LMFDB - Embedded newform 560.2.bj.a.97.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [560,2,Mod(97,560)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(560, base_ring=CyclotomicField(4))

chi = DirichletCharacter(H, H._module([0, 0, 1, 2]))

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

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

chi := DirichletCharacter("560.97");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 560 = 2^{4} \cdot 5 \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	560.bj (of order $4$, 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:	$4.47162251319$
Analytic rank:	$0$
Dimension:	$4$
Relative dimension:	$2$ over $\Q(i)$
Coefficient field:	$\Q(i, \sqrt{10})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} + 25 $ x^4 + 25
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 35)
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			97.1
Root			$-1.58114 - 1.58114i$ of defining polynomial
Character	$\chi$	$=$	560.97
Dual form			560.2.bj.a.433.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.58114 - 1.58114i) q^{3} +(-1.58114 - 1.58114i) q^{5} +(0.581139 - 2.58114i) q^{7} +2.00000i q^{9} +O(q^{10})$	\(q+(-1.58114 - 1.58114i) q^{3} +(-1.58114 - 1.58114i) q^{5} +(0.581139 - 2.58114i) q^{7} +2.00000i q^{9} +1.00000 q^{11} +(-1.58114 - 1.58114i) q^{13} +5.00000i q^{15} +(1.58114 - 1.58114i) q^{17} -3.16228 q^{19} +(-5.00000 + 3.16228i) q^{21} +(-2.00000 + 2.00000i) q^{23} +5.00000i q^{25} +(-1.58114 + 1.58114i) q^{27} +3.00000i q^{29} +3.16228i q^{31} +(-1.58114 - 1.58114i) q^{33} +(-5.00000 + 3.16228i) q^{35} +(-6.00000 - 6.00000i) q^{37} +5.00000i q^{39} +9.48683i q^{41} +(3.00000 - 3.00000i) q^{43} +(3.16228 - 3.16228i) q^{45} +(4.74342 - 4.74342i) q^{47} +(-6.32456 - 3.00000i) q^{49} -5.00000 q^{51} +(1.00000 - 1.00000i) q^{53} +(-1.58114 - 1.58114i) q^{55} +(5.00000 + 5.00000i) q^{57} -9.48683 q^{59} -6.32456i q^{61} +(5.16228 + 1.16228i) q^{63} +5.00000i q^{65} +(1.00000 + 1.00000i) q^{67} +6.32456 q^{69} +6.00000 q^{71} +(7.90569 - 7.90569i) q^{75} +(0.581139 - 2.58114i) q^{77} -13.0000i q^{79} +11.0000 q^{81} +(3.16228 + 3.16228i) q^{83} -5.00000 q^{85} +(4.74342 - 4.74342i) q^{87} -6.32456 q^{89} +(-5.00000 + 3.16228i) q^{91} +(5.00000 - 5.00000i) q^{93} +(5.00000 + 5.00000i) q^{95} +(-1.58114 + 1.58114i) q^{97} +2.00000i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q - 4 q^{7}+O(q^{10}) $ 4 * q - 4 * q^7	$ 4 q - 4 q^{7} + 4 q^{11} - 20 q^{21} - 8 q^{23} - 20 q^{35} - 24 q^{37} + 12 q^{43} - 20 q^{51} + 4 q^{53} + 20 q^{57} + 8 q^{63} + 4 q^{67} + 24 q^{71} - 4 q^{77} + 44 q^{81} - 20 q^{85} - 20 q^{91} + 20 q^{93} + 20 q^{95}+O(q^{100}) $ 4 * q - 4 * q^7 + 4 * q^11 - 20 * q^21 - 8 * q^23 - 20 * q^35 - 24 * q^37 + 12 * q^43 - 20 * q^51 + 4 * q^53 + 20 * q^57 + 8 * q^63 + 4 * q^67 + 24 * q^71 - 4 * q^77 + 44 * q^81 - 20 * q^85 - 20 * q^91 + 20 * q^93 + 20 * q^95

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/560\mathbb{Z}\right)^\times$.

$n$	$241$	$337$	$351$	$421$
$\chi(n)$	$-1$	$e\left(\frac{1}{4}\right)$	$1$	$1$

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
$2$		0			0
$3$	−1.58114	−	1.58114i	−0.912871	−	0.912871i	0.0836263	−	0.996497i	$-0.473350\pi$
$3$	−1.58114	−	1.58114i	−0.912871	−	0.912871i	−0.996497	+	0.0836263i	$0.973350\pi$
$4$		0			0
$5$	−1.58114	−	1.58114i	−0.707107	−	0.707107i
$5$	−1.58114	−	1.58114i	−0.707107	−	0.707107i
$6$		0			0
$7$	0.581139	−	2.58114i	0.219650	−	0.975579i
$7$	0.581139	−	2.58114i	0.219650	−	0.975579i
$8$		0			0
$9$			2.00000i			0.666667i
$10$		0			0
$11$	1.00000			0.301511			0.150756	−	0.988571i	$-0.451829\pi$
$11$	1.00000			0.301511			0.150756	+	0.988571i	$0.451829\pi$
$12$		0			0
$13$	−1.58114	−	1.58114i	−0.438529	−	0.438529i	0.452988	−	0.891517i	$-0.350358\pi$
$13$	−1.58114	−	1.58114i	−0.438529	−	0.438529i	−0.891517	+	0.452988i	$0.850358\pi$
$14$		0			0
$15$			5.00000i			1.29099i
$16$		0			0
$17$	1.58114	−	1.58114i	0.383482	−	0.383482i	−0.488873	−	0.872355i	$-0.662592\pi$
$17$	1.58114	−	1.58114i	0.383482	−	0.383482i	0.872355	+	0.488873i	$0.162592\pi$
$18$		0			0
$19$	−3.16228			−0.725476			−0.362738	−	0.931891i	$-0.618158\pi$
$19$	−3.16228			−0.725476			−0.362738	+	0.931891i	$0.618158\pi$
$20$		0			0
$21$	−5.00000	+	3.16228i	−1.09109	+	0.690066i
$22$		0			0
$23$	−2.00000	+	2.00000i	−0.417029	+	0.417029i	−0.884178	−	0.467150i	$-0.845281\pi$
$23$	−2.00000	+	2.00000i	−0.417029	+	0.417029i	0.467150	+	0.884178i	$0.345281\pi$
$24$		0			0
$25$			5.00000i			1.00000i
$26$		0			0
$27$	−1.58114	+	1.58114i	−0.304290	+	0.304290i
$28$		0			0
$29$			3.00000i			0.557086i	0.960424	+	0.278543i	$0.0898515\pi$
$29$			3.00000i			0.557086i	−0.960424	+	0.278543i	$0.910149\pi$
$30$		0			0
$31$			3.16228i			0.567962i	0.958830	+	0.283981i	$0.0916552\pi$
$31$			3.16228i			0.567962i	−0.958830	+	0.283981i	$0.908345\pi$
$32$		0			0
$33$	−1.58114	−	1.58114i	−0.275241	−	0.275241i
$34$		0			0
$35$	−5.00000	+	3.16228i	−0.845154	+	0.534522i
$36$		0			0
$37$	−6.00000	−	6.00000i	−0.986394	−	0.986394i	0.0135147	−	0.999909i	$-0.495698\pi$
$37$	−6.00000	−	6.00000i	−0.986394	−	0.986394i	−0.999909	+	0.0135147i	$0.995698\pi$
$38$		0			0
$39$			5.00000i			0.800641i
$40$		0			0
$41$			9.48683i			1.48159i	0.671729	+	0.740797i	$0.265552\pi$
$41$			9.48683i			1.48159i	−0.671729	+	0.740797i	$0.734448\pi$
$42$		0			0
$43$	3.00000	−	3.00000i	0.457496	−	0.457496i	−0.440337	−	0.897833i	$-0.645141\pi$
$43$	3.00000	−	3.00000i	0.457496	−	0.457496i	0.897833	+	0.440337i	$0.145141\pi$
$44$		0			0
$45$	3.16228	−	3.16228i	0.471405	−	0.471405i
$46$		0			0
$47$	4.74342	−	4.74342i	0.691898	−	0.691898i	−0.270751	−	0.962649i	$-0.587272\pi$
$47$	4.74342	−	4.74342i	0.691898	−	0.691898i	0.962649	+	0.270751i	$0.0872720\pi$
$48$		0			0
$49$	−6.32456	−	3.00000i	−0.903508	−	0.428571i
$50$		0			0
$51$	−5.00000			−0.700140
$52$		0			0
$53$	1.00000	−	1.00000i	0.137361	−	0.137361i	−0.635083	−	0.772444i	$-0.719034\pi$
$53$	1.00000	−	1.00000i	0.137361	−	0.137361i	0.772444	+	0.635083i	$0.219034\pi$
$54$		0			0
$55$	−1.58114	−	1.58114i	−0.213201	−	0.213201i
$56$		0			0
$57$	5.00000	+	5.00000i	0.662266	+	0.662266i
$58$		0			0
$59$	−9.48683			−1.23508			−0.617540	−	0.786539i	$-0.711871\pi$
$59$	−9.48683			−1.23508			−0.617540	+	0.786539i	$0.711871\pi$
$60$		0			0
$61$		−	6.32456i		−	0.809776i	−0.914366	−	0.404888i	$-0.867310\pi$
