LMFDB - Embedded newform 297.2.e.b.199.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [297,2,Mod(100,297)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(297, base_ring=CyclotomicField(6))

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

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

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

chi := DirichletCharacter("297.100");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 297 = 3^{3} \cdot 11 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	297.e (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:	$2.37155694003$
Analytic rank:	$0$
Dimension:	$2$
Coefficient field:	$\Q(\zeta_{6})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{2} - x + 1 $ x^2 - x + 1
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 99)
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			199.1
Root			$0.500000 - 0.866025i$ of defining polynomial
Character	$\chi$	$=$	297.199
Dual form			297.2.e.b.100.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.00000 - 1.73205i) q^{4} +(-1.50000 + 2.59808i) q^{5} +(2.00000 + 3.46410i) q^{7} +(0.500000 + 0.866025i) q^{11} +(-1.00000 + 1.73205i) q^{13} +(-2.00000 - 3.46410i) q^{16} +6.00000 q^{17} +2.00000 q^{19} +(3.00000 + 5.19615i) q^{20} +(1.50000 - 2.59808i) q^{23} +(-2.00000 - 3.46410i) q^{25} +8.00000 q^{28} +(-3.00000 - 5.19615i) q^{29} +(-4.00000 + 6.92820i) q^{31} -12.0000 q^{35} +2.00000 q^{37} +(-4.00000 - 6.92820i) q^{43} +2.00000 q^{44} +(1.50000 + 2.59808i) q^{47} +(-4.50000 + 7.79423i) q^{49} +(2.00000 + 3.46410i) q^{52} -3.00000 q^{53} -3.00000 q^{55} +(-4.00000 - 6.92820i) q^{61} -8.00000 q^{64} +(-3.00000 - 5.19615i) q^{65} +(6.50000 - 11.2583i) q^{67} +(6.00000 - 10.3923i) q^{68} +2.00000 q^{73} +(2.00000 - 3.46410i) q^{76} +(-2.00000 + 3.46410i) q^{77} +(-1.00000 - 1.73205i) q^{79} +12.0000 q^{80} +(-9.00000 - 15.5885i) q^{83} +(-9.00000 + 15.5885i) q^{85} -3.00000 q^{89} -8.00000 q^{91} +(-3.00000 - 5.19615i) q^{92} +(-3.00000 + 5.19615i) q^{95} +(-1.00000 - 1.73205i) q^{97} +O(q^{100})$
$\operatorname{Tr}(f)(q)$	$=$	$ 2 q + 2 q^{4} - 3 q^{5} + 4 q^{7} + q^{11} - 2 q^{13} - 4 q^{16} + 12 q^{17} + 4 q^{19} + 6 q^{20} + 3 q^{23} - 4 q^{25} + 16 q^{28} - 6 q^{29} - 8 q^{31} - 24 q^{35} + 4 q^{37} - 8 q^{43} + 4 q^{44} + 3 q^{47}+ \cdots - 2 q^{97}+O(q^{100}) $ 2 * q + 2 * q^4 - 3 * q^5 + 4 * q^7 + q^11 - 2 * q^13 - 4 * q^16 + 12 * q^17 + 4 * q^19 + 6 * q^20 + 3 * q^23 - 4 * q^25 + 16 * q^28 - 6 * q^29 - 8 * q^31 - 24 * q^35 + 4 * q^37 - 8 * q^43 + 4 * q^44 + 3 * q^47 - 9 * q^49 + 4 * q^52 - 6 * q^53 - 6 * q^55 - 8 * q^61 - 16 * q^64 - 6 * q^65 + 13 * q^67 + 12 * q^68 + 4 * q^73 + 4 * q^76 - 4 * q^77 - 2 * q^79 + 24 * q^80 - 18 * q^83 - 18 * q^85 - 6 * q^89 - 16 * q^91 - 6 * q^92 - 6 * q^95 - 2 * q^97

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/297\mathbb{Z}\right)^\times$.

$n$	$56$	$244$
$\chi(n)$	$e\left(\frac{1}{3}\right)$	$1$

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		0.866025	−	0.500000i	$-0.166667\pi$
$2$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$3$		0			0
$3$		0			0
$4$	1.00000	−	1.73205i	0.500000	−	0.866025i
$5$	−1.50000	+	2.59808i	−0.670820	+	1.16190i	0.306851	+	0.951757i	$0.400725\pi$
$5$	−1.50000	+	2.59808i	−0.670820	+	1.16190i	−0.977672	+	0.210138i	$0.932609\pi$
$6$		0			0
$7$	2.00000	+	3.46410i	0.755929	+	1.30931i	0.944911	+	0.327327i	$0.106148\pi$
$7$	2.00000	+	3.46410i	0.755929	+	1.30931i	−0.188982	+	0.981981i	$0.560519\pi$
$8$		0			0
$9$		0			0
$10$		0			0
$11$	0.500000	+	0.866025i	0.150756	+	0.261116i
$11$	0.500000	+	0.866025i	0.150756	+	0.261116i
$12$		0			0
$13$	−1.00000	+	1.73205i	−0.277350	+	0.480384i	−0.970725	−	0.240192i	$-0.922790\pi$
$13$	−1.00000	+	1.73205i	−0.277350	+	0.480384i	0.693375	+	0.720577i	$0.256123\pi$
$14$		0			0
$15$		0			0
$16$	−2.00000	−	3.46410i	−0.500000	−	0.866025i
$17$	6.00000			1.45521			0.727607	−	0.685994i	$-0.240633\pi$
$17$	6.00000			1.45521			0.727607	+	0.685994i	$0.240633\pi$
$18$		0			0
$19$	2.00000			0.458831			0.229416	−	0.973329i	$-0.426318\pi$
$19$	2.00000			0.458831			0.229416	+	0.973329i	$0.426318\pi$
$20$	3.00000	+	5.19615i	0.670820	+	1.16190i
$21$		0			0
$22$		0			0
$23$	1.50000	−	2.59808i	0.312772	−	0.541736i	−0.666190	−	0.745782i	$-0.732076\pi$
$23$	1.50000	−	2.59808i	0.312772	−	0.541736i	0.978961	+	0.204046i	$0.0654092\pi$
$24$		0			0
$25$	−2.00000	−	3.46410i	−0.400000	−	0.692820i
$26$		0			0
$27$		0			0
$28$	8.00000			1.51186
$29$	−3.00000	−	5.19615i	−0.557086	−	0.964901i	−0.997738	−	0.0672232i	$-0.978586\pi$
$29$	−3.00000	−	5.19615i	−0.557086	−	0.964901i	0.440652	−	0.897678i	$-0.354747\pi$
$30$		0			0
$31$	−4.00000	+	6.92820i	−0.718421	+	1.24434i	0.243204	+	0.969975i	$0.421802\pi$
$31$	−4.00000	+	6.92820i	−0.718421	+	1.24434i	−0.961625	+	0.274367i	$0.911532\pi$
$32$		0			0
$33$		0			0
$34$		0			0
$35$	−12.0000			−2.02837
$36$		0			0
$37$	2.00000			0.328798			0.164399	−	0.986394i	$-0.447432\pi$
$37$	2.00000			0.328798			0.164399	+	0.986394i	$0.447432\pi$
$38$		0			0
$39$		0			0
$40$		0			0
$41$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$41$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$42$		0			0
$43$	−4.00000	−	6.92820i	−0.609994	−	1.05654i	−0.991241	−	0.132068i	$-0.957838\pi$
$43$	−4.00000	−	6.92820i	−0.609994	−	1.05654i	0.381246	−	0.924473i	$-0.375495\pi$
$44$	2.00000			0.301511
$45$		0			0
$46$		0			0
$47$	1.50000	+	2.59808i	0.218797	+	0.378968i	0.954441	−	0.298401i	$-0.0964533\pi$
$47$	1.50000	+	2.59808i	0.218797	+	0.378968i	−0.735643	+	0.677369i	$0.763120\pi$
$48$		0			0
$49$	−4.50000	+	7.79423i	−0.642857	+	1.11346i
$50$		0			0
$51$		0			0
$52$	2.00000	+	3.46410i	0.277350	+	0.480384i
$53$	−3.00000			−0.412082			−0.206041	−	0.978543i	$-0.566058\pi$
$53$	−3.00000			−0.412082			−0.206041	+	0.978543i	$0.566058\pi$
$54$		0			0
$55$	−3.00000			−0.404520
$56$		0			0
$57$		0			0
$58$		0			0
$59$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$59$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$60$		0			0
$61$	−4.00000	−	6.92820i	−0.512148	−	0.887066i	−0.999901	−	0.0140840i	$-0.995517\pi$
