LMFDB - Embedded newform 705.1.p.a.614.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [705,1,Mod(14,705)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(705, base_ring=CyclotomicField(46))

chi = DirichletCharacter(H, H._module([23, 23, 4]))

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

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

chi := DirichletCharacter("705.14");

S:= CuspForms(chi, 1);

N := Newforms(S);

Level:	$ N $	$=$	$ 705 = 3 \cdot 5 \cdot 47 $
Weight:	$ k $	$=$	$ 1 $
Character orbit:	$[\chi]$	$=$	705.p (of order $46$, degree $22$, 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:	$0.351840833906$
Analytic rank:	$0$
Dimension:	$22$
Coefficient field:	$\Q(\zeta_{46})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{22} - x^{21} + x^{20} - x^{19} + x^{18} - x^{17} + x^{16} - x^{15} + x^{14} - x^{13} + x^{12} + \cdots + 1 $ x^22 - x^21 + x^20 - x^19 + x^18 - x^17 + x^16 - x^15 + x^14 - x^13 + x^12 - x^11 + x^10 - x^9 + x^8 - x^7 + x^6 - x^5 + x^4 - x^3 + x^2 - x + 1
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Projective image:	$D_{23}$
Projective field:	Galois closure of $\mathbb{Q}[x]/(x^{23} - \cdots)$

Embedding invariants

Embedding label			614.1
Root			$-0.203456 + 0.979084i$ of defining polynomial
Character	$\chi$	$=$	705.614
Dual form			705.1.p.a.674.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.347674 - 0.211425i) q^{2} +(-0.576680 + 0.816970i) q^{3} +(-0.383889 + 0.740871i) q^{4} +(0.203456 + 0.979084i) q^{5} +(-0.0277687 + 0.405963i) q^{6} +(0.0509395 + 0.744708i) q^{8} +(-0.334880 - 0.942261i) q^{9} +O(q^{10})$	\(q+(0.347674 - 0.211425i) q^{2} +(-0.576680 + 0.816970i) q^{3} +(-0.383889 + 0.740871i) q^{4} +(0.203456 + 0.979084i) q^{5} +(-0.0277687 + 0.405963i) q^{6} +(0.0509395 + 0.744708i) q^{8} +(-0.334880 - 0.942261i) q^{9} +(0.277739 + 0.297386i) q^{10} +(-0.383889 - 0.740871i) q^{12} +(-0.917211 - 0.398401i) q^{15} +(-0.306035 - 0.433553i) q^{16} +(-1.90790 + 0.262234i) q^{17} +(-0.315646 - 0.256797i) q^{18} +(0.187206 - 0.900885i) q^{19} +(-0.803480 - 0.225125i) q^{20} +(1.46007 + 0.887885i) q^{23} +(-0.637780 - 0.387843i) q^{24} +(-0.917211 + 0.398401i) q^{25} +(0.962917 + 0.269797i) q^{27} +(-0.403122 + 0.0554078i) q^{30} +(1.14262 + 1.61872i) q^{31} +(-0.882715 - 0.383417i) q^{32} +(-0.607882 + 0.494549i) q^{34} +(0.826651 + 0.113621i) q^{36} +(-0.125383 - 0.352794i) q^{38} +(-0.718768 + 0.201389i) q^{40} +(0.854419 - 0.519584i) q^{45} +0.695347 q^{46} +(0.682553 - 0.730836i) q^{47} +0.530684 q^{48} +(0.854419 - 0.519584i) q^{49} +(-0.234658 + 0.332435i) q^{50} +(0.886009 - 1.70992i) q^{51} +(0.0457060 - 0.668198i) q^{53} +(0.391823 - 0.109784i) q^{54} +(0.628038 + 0.672464i) q^{57} +(0.647271 - 0.526594i) q^{60} +(-1.05893 + 1.13384i) q^{61} +(0.739496 + 0.321209i) q^{62} +(0.137780 - 0.0189375i) q^{64} +(0.538138 - 1.51418i) q^{68} +(-1.56737 + 0.680803i) q^{69} +(0.684651 - 0.297386i) q^{72} +(0.203456 - 0.979084i) q^{75} +(0.595574 + 0.484535i) q^{76} +(1.81734 + 0.789381i) q^{79} +(0.362220 - 0.387843i) q^{80} +(-0.775711 + 0.631088i) q^{81} +(0.135214 + 0.0185847i) q^{83} +(-0.644923 - 1.81464i) q^{85} +(0.187206 - 0.361291i) q^{90} +(-1.21831 + 0.740871i) q^{92} -1.98137 q^{93} +(0.0827887 - 0.398401i) q^{94} +0.920130 q^{95} +(0.822285 - 0.500042i) q^{96} +(0.187206 - 0.361291i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 22 q - 2 q^{2} - q^{3} - 3 q^{4} - q^{5} - 2 q^{6} - 4 q^{8} - q^{9}+O(q^{10}) $ 22 * q - 2 * q^2 - q^3 - 3 * q^4 - q^5 - 2 * q^6 - 4 * q^8 - q^9	$ 22 q - 2 q^{2} - q^{3} - 3 q^{4} - q^{5} - 2 q^{6} - 4 q^{8} - q^{9} - 2 q^{10} - 3 q^{12} - q^{15} - 5 q^{16} - 2 q^{17} - 2 q^{18} - 2 q^{19} - 3 q^{20} + 21 q^{23} - 4 q^{24} - q^{25} - q^{27} - 2 q^{30} - 2 q^{31} - 6 q^{32} - 4 q^{34} - 3 q^{36} - 4 q^{38} - 4 q^{40} - q^{45} - 4 q^{46} - q^{47} + 18 q^{48} - q^{49} - 2 q^{50} - 2 q^{51} - 2 q^{53} - 2 q^{54} - 2 q^{57} - 3 q^{60} - 2 q^{61} - 4 q^{62} - 7 q^{64} - 6 q^{68} - 2 q^{69} - 4 q^{72} - q^{75} + 17 q^{76} - 2 q^{79} + 18 q^{80} - q^{81} - 2 q^{83} - 2 q^{85} - 2 q^{90} + 17 q^{92} - 2 q^{93} + 21 q^{94} - 2 q^{95} + 17 q^{96} - 2 q^{98}+O(q^{100}) $ 22 * q - 2 * q^2 - q^3 - 3 * q^4 - q^5 - 2 * q^6 - 4 * q^8 - q^9 - 2 * q^10 - 3 * q^12 - q^15 - 5 * q^16 - 2 * q^17 - 2 * q^18 - 2 * q^19 - 3 * q^20 + 21 * q^23 - 4 * q^24 - q^25 - q^27 - 2 * q^30 - 2 * q^31 - 6 * q^32 - 4 * q^34 - 3 * q^36 - 4 * q^38 - 4 * q^40 - q^45 - 4 * q^46 - q^47 + 18 * q^48 - q^49 - 2 * q^50 - 2 * q^51 - 2 * q^53 - 2 * q^54 - 2 * q^57 - 3 * q^60 - 2 * q^61 - 4 * q^62 - 7 * q^64 - 6 * q^68 - 2 * q^69 - 4 * q^72 - q^75 + 17 * q^76 - 2 * q^79 + 18 * q^80 - q^81 - 2 * q^83 - 2 * q^85 - 2 * q^90 + 17 * q^92 - 2 * q^93 + 21 * q^94 - 2 * q^95 + 17 * q^96 - 2 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/705\mathbb{Z}\right)^\times$.

$n$	$142$	$236$	$616$
$\chi(n)$	$-1$	$-1$	$e\left(\frac{10}{23}\right)$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$	0.347674	−	0.211425i	0.347674	−	0.211425i	−0.334880	−	0.942261i	$-0.608696\pi$
$2$	0.347674	−	0.211425i	0.347674	−	0.211425i	0.682553	+	0.730836i	$0.260870\pi$
$3$	−0.576680	+	0.816970i	−0.576680	+	0.816970i
$3$	−0.576680	+	0.816970i	−0.576680	+	0.816970i
$4$	−0.383889	+	0.740871i	−0.383889	+	0.740871i
$5$	0.203456	+	0.979084i	0.203456	+	0.979084i
$5$	0.203456	+	0.979084i	0.203456	+	0.979084i
$6$	−0.0277687	+	0.405963i	−0.0277687	+	0.405963i
$7$		0			0		0.962917	−	0.269797i	$-0.0869565\pi$
$7$		0			0		−0.962917	+	0.269797i	$0.913043\pi$
$8$	0.0509395	+	0.744708i	0.0509395	+	0.744708i
$9$	−0.334880	−	0.942261i	−0.334880	−	0.942261i
$10$	0.277739	+	0.297386i	0.277739	+	0.297386i
$11$		0			0		−0.990686	−	0.136167i	$-0.956522\pi$
$11$		0			0		0.990686	+	0.136167i	$0.0434783\pi$
$12$	−0.383889	−	0.740871i	−0.383889	−	0.740871i
$13$		0			0		0.775711	−	0.631088i	$-0.217391\pi$
$13$		0			0		−0.775711	+	0.631088i	$0.782609\pi$
$14$		0			0
$15$	−0.917211	−	0.398401i	−0.917211	−	0.398401i
$16$	−0.306035	−	0.433553i	−0.306035	−	0.433553i
$17$	−1.90790	+	0.262234i	−1.90790	+	0.262234i	−0.990686	−	0.136167i	$-0.956522\pi$
$17$	−1.90790	+	0.262234i	−1.90790	+	0.262234i	−0.917211	+	0.398401i	$0.869565\pi$
$18$	−0.315646	−	0.256797i	−0.315646	−	0.256797i
$19$	0.187206	−	0.900885i	0.187206	−	0.900885i	−0.775711	−	0.631088i	$-0.782609\pi$
$19$	0.187206	−	0.900885i	0.187206	−	0.900885i	0.962917	−	0.269797i	$-0.0869565\pi$
$20$	−0.803480	−	0.225125i	−0.803480	−	0.225125i
$21$		0			0
$22$		0			0
$23$	1.46007	+	0.887885i	1.46007	+	0.887885i	1.00000			$0$
$23$	1.46007	+	0.887885i	1.46007	+	0.887885i	0.460065	+	0.887885i	$0.347826\pi$
$24$	−0.637780	−	0.387843i	−0.637780	−	0.387843i
$25$	−0.917211	+	0.398401i	−0.917211	+	0.398401i
$26$		0			0
$27$	0.962917	+	0.269797i	0.962917	+	0.269797i
$28$		0			0
$29$		0			0		−0.775711	−	0.631088i	$-0.782609\pi$
$29$		0			0		0.775711	+	0.631088i	$0.217391\pi$
$30$	−0.403122	+	0.0554078i	−0.403122	+	0.0554078i
