LMFDB - Embedded newform 1775.1.p.b.141.2

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			141.2
Root			$-0.995974 + 0.0896393i$ of defining polynomial
Character	$\chi$	$=$	1775.141
Dual form			1775.1.p.b.1561.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.21850 - 0.885289i) q^{2} +(-0.595762 - 1.83357i) q^{3} +(0.391978 + 1.20638i) q^{4} +(-0.691063 + 0.722795i) q^{5} +(-0.897302 + 2.76161i) q^{6} +(0.124951 - 0.384559i) q^{8} +(-2.19802 + 1.59695i) q^{9} +O(q^{10})$	\(q+(-1.21850 - 0.885289i) q^{2} +(-0.595762 - 1.83357i) q^{3} +(0.391978 + 1.20638i) q^{4} +(-0.691063 + 0.722795i) q^{5} +(-0.897302 + 2.76161i) q^{6} +(0.124951 - 0.384559i) q^{8} +(-2.19802 + 1.59695i) q^{9} +(1.48194 - 0.268932i) q^{10} +(1.97846 - 1.43743i) q^{12} +(1.73700 + 0.836496i) q^{15} +(0.533514 - 0.387620i) q^{16} +4.09204 q^{18} +(-0.615546 + 1.89446i) q^{19} +(-1.14285 - 0.550367i) q^{20} -0.779555 q^{24} +(-0.0448648 - 0.998993i) q^{25} +(2.67789 + 1.94560i) q^{27} +(-0.340473 - 1.04787i) q^{29} +(-1.37599 - 2.55701i) q^{30} -1.39759 q^{32} +(-2.78811 - 2.02568i) q^{36} +(1.61152 - 1.17084i) q^{37} +(2.42718 - 1.76345i) q^{38} +(0.191608 + 0.356068i) q^{40} +0.947737 q^{43} +(0.364698 - 2.69231i) q^{45} +(-1.02857 - 0.747303i) q^{48} +1.00000 q^{49} +(-0.829730 + 1.25699i) q^{50} +(-1.54058 - 4.74141i) q^{54} +3.84033 q^{57} +(-0.512801 + 1.57824i) q^{58} +(-0.328269 + 2.42338i) q^{60} +(1.16944 + 0.849649i) q^{64} +(0.309017 + 0.951057i) q^{71} +(0.339478 + 1.04481i) q^{72} +(-0.766736 - 0.557066i) q^{73} -3.00016 q^{74} +(-1.80499 + 0.677425i) q^{75} -2.52672 q^{76} +(0.0829607 + 0.255327i) q^{79} +(-0.0885214 + 0.653491i) q^{80} +(1.13243 - 3.48527i) q^{81} +(-0.137526 + 0.423260i) q^{83} +(-1.15481 - 0.839021i) q^{86} +(-1.71850 + 1.24856i) q^{87} +(1.55972 + 1.13321i) q^{89} +(-2.82785 + 2.95770i) q^{90} +(-0.943922 - 1.75410i) q^{95} +(0.832630 + 2.56257i) q^{96} +(-1.21850 - 0.885289i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $\left(\mathbb{Z}/1775\mathbb{Z}\right)^\times$.

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

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 $

$2$	−1.21850	−	0.885289i	−1.21850	−	0.885289i	−0.222521	−	0.974928i	$-0.571429\pi$
$2$	−1.21850	−	0.885289i	−1.21850	−	0.885289i	−0.995974	+	0.0896393i	$0.971429\pi$
$3$	−0.595762	−	1.83357i	−0.595762	−	1.83357i	−0.550897	−	0.834573i	$-0.685714\pi$
$3$	−0.595762	−	1.83357i	−0.595762	−	1.83357i	−0.0448648	−	0.998993i	$-0.514286\pi$
$4$	0.391978	+	1.20638i	0.391978	+	1.20638i
$5$	−0.691063	+	0.722795i	−0.691063	+	0.722795i
$5$	−0.691063	+	0.722795i	−0.691063	+	0.722795i
$6$	−0.897302	+	2.76161i	−0.897302	+	2.76161i
$7$		0			0		1.00000			$0$
$7$		0			0		−1.00000			$\pi$
$8$	0.124951	−	0.384559i	0.124951	−	0.384559i
$9$	−2.19802	+	1.59695i	−2.19802	+	1.59695i
$10$	1.48194	−	0.268932i	1.48194	−	0.268932i
$11$		0			0		−0.809017	−	0.587785i	$-0.800000\pi$
$11$		0			0		0.809017	+	0.587785i	$0.200000\pi$
$12$	1.97846	−	1.43743i	1.97846	−	1.43743i
$13$		0			0		0.809017	−	0.587785i	$-0.200000\pi$
$13$		0			0		−0.809017	+	0.587785i	$0.800000\pi$
$14$		0			0
$15$	1.73700	+	0.836496i	1.73700	+	0.836496i
$16$	0.533514	−	0.387620i	0.533514	−	0.387620i
$17$		0			0		0.309017	−	0.951057i	$-0.400000\pi$
$17$		0			0		−0.309017	+	0.951057i	$0.600000\pi$
$18$	4.09204			4.09204
$19$	−0.615546	+	1.89446i	−0.615546	+	1.89446i	−0.222521	+	0.974928i	$0.571429\pi$
$19$	−0.615546	+	1.89446i	−0.615546	+	1.89446i	−0.393025	+	0.919528i	$0.628571\pi$
$20$	−1.14285	−	0.550367i	−1.14285	−	0.550367i
$21$		0			0
$22$		0			0
$23$		0			0		−0.809017	−	0.587785i	$-0.800000\pi$
$23$		0			0		0.809017	+	0.587785i	$0.200000\pi$
$24$	−0.779555			−0.779555
$25$	−0.0448648	−	0.998993i	−0.0448648	−	0.998993i
$26$		0			0
$27$	2.67789	+	1.94560i	2.67789	+	1.94560i
$28$		0			0
$29$	−0.340473	−	1.04787i	−0.340473	−	1.04787i	−0.963963	−	0.266037i	$-0.914286\pi$
$29$	−0.340473	−	1.04787i	−0.340473	−	1.04787i	0.623490	−	0.781831i	$-0.285714\pi$
$30$	−1.37599	−	2.55701i	−1.37599	−	2.55701i
$31$		0			0		0.309017	−	0.951057i	$-0.400000\pi$
$31$		0			0		−0.309017	+	0.951057i	$0.600000\pi$
$32$	−1.39759			−1.39759
$33$		0			0
$34$		0			0
$35$		0			0
$36$	−2.78811	−	2.02568i	−2.78811	−	2.02568i
$37$	1.61152	−	1.17084i	1.61152	−	1.17084i	0.753071	−	0.657939i	$-0.228571\pi$
$37$	1.61152	−	1.17084i	1.61152	−	1.17084i	0.858449	−	0.512899i	$-0.171429\pi$
$38$	2.42718	−	1.76345i	2.42718	−	1.76345i
$39$		0			0
$40$	0.191608	+	0.356068i	0.191608	+	0.356068i
$41$		0			0		0.809017	−	0.587785i	$-0.200000\pi$
$41$		0			0		−0.809017	+	0.587785i	$0.800000\pi$
$42$		0			0
$43$	0.947737			0.947737			0.473869	−	0.880596i	$-0.342857\pi$
$43$	0.947737			0.947737			0.473869	+	0.880596i	$0.342857\pi$
$44$		0			0
$45$	0.364698	−	2.69231i	0.364698	−	2.69231i
$46$		0			0
$47$		0			0		−0.309017	−	0.951057i	$-0.600000\pi$
$47$		0			0		0.309017	+	0.951057i	$0.400000\pi$
$48$	−1.02857	−	0.747303i	−1.02857	−	0.747303i
$49$	1.00000			1.00000
$50$	−0.829730	+	1.25699i	−0.829730	+	1.25699i
$51$		0			0
$52$		0			0
$53$		0			0		−0.309017	−	0.951057i	$-0.600000\pi$
$53$		0			0		0.309017	+	0.951057i	$0.400000\pi$
$54$	−1.54058	−	4.74141i	−1.54058	−	4.74141i
$55$		0			0
$56$		0			0
$57$	3.84033			3.84033
$58$	−0.512801	+	1.57824i	−0.512801	+	1.57824i
$59$		0			0		0.809017	−	0.587785i	$-0.200000\pi$
$59$		0			0		−0.809017	+	0.587785i	$0.800000\pi$
$60$	−0.328269	+	2.42338i	−0.328269	+	2.42338i
$61$		0			0		−0.809017	−	0.587785i	$-0.800000\pi$
$61$		0			0		0.809017	+	0.587785i	$0.200000\pi$
$62$		0			0
$63$		0			0
$64$	1.16944	+	0.849649i	1.16944	+	0.849649i
$65$		0			0
$66$		0			0
$67$		0			0		0.309017	−	0.951057i	$-0.400000\pi$
$67$		0			0		−0.309017	+	0.951057i	$0.600000\pi$