$61$		−	6.32456i		−	0.809776i	0.914366	−	0.404888i	$-0.132690\pi$
$62$		0			0
$63$	5.16228	+	1.16228i	0.650386	+	0.146433i
$64$		0			0
$65$			5.00000i			0.620174i
$66$		0			0
$67$	1.00000	+	1.00000i	0.122169	+	0.122169i	0.765548	−	0.643379i	$-0.222468\pi$
$67$	1.00000	+	1.00000i	0.122169	+	0.122169i	−0.643379	+	0.765548i	$0.722468\pi$
$68$		0			0
$69$	6.32456			0.761387
$70$		0			0
$71$	6.00000			0.712069			0.356034	−	0.934473i	$-0.384129\pi$
$71$	6.00000			0.712069			0.356034	+	0.934473i	$0.384129\pi$
$72$		0			0
$73$		0			0		0.707107	−	0.707107i	$-0.250000\pi$
$73$		0			0		−0.707107	+	0.707107i	$0.750000\pi$
$74$		0			0
$75$	7.90569	−	7.90569i	0.912871	−	0.912871i
$76$		0			0
$77$	0.581139	−	2.58114i	0.0662269	−	0.294148i
$78$		0			0
$79$		−	13.0000i		−	1.46261i	−0.682048	−	0.731307i	$-0.738911\pi$
$79$		−	13.0000i		−	1.46261i	0.682048	−	0.731307i	$-0.261089\pi$
$80$		0			0
$81$	11.0000			1.22222
$82$		0			0
$83$	3.16228	+	3.16228i	0.347105	+	0.347105i	0.859030	−	0.511925i	$-0.171067\pi$
$83$	3.16228	+	3.16228i	0.347105	+	0.347105i	−0.511925	+	0.859030i	$0.671067\pi$
$84$		0			0
$85$	−5.00000			−0.542326
$86$		0			0
$87$	4.74342	−	4.74342i	0.508548	−	0.508548i
$88$		0			0
$89$	−6.32456			−0.670402			−0.335201	−	0.942147i	$-0.608804\pi$
$89$	−6.32456			−0.670402			−0.335201	+	0.942147i	$0.608804\pi$
$90$		0			0
$91$	−5.00000	+	3.16228i	−0.524142	+	0.331497i
$92$		0			0
$93$	5.00000	−	5.00000i	0.518476	−	0.518476i
$94$		0			0
$95$	5.00000	+	5.00000i	0.512989	+	0.512989i
$96$		0			0
$97$	−1.58114	+	1.58114i	−0.160540	+	0.160540i	−0.782806	−	0.622266i	$-0.786212\pi$
$97$	−1.58114	+	1.58114i	−0.160540	+	0.160540i	0.622266	+	0.782806i	$0.286212\pi$
$98$		0			0
$99$			2.00000i			0.201008i
$100$		0			0
$101$			3.16228i			0.314658i	0.987546	+	0.157329i	$0.0502884\pi$
$101$			3.16228i			0.314658i	−0.987546	+	0.157329i	$0.949712\pi$
$102$		0			0
$103$	−11.0680	−	11.0680i	−1.09056	−	1.09056i	−0.995469	−	0.0950911i	$-0.969686\pi$
$103$	−11.0680	−	11.0680i	−1.09056	−	1.09056i	−0.0950911	−	0.995469i	$-0.530314\pi$
$104$		0			0
$105$	12.9057	+	2.90569i	1.25947	+	0.283567i
$106$		0			0
$107$	3.00000	+	3.00000i	0.290021	+	0.290021i	0.837088	−	0.547068i	$-0.184256\pi$
$107$	3.00000	+	3.00000i	0.290021	+	0.290021i	−0.547068	+	0.837088i	$0.684256\pi$
$108$		0			0
$109$		−	7.00000i		−	0.670478i	−0.942133	−	0.335239i	$-0.891183\pi$
$109$		−	7.00000i		−	0.670478i	0.942133	−	0.335239i	$-0.108817\pi$
$110$		0			0
$111$			18.9737i			1.80090i
$112$		0			0
$113$	12.0000	−	12.0000i	1.12887	−	1.12887i	0.138503	−	0.990362i	$-0.455771\pi$
$113$	12.0000	−	12.0000i	1.12887	−	1.12887i	0.990362	−	0.138503i	$-0.0442291\pi$
$114$		0			0
$115$	6.32456			0.589768
$116$		0			0
$117$	3.16228	−	3.16228i	0.292353	−	0.292353i
$118$		0			0
$119$	−3.16228	−	5.00000i	−0.289886	−	0.458349i
$120$		0			0
$121$	−10.0000			−0.909091
$122$		0			0
$123$	15.0000	−	15.0000i	1.35250	−	1.35250i
$124$		0			0
$125$	7.90569	−	7.90569i	0.707107	−	0.707107i
$126$		0			0
$127$	−9.00000	−	9.00000i	−0.798621	−	0.798621i	0.184257	−	0.982878i	$-0.441012\pi$
$127$	−9.00000	−	9.00000i	−0.798621	−	0.798621i	−0.982878	+	0.184257i	$0.941012\pi$
$128$		0			0
$129$	−9.48683			−0.835269
$130$		0			0
$131$		0			0		1.00000			$0$
$131$		0			0		−1.00000			$\pi$
$132$		0			0
$133$	−1.83772	+	8.16228i	−0.159351	+	0.707759i
$134$		0			0
$135$	5.00000			0.430331
$136$		0			0
$137$	2.00000	+	2.00000i	0.170872	+	0.170872i	0.787362	−	0.616491i	$-0.211446\pi$
$137$	2.00000	+	2.00000i	0.170872	+	0.170872i	−0.616491	+	0.787362i	$0.711446\pi$
$138$		0			0
$139$	18.9737			1.60933			0.804663	−	0.593732i	$-0.202346\pi$
$139$	18.9737			1.60933			0.804663	+	0.593732i	$0.202346\pi$
$140$		0			0
$141$	−15.0000			−1.26323
$142$		0			0
$143$	−1.58114	−	1.58114i	−0.132221	−	0.132221i
$144$		0			0
$145$	4.74342	−	4.74342i	0.393919	−	0.393919i
$146$		0			0
$147$	5.25658	+	14.7434i	0.433556	+	1.21602i
$148$		0			0
$149$		−	12.0000i		−	0.983078i	−0.870855	−	0.491539i	$-0.836434\pi$
$149$		−	12.0000i		−	0.983078i	0.870855	−	0.491539i	$-0.163566\pi$
$150$		0			0
$151$	−9.00000			−0.732410			−0.366205	−	0.930534i	$-0.619343\pi$
$151$	−9.00000			−0.732410			−0.366205	+	0.930534i	$0.619343\pi$
$152$		0			0
$153$	3.16228	+	3.16228i	0.255655	+	0.255655i
$154$		0			0
$155$	5.00000	−	5.00000i	0.401610	−	0.401610i
$156$		0			0
$157$	6.32456	−	6.32456i	0.504754	−	0.504754i	−0.408157	−	0.912912i	$-0.633828\pi$
$157$	6.32456	−	6.32456i	0.504754	−	0.504754i	0.912912	+	0.408157i	$0.133828\pi$
$158$		0			0
$159$	−3.16228			−0.250785
$160$		0			0
$161$	4.00000	+	6.32456i	0.315244	+	0.498445i
$162$		0			0
$163$	−6.00000	+	6.00000i	−0.469956	+	0.469956i	−0.901900	−	0.431944i	$-0.857828\pi$
$163$	−6.00000	+	6.00000i	−0.469956	+	0.469956i	0.431944	+	0.901900i	$0.357828\pi$
$164$		0			0
$165$			5.00000i			0.389249i
$166$		0			0
$167$	−11.0680	+	11.0680i	−0.856465	+	0.856465i	−0.990920	−	0.134454i	$-0.957072\pi$
$167$	−11.0680	+	11.0680i	−0.856465	+	0.856465i	0.134454	+	0.990920i	$0.457072\pi$
$168$		0			0
$169$		−	8.00000i		−	0.615385i
$170$		0			0
$171$		−	6.32456i		−	0.483651i
$172$		0			0
$173$	−11.0680	−	11.0680i	−0.841482	−	0.841482i	0.147569	−	0.989052i	$-0.452855\pi$
$173$	−11.0680	−	11.0680i	−0.841482	−	0.841482i	−0.989052	+	0.147569i	$0.952855\pi$
$174$		0			0
$175$	12.9057	+	2.90569i	0.975579	+	0.219650i
$176$		0			0
$177$	15.0000	+	15.0000i	1.12747	+	1.12747i
$178$		0			0
$179$			6.00000i			0.448461i	0.974536	+	0.224231i	$0.0719869\pi$
$179$			6.00000i			0.448461i	−0.974536	+	0.224231i	$0.928013\pi$
$180$		0			0
$181$			22.1359i			1.64535i	0.568511	+	0.822676i	$0.307520\pi$
$181$			22.1359i			1.64535i	−0.568511	+	0.822676i	$0.692480\pi$
$182$		0			0
$183$	−10.0000	+	10.0000i	−0.739221	+	0.739221i
$184$		0			0
$185$			18.9737i			1.39497i
$186$		0			0
$187$	1.58114	−	1.58114i	0.115624	−	0.115624i
$188$		0			0
$189$	3.16228	+	5.00000i	0.230022	+	0.363696i
$190$		0			0
$191$	3.00000			0.217072			0.108536	−	0.994092i	$-0.465384\pi$
$191$	3.00000			0.217072			0.108536	+	0.994092i	$0.465384\pi$
$192$		0			0
$193$	−8.00000	+	8.00000i	−0.575853	+	0.575853i	−0.933758	−	0.357905i	$-0.883491\pi$
$193$	−8.00000	+	8.00000i	−0.575853	+	0.575853i	0.357905	+	0.933758i	$0.383491\pi$
$194$		0			0
$195$	7.90569	−	7.90569i	0.566139	−	0.566139i
$196$		0			0
$197$	−1.00000	−	1.00000i	−0.0712470	−	0.0712470i	0.670585	−	0.741832i	$-0.266043\pi$