$61$	−4.00000	−	6.92820i	−0.512148	−	0.887066i	0.487753	−	0.872982i	$-0.337817\pi$
$62$		0			0
$63$		0			0
$64$	−8.00000			−1.00000
$65$	−3.00000	−	5.19615i	−0.372104	−	0.644503i
$66$		0			0
$67$	6.50000	−	11.2583i	0.794101	−	1.37542i	−0.129307	−	0.991605i	$-0.541275\pi$
$67$	6.50000	−	11.2583i	0.794101	−	1.37542i	0.923408	−	0.383819i	$-0.125391\pi$
$68$	6.00000	−	10.3923i	0.727607	−	1.26025i
$69$		0			0
$70$		0			0
$71$		0			0			−	1.00000i	$-0.5\pi$
$71$		0			0				1.00000i	$0.5\pi$
$72$		0			0
$73$	2.00000			0.234082			0.117041	−	0.993127i	$-0.462659\pi$
$73$	2.00000			0.234082			0.117041	+	0.993127i	$0.462659\pi$
$74$		0			0
$75$		0			0
$76$	2.00000	−	3.46410i	0.229416	−	0.397360i
$77$	−2.00000	+	3.46410i	−0.227921	+	0.394771i
$78$		0			0
$79$	−1.00000	−	1.73205i	−0.112509	−	0.194871i	0.804272	−	0.594261i	$-0.202555\pi$
$79$	−1.00000	−	1.73205i	−0.112509	−	0.194871i	−0.916781	+	0.399390i	$0.869222\pi$
$80$	12.0000			1.34164
$81$		0			0
$82$		0			0
$83$	−9.00000	−	15.5885i	−0.987878	−	1.71106i	−0.628372	−	0.777913i	$-0.716279\pi$
$83$	−9.00000	−	15.5885i	−0.987878	−	1.71106i	−0.359506	−	0.933143i	$-0.617055\pi$
$84$		0			0
$85$	−9.00000	+	15.5885i	−0.976187	+	1.69081i
$86$		0			0
$87$		0			0
$88$		0			0
$89$	−3.00000			−0.317999			−0.159000	−	0.987279i	$-0.550827\pi$
$89$	−3.00000			−0.317999			−0.159000	+	0.987279i	$0.550827\pi$
$90$		0			0
$91$	−8.00000			−0.838628
$92$	−3.00000	−	5.19615i	−0.312772	−	0.541736i
$93$		0			0
$94$		0			0
$95$	−3.00000	+	5.19615i	−0.307794	+	0.533114i
$96$		0			0
$97$	−1.00000	−	1.73205i	−0.101535	−	0.175863i	0.810782	−	0.585348i	$-0.199042\pi$
$97$	−1.00000	−	1.73205i	−0.101535	−	0.175863i	−0.912317	+	0.409484i	$0.865709\pi$
$98$		0			0
$99$		0			0
$100$	−8.00000			−0.800000
$101$	3.00000	+	5.19615i	0.298511	+	0.517036i	0.975796	−	0.218685i	$-0.0701767\pi$
$101$	3.00000	+	5.19615i	0.298511	+	0.517036i	−0.677284	+	0.735721i	$0.736843\pi$
$102$		0			0
$103$	−2.50000	+	4.33013i	−0.246332	+	0.426660i	−0.962505	−	0.271263i	$-0.912559\pi$
$103$	−2.50000	+	4.33013i	−0.246332	+	0.426660i	0.716173	+	0.697923i	$0.245892\pi$
$104$		0			0
$105$		0			0
$106$		0			0
$107$	12.0000			1.16008			0.580042	−	0.814587i	$-0.303036\pi$
$107$	12.0000			1.16008			0.580042	+	0.814587i	$0.303036\pi$
$108$		0			0
$109$	14.0000			1.34096			0.670478	−	0.741929i	$-0.266089\pi$
$109$	14.0000			1.34096			0.670478	+	0.741929i	$0.266089\pi$
$110$		0			0
$111$		0			0
$112$	8.00000	−	13.8564i	0.755929	−	1.30931i
$113$	−3.00000	+	5.19615i	−0.282216	+	0.488813i	−0.971930	−	0.235269i	$-0.924403\pi$
$113$	−3.00000	+	5.19615i	−0.282216	+	0.488813i	0.689714	+	0.724082i	$0.257736\pi$
$114$		0			0
$115$	4.50000	+	7.79423i	0.419627	+	0.726816i
$116$	−12.0000			−1.11417
$117$		0			0
$118$		0			0
$119$	12.0000	+	20.7846i	1.10004	+	1.90532i
$120$		0			0
$121$	−0.500000	+	0.866025i	−0.0454545	+	0.0787296i
$122$		0			0
$123$		0			0
$124$	8.00000	+	13.8564i	0.718421	+	1.24434i
$125$	−3.00000			−0.268328
$126$		0			0
$127$	−4.00000			−0.354943			−0.177471	−	0.984126i	$-0.556792\pi$
$127$	−4.00000			−0.354943			−0.177471	+	0.984126i	$0.556792\pi$
$128$		0			0
$129$		0			0
$130$		0			0
$131$	9.00000	−	15.5885i	0.786334	−	1.36197i	−0.141865	−	0.989886i	$-0.545310\pi$
$131$	9.00000	−	15.5885i	0.786334	−	1.36197i	0.928199	−	0.372084i	$-0.121357\pi$
$132$		0			0
$133$	4.00000	+	6.92820i	0.346844	+	0.600751i
$134$		0			0
$135$		0			0
$136$		0			0
$137$	9.00000	+	15.5885i	0.768922	+	1.33181i	0.938148	+	0.346235i	$0.112540\pi$
$137$	9.00000	+	15.5885i	0.768922	+	1.33181i	−0.169226	+	0.985577i	$0.554127\pi$
$138$		0			0
$139$	5.00000	−	8.66025i	0.424094	−	0.734553i	−0.572241	−	0.820086i	$-0.693926\pi$
$139$	5.00000	−	8.66025i	0.424094	−	0.734553i	0.996335	+	0.0855324i	$0.0272591\pi$
$140$	−12.0000	+	20.7846i	−1.01419	+	1.75662i
$141$		0			0
$142$		0			0
$143$	−2.00000			−0.167248
$144$		0			0
$145$	18.0000			1.49482
$146$		0			0
$147$		0			0
$148$	2.00000	−	3.46410i	0.164399	−	0.284747i
$149$	−6.00000	+	10.3923i	−0.491539	+	0.851371i	−0.999953	−	0.00974235i	$-0.996899\pi$
$149$	−6.00000	+	10.3923i	−0.491539	+	0.851371i	0.508413	+	0.861113i	$0.330232\pi$
$150$		0			0
$151$	−4.00000	−	6.92820i	−0.325515	−	0.563809i	0.656101	−	0.754673i	$-0.272204\pi$
$151$	−4.00000	−	6.92820i	−0.325515	−	0.563809i	−0.981617	+	0.190864i	$0.938871\pi$
$152$		0			0
$153$		0			0
$154$		0			0
$155$	−12.0000	−	20.7846i	−0.963863	−	1.66946i
$156$		0			0
$157$	3.50000	−	6.06218i	0.279330	−	0.483814i	−0.691888	−	0.722005i	$-0.743221\pi$
$157$	3.50000	−	6.06218i	0.279330	−	0.483814i	0.971219	+	0.238190i	$0.0765542\pi$
$158$		0			0
$159$		0			0
$160$		0			0
$161$	12.0000			0.945732
$162$		0			0
$163$	−1.00000			−0.0783260			−0.0391630	−	0.999233i	$-0.512469\pi$
$163$	−1.00000			−0.0783260			−0.0391630	+	0.999233i	$0.512469\pi$
$164$		0			0
$165$		0			0
$166$		0			0
$167$	9.00000	−	15.5885i	0.696441	−	1.20627i	−0.273252	−	0.961943i	$-0.588099\pi$
$167$	9.00000	−	15.5885i	0.696441	−	1.20627i	0.969693	−	0.244328i	$-0.0785675\pi$
$168$		0			0
$169$	4.50000	+	7.79423i	0.346154	+	0.599556i
$170$		0			0
$171$		0			0
$172$	−16.0000			−1.21999
$173$	9.00000	+	15.5885i	0.684257	+	1.18517i	0.973670	+	0.227964i	$0.0732068\pi$
$173$	9.00000	+	15.5885i	0.684257	+	1.18517i	−0.289412	+	0.957205i	$0.593460\pi$
$174$		0			0
$175$	8.00000	−	13.8564i	0.604743	−	1.04745i
$176$	2.00000	−	3.46410i	0.150756	−	0.261116i
$177$		0			0
$178$		0			0
$179$	−15.0000			−1.12115			−0.560576	−	0.828103i	$-0.689420\pi$
$179$	−15.0000			−1.12115			−0.560576	+	0.828103i	$0.689420\pi$
$180$		0			0
$181$	−1.00000			−0.0743294			−0.0371647	−	0.999309i	$-0.511833\pi$
$181$	−1.00000			−0.0743294			−0.0371647	+	0.999309i	$0.511833\pi$
$182$		0			0
$183$		0			0
$184$		0			0
$185$	−3.00000	+	5.19615i	−0.220564	+	0.382029i
$186$		0			0
$187$	3.00000	+	5.19615i	0.219382	+	0.379980i
$188$	6.00000			0.437595
$189$		0			0
$190$		0			0
$191$	1.50000	+	2.59808i	0.108536	+	0.187990i	0.915177	−	0.403051i	$-0.132050\pi$
$191$	1.50000	+	2.59808i	0.108536	+	0.187990i	−0.806641	+	0.591041i	$0.798717\pi$
$192$		0			0
$193$	2.00000	−	3.46410i	0.143963	−	0.249351i	−0.785022	−	0.619467i	$-0.787349\pi$