$68$		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
$72$	0.339478	+	1.04481i	0.339478	+	1.04481i
$73$	−0.766736	−	0.557066i	−0.766736	−	0.557066i	0.134233	−	0.990950i	$-0.457143\pi$
$73$	−0.766736	−	0.557066i	−0.766736	−	0.557066i	−0.900969	+	0.433884i	$0.857143\pi$
$74$	−3.00016			−3.00016
$75$	−1.80499	+	0.677425i	−1.80499	+	0.677425i
$76$	−2.52672			−2.52672
$77$		0			0
$78$		0			0
$79$	0.0829607	+	0.255327i	0.0829607	+	0.255327i	0.983930	−	0.178557i	$-0.0571429\pi$
$79$	0.0829607	+	0.255327i	0.0829607	+	0.255327i	−0.900969	+	0.433884i	$0.857143\pi$
$80$	−0.0885214	+	0.653491i	−0.0885214	+	0.653491i
$81$	1.13243	−	3.48527i	1.13243	−	3.48527i
$82$		0			0
$83$	−0.137526	+	0.423260i	−0.137526	+	0.423260i	−0.995974	−	0.0896393i	$-0.971429\pi$
$83$	−0.137526	+	0.423260i	−0.137526	+	0.423260i	0.858449	+	0.512899i	$0.171429\pi$
$84$		0			0
$85$		0			0
$86$	−1.15481	−	0.839021i	−1.15481	−	0.839021i
$87$	−1.71850	+	1.24856i	−1.71850	+	1.24856i
$88$		0			0
$89$	1.55972	+	1.13321i	1.55972	+	1.13321i	0.936235	+	0.351375i	$0.114286\pi$
$89$	1.55972	+	1.13321i	1.55972	+	1.13321i	0.623490	+	0.781831i	$0.285714\pi$
$90$	−2.82785	+	2.95770i	−2.82785	+	2.95770i
$91$		0			0
$92$		0			0
$93$		0			0
$94$		0			0
$95$	−0.943922	−	1.75410i	−0.943922	−	1.75410i
$96$	0.832630	+	2.56257i	0.832630	+	2.56257i
$97$		0			0		−0.309017	−	0.951057i	$-0.600000\pi$
$97$		0			0		0.309017	+	0.951057i	$0.400000\pi$
$98$	−1.21850	−	0.885289i	−1.21850	−	0.885289i
$99$		0			0
$100$	1.18758	−	0.445707i	1.18758	−	0.445707i
$101$	1.71690			1.71690			0.858449	−	0.512899i	$-0.171429\pi$
$101$	1.71690			1.71690			0.858449	+	0.512899i	$0.171429\pi$
$102$		0			0
$103$	0.385338	+	1.18595i	0.385338	+	1.18595i	0.936235	+	0.351375i	$0.114286\pi$
$103$	0.385338	+	1.18595i	0.385338	+	1.18595i	−0.550897	+	0.834573i	$0.685714\pi$
$104$		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	$0.800000\pi$
$108$	−1.29747	+	3.99319i	−1.29747	+	3.99319i
$109$	−1.00883	+	0.732956i	−1.00883	+	0.732956i	−0.963963	−	0.266037i	$-0.914286\pi$
$109$	−1.00883	+	0.732956i	−1.00883	+	0.732956i	−0.0448648	+	0.998993i	$0.514286\pi$
$110$		0			0
$111$	−3.10689	−	2.25729i	−3.10689	−	2.25729i
$112$		0			0
$113$		0			0		0.809017	−	0.587785i	$-0.200000\pi$
$113$		0			0		−0.809017	+	0.587785i	$0.800000\pi$
$114$	−4.67942	−	3.39980i	−4.67942	−	3.39980i
$115$		0			0
$116$	1.13067	−	0.821482i	1.13067	−	0.821482i
$117$		0			0
$118$		0			0
$119$		0			0
$120$	0.538721	−	0.563458i	0.538721	−	0.563458i
$121$	0.309017	+	0.951057i	0.309017	+	0.951057i
$122$		0			0
$123$		0			0
$124$		0			0
$125$	0.753071	+	0.657939i	0.753071	+	0.657939i
$126$		0			0
$127$		0			0		−0.809017	−	0.587785i	$-0.800000\pi$
$127$		0			0		0.809017	+	0.587785i	$0.200000\pi$
$128$	−0.240896	−	0.741401i	−0.240896	−	0.741401i
$129$	−0.564626	−	1.73774i	−0.564626	−	1.73774i
$130$		0			0
$131$	0.608102	−	1.87155i	0.608102	−	1.87155i	0.134233	−	0.990950i	$-0.457143\pi$
$131$	0.608102	−	1.87155i	0.608102	−	1.87155i	0.473869	−	0.880596i	$-0.342857\pi$
$132$		0			0
$133$		0			0
$134$		0			0
$135$	−3.25686	+	0.591032i	−3.25686	+	0.591032i
$136$		0			0
$137$		0			0		0.809017	−	0.587785i	$-0.200000\pi$
$137$		0			0		−0.809017	+	0.587785i	$0.800000\pi$
$138$		0			0
$139$		0			0		−0.809017	−	0.587785i	$-0.800000\pi$
$139$		0			0		0.809017	+	0.587785i	$0.200000\pi$
$140$		0			0
$141$		0			0
$142$	0.465424	−	1.43243i	0.465424	−	1.43243i
$143$		0			0
$144$	−0.553661	+	1.70399i	−0.553661	+	1.70399i
$145$	0.992682	+	0.478050i	0.992682	+	0.478050i
$146$	0.441099	+	1.35756i	0.441099	+	1.35756i
$147$	−0.595762	−	1.83357i	−0.595762	−	1.83357i
$148$	2.04416	+	1.48517i	2.04416	+	1.48517i
$149$		0			0		1.00000			$0$
$149$		0			0		−1.00000			$\pi$
$150$	2.79909	+	0.772500i	2.79909	+	0.772500i
$151$	1.87247			1.87247			0.936235	−	0.351375i	$-0.114286\pi$
$151$	1.87247			1.87247			0.936235	+	0.351375i	$0.114286\pi$
$152$	0.651617	+	0.473427i	0.651617	+	0.473427i
$153$		0			0
$154$		0			0
$155$		0			0
$156$		0			0
$157$	−0.0897297			−0.0897297			−0.0448648	−	0.998993i	$-0.514286\pi$
$157$	−0.0897297			−0.0897297			−0.0448648	+	0.998993i	$0.514286\pi$
$158$	0.124951	−	0.384559i	0.124951	−	0.384559i
$159$		0			0
$160$	0.965821	−	1.01017i	0.965821	−	1.01017i
$161$		0			0
$162$	−4.46534	+	3.24426i	−4.46534	+	3.24426i
$163$		0			0		0.809017	−	0.587785i	$-0.200000\pi$
$163$		0			0		−0.809017	+	0.587785i	$0.800000\pi$
$164$		0			0
$165$		0			0
$166$	0.542281	−	0.393990i	0.542281	−	0.393990i
$167$	−0.556829	+	1.71374i	−0.556829	+	1.71374i	0.134233	+	0.990950i	$0.457143\pi$
$167$	−0.556829	+	1.71374i	−0.556829	+	1.71374i	−0.691063	+	0.722795i	$0.742857\pi$
$168$		0			0
$169$	0.309017	−	0.951057i	0.309017	−	0.951057i
$170$		0			0
$171$	−1.67238	−	5.14704i	−1.67238	−	5.14704i
$172$	0.371492	+	1.14333i	0.371492	+	1.14333i
$173$		0			0		−0.809017	−	0.587785i	$-0.800000\pi$
$173$		0			0		0.809017	+	0.587785i	$0.200000\pi$
$174$	3.19931			3.19931
$175$		0			0
$176$		0			0
$177$		0			0
$178$	−0.897302	−	2.76161i	−0.897302	−	2.76161i
$179$	0.292867	+	0.901352i	0.292867	+	0.901352i	0.983930	+	0.178557i	$0.0571429\pi$
$179$	0.292867	+	0.901352i	0.292867	+	0.901352i	−0.691063	+	0.722795i	$0.742857\pi$
$180$	3.39091	−	0.615359i	3.39091	−	0.615359i
$181$		0			0		0.309017	−	0.951057i	$-0.400000\pi$
$181$		0			0		−0.309017	+	0.951057i	$0.600000\pi$
$182$		0			0
$183$		0			0
$184$		0			0
$185$	−0.267386	+	1.97392i	−0.267386	+	1.97392i
$186$		0			0
$187$		0			0
$188$		0			0
$189$		0			0
$190$	−0.402721	+	2.97301i	−0.402721	+	2.97301i
$191$	0.0725928	−	0.0527418i	0.0725928	−	0.0527418i	−0.550897	−	0.834573i	$-0.685714\pi$
$191$	0.0725928	−	0.0527418i	0.0725928	−	0.0527418i	0.623490	+	0.781831i	$0.285714\pi$
$192$	0.861179	−	2.65044i	0.861179	−	2.65044i