$197$	−1.00000	−	1.00000i	−0.0712470	−	0.0712470i	−0.741832	+	0.670585i	$0.766043\pi$
$198$		0			0
$199$	9.48683			0.672504			0.336252	−	0.941772i	$-0.390841\pi$
$199$	9.48683			0.672504			0.336252	+	0.941772i	$0.390841\pi$
$200$		0			0
$201$		−	3.16228i		−	0.223050i
$202$		0			0
$203$	7.74342	+	1.74342i	0.543481	+	0.122364i
$204$		0			0
$205$	15.0000	−	15.0000i	1.04765	−	1.04765i
$206$		0			0
$207$	−4.00000	−	4.00000i	−0.278019	−	0.278019i
$208$		0			0
$209$	−3.16228			−0.218739
$210$		0			0
$211$	−17.0000			−1.17033			−0.585164	−	0.810915i	$-0.698970\pi$
$211$	−17.0000			−1.17033			−0.585164	+	0.810915i	$0.698970\pi$
$212$		0			0
$213$	−9.48683	−	9.48683i	−0.650027	−	0.650027i
$214$		0			0
$215$	−9.48683			−0.646997
$216$		0			0
$217$	8.16228	+	1.83772i	0.554092	+	0.124753i
$218$		0			0
$219$		0			0
$220$		0			0
$221$	−5.00000			−0.336336
$222$		0			0
$223$	−14.2302	−	14.2302i	−0.952928	−	0.952928i	0.0460129	−	0.998941i	$-0.485348\pi$
$223$	−14.2302	−	14.2302i	−0.952928	−	0.952928i	−0.998941	+	0.0460129i	$0.985348\pi$
$224$		0			0
$225$	−10.0000			−0.666667
$226$		0			0
$227$	1.58114	−	1.58114i	0.104944	−	0.104944i	−0.652685	−	0.757629i	$-0.726358\pi$
$227$	1.58114	−	1.58114i	0.104944	−	0.104944i	0.757629	+	0.652685i	$0.226358\pi$
$228$		0			0
$229$	15.8114			1.04485			0.522423	−	0.852686i	$-0.325028\pi$
$229$	15.8114			1.04485			0.522423	+	0.852686i	$0.325028\pi$
$230$		0			0
$231$	−5.00000	+	3.16228i	−0.328976	+	0.208063i
$232$		0			0
$233$	−18.0000	+	18.0000i	−1.17922	+	1.17922i	−0.199276	+	0.979943i	$0.563859\pi$
$233$	−18.0000	+	18.0000i	−1.17922	+	1.17922i	−0.979943	+	0.199276i	$0.936141\pi$
$234$		0			0
$235$	−15.0000			−0.978492
$236$		0			0
$237$	−20.5548	+	20.5548i	−1.33518	+	1.33518i
$238$		0			0
$239$		−	19.0000i		−	1.22901i	−0.788914	−	0.614504i	$-0.789356\pi$
$239$		−	19.0000i		−	1.22901i	0.788914	−	0.614504i	$-0.210644\pi$
$240$		0			0
$241$		−	25.2982i		−	1.62960i	−0.579741	−	0.814801i	$-0.696846\pi$
$241$		−	25.2982i		−	1.62960i	0.579741	−	0.814801i	$-0.303154\pi$
$242$		0			0
$243$	−12.6491	−	12.6491i	−0.811441	−	0.811441i
$244$		0			0
$245$	5.25658	+	14.7434i	0.335831	+	0.941922i
$246$		0			0
$247$	5.00000	+	5.00000i	0.318142	+	0.318142i
$248$		0			0
$249$		−	10.0000i		−	0.633724i
$250$		0			0
$251$			12.6491i			0.798405i	0.916863	+	0.399202i	$0.130713\pi$
$251$			12.6491i			0.798405i	−0.916863	+	0.399202i	$0.869287\pi$
$252$		0			0
$253$	−2.00000	+	2.00000i	−0.125739	+	0.125739i
$254$		0			0
$255$	7.90569	+	7.90569i	0.495074	+	0.495074i
$256$		0			0
$257$	12.6491	−	12.6491i	0.789030	−	0.789030i	−0.192305	−	0.981335i	$-0.561596\pi$
$257$	12.6491	−	12.6491i	0.789030	−	0.789030i	0.981335	+	0.192305i	$0.0615964\pi$
$258$		0			0
$259$	−18.9737	+	12.0000i	−1.17897	+	0.745644i
$260$		0			0
$261$	−6.00000			−0.371391
$262$		0			0
$263$	−7.00000	+	7.00000i	−0.431638	+	0.431638i	−0.889185	−	0.457547i	$-0.848728\pi$
$263$	−7.00000	+	7.00000i	−0.431638	+	0.431638i	0.457547	+	0.889185i	$0.348728\pi$
$264$		0			0
$265$	−3.16228			−0.194257
$266$		0			0
$267$	10.0000	+	10.0000i	0.611990	+	0.611990i
$268$		0			0
$269$	−18.9737			−1.15684			−0.578422	−	0.815737i	$-0.696331\pi$
$269$	−18.9737			−1.15684			−0.578422	+	0.815737i	$0.696331\pi$
$270$		0			0
$271$		−	12.6491i		−	0.768379i	−0.923254	−	0.384189i	$-0.874481\pi$
$271$		−	12.6491i		−	0.768379i	0.923254	−	0.384189i	$-0.125519\pi$
$272$		0			0
$273$	12.9057	+	2.90569i	0.781088	+	0.175861i
$274$		0			0
$275$			5.00000i			0.301511i
$276$		0			0
$277$	−18.0000	−	18.0000i	−1.08152	−	1.08152i	−0.996368	−	0.0851468i	$-0.972864\pi$
$277$	−18.0000	−	18.0000i	−1.08152	−	1.08152i	−0.0851468	−	0.996368i	$-0.527136\pi$
$278$		0			0
$279$	−6.32456			−0.378641
$280$		0			0
$281$	9.00000			0.536895			0.268447	−	0.963294i	$-0.413489\pi$
$281$	9.00000			0.536895			0.268447	+	0.963294i	$0.413489\pi$
$282$		0			0
$283$	4.74342	+	4.74342i	0.281967	+	0.281967i	0.833893	−	0.551926i	$-0.186107\pi$
$283$	4.74342	+	4.74342i	0.281967	+	0.281967i	−0.551926	+	0.833893i	$0.686107\pi$
$284$		0			0
$285$		−	15.8114i		−	0.936586i
$286$		0			0
$287$	24.4868	+	5.51317i	1.44541	+	0.325432i
$288$		0			0
$289$			12.0000i			0.705882i
$290$		0			0
$291$	5.00000			0.293105
$292$		0			0
$293$	−7.90569	−	7.90569i	−0.461856	−	0.461856i	0.437408	−	0.899263i	$-0.355897\pi$
$293$	−7.90569	−	7.90569i	−0.461856	−	0.461856i	−0.899263	+	0.437408i	$0.855897\pi$
$294$		0			0
$295$	15.0000	+	15.0000i	0.873334	+	0.873334i
$296$		0			0
$297$	−1.58114	+	1.58114i	−0.0917470	+	0.0917470i
$298$		0			0
$299$	6.32456			0.365758
$300$		0			0
$301$	−6.00000	−	9.48683i	−0.345834	−	0.546812i
$302$		0			0
$303$	5.00000	−	5.00000i	0.287242	−	0.287242i
$304$		0			0
$305$	−10.0000	+	10.0000i	−0.572598	+	0.572598i
$306$		0			0
$307$	4.74342	−	4.74342i	0.270721	−	0.270721i	−0.558669	−	0.829390i	$-0.688688\pi$
$307$	4.74342	−	4.74342i	0.270721	−	0.270721i	0.829390	+	0.558669i	$0.188688\pi$
$308$		0			0
$309$			35.0000i			1.99108i
$310$		0			0
$311$		−	22.1359i		−	1.25521i	−0.778530	−	0.627607i	$-0.784034\pi$
$311$		−	22.1359i		−	1.25521i	0.778530	−	0.627607i	$-0.215966\pi$
$312$		0			0
$313$	−14.2302	−	14.2302i	−0.804341	−	0.804341i	0.179430	−	0.983771i	$-0.442575\pi$
$313$	−14.2302	−	14.2302i	−0.804341	−	0.804341i	−0.983771	+	0.179430i	$0.942575\pi$
$314$		0			0
$315$	−6.32456	−	10.0000i	−0.356348	−	0.563436i
$316$		0			0
$317$	19.0000	+	19.0000i	1.06715	+	1.06715i	0.997577	+	0.0695692i	$0.0221625\pi$
$317$	19.0000	+	19.0000i	1.06715	+	1.06715i	0.0695692	+	0.997577i	$0.477838\pi$
$318$		0			0
$319$			3.00000i			0.167968i
$320$		0			0
$321$		−	9.48683i		−	0.529503i
$322$		0			0
$323$	−5.00000	+	5.00000i	−0.278207	+	0.278207i
$324$		0			0
$325$	7.90569	−	7.90569i	0.438529	−	0.438529i
$326$		0			0
$327$	−11.0680	+	11.0680i	−0.612060	+	0.612060i
$328$		0			0
$329$	−9.48683	−	15.0000i	−0.523026	−	0.826977i
$330$		0			0
$331$	6.00000			0.329790			0.164895	−	0.986311i	$-0.447272\pi$
$331$	6.00000			0.329790			0.164895	+	0.986311i	$0.447272\pi$
$332$		0			0
$333$	12.0000	−	12.0000i	0.657596	−	0.657596i
$334$		0			0
$335$		−	3.16228i		−	0.172774i
$336$		0			0
$337$	−8.00000	−	8.00000i	−0.435788	−	0.435788i	0.454804	−	0.890592i	$-0.349709\pi$
$337$	−8.00000	−	8.00000i	−0.435788	−	0.435788i	−0.890592	+	0.454804i	$0.849709\pi$
$338$		0			0
$339$	−37.9473			−2.06102
$340$		0			0
$341$			3.16228i			0.171247i