$193$	2.00000	−	3.46410i	0.143963	−	0.249351i	0.928986	+	0.370116i	$0.120682\pi$
$194$		0			0
$195$		0			0
$196$	9.00000	+	15.5885i	0.642857	+	1.11346i
$197$	−18.0000			−1.28245			−0.641223	−	0.767354i	$-0.721573\pi$
$197$	−18.0000			−1.28245			−0.641223	+	0.767354i	$0.721573\pi$
$198$		0			0
$199$	11.0000			0.779769			0.389885	−	0.920864i	$-0.372515\pi$
$199$	11.0000			0.779769			0.389885	+	0.920864i	$0.372515\pi$
$200$		0			0
$201$		0			0
$202$		0			0
$203$	12.0000	−	20.7846i	0.842235	−	1.45879i
$204$		0			0
$205$		0			0
$206$		0			0
$207$		0			0
$208$	8.00000			0.554700
$209$	1.00000	+	1.73205i	0.0691714	+	0.119808i
$210$		0			0
$211$	2.00000	−	3.46410i	0.137686	−	0.238479i	−0.788935	−	0.614477i	$-0.789367\pi$
$211$	2.00000	−	3.46410i	0.137686	−	0.238479i	0.926620	+	0.375999i	$0.122700\pi$
$212$	−3.00000	+	5.19615i	−0.206041	+	0.356873i
$213$		0			0
$214$		0			0
$215$	24.0000			1.63679
$216$		0			0
$217$	−32.0000			−2.17230
$218$		0			0
$219$		0			0
$220$	−3.00000	+	5.19615i	−0.202260	+	0.350325i
$221$	−6.00000	+	10.3923i	−0.403604	+	0.699062i
$222$		0			0
$223$	−5.50000	−	9.52628i	−0.368307	−	0.637927i	0.620994	−	0.783815i	$-0.286729\pi$
$223$	−5.50000	−	9.52628i	−0.368307	−	0.637927i	−0.989301	+	0.145889i	$0.953396\pi$
$224$		0			0
$225$		0			0
$226$		0			0
$227$	9.00000	+	15.5885i	0.597351	+	1.03464i	0.993210	+	0.116331i	$0.0371134\pi$
$227$	9.00000	+	15.5885i	0.597351	+	1.03464i	−0.395860	+	0.918311i	$0.629553\pi$
$228$		0			0
$229$	−11.5000	+	19.9186i	−0.759941	+	1.31626i	0.182939	+	0.983124i	$0.441439\pi$
$229$	−11.5000	+	19.9186i	−0.759941	+	1.31626i	−0.942880	+	0.333133i	$0.891894\pi$
$230$		0			0
$231$		0			0
$232$		0			0
$233$	6.00000			0.393073			0.196537	−	0.980497i	$-0.437031\pi$
$233$	6.00000			0.393073			0.196537	+	0.980497i	$0.437031\pi$
$234$		0			0
$235$	−9.00000			−0.587095
$236$		0			0
$237$		0			0
$238$		0			0
$239$	−6.00000	+	10.3923i	−0.388108	+	0.672222i	−0.992195	−	0.124696i	$-0.960204\pi$
$239$	−6.00000	+	10.3923i	−0.388108	+	0.672222i	0.604087	+	0.796918i	$0.293538\pi$
$240$		0			0
$241$	−1.00000	−	1.73205i	−0.0644157	−	0.111571i	0.832019	−	0.554747i	$-0.187185\pi$
$241$	−1.00000	−	1.73205i	−0.0644157	−	0.111571i	−0.896435	+	0.443176i	$0.853852\pi$
$242$		0			0
$243$		0			0
$244$	−16.0000			−1.02430
$245$	−13.5000	−	23.3827i	−0.862483	−	1.49387i
$246$		0			0
$247$	−2.00000	+	3.46410i	−0.127257	+	0.220416i
$248$		0			0
$249$		0			0
$250$		0			0
$251$	15.0000			0.946792			0.473396	−	0.880850i	$-0.343028\pi$
$251$	15.0000			0.946792			0.473396	+	0.880850i	$0.343028\pi$
$252$		0			0
$253$	3.00000			0.188608
$254$		0			0
$255$		0			0
$256$	−8.00000	+	13.8564i	−0.500000	+	0.866025i
$257$	3.00000	−	5.19615i	0.187135	−	0.324127i	−0.757159	−	0.653231i	$-0.773413\pi$
$257$	3.00000	−	5.19615i	0.187135	−	0.324127i	0.944294	+	0.329104i	$0.106747\pi$
$258$		0			0
$259$	4.00000	+	6.92820i	0.248548	+	0.430498i
$260$	−12.0000			−0.744208
$261$		0			0
$262$		0			0
$263$	−12.0000	−	20.7846i	−0.739952	−	1.28163i	−0.952517	−	0.304487i	$-0.901515\pi$
$263$	−12.0000	−	20.7846i	−0.739952	−	1.28163i	0.212565	−	0.977147i	$-0.431818\pi$
$264$		0			0
$265$	4.50000	−	7.79423i	0.276433	−	0.478796i
$266$		0			0
$267$		0			0
$268$	−13.0000	−	22.5167i	−0.794101	−	1.37542i
$269$	−27.0000			−1.64622			−0.823110	−	0.567883i	$-0.807763\pi$
$269$	−27.0000			−1.64622			−0.823110	+	0.567883i	$0.807763\pi$
$270$		0			0
$271$	2.00000			0.121491			0.0607457	−	0.998153i	$-0.480652\pi$
$271$	2.00000			0.121491			0.0607457	+	0.998153i	$0.480652\pi$
$272$	−12.0000	−	20.7846i	−0.727607	−	1.26025i
$273$		0			0
$274$		0			0
$275$	2.00000	−	3.46410i	0.120605	−	0.208893i
$276$		0			0
$277$	−1.00000	−	1.73205i	−0.0600842	−	0.104069i	0.834419	−	0.551131i	$-0.185804\pi$
$277$	−1.00000	−	1.73205i	−0.0600842	−	0.104069i	−0.894503	+	0.447062i	$0.852470\pi$
$278$		0			0
$279$		0			0
$280$		0			0
$281$	−6.00000	−	10.3923i	−0.357930	−	0.619953i	0.629685	−	0.776851i	$-0.283184\pi$
$281$	−6.00000	−	10.3923i	−0.357930	−	0.619953i	−0.987615	+	0.156898i	$0.949851\pi$
$282$		0			0
$283$	5.00000	−	8.66025i	0.297219	−	0.514799i	−0.678280	−	0.734804i	$-0.737274\pi$
$283$	5.00000	−	8.66025i	0.297219	−	0.514799i	0.975499	+	0.220005i	$0.0706075\pi$
$284$		0			0
$285$		0			0
$286$		0			0
$287$		0			0
$288$		0			0
$289$	19.0000			1.11765
$290$		0			0
$291$		0			0
$292$	2.00000	−	3.46410i	0.117041	−	0.202721i
$293$	3.00000	−	5.19615i	0.175262	−	0.303562i	−0.764990	−	0.644042i	$-0.777256\pi$
$293$	3.00000	−	5.19615i	0.175262	−	0.303562i	0.940252	+	0.340480i	$0.110589\pi$
$294$		0			0
$295$		0			0
$296$		0			0
$297$		0			0
$298$		0			0
$299$	3.00000	+	5.19615i	0.173494	+	0.300501i
$300$		0			0
$301$	16.0000	−	27.7128i	0.922225	−	1.59734i
$302$		0			0
$303$		0			0
$304$	−4.00000	−	6.92820i	−0.229416	−	0.397360i
$305$	24.0000			1.37424
$306$		0			0
$307$	−16.0000			−0.913168			−0.456584	−	0.889680i	$-0.650927\pi$
$307$	−16.0000			−0.913168			−0.456584	+	0.889680i	$0.650927\pi$
$308$	4.00000	+	6.92820i	0.227921	+	0.394771i
$309$		0			0
$310$		0			0
$311$	−1.50000	+	2.59808i	−0.0850572	+	0.147323i	−0.905416	−	0.424526i	$-0.860441\pi$
$311$	−1.50000	+	2.59808i	−0.0850572	+	0.147323i	0.820358	+	0.571850i	$0.193774\pi$
$312$		0			0
$313$	−5.50000	−	9.52628i	−0.310878	−	0.538457i	0.667674	−	0.744453i	$-0.267290\pi$
$313$	−5.50000	−	9.52628i	−0.310878	−	0.538457i	−0.978553	+	0.205996i	$0.933957\pi$
$314$		0			0
$315$		0			0
$316$	−4.00000			−0.225018
$317$	−13.5000	−	23.3827i	−0.758236	−	1.31330i	−0.943750	−	0.330661i	$-0.892728\pi$
$317$	−13.5000	−	23.3827i	−0.758236	−	1.31330i	0.185514	−	0.982642i	$-0.440605\pi$
$318$		0			0
$319$	3.00000	−	5.19615i	0.167968	−	0.290929i
$320$	12.0000	−	20.7846i	0.670820	−	1.16190i
$321$		0			0
$322$		0			0
$323$	12.0000			0.667698
$324$		0			0
$325$	8.00000			0.443760
$326$		0			0
$327$		0			0
$328$		0			0
$329$	−6.00000	+	10.3923i	−0.330791	+	0.572946i
$330$		0			0
$331$	−14.5000	−	25.1147i	−0.796992	−	1.38043i	−0.921567	−	0.388221i	$-0.873090\pi$
$331$	−14.5000	−	25.1147i	−0.796992	−	1.38043i	0.124574	−	0.992210i	$-0.460243\pi$