$31$	1.14262	+	1.61872i	1.14262	+	1.61872i	0.682553	+	0.730836i	$0.260870\pi$
$31$	1.14262	+	1.61872i	1.14262	+	1.61872i	0.460065	+	0.887885i	$0.347826\pi$
$32$	−0.882715	−	0.383417i	−0.882715	−	0.383417i
$33$		0			0
$34$	−0.607882	+	0.494549i	−0.607882	+	0.494549i
$35$		0			0
$36$	0.826651	+	0.113621i	0.826651	+	0.113621i
$37$		0			0		−0.682553	−	0.730836i	$-0.739130\pi$
$37$		0			0		0.682553	+	0.730836i	$0.260870\pi$
$38$	−0.125383	−	0.352794i	−0.125383	−	0.352794i
$39$		0			0
$40$	−0.718768	+	0.201389i	−0.718768	+	0.201389i
$41$		0			0		0.0682424	−	0.997669i	$-0.478261\pi$
$41$		0			0		−0.0682424	+	0.997669i	$0.521739\pi$
$42$		0			0
$43$		0			0		0.460065	−	0.887885i	$-0.347826\pi$
$43$		0			0		−0.460065	+	0.887885i	$0.652174\pi$
$44$		0			0
$45$	0.854419	−	0.519584i	0.854419	−	0.519584i
$46$	0.695347			0.695347
$47$	0.682553	−	0.730836i	0.682553	−	0.730836i
$47$	0.682553	−	0.730836i	0.682553	−	0.730836i
$48$	0.530684			0.530684
$49$	0.854419	−	0.519584i	0.854419	−	0.519584i
$50$	−0.234658	+	0.332435i	−0.234658	+	0.332435i
$51$	0.886009	−	1.70992i	0.886009	−	1.70992i
$52$		0			0
$53$	0.0457060	−	0.668198i	0.0457060	−	0.668198i	−0.917211	−	0.398401i	$-0.869565\pi$
$53$	0.0457060	−	0.668198i	0.0457060	−	0.668198i	0.962917	−	0.269797i	$-0.0869565\pi$
$54$	0.391823	−	0.109784i	0.391823	−	0.109784i
$55$		0			0
$56$		0			0
$57$	0.628038	+	0.672464i	0.628038	+	0.672464i
$58$		0			0
$59$		0			0		−0.460065	−	0.887885i	$-0.652174\pi$
$59$		0			0		0.460065	+	0.887885i	$0.347826\pi$
$60$	0.647271	−	0.526594i	0.647271	−	0.526594i
$61$	−1.05893	+	1.13384i	−1.05893	+	1.13384i	−0.0682424	+	0.997669i	$0.521739\pi$
$61$	−1.05893	+	1.13384i	−1.05893	+	1.13384i	−0.990686	+	0.136167i	$0.956522\pi$
$62$	0.739496	+	0.321209i	0.739496	+	0.321209i
$63$		0			0
$64$	0.137780	−	0.0189375i	0.137780	−	0.0189375i
$65$		0			0
$66$		0			0
$67$		0			0		−0.962917	−	0.269797i	$-0.913043\pi$
$67$		0			0		0.962917	+	0.269797i	$0.0869565\pi$
$68$	0.538138	−	1.51418i	0.538138	−	1.51418i
$69$	−1.56737	+	0.680803i	−1.56737	+	0.680803i
$70$		0			0
$71$		0			0		−0.854419	−	0.519584i	$-0.826087\pi$
$71$		0			0		0.854419	+	0.519584i	$0.173913\pi$
$72$	0.684651	−	0.297386i	0.684651	−	0.297386i
$73$		0			0		0.334880	−	0.942261i	$-0.391304\pi$
$73$		0			0		−0.334880	+	0.942261i	$0.608696\pi$
$74$		0			0
$75$	0.203456	−	0.979084i	0.203456	−	0.979084i
$76$	0.595574	+	0.484535i	0.595574	+	0.484535i
$77$		0			0
$78$		0			0
$79$	1.81734	+	0.789381i	1.81734	+	0.789381i	0.962917	+	0.269797i	$0.0869565\pi$
$79$	1.81734	+	0.789381i	1.81734	+	0.789381i	0.854419	+	0.519584i	$0.173913\pi$
$80$	0.362220	−	0.387843i	0.362220	−	0.387843i
$81$	−0.775711	+	0.631088i	−0.775711	+	0.631088i
$82$		0			0
$83$	0.135214	+	0.0185847i	0.135214	+	0.0185847i	0.203456	−	0.979084i	$-0.434783\pi$
$83$	0.135214	+	0.0185847i	0.135214	+	0.0185847i	−0.0682424	+	0.997669i	$0.521739\pi$
$84$		0			0
$85$	−0.644923	−	1.81464i	−0.644923	−	1.81464i
$86$		0			0
$87$		0			0
$88$		0			0
$89$		0			0		−0.203456	−	0.979084i	$-0.565217\pi$
$89$		0			0		0.203456	+	0.979084i	$0.434783\pi$
$90$	0.187206	−	0.361291i	0.187206	−	0.361291i
$91$		0			0
$92$	−1.21831	+	0.740871i	−1.21831	+	0.740871i
$93$	−1.98137			−1.98137
$94$	0.0827887	−	0.398401i	0.0827887	−	0.398401i
$95$	0.920130			0.920130
$96$	0.822285	−	0.500042i	0.822285	−	0.500042i
$97$		0			0		0.576680	−	0.816970i	$-0.304348\pi$
$97$		0			0		−0.576680	+	0.816970i	$0.695652\pi$
$98$	0.187206	−	0.361291i	0.187206	−	0.361291i
$99$		0			0
$100$	0.0569430	−	0.832477i	0.0569430	−	0.832477i
$101$		0			0		0.962917	−	0.269797i	$-0.0869565\pi$
$101$		0			0		−0.962917	+	0.269797i	$0.913043\pi$
$102$	−0.0534778	−	0.781818i	−0.0534778	−	0.781818i
$103$		0			0		−0.334880	−	0.942261i	$-0.608696\pi$
$103$		0			0		0.334880	+	0.942261i	$0.391304\pi$
$104$		0			0
$105$		0			0
$106$	−0.125383	−	0.241978i	−0.125383	−	0.241978i
$107$	0.894675	−	0.727872i	0.894675	−	0.727872i	−0.0682424	−	0.997669i	$-0.521739\pi$
$107$	0.894675	−	0.727872i	0.894675	−	0.727872i	0.962917	+	0.269797i	$0.0869565\pi$
$108$	−0.569538	+	0.609826i	−0.569538	+	0.609826i
$109$	0.125185	+	0.0543757i	0.125185	+	0.0543757i	0.460065	−	0.887885i	$-0.347826\pi$
$109$	0.125185	+	0.0543757i	0.125185	+	0.0543757i	−0.334880	+	0.942261i	$0.608696\pi$
$110$		0			0
$111$		0			0
$112$		0			0
$113$	0.277739	−	1.33655i	0.277739	−	1.33655i	−0.576680	−	0.816970i	$-0.695652\pi$
$113$	0.277739	−	1.33655i	0.277739	−	1.33655i	0.854419	−	0.519584i	$-0.173913\pi$
$114$	0.360528	+	0.101015i	0.360528	+	0.101015i
$115$	−0.572255	+	1.61017i	−0.572255	+	1.61017i
$116$		0			0
$117$		0			0
$118$		0			0
$119$		0			0
$120$	0.249970	−	0.703349i	0.249970	−	0.703349i
$121$	0.962917	+	0.269797i	0.962917	+	0.269797i
$122$	−0.128440	+	0.618088i	−0.128440	+	0.618088i
$123$		0			0
$124$	−1.63790	+	0.225125i	−1.63790	+	0.225125i
$125$	−0.576680	−	0.816970i	−0.576680	−	0.816970i
$126$		0			0
$127$		0			0		0.682553	−	0.730836i	$-0.260870\pi$
$127$		0			0		−0.682553	+	0.730836i	$0.739130\pi$
$128$	0.790436	−	0.643067i	0.790436	−	0.643067i
$129$		0			0
$130$		0			0
$131$		0			0		−0.682553	−	0.730836i	$-0.739130\pi$
$131$		0			0		0.682553	+	0.730836i	$0.260870\pi$
$132$		0			0
$133$		0			0
$134$		0			0
$135$	−0.0682424	+	0.997669i	−0.0682424	+	0.997669i
$136$	−0.292475	−	1.40747i	−0.292475	−	1.40747i
$137$	−0.0627919	+	0.121183i	−0.0627919	+	0.121183i	−0.917211	−	0.398401i	$-0.869565\pi$
$137$	−0.0627919	+	0.121183i	−0.0627919	+	0.121183i	0.854419	+	0.519584i	$0.173913\pi$
$138$	−0.400993	+	0.568078i	−0.400993	+	0.568078i
$139$	−1.56737	+	0.953137i	−1.56737	+	0.953137i	−0.576680	+	0.816970i	$0.695652\pi$
$139$	−1.56737	+	0.953137i	−1.56737	+	0.953137i	−0.990686	+	0.136167i	$0.956522\pi$
$140$		0			0
$141$	0.203456	+	0.979084i	0.203456	+	0.979084i
$142$		0			0
$143$		0			0
$144$	−0.306035	+	0.433553i	−0.306035	+	0.433553i
$145$		0			0
$146$		0			0
$147$	−0.0682424	+	0.997669i	−0.0682424	+	0.997669i
$148$		0			0
$149$		0			0		−0.0682424	−	0.997669i	$-0.521739\pi$
$149$		0			0		0.0682424	+	0.997669i	$0.478261\pi$
$150$	−0.136267	−	0.383417i	−0.136267	−	0.383417i
$151$	−1.05893	−	1.13384i	−1.05893	−	1.13384i	−0.990686	−	0.136167i	$-0.956522\pi$
$151$	−1.05893	−	1.13384i	−1.05893	−	1.13384i	−0.0682424	−	0.997669i	$-0.521739\pi$
$152$	0.680433	+	0.0935233i	0.680433	+	0.0935233i
$153$	0.886009	+	1.70992i	0.886009	+	1.70992i
$154$		0			0
$155$	−1.35239	+	1.44806i	−1.35239	+	1.44806i
$156$		0			0
$157$		0			0		−0.576680	−	0.816970i	$-0.695652\pi$
$157$		0			0		0.576680	+	0.816970i	$0.304348\pi$
$158$	0.798735	−	0.109784i	0.798735	−	0.109784i
$159$	0.519540	+	0.422677i	0.519540	+	0.422677i
$160$	0.195804	−	0.942261i	0.195804	−	0.942261i
$161$		0			0
$162$	−0.136267	+	0.383417i	−0.136267	+	0.383417i
$163$		0			0		0.917211	−	0.398401i	$-0.130435\pi$
$163$		0			0		−0.917211	+	0.398401i	$0.869565\pi$
$164$		0			0
$165$		0			0
$166$	0.0509395	−	0.0221261i	0.0509395	−	0.0221261i