$193$		0			0		1.00000			$0$
$193$		0			0		−1.00000			$\pi$
$194$		0			0
$195$		0			0
$196$	0.391978	+	1.20638i	0.391978	+	1.20638i
$197$		0			0		−0.309017	−	0.951057i	$-0.600000\pi$
$197$		0			0		0.309017	+	0.951057i	$0.400000\pi$
$198$		0			0
$199$	1.50614			1.50614			0.753071	−	0.657939i	$-0.228571\pi$
$199$	1.50614			1.50614			0.753071	+	0.657939i	$0.228571\pi$
$200$	−0.389777	−	0.107572i	−0.389777	−	0.107572i
$201$		0			0
$202$	−2.09203	−	1.51995i	−2.09203	−	1.51995i
$203$		0			0
$204$		0			0
$205$		0			0
$206$	0.580374	−	1.78621i	0.580374	−	1.78621i
$207$		0			0
$208$		0			0
$209$		0			0
$210$		0			0
$211$		0			0		−0.809017	−	0.587785i	$-0.800000\pi$
$211$		0			0		0.809017	+	0.587785i	$0.200000\pi$
$212$		0			0
$213$	1.55972	−	1.13321i	1.55972	−	1.13321i
$214$	1.97157	+	1.43243i	1.97157	+	1.43243i
$215$	−0.654946	+	0.685020i	−0.654946	+	0.685020i
$216$	1.08280	−	0.786701i	1.08280	−	0.786701i
$217$		0			0
$218$	1.87813			1.87813
$219$	−0.564626	+	1.73774i	−0.564626	+	1.73774i
$220$		0			0
$221$		0			0
$222$	1.78738	+	5.50099i	1.78738	+	5.50099i
$223$	1.61152	+	1.17084i	1.61152	+	1.17084i	0.858449	+	0.512899i	$0.171429\pi$
$223$	1.61152	+	1.17084i	1.61152	+	1.17084i	0.753071	+	0.657939i	$0.228571\pi$
$224$		0			0
$225$	1.69396	+	2.12416i	1.69396	+	2.12416i
$226$		0			0
$227$		0			0		−0.809017	−	0.587785i	$-0.800000\pi$
$227$		0			0		0.809017	+	0.587785i	$0.200000\pi$
$228$	1.50532	+	4.63291i	1.50532	+	4.63291i
$229$	−0.427100	−	1.31448i	−0.427100	−	1.31448i	−0.900969	−	0.433884i	$-0.857143\pi$
$229$	−0.427100	−	1.31448i	−0.427100	−	1.31448i	0.473869	−	0.880596i	$-0.342857\pi$
$230$		0			0
$231$		0			0
$232$	−0.445509			−0.445509
$233$	0.530551	−	1.63287i	0.530551	−	1.63287i	−0.222521	−	0.974928i	$-0.571429\pi$
$233$	0.530551	−	1.63287i	0.530551	−	1.63287i	0.753071	−	0.657939i	$-0.228571\pi$
$234$		0			0
$235$		0			0
$236$		0			0
$237$	0.418734	−	0.304228i	0.418734	−	0.304228i
$238$		0			0
$239$		0			0		−0.809017	−	0.587785i	$-0.800000\pi$
$239$		0			0		0.809017	+	0.587785i	$0.200000\pi$
$240$	1.25096	−	0.227015i	1.25096	−	0.227015i
$241$		0			0		0.809017	−	0.587785i	$-0.200000\pi$
$241$		0			0		−0.809017	+	0.587785i	$0.800000\pi$
$242$	0.465424	−	1.43243i	0.465424	−	1.43243i
$243$	−3.75509			−3.75509
$244$		0			0
$245$	−0.691063	+	0.722795i	−0.691063	+	0.722795i
$246$		0			0
$247$		0			0
$248$		0			0
$249$	0.858008			0.858008
$250$	−0.335148	−	1.46838i	−0.335148	−	1.46838i
$251$	−0.786050			−0.786050			−0.393025	−	0.919528i	$-0.628571\pi$
$251$	−0.786050			−0.786050			−0.393025	+	0.919528i	$0.628571\pi$
$252$		0			0
$253$		0			0
$254$		0			0
$255$		0			0
$256$	0.0838636	−	0.258106i	0.0838636	−	0.258106i
$257$		0			0		1.00000			$0$
$257$		0			0		−1.00000			$\pi$
$258$	−0.850407	+	2.61728i	−0.850407	+	2.61728i
$259$		0			0
$260$		0			0
$261$	2.42176	+	1.75951i	2.42176	+	1.75951i
$262$	−2.39783	+	1.74212i	−2.39783	+	1.74212i
$263$	−0.217194	+	0.157801i	−0.217194	+	0.157801i	−0.691063	−	0.722795i	$-0.742857\pi$
$263$	−0.217194	+	0.157801i	−0.217194	+	0.157801i	0.473869	+	0.880596i	$0.342857\pi$
$264$		0			0
$265$		0			0
$266$		0			0
$267$	1.14858	−	3.53498i	1.14858	−	3.53498i
$268$		0			0
$269$		0			0		0.309017	−	0.951057i	$-0.400000\pi$
$269$		0			0		−0.309017	+	0.951057i	$0.600000\pi$
$270$	4.49170	+	2.16309i	4.49170	+	2.16309i
$271$	−0.0277280	−	0.0853380i	−0.0277280	−	0.0853380i	0.936235	−	0.351375i	$-0.114286\pi$
$271$	−0.0277280	−	0.0853380i	−0.0277280	−	0.0853380i	−0.963963	+	0.266037i	$0.914286\pi$
$272$		0			0
$273$		0			0
$274$		0			0
$275$		0			0
$276$		0			0
$277$	−1.38900	−	1.00917i	−1.38900	−	1.00917i	−0.995974	−	0.0896393i	$-0.971429\pi$
$277$	−1.38900	−	1.00917i	−1.38900	−	1.00917i	−0.393025	−	0.919528i	$-0.628571\pi$
$278$		0			0
$279$		0			0
$280$		0			0
$281$		0			0		0.309017	−	0.951057i	$-0.400000\pi$
$281$		0			0		−0.309017	+	0.951057i	$0.600000\pi$
$282$		0			0
$283$		0			0		0.309017	−	0.951057i	$-0.400000\pi$
$283$		0			0		−0.309017	+	0.951057i	$0.600000\pi$
$284$	−1.02621	+	0.745586i	−1.02621	+	0.745586i
$285$	−2.65391	+	2.77577i	−2.65391	+	2.77577i
$286$		0			0
$287$		0			0
$288$	3.07192	−	2.23188i	3.07192	−	2.23188i
$289$	−0.809017	−	0.587785i	−0.809017	−	0.587785i
$290$	−0.786366	−	1.46131i	−0.786366	−	1.46131i
$291$		0			0
$292$	0.371492	−	1.14333i	0.371492	−	1.14333i
$293$	2.00000			2.00000			1.00000			$0$
$293$	2.00000			2.00000			1.00000			$0$
$294$	−0.897302	+	2.76161i	−0.897302	+	2.76161i
$295$		0			0
$296$	−0.248895	−	0.766021i	−0.248895	−	0.766021i
$297$		0			0
$298$		0			0
$299$		0			0
$300$	−1.52475	−	1.91198i	−1.52475	−	1.91198i
$301$		0			0
$302$	−2.28160	−	1.65768i	−2.28160	−	1.65768i
$303$	−1.02286	−	3.14805i	−1.02286	−	3.14805i
$304$	0.405927	+	1.24932i	0.405927	+	1.24932i
$305$		0			0
$306$		0			0
$307$		0			0		1.00000			$0$
$307$		0			0		−1.00000			$\pi$
$308$		0			0
$309$	1.94494	−	1.41309i	1.94494	−	1.41309i
$310$		0			0
$311$	1.61152	+	1.17084i	1.61152	+	1.17084i	0.858449	+	0.512899i	$0.171429\pi$
$311$	1.61152	+	1.17084i	1.61152	+	1.17084i	0.753071	+	0.657939i	$0.228571\pi$
$312$		0			0
$313$	0.360046	−	0.261589i	0.360046	−	0.261589i	−0.393025	−	0.919528i	$-0.628571\pi$
$313$	0.360046	−	0.261589i	0.360046	−	0.261589i	0.753071	+	0.657939i	$0.228571\pi$
$314$	0.109335	+	0.0794366i	0.109335	+	0.0794366i
$315$		0			0
$316$	−0.275503	+	0.200165i	−0.275503	+	0.200165i
$317$		0			0		0.309017	−	0.951057i	$-0.400000\pi$
$317$		0			0		−0.309017	+	0.951057i	$0.600000\pi$
$318$		0			0
$319$		0			0
$320$	−1.42228	+	0.258106i	−1.42228	+	0.258106i
$321$	0.963963	+	2.96677i	0.963963	+	2.96677i
$322$		0			0
$323$		0			0
$324$	4.64847			4.64847
$325$		0			0
$326$		0			0
$327$	1.94494	+	1.41309i	1.94494	+	1.41309i
$328$		0			0
$329$		0			0
