LMFDB - Embedded newform 1176.2.q.n.961.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1176,2,Mod(361,1176)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1176, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 0, 0, 4]))

N = Newforms(chi, 2, names="a")

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

chi := DirichletCharacter("1176.361");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1176 = 2^{3} \cdot 3 \cdot 7^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1176.q (of order $3$, degree $2$, not 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:	$9.39040727770$
Analytic rank:	$0$
Dimension:	$4$
Relative dimension:	$2$ over $\Q(\zeta_{3})$
Coefficient field:	$\Q(\sqrt{2}, \sqrt{-3})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} + 2x^{2} + 4 $ x^4 + 2*x^2 + 4
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			961.2
Root			$0.707107 + 1.22474i$ of defining polynomial
Character	$\chi$	$=$	1176.961
Dual form			1176.2.q.n.361.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.500000 + 0.866025i) q^{3} +(-0.292893 + 0.507306i) q^{5} +(-0.500000 + 0.866025i) q^{9} +O(q^{10})$	\(q+(0.500000 + 0.866025i) q^{3} +(-0.292893 + 0.507306i) q^{5} +(-0.500000 + 0.866025i) q^{9} +(2.41421 + 4.18154i) q^{11} +4.24264 q^{13} -0.585786 q^{15} +(-2.29289 - 3.97141i) q^{17} +(-0.585786 + 1.01461i) q^{19} +(-0.414214 + 0.717439i) q^{23} +(2.32843 + 4.03295i) q^{25} -1.00000 q^{27} -2.82843 q^{29} +(-1.41421 - 2.44949i) q^{31} +(-2.41421 + 4.18154i) q^{33} +(-4.82843 + 8.36308i) q^{37} +(2.12132 + 3.67423i) q^{39} +1.75736 q^{41} +11.3137 q^{43} +(-0.292893 - 0.507306i) q^{45} +(-6.24264 + 10.8126i) q^{47} +(2.29289 - 3.97141i) q^{51} +(1.00000 + 1.73205i) q^{53} -2.82843 q^{55} -1.17157 q^{57} +(4.24264 + 7.34847i) q^{59} +(1.53553 - 2.65962i) q^{61} +(-1.24264 + 2.15232i) q^{65} +(5.65685 + 9.79796i) q^{67} -0.828427 q^{69} +6.48528 q^{71} +(-8.12132 - 14.0665i) q^{73} +(-2.32843 + 4.03295i) q^{75} +(-1.17157 + 2.02922i) q^{79} +(-0.500000 - 0.866025i) q^{81} -4.00000 q^{83} +2.68629 q^{85} +(-1.41421 - 2.44949i) q^{87} +(-7.12132 + 12.3345i) q^{89} +(1.41421 - 2.44949i) q^{93} +(-0.343146 - 0.594346i) q^{95} +8.24264 q^{97} -4.82843 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q + 2 q^{3} - 4 q^{5} - 2 q^{9}+O(q^{10}) $ 4 * q + 2 * q^3 - 4 * q^5 - 2 * q^9	$ 4 q + 2 q^{3} - 4 q^{5} - 2 q^{9} + 4 q^{11} - 8 q^{15} - 12 q^{17} - 8 q^{19} + 4 q^{23} - 2 q^{25} - 4 q^{27} - 4 q^{33} - 8 q^{37} + 24 q^{41} - 4 q^{45} - 8 q^{47} + 12 q^{51} + 4 q^{53} - 16 q^{57} - 8 q^{61} + 12 q^{65} + 8 q^{69} - 8 q^{71} - 24 q^{73} + 2 q^{75} - 16 q^{79} - 2 q^{81} - 16 q^{83} + 56 q^{85} - 20 q^{89} - 24 q^{95} + 16 q^{97} - 8 q^{99}+O(q^{100}) $ 4 * q + 2 * q^3 - 4 * q^5 - 2 * q^9 + 4 * q^11 - 8 * q^15 - 12 * q^17 - 8 * q^19 + 4 * q^23 - 2 * q^25 - 4 * q^27 - 4 * q^33 - 8 * q^37 + 24 * q^41 - 4 * q^45 - 8 * q^47 + 12 * q^51 + 4 * q^53 - 16 * q^57 - 8 * q^61 + 12 * q^65 + 8 * q^69 - 8 * q^71 - 24 * q^73 + 2 * q^75 - 16 * q^79 - 2 * q^81 - 16 * q^83 + 56 * q^85 - 20 * q^89 - 24 * q^95 + 16 * q^97 - 8 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1176\mathbb{Z}\right)^\times$.

$n$	$295$	$589$	$785$	$1081$
$\chi(n)$	$1$	$1$	$1$	$e\left(\frac{1}{3}\right)$

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			0
$2$		0			0
$3$	0.500000	+	0.866025i	0.288675	+	0.500000i
$3$	0.500000	+	0.866025i	0.288675	+	0.500000i
$4$		0			0
$5$	−0.292893	+	0.507306i	−0.130986	+	0.226874i	−0.924057	−	0.382255i	$-0.875148\pi$
$5$	−0.292893	+	0.507306i	−0.130986	+	0.226874i	0.793071	+	0.609129i	$0.208481\pi$
$6$		0			0
$7$		0			0
$7$		0			0
$8$		0			0
$9$	−0.500000	+	0.866025i	−0.166667	+	0.288675i
$10$		0			0
$11$	2.41421	+	4.18154i	0.727913	+	1.26078i	0.957764	+	0.287556i	$0.0928428\pi$
$11$	2.41421	+	4.18154i	0.727913	+	1.26078i	−0.229851	+	0.973226i	$0.573824\pi$
$12$		0			0
$13$	4.24264			1.17670			0.588348	−	0.808608i	$-0.299778\pi$
$13$	4.24264			1.17670			0.588348	+	0.808608i	$0.299778\pi$
$14$		0			0
$15$	−0.585786			−0.151249
$16$		0			0
$17$	−2.29289	−	3.97141i	−0.556108	−	0.963208i	−0.997816	−	0.0660490i	$-0.978961\pi$
$17$	−2.29289	−	3.97141i	−0.556108	−	0.963208i	0.441708	−	0.897159i	$-0.354373\pi$
$18$		0			0
$19$	−0.585786	+	1.01461i	−0.134389	+	0.232768i	−0.925364	−	0.379080i	$-0.876240\pi$
$19$	−0.585786	+	1.01461i	−0.134389	+	0.232768i	0.790975	+	0.611848i	$0.209574\pi$
$20$		0			0
$21$		0			0
$22$		0			0
$23$	−0.414214	+	0.717439i	−0.0863695	+	0.149596i	−0.905974	−	0.423333i	$-0.860860\pi$
$23$	−0.414214	+	0.717439i	−0.0863695	+	0.149596i	0.819604	+	0.572930i	$0.194193\pi$
$24$		0			0
$25$	2.32843	+	4.03295i	0.465685	+	0.806591i
$26$		0			0
$27$	−1.00000			−0.192450
$28$		0			0
$29$	−2.82843			−0.525226			−0.262613	−	0.964901i	$-0.584584\pi$
$29$	−2.82843			−0.525226			−0.262613	+	0.964901i	$0.584584\pi$
$30$		0			0
$31$	−1.41421	−	2.44949i	−0.254000	−	0.439941i	0.710623	−	0.703573i	$-0.248413\pi$
$31$	−1.41421	−	2.44949i	−0.254000	−	0.439941i	−0.964623	+	0.263631i	$0.915080\pi$
$32$		0			0
$33$	−2.41421	+	4.18154i	−0.420261	+	0.727913i
$34$		0			0
$35$		0			0
$36$		0			0
$37$	−4.82843	+	8.36308i	−0.793789	+	1.37488i	0.129817	+	0.991538i	$0.458561\pi$
$37$	−4.82843	+	8.36308i	−0.793789	+	1.37488i	−0.923606	+	0.383344i	$0.874772\pi$
$38$		0			0
$39$	2.12132	+	3.67423i	0.339683	+	0.588348i
$40$		0			0
$41$	1.75736			0.274453			0.137227	−	0.990540i	$-0.456181\pi$
$41$	1.75736			0.274453			0.137227	+	0.990540i	$0.456181\pi$
$42$		0			0
$43$	11.3137			1.72532			0.862662	−	0.505781i	$-0.168795\pi$
$43$	11.3137			1.72532			0.862662	+	0.505781i	$0.168795\pi$
$44$		0			0
$45$	−0.292893	−	0.507306i	−0.0436619	−	0.0756247i
$46$		0			0
$47$	−6.24264	+	10.8126i	−0.910583	+	1.57718i	−0.0973398	+	0.995251i	$0.531033\pi$
$47$	−6.24264	+	10.8126i	−0.910583	+	1.57718i	−0.813243	+	0.581924i	$0.802300\pi$
$48$		0			0
$49$		0			0
$50$		0			0
$51$	2.29289	−	3.97141i	0.321069	−	0.556108i
$52$		0			0
$53$	1.00000	+	1.73205i	0.137361	+	0.237915i	0.926497	−	0.376303i	$-0.122805\pi$
$53$	1.00000	+	1.73205i	0.137361	+	0.237915i	−0.789136	+	0.614218i	$0.789471\pi$
$54$		0			0
$55$	−2.82843			−0.381385
$56$		0			0
$57$	−1.17157			−0.155179
$58$		0			0
$59$	4.24264	+	7.34847i	0.552345	+	0.956689i	0.998105	+	0.0615367i	$0.0196001\pi$
$59$	4.24264	+	7.34847i	0.552345	+	0.956689i	−0.445760	+	0.895152i	$0.647067\pi$