$167$	0.224289	−	0.631088i	0.224289	−	0.631088i	−0.775711	−	0.631088i	$-0.782609\pi$
$167$	0.224289	−	0.631088i	0.224289	−	0.631088i	1.00000			$0$
$168$		0			0
$169$	0.203456	−	0.979084i	0.203456	−	0.979084i
$170$	−0.607882	−	0.494549i	−0.607882	−	0.494549i
$171$	−0.911560	+	0.125291i	−0.911560	+	0.125291i
$172$		0			0
$173$	−1.25209	−	0.543860i	−1.25209	−	0.543860i	−0.334880	−	0.942261i	$-0.608696\pi$
$173$	−1.25209	−	0.543860i	−1.25209	−	0.543860i	−0.917211	+	0.398401i	$0.869565\pi$
$174$		0			0
$175$		0			0
$176$		0			0
$177$		0			0
$178$		0			0
$179$		0			0		−0.334880	−	0.942261i	$-0.608696\pi$
$179$		0			0		0.334880	+	0.942261i	$0.391304\pi$
$180$	0.0569430	+	0.832477i	0.0569430	+	0.832477i
$181$	1.31448	−	0.368301i	1.31448	−	0.368301i	0.460065	−	0.887885i	$-0.347826\pi$
$181$	1.31448	−	0.368301i	1.31448	−	0.368301i	0.854419	+	0.519584i	$0.173913\pi$
$182$		0			0
$183$	−0.315646	−	1.51897i	−0.315646	−	1.51897i
$184$	−0.586841	+	1.13255i	−0.586841	+	1.13255i
$185$		0			0
$186$	−0.688871	+	0.418911i	−0.688871	+	0.418911i
$187$		0			0
$188$	0.279431	+	0.786244i	0.279431	+	0.786244i
$189$		0			0
$190$	0.319905	−	0.194538i	0.319905	−	0.194538i
$191$		0			0		0.576680	−	0.816970i	$-0.304348\pi$
$191$		0			0		−0.576680	+	0.816970i	$0.695652\pi$
$192$	−0.0639838	+	0.123483i	−0.0639838	+	0.123483i
$193$		0			0		−0.203456	−	0.979084i	$-0.565217\pi$
$193$		0			0		0.203456	+	0.979084i	$0.434783\pi$
$194$		0			0
$195$		0			0
$196$	0.0569430	+	0.832477i	0.0569430	+	0.832477i
$197$	0.519540	+	1.46184i	0.519540	+	1.46184i	0.854419	+	0.519584i	$0.173913\pi$
$197$	0.519540	+	1.46184i	0.519540	+	1.46184i	−0.334880	+	0.942261i	$0.608696\pi$
$198$		0			0
$199$	0.663521	+	0.0911989i	0.663521	+	0.0911989i	0.460065	−	0.887885i	$-0.347826\pi$
$199$	0.663521	+	0.0911989i	0.663521	+	0.0911989i	0.203456	+	0.979084i	$0.434783\pi$
$200$	−0.343415	−	0.662761i	−0.343415	−	0.662761i
$201$		0			0
$202$		0			0
$203$		0			0
$204$	0.926702	+	1.31284i	0.926702	+	1.31284i
$205$		0			0
$206$		0			0
$207$	0.347674	−	1.67310i	0.347674	−	1.67310i
$208$		0			0
$209$		0			0
$210$		0			0
$211$	−0.985454	−	0.599268i	−0.985454	−	0.599268i	−0.0682424	−	0.997669i	$-0.521739\pi$
$211$	−0.985454	−	0.599268i	−0.985454	−	0.599268i	−0.917211	+	0.398401i	$0.869565\pi$
$212$	0.477503	+	0.290376i	0.477503	+	0.290376i
$213$		0			0
$214$	0.157164	−	0.442218i	0.157164	−	0.442218i
$215$		0			0
$216$	−0.151869	+	0.730836i	−0.151869	+	0.730836i
$217$		0			0
$218$	0.0550200	−	0.00756233i	0.0550200	−	0.00756233i
$219$		0			0
$220$		0			0
$221$		0			0
$222$		0			0
$223$		0			0		−0.460065	−	0.887885i	$-0.652174\pi$
$223$		0			0		0.460065	+	0.887885i	$0.347826\pi$
$224$		0			0
$225$	0.682553	+	0.730836i	0.682553	+	0.730836i
$226$	−0.186018	−	0.523405i	−0.186018	−	0.523405i
$227$	0.105873	+	1.54781i	0.105873	+	1.54781i	0.682553	+	0.730836i	$0.260870\pi$
$227$	0.105873	+	1.54781i	0.105873	+	1.54781i	−0.576680	+	0.816970i	$0.695652\pi$
$228$	−0.739306	+	0.207144i	−0.739306	+	0.207144i
$229$	0.105873	−	1.54781i	0.105873	−	1.54781i	−0.576680	−	0.816970i	$-0.695652\pi$
$229$	0.105873	−	1.54781i	0.105873	−	1.54781i	0.682553	−	0.730836i	$-0.260870\pi$
$230$	0.141473	+	0.680803i	0.141473	+	0.680803i
$231$		0			0
$232$		0			0
$233$	−0.572255	+	0.347996i	−0.572255	+	0.347996i	−0.775711	−	0.631088i	$-0.782609\pi$
$233$	−0.572255	+	0.347996i	−0.572255	+	0.347996i	0.203456	+	0.979084i	$0.434783\pi$
$234$		0			0
$235$	0.854419	+	0.519584i	0.854419	+	0.519584i
$236$		0			0
$237$	−1.69292	+	1.02949i	−1.69292	+	1.02949i
$238$		0			0
$239$		0			0		0.460065	−	0.887885i	$-0.347826\pi$
$239$		0			0		−0.460065	+	0.887885i	$0.652174\pi$
$240$	0.107971	+	0.519584i	0.107971	+	0.519584i
$241$	0.0457060	−	0.668198i	0.0457060	−	0.668198i	−0.917211	−	0.398401i	$-0.869565\pi$
$241$	0.0457060	−	0.668198i	0.0457060	−	0.668198i	0.962917	−	0.269797i	$-0.0869565\pi$
$242$	0.391823	−	0.109784i	0.391823	−	0.109784i
$243$	−0.0682424	−	0.997669i	−0.0682424	−	0.997669i
$244$	−0.433516	−	1.21980i	−0.433516	−	1.21980i
$245$	0.682553	+	0.730836i	0.682553	+	0.730836i
$246$		0			0
$247$		0			0
$248$	−1.14727	+	0.933374i	−1.14727	+	0.933374i
$249$	−0.0931581	+	0.0997480i	−0.0931581	+	0.0997480i
$250$	−0.373224	−	0.162114i	−0.373224	−	0.162114i
$251$		0			0		−0.576680	−	0.816970i	$-0.695652\pi$
$251$		0			0		0.576680	+	0.816970i	$0.304348\pi$
$252$		0			0
$253$		0			0
$254$		0			0
$255$	1.85442	+	0.519584i	1.85442	+	0.519584i
$256$	0.0922795	−	0.259650i	0.0922795	−	0.259650i
$257$	−1.76640	+	0.767255i	−1.76640	+	0.767255i	−0.775711	+	0.631088i	$0.782609\pi$
$257$	−1.76640	+	0.767255i	−1.76640	+	0.767255i	−0.990686	+	0.136167i	$0.956522\pi$
$258$		0			0
$259$		0			0
$260$		0			0
$261$		0			0
$262$		0			0
$263$	0.347674	−	1.67310i	0.347674	−	1.67310i	−0.334880	−	0.942261i	$-0.608696\pi$
$263$	0.347674	−	1.67310i	0.347674	−	1.67310i	0.682553	−	0.730836i	$-0.260870\pi$
$264$		0			0
$265$	0.663521	−	0.0911989i	0.663521	−	0.0911989i
$266$		0			0
$267$		0			0
$268$		0			0
$269$		0			0		0.775711	−	0.631088i	$-0.217391\pi$
$269$		0			0		−0.775711	+	0.631088i	$0.782609\pi$
$270$	0.187206	+	0.361291i	0.187206	+	0.361291i
$271$	−0.911560	−	0.125291i	−0.911560	−	0.125291i	−0.334880	−	0.942261i	$-0.608696\pi$
$271$	−0.911560	−	0.125291i	−0.911560	−	0.125291i	−0.576680	+	0.816970i	$0.695652\pi$
$272$	0.697575	+	0.746921i	0.697575	+	0.746921i
$273$		0			0
$274$	0.00379000	+	0.0554078i	0.00379000	+	0.0554078i
$275$		0			0
$276$	0.0973064	−	1.42257i	0.0973064	−	1.42257i
$277$		0			0		−0.203456	−	0.979084i	$-0.565217\pi$
$277$		0			0		0.203456	+	0.979084i	$0.434783\pi$
$278$	−0.343415	+	0.662761i	−0.343415	+	0.662761i
$279$	1.14262	−	1.61872i	1.14262	−	1.61872i
$280$		0			0
$281$		0			0		1.00000			$0$
$281$		0			0		−1.00000			$\pi$
$282$	0.277739	+	0.297386i	0.277739	+	0.297386i
$283$		0			0		1.00000			$0$
$283$		0			0		−1.00000			$\pi$
$284$		0			0
$285$	−0.530621	+	0.751719i	−0.530621	+	0.751719i
$286$		0			0
$287$		0			0
$288$	−0.0656758	+	0.960147i	−0.0656758	+	0.960147i
$289$	2.60839	−	0.730836i	2.60839	−	0.730836i
$290$		0			0
$291$		0			0
$292$		0			0
$293$	−0.403122	−	0.0554078i	−0.403122	−	0.0554078i	−0.0682424	−	0.997669i	$-0.521739\pi$
$293$	−0.403122	−	0.0554078i	−0.403122	−	0.0554078i	−0.334880	+	0.942261i	$0.608696\pi$
$294$	0.187206	+	0.361291i	0.187206	+	0.361291i
$295$		0			0
$296$		0			0
$297$		0			0
$298$		0			0
$299$		0			0
$300$	0.647271	+	0.526594i	0.647271	+	0.526594i
$301$		0			0
$302$	−0.607882	−	0.170321i	−0.607882	−	0.170321i
$303$		0			0
$304$	−0.447872	+	0.194538i	−0.447872	+	0.194538i
$305$	−1.32557	−	0.806094i	−1.32557	−	0.806094i
$306$	0.669562	+	0.407169i	0.669562	+	0.407169i
$307$		0			0		0.917211	−	0.398401i	$-0.130435\pi$
$307$		0			0		−0.917211	+	0.398401i	$0.869565\pi$
$308$		0			0
$309$		0			0
$310$	−0.164035	+	0.789381i	−0.164035	+	0.789381i
$311$		0			0		−0.775711	−	0.631088i	$-0.782609\pi$
$311$		0			0		0.775711	+	0.631088i	$0.217391\pi$