$332$	−36.0000			−1.97576
$333$		0			0
$334$		0			0
$335$	19.5000	+	33.7750i	1.06540	+	1.84532i
$336$		0			0
$337$	−16.0000	+	27.7128i	−0.871576	+	1.50961i	−0.0112091	+	0.999937i	$0.503568\pi$
$337$	−16.0000	+	27.7128i	−0.871576	+	1.50961i	−0.860366	+	0.509676i	$0.829765\pi$
$338$		0			0
$339$		0			0
$340$	18.0000	+	31.1769i	0.976187	+	1.69081i
$341$	−8.00000			−0.433224
$342$		0			0
$343$	−8.00000			−0.431959
$344$		0			0
$345$		0			0
$346$		0			0
$347$	6.00000	−	10.3923i	0.322097	−	0.557888i	−0.658824	−	0.752297i	$-0.728946\pi$
$347$	6.00000	−	10.3923i	0.322097	−	0.557888i	0.980921	+	0.194409i	$0.0622790\pi$
$348$		0			0
$349$	14.0000	+	24.2487i	0.749403	+	1.29800i	0.948109	+	0.317945i	$0.102993\pi$
$349$	14.0000	+	24.2487i	0.749403	+	1.29800i	−0.198706	+	0.980059i	$0.563674\pi$
$350$		0			0
$351$		0			0
$352$		0			0
$353$	7.50000	+	12.9904i	0.399185	+	0.691408i	0.993626	−	0.112731i	$-0.0359599\pi$
$353$	7.50000	+	12.9904i	0.399185	+	0.691408i	−0.594441	+	0.804139i	$0.702627\pi$
$354$		0			0
$355$		0			0
$356$	−3.00000	+	5.19615i	−0.159000	+	0.275396i
$357$		0			0
$358$		0			0
$359$	6.00000			0.316668			0.158334	−	0.987386i	$-0.449388\pi$
$359$	6.00000			0.316668			0.158334	+	0.987386i	$0.449388\pi$
$360$		0			0
$361$	−15.0000			−0.789474
$362$		0			0
$363$		0			0
$364$	−8.00000	+	13.8564i	−0.419314	+	0.726273i
$365$	−3.00000	+	5.19615i	−0.157027	+	0.271979i
$366$		0			0
$367$	9.50000	+	16.4545i	0.495896	+	0.858917i	0.999989	−	0.00473247i	$-0.00150640\pi$
$367$	9.50000	+	16.4545i	0.495896	+	0.858917i	−0.504093	+	0.863649i	$0.668173\pi$
$368$	−12.0000			−0.625543
$369$		0			0
$370$		0			0
$371$	−6.00000	−	10.3923i	−0.311504	−	0.539542i
$372$		0			0
$373$	−4.00000	+	6.92820i	−0.207112	+	0.358729i	−0.950804	−	0.309794i	$-0.899740\pi$
$373$	−4.00000	+	6.92820i	−0.207112	+	0.358729i	0.743691	+	0.668523i	$0.233073\pi$
$374$		0			0
$375$		0			0
$376$		0			0
$377$	12.0000			0.618031
$378$		0			0
$379$	−13.0000			−0.667765			−0.333883	−	0.942615i	$-0.608359\pi$
$379$	−13.0000			−0.667765			−0.333883	+	0.942615i	$0.608359\pi$
$380$	6.00000	+	10.3923i	0.307794	+	0.533114i
$381$		0			0
$382$		0			0
$383$	−13.5000	+	23.3827i	−0.689818	+	1.19480i	0.282079	+	0.959391i	$0.408976\pi$
$383$	−13.5000	+	23.3827i	−0.689818	+	1.19480i	−0.971897	+	0.235408i	$0.924357\pi$
$384$		0			0
$385$	−6.00000	−	10.3923i	−0.305788	−	0.529641i
$386$		0			0
$387$		0			0
$388$	−4.00000			−0.203069
$389$	15.0000	+	25.9808i	0.760530	+	1.31728i	0.942578	+	0.333987i	$0.108394\pi$
$389$	15.0000	+	25.9808i	0.760530	+	1.31728i	−0.182047	+	0.983290i	$0.558272\pi$
$390$		0			0
$391$	9.00000	−	15.5885i	0.455150	−	0.788342i
$392$		0			0
$393$		0			0
$394$		0			0
$395$	6.00000			0.301893
$396$		0			0
$397$	17.0000			0.853206			0.426603	−	0.904439i	$-0.359710\pi$
$397$	17.0000			0.853206			0.426603	+	0.904439i	$0.359710\pi$
$398$		0			0
$399$		0			0
$400$	−8.00000	+	13.8564i	−0.400000	+	0.692820i
$401$	10.5000	−	18.1865i	0.524345	−	0.908192i	−0.475253	−	0.879849i	$-0.657644\pi$
$401$	10.5000	−	18.1865i	0.524345	−	0.908192i	0.999598	−	0.0283431i	$-0.00902310\pi$
$402$		0			0
$403$	−8.00000	−	13.8564i	−0.398508	−	0.690237i
$404$	12.0000			0.597022
$405$		0			0
$406$		0			0
$407$	1.00000	+	1.73205i	0.0495682	+	0.0858546i
$408$		0			0
$409$	−16.0000	+	27.7128i	−0.791149	+	1.37031i	0.134107	+	0.990967i	$0.457183\pi$
$409$	−16.0000	+	27.7128i	−0.791149	+	1.37031i	−0.925256	+	0.379344i	$0.876150\pi$
$410$		0			0
$411$		0			0
$412$	5.00000	+	8.66025i	0.246332	+	0.426660i
$413$		0			0
$414$		0			0
$415$	54.0000			2.65076
$416$		0			0
$417$		0			0
$418$		0			0
$419$	−10.5000	+	18.1865i	−0.512959	+	0.888470i	0.486928	+	0.873442i	$0.338117\pi$
$419$	−10.5000	+	18.1865i	−0.512959	+	0.888470i	−0.999887	+	0.0150285i	$0.995216\pi$
$420$		0			0
$421$	3.50000	+	6.06218i	0.170580	+	0.295452i	0.938623	−	0.344946i	$-0.112103\pi$
$421$	3.50000	+	6.06218i	0.170580	+	0.295452i	−0.768043	+	0.640398i	$0.778769\pi$
$422$		0			0
$423$		0			0
$424$		0			0
$425$	−12.0000	−	20.7846i	−0.582086	−	1.00820i
$426$		0			0
$427$	16.0000	−	27.7128i	0.774294	−	1.34112i
$428$	12.0000	−	20.7846i	0.580042	−	1.00466i
$429$		0			0
$430$		0			0
$431$	12.0000			0.578020			0.289010	−	0.957326i	$-0.406674\pi$
$431$	12.0000			0.578020			0.289010	+	0.957326i	$0.406674\pi$
$432$		0			0
$433$	17.0000			0.816968			0.408484	−	0.912766i	$-0.366058\pi$
$433$	17.0000			0.816968			0.408484	+	0.912766i	$0.366058\pi$
$434$		0			0
$435$		0			0
$436$	14.0000	−	24.2487i	0.670478	−	1.16130i
$437$	3.00000	−	5.19615i	0.143509	−	0.248566i
$438$		0			0
$439$	−13.0000	−	22.5167i	−0.620456	−	1.07466i	−0.989401	−	0.145210i	$-0.953614\pi$
$439$	−13.0000	−	22.5167i	−0.620456	−	1.07466i	0.368945	−	0.929451i	$-0.379719\pi$
$440$		0			0
$441$		0			0
$442$		0			0
$443$	6.00000	+	10.3923i	0.285069	+	0.493753i	0.972626	−	0.232377i	$-0.0746503\pi$
$443$	6.00000	+	10.3923i	0.285069	+	0.493753i	−0.687557	+	0.726130i	$0.741317\pi$
$444$		0			0
$445$	4.50000	−	7.79423i	0.213320	−	0.369482i
$446$		0			0
$447$		0			0
$448$	−16.0000	−	27.7128i	−0.755929	−	1.30931i
$449$	−30.0000			−1.41579			−0.707894	−	0.706319i	$-0.750354\pi$
$449$	−30.0000			−1.41579			−0.707894	+	0.706319i	$0.750354\pi$
$450$		0			0
$451$		0			0
$452$	6.00000	+	10.3923i	0.282216	+	0.488813i
$453$		0			0
$454$		0			0
$455$	12.0000	−	20.7846i	0.562569	−	0.974398i
$456$		0			0
$457$	5.00000	+	8.66025i	0.233890	+	0.405110i	0.958950	−	0.283577i	$-0.0915211\pi$
$457$	5.00000	+	8.66025i	0.233890	+	0.405110i	−0.725059	+	0.688686i	$0.758188\pi$
$458$		0			0
$459$		0			0
$460$	18.0000			0.839254
$461$	15.0000	+	25.9808i	0.698620	+	1.21004i	0.968945	+	0.247276i	$0.0795353\pi$
$461$	15.0000	+	25.9808i	0.698620	+	1.21004i	−0.270326	+	0.962769i	$0.587131\pi$
$462$		0			0
$463$	−14.5000	+	25.1147i	−0.673872	+	1.16718i	0.302925	+	0.953014i	$0.402037\pi$
$463$	−14.5000	+	25.1147i	−0.673872	+	1.16718i	−0.976797	+	0.214166i	$0.931297\pi$
$464$	−12.0000	+	20.7846i	−0.557086	+	0.964901i
$465$		0			0
$466$		0			0
$467$	−15.0000			−0.694117			−0.347059	−	0.937843i	$-0.612820\pi$
$467$	−15.0000			−0.694117			−0.347059	+	0.937843i	$0.612820\pi$