$60$		0			0
$61$	1.53553	−	2.65962i	0.196605	−	0.340530i	−0.750821	−	0.660506i	$-0.770342\pi$
$61$	1.53553	−	2.65962i	0.196605	−	0.340530i	0.947425	+	0.319976i	$0.103675\pi$
$62$		0			0
$63$		0			0
$64$		0			0
$65$	−1.24264	+	2.15232i	−0.154131	+	0.266962i
$66$		0			0
$67$	5.65685	+	9.79796i	0.691095	+	1.19701i	0.971480	+	0.237124i	$0.0762046\pi$
$67$	5.65685	+	9.79796i	0.691095	+	1.19701i	−0.280385	+	0.959888i	$0.590462\pi$
$68$		0			0
$69$	−0.828427			−0.0997309
$70$		0			0
$71$	6.48528			0.769661			0.384831	−	0.922987i	$-0.374260\pi$
$71$	6.48528			0.769661			0.384831	+	0.922987i	$0.374260\pi$
$72$		0			0
$73$	−8.12132	−	14.0665i	−0.950529	−	1.64636i	−0.744284	−	0.667864i	$-0.767209\pi$
$73$	−8.12132	−	14.0665i	−0.950529	−	1.64636i	−0.206245	−	0.978500i	$-0.566124\pi$
$74$		0			0
$75$	−2.32843	+	4.03295i	−0.268864	+	0.465685i
$76$		0			0
$77$		0			0
$78$		0			0
$79$	−1.17157	+	2.02922i	−0.131812	+	0.228306i	−0.924375	−	0.381485i	$-0.875413\pi$
$79$	−1.17157	+	2.02922i	−0.131812	+	0.228306i	0.792563	+	0.609790i	$0.208746\pi$
$80$		0			0
$81$	−0.500000	−	0.866025i	−0.0555556	−	0.0962250i
$82$		0			0
$83$	−4.00000			−0.439057			−0.219529	−	0.975606i	$-0.570452\pi$
$83$	−4.00000			−0.439057			−0.219529	+	0.975606i	$0.570452\pi$
$84$		0			0
$85$	2.68629			0.291369
$86$		0			0
$87$	−1.41421	−	2.44949i	−0.151620	−	0.262613i
$88$		0			0
$89$	−7.12132	+	12.3345i	−0.754858	+	1.30745i	0.190586	+	0.981670i	$0.438961\pi$
$89$	−7.12132	+	12.3345i	−0.754858	+	1.30745i	−0.945445	+	0.325783i	$0.894372\pi$
$90$		0			0
$91$		0			0
$92$		0			0
$93$	1.41421	−	2.44949i	0.146647	−	0.254000i
$94$		0			0
$95$	−0.343146	−	0.594346i	−0.0352060	−	0.0609786i
$96$		0			0
$97$	8.24264			0.836913			0.418457	−	0.908237i	$-0.362571\pi$
$97$	8.24264			0.836913			0.418457	+	0.908237i	$0.362571\pi$
$98$		0			0
$99$	−4.82843			−0.485275
$100$		0			0
$101$	−7.36396	−	12.7548i	−0.732742	−	1.26915i	−0.955707	−	0.294319i	$-0.904907\pi$
$101$	−7.36396	−	12.7548i	−0.732742	−	1.26915i	0.222966	−	0.974826i	$-0.428426\pi$
$102$		0			0
$103$	7.07107	−	12.2474i	0.696733	−	1.20678i	−0.272860	−	0.962054i	$-0.587970\pi$
$103$	7.07107	−	12.2474i	0.696733	−	1.20678i	0.969593	−	0.244723i	$-0.0786971\pi$
$104$		0			0
$105$		0			0
$106$		0			0
$107$	−3.58579	+	6.21076i	−0.346651	+	0.600417i	−0.985652	−	0.168788i	$-0.946015\pi$
$107$	−3.58579	+	6.21076i	−0.346651	+	0.600417i	0.639001	+	0.769206i	$0.279348\pi$
$108$		0			0
$109$	−9.65685	−	16.7262i	−0.924959	−	1.60208i	−0.791627	−	0.611004i	$-0.790766\pi$
$109$	−9.65685	−	16.7262i	−0.924959	−	1.60208i	−0.133332	−	0.991071i	$-0.542568\pi$
$110$		0			0
$111$	−9.65685			−0.916588
$112$		0			0
$113$	−10.0000			−0.940721			−0.470360	−	0.882474i	$-0.655876\pi$
$113$	−10.0000			−0.940721			−0.470360	+	0.882474i	$0.655876\pi$
$114$		0			0
$115$	−0.242641	−	0.420266i	−0.0226264	−	0.0391900i
$116$		0			0
$117$	−2.12132	+	3.67423i	−0.196116	+	0.339683i
$118$		0			0
$119$		0			0
$120$		0			0
$121$	−6.15685	+	10.6640i	−0.559714	+	0.969453i
$122$		0			0
$123$	0.878680	+	1.52192i	0.0792279	+	0.137227i
$124$		0			0
$125$	−5.65685			−0.505964
$126$		0			0
$127$	20.0000			1.77471			0.887357	−	0.461084i	$-0.152539\pi$
$127$	20.0000			1.77471			0.887357	+	0.461084i	$0.152539\pi$
$128$		0			0
$129$	5.65685	+	9.79796i	0.498058	+	0.862662i
$130$		0			0
$131$	2.00000	−	3.46410i	0.174741	−	0.302660i	−0.765331	−	0.643637i	$-0.777425\pi$
$131$	2.00000	−	3.46410i	0.174741	−	0.302660i	0.940072	+	0.340977i	$0.110758\pi$
$132$		0			0
$133$		0			0
$134$		0			0
$135$	0.292893	−	0.507306i	0.0252082	−	0.0436619i
$136$		0			0
$137$	7.41421	+	12.8418i	0.633439	+	1.09715i	0.986844	+	0.161678i	$0.0516906\pi$
$137$	7.41421	+	12.8418i	0.633439	+	1.09715i	−0.353405	+	0.935471i	$0.614976\pi$
$138$		0			0
$139$	12.9706			1.10015			0.550074	−	0.835116i	$-0.314599\pi$
$139$	12.9706			1.10015			0.550074	+	0.835116i	$0.314599\pi$
$140$		0			0
$141$	−12.4853			−1.05145
$142$		0			0
$143$	10.2426	+	17.7408i	0.856533	+	1.48356i
$144$		0			0
$145$	0.828427	−	1.43488i	0.0687971	−	0.119160i
$146$		0			0
$147$		0			0
$148$		0			0
$149$	10.6569	−	18.4582i	0.873044	−	1.51216i	0.0142111	−	0.999899i	$-0.495476\pi$
$149$	10.6569	−	18.4582i	0.873044	−	1.51216i	0.858832	−	0.512257i	$-0.171190\pi$
$150$		0			0
$151$	−0.828427	−	1.43488i	−0.0674164	−	0.116769i	0.830347	−	0.557247i	$-0.188142\pi$
$151$	−0.828427	−	1.43488i	−0.0674164	−	0.116769i	−0.897763	+	0.440478i	$0.854809\pi$
$152$		0			0
$153$	4.58579			0.370739
$154$		0			0
$155$	1.65685			0.133082
$156$		0			0
$157$	4.12132	+	7.13834i	0.328917	+	0.569701i	0.982297	−	0.187329i	$-0.0599830\pi$
$157$	4.12132	+	7.13834i	0.328917	+	0.569701i	−0.653380	+	0.757030i	$0.726650\pi$
$158$		0			0
$159$	−1.00000	+	1.73205i	−0.0793052	+	0.137361i
$160$		0			0
$161$		0			0
$162$		0			0
$163$	2.82843	−	4.89898i	0.221540	−	0.383718i	−0.733736	−	0.679435i	$-0.762225\pi$
$163$	2.82843	−	4.89898i	0.221540	−	0.383718i	0.955276	+	0.295717i	$0.0955585\pi$
$164$		0			0
$165$	−1.41421	−	2.44949i	−0.110096	−	0.190693i
$166$		0			0
$167$	−9.17157			−0.709718			−0.354859	−	0.934920i	$-0.615471\pi$
$167$	−9.17157			−0.709718			−0.354859	+	0.934920i	$0.615471\pi$
$168$		0			0
$169$	5.00000			0.384615
$170$		0			0
$171$	−0.585786	−	1.01461i	−0.0447962	−	0.0775893i
$172$		0			0
$173$	9.70711	−	16.8132i	0.738018	−	1.27828i	−0.215369	−	0.976533i	$-0.569095\pi$
$173$	9.70711	−	16.8132i	0.738018	−	1.27828i	0.953387	−	0.301751i	$-0.0975712\pi$
$174$		0			0
$175$		0			0
$176$		0			0
$177$	−4.24264	+	7.34847i	−0.318896	+	0.552345i
$178$		0			0
$179$	−5.24264	−	9.08052i	−0.391853	−	0.678710i	0.600841	−	0.799369i	$-0.294833\pi$
$179$	−5.24264	−	9.08052i	−0.391853	−	0.678710i	−0.992694	+	0.120659i	$0.961499\pi$
$180$		0			0
$181$	7.07107			0.525588			0.262794	−	0.964852i	$-0.415356\pi$
$181$	7.07107			0.525588			0.262794	+	0.964852i	$0.415356\pi$
$182$		0			0
$183$	3.07107			0.227020
$184$		0			0
$185$	−2.82843	−	4.89898i	−0.207950	−	0.360180i
$186$		0			0
$187$	11.0711	−	19.1757i	0.809597	−	1.40226i
$188$		0			0
$189$		0			0
$190$		0			0
$191$	8.07107	−	13.9795i	0.584002	−	1.01152i	−0.410997	−	0.911637i	$-0.634819\pi$
$191$	8.07107	−	13.9795i	0.584002	−	1.01152i	0.994999	−	0.0998844i	$-0.0318473\pi$
$192$		0			0
$193$	−1.00000	−	1.73205i	−0.0719816	−	0.124676i	0.827788	−	0.561041i	$-0.189599\pi$
$193$	−1.00000	−	1.73205i	−0.0719816	−	0.124676i	−0.899770	+	0.436365i	$0.856266\pi$
