LMFDB - Embedded newform 1775.1.p.b.1561.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1775,1,Mod(141,1775)]

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([2, 5]))

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

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

chi := DirichletCharacter("1775.141");

S:= CuspForms(chi, 1);

N := Newforms(S);

Level:	$ N $	$=$	$ 1775 = 5^{2} \cdot 71 $
Weight:	$ k $	$=$	$ 1 $
Character orbit:	$[\chi]$	$=$	1775.p (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:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Projective image:	$D_{35}$
Projective field:	Galois closure of $\mathbb{Q}[x]/(x^{35} + \cdots)$

Embedding invariants

Embedding label			1561.1
Root			$-0.691063 + 0.722795i$ of defining polynomial
Character	$\chi$	$=$	1775.1561
Dual form			1775.1.p.b.141.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.59203 + 1.15668i) q^{2} +(0.465424 - 1.43243i) q^{3} +(0.887642 - 2.73188i) q^{4} +(-0.550897 + 0.834573i) q^{5} +(0.915888 + 2.81881i) q^{6} +(1.13865 + 3.50441i) q^{8} +(-1.02621 - 0.745586i) q^{9} +O(q^{10})$	\(q+(-1.59203 + 1.15668i) q^{2} +(0.465424 - 1.43243i) q^{3} +(0.887642 - 2.73188i) q^{4} +(-0.550897 + 0.834573i) q^{5} +(0.915888 + 2.81881i) q^{6} +(1.13865 + 3.50441i) q^{8} +(-1.02621 - 0.745586i) q^{9} +(-0.0882877 - 1.96588i) q^{10} +(-3.50009 - 2.54296i) q^{12} +(0.939065 + 1.17755i) q^{15} +(-3.54237 - 2.57368i) q^{16} +2.49616 q^{18} +(-0.427100 - 1.31448i) q^{19} +(1.79096 + 2.24579i) q^{20} +5.54977 q^{24} +(-0.393025 - 0.919528i) q^{25} +(-0.327125 + 0.237670i) q^{27} +(0.530551 - 1.63287i) q^{29} +(-2.85707 - 0.788501i) q^{30} +4.93174 q^{32} +(-2.94776 + 2.14167i) q^{36} +(1.11816 + 0.812393i) q^{37} +(2.20039 + 1.59867i) q^{38} +(-3.55197 - 0.980281i) q^{40} -1.92793 q^{43} +(1.18758 - 0.445707i) q^{45} +(-5.33532 + 3.87634i) q^{48} +1.00000 q^{49} +(1.68931 + 1.00931i) q^{50} +(0.245885 - 0.756757i) q^{54} -2.08168 q^{57} +(1.04405 + 3.21325i) q^{58} +(4.05048 - 1.52017i) q^{60} +(-4.30911 + 3.13075i) q^{64} +(0.309017 - 0.951057i) q^{71} +(1.44434 - 4.44523i) q^{72} +(1.55972 - 1.13321i) q^{73} -2.71983 q^{74} +(-1.50008 + 0.135010i) q^{75} -3.97011 q^{76} +(0.578625 - 1.78082i) q^{79} +(4.09941 - 1.53853i) q^{80} +(-0.203784 - 0.627183i) q^{81} +(-0.556829 - 1.71374i) q^{83} +(3.06932 - 2.22999i) q^{86} +(-2.09203 - 1.51995i) q^{87} +(-1.21850 + 0.885289i) q^{89} +(-1.37513 + 2.08323i) q^{90} +(1.33232 + 0.367696i) q^{95} +(2.29535 - 7.06435i) q^{96} +(-1.59203 + 1.15668i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 24 q - 3 q^{2} + 2 q^{3} - 9 q^{4} + q^{5} - q^{6} - q^{8} - 4 q^{9}+O(q^{10}) $ 24 * q - 3 * q^2 + 2 * q^3 - 9 * q^4 + q^5 - q^6 - q^8 - 4 * q^9	$ 24 q - 3 q^{2} + 2 q^{3} - 9 q^{4} + q^{5} - q^{6} - q^{8} - 4 q^{9} - 3 q^{10} - 4 q^{12} + 2 q^{15} - 7 q^{16} - 8 q^{18} - 3 q^{19} - 9 q^{20} - 16 q^{24} + q^{25} - q^{27} - 3 q^{29} - 3 q^{30} - 4 q^{32} - 3 q^{36} + 2 q^{37} + 20 q^{38} - q^{40} + 2 q^{43} - 2 q^{45} - 14 q^{48} + 24 q^{49} + 2 q^{50} - 2 q^{54} + 4 q^{57} - q^{58} + 29 q^{60} - 10 q^{64} - 6 q^{71} + 23 q^{72} - 3 q^{73} - 10 q^{74} - 5 q^{75} - 4 q^{76} - 3 q^{79} + 28 q^{80} - 7 q^{81} + 2 q^{83} + 4 q^{86} - 15 q^{87} - 3 q^{89} - 6 q^{90} + 2 q^{95} + 23 q^{96} - 3 q^{98}+O(q^{100}) $ 24 * q - 3 * q^2 + 2 * q^3 - 9 * q^4 + q^5 - q^6 - q^8 - 4 * q^9 - 3 * q^10 - 4 * q^12 + 2 * q^15 - 7 * q^16 - 8 * q^18 - 3 * q^19 - 9 * q^20 - 16 * q^24 + q^25 - q^27 - 3 * q^29 - 3 * q^30 - 4 * q^32 - 3 * q^36 + 2 * q^37 + 20 * q^38 - q^40 + 2 * q^43 - 2 * q^45 - 14 * q^48 + 24 * q^49 + 2 * q^50 - 2 * q^54 + 4 * q^57 - q^58 + 29 * q^60 - 10 * q^64 - 6 * q^71 + 23 * q^72 - 3 * q^73 - 10 * q^74 - 5 * q^75 - 4 * q^76 - 3 * q^79 + 28 * q^80 - 7 * q^81 + 2 * q^83 + 4 * q^86 - 15 * q^87 - 3 * q^89 - 6 * q^90 + 2 * q^95 + 23 * q^96 - 3 * q^98