$342$		0			0
$343$	−11.4189	+	14.5811i	−0.616561	+	0.787307i
$344$		0			0
$345$	−10.0000	−	10.0000i	−0.538382	−	0.538382i
$346$		0			0
$347$	−24.0000	−	24.0000i	−1.28839	−	1.28839i	−0.935766	−	0.352621i	$-0.885290\pi$
$347$	−24.0000	−	24.0000i	−1.28839	−	1.28839i	−0.352621	−	0.935766i	$-0.614710\pi$
$348$		0			0
$349$	34.7851			1.86200			0.931001	−	0.365018i	$-0.118937\pi$
$349$	34.7851			1.86200			0.931001	+	0.365018i	$0.118937\pi$
$350$		0			0
$351$	5.00000			0.266880
$352$		0			0
$353$	14.2302	+	14.2302i	0.757400	+	0.757400i	0.975848	−	0.218449i	$-0.0700996\pi$
$353$	14.2302	+	14.2302i	0.757400	+	0.757400i	−0.218449	+	0.975848i	$0.570100\pi$
$354$		0			0
$355$	−9.48683	−	9.48683i	−0.503509	−	0.503509i
$356$		0			0
$357$	−2.90569	+	12.9057i	−0.153786	+	0.683042i
$358$		0			0
$359$			22.0000i			1.16112i	0.814219	+	0.580558i	$0.197165\pi$
$359$			22.0000i			1.16112i	−0.814219	+	0.580558i	$0.802835\pi$
$360$		0			0
$361$	−9.00000			−0.473684
$362$		0			0
$363$	15.8114	+	15.8114i	0.829883	+	0.829883i
$364$		0			0
$365$		0			0
$366$		0			0
$367$	17.3925	−	17.3925i	0.907883	−	0.907883i	−0.0882186	−	0.996101i	$-0.528117\pi$
$367$	17.3925	−	17.3925i	0.907883	−	0.907883i	0.996101	+	0.0882186i	$0.0281174\pi$
$368$		0			0
$369$	−18.9737			−0.987730
$370$		0			0
$371$	−2.00000	−	3.16228i	−0.103835	−	0.164177i
$372$		0			0
$373$	12.0000	−	12.0000i	0.621336	−	0.621336i	−0.324537	−	0.945873i	$-0.605208\pi$
$373$	12.0000	−	12.0000i	0.621336	−	0.621336i	0.945873	+	0.324537i	$0.105208\pi$
$374$		0			0
$375$	−25.0000			−1.29099
$376$		0			0
$377$	4.74342	−	4.74342i	0.244298	−	0.244298i
$378$		0			0
$379$		−	8.00000i		−	0.410932i	−0.978664	−	0.205466i	$-0.934129\pi$
$379$		−	8.00000i		−	0.410932i	0.978664	−	0.205466i	$-0.0658711\pi$
$380$		0			0
$381$			28.4605i			1.45808i
$382$		0			0
$383$	15.8114	+	15.8114i	0.807924	+	0.807924i	0.984319	−	0.176395i	$-0.0564437\pi$
$383$	15.8114	+	15.8114i	0.807924	+	0.807924i	−0.176395	+	0.984319i	$0.556444\pi$
$384$		0			0
$385$	−5.00000	+	3.16228i	−0.254824	+	0.161165i
$386$		0			0
$387$	6.00000	+	6.00000i	0.304997	+	0.304997i
$388$		0			0
$389$			23.0000i			1.16615i	0.812420	+	0.583073i	$0.198150\pi$
$389$			23.0000i			1.16615i	−0.812420	+	0.583073i	$0.801850\pi$
$390$		0			0
$391$			6.32456i			0.319847i
$392$		0			0
$393$		0			0
$394$		0			0
$395$	−20.5548	+	20.5548i	−1.03422	+	1.03422i
$396$		0			0
$397$	−23.7171	+	23.7171i	−1.19033	+	1.19033i	−0.213351	+	0.976976i	$0.568438\pi$
$397$	−23.7171	+	23.7171i	−1.19033	+	1.19033i	−0.976976	+	0.213351i	$0.931562\pi$
$398$		0			0
$399$	15.8114	−	10.0000i	0.791559	−	0.500626i
$400$		0			0
$401$	−1.00000			−0.0499376			−0.0249688	−	0.999688i	$-0.507949\pi$
$401$	−1.00000			−0.0499376			−0.0249688	+	0.999688i	$0.507949\pi$
$402$		0			0
$403$	5.00000	−	5.00000i	0.249068	−	0.249068i
$404$		0			0
$405$	−17.3925	−	17.3925i	−0.864242	−	0.864242i
$406$		0			0
$407$	−6.00000	−	6.00000i	−0.297409	−	0.297409i
$408$		0			0
$409$	3.16228			0.156365			0.0781823	−	0.996939i	$-0.475088\pi$
$409$	3.16228			0.156365			0.0781823	+	0.996939i	$0.475088\pi$
$410$		0			0
$411$		−	6.32456i		−	0.311967i
$412$		0			0
$413$	−5.51317	+	24.4868i	−0.271285	+	1.20492i
$414$		0			0
$415$		−	10.0000i		−	0.490881i
$416$		0			0
$417$	−30.0000	−	30.0000i	−1.46911	−	1.46911i
$418$		0			0
$419$	15.8114			0.772437			0.386218	−	0.922407i	$-0.373781\pi$
$419$	15.8114			0.772437			0.386218	+	0.922407i	$0.373781\pi$
$420$		0			0
$421$	19.0000			0.926003			0.463002	−	0.886357i	$-0.346772\pi$
$421$	19.0000			0.926003			0.463002	+	0.886357i	$0.346772\pi$
$422$		0			0
$423$	9.48683	+	9.48683i	0.461266	+	0.461266i
$424$		0			0
$425$	7.90569	+	7.90569i	0.383482	+	0.383482i
$426$		0			0
$427$	−16.3246	−	3.67544i	−0.790001	−	0.177867i
$428$		0			0
$429$			5.00000i			0.241402i
$430$		0			0
$431$	23.0000			1.10787			0.553936	−	0.832560i	$-0.313125\pi$
$431$	23.0000			1.10787			0.553936	+	0.832560i	$0.313125\pi$
$432$		0			0
$433$	9.48683	+	9.48683i	0.455908	+	0.455908i	0.897310	−	0.441402i	$-0.145519\pi$
$433$	9.48683	+	9.48683i	0.455908	+	0.455908i	−0.441402	+	0.897310i	$0.645519\pi$
$434$		0			0
$435$	−15.0000			−0.719195
$436$		0			0
$437$	6.32456	−	6.32456i	0.302545	−	0.302545i
$438$		0			0
$439$	12.6491			0.603709			0.301855	−	0.953354i	$-0.402394\pi$
$439$	12.6491			0.603709			0.301855	+	0.953354i	$0.402394\pi$
$440$		0			0
$441$	6.00000	−	12.6491i	0.285714	−	0.602339i
$442$		0			0
$443$	−1.00000	+	1.00000i	−0.0475114	+	0.0475114i	−0.730463	−	0.682952i	$-0.760696\pi$
$443$	−1.00000	+	1.00000i	−0.0475114	+	0.0475114i	0.682952	+	0.730463i	$0.260696\pi$
$444$		0			0
$445$	10.0000	+	10.0000i	0.474045	+	0.474045i
$446$		0			0
$447$	−18.9737	+	18.9737i	−0.897424	+	0.897424i
$448$		0			0
$449$		−	17.0000i		−	0.802280i	−0.916017	−	0.401140i	$-0.868614\pi$
$449$		−	17.0000i		−	0.802280i	0.916017	−	0.401140i	$-0.131386\pi$
$450$		0			0
$451$			9.48683i			0.446718i
$452$		0			0
$453$	14.2302	+	14.2302i	0.668595	+	0.668595i
$454$		0			0
$455$	12.9057	+	2.90569i	0.605028	+	0.136221i
$456$		0			0
$457$	−1.00000	−	1.00000i	−0.0467780	−	0.0467780i	0.683331	−	0.730109i	$-0.260531\pi$
$457$	−1.00000	−	1.00000i	−0.0467780	−	0.0467780i	−0.730109	+	0.683331i	$0.760531\pi$
$458$		0			0
$459$			5.00000i			0.233380i
$460$		0			0
$461$			6.32456i			0.294564i	0.989095	+	0.147282i	$0.0470525\pi$
$461$			6.32456i			0.294564i	−0.989095	+	0.147282i	$0.952948\pi$
$462$		0			0
$463$	4.00000	−	4.00000i	0.185896	−	0.185896i	−0.608023	−	0.793919i	$-0.708037\pi$
$463$	4.00000	−	4.00000i	0.185896	−	0.185896i	0.793919	+	0.608023i	$0.208037\pi$
$464$		0			0
$465$	−15.8114			−0.733236
$466$		0			0
$467$	11.0680	−	11.0680i	0.512165	−	0.512165i	−0.403025	−	0.915189i	$-0.632041\pi$
$467$	11.0680	−	11.0680i	0.512165	−	0.512165i	0.915189	+	0.403025i	$0.132041\pi$
$468$		0			0
$469$	3.16228	−	2.00000i	0.146020	−	0.0923514i
$470$		0			0
$471$	−20.0000			−0.921551
$472$		0			0
$473$	3.00000	−	3.00000i	0.137940	−	0.137940i
$474$		0			0
$475$		−	15.8114i		−	0.725476i
$476$		0			0
$477$	2.00000	+	2.00000i	0.0915737	+	0.0915737i
$478$		0			0
$479$	6.32456			0.288976			0.144488	−	0.989507i	$-0.453846\pi$
$479$	6.32456			0.288976			0.144488	+	0.989507i	$0.453846\pi$
$480$		0			0
$481$			18.9737i			0.865125i
$482$		0			0
$483$	3.67544	−	16.3246i	0.167239	−	0.742793i
$484$		0			0
$485$	5.00000			0.227038
$486$		0			0
