LMFDB - Embedded newform 1416.1.u.b.731.1

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [1416,1,Mod(11,1416)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("1416.11"); S:= CuspForms(chi, 1); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(1416, base_ring=CyclotomicField(58)) chi = DirichletCharacter(H, H._module([29, 29, 29, 25])) B = ModularForms(chi, 1).cuspidal_submodule().basis() N = [B[i] for i in range(len(B))]

Level:	$ N $	$=$	$ 1416 = 2^{3} \cdot 3 \cdot 59 $
Weight:	$ k $	$=$	$ 1 $
Character orbit:	$[\chi]$	$=$	1416.u (of order $58$, degree $28$, minimal)

Newform invariants

comment:select newform

sage:traces = [28,1] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(2)] == traces)

gp:f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$0.706676057888$
Analytic rank:	$0$
Dimension:	$28$
Coefficient field:	$\Q(\zeta_{58})$
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{28} - x^{27} + x^{26} - x^{25} + x^{24} - x^{23} + x^{22} - x^{21} + x^{20} - x^{19} + x^{18} + \cdots + 1 $ x^28 - x^27 + x^26 - x^25 + x^24 - x^23 + x^22 - x^21 + x^20 - x^19 + x^18 - x^17 + x^16 - x^15 + x^14 - x^13 + x^12 - x^11 + x^10 - x^9 + x^8 - x^7 + x^6 - x^5 + x^4 - x^3 + x^2 - x + 1
Coefficient ring:	$\Z[a_1, a_2]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Projective image:	$D_{58}$
Projective field:	Galois closure of $\mathbb{Q}[x]/(x^{58} - \cdots)$

Embedding invariants

Embedding label			731.1
Root			$0.370138 + 0.928977i$ of defining polynomial
Character	$\chi$	$=$	1416.731
Dual form			1416.1.u.b.1139.1

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.725995 - 0.687699i) q^{2} +(0.267528 + 0.963550i) q^{3} +(0.0541389 - 0.998533i) q^{4} +(0.856857 + 0.515554i) q^{6} +(-0.647386 - 0.762162i) q^{8} +(-0.856857 + 0.515554i) q^{9} +(1.70367 - 0.185285i) q^{11} +(0.976621 - 0.214970i) q^{12} +(-0.994138 - 0.108119i) q^{16} +(1.34676 - 0.714006i) q^{17} +(-0.267528 + 0.963550i) q^{18} +(-1.62401 + 0.977132i) q^{19} +(1.10944 - 1.30613i) q^{22} +(0.561187 - 0.827689i) q^{24} +(0.947653 + 0.319302i) q^{25} +(-0.725995 - 0.687699i) q^{27} +(-0.796093 + 0.605174i) q^{32} +(0.634311 + 1.59200i) q^{33} +(0.486719 - 1.44453i) q^{34} +(0.468408 + 0.883512i) q^{36} +(-0.507048 + 1.82622i) q^{38} +(-0.780134 - 0.310834i) q^{41} +(0.0464848 - 0.427421i) q^{43} +(-0.0927786 - 1.71120i) q^{44} +(-0.161782 - 0.986827i) q^{48} +(-0.561187 - 0.827689i) q^{49} +(0.907575 - 0.419889i) q^{50} +(1.04828 + 1.10665i) q^{51} -1.00000 q^{54} +(-1.37598 - 1.30340i) q^{57} +(0.370138 + 0.928977i) q^{59} +(-0.161782 + 0.986827i) q^{64} +(1.55533 + 0.719570i) q^{66} +(-1.46876 + 1.24758i) q^{67} +(-0.640047 - 1.38344i) q^{68} +(0.947653 + 0.319302i) q^{72} +(-1.32527 + 0.367958i) q^{73} +(-0.0541389 + 0.998533i) q^{75} +(0.887777 + 1.67453i) q^{76} +(0.468408 - 0.883512i) q^{81} +(-0.780134 + 0.310834i) q^{82} +(0.589329 + 0.447996i) q^{83} +(-0.260189 - 0.342273i) q^{86} +(-1.24415 - 1.17852i) q^{88} +(-1.15592 - 1.09495i) q^{89} +(-0.796093 - 0.605174i) q^{96} +(-1.79023 - 0.497055i) q^{97} +(-0.976621 - 0.214970i) q^{98} +(-1.36428 + 1.03710i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 28 q + q^{2} - q^{3} - q^{4} + q^{6} + q^{8} - q^{9} - 2 q^{11} - q^{12} - q^{16} + q^{18} + 2 q^{19} + 2 q^{22} + q^{24} + q^{25} - q^{27} + q^{32} - 2 q^{33} - q^{36} - 2 q^{38} - 2 q^{44}+ \cdots - 2 q^{99}+O(q^{100}) $ 28 * q + q^2 - q^3 - q^4 + q^6 + q^8 - q^9 - 2 * q^11 - q^12 - q^16 + q^18 + 2 * q^19 + 2 * q^22 + q^24 + q^25 - q^27 + q^32 - 2 * q^33 - q^36 - 2 * q^38 - 2 * q^44 - q^48 - q^49 - q^50 - 28 * q^54 + 2 * q^57 + q^59 - q^64 + 2 * q^66 + q^72 + q^75 + 2 * q^76 - q^81 + 2 * q^83 + 2 * q^88 - 2 * q^89 + q^96 + q^98 - 2 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1416\mathbb{Z}\right)^\times$.

$n$	$473$	$709$	$769$	$1063$
$\chi(n)$	$-1$	$-1$	$e\left(\frac{15}{58}\right)$	$-1$