$468$		0			0
$469$	52.0000			2.40114
$470$		0			0
$471$		0			0
$472$		0			0
$473$	4.00000	−	6.92820i	0.183920	−	0.318559i
$474$		0			0
$475$	−4.00000	−	6.92820i	−0.183533	−	0.317888i
$476$	48.0000			2.20008
$477$		0			0
$478$		0			0
$479$	−3.00000	−	5.19615i	−0.137073	−	0.237418i	0.789314	−	0.613990i	$-0.210436\pi$
$479$	−3.00000	−	5.19615i	−0.137073	−	0.237418i	−0.926388	+	0.376571i	$0.877103\pi$
$480$		0			0
$481$	−2.00000	+	3.46410i	−0.0911922	+	0.157949i
$482$		0			0
$483$		0			0
$484$	1.00000	+	1.73205i	0.0454545	+	0.0787296i
$485$	6.00000			0.272446
$486$		0			0
$487$	8.00000			0.362515			0.181257	−	0.983436i	$-0.441983\pi$
$487$	8.00000			0.362515			0.181257	+	0.983436i	$0.441983\pi$
$488$		0			0
$489$		0			0
$490$		0			0
$491$	−15.0000	+	25.9808i	−0.676941	+	1.17250i	0.298957	+	0.954267i	$0.403361\pi$
$491$	−15.0000	+	25.9808i	−0.676941	+	1.17250i	−0.975898	+	0.218229i	$0.929972\pi$
$492$		0			0
$493$	−18.0000	−	31.1769i	−0.810679	−	1.40414i
$494$		0			0
$495$		0			0
$496$	32.0000			1.43684
$497$		0			0
$498$		0			0
$499$	−20.5000	+	35.5070i	−0.917706	+	1.58951i	−0.114816	+	0.993387i	$0.536628\pi$
$499$	−20.5000	+	35.5070i	−0.917706	+	1.58951i	−0.802890	+	0.596127i	$0.796706\pi$
$500$	−3.00000	+	5.19615i	−0.134164	+	0.232379i
$501$		0			0
$502$		0			0
$503$	−6.00000			−0.267527			−0.133763	−	0.991013i	$-0.542706\pi$
$503$	−6.00000			−0.267527			−0.133763	+	0.991013i	$0.542706\pi$
$504$		0			0
$505$	−18.0000			−0.800989
$506$		0			0
$507$		0			0
$508$	−4.00000	+	6.92820i	−0.177471	+	0.307389i
$509$	−4.50000	+	7.79423i	−0.199459	+	0.345473i	−0.948353	−	0.317217i	$-0.897252\pi$
$509$	−4.50000	+	7.79423i	−0.199459	+	0.345473i	0.748894	+	0.662690i	$0.230585\pi$
$510$		0			0
$511$	4.00000	+	6.92820i	0.176950	+	0.306486i
$512$		0			0
$513$		0			0
$514$		0			0
$515$	−7.50000	−	12.9904i	−0.330489	−	0.572425i
$516$		0			0
$517$	−1.50000	+	2.59808i	−0.0659699	+	0.114263i
$518$		0			0
$519$		0			0
$520$		0			0
$521$	−42.0000			−1.84005			−0.920027	−	0.391856i	$-0.871833\pi$
$521$	−42.0000			−1.84005			−0.920027	+	0.391856i	$0.871833\pi$
$522$		0			0
$523$	−34.0000			−1.48672			−0.743358	−	0.668894i	$-0.766768\pi$
$523$	−34.0000			−1.48672			−0.743358	+	0.668894i	$0.766768\pi$
$524$	−18.0000	−	31.1769i	−0.786334	−	1.36197i
$525$		0			0
$526$		0			0
$527$	−24.0000	+	41.5692i	−1.04546	+	1.81078i
$528$		0			0
$529$	7.00000	+	12.1244i	0.304348	+	0.527146i
$530$		0			0
$531$		0			0
$532$	16.0000			0.693688
$533$		0			0
$534$		0			0
$535$	−18.0000	+	31.1769i	−0.778208	+	1.34790i
$536$		0			0
$537$		0			0
$538$		0			0
$539$	−9.00000			−0.387657
$540$		0			0
$541$	14.0000			0.601907			0.300954	−	0.953639i	$-0.402695\pi$
$541$	14.0000			0.601907			0.300954	+	0.953639i	$0.402695\pi$
$542$		0			0
$543$		0			0
$544$		0			0
$545$	−21.0000	+	36.3731i	−0.899541	+	1.55805i
$546$		0			0
$547$	14.0000	+	24.2487i	0.598597	+	1.03680i	0.993028	+	0.117875i	$0.0376081\pi$
$547$	14.0000	+	24.2487i	0.598597	+	1.03680i	−0.394432	+	0.918925i	$0.629059\pi$
$548$	36.0000			1.53784
$549$		0			0
$550$		0			0
$551$	−6.00000	−	10.3923i	−0.255609	−	0.442727i
$552$		0			0
$553$	4.00000	−	6.92820i	0.170097	−	0.294617i
$554$		0			0
$555$		0			0
$556$	−10.0000	−	17.3205i	−0.424094	−	0.734553i
$557$	30.0000			1.27114			0.635570	−	0.772043i	$-0.280765\pi$
$557$	30.0000			1.27114			0.635570	+	0.772043i	$0.280765\pi$
$558$		0			0
$559$	16.0000			0.676728
$560$	24.0000	+	41.5692i	1.01419	+	1.75662i
$561$		0			0
$562$		0			0
$563$	12.0000	−	20.7846i	0.505740	−	0.875967i	−0.494238	−	0.869326i	$-0.664553\pi$
$563$	12.0000	−	20.7846i	0.505740	−	0.875967i	0.999978	−	0.00664037i	$-0.00211371\pi$
$564$		0			0
$565$	−9.00000	−	15.5885i	−0.378633	−	0.655811i
$566$		0			0
$567$		0			0
$568$		0			0
$569$	−21.0000	−	36.3731i	−0.880366	−	1.52484i	−0.850935	−	0.525271i	$-0.823964\pi$
$569$	−21.0000	−	36.3731i	−0.880366	−	1.52484i	−0.0294311	−	0.999567i	$-0.509370\pi$
$570$		0			0
$571$	−10.0000	+	17.3205i	−0.418487	+	0.724841i	−0.995788	−	0.0916910i	$-0.970773\pi$
$571$	−10.0000	+	17.3205i	−0.418487	+	0.724841i	0.577301	+	0.816532i	$0.304106\pi$
$572$	−2.00000	+	3.46410i	−0.0836242	+	0.144841i
$573$		0			0
$574$		0			0
$575$	−12.0000			−0.500435
$576$		0			0
$577$	−7.00000			−0.291414			−0.145707	−	0.989328i	$-0.546546\pi$
$577$	−7.00000			−0.291414			−0.145707	+	0.989328i	$0.546546\pi$
$578$		0			0
$579$		0			0
$580$	18.0000	−	31.1769i	0.747409	−	1.29455i
$581$	36.0000	−	62.3538i	1.49353	−	2.58687i
$582$		0			0
$583$	−1.50000	−	2.59808i	−0.0621237	−	0.107601i
$584$		0			0
$585$		0			0
$586$		0			0
$587$	−1.50000	−	2.59808i	−0.0619116	−	0.107234i	0.833408	−	0.552658i	$-0.186386\pi$
$587$	−1.50000	−	2.59808i	−0.0619116	−	0.107234i	−0.895320	+	0.445424i	$0.853053\pi$
$588$		0			0
$589$	−8.00000	+	13.8564i	−0.329634	+	0.570943i
$590$		0			0
$591$		0			0
$592$	−4.00000	−	6.92820i	−0.164399	−	0.284747i
$593$	36.0000			1.47834			0.739171	−	0.673517i	$-0.235217\pi$
$593$	36.0000			1.47834			0.739171	+	0.673517i	$0.235217\pi$
$594$		0			0
$595$	−72.0000			−2.95171
$596$	12.0000	+	20.7846i	0.491539	+	0.851371i
$597$		0			0
$598$		0			0
$599$	12.0000	−	20.7846i	0.490307	−	0.849236i	−0.509631	−	0.860393i	$-0.670218\pi$
$599$	12.0000	−	20.7846i	0.490307	−	0.849236i	0.999938	+	0.0111569i	$0.00355143\pi$
$600$		0			0
$601$	20.0000	+	34.6410i	0.815817	+	1.41304i	0.908740	+	0.417363i	$0.137046\pi$
$601$	20.0000	+	34.6410i	0.815817	+	1.41304i	−0.0929227	+	0.995673i	$0.529621\pi$
$602$		0			0
$603$		0			0
$604$	−16.0000			−0.651031
$605$	−1.50000	−	2.59808i	−0.0609837	−	0.105627i
$606$		0			0
$607$	14.0000	−	24.2487i	0.568242	−	0.984225i	−0.428497	−	0.903543i	$-0.640957\pi$
$607$	14.0000	−	24.2487i	0.568242	−	0.984225i	0.996740	−	0.0806818i	$-0.0257098\pi$
$608$		0			0
$609$		0			0
$610$		0			0
$611$	−6.00000			−0.242734
$612$		0			0
$613$	−16.0000			−0.646234			−0.323117	−	0.946359i	$-0.604731\pi$
$613$	−16.0000			−0.646234			−0.323117	+	0.946359i	$0.604731\pi$
$614$		0			0
$615$		0			0
$616$		0			0
$617$	4.50000	−	7.79423i	0.181163	−	0.313784i	−0.761114	−	0.648618i	$-0.775347\pi$