$312$		0			0
$313$		0			0		−0.576680	−	0.816970i	$-0.695652\pi$
$313$		0			0		0.576680	+	0.816970i	$0.304348\pi$
$314$		0			0
$315$		0			0
$316$	−1.28248	+	1.04338i	−1.28248	+	1.04338i
$317$	−0.530621	−	1.02405i	−0.530621	−	1.02405i	−0.990686	−	0.136167i	$-0.956522\pi$
$317$	−0.530621	−	1.02405i	−0.530621	−	1.02405i	0.460065	−	0.887885i	$-0.347826\pi$
$318$	0.269995	+	0.0371099i	0.269995	+	0.0371099i
$319$		0			0
$320$	0.0465736	+	0.131045i	0.0465736	+	0.131045i
$321$	0.0787081	+	1.15067i	0.0787081	+	1.15067i
$322$		0			0
$323$	−0.120927	+	1.76789i	−0.120927	+	1.76789i
$324$	−0.169768	−	0.816970i	−0.169768	−	0.816970i
$325$		0			0
$326$		0			0
$327$	−0.116615	+	0.0709153i	−0.116615	+	0.0709153i
$328$		0			0
$329$		0			0
$330$		0			0
$331$	−0.116615	+	0.0709153i	−0.116615	+	0.0709153i	−0.576680	−	0.816970i	$-0.695652\pi$
$331$	−0.116615	+	0.0709153i	−0.116615	+	0.0709153i	0.460065	+	0.887885i	$0.347826\pi$
$332$	−0.0656758	+	0.0930415i	−0.0656758	+	0.0930415i
$333$		0			0
$334$	−0.0554485	−	0.266833i	−0.0554485	−	0.266833i
$335$		0			0
$336$		0			0
$337$		0			0		−0.0682424	−	0.997669i	$-0.521739\pi$
$337$		0			0		0.0682424	+	0.997669i	$0.478261\pi$
$338$	−0.136267	−	0.383417i	−0.136267	−	0.383417i
$339$	0.931758	+	0.997669i	0.931758	+	0.997669i
$340$	1.59199	+	0.218814i	1.59199	+	0.218814i
$341$		0			0
$342$	−0.290436	+	0.236287i	−0.290436	+	0.236287i
$343$		0			0
$344$		0			0
$345$	−0.985454	−	1.39607i	−0.985454	−	1.39607i
$346$	−0.550304	+	0.0756376i	−0.550304	+	0.0756376i
$347$	−1.05893	−	0.861502i	−1.05893	−	0.861502i	−0.0682424	−	0.997669i	$-0.521739\pi$
$347$	−1.05893	−	0.861502i	−1.05893	−	0.861502i	−0.990686	+	0.136167i	$0.956522\pi$
$348$		0			0
$349$	−1.76640	−	0.494921i	−1.76640	−	0.494921i	−0.775711	−	0.631088i	$-0.782609\pi$
$349$	−1.76640	−	0.494921i	−1.76640	−	0.494921i	−0.990686	+	0.136167i	$0.956522\pi$
$350$		0			0
$351$		0			0
$352$		0			0
$353$	0.786177	+	0.478085i	0.786177	+	0.478085i	0.854419	−	0.519584i	$-0.173913\pi$
$353$	0.786177	+	0.478085i	0.786177	+	0.478085i	−0.0682424	+	0.997669i	$0.521739\pi$
$354$		0			0
$355$		0			0
$356$		0			0
$357$		0			0
$358$		0			0
$359$		0			0		0.990686	−	0.136167i	$-0.0434783\pi$
$359$		0			0		−0.990686	+	0.136167i	$0.956522\pi$
$360$	0.430462	+	0.609826i	0.430462	+	0.609826i
$361$	0.140664	+	0.0610990i	0.140664	+	0.0610990i
$362$	0.379143	−	0.405963i	0.379143	−	0.405963i
$363$	−0.775711	+	0.631088i	−0.775711	+	0.631088i
$364$		0			0
$365$		0			0
$366$	−0.430891	−	0.461371i	−0.430891	−	0.461371i
$367$		0			0		−0.334880	−	0.942261i	$-0.608696\pi$
$367$		0			0		0.334880	+	0.942261i	$0.391304\pi$
$368$	−0.0618858	−	0.904739i	−0.0618858	−	0.904739i
$369$		0			0
$370$		0			0
$371$		0			0
$372$	0.760626	−	1.46794i	0.760626	−	1.46794i
$373$		0			0		0.576680	−	0.816970i	$-0.304348\pi$
$373$		0			0		−0.576680	+	0.816970i	$0.695652\pi$
$374$		0			0
$375$	1.00000			1.00000
$376$	0.579029	+	0.471075i	0.579029	+	0.471075i
$377$		0			0
$378$		0			0
$379$	0.665120	−	0.942261i	0.665120	−	0.942261i	−0.334880	−	0.942261i	$-0.608696\pi$
$379$	0.665120	−	0.942261i	0.665120	−	0.942261i	1.00000			$0$
$380$	−0.353228	+	0.681698i	−0.353228	+	0.681698i
$381$		0			0
$382$		0			0
$383$	1.31448	−	0.368301i	1.31448	−	0.368301i	0.460065	−	0.887885i	$-0.347826\pi$
$383$	1.31448	−	0.368301i	1.31448	−	0.368301i	0.854419	+	0.519584i	$0.173913\pi$
$384$	0.0695378	+	1.01661i	0.0695378	+	1.01661i
$385$		0			0
$386$		0			0
$387$		0			0
$388$		0			0
$389$		0			0		0.775711	−	0.631088i	$-0.217391\pi$
$389$		0			0		−0.775711	+	0.631088i	$0.782609\pi$
$390$		0			0
$391$	−3.01849	−	1.31111i	−3.01849	−	1.31111i
$392$	0.430462	+	0.609826i	0.430462	+	0.609826i
$393$		0			0
$394$	0.489701	+	0.398401i	0.489701	+	0.398401i
$395$	−0.403122	+	1.93993i	−0.403122	+	1.93993i
$396$		0			0
$397$		0			0		0.334880	−	0.942261i	$-0.391304\pi$
$397$		0			0		−0.334880	+	0.942261i	$0.608696\pi$
$398$	0.249970	−	0.108577i	0.249970	−	0.108577i
$399$		0			0
$400$	0.453426	+	0.275735i	0.453426	+	0.275735i
$401$		0			0		0.917211	−	0.398401i	$-0.130435\pi$
$401$		0			0		−0.917211	+	0.398401i	$0.869565\pi$
$402$		0			0
$403$		0			0
$404$		0			0
$405$	−0.775711	−	0.631088i	−0.775711	−	0.631088i
$406$		0			0
$407$		0			0
$408$	1.31852	+	0.572716i	1.31852	+	0.572716i
$409$	−1.25209	+	1.34066i	−1.25209	+	1.34066i	−0.334880	+	0.942261i	$0.608696\pi$
$409$	−1.25209	+	1.34066i	−1.25209	+	1.34066i	−0.917211	+	0.398401i	$0.869565\pi$
$410$		0			0
$411$	−0.0627919	−	0.121183i	−0.0627919	−	0.121183i
$412$		0			0
$413$		0			0
$414$	−0.232858	−	0.655198i	−0.232858	−	0.655198i
$415$	0.00931405	+	0.136167i	0.00931405	+	0.136167i
$416$		0			0
$417$	0.125185	−	1.83015i	0.125185	−	1.83015i
$418$		0			0
$419$		0			0		0.460065	−	0.887885i	$-0.347826\pi$
$419$		0			0		−0.460065	+	0.887885i	$0.652174\pi$
$420$		0			0
$421$	−0.985454	+	0.599268i	−0.985454	+	0.599268i	−0.917211	−	0.398401i	$-0.869565\pi$
$421$	−0.985454	+	0.599268i	−0.985454	+	0.599268i	−0.0682424	+	0.997669i	$0.521739\pi$
$422$	−0.469316			−0.469316
$423$	−0.917211	−	0.398401i	−0.917211	−	0.398401i
$424$	0.499941			0.499941
$425$	1.64547	−	1.00063i	1.64547	−	1.00063i
$426$		0			0
$427$		0			0
$428$	0.195804	+	0.942261i	0.195804	+	0.942261i
$429$		0			0
$430$		0			0
$431$		0			0		−0.0682424	−	0.997669i	$-0.521739\pi$
$431$		0			0		0.0682424	+	0.997669i	$0.478261\pi$
$432$	−0.177715	−	0.500042i	−0.177715	−	0.500042i
$433$		0			0		−0.682553	−	0.730836i	$-0.739130\pi$
$433$		0			0		0.682553	+	0.730836i	$0.260870\pi$
$434$		0			0
$435$		0			0
$436$	−0.0883427	+	0.0718721i	−0.0883427	+	0.0718721i
$437$	1.07322	−	1.14913i	1.07322	−	1.14913i
$438$		0			0
$439$	0.0787081	+	0.111504i	0.0787081	+	0.111504i	0.854419	−	0.519584i	$-0.173913\pi$
$439$	0.0787081	+	0.111504i	0.0787081	+	0.111504i	−0.775711	+	0.631088i	$0.782609\pi$
$440$		0			0
$441$	−0.775711	−	0.631088i	−0.775711	−	0.631088i
$442$		0			0
$443$	−0.131424	−	0.0368232i	−0.131424	−	0.0368232i	0.203456	−	0.979084i	$-0.434783\pi$
$443$	−0.131424	−	0.0368232i	−0.131424	−	0.0368232i	−0.334880	+	0.942261i	$0.608696\pi$
$444$		0			0
$445$		0			0
$446$		0			0
$447$		0			0
$448$		0			0
$449$		0			0		0.334880	−	0.942261i	$-0.391304\pi$
$449$		0			0		−0.334880	+	0.942261i	$0.608696\pi$
$450$	0.391823	+	0.109784i	0.391823	+	0.109784i
$451$		0			0
$452$	0.883594	+	0.718857i	0.883594	+	0.718857i
$453$	1.53697	−	0.211252i	1.53697	−	0.211252i
$454$	0.364054	+	0.515747i	0.364054	+	0.515747i
$455$		0			0
$456$	−0.468798	+	0.501960i	−0.468798	+	0.501960i
$457$		0			0		0.775711	−	0.631088i	$-0.217391\pi$
$457$		0			0		−0.775711	+	0.631088i	$0.782609\pi$
$458$	−0.290436	−	0.560515i	−0.290436	−	0.560515i
$459$	−1.90790	−	0.262234i	−1.90790	−	0.262234i
$460$	−0.973248	−	1.04209i	−0.973248	−	1.04209i
$461$		0			0		−0.334880	−	0.942261i	$-0.608696\pi$
$461$		0			0		0.334880	+	0.942261i	$0.391304\pi$
$462$		0			0
$463$		0			0		0.962917	−	0.269797i	$-0.0869565\pi$