$487$	−4.00000	−	4.00000i	−0.181257	−	0.181257i	0.610646	−	0.791904i	$-0.290910\pi$
$487$	−4.00000	−	4.00000i	−0.181257	−	0.181257i	−0.791904	+	0.610646i	$0.790910\pi$
$488$		0			0
$489$	18.9737			0.858019
$490$		0			0
$491$	41.0000			1.85030			0.925152	−	0.379597i	$-0.123937\pi$
$491$	41.0000			1.85030			0.925152	+	0.379597i	$0.123937\pi$
$492$		0			0
$493$	4.74342	+	4.74342i	0.213633	+	0.213633i
$494$		0			0
$495$	3.16228	−	3.16228i	0.142134	−	0.142134i
$496$		0			0
$497$	3.48683	−	15.4868i	0.156406	−	0.694679i
$498$		0			0
$499$		−	19.0000i		−	0.850557i	−0.905063	−	0.425278i	$-0.860176\pi$
$499$		−	19.0000i		−	0.850557i	0.905063	−	0.425278i	$-0.139824\pi$
$500$		0			0
$501$	35.0000			1.56368
$502$		0			0
$503$	−7.90569	−	7.90569i	−0.352497	−	0.352497i	0.508541	−	0.861038i	$-0.330185\pi$
$503$	−7.90569	−	7.90569i	−0.352497	−	0.352497i	−0.861038	+	0.508541i	$0.830185\pi$
$504$		0			0
$505$	5.00000	−	5.00000i	0.222497	−	0.222497i
$506$		0			0
$507$	−12.6491	+	12.6491i	−0.561767	+	0.561767i
$508$		0			0
$509$	18.9737			0.840993			0.420496	−	0.907294i	$-0.361856\pi$
$509$	18.9737			0.840993			0.420496	+	0.907294i	$0.361856\pi$
$510$		0			0
$511$		0			0
$512$		0			0
$513$	5.00000	−	5.00000i	0.220755	−	0.220755i
$514$		0			0
$515$			35.0000i			1.54228i
$516$		0			0
$517$	4.74342	−	4.74342i	0.208615	−	0.208615i
$518$		0			0
$519$			35.0000i			1.53633i
$520$		0			0
$521$		−	41.1096i		−	1.80104i	−0.434810	−	0.900522i	$-0.643184\pi$
$521$		−	41.1096i		−	1.80104i	0.434810	−	0.900522i	$-0.356816\pi$
$522$		0			0
$523$	18.9737	+	18.9737i	0.829660	+	0.829660i	0.987470	−	0.157809i	$-0.0504431\pi$
$523$	18.9737	+	18.9737i	0.829660	+	0.829660i	−0.157809	+	0.987470i	$0.550443\pi$
$524$		0			0
$525$	−15.8114	−	25.0000i	−0.690066	−	1.09109i
$526$		0			0
$527$	5.00000	+	5.00000i	0.217803	+	0.217803i
$528$		0			0
$529$			15.0000i			0.652174i
$530$		0			0
$531$		−	18.9737i		−	0.823387i
$532$		0			0
$533$	15.0000	−	15.0000i	0.649722	−	0.649722i
$534$		0			0
$535$		−	9.48683i		−	0.410152i
$536$		0			0
$537$	9.48683	−	9.48683i	0.409387	−	0.409387i
$538$		0			0
$539$	−6.32456	−	3.00000i	−0.272418	−	0.129219i
$540$		0			0
$541$	9.00000			0.386940			0.193470	−	0.981106i	$-0.438026\pi$
$541$	9.00000			0.386940			0.193470	+	0.981106i	$0.438026\pi$
$542$		0			0
$543$	35.0000	−	35.0000i	1.50199	−	1.50199i
$544$		0			0
$545$	−11.0680	+	11.0680i	−0.474100	+	0.474100i
$546$		0			0
$547$	−14.0000	−	14.0000i	−0.598597	−	0.598597i	0.341342	−	0.939939i	$-0.389118\pi$
$547$	−14.0000	−	14.0000i	−0.598597	−	0.598597i	−0.939939	+	0.341342i	$0.889118\pi$
$548$		0			0
$549$	12.6491			0.539851
$550$		0			0
$551$		−	9.48683i		−	0.404153i
$552$		0			0
$553$	−33.5548	−	7.55480i	−1.42690	−	0.321263i
$554$		0			0
$555$	30.0000	−	30.0000i	1.27343	−	1.27343i
$556$		0			0
$557$	−6.00000	−	6.00000i	−0.254228	−	0.254228i	0.568473	−	0.822702i	$-0.307534\pi$
$557$	−6.00000	−	6.00000i	−0.254228	−	0.254228i	−0.822702	+	0.568473i	$0.807534\pi$
$558$		0			0
$559$	−9.48683			−0.401250
$560$		0			0
$561$	−5.00000			−0.211100
$562$		0			0
$563$	−9.48683	−	9.48683i	−0.399822	−	0.399822i	0.478348	−	0.878170i	$-0.341236\pi$
$563$	−9.48683	−	9.48683i	−0.399822	−	0.399822i	−0.878170	+	0.478348i	$0.841236\pi$
$564$		0			0
$565$	−37.9473			−1.59646
$566$		0			0
$567$	6.39253	−	28.3925i	0.268461	−	1.19237i
$568$		0			0
$569$		−	32.0000i		−	1.34151i	−0.741679	−	0.670755i	$-0.765970\pi$
$569$		−	32.0000i		−	1.34151i	0.741679	−	0.670755i	$-0.234030\pi$
$570$		0			0
$571$	26.0000			1.08807			0.544033	−	0.839064i	$-0.316897\pi$
$571$	26.0000			1.08807			0.544033	+	0.839064i	$0.316897\pi$
$572$		0			0
$573$	−4.74342	−	4.74342i	−0.198159	−	0.198159i
$574$		0			0
$575$	−10.0000	−	10.0000i	−0.417029	−	0.417029i
$576$		0			0
$577$	20.5548	−	20.5548i	0.855708	−	0.855708i	−0.135121	−	0.990829i	$-0.543142\pi$
$577$	20.5548	−	20.5548i	0.855708	−	0.855708i	0.990829	+	0.135121i	$0.0431424\pi$
$578$		0			0
$579$	25.2982			1.05136
$580$		0			0
$581$	10.0000	−	6.32456i	0.414870	−	0.262387i
$582$		0			0
$583$	1.00000	−	1.00000i	0.0414158	−	0.0414158i
$584$		0			0
$585$	−10.0000			−0.413449
$586$		0			0
$587$	15.8114	−	15.8114i	0.652606	−	0.652606i	−0.301014	−	0.953620i	$-0.597325\pi$
$587$	15.8114	−	15.8114i	0.652606	−	0.652606i	0.953620	+	0.301014i	$0.0973251\pi$
$588$		0			0
$589$		−	10.0000i		−	0.412043i
$590$		0			0
$591$			3.16228i			0.130079i
$592$		0			0
$593$	20.5548	+	20.5548i	0.844085	+	0.844085i	0.989387	−	0.145303i	$-0.0464156\pi$
$593$	20.5548	+	20.5548i	0.844085	+	0.844085i	−0.145303	+	0.989387i	$0.546416\pi$
$594$		0			0
$595$	−2.90569	+	12.9057i	−0.119122	+	0.529082i
$596$		0			0
$597$	−15.0000	−	15.0000i	−0.613909	−	0.613909i
$598$		0			0
$599$		−	13.0000i		−	0.531166i	−0.964088	−	0.265583i	$-0.914436\pi$
$599$		−	13.0000i		−	0.531166i	0.964088	−	0.265583i	$-0.0855644\pi$
$600$		0			0
$601$		−	22.1359i		−	0.902944i	−0.892285	−	0.451472i	$-0.850899\pi$
$601$		−	22.1359i		−	0.902944i	0.892285	−	0.451472i	$-0.149101\pi$
$602$		0			0
$603$	−2.00000	+	2.00000i	−0.0814463	+	0.0814463i
$604$		0			0
$605$	15.8114	+	15.8114i	0.642824	+	0.642824i
$606$		0			0
$607$	−14.2302	+	14.2302i	−0.577588	+	0.577588i	−0.934238	−	0.356650i	$-0.883919\pi$
$607$	−14.2302	+	14.2302i	−0.577588	+	0.577588i	0.356650	+	0.934238i	$0.383919\pi$
$608$		0			0
$609$	−9.48683	−	15.0000i	−0.384426	−	0.607831i
$610$		0			0
$611$	−15.0000			−0.606835
$612$		0			0
$613$	17.0000	−	17.0000i	0.686624	−	0.686624i	−0.274861	−	0.961484i	$-0.588632\pi$
$613$	17.0000	−	17.0000i	0.686624	−	0.686624i	0.961484	+	0.274861i	$0.0886317\pi$
$614$		0			0
$615$	−47.4342			−1.91273
$616$		0			0
$617$	4.00000	+	4.00000i	0.161034	+	0.161034i	0.783025	−	0.621991i	$-0.213676\pi$
$617$	4.00000	+	4.00000i	0.161034	+	0.161034i	−0.621991	+	0.783025i	$0.713676\pi$
$618$		0			0
$619$	25.2982			1.01682			0.508411	−	0.861115i	$-0.330233\pi$
$619$	25.2982			1.01682			0.508411	+	0.861115i	$0.330233\pi$
$620$		0			0
$621$		−	6.32456i		−	0.253796i
$622$		0			0
$623$	−3.67544	+	16.3246i	−0.147254	+	0.654029i
$624$		0			0
$625$	−25.0000			−1.00000
$626$		0			0
$627$	5.00000	+	5.00000i	0.199681	+	0.199681i
$628$		0			0
$629$	−18.9737			−0.756530
$630$		0			0
$631$	31.0000			1.23409			0.617045	−	0.786928i	$-0.288330\pi$
$631$	31.0000			1.23409			0.617045	+	0.786928i	$0.288330\pi$
$632$		0			0
$633$	26.8794	+	26.8794i	1.06836	+	1.06836i
$634$		0			0