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 $

$2$	0.725995	−	0.687699i	0.725995	−	0.687699i
$2$	0.725995	−	0.687699i	0.725995	−	0.687699i
$3$	0.267528	+	0.963550i	0.267528	+	0.963550i
$3$	0.267528	+	0.963550i	0.267528	+	0.963550i
$4$	0.0541389	−	0.998533i	0.0541389	−	0.998533i
$5$		0			0		−0.986827	−	0.161782i	$-0.948276\pi$
$5$		0			0		0.986827	+	0.161782i	$0.0517241\pi$
$6$	0.856857	+	0.515554i	0.856857	+	0.515554i
$7$		0			0		0.468408	−	0.883512i	$-0.344828\pi$
$7$		0			0		−0.468408	+	0.883512i	$0.655172\pi$
$8$	−0.647386	−	0.762162i	−0.647386	−	0.762162i
$9$	−0.856857	+	0.515554i	−0.856857	+	0.515554i
$10$		0			0
$11$	1.70367	−	0.185285i	1.70367	−	0.185285i	0.796093	−	0.605174i	$-0.206897\pi$
$11$	1.70367	−	0.185285i	1.70367	−	0.185285i	0.907575	+	0.419889i	$0.137931\pi$
$12$	0.976621	−	0.214970i	0.976621	−	0.214970i
$13$		0			0		0.419889	−	0.907575i	$-0.362069\pi$
$13$		0			0		−0.419889	+	0.907575i	$0.637931\pi$
$14$		0			0
$15$		0			0
$16$	−0.994138	−	0.108119i	−0.994138	−	0.108119i
$17$	1.34676	−	0.714006i	1.34676	−	0.714006i	0.370138	−	0.928977i	$-0.379310\pi$
$17$	1.34676	−	0.714006i	1.34676	−	0.714006i	0.976621	+	0.214970i	$0.0689655\pi$
$18$	−0.267528	+	0.963550i	−0.267528	+	0.963550i
$19$	−1.62401	+	0.977132i	−1.62401	+	0.977132i	−0.647386	+	0.762162i	$0.724138\pi$
$19$	−1.62401	+	0.977132i	−1.62401	+	0.977132i	−0.976621	+	0.214970i	$0.931034\pi$
$20$		0			0
$21$		0			0
$22$	1.10944	−	1.30613i	1.10944	−	1.30613i
$23$		0			0		−0.370138	−	0.928977i	$-0.620690\pi$
$23$		0			0		0.370138	+	0.928977i	$0.379310\pi$
$24$	0.561187	−	0.827689i	0.561187	−	0.827689i
$25$	0.947653	+	0.319302i	0.947653	+	0.319302i
$26$		0			0
$27$	−0.725995	−	0.687699i	−0.725995	−	0.687699i
$28$		0			0
$29$		0			0		0.687699	−	0.725995i	$-0.258621\pi$
$29$		0			0		−0.687699	+	0.725995i	$0.741379\pi$
$30$		0			0
$31$		0			0		0.515554	−	0.856857i	$-0.327586\pi$
$31$		0			0		−0.515554	+	0.856857i	$0.672414\pi$
$32$	−0.796093	+	0.605174i	−0.796093	+	0.605174i
$33$	0.634311	+	1.59200i	0.634311	+	1.59200i
$34$	0.486719	−	1.44453i	0.486719	−	1.44453i
$35$		0			0
$36$	0.468408	+	0.883512i	0.468408	+	0.883512i
$37$		0			0		−0.762162	−	0.647386i	$-0.775862\pi$
$37$		0			0		0.762162	+	0.647386i	$0.224138\pi$
$38$	−0.507048	+	1.82622i	−0.507048	+	1.82622i
$39$		0			0
$40$		0			0
$41$	−0.780134	−	0.310834i	−0.780134	−	0.310834i	−0.0541389	−	0.998533i	$-0.517241\pi$
$41$	−0.780134	−	0.310834i	−0.780134	−	0.310834i	−0.725995	+	0.687699i	$0.758621\pi$
$42$		0			0
$43$	0.0464848	−	0.427421i	0.0464848	−	0.427421i	−0.947653	−	0.319302i	$-0.896552\pi$
$43$	0.0464848	−	0.427421i	0.0464848	−	0.427421i	0.994138	−	0.108119i	$-0.0344828\pi$
$44$	−0.0927786	−	1.71120i	−0.0927786	−	1.71120i
$45$		0			0
$46$		0			0
$47$		0			0		−0.161782	−	0.986827i	$-0.551724\pi$
$47$		0			0		0.161782	+	0.986827i	$0.448276\pi$
$48$	−0.161782	−	0.986827i	−0.161782	−	0.986827i
$49$	−0.561187	−	0.827689i	−0.561187	−	0.827689i
$50$	0.907575	−	0.419889i	0.907575	−	0.419889i
$51$	1.04828	+	1.10665i	1.04828	+	1.10665i
$52$		0			0
$53$		0			0		−0.827689	−	0.561187i	$-0.810345\pi$
$53$		0			0		0.827689	+	0.561187i	$0.189655\pi$
$54$	−1.00000			−1.00000
$55$		0			0
$56$		0			0
$57$	−1.37598	−	1.30340i	−1.37598	−	1.30340i
$58$		0			0
$59$	0.370138	+	0.928977i	0.370138	+	0.928977i
$59$	0.370138	+	0.928977i	0.370138	+	0.928977i
$60$		0			0
$61$		0			0		−0.687699	−	0.725995i	$-0.741379\pi$
$61$		0			0		0.687699	+	0.725995i	$0.258621\pi$
$62$		0			0
$63$		0			0
$64$	−0.161782	+	0.986827i	−0.161782	+	0.986827i
$65$		0			0
$66$	1.55533	+	0.719570i	1.55533	+	0.719570i
$67$	−1.46876	+	1.24758i	−1.46876	+	1.24758i	−0.561187	+	0.827689i	$0.689655\pi$
$67$	−1.46876	+	1.24758i	−1.46876	+	1.24758i	−0.907575	+	0.419889i	$0.862069\pi$
$68$	−0.640047	−	1.38344i	−0.640047	−	1.38344i
$69$		0			0
$70$		0			0
$71$		0			0		0.986827	−	0.161782i	$-0.0517241\pi$
$71$		0			0		−0.986827	+	0.161782i	$0.948276\pi$
$72$	0.947653	+	0.319302i	0.947653	+	0.319302i
$73$	−1.32527	+	0.367958i	−1.32527	+	0.367958i	−0.856857	−	0.515554i	$-0.827586\pi$
$73$	−1.32527	+	0.367958i	−1.32527	+	0.367958i	−0.468408	+	0.883512i	$0.655172\pi$
$74$		0			0
$75$	−0.0541389	+	0.998533i	−0.0541389	+	0.998533i
$76$	0.887777	+	1.67453i	0.887777	+	1.67453i
$77$		0			0
$78$		0			0
$79$		0			0		−0.976621	−	0.214970i	$-0.931034\pi$
$79$		0			0		0.976621	+	0.214970i	$0.0689655\pi$
$80$		0			0
$81$	0.468408	−	0.883512i	0.468408	−	0.883512i
$82$	−0.780134	+	0.310834i	−0.780134	+	0.310834i
$83$	0.589329	+	0.447996i	0.589329	+	0.447996i	0.856857	−	0.515554i	$-0.172414\pi$
$83$	0.589329	+	0.447996i	0.589329	+	0.447996i	−0.267528	+	0.963550i	$0.586207\pi$
$84$		0			0
$85$		0			0
$86$	−0.260189	−	0.342273i	−0.260189	−	0.342273i
$87$		0			0
$88$	−1.24415	−	1.17852i	−1.24415	−	1.17852i
$89$	−1.15592	−	1.09495i	−1.15592	−	1.09495i	−0.994138	−	0.108119i	$-0.965517\pi$
$89$	−1.15592	−	1.09495i	−1.15592	−	1.09495i	−0.161782	−	0.986827i	$-0.551724\pi$
$90$		0			0
$91$		0			0
$92$		0			0
$93$		0			0
$94$		0			0
$95$		0			0
$96$	−0.796093	−	0.605174i	−0.796093	−	0.605174i
$97$	−1.79023	−	0.497055i	−1.79023	−	0.497055i	−0.796093	−	0.605174i	$-0.793103\pi$
$97$	−1.79023	−	0.497055i	−1.79023	−	0.497055i	−0.994138	+	0.108119i	$0.965517\pi$
$98$	−0.976621	−	0.214970i	−0.976621	−	0.214970i
$99$	−1.36428	+	1.03710i	−1.36428	+	1.03710i
$100$	0.370138	−	0.928977i	0.370138	−	0.928977i
$101$		0			0		−0.468408	−	0.883512i	$-0.655172\pi$
$101$		0			0		0.468408	+	0.883512i	$0.344828\pi$
$102$	1.52209	+	0.0825252i	1.52209	+	0.0825252i
$103$		0			0		0.998533	−	0.0541389i	$-0.0172414\pi$
$103$		0			0		−0.998533	+	0.0541389i	$0.982759\pi$
$104$		0			0
$105$		0			0
$106$		0			0
$107$	0.178978	+	1.64567i	0.178978	+	1.64567i	0.647386	+	0.762162i	$0.275862\pi$
$107$	0.178978	+	1.64567i	0.178978	+	1.64567i	−0.468408	+	0.883512i	$0.655172\pi$
$108$	−0.725995	+	0.687699i	−0.725995	+	0.687699i
$109$		0			0		−0.419889	−	0.907575i	$-0.637931\pi$
$109$		0			0		0.419889	+	0.907575i	$0.362069\pi$
$110$		0			0
$111$		0			0
$112$		0			0
$113$	0.293659	−	1.79124i	0.293659	−	1.79124i	−0.267528	−	0.963550i	$-0.586207\pi$
$113$	0.293659	−	1.79124i	0.293659	−	1.79124i	0.561187	−	0.827689i	$-0.310345\pi$
$114$	−1.89531			−1.89531
$115$		0			0
$116$		0			0
$117$		0			0
$118$	0.907575	+	0.419889i	0.907575	+	0.419889i
$119$		0			0
$120$		0			0
$121$	1.89154	−	0.416358i	1.89154	−	0.416358i
$122$		0			0
$123$	0.0907960	−	0.834855i	0.0907960	−	0.834855i
$124$		0			0
$125$		0			0
$126$		0			0
$127$		0			0		0.907575	−	0.419889i	$-0.137931\pi$
$127$		0			0		−0.907575	+	0.419889i	$0.862069\pi$
$128$	0.561187	+	0.827689i	0.561187	+	0.827689i
$129$	0.424277	−	0.0695567i	0.424277	−	0.0695567i
$130$		0			0
$131$	−1.31779	−	0.609675i	−1.31779	−	0.609675i	−0.370138	−	0.928977i	$-0.620690\pi$
$131$	−1.31779	−	0.609675i	−1.31779	−	0.609675i	−0.947653	+	0.319302i	$0.896552\pi$
$132$	1.62401	−	0.547192i	1.62401	−	0.547192i
$133$		0			0
$134$	−0.208356	+	1.91580i	−0.208356	+	1.91580i
$135$		0			0
$136$	−1.41606	−	0.564211i	−1.41606	−	0.564211i
$137$	0.624000	+	1.03710i	0.624000	+	1.03710i	0.994138	+	0.108119i	$0.0344828\pi$
$137$	0.624000	+	1.03710i	0.624000	+	1.03710i	−0.370138	+	0.928977i	$0.620690\pi$
$138$		0			0
