LMFDB - Embedded newform 1775.1.bb.b.1419.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1775,1,Mod(354,1775)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1775, base_ring=CyclotomicField(10))

chi = DirichletCharacter(H, H._module([1, 5]))

N = Newforms(chi, 1, names="a")

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

chi := DirichletCharacter("1775.354");

S:= CuspForms(chi, 1);

N := Newforms(S);

Level:	$ N $	$=$	$ 1775 = 5^{2} \cdot 71 $
Weight:	$ k $	$=$	$ 1 $
Character orbit:	$[\chi]$	$=$	1775.bb (of order $10$, degree $4$, 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:	$0.885840397424$
Analytic rank:	$0$
Dimension:	$24$
Relative dimension:	$6$ over $\Q(\zeta_{10})$
Coefficient field:	$\Q(\zeta_{35})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{24} - x^{23} + x^{19} - x^{18} + x^{17} - x^{16} + x^{14} - x^{13} + x^{12} - x^{11} + x^{10} + \cdots + 1 $ x^24 - x^23 + x^19 - x^18 + x^17 - x^16 + x^14 - x^13 + x^12 - x^11 + x^10 - x^8 + x^7 - x^6 + x^5 - x + 1
Coefficient ring:	$\Z[a_1, \ldots, a_{4}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Projective image:	$D_{70}$
Projective field:	Galois closure of $\mathbb{Q}[x]/(x^{70} + \cdots)$

Embedding invariants

Embedding label			1419.1
Root			$0.936235 + 0.351375i$ of defining polynomial
Character	$\chi$	$=$	1775.1419
Dual form			1775.1.bb.b.354.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.88490 + 0.612441i) q^{2} +(0.602949 + 0.829888i) q^{3} +(2.36874 - 1.72099i) q^{4} +(0.0448648 + 0.998993i) q^{5} +(-1.64476 - 1.19498i) q^{6} +(-2.24590 + 3.09122i) q^{8} +(-0.0161501 + 0.0497048i) q^{9} +O(q^{10})$	\(q+(-1.88490 + 0.612441i) q^{2} +(0.602949 + 0.829888i) q^{3} +(2.36874 - 1.72099i) q^{4} +(0.0448648 + 0.998993i) q^{5} +(-1.64476 - 1.19498i) q^{6} +(-2.24590 + 3.09122i) q^{8} +(-0.0161501 + 0.0497048i) q^{9} +(-0.696390 - 1.85552i) q^{10} +(2.85646 + 0.928121i) q^{12} +(-0.802002 + 0.639575i) q^{15} +(1.43533 - 4.41749i) q^{16} -0.103579i q^{18} +(1.59203 + 1.15668i) q^{19} +(1.82553 + 2.28914i) q^{20} -3.91953 q^{24} +(-0.995974 + 0.0896393i) q^{25} +(0.924605 - 0.300422i) q^{27} +(-0.635928 + 0.462029i) q^{29} +(1.11999 - 1.69671i) q^{30} +5.38462i q^{32} +(0.0472862 + 0.145532i) q^{36} +(-0.339635 - 0.110354i) q^{37} +(-3.70921 - 1.20520i) q^{38} +(-3.18887 - 2.10495i) q^{40} +1.66915i q^{43} +(-0.0503793 - 0.0139038i) q^{45} +(4.53145 - 1.47236i) q^{48} -1.00000 q^{49} +(1.82241 - 0.778936i) q^{50} +(-1.55880 + 1.13253i) q^{54} +2.01863i q^{57} +(0.915694 - 1.26035i) q^{58} +(-0.799032 + 2.89523i) q^{60} +(-1.86243 - 5.73197i) q^{64} +(0.809017 - 0.587785i) q^{71} +(-0.117377 - 0.161555i) q^{72} +(1.58745 - 0.515795i) q^{73} +0.707764 q^{74} +(-0.674913 - 0.772500i) q^{75} +5.76175 q^{76} +(-1.55972 + 1.13321i) q^{79} +(4.47744 + 1.23569i) q^{80} +(0.849089 + 0.616899i) q^{81} +(0.510061 - 0.702039i) q^{83} +(-1.02225 - 3.14617i) q^{86} +(-0.766864 - 0.249169i) q^{87} +(0.530551 + 1.63287i) q^{89} +(0.103475 - 0.00464707i) q^{90} +(-1.08409 + 1.64232i) q^{95} +(-4.46863 + 3.24665i) q^{96} +(1.88490 - 0.612441i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 24 q - 5 q^{2} + 3 q^{4} - q^{5} + 5 q^{6} - 5 q^{8} + 8 q^{9}+O(q^{10}) $ 24 * q - 5 * q^2 + 3 * q^4 - q^5 + 5 * q^6 - 5 * q^8 + 8 * q^9	$ 24 q - 5 q^{2} + 3 q^{4} - q^{5} + 5 q^{6} - 5 q^{8} + 8 q^{9} - 5 q^{10} + 10 q^{12} - 11 q^{16} + 3 q^{19} + q^{20} - 4 q^{24} + q^{25} - 5 q^{27} + 3 q^{29} + 7 q^{30} - 11 q^{36} - 30 q^{38} - 5 q^{40} + 4 q^{45} + 10 q^{48} - 24 q^{49} - 10 q^{54} + 5 q^{58} - 23 q^{60} + 8 q^{64} + 6 q^{71} + 25 q^{72} - 5 q^{73} - 14 q^{74} - 7 q^{75} + 8 q^{76} + 3 q^{79} + 22 q^{80} - q^{81} - 5 q^{87} - 3 q^{89} + 12 q^{90} + 2 q^{95} - 11 q^{96} + 5 q^{98}+O(q^{100}) $ 24 * q - 5 * q^2 + 3 * q^4 - q^5 + 5 * q^6 - 5 * q^8 + 8 * q^9 - 5 * q^10 + 10 * q^12 - 11 * q^16 + 3 * q^19 + q^20 - 4 * q^24 + q^25 - 5 * q^27 + 3 * q^29 + 7 * q^30 - 11 * q^36 - 30 * q^38 - 5 * q^40 + 4 * q^45 + 10 * q^48 - 24 * q^49 - 10 * q^54 + 5 * q^58 - 23 * q^60 + 8 * q^64 + 6 * q^71 + 25 * q^72 - 5 * q^73 - 14 * q^74 - 7 * q^75 + 8 * q^76 + 3 * q^79 + 22 * q^80 - q^81 - 5 * q^87 - 3 * q^89 + 12 * q^90 + 2 * q^95 - 11 * q^96 + 5 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1775\mathbb{Z}\right)^\times$.