Display 100 coefficients 10 coefficients

Character values

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

$n$	$427$	$1001$
$\chi(n)$	$e\left(\frac{4}{5}\right)$	$-1$

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 $

$2$	−1.59203	+	1.15668i	−1.59203	+	1.15668i	−0.691063	+	0.722795i	$0.742857\pi$
$2$	−1.59203	+	1.15668i	−1.59203	+	1.15668i	−0.900969	+	0.433884i	$0.857143\pi$
$3$	0.465424	−	1.43243i	0.465424	−	1.43243i	−0.393025	−	0.919528i	$-0.628571\pi$
$3$	0.465424	−	1.43243i	0.465424	−	1.43243i	0.858449	−	0.512899i	$-0.171429\pi$
$4$	0.887642	−	2.73188i	0.887642	−	2.73188i
$5$	−0.550897	+	0.834573i	−0.550897	+	0.834573i
$5$	−0.550897	+	0.834573i	−0.550897	+	0.834573i
$6$	0.915888	+	2.81881i	0.915888	+	2.81881i
$7$		0			0		1.00000			$0$
$7$		0			0		−1.00000			$\pi$
$8$	1.13865	+	3.50441i	1.13865	+	3.50441i
$9$	−1.02621	−	0.745586i	−1.02621	−	0.745586i
$10$	−0.0882877	−	1.96588i	−0.0882877	−	1.96588i
$11$		0			0		0.809017	−	0.587785i	$-0.200000\pi$
$11$		0			0		−0.809017	+	0.587785i	$0.800000\pi$
$12$	−3.50009	−	2.54296i	−3.50009	−	2.54296i
$13$		0			0		−0.809017	−	0.587785i	$-0.800000\pi$
$13$		0			0		0.809017	+	0.587785i	$0.200000\pi$
$14$		0			0
$15$	0.939065	+	1.17755i	0.939065	+	1.17755i
$16$	−3.54237	−	2.57368i	−3.54237	−	2.57368i
$17$		0			0		−0.309017	−	0.951057i	$-0.600000\pi$
$17$		0			0		0.309017	+	0.951057i	$0.400000\pi$
$18$	2.49616			2.49616
$19$	−0.427100	−	1.31448i	−0.427100	−	1.31448i	−0.900969	−	0.433884i	$-0.857143\pi$
$19$	−0.427100	−	1.31448i	−0.427100	−	1.31448i	0.473869	−	0.880596i	$-0.342857\pi$
$20$	1.79096	+	2.24579i	1.79096	+	2.24579i
$21$		0			0
$22$		0			0
$23$		0			0		0.809017	−	0.587785i	$-0.200000\pi$
$23$		0			0		−0.809017	+	0.587785i	$0.800000\pi$
$24$	5.54977			5.54977
$25$	−0.393025	−	0.919528i	−0.393025	−	0.919528i
$26$		0			0
$27$	−0.327125	+	0.237670i	−0.327125	+	0.237670i
$28$		0			0
$29$	0.530551	−	1.63287i	0.530551	−	1.63287i	−0.222521	−	0.974928i	$-0.571429\pi$
$29$	0.530551	−	1.63287i	0.530551	−	1.63287i	0.753071	−	0.657939i	$-0.228571\pi$
$30$	−2.85707	−	0.788501i	−2.85707	−	0.788501i
$31$		0			0		−0.309017	−	0.951057i	$-0.600000\pi$
$31$		0			0		0.309017	+	0.951057i	$0.400000\pi$
$32$	4.93174			4.93174
$33$		0			0
$34$		0			0
$35$		0			0
$36$	−2.94776	+	2.14167i	−2.94776	+	2.14167i
$37$	1.11816	+	0.812393i	1.11816	+	0.812393i	0.983930	−	0.178557i	$-0.0571429\pi$
$37$	1.11816	+	0.812393i	1.11816	+	0.812393i	0.134233	+	0.990950i	$0.457143\pi$
$38$	2.20039	+	1.59867i	2.20039	+	1.59867i
$39$		0			0
$40$	−3.55197	−	0.980281i	−3.55197	−	0.980281i
$41$		0			0		−0.809017	−	0.587785i	$-0.800000\pi$
$41$		0			0		0.809017	+	0.587785i	$0.200000\pi$
$42$		0			0
$43$	−1.92793			−1.92793			−0.963963	−	0.266037i	$-0.914286\pi$
$43$	−1.92793			−1.92793			−0.963963	+	0.266037i	$0.914286\pi$
$44$		0			0
$45$	1.18758	−	0.445707i	1.18758	−	0.445707i
$46$		0			0
$47$		0			0		0.309017	−	0.951057i	$-0.400000\pi$
$47$		0			0		−0.309017	+	0.951057i	$0.600000\pi$
$48$	−5.33532	+	3.87634i	−5.33532	+	3.87634i
$49$	1.00000			1.00000
$50$	1.68931	+	1.00931i	1.68931	+	1.00931i
$51$		0			0
$52$		0			0
$53$		0			0		0.309017	−	0.951057i	$-0.400000\pi$
$53$		0			0		−0.309017	+	0.951057i	$0.600000\pi$
$54$	0.245885	−	0.756757i	0.245885	−	0.756757i
$55$		0			0
$56$		0			0
$57$	−2.08168			−2.08168
$58$	1.04405	+	3.21325i	1.04405	+	3.21325i
$59$		0			0		−0.809017	−	0.587785i	$-0.800000\pi$
$59$		0			0		0.809017	+	0.587785i	$0.200000\pi$
$60$	4.05048	−	1.52017i	4.05048	−	1.52017i
$61$		0			0		0.809017	−	0.587785i	$-0.200000\pi$
$61$		0			0		−0.809017	+	0.587785i	$0.800000\pi$
$62$		0			0
$63$		0			0
$64$	−4.30911	+	3.13075i	−4.30911	+	3.13075i
$65$		0			0
$66$		0			0
$67$		0			0		−0.309017	−	0.951057i	$-0.600000\pi$
$67$		0			0		0.309017	+	0.951057i	$0.400000\pi$
$68$		0			0
$69$		0			0
$70$		0			0
$71$	0.309017	−	0.951057i	0.309017	−	0.951057i
$71$	0.309017	−	0.951057i	0.309017	−	0.951057i
$72$	1.44434	−	4.44523i	1.44434	−	4.44523i
$73$	1.55972	−	1.13321i	1.55972	−	1.13321i	0.623490	−	0.781831i	$-0.285714\pi$
$73$	1.55972	−	1.13321i	1.55972	−	1.13321i	0.936235	−	0.351375i	$-0.114286\pi$
$74$	−2.71983			−2.71983
$75$	−1.50008	+	0.135010i	−1.50008	+	0.135010i
$76$	−3.97011			−3.97011
$77$		0			0
$78$		0			0
$79$	0.578625	−	1.78082i	0.578625	−	1.78082i	−0.0448648	−	0.998993i	$-0.514286\pi$
$79$	0.578625	−	1.78082i	0.578625	−	1.78082i	0.623490	−	0.781831i	$-0.285714\pi$
$80$	4.09941	−	1.53853i	4.09941	−	1.53853i
$81$	−0.203784	−	0.627183i	−0.203784	−	0.627183i
$82$		0			0
$83$	−0.556829	−	1.71374i	−0.556829	−	1.71374i	−0.691063	−	0.722795i	$-0.742857\pi$
$83$	−0.556829	−	1.71374i	−0.556829	−	1.71374i	0.134233	−	0.990950i	$-0.457143\pi$
$84$		0			0
$85$		0			0
$86$	3.06932	−	2.22999i	3.06932	−	2.22999i
$87$	−2.09203	−	1.51995i	−2.09203	−	1.51995i
$88$		0			0
$89$	−1.21850	+	0.885289i	−1.21850	+	0.885289i	−0.995974	−	0.0896393i	$-0.971429\pi$
$89$	−1.21850	+	0.885289i	−1.21850	+	0.885289i	−0.222521	+	0.974928i	$0.571429\pi$
$90$	−1.37513	+	2.08323i	−1.37513	+	2.08323i
$91$		0			0
$92$		0			0
$93$		0			0
$94$		0			0
$95$	1.33232	+	0.367696i	1.33232	+	0.367696i
$96$	2.29535	−	7.06435i	2.29535	−	7.06435i
$97$		0			0		0.309017	−	0.951057i	$-0.400000\pi$
$97$		0			0		−0.309017	+	0.951057i	$0.600000\pi$
$98$	−1.59203	+	1.15668i	−1.59203	+	1.15668i
$99$		0			0
$100$	−2.86091	+	0.257486i	−2.86091	+	0.257486i
$101$	0.268467			0.268467			0.134233	−	0.990950i	$-0.457143\pi$
$101$	0.268467			0.268467			0.134233	+	0.990950i	$0.457143\pi$
$102$		0			0
$103$	−0.137526	+	0.423260i	−0.137526	+	0.423260i	−0.995974	−	0.0896393i	$-0.971429\pi$
$103$	−0.137526	+	0.423260i	−0.137526	+	0.423260i	0.858449	+	0.512899i	$0.171429\pi$
$104$		0			0
$105$		0			0
$106$		0			0
$107$	−1.61803			−1.61803			−0.809017	−	0.587785i	$-0.800000\pi$
$107$	−1.61803			−1.61803			−0.809017	+	0.587785i	$0.800000\pi$
$108$	0.358917	+	1.10463i	0.358917	+	1.10463i
$109$	0.360046	+	0.261589i	0.360046	+	0.261589i	0.753071	−	0.657939i	$-0.228571\pi$
$109$	0.360046	+	0.261589i	0.360046	+	0.261589i	−0.393025	+	0.919528i	$0.628571\pi$
$110$		0			0
$111$	1.68411	−	1.22358i	1.68411	−	1.22358i
$112$		0			0
$113$		0			0		−0.809017	−	0.587785i	$-0.800000\pi$
$113$		0			0		0.809017	+	0.587785i	$0.200000\pi$
$114$	3.31410	−	2.40783i	3.31410	−	2.40783i
$115$		0			0
$116$	−3.98986	−	2.89880i	−3.98986	−	2.89880i
$117$		0			0
$118$		0			0
$119$		0			0
$120$	−3.05735	+	4.63169i	−3.05735	+	4.63169i
$121$	0.309017	−	0.951057i	0.309017	−	0.951057i
$122$		0			0
$123$		0			0
$124$		0			0
$125$	0.983930	+	0.178557i	0.983930	+	0.178557i
$126$		0			0
$127$		0			0		0.809017	−	0.587785i	$-0.200000\pi$
$127$		0			0		−0.809017	+	0.587785i	$0.800000\pi$
$128$	1.71497	−	5.27815i	1.71497	−	5.27815i
$129$	−0.897302	+	2.76161i	−0.897302	+	2.76161i
$130$		0			0
$131$	−0.0277280	−	0.0853380i	−0.0277280	−	0.0853380i	0.936235	−	0.351375i	$-0.114286\pi$
$131$	−0.0277280	−	0.0853380i	−0.0277280	−	0.0853380i	−0.963963	+	0.266037i	$0.914286\pi$