$139$	−0.143143	+	0.515554i	−0.143143	+	0.515554i	0.856857	+	0.515554i	$0.172414\pi$
$139$	−0.143143	+	0.515554i	−0.143143	+	0.515554i	−1.00000			$1.00000\pi$
$140$		0			0
$141$		0			0
$142$		0			0
$143$		0			0
$144$	0.907575	−	0.419889i	0.907575	−	0.419889i
$145$		0			0
$146$	−0.709092	+	1.17852i	−0.709092	+	1.17852i
$147$	0.647386	−	0.762162i	0.647386	−	0.762162i
$148$		0			0
$149$		0			0		−0.856857	−	0.515554i	$-0.827586\pi$
$149$		0			0		0.856857	+	0.515554i	$0.172414\pi$
$150$	0.647386	+	0.762162i	0.647386	+	0.762162i
$151$		0			0		−0.319302	−	0.947653i	$-0.603448\pi$
$151$		0			0		0.319302	+	0.947653i	$0.396552\pi$
$152$	1.79609	+	0.605174i	1.79609	+	0.605174i
$153$	−0.785871	+	1.30613i	−0.785871	+	1.30613i
$154$		0			0
$155$		0			0
$156$		0			0
$157$		0			0		0.214970	−	0.976621i	$-0.431034\pi$
$157$		0			0		−0.214970	+	0.976621i	$0.568966\pi$
$158$		0			0
$159$		0			0
$160$		0			0
$161$		0			0
$162$	−0.267528	−	0.963550i	−0.267528	−	0.963550i
$163$	−0.522547	−	1.88205i	−0.522547	−	1.88205i	−0.468408	−	0.883512i	$-0.655172\pi$
$163$	−0.522547	−	1.88205i	−0.522547	−	1.88205i	−0.0541389	−	0.998533i	$-0.517241\pi$
$164$	−0.352614	+	0.762162i	−0.352614	+	0.762162i
$165$		0			0
$166$	0.735937	−	0.0800379i	0.735937	−	0.0800379i
$167$		0			0		0.827689	−	0.561187i	$-0.189655\pi$
$167$		0			0		−0.827689	+	0.561187i	$0.810345\pi$
$168$		0			0
$169$	−0.647386	−	0.762162i	−0.647386	−	0.762162i
$170$		0			0
$171$	0.887777	−	1.67453i	0.887777	−	1.67453i
$172$	−0.424277	−	0.0695567i	−0.424277	−	0.0695567i
$173$		0			0		0.0541389	−	0.998533i	$-0.482759\pi$
$173$		0			0		−0.0541389	+	0.998533i	$0.517241\pi$
$174$		0			0
$175$		0			0
$176$	−1.71371			−1.71371
$177$	−0.796093	+	0.605174i	−0.796093	+	0.605174i
$178$	−1.59219			−1.59219
$179$	−0.234906	+	0.222515i	−0.234906	+	0.222515i	−0.796093	−	0.605174i	$-0.793103\pi$
$179$	−0.234906	+	0.222515i	−0.234906	+	0.222515i	0.561187	+	0.827689i	$0.310345\pi$
$180$		0			0
$181$		0			0		0.0541389	−	0.998533i	$-0.482759\pi$
$181$		0			0		−0.0541389	+	0.998533i	$0.517241\pi$
$182$		0			0
$183$		0			0
$184$		0			0
$185$		0			0
$186$		0			0
$187$	2.16214	−	1.46596i	2.16214	−	1.46596i
$188$		0			0
$189$		0			0
$190$		0			0
$191$		0			0		−0.267528	−	0.963550i	$-0.586207\pi$
$191$		0			0		0.267528	+	0.963550i	$0.413793\pi$
$192$	−0.994138	+	0.108119i	−0.994138	+	0.108119i
$193$	1.11579	+	0.121350i	1.11579	+	0.121350i	0.647386	−	0.762162i	$-0.275862\pi$
$193$	1.11579	+	0.121350i	1.11579	+	0.121350i	0.468408	+	0.883512i	$0.344828\pi$
$194$	−1.64152	+	0.870281i	−1.64152	+	0.870281i
$195$		0			0
$196$	−0.856857	+	0.515554i	−0.856857	+	0.515554i
$197$		0			0		0.214970	−	0.976621i	$-0.431034\pi$
$197$		0			0		−0.214970	+	0.976621i	$0.568966\pi$
$198$	−0.277248	+	1.69114i	−0.277248	+	1.69114i
$199$		0			0		0.647386	−	0.762162i	$-0.275862\pi$
$199$		0			0		−0.647386	+	0.762162i	$0.724138\pi$
$200$	−0.370138	−	0.928977i	−0.370138	−	0.928977i
$201$	−1.59504	−	1.08146i	−1.59504	−	1.08146i
$202$		0			0
$203$		0			0
$204$	1.16178	−	0.986827i	1.16178	−	0.986827i
$205$		0			0
$206$		0			0
$207$		0			0
$208$		0			0
$209$	−2.58572	+	1.96561i	−2.58572	+	1.96561i
$210$		0			0
$211$	−0.564213	+	1.67453i	−0.564213	+	1.67453i	0.161782	+	0.986827i	$0.448276\pi$
$211$	−0.564213	+	1.67453i	−0.564213	+	1.67453i	−0.725995	+	0.687699i	$0.758621\pi$
$212$		0			0
$213$		0			0
$214$	1.26167	+	1.07167i	1.26167	+	1.07167i
$215$		0			0
$216$	−0.0541389	+	0.998533i	−0.0541389	+	0.998533i
$217$		0			0
$218$		0			0
$219$	−0.709092	−	1.17852i	−0.709092	−	1.17852i
$220$		0			0
$221$		0			0
$222$		0			0
$223$		0			0		−0.907575	−	0.419889i	$-0.862069\pi$
$223$		0			0		0.907575	+	0.419889i	$0.137931\pi$
$224$		0			0
$225$	−0.976621	+	0.214970i	−0.976621	+	0.214970i
$226$	−1.01864	−	1.50238i	−1.01864	−	1.50238i
$227$	1.01864	−	0.471273i	1.01864	−	0.471273i	0.161782	−	0.986827i	$-0.448276\pi$
$227$	1.01864	−	0.471273i	1.01864	−	0.471273i	0.856857	+	0.515554i	$0.172414\pi$
$228$	−1.37598	+	1.30340i	−1.37598	+	1.30340i
$229$		0			0		−0.883512	−	0.468408i	$-0.844828\pi$
$229$		0			0		0.883512	+	0.468408i	$0.155172\pi$
$230$		0			0
$231$		0			0
$232$		0			0
$233$	0.522547	−	0.115021i	0.522547	−	0.115021i	0.0541389	−	0.998533i	$-0.482759\pi$
$233$	0.522547	−	0.115021i	0.522547	−	0.115021i	0.468408	+	0.883512i	$0.344828\pi$
$234$		0			0
$235$		0			0
$236$	0.947653	−	0.319302i	0.947653	−	0.319302i
$237$		0			0
$238$		0			0
$239$		0			0		−0.214970	−	0.976621i	$-0.568966\pi$
$239$		0			0		0.214970	+	0.976621i	$0.431034\pi$
$240$		0			0
$241$	−0.234906	+	1.43286i	−0.234906	+	1.43286i	0.561187	+	0.827689i	$0.310345\pi$
$241$	−0.234906	+	1.43286i	−0.234906	+	1.43286i	−0.796093	+	0.605174i	$0.793103\pi$
$242$	1.08692	−	1.60308i	1.08692	−	1.60308i
$243$	0.976621	+	0.214970i	0.976621	+	0.214970i
$244$		0			0
$245$		0			0
$246$	−0.508212	−	0.668542i	−0.508212	−	0.668542i
$247$		0			0
$248$		0			0
$249$	−0.274005	+	0.687699i	−0.274005	+	0.687699i
$250$		0			0
$251$	−1.76443	+	0.0956648i	−1.76443	+	0.0956648i	−0.907575	−	0.419889i	$-0.862069\pi$
$251$	−1.76443	+	0.0956648i	−1.76443	+	0.0956648i	−0.856857	+	0.515554i	$0.827586\pi$
$252$		0			0
$253$		0			0
$254$		0			0
$255$		0			0
$256$	0.976621	+	0.214970i	0.976621	+	0.214970i
$257$	1.70262	+	0.472729i	1.70262	+	0.472729i	0.976621	−	0.214970i	$-0.0689655\pi$
$257$	1.70262	+	0.472729i	1.70262	+	0.472729i	0.725995	+	0.687699i	$0.241379\pi$
$258$	0.260189	−	0.342273i	0.260189	−	0.342273i
$259$		0			0
$260$		0			0
$261$		0			0
$262$	−1.37598	+	0.463623i	−1.37598	+	0.463623i
$263$		0			0		−0.605174	−	0.796093i	$-0.706897\pi$
$263$		0			0		0.605174	+	0.796093i	$0.293103\pi$
$264$	0.802718	−	1.51409i	0.802718	−	1.51409i
$265$		0			0
$266$		0			0
$267$	0.745793	−	1.40672i	0.745793	−	1.40672i
$268$	1.16623	+	1.53415i	1.16623	+	1.53415i
$269$		0			0		0.947653	−	0.319302i	$-0.103448\pi$
$269$		0			0		−0.947653	+	0.319302i	$0.896552\pi$
$270$		0			0
$271$		0			0		−0.796093	−	0.605174i	$-0.793103\pi$
$271$		0			0		0.796093	+	0.605174i	$0.206897\pi$
$272$	−1.41606	+	0.564211i	−1.41606	+	0.564211i
$273$		0			0
$274$	1.16623	+	0.323803i	1.16623	+	0.323803i
$275$	1.67365	+	0.368398i	1.67365	+	0.368398i
$276$		0			0
$277$		0			0		0.370138	−	0.928977i	$-0.379310\pi$
$277$		0			0		−0.370138	+	0.928977i	$0.620690\pi$
$278$	0.250625	+	0.472729i	0.250625	+	0.472729i
$279$		0			0
$280$		0			0
$281$	1.90171	−	0.528008i	1.90171	−	0.528008i	0.907575	−	0.419889i	$-0.137931\pi$
$281$	1.90171	−	0.528008i	1.90171	−	0.528008i	0.994138	−	0.108119i	$-0.0344828\pi$
$282$		0			0
$283$	1.19440	−	0.195813i	1.19440	−	0.195813i	0.468408	−	0.883512i	$-0.344828\pi$
$283$	1.19440	−	0.195813i	1.19440	−	0.195813i	0.725995	+	0.687699i	$0.241379\pi$
$284$		0			0
$285$		0			0
$286$		0			0
$287$		0			0
$288$	0.370138	−	0.928977i	0.370138	−	0.928977i
$289$	0.742767	−	1.09550i	0.742767	−	1.09550i
$290$		0			0
$291$		−	1.85795i		−	1.85795i
$292$	0.295670	+	1.34324i	0.295670	+	1.34324i
$293$		0			0		−0.687699	−	0.725995i	$-0.741379\pi$
$293$		0			0		0.687699	+	0.725995i	$0.258621\pi$
$294$	−0.0541389	−	0.998533i	−0.0541389	−	0.998533i
$295$		0			0
$296$		0			0
$297$	−1.36428	−	1.03710i	−1.36428	−	1.03710i
$298$		0			0
$299$		0			0
$300$	0.994138	+	0.108119i	0.994138	+	0.108119i
$301$		0			0