$n$	$427$	$1001$
$\chi(n)$	$e\left(\frac{9}{10}\right)$	$-1$

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 $

$2$	−1.88490	+	0.612441i	−1.88490	+	0.612441i	−0.900969	+	0.433884i	$0.857143\pi$
$2$	−1.88490	+	0.612441i	−1.88490	+	0.612441i	−0.983930	+	0.178557i	$0.942857\pi$
$3$	0.602949	+	0.829888i	0.602949	+	0.829888i	0.995974	−	0.0896393i	$-0.0285714\pi$
$3$	0.602949	+	0.829888i	0.602949	+	0.829888i	−0.393025	+	0.919528i	$0.628571\pi$
$4$	2.36874	−	1.72099i	2.36874	−	1.72099i
$5$	0.0448648	+	0.998993i	0.0448648	+	0.998993i
$5$	0.0448648	+	0.998993i	0.0448648	+	0.998993i
$6$	−1.64476	−	1.19498i	−1.64476	−	1.19498i
$7$		0			0			−	1.00000i	$-0.5\pi$
$7$		0			0				1.00000i	$0.5\pi$
$8$	−2.24590	+	3.09122i	−2.24590	+	3.09122i
$9$	−0.0161501	+	0.0497048i	−0.0161501	+	0.0497048i
$10$	−0.696390	−	1.85552i	−0.696390	−	1.85552i
$11$		0			0		−0.309017	−	0.951057i	$-0.600000\pi$
$11$		0			0		0.309017	+	0.951057i	$0.400000\pi$
$12$	2.85646	+	0.928121i	2.85646	+	0.928121i
$13$		0			0		−0.951057	−	0.309017i	$-0.900000\pi$
$13$		0			0		0.951057	+	0.309017i	$0.100000\pi$
$14$		0			0
$15$	−0.802002	+	0.639575i	−0.802002	+	0.639575i
$16$	1.43533	−	4.41749i	1.43533	−	4.41749i
$17$		0			0		0.587785	−	0.809017i	$-0.300000\pi$
$17$		0			0		−0.587785	+	0.809017i	$0.700000\pi$
$18$		−	0.103579i		−	0.103579i
$19$	1.59203	+	1.15668i	1.59203	+	1.15668i	0.900969	+	0.433884i	$0.142857\pi$
$19$	1.59203	+	1.15668i	1.59203	+	1.15668i	0.691063	+	0.722795i	$0.257143\pi$
$20$	1.82553	+	2.28914i	1.82553	+	2.28914i
$21$		0			0
$22$		0			0
$23$		0			0		0.951057	−	0.309017i	$-0.100000\pi$
$23$		0			0		−0.951057	+	0.309017i	$0.900000\pi$
$24$	−3.91953			−3.91953
$25$	−0.995974	+	0.0896393i	−0.995974	+	0.0896393i
$26$		0			0
$27$	0.924605	−	0.300422i	0.924605	−	0.300422i
$28$		0			0
$29$	−0.635928	+	0.462029i	−0.635928	+	0.462029i	−0.858449	−	0.512899i	$-0.828571\pi$
$29$	−0.635928	+	0.462029i	−0.635928	+	0.462029i	0.222521	+	0.974928i	$0.428571\pi$
$30$	1.11999	−	1.69671i	1.11999	−	1.69671i
$31$		0			0		−0.809017	−	0.587785i	$-0.800000\pi$
$31$		0			0		0.809017	+	0.587785i	$0.200000\pi$
$32$			5.38462i			5.38462i
$33$		0			0
$34$		0			0
$35$		0			0
$36$	0.0472862	+	0.145532i	0.0472862	+	0.145532i
$37$	−0.339635	−	0.110354i	−0.339635	−	0.110354i	0.134233	−	0.990950i	$-0.457143\pi$
$37$	−0.339635	−	0.110354i	−0.339635	−	0.110354i	−0.473869	+	0.880596i	$0.657143\pi$
$38$	−3.70921	−	1.20520i	−3.70921	−	1.20520i
$39$		0			0
$40$	−3.18887	−	2.10495i	−3.18887	−	2.10495i
$41$		0			0		0.309017	−	0.951057i	$-0.400000\pi$
$41$		0			0		−0.309017	+	0.951057i	$0.600000\pi$
$42$		0			0
$43$			1.66915i			1.66915i	0.550897	+	0.834573i	$0.314286\pi$
$43$			1.66915i			1.66915i	−0.550897	+	0.834573i	$0.685714\pi$
$44$		0			0
$45$	−0.0503793	−	0.0139038i	−0.0503793	−	0.0139038i
$46$		0			0
$47$		0			0		−0.587785	−	0.809017i	$-0.700000\pi$
$47$		0			0		0.587785	+	0.809017i	$0.300000\pi$
$48$	4.53145	−	1.47236i	4.53145	−	1.47236i
$49$	−1.00000			−1.00000
$50$	1.82241	−	0.778936i	1.82241	−	0.778936i
$51$		0			0
$52$		0			0
$53$		0			0		−0.587785	−	0.809017i	$-0.700000\pi$
$53$		0			0		0.587785	+	0.809017i	$0.300000\pi$
$54$	−1.55880	+	1.13253i	−1.55880	+	1.13253i
$55$		0			0
$56$		0			0
$57$			2.01863i			2.01863i
$58$	0.915694	−	1.26035i	0.915694	−	1.26035i
$59$		0			0		0.309017	−	0.951057i	$-0.400000\pi$
$59$		0			0		−0.309017	+	0.951057i	$0.600000\pi$
$60$	−0.799032	+	2.89523i	−0.799032	+	2.89523i
$61$		0			0		−0.309017	−	0.951057i	$-0.600000\pi$
$61$		0			0		0.309017	+	0.951057i	$0.400000\pi$
$62$		0			0
$63$		0			0
$64$	−1.86243	−	5.73197i	−1.86243	−	5.73197i
$65$		0			0
$66$		0			0
$67$		0			0		0.587785	−	0.809017i	$-0.300000\pi$
$67$		0			0		−0.587785	+	0.809017i	$0.700000\pi$
$68$		0			0
$69$		0			0
$70$		0			0
$71$	0.809017	−	0.587785i	0.809017	−	0.587785i
$71$	0.809017	−	0.587785i	0.809017	−	0.587785i
$72$	−0.117377	−	0.161555i	−0.117377	−	0.161555i
$73$	1.58745	−	0.515795i	1.58745	−	0.515795i	0.623490	−	0.781831i	$-0.285714\pi$
$73$	1.58745	−	0.515795i	1.58745	−	0.515795i	0.963963	+	0.266037i	$0.0857143\pi$
$74$	0.707764			0.707764
$75$	−0.674913	−	0.772500i	−0.674913	−	0.772500i
$76$	5.76175			5.76175
$77$		0			0
$78$		0			0
$79$	−1.55972	+	1.13321i	−1.55972	+	1.13321i	−0.623490	+	0.781831i	$0.714286\pi$
$79$	−1.55972	+	1.13321i	−1.55972	+	1.13321i	−0.936235	+	0.351375i	$0.885714\pi$
$80$	4.47744	+	1.23569i	4.47744	+	1.23569i
$81$	0.849089	+	0.616899i	0.849089	+	0.616899i
$82$		0			0
$83$	0.510061	−	0.702039i	0.510061	−	0.702039i	−0.473869	−	0.880596i	$-0.657143\pi$
$83$	0.510061	−	0.702039i	0.510061	−	0.702039i	0.983930	+	0.178557i	$0.0571429\pi$
$84$		0			0
$85$		0			0
$86$	−1.02225	−	3.14617i	−1.02225	−	3.14617i
$87$	−0.766864	−	0.249169i	−0.766864	−	0.249169i
$88$		0			0
$89$	0.530551	+	1.63287i	0.530551	+	1.63287i	0.753071	+	0.657939i	$0.228571\pi$
$89$	0.530551	+	1.63287i	0.530551	+	1.63287i	−0.222521	+	0.974928i	$0.571429\pi$
$90$	0.103475	−	0.00464707i	0.103475	−	0.00464707i
$91$		0			0
$92$		0			0
$93$		0			0
$94$		0			0
$95$	−1.08409	+	1.64232i	−1.08409	+	1.64232i
$96$	−4.46863	+	3.24665i	−4.46863	+	3.24665i
$97$		0			0		−0.587785	−	0.809017i	$-0.700000\pi$
$97$		0			0		0.587785	+	0.809017i	$0.300000\pi$
$98$	1.88490	−	0.612441i	1.88490	−	0.612441i
$99$		0			0
$100$	−2.20494	+	1.92640i	−2.20494	+	1.92640i
$101$	0.947737			0.947737			0.473869	−	0.880596i	$-0.342857\pi$
$101$	0.947737			0.947737			0.473869	+	0.880596i	$0.342857\pi$
$102$		0			0
$103$	−1.14610	−	1.57747i	−1.14610	−	1.57747i	−0.753071	−	0.657939i	$-0.771429\pi$
$103$	−1.14610	−	1.57747i	−1.14610	−	1.57747i	−0.393025	−	0.919528i	$-0.628571\pi$
$104$		0			0
$105$		0			0
$106$		0			0
$107$		−	1.90211i		−	1.90211i	−0.309017	−	0.951057i	$-0.600000\pi$
$107$		−	1.90211i		−	1.90211i	0.309017	−	0.951057i	$-0.400000\pi$
$108$	1.67313	−	2.30286i	1.67313	−	2.30286i
$109$	−0.137526	+	0.423260i	−0.137526	+	0.423260i	−0.995974	−	0.0896393i	$-0.971429\pi$
$109$	−0.137526	+	0.423260i	−0.137526	+	0.423260i	0.858449	+	0.512899i	$0.171429\pi$
$110$		0			0
$111$	−0.113201	−	0.348397i	−0.113201	−	0.348397i
$112$		0			0
$113$		0			0		−0.951057	−	0.309017i	$-0.900000\pi$
$113$		0			0		0.951057	+	0.309017i	$0.100000\pi$
$114$	−1.23629	−	3.80491i	−1.23629	−	3.80491i
$115$		0			0
$116$	−0.711201	+	2.18885i	−0.711201	+	2.18885i
$117$		0			0
$118$		0			0
$119$		0			0
$120$	−0.175849	−	3.91558i	−0.175849	−	3.91558i
$121$	−0.809017	+	0.587785i	−0.809017	+	0.587785i
$122$		0			0
$123$		0			0
$124$		0			0
$125$	−0.134233	−	0.990950i	−0.134233	−	0.990950i
$126$		0			0
$127$		0			0		0.951057	−	0.309017i	$-0.100000\pi$
$127$		0			0		−0.951057	+	0.309017i	$0.900000\pi$
$128$	3.85598	+	5.30730i	3.85598	+	5.30730i
$129$	−1.38521	+	1.00641i	−1.38521	+	1.00641i
$130$		0			0
$131$	−1.51486	−	1.10061i	−1.51486	−	1.10061i	−0.963963	−	0.266037i	$-0.914286\pi$
$131$	−1.51486	−	1.10061i	−1.51486	−	1.10061i	−0.550897	−	0.834573i	$-0.685714\pi$
$132$		0			0
$133$		0			0
$134$		0			0
$135$	0.341602	+	0.910196i	0.341602	+	0.910196i