$617$	4.50000	−	7.79423i	0.181163	−	0.313784i	0.942277	+	0.334835i	$0.108680\pi$
$618$		0			0
$619$	−22.0000	−	38.1051i	−0.884255	−	1.53157i	−0.846566	−	0.532284i	$-0.821334\pi$
$619$	−22.0000	−	38.1051i	−0.884255	−	1.53157i	−0.0376891	−	0.999290i	$-0.512000\pi$
$620$	−48.0000			−1.92773
$621$		0			0
$622$		0			0
$623$	−6.00000	−	10.3923i	−0.240385	−	0.416359i
$624$		0			0
$625$	14.5000	−	25.1147i	0.580000	−	1.00459i
$626$		0			0
$627$		0			0
$628$	−7.00000	−	12.1244i	−0.279330	−	0.483814i
$629$	12.0000			0.478471
$630$		0			0
$631$	−31.0000			−1.23409			−0.617045	−	0.786928i	$-0.711670\pi$
$631$	−31.0000			−1.23409			−0.617045	+	0.786928i	$0.711670\pi$
$632$		0			0
$633$		0			0
$634$		0			0
$635$	6.00000	−	10.3923i	0.238103	−	0.412406i
$636$		0			0
$637$	−9.00000	−	15.5885i	−0.356593	−	0.617637i
$638$		0			0
$639$		0			0
$640$		0			0
$641$	−16.5000	−	28.5788i	−0.651711	−	1.12880i	−0.982708	−	0.185164i	$-0.940718\pi$
$641$	−16.5000	−	28.5788i	−0.651711	−	1.12880i	0.330997	−	0.943632i	$-0.392615\pi$
$642$		0			0
$643$	15.5000	−	26.8468i	0.611260	−	1.05873i	−0.379768	−	0.925082i	$-0.623996\pi$
$643$	15.5000	−	26.8468i	0.611260	−	1.05873i	0.991028	−	0.133652i	$-0.0426705\pi$
$644$	12.0000	−	20.7846i	0.472866	−	0.819028i
$645$		0			0
$646$		0			0
$647$	−21.0000			−0.825595			−0.412798	−	0.910823i	$-0.635448\pi$
$647$	−21.0000			−0.825595			−0.412798	+	0.910823i	$0.635448\pi$
$648$		0			0
$649$		0			0
$650$		0			0
$651$		0			0
$652$	−1.00000	+	1.73205i	−0.0391630	+	0.0678323i
$653$	9.00000	−	15.5885i	0.352197	−	0.610023i	−0.634437	−	0.772975i	$-0.718768\pi$
$653$	9.00000	−	15.5885i	0.352197	−	0.610023i	0.986634	+	0.162951i	$0.0521013\pi$
$654$		0			0
$655$	27.0000	+	46.7654i	1.05498	+	1.82727i
$656$		0			0
$657$		0			0
$658$		0			0
$659$	−12.0000	−	20.7846i	−0.467454	−	0.809653i	0.531855	−	0.846836i	$-0.321495\pi$
$659$	−12.0000	−	20.7846i	−0.467454	−	0.809653i	−0.999309	+	0.0371821i	$0.988162\pi$
$660$		0			0
$661$	−7.00000	+	12.1244i	−0.272268	+	0.471583i	−0.969442	−	0.245319i	$-0.921107\pi$
$661$	−7.00000	+	12.1244i	−0.272268	+	0.471583i	0.697174	+	0.716902i	$0.254441\pi$
$662$		0			0
$663$		0			0
$664$		0			0
$665$	−24.0000			−0.930680
$666$		0			0
$667$	−18.0000			−0.696963
$668$	−18.0000	−	31.1769i	−0.696441	−	1.20627i
$669$		0			0
$670$		0			0
$671$	4.00000	−	6.92820i	0.154418	−	0.267460i
$672$		0			0
$673$	17.0000	+	29.4449i	0.655302	+	1.13502i	0.981818	+	0.189824i	$0.0607919\pi$
$673$	17.0000	+	29.4449i	0.655302	+	1.13502i	−0.326516	+	0.945192i	$0.605875\pi$
$674$		0			0
$675$		0			0
$676$	18.0000			0.692308
$677$	18.0000	+	31.1769i	0.691796	+	1.19823i	0.971249	+	0.238067i	$0.0765137\pi$
$677$	18.0000	+	31.1769i	0.691796	+	1.19823i	−0.279453	+	0.960159i	$0.590153\pi$
$678$		0			0
$679$	4.00000	−	6.92820i	0.153506	−	0.265880i
$680$		0			0
$681$		0			0
$682$		0			0
$683$	−15.0000			−0.573959			−0.286980	−	0.957937i	$-0.592651\pi$
$683$	−15.0000			−0.573959			−0.286980	+	0.957937i	$0.592651\pi$
$684$		0			0
$685$	−54.0000			−2.06323
$686$		0			0
$687$		0			0
$688$	−16.0000	+	27.7128i	−0.609994	+	1.05654i
$689$	3.00000	−	5.19615i	0.114291	−	0.197958i
$690$		0			0
$691$	12.5000	+	21.6506i	0.475522	+	0.823629i	0.999607	−	0.0280373i	$-0.00892572\pi$
$691$	12.5000	+	21.6506i	0.475522	+	0.823629i	−0.524084	+	0.851666i	$0.675592\pi$
$692$	36.0000			1.36851
$693$		0			0
$694$		0			0
$695$	15.0000	+	25.9808i	0.568982	+	0.985506i
$696$		0			0
$697$		0			0
$698$		0			0
$699$		0			0
$700$	−16.0000	−	27.7128i	−0.604743	−	1.04745i
$701$	−36.0000			−1.35970			−0.679851	−	0.733351i	$-0.737955\pi$
$701$	−36.0000			−1.35970			−0.679851	+	0.733351i	$0.737955\pi$
$702$		0			0
$703$	4.00000			0.150863
$704$	−4.00000	−	6.92820i	−0.150756	−	0.261116i
$705$		0			0
$706$		0			0
$707$	−12.0000	+	20.7846i	−0.451306	+	0.781686i
$708$		0			0
$709$	−11.5000	−	19.9186i	−0.431892	−	0.748058i	0.565145	−	0.824992i	$-0.308820\pi$
$709$	−11.5000	−	19.9186i	−0.431892	−	0.748058i	−0.997036	+	0.0769337i	$0.975487\pi$
$710$		0			0
$711$		0			0
$712$		0			0
$713$	12.0000	+	20.7846i	0.449404	+	0.778390i
$714$		0			0
$715$	3.00000	−	5.19615i	0.112194	−	0.194325i
$716$	−15.0000	+	25.9808i	−0.560576	+	0.970947i
$717$		0			0
$718$		0			0
$719$	3.00000			0.111881			0.0559406	−	0.998434i	$-0.482184\pi$
$719$	3.00000			0.111881			0.0559406	+	0.998434i	$0.482184\pi$
$720$		0			0
$721$	−20.0000			−0.744839
$722$		0			0
$723$		0			0
$724$	−1.00000	+	1.73205i	−0.0371647	+	0.0643712i
$725$	−12.0000	+	20.7846i	−0.445669	+	0.771921i
$726$		0			0
$727$	14.0000	+	24.2487i	0.519231	+	0.899335i	0.999750	+	0.0223506i	$0.00711500\pi$
$727$	14.0000	+	24.2487i	0.519231	+	0.899335i	−0.480519	+	0.876984i	$0.659552\pi$
$728$		0			0
$729$		0			0
$730$		0			0
$731$	−24.0000	−	41.5692i	−0.887672	−	1.53749i
$732$		0			0
$733$	20.0000	−	34.6410i	0.738717	−	1.27950i	−0.214356	−	0.976756i	$-0.568765\pi$
$733$	20.0000	−	34.6410i	0.738717	−	1.27950i	0.953073	−	0.302740i	$-0.0979013\pi$
$734$		0			0
$735$		0			0
$736$		0			0
$737$	13.0000			0.478861
$738$		0			0
$739$	−10.0000			−0.367856			−0.183928	−	0.982940i	$-0.558881\pi$
$739$	−10.0000			−0.367856			−0.183928	+	0.982940i	$0.558881\pi$
$740$	6.00000	+	10.3923i	0.220564	+	0.382029i
$741$		0			0
$742$		0			0
$743$	−3.00000	+	5.19615i	−0.110059	+	0.190628i	−0.915794	−	0.401648i	$-0.868437\pi$
$743$	−3.00000	+	5.19615i	−0.110059	+	0.190628i	0.805735	+	0.592277i	$0.201771\pi$
$744$		0			0
$745$	−18.0000	−	31.1769i	−0.659469	−	1.14223i
$746$		0			0
$747$		0			0
$748$	12.0000			0.438763
$749$	24.0000	+	41.5692i	0.876941	+	1.51891i
$750$		0			0
$751$	8.00000	−	13.8564i	0.291924	−	0.505627i	−0.682341	−	0.731034i	$-0.739038\pi$
$751$	8.00000	−	13.8564i	0.291924	−	0.505627i	0.974265	+	0.225407i	$0.0723712\pi$
$752$	6.00000	−	10.3923i	0.218797	−	0.378968i
$753$		0			0
$754$		0			0
$755$	24.0000			0.873449
$756$		0			0
$757$	29.0000			1.05402			0.527011	−	0.849858i	$-0.323312\pi$
$757$	29.0000			1.05402			0.527011	+	0.849858i	$0.323312\pi$
$758$		0			0
$759$		0			0
$760$		0			0
$761$	6.00000	−	10.3923i	0.217500	−	0.376721i	−0.736543	−	0.676391i	$-0.763543\pi$
$761$	6.00000	−	10.3923i	0.217500	−	0.376721i	0.954043	+	0.299670i	$0.0968765\pi$