$132$		0			0
$133$		0			0
$134$		0			0
$135$	−0.0181410	−	0.403942i	−0.0181410	−	0.403942i
$136$		0			0
$137$		0			0		−0.809017	−	0.587785i	$-0.800000\pi$
$137$		0			0		0.809017	+	0.587785i	$0.200000\pi$
$138$		0			0
$139$		0			0		0.809017	−	0.587785i	$-0.200000\pi$
$139$		0			0		−0.809017	+	0.587785i	$0.800000\pi$
$140$		0			0
$141$		0			0
$142$	0.608102	+	1.87155i	0.608102	+	1.87155i
$143$		0			0
$144$	1.71632	+	5.28229i	1.71632	+	5.28229i
$145$	1.07047	+	1.34232i	1.07047	+	1.34232i
$146$	−1.17238	+	3.60820i	−1.17238	+	3.60820i
$147$	0.465424	−	1.43243i	0.465424	−	1.43243i
$148$	3.21189	−	2.33357i	3.21189	−	2.33357i
$149$		0			0		1.00000			$0$
$149$		0			0		−1.00000			$\pi$
$150$	2.23201	−	1.95005i	2.23201	−	1.95005i
$151$	−1.99195			−1.99195			−0.995974	−	0.0896393i	$-0.971429\pi$
$151$	−1.99195			−1.99195			−0.995974	+	0.0896393i	$0.971429\pi$
$152$	4.12016	−	2.99347i	4.12016	−	2.99347i
$153$		0			0
$154$		0			0
$155$		0			0
$156$		0			0
$157$	−0.786050			−0.786050			−0.393025	−	0.919528i	$-0.628571\pi$
$157$	−0.786050			−0.786050			−0.393025	+	0.919528i	$0.628571\pi$
$158$	1.13865	+	3.50441i	1.13865	+	3.50441i
$159$		0			0
$160$	−2.71688	+	4.11590i	−2.71688	+	4.11590i
$161$		0			0
$162$	1.04988	+	0.762782i	1.04988	+	0.762782i
$163$		0			0		−0.809017	−	0.587785i	$-0.800000\pi$
$163$		0			0		0.809017	+	0.587785i	$0.200000\pi$
$164$		0			0
$165$		0			0
$166$	2.86874	+	2.08426i	2.86874	+	2.08426i
$167$	0.385338	+	1.18595i	0.385338	+	1.18595i	0.936235	+	0.351375i	$0.114286\pi$
$167$	0.385338	+	1.18595i	0.385338	+	1.18595i	−0.550897	+	0.834573i	$0.685714\pi$
$168$		0			0
$169$	0.309017	+	0.951057i	0.309017	+	0.951057i
$170$		0			0
$171$	−0.541762	+	1.66737i	−0.541762	+	1.66737i
$172$	−1.71131	+	5.26686i	−1.71131	+	5.26686i
$173$		0			0		0.809017	−	0.587785i	$-0.200000\pi$
$173$		0			0		−0.809017	+	0.587785i	$0.800000\pi$
$174$	5.08867			5.08867
$175$		0			0
$176$		0			0
$177$		0			0
$178$	0.915888	−	2.81881i	0.915888	−	2.81881i
$179$	−0.595762	+	1.83357i	−0.595762	+	1.83357i	−0.0448648	+	0.998993i	$0.514286\pi$
$179$	−0.595762	+	1.83357i	−0.595762	+	1.83357i	−0.550897	+	0.834573i	$0.685714\pi$
$180$	−0.163471	−	3.63996i	−0.163471	−	3.63996i
$181$		0			0		−0.309017	−	0.951057i	$-0.600000\pi$
$181$		0			0		0.309017	+	0.951057i	$0.400000\pi$
$182$		0			0
$183$		0			0
$184$		0			0
$185$	−1.29399	+	0.485644i	−1.29399	+	0.485644i
$186$		0			0
$187$		0			0
$188$		0			0
$189$		0			0
$190$	−2.54640	+	0.955679i	−2.54640	+	0.955679i
$191$	0.635928	+	0.462029i	0.635928	+	0.462029i	0.858449	−	0.512899i	$-0.171429\pi$
$191$	0.635928	+	0.462029i	0.635928	+	0.462029i	−0.222521	+	0.974928i	$0.571429\pi$
$192$	2.47901	+	7.62961i	2.47901	+	7.62961i
$193$		0			0		1.00000			$0$
$193$		0			0		−1.00000			$\pi$
$194$		0			0
$195$		0			0
$196$	0.887642	−	2.73188i	0.887642	−	2.73188i
$197$		0			0		0.309017	−	0.951057i	$-0.400000\pi$
$197$		0			0		−0.309017	+	0.951057i	$0.600000\pi$
$198$		0			0
$199$	1.96786			1.96786			0.983930	−	0.178557i	$-0.0571429\pi$
$199$	1.96786			1.96786			0.983930	+	0.178557i	$0.0571429\pi$
$200$	2.77489	−	2.42434i	2.77489	−	2.42434i
$201$		0			0
$202$	−0.427407	+	0.310529i	−0.427407	+	0.310529i
$203$		0			0
$204$		0			0
$205$		0			0
$206$	−0.270631	−	0.832916i	−0.270631	−	0.832916i
$207$		0			0
$208$		0			0
$209$		0			0
$210$		0			0
$211$		0			0		0.809017	−	0.587785i	$-0.200000\pi$
$211$		0			0		−0.809017	+	0.587785i	$0.800000\pi$
$212$		0			0
$213$	−1.21850	−	0.885289i	−1.21850	−	0.885289i
$214$	2.57596	−	1.87155i	2.57596	−	1.87155i
$215$	1.06209	−	1.60900i	1.06209	−	1.60900i
$216$	−1.20538	−	0.875757i	−1.20538	−	0.875757i
$217$		0			0
$218$	−0.875780			−0.875780
$219$	−0.897302	−	2.76161i	−0.897302	−	2.76161i
$220$		0			0
$221$		0			0
$222$	−1.26587	+	3.89596i	−1.26587	+	3.89596i
$223$	1.11816	−	0.812393i	1.11816	−	0.812393i	0.134233	−	0.990950i	$-0.457143\pi$
$223$	1.11816	−	0.812393i	1.11816	−	0.812393i	0.983930	+	0.178557i	$0.0571429\pi$
$224$		0			0
$225$	−0.282260	+	1.23666i	−0.282260	+	1.23666i
$226$		0			0
$227$		0			0		0.809017	−	0.587785i	$-0.200000\pi$
$227$		0			0		−0.809017	+	0.587785i	$0.800000\pi$
$228$	−1.84778	+	5.68690i	−1.84778	+	5.68690i
$229$	−0.340473	+	1.04787i	−0.340473	+	1.04787i	0.623490	+	0.781831i	$0.285714\pi$
$229$	−0.340473	+	1.04787i	−0.340473	+	1.04787i	−0.963963	+	0.266037i	$0.914286\pi$
$230$		0			0
$231$		0			0
$232$	6.32635			6.32635
$233$	0.0829607	+	0.255327i	0.0829607	+	0.255327i	0.983930	−	0.178557i	$-0.0571429\pi$
$233$	0.0829607	+	0.255327i	0.0829607	+	0.255327i	−0.900969	+	0.433884i	$0.857143\pi$
$234$		0			0
$235$		0			0
$236$		0			0
$237$	−2.28160	−	1.65768i	−2.28160	−	1.65768i
$238$		0			0
$239$		0			0		0.809017	−	0.587785i	$-0.200000\pi$
$239$		0			0		−0.809017	+	0.587785i	$0.800000\pi$
$240$	−0.295875	−	6.58818i	−0.295875	−	6.58818i
$241$		0			0		−0.809017	−	0.587785i	$-0.800000\pi$
$241$		0			0		0.809017	+	0.587785i	$0.200000\pi$
$242$	0.608102	+	1.87155i	0.608102	+	1.87155i
$243$	−1.39759			−1.39759
$244$		0			0
$245$	−0.550897	+	0.834573i	−0.550897	+	0.834573i
$246$		0			0
$247$		0			0
$248$		0			0
$249$	−2.71398			−2.71398
$250$	−1.77298	+	0.853822i	−1.77298	+	0.853822i
$251$	0.947737			0.947737			0.473869	−	0.880596i	$-0.342857\pi$
$251$	0.947737			0.947737			0.473869	+	0.880596i	$0.342857\pi$
$252$		0			0
$253$		0			0
$254$		0			0
$255$		0			0
$256$	1.72889	+	5.32099i	1.72889	+	5.32099i
$257$		0			0		1.00000			$0$
$257$		0			0		−1.00000			$\pi$
$258$	−1.76576	−	5.43447i	−1.76576	−	5.43447i
$259$		0			0
$260$		0			0
$261$	−1.76190	+	1.28009i	−1.76190	+	1.28009i
$262$	0.142852	+	0.103788i	0.142852	+	0.103788i
$263$	−1.51486	−	1.10061i	−1.51486	−	1.10061i	−0.963963	−	0.266037i	$-0.914286\pi$
$263$	−1.51486	−	1.10061i	−1.51486	−	1.10061i	−0.550897	−	0.834573i	$-0.685714\pi$
$264$		0			0
$265$		0			0
$266$		0			0
$267$	0.700995	+	2.15744i	0.700995	+	2.15744i
$268$		0			0
$269$		0			0		−0.309017	−	0.951057i	$-0.600000\pi$
$269$		0			0		0.309017	+	0.951057i	$0.400000\pi$
$270$	0.496112	+	0.622105i	0.496112	+	0.622105i
$271$	−0.242903	+	0.747578i	−0.242903	+	0.747578i	0.753071	+	0.657939i	$0.228571\pi$
$271$	−0.242903	+	0.747578i	−0.242903	+	0.747578i	−0.995974	+	0.0896393i	$0.971429\pi$
$272$		0			0
$273$		0			0
$274$		0			0
$275$		0			0
$276$		0			0
$277$	−0.217194	+	0.157801i	−0.217194	+	0.157801i	−0.691063	−	0.722795i	$-0.742857\pi$
$277$	−0.217194	+	0.157801i	−0.217194	+	0.157801i	0.473869	+	0.880596i	$0.342857\pi$
$278$		0			0
$279$		0			0
$280$		0			0
$281$		0			0		−0.309017	−	0.951057i	$-0.600000\pi$
$281$		0			0		0.309017	+	0.951057i	$0.400000\pi$
$282$		0			0
$283$		0			0		−0.309017	−	0.951057i	$-0.600000\pi$
$283$		0			0		0.309017	+	0.951057i	$0.400000\pi$
$284$	−2.32388	−	1.68840i	−2.32388	−	1.68840i
$285$	1.14679	−	1.73731i	1.14679	−	1.73731i
$286$		0			0
$287$		0			0
$288$	−5.06100	−	3.67703i	−5.06100	−	3.67703i
$289$	−0.809017	+	0.587785i	−0.809017	+	0.587785i
$290$	−3.25686	−	0.898835i	−3.25686	−	0.898835i
$291$		0			0