$194$		0			0
$195$	−2.48528			−0.177975
$196$		0			0
$197$	−25.3137			−1.80353			−0.901764	−	0.432230i	$-0.857727\pi$
$197$	−25.3137			−1.80353			−0.901764	+	0.432230i	$0.857727\pi$
$198$		0			0
$199$	−2.82843	−	4.89898i	−0.200502	−	0.347279i	0.748188	−	0.663486i	$-0.230924\pi$
$199$	−2.82843	−	4.89898i	−0.200502	−	0.347279i	−0.948690	+	0.316207i	$0.897591\pi$
$200$		0			0
$201$	−5.65685	+	9.79796i	−0.399004	+	0.691095i
$202$		0			0
$203$		0			0
$204$		0			0
$205$	−0.514719	+	0.891519i	−0.0359495	+	0.0622664i
$206$		0			0
$207$	−0.414214	−	0.717439i	−0.0287898	−	0.0498655i
$208$		0			0
$209$	−5.65685			−0.391293
$210$		0			0
$211$	−9.65685			−0.664805			−0.332403	−	0.943138i	$-0.607859\pi$
$211$	−9.65685			−0.664805			−0.332403	+	0.943138i	$0.607859\pi$
$212$		0			0
$213$	3.24264	+	5.61642i	0.222182	+	0.384831i
$214$		0			0
$215$	−3.31371	+	5.73951i	−0.225993	+	0.391431i
$216$		0			0
$217$		0			0
$218$		0			0
$219$	8.12132	−	14.0665i	0.548788	−	0.950529i
$220$		0			0
$221$	−9.72792	−	16.8493i	−0.654371	−	1.13340i
$222$		0			0
$223$	2.34315			0.156909			0.0784543	−	0.996918i	$-0.475002\pi$
$223$	2.34315			0.156909			0.0784543	+	0.996918i	$0.475002\pi$
$224$		0			0
$225$	−4.65685			−0.310457
$226$		0			0
$227$	5.41421	+	9.37769i	0.359354	+	0.622419i	0.987853	−	0.155391i	$-0.0496637\pi$
$227$	5.41421	+	9.37769i	0.359354	+	0.622419i	−0.628499	+	0.777810i	$0.716330\pi$
$228$		0			0
$229$	11.2929	−	19.5599i	0.746255	−	1.29255i	−0.203351	−	0.979106i	$-0.565183\pi$
$229$	11.2929	−	19.5599i	0.746255	−	1.29255i	0.949606	−	0.313446i	$-0.101484\pi$
$230$		0			0
$231$		0			0
$232$		0			0
$233$	4.58579	−	7.94282i	0.300425	−	0.520351i	−0.675807	−	0.737078i	$-0.736205\pi$
$233$	4.58579	−	7.94282i	0.300425	−	0.520351i	0.976232	+	0.216727i	$0.0695382\pi$
$234$		0			0
$235$	−3.65685	−	6.33386i	−0.238547	−	0.413175i
$236$		0			0
$237$	−2.34315			−0.152204
$238$		0			0
$239$	−7.17157			−0.463890			−0.231945	−	0.972729i	$-0.574509\pi$
$239$	−7.17157			−0.463890			−0.231945	+	0.972729i	$0.574509\pi$
$240$		0			0
$241$	2.94975	+	5.10911i	0.190010	+	0.329107i	0.945253	−	0.326338i	$-0.105815\pi$
$241$	2.94975	+	5.10911i	0.190010	+	0.329107i	−0.755243	+	0.655445i	$0.772481\pi$
$242$		0			0
$243$	0.500000	−	0.866025i	0.0320750	−	0.0555556i
$244$		0			0
$245$		0			0
$246$		0			0
$247$	−2.48528	+	4.30463i	−0.158135	+	0.273897i
$248$		0			0
$249$	−2.00000	−	3.46410i	−0.126745	−	0.219529i
$250$		0			0
$251$	22.1421			1.39760			0.698800	−	0.715317i	$-0.253718\pi$
$251$	22.1421			1.39760			0.698800	+	0.715317i	$0.253718\pi$
$252$		0			0
$253$	−4.00000			−0.251478
$254$		0			0
$255$	1.34315	+	2.32640i	0.0841110	+	0.145685i
$256$		0			0
$257$	0.292893	−	0.507306i	0.0182702	−	0.0316449i	−0.856746	−	0.515739i	$-0.827517\pi$
$257$	0.292893	−	0.507306i	0.0182702	−	0.0316449i	0.875016	+	0.484094i	$0.160851\pi$
$258$		0			0
$259$		0			0
$260$		0			0
$261$	1.41421	−	2.44949i	0.0875376	−	0.151620i
$262$		0			0
$263$	−4.07107	−	7.05130i	−0.251033	−	0.434802i	0.712778	−	0.701390i	$-0.247437\pi$
$263$	−4.07107	−	7.05130i	−0.251033	−	0.434802i	−0.963810	+	0.266589i	$0.914104\pi$
$264$		0			0
$265$	−1.17157			−0.0719691
$266$		0			0
$267$	−14.2426			−0.871635
$268$		0			0
$269$	9.94975	+	17.2335i	0.606647	+	1.05074i	0.991789	+	0.127886i	$0.0408191\pi$
$269$	9.94975	+	17.2335i	0.606647	+	1.05074i	−0.385142	+	0.922857i	$0.625848\pi$
$270$		0			0
$271$	11.0711	−	19.1757i	0.672519	−	1.16484i	−0.304668	−	0.952459i	$-0.598545\pi$
$271$	11.0711	−	19.1757i	0.672519	−	1.16484i	0.977187	−	0.212379i	$-0.0681212\pi$
$272$		0			0
$273$		0			0
$274$		0			0
$275$	−11.2426	+	19.4728i	−0.677957	+	1.17426i
$276$		0			0
$277$	−8.31371	−	14.3998i	−0.499522	−	0.865198i	0.500478	−	0.865750i	$-0.333158\pi$
$277$	−8.31371	−	14.3998i	−0.499522	−	0.865198i	−1.00000		0.000551476i	$0.999824\pi$
$278$		0			0
$279$	2.82843			0.169334
$280$		0			0
$281$	6.82843			0.407350			0.203675	−	0.979039i	$-0.434711\pi$
$281$	6.82843			0.407350			0.203675	+	0.979039i	$0.434711\pi$
$282$		0			0
$283$	−1.07107	−	1.85514i	−0.0636684	−	0.110277i	0.832434	−	0.554124i	$-0.186947\pi$
$283$	−1.07107	−	1.85514i	−0.0636684	−	0.110277i	−0.896103	+	0.443847i	$0.853613\pi$
$284$		0			0
$285$	0.343146	−	0.594346i	0.0203262	−	0.0352060i
$286$		0			0
$287$		0			0
$288$		0			0
$289$	−2.01472	+	3.48960i	−0.118513	+	0.205270i
$290$		0			0
$291$	4.12132	+	7.13834i	0.241596	+	0.418457i
$292$		0			0
$293$	−10.2426			−0.598381			−0.299191	−	0.954193i	$-0.596717\pi$
$293$	−10.2426			−0.598381			−0.299191	+	0.954193i	$0.596717\pi$
$294$		0			0
$295$	−4.97056			−0.289397
$296$		0			0
$297$	−2.41421	−	4.18154i	−0.140087	−	0.242638i
$298$		0			0
$299$	−1.75736	+	3.04384i	−0.101631	+	0.176030i
$300$		0			0
$301$		0			0
$302$		0			0
$303$	7.36396	−	12.7548i	0.423049	−	0.732742i
$304$		0			0
$305$	0.899495	+	1.55797i	0.0515049	+	0.0892092i
$306$		0			0
$307$	−28.4853			−1.62574			−0.812870	−	0.582445i	$-0.802096\pi$
$307$	−28.4853			−1.62574			−0.812870	+	0.582445i	$0.802096\pi$
$308$		0			0
$309$	14.1421			0.804518
$310$		0			0
$311$	7.89949	+	13.6823i	0.447939	+	0.775854i	0.998252	−	0.0591052i	$-0.0188247\pi$
$311$	7.89949	+	13.6823i	0.447939	+	0.775854i	−0.550312	+	0.834959i	$0.685491\pi$
$312$		0			0
$313$	−1.63604	+	2.83370i	−0.0924744	+	0.160170i	−0.908552	−	0.417772i	$-0.862811\pi$
$313$	−1.63604	+	2.83370i	−0.0924744	+	0.160170i	0.816077	+	0.577943i	$0.196144\pi$
$314$		0			0
$315$		0			0
$316$		0			0
$317$	11.0000	−	19.0526i	0.617822	−	1.07010i	−0.372061	−	0.928208i	$-0.621349\pi$
$317$	11.0000	−	19.0526i	0.617822	−	1.07010i	0.989882	−	0.141890i	$-0.0453179\pi$
$318$		0			0
$319$	−6.82843	−	11.8272i	−0.382319	−	0.662195i
$320$		0			0
$321$	−7.17157			−0.400278
$322$		0			0
$323$	5.37258			0.298939
$324$		0			0
$325$	9.87868	+	17.1104i	0.547971	+	0.949113i
$326$		0			0
$327$	9.65685	−	16.7262i	0.534025	−	0.924959i
$328$		0			0
$329$		0			0
$330$		0			0
$331$	7.65685	−	13.2621i	0.420859	−	0.728949i	−0.575165	−	0.818037i	$-0.695062\pi$
$331$	7.65685	−	13.2621i	0.420859	−	0.728949i	0.996024	+	0.0890887i	$0.0283955\pi$
$332$		0			0
$333$	−4.82843	−	8.36308i	−0.264596	−	0.458294i
$334$		0			0
$335$	−6.62742			−0.362094
$336$		0			0
$337$	21.6569			1.17972			0.589862	−	0.807504i	$-0.299182\pi$
$337$	21.6569			1.17972			0.589862	+	0.807504i	$0.299182\pi$
$338$		0			0
$339$	−5.00000	−	8.66025i	−0.271563	−	0.470360i