$635$			28.4605i			1.12942i
$636$		0			0
$637$	5.25658	+	14.7434i	0.208273	+	0.584155i
$638$		0			0
$639$			12.0000i			0.474713i
$640$		0			0
$641$	44.0000			1.73790			0.868948	−	0.494904i	$-0.164797\pi$
$641$	44.0000			1.73790			0.868948	+	0.494904i	$0.164797\pi$
$642$		0			0
$643$	−4.74342	−	4.74342i	−0.187062	−	0.187062i	0.607363	−	0.794425i	$-0.292228\pi$
$643$	−4.74342	−	4.74342i	−0.187062	−	0.187062i	−0.794425	+	0.607363i	$0.792228\pi$
$644$		0			0
$645$	15.0000	+	15.0000i	0.590624	+	0.590624i
$646$		0			0
$647$	−12.6491	+	12.6491i	−0.497288	+	0.497288i	−0.910593	−	0.413305i	$-0.864374\pi$
$647$	−12.6491	+	12.6491i	−0.497288	+	0.497288i	0.413305	+	0.910593i	$0.364374\pi$
$648$		0			0
$649$	−9.48683			−0.372391
$650$		0			0
$651$	−10.0000	−	15.8114i	−0.391931	−	0.619697i
$652$		0			0
$653$	−19.0000	+	19.0000i	−0.743527	+	0.743527i	−0.973255	−	0.229728i	$-0.926216\pi$
$653$	−19.0000	+	19.0000i	−0.743527	+	0.743527i	0.229728	+	0.973255i	$0.426216\pi$
$654$		0			0
$655$		0			0
$656$		0			0
$657$		0			0
$658$		0			0
$659$			1.00000i			0.0389545i	0.999810	+	0.0194772i	$0.00620019\pi$
$659$			1.00000i			0.0389545i	−0.999810	+	0.0194772i	$0.993800\pi$
$660$		0			0
$661$			12.6491i			0.491993i	0.969271	+	0.245997i	$0.0791152\pi$
$661$			12.6491i			0.491993i	−0.969271	+	0.245997i	$0.920885\pi$
$662$		0			0
$663$	7.90569	+	7.90569i	0.307032	+	0.307032i
$664$		0			0
$665$	15.8114	−	10.0000i	0.613139	−	0.387783i
$666$		0			0
$667$	−6.00000	−	6.00000i	−0.232321	−	0.232321i
$668$		0			0
$669$			45.0000i			1.73980i
$670$		0			0
$671$		−	6.32456i		−	0.244157i
$672$		0			0
$673$	−24.0000	+	24.0000i	−0.925132	+	0.925132i	−0.997386	−	0.0722542i	$-0.976981\pi$
$673$	−24.0000	+	24.0000i	−0.925132	+	0.925132i	0.0722542	+	0.997386i	$0.476981\pi$
$674$		0			0
$675$	−7.90569	−	7.90569i	−0.304290	−	0.304290i
$676$		0			0
$677$	−14.2302	+	14.2302i	−0.546913	+	0.546913i	−0.925547	−	0.378634i	$-0.876394\pi$
$677$	−14.2302	+	14.2302i	−0.546913	+	0.546913i	0.378634	+	0.925547i	$0.376394\pi$
$678$		0			0
$679$	3.16228	+	5.00000i	0.121357	+	0.191882i
$680$		0			0
$681$	−5.00000			−0.191600
$682$		0			0
$683$	−32.0000	+	32.0000i	−1.22445	+	1.22445i	−0.258411	+	0.966035i	$0.583199\pi$
$683$	−32.0000	+	32.0000i	−1.22445	+	1.22445i	−0.966035	+	0.258411i	$0.916801\pi$
$684$		0			0
$685$		−	6.32456i		−	0.241649i
$686$		0			0
$687$	−25.0000	−	25.0000i	−0.953809	−	0.953809i
$688$		0			0
$689$	−3.16228			−0.120473
$690$		0			0
$691$			31.6228i			1.20299i	0.798878	+	0.601494i	$0.205427\pi$
$691$			31.6228i			1.20299i	−0.798878	+	0.601494i	$0.794573\pi$
$692$		0			0
$693$	5.16228	+	1.16228i	0.196099	+	0.0441513i
$694$		0			0
$695$	−30.0000	−	30.0000i	−1.13796	−	1.13796i
$696$		0			0
$697$	15.0000	+	15.0000i	0.568166	+	0.568166i
$698$		0			0
$699$	56.9210			2.15295
$700$		0			0
$701$	−13.0000			−0.491003			−0.245502	−	0.969396i	$-0.578953\pi$
$701$	−13.0000			−0.491003			−0.245502	+	0.969396i	$0.578953\pi$
$702$		0			0
$703$	18.9737	+	18.9737i	0.715605	+	0.715605i
$704$		0			0
$705$	23.7171	+	23.7171i	0.893237	+	0.893237i
$706$		0			0
$707$	8.16228	+	1.83772i	0.306974	+	0.0691147i
$708$		0			0
$709$			9.00000i			0.338002i	0.985616	+	0.169001i	$0.0540541\pi$
$709$			9.00000i			0.338002i	−0.985616	+	0.169001i	$0.945946\pi$
$710$		0			0
$711$	26.0000			0.975076
$712$		0			0
$713$	−6.32456	−	6.32456i	−0.236856	−	0.236856i
$714$		0			0
$715$			5.00000i			0.186989i
$716$		0			0
$717$	−30.0416	+	30.0416i	−1.12193	+	1.12193i
$718$		0			0
$719$	−31.6228			−1.17933			−0.589665	−	0.807648i	$-0.700740\pi$
$719$	−31.6228			−1.17933			−0.589665	+	0.807648i	$0.700740\pi$
$720$		0			0
$721$	−35.0000	+	22.1359i	−1.30347	+	0.824386i
$722$		0			0
$723$	−40.0000	+	40.0000i	−1.48762	+	1.48762i
$724$		0			0
$725$	−15.0000			−0.557086
$726$		0			0
$727$	−9.48683	+	9.48683i	−0.351847	+	0.351847i	−0.860796	−	0.508949i	$-0.830034\pi$
$727$	−9.48683	+	9.48683i	−0.351847	+	0.351847i	0.508949	+	0.860796i	$0.330034\pi$
$728$		0			0
$729$			7.00000i			0.259259i
$730$		0			0
$731$		−	9.48683i		−	0.350883i
$732$		0			0
$733$	17.3925	+	17.3925i	0.642408	+	0.642408i	0.951147	−	0.308739i	$-0.0999070\pi$
$733$	17.3925	+	17.3925i	0.642408	+	0.642408i	−0.308739	+	0.951147i	$0.599907\pi$
$734$		0			0
$735$	15.0000	−	31.6228i	0.553283	−	1.16642i
$736$		0			0
$737$	1.00000	+	1.00000i	0.0368355	+	0.0368355i
$738$		0			0
$739$			37.0000i			1.36107i	0.732717	+	0.680534i	$0.238252\pi$
$739$			37.0000i			1.36107i	−0.732717	+	0.680534i	$0.761748\pi$
$740$		0			0
$741$		−	15.8114i		−	0.580846i
$742$		0			0
$743$	9.00000	−	9.00000i	0.330178	−	0.330178i	−0.522476	−	0.852654i	$-0.674992\pi$
$743$	9.00000	−	9.00000i	0.330178	−	0.330178i	0.852654	+	0.522476i	$0.174992\pi$
$744$		0			0
$745$	−18.9737	+	18.9737i	−0.695141	+	0.695141i
$746$		0			0
$747$	−6.32456	+	6.32456i	−0.231403	+	0.231403i
$748$		0			0
$749$	9.48683	−	6.00000i	0.346641	−	0.219235i
$750$		0			0
$751$	−37.0000			−1.35015			−0.675075	−	0.737749i	$-0.735889\pi$
$751$	−37.0000			−1.35015			−0.675075	+	0.737749i	$0.735889\pi$
$752$		0			0
$753$	20.0000	−	20.0000i	0.728841	−	0.728841i
$754$		0			0
$755$	14.2302	+	14.2302i	0.517892	+	0.517892i
$756$		0			0
$757$	−16.0000	−	16.0000i	−0.581530	−	0.581530i	0.353794	−	0.935324i	$-0.384892\pi$
$757$	−16.0000	−	16.0000i	−0.581530	−	0.581530i	−0.935324	+	0.353794i	$0.884892\pi$
$758$		0			0
$759$	6.32456			0.229567
$760$		0			0
$761$		−	25.2982i		−	0.917060i	−0.888679	−	0.458530i	$-0.848376\pi$
$761$		−	25.2982i		−	0.917060i	0.888679	−	0.458530i	$-0.151624\pi$
$762$		0			0
$763$	−18.0680	−	4.06797i	−0.654104	−	0.147270i
$764$		0			0
$765$		−	10.0000i		−	0.361551i
$766$		0			0
$767$	15.0000	+	15.0000i	0.541619	+	0.541619i
$768$		0			0
$769$	−22.1359			−0.798243			−0.399121	−	0.916898i	$-0.630685\pi$
$769$	−22.1359			−0.798243			−0.399121	+	0.916898i	$0.630685\pi$
$770$		0			0
$771$	−40.0000			−1.44056
$772$		0			0
$773$	−36.3662	−	36.3662i	−1.30800	−	1.30800i	−0.922856	−	0.385145i	$-0.874151\pi$
$773$	−36.3662	−	36.3662i	−1.30800	−	1.30800i	−0.385145	−	0.922856i	$-0.625849\pi$
$774$		0			0
$775$	−15.8114			−0.567962
$776$		0			0
$777$	48.9737	+	11.0263i	1.75692	+	0.395568i
$778$		0			0
$779$		−	30.0000i		−	1.07486i
$780$		0			0
$781$	6.00000			0.214697
$782$		0			0
$783$	−4.74342	−	4.74342i	−0.169516	−	0.169516i
$784$		0			0
$785$	−20.0000			−0.713831
$786$		0			0