$136$		0			0
$137$		0			0		−0.951057	−	0.309017i	$-0.900000\pi$
$137$		0			0		0.951057	+	0.309017i	$0.100000\pi$
$138$		0			0
$139$		0			0		−0.309017	−	0.951057i	$-0.600000\pi$
$139$		0			0		0.309017	+	0.951057i	$0.400000\pi$
$140$		0			0
$141$		0			0
$142$	−1.16493	+	1.60339i	−1.16493	+	1.60339i
$143$		0			0
$144$	0.196390	+	0.142685i	0.196390	+	0.142685i
$145$	−0.490094	−	0.614559i	−0.490094	−	0.614559i
$146$	−2.67629	+	1.94444i	−2.67629	+	1.94444i
$147$	−0.602949	−	0.829888i	−0.602949	−	0.829888i
$148$	−0.994427	+	0.323109i	−0.994427	+	0.323109i
$149$		0			0		1.00000			$0$
$149$		0			0		−1.00000			$\pi$
$150$	1.74525	+	1.04274i	1.74525	+	1.04274i
$151$	−1.50614			−1.50614			−0.753071	−	0.657939i	$-0.771429\pi$
$151$	−1.50614			−1.50614			−0.753071	+	0.657939i	$0.771429\pi$
$152$	−7.15109	+	2.32353i	−7.15109	+	2.32353i
$153$		0			0
$154$		0			0
$155$		0			0
$156$		0			0
$157$		−	0.179279i		−	0.179279i	−0.995974	−	0.0896393i	$-0.971429\pi$
$157$		−	0.179279i		−	0.179279i	0.995974	−	0.0896393i	$-0.0285714\pi$
$158$	2.24590	−	3.09122i	2.24590	−	3.09122i
$159$		0			0
$160$	−5.37920	+	0.241580i	−5.37920	+	0.241580i
$161$		0			0
$162$	−1.97826	−	0.642776i	−1.97826	−	0.642776i
$163$		0			0		−0.951057	−	0.309017i	$-0.900000\pi$
$163$		0			0		0.951057	+	0.309017i	$0.100000\pi$
$164$		0			0
$165$		0			0
$166$	−0.531456	+	1.63565i	−0.531456	+	1.63565i
$167$	−0.919098	+	1.26503i	−0.919098	+	1.26503i	0.0448648	+	0.998993i	$0.485714\pi$
$167$	−0.919098	+	1.26503i	−0.919098	+	1.26503i	−0.963963	+	0.266037i	$0.914286\pi$
$168$		0			0
$169$	0.809017	+	0.587785i	0.809017	+	0.587785i
$170$		0			0
$171$	−0.0832038	+	0.0604511i	−0.0832038	+	0.0604511i
$172$	2.87259	+	3.95378i	2.87259	+	3.95378i
$173$		0			0		0.951057	−	0.309017i	$-0.100000\pi$
$173$		0			0		−0.951057	+	0.309017i	$0.900000\pi$
$174$	1.59806			1.59806
$175$		0			0
$176$		0			0
$177$		0			0
$178$	−2.00007	−	2.75286i	−2.00007	−	2.75286i
$179$	0.891370	−	0.647618i	0.891370	−	0.647618i	−0.0448648	−	0.998993i	$-0.514286\pi$
$179$	0.891370	−	0.647618i	0.891370	−	0.647618i	0.936235	+	0.351375i	$0.114286\pi$
$180$	−0.143264	+	0.0537678i	−0.143264	+	0.0537678i
$181$		0			0		−0.809017	−	0.587785i	$-0.800000\pi$
$181$		0			0		0.809017	+	0.587785i	$0.200000\pi$
$182$		0			0
$183$		0			0
$184$		0			0
$185$	0.0950054	−	0.344244i	0.0950054	−	0.344244i
$186$		0			0
$187$		0			0
$188$		0			0
$189$		0			0
$190$	1.03757	−	3.75955i	1.03757	−	3.75955i
$191$	0.615546	−	1.89446i	0.615546	−	1.89446i	0.222521	−	0.974928i	$-0.428571\pi$
$191$	0.615546	−	1.89446i	0.615546	−	1.89446i	0.393025	−	0.919528i	$-0.371429\pi$
$192$	3.63394	−	5.00170i	3.63394	−	5.00170i
$193$		0			0			−	1.00000i	$-0.5\pi$
$193$		0			0				1.00000i	$0.5\pi$
$194$		0			0
$195$		0			0
$196$	−2.36874	+	1.72099i	−2.36874	+	1.72099i
$197$		0			0		−0.587785	−	0.809017i	$-0.700000\pi$
$197$		0			0		0.587785	+	0.809017i	$0.300000\pi$
$198$		0			0
$199$	0.268467			0.268467			0.134233	−	0.990950i	$-0.457143\pi$
$199$	0.268467			0.268467			0.134233	+	0.990950i	$0.457143\pi$
$200$	1.95977	−	3.28009i	1.95977	−	3.28009i
$201$		0			0
$202$	−1.78639	+	0.580433i	−1.78639	+	0.580433i
$203$		0			0
$204$		0			0
$205$		0			0
$206$	3.12638	+	2.27145i	3.12638	+	2.27145i
$207$		0			0
$208$		0			0
$209$		0			0
$210$		0			0
$211$		0			0		−0.309017	−	0.951057i	$-0.600000\pi$
$211$		0			0		0.309017	+	0.951057i	$0.400000\pi$
$212$		0			0
$213$	0.975592	+	0.316989i	0.975592	+	0.316989i
$214$	1.16493	+	3.58529i	1.16493	+	3.58529i
$215$	−1.66747	+	0.0748860i	−1.66747	+	0.0748860i
$216$	−1.14790	+	3.53288i	−1.14790	+	3.53288i
$217$		0			0
$218$		−	0.882028i		−	0.882028i
$219$	1.38521	+	1.00641i	1.38521	+	1.00641i
$220$		0			0
$221$		0			0
$222$	0.426746	+	0.587365i	0.426746	+	0.587365i
$223$	0.339635	−	0.110354i	0.339635	−	0.110354i	−0.134233	−	0.990950i	$-0.542857\pi$
$223$	0.339635	−	0.110354i	0.339635	−	0.110354i	0.473869	+	0.880596i	$0.342857\pi$
$224$		0			0
$225$	0.0116295	−	0.0509523i	0.0116295	−	0.0509523i
$226$		0			0
$227$		0			0		0.951057	−	0.309017i	$-0.100000\pi$
$227$		0			0		−0.951057	+	0.309017i	$0.900000\pi$
$228$	3.47404	+	4.78161i	3.47404	+	4.78161i
$229$	−0.0725928	+	0.0527418i	−0.0725928	+	0.0527418i	−0.623490	−	0.781831i	$-0.714286\pi$
$229$	−0.0725928	+	0.0527418i	−0.0725928	+	0.0527418i	0.550897	+	0.834573i	$0.314286\pi$
$230$		0			0
$231$		0			0
$232$		−	3.00346i		−	3.00346i
$233$	−1.03520	+	1.42483i	−1.03520	+	1.42483i	−0.134233	+	0.990950i	$0.542857\pi$
$233$	−1.03520	+	1.42483i	−1.03520	+	1.42483i	−0.900969	+	0.433884i	$0.857143\pi$
$234$		0			0
$235$		0			0
$236$		0			0
$237$	−1.88087	−	0.611132i	−1.88087	−	0.611132i
$238$		0			0
$239$		0			0		−0.309017	−	0.951057i	$-0.600000\pi$
$239$		0			0		0.309017	+	0.951057i	$0.400000\pi$
$240$	1.67418	+	4.46083i	1.67418	+	4.46083i
$241$		0			0		0.309017	−	0.951057i	$-0.400000\pi$
$241$		0			0		−0.309017	+	0.951057i	$0.600000\pi$
$242$	1.16493	−	1.60339i	1.16493	−	1.60339i
$243$			0.104420i			0.104420i
$244$		0			0
$245$	−0.0448648	−	0.998993i	−0.0448648	−	0.998993i
$246$		0			0
$247$		0			0
$248$		0			0
$249$	0.890155			0.890155
$250$	0.859914	+	1.78563i	0.859914	+	1.78563i
$251$	1.38213			1.38213			0.691063	−	0.722795i	$-0.257143\pi$
$251$	1.38213			1.38213			0.691063	+	0.722795i	$0.257143\pi$
$252$		0			0
$253$		0			0
$254$		0			0
$255$		0			0
$256$	−5.64264	−	4.09962i	−5.64264	−	4.09962i
$257$		0			0			−	1.00000i	$-0.5\pi$
$257$		0			0				1.00000i	$0.5\pi$
$258$	1.99460	−	2.74534i	1.99460	−	2.74534i
$259$		0			0
$260$		0			0
$261$	−0.0126948	−	0.0390704i	−0.0126948	−	0.0390704i
$262$	3.52942	+	1.14678i	3.52942	+	1.14678i
$263$	0.506032	+	0.164420i	0.506032	+	0.164420i	0.550897	−	0.834573i	$-0.314286\pi$
$263$	0.506032	+	0.164420i	0.506032	+	0.164420i	−0.0448648	+	0.998993i	$0.514286\pi$
$264$		0			0
$265$		0			0
$266$		0			0
$267$	−1.03520	+	1.42483i	−1.03520	+	1.42483i
$268$		0			0
$269$		0			0		−0.809017	−	0.587785i	$-0.800000\pi$
$269$		0			0		0.809017	+	0.587785i	$0.200000\pi$
$270$	−1.20133	−	1.50642i	−1.20133	−	1.50642i
$271$	1.61152	−	1.17084i	1.61152	−	1.17084i	0.753071	−	0.657939i	$-0.228571\pi$
$271$	1.61152	−	1.17084i	1.61152	−	1.17084i	0.858449	−	0.512899i	$-0.171429\pi$
$272$		0			0
$273$		0			0
$274$		0			0
$275$		0			0
$276$		0			0
$277$	1.67499	−	0.544238i	1.67499	−	0.544238i	0.691063	−	0.722795i	$-0.257143\pi$
$277$	1.67499	−	0.544238i	1.67499	−	0.544238i	0.983930	+	0.178557i	$0.0571429\pi$
$278$		0			0
$279$		0			0
$280$		0			0
$281$		0			0		−0.809017	−	0.587785i	$-0.800000\pi$
$281$		0			0		0.809017	+	0.587785i	$0.200000\pi$
$282$		0			0
$283$		0			0		0.587785	−	0.809017i	$-0.300000\pi$
$283$		0			0		−0.587785	+	0.809017i	$0.700000\pi$
$284$	0.904779	−	2.78462i	0.904779	−	2.78462i
$285$	−2.01659	+	0.0905654i	−2.01659	+	0.0905654i
$286$		0			0
$287$		0			0
$288$	−0.267641	−	0.0869619i	−0.267641	−	0.0869619i
$289$	−0.309017	−	0.951057i	−0.309017	−	0.951057i
$290$	1.30016	+	0.858227i	1.30016	+	0.858227i
$291$		0			0
$292$	2.87259	−	3.95378i	2.87259	−	3.95378i
$293$		0			0		1.00000			$0$