$463$		0			0		−0.962917	+	0.269797i	$0.913043\pi$
$464$		0			0
$465$	−0.403122	−	1.93993i	−0.403122	−	1.93993i
$466$	−0.125383	+	0.241978i	−0.125383	+	0.241978i
$467$	1.05788	−	1.49867i	1.05788	−	1.49867i	0.203456	−	0.979084i	$-0.434783\pi$
$467$	1.05788	−	1.49867i	1.05788	−	1.49867i	0.854419	−	0.519584i	$-0.173913\pi$
$468$		0			0
$469$		0			0
$470$	0.406912			0.406912
$471$		0			0
$472$		0			0
$473$		0			0
$474$	−0.370925	+	0.715852i	−0.370925	+	0.715852i
$475$	0.187206	+	0.900885i	0.187206	+	0.900885i
$476$		0			0
$477$	−0.644923	+	0.180699i	−0.644923	+	0.180699i
$478$		0			0
$479$		0			0		−0.334880	−	0.942261i	$-0.608696\pi$
$479$		0			0		0.334880	+	0.942261i	$0.391304\pi$
$480$	0.656882	+	0.703349i	0.656882	+	0.703349i
$481$		0			0
$482$	−0.125383	−	0.241978i	−0.125383	−	0.241978i
$483$		0			0
$484$	−0.569538	+	0.609826i	−0.569538	+	0.609826i
$485$		0			0
$486$	−0.234658	−	0.332435i	−0.234658	−	0.332435i
$487$		0			0		0.990686	−	0.136167i	$-0.0434783\pi$
$487$		0			0		−0.990686	+	0.136167i	$0.956522\pi$
$488$	−0.898318	−	0.730836i	−0.898318	−	0.730836i
$489$		0			0
$490$	0.391823	+	0.109784i	0.391823	+	0.109784i
$491$		0			0		0.334880	−	0.942261i	$-0.391304\pi$
$491$		0			0		−0.334880	+	0.942261i	$0.608696\pi$
$492$		0			0
$493$		0			0
$494$		0			0
$495$		0			0
$496$	0.352120	−	0.990770i	0.352120	−	0.990770i
$497$		0			0
$498$	−0.0112994	+	0.0543757i	−0.0112994	+	0.0543757i
$499$	−1.32557	−	1.07843i	−1.32557	−	1.07843i	−0.990686	−	0.136167i	$-0.956522\pi$
$499$	−1.32557	−	1.07843i	−1.32557	−	1.07843i	−0.334880	−	0.942261i	$-0.608696\pi$
$500$	0.826651	−	0.113621i	0.826651	−	0.113621i
$501$	0.386237	+	0.547173i	0.386237	+	0.547173i
$502$		0			0
$503$	0.277739	−	0.297386i	0.277739	−	0.297386i	−0.576680	−	0.816970i	$-0.695652\pi$
$503$	0.277739	−	0.297386i	0.277739	−	0.297386i	0.854419	+	0.519584i	$0.173913\pi$
$504$		0			0
$505$		0			0
$506$		0			0
$507$	0.682553	+	0.730836i	0.682553	+	0.730836i
$508$		0			0
$509$		0			0		−0.0682424	−	0.997669i	$-0.521739\pi$
$509$		0			0		0.0682424	+	0.997669i	$0.478261\pi$
$510$	0.754586	−	0.211425i	0.754586	−	0.211425i
$511$		0			0
$512$	0.184505	+	0.887885i	0.184505	+	0.887885i
$513$	0.423320	−	0.816970i	0.423320	−	0.816970i
$514$	−0.451913	+	0.640215i	−0.451913	+	0.640215i
$515$		0			0
$516$		0			0
$517$		0			0
$518$		0			0
$519$	1.16637	−	0.709287i	1.16637	−	0.709287i
$520$		0			0
$521$		0			0		0.460065	−	0.887885i	$-0.347826\pi$
$521$		0			0		−0.460065	+	0.887885i	$0.652174\pi$
$522$		0			0
$523$		0			0		0.0682424	−	0.997669i	$-0.478261\pi$
$523$		0			0		−0.0682424	+	0.997669i	$0.521739\pi$
$524$		0			0
$525$		0			0
$526$	−0.232858	−	0.655198i	−0.232858	−	0.655198i
$527$	−2.60448	−	2.78872i	−2.60448	−	2.78872i
$528$		0			0
$529$	0.883385	+	1.70486i	0.883385	+	1.70486i
$530$	0.211407	−	0.171992i	0.211407	−	0.171992i
$531$		0			0
$532$		0			0
$533$		0			0
$534$		0			0
$535$	0.894675	+	0.727872i	0.894675	+	0.727872i
$536$		0			0
$537$		0			0
$538$		0			0
$539$		0			0
$540$	−0.712947	−	0.433553i	−0.712947	−	0.433553i
$541$	−1.69292	−	1.02949i	−1.69292	−	1.02949i	−0.917211	−	0.398401i	$-0.869565\pi$
$541$	−1.69292	−	1.02949i	−1.69292	−	1.02949i	−0.775711	−	0.631088i	$-0.782609\pi$
$542$	−0.343415	+	0.149166i	−0.343415	+	0.149166i
$543$	−0.457146	+	1.28629i	−0.457146	+	1.28629i
$544$	1.78468	+	0.500042i	1.78468	+	0.500042i
$545$	−0.0277687	+	0.133630i	−0.0277687	+	0.133630i
$546$		0			0
$547$		0			0		0.990686	−	0.136167i	$-0.0434783\pi$
$547$		0			0		−0.990686	+	0.136167i	$0.956522\pi$
$548$	−0.0656758	−	0.0930415i	−0.0656758	−	0.0930415i
$549$	1.42298	+	0.618088i	1.42298	+	0.618088i
$550$		0			0
$551$		0			0
$552$	−0.586841	−	1.13255i	−0.586841	−	1.13255i
$553$		0			0
$554$		0			0
$555$		0			0
$556$	−0.104458	−	1.52712i	−0.104458	−	1.52712i
$557$	1.85442	−	0.519584i	1.85442	−	0.519584i	0.854419	−	0.519584i	$-0.173913\pi$
$557$	1.85442	−	0.519584i	1.85442	−	0.519584i	1.00000			$0$
$558$	0.0550200	−	0.804365i	0.0550200	−	0.804365i
$559$		0			0
$560$		0			0
$561$		0			0
$562$		0			0
$563$	1.92583			1.92583			0.962917	−	0.269797i	$-0.0869565\pi$
$563$	1.92583			1.92583			0.962917	+	0.269797i	$0.0869565\pi$
$564$	−0.803480	−	0.225125i	−0.803480	−	0.225125i
$565$	1.36511			1.36511
$566$		0			0
$567$		0			0
$568$		0			0
$569$		0			0		−0.203456	−	0.979084i	$-0.565217\pi$
$569$		0			0		0.203456	+	0.979084i	$0.434783\pi$
$570$	−0.0255508	+	0.373539i	−0.0255508	+	0.373539i
$571$	0.886009	−	0.248248i	0.886009	−	0.248248i	0.203456	−	0.979084i	$-0.434783\pi$
$571$	0.886009	−	0.248248i	0.886009	−	0.248248i	0.682553	+	0.730836i	$0.260870\pi$
$572$		0			0
$573$		0			0
$574$		0			0
$575$	−1.69292	−	0.232687i	−1.69292	−	0.232687i
$576$	−0.0639838	−	0.123483i	−0.0639838	−	0.123483i
$577$		0			0		0.775711	−	0.631088i	$-0.217391\pi$
$577$		0			0		−0.775711	+	0.631088i	$0.782609\pi$
$578$	0.752350	−	0.805571i	0.752350	−	0.805571i
$579$		0			0
$580$		0			0
$581$		0			0
$582$		0			0
$583$		0			0
$584$		0			0
$585$		0			0
$586$	−0.151869	+	0.0659662i	−0.151869	+	0.0659662i
$587$	0.786177	+	0.478085i	0.786177	+	0.478085i	0.854419	−	0.519584i	$-0.173913\pi$
$587$	0.786177	+	0.478085i	0.786177	+	0.478085i	−0.0682424	+	0.997669i	$0.521739\pi$
$588$	−0.712947	−	0.433553i	−0.712947	−	0.433553i
$589$	1.67219	−	0.726333i	1.67219	−	0.726333i
$590$		0			0
$591$	−1.49389	−	0.418569i	−1.49389	−	0.418569i
$592$		0			0
$593$	−0.315646	−	0.256797i	−0.315646	−	0.256797i	0.460065	−	0.887885i	$-0.347826\pi$
$593$	−0.315646	−	0.256797i	−0.315646	−	0.256797i	−0.775711	+	0.631088i	$0.782609\pi$
$594$		0			0
$595$		0			0
$596$		0			0
$597$	−0.457146	+	0.489484i	−0.457146	+	0.489484i
$598$		0			0
$599$		0			0		−0.460065	−	0.887885i	$-0.652174\pi$
$599$		0			0		0.460065	+	0.887885i	$0.347826\pi$
$600$	0.739496	+	0.101641i	0.739496	+	0.101641i
$601$	0.931758	+	0.997669i	0.931758	+	0.997669i	1.00000			$0$
$601$	0.931758	+	0.997669i	0.931758	+	0.997669i	−0.0682424	+	0.997669i	$0.521739\pi$
$602$		0			0
$603$		0			0
$604$	1.24654	−	0.349263i	1.24654	−	0.349263i
$605$	−0.0682424	+	0.997669i	−0.0682424	+	0.997669i
$606$		0			0
$607$		0			0		0.460065	−	0.887885i	$-0.347826\pi$
$607$		0			0		−0.460065	+	0.887885i	$0.652174\pi$
$608$	−0.510664	+	0.723447i	−0.510664	+	0.723447i
$609$		0			0
$610$	−0.631293			−0.631293
$611$		0			0
$612$	−1.60696			−1.60696
$613$		0			0		0.854419	−	0.519584i	$-0.173913\pi$
$613$		0			0		−0.854419	+	0.519584i	$0.826087\pi$
$614$		0			0
$615$		0			0
$616$		0			0
$617$	0.135214	−	1.97675i	0.135214	−	1.97675i	−0.0682424	−	0.997669i	$-0.521739\pi$
$617$	0.135214	−	1.97675i	0.135214	−	1.97675i	0.203456	−	0.979084i	$-0.434783\pi$
$618$		0			0
$619$	0.105873	+	1.54781i	0.105873	+	1.54781i	0.682553	+	0.730836i	$0.260870\pi$
$619$	0.105873	+	1.54781i	0.105873	+	1.54781i	−0.576680	+	0.816970i	$0.695652\pi$
$620$	−0.553657	−	1.55784i	−0.553657	−	1.55784i
$621$	1.16637	+	1.24888i	1.16637	+	1.24888i
$622$		0			0
$623$		0			0
$624$		0			0
$625$	0.682553	−	0.730836i	0.682553	−	0.730836i