$340$		0			0
$341$	6.82843	−	11.8272i	0.369780	−	0.640478i
$342$		0			0
$343$		0			0
$344$		0			0
$345$	0.242641	−	0.420266i	0.0130633	−	0.0226264i
$346$		0			0
$347$	−7.24264	−	12.5446i	−0.388805	−	0.673431i	0.603484	−	0.797375i	$-0.293779\pi$
$347$	−7.24264	−	12.5446i	−0.388805	−	0.673431i	−0.992289	+	0.123945i	$0.960445\pi$
$348$		0			0
$349$	13.4142			0.718046			0.359023	−	0.933329i	$-0.383110\pi$
$349$	13.4142			0.718046			0.359023	+	0.933329i	$0.383110\pi$
$350$		0			0
$351$	−4.24264			−0.226455
$352$		0			0
$353$	−15.8492	−	27.4517i	−0.843570	−	1.46111i	−0.886857	−	0.462044i	$-0.847116\pi$
$353$	−15.8492	−	27.4517i	−0.843570	−	1.46111i	0.0432872	−	0.999063i	$-0.486217\pi$
$354$		0			0
$355$	−1.89949	+	3.29002i	−0.100815	+	0.174616i
$356$		0			0
$357$		0			0
$358$		0			0
$359$	−11.5858	+	20.0672i	−0.611474	+	1.05910i	0.379518	+	0.925184i	$0.376090\pi$
$359$	−11.5858	+	20.0672i	−0.611474	+	1.05910i	−0.990992	+	0.133920i	$0.957243\pi$
$360$		0			0
$361$	8.81371	+	15.2658i	0.463879	+	0.803463i
$362$		0			0
$363$	−12.3137			−0.646302
$364$		0			0
$365$	9.51472			0.498023
$366$		0			0
$367$	−13.6569	−	23.6544i	−0.712882	−	1.23475i	−0.963771	−	0.266732i	$-0.914056\pi$
$367$	−13.6569	−	23.6544i	−0.712882	−	1.23475i	0.250889	−	0.968016i	$-0.419277\pi$
$368$		0			0
$369$	−0.878680	+	1.52192i	−0.0457422	+	0.0792279i
$370$		0			0
$371$		0			0
$372$		0			0
$373$	8.65685	−	14.9941i	0.448235	−	0.776366i	−0.550036	−	0.835141i	$-0.685386\pi$
$373$	8.65685	−	14.9941i	0.448235	−	0.776366i	0.998271	+	0.0587751i	$0.0187195\pi$
$374$		0			0
$375$	−2.82843	−	4.89898i	−0.146059	−	0.252982i
$376$		0			0
$377$	−12.0000			−0.618031
$378$		0			0
$379$	−0.686292			−0.0352524			−0.0176262	−	0.999845i	$-0.505611\pi$
$379$	−0.686292			−0.0352524			−0.0176262	+	0.999845i	$0.505611\pi$
$380$		0			0
$381$	10.0000	+	17.3205i	0.512316	+	0.887357i
$382$		0			0
$383$	−12.4853	+	21.6251i	−0.637968	+	1.10499i	0.347910	+	0.937528i	$0.386892\pi$
$383$	−12.4853	+	21.6251i	−0.637968	+	1.10499i	−0.985878	+	0.167465i	$0.946442\pi$
$384$		0			0
$385$		0			0
$386$		0			0
$387$	−5.65685	+	9.79796i	−0.287554	+	0.498058i
$388$		0			0
$389$	−1.89949	−	3.29002i	−0.0963082	−	0.166811i	0.813846	−	0.581081i	$-0.197370\pi$
$389$	−1.89949	−	3.29002i	−0.0963082	−	0.166811i	−0.910154	+	0.414270i	$0.864037\pi$
$390$		0			0
$391$	3.79899			0.192123
$392$		0			0
$393$	4.00000			0.201773
$394$		0			0
$395$	−0.686292	−	1.18869i	−0.0345311	−	0.0598096i
$396$		0			0
$397$	3.87868	−	6.71807i	0.194665	−	0.337170i	−0.752125	−	0.659020i	$-0.770971\pi$
$397$	3.87868	−	6.71807i	0.194665	−	0.337170i	0.946791	+	0.321850i	$0.104305\pi$
$398$		0			0
$399$		0			0
$400$		0			0
$401$	−3.41421	+	5.91359i	−0.170498	+	0.295311i	−0.938594	−	0.345024i	$-0.887871\pi$
$401$	−3.41421	+	5.91359i	−0.170498	+	0.295311i	0.768096	+	0.640334i	$0.221204\pi$
$402$		0			0
$403$	−6.00000	−	10.3923i	−0.298881	−	0.517678i
$404$		0			0
$405$	0.585786			0.0291080
$406$		0			0
$407$	−46.6274			−2.31124
$408$		0			0
$409$	−0.121320	−	0.210133i	−0.00599890	−	0.0103904i	0.863010	−	0.505186i	$-0.168576\pi$
$409$	−0.121320	−	0.210133i	−0.00599890	−	0.0103904i	−0.869009	+	0.494796i	$0.835243\pi$
$410$		0			0
$411$	−7.41421	+	12.8418i	−0.365716	+	0.633439i
$412$		0			0
$413$		0			0
$414$		0			0
$415$	1.17157	−	2.02922i	0.0575103	−	0.0996107i
$416$		0			0
$417$	6.48528	+	11.2328i	0.317586	+	0.550074i
$418$		0			0
$419$	24.4853			1.19618			0.598092	−	0.801427i	$-0.295926\pi$
$419$	24.4853			1.19618			0.598092	+	0.801427i	$0.295926\pi$
$420$		0			0
$421$	−2.68629			−0.130922			−0.0654609	−	0.997855i	$-0.520852\pi$
$421$	−2.68629			−0.130922			−0.0654609	+	0.997855i	$0.520852\pi$
$422$		0			0
$423$	−6.24264	−	10.8126i	−0.303528	−	0.525725i
$424$		0			0
$425$	10.6777	−	18.4943i	0.517943	−	0.897104i
$426$		0			0
$427$		0			0
$428$		0			0
$429$	−10.2426	+	17.7408i	−0.494519	+	0.856533i
$430$		0			0
$431$	−10.0711	−	17.4436i	−0.485106	−	0.840229i	0.514747	−	0.857342i	$-0.327886\pi$
$431$	−10.0711	−	17.4436i	−0.485106	−	0.840229i	−0.999854	+	0.0171133i	$0.994552\pi$
$432$		0			0
$433$	15.0711			0.724269			0.362135	−	0.932126i	$-0.382048\pi$
$433$	15.0711			0.724269			0.362135	+	0.932126i	$0.382048\pi$
$434$		0			0
$435$	1.65685			0.0794401
$436$		0			0
$437$	−0.485281	−	0.840532i	−0.0232142	−	0.0402081i
$438$		0			0
$439$	−17.6569	+	30.5826i	−0.842716	+	1.45963i	0.0448746	+	0.998993i	$0.485711\pi$
$439$	−17.6569	+	30.5826i	−0.842716	+	1.45963i	−0.887590	+	0.460634i	$0.847622\pi$
$440$		0			0
$441$		0			0
$442$		0			0
$443$	8.41421	−	14.5738i	0.399771	−	0.692424i	−0.593926	−	0.804520i	$-0.702423\pi$
$443$	8.41421	−	14.5738i	0.399771	−	0.692424i	0.993697	+	0.112095i	$0.0357562\pi$
$444$		0			0
$445$	−4.17157	−	7.22538i	−0.197752	−	0.342516i
$446$		0			0
$447$	21.3137			1.00810
$448$		0			0
$449$	28.6274			1.35101			0.675506	−	0.737355i	$-0.263925\pi$
$449$	28.6274			1.35101			0.675506	+	0.737355i	$0.263925\pi$
$450$		0			0
$451$	4.24264	+	7.34847i	0.199778	+	0.346026i
$452$		0			0
$453$	0.828427	−	1.43488i	0.0389229	−	0.0674164i
$454$		0			0
$455$		0			0
$456$		0			0
$457$	−10.3137	+	17.8639i	−0.482455	+	0.835636i	−0.999797	−	0.0201422i	$-0.993588\pi$
$457$	−10.3137	+	17.8639i	−0.482455	+	0.835636i	0.517342	+	0.855779i	$0.326921\pi$
$458$		0			0
$459$	2.29289	+	3.97141i	0.107023	+	0.185369i
$460$		0			0
$461$	−20.3848			−0.949414			−0.474707	−	0.880144i	$-0.657446\pi$
$461$	−20.3848			−0.949414			−0.474707	+	0.880144i	$0.657446\pi$
$462$		0			0
$463$	−9.65685			−0.448792			−0.224396	−	0.974498i	$-0.572041\pi$
$463$	−9.65685			−0.448792			−0.224396	+	0.974498i	$0.572041\pi$
$464$		0			0
$465$	0.828427	+	1.43488i	0.0384174	+	0.0665409i
$466$		0			0
$467$	6.58579	−	11.4069i	0.304754	−	0.527849i	−0.672453	−	0.740140i	$-0.734759\pi$
$467$	6.58579	−	11.4069i	0.304754	−	0.527849i	0.977206	+	0.212291i	$0.0680925\pi$
$468$		0			0
$469$		0			0
$470$		0			0
$471$	−4.12132	+	7.13834i	−0.189900	+	0.328917i
$472$		0			0
$473$	27.3137	+	47.3087i	1.25589	+	2.17526i
$474$		0			0
$475$	−5.45584			−0.250331
$476$		0			0
$477$	−2.00000			−0.0915737
$478$		0			0
$479$	−8.58579	−	14.8710i	−0.392295	−	0.679474i	0.600457	−	0.799657i	$-0.294985\pi$
$479$	−8.58579	−	14.8710i	−0.392295	−	0.679474i	−0.992752	+	0.120183i	$0.961652\pi$
$480$		0			0
$481$	−20.4853	+	35.4815i	−0.934048	+	1.61782i
$482$		0			0
$483$		0			0
$484$		0			0
$485$	−2.41421	+	4.18154i	−0.109624	+	0.189874i