$293$		0			0		−1.00000			$\pi$
$294$	1.64476	+	1.19498i	1.64476	+	1.19498i
$295$		0			0
$296$	1.10392	−	0.802042i	1.10392	−	0.802042i
$297$		0			0
$298$		0			0
$299$		0			0
$300$	−2.92816	−	0.668333i	−2.92816	−	0.668333i
$301$		0			0
$302$	2.83893	−	0.922423i	2.83893	−	0.922423i
$303$	0.571438	+	0.786516i	0.571438	+	0.786516i
$304$	7.39471	−	5.37257i	7.39471	−	5.37257i
$305$		0			0
$306$		0			0
$307$		0			0			−	1.00000i	$-0.5\pi$
$307$		0			0				1.00000i	$0.5\pi$
$308$		0			0
$309$	0.618083	−	1.90226i	0.618083	−	1.90226i
$310$		0			0
$311$	−0.608102	−	1.87155i	−0.608102	−	1.87155i	−0.473869	−	0.880596i	$-0.657143\pi$
$311$	−0.608102	−	1.87155i	−0.608102	−	1.87155i	−0.134233	−	0.990950i	$-0.542857\pi$
$312$		0			0
$313$	−0.825296	−	0.268155i	−0.825296	−	0.268155i	−0.134233	−	0.990950i	$-0.542857\pi$
$313$	−0.825296	−	0.268155i	−0.825296	−	0.268155i	−0.691063	+	0.722795i	$0.742857\pi$
$314$	0.109798	+	0.337922i	0.109798	+	0.337922i
$315$		0			0
$316$	−1.74435	+	5.36855i	−1.74435	+	5.36855i
$317$		0			0		0.587785	−	0.809017i	$-0.300000\pi$
$317$		0			0		−0.587785	+	0.809017i	$0.700000\pi$
$318$		0			0
$319$		0			0
$320$	5.64264	−	2.11772i	5.64264	−	2.11772i
$321$	1.57854	−	1.14688i	1.57854	−	1.14688i
$322$		0			0
$323$		0			0
$324$	3.07295			3.07295
$325$		0			0
$326$		0			0
$327$	−0.434179	+	0.141073i	−0.434179	+	0.141073i
$328$		0			0
$329$		0			0
$330$		0			0
$331$		0			0		−0.809017	−	0.587785i	$-0.800000\pi$
$331$		0			0		0.809017	+	0.587785i	$0.200000\pi$
$332$		−	2.54076i		−	2.54076i
$333$	0.0109703	−	0.0150993i	0.0109703	−	0.0150993i
$334$	0.957651	−	2.94735i	0.957651	−	2.94735i
$335$		0			0
$336$		0			0
$337$		0			0		−0.951057	−	0.309017i	$-0.900000\pi$
$337$		0			0		0.951057	+	0.309017i	$0.100000\pi$
$338$	−1.88490	−	0.612441i	−1.88490	−	0.612441i
$339$		0			0
$340$		0			0
$341$		0			0
$342$	0.119808	−	0.164902i	0.119808	−	0.164902i
$343$		0			0
$344$	−5.15970	−	3.74874i	−5.15970	−	3.74874i
$345$		0			0
$346$		0			0
$347$		0			0		−0.587785	−	0.809017i	$-0.700000\pi$
$347$		0			0		0.587785	+	0.809017i	$0.300000\pi$
$348$	−2.24532	+	0.729549i	−2.24532	+	0.729549i
$349$		0			0		1.00000			$0$
$349$		0			0		−1.00000			$\pi$
$350$		0			0
$351$		0			0
$352$		0			0
$353$		0			0		−0.587785	−	0.809017i	$-0.700000\pi$
$353$		0			0		0.587785	+	0.809017i	$0.300000\pi$
$354$		0			0
$355$	0.623490	+	0.781831i	0.623490	+	0.781831i
$356$	4.06689	+	2.95477i	4.06689	+	2.95477i
$357$		0			0
$358$	−1.28351	+	1.76661i	−1.28351	+	1.76661i
$359$	−0.0277280	+	0.0853380i	−0.0277280	+	0.0853380i	−0.963963	−	0.266037i	$-0.914286\pi$
$359$	−0.0277280	+	0.0853380i	−0.0277280	+	0.0853380i	0.936235	+	0.351375i	$0.114286\pi$
$360$	0.156127	−	0.124507i	0.156127	−	0.124507i
$361$	0.887642	+	2.73188i	0.887642	+	2.73188i
$362$		0			0
$363$	−0.975592	−	0.316989i	−0.975592	−	0.316989i
$364$		0			0
$365$	0.586496	+	1.56271i	0.586496	+	1.56271i
$366$		0			0
$367$	0.919098	−	1.26503i	0.919098	−	1.26503i	−0.0448648	−	0.998993i	$-0.514286\pi$
$367$	0.919098	−	1.26503i	0.919098	−	1.26503i	0.963963	−	0.266037i	$-0.0857143\pi$
$368$		0			0
$369$		0			0
$370$	0.0317537	+	0.707051i	0.0317537	+	0.707051i
$371$		0			0
$372$		0			0
$373$	1.90020	−	0.617412i	1.90020	−	0.617412i	0.936235	−	0.351375i	$-0.114286\pi$
$373$	1.90020	−	0.617412i	1.90020	−	0.617412i	0.963963	−	0.266037i	$-0.0857143\pi$
$374$		0			0
$375$	0.741442	−	0.708891i	0.741442	−	0.708891i
$376$		0			0
$377$		0			0
$378$		0			0
$379$	−0.360046	+	0.261589i	−0.360046	+	0.261589i	−0.753071	−	0.657939i	$-0.771429\pi$
$379$	−0.360046	+	0.261589i	−0.360046	+	0.261589i	0.393025	+	0.919528i	$0.371429\pi$
$380$	0.258500	+	5.75594i	0.258500	+	5.75594i
$381$		0			0
$382$			3.94784i			3.94784i
$383$		0			0		0.587785	−	0.809017i	$-0.300000\pi$
$383$		0			0		−0.587785	+	0.809017i	$0.700000\pi$
$384$	−2.07951	+	6.40007i	−2.07951	+	6.40007i
$385$		0			0
$386$		0			0
$387$	−0.0829645	−	0.0269568i	−0.0829645	−	0.0269568i
$388$		0			0
$389$		0			0		−0.309017	−	0.951057i	$-0.600000\pi$
$389$		0			0		0.309017	+	0.951057i	$0.400000\pi$
$390$		0			0
$391$		0			0
$392$	2.24590	−	3.09122i	2.24590	−	3.09122i
$393$		−	1.92078i		−	1.92078i
$394$		0			0
$395$	−1.20204	−	1.50731i	−1.20204	−	1.50731i
$396$		0			0
$397$		0			0		−0.587785	−	0.809017i	$-0.700000\pi$
$397$		0			0		0.587785	+	0.809017i	$0.300000\pi$
$398$	−0.506032	+	0.164420i	−0.506032	+	0.164420i
$399$		0			0
$400$	−1.03357	+	4.52837i	−1.03357	+	4.52837i
$401$		0			0		1.00000			$0$
$401$		0			0		−1.00000			$\pi$
$402$		0			0
$403$		0			0
$404$	2.24494	−	1.63105i	2.24494	−	1.63105i
$405$	−0.578184	+	0.875911i	−0.578184	+	0.875911i
$406$		0			0
$407$		0			0
$408$		0			0
$409$	−0.465424	+	1.43243i	−0.465424	+	1.43243i	0.393025	+	0.919528i	$0.371429\pi$
$409$	−0.465424	+	1.43243i	−0.465424	+	1.43243i	−0.858449	+	0.512899i	$0.828571\pi$
$410$		0			0
$411$		0			0
$412$	−5.42961	−	1.76419i	−5.42961	−	1.76419i
$413$		0			0
$414$		0			0
$415$	0.724216	+	0.478050i	0.724216	+	0.478050i
$416$		0			0
$417$		0			0
$418$		0			0
$419$	0.360046	+	0.261589i	0.360046	+	0.261589i	0.753071	−	0.657939i	$-0.228571\pi$
$419$	0.360046	+	0.261589i	0.360046	+	0.261589i	−0.393025	+	0.919528i	$0.628571\pi$
$420$		0			0
$421$		0			0		0.809017	−	0.587785i	$-0.200000\pi$
$421$		0			0		−0.809017	+	0.587785i	$0.800000\pi$
$422$		0			0
$423$		0			0
$424$		0			0
$425$		0			0
$426$	−2.03303			−2.03303
$427$		0			0
$428$	−3.27352	−	4.50561i	−3.27352	−	4.50561i
$429$		0			0
$430$	3.09714	−	1.16238i	3.09714	−	1.16238i
$431$	1.11816	+	0.812393i	1.11816	+	0.812393i	0.983930	−	0.178557i	$-0.0571429\pi$
$431$	1.11816	+	0.812393i	1.11816	+	0.812393i	0.134233	+	0.990950i	$0.457143\pi$
$432$		−	4.51564i		−	4.51564i
$433$		0			0		0.587785	−	0.809017i	$-0.300000\pi$
$433$		0			0		−0.587785	+	0.809017i	$0.700000\pi$
$434$		0			0
$435$	0.214513	−	0.777271i	0.214513	−	0.777271i
$436$	0.402664	+	1.23927i	0.402664	+	1.23927i
$437$		0			0
$438$	−3.22734	−	1.04863i	−3.22734	−	1.04863i
$439$		0			0		−0.309017	−	0.951057i	$-0.600000\pi$
$439$		0			0		0.309017	+	0.951057i	$0.400000\pi$
$440$		0			0
$441$	0.0161501	−	0.0497048i	0.0161501	−	0.0497048i
$442$		0			0
$443$		0			0			−	1.00000i	$-0.5\pi$
$443$		0			0				1.00000i	$0.5\pi$
$444$	−0.867734	−	0.630445i	−0.867734	−	0.630445i
$445$	−1.60742	+	0.603275i	−1.60742	+	0.603275i
$446$	−0.572593	+	0.416013i	−0.572593	+	0.416013i
$447$		0			0
$448$		0			0
$449$		0			0		1.00000			$0$
$449$		0			0		−1.00000			$\pi$
$450$	0.00928478	+	0.103162i	0.00928478	+	0.103162i
$451$		0			0
$452$		0			0
$453$	−0.908128	−	1.24993i	−0.908128	−	1.24993i
$454$		0			0
$455$		0			0
$456$	−6.24002	−	4.53364i	−6.24002	−	4.53364i
$457$		0			0			−	1.00000i	$-0.5\pi$
$457$		0			0				1.00000i	$0.5\pi$
$458$	0.104529	−	0.143872i	0.104529	−	0.143872i
$459$		0			0
$460$		0			0
$461$		0			0		−0.309017	−	0.951057i	$-0.600000\pi$
$461$		0			0		0.309017	+	0.951057i	$0.400000\pi$
$462$		0			0
$463$	−1.67499	−	0.544238i	−1.67499	−	0.544238i	−0.691063	−	0.722795i	$-0.742857\pi$
