			0
$916$		0			0
$917$		−	540.627i		−	0.589561i
$918$		0			0
$919$	−940.127			−1.02299			−0.511494	−	0.859287i	$-0.670908\pi$
$919$	−940.127			−1.02299			−0.511494	+	0.859287i	$0.670908\pi$
$920$		0			0
$921$		0			0
$922$		0			0
$923$	−1092.36	−	192.613i	−1.18349	−	0.208681i
$924$		0			0
$925$	−65.6257	+	55.0665i	−0.0709467	+	0.0595314i
$926$		0			0
$927$		0			0
$928$		0			0
$929$	272.955	−	48.1294i	0.293816	−	0.0518078i	−0.0247970	−	0.999693i	$-0.507894\pi$
$929$	272.955	−	48.1294i	0.293816	−	0.0518078i	0.318613	+	0.947885i	$0.396783\pi$
$930$		0			0
$931$	−2279.43	+	829.643i	−2.44836	+	0.891131i
$932$		0			0
$933$		0			0
$934$		0			0
$935$	−2180.66	−	1259.00i	−2.33225	−	1.34653i
$936$		0			0
$937$	468.807	+	811.997i	0.500327	+	0.866592i	1.00000		0.000378066i	$0.000120342\pi$
$937$	468.807	+	811.997i	0.500327	+	0.866592i	−0.499673	+	0.866214i	$0.666546\pi$
$938$		0			0
$939$		0			0
$940$		0			0
$941$	−579.952	+	691.160i	−0.616315	+	0.734495i	−0.980432	−	0.196858i	$-0.936926\pi$
$941$	−579.952	+	691.160i	−0.616315	+	0.734495i	0.364117	+	0.931353i	$0.381371\pi$
$942$		0			0
$943$	−17.2698	−	6.28570i	−0.0183137	−	0.00666564i
$944$		0			0
$945$		0			0
$946$		0			0
$947$	−208.635	+	573.219i	−0.220311	+	0.605300i	−0.999776	−	0.0211454i	$-0.993269\pi$
$947$	−208.635	+	573.219i	−0.220311	+	0.605300i	0.779465	+	0.626446i	$0.215491\pi$
$948$		0			0
$949$	34.5908	+	29.0251i	0.0364497	+	0.0305849i
$950$		0			0
$951$		0			0
$952$		0			0
$953$	1125.59	−	649.858i	1.18110	−	0.681908i	0.224830	−	0.974398i	$-0.427817\pi$
$953$	1125.59	−	649.858i	1.18110	−	0.681908i	0.956269	+	0.292490i	$0.0944838\pi$
$954$		0			0
$955$	−270.088	+	467.806i	−0.282815	+	0.489849i
$956$		0			0
$957$		0			0
$958$		0			0
$959$	878.233	+	2412.93i	0.915780	+	2.51608i
$960$		0			0
$961$	−127.913	−	725.429i	−0.133104	−	0.754869i
$962$		0			0
$963$		0			0
$964$		0			0
$965$	−784.204	−	934.578i	−0.812647	−	0.968475i
$966$		0			0
$967$	176.440	−	1000.64i	0.182461	−	1.03479i	−0.746714	−	0.665145i	$-0.768370\pi$
$967$	176.440	−	1000.64i	0.182461	−	1.03479i	0.929175	−	0.369641i	$-0.120519\pi$
$968$		0			0
$969$		0			0
$970$		0			0
$971$			455.462i			0.469065i	0.972108	+	0.234532i	$0.0753559\pi$
$971$			455.462i			0.469065i	−0.972108	+	0.234532i	$0.924644\pi$
$972$		0			0
$973$	2088.62			2.14658
$974$		0			0
$975$		0			0
$976$		0			0
$977$	−1060.32	−	186.964i	−1.08529	−	0.191365i	−0.397734	−	0.917501i	$-0.630203\pi$
$977$	−1060.32	−	186.964i	−1.08529	−	0.191365i	−0.687551	+	0.726136i	$0.741314\pi$
$978$		0			0
$979$	−839.297	+	704.254i	−0.857300	+	0.719361i
$980$		0			0
$981$		0			0
$982$		0			0
$983$	1690.45	−	298.071i	1.71968	−	0.303226i	0.775181	−	0.631739i	$-0.217659\pi$
$983$	1690.45	−	298.071i	1.71968	−	0.303226i	0.944499	+	0.328513i	$0.106547\pi$
$984$		0			0
$985$	−1095.40	+	398.693i	−1.11208	+	0.404765i
$986$		0			0
$987$		0			0
$988$		0			0
$989$	−432.484	−	249.695i	−0.437294	−	0.252472i
$990$		0			0
$991$	−916.942	−	1588.19i	−0.925270	−	1.60261i	−0.791127	−	0.611652i	$-0.790505\pi$
$991$	−916.942	−	1588.19i	−0.925270	−	1.60261i	−0.134143	−	0.990962i	$-0.542828\pi$
$992$		0			0
$993$		0			0
$994$		0			0
$995$	−1124.15	+	1339.71i	−1.12980	+	1.34644i
$996$		0			0
$997$	464.326	+	169.001i	0.465723	+	0.169509i	0.564214	−	0.825629i	$-0.309179\pi$
$997$	464.326	+	169.001i	0.465723	+	0.169509i	−0.0984911	+	0.995138i	$0.531402\pi$
$998$		0			0
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	324.3.k.a.17.5		36
3.2	odd	2		108.3.k.a.77.3	✓	36
12.11	even	2		432.3.bc.b.401.4		36
27.7	even	9		108.3.k.a.101.3	yes	36
27.13	even	9		2916.3.c.b.1457.30		36
27.14	odd	18		2916.3.c.b.1457.7		36
27.20	odd	18	inner	324.3.k.a.305.5		36
108.7	odd	18		432.3.bc.b.209.4		36