$302$		0			0
$303$		0			0
$304$	1.72013	−	0.795818i	1.72013	−	0.795818i
$305$		0			0
$306$	0.327685	+	1.48869i	0.327685	+	1.48869i
$307$	0.293659	+	1.79124i	0.293659	+	1.79124i	0.561187	+	0.827689i	$0.310345\pi$
$307$	0.293659	+	1.79124i	0.293659	+	1.79124i	−0.267528	+	0.963550i	$0.586207\pi$
$308$		0			0
$309$		0			0
$310$		0			0
$311$		0			0		0.108119	−	0.994138i	$-0.465517\pi$
$311$		0			0		−0.108119	+	0.994138i	$0.534483\pi$
$312$		0			0
$313$	1.12439	+	0.447996i	1.12439	+	0.447996i	0.856857	−	0.515554i	$-0.172414\pi$
$313$	1.12439	+	0.447996i	1.12439	+	0.447996i	0.267528	+	0.963550i	$0.413793\pi$
$314$		0			0
$315$		0			0
$316$		0			0
$317$		0			0		−0.762162	−	0.647386i	$-0.775862\pi$
$317$		0			0		0.762162	+	0.647386i	$0.224138\pi$
$318$		0			0
$319$		0			0
$320$		0			0
$321$	−1.53781	+	0.612719i	−1.53781	+	0.612719i
$322$		0			0
$323$	−1.48947	+	2.47551i	−1.48947	+	2.47551i
$324$	−0.856857	−	0.515554i	−0.856857	−	0.515554i
$325$		0			0
$326$	−1.67365	−	1.00700i	−1.67365	−	1.00700i
$327$		0			0
$328$	0.268142	+	0.795818i	0.268142	+	0.795818i
$329$		0			0
$330$		0			0
$331$	−0.415433	−	1.04266i	−0.415433	−	1.04266i	−0.976621	−	0.214970i	$-0.931034\pi$
$331$	−0.415433	−	1.04266i	−0.415433	−	1.04266i	0.561187	−	0.827689i	$-0.310345\pi$
$332$	0.479245	−	0.564211i	0.479245	−	0.564211i
$333$		0			0
$334$		0			0
$335$		0			0
$336$		0			0
$337$	1.74375	−	0.924476i	1.74375	−	0.924476i	0.796093	−	0.605174i	$-0.206897\pi$
$337$	1.74375	−	0.924476i	1.74375	−	0.924476i	0.947653	−	0.319302i	$-0.103448\pi$
$338$	−0.994138	−	0.108119i	−0.994138	−	0.108119i
$339$	1.80451	−	0.196252i	1.80451	−	0.196252i
$340$		0			0
$341$		0			0
$342$	−0.507048	−	1.82622i	−0.507048	−	1.82622i
$343$		0			0
$344$	−0.355857	+	0.241277i	−0.355857	+	0.241277i
$345$		0			0
$346$		0			0
$347$	0.438813	−	0.827689i	0.438813	−	0.827689i	−0.561187	−	0.827689i	$-0.689655\pi$
$347$	0.438813	−	0.827689i	0.438813	−	0.827689i	1.00000			$0$
$348$		0			0
$349$		0			0		−0.986827	−	0.161782i	$-0.948276\pi$
$349$		0			0		0.986827	+	0.161782i	$0.0517241\pi$
$350$		0			0
$351$		0			0
$352$	−1.24415	+	1.17852i	−1.24415	+	1.17852i
$353$	0.323564			0.323564			0.161782	−	0.986827i	$-0.448276\pi$
$353$	0.323564			0.323564			0.161782	+	0.986827i	$0.448276\pi$
$354$	−0.161782	+	0.986827i	−0.161782	+	0.986827i
$355$		0			0
$356$	−1.15592	+	1.09495i	−1.15592	+	1.09495i
$357$		0			0
$358$	−0.0175174	+	0.323089i	−0.0175174	+	0.323089i
$359$		0			0		−0.986827	−	0.161782i	$-0.948276\pi$
$359$		0			0		0.986827	+	0.161782i	$0.0517241\pi$
$360$		0			0
$361$	1.21420	−	2.29023i	1.21420	−	2.29023i
$362$		0			0
$363$	0.907221	+	1.71120i	0.907221	+	1.71120i
$364$		0			0
$365$		0			0
$366$		0			0
$367$		0			0		0.419889	−	0.907575i	$-0.362069\pi$
$367$		0			0		−0.419889	+	0.907575i	$0.637931\pi$
$368$		0			0
$369$	0.828715	−	0.135861i	0.828715	−	0.135861i
$370$		0			0
$371$		0			0
$372$		0			0
$373$		0			0		0.856857	−	0.515554i	$-0.172414\pi$
$373$		0			0		−0.856857	+	0.515554i	$0.827586\pi$
$374$	0.561558	−	2.55118i	0.561558	−	2.55118i
$375$		0			0
$376$		0			0
$377$		0			0
$378$		0			0
$379$	0.701525	+	0.236371i	0.701525	+	0.236371i	0.647386	−	0.762162i	$-0.275862\pi$
$379$	0.701525	+	0.236371i	0.701525	+	0.236371i	0.0541389	+	0.998533i	$0.482759\pi$
$380$		0			0
$381$		0			0
$382$		0			0
$383$		0			0		0.687699	−	0.725995i	$-0.258621\pi$
$383$		0			0		−0.687699	+	0.725995i	$0.741379\pi$
$384$	−0.647386	+	0.762162i	−0.647386	+	0.762162i
$385$		0			0
$386$	0.893514	−	0.679232i	0.893514	−	0.679232i
$387$	0.180527	+	0.390204i	0.180527	+	0.390204i
$388$	−0.593247	+	1.76070i	−0.593247	+	1.76070i
$389$		0			0		0.605174	−	0.796093i	$-0.293103\pi$
$389$		0			0		−0.605174	+	0.796093i	$0.706897\pi$
$390$		0			0
$391$		0			0
$392$	−0.267528	+	0.963550i	−0.267528	+	0.963550i
$393$	0.234906	−	1.43286i	0.234906	−	1.43286i
$394$		0			0
$395$		0			0
$396$	0.961714	+	1.41842i	0.961714	+	1.41842i
$397$		0			0		0.108119	−	0.994138i	$-0.465517\pi$
$397$		0			0		−0.108119	+	0.994138i	$0.534483\pi$
$398$		0			0
$399$		0			0
$400$	−0.907575	−	0.419889i	−0.907575	−	0.419889i
$401$	0.321667	+	1.96208i	0.321667	+	1.96208i	0.267528	+	0.963550i	$0.413793\pi$
$401$	0.321667	+	1.96208i	0.321667	+	1.96208i	0.0541389	+	0.998533i	$0.482759\pi$
$402$	−1.90171	+	0.311770i	−1.90171	+	0.311770i
$403$		0			0
$404$		0			0
$405$		0			0
$406$		0			0
$407$		0			0
$408$	0.164808	−	1.51539i	0.164808	−	1.51539i
$409$	0.215921	+	0.0117069i	0.215921	+	0.0117069i	0.161782	−	0.986827i	$-0.448276\pi$
$409$	0.215921	+	0.0117069i	0.215921	+	0.0117069i	0.0541389	+	0.998533i	$0.482759\pi$
$410$		0			0
$411$	−0.832356	+	0.878708i	−0.832356	+	0.878708i
$412$		0			0
$413$		0			0
$414$		0			0
$415$		0			0
$416$		0			0
$417$	−0.535057			−0.535057
$418$	−0.525470	+	3.20523i	−0.525470	+	3.20523i
$419$	0.300267	−	0.442861i	0.300267	−	0.442861i	−0.647386	−	0.762162i	$-0.724138\pi$
$419$	0.300267	−	0.442861i	0.300267	−	0.442861i	0.947653	+	0.319302i	$0.103448\pi$
$420$		0			0
$421$		0			0		0.762162	−	0.647386i	$-0.224138\pi$
$421$		0			0		−0.762162	+	0.647386i	$0.775862\pi$
$422$	0.741954	+	1.60371i	0.741954	+	1.60371i
$423$		0			0
$424$		0			0
$425$	1.50424	−	0.246608i	1.50424	−	0.246608i
$426$		0			0
$427$		0			0
$428$	1.65295	−	0.0896204i	1.65295	−	0.0896204i
$429$		0			0
$430$		0			0
$431$		0			0		0.370138	−	0.928977i	$-0.379310\pi$
$431$		0			0		−0.370138	+	0.928977i	$0.620690\pi$
$432$	0.647386	+	0.762162i	0.647386	+	0.762162i
$433$	−1.90758	−	0.419889i	−1.90758	−	0.419889i	−0.907575	−	0.419889i	$-0.862069\pi$
$433$	−1.90758	−	0.419889i	−1.90758	−	0.419889i	−1.00000			$\pi$
$434$		0			0
$435$		0			0
$436$		0			0
$437$		0			0
$438$	−1.32527	−	0.367958i	−1.32527	−	0.367958i
$439$		0			0		0.947653	−	0.319302i	$-0.103448\pi$
$439$		0			0		−0.947653	+	0.319302i	$0.896552\pi$
$440$		0			0
$441$	0.907575	+	0.419889i	0.907575	+	0.419889i
$442$		0			0
$443$	0.939999	+	0.890414i	0.939999	+	0.890414i	0.994138	−	0.108119i	$-0.0344828\pi$
$443$	0.939999	+	0.890414i	0.939999	+	0.890414i	−0.0541389	+	0.998533i	$0.517241\pi$
$444$		0			0
$445$		0			0
$446$		0			0
$447$		0			0
$448$		0			0
$449$	−0.957875	+	0.381652i	−0.957875	+	0.381652i	−0.796093	−	0.605174i	$-0.793103\pi$
$449$	−0.957875	+	0.381652i	−0.957875	+	0.381652i	−0.161782	+	0.986827i	$0.551724\pi$
$450$	−0.561187	+	0.827689i	−0.561187	+	0.827689i
$451$	−1.38668	−	0.385011i	−1.38668	−	0.385011i
$452$	−1.77271	−	0.390204i	−1.77271	−	0.390204i
$453$		0			0
$454$	0.415433	−	1.04266i	0.415433	−	1.04266i
$455$		0			0
$456$	−0.102610	+	1.89253i	−0.102610	+	1.89253i
$457$	−0.637666	+	0.0345733i	−0.637666	+	0.0345733i	−0.370138	−	0.928977i	$-0.620690\pi$
$457$	−0.637666	+	0.0345733i	−0.637666	+	0.0345733i	−0.267528	+	0.963550i	$0.586207\pi$
$458$		0			0
$459$	−1.46876	−	0.407800i	−1.46876	−	0.407800i
$460$		0			0
$461$		0			0		−0.108119	−	0.994138i	$-0.534483\pi$
$461$		0			0		0.108119	+	0.994138i	$0.465517\pi$
$462$		0			0
$463$		0			0		−0.419889	−	0.907575i	$-0.637931\pi$
$463$		0			0		0.419889	+	0.907575i	$0.362069\pi$
$464$		0			0
$465$		0			0
$466$	0.300267	−	0.442861i	0.300267	−	0.442861i
$467$	0.321667	−	1.96208i	0.321667	−	1.96208i	0.0541389	−	0.998533i	$-0.482759\pi$
$467$	0.321667	−	1.96208i	0.321667	−	1.96208i	0.267528	−	0.963550i	$-0.413793\pi$