$292$	−1.71131	−	5.26686i	−1.71131	−	5.26686i
$293$	2.00000			2.00000			1.00000			$0$
$293$	2.00000			2.00000			1.00000			$0$
$294$	0.915888	+	2.81881i	0.915888	+	2.81881i
$295$		0			0
$296$	−1.57376	+	4.84354i	−1.57376	+	4.84354i
$297$		0			0
$298$		0			0
$299$		0			0
$300$	−0.962703	+	4.21788i	−0.962703	+	4.21788i
$301$		0			0
$302$	3.17124	−	2.30404i	3.17124	−	2.30404i
$303$	0.124951	−	0.384559i	0.124951	−	0.384559i
$304$	−1.87011	+	5.75560i	−1.87011	+	5.75560i
$305$		0			0
$306$		0			0
$307$		0			0		1.00000			$0$
$307$		0			0		−1.00000			$\pi$
$308$		0			0
$309$	0.542281	+	0.393990i	0.542281	+	0.393990i
$310$		0			0
$311$	1.11816	−	0.812393i	1.11816	−	0.812393i	0.134233	−	0.990950i	$-0.457143\pi$
$311$	1.11816	−	0.812393i	1.11816	−	0.812393i	0.983930	+	0.178557i	$0.0571429\pi$
$312$		0			0
$313$	1.45780	+	1.05915i	1.45780	+	1.05915i	0.983930	+	0.178557i	$0.0571429\pi$
$313$	1.45780	+	1.05915i	1.45780	+	1.05915i	0.473869	+	0.880596i	$0.342857\pi$
$314$	1.25142	−	0.909207i	1.25142	−	0.909207i
$315$		0			0
$316$	−4.35139	−	3.16147i	−4.35139	−	3.16147i
$317$		0			0		−0.309017	−	0.951057i	$-0.600000\pi$
$317$		0			0		0.309017	+	0.951057i	$0.400000\pi$
$318$		0			0
$319$		0			0
$320$	−0.238966	−	5.32099i	−0.238966	−	5.32099i
$321$	−0.753071	+	2.31772i	−0.753071	+	2.31772i
$322$		0			0
$323$		0			0
$324$	−1.89428			−1.89428
$325$		0			0
$326$		0			0
$327$	0.542281	−	0.393990i	0.542281	−	0.393990i
$328$		0			0
$329$		0			0
$330$		0			0
$331$		0			0		−0.309017	−	0.951057i	$-0.600000\pi$
$331$		0			0		0.309017	+	0.951057i	$0.400000\pi$
$332$	−5.17601			−5.17601
$333$	−0.541762	−	1.66737i	−0.541762	−	1.66737i
$334$	−1.98523	−	1.44235i	−1.98523	−	1.44235i
$335$		0			0
$336$		0			0
$337$		0			0		−0.809017	−	0.587785i	$-0.800000\pi$
$337$		0			0		0.809017	+	0.587785i	$0.200000\pi$
$338$	−1.59203	−	1.15668i	−1.59203	−	1.15668i
$339$		0			0
$340$		0			0
$341$		0			0
$342$	−1.06611	−	3.28116i	−1.06611	−	3.28116i
$343$		0			0
$344$	−2.19524	−	6.75625i	−2.19524	−	6.75625i
$345$		0			0
$346$		0			0
$347$		0			0		0.309017	−	0.951057i	$-0.400000\pi$
$347$		0			0		−0.309017	+	0.951057i	$0.600000\pi$
$348$	−6.00930	+	4.36601i	−6.00930	+	4.36601i
$349$		0			0		1.00000			$0$
$349$		0			0		−1.00000			$\pi$
$350$		0			0
$351$		0			0
$352$		0			0
$353$		0			0		0.309017	−	0.951057i	$-0.400000\pi$
$353$		0			0		−0.309017	+	0.951057i	$0.600000\pi$
$354$		0			0
$355$	0.623490	+	0.781831i	0.623490	+	0.781831i
$356$	1.33692	+	4.11460i	1.33692	+	4.11460i
$357$		0			0
$358$	−1.17238	−	3.60820i	−1.17238	−	3.60820i
$359$	0.891370	+	0.647618i	0.891370	+	0.647618i	0.936235	−	0.351375i	$-0.114286\pi$
$359$	0.891370	+	0.647618i	0.891370	+	0.647618i	−0.0448648	+	0.998993i	$0.514286\pi$
$360$	2.91419	+	3.65427i	2.91419	+	3.65427i
$361$	−0.736424	+	0.535043i	−0.736424	+	0.535043i
$362$		0			0
$363$	−1.21850	−	0.885289i	−1.21850	−	0.885289i
$364$		0			0
$365$	0.0864961	+	1.92598i	0.0864961	+	1.92598i
$366$		0			0
$367$	0.385338	+	1.18595i	0.385338	+	1.18595i	0.936235	+	0.351375i	$0.114286\pi$
$367$	0.385338	+	1.18595i	0.385338	+	1.18595i	−0.550897	+	0.834573i	$0.685714\pi$
$368$		0			0
$369$		0			0
$370$	1.49835	−	2.26990i	1.49835	−	2.26990i
$371$		0			0
$372$		0			0
$373$	0.891370	−	0.647618i	0.891370	−	0.647618i	−0.0448648	−	0.998993i	$-0.514286\pi$
$373$	0.891370	−	0.647618i	0.891370	−	0.647618i	0.936235	+	0.351375i	$0.114286\pi$
$374$		0			0
$375$	0.713714	−	1.32630i	0.713714	−	1.32630i
$376$		0			0
$377$		0			0
$378$		0			0
$379$	−0.137526	+	0.423260i	−0.137526	+	0.423260i	−0.995974	−	0.0896393i	$-0.971429\pi$
$379$	−0.137526	+	0.423260i	−0.137526	+	0.423260i	0.858449	+	0.512899i	$0.171429\pi$
$380$	2.18712	−	3.31335i	2.18712	−	3.31335i
$381$		0			0
$382$	−1.54684			−1.54684
$383$		0			0		−0.309017	−	0.951057i	$-0.600000\pi$
$383$		0			0		0.309017	+	0.951057i	$0.400000\pi$
$384$	−6.76237	−	4.91315i	−6.76237	−	4.91315i
$385$		0			0
$386$		0			0
$387$	1.97846	+	1.43743i	1.97846	+	1.43743i
$388$		0			0
$389$		0			0		0.809017	−	0.587785i	$-0.200000\pi$
$389$		0			0		−0.809017	+	0.587785i	$0.800000\pi$
$390$		0			0
$391$		0			0
$392$	1.13865	+	3.50441i	1.13865	+	3.50441i
$393$	−0.135146			−0.135146
$394$		0			0
$395$	1.16747	+	1.46396i	1.16747	+	1.46396i
$396$		0			0
$397$		0			0		0.309017	−	0.951057i	$-0.400000\pi$
$397$		0			0		−0.309017	+	0.951057i	$0.600000\pi$
$398$	−3.13289	+	2.27618i	−3.13289	+	2.27618i
$399$		0			0
$400$	−0.974333	+	4.26883i	−0.974333	+	4.26883i
$401$		0			0		1.00000			$0$
$401$		0			0		−1.00000			$\pi$
$402$		0			0
$403$		0			0
$404$	0.238302	−	0.733419i	0.238302	−	0.733419i
$405$	0.635694	+	0.175440i	0.635694	+	0.175440i
$406$		0			0
$407$		0			0
$408$		0			0
$409$	1.61152	+	1.17084i	1.61152	+	1.17084i	0.858449	+	0.512899i	$0.171429\pi$
$409$	1.61152	+	1.17084i	1.61152	+	1.17084i	0.753071	+	0.657939i	$0.228571\pi$
$410$		0			0
$411$		0			0
$412$	1.03422	+	0.751407i	1.03422	+	0.751407i
$413$		0			0
$414$		0			0
$415$	1.73700	+	0.479382i	1.73700	+	0.479382i
$416$		0			0
$417$		0			0
$418$		0			0
$419$	−0.137526	−	0.423260i	−0.137526	−	0.423260i	0.858449	−	0.512899i	$-0.171429\pi$
$419$	−0.137526	−	0.423260i	−0.137526	−	0.423260i	−0.995974	+	0.0896393i	$0.971429\pi$
$420$		0			0
$421$		0			0		0.309017	−	0.951057i	$-0.400000\pi$
$421$		0			0		−0.309017	+	0.951057i	$0.600000\pi$
$422$		0			0
$423$		0			0
$424$		0			0
$425$		0			0
$426$	2.96388			2.96388
$427$		0			0
$428$	−1.43623	+	4.42028i	−1.43623	+	4.42028i
$429$		0			0
$430$	0.170212	+	3.79007i	0.170212	+	3.79007i
$431$	0.292867	+	0.901352i	0.292867	+	0.901352i	0.983930	+	0.178557i	$0.0571429\pi$
$431$	0.292867	+	0.901352i	0.292867	+	0.901352i	−0.691063	+	0.722795i	$0.742857\pi$
$432$	1.77049			1.77049
$433$		0			0		−0.309017	−	0.951057i	$-0.600000\pi$
$433$		0			0		0.309017	+	0.951057i	$0.400000\pi$
$434$		0			0
$435$	2.42100	−	0.908618i	2.42100	−	0.908618i
$436$	1.03422	−	0.751407i	1.03422	−	0.751407i
$437$		0			0
$438$	4.62283	+	3.35868i	4.62283	+	3.35868i
$439$		0			0		0.809017	−	0.587785i	$-0.200000\pi$
$439$		0			0		−0.809017	+	0.587785i	$0.800000\pi$
$440$		0			0
$441$	−1.02621	−	0.745586i	−1.02621	−	0.745586i
$442$		0			0
$443$		0			0		1.00000			$0$
$443$		0			0		−1.00000			$\pi$
$444$	−1.84778	−	5.68690i	−1.84778	−	5.68690i
$445$	−0.0675728	−	1.50463i	−0.0675728	−	1.50463i
$446$	−0.840473	+	2.58671i	−0.840473	+	2.58671i
$447$		0			0
$448$		0			0
$449$		0			0		1.00000			$0$
$449$		0			0		−1.00000			$\pi$
$450$	−0.981055	−	2.29529i	−0.981055	−	2.29529i
$451$		0			0
$452$		0			0
$453$	−0.927100	+	2.85332i	−0.927100	+	2.85332i
$454$		0			0
$455$		0			0
$456$	−2.37031	−	7.29506i	−2.37031	−	7.29506i
$457$		0			0		1.00000			$0$
$457$		0			0		−1.00000			$\pi$
$458$	−0.670003	−	2.06206i	−0.670003	−	2.06206i
$459$		0			0
$460$		0			0
$461$		0			0		0.809017	−	0.587785i	$-0.200000\pi$
$461$		0			0		−0.809017	+	0.587785i	$0.800000\pi$
$462$		0			0
$463$	−0.217194	−	0.157801i	−0.217194	−	0.157801i	0.473869	−	0.880596i	$-0.342857\pi$