$787$	−17.3925	+	17.3925i	−0.619977	+	0.619977i	−0.945525	−	0.325549i	$-0.894451\pi$
$787$	−17.3925	+	17.3925i	−0.619977	+	0.619977i	0.325549	+	0.945525i	$0.394451\pi$
$788$		0			0
$789$	22.1359			0.788060
$790$		0			0
$791$	−24.0000	−	37.9473i	−0.853342	−	1.34925i
$792$		0			0
$793$	−10.0000	+	10.0000i	−0.355110	+	0.355110i
$794$		0			0
$795$	5.00000	+	5.00000i	0.177332	+	0.177332i
$796$		0			0
$797$	1.58114	−	1.58114i	0.0560068	−	0.0560068i	−0.678549	−	0.734555i	$-0.737391\pi$
$797$	1.58114	−	1.58114i	0.0560068	−	0.0560068i	0.734555	+	0.678549i	$0.237391\pi$
$798$		0			0
$799$		−	15.0000i		−	0.530662i
$800$		0			0
$801$		−	12.6491i		−	0.446934i
$802$		0			0
$803$		0			0
$804$		0			0
$805$	3.67544	−	16.3246i	0.129542	−	0.575365i
$806$		0			0
$807$	30.0000	+	30.0000i	1.05605	+	1.05605i
$808$		0			0
$809$			3.00000i			0.105474i	0.998608	+	0.0527372i	$0.0167946\pi$
$809$			3.00000i			0.105474i	−0.998608	+	0.0527372i	$0.983205\pi$
$810$		0			0
$811$		−	37.9473i		−	1.33251i	−0.745724	−	0.666256i	$-0.767896\pi$
$811$		−	37.9473i		−	1.33251i	0.745724	−	0.666256i	$-0.232104\pi$
$812$		0			0
$813$	−20.0000	+	20.0000i	−0.701431	+	0.701431i
$814$		0			0
$815$	18.9737			0.664619
$816$		0			0
$817$	−9.48683	+	9.48683i	−0.331902	+	0.331902i
$818$		0			0
$819$	−6.32456	−	10.0000i	−0.220998	−	0.349428i
$820$		0			0
$821$	−23.0000			−0.802706			−0.401353	−	0.915924i	$-0.631460\pi$
$821$	−23.0000			−0.802706			−0.401353	+	0.915924i	$0.631460\pi$
$822$		0			0
$823$	3.00000	−	3.00000i	0.104573	−	0.104573i	−0.652884	−	0.757458i	$-0.726441\pi$
$823$	3.00000	−	3.00000i	0.104573	−	0.104573i	0.757458	+	0.652884i	$0.226441\pi$
$824$		0			0
$825$	7.90569	−	7.90569i	0.275241	−	0.275241i
$826$		0			0
$827$	26.0000	+	26.0000i	0.904109	+	0.904109i	0.995789	−	0.0916799i	$-0.0292237\pi$
$827$	26.0000	+	26.0000i	0.904109	+	0.904109i	−0.0916799	+	0.995789i	$0.529224\pi$
$828$		0			0
$829$	28.4605			0.988474			0.494237	−	0.869327i	$-0.335448\pi$
$829$	28.4605			0.988474			0.494237	+	0.869327i	$0.335448\pi$
$830$		0			0
$831$			56.9210i			1.97457i
$832$		0			0
$833$	−14.7434	+	5.25658i	−0.510829	+	0.182130i
$834$		0			0
$835$	35.0000			1.21122
$836$		0			0
$837$	−5.00000	−	5.00000i	−0.172825	−	0.172825i
$838$		0			0
$839$	−50.5964			−1.74678			−0.873392	−	0.487019i	$-0.838084\pi$
$839$	−50.5964			−1.74678			−0.873392	+	0.487019i	$0.838084\pi$
$840$		0			0
$841$	20.0000			0.689655
$842$		0			0
$843$	−14.2302	−	14.2302i	−0.490116	−	0.490116i
$844$		0			0
$845$	−12.6491	+	12.6491i	−0.435143	+	0.435143i
$846$		0			0
$847$	−5.81139	+	25.8114i	−0.199682	+	0.886890i
$848$		0			0
$849$		−	15.0000i		−	0.514799i
$850$		0			0
$851$	24.0000			0.822709
$852$		0			0
$853$		0			0		0.707107	−	0.707107i	$-0.250000\pi$
$853$		0			0		−0.707107	+	0.707107i	$0.750000\pi$
$854$		0			0
$855$	−10.0000	+	10.0000i	−0.341993	+	0.341993i
$856$		0			0
$857$	−31.6228	+	31.6228i	−1.08021	+	1.08021i	−0.0837245	+	0.996489i	$0.526682\pi$
$857$	−31.6228	+	31.6228i	−1.08021	+	1.08021i	−0.996489	+	0.0837245i	$0.973318\pi$
$858$		0			0
$859$	−12.6491			−0.431582			−0.215791	−	0.976440i	$-0.569233\pi$
$859$	−12.6491			−0.431582			−0.215791	+	0.976440i	$0.569233\pi$
$860$		0			0
$861$	−30.0000	−	47.4342i	−1.02240	−	1.61655i
$862$		0			0
$863$	13.0000	−	13.0000i	0.442525	−	0.442525i	−0.450335	−	0.892860i	$-0.648695\pi$
$863$	13.0000	−	13.0000i	0.442525	−	0.442525i	0.892860	+	0.450335i	$0.148695\pi$
$864$		0			0
$865$			35.0000i			1.19004i
$866$		0			0
$867$	18.9737	−	18.9737i	0.644379	−	0.644379i
$868$		0			0
$869$		−	13.0000i		−	0.440995i
$870$		0			0
$871$		−	3.16228i		−	0.107150i
$872$		0			0
$873$	−3.16228	−	3.16228i	−0.107027	−	0.107027i
$874$		0			0
$875$	−15.8114	−	25.0000i	−0.534522	−	0.845154i
$876$		0			0
$877$	17.0000	+	17.0000i	0.574049	+	0.574049i	0.933257	−	0.359208i	$-0.116953\pi$
$877$	17.0000	+	17.0000i	0.574049	+	0.574049i	−0.359208	+	0.933257i	$0.616953\pi$
$878$		0			0
$879$			25.0000i			0.843229i
$880$		0			0
$881$		−	37.9473i		−	1.27848i	−0.769008	−	0.639239i	$-0.779249\pi$
$881$		−	37.9473i		−	1.27848i	0.769008	−	0.639239i	$-0.220751\pi$
$882$		0			0
$883$	18.0000	−	18.0000i	0.605748	−	0.605748i	−0.336084	−	0.941832i	$-0.609103\pi$
$883$	18.0000	−	18.0000i	0.605748	−	0.605748i	0.941832	+	0.336084i	$0.109103\pi$
$884$		0			0
$885$		−	47.4342i		−	1.59448i
$886$		0			0
$887$	−3.16228	+	3.16228i	−0.106179	+	0.106179i	−0.758200	−	0.652022i	$-0.773921\pi$
$887$	−3.16228	+	3.16228i	−0.106179	+	0.106179i	0.652022	+	0.758200i	$0.273921\pi$
$888$		0			0
$889$	−28.4605	+	18.0000i	−0.954534	+	0.603701i
$890$		0			0
$891$	11.0000			0.368514
$892$		0			0
$893$	−15.0000	+	15.0000i	−0.501956	+	0.501956i
$894$		0			0
$895$	9.48683	−	9.48683i	0.317110	−	0.317110i
$896$		0			0
$897$	−10.0000	−	10.0000i	−0.333890	−	0.333890i
$898$		0			0
$899$	−9.48683			−0.316404
$900$		0			0
$901$		−	3.16228i		−	0.105351i
$902$		0			0
$903$	−5.51317	+	24.4868i	−0.183467	+	0.814871i
$904$		0			0
$905$	35.0000	−	35.0000i	1.16344	−	1.16344i
$906$		0			0
$907$	−22.0000	−	22.0000i	−0.730498	−	0.730498i	0.240220	−	0.970718i	$-0.422780\pi$
$907$	−22.0000	−	22.0000i	−0.730498	−	0.730498i	−0.970718	+	0.240220i	$0.922780\pi$
$908$		0			0
$909$	−6.32456			−0.209772
$910$		0			0
$911$	−54.0000			−1.78910			−0.894550	−	0.446968i	$-0.852504\pi$
$911$	−54.0000			−1.78910			−0.894550	+	0.446968i	$0.852504\pi$
$912$		0			0
$913$	3.16228	+	3.16228i	0.104656	+	0.104656i
$914$		0			0
$915$	31.6228			1.04542
$916$		0			0
$917$		0			0
$918$		0			0
$919$			27.0000i			0.890648i	0.895370	+	0.445324i	$0.146911\pi$
$919$			27.0000i			0.890648i	−0.895370	+	0.445324i	$0.853089\pi$
$920$		0			0
$921$	−15.0000			−0.494267
$922$		0			0
$923$	−9.48683	−	9.48683i	−0.312263	−	0.312263i
$924$		0			0
$925$	30.0000	−	30.0000i	0.986394	−	0.986394i
$926$		0			0
$927$	22.1359	−	22.1359i	0.727040	−	0.727040i
$928$		0			0
$929$	3.16228			0.103751			0.0518755	−	0.998654i	$-0.483480\pi$
$929$	3.16228			0.103751			0.0518755	+	0.998654i	$0.483480\pi$
$930$		0			0
$931$	20.0000	+	9.48683i	0.655474	+	0.310918i
$932$		0			0
$933$	−35.0000	+	35.0000i	−1.14585	+	1.14585i
$934$		0			0
$935$	−5.00000			−0.163517
$936$		0			0
$937$	−14.2302	+	14.2302i	−0.464882	+	0.464882i	−0.900252	−	0.435370i	$-0.856618\pi$
$937$	−14.2302	+	14.2302i	−0.464882	+	0.464882i	0.435370	+	0.900252i	$0.356618\pi$
$938$		0			0
$939$			45.0000i			1.46852i
$940$		0			0