$468$		0			0
$469$		0			0
$470$		0			0
$471$		0			0
$472$	0.468408	−	0.883512i	0.468408	−	0.883512i
$473$		−	0.736796i		−	0.736796i
$474$		0			0
$475$	−1.85100	+	0.407435i	−1.85100	+	0.407435i
$476$		0			0
$477$		0			0
$478$		0			0
$479$		0			0		−0.883512	−	0.468408i	$-0.844828\pi$
$479$		0			0		0.883512	+	0.468408i	$0.155172\pi$
$480$		0			0
$481$		0			0
$482$	0.814839	+	1.20180i	0.814839	+	1.20180i
$483$		0			0
$484$	−0.313342	−	1.91130i	−0.313342	−	1.91130i
$485$		0			0
$486$	0.856857	−	0.515554i	0.856857	−	0.515554i
$487$		0			0		−0.0541389	−	0.998533i	$-0.517241\pi$
$487$		0			0		0.0541389	+	0.998533i	$0.482759\pi$
$488$		0			0
$489$	1.67365	−	1.00700i	1.67365	−	1.00700i
$490$		0			0
$491$	−0.993524	−	1.65125i	−0.993524	−	1.65125i	−0.725995	−	0.687699i	$-0.758621\pi$
$491$	−0.993524	−	1.65125i	−0.993524	−	1.65125i	−0.267528	−	0.963550i	$-0.586207\pi$
$492$	−0.828715	−	0.135861i	−0.828715	−	0.135861i
$493$		0			0
$494$		0			0
$495$		0			0
$496$		0			0
$497$		0			0
$498$	0.274005	+	0.687699i	0.274005	+	0.687699i
$499$	1.03076	−	0.783563i	1.03076	−	0.783563i	0.0541389	−	0.998533i	$-0.482759\pi$
$499$	1.03076	−	0.783563i	1.03076	−	0.783563i	0.976621	+	0.214970i	$0.0689655\pi$
$500$		0			0
$501$		0			0
$502$	−1.21518	+	1.28285i	−1.21518	+	1.28285i
$503$		0			0		−0.856857	−	0.515554i	$-0.827586\pi$
$503$		0			0		0.856857	+	0.515554i	$0.172414\pi$
$504$		0			0
$505$		0			0
$506$		0			0
$507$	0.561187	−	0.827689i	0.561187	−	0.827689i
$508$		0			0
$509$		0			0		0.647386	−	0.762162i	$-0.275862\pi$
$509$		0			0		−0.647386	+	0.762162i	$0.724138\pi$
$510$		0			0
$511$		0			0
$512$	0.856857	−	0.515554i	0.856857	−	0.515554i
$513$	1.85100	+	0.407435i	1.85100	+	0.407435i
$514$	1.56119	−	0.827689i	1.56119	−	0.827689i
$515$		0			0
$516$	−0.0464848	−	0.427421i	−0.0464848	−	0.427421i
$517$		0			0
$518$		0			0
$519$		0			0
$520$		0			0
$521$	−1.53781	+	1.04266i	−1.53781	+	1.04266i	−0.561187	+	0.827689i	$0.689655\pi$
$521$	−1.53781	+	1.04266i	−1.53781	+	1.04266i	−0.976621	+	0.214970i	$0.931034\pi$
$522$		0			0
$523$	0.606482	+	0.714006i	0.606482	+	0.714006i	0.976621	−	0.214970i	$-0.0689655\pi$
$523$	0.606482	+	0.714006i	0.606482	+	0.714006i	−0.370138	+	0.928977i	$0.620690\pi$
$524$	−0.680125	+	1.28285i	−0.680125	+	1.28285i
$525$		0			0
$526$		0			0
$527$		0			0
$528$	−0.458467	−	1.65125i	−0.458467	−	1.65125i
$529$	−0.725995	+	0.687699i	−0.725995	+	0.687699i
$530$		0			0
$531$	−0.796093	−	0.605174i	−0.796093	−	0.605174i
$532$		0			0
$533$		0			0
$534$	−0.425955	−	1.53415i	−0.425955	−	1.53415i
$535$		0			0
$536$	1.90171	+	0.311770i	1.90171	+	0.311770i
$537$	−0.277248	−	0.166815i	−0.277248	−	0.166815i
$538$		0			0
$539$	−1.10944	−	1.30613i	−1.10944	−	1.30613i
$540$		0			0
$541$		0			0		0.827689	−	0.561187i	$-0.189655\pi$
$541$		0			0		−0.827689	+	0.561187i	$0.810345\pi$
$542$		0			0
$543$		0			0
$544$	−0.640047	+	1.38344i	−0.640047	+	1.38344i
$545$		0			0
$546$		0			0
$547$	1.44348	+	0.156988i	1.44348	+	0.156988i	0.796093	−	0.605174i	$-0.206897\pi$
$547$	1.44348	+	0.156988i	1.44348	+	0.156988i	0.647386	+	0.762162i	$0.275862\pi$
$548$	1.06936	−	0.566937i	1.06936	−	0.566937i
$549$		0			0
$550$	1.46841	−	0.883512i	1.46841	−	0.883512i
$551$		0			0
$552$		0			0
$553$		0			0
$554$		0			0
$555$		0			0
$556$	0.507048	+	0.170844i	0.507048	+	0.170844i
$557$		0			0		−0.319302	−	0.947653i	$-0.603448\pi$
$557$		0			0		0.319302	+	0.947653i	$0.396552\pi$
$558$		0			0
$559$		0			0
$560$		0			0
$561$	1.99096	+	1.69114i	1.99096	+	1.69114i
$562$	1.01752	−	1.69114i	1.01752	−	1.69114i
$563$	1.44503	−	1.09848i	1.44503	−	1.09848i	0.468408	−	0.883512i	$-0.344828\pi$
$563$	1.44503	−	1.09848i	1.44503	−	1.09848i	0.976621	−	0.214970i	$-0.0689655\pi$
$564$		0			0
$565$		0			0
$566$	0.732472	−	0.963550i	0.732472	−	0.963550i
$567$		0			0
$568$		0			0
$569$	0.388449	−	1.39907i	0.388449	−	1.39907i	−0.468408	−	0.883512i	$-0.655172\pi$
$569$	0.388449	−	1.39907i	0.388449	−	1.39907i	0.856857	−	0.515554i	$-0.172414\pi$
$570$		0			0
$571$	−0.853437	−	1.41842i	−0.853437	−	1.41842i	−0.907575	−	0.419889i	$-0.862069\pi$
$571$	−0.853437	−	1.41842i	−0.853437	−	1.41842i	0.0541389	−	0.998533i	$-0.482759\pi$
$572$		0			0
$573$		0			0
$574$		0			0
$575$		0			0
$576$	−0.370138	−	0.928977i	−0.370138	−	0.928977i
$577$	0.671857	+	0.310834i	0.671857	+	0.310834i	0.725995	−	0.687699i	$-0.241379\pi$
$577$	0.671857	+	0.310834i	0.671857	+	0.310834i	−0.0541389	+	0.998533i	$0.517241\pi$
$578$	−0.214129	−	1.30613i	−0.214129	−	1.30613i
$579$	0.181580	+	1.10759i	0.181580	+	1.10759i
$580$		0			0
$581$		0			0
$582$	−1.27771	−	1.34887i	−1.27771	−	1.34887i
$583$		0			0
$584$	1.13840	+	0.771856i	1.13840	+	0.771856i
$585$		0			0
$586$		0			0
$587$	1.26450	−	0.278338i	1.26450	−	0.278338i	0.468408	−	0.883512i	$-0.344828\pi$
$587$	1.26450	−	0.278338i	1.26450	−	0.278338i	0.796093	+	0.605174i	$0.206897\pi$
$588$	−0.725995	−	0.687699i	−0.725995	−	0.687699i
$589$		0			0
$590$		0			0
$591$		0			0
$592$		0			0
$593$	−0.221658	−	1.00700i	−0.221658	−	1.00700i	−0.947653	−	0.319302i	$-0.896552\pi$
$593$	−0.221658	−	1.00700i	−0.221658	−	1.00700i	0.725995	−	0.687699i	$-0.241379\pi$
$594$	−1.70367	+	0.185285i	−1.70367	+	0.185285i
$595$		0			0
$596$		0			0
$597$		0			0
$598$		0			0
$599$		0			0		−0.419889	−	0.907575i	$-0.637931\pi$
$599$		0			0		0.419889	+	0.907575i	$0.362069\pi$
$600$	0.796093	−	0.605174i	0.796093	−	0.605174i
$601$	0.0690451	+	0.634860i	0.0690451	+	0.634860i	0.976621	+	0.214970i	$0.0689655\pi$
$601$	0.0690451	+	0.634860i	0.0690451	+	0.634860i	−0.907575	+	0.419889i	$0.862069\pi$
$602$		0			0
$603$	0.615326	−	1.82622i	0.615326	−	1.82622i
$604$		0			0
$605$		0			0
$606$		0			0
$607$		0			0		−0.468408	−	0.883512i	$-0.655172\pi$
$607$		0			0		0.468408	+	0.883512i	$0.344828\pi$
$608$	0.701525	−	1.76070i	0.701525	−	1.76070i
$609$		0			0
$610$		0			0
$611$		0			0
$612$	1.26167	+	0.855431i	1.26167	+	0.855431i
$613$		0			0		0.928977	−	0.370138i	$-0.120690\pi$
$613$		0			0		−0.928977	+	0.370138i	$0.879310\pi$
$614$	1.44503	+	1.09848i	1.44503	+	1.09848i
$615$		0			0
$616$		0			0
$617$	0.386466	+	0.508387i	0.386466	+	0.508387i	0.947653	−	0.319302i	$-0.103448\pi$
$617$	0.386466	+	0.508387i	0.386466	+	0.508387i	−0.561187	+	0.827689i	$0.689655\pi$
$618$		0			0
$619$	−1.15592	−	1.09495i	−1.15592	−	1.09495i	−0.994138	−	0.108119i	$-0.965517\pi$
$619$	−1.15592	−	1.09495i	−1.15592	−	1.09495i	−0.161782	−	0.986827i	$-0.551724\pi$
$620$		0			0
$621$		0			0
$622$		0			0
$623$		0			0
$624$		0			0
$625$	0.796093	+	0.605174i	0.796093	+	0.605174i
$626$	1.12439	−	0.447996i	1.12439	−	0.447996i
$627$	−2.58572	−	1.96561i	−2.58572	−	1.96561i
$628$		0			0
$629$		0			0
$630$		0			0
$631$		0			0		0.370138	−	0.928977i	$-0.379310\pi$
$631$		0			0		−0.370138	+	0.928977i	$0.620690\pi$
$632$		0			0
$633$	−1.76443	−	0.0956648i	−1.76443	−	0.0956648i
$634$		0			0
$635$		0			0
$636$		0			0
$637$		0			0
$638$		0			0
$639$		0			0
$640$		0			0
$641$	−1.26167	+	1.07167i	−1.26167	+	1.07167i	−0.267528	+	0.963550i	$0.586207\pi$
$641$	−1.26167	+	1.07167i	−1.26167	+	1.07167i	−0.994138	+	0.108119i	$0.965517\pi$
$642$	−0.695075	+	1.50238i	−0.695075	+	1.50238i
$643$	−0.726610	+	1.07167i	−0.726610	+	1.07167i	0.267528	+	0.963550i	$0.413793\pi$