$330$		0			0
$331$		0			0		0.309017	−	0.951057i	$-0.400000\pi$
$331$		0			0		−0.309017	+	0.951057i	$0.600000\pi$
$332$	−0.564521			−0.564521
$333$	−1.67238	+	5.14704i	−1.67238	+	5.14704i
$334$	2.19565	−	1.59523i	2.19565	−	1.59523i
$335$		0			0
$336$		0			0
$337$		0			0		0.809017	−	0.587785i	$-0.200000\pi$
$337$		0			0		−0.809017	+	0.587785i	$0.800000\pi$
$338$	−1.21850	+	0.885289i	−1.21850	+	0.885289i
$339$		0			0
$340$		0			0
$341$		0			0
$342$	−2.51884	+	7.75218i	−2.51884	+	7.75218i
$343$		0			0
$344$	0.118420	−	0.364461i	0.118420	−	0.364461i
$345$		0			0
$346$		0			0
$347$		0			0		−0.309017	−	0.951057i	$-0.600000\pi$
$347$		0			0		0.309017	+	0.951057i	$0.400000\pi$
$348$	−2.17985	−	1.58376i	−2.17985	−	1.58376i
$349$		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	$-0.600000\pi$
$353$		0			0		0.309017	+	0.951057i	$0.400000\pi$
$354$		0			0
$355$	−0.900969	−	0.433884i	−0.900969	−	0.433884i
$356$	−0.755704	+	2.32582i	−0.755704	+	2.32582i
$357$		0			0
$358$	0.441099	−	1.35756i	0.441099	−	1.35756i
$359$	1.11816	−	0.812393i	1.11816	−	0.812393i	0.134233	−	0.990950i	$-0.457143\pi$
$359$	1.11816	−	0.812393i	1.11816	−	0.812393i	0.983930	+	0.178557i	$0.0571429\pi$
$360$	−0.989782	−	0.476654i	−0.989782	−	0.476654i
$361$	−2.40105	−	1.74446i	−2.40105	−	1.74446i
$362$		0			0
$363$	1.55972	−	1.13321i	1.55972	−	1.13321i
$364$		0			0
$365$	0.932507	−	0.169225i	0.932507	−	0.169225i
$366$		0			0
$367$	−0.556829	+	1.71374i	−0.556829	+	1.71374i	0.134233	+	0.990950i	$0.457143\pi$
$367$	−0.556829	+	1.71374i	−0.556829	+	1.71374i	−0.691063	+	0.722795i	$0.742857\pi$
$368$		0			0
$369$		0			0
$370$	2.07330	−	2.16850i	2.07330	−	2.16850i
$371$		0			0
$372$		0			0
$373$	1.11816	+	0.812393i	1.11816	+	0.812393i	0.983930	−	0.178557i	$-0.0571429\pi$
$373$	1.11816	+	0.812393i	1.11816	+	0.812393i	0.134233	+	0.990950i	$0.457143\pi$
$374$		0			0
$375$	0.757723	−	1.77278i	0.757723	−	1.77278i
$376$		0			0
$377$		0			0
$378$		0			0
$379$	0.385338	+	1.18595i	0.385338	+	1.18595i	0.936235	+	0.351375i	$0.114286\pi$
$379$	0.385338	+	1.18595i	0.385338	+	1.18595i	−0.550897	+	0.834573i	$0.685714\pi$
$380$	1.74612	−	1.82630i	1.74612	−	1.82630i
$381$		0			0
$382$	−0.135146			−0.135146
$383$		0			0		0.309017	−	0.951057i	$-0.400000\pi$
$383$		0			0		−0.309017	+	0.951057i	$0.600000\pi$
$384$	−1.21589	+	0.883396i	−1.21589	+	0.883396i
$385$		0			0
$386$		0			0
$387$	−2.08314	+	1.51349i	−2.08314	+	1.51349i
$388$		0			0
$389$		0			0		−0.809017	−	0.587785i	$-0.800000\pi$
$389$		0			0		0.809017	+	0.587785i	$0.200000\pi$
$390$		0			0
$391$		0			0
$392$	0.124951	−	0.384559i	0.124951	−	0.384559i
$393$	−3.79389			−3.79389
$394$		0			0
$395$	−0.241880	−	0.116483i	−0.241880	−	0.116483i
$396$		0			0
$397$		0			0		−0.309017	−	0.951057i	$-0.600000\pi$
$397$		0			0		0.309017	+	0.951057i	$0.400000\pi$
$398$	−1.83523	−	1.33337i	−1.83523	−	1.33337i
$399$		0			0
$400$	−0.411166	−	0.515586i	−0.411166	−	0.515586i
$401$		0			0		1.00000			$0$
$401$		0			0		−1.00000			$\pi$
$402$		0			0
$403$		0			0
$404$	0.672986	+	2.07124i	0.672986	+	2.07124i
$405$	1.73656	+	3.22706i	1.73656	+	3.22706i
$406$		0			0
$407$		0			0
$408$		0			0
$409$	−1.51486	+	1.10061i	−1.51486	+	1.10061i	−0.550897	+	0.834573i	$0.685714\pi$
$409$	−1.51486	+	1.10061i	−1.51486	+	1.10061i	−0.963963	+	0.266037i	$0.914286\pi$
$410$		0			0
$411$		0			0
$412$	−1.27966	+	0.929730i	−1.27966	+	0.929730i
$413$		0			0
$414$		0			0
$415$	−0.210891	−	0.391902i	−0.210891	−	0.391902i
$416$		0			0
$417$		0			0
$418$		0			0
$419$	0.385338	−	1.18595i	0.385338	−	1.18595i	−0.550897	−	0.834573i	$-0.685714\pi$
$419$	0.385338	−	1.18595i	0.385338	−	1.18595i	0.936235	−	0.351375i	$-0.114286\pi$
$420$		0			0
$421$		0			0		−0.309017	−	0.951057i	$-0.600000\pi$
$421$		0			0		0.309017	+	0.951057i	$0.400000\pi$
$422$		0			0
$423$		0			0
$424$		0			0
$425$		0			0
$426$	−2.90373			−2.90373
$427$		0			0
$428$	−0.634233	−	1.95197i	−0.634233	−	1.95197i
$429$		0			0
$430$	1.40449	−	0.254877i	1.40449	−	0.254877i
$431$	−0.242903	+	0.747578i	−0.242903	+	0.747578i	0.753071	+	0.657939i	$0.228571\pi$
$431$	−0.242903	+	0.747578i	−0.242903	+	0.747578i	−0.995974	+	0.0896393i	$0.971429\pi$
$432$	2.18284			2.18284
$433$		0			0		0.309017	−	0.951057i	$-0.400000\pi$
$433$		0			0		−0.309017	+	0.951057i	$0.600000\pi$
$434$		0			0
$435$	0.285135	−	2.10495i	0.285135	−	2.10495i
$436$	−1.27966	−	0.929730i	−1.27966	−	0.929730i
$437$		0			0
$438$	2.22639	−	1.61757i	2.22639	−	1.61757i
$439$		0			0		−0.809017	−	0.587785i	$-0.800000\pi$
$439$		0			0		0.809017	+	0.587785i	$0.200000\pi$
$440$		0			0
$441$	−2.19802	+	1.59695i	−2.19802	+	1.59695i
$442$		0			0
$443$		0			0		1.00000			$0$
$443$		0			0		−1.00000			$\pi$
$444$	1.50532	−	4.63291i	1.50532	−	4.63291i
$445$	−1.89694	+	0.344244i	−1.89694	+	0.344244i
$446$	−0.927100	−	2.85332i	−0.927100	−	2.85332i
$447$		0			0
$448$		0			0
$449$		0			0		1.00000			$0$
$449$		0			0		−1.00000			$\pi$
$450$	−0.183589	−	4.08792i	−0.183589	−	4.08792i
$451$		0			0
$452$		0			0
$453$	−1.11555	−	3.43330i	−1.11555	−	3.43330i
$454$		0			0
$455$		0			0
$456$	0.479852	−	1.47683i	0.479852	−	1.47683i
$457$		0			0		1.00000			$0$
$457$		0			0		−1.00000			$\pi$
$458$	−0.643274	+	1.97979i	−0.643274	+	1.97979i
$459$		0			0
$460$		0			0
$461$		0			0		−0.809017	−	0.587785i	$-0.800000\pi$
$461$		0			0		0.809017	+	0.587785i	$0.200000\pi$
$462$		0			0
$463$	−1.38900	+	1.00917i	−1.38900	+	1.00917i	−0.393025	+	0.919528i	$0.628571\pi$
$463$	−1.38900	+	1.00917i	−1.38900	+	1.00917i	−0.995974	+	0.0896393i	$0.971429\pi$
$464$	−0.587822	−	0.427078i	−0.587822	−	0.427078i
$465$		0			0
$466$	−2.09203	+	1.51995i	−2.09203	+	1.51995i
$467$		0			0		0.309017	−	0.951057i	$-0.400000\pi$
$467$		0			0		−0.309017	+	0.951057i	$0.600000\pi$
$468$		0			0