$463$	−0.217194	−	0.157801i	−0.217194	−	0.157801i	−0.691063	+	0.722795i	$0.742857\pi$
$464$	−6.08189	+	4.41875i	−6.08189	+	4.41875i
$465$		0			0
$466$	−0.427407	−	0.310529i	−0.427407	−	0.310529i
$467$		0			0		−0.309017	−	0.951057i	$-0.600000\pi$
$467$		0			0		0.309017	+	0.951057i	$0.400000\pi$
$468$		0			0
$469$		0			0
$470$		0			0
$471$	−0.365846	+	1.12596i	−0.365846	+	1.12596i
$472$		0			0
$473$		0			0
$474$	5.54977			5.54977
$475$	−1.04084	+	0.909354i	−1.04084	+	0.909354i
$476$		0			0
$477$		0			0
$478$		0			0
$479$		0			0		0.309017	−	0.951057i	$-0.400000\pi$
$479$		0			0		−0.309017	+	0.951057i	$0.600000\pi$
$480$	4.63122	+	5.80737i	4.63122	+	5.80737i
$481$		0			0
$482$		0			0
$483$		0			0
$484$	−2.32388	−	1.68840i	−2.32388	−	1.68840i
$485$		0			0
$486$	2.22501	−	1.61656i	2.22501	−	1.61656i
$487$		0			0		−0.809017	−	0.587785i	$-0.800000\pi$
$487$		0			0		0.809017	+	0.587785i	$0.200000\pi$
$488$		0			0
$489$		0			0
$490$	−0.0882877	−	1.96588i	−0.0882877	−	1.96588i
$491$		0			0		−0.809017	−	0.587785i	$-0.800000\pi$
$491$		0			0		0.809017	+	0.587785i	$0.200000\pi$
$492$		0			0
$493$		0			0
$494$		0			0
$495$		0			0
$496$		0			0
$497$		0			0
$498$	4.32073	−	3.13920i	4.32073	−	3.13920i
$499$	1.50614			1.50614			0.753071	−	0.657939i	$-0.228571\pi$
$499$	1.50614			1.50614			0.753071	+	0.657939i	$0.228571\pi$
$500$	1.36117	−	2.52948i	1.36117	−	2.52948i
$501$	1.87813			1.87813
$502$	−1.50883	+	1.09623i	−1.50883	+	1.09623i
$503$	−0.242903	+	0.747578i	−0.242903	+	0.747578i	0.753071	+	0.657939i	$0.228571\pi$
$503$	−0.242903	+	0.747578i	−0.242903	+	0.747578i	−0.995974	+	0.0896393i	$0.971429\pi$
$504$		0			0
$505$	−0.147897	+	0.224055i	−0.147897	+	0.224055i
$506$		0			0
$507$	1.50614			1.50614
$508$		0			0
$509$	−0.500000	−	0.363271i	−0.500000	−	0.363271i	0.309017	−	0.951057i	$-0.400000\pi$
$509$	−0.500000	−	0.363271i	−0.500000	−	0.363271i	−0.809017	+	0.587785i	$0.800000\pi$
$510$		0			0
$511$		0			0
$512$	−4.41727	−	3.20933i	−4.41727	−	3.20933i
$513$	0.452128	+	0.328490i	0.452128	+	0.328490i
$514$		0			0
$515$	−0.277479	−	0.347948i	−0.277479	−	0.347948i
$516$	6.74791	+	4.90265i	6.74791	+	4.90265i
$517$		0			0
$518$		0			0
$519$		0			0
$520$		0			0
$521$	−0.0277280	+	0.0853380i	−0.0277280	+	0.0853380i	−0.963963	−	0.266037i	$-0.914286\pi$
$521$	−0.0277280	+	0.0853380i	−0.0277280	+	0.0853380i	0.936235	+	0.351375i	$0.114286\pi$
$522$	1.32434	−	4.07590i	1.32434	−	4.07590i
$523$		0			0		0.809017	−	0.587785i	$-0.200000\pi$
$523$		0			0		−0.809017	+	0.587785i	$0.800000\pi$
$524$	−0.257746			−0.257746
$525$		0			0
$526$	3.68476			3.68476
$527$		0			0
$528$		0			0
$529$	0.309017	−	0.951057i	0.309017	−	0.951057i
$530$		0			0
$531$		0			0
$532$		0			0
$533$		0			0
$534$	−3.61147	−	2.62389i	−3.61147	−	2.62389i
$535$	0.891370	−	1.35037i	0.891370	−	1.35037i
$536$		0			0
$537$	2.34917	+	1.70677i	2.34917	+	1.70677i
$538$		0			0
$539$		0			0
$540$	−1.11962	−	0.308997i	−1.11962	−	0.308997i
$541$		0			0		−0.809017	−	0.587785i	$-0.800000\pi$
$541$		0			0		0.809017	+	0.587785i	$0.200000\pi$
$542$	−0.477999	−	1.47113i	−0.477999	−	1.47113i
$543$		0			0
$544$		0			0
$545$	−0.416664	+	0.156377i	−0.416664	+	0.156377i
$546$		0			0
$547$	0.292867	−	0.901352i	0.292867	−	0.901352i	−0.691063	−	0.722795i	$-0.742857\pi$
$547$	0.292867	−	0.901352i	0.292867	−	0.901352i	0.983930	−	0.178557i	$-0.0571429\pi$
$548$		0			0
$549$		0			0
$550$		0			0
$551$	−2.37297			−2.37297
$552$		0			0
$553$		0			0
$554$	0.163255	−	0.502447i	0.163255	−	0.502447i
$555$	0.0933941	+	2.07958i	0.0933941	+	2.07958i
$556$		0			0
$557$	−0.445042			−0.445042			−0.222521	−	0.974928i	$-0.571429\pi$
$557$	−0.445042			−0.445042			−0.222521	+	0.974928i	$0.571429\pi$
$558$		0			0
$559$		0			0
$560$		0			0
$561$		0			0
$562$		0			0
$563$		0			0		−0.809017	−	0.587785i	$-0.800000\pi$
$563$		0			0		0.809017	+	0.587785i	$0.200000\pi$
$564$		0			0
$565$		0			0
$566$		0			0
$567$		0			0
$568$	3.68476			3.68476
$569$	0.578625	+	1.78082i	0.578625	+	1.78082i	0.623490	+	0.781831i	$0.285714\pi$
$569$	0.578625	+	1.78082i	0.578625	+	1.78082i	−0.0448648	+	0.998993i	$0.514286\pi$
$570$	0.183787	+	4.09232i	0.183787	+	4.09232i
$571$	−0.427100	+	1.31448i	−0.427100	+	1.31448i	0.473869	+	0.880596i	$0.342857\pi$
$571$	−0.427100	+	1.31448i	−0.427100	+	1.31448i	−0.900969	+	0.433884i	$0.857143\pi$
$572$		0			0
$573$	0.957798	−	0.695881i	0.957798	−	0.695881i
$574$		0			0
$575$		0			0
$576$	6.75630			6.75630
$577$	−1.00883	+	0.732956i	−1.00883	+	0.732956i	−0.963963	−	0.266037i	$-0.914286\pi$
$577$	−1.00883	+	0.732956i	−1.00883	+	0.732956i	−0.0448648	+	0.998993i	$0.514286\pi$
$578$	0.608102	−	1.87155i	0.608102	−	1.87155i
$579$		0			0
$580$	4.61726	−	1.73289i	4.61726	−	1.73289i
$581$		0			0
$582$		0			0
$583$		0			0
$584$	5.74721	+	4.17559i	5.74721	+	4.17559i
$585$		0			0
$586$	−3.18406	+	2.31336i	−3.18406	+	2.31336i
$587$	−1.21850	−	0.885289i	−1.21850	−	0.885289i	−0.222521	−	0.974928i	$-0.571429\pi$
$587$	−1.21850	−	0.885289i	−1.21850	−	0.885289i	−0.995974	+	0.0896393i	$0.971429\pi$
$588$	−3.50009	−	2.54296i	−3.50009	−	2.54296i
$589$		0			0
$590$		0			0
$591$		0			0
$592$	−1.87011	−	5.75560i	−1.87011	−	5.75560i
$593$	−1.99195			−1.99195			−0.995974	−	0.0896393i	$-0.971429\pi$
$593$	−1.99195			−1.99195			−0.995974	+	0.0896393i	$0.971429\pi$
$594$		0			0
$595$		0			0
$596$		0			0
$597$	0.915888	−	2.81881i	0.915888	−	2.81881i
$598$		0			0
$599$		0			0		1.00000			$0$
$599$		0			0		−1.00000			$\pi$
$600$	−2.18120	−	5.10317i	−2.18120	−	5.10317i
$601$		0			0		1.00000			$0$
$601$		0			0		−1.00000			$\pi$
$602$		0			0
$603$		0			0
$604$	−1.76814	+	5.44177i	−1.76814	+	5.44177i
$605$	0.623490	+	0.781831i	0.623490	+	0.781831i
$606$	0.245885	+	0.756757i	0.245885	+	0.756757i
$607$		0			0		1.00000			$0$
$607$		0			0		−1.00000			$\pi$
$608$	−2.10635	−	6.48267i	−2.10635	−	6.48267i
$609$		0			0
$610$		0			0
$611$		0			0
$612$		0			0
$613$	0.360046	+	0.261589i	0.360046	+	0.261589i	0.753071	−	0.657939i	$-0.228571\pi$
$613$	0.360046	+	0.261589i	0.360046	+	0.261589i	−0.393025	+	0.919528i	$0.628571\pi$
$614$		0			0
$615$		0			0
$616$		0			0
$617$	−0.0277280	−	0.0853380i	−0.0277280	−	0.0853380i	0.936235	−	0.351375i	$-0.114286\pi$
$617$	−0.0277280	−	0.0853380i	−0.0277280	−	0.0853380i	−0.963963	+	0.266037i	$0.914286\pi$
$618$	−1.31905			−1.31905
$619$		0			0		−0.309017	−	0.951057i	$-0.600000\pi$
$619$		0			0		0.309017	+	0.951057i	$0.400000\pi$
$620$		0			0
$621$		0			0
$622$	−0.840473	+	2.58671i	−0.840473	+	2.58671i
$623$		0			0
$624$		0			0
$625$	−0.691063	+	0.722795i	−0.691063	+	0.722795i
$626$	−3.54596			−3.54596
$627$		0			0
$628$	−0.697731	+	2.14740i	−0.697731	+	2.14740i
$629$		0			0
$630$		0			0
$631$		0			0		−0.309017	−	0.951057i	$-0.600000\pi$
$631$		0			0		0.309017	+	0.951057i	$0.400000\pi$
$632$	6.89960			6.89960
$633$		0			0
$634$		0			0
$635$		0			0
$636$		0			0
$637$		0			0
$638$		0			0
$639$	−1.02621	+	0.745586i	−1.02621	+	0.745586i
$640$	3.46023	+	4.33899i	3.46023	+	4.33899i