$626$		0			0
$627$		0			0
$628$		0			0
$629$		0			0
$630$		0			0
$631$	1.64547	+	0.461039i	1.64547	+	0.461039i	0.962917	−	0.269797i	$-0.0869565\pi$
$631$	1.64547	+	0.461039i	1.64547	+	0.461039i	0.682553	+	0.730836i	$0.260870\pi$
$632$	−0.495284	+	1.39360i	−0.495284	+	1.39360i
$633$	1.05788	−	0.459500i	1.05788	−	0.459500i
$634$	−0.400993	−	0.243849i	−0.400993	−	0.243849i
$635$		0			0
$636$	−0.512595	+	0.222651i	−0.512595	+	0.222651i
$637$		0			0
$638$		0			0
$639$		0			0
$640$	0.790436	+	0.643067i	0.790436	+	0.643067i
$641$		0			0		0.990686	−	0.136167i	$-0.0434783\pi$
$641$		0			0		−0.990686	+	0.136167i	$0.956522\pi$
$642$	0.270645	+	0.383417i	0.270645	+	0.383417i
$643$		0			0		−0.917211	−	0.398401i	$-0.869565\pi$
$643$		0			0		0.917211	+	0.398401i	$0.130435\pi$
$644$		0			0
$645$		0			0
$646$	0.331732	+	0.640215i	0.331732	+	0.640215i
$647$	0.663521	+	0.0911989i	0.663521	+	0.0911989i	0.460065	−	0.887885i	$-0.347826\pi$
$647$	0.663521	+	0.0911989i	0.663521	+	0.0911989i	0.203456	+	0.979084i	$0.434783\pi$
$648$	−0.509491	−	0.545531i	−0.509491	−	0.545531i
$649$		0			0
$650$		0			0
$651$		0			0
$652$		0			0
$653$	0.187206	+	0.900885i	0.187206	+	0.900885i	0.962917	+	0.269797i	$0.0869565\pi$
$653$	0.187206	+	0.900885i	0.187206	+	0.900885i	−0.775711	+	0.631088i	$0.782609\pi$
$654$	−0.0255508	+	0.0493108i	−0.0255508	+	0.0493108i
$655$		0			0
$656$		0			0
$657$		0			0
$658$		0			0
$659$		0			0		1.00000			$0$
$659$		0			0		−1.00000			$\pi$
$660$		0			0
$661$	−1.11059	+	1.57335i	−1.11059	+	1.57335i	−0.334880	+	0.942261i	$0.608696\pi$
$661$	−1.11059	+	1.57335i	−1.11059	+	1.57335i	−0.775711	+	0.631088i	$0.782609\pi$
$662$	−0.0255508	+	0.0493108i	−0.0255508	+	0.0493108i
$663$		0			0
$664$	−0.00695246	+	0.101641i	−0.00695246	+	0.101641i
$665$		0			0
$666$		0			0
$667$		0			0
$668$	0.381453	+	0.408437i	0.381453	+	0.408437i
$669$		0			0
$670$		0			0
$671$		0			0
$672$		0			0
$673$		0			0		−0.917211	−	0.398401i	$-0.869565\pi$
$673$		0			0		0.917211	+	0.398401i	$0.130435\pi$
$674$		0			0
$675$	−0.990686	+	0.136167i	−0.990686	+	0.136167i
$676$	0.647271	+	0.526594i	0.647271	+	0.526594i
$677$	−0.373224	+	1.79605i	−0.373224	+	1.79605i	0.203456	+	0.979084i	$0.434783\pi$
$677$	−0.373224	+	1.79605i	−0.373224	+	1.79605i	−0.576680	+	0.816970i	$0.695652\pi$
$678$	0.534880	+	0.149866i	0.534880	+	0.149866i
$679$		0			0
$680$	1.31852	−	0.572716i	1.31852	−	0.572716i
$681$	−1.32557	−	0.806094i	−1.32557	−	0.806094i
$682$		0			0
$683$	−1.56737	+	0.680803i	−1.56737	+	0.680803i	−0.990686	−	0.136167i	$-0.956522\pi$
$683$	−1.56737	+	0.680803i	−1.56737	+	0.680803i	−0.576680	+	0.816970i	$0.695652\pi$
$684$	0.257113	−	0.723447i	0.257113	−	0.723447i
$685$	−0.131424	−	0.0368232i	−0.131424	−	0.0368232i
$686$		0			0
$687$	1.20346	+	0.979084i	1.20346	+	0.979084i
$688$		0			0
$689$		0			0
$690$	−0.637780	−	0.277027i	−0.637780	−	0.277027i
$691$	1.31448	−	1.40747i	1.31448	−	1.40747i	0.460065	−	0.887885i	$-0.347826\pi$
$691$	1.31448	−	1.40747i	1.31448	−	1.40747i	0.854419	−	0.519584i	$-0.173913\pi$
$692$	0.883594	−	0.718857i	0.883594	−	0.718857i
$693$		0			0
$694$	−0.550304	−	0.0756376i	−0.550304	−	0.0756376i
$695$	−1.25209	−	1.34066i	−1.25209	−	1.34066i
$696$		0			0
$697$		0			0
$698$	−0.718768	+	0.201389i	−0.718768	+	0.201389i
$699$	0.0457060	−	0.668198i	0.0457060	−	0.668198i
$700$		0			0
$701$		0			0		0.460065	−	0.887885i	$-0.347826\pi$
$701$		0			0		−0.460065	+	0.887885i	$0.652174\pi$
$702$		0			0
$703$		0			0
$704$		0			0
$705$	−0.917211	+	0.398401i	−0.917211	+	0.398401i
$706$	0.374412			0.374412
$707$		0			0
$708$		0			0
$709$	0.786177	−	1.51725i	0.786177	−	1.51725i	−0.0682424	−	0.997669i	$-0.521739\pi$
$709$	0.786177	−	1.51725i	0.786177	−	1.51725i	0.854419	−	0.519584i	$-0.173913\pi$
$710$		0			0
$711$	0.135214	−	1.97675i	0.135214	−	1.97675i
$712$		0			0
$713$	0.231058	+	3.37795i	0.231058	+	3.37795i
$714$		0			0
$715$		0			0
$716$		0			0
$717$		0			0
$718$		0			0
$719$		0			0		0.682553	−	0.730836i	$-0.260870\pi$
$719$		0			0		−0.682553	+	0.730836i	$0.739130\pi$
$720$	−0.486749	−	0.211425i	−0.486749	−	0.211425i
$721$		0			0
$722$	0.0618231	−	0.00849738i	0.0618231	−	0.00849738i
$723$	0.519540	+	0.422677i	0.519540	+	0.422677i
$724$	−0.231752	+	1.11525i	−0.231752	+	1.11525i
$725$		0			0
$726$	−0.136267	+	0.383417i	−0.136267	+	0.383417i
$727$		0			0		0.917211	−	0.398401i	$-0.130435\pi$
$727$		0			0		−0.917211	+	0.398401i	$0.869565\pi$
$728$		0			0
$729$	0.854419	+	0.519584i	0.854419	+	0.519584i
$730$		0			0
$731$		0			0
$732$	1.24654	+	0.349263i	1.24654	+	0.349263i
$733$		0			0		0.203456	−	0.979084i	$-0.434783\pi$
$733$		0			0		−0.203456	+	0.979084i	$0.565217\pi$
$734$		0			0
$735$	−0.990686	+	0.136167i	−0.990686	+	0.136167i
$736$	−0.948391	−	1.34356i	−0.948391	−	1.34356i
$737$		0			0
$738$		0			0
$739$	−1.05893	+	0.861502i	−1.05893	+	0.861502i	−0.990686	−	0.136167i	$-0.956522\pi$
$739$	−1.05893	+	0.861502i	−1.05893	+	0.861502i	−0.0682424	+	0.997669i	$0.521739\pi$
$740$		0			0
$741$		0			0
$742$		0			0
$743$	−0.308133	−	0.867003i	−0.308133	−	0.867003i	−0.990686	−	0.136167i	$-0.956522\pi$
$743$	−0.308133	−	0.867003i	−0.308133	−	0.867003i	0.682553	−	0.730836i	$-0.260870\pi$
$744$	−0.100930	−	1.47554i	−0.100930	−	1.47554i
$745$		0			0
$746$		0			0
$747$	−0.0277687	−	0.133630i	−0.0277687	−	0.133630i
$748$		0			0
$749$		0			0
$750$	0.347674	−	0.211425i	0.347674	−	0.211425i
$751$	−1.15336			−1.15336			−0.576680	−	0.816970i	$-0.695652\pi$
$751$	−1.15336			−1.15336			−0.576680	+	0.816970i	$0.695652\pi$
$752$	−0.525741	−	0.0722614i	−0.525741	−	0.0722614i
$753$		0			0
$754$		0			0
$755$	0.894675	−	1.26747i	0.894675	−	1.26747i
$756$		0			0
$757$		0			0		−0.203456	−	0.979084i	$-0.565217\pi$
$757$		0			0		0.203456	+	0.979084i	$0.434783\pi$
$758$	0.0320273	−	0.468222i	0.0320273	−	0.468222i
$759$		0			0
$760$	0.0468709	+	0.685229i	0.0468709	+	0.685229i
$761$		0			0		−0.334880	−	0.942261i	$-0.608696\pi$
$761$		0			0		0.334880	+	0.942261i	$0.391304\pi$
$762$		0			0
$763$		0			0
$764$		0			0
$765$	−1.49389	+	1.21537i	−1.49389	+	1.21537i
$766$	0.379143	−	0.405963i	0.379143	−	0.405963i
$767$		0			0
$768$	0.158910	+	0.225125i	0.158910	+	0.225125i
$769$	−1.90790	+	0.262234i	−1.90790	+	0.262234i	−0.990686	−	0.136167i	$-0.956522\pi$
$769$	−1.90790	+	0.262234i	−1.90790	+	0.262234i	−0.917211	+	0.398401i	$0.869565\pi$
$770$		0			0
$771$	0.391823	−	1.88555i	0.391823	−	1.88555i
$772$		0			0
$773$	0.614311	−	1.72850i	0.614311	−	1.72850i	−0.0682424	−	0.997669i	$-0.521739\pi$
$773$	0.614311	−	1.72850i	0.614311	−	1.72850i	0.682553	−	0.730836i	$-0.260870\pi$
$774$		0			0
$775$	−1.69292	−	1.02949i	−1.69292	−	1.02949i
$776$		0			0
$777$		0			0
$778$		0			0
$779$		0			0
$780$		0			0
$781$		0			0
$782$	−1.32665	+	0.182344i	−1.32665	+	0.182344i
$783$		0			0
$784$	−0.486749	−	0.211425i	−0.486749	−	0.211425i
$785$		0			0
$786$		0			0
$787$		0			0		−0.460065	−	0.887885i	$-0.652174\pi$
$787$		0			0		0.460065	+	0.887885i	$0.347826\pi$