$469$		0			0
$470$		0			0
$471$	0.0534575	+	0.164525i	0.0534575	+	0.164525i
$472$		0			0
$473$		0			0
$474$	−0.779555			−0.779555
$475$	1.92016	+	0.529932i	1.92016	+	0.529932i
$476$		0			0
$477$		0			0
$478$		0			0
$479$		0			0		−0.309017	−	0.951057i	$-0.600000\pi$
$479$		0			0		0.309017	+	0.951057i	$0.400000\pi$
$480$	−2.42761	−	1.16908i	−2.42761	−	1.16908i
$481$		0			0
$482$		0			0
$483$		0			0
$484$	−1.02621	+	0.745586i	−1.02621	+	0.745586i
$485$		0			0
$486$	4.57556	+	3.32434i	4.57556	+	3.32434i
$487$		0			0		0.809017	−	0.587785i	$-0.200000\pi$
$487$		0			0		−0.809017	+	0.587785i	$0.800000\pi$
$488$		0			0
$489$		0			0
$490$	1.48194	−	0.268932i	1.48194	−	0.268932i
$491$		0			0		0.809017	−	0.587785i	$-0.200000\pi$
$491$		0			0		−0.809017	+	0.587785i	$0.800000\pi$
$492$		0			0
$493$		0			0
$494$		0			0
$495$		0			0
$496$		0			0
$497$		0			0
$498$	−1.04548	−	0.759584i	−1.04548	−	0.759584i
$499$	−1.92793			−1.92793			−0.963963	−	0.266037i	$-0.914286\pi$
$499$	−1.92793			−1.92793			−0.963963	+	0.266037i	$0.914286\pi$
$500$	−0.498539	+	1.16639i	−0.498539	+	1.16639i
$501$	3.47400			3.47400
$502$	0.957798	+	0.695881i	0.957798	+	0.695881i
$503$	−0.0277280	−	0.0853380i	−0.0277280	−	0.0853380i	0.936235	−	0.351375i	$-0.114286\pi$
$503$	−0.0277280	−	0.0853380i	−0.0277280	−	0.0853380i	−0.963963	+	0.266037i	$0.914286\pi$
$504$		0			0
$505$	−1.18648	+	1.24096i	−1.18648	+	1.24096i
$506$		0			0
$507$	−1.92793			−1.92793
$508$		0			0
$509$	−0.500000	+	0.363271i	−0.500000	+	0.363271i	−0.809017	−	0.587785i	$-0.800000\pi$
$509$	−0.500000	+	0.363271i	−0.500000	+	0.363271i	0.309017	+	0.951057i	$0.400000\pi$
$510$		0			0
$511$		0			0
$512$	−0.961358	+	0.698468i	−0.961358	+	0.698468i
$513$	−5.33421	+	3.87553i	−5.33421	+	3.87553i
$514$		0			0
$515$	−1.12349	−	0.541044i	−1.12349	−	0.541044i
$516$	1.87506	−	1.36231i	1.87506	−	1.36231i
$517$		0			0
$518$		0			0
$519$		0			0
$520$		0			0
$521$	0.608102	+	1.87155i	0.608102	+	1.87155i	0.473869	+	0.880596i	$0.342857\pi$
$521$	0.608102	+	1.87155i	0.608102	+	1.87155i	0.134233	+	0.990950i	$0.457143\pi$
$522$	−1.39323	−	4.28792i	−1.39323	−	4.28792i
$523$		0			0		−0.809017	−	0.587785i	$-0.800000\pi$
$523$		0			0		0.809017	+	0.587785i	$0.200000\pi$
$524$	2.49616			2.49616
$525$		0			0
$526$	0.404349			0.404349
$527$		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
$534$	−4.52902	+	3.29053i	−4.52902	+	3.29053i
$535$	1.11816	−	1.16951i	1.11816	−	1.16951i
$536$		0			0
$537$	1.47821	−	1.07398i	1.47821	−	1.07398i
$538$		0			0
$539$		0			0
$540$	−1.98963	−	3.69735i	−1.98963	−	3.69735i
$541$		0			0		0.809017	−	0.587785i	$-0.200000\pi$
$541$		0			0		−0.809017	+	0.587785i	$0.800000\pi$
$542$	−0.0417623	+	0.128531i	−0.0417623	+	0.128531i
$543$		0			0
$544$		0			0
$545$	0.167386	−	1.23569i	0.167386	−	1.23569i
$546$		0			0
$547$	−0.242903	−	0.747578i	−0.242903	−	0.747578i	−0.995974	−	0.0896393i	$-0.971429\pi$
$547$	−0.242903	−	0.747578i	−0.242903	−	0.747578i	0.753071	−	0.657939i	$-0.228571\pi$
$548$		0			0
$549$		0			0
$550$		0			0
$551$	2.19472			2.19472
$552$		0			0
$553$		0			0
$554$	0.799085	+	2.45933i	0.799085	+	2.45933i
$555$	3.77861	−	0.685717i	3.77861	−	0.685717i
$556$		0			0
$557$	1.24698			1.24698			0.623490	−	0.781831i	$-0.285714\pi$
$557$	1.24698			1.24698			0.623490	+	0.781831i	$0.285714\pi$
$558$		0			0
$559$		0			0
$560$		0			0
$561$		0			0
$562$		0			0
$563$		0			0		0.809017	−	0.587785i	$-0.200000\pi$
$563$		0			0		−0.809017	+	0.587785i	$0.800000\pi$
$564$		0			0
$565$		0			0
$566$		0			0
$567$		0			0
$568$	0.404349			0.404349
$569$	0.0829607	−	0.255327i	0.0829607	−	0.255327i	−0.900969	−	0.433884i	$-0.857143\pi$
$569$	0.0829607	−	0.255327i	0.0829607	−	0.255327i	0.983930	+	0.178557i	$0.0571429\pi$
$570$	5.69113	−	1.03279i	5.69113	−	1.03279i
$571$	−0.615546	−	1.89446i	−0.615546	−	1.89446i	−0.393025	−	0.919528i	$-0.628571\pi$
$571$	−0.615546	−	1.89446i	−0.615546	−	1.89446i	−0.222521	−	0.974928i	$-0.571429\pi$
$572$		0			0
$573$	−0.139954	−	0.101682i	−0.139954	−	0.101682i
$574$		0			0
$575$		0			0
$576$	−3.92730			−3.92730
$577$	1.45780	+	1.05915i	1.45780	+	1.05915i	0.983930	+	0.178557i	$0.0571429\pi$
$577$	1.45780	+	1.05915i	1.45780	+	1.05915i	0.473869	+	0.880596i	$0.342857\pi$
$578$	0.465424	+	1.43243i	0.465424	+	1.43243i
$579$		0			0
$580$	−0.187603	+	1.38494i	−0.187603	+	1.38494i
$581$		0			0
$582$		0			0
$583$		0			0
$584$	−0.310029	+	0.225249i	−0.310029	+	0.225249i
$585$		0			0
$586$	−2.43699	−	1.77058i	−2.43699	−	1.77058i
$587$	1.55972	−	1.13321i	1.55972	−	1.13321i	0.623490	−	0.781831i	$-0.285714\pi$
$587$	1.55972	−	1.13321i	1.55972	−	1.13321i	0.936235	−	0.351375i	$-0.114286\pi$
$588$	1.97846	−	1.43743i	1.97846	−	1.43743i
$589$		0			0
$590$		0			0
$591$		0			0
$592$	0.405927	−	1.24932i	0.405927	−	1.24932i
$593$	1.87247			1.87247			0.936235	−	0.351375i	$-0.114286\pi$
$593$	1.87247			1.87247			0.936235	+	0.351375i	$0.114286\pi$
$594$		0			0
$595$		0			0
$596$		0			0
$597$	−0.897302	−	2.76161i	−0.897302	−	2.76161i
$598$		0			0
$599$		0			0		1.00000			$0$
$599$		0			0		−1.00000			$\pi$
$600$	0.0349746	+	0.778770i	0.0349746	+	0.778770i
$601$		0			0		1.00000			$0$
$601$		0			0		−1.00000			$\pi$
$602$		0			0
$603$		0			0
$604$	0.733966	+	2.25892i	0.733966	+	2.25892i
$605$	−0.900969	−	0.433884i	−0.900969	−	0.433884i
$606$	−1.54058	+	4.74141i	−1.54058	+	4.74141i
$607$		0			0		1.00000			$0$
$607$		0			0		−1.00000			$\pi$
$608$	0.860280	−	2.64767i	0.860280	−	2.64767i
$609$		0			0
$610$		0			0
$611$		0			0
$612$		0			0
$613$	−1.00883	+	0.732956i	−1.00883	+	0.732956i	−0.963963	−	0.266037i	$-0.914286\pi$
$613$	−1.00883	+	0.732956i	−1.00883	+	0.732956i	−0.0448648	+	0.998993i	$0.514286\pi$
$614$		0			0
$615$		0			0
$616$		0			0