$641$	−1.59203	−	1.15668i	−1.59203	−	1.15668i	−0.900969	−	0.433884i	$-0.857143\pi$
$641$	−1.59203	−	1.15668i	−1.59203	−	1.15668i	−0.691063	−	0.722795i	$-0.742857\pi$
$642$	−1.48194	−	4.56094i	−1.48194	−	4.56094i
$643$	−1.61803			−1.61803			−0.809017	−	0.587785i	$-0.800000\pi$
$643$	−1.61803			−1.61803			−0.809017	+	0.587785i	$0.800000\pi$
$644$		0			0
$645$	−1.81045	−	2.27023i	−1.81045	−	2.27023i
$646$		0			0
$647$	0.190983	−	0.587785i	0.190983	−	0.587785i	−0.809017	−	0.587785i	$-0.800000\pi$
$647$	0.190983	−	0.587785i	0.190983	−	0.587785i	1.00000			$0$
$648$	1.96587	−	1.42829i	1.96587	−	1.42829i
$649$		0			0
$650$		0			0
$651$		0			0
$652$		0			0
$653$		0			0		0.309017	−	0.951057i	$-0.400000\pi$
$653$		0			0		−0.309017	+	0.951057i	$0.600000\pi$
$654$	−0.407609	+	1.25449i	−0.407609	+	1.25449i
$655$	0.0864961	+	0.0238714i	0.0864961	+	0.0238714i
$656$		0			0
$657$	−2.44551			−2.44551
$658$		0			0
$659$	0.635928	+	0.462029i	0.635928	+	0.462029i	0.858449	−	0.512899i	$-0.171429\pi$
$659$	0.635928	+	0.462029i	0.635928	+	0.462029i	−0.222521	+	0.974928i	$0.571429\pi$
$660$		0			0
$661$		0			0		0.809017	−	0.587785i	$-0.200000\pi$
$661$		0			0		−0.809017	+	0.587785i	$0.800000\pi$
$662$		0			0
$663$		0			0
$664$	5.37163	−	3.90272i	5.37163	−	3.90272i
$665$		0			0
$666$	2.79112	+	2.02787i	2.79112	+	2.02787i
$667$		0			0
$668$	3.58191			3.58191
$669$	−0.643274	−	1.97979i	−0.643274	−	1.97979i
$670$		0			0
$671$		0			0
$672$		0			0
$673$		0			0		0.809017	−	0.587785i	$-0.200000\pi$
$673$		0			0		−0.809017	+	0.587785i	$0.800000\pi$
$674$		0			0
$675$	0.347113	+	0.207390i	0.347113	+	0.207390i
$676$	2.87247			2.87247
$677$	0.635928	−	0.462029i	0.635928	−	0.462029i	−0.222521	−	0.974928i	$-0.571429\pi$
$677$	0.635928	−	0.462029i	0.635928	−	0.462029i	0.858449	+	0.512899i	$0.171429\pi$
$678$		0			0
$679$		0			0
$680$		0			0
$681$		0			0
$682$		0			0
$683$		0			0		−0.309017	−	0.951057i	$-0.600000\pi$
$683$		0			0		0.309017	+	0.951057i	$0.400000\pi$
$684$	4.07417	+	2.96006i	4.07417	+	2.96006i
$685$		0			0
$686$		0			0
$687$	1.34253	+	0.975406i	1.34253	+	0.975406i
$688$	6.82943	+	4.96187i	6.82943	+	4.96187i
$689$		0			0
$690$		0			0
$691$		0			0		−0.809017	−	0.587785i	$-0.800000\pi$
$691$		0			0		0.809017	+	0.587785i	$0.200000\pi$
$692$		0			0
$693$		0			0
$694$		0			0
$695$		0			0
$696$	2.94443	−	9.06203i	2.94443	−	9.06203i
$697$		0			0
$698$		0			0
$699$	0.404349			0.404349
$700$		0			0
$701$		0			0		1.00000			$0$
$701$		0			0		−1.00000			$\pi$
$702$		0			0
$703$	0.590306	−	1.81678i	0.590306	−	1.81678i
$704$		0			0
$705$		0			0
$706$		0			0
$707$		0			0
$708$		0			0
$709$		0			0		−0.809017	−	0.587785i	$-0.800000\pi$
$709$		0			0		0.809017	+	0.587785i	$0.200000\pi$
$710$	−1.89694	−	0.523523i	−1.89694	−	0.523523i
$711$	−1.92155	+	1.39609i	−1.92155	+	1.39609i
$712$	−4.48986	−	3.26207i	−4.48986	−	3.26207i
$713$		0			0
$714$		0			0
$715$		0			0
$716$	4.48026	+	3.25510i	4.48026	+	3.25510i
$717$		0			0
$718$	−2.16818			−2.16818
$719$	0.608102	+	1.87155i	0.608102	+	1.87155i	0.473869	+	0.880596i	$0.342857\pi$
$719$	0.608102	+	1.87155i	0.608102	+	1.87155i	0.134233	+	0.990950i	$0.457143\pi$
$720$	−5.35397	−	1.47760i	−5.35397	−	1.47760i
$721$		0			0
$722$	0.553537	−	1.70361i	0.553537	−	1.70361i
$723$		0			0
$724$		0			0
$725$	−1.70999	+	0.153902i	−1.70999	+	0.153902i
$726$	2.96388			2.96388
$727$		0			0		0.809017	−	0.587785i	$-0.200000\pi$
$727$		0			0		−0.809017	+	0.587785i	$0.800000\pi$
$728$		0			0
$729$	−0.446687	+	1.37476i	−0.446687	+	1.37476i
$730$	−2.36545	−	2.96618i	−2.36545	−	2.96618i
$731$		0			0
$732$		0			0
$733$		0			0		−0.309017	−	0.951057i	$-0.600000\pi$
$733$		0			0		0.309017	+	0.951057i	$0.400000\pi$
$734$	−1.98523	−	1.44235i	−1.98523	−	1.44235i
$735$	0.939065	+	1.17755i	0.939065	+	1.17755i
$736$		0			0
$737$		0			0
$738$		0			0
$739$	−0.500000	+	0.363271i	−0.500000	+	0.363271i	−0.809017	−	0.587785i	$-0.800000\pi$
$739$	−0.500000	+	0.363271i	−0.500000	+	0.363271i	0.309017	+	0.951057i	$0.400000\pi$
$740$	0.178118	+	3.96612i	0.178118	+	3.96612i
$741$		0			0
$742$		0			0
$743$		0			0		1.00000			$0$
$743$		0			0		−1.00000			$\pi$
$744$		0			0
$745$		0			0
$746$	−0.670003	+	2.06206i	−0.670003	+	2.06206i
$747$	−0.706319	+	2.17383i	−0.706319	+	2.17383i
$748$		0			0
$749$		0			0
$750$	0.397851	+	2.93705i	0.397851	+	2.93705i
$751$		0			0		1.00000			$0$
$751$		0			0		−1.00000			$\pi$
$752$		0			0
$753$	0.441099	−	1.35756i	0.441099	−	1.35756i
$754$		0			0
$755$	1.09736	−	1.66243i	1.09736	−	1.66243i
$756$		0			0
$757$		0			0		1.00000			$0$
$757$		0			0		−1.00000			$\pi$
$758$	−0.270631	−	0.832916i	−0.270631	−	0.832916i
$759$		0			0
$760$	0.228487	+	5.08767i	0.228487	+	5.08767i
$761$		0			0		0.809017	−	0.587785i	$-0.200000\pi$
$761$		0			0		−0.809017	+	0.587785i	$0.800000\pi$
$762$		0			0
$763$		0			0
$764$	1.82668	−	1.32716i	1.82668	−	1.32716i
$765$		0			0
$766$		0			0
$767$		0			0
$768$	8.42659			8.42659
$769$		0			0		−0.309017	−	0.951057i	$-0.600000\pi$
$769$		0			0		0.309017	+	0.951057i	$0.400000\pi$
$770$		0			0
$771$		0			0
$772$		0			0
$773$		0			0		0.809017	−	0.587785i	$-0.200000\pi$
$773$		0			0		−0.809017	+	0.587785i	$0.800000\pi$
$774$	−4.81242			−4.81242
$775$		0			0
$776$		0			0
$777$		0			0
$778$		0			0
$779$		0			0
$780$		0			0
$781$		0			0
$782$		0			0
$783$	0.214528	+	0.660248i	0.214528	+	0.660248i
$784$	−3.54237	−	2.57368i	−3.54237	−	2.57368i
$785$	0.433033	−	0.656016i	0.433033	−	0.656016i
$786$	0.215156	−	0.156320i	0.215156	−	0.156320i
$787$	1.61152	+	1.17084i	1.61152	+	1.17084i	0.858449	+	0.512899i	$0.171429\pi$
$787$	1.61152	+	1.17084i	1.61152	+	1.17084i	0.753071	+	0.657939i	$0.228571\pi$
$788$		0			0
$789$	−2.28160	+	1.65768i	−2.28160	+	1.65768i
$790$	−3.55197	−	0.980281i	−3.55197	−	0.980281i
$791$		0			0
$792$		0			0
$793$		0			0
$794$		0			0
$795$		0			0
$796$	1.74675	−	5.37596i	1.74675	−	5.37596i
$797$	0.608102	−	1.87155i	0.608102	−	1.87155i	0.134233	−	0.990950i	$-0.457143\pi$
$797$	0.608102	−	1.87155i	0.608102	−	1.87155i	0.473869	−	0.880596i	$-0.342857\pi$
$798$		0			0
$799$		0			0
$800$	−1.93830	−	4.53487i	−1.93830	−	4.53487i
$801$	1.91049			1.91049
$802$		0			0
$803$		0			0
$804$		0			0
$805$		0			0
$806$		0			0
$807$		0			0
$808$	0.305690	+	0.940817i	0.305690	+	0.940817i
$809$		0			0		−0.809017	−	0.587785i	$-0.800000\pi$
$809$		0			0		0.809017	+	0.587785i	$0.200000\pi$
$810$	−1.21497	+	0.455987i	−1.21497	+	0.455987i
$811$	1.55972	−	1.13321i	1.55972	−	1.13321i	0.623490	−	0.781831i	$-0.285714\pi$
$811$	1.55972	−	1.13321i	1.55972	−	1.13321i	0.936235	−	0.351375i	$-0.114286\pi$
$812$		0			0
$813$	0.957798	+	0.695881i	0.957798	+	0.695881i
$814$		0			0
$815$		0			0
$816$		0			0
$817$	0.823417	+	2.53422i	0.823417	+	2.53422i
$818$	−3.91987			−3.91987
$819$		0			0
$820$		0			0
$821$	−0.556829	+	1.71374i	−0.556829	+	1.71374i	0.134233	+	0.990950i	$0.457143\pi$
$821$	−0.556829	+	1.71374i	−0.556829	+	1.71374i	−0.691063	+	0.722795i	$0.742857\pi$
$822$		0			0
$823$		0			0		0.809017	−	0.587785i	$-0.200000\pi$