$762$		0			0
$763$	28.0000	+	48.4974i	1.01367	+	1.75572i
$764$	6.00000			0.217072
$765$		0			0
$766$		0			0
$767$		0			0
$768$		0			0
$769$	−4.00000	+	6.92820i	−0.144244	+	0.249837i	−0.929091	−	0.369852i	$-0.879408\pi$
$769$	−4.00000	+	6.92820i	−0.144244	+	0.249837i	0.784847	+	0.619690i	$0.212742\pi$
$770$		0			0
$771$		0			0
$772$	−4.00000	−	6.92820i	−0.143963	−	0.249351i
$773$	−18.0000			−0.647415			−0.323708	−	0.946157i	$-0.604929\pi$
$773$	−18.0000			−0.647415			−0.323708	+	0.946157i	$0.604929\pi$
$774$		0			0
$775$	32.0000			1.14947
$776$		0			0
$777$		0			0
$778$		0			0
$779$		0			0
$780$		0			0
$781$		0			0
$782$		0			0
$783$		0			0
$784$	36.0000			1.28571
$785$	10.5000	+	18.1865i	0.374761	+	0.649105i
$786$		0			0
$787$	−16.0000	+	27.7128i	−0.570338	+	0.987855i	0.426193	+	0.904632i	$0.359855\pi$
$787$	−16.0000	+	27.7128i	−0.570338	+	0.987855i	−0.996531	+	0.0832226i	$0.973479\pi$
$788$	−18.0000	+	31.1769i	−0.641223	+	1.11063i
$789$		0			0
$790$		0			0
$791$	−24.0000			−0.853342
$792$		0			0
$793$	16.0000			0.568177
$794$		0			0
$795$		0			0
$796$	11.0000	−	19.0526i	0.389885	−	0.675300i
$797$	15.0000	−	25.9808i	0.531327	−	0.920286i	−0.468004	−	0.883726i	$-0.655027\pi$
$797$	15.0000	−	25.9808i	0.531327	−	0.920286i	0.999331	−	0.0365596i	$-0.0116399\pi$
$798$		0			0
$799$	9.00000	+	15.5885i	0.318397	+	0.551480i
$800$		0			0
$801$		0			0
$802$		0			0
$803$	1.00000	+	1.73205i	0.0352892	+	0.0611227i
$804$		0			0
$805$	−18.0000	+	31.1769i	−0.634417	+	1.09884i
$806$		0			0
$807$		0			0
$808$		0			0
$809$	6.00000			0.210949			0.105474	−	0.994422i	$-0.466364\pi$
$809$	6.00000			0.210949			0.105474	+	0.994422i	$0.466364\pi$
$810$		0			0
$811$	8.00000			0.280918			0.140459	−	0.990086i	$-0.455142\pi$
$811$	8.00000			0.280918			0.140459	+	0.990086i	$0.455142\pi$
$812$	−24.0000	−	41.5692i	−0.842235	−	1.45879i
$813$		0			0
$814$		0			0
$815$	1.50000	−	2.59808i	0.0525427	−	0.0910066i
$816$		0			0
$817$	−8.00000	−	13.8564i	−0.279885	−	0.484774i
$818$		0			0
$819$		0			0
$820$		0			0
$821$	6.00000	+	10.3923i	0.209401	+	0.362694i	0.951526	−	0.307568i	$-0.0995151\pi$
$821$	6.00000	+	10.3923i	0.209401	+	0.362694i	−0.742125	+	0.670262i	$0.766182\pi$
$822$		0			0
$823$	24.5000	−	42.4352i	0.854016	−	1.47920i	−0.0235383	−	0.999723i	$-0.507493\pi$
$823$	24.5000	−	42.4352i	0.854016	−	1.47920i	0.877555	−	0.479477i	$-0.159174\pi$
$824$		0			0
$825$		0			0
$826$		0			0
$827$	−18.0000			−0.625921			−0.312961	−	0.949766i	$-0.601321\pi$
$827$	−18.0000			−0.625921			−0.312961	+	0.949766i	$0.601321\pi$
$828$		0			0
$829$	−7.00000			−0.243120			−0.121560	−	0.992584i	$-0.538790\pi$
$829$	−7.00000			−0.243120			−0.121560	+	0.992584i	$0.538790\pi$
$830$		0			0
$831$		0			0
$832$	8.00000	−	13.8564i	0.277350	−	0.480384i
$833$	−27.0000	+	46.7654i	−0.935495	+	1.62032i
$834$		0			0
$835$	27.0000	+	46.7654i	0.934374	+	1.61838i
$836$	4.00000			0.138343
$837$		0			0
$838$		0			0
$839$	7.50000	+	12.9904i	0.258929	+	0.448478i	0.965955	−	0.258709i	$-0.0832972\pi$
$839$	7.50000	+	12.9904i	0.258929	+	0.448478i	−0.707026	+	0.707187i	$0.749964\pi$
$840$		0			0
$841$	−3.50000	+	6.06218i	−0.120690	+	0.209041i
$842$		0			0
$843$		0			0
$844$	−4.00000	−	6.92820i	−0.137686	−	0.238479i
$845$	−27.0000			−0.928828
$846$		0			0
$847$	−4.00000			−0.137442
$848$	6.00000	+	10.3923i	0.206041	+	0.356873i
$849$		0			0
$850$		0			0
$851$	3.00000	−	5.19615i	0.102839	−	0.178122i
$852$		0			0
$853$	−22.0000	−	38.1051i	−0.753266	−	1.30469i	−0.946232	−	0.323489i	$-0.895144\pi$
$853$	−22.0000	−	38.1051i	−0.753266	−	1.30469i	0.192966	−	0.981205i	$-0.438189\pi$
$854$		0			0
$855$		0			0
$856$		0			0
$857$	−6.00000	−	10.3923i	−0.204956	−	0.354994i	0.745163	−	0.666883i	$-0.232372\pi$
$857$	−6.00000	−	10.3923i	−0.204956	−	0.354994i	−0.950119	+	0.311888i	$0.899038\pi$
$858$		0			0
$859$	6.50000	−	11.2583i	0.221777	−	0.384129i	−0.733571	−	0.679613i	$-0.762148\pi$
$859$	6.50000	−	11.2583i	0.221777	−	0.384129i	0.955348	+	0.295484i	$0.0954809\pi$
$860$	24.0000	−	41.5692i	0.818393	−	1.41750i
$861$		0			0
$862$		0			0
$863$	36.0000			1.22545			0.612727	−	0.790295i	$-0.290072\pi$
$863$	36.0000			1.22545			0.612727	+	0.790295i	$0.290072\pi$
$864$		0			0
$865$	−54.0000			−1.83606
$866$		0			0
$867$		0			0
$868$	−32.0000	+	55.4256i	−1.08615	+	1.88127i
$869$	1.00000	−	1.73205i	0.0339227	−	0.0587558i
$870$		0			0
$871$	13.0000	+	22.5167i	0.440488	+	0.762948i
$872$		0			0
$873$		0			0
$874$		0			0
$875$	−6.00000	−	10.3923i	−0.202837	−	0.351324i
$876$		0			0
$877$	20.0000	−	34.6410i	0.675352	−	1.16974i	−0.301014	−	0.953620i	$-0.597325\pi$
$877$	20.0000	−	34.6410i	0.675352	−	1.16974i	0.976366	−	0.216124i	$-0.0693416\pi$
$878$		0			0
$879$		0			0
$880$	6.00000	+	10.3923i	0.202260	+	0.350325i
$881$	39.0000			1.31394			0.656972	−	0.753915i	$-0.271837\pi$
$881$	39.0000			1.31394			0.656972	+	0.753915i	$0.271837\pi$
$882$		0			0
$883$	5.00000			0.168263			0.0841317	−	0.996455i	$-0.473188\pi$
$883$	5.00000			0.168263			0.0841317	+	0.996455i	$0.473188\pi$
$884$	12.0000	+	20.7846i	0.403604	+	0.699062i
$885$		0			0
$886$		0			0
$887$	−15.0000	+	25.9808i	−0.503651	+	0.872349i	0.496340	+	0.868128i	$0.334677\pi$
$887$	−15.0000	+	25.9808i	−0.503651	+	0.872349i	−0.999991	+	0.00422062i	$0.998657\pi$
$888$		0			0
$889$	−8.00000	−	13.8564i	−0.268311	−	0.464729i
$890$		0			0
$891$		0			0
$892$	−22.0000			−0.736614
$893$	3.00000	+	5.19615i	0.100391	+	0.173883i
$894$		0			0
$895$	22.5000	−	38.9711i	0.752092	−	1.30266i
$896$		0			0
$897$		0			0
$898$		0			0
$899$	48.0000			1.60089
$900$		0			0
$901$	−18.0000			−0.599667
$902$		0			0
$903$		0			0
$904$		0			0
$905$	1.50000	−	2.59808i	0.0498617	−	0.0863630i
$906$		0			0
$907$	14.0000	+	24.2487i	0.464862	+	0.805165i	0.999195	−	0.0401089i	$-0.0127705\pi$
$907$	14.0000	+	24.2487i	0.464862	+	0.805165i	−0.534333	+	0.845274i	$0.679437\pi$
$908$	36.0000			1.19470
$909$		0			0
$910$		0			0
$911$	−7.50000	−	12.9904i	−0.248486	−	0.430391i	0.714620	−	0.699513i	$-0.246600\pi$
$911$	−7.50000	−	12.9904i	−0.248486	−	0.430391i	−0.963106	+	0.269122i	$0.913266\pi$
$912$		0			0
$913$	9.00000	−	15.5885i	0.297857	−	0.515903i