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
108.3.k.a.77.3	✓	36	3.2	odd	2
108.3.k.a.101.3	yes	36	27.7	even	9
324.3.k.a.17.5		36	1.1	even	1	trivial
324.3.k.a.305.5		36	27.20	odd	18	inner
432.3.bc.b.209.4		36	108.7	odd	18
432.3.bc.b.401.4		36	12.11	even	2
2916.3.c.b.1457.7		36	27.14	odd	18
2916.3.c.b.1457.30		36	27.13	even	9

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:	\( N \)	\(=\)	\( 324 = 2^{2} \cdot 3^{4} \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	324.k (of order \(18\), degree \(6\), not minimal)

\(f(q)\)	\(=\)	\(q+(5.13754 + 0.905886i) q^{5} +(-8.93347 + 7.49607i) q^{7} +O(q^{10})\)	\(q+(5.13754 + 0.905886i) q^{5} +(-8.93347 + 7.49607i) q^{7} +(-16.7592 + 2.95510i) q^{11} +(-12.2141 + 4.44559i) q^{13} +(24.5630 + 14.1815i) q^{17} +(-13.9412 - 24.1469i) q^{19} +(-6.09173 + 7.25984i) q^{23} +(2.08134 + 0.757544i) q^{25} +(-4.43920 + 12.1966i) q^{29} +(11.4748 + 9.62853i) q^{31} +(-52.6866 + 30.4186i) q^{35} +(-19.3390 + 33.4961i) q^{37} +(0.663254 + 1.82228i) q^{41} +(9.15032 + 51.8940i) q^{43} +(-1.66892 - 1.98894i) q^{47} +(15.1070 - 85.6762i) q^{49} +14.7096i q^{53} -88.7782 q^{55} +(16.7995 + 2.96221i) q^{59} +(-17.6298 + 14.7932i) q^{61} +(-66.7778 + 11.7747i) q^{65} +(50.8610 - 18.5119i) q^{67} +(73.9041 + 42.6686i) q^{71} +(-1.73700 - 3.00857i) q^{73} +(127.566 - 152.028i) q^{77} +(-15.2280 - 5.54254i) q^{79} +(31.4813 - 86.4941i) q^{83} +(113.347 + 95.1090i) q^{85} +(55.7558 - 32.1906i) q^{89} +(75.7903 - 131.273i) q^{91} +(-49.7492 - 136.685i) q^{95} +(7.70330 + 43.6876i) q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 36 q + 9 q^{5}+O(q^{10}) \) 36 * q + 9 * q^5	\( 36 q + 9 q^{5} - 36 q^{11} + 18 q^{23} - 9 q^{25} + 18 q^{29} + 45 q^{31} + 243 q^{35} + 198 q^{41} + 90 q^{43} + 243 q^{47} + 72 q^{49} - 252 q^{59} - 144 q^{61} - 747 q^{65} + 108 q^{67} - 324 q^{71} - 63 q^{73} - 495 q^{77} + 36 q^{79} + 27 q^{83} - 180 q^{85} + 567 q^{89} + 99 q^{91} + 1044 q^{95} - 216 q^{97}+O(q^{100}) \) 36 * q + 9 * q^5 - 36 * q^11 + 18 * q^23 - 9 * q^25 + 18 * q^29 + 45 * q^31 + 243 * q^35 + 198 * q^41 + 90 * q^43 + 243 * q^47 + 72 * q^49 - 252 * q^59 - 144 * q^61 - 747 * q^65 + 108 * q^67 - 324 * q^71 - 63 * q^73 - 495 * q^77 + 36 * q^79 + 27 * q^83 - 180 * q^85 + 567 * q^89 + 99 * q^91 + 1044 * q^95 - 216 * q^97

Introduction

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