$643$	−0.726610	+	1.07167i	−0.726610	+	1.07167i	−0.994138	+	0.108119i	$0.965517\pi$
$644$		0			0
$645$		0			0
$646$	0.621063	+	2.82152i	0.621063	+	2.82152i
$647$		0			0		−0.687699	−	0.725995i	$-0.741379\pi$
$647$		0			0		0.687699	+	0.725995i	$0.258621\pi$
$648$	−0.976621	+	0.214970i	−0.976621	+	0.214970i
$649$	0.802718	+	1.51409i	0.802718	+	1.51409i
$650$		0			0
$651$		0			0
$652$	−1.90758	+	0.419889i	−1.90758	+	0.419889i
$653$		0			0		−0.998533	−	0.0541389i	$-0.982759\pi$
$653$		0			0		0.998533	+	0.0541389i	$0.0172414\pi$
$654$		0			0
$655$		0			0
$656$	0.741954	+	0.393359i	0.741954	+	0.393359i
$657$	0.945861	−	0.998533i	0.945861	−	0.998533i
$658$		0			0
$659$	−1.11579	−	1.64567i	−1.11579	−	1.64567i	−0.647386	−	0.762162i	$-0.724138\pi$
$659$	−1.11579	−	1.64567i	−1.11579	−	1.64567i	−0.468408	−	0.883512i	$-0.655172\pi$
$660$		0			0
$661$		0			0		−0.161782	−	0.986827i	$-0.551724\pi$
$661$		0			0		0.161782	+	0.986827i	$0.448276\pi$
$662$	−1.01864	−	0.471273i	−1.01864	−	0.471273i
$663$		0			0
$664$	−0.0400778	−	0.739191i	−0.0400778	−	0.739191i
$665$		0			0
$666$		0			0
$667$		0			0
$668$		0			0
$669$		0			0
$670$		0			0
$671$		0			0
$672$		0			0
$673$	0.624000	−	0.820858i	0.624000	−	0.820858i	−0.370138	−	0.928977i	$-0.620690\pi$
$673$	0.624000	−	0.820858i	0.624000	−	0.820858i	0.994138	+	0.108119i	$0.0344828\pi$
$674$	0.630190	−	1.87034i	0.630190	−	1.87034i
$675$	−0.468408	−	0.883512i	−0.468408	−	0.883512i
$676$	−0.796093	+	0.605174i	−0.796093	+	0.605174i
$677$		0			0		0.515554	−	0.856857i	$-0.327586\pi$
$677$		0			0		−0.515554	+	0.856857i	$0.672414\pi$
$678$	1.17510	−	1.38344i	1.17510	−	1.38344i
$679$		0			0
$680$		0			0
$681$	0.726610	+	0.855431i	0.726610	+	0.855431i
$682$		0			0
$683$	−1.85100	−	0.623673i	−1.85100	−	0.623673i	−0.994138	−	0.108119i	$-0.965517\pi$
$683$	−1.85100	−	0.623673i	−1.85100	−	0.623673i	−0.856857	−	0.515554i	$-0.827586\pi$
$684$	−1.62401	−	0.977132i	−1.62401	−	0.977132i
$685$		0			0
$686$		0			0
$687$		0			0
$688$	−0.0924246	+	0.419889i	−0.0924246	+	0.419889i
$689$		0			0
$690$		0			0
$691$	−0.191049	+	0.101288i	−0.191049	+	0.101288i	−0.561187	−	0.827689i	$-0.689655\pi$
$691$	−0.191049	+	0.101288i	−0.191049	+	0.101288i	0.370138	+	0.928977i	$0.379310\pi$
$692$		0			0
$693$		0			0
$694$	−0.250625	−	0.902670i	−0.250625	−	0.902670i
$695$		0			0
$696$		0			0
$697$	−1.27259	+	0.138403i	−1.27259	+	0.138403i
$698$		0			0
$699$	0.250625	+	0.472729i	0.250625	+	0.472729i
$700$		0			0
$701$		0			0		0.468408	−	0.883512i	$-0.344828\pi$
$701$		0			0		−0.468408	+	0.883512i	$0.655172\pi$
$702$		0			0
$703$		0			0
$704$	−0.0927786	+	1.71120i	−0.0927786	+	1.71120i
$705$		0			0
$706$	0.234906	−	0.222515i	0.234906	−	0.222515i
$707$		0			0
$708$	0.561187	+	0.827689i	0.561187	+	0.827689i
$709$		0			0		1.00000			$0$
$709$		0			0		−1.00000			$\pi$
$710$		0			0
$711$		0			0
$712$	−0.0861992	+	1.58985i	−0.0861992	+	1.58985i
$713$		0			0
$714$		0			0
$715$		0			0
$716$	0.209471	+	0.246608i	0.209471	+	0.246608i
$717$		0			0
$718$		0			0
$719$		0			0		0.994138	−	0.108119i	$-0.0344828\pi$
$719$		0			0		−0.994138	+	0.108119i	$0.965517\pi$
$720$		0			0
$721$		0			0
$722$	−0.693483	−	2.49770i	−0.693483	−	2.49770i
$723$	−1.44348	+	0.156988i	−1.44348	+	0.156988i
$724$		0			0
$725$		0			0
$726$	1.83543	+	0.618429i	1.83543	+	0.618429i
$727$		0			0		0.856857	−	0.515554i	$-0.172414\pi$
$727$		0			0		−0.856857	+	0.515554i	$0.827586\pi$
$728$		0			0
$729$	0.0541389	+	0.998533i	0.0541389	+	0.998533i
$730$		0			0
$731$	−0.242577	−	0.608823i	−0.242577	−	0.608823i
$732$		0			0
$733$		0			0		−0.947653	−	0.319302i	$-0.896552\pi$
$733$		0			0		0.947653	+	0.319302i	$0.103448\pi$
$734$		0			0
$735$		0			0
$736$		0			0
$737$	−2.27113	+	2.39760i	−2.27113	+	2.39760i
$738$	0.508212	−	0.668542i	0.508212	−	0.668542i
$739$	−0.957875	+	1.59200i	−0.957875	+	1.59200i	−0.161782	+	0.986827i	$0.551724\pi$
$739$	−0.957875	+	1.59200i	−0.957875	+	1.59200i	−0.796093	+	0.605174i	$0.793103\pi$
$740$		0			0
$741$		0			0
$742$		0			0
$743$		0			0		0.605174	−	0.796093i	$-0.293103\pi$
$743$		0			0		−0.605174	+	0.796093i	$0.706897\pi$
$744$		0			0
$745$		0			0
$746$		0			0
$747$	−0.735937	−	0.0800379i	−0.735937	−	0.0800379i
$748$	−1.34676	−	2.23833i	−1.34676	−	2.23833i
$749$		0			0
$750$		0			0
$751$		0			0		0.108119	−	0.994138i	$-0.465517\pi$
$751$		0			0		−0.108119	+	0.994138i	$0.534483\pi$
$752$		0			0
$753$	−0.564213	−	1.67453i	−0.564213	−	1.67453i
$754$		0			0
$755$		0			0
$756$		0			0
$757$		0			0		−0.561187	−	0.827689i	$-0.689655\pi$
$757$		0			0		0.561187	+	0.827689i	$0.310345\pi$
$758$	0.671857	−	0.310834i	0.671857	−	0.310834i
$759$		0			0
$760$		0			0
$761$	1.37014	+	0.928977i	1.37014	+	0.928977i	1.00000			$0$
$761$	1.37014	+	0.928977i	1.37014	+	0.928977i	0.370138	+	0.928977i	$0.379310\pi$
$762$		0			0
$763$		0			0
$764$		0			0
$765$		0			0
$766$		0			0
$767$		0			0
$768$	0.0541389	+	0.998533i	0.0541389	+	0.998533i
$769$	0.577515	+	0.609675i	0.577515	+	0.609675i	0.947653	−	0.319302i	$-0.103448\pi$
$769$	0.577515	+	0.609675i	0.577515	+	0.609675i	−0.370138	+	0.928977i	$0.620690\pi$
$770$		0			0
$771$			1.76702i			1.76702i
$772$	0.181580	−	1.10759i	0.181580	−	1.10759i
$773$		0			0		0.561187	−	0.827689i	$-0.310345\pi$
$773$		0			0		−0.561187	+	0.827689i	$0.689655\pi$
$774$	0.399405	+	0.159138i	0.399405	+	0.159138i
$775$		0			0
$776$	0.780134	+	1.68623i	0.780134	+	1.68623i
$777$		0			0
$778$		0			0
$779$	1.57067	−	0.257498i	1.57067	−	0.257498i
$780$		0			0
$781$		0			0
$782$		0			0
$783$		0			0
$784$	0.468408	+	0.883512i	0.468408	+	0.883512i
$785$		0			0
$786$	−0.814839	−	1.20180i	−0.814839	−	1.20180i
$787$	1.94179	+	0.427421i	1.94179	+	0.427421i	0.994138	+	0.108119i	$0.0344828\pi$
$787$	1.94179	+	0.427421i	1.94179	+	0.427421i	0.947653	+	0.319302i	$0.103448\pi$
$788$		0			0
$789$		0			0
$790$		0			0
$791$		0			0
$792$	1.67365	+	0.368398i	1.67365	+	0.368398i
$793$		0			0
$794$		0			0
$795$		0			0
$796$		0			0
$797$		0			0		−0.725995	−	0.687699i	$-0.758621\pi$
$797$		0			0		0.725995	+	0.687699i	$0.241379\pi$
$798$		0			0
$799$		0			0
$800$	−0.947653	+	0.319302i	−0.947653	+	0.319302i
$801$	1.55496	+	0.342273i	1.55496	+	0.342273i
$802$	1.58285	+	1.20325i	1.58285	+	1.20325i
$803$	−2.18964	+	0.872431i	−2.18964	+	0.872431i
$804$	−1.16623	+	1.53415i	−1.16623	+	1.53415i
$805$		0			0
$806$		0			0
$807$		0			0
$808$		0			0
$809$	−0.346752	−	0.654043i	−0.346752	−	0.654043i	0.647386	−	0.762162i	$-0.275862\pi$
$809$	−0.346752	−	0.654043i	−0.346752	−	0.654043i	−0.994138	+	0.108119i	$0.965517\pi$
$810$		0			0
$811$	0.838547	−	0.0454647i	0.838547	−	0.0454647i	0.370138	−	0.928977i	$-0.379310\pi$
$811$	0.838547	−	0.0454647i	0.838547	−	0.0454647i	0.468408	+	0.883512i	$0.344828\pi$
$812$		0			0
$813$		0			0
$814$		0			0
$815$		0			0
$816$	−0.922482	−	1.21350i	−0.922482	−	1.21350i
$817$	0.342155	+	0.739556i	0.342155	+	0.739556i
$818$	0.164808	−	0.139990i	0.164808	−	0.139990i
$819$		0			0
$820$		0			0
$821$		0			0		0.161782	−	0.986827i	$-0.448276\pi$
$821$		0			0		−0.161782	+	0.986827i	$0.551724\pi$
$822$			1.21035i			1.21035i
$823$		0			0		−0.214970	−	0.976621i	$-0.568966\pi$
$823$		0			0		0.214970	+	0.976621i	$0.431034\pi$
$824$		0			0
$825$	0.0927786	+	1.71120i	0.0927786	+	1.71120i
$826$		0			0