$486$		0			0
$487$	14.4853	+	25.0892i	0.656391	+	1.13690i	0.981543	+	0.191241i	$0.0612510\pi$
$487$	14.4853	+	25.0892i	0.656391	+	1.13690i	−0.325152	+	0.945662i	$0.605416\pi$
$488$		0			0
$489$	5.65685			0.255812
$490$		0			0
$491$	24.8284			1.12049			0.560246	−	0.828327i	$-0.310707\pi$
$491$	24.8284			1.12049			0.560246	+	0.828327i	$0.310707\pi$
$492$		0			0
$493$	6.48528	+	11.2328i	0.292082	+	0.505902i
$494$		0			0
$495$	1.41421	−	2.44949i	0.0635642	−	0.110096i
$496$		0			0
$497$		0			0
$498$		0			0
$499$	−4.48528	+	7.76874i	−0.200789	+	0.347776i	−0.948783	−	0.315929i	$-0.897684\pi$
$499$	−4.48528	+	7.76874i	−0.200789	+	0.347776i	0.747994	+	0.663705i	$0.231017\pi$
$500$		0			0
$501$	−4.58579	−	7.94282i	−0.204878	−	0.354859i
$502$		0			0
$503$	3.31371			0.147751			0.0738755	−	0.997267i	$-0.476463\pi$
$503$	3.31371			0.147751			0.0738755	+	0.997267i	$0.476463\pi$
$504$		0			0
$505$	8.62742			0.383915
$506$		0			0
$507$	2.50000	+	4.33013i	0.111029	+	0.192308i
$508$		0			0
$509$	−0.192388	+	0.333226i	−0.00852746	+	0.0147700i	−0.870258	−	0.492597i	$-0.836048\pi$
$509$	−0.192388	+	0.333226i	−0.00852746	+	0.0147700i	0.861730	+	0.507367i	$0.169381\pi$
$510$		0			0
$511$		0			0
$512$		0			0
$513$	0.585786	−	1.01461i	0.0258631	−	0.0447962i
$514$		0			0
$515$	4.14214	+	7.17439i	0.182524	+	0.316141i
$516$		0			0
$517$	−60.2843			−2.65130
$518$		0			0
$519$	19.4142			0.852189
$520$		0			0
$521$	−2.87868	−	4.98602i	−0.126117	−	0.218441i	0.796052	−	0.605228i	$-0.206918\pi$
$521$	−2.87868	−	4.98602i	−0.126117	−	0.218441i	−0.922169	+	0.386787i	$0.873585\pi$
$522$		0			0
$523$	−14.4853	+	25.0892i	−0.633397	+	1.09708i	0.353455	+	0.935451i	$0.385007\pi$
$523$	−14.4853	+	25.0892i	−0.633397	+	1.09708i	−0.986852	+	0.161625i	$0.948327\pi$
$524$		0			0
$525$		0			0
$526$		0			0
$527$	−6.48528	+	11.2328i	−0.282503	+	0.489310i
$528$		0			0
$529$	11.1569	+	19.3242i	0.485081	+	0.840184i
$530$		0			0
$531$	−8.48528			−0.368230
$532$		0			0
$533$	7.45584			0.322948
$534$		0			0
$535$	−2.10051	−	3.63818i	−0.0908128	−	0.157292i
$536$		0			0
$537$	5.24264	−	9.08052i	0.226237	−	0.391853i
$538$		0			0
$539$		0			0
$540$		0			0
$541$	9.00000	−	15.5885i	0.386940	−	0.670200i	−0.605096	−	0.796152i	$-0.706865\pi$
$541$	9.00000	−	15.5885i	0.386940	−	0.670200i	0.992036	+	0.125952i	$0.0401986\pi$
$542$		0			0
$543$	3.53553	+	6.12372i	0.151724	+	0.262794i
$544$		0			0
$545$	11.3137			0.484626
$546$		0			0
$547$	−36.9706			−1.58075			−0.790374	−	0.612625i	$-0.790114\pi$
$547$	−36.9706			−1.58075			−0.790374	+	0.612625i	$0.790114\pi$
$548$		0			0
$549$	1.53553	+	2.65962i	0.0655350	+	0.113510i
$550$		0			0
$551$	1.65685	−	2.86976i	0.0705844	−	0.122256i
$552$		0			0
$553$		0			0
$554$		0			0
$555$	2.82843	−	4.89898i	0.120060	−	0.207950i
$556$		0			0
$557$	6.31371	+	10.9357i	0.267520	+	0.463359i	0.968221	−	0.250097i	$-0.0804624\pi$
$557$	6.31371	+	10.9357i	0.267520	+	0.463359i	−0.700700	+	0.713456i	$0.747129\pi$
$558$		0			0
$559$	48.0000			2.03018
$560$		0			0
$561$	22.1421			0.934842
$562$		0			0
$563$	−15.0711	−	26.1039i	−0.635170	−	1.10015i	−0.986479	−	0.163887i	$-0.947597\pi$
$563$	−15.0711	−	26.1039i	−0.635170	−	1.10015i	0.351309	−	0.936259i	$-0.385737\pi$
$564$		0			0
$565$	2.92893	−	5.07306i	0.123221	−	0.213425i
$566$		0			0
$567$		0			0
$568$		0			0
$569$	17.0711	−	29.5680i	0.715656	−	1.23955i	−0.247049	−	0.969003i	$-0.579461\pi$
$569$	17.0711	−	29.5680i	0.715656	−	1.23955i	0.962706	−	0.270550i	$-0.0872057\pi$
$570$		0			0
$571$	15.1716	+	26.2779i	0.634911	+	1.09970i	0.986534	+	0.163556i	$0.0522964\pi$
$571$	15.1716	+	26.2779i	0.634911	+	1.09970i	−0.351624	+	0.936141i	$0.614370\pi$
$572$		0			0
$573$	16.1421			0.674347
$574$		0			0
$575$	−3.85786			−0.160884
$576$		0			0
$577$	14.6066	+	25.2994i	0.608081	+	1.05323i	0.991556	+	0.129676i	$0.0413937\pi$
$577$	14.6066	+	25.2994i	0.608081	+	1.05323i	−0.383476	+	0.923551i	$0.625273\pi$
$578$		0			0
$579$	1.00000	−	1.73205i	0.0415586	−	0.0719816i
$580$		0			0
$581$		0			0
$582$		0			0
$583$	−4.82843	+	8.36308i	−0.199973	+	0.346363i
$584$		0			0
$585$	−1.24264	−	2.15232i	−0.0513769	−	0.0889873i
$586$		0			0
$587$	3.79899			0.156801			0.0784005	−	0.996922i	$-0.475019\pi$
$587$	3.79899			0.156801			0.0784005	+	0.996922i	$0.475019\pi$
$588$		0			0
$589$	3.31371			0.136539
$590$		0			0
$591$	−12.6569	−	21.9223i	−0.520633	−	0.901764i
$592$		0			0
$593$	−22.2929	+	38.6124i	−0.915459	+	1.58562i	−0.109232	+	0.994016i	$0.534839\pi$
$593$	−22.2929	+	38.6124i	−0.915459	+	1.58562i	−0.806227	+	0.591606i	$0.798494\pi$
$594$		0			0
$595$		0			0
$596$		0			0
$597$	2.82843	−	4.89898i	0.115760	−	0.200502i
$598$		0			0
$599$	13.7279	+	23.7775i	0.560908	+	0.971521i	0.997418	+	0.0718211i	$0.0228811\pi$
$599$	13.7279	+	23.7775i	0.560908	+	0.971521i	−0.436510	+	0.899699i	$0.643786\pi$
$600$		0			0
$601$	−3.75736			−0.153266			−0.0766329	−	0.997059i	$-0.524417\pi$
$601$	−3.75736			−0.153266			−0.0766329	+	0.997059i	$0.524417\pi$
$602$		0			0
$603$	−11.3137			−0.460730
$604$		0			0
$605$	−3.60660	−	6.24682i	−0.146629	−	0.253969i
$606$		0			0
$607$	4.48528	−	7.76874i	0.182052	−	0.315323i	−0.760527	−	0.649306i	$-0.775059\pi$
$607$	4.48528	−	7.76874i	0.182052	−	0.315323i	0.942579	+	0.333983i	$0.108393\pi$
$608$		0			0
$609$		0			0
$610$		0			0
$611$	−26.4853	+	45.8739i	−1.07148	+	1.85586i
$612$		0			0
$613$	10.8284	+	18.7554i	0.437356	+	0.757523i	0.997485	−	0.0708828i	$-0.0225816\pi$
$613$	10.8284	+	18.7554i	0.437356	+	0.757523i	−0.560129	+	0.828406i	$0.689248\pi$
$614$		0			0
$615$	−1.02944			−0.0415109
$616$		0			0
$617$	12.4853			0.502639			0.251319	−	0.967904i	$-0.419136\pi$
$617$	12.4853			0.502639			0.251319	+	0.967904i	$0.419136\pi$
$618$		0			0
$619$	−11.1716	−	19.3497i	−0.449023	−	0.777731i	0.549299	−	0.835626i	$-0.314895\pi$
$619$	−11.1716	−	19.3497i	−0.449023	−	0.777731i	−0.998323	+	0.0578943i	$0.981561\pi$
$620$		0			0
$621$	0.414214	−	0.717439i	0.0166218	−	0.0287898i
$622$		0			0
$623$		0			0
$624$		0			0
$625$	−9.98528	+	17.2950i	−0.399411	+	0.691801i
$626$		0			0
$627$	−2.82843	−	4.89898i	−0.112956	−	0.195646i
$628$		0			0
$629$	44.2843			1.76573
$630$		0			0
$631$	−36.9706			−1.47177			−0.735887	−	0.677104i	$-0.763235\pi$
$631$	−36.9706			−1.47177			−0.735887	+	0.677104i	$0.763235\pi$
$632$		0			0
$633$	−4.82843	−	8.36308i	−0.191913	−	0.332403i
$634$		0			0
$635$	−5.85786	+	10.1461i	−0.232462	+	0.402636i