$617$	0.608102	−	1.87155i	0.608102	−	1.87155i	0.134233	−	0.990950i	$-0.457143\pi$
$617$	0.608102	−	1.87155i	0.608102	−	1.87155i	0.473869	−	0.880596i	$-0.342857\pi$
$618$	−3.62089			−3.62089
$619$		0			0		0.309017	−	0.951057i	$-0.400000\pi$
$619$		0			0		−0.309017	+	0.951057i	$0.600000\pi$
$620$		0			0
$621$		0			0
$622$	−0.927100	−	2.85332i	−0.927100	−	2.85332i
$623$		0			0
$624$		0			0
$625$	−0.995974	+	0.0896393i	−0.995974	+	0.0896393i
$626$	−0.670297			−0.670297
$627$		0			0
$628$	−0.0351720	−	0.108248i	−0.0351720	−	0.108248i
$629$		0			0
$630$		0			0
$631$		0			0		0.309017	−	0.951057i	$-0.400000\pi$
$631$		0			0		−0.309017	+	0.951057i	$0.600000\pi$
$632$	0.108554			0.108554
$633$		0			0
$634$		0			0
$635$		0			0
$636$		0			0
$637$		0			0
$638$		0			0
$639$	−2.19802	−	1.59695i	−2.19802	−	1.59695i
$640$	0.702355	+	0.338236i	0.702355	+	0.338236i
$641$	−1.21850	+	0.885289i	−1.21850	+	0.885289i	−0.995974	−	0.0896393i	$-0.971429\pi$
$641$	−1.21850	+	0.885289i	−1.21850	+	0.885289i	−0.222521	+	0.974928i	$0.571429\pi$
$642$	1.45187	−	4.46838i	1.45187	−	4.46838i
$643$	−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
$645$	1.64622	+	0.792778i	1.64622	+	0.792778i
$646$		0			0
$647$	0.190983	+	0.587785i	0.190983	+	0.587785i	1.00000			$0$
$647$	0.190983	+	0.587785i	0.190983	+	0.587785i	−0.809017	+	0.587785i	$0.800000\pi$
$648$	−1.19879	−	0.870975i	−1.19879	−	0.870975i
$649$		0			0
$650$		0			0
$651$		0			0
$652$		0			0
$653$		0			0		−0.309017	−	0.951057i	$-0.600000\pi$
$653$		0			0		0.309017	+	0.951057i	$0.400000\pi$
$654$	−1.11892	−	3.44368i	−1.11892	−	3.44368i
$655$	0.932507	+	1.73289i	0.932507	+	1.73289i
$656$		0			0
$657$	2.57491			2.57491
$658$		0			0
$659$	0.0725928	−	0.0527418i	0.0725928	−	0.0527418i	−0.550897	−	0.834573i	$-0.685714\pi$
$659$	0.0725928	−	0.0527418i	0.0725928	−	0.0527418i	0.623490	+	0.781831i	$0.285714\pi$
$660$		0			0
$661$		0			0		−0.809017	−	0.587785i	$-0.800000\pi$
$661$		0			0		0.809017	+	0.587785i	$0.200000\pi$
$662$		0			0
$663$		0			0
$664$	0.145584	+	0.105773i	0.145584	+	0.105773i
$665$		0			0
$666$	6.59440	−	4.79111i	6.59440	−	4.79111i
$667$		0			0
$668$	−2.28570			−2.28570
$669$	1.18673	−	3.65237i	1.18673	−	3.65237i
$670$		0			0
$671$		0			0
$672$		0			0
$673$		0			0		−0.809017	−	0.587785i	$-0.800000\pi$
$673$		0			0		0.809017	+	0.587785i	$0.200000\pi$
$674$		0			0
$675$	1.82350	−	2.76248i	1.82350	−	2.76248i
$676$	1.26847			1.26847
$677$	0.0725928	+	0.0527418i	0.0725928	+	0.0527418i	0.623490	−	0.781831i	$-0.285714\pi$
$677$	0.0725928	+	0.0527418i	0.0725928	+	0.0527418i	−0.550897	+	0.834573i	$0.685714\pi$
$678$		0			0
$679$		0			0
$680$		0			0
$681$		0			0
$682$		0			0
$683$		0			0		0.309017	−	0.951057i	$-0.400000\pi$
$683$		0			0		−0.309017	+	0.951057i	$0.600000\pi$
$684$	5.55377	−	4.03505i	5.55377	−	4.03505i
$685$		0			0
$686$		0			0
$687$	−2.15573	+	1.56623i	−2.15573	+	1.56623i
$688$	0.505631	−	0.367362i	0.505631	−	0.367362i
$689$		0			0
$690$		0			0
$691$		0			0		0.809017	−	0.587785i	$-0.200000\pi$
$691$		0			0		−0.809017	+	0.587785i	$0.800000\pi$
$692$		0			0
$693$		0			0
$694$		0			0
$695$		0			0
$696$	0.265417	+	0.816871i	0.265417	+	0.816871i
$697$		0			0
$698$		0			0
$699$	−3.31005			−3.31005
$700$		0			0
$701$		0			0		1.00000			$0$
$701$		0			0		−1.00000			$\pi$
$702$		0			0
$703$	1.22614	+	3.77366i	1.22614	+	3.77366i
$704$		0			0
$705$		0			0
$706$		0			0
$707$		0			0
$708$		0			0
$709$		0			0		0.809017	−	0.587785i	$-0.200000\pi$
$709$		0			0		−0.809017	+	0.587785i	$0.800000\pi$
$710$	0.713714	+	1.32630i	0.713714	+	1.32630i
$711$	−0.590094	−	0.428728i	−0.590094	−	0.428728i
$712$	0.630673	−	0.458211i	0.630673	−	0.458211i
$713$		0			0
$714$		0			0
$715$		0			0
$716$	−0.972578	+	0.706620i	−0.972578	+	0.706620i
$717$		0			0
$718$	−2.08168			−2.08168
$719$	0.465424	−	1.43243i	0.465424	−	1.43243i	−0.393025	−	0.919528i	$-0.628571\pi$
$719$	0.465424	−	1.43243i	0.465424	−	1.43243i	0.858449	−	0.512899i	$-0.171429\pi$
$720$	−0.849022	−	1.57775i	−0.849022	−	1.57775i
$721$		0			0
$722$	1.38131	+	4.25124i	1.38131	+	4.25124i
$723$		0			0
$724$		0			0
$725$	−1.03154	+	0.387143i	−1.03154	+	0.387143i
$726$	−2.90373			−2.90373
$727$		0			0		−0.809017	−	0.587785i	$-0.800000\pi$
$727$		0			0		0.809017	+	0.587785i	$0.200000\pi$
$728$		0			0
$729$	1.10471	+	3.39994i	1.10471	+	3.39994i
$730$	−1.28607	−	0.619338i	−1.28607	−	0.619338i
$731$		0			0
$732$		0			0
$733$		0			0		0.309017	−	0.951057i	$-0.400000\pi$
$733$		0			0		−0.309017	+	0.951057i	$0.600000\pi$
$734$	2.19565	−	1.59523i	2.19565	−	1.59523i
$735$	1.73700	+	0.836496i	1.73700	+	0.836496i
$736$		0			0
$737$		0			0
$738$		0			0
$739$	−0.500000	−	0.363271i	−0.500000	−	0.363271i	0.309017	−	0.951057i	$-0.400000\pi$
$739$	−0.500000	−	0.363271i	−0.500000	−	0.363271i	−0.809017	+	0.587785i	$0.800000\pi$
$740$	−2.48611	+	0.451163i	−2.48611	+	0.451163i
$741$		0			0
$742$		0			0
$743$		0			0		1.00000			$0$
$743$		0			0		−1.00000			$\pi$
$744$		0			0
$745$		0			0
$746$	−0.643274	−	1.97979i	−0.643274	−	1.97979i
$747$	−0.373643	−	1.14995i	−0.373643	−	1.14995i
$748$		0			0
$749$		0			0
$750$	−2.49270	+	1.48932i	−2.49270	+	1.48932i
$751$		0			0		1.00000			$0$
$751$		0			0		−1.00000			$\pi$
$752$		0			0
$753$	0.468299	+	1.44127i	0.468299	+	1.44127i
$754$		0			0
$755$	−1.29399	+	1.35341i	−1.29399	+	1.35341i
$756$		0			0
$757$		0			0		1.00000			$0$
$757$		0			0		−1.00000			$\pi$
$758$	0.580374	−	1.78621i	0.580374	−	1.78621i
$759$		0			0
$760$	−0.792499	+	0.143817i	−0.792499	+	0.143817i
$761$		0			0		−0.809017	−	0.587785i	$-0.800000\pi$
$761$		0			0		0.809017	+	0.587785i	$0.200000\pi$
$762$		0			0
$763$		0			0
$764$	0.0920816	+	0.0669012i	0.0920816	+	0.0669012i
$765$		0			0
$766$		0			0
$767$		0			0
$768$	−0.523217			−0.523217
$769$		0			0		0.309017	−	0.951057i	$-0.400000\pi$