$463$	−1.67499	−	0.544238i	−1.67499	−	0.544238i	−0.983930	+	0.178557i	$0.942857\pi$
$464$	1.12824	+	3.47237i	1.12824	+	3.47237i
$465$		0			0
$466$	1.07862	−	3.31967i	1.07862	−	3.31967i
$467$		0			0		0.587785	−	0.809017i	$-0.300000\pi$
$467$		0			0		−0.587785	+	0.809017i	$0.700000\pi$
$468$		0			0
$469$		0			0
$470$		0			0
$471$	0.148781	−	0.108096i	0.148781	−	0.108096i
$472$		0			0
$473$		0			0
$474$	3.91953			3.91953
$475$	−1.68931	−	1.00931i	−1.68931	−	1.00931i
$476$		0			0
$477$		0			0
$478$		0			0
$479$		0			0		0.809017	−	0.587785i	$-0.200000\pi$
$479$		0			0		−0.809017	+	0.587785i	$0.800000\pi$
$480$	−3.44387	−	4.31847i	−3.44387	−	4.31847i
$481$		0			0
$482$		0			0
$483$		0			0
$484$	−0.904779	+	2.78462i	−0.904779	+	2.78462i
$485$		0			0
$486$	−0.0639511	−	0.196821i	−0.0639511	−	0.196821i
$487$		0			0		−0.951057	−	0.309017i	$-0.900000\pi$
$487$		0			0		0.951057	+	0.309017i	$0.100000\pi$
$488$		0			0
$489$		0			0
$490$	0.696390	+	1.85552i	0.696390	+	1.85552i
$491$		0			0		0.309017	−	0.951057i	$-0.400000\pi$
$491$		0			0		−0.309017	+	0.951057i	$0.600000\pi$
$492$		0			0
$493$		0			0
$494$		0			0
$495$		0			0
$496$		0			0
$497$		0			0
$498$	−1.67785	+	0.545167i	−1.67785	+	0.545167i
$499$	1.71690			1.71690			0.858449	−	0.512899i	$-0.171429\pi$
$499$	1.71690			1.71690			0.858449	+	0.512899i	$0.171429\pi$
$500$	−2.02338	−	2.11629i	−2.02338	−	2.11629i
$501$	−1.60400			−1.60400
$502$	−2.60517	+	0.846470i	−2.60517	+	0.846470i
$503$	−0.105377	−	0.145039i	−0.105377	−	0.145039i	0.753071	−	0.657939i	$-0.228571\pi$
$503$	−0.105377	−	0.145039i	−0.105377	−	0.145039i	−0.858449	+	0.512899i	$0.828571\pi$
$504$		0			0
$505$	0.0425201	+	0.946783i	0.0425201	+	0.946783i
$506$		0			0
$507$			1.02580i			1.02580i
$508$		0			0
$509$	−0.500000	+	1.53884i	−0.500000	+	1.53884i	0.309017	+	0.951057i	$0.400000\pi$
$509$	−0.500000	+	1.53884i	−0.500000	+	1.53884i	−0.809017	+	0.587785i	$0.800000\pi$
$510$		0			0
$511$		0			0
$512$	6.90746	+	2.24437i	6.90746	+	2.24437i
$513$	1.81949	+	0.591189i	1.81949	+	0.591189i
$514$		0			0
$515$	1.52446	−	1.21572i	1.52446	−	1.21572i
$516$	−1.54917	+	4.76785i	−1.54917	+	4.76785i
$517$		0			0
$518$		0			0
$519$		0			0
$520$		0			0
$521$	1.51486	−	1.10061i	1.51486	−	1.10061i	0.550897	−	0.834573i	$-0.314286\pi$
$521$	1.51486	−	1.10061i	1.51486	−	1.10061i	0.963963	−	0.266037i	$-0.0857143\pi$
$522$	0.0478566	+	0.0658690i	0.0478566	+	0.0658690i
$523$		0			0		0.951057	−	0.309017i	$-0.100000\pi$
$523$		0			0		−0.951057	+	0.309017i	$0.900000\pi$
$524$	−5.48245			−5.48245
$525$		0			0
$526$	−1.05452			−1.05452
$527$		0			0
$528$		0			0
$529$	0.809017	−	0.587785i	0.809017	−	0.587785i
$530$		0			0
$531$		0			0
$532$		0			0
$533$		0			0
$534$	1.07862	−	3.31967i	1.07862	−	3.31967i
$535$	1.90020	−	0.0853380i	1.90020	−	0.0853380i
$536$		0			0
$537$	1.07490	+	0.349257i	1.07490	+	0.349257i
$538$		0			0
$539$		0			0
$540$	2.37561	+	1.56812i	2.37561	+	1.56812i
$541$		0			0		0.309017	−	0.951057i	$-0.400000\pi$
$541$		0			0		−0.309017	+	0.951057i	$0.600000\pi$
$542$	−2.32048	+	3.19387i	−2.32048	+	3.19387i
$543$		0			0
$544$		0			0
$545$	−0.429004	−	0.118398i	−0.429004	−	0.118398i
$546$		0			0
$547$	0.849696	+	1.16951i	0.849696	+	1.16951i	0.983930	+	0.178557i	$0.0571429\pi$
$547$	0.849696	+	1.16951i	0.849696	+	1.16951i	−0.134233	+	0.990950i	$0.542857\pi$
$548$		0			0
$549$		0			0
$550$		0			0
$551$	−1.54684			−1.54684
$552$		0			0
$553$		0			0
$554$	−2.82388	+	2.05167i	−2.82388	+	2.05167i
$555$	0.342968	−	0.128718i	0.342968	−	0.128718i
$556$		0			0
$557$		−	1.94986i		−	1.94986i	−0.222521	−	0.974928i	$-0.571429\pi$
$557$		−	1.94986i		−	1.94986i	0.222521	−	0.974928i	$-0.428571\pi$
$558$		0			0
$559$		0			0
$560$		0			0
$561$		0			0
$562$		0			0
$563$		0			0		−0.951057	−	0.309017i	$-0.900000\pi$
$563$		0			0		0.951057	+	0.309017i	$0.100000\pi$
$564$		0			0
$565$		0			0
$566$		0			0
$567$		0			0
$568$			3.82096i			3.82096i
$569$	−1.55972	−	1.13321i	−1.55972	−	1.13321i	−0.936235	−	0.351375i	$-0.885714\pi$
$569$	−1.55972	−	1.13321i	−1.55972	−	1.13321i	−0.623490	−	0.781831i	$-0.714286\pi$
$570$	3.74561	−	1.40575i	3.74561	−	1.40575i
$571$	1.59203	−	1.15668i	1.59203	−	1.15668i	0.691063	−	0.722795i	$-0.257143\pi$
$571$	1.59203	−	1.15668i	1.59203	−	1.15668i	0.900969	−	0.433884i	$-0.142857\pi$
$572$		0			0
$573$	1.94333	−	0.631426i	1.94333	−	0.631426i
$574$		0			0
$575$		0			0
$576$	0.314984			0.314984
$577$	1.48713	−	0.483198i	1.48713	−	0.483198i	0.550897	−	0.834573i	$-0.314286\pi$
$577$	1.48713	−	0.483198i	1.48713	−	0.483198i	0.936235	+	0.351375i	$0.114286\pi$
$578$	1.16493	+	1.60339i	1.16493	+	1.60339i
$579$		0			0
$580$	−2.21856	−	0.612283i	−2.21856	−	0.612283i
$581$		0			0
$582$		0			0
$583$		0			0
$584$	−1.97083	+	6.06559i	−1.97083	+	6.06559i
$585$		0			0
$586$		0			0
$587$	−0.975592	−	0.316989i	−0.975592	−	0.316989i	−0.222521	−	0.974928i	$-0.571429\pi$
$587$	−0.975592	−	0.316989i	−0.975592	−	0.316989i	−0.753071	+	0.657939i	$0.771429\pi$
$588$	−2.85646	−	0.928121i	−2.85646	−	0.928121i
$589$		0			0
$590$		0			0
$591$		0			0
$592$	−0.974977	+	1.34194i	−0.974977	+	1.34194i
$593$			1.31588i			1.31588i	0.753071	+	0.657939i	$0.228571\pi$
$593$			1.31588i			1.31588i	−0.753071	+	0.657939i	$0.771429\pi$
$594$		0			0
$595$		0			0
$596$		0			0
$597$	0.161872	+	0.222797i	0.161872	+	0.222797i
$598$		0			0
$599$		0			0		1.00000			$0$
$599$		0			0		−1.00000			$\pi$
$600$	3.90375	−	0.351344i	3.90375	−	0.351344i
$601$		0			0		1.00000			$0$
$601$		0			0		−1.00000			$\pi$
$602$		0			0
$603$		0			0
$604$	−3.56766	+	2.59206i	−3.56766	+	2.59206i
$605$	−0.623490	−	0.781831i	−0.623490	−	0.781831i
$606$	−1.55880	−	1.13253i	−1.55880	−	1.13253i
$607$		0			0			−	1.00000i	$-0.5\pi$
$607$		0			0				1.00000i	$0.5\pi$
$608$	−6.22827	+	8.57248i	−6.22827	+	8.57248i
$609$		0			0
$610$		0			0
$611$		0			0
$612$		0			0
$613$	−1.85442	−	0.602539i	−1.85442	−	0.602539i	−0.995974	−	0.0896393i	$-0.971429\pi$
$613$	−1.85442	−	0.602539i	−1.85442	−	0.602539i	−0.858449	−	0.512899i	$-0.828571\pi$
$614$		0			0
$615$		0			0
$616$		0			0
$617$	−0.413066	+	0.568536i	−0.413066	+	0.568536i	−0.963963	−	0.266037i	$-0.914286\pi$
$617$	−0.413066	+	0.568536i	−0.413066	+	0.568536i	0.550897	+	0.834573i	$0.314286\pi$
$618$			3.96411i			3.96411i
$619$		0			0		−0.809017	−	0.587785i	$-0.800000\pi$
$619$		0			0		0.809017	+	0.587785i	$0.200000\pi$
$620$		0			0
$621$		0			0
$622$	2.29242	+	3.15525i	2.29242	+	3.15525i
$623$		0			0
$624$		0			0
$625$	0.983930	−	0.178557i	0.983930	−	0.178557i
$626$	1.71983			1.71983
$627$		0			0
$628$	−0.308537	−	0.424665i	−0.308537	−	0.424665i
$629$		0			0
$630$		0			0
$631$		0			0		−0.809017	−	0.587785i	$-0.800000\pi$
$631$		0			0		0.809017	+	0.587785i	$0.200000\pi$
$632$		−	7.36652i		−	7.36652i
$633$		0			0
$634$		0			0
$635$		0			0
$636$		0			0
$637$		0			0
$638$		0			0
$639$	0.0161501	+	0.0497048i	0.0161501	+	0.0497048i
$640$	−5.12896	+	4.09021i	−5.12896	+	4.09021i
$641$	0.0829607	−	0.255327i	0.0829607	−	0.255327i	−0.900969	−	0.433884i	$-0.857143\pi$
$641$	0.0829607	−	0.255327i	0.0829607	−	0.255327i	0.983930	+	0.178557i	$0.0571429\pi$