$827$			0.429941i			0.429941i	0.976621	+	0.214970i	$0.0689655\pi$
$827$			0.429941i			0.429941i	−0.976621	+	0.214970i	$0.931034\pi$
$828$		0			0
$829$		0			0		0.976621	−	0.214970i	$-0.0689655\pi$
$829$		0			0		−0.976621	+	0.214970i	$0.931034\pi$
$830$		0			0
$831$		0			0
$832$		0			0
$833$	−1.34676	−	0.714006i	−1.34676	−	0.714006i
$834$	−0.388449	+	0.367958i	−0.388449	+	0.367958i
$835$		0			0
$836$	1.82274	+	2.68835i	1.82274	+	2.68835i
$837$		0			0
$838$	−0.0865625	−	0.528008i	−0.0865625	−	0.528008i
$839$		0			0		−0.907575	−	0.419889i	$-0.862069\pi$
$839$		0			0		0.907575	+	0.419889i	$0.137931\pi$
$840$		0			0
$841$	−0.0541389	−	0.998533i	−0.0541389	−	0.998533i
$842$		0			0
$843$	1.01752	+	1.69114i	1.01752	+	1.69114i
$844$	1.64152	+	0.654043i	1.64152	+	0.654043i
$845$		0			0
$846$		0			0
$847$		0			0
$848$		0			0
$849$	0.508212	+	1.09848i	0.508212	+	1.09848i
$850$	0.922482	−	1.21350i	0.922482	−	1.21350i
$851$		0			0
$852$		0			0
$853$		0			0		0.796093	−	0.605174i	$-0.206897\pi$
$853$		0			0		−0.796093	+	0.605174i	$0.793103\pi$
$854$		0			0
$855$		0			0
$856$	1.13840	−	1.20180i	1.13840	−	1.20180i
$857$	1.70367	+	1.02506i	1.70367	+	1.02506i	0.907575	+	0.419889i	$0.137931\pi$
$857$	1.70367	+	1.02506i	1.70367	+	1.02506i	0.796093	+	0.605174i	$0.206897\pi$
$858$		0			0
$859$	0.439167	+	1.30340i	0.439167	+	1.30340i	0.907575	+	0.419889i	$0.137931\pi$
$859$	0.439167	+	1.30340i	0.439167	+	1.30340i	−0.468408	+	0.883512i	$0.655172\pi$
$860$		0			0
$861$		0			0
$862$		0			0
$863$		0			0		0.647386	−	0.762162i	$-0.275862\pi$
$863$		0			0		−0.647386	+	0.762162i	$0.724138\pi$
$864$	0.994138	+	0.108119i	0.994138	+	0.108119i
$865$		0			0
$866$	−1.67365	+	1.00700i	−1.67365	+	1.00700i
$867$	1.25428	+	0.422616i	1.25428	+	0.422616i
$868$		0			0
$869$		0			0
$870$		0			0
$871$		0			0
$872$		0			0
$873$	1.79023	−	0.497055i	1.79023	−	0.497055i
$874$		0			0
$875$		0			0
$876$	−1.21518	+	0.644248i	−1.21518	+	0.644248i
$877$		0			0		−0.647386	−	0.762162i	$-0.724138\pi$
$877$		0			0		0.647386	+	0.762162i	$0.275862\pi$
$878$		0			0
$879$		0			0
$880$		0			0
$881$	0.0507182	−	0.935443i	0.0507182	−	0.935443i	−0.856857	−	0.515554i	$-0.827586\pi$
$881$	0.0507182	−	0.935443i	0.0507182	−	0.935443i	0.907575	−	0.419889i	$-0.137931\pi$
$882$	0.947653	−	0.319302i	0.947653	−	0.319302i
$883$	−1.31779	+	1.24828i	−1.31779	+	1.24828i	−0.370138	+	0.928977i	$0.620690\pi$
$883$	−1.31779	+	1.24828i	−1.31779	+	1.24828i	−0.947653	+	0.319302i	$0.896552\pi$
$884$		0			0
$885$		0			0
$886$	1.29477			1.29477
$887$		0			0		0.725995	−	0.687699i	$-0.241379\pi$
$887$		0			0		−0.725995	+	0.687699i	$0.758621\pi$
$888$		0			0
$889$		0			0
$890$		0			0
$891$	0.634311	−	1.59200i	0.634311	−	1.59200i
$892$		0			0
$893$		0			0
$894$		0			0
$895$		0			0
$896$		0			0
$897$		0			0
$898$	−0.432951	+	0.935808i	−0.432951	+	0.935808i
$899$		0			0
$900$	0.161782	+	0.986827i	0.161782	+	0.986827i
$901$		0			0
$902$	−1.27150	+	0.674105i	−1.27150	+	0.674105i
$903$		0			0
$904$	−1.55533	+	0.935808i	−1.55533	+	0.935808i
$905$		0			0
$906$		0			0
$907$	−0.606482	+	0.714006i	−0.606482	+	0.714006i	−0.976621	−	0.214970i	$-0.931034\pi$
$907$	−0.606482	+	0.714006i	−0.606482	+	0.714006i	0.370138	+	0.928977i	$0.379310\pi$
$908$	−0.415433	−	1.04266i	−0.415433	−	1.04266i
$909$		0			0
$910$		0			0
$911$		0			0		−0.319302	−	0.947653i	$-0.603448\pi$
$911$		0			0		0.319302	+	0.947653i	$0.396552\pi$
$912$	1.22700	+	1.44453i	1.22700	+	1.44453i
$913$	1.08703	+	0.654043i	1.08703	+	0.654043i
$914$	−0.439167	+	0.463623i	−0.439167	+	0.463623i
$915$		0			0
$916$		0			0
$917$		0			0
$918$	−1.34676	+	0.714006i	−1.34676	+	0.714006i
$919$		0			0		0.319302	−	0.947653i	$-0.396552\pi$
$919$		0			0		−0.319302	+	0.947653i	$0.603448\pi$
$920$		0			0
$921$	−1.64739	+	0.762162i	−1.64739	+	0.762162i
$922$		0			0
$923$		0			0
$924$		0			0
$925$		0			0
$926$		0			0
$927$		0			0
$928$		0			0
$929$	−0.0607641	−	1.12073i	−0.0607641	−	1.12073i	−0.856857	−	0.515554i	$-0.827586\pi$
$929$	−0.0607641	−	1.12073i	−0.0607641	−	1.12073i	0.796093	−	0.605174i	$-0.206897\pi$
$930$		0			0
$931$	1.72013	+	0.795818i	1.72013	+	0.795818i
$932$	−0.0865625	−	0.528008i	−0.0865625	−	0.528008i
$933$		0			0
$934$	−1.11579	−	1.64567i	−1.11579	−	1.64567i
$935$		0			0
$936$		0			0
$937$	−1.70262	−	0.902670i	−1.70262	−	0.902670i	−0.976621	−	0.214970i	$-0.931034\pi$
$937$	−1.70262	−	0.902670i	−1.70262	−	0.902670i	−0.725995	−	0.687699i	$-0.758621\pi$
$938$		0			0
$939$	−0.130862	+	1.20325i	−0.130862	+	1.20325i
$940$		0			0
$941$		0			0		0.976621	−	0.214970i	$-0.0689655\pi$
$941$		0			0		−0.976621	+	0.214970i	$0.931034\pi$
$942$		0			0
$943$		0			0
$944$	−0.267528	−	0.963550i	−0.267528	−	0.963550i
$945$		0			0
$946$	−0.506694	−	0.534910i	−0.506694	−	0.534910i
$947$	−0.260189	−	1.18205i	−0.260189	−	1.18205i	−0.907575	−	0.419889i	$-0.862069\pi$
$947$	−0.260189	−	1.18205i	−0.260189	−	1.18205i	0.647386	−	0.762162i	$-0.275862\pi$
$948$		0			0
$949$		0			0
$950$	−1.06362	+	1.56872i	−1.06362	+	1.56872i
$951$		0			0
$952$		0			0
$953$	0.828715	+	1.79124i	0.828715	+	1.79124i	0.561187	+	0.827689i	$0.310345\pi$
$953$	0.828715	+	1.79124i	0.828715	+	1.79124i	0.267528	+	0.963550i	$0.413793\pi$
$954$		0			0
$955$		0			0
$956$		0			0
$957$		0			0
$958$		0			0
$959$		0			0
$960$		0			0
$961$	−0.468408	−	0.883512i	−0.468408	−	0.883512i
$962$		0			0
$963$	−1.00179	−	1.31783i	−1.00179	−	1.31783i
$964$	1.41804	+	0.312135i	1.41804	+	0.312135i
$965$		0			0
$966$		0			0
$967$		0			0		0.928977	−	0.370138i	$-0.120690\pi$
$967$		0			0		−0.928977	+	0.370138i	$0.879310\pi$
$968$	−1.54189	−	1.17211i	−1.54189	−	1.17211i
$969$	−2.78375	−	0.772906i	−2.78375	−	0.772906i
$970$		0			0
$971$	−0.624000	−	0.820858i	−0.624000	−	0.820858i	0.370138	−	0.928977i	$-0.379310\pi$
$971$	−0.624000	−	0.820858i	−0.624000	−	0.820858i	−0.994138	+	0.108119i	$0.965517\pi$
$972$	0.267528	−	0.963550i	0.267528	−	0.963550i
$973$		0			0
$974$		0			0
$975$		0			0
$976$		0			0
$977$	−0.306626	+	0.103314i	−0.306626	+	0.103314i	−0.468408	−	0.883512i	$-0.655172\pi$
$977$	−0.306626	+	0.103314i	−0.306626	+	0.103314i	0.161782	+	0.986827i	$0.448276\pi$
$978$	0.522547	−	1.88205i	0.522547	−	1.88205i
$979$	−2.17218	−	1.65125i	−2.17218	−	1.65125i
$980$		0			0
$981$		0			0
$982$	−1.85686	−	0.515554i	−1.85686	−	0.515554i
$983$		0			0		−0.976621	−	0.214970i	$-0.931034\pi$
$983$		0			0		0.976621	+	0.214970i	$0.0689655\pi$
$984$	−0.695075	+	0.471273i	−0.695075	+	0.471273i
$985$		0			0
$986$		0			0
$987$		0			0
$988$		0			0
$989$		0			0
$990$		0			0
$991$		0			0		0.986827	−	0.161782i	$-0.0517241\pi$
$991$		0			0		−0.986827	+	0.161782i	$0.948276\pi$
$992$		0			0
$993$	0.893514	−	0.679232i	0.893514	−	0.679232i
$994$		0			0
$995$		0			0
$996$	0.671857	+	0.310834i	0.671857	+	0.310834i
$997$		0			0		0.561187	−	0.827689i	$-0.310345\pi$
$997$		0			0		−0.561187	+	0.827689i	$0.689655\pi$
$998$	0.209471	−	1.27772i	0.209471	−	1.27772i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1416.1.u.b.731.1	yes	28
3.2	odd	2		1416.1.u.a.731.1	✓	28
8.3	odd	2	CM	1416.1.u.b.731.1	yes	28
24.11	even	2		1416.1.u.a.731.1	✓	28
59.18	odd	58		1416.1.u.a.1139.1	yes	28
177.77	even	58	inner	1416.1.u.b.1139.1	yes	28
472.195	even	58		1416.1.u.a.1139.1	yes	28
1416.1139	odd	58	inner	1416.1.u.b.1139.1	yes	28