$823$		0			0		−0.809017	+	0.587785i	$0.800000\pi$
$824$	−1.63987			−1.63987
$825$		0			0
$826$		0			0
$827$		0			0		0.809017	−	0.587785i	$-0.200000\pi$
$827$		0			0		−0.809017	+	0.587785i	$0.800000\pi$
$828$		0			0
$829$	−0.427100	+	1.31448i	−0.427100	+	1.31448i	0.473869	+	0.880596i	$0.342857\pi$
$829$	−0.427100	+	1.31448i	−0.427100	+	1.31448i	−0.900969	+	0.433884i	$0.857143\pi$
$830$	−3.31985	+	1.24596i	−3.31985	+	1.24596i
$831$	0.124951	+	0.384559i	0.124951	+	0.384559i
$832$		0			0
$833$		0			0
$834$		0			0
$835$	−1.20204	−	0.331743i	−1.20204	−	0.331743i
$836$		0			0
$837$		0			0
$838$	0.708521	+	0.514770i	0.708521	+	0.514770i
$839$	1.45780	−	1.05915i	1.45780	−	1.05915i	0.473869	−	0.880596i	$-0.342857\pi$
$839$	1.45780	−	1.05915i	1.45780	−	1.05915i	0.983930	−	0.178557i	$-0.0571429\pi$
$840$		0			0
$841$	−1.57575	−	1.14485i	−1.57575	−	1.14485i
$842$		0			0
$843$		0			0
$844$		0			0
$845$	−0.963963	−	0.266037i	−0.963963	−	0.266037i
$846$		0			0
$847$		0			0
$848$		0			0
$849$		0			0
$850$		0			0
$851$		0			0
$852$	−3.50009	+	2.54296i	−3.50009	+	2.54296i
$853$	−0.615546	+	1.89446i	−0.615546	+	1.89446i	−0.222521	+	0.974928i	$0.571429\pi$
$853$	−0.615546	+	1.89446i	−0.615546	+	1.89446i	−0.393025	+	0.919528i	$0.628571\pi$
$854$		0			0
$855$	−1.09309	−	1.37069i	−1.09309	−	1.37069i
$856$	−1.84238	−	5.67026i	−1.84238	−	5.67026i
$857$	1.50614			1.50614			0.753071	−	0.657939i	$-0.228571\pi$
$857$	1.50614			1.50614			0.753071	+	0.657939i	$0.228571\pi$
$858$		0			0
$859$		0			0		−0.809017	−	0.587785i	$-0.800000\pi$
$859$		0			0		0.809017	+	0.587785i	$0.200000\pi$
$860$	−3.45283	−	4.32971i	−3.45283	−	4.32971i
$861$		0			0
$862$	−1.50883	−	1.09623i	−1.50883	−	1.09623i
$863$		0			0		−0.809017	−	0.587785i	$-0.800000\pi$
$863$		0			0		0.809017	+	0.587785i	$0.200000\pi$
$864$	−1.61330	+	1.17213i	−1.61330	+	1.17213i
$865$		0			0
$866$		0			0
$867$	0.465424	+	1.43243i	0.465424	+	1.43243i
$868$		0			0
$869$		0			0
$870$	−2.80333	+	4.24687i	−2.80333	+	4.24687i
$871$		0			0
$872$	−0.506748	+	1.55961i	−0.506748	+	1.55961i
$873$		0			0
$874$		0			0
$875$		0			0
$876$	−8.34088			−8.34088
$877$	0.0725928	−	0.0527418i	0.0725928	−	0.0527418i	−0.550897	−	0.834573i	$-0.685714\pi$
$877$	0.0725928	−	0.0527418i	0.0725928	−	0.0527418i	0.623490	+	0.781831i	$0.285714\pi$
$878$		0			0
$879$	0.930848	−	2.86485i	0.930848	−	2.86485i
$880$		0			0
$881$	0.385338	+	1.18595i	0.385338	+	1.18595i	0.936235	+	0.351375i	$0.114286\pi$
$881$	0.385338	+	1.18595i	0.385338	+	1.18595i	−0.550897	+	0.834573i	$0.685714\pi$
$882$	2.49616			2.49616
$883$		0			0		−0.309017	−	0.951057i	$-0.600000\pi$
$883$		0			0		0.309017	+	0.951057i	$0.400000\pi$
$884$		0			0
$885$		0			0
$886$		0			0
$887$		0			0		−0.809017	−	0.587785i	$-0.800000\pi$
$887$		0			0		0.809017	+	0.587785i	$0.200000\pi$
$888$	6.20555	+	4.50859i	6.20555	+	4.50859i
$889$		0			0
$890$	1.84795	+	2.31725i	1.84795	+	2.31725i
$891$		0			0
$892$	−1.22683	−	3.77580i	−1.22683	−	3.77580i
$893$		0			0
$894$		0			0
$895$	−1.20204	−	1.50731i	−1.20204	−	1.50731i
$896$		0			0
$897$		0			0
$898$		0			0
$899$		0			0
$900$	3.12787	+	1.86882i	3.12787	+	1.86882i
$901$		0			0
$902$		0			0
$903$		0			0
$904$		0			0
$905$		0			0
$906$	−1.82440	−	5.61493i	−1.82440	−	5.61493i
$907$		0			0		1.00000			$0$
$907$		0			0		−1.00000			$\pi$
$908$		0			0
$909$	−0.275503	−	0.200165i	−0.275503	−	0.200165i
$910$		0			0
$911$		0			0		0.809017	−	0.587785i	$-0.200000\pi$
$911$		0			0		−0.809017	+	0.587785i	$0.800000\pi$
$912$	7.37408	+	5.35758i	7.37408	+	5.35758i
$913$		0			0
$914$		0			0
$915$		0			0
$916$	2.56043	+	1.86026i	2.56043	+	1.86026i
$917$		0			0
$918$		0			0
$919$		0			0		−0.309017	−	0.951057i	$-0.600000\pi$
$919$		0			0		0.309017	+	0.951057i	$0.400000\pi$
$920$		0			0
$921$		0			0
$922$		0			0
$923$		0			0
$924$		0			0
$925$	0.307552	−	1.34747i	0.307552	−	1.34747i
$926$	0.528304			0.528304
$927$	0.456707	−	0.331817i	0.456707	−	0.331817i
$928$	2.61654	−	8.05287i	2.61654	−	8.05287i
$929$	0.292867	−	0.901352i	0.292867	−	0.901352i	−0.691063	−	0.722795i	$-0.742857\pi$
$929$	0.292867	−	0.901352i	0.292867	−	0.901352i	0.983930	−	0.178557i	$-0.0571429\pi$
$930$		0			0
$931$	−0.427100	−	1.31448i	−0.427100	−	1.31448i
$932$	0.771162			0.771162
$933$	−0.643274	−	1.97979i	−0.643274	−	1.97979i
$934$		0			0
$935$		0			0
$936$		0			0
$937$		0			0		−0.809017	−	0.587785i	$-0.800000\pi$
$937$		0			0		0.809017	+	0.587785i	$0.200000\pi$
$938$		0			0
$939$	2.19565	−	1.59523i	2.19565	−	1.59523i
$940$		0			0
$941$	−1.59203	−	1.15668i	−1.59203	−	1.15668i	−0.900969	−	0.433884i	$-0.857143\pi$
$941$	−1.59203	−	1.15668i	−1.59203	−	1.15668i	−0.691063	−	0.722795i	$-0.742857\pi$
$942$	−0.719934	−	2.21573i	−0.719934	−	2.21573i
$943$		0			0
$944$		0			0
$945$		0			0
$946$		0			0
$947$	−0.0277280	+	0.0853380i	−0.0277280	+	0.0853380i	−0.963963	−	0.266037i	$-0.914286\pi$
$947$	−0.0277280	+	0.0853380i	−0.0277280	+	0.0853380i	0.936235	+	0.351375i	$0.114286\pi$
$948$	−6.55381	+	4.76162i	−6.55381	+	4.76162i
$949$		0			0
$950$	0.605219	−	2.65164i	0.605219	−	2.65164i
$951$		0			0
$952$		0			0
$953$	0.578625	−	1.78082i	0.578625	−	1.78082i	−0.0448648	−	0.998993i	$-0.514286\pi$
$953$	0.578625	−	1.78082i	0.578625	−	1.78082i	0.623490	−	0.781831i	$-0.285714\pi$
$954$		0			0
$955$	−0.735927	+	0.276198i	−0.735927	+	0.276198i
$956$		0			0
$957$		0			0
$958$		0			0
$959$		0			0
$960$	−7.73315	−	2.13421i	−7.73315	−	2.13421i
$961$	−0.809017	+	0.587785i	−0.809017	+	0.587785i
$962$		0			0
$963$	1.66044	+	1.20638i	1.66044	+	1.20638i
$964$		0			0
$965$		0			0
$966$		0			0
$967$		0			0		−0.309017	−	0.951057i	$-0.600000\pi$
$967$		0			0		0.309017	+	0.951057i	$0.400000\pi$
$968$	3.68476			3.68476
$969$		0			0
$970$		0			0
$971$	0.190983	−	0.587785i	0.190983	−	0.587785i	−0.809017	−	0.587785i	$-0.800000\pi$
$971$	0.190983	−	0.587785i	0.190983	−	0.587785i	1.00000			$0$
$972$	−1.24056	+	3.81805i	−1.24056	+	3.81805i
$973$		0			0
$974$		0			0
$975$		0			0
$976$		0			0
$977$	−1.38900	+	1.00917i	−1.38900	+	1.00917i	−0.393025	+	0.919528i	$0.628571\pi$
$977$	−1.38900	+	1.00917i	−1.38900	+	1.00917i	−0.995974	+	0.0896393i	$0.971429\pi$
$978$		0			0
$979$		0			0
$980$	1.79096	+	2.24579i	1.79096	+	2.24579i
$981$	−0.174446	−	0.536891i	−0.174446	−	0.536891i
$982$		0			0
$983$	0.292867	+	0.901352i	0.292867	+	0.901352i	0.983930	+	0.178557i	$0.0571429\pi$
$983$	0.292867	+	0.901352i	0.292867	+	0.901352i	−0.691063	+	0.722795i	$0.742857\pi$
$984$		0			0
$985$		0			0
$986$		0			0
$987$		0			0
$988$		0			0
$989$		0			0
$990$		0			0
$991$		0			0		−0.809017	−	0.587785i	$-0.800000\pi$
$991$		0			0		0.809017	+	0.587785i	$0.200000\pi$
$992$		0			0
$993$		0			0
$994$		0			0
$995$	−1.08409	+	1.64232i	−1.08409	+	1.64232i
$996$	−2.40904	+	7.41426i	−2.40904	+	7.41426i
$997$	0.578625	−	1.78082i	0.578625	−	1.78082i	−0.0448648	−	0.998993i	$-0.514286\pi$
$997$	0.578625	−	1.78082i	0.578625	−	1.78082i	0.623490	−	0.781831i	$-0.285714\pi$
$998$	−2.39783	+	1.74212i	−2.39783	+	1.74212i
$999$	−0.558861			−0.558861