$642$	−2.27300	+	3.12851i	−2.27300	+	3.12851i
$643$		−	1.90211i		−	1.90211i	−0.309017	−	0.951057i	$-0.600000\pi$
$643$		−	1.90211i		−	1.90211i	0.309017	−	0.951057i	$-0.400000\pi$
$644$		0			0
$645$	−1.06754	−	1.33866i	−1.06754	−	1.33866i
$646$		0			0
$647$	0.690983	+	0.951057i	0.690983	+	0.951057i	1.00000			$0$
$647$	0.690983	+	0.951057i	0.690983	+	0.951057i	−0.309017	+	0.951057i	$0.600000\pi$
$648$	−3.81394	+	1.23922i	−3.81394	+	1.23922i
$649$		0			0
$650$		0			0
$651$		0			0
$652$		0			0
$653$		0			0		−0.587785	−	0.809017i	$-0.700000\pi$
$653$		0			0		0.587785	+	0.809017i	$0.300000\pi$
$654$	0.731985	−	0.531818i	0.731985	−	0.531818i
$655$	1.03154	−	1.56271i	1.03154	−	1.56271i
$656$		0			0
$657$			0.0872341i			0.0872341i
$658$		0			0
$659$	0.615546	−	1.89446i	0.615546	−	1.89446i	0.222521	−	0.974928i	$-0.428571\pi$
$659$	0.615546	−	1.89446i	0.615546	−	1.89446i	0.393025	−	0.919528i	$-0.371429\pi$
$660$		0			0
$661$		0			0		−0.309017	−	0.951057i	$-0.600000\pi$
$661$		0			0		0.309017	+	0.951057i	$0.400000\pi$
$662$		0			0
$663$		0			0
$664$	1.02461	+	3.15342i	1.02461	+	3.15342i
$665$		0			0
$666$	−0.0114304	+	0.0351792i	−0.0114304	+	0.0351792i
$667$		0			0
$668$			4.57829i			4.57829i
$669$	0.296365	+	0.215321i	0.296365	+	0.215321i
$670$		0			0
$671$		0			0
$672$		0			0
$673$		0			0		0.951057	−	0.309017i	$-0.100000\pi$
$673$		0			0		−0.951057	+	0.309017i	$0.900000\pi$
$674$		0			0
$675$	−0.893953	+	0.382094i	−0.893953	+	0.382094i
$676$	2.92793			2.92793
$677$	−0.170504	+	0.0554001i	−0.170504	+	0.0554001i	−0.393025	−	0.919528i	$-0.628571\pi$
$677$	−0.170504	+	0.0554001i	−0.170504	+	0.0554001i	0.222521	+	0.974928i	$0.428571\pi$
$678$		0			0
$679$		0			0
$680$		0			0
$681$		0			0
$682$		0			0
$683$		0			0		0.587785	−	0.809017i	$-0.300000\pi$
$683$		0			0		−0.587785	+	0.809017i	$0.700000\pi$
$684$	−0.0930525	+	0.286386i	−0.0930525	+	0.286386i
$685$		0			0
$686$		0			0
$687$	−0.0875396	−	0.0284433i	−0.0875396	−	0.0284433i
$688$	7.37344	+	2.39577i	7.37344	+	2.39577i
$689$		0			0
$690$		0			0
$691$		0			0		0.309017	−	0.951057i	$-0.400000\pi$
$691$		0			0		−0.309017	+	0.951057i	$0.600000\pi$
$692$		0			0
$693$		0			0
$694$		0			0
$695$		0			0
$696$	2.49254	−	1.81094i	2.49254	−	1.81094i
$697$		0			0
$698$		0			0
$699$	−1.80663			−1.80663
$700$		0			0
$701$		0			0		1.00000			$0$
$701$		0			0		−1.00000			$\pi$
$702$		0			0
$703$	−0.413066	−	0.568536i	−0.413066	−	0.568536i
$704$		0			0
$705$		0			0
$706$		0			0
$707$		0			0
$708$		0			0
$709$		0			0		0.309017	−	0.951057i	$-0.400000\pi$
$709$		0			0		−0.309017	+	0.951057i	$0.600000\pi$
$710$	−1.65404	−	1.09182i	−1.65404	−	1.09182i
$711$	−0.0311361	−	0.0958271i	−0.0311361	−	0.0958271i
$712$	−6.23911	−	2.02721i	−6.23911	−	2.02721i
$713$		0			0
$714$		0			0
$715$		0			0
$716$	0.996880	−	3.06808i	0.996880	−	3.06808i
$717$		0			0
$718$		−	0.177835i		−	0.177835i
$719$	0.217194	+	0.157801i	0.217194	+	0.157801i	0.691063	−	0.722795i	$-0.257143\pi$
$719$	0.217194	+	0.157801i	0.217194	+	0.157801i	−0.473869	+	0.880596i	$0.657143\pi$
$720$	−0.133731	+	0.202593i	−0.133731	+	0.202593i
$721$		0			0
$722$	−3.34623	−	4.60569i	−3.34623	−	4.60569i
$723$		0			0
$724$		0			0
$725$	0.591952	−	0.517173i	0.591952	−	0.517173i
$726$	2.03303			2.03303
$727$		0			0		0.951057	−	0.309017i	$-0.100000\pi$
$727$		0			0		−0.951057	+	0.309017i	$0.900000\pi$
$728$		0			0
$729$	0.762432	−	0.553939i	0.762432	−	0.553939i
$730$	−2.06255	−	2.58636i	−2.06255	−	2.58636i
$731$		0			0
$732$		0			0
$733$		0			0		0.587785	−	0.809017i	$-0.300000\pi$
$733$		0			0		−0.587785	+	0.809017i	$0.700000\pi$
$734$	−0.957651	+	2.94735i	−0.957651	+	2.94735i
$735$	0.802002	−	0.639575i	0.802002	−	0.639575i
$736$		0			0
$737$		0			0
$738$		0			0
$739$	−0.500000	−	1.53884i	−0.500000	−	1.53884i	−0.809017	−	0.587785i	$-0.800000\pi$
$739$	−0.500000	−	1.53884i	−0.500000	−	1.53884i	0.309017	−	0.951057i	$-0.400000\pi$
$740$	−0.367398	−	0.978930i	−0.367398	−	0.978930i
$741$		0			0
$742$		0			0
$743$		0			0			−	1.00000i	$-0.5\pi$
$743$		0			0				1.00000i	$0.5\pi$
$744$		0			0
$745$		0			0
$746$	−3.20355	+	2.32752i	−3.20355	+	2.32752i
$747$	0.0266571	+	0.0366904i	0.0266571	+	0.0366904i
$748$		0			0
$749$		0			0
$750$	−0.963389	+	1.79028i	−0.963389	+	1.79028i
$751$		0			0		1.00000			$0$
$751$		0			0		−1.00000			$\pi$
$752$		0			0
$753$	0.833351	+	1.14701i	0.833351	+	1.14701i
$754$		0			0
$755$	−0.0675728	−	1.50463i	−0.0675728	−	1.50463i
$756$		0			0
$757$		0			0			−	1.00000i	$-0.5\pi$
$757$		0			0				1.00000i	$0.5\pi$
$758$	0.518443	−	0.713576i	0.518443	−	0.713576i
$759$		0			0
$760$	−2.64202	−	7.03965i	−2.64202	−	7.03965i
$761$		0			0		−0.309017	−	0.951057i	$-0.600000\pi$
$761$		0			0		0.309017	+	0.951057i	$0.400000\pi$
$762$		0			0
$763$		0			0
$764$	−1.80227	−	5.54683i	−1.80227	−	5.54683i
$765$		0			0
$766$		0			0
$767$		0			0
$768$		−	7.15462i		−	7.15462i
$769$		0			0		−0.809017	−	0.587785i	$-0.800000\pi$
$769$		0			0		0.809017	+	0.587785i	$0.200000\pi$
$770$		0			0
$771$		0			0
$772$		0			0
$773$		0			0		0.951057	−	0.309017i	$-0.100000\pi$
$773$		0			0		−0.951057	+	0.309017i	$0.900000\pi$
$774$	0.172889			0.172889
$775$		0			0
$776$		0			0
$777$		0			0
$778$		0			0
$779$		0			0
$780$		0			0
$781$		0			0
$782$		0			0
$783$	−0.449178	+	0.618241i	−0.449178	+	0.618241i
$784$	−1.43533	+	4.41749i	−1.43533	+	4.41749i
$785$	0.179098	−	0.00804330i	0.179098	−	0.00804330i
$786$	1.17636	+	3.62047i	1.17636	+	3.62047i
$787$	1.25147	+	0.406628i	1.25147	+	0.406628i	0.858449	−	0.512899i	$-0.171429\pi$
$787$	1.25147	+	0.406628i	1.25147	+	0.406628i	0.393025	+	0.919528i	$0.371429\pi$
$788$		0			0
$789$	0.168662	+	0.519087i	0.168662	+	0.519087i
$790$	3.18887	+	2.10495i	3.18887	+	2.10495i
$791$		0			0
$792$		0			0
$793$		0			0
$794$		0			0
$795$		0			0
$796$	0.635928	−	0.462029i	0.635928	−	0.462029i
$797$	1.16493	+	1.60339i	1.16493	+	1.60339i	0.691063	+	0.722795i	$0.257143\pi$
$797$	1.16493	+	1.60339i	1.16493	+	1.60339i	0.473869	+	0.880596i	$0.342857\pi$
$798$		0			0
$799$		0			0
$800$	−0.482673	−	5.36294i	−0.482673	−	5.36294i
$801$	−0.0897297			−0.0897297
$802$		0			0
$803$		0			0
$804$		0			0
$805$		0			0
$806$		0			0
$807$		0			0
$808$	−2.12852	+	2.92966i	−2.12852	+	2.92966i
$809$		0			0		0.309017	−	0.951057i	$-0.400000\pi$
$809$		0			0		−0.309017	+	0.951057i	$0.600000\pi$
$810$	0.553374	−	2.00511i	0.553374	−	2.00511i
$811$	−0.340473	−	1.04787i	−0.340473	−	1.04787i	−0.963963	−	0.266037i	$-0.914286\pi$
$811$	−0.340473	−	1.04787i	−0.340473	−	1.04787i	0.623490	−	0.781831i	$-0.285714\pi$
$812$		0			0
$813$	1.94333	+	0.631426i	1.94333	+	0.631426i
$814$		0			0
$815$		0			0
$816$		0			0
$817$	−1.93067	+	2.65733i	−1.93067	+	2.65733i
$818$		−	2.98502i		−	2.98502i
$819$		0			0
$820$		0			0
$821$	−1.45780	+	1.05915i	−1.45780	+	1.05915i	−0.473869	+	0.880596i	$0.657143\pi$
$821$	−1.45780	+	1.05915i	−1.45780	+	1.05915i	−0.983930	+	0.178557i	$0.942857\pi$
$822$		0			0
$823$		0			0		0.951057	−	0.309017i	$-0.100000\pi$
$823$		0			0		−0.951057	+	0.309017i	$0.900000\pi$