$636$		0			0
$637$		0			0
$638$		0			0
$639$	−3.24264	+	5.61642i	−0.128277	+	0.222182i
$640$		0			0
$641$	13.5563	+	23.4803i	0.535444	+	0.927416i	0.999142	+	0.0414223i	$0.0131889\pi$
$641$	13.5563	+	23.4803i	0.535444	+	0.927416i	−0.463698	+	0.885993i	$0.653478\pi$
$642$		0			0
$643$	−7.79899			−0.307562			−0.153781	−	0.988105i	$-0.549145\pi$
$643$	−7.79899			−0.307562			−0.153781	+	0.988105i	$0.549145\pi$
$644$		0			0
$645$	−6.62742			−0.260954
$646$		0			0
$647$	19.8995	+	34.4669i	0.782330	+	1.35504i	0.930581	+	0.366085i	$0.119302\pi$
$647$	19.8995	+	34.4669i	0.782330	+	1.35504i	−0.148251	+	0.988950i	$0.547364\pi$
$648$		0			0
$649$	−20.4853	+	35.4815i	−0.804118	+	1.39277i
$650$		0			0
$651$		0			0
$652$		0			0
$653$	−8.92893	+	15.4654i	−0.349416	+	0.605206i	−0.986146	−	0.165881i	$-0.946953\pi$
$653$	−8.92893	+	15.4654i	−0.349416	+	0.605206i	0.636730	+	0.771087i	$0.280287\pi$
$654$		0			0
$655$	1.17157	+	2.02922i	0.0457771	+	0.0792883i
$656$		0			0
$657$	16.2426			0.633686
$658$		0			0
$659$	38.4853			1.49917			0.749587	−	0.661906i	$-0.230252\pi$
$659$	38.4853			1.49917			0.749587	+	0.661906i	$0.230252\pi$
$660$		0			0
$661$	−9.53553	−	16.5160i	−0.370889	−	0.642399i	0.618813	−	0.785538i	$-0.287614\pi$
$661$	−9.53553	−	16.5160i	−0.370889	−	0.642399i	−0.989703	+	0.143139i	$0.954280\pi$
$662$		0			0
$663$	9.72792	−	16.8493i	0.377801	−	0.654371i
$664$		0			0
$665$		0			0
$666$		0			0
$667$	1.17157	−	2.02922i	0.0453635	−	0.0785719i
$668$		0			0
$669$	1.17157	+	2.02922i	0.0452956	+	0.0784543i
$670$		0			0
$671$	14.8284			0.572445
$672$		0			0
$673$	−0.686292			−0.0264546			−0.0132273	−	0.999913i	$-0.504211\pi$
$673$	−0.686292			−0.0264546			−0.0132273	+	0.999913i	$0.504211\pi$
$674$		0			0
$675$	−2.32843	−	4.03295i	−0.0896212	−	0.155228i
$676$		0			0
$677$	15.8492	−	27.4517i	0.609136	−	1.05505i	−0.382247	−	0.924060i	$-0.624850\pi$
$677$	15.8492	−	27.4517i	0.609136	−	1.05505i	0.991383	−	0.130994i	$-0.0418169\pi$
$678$		0			0
$679$		0			0
$680$		0			0
$681$	−5.41421	+	9.37769i	−0.207473	+	0.359354i
$682$		0			0
$683$	−18.8995	−	32.7349i	−0.723169	−	1.25257i	−0.959723	−	0.280947i	$-0.909351\pi$
$683$	−18.8995	−	32.7349i	−0.723169	−	1.25257i	0.236554	−	0.971618i	$-0.423982\pi$
$684$		0			0
$685$	−8.68629			−0.331886
$686$		0			0
$687$	22.5858			0.861701
$688$		0			0
$689$	4.24264	+	7.34847i	0.161632	+	0.279954i
$690$		0			0
$691$	−15.6569	+	27.1185i	−0.595615	+	1.03164i	0.397845	+	0.917453i	$0.369758\pi$
$691$	−15.6569	+	27.1185i	−0.595615	+	1.03164i	−0.993460	+	0.114182i	$0.963575\pi$
$692$		0			0
$693$		0			0
$694$		0			0
$695$	−3.79899	+	6.58004i	−0.144104	+	0.249595i
$696$		0			0
$697$	−4.02944	−	6.97919i	−0.152626	−	0.264356i
$698$		0			0
$699$	9.17157			0.346901
$700$		0			0
$701$	22.1421			0.836297			0.418148	−	0.908379i	$-0.362679\pi$
$701$	22.1421			0.836297			0.418148	+	0.908379i	$0.362679\pi$
$702$		0			0
$703$	−5.65685	−	9.79796i	−0.213352	−	0.369537i
$704$		0			0
$705$	3.65685	−	6.33386i	0.137725	−	0.238547i
$706$		0			0
$707$		0			0
$708$		0			0
$709$	19.3137	−	33.4523i	0.725342	−	1.25633i	−0.233492	−	0.972359i	$-0.575015\pi$
$709$	19.3137	−	33.4523i	0.725342	−	1.25633i	0.958833	−	0.283970i	$-0.0916515\pi$
$710$		0			0
$711$	−1.17157	−	2.02922i	−0.0439374	−	0.0761018i
$712$		0			0
$713$	2.34315			0.0877515
$714$		0			0
$715$	−12.0000			−0.448775
$716$		0			0
$717$	−3.58579	−	6.21076i	−0.133914	−	0.231945i
$718$		0			0
$719$	−19.3137	+	33.4523i	−0.720280	+	1.24756i	0.240608	+	0.970622i	$0.422653\pi$
$719$	−19.3137	+	33.4523i	−0.720280	+	1.24756i	−0.960888	+	0.276939i	$0.910680\pi$
$720$		0			0
$721$		0			0
$722$		0			0
$723$	−2.94975	+	5.10911i	−0.109702	+	0.190010i
$724$		0			0
$725$	−6.58579	−	11.4069i	−0.244590	−	0.423642i
$726$		0			0
$727$	−38.1421			−1.41461			−0.707307	−	0.706907i	$-0.750090\pi$
$727$	−38.1421			−1.41461			−0.707307	+	0.706907i	$0.750090\pi$
$728$		0			0
$729$	1.00000			0.0370370
$730$		0			0
$731$	−25.9411	−	44.9313i	−0.959467	−	1.66185i
$732$		0			0
$733$	−20.0208	+	34.6771i	−0.739486	+	1.28083i	0.213241	+	0.977000i	$0.431598\pi$
$733$	−20.0208	+	34.6771i	−0.739486	+	1.28083i	−0.952727	+	0.303827i	$0.901735\pi$
$734$		0			0
$735$		0			0
$736$		0			0
$737$	−27.3137	+	47.3087i	−1.00611	+	1.74264i
$738$		0			0
$739$	0.485281	+	0.840532i	0.0178514	+	0.0309195i	0.874813	−	0.484461i	$-0.160984\pi$
$739$	0.485281	+	0.840532i	0.0178514	+	0.0309195i	−0.856962	+	0.515380i	$0.827651\pi$
$740$		0			0
$741$	−4.97056			−0.182598
$742$		0			0
$743$	0.828427			0.0303920			0.0151960	−	0.999885i	$-0.495163\pi$
$743$	0.828427			0.0303920			0.0151960	+	0.999885i	$0.495163\pi$
$744$		0			0
$745$	6.24264	+	10.8126i	0.228713	+	0.396142i
$746$		0			0
$747$	2.00000	−	3.46410i	0.0731762	−	0.126745i
$748$		0			0
$749$		0			0
$750$		0			0
$751$	18.1421	−	31.4231i	0.662016	−	1.14665i	−0.318069	−	0.948067i	$-0.603034\pi$
$751$	18.1421	−	31.4231i	0.662016	−	1.14665i	0.980085	−	0.198578i	$-0.0636322\pi$
$752$		0			0
$753$	11.0711	+	19.1757i	0.403452	+	0.698800i
$754$		0			0
$755$	0.970563			0.0353224
$756$		0			0
$757$	−25.9411			−0.942846			−0.471423	−	0.881907i	$-0.656260\pi$
$757$	−25.9411			−0.942846			−0.471423	+	0.881907i	$0.656260\pi$
$758$		0			0
$759$	−2.00000	−	3.46410i	−0.0725954	−	0.125739i
$760$		0			0
$761$	6.05025	−	10.4793i	0.219321	−	0.379876i	−0.735279	−	0.677764i	$-0.762949\pi$
$761$	6.05025	−	10.4793i	0.219321	−	0.379876i	0.954601	+	0.297888i	$0.0962823\pi$
$762$		0			0
$763$		0			0
$764$		0			0
$765$	−1.34315	+	2.32640i	−0.0485615	+	0.0841110i
$766$		0			0
$767$	18.0000	+	31.1769i	0.649942	+	1.12573i
$768$		0			0
$769$	−18.8701			−0.680472			−0.340236	−	0.940340i	$-0.610507\pi$
$769$	−18.8701			−0.680472			−0.340236	+	0.940340i	$0.610507\pi$
$770$		0			0
$771$	0.585786			0.0210966
$772$		0			0
$773$	18.6777	+	32.3507i	0.671789	+	1.16357i	0.977396	+	0.211415i	$0.0678072\pi$
$773$	18.6777	+	32.3507i	0.671789	+	1.16357i	−0.305607	+	0.952158i	$0.598859\pi$
$774$		0			0
$775$	6.58579	−	11.4069i	0.236568	−	0.409749i
$776$		0			0
$777$		0			0
$778$		0			0
$779$	−1.02944	+	1.78304i	−0.0368834	+	0.0638840i
$780$		0			0
$781$	15.6569	+	27.1185i	0.560246	+	0.970375i
$782$		0			0
$783$	2.82843			0.101080
$784$		0			0
$785$	−4.82843			−0.172334
$786$		0			0
$787$	3.65685	+	6.33386i	0.130353	+	0.225778i	0.923813	−	0.382845i	$-0.125056\pi$
$787$	3.65685	+	6.33386i	0.130353	+	0.225778i	−0.793460	+	0.608623i	$0.791722\pi$