$788$	−1.28248	−	0.176273i	−1.28248	−	0.176273i
$789$	1.16637	+	1.24888i	1.16637	+	1.24888i
$790$	0.269995	+	0.759692i	0.269995	+	0.759692i
$791$		0			0
$792$		0			0
$793$		0			0
$794$		0			0
$795$	−0.308133	+	0.594669i	−0.308133	+	0.594669i
$796$	−0.322285	+	0.456574i	−0.322285	+	0.456574i
$797$	−1.56737	+	0.953137i	−1.56737	+	0.953137i	−0.576680	+	0.816970i	$0.695652\pi$
$797$	−1.56737	+	0.953137i	−1.56737	+	0.953137i	−0.990686	+	0.136167i	$0.956522\pi$
$798$		0			0
$799$	−1.11059	+	1.57335i	−1.11059	+	1.57335i
$800$	0.962390			0.962390
$801$		0			0
$802$		0			0
$803$		0			0
$804$		0			0
$805$		0			0
$806$		0			0
$807$		0			0
$808$		0			0
$809$		0			0		−0.682553	−	0.730836i	$-0.739130\pi$
$809$		0			0		0.682553	+	0.730836i	$0.260870\pi$
$810$	−0.403122	−	0.0554078i	−0.403122	−	0.0554078i
$811$	0.628038	+	1.21206i	0.628038	+	1.21206i	0.962917	+	0.269797i	$0.0869565\pi$
$811$	0.628038	+	1.21206i	0.628038	+	1.21206i	−0.334880	+	0.942261i	$0.608696\pi$
$812$		0			0
$813$	0.628038	−	0.672464i	0.628038	−	0.672464i
$814$		0			0
$815$		0			0
$816$	−1.01249	+	0.139164i	−1.01249	+	0.139164i
$817$		0			0
$818$	−0.151869	+	0.730836i	−0.151869	+	0.730836i
$819$		0			0
$820$		0			0
$821$		0			0		0.917211	−	0.398401i	$-0.130435\pi$
$821$		0			0		−0.917211	+	0.398401i	$0.869565\pi$
$822$	−0.0474522	−	0.0288563i	−0.0474522	−	0.0288563i
$823$		0			0		−0.854419	−	0.519584i	$-0.826087\pi$
$823$		0			0		0.854419	+	0.519584i	$0.173913\pi$
$824$		0			0
$825$		0			0
$826$		0			0
$827$	−0.373224	+	1.79605i	−0.373224	+	1.79605i	0.203456	+	0.979084i	$0.434783\pi$
$827$	−0.373224	+	1.79605i	−0.373224	+	1.79605i	−0.576680	+	0.816970i	$0.695652\pi$
$828$	1.10608	+	0.899864i	1.10608	+	0.899864i
$829$	−0.403122	+	0.0554078i	−0.403122	+	0.0554078i	−0.334880	−	0.942261i	$-0.608696\pi$
$829$	−0.403122	+	0.0554078i	−0.403122	+	0.0554078i	−0.0682424	+	0.997669i	$0.521739\pi$
$830$	0.0320273	+	0.0453723i	0.0320273	+	0.0453723i
$831$		0			0
$832$		0			0
$833$	−1.49389	+	1.21537i	−1.49389	+	1.21537i
$834$	−0.343415	−	0.662761i	−0.343415	−	0.662761i
$835$	0.663521	+	0.0911989i	0.663521	+	0.0911989i
$836$		0			0
$837$	0.663521	+	1.86697i	0.663521	+	1.86697i
$838$		0			0
$839$		0			0		0.962917	−	0.269797i	$-0.0869565\pi$
$839$		0			0		−0.962917	+	0.269797i	$0.913043\pi$
$840$		0			0
$841$	0.203456	+	0.979084i	0.203456	+	0.979084i
$842$	−0.215916	+	0.416699i	−0.215916	+	0.416699i
$843$		0			0
$844$	0.822285	−	0.500042i	0.822285	−	0.500042i
$845$	1.00000			1.00000
$846$	−0.403122	+	0.0554078i	−0.403122	+	0.0554078i
$847$		0			0
$848$	−0.303687	+	0.184676i	−0.303687	+	0.184676i
$849$		0			0
$850$	0.360528	−	0.695787i	0.360528	−	0.695787i
$851$		0			0
$852$		0			0
$853$		0			0		0.962917	−	0.269797i	$-0.0869565\pi$
$853$		0			0		−0.962917	+	0.269797i	$0.913043\pi$
$854$		0			0
$855$	−0.308133	−	0.867003i	−0.308133	−	0.867003i
$856$	0.587627	+	0.629195i	0.587627	+	0.629195i
$857$	1.14262	+	0.157049i	1.14262	+	0.157049i	0.682553	−	0.730836i	$-0.260870\pi$
$857$	1.14262	+	0.157049i	1.14262	+	0.157049i	0.460065	+	0.887885i	$0.347826\pi$
$858$		0			0
$859$	−0.315646	+	0.256797i	−0.315646	+	0.256797i	−0.775711	−	0.631088i	$-0.782609\pi$
$859$	−0.315646	+	0.256797i	−0.315646	+	0.256797i	0.460065	+	0.887885i	$0.347826\pi$
$860$		0			0
$861$		0			0
$862$		0			0
$863$	1.96292	−	0.269797i	1.96292	−	0.269797i	0.962917	−	0.269797i	$-0.0869565\pi$
$863$	1.96292	−	0.269797i	1.96292	−	0.269797i	1.00000			$0$
$864$	−0.746537	−	0.607353i	−0.746537	−	0.607353i
$865$	0.277739	−	1.33655i	0.277739	−	1.33655i
$866$		0			0
$867$	−0.907135	+	2.55243i	−0.907135	+	2.55243i
$868$		0			0
$869$		0			0
$870$		0			0
$871$		0			0
$872$	−0.0341172	+	0.0959965i	−0.0341172	+	0.0959965i
$873$		0			0
$874$	0.130173	−	0.626428i	0.130173	−	0.626428i
$875$		0			0
$876$		0			0
$877$		0			0		−0.576680	−	0.816970i	$-0.695652\pi$
$877$		0			0		0.576680	+	0.816970i	$0.304348\pi$
$878$	0.0509395	+	0.0221261i	0.0509395	+	0.0221261i
$879$	0.277739	−	0.297386i	0.277739	−	0.297386i
$880$		0			0
$881$		0			0		−0.460065	−	0.887885i	$-0.652174\pi$
$881$		0			0		0.460065	+	0.887885i	$0.347826\pi$
$882$	−0.403122	−	0.0554078i	−0.403122	−	0.0554078i
$883$		0			0		−0.682553	−	0.730836i	$-0.739130\pi$
$883$		0			0		0.682553	+	0.730836i	$0.260870\pi$
$884$		0			0
$885$		0			0
$886$	−0.0534778	+	0.0149838i	−0.0534778	+	0.0149838i
$887$	−0.0627919	+	0.917985i	−0.0627919	+	0.917985i	0.854419	+	0.519584i	$0.173913\pi$
$887$	−0.0627919	+	0.917985i	−0.0627919	+	0.917985i	−0.917211	+	0.398401i	$0.869565\pi$
$888$		0			0
$889$		0			0
$890$		0			0
$891$		0			0
$892$		0			0
$893$	−0.530621	−	0.751719i	−0.530621	−	0.751719i
$894$		0			0
$895$		0			0
$896$		0			0
$897$		0			0
$898$		0			0
$899$		0			0
$900$	−0.803480	+	0.225125i	−0.803480	+	0.225125i
$901$	0.0880222	+	1.28684i	0.0880222	+	1.28684i
$902$		0			0
$903$		0			0
$904$	1.00949	+	0.138751i	1.00949	+	0.138751i
$905$	0.628038	+	1.21206i	0.628038	+	1.21206i
$906$	0.489701	−	0.398401i	0.489701	−	0.398401i
$907$		0			0		0.682553	−	0.730836i	$-0.260870\pi$
$907$		0			0		−0.682553	+	0.730836i	$0.739130\pi$
$908$	−1.18737	−	0.515747i	−1.18737	−	0.515747i
$909$		0			0
$910$		0			0
$911$		0			0		−0.775711	−	0.631088i	$-0.782609\pi$
$911$		0			0		0.775711	+	0.631088i	$0.217391\pi$
$912$	0.0993472	−	0.478085i	0.0993472	−	0.478085i
$913$		0			0
$914$		0			0
$915$	1.42298	−	0.618088i	1.42298	−	0.618088i
$916$	1.10608	+	0.672623i	1.10608	+	0.672623i
$917$		0			0
$918$	−0.718768	+	0.312205i	−0.718768	+	0.312205i
$919$	−0.572255	+	1.61017i	−0.572255	+	1.61017i	0.203456	+	0.979084i	$0.434783\pi$
$919$	−0.572255	+	1.61017i	−0.572255	+	1.61017i	−0.775711	+	0.631088i	$0.782609\pi$
$920$	−1.22826	−	0.344142i	−1.22826	−	0.344142i
$921$		0			0
$922$		0			0
$923$		0			0
$924$		0			0
$925$		0			0
$926$		0			0
$927$		0			0
$928$		0			0
$929$		0			0		−0.990686	−	0.136167i	$-0.956522\pi$
$929$		0			0		0.990686	+	0.136167i	$0.0434783\pi$
$930$	−0.550304	−	0.589232i	−0.550304	−	0.589232i
$931$	−0.308133	−	0.867003i	−0.308133	−	0.867003i
$932$	−0.0381381	−	0.557559i	−0.0381381	−	0.557559i
$933$		0			0
$934$	0.0509395	−	0.744708i	0.0509395	−	0.744708i
$935$		0			0
$936$		0			0
$937$		0			0		0.576680	−	0.816970i	$-0.304348\pi$
$937$		0			0		−0.576680	+	0.816970i	$0.695652\pi$
$938$		0			0
$939$		0			0
$940$	−0.712947	+	0.433553i	−0.712947	+	0.433553i
$941$		0			0		1.00000			$0$
$941$		0			0		−1.00000			$\pi$
$942$		0			0
$943$		0			0
$944$		0			0
$945$		0			0
$946$		0			0
$947$	−1.76640	+	0.494921i	−1.76640	+	0.494921i	−0.990686	−	0.136167i	$-0.956522\pi$
$947$	−1.76640	+	0.494921i	−1.76640	+	0.494921i	−0.775711	+	0.631088i	$0.782609\pi$
$948$	−0.112825	−	1.64945i	−0.112825	−	1.64945i
$949$		0			0
$950$	0.255556	+	0.273634i	0.255556	+	0.273634i
$951$	1.14262	+	0.157049i	1.14262	+	0.157049i
$952$		0			0
$953$	−0.315646	+	0.256797i	−0.315646	+	0.256797i	−0.775711	−	0.631088i	$-0.782609\pi$
$953$	−0.315646	+	0.256797i	−0.315646	+	0.256797i	0.460065	+	0.887885i	$0.347826\pi$