$769$		0			0		−0.309017	+	0.951057i	$0.600000\pi$
$770$		0			0
$771$		0			0
$772$		0			0
$773$		0			0		−0.809017	−	0.587785i	$-0.800000\pi$
$773$		0			0		0.809017	+	0.587785i	$0.200000\pi$
$774$	3.87818			3.87818
$775$		0			0
$776$		0			0
$777$		0			0
$778$		0			0
$779$		0			0
$780$		0			0
$781$		0			0
$782$		0			0
$783$	1.12698	−	3.46850i	1.12698	−	3.46850i
$784$	0.533514	−	0.387620i	0.533514	−	0.387620i
$785$	0.0620088	−	0.0648561i	0.0620088	−	0.0648561i
$786$	4.62283	+	3.35868i	4.62283	+	3.35868i
$787$	−1.51486	+	1.10061i	−1.51486	+	1.10061i	−0.550897	+	0.834573i	$0.685714\pi$
$787$	−1.51486	+	1.10061i	−1.51486	+	1.10061i	−0.963963	+	0.266037i	$0.914286\pi$
$788$		0			0
$789$	0.418734	+	0.304228i	0.418734	+	0.304228i
$790$	0.191608	+	0.356068i	0.191608	+	0.356068i
$791$		0			0
$792$		0			0
$793$		0			0
$794$		0			0
$795$		0			0
$796$	0.590374	+	1.81699i	0.590374	+	1.81699i
$797$	0.465424	+	1.43243i	0.465424	+	1.43243i	0.858449	+	0.512899i	$0.171429\pi$
$797$	0.465424	+	1.43243i	0.465424	+	1.43243i	−0.393025	+	0.919528i	$0.628571\pi$
$798$		0			0
$799$		0			0
$800$	0.0627026	+	1.39618i	0.0627026	+	1.39618i
$801$	−5.23798			−5.23798
$802$		0			0
$803$		0			0
$804$		0			0
$805$		0			0
$806$		0			0
$807$		0			0
$808$	0.214528	−	0.660248i	0.214528	−	0.660248i
$809$		0			0		0.809017	−	0.587785i	$-0.200000\pi$
$809$		0			0		−0.809017	+	0.587785i	$0.800000\pi$
$810$	0.740896	−	5.46951i	0.740896	−	5.46951i
$811$	−0.766736	−	0.557066i	−0.766736	−	0.557066i	0.134233	−	0.990950i	$-0.457143\pi$
$811$	−0.766736	−	0.557066i	−0.766736	−	0.557066i	−0.900969	+	0.433884i	$0.857143\pi$
$812$		0			0
$813$	−0.139954	+	0.101682i	−0.139954	+	0.101682i
$814$		0			0
$815$		0			0
$816$		0			0
$817$	−0.583376	+	1.79545i	−0.583376	+	1.79545i
$818$	2.82021			2.82021
$819$		0			0
$820$		0			0
$821$	−0.137526	−	0.423260i	−0.137526	−	0.423260i	0.858449	−	0.512899i	$-0.171429\pi$
$821$	−0.137526	−	0.423260i	−0.137526	−	0.423260i	−0.995974	+	0.0896393i	$0.971429\pi$
$822$		0			0
$823$		0			0		−0.809017	−	0.587785i	$-0.800000\pi$
$823$		0			0		0.809017	+	0.587785i	$0.200000\pi$
$824$	0.504215			0.504215
$825$		0			0
$826$		0			0
$827$		0			0		−0.809017	−	0.587785i	$-0.800000\pi$
$827$		0			0		0.809017	+	0.587785i	$0.200000\pi$
$828$		0			0
$829$	−0.615546	−	1.89446i	−0.615546	−	1.89446i	−0.393025	−	0.919528i	$-0.628571\pi$
$829$	−0.615546	−	1.89446i	−0.615546	−	1.89446i	−0.222521	−	0.974928i	$-0.571429\pi$
$830$	−0.0899761	+	0.664230i	−0.0899761	+	0.664230i
$831$	−1.02286	+	3.14805i	−1.02286	+	3.14805i
$832$		0			0
$833$		0			0
$834$		0			0
$835$	−0.853882	−	1.58678i	−0.853882	−	1.58678i
$836$		0			0
$837$		0			0
$838$	−1.51944	+	1.10394i	−1.51944	+	1.10394i
$839$	0.360046	+	0.261589i	0.360046	+	0.261589i	0.753071	−	0.657939i	$-0.228571\pi$
$839$	0.360046	+	0.261589i	0.360046	+	0.261589i	−0.393025	+	0.919528i	$0.628571\pi$
$840$		0			0
$841$	−0.173089	+	0.125757i	−0.173089	+	0.125757i
$842$		0			0
$843$		0			0
$844$		0			0
$845$	0.473869	+	0.880596i	0.473869	+	0.880596i
$846$		0			0
$847$		0			0
$848$		0			0
$849$		0			0
$850$		0			0
$851$		0			0
$852$	1.97846	+	1.43743i	1.97846	+	1.43743i
$853$	0.578625	+	1.78082i	0.578625	+	1.78082i	0.623490	+	0.781831i	$0.285714\pi$
$853$	0.578625	+	1.78082i	0.578625	+	1.78082i	−0.0448648	+	0.998993i	$0.514286\pi$
$854$		0			0
$855$	4.87597	+	2.34814i	4.87597	+	2.34814i
$856$	−0.202174	+	0.622229i	−0.202174	+	0.622229i
$857$	−1.92793			−1.92793			−0.963963	−	0.266037i	$-0.914286\pi$
$857$	−1.92793			−1.92793			−0.963963	+	0.266037i	$0.914286\pi$
$858$		0			0
$859$		0			0		0.809017	−	0.587785i	$-0.200000\pi$
$859$		0			0		−0.809017	+	0.587785i	$0.800000\pi$
$860$	−1.08312	−	0.521603i	−1.08312	−	0.521603i
$861$		0			0
$862$	0.957798	−	0.695881i	0.957798	−	0.695881i
$863$		0			0		0.809017	−	0.587785i	$-0.200000\pi$
$863$		0			0		−0.809017	+	0.587785i	$0.800000\pi$
$864$	−3.74259	−	2.71915i	−3.74259	−	2.71915i
$865$		0			0
$866$		0			0
$867$	−0.595762	+	1.83357i	−0.595762	+	1.83357i
$868$		0			0
$869$		0			0
$870$	−2.21093	+	2.31245i	−2.21093	+	2.31245i
$871$		0			0
$872$	0.155811	+	0.479537i	0.155811	+	0.479537i
$873$		0			0
$874$		0			0
$875$		0			0
$876$	−2.31770			−2.31770
$877$	−1.59203	−	1.15668i	−1.59203	−	1.15668i	−0.900969	−	0.433884i	$-0.857143\pi$
$877$	−1.59203	−	1.15668i	−1.59203	−	1.15668i	−0.691063	−	0.722795i	$-0.742857\pi$
$878$		0			0
$879$	−1.19152	−	3.66713i	−1.19152	−	3.66713i
$880$		0			0
$881$	−0.556829	+	1.71374i	−0.556829	+	1.71374i	0.134233	+	0.990950i	$0.457143\pi$
$881$	−0.556829	+	1.71374i	−0.556829	+	1.71374i	−0.691063	+	0.722795i	$0.742857\pi$
$882$	4.09204			4.09204
$883$		0			0		0.309017	−	0.951057i	$-0.400000\pi$
$883$		0			0		−0.309017	+	0.951057i	$0.600000\pi$
$884$		0			0
$885$		0			0
$886$		0			0
$887$		0			0		0.809017	−	0.587785i	$-0.200000\pi$
$887$		0			0		−0.809017	+	0.587785i	$0.800000\pi$
$888$	−1.25627	+	0.912732i	−1.25627	+	0.912732i
$889$		0			0
$890$	2.61617	+	1.25988i	2.61617	+	1.25988i
$891$		0			0
$892$	−0.780799	+	2.40305i	−0.780799	+	2.40305i
$893$		0			0
$894$		0			0
$895$	−0.853882	−	0.411208i	−0.853882	−	0.411208i
$896$		0			0
$897$		0			0
$898$		0			0
$899$		0			0
$900$	−1.89855	+	2.87618i	−1.89855	+	2.87618i
$901$		0			0
$902$		0			0
$903$		0			0
$904$		0			0
$905$		0			0
$906$	−1.68017	+	5.17104i	−1.68017	+	5.17104i
$907$		0			0		1.00000			$0$
$907$		0			0		−1.00000			$\pi$
$908$		0			0
$909$	−3.77377	+	2.74180i	−3.77377	+	2.74180i
$910$		0			0
$911$		0			0		−0.809017	−	0.587785i	$-0.800000\pi$
$911$		0			0		0.809017	+	0.587785i	$0.200000\pi$
$912$	2.04887	−	1.48859i	2.04887	−	1.48859i
$913$		0			0
$914$		0			0
$915$		0			0
$916$	1.41835	−	1.03049i	1.41835	−	1.03049i
$917$		0			0
$918$		0			0