$914$		0			0
$915$		0			0
$916$	23.0000	+	39.8372i	0.759941	+	1.31626i
$917$	72.0000			2.37765
$918$		0			0
$919$	56.0000			1.84727			0.923635	−	0.383274i	$-0.125203\pi$
$919$	56.0000			1.84727			0.923635	+	0.383274i	$0.125203\pi$
$920$		0			0
$921$		0			0
$922$		0			0
$923$		0			0
$924$		0			0
$925$	−4.00000	−	6.92820i	−0.131519	−	0.227798i
$926$		0			0
$927$		0			0
$928$		0			0
$929$	10.5000	+	18.1865i	0.344494	+	0.596681i	0.985262	−	0.171054i	$-0.0547172\pi$
$929$	10.5000	+	18.1865i	0.344494	+	0.596681i	−0.640768	+	0.767735i	$0.721384\pi$
$930$		0			0
$931$	−9.00000	+	15.5885i	−0.294963	+	0.510891i
$932$	6.00000	−	10.3923i	0.196537	−	0.340411i
$933$		0			0
$934$		0			0
$935$	−18.0000			−0.588663
$936$		0			0
$937$	−28.0000			−0.914720			−0.457360	−	0.889282i	$-0.651205\pi$
$937$	−28.0000			−0.914720			−0.457360	+	0.889282i	$0.651205\pi$
$938$		0			0
$939$		0			0
$940$	−9.00000	+	15.5885i	−0.293548	+	0.508439i
$941$	−27.0000	+	46.7654i	−0.880175	+	1.52451i	−0.0290288	+	0.999579i	$0.509241\pi$
$941$	−27.0000	+	46.7654i	−0.880175	+	1.52451i	−0.851146	+	0.524929i	$0.824092\pi$
$942$		0			0
$943$		0			0
$944$		0			0
$945$		0			0
$946$		0			0
$947$	1.50000	+	2.59808i	0.0487435	+	0.0844261i	0.889368	−	0.457193i	$-0.151145\pi$
$947$	1.50000	+	2.59808i	0.0487435	+	0.0844261i	−0.840624	+	0.541619i	$0.817812\pi$
$948$		0			0
$949$	−2.00000	+	3.46410i	−0.0649227	+	0.112449i
$950$		0			0
$951$		0			0
$952$		0			0
$953$	−6.00000			−0.194359			−0.0971795	−	0.995267i	$-0.530982\pi$
$953$	−6.00000			−0.194359			−0.0971795	+	0.995267i	$0.530982\pi$
$954$		0			0
$955$	−9.00000			−0.291233
$956$	12.0000	+	20.7846i	0.388108	+	0.672222i
$957$		0			0
$958$		0			0
$959$	−36.0000	+	62.3538i	−1.16250	+	2.01351i
$960$		0			0
$961$	−16.5000	−	28.5788i	−0.532258	−	0.921898i
$962$		0			0
$963$		0			0
$964$	−4.00000			−0.128831
$965$	6.00000	+	10.3923i	0.193147	+	0.334540i
$966$		0			0
$967$	20.0000	−	34.6410i	0.643157	−	1.11398i	−0.341567	−	0.939857i	$-0.610958\pi$
$967$	20.0000	−	34.6410i	0.643157	−	1.11398i	0.984724	−	0.174123i	$-0.0557089\pi$
$968$		0			0
$969$		0			0
$970$		0			0
$971$	−27.0000			−0.866471			−0.433236	−	0.901281i	$-0.642628\pi$
$971$	−27.0000			−0.866471			−0.433236	+	0.901281i	$0.642628\pi$
$972$		0			0
$973$	40.0000			1.28234
$974$		0			0
$975$		0			0
$976$	−16.0000	+	27.7128i	−0.512148	+	0.887066i
$977$	22.5000	−	38.9711i	0.719839	−	1.24680i	−0.241225	−	0.970469i	$-0.577549\pi$
$977$	22.5000	−	38.9711i	0.719839	−	1.24680i	0.961063	−	0.276328i	$-0.0891176\pi$
$978$		0			0
$979$	−1.50000	−	2.59808i	−0.0479402	−	0.0830349i
$980$	−54.0000			−1.72497
$981$		0			0
$982$		0			0
$983$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$983$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$984$		0			0
$985$	27.0000	−	46.7654i	0.860292	−	1.49007i
$986$		0			0
$987$		0			0
$988$	4.00000	+	6.92820i	0.127257	+	0.220416i
$989$	−24.0000			−0.763156
$990$		0			0
$991$	−16.0000			−0.508257			−0.254128	−	0.967170i	$-0.581789\pi$
$991$	−16.0000			−0.508257			−0.254128	+	0.967170i	$0.581789\pi$
$992$		0			0
$993$		0			0
$994$		0			0
$995$	−16.5000	+	28.5788i	−0.523085	+	0.906010i
$996$		0			0
$997$	5.00000	+	8.66025i	0.158352	+	0.274273i	0.934274	−	0.356555i	$-0.116049\pi$
$997$	5.00000	+	8.66025i	0.158352	+	0.274273i	−0.775923	+	0.630828i	$0.782715\pi$
$998$		0			0
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	297.2.e.b.199.1		2
3.2	odd	2		99.2.e.b.67.1	yes	2
9.2	odd	6		99.2.e.b.34.1	✓	2
9.4	even	3		891.2.a.e.1.1		1
9.5	odd	6		891.2.a.d.1.1		1
9.7	even	3	inner	297.2.e.b.100.1		2
33.32	even	2		1089.2.e.b.364.1		2
99.32	even	6		9801.2.a.f.1.1		1
99.65	even	6		1089.2.e.b.727.1		2
99.76	odd	6		9801.2.a.g.1.1		1

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
99.2.e.b.34.1	✓	2	9.2	odd	6
99.2.e.b.67.1	yes	2	3.2	odd	2
297.2.e.b.100.1		2	9.7	even	3	inner
297.2.e.b.199.1		2	1.1	even	1	trivial
891.2.a.d.1.1		1	9.5	odd	6
891.2.a.e.1.1		1	9.4	even	3
1089.2.e.b.364.1		2	33.32	even	2
1089.2.e.b.727.1		2	99.65	even	6
9801.2.a.f.1.1		1	99.32	even	6
9801.2.a.g.1.1		1	99.76	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:	\( N \)	\(=\)	\( 297 = 3^{3} \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	297.e (of order \(3\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(1.00000 - 1.73205i) q^{4} +(-1.50000 + 2.59808i) q^{5} +(2.00000 + 3.46410i) q^{7} +(0.500000 + 0.866025i) q^{11} +(-1.00000 + 1.73205i) q^{13} +(-2.00000 - 3.46410i) q^{16} +6.00000 q^{17} +2.00000 q^{19} +(3.00000 + 5.19615i) q^{20} +(1.50000 - 2.59808i) q^{23} +(-2.00000 - 3.46410i) q^{25} +8.00000 q^{28} +(-3.00000 - 5.19615i) q^{29} +(-4.00000 + 6.92820i) q^{31} -12.0000 q^{35} +2.00000 q^{37} +(-4.00000 - 6.92820i) q^{43} +2.00000 q^{44} +(1.50000 + 2.59808i) q^{47} +(-4.50000 + 7.79423i) q^{49} +(2.00000 + 3.46410i) q^{52} -3.00000 q^{53} -3.00000 q^{55} +(-4.00000 - 6.92820i) q^{61} -8.00000 q^{64} +(-3.00000 - 5.19615i) q^{65} +(6.50000 - 11.2583i) q^{67} +(6.00000 - 10.3923i) q^{68} +2.00000 q^{73} +(2.00000 - 3.46410i) q^{76} +(-2.00000 + 3.46410i) q^{77} +(-1.00000 - 1.73205i) q^{79} +12.0000 q^{80} +(-9.00000 - 15.5885i) q^{83} +(-9.00000 + 15.5885i) q^{85} -3.00000 q^{89} -8.00000 q^{91} +(-3.00000 - 5.19615i) q^{92} +(-3.00000 + 5.19615i) q^{95} +(-1.00000 - 1.73205i) q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q + 2 q^{4} - 3 q^{5} + 4 q^{7} + q^{11} - 2 q^{13} - 4 q^{16} + 12 q^{17} + 4 q^{19} + 6 q^{20} + 3 q^{23} - 4 q^{25} + 16 q^{28} - 6 q^{29} - 8 q^{31} - 24 q^{35} + 4 q^{37} - 8 q^{43} + 4 q^{44} + 3 q^{47}+ \cdots - 2 q^{97}+O(q^{100}) \) 2 * q + 2 * q^4 - 3 * q^5 + 4 * q^7 + q^11 - 2 * q^13 - 4 * q^16 + 12 * q^17 + 4 * q^19 + 6 * q^20 + 3 * q^23 - 4 * q^25 + 16 * q^28 - 6 * q^29 - 8 * q^31 - 24 * q^35 + 4 * q^37 - 8 * q^43 + 4 * q^44 + 3 * q^47 - 9 * q^49 + 4 * q^52 - 6 * q^53 - 6 * q^55 - 8 * q^61 - 16 * q^64 - 6 * q^65 + 13 * q^67 + 12 * q^68 + 4 * q^73 + 4 * q^76 - 4 * q^77 - 2 * q^79 + 24 * q^80 - 18 * q^83 - 18 * q^85 - 6 * q^89 - 16 * q^91 - 6 * q^92 - 6 * q^95 - 2 * q^97

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