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1775.1.p.b.1561.1	yes	24
25.16	even	5	inner	1775.1.p.b.141.1	✓	24
71.70	odd	2	CM	1775.1.p.b.1561.1	yes	24
1775.141	odd	10	inner	1775.1.p.b.141.1	✓	24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1775.1.p.b.141.1	✓	24	25.16	even	5	inner
1775.1.p.b.141.1	✓	24	1775.141	odd	10	inner
1775.1.p.b.1561.1	yes	24	1.1	even	1	trivial
1775.1.p.b.1561.1	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.p (of order \(10\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.59203 + 1.15668i) q^{2} +(0.465424 - 1.43243i) q^{3} +(0.887642 - 2.73188i) q^{4} +(-0.550897 + 0.834573i) q^{5} +(0.915888 + 2.81881i) q^{6} +(1.13865 + 3.50441i) q^{8} +(-1.02621 - 0.745586i) q^{9} +O(q^{10})\)	\(q+(-1.59203 + 1.15668i) q^{2} +(0.465424 - 1.43243i) q^{3} +(0.887642 - 2.73188i) q^{4} +(-0.550897 + 0.834573i) q^{5} +(0.915888 + 2.81881i) q^{6} +(1.13865 + 3.50441i) q^{8} +(-1.02621 - 0.745586i) q^{9} +(-0.0882877 - 1.96588i) q^{10} +(-3.50009 - 2.54296i) q^{12} +(0.939065 + 1.17755i) q^{15} +(-3.54237 - 2.57368i) q^{16} +2.49616 q^{18} +(-0.427100 - 1.31448i) q^{19} +(1.79096 + 2.24579i) q^{20} +5.54977 q^{24} +(-0.393025 - 0.919528i) q^{25} +(-0.327125 + 0.237670i) q^{27} +(0.530551 - 1.63287i) q^{29} +(-2.85707 - 0.788501i) q^{30} +4.93174 q^{32} +(-2.94776 + 2.14167i) q^{36} +(1.11816 + 0.812393i) q^{37} +(2.20039 + 1.59867i) q^{38} +(-3.55197 - 0.980281i) q^{40} -1.92793 q^{43} +(1.18758 - 0.445707i) q^{45} +(-5.33532 + 3.87634i) q^{48} +1.00000 q^{49} +(1.68931 + 1.00931i) q^{50} +(0.245885 - 0.756757i) q^{54} -2.08168 q^{57} +(1.04405 + 3.21325i) q^{58} +(4.05048 - 1.52017i) q^{60} +(-4.30911 + 3.13075i) q^{64} +(0.309017 - 0.951057i) q^{71} +(1.44434 - 4.44523i) q^{72} +(1.55972 - 1.13321i) q^{73} -2.71983 q^{74} +(-1.50008 + 0.135010i) q^{75} -3.97011 q^{76} +(0.578625 - 1.78082i) q^{79} +(4.09941 - 1.53853i) q^{80} +(-0.203784 - 0.627183i) q^{81} +(-0.556829 - 1.71374i) q^{83} +(3.06932 - 2.22999i) q^{86} +(-2.09203 - 1.51995i) q^{87} +(-1.21850 + 0.885289i) q^{89} +(-1.37513 + 2.08323i) q^{90} +(1.33232 + 0.367696i) q^{95} +(2.29535 - 7.06435i) q^{96} +(-1.59203 + 1.15668i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q - 3 q^{2} + 2 q^{3} - 9 q^{4} + q^{5} - q^{6} - q^{8} - 4 q^{9}+O(q^{10}) \) 24 * q - 3 * q^2 + 2 * q^3 - 9 * q^4 + q^5 - q^6 - q^8 - 4 * q^9	\( 24 q - 3 q^{2} + 2 q^{3} - 9 q^{4} + q^{5} - q^{6} - q^{8} - 4 q^{9} - 3 q^{10} - 4 q^{12} + 2 q^{15} - 7 q^{16} - 8 q^{18} - 3 q^{19} - 9 q^{20} - 16 q^{24} + q^{25} - q^{27} - 3 q^{29} - 3 q^{30} - 4 q^{32} - 3 q^{36} + 2 q^{37} + 20 q^{38} - q^{40} + 2 q^{43} - 2 q^{45} - 14 q^{48} + 24 q^{49} + 2 q^{50} - 2 q^{54} + 4 q^{57} - q^{58} + 29 q^{60} - 10 q^{64} - 6 q^{71} + 23 q^{72} - 3 q^{73} - 10 q^{74} - 5 q^{75} - 4 q^{76} - 3 q^{79} + 28 q^{80} - 7 q^{81} + 2 q^{83} + 4 q^{86} - 15 q^{87} - 3 q^{89} - 6 q^{90} + 2 q^{95} + 23 q^{96} - 3 q^{98}+O(q^{100}) \) 24 * q - 3 * q^2 + 2 * q^3 - 9 * q^4 + q^5 - q^6 - q^8 - 4 * q^9 - 3 * q^10 - 4 * q^12 + 2 * q^15 - 7 * q^16 - 8 * q^18 - 3 * q^19 - 9 * q^20 - 16 * q^24 + q^25 - q^27 - 3 * q^29 - 3 * q^30 - 4 * q^32 - 3 * q^36 + 2 * q^37 + 20 * q^38 - q^40 + 2 * q^43 - 2 * q^45 - 14 * q^48 + 24 * q^49 + 2 * q^50 - 2 * q^54 + 4 * q^57 - q^58 + 29 * q^60 - 10 * q^64 - 6 * q^71 + 23 * q^72 - 3 * q^73 - 10 * q^74 - 5 * q^75 - 4 * q^76 - 3 * q^79 + 28 * q^80 - 7 * q^81 + 2 * q^83 + 4 * q^86 - 15 * q^87 - 3 * q^89 - 6 * q^90 + 2 * q^95 + 23 * q^96 - 3 * q^98

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