$824$	7.45031			7.45031
$825$		0			0
$826$		0			0
$827$		0			0		0.951057	−	0.309017i	$-0.100000\pi$
$827$		0			0		−0.951057	+	0.309017i	$0.900000\pi$
$828$		0			0
$829$	−1.59203	+	1.15668i	−1.59203	+	1.15668i	−0.691063	+	0.722795i	$0.742857\pi$
$829$	−1.59203	+	1.15668i	−1.59203	+	1.15668i	−0.900969	+	0.433884i	$0.857143\pi$
$830$	−1.65785	−	0.457538i	−1.65785	−	0.457538i
$831$	1.46159	+	1.06191i	1.46159	+	1.06191i
$832$		0			0
$833$		0			0
$834$		0			0
$835$	−1.30499	−	0.861417i	−1.30499	−	0.861417i
$836$		0			0
$837$		0			0
$838$	−0.838859	−	0.272562i	−0.838859	−	0.272562i
$839$	−0.556829	−	1.71374i	−0.556829	−	1.71374i	−0.691063	−	0.722795i	$-0.742857\pi$
$839$	−0.556829	−	1.71374i	−0.556829	−	1.71374i	0.134233	−	0.990950i	$-0.457143\pi$
$840$		0			0
$841$	−0.118083	+	0.363423i	−0.118083	+	0.363423i
$842$		0			0
$843$		0			0
$844$		0			0
$845$	−0.550897	+	0.834573i	−0.550897	+	0.834573i
$846$		0			0
$847$		0			0
$848$		0			0
$849$		0			0
$850$		0			0
$851$		0			0
$852$	2.85646	−	0.928121i	2.85646	−	0.928121i
$853$	−0.773453	−	1.06457i	−0.773453	−	1.06457i	−0.995974	−	0.0896393i	$-0.971429\pi$
$853$	−0.773453	−	1.06457i	−0.773453	−	1.06457i	0.222521	−	0.974928i	$-0.428571\pi$
$854$		0			0
$855$	−0.0641232	−	0.0804079i	−0.0641232	−	0.0804079i
$856$	5.87985	+	4.27196i	5.87985	+	4.27196i
$857$		−	1.02580i		−	1.02580i	−0.858449	−	0.512899i	$-0.828571\pi$
$857$		−	1.02580i		−	1.02580i	0.858449	−	0.512899i	$-0.171429\pi$
$858$		0			0
$859$		0			0		0.309017	−	0.951057i	$-0.400000\pi$
$859$		0			0		−0.309017	+	0.951057i	$0.600000\pi$
$860$	−3.82092	+	3.04708i	−3.82092	+	3.04708i
$861$		0			0
$862$	−2.60517	−	0.846470i	−2.60517	−	0.846470i
$863$		0			0		−0.951057	−	0.309017i	$-0.900000\pi$
$863$		0			0		0.951057	+	0.309017i	$0.100000\pi$
$864$	1.61766	+	4.97865i	1.61766	+	4.97865i
$865$		0			0
$866$		0			0
$867$	0.602949	−	0.829888i	0.602949	−	0.829888i
$868$		0			0
$869$		0			0
$870$	0.0716968	+	1.59645i	0.0716968	+	1.59645i
$871$		0			0
$872$	−0.999520	−	1.37572i	−0.999520	−	1.37572i
$873$		0			0
$874$		0			0
$875$		0			0
$876$	5.01322			5.01322
$877$	0.668355	−	0.217162i	0.668355	−	0.217162i	0.0448648	−	0.998993i	$-0.485714\pi$
$877$	0.668355	−	0.217162i	0.668355	−	0.217162i	0.623490	+	0.781831i	$0.285714\pi$
$878$		0			0
$879$		0			0
$880$		0			0
$881$	1.00883	+	0.732956i	1.00883	+	0.732956i	0.963963	−	0.266037i	$-0.0857143\pi$
$881$	1.00883	+	0.732956i	1.00883	+	0.732956i	0.0448648	+	0.998993i	$0.485714\pi$
$882$			0.103579i			0.103579i
$883$		0			0		0.587785	−	0.809017i	$-0.300000\pi$
$883$		0			0		−0.587785	+	0.809017i	$0.700000\pi$
$884$		0			0
$885$		0			0
$886$		0			0
$887$		0			0		−0.951057	−	0.309017i	$-0.900000\pi$
$887$		0			0		0.951057	+	0.309017i	$0.100000\pi$
$888$	1.33121	+	0.432537i	1.33121	+	0.432537i
$889$		0			0
$890$	2.66035	−	2.12156i	2.66035	−	2.12156i
$891$		0			0
$892$	0.614590	−	0.845910i	0.614590	−	0.845910i
$893$		0			0
$894$		0			0
$895$	0.686957	+	0.861417i	0.686957	+	0.861417i
$896$		0			0
$897$		0			0
$898$		0			0
$899$		0			0
$900$	−0.0601412	−	0.140707i	−0.0601412	−	0.140707i
$901$		0			0
$902$		0			0
$903$		0			0
$904$		0			0
$905$		0			0
$906$	2.47724	+	1.79982i	2.47724	+	1.79982i
$907$		0			0			−	1.00000i	$-0.5\pi$
$907$		0			0				1.00000i	$0.5\pi$
$908$		0			0
$909$	−0.0153060	+	0.0471071i	−0.0153060	+	0.0471071i
$910$		0			0
$911$		0			0		−0.309017	−	0.951057i	$-0.600000\pi$
$911$		0			0		0.309017	+	0.951057i	$0.400000\pi$
$912$	8.91726	+	2.89739i	8.91726	+	2.89739i
$913$		0			0
$914$		0			0
$915$		0			0
$916$	−0.0811855	+	0.249863i	−0.0811855	+	0.249863i
$917$		0			0
$918$		0			0
$919$		0			0		−0.809017	−	0.587785i	$-0.800000\pi$
$919$		0			0		0.809017	+	0.587785i	$0.200000\pi$
$920$		0			0
$921$		0			0
$922$		0			0
$923$		0			0
$924$		0			0
$925$	0.348160	+	0.0794653i	0.348160	+	0.0794653i
$926$	3.49050			3.49050
$927$	0.0969171	−	0.0314903i	0.0969171	−	0.0314903i
$928$	−2.48785	−	3.42423i	−2.48785	−	3.42423i
$929$	−1.11816	+	0.812393i	−1.11816	+	0.812393i	−0.983930	−	0.178557i	$-0.942857\pi$
$929$	−1.11816	+	0.812393i	−1.11816	+	0.812393i	−0.134233	+	0.990950i	$0.542857\pi$
$930$		0			0
$931$	−1.59203	−	1.15668i	−1.59203	−	1.15668i
$932$			5.15664i			5.15664i
$933$	1.18652	−	1.63310i	1.18652	−	1.63310i
$934$		0			0
$935$		0			0
$936$		0			0
$937$		0			0		−0.951057	−	0.309017i	$-0.900000\pi$
$937$		0			0		0.951057	+	0.309017i	$0.100000\pi$
$938$		0			0
$939$	−0.275073	−	0.846587i	−0.275073	−	0.846587i
$940$		0			0
$941$	−0.0829607	+	0.255327i	−0.0829607	+	0.255327i	−0.983930	−	0.178557i	$-0.942857\pi$
$941$	−0.0829607	+	0.255327i	−0.0829607	+	0.255327i	0.900969	+	0.433884i	$0.142857\pi$
$942$	−0.214235	+	0.294870i	−0.214235	+	0.294870i
$943$		0			0
$944$		0			0
$945$		0			0
$946$		0			0
$947$	−0.413066	−	0.568536i	−0.413066	−	0.568536i	0.550897	−	0.834573i	$-0.314286\pi$
$947$	−0.413066	−	0.568536i	−0.413066	−	0.568536i	−0.963963	+	0.266037i	$0.914286\pi$
$948$	−5.50705	+	1.78935i	−5.50705	+	1.78935i
$949$		0			0
$950$	3.80232	+	0.867854i	3.80232	+	0.867854i
$951$		0			0
$952$		0			0
$953$	0.312745	+	0.430457i	0.312745	+	0.430457i	0.936235	−	0.351375i	$-0.114286\pi$
$953$	0.312745	+	0.430457i	0.312745	+	0.430457i	−0.623490	+	0.781831i	$0.714286\pi$
$954$		0			0
$955$	1.92016	+	0.529932i	1.92016	+	0.529932i
$956$		0			0
$957$		0			0
$958$		0			0
$959$		0			0
$960$	5.15970	+	3.40588i	5.15970	+	3.40588i
$961$	0.309017	+	0.951057i	0.309017	+	0.951057i
$962$		0			0
$963$	0.0945441	+	0.0307192i	0.0945441	+	0.0307192i
$964$		0			0
$965$		0			0
$966$		0			0
$967$		0			0		0.587785	−	0.809017i	$-0.300000\pi$
$967$		0			0		−0.587785	+	0.809017i	$0.700000\pi$
$968$		−	3.82096i		−	3.82096i
$969$		0			0
$970$		0			0
$971$	−1.30902	+	0.951057i	−1.30902	+	0.951057i	−0.309017	+	0.951057i	$0.600000\pi$
$971$	−1.30902	+	0.951057i	−1.30902	+	0.951057i	−1.00000			$\pi$
$972$	0.179706	+	0.247344i	0.179706	+	0.247344i
$973$		0			0
$974$		0			0
$975$		0			0
$976$		0			0
$977$	1.74905	−	0.568299i	1.74905	−	0.568299i	0.753071	−	0.657939i	$-0.228571\pi$
$977$	1.74905	−	0.568299i	1.74905	−	0.568299i	0.995974	+	0.0896393i	$0.0285714\pi$
$978$		0			0
$979$		0			0
$980$	−1.82553	−	2.28914i	−1.82553	−	2.28914i
$981$	−0.0188170	−	0.0136713i	−0.0188170	−	0.0136713i
$982$		0			0
$983$	−0.849696	+	1.16951i	−0.849696	+	1.16951i	0.134233	+	0.990950i	$0.457143\pi$
$983$	−0.849696	+	1.16951i	−0.849696	+	1.16951i	−0.983930	+	0.178557i	$0.942857\pi$
$984$		0			0
$985$		0			0
$986$		0			0
$987$		0			0
$988$		0			0
$989$		0			0
$990$		0			0
$991$		0			0		0.309017	−	0.951057i	$-0.400000\pi$
$991$		0			0		−0.309017	+	0.951057i	$0.600000\pi$
$992$		0			0
$993$		0			0
$994$		0			0
$995$	0.0120447	+	0.268196i	0.0120447	+	0.268196i
$996$	2.10855	−	1.53195i	2.10855	−	1.53195i
$997$	−0.312745	−	0.430457i	−0.312745	−	0.430457i	0.623490	−	0.781831i	$-0.285714\pi$
$997$	−0.312745	−	0.430457i	−0.312745	−	0.430457i	−0.936235	+	0.351375i	$0.885714\pi$
$998$	−3.23618	+	1.05150i	−3.23618	+	1.05150i
$999$	−0.347182			−0.347182