$941$			37.9473i			1.23705i	0.785766	+	0.618524i	$0.212269\pi$
$941$			37.9473i			1.23705i	−0.785766	+	0.618524i	$0.787731\pi$
$942$		0			0
$943$	−18.9737	−	18.9737i	−0.617868	−	0.617868i
$944$		0			0
$945$	2.90569	−	12.9057i	0.0945222	−	0.419822i
$946$		0			0
$947$	−7.00000	−	7.00000i	−0.227469	−	0.227469i	0.584165	−	0.811635i	$-0.301422\pi$
$947$	−7.00000	−	7.00000i	−0.227469	−	0.227469i	−0.811635	+	0.584165i	$0.801422\pi$
$948$		0			0
$949$		0			0
$950$		0			0
$951$		−	60.0833i		−	1.94833i
$952$		0			0
$953$	−3.00000	+	3.00000i	−0.0971795	+	0.0971795i	−0.754025	−	0.656846i	$-0.771890\pi$
$953$	−3.00000	+	3.00000i	−0.0971795	+	0.0971795i	0.656846	+	0.754025i	$0.271890\pi$
$954$		0			0
$955$	−4.74342	−	4.74342i	−0.153493	−	0.153493i
$956$		0			0
$957$	4.74342	−	4.74342i	0.153333	−	0.153333i
$958$		0			0
$959$	6.32456	−	4.00000i	0.204231	−	0.129167i
$960$		0			0
$961$	21.0000			0.677419
$962$		0			0
$963$	−6.00000	+	6.00000i	−0.193347	+	0.193347i
$964$		0			0
$965$	25.2982			0.814379
$966$		0			0
$967$	33.0000	+	33.0000i	1.06121	+	1.06121i	0.998000	+	0.0632081i	$0.0201332\pi$
$967$	33.0000	+	33.0000i	1.06121	+	1.06121i	0.0632081	+	0.998000i	$0.479867\pi$
$968$		0			0
$969$	15.8114			0.507935
$970$		0			0
$971$		−	34.7851i		−	1.11631i	−0.829738	−	0.558153i	$-0.811510\pi$
$971$		−	34.7851i		−	1.11631i	0.829738	−	0.558153i	$-0.188490\pi$
$972$		0			0
$973$	11.0263	−	48.9737i	0.353488	−	1.57002i
$974$		0			0
$975$	−25.0000			−0.800641
$976$		0			0
$977$	−1.00000	−	1.00000i	−0.0319928	−	0.0319928i	0.690929	−	0.722922i	$-0.257202\pi$
$977$	−1.00000	−	1.00000i	−0.0319928	−	0.0319928i	−0.722922	+	0.690929i	$0.757202\pi$
$978$		0			0
$979$	−6.32456			−0.202134
$980$		0			0
$981$	14.0000			0.446986
$982$		0			0
$983$	20.5548	+	20.5548i	0.655596	+	0.655596i	0.954335	−	0.298739i	$-0.0965658\pi$
$983$	20.5548	+	20.5548i	0.655596	+	0.655596i	−0.298739	+	0.954335i	$0.596566\pi$
$984$		0			0
$985$			3.16228i			0.100759i
$986$		0			0
$987$	−8.71708	+	38.7171i	−0.277468	+	1.23238i
$988$		0			0
$989$			12.0000i			0.381578i
$990$		0			0
$991$	−4.00000			−0.127064			−0.0635321	−	0.997980i	$-0.520237\pi$
$991$	−4.00000			−0.127064			−0.0635321	+	0.997980i	$0.520237\pi$
$992$		0			0
$993$	−9.48683	−	9.48683i	−0.301056	−	0.301056i
$994$		0			0
$995$	−15.0000	−	15.0000i	−0.475532	−	0.475532i
$996$		0			0
$997$	14.2302	−	14.2302i	0.450677	−	0.450677i	−0.444902	−	0.895579i	$-0.646762\pi$
$997$	14.2302	−	14.2302i	0.450677	−	0.450677i	0.895579	+	0.444902i	$0.146762\pi$
$998$		0			0
$999$	18.9737			0.600300

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	560.2.bj.a.97.1		4
4.3	odd	2		35.2.f.a.27.2	yes	4
5.3	odd	4	inner	560.2.bj.a.433.2		4
7.6	odd	2	inner	560.2.bj.a.97.2		4
12.11	even	2		315.2.p.c.307.2		4
20.3	even	4		35.2.f.a.13.1	✓	4
20.7	even	4		175.2.f.c.118.2		4
20.19	odd	2		175.2.f.c.132.1		4
28.3	even	6		245.2.l.c.117.1		8
28.11	odd	6		245.2.l.c.117.2		8
28.19	even	6		245.2.l.c.227.2		8
28.23	odd	6		245.2.l.c.227.1		8
28.27	even	2		35.2.f.a.27.1	yes	4
35.13	even	4	inner	560.2.bj.a.433.1		4
60.23	odd	4		315.2.p.c.118.1		4
84.83	odd	2		315.2.p.c.307.1		4
140.3	odd	12		245.2.l.c.68.1		8
140.23	even	12		245.2.l.c.178.1		8
140.27	odd	4		175.2.f.c.118.1		4
140.83	odd	4		35.2.f.a.13.2	yes	4
140.103	odd	12		245.2.l.c.178.2		8
140.123	even	12		245.2.l.c.68.2		8
140.139	even	2		175.2.f.c.132.2		4
420.83	even	4		315.2.p.c.118.2		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
35.2.f.a.13.1	✓	4	20.3	even	4
35.2.f.a.13.2	yes	4	140.83	odd	4
35.2.f.a.27.1	yes	4	28.27	even	2
35.2.f.a.27.2	yes	4	4.3	odd	2
175.2.f.c.118.1		4	140.27	odd	4
175.2.f.c.118.2		4	20.7	even	4
175.2.f.c.132.1		4	20.19	odd	2
175.2.f.c.132.2		4	140.139	even	2
245.2.l.c.68.1		8	140.3	odd	12
245.2.l.c.68.2		8	140.123	even	12
245.2.l.c.117.1		8	28.3	even	6
245.2.l.c.117.2		8	28.11	odd	6
245.2.l.c.178.1		8	140.23	even	12
245.2.l.c.178.2		8	140.103	odd	12
245.2.l.c.227.1		8	28.23	odd	6
245.2.l.c.227.2		8	28.19	even	6
315.2.p.c.118.1		4	60.23	odd	4
315.2.p.c.118.2		4	420.83	even	4
315.2.p.c.307.1		4	84.83	odd	2
315.2.p.c.307.2		4	12.11	even	2
560.2.bj.a.97.1		4	1.1	even	1	trivial
560.2.bj.a.97.2		4	7.6	odd	2	inner
560.2.bj.a.433.1		4	35.13	even	4	inner
560.2.bj.a.433.2		4	5.3	odd	4	inner

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:	\( N \)	\(=\)	\( 560 = 2^{4} \cdot 5 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	560.bj (of order \(4\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(-1.58114 - 1.58114i) q^{3} +(-1.58114 - 1.58114i) q^{5} +(0.581139 - 2.58114i) q^{7} +2.00000i q^{9} +O(q^{10})\)	\(q+(-1.58114 - 1.58114i) q^{3} +(-1.58114 - 1.58114i) q^{5} +(0.581139 - 2.58114i) q^{7} +2.00000i q^{9} +1.00000 q^{11} +(-1.58114 - 1.58114i) q^{13} +5.00000i q^{15} +(1.58114 - 1.58114i) q^{17} -3.16228 q^{19} +(-5.00000 + 3.16228i) q^{21} +(-2.00000 + 2.00000i) q^{23} +5.00000i q^{25} +(-1.58114 + 1.58114i) q^{27} +3.00000i q^{29} +3.16228i q^{31} +(-1.58114 - 1.58114i) q^{33} +(-5.00000 + 3.16228i) q^{35} +(-6.00000 - 6.00000i) q^{37} +5.00000i q^{39} +9.48683i q^{41} +(3.00000 - 3.00000i) q^{43} +(3.16228 - 3.16228i) q^{45} +(4.74342 - 4.74342i) q^{47} +(-6.32456 - 3.00000i) q^{49} -5.00000 q^{51} +(1.00000 - 1.00000i) q^{53} +(-1.58114 - 1.58114i) q^{55} +(5.00000 + 5.00000i) q^{57} -9.48683 q^{59} -6.32456i q^{61} +(5.16228 + 1.16228i) q^{63} +5.00000i q^{65} +(1.00000 + 1.00000i) q^{67} +6.32456 q^{69} +6.00000 q^{71} +(7.90569 - 7.90569i) q^{75} +(0.581139 - 2.58114i) q^{77} -13.0000i q^{79} +11.0000 q^{81} +(3.16228 + 3.16228i) q^{83} -5.00000 q^{85} +(4.74342 - 4.74342i) q^{87} -6.32456 q^{89} +(-5.00000 + 3.16228i) q^{91} +(5.00000 - 5.00000i) q^{93} +(5.00000 + 5.00000i) q^{95} +(-1.58114 + 1.58114i) q^{97} +2.00000i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q - 4 q^{7}+O(q^{10}) \) 4 * q - 4 * q^7	\( 4 q - 4 q^{7} + 4 q^{11} - 20 q^{21} - 8 q^{23} - 20 q^{35} - 24 q^{37} + 12 q^{43} - 20 q^{51} + 4 q^{53} + 20 q^{57} + 8 q^{63} + 4 q^{67} + 24 q^{71} - 4 q^{77} + 44 q^{81} - 20 q^{85} - 20 q^{91} + 20 q^{93} + 20 q^{95}+O(q^{100}) \) 4 * q - 4 * q^7 + 4 * q^11 - 20 * q^21 - 8 * q^23 - 20 * q^35 - 24 * q^37 + 12 * q^43 - 20 * q^51 + 4 * q^53 + 20 * q^57 + 8 * q^63 + 4 * q^67 + 24 * q^71 - 4 * q^77 + 44 * q^81 - 20 * q^85 - 20 * q^91 + 20 * q^93 + 20 * q^95

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