$788$		0			0
$789$	4.07107	−	7.05130i	0.144934	−	0.251033i
$790$		0			0
$791$		0			0
$792$		0			0
$793$	6.51472	−	11.2838i	0.231344	−	0.400700i
$794$		0			0
$795$	−0.585786	−	1.01461i	−0.0207757	−	0.0359846i
$796$		0			0
$797$	−36.5858			−1.29594			−0.647968	−	0.761668i	$-0.724381\pi$
$797$	−36.5858			−1.29594			−0.647968	+	0.761668i	$0.724381\pi$
$798$		0			0
$799$	57.2548			2.02553
$800$		0			0
$801$	−7.12132	−	12.3345i	−0.251619	−	0.435818i
$802$		0			0
$803$	39.2132	−	67.9193i	1.38380	−	2.39682i
$804$		0			0
$805$		0			0
$806$		0			0
$807$	−9.94975	+	17.2335i	−0.350248	+	0.606647i
$808$		0			0
$809$	−20.3137	−	35.1844i	−0.714192	−	1.23702i	−0.963270	−	0.268533i	$-0.913461\pi$
$809$	−20.3137	−	35.1844i	−0.714192	−	1.23702i	0.249078	−	0.968483i	$-0.419872\pi$
$810$		0			0
$811$	14.3431			0.503656			0.251828	−	0.967772i	$-0.418968\pi$
$811$	14.3431			0.503656			0.251828	+	0.967772i	$0.418968\pi$
$812$		0			0
$813$	22.1421			0.776559
$814$		0			0
$815$	1.65685	+	2.86976i	0.0580371	+	0.100523i
$816$		0			0
$817$	−6.62742	+	11.4790i	−0.231864	+	0.401600i
$818$		0			0
$819$		0			0
$820$		0			0
$821$	16.6569	−	28.8505i	0.581328	−	1.00689i	−0.413994	−	0.910280i	$-0.635867\pi$
$821$	16.6569	−	28.8505i	0.581328	−	1.00689i	0.995322	−	0.0966104i	$-0.0308001\pi$
$822$		0			0
$823$	−4.48528	−	7.76874i	−0.156347	−	0.270801i	0.777202	−	0.629252i	$-0.216639\pi$
$823$	−4.48528	−	7.76874i	−0.156347	−	0.270801i	−0.933549	+	0.358451i	$0.883305\pi$
$824$		0			0
$825$	−22.4853			−0.782837
$826$		0			0
$827$	11.8579			0.412338			0.206169	−	0.978516i	$-0.433900\pi$
$827$	11.8579			0.412338			0.206169	+	0.978516i	$0.433900\pi$
$828$		0			0
$829$	1.19239	+	2.06528i	0.0414134	+	0.0717300i	0.885989	−	0.463706i	$-0.153481\pi$
$829$	1.19239	+	2.06528i	0.0414134	+	0.0717300i	−0.844576	+	0.535436i	$0.820147\pi$
$830$		0			0
$831$	8.31371	−	14.3998i	0.288399	−	0.499522i
$832$		0			0
$833$		0			0
$834$		0			0
$835$	2.68629	−	4.65279i	0.0929630	−	0.161017i
$836$		0			0
$837$	1.41421	+	2.44949i	0.0488824	+	0.0846668i
$838$		0			0
$839$	−15.7990			−0.545442			−0.272721	−	0.962093i	$-0.587924\pi$
$839$	−15.7990			−0.545442			−0.272721	+	0.962093i	$0.587924\pi$
$840$		0			0
$841$	−21.0000			−0.724138
$842$		0			0
$843$	3.41421	+	5.91359i	0.117592	+	0.203675i
$844$		0			0
$845$	−1.46447	+	2.53653i	−0.0503792	+	0.0872593i
$846$		0			0
$847$		0			0
$848$		0			0
$849$	1.07107	−	1.85514i	0.0367590	−	0.0636684i
$850$		0			0
$851$	−4.00000	−	6.92820i	−0.137118	−	0.237496i
$852$		0			0
$853$	19.0711			0.652981			0.326490	−	0.945200i	$-0.394134\pi$
$853$	19.0711			0.652981			0.326490	+	0.945200i	$0.394134\pi$
$854$		0			0
$855$	0.686292			0.0234707
$856$		0			0
$857$	−15.6066	−	27.0314i	−0.533111	−	0.923376i	−0.999252	−	0.0386654i	$-0.987689\pi$
$857$	−15.6066	−	27.0314i	−0.533111	−	0.923376i	0.466141	−	0.884711i	$-0.345644\pi$
$858$		0			0
$859$	−26.7279	+	46.2941i	−0.911945	+	1.57953i	−0.100631	+	0.994924i	$0.532086\pi$
$859$	−26.7279	+	46.2941i	−0.911945	+	1.57953i	−0.811314	+	0.584611i	$0.801247\pi$
$860$		0			0
$861$		0			0
$862$		0			0
$863$	21.0416	−	36.4452i	0.716265	−	1.24061i	−0.246204	−	0.969218i	$-0.579183\pi$
$863$	21.0416	−	36.4452i	0.716265	−	1.24061i	0.962469	−	0.271390i	$-0.0874833\pi$
$864$		0			0
$865$	5.68629	+	9.84895i	0.193340	+	0.334874i
$866$		0			0
$867$	−4.02944			−0.136847
$868$		0			0
$869$	−11.3137			−0.383791
$870$		0			0
$871$	24.0000	+	41.5692i	0.813209	+	1.40852i
$872$		0			0
$873$	−4.12132	+	7.13834i	−0.139486	+	0.241596i
$874$		0			0
$875$		0			0
$876$		0			0
$877$	−14.1421	+	24.4949i	−0.477546	+	0.827134i	−0.999669	−	0.0257364i	$-0.991807\pi$
$877$	−14.1421	+	24.4949i	−0.477546	+	0.827134i	0.522123	+	0.852870i	$0.325140\pi$
$878$		0			0
$879$	−5.12132	−	8.87039i	−0.172738	−	0.299191i
$880$		0			0
$881$	−18.0416			−0.607838			−0.303919	−	0.952698i	$-0.598295\pi$
$881$	−18.0416			−0.607838			−0.303919	+	0.952698i	$0.598295\pi$
$882$		0			0
$883$	−21.6569			−0.728811			−0.364406	−	0.931240i	$-0.618728\pi$
$883$	−21.6569			−0.728811			−0.364406	+	0.931240i	$0.618728\pi$
$884$		0			0
$885$	−2.48528	−	4.30463i	−0.0835418	−	0.144699i
$886$		0			0
$887$	0.100505	−	0.174080i	0.00337463	−	0.00584503i	−0.864333	−	0.502920i	$-0.832259\pi$
$887$	0.100505	−	0.174080i	0.00337463	−	0.00584503i	0.867708	+	0.497075i	$0.165592\pi$
$888$		0			0
$889$		0			0
$890$		0			0
$891$	2.41421	−	4.18154i	0.0808792	−	0.140087i
$892$		0			0
$893$	−7.31371	−	12.6677i	−0.244744	−	0.423909i
$894$		0			0
$895$	6.14214			0.205309
$896$		0			0
$897$	−3.51472			−0.117353
$898$		0			0
$899$	4.00000	+	6.92820i	0.133407	+	0.231069i
$900$		0			0
$901$	4.58579	−	7.94282i	0.152775	−	0.264614i
$902$		0			0
$903$		0			0
$904$		0			0
$905$	−2.07107	+	3.58719i	−0.0688446	+	0.119242i
$906$		0			0
$907$	−21.1716	−	36.6702i	−0.702991	−	1.21762i	−0.967412	−	0.253208i	$-0.918514\pi$
$907$	−21.1716	−	36.6702i	−0.702991	−	1.21762i	0.264421	−	0.964407i	$-0.414819\pi$
$908$		0			0
$909$	14.7279			0.488494
$910$		0			0
$911$	−10.4853			−0.347393			−0.173696	−	0.984799i	$-0.555571\pi$
$911$	−10.4853			−0.347393			−0.173696	+	0.984799i	$0.555571\pi$
$912$		0			0
$913$	−9.65685	−	16.7262i	−0.319595	−	0.553555i
$914$		0			0
$915$	−0.899495	+	1.55797i	−0.0297364	+	0.0515049i
$916$		0			0
$917$		0			0
$918$		0			0
$919$	−4.34315	+	7.52255i	−0.143267	+	0.248146i	−0.928725	−	0.370769i	$-0.879094\pi$
$919$	−4.34315	+	7.52255i	−0.143267	+	0.248146i	0.785458	+	0.618915i	$0.212427\pi$
$920$		0			0
$921$	−14.2426	−	24.6690i	−0.469311	−	0.812870i
$922$		0			0
$923$	27.5147			0.905658
$924$		0			0
$925$	−44.9706			−1.47862
$926$		0			0
$927$	7.07107	+	12.2474i	0.232244	+	0.402259i
$928$		0			0
$929$	−1.94975	+	3.37706i	−0.0639691	+	0.110798i	−0.896236	−	0.443577i	$-0.853709\pi$
$929$	−1.94975	+	3.37706i	−0.0639691	+	0.110798i	0.832267	+	0.554375i	$0.187043\pi$
$930$		0			0
$931$		0			0
$932$		0			0
$933$	−7.89949	+	13.6823i	−0.258618	+	0.447939i
$934$		0			0
$935$	6.48528	+	11.2328i	0.212091	+	0.367353i
$936$		0			0
$937$	−19.3553			−0.632311			−0.316156	−	0.948707i	$-0.602392\pi$
$937$	−19.3553			−0.632311			−0.316156	+	0.948707i	$0.602392\pi$
$938$		0			0
$939$	−3.27208			−0.106780
$940$		0			0
$941$	−5.36396	−	9.29065i	−0.174860	−	0.302867i	0.765253	−	0.643730i	$-0.222614\pi$
$941$	−5.36396	−	9.29065i	−0.174860	−	0.302867i	−0.940113	+	0.340863i	$0.889281\pi$
$942$		0			0