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1775.1.bb.b.1419.1	yes	24
25.4	even	10	inner	1775.1.bb.b.354.1	✓	24
71.70	odd	2	CM	1775.1.bb.b.1419.1	yes	24
1775.354	odd	10	inner	1775.1.bb.b.354.1	✓	24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1775.1.bb.b.354.1	✓	24	25.4	even	10	inner
1775.1.bb.b.354.1	✓	24	1775.354	odd	10	inner
1775.1.bb.b.1419.1	yes	24	1.1	even	1	trivial
1775.1.bb.b.1419.1	yes	24	71.70	odd	2	CM

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:	\( N \)	\(=\)	\( 1775 = 5^{2} \cdot 71 \)
Weight:	\( k \)	\(=\)	\( 1 \)
Character orbit:	\([\chi]\)	\(=\)	1775.bb (of order \(10\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.88490 + 0.612441i) q^{2} +(0.602949 + 0.829888i) q^{3} +(2.36874 - 1.72099i) q^{4} +(0.0448648 + 0.998993i) q^{5} +(-1.64476 - 1.19498i) q^{6} +(-2.24590 + 3.09122i) q^{8} +(-0.0161501 + 0.0497048i) q^{9} +O(q^{10})\)	\(q+(-1.88490 + 0.612441i) q^{2} +(0.602949 + 0.829888i) q^{3} +(2.36874 - 1.72099i) q^{4} +(0.0448648 + 0.998993i) q^{5} +(-1.64476 - 1.19498i) q^{6} +(-2.24590 + 3.09122i) q^{8} +(-0.0161501 + 0.0497048i) q^{9} +(-0.696390 - 1.85552i) q^{10} +(2.85646 + 0.928121i) q^{12} +(-0.802002 + 0.639575i) q^{15} +(1.43533 - 4.41749i) q^{16} -0.103579i q^{18} +(1.59203 + 1.15668i) q^{19} +(1.82553 + 2.28914i) q^{20} -3.91953 q^{24} +(-0.995974 + 0.0896393i) q^{25} +(0.924605 - 0.300422i) q^{27} +(-0.635928 + 0.462029i) q^{29} +(1.11999 - 1.69671i) q^{30} +5.38462i q^{32} +(0.0472862 + 0.145532i) q^{36} +(-0.339635 - 0.110354i) q^{37} +(-3.70921 - 1.20520i) q^{38} +(-3.18887 - 2.10495i) q^{40} +1.66915i q^{43} +(-0.0503793 - 0.0139038i) q^{45} +(4.53145 - 1.47236i) q^{48} -1.00000 q^{49} +(1.82241 - 0.778936i) q^{50} +(-1.55880 + 1.13253i) q^{54} +2.01863i q^{57} +(0.915694 - 1.26035i) q^{58} +(-0.799032 + 2.89523i) q^{60} +(-1.86243 - 5.73197i) q^{64} +(0.809017 - 0.587785i) q^{71} +(-0.117377 - 0.161555i) q^{72} +(1.58745 - 0.515795i) q^{73} +0.707764 q^{74} +(-0.674913 - 0.772500i) q^{75} +5.76175 q^{76} +(-1.55972 + 1.13321i) q^{79} +(4.47744 + 1.23569i) q^{80} +(0.849089 + 0.616899i) q^{81} +(0.510061 - 0.702039i) q^{83} +(-1.02225 - 3.14617i) q^{86} +(-0.766864 - 0.249169i) q^{87} +(0.530551 + 1.63287i) q^{89} +(0.103475 - 0.00464707i) q^{90} +(-1.08409 + 1.64232i) q^{95} +(-4.46863 + 3.24665i) q^{96} +(1.88490 - 0.612441i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q - 5 q^{2} + 3 q^{4} - q^{5} + 5 q^{6} - 5 q^{8} + 8 q^{9}+O(q^{10}) \) 24 * q - 5 * q^2 + 3 * q^4 - q^5 + 5 * q^6 - 5 * q^8 + 8 * q^9	\( 24 q - 5 q^{2} + 3 q^{4} - q^{5} + 5 q^{6} - 5 q^{8} + 8 q^{9} - 5 q^{10} + 10 q^{12} - 11 q^{16} + 3 q^{19} + q^{20} - 4 q^{24} + q^{25} - 5 q^{27} + 3 q^{29} + 7 q^{30} - 11 q^{36} - 30 q^{38} - 5 q^{40} + 4 q^{45} + 10 q^{48} - 24 q^{49} - 10 q^{54} + 5 q^{58} - 23 q^{60} + 8 q^{64} + 6 q^{71} + 25 q^{72} - 5 q^{73} - 14 q^{74} - 7 q^{75} + 8 q^{76} + 3 q^{79} + 22 q^{80} - q^{81} - 5 q^{87} - 3 q^{89} + 12 q^{90} + 2 q^{95} - 11 q^{96} + 5 q^{98}+O(q^{100}) \) 24 * q - 5 * q^2 + 3 * q^4 - q^5 + 5 * q^6 - 5 * q^8 + 8 * q^9 - 5 * q^10 + 10 * q^12 - 11 * q^16 + 3 * q^19 + q^20 - 4 * q^24 + q^25 - 5 * q^27 + 3 * q^29 + 7 * q^30 - 11 * q^36 - 30 * q^38 - 5 * q^40 + 4 * q^45 + 10 * q^48 - 24 * q^49 - 10 * q^54 + 5 * q^58 - 23 * q^60 + 8 * q^64 + 6 * q^71 + 25 * q^72 - 5 * q^73 - 14 * q^74 - 7 * q^75 + 8 * q^76 + 3 * q^79 + 22 * q^80 - q^81 - 5 * q^87 - 3 * q^89 + 12 * q^90 + 2 * q^95 - 11 * q^96 + 5 * q^98

Introduction

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