$954$	−0.186018	+	0.199177i	−0.186018	+	0.199177i
$955$		0			0
$956$		0			0
$957$		0			0
$958$		0			0
$959$		0			0
$960$	−0.133918	−	0.0375221i	−0.133918	−	0.0375221i
$961$	−0.979802	+	2.75690i	−0.979802	+	2.75690i
$962$		0			0
$963$	−0.985454	−	0.599268i	−0.985454	−	0.599268i
$964$	0.477503	+	0.290376i	0.477503	+	0.290376i
$965$		0			0
$966$		0			0
$967$		0			0		−0.962917	−	0.269797i	$-0.913043\pi$
$967$		0			0		0.962917	+	0.269797i	$0.0869565\pi$
$968$	−0.151869	+	0.730836i	−0.151869	+	0.730836i
$969$	−1.37457	−	1.11830i	−1.37457	−	1.11830i
$970$		0			0
$971$		0			0		−0.576680	−	0.816970i	$-0.695652\pi$
$971$		0			0		0.576680	+	0.816970i	$0.304348\pi$
$972$	0.765342	+	0.332435i	0.765342	+	0.332435i
$973$		0			0
$974$		0			0
$975$		0			0
$976$	0.815646	+	0.112108i	0.815646	+	0.112108i
$977$	0.931758	+	0.997669i	0.931758	+	0.997669i	1.00000			$0$
$977$	0.931758	+	0.997669i	0.931758	+	0.997669i	−0.0682424	+	0.997669i	$0.521739\pi$
$978$		0			0
$979$		0			0
$980$	−0.803480	+	0.225125i	−0.803480	+	0.225125i
$981$	0.00931405	−	0.136167i	0.00931405	−	0.136167i
$982$		0			0
$983$	−0.713755	+	1.37749i	−0.713755	+	1.37749i	0.203456	+	0.979084i	$0.434783\pi$
$983$	−0.713755	+	1.37749i	−0.713755	+	1.37749i	−0.917211	+	0.398401i	$0.869565\pi$
$984$		0			0
$985$	−1.32557	+	0.806094i	−1.32557	+	0.806094i
$986$		0			0
$987$		0			0
$988$		0			0
$989$		0			0
$990$		0			0
$991$	−0.530621	+	1.02405i	−0.530621	+	1.02405i	0.460065	+	0.887885i	$0.347826\pi$
$991$	−0.530621	+	1.02405i	−0.530621	+	1.02405i	−0.990686	+	0.136167i	$0.956522\pi$
$992$	−0.387961	−	1.86697i	−0.387961	−	1.86697i
$993$	0.00931405	−	0.136167i	0.00931405	−	0.136167i
$994$		0			0
$995$	0.0457060	+	0.668198i	0.0457060	+	0.668198i
$996$	−0.0381381	−	0.107310i	−0.0381381	−	0.107310i
$997$		0			0		−0.682553	−	0.730836i	$-0.739130\pi$
$997$		0			0		0.682553	+	0.730836i	$0.260870\pi$
$998$	−0.688871	−	0.0946831i	−0.688871	−	0.0946831i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	705.1.p.a.614.1	✓	22
3.2	odd	2		705.1.p.b.614.1	yes	22
5.2	odd	4		3525.1.bd.a.1601.2		44
5.3	odd	4		3525.1.bd.a.1601.1		44
5.4	even	2		705.1.p.b.614.1	yes	22
15.2	even	4		3525.1.bd.a.1601.1		44
15.8	even	4		3525.1.bd.a.1601.2		44
15.14	odd	2	CM	705.1.p.a.614.1	✓	22
47.16	even	23	inner	705.1.p.a.674.1	yes	22
141.110	odd	46		705.1.p.b.674.1	yes	22
235.63	odd	92		3525.1.bd.a.251.2		44
235.157	odd	92		3525.1.bd.a.251.1		44
235.204	even	46		705.1.p.b.674.1	yes	22
705.392	even	92		3525.1.bd.a.251.2		44
705.533	even	92		3525.1.bd.a.251.1		44
705.674	odd	46	inner	705.1.p.a.674.1	yes	22

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
705.1.p.a.614.1	✓	22	1.1	even	1	trivial
705.1.p.a.614.1	✓	22	15.14	odd	2	CM
705.1.p.a.674.1	yes	22	47.16	even	23	inner
705.1.p.a.674.1	yes	22	705.674	odd	46	inner
705.1.p.b.614.1	yes	22	3.2	odd	2
705.1.p.b.614.1	yes	22	5.4	even	2
705.1.p.b.674.1	yes	22	141.110	odd	46
705.1.p.b.674.1	yes	22	235.204	even	46
3525.1.bd.a.251.1		44	235.157	odd	92
3525.1.bd.a.251.1		44	705.533	even	92
3525.1.bd.a.251.2		44	235.63	odd	92
3525.1.bd.a.251.2		44	705.392	even	92
3525.1.bd.a.1601.1		44	5.3	odd	4
3525.1.bd.a.1601.1		44	15.2	even	4
3525.1.bd.a.1601.2		44	5.2	odd	4
3525.1.bd.a.1601.2		44	15.8	even	4

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:	\( N \)	\(=\)	\( 705 = 3 \cdot 5 \cdot 47 \)
Weight:	\( k \)	\(=\)	\( 1 \)
Character orbit:	\([\chi]\)	\(=\)	705.p (of order \(46\), degree \(22\), minimal)

\(f(q)\)	\(=\)	\(q+(0.347674 - 0.211425i) q^{2} +(-0.576680 + 0.816970i) q^{3} +(-0.383889 + 0.740871i) q^{4} +(0.203456 + 0.979084i) q^{5} +(-0.0277687 + 0.405963i) q^{6} +(0.0509395 + 0.744708i) q^{8} +(-0.334880 - 0.942261i) q^{9} +O(q^{10})\)	\(q+(0.347674 - 0.211425i) q^{2} +(-0.576680 + 0.816970i) q^{3} +(-0.383889 + 0.740871i) q^{4} +(0.203456 + 0.979084i) q^{5} +(-0.0277687 + 0.405963i) q^{6} +(0.0509395 + 0.744708i) q^{8} +(-0.334880 - 0.942261i) q^{9} +(0.277739 + 0.297386i) q^{10} +(-0.383889 - 0.740871i) q^{12} +(-0.917211 - 0.398401i) q^{15} +(-0.306035 - 0.433553i) q^{16} +(-1.90790 + 0.262234i) q^{17} +(-0.315646 - 0.256797i) q^{18} +(0.187206 - 0.900885i) q^{19} +(-0.803480 - 0.225125i) q^{20} +(1.46007 + 0.887885i) q^{23} +(-0.637780 - 0.387843i) q^{24} +(-0.917211 + 0.398401i) q^{25} +(0.962917 + 0.269797i) q^{27} +(-0.403122 + 0.0554078i) q^{30} +(1.14262 + 1.61872i) q^{31} +(-0.882715 - 0.383417i) q^{32} +(-0.607882 + 0.494549i) q^{34} +(0.826651 + 0.113621i) q^{36} +(-0.125383 - 0.352794i) q^{38} +(-0.718768 + 0.201389i) q^{40} +(0.854419 - 0.519584i) q^{45} +0.695347 q^{46} +(0.682553 - 0.730836i) q^{47} +0.530684 q^{48} +(0.854419 - 0.519584i) q^{49} +(-0.234658 + 0.332435i) q^{50} +(0.886009 - 1.70992i) q^{51} +(0.0457060 - 0.668198i) q^{53} +(0.391823 - 0.109784i) q^{54} +(0.628038 + 0.672464i) q^{57} +(0.647271 - 0.526594i) q^{60} +(-1.05893 + 1.13384i) q^{61} +(0.739496 + 0.321209i) q^{62} +(0.137780 - 0.0189375i) q^{64} +(0.538138 - 1.51418i) q^{68} +(-1.56737 + 0.680803i) q^{69} +(0.684651 - 0.297386i) q^{72} +(0.203456 - 0.979084i) q^{75} +(0.595574 + 0.484535i) q^{76} +(1.81734 + 0.789381i) q^{79} +(0.362220 - 0.387843i) q^{80} +(-0.775711 + 0.631088i) q^{81} +(0.135214 + 0.0185847i) q^{83} +(-0.644923 - 1.81464i) q^{85} +(0.187206 - 0.361291i) q^{90} +(-1.21831 + 0.740871i) q^{92} -1.98137 q^{93} +(0.0827887 - 0.398401i) q^{94} +0.920130 q^{95} +(0.822285 - 0.500042i) q^{96} +(0.187206 - 0.361291i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 22 q - 2 q^{2} - q^{3} - 3 q^{4} - q^{5} - 2 q^{6} - 4 q^{8} - q^{9}+O(q^{10}) \) 22 * q - 2 * q^2 - q^3 - 3 * q^4 - q^5 - 2 * q^6 - 4 * q^8 - q^9	\( 22 q - 2 q^{2} - q^{3} - 3 q^{4} - q^{5} - 2 q^{6} - 4 q^{8} - q^{9} - 2 q^{10} - 3 q^{12} - q^{15} - 5 q^{16} - 2 q^{17} - 2 q^{18} - 2 q^{19} - 3 q^{20} + 21 q^{23} - 4 q^{24} - q^{25} - q^{27} - 2 q^{30} - 2 q^{31} - 6 q^{32} - 4 q^{34} - 3 q^{36} - 4 q^{38} - 4 q^{40} - q^{45} - 4 q^{46} - q^{47} + 18 q^{48} - q^{49} - 2 q^{50} - 2 q^{51} - 2 q^{53} - 2 q^{54} - 2 q^{57} - 3 q^{60} - 2 q^{61} - 4 q^{62} - 7 q^{64} - 6 q^{68} - 2 q^{69} - 4 q^{72} - q^{75} + 17 q^{76} - 2 q^{79} + 18 q^{80} - q^{81} - 2 q^{83} - 2 q^{85} - 2 q^{90} + 17 q^{92} - 2 q^{93} + 21 q^{94} - 2 q^{95} + 17 q^{96} - 2 q^{98}+O(q^{100}) \) 22 * q - 2 * q^2 - q^3 - 3 * q^4 - q^5 - 2 * q^6 - 4 * q^8 - q^9 - 2 * q^10 - 3 * q^12 - q^15 - 5 * q^16 - 2 * q^17 - 2 * q^18 - 2 * q^19 - 3 * q^20 + 21 * q^23 - 4 * q^24 - q^25 - q^27 - 2 * q^30 - 2 * q^31 - 6 * q^32 - 4 * q^34 - 3 * q^36 - 4 * q^38 - 4 * q^40 - q^45 - 4 * q^46 - q^47 + 18 * q^48 - q^49 - 2 * q^50 - 2 * q^51 - 2 * q^53 - 2 * q^54 - 2 * q^57 - 3 * q^60 - 2 * q^61 - 4 * q^62 - 7 * q^64 - 6 * q^68 - 2 * q^69 - 4 * q^72 - q^75 + 17 * q^76 - 2 * q^79 + 18 * q^80 - q^81 - 2 * q^83 - 2 * q^85 - 2 * q^90 + 17 * q^92 - 2 * q^93 + 21 * q^94 - 2 * q^95 + 17 * q^96 - 2 * q^98

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