$943$	−0.727922	+	1.26080i	−0.0237044	+	0.0410572i
$944$		0			0
$945$		0			0
$946$		0			0
$947$	−7.38478	+	12.7908i	−0.239973	+	0.415645i	−0.960706	−	0.277567i	$-0.910472\pi$
$947$	−7.38478	+	12.7908i	−0.239973	+	0.415645i	0.720733	+	0.693212i	$0.243805\pi$
$948$		0			0
$949$	−34.4558	−	59.6793i	−1.11848	−	1.93727i
$950$		0			0
$951$	22.0000			0.713399
$952$		0			0
$953$	2.00000			0.0647864			0.0323932	−	0.999475i	$-0.489687\pi$
$953$	2.00000			0.0647864			0.0323932	+	0.999475i	$0.489687\pi$
$954$		0			0
$955$	4.72792	+	8.18900i	0.152992	+	0.264990i
$956$		0			0
$957$	6.82843	−	11.8272i	0.220732	−	0.382319i
$958$		0			0
$959$		0			0
$960$		0			0
$961$	11.5000	−	19.9186i	0.370968	−	0.642535i
$962$		0			0
$963$	−3.58579	−	6.21076i	−0.115550	−	0.200139i
$964$		0			0
$965$	1.17157			0.0377143
$966$		0			0
$967$	−8.68629			−0.279332			−0.139666	−	0.990199i	$-0.544603\pi$
$967$	−8.68629			−0.279332			−0.139666	+	0.990199i	$0.544603\pi$
$968$		0			0
$969$	2.68629	+	4.65279i	0.0862961	+	0.149469i
$970$		0			0
$971$	10.0000	−	17.3205i	0.320915	−	0.555842i	−0.659762	−	0.751475i	$-0.729343\pi$
$971$	10.0000	−	17.3205i	0.320915	−	0.555842i	0.980677	+	0.195633i	$0.0626762\pi$
$972$		0			0
$973$		0			0
$974$		0			0
$975$	−9.87868	+	17.1104i	−0.316371	+	0.547971i
$976$		0			0
$977$	−15.8995	−	27.5387i	−0.508670	−	0.881042i	−0.999950	−	0.0100402i	$-0.996804\pi$
$977$	−15.8995	−	27.5387i	−0.508670	−	0.881042i	0.491280	−	0.871002i	$-0.336529\pi$
$978$		0			0
$979$	−68.7696			−2.19788
$980$		0			0
$981$	19.3137			0.616639
$982$		0			0
$983$	−23.3137	−	40.3805i	−0.743592	−	1.28794i	−0.950850	−	0.309652i	$-0.899787\pi$
$983$	−23.3137	−	40.3805i	−0.743592	−	1.28794i	0.207258	−	0.978286i	$-0.433546\pi$
$984$		0			0
$985$	7.41421	−	12.8418i	0.236236	−	0.409174i
$986$		0			0
$987$		0			0
$988$		0			0
$989$	−4.68629	+	8.11689i	−0.149015	+	0.258102i
$990$		0			0
$991$	−13.3137	−	23.0600i	−0.422924	−	0.732526i	0.573300	−	0.819345i	$-0.305663\pi$
$991$	−13.3137	−	23.0600i	−0.422924	−	0.732526i	−0.996224	+	0.0868198i	$0.972330\pi$
$992$		0			0
$993$	15.3137			0.485966
$994$		0			0
$995$	3.31371			0.105052
$996$		0			0
$997$	8.80761	+	15.2552i	0.278940	+	0.483138i	0.971122	−	0.238585i	$-0.0766837\pi$
$997$	8.80761	+	15.2552i	0.278940	+	0.483138i	−0.692182	+	0.721723i	$0.743350\pi$
$998$		0			0
$999$	4.82843	−	8.36308i	0.152765	−	0.264596i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1176.2.q.n.961.2		4
3.2	odd	2		3528.2.s.bl.3313.1		4
4.3	odd	2		2352.2.q.ba.961.2		4
7.2	even	3		1176.2.a.l.1.1	✓	2
7.3	odd	6		1176.2.q.m.361.1		4
7.4	even	3	inner	1176.2.q.n.361.2		4
7.5	odd	6		1176.2.a.m.1.2	yes	2
7.6	odd	2		1176.2.q.m.961.1		4
21.2	odd	6		3528.2.a.bc.1.2		2
21.5	even	6		3528.2.a.bm.1.1		2
21.11	odd	6		3528.2.s.bl.361.1		4
21.17	even	6		3528.2.s.bc.361.2		4
21.20	even	2		3528.2.s.bc.3313.2		4
28.3	even	6		2352.2.q.bg.1537.1		4
28.11	odd	6		2352.2.q.ba.1537.2		4
28.19	even	6		2352.2.a.z.1.2		2
28.23	odd	6		2352.2.a.bg.1.1		2
28.27	even	2		2352.2.q.bg.961.1		4
56.5	odd	6		9408.2.a.dr.1.1		2
56.19	even	6		9408.2.a.ed.1.1		2
56.37	even	6		9408.2.a.dv.1.2		2
56.51	odd	6		9408.2.a.dh.1.2		2
84.23	even	6		7056.2.a.ce.1.2		2
84.47	odd	6		7056.2.a.cw.1.1		2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1176.2.a.l.1.1	✓	2	7.2	even	3
1176.2.a.m.1.2	yes	2	7.5	odd	6
1176.2.q.m.361.1		4	7.3	odd	6
1176.2.q.m.961.1		4	7.6	odd	2
1176.2.q.n.361.2		4	7.4	even	3	inner
1176.2.q.n.961.2		4	1.1	even	1	trivial
2352.2.a.z.1.2		2	28.19	even	6
2352.2.a.bg.1.1		2	28.23	odd	6
2352.2.q.ba.961.2		4	4.3	odd	2
2352.2.q.ba.1537.2		4	28.11	odd	6
2352.2.q.bg.961.1		4	28.27	even	2
2352.2.q.bg.1537.1		4	28.3	even	6
3528.2.a.bc.1.2		2	21.2	odd	6
3528.2.a.bm.1.1		2	21.5	even	6
3528.2.s.bc.361.2		4	21.17	even	6
3528.2.s.bc.3313.2		4	21.20	even	2
3528.2.s.bl.361.1		4	21.11	odd	6
3528.2.s.bl.3313.1		4	3.2	odd	2
7056.2.a.ce.1.2		2	84.23	even	6
7056.2.a.cw.1.1		2	84.47	odd	6
9408.2.a.dh.1.2		2	56.51	odd	6
9408.2.a.dr.1.1		2	56.5	odd	6
9408.2.a.dv.1.2		2	56.37	even	6
9408.2.a.ed.1.1		2	56.19	even	6

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:	\( N \)	\(=\)	\( 1176 = 2^{3} \cdot 3 \cdot 7^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1176.q (of order \(3\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(0.500000 + 0.866025i) q^{3} +(-0.292893 + 0.507306i) q^{5} +(-0.500000 + 0.866025i) q^{9} +O(q^{10})\)	\(q+(0.500000 + 0.866025i) q^{3} +(-0.292893 + 0.507306i) q^{5} +(-0.500000 + 0.866025i) q^{9} +(2.41421 + 4.18154i) q^{11} +4.24264 q^{13} -0.585786 q^{15} +(-2.29289 - 3.97141i) q^{17} +(-0.585786 + 1.01461i) q^{19} +(-0.414214 + 0.717439i) q^{23} +(2.32843 + 4.03295i) q^{25} -1.00000 q^{27} -2.82843 q^{29} +(-1.41421 - 2.44949i) q^{31} +(-2.41421 + 4.18154i) q^{33} +(-4.82843 + 8.36308i) q^{37} +(2.12132 + 3.67423i) q^{39} +1.75736 q^{41} +11.3137 q^{43} +(-0.292893 - 0.507306i) q^{45} +(-6.24264 + 10.8126i) q^{47} +(2.29289 - 3.97141i) q^{51} +(1.00000 + 1.73205i) q^{53} -2.82843 q^{55} -1.17157 q^{57} +(4.24264 + 7.34847i) q^{59} +(1.53553 - 2.65962i) q^{61} +(-1.24264 + 2.15232i) q^{65} +(5.65685 + 9.79796i) q^{67} -0.828427 q^{69} +6.48528 q^{71} +(-8.12132 - 14.0665i) q^{73} +(-2.32843 + 4.03295i) q^{75} +(-1.17157 + 2.02922i) q^{79} +(-0.500000 - 0.866025i) q^{81} -4.00000 q^{83} +2.68629 q^{85} +(-1.41421 - 2.44949i) q^{87} +(-7.12132 + 12.3345i) q^{89} +(1.41421 - 2.44949i) q^{93} +(-0.343146 - 0.594346i) q^{95} +8.24264 q^{97} -4.82843 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q + 2 q^{3} - 4 q^{5} - 2 q^{9}+O(q^{10}) \) 4 * q + 2 * q^3 - 4 * q^5 - 2 * q^9	\( 4 q + 2 q^{3} - 4 q^{5} - 2 q^{9} + 4 q^{11} - 8 q^{15} - 12 q^{17} - 8 q^{19} + 4 q^{23} - 2 q^{25} - 4 q^{27} - 4 q^{33} - 8 q^{37} + 24 q^{41} - 4 q^{45} - 8 q^{47} + 12 q^{51} + 4 q^{53} - 16 q^{57} - 8 q^{61} + 12 q^{65} + 8 q^{69} - 8 q^{71} - 24 q^{73} + 2 q^{75} - 16 q^{79} - 2 q^{81} - 16 q^{83} + 56 q^{85} - 20 q^{89} - 24 q^{95} + 16 q^{97} - 8 q^{99}+O(q^{100}) \) 4 * q + 2 * q^3 - 4 * q^5 - 2 * q^9 + 4 * q^11 - 8 * q^15 - 12 * q^17 - 8 * q^19 + 4 * q^23 - 2 * q^25 - 4 * q^27 - 4 * q^33 - 8 * q^37 + 24 * q^41 - 4 * q^45 - 8 * q^47 + 12 * q^51 + 4 * q^53 - 16 * q^57 - 8 * q^61 + 12 * q^65 + 8 * q^69 - 8 * q^71 - 24 * q^73 + 2 * q^75 - 16 * q^79 - 2 * q^81 - 16 * q^83 + 56 * q^85 - 20 * q^89 - 24 * q^95 + 16 * q^97 - 8 * q^99

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