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1416.1.u.a.731.1	✓	28	3.2	odd	2
1416.1.u.a.731.1	✓	28	24.11	even	2
1416.1.u.a.1139.1	yes	28	59.18	odd	58
1416.1.u.a.1139.1	yes	28	472.195	even	58
1416.1.u.b.731.1	yes	28	1.1	even	1	trivial
1416.1.u.b.731.1	yes	28	8.3	odd	2	CM
1416.1.u.b.1139.1	yes	28	177.77	even	58	inner
1416.1.u.b.1139.1	yes	28	1416.1139	odd	58	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 $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 1416 = 2^{3} \cdot 3 \cdot 59 \)
Weight:	\( k \)	\(=\)	\( 1 \)
Character orbit:	\([\chi]\)	\(=\)	1416.u (of order \(58\), degree \(28\), minimal)

\(f(q)\)	\(=\)	\(q+(0.725995 - 0.687699i) q^{2} +(0.267528 + 0.963550i) q^{3} +(0.0541389 - 0.998533i) q^{4} +(0.856857 + 0.515554i) q^{6} +(-0.647386 - 0.762162i) q^{8} +(-0.856857 + 0.515554i) q^{9} +(1.70367 - 0.185285i) q^{11} +(0.976621 - 0.214970i) q^{12} +(-0.994138 - 0.108119i) q^{16} +(1.34676 - 0.714006i) q^{17} +(-0.267528 + 0.963550i) q^{18} +(-1.62401 + 0.977132i) q^{19} +(1.10944 - 1.30613i) q^{22} +(0.561187 - 0.827689i) q^{24} +(0.947653 + 0.319302i) q^{25} +(-0.725995 - 0.687699i) q^{27} +(-0.796093 + 0.605174i) q^{32} +(0.634311 + 1.59200i) q^{33} +(0.486719 - 1.44453i) q^{34} +(0.468408 + 0.883512i) q^{36} +(-0.507048 + 1.82622i) q^{38} +(-0.780134 - 0.310834i) q^{41} +(0.0464848 - 0.427421i) q^{43} +(-0.0927786 - 1.71120i) q^{44} +(-0.161782 - 0.986827i) q^{48} +(-0.561187 - 0.827689i) q^{49} +(0.907575 - 0.419889i) q^{50} +(1.04828 + 1.10665i) q^{51} -1.00000 q^{54} +(-1.37598 - 1.30340i) q^{57} +(0.370138 + 0.928977i) q^{59} +(-0.161782 + 0.986827i) q^{64} +(1.55533 + 0.719570i) q^{66} +(-1.46876 + 1.24758i) q^{67} +(-0.640047 - 1.38344i) q^{68} +(0.947653 + 0.319302i) q^{72} +(-1.32527 + 0.367958i) q^{73} +(-0.0541389 + 0.998533i) q^{75} +(0.887777 + 1.67453i) q^{76} +(0.468408 - 0.883512i) q^{81} +(-0.780134 + 0.310834i) q^{82} +(0.589329 + 0.447996i) q^{83} +(-0.260189 - 0.342273i) q^{86} +(-1.24415 - 1.17852i) q^{88} +(-1.15592 - 1.09495i) q^{89} +(-0.796093 - 0.605174i) q^{96} +(-1.79023 - 0.497055i) q^{97} +(-0.976621 - 0.214970i) q^{98} +(-1.36428 + 1.03710i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 28 q + q^{2} - q^{3} - q^{4} + q^{6} + q^{8} - q^{9} - 2 q^{11} - q^{12} - q^{16} + q^{18} + 2 q^{19} + 2 q^{22} + q^{24} + q^{25} - q^{27} + q^{32} - 2 q^{33} - q^{36} - 2 q^{38} - 2 q^{44}+ \cdots - 2 q^{99}+O(q^{100}) \) 28 * q + q^2 - q^3 - q^4 + q^6 + q^8 - q^9 - 2 * q^11 - q^12 - q^16 + q^18 + 2 * q^19 + 2 * q^22 + q^24 + q^25 - q^27 + q^32 - 2 * q^33 - q^36 - 2 * q^38 - 2 * q^44 - q^48 - q^49 - q^50 - 28 * q^54 + 2 * q^57 + q^59 - q^64 + 2 * q^66 + q^72 + q^75 + 2 * q^76 - q^81 + 2 * q^83 + 2 * q^88 - 2 * q^89 + q^96 + q^98 - 2 * q^99

Introduction

L-functions

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