$919$		0			0		0.309017	−	0.951057i	$-0.400000\pi$
$919$		0			0		−0.309017	+	0.951057i	$0.600000\pi$
$920$		0			0
$921$		0			0
$922$		0			0
$923$		0			0
$924$		0			0
$925$	−1.24196	−	1.55737i	−1.24196	−	1.55737i
$926$	2.58589			2.58589
$927$	−2.74088	−	1.99137i	−2.74088	−	1.99137i
$928$	0.475841	+	1.46449i	0.475841	+	1.46449i
$929$	−0.242903	−	0.747578i	−0.242903	−	0.747578i	−0.995974	−	0.0896393i	$-0.971429\pi$
$929$	−0.242903	−	0.747578i	−0.242903	−	0.747578i	0.753071	−	0.657939i	$-0.228571\pi$
$930$		0			0
$931$	−0.615546	+	1.89446i	−0.615546	+	1.89446i
$932$	2.17783			2.17783
$933$	1.18673	−	3.65237i	1.18673	−	3.65237i
$934$		0			0
$935$		0			0
$936$		0			0
$937$		0			0		0.809017	−	0.587785i	$-0.200000\pi$
$937$		0			0		−0.809017	+	0.587785i	$0.800000\pi$
$938$		0			0
$939$	−0.694143	−	0.504324i	−0.694143	−	0.504324i
$940$		0			0
$941$	−1.21850	+	0.885289i	−1.21850	+	0.885289i	−0.995974	−	0.0896393i	$-0.971429\pi$
$941$	−1.21850	+	0.885289i	−1.21850	+	0.885289i	−0.222521	+	0.974928i	$0.571429\pi$
$942$	0.0805146	−	0.247799i	0.0805146	−	0.247799i
$943$		0			0
$944$		0			0
$945$		0			0
$946$		0			0
$947$	0.608102	+	1.87155i	0.608102	+	1.87155i	0.473869	+	0.880596i	$0.342857\pi$
$947$	0.608102	+	1.87155i	0.608102	+	1.87155i	0.134233	+	0.990950i	$0.457143\pi$
$948$	0.531150	+	0.385903i	0.531150	+	0.385903i
$949$		0			0
$950$	−1.87057	−	2.34562i	−1.87057	−	2.34562i
$951$		0			0
$952$		0			0
$953$	0.0829607	+	0.255327i	0.0829607	+	0.255327i	0.983930	−	0.178557i	$-0.0571429\pi$
$953$	0.0829607	+	0.255327i	0.0829607	+	0.255327i	−0.900969	+	0.433884i	$0.857143\pi$
$954$		0			0
$955$	−0.0120447	+	0.0889176i	−0.0120447	+	0.0889176i
$956$		0			0
$957$		0			0
$958$		0			0
$959$		0			0
$960$	1.32059	+	2.45407i	1.32059	+	2.45407i
$961$	−0.809017	−	0.587785i	−0.809017	−	0.587785i
$962$		0			0
$963$	3.55647	−	2.58392i	3.55647	−	2.58392i
$964$		0			0
$965$		0			0
$966$		0			0
$967$		0			0		0.309017	−	0.951057i	$-0.400000\pi$
$967$		0			0		−0.309017	+	0.951057i	$0.600000\pi$
$968$	0.404349			0.404349
$969$		0			0
$970$		0			0
$971$	0.190983	+	0.587785i	0.190983	+	0.587785i	1.00000			$0$
$971$	0.190983	+	0.587785i	0.190983	+	0.587785i	−0.809017	+	0.587785i	$0.800000\pi$
$972$	−1.47191	−	4.53008i	−1.47191	−	4.53008i
$973$		0			0
$974$		0			0
$975$		0			0
$976$		0			0
$977$	0.891370	+	0.647618i	0.891370	+	0.647618i	0.936235	−	0.351375i	$-0.114286\pi$
$977$	0.891370	+	0.647618i	0.891370	+	0.647618i	−0.0448648	+	0.998993i	$0.514286\pi$
$978$		0			0
$979$		0			0
$980$	−1.14285	−	0.550367i	−1.14285	−	0.550367i
$981$	1.04692	−	3.22210i	1.04692	−	3.22210i
$982$		0			0
$983$	−0.242903	+	0.747578i	−0.242903	+	0.747578i	0.753071	+	0.657939i	$0.228571\pi$
$983$	−0.242903	+	0.747578i	−0.242903	+	0.747578i	−0.995974	+	0.0896393i	$0.971429\pi$
$984$		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	$-0.200000\pi$
$991$		0			0		−0.809017	+	0.587785i	$0.800000\pi$
$992$		0			0
$993$		0			0
$994$		0			0
$995$	−1.04084	+	1.08863i	−1.04084	+	1.08863i
$996$	0.336320	+	1.03509i	0.336320	+	1.03509i
$997$	0.0829607	+	0.255327i	0.0829607	+	0.255327i	0.983930	−	0.178557i	$-0.0571429\pi$
$997$	0.0829607	+	0.255327i	0.0829607	+	0.255327i	−0.900969	+	0.433884i	$0.857143\pi$
$998$	2.34917	+	1.70677i	2.34917	+	1.70677i
$999$	6.59345			6.59345

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1775.1.p.b.141.2	✓	24
25.11	even	5	inner	1775.1.p.b.1561.2	yes	24
71.70	odd	2	CM	1775.1.p.b.141.2	✓	24
1775.1561	odd	10	inner	1775.1.p.b.1561.2	yes	24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1775.1.p.b.141.2	✓	24	1.1	even	1	trivial
1775.1.p.b.141.2	✓	24	71.70	odd	2	CM
1775.1.p.b.1561.2	yes	24	25.11	even	5	inner
1775.1.p.b.1561.2	yes	24	1775.1561	odd	10	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

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

\(f(q)\)	\(=\)	\(q+(-1.21850 - 0.885289i) q^{2} +(-0.595762 - 1.83357i) q^{3} +(0.391978 + 1.20638i) q^{4} +(-0.691063 + 0.722795i) q^{5} +(-0.897302 + 2.76161i) q^{6} +(0.124951 - 0.384559i) q^{8} +(-2.19802 + 1.59695i) q^{9} +O(q^{10})\)	\(q+(-1.21850 - 0.885289i) q^{2} +(-0.595762 - 1.83357i) q^{3} +(0.391978 + 1.20638i) q^{4} +(-0.691063 + 0.722795i) q^{5} +(-0.897302 + 2.76161i) q^{6} +(0.124951 - 0.384559i) q^{8} +(-2.19802 + 1.59695i) q^{9} +(1.48194 - 0.268932i) q^{10} +(1.97846 - 1.43743i) q^{12} +(1.73700 + 0.836496i) q^{15} +(0.533514 - 0.387620i) q^{16} +4.09204 q^{18} +(-0.615546 + 1.89446i) q^{19} +(-1.14285 - 0.550367i) q^{20} -0.779555 q^{24} +(-0.0448648 - 0.998993i) q^{25} +(2.67789 + 1.94560i) q^{27} +(-0.340473 - 1.04787i) q^{29} +(-1.37599 - 2.55701i) q^{30} -1.39759 q^{32} +(-2.78811 - 2.02568i) q^{36} +(1.61152 - 1.17084i) q^{37} +(2.42718 - 1.76345i) q^{38} +(0.191608 + 0.356068i) q^{40} +0.947737 q^{43} +(0.364698 - 2.69231i) q^{45} +(-1.02857 - 0.747303i) q^{48} +1.00000 q^{49} +(-0.829730 + 1.25699i) q^{50} +(-1.54058 - 4.74141i) q^{54} +3.84033 q^{57} +(-0.512801 + 1.57824i) q^{58} +(-0.328269 + 2.42338i) q^{60} +(1.16944 + 0.849649i) q^{64} +(0.309017 + 0.951057i) q^{71} +(0.339478 + 1.04481i) q^{72} +(-0.766736 - 0.557066i) q^{73} -3.00016 q^{74} +(-1.80499 + 0.677425i) q^{75} -2.52672 q^{76} +(0.0829607 + 0.255327i) q^{79} +(-0.0885214 + 0.653491i) q^{80} +(1.13243 - 3.48527i) q^{81} +(-0.137526 + 0.423260i) q^{83} +(-1.15481 - 0.839021i) q^{86} +(-1.71850 + 1.24856i) q^{87} +(1.55972 + 1.13321i) q^{89} +(-2.82785 + 2.95770i) q^{90} +(-0.943922 - 1.75410i) q^{95} +(0.832630 + 2.56257i) q^{96} +(-1.21850 - 0.885289i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q - 3 q^{2} + 2 q^{3} - 9 q^{4} + q^{5} - q^{6} - q^{8} - 4 q^{9}+O(q^{10}) \) 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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