LMFDB - Embedded newform 912.2.bo.g.529.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [912,2,Mod(289,912)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(912, base_ring=CyclotomicField(18))

chi = DirichletCharacter(H, H._module([0, 0, 0, 2]))

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

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

chi := DirichletCharacter("912.289");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 912 = 2^{4} \cdot 3 \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	912.bo (of order $9$, degree $6$, 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:	$7.28235666434$
Analytic rank:	$0$
Dimension:	$12$
Relative dimension:	$2$ over $\Q(\zeta_{9})$
Coefficient field:	$\mathbb{Q}[x]/(x^{12} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{12} - 3 x^{11} + 27 x^{10} + 309 x^{8} + 42 x^{7} + 2059 x^{6} + 1245 x^{5} + 8226 x^{4} + \cdots + 16129 $ x^12 - 3x^11 + 27x^10 + 309x^8 + 42x^7 + 2059x^6 + 1245x^5 + 8226x^4 + 2250x^3 + 14496x^2 + 6096x + 16129
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 228)
Sato-Tate group:	$\mathrm{SU}(2)[C_{9}]$

Embedding invariants

Embedding label			529.2
Root			$-0.629732 - 1.09073i$ of defining polynomial
Character	$\chi$	$=$	912.529
Dual form			912.2.bo.g.481.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.939693 + 0.342020i) q^{3} +(0.392352 - 2.22514i) q^{5} +(2.18351 + 3.78195i) q^{7} +(0.766044 - 0.642788i) q^{9} +O(q^{10})$	\(q+(-0.939693 + 0.342020i) q^{3} +(0.392352 - 2.22514i) q^{5} +(2.18351 + 3.78195i) q^{7} +(0.766044 - 0.642788i) q^{9} +(1.08468 - 1.87871i) q^{11} +(-0.570168 - 0.207524i) q^{13} +(0.392352 + 2.22514i) q^{15} +(4.25293 + 3.56863i) q^{17} +(-4.26937 + 0.878888i) q^{19} +(-3.34533 - 2.80706i) q^{21} +(-0.944939 - 5.35902i) q^{23} +(-0.0988321 - 0.0359720i) q^{25} +(-0.500000 + 0.866025i) q^{27} +(-1.22757 + 1.03005i) q^{29} +(3.37280 + 5.84187i) q^{31} +(-0.376704 + 2.13640i) q^{33} +(9.27206 - 3.37475i) q^{35} +6.55866 q^{37} +0.606760 q^{39} +(6.77909 - 2.46739i) q^{41} +(0.244654 - 1.38750i) q^{43} +(-1.12973 - 1.95675i) q^{45} +(7.98289 - 6.69844i) q^{47} +(-6.03542 + 10.4537i) q^{49} +(-5.21699 - 1.89883i) q^{51} +(1.95158 + 11.0680i) q^{53} +(-3.75482 - 3.15067i) q^{55} +(3.71130 - 2.28610i) q^{57} +(5.10210 + 4.28117i) q^{59} +(-1.28393 - 7.28155i) q^{61} +(4.10365 + 1.49361i) q^{63} +(-0.685476 + 1.18728i) q^{65} +(8.37325 - 7.02599i) q^{67} +(2.72084 + 4.71264i) q^{69} +(-2.10032 + 11.9115i) q^{71} +(-0.491424 + 0.178864i) q^{73} +0.105175 q^{75} +9.47360 q^{77} +(9.14536 - 3.32864i) q^{79} +(0.173648 - 0.984808i) q^{81} +(-6.51587 - 11.2858i) q^{83} +(9.60935 - 8.06320i) q^{85} +(0.801239 - 1.38779i) q^{87} +(-4.30653 - 1.56745i) q^{89} +(-0.460121 - 2.60947i) q^{91} +(-5.16744 - 4.33599i) q^{93} +(0.280550 + 9.84478i) q^{95} +(-7.83934 - 6.57799i) q^{97} +(-0.376704 - 2.13640i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q - 6 q^{5} + 9 q^{7}+O(q^{10}) $ 12 * q - 6 * q^5 + 9 * q^7	$ 12 q - 6 q^{5} + 9 q^{7} + 9 q^{11} - 3 q^{13} - 6 q^{15} + 12 q^{17} - 9 q^{19} + 6 q^{21} - 15 q^{23} + 12 q^{25} - 6 q^{27} - 24 q^{29} + 6 q^{31} - 9 q^{33} + 42 q^{35} + 12 q^{37} - 18 q^{39} + 6 q^{41} + 39 q^{43} - 3 q^{45} + 3 q^{47} - 21 q^{49} + 3 q^{51} + 18 q^{53} - 45 q^{55} + 3 q^{57} + 33 q^{61} - 3 q^{63} - 33 q^{65} + 27 q^{67} + 12 q^{69} - 6 q^{71} - 24 q^{73} + 30 q^{75} - 18 q^{79} - 3 q^{83} + 39 q^{85} + 9 q^{87} - 15 q^{89} - 18 q^{91} - 6 q^{93} + 30 q^{95} - 15 q^{97} - 9 q^{99}+O(q^{100}) $ 12 * q - 6 * q^5 + 9 * q^7 + 9 * q^11 - 3 * q^13 - 6 * q^15 + 12 * q^17 - 9 * q^19 + 6 * q^21 - 15 * q^23 + 12 * q^25 - 6 * q^27 - 24 * q^29 + 6 * q^31 - 9 * q^33 + 42 * q^35 + 12 * q^37 - 18 * q^39 + 6 * q^41 + 39 * q^43 - 3 * q^45 + 3 * q^47 - 21 * q^49 + 3 * q^51 + 18 * q^53 - 45 * q^55 + 3 * q^57 + 33 * q^61 - 3 * q^63 - 33 * q^65 + 27 * q^67 + 12 * q^69 - 6 * q^71 - 24 * q^73 + 30 * q^75 - 18 * q^79 - 3 * q^83 + 39 * q^85 + 9 * q^87 - 15 * q^89 - 18 * q^91 - 6 * q^93 + 30 * q^95 - 15 * q^97 - 9 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/912\mathbb{Z}\right)^\times$.

$n$	$97$	$229$	$305$	$799$
$\chi(n)$	$e\left(\frac{2}{9}\right)$	$1$	$1$	$1$

Coefficient data

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

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

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

$2$		0			0
$2$		0			0
$3$	−0.939693	+	0.342020i	−0.542532	+	0.197465i
$3$	−0.939693	+	0.342020i	−0.542532	+	0.197465i
$4$		0			0
$5$	0.392352	−	2.22514i	0.175465	−	0.995112i	−0.762141	−	0.647411i	$-0.775852\pi$
$5$	0.392352	−	2.22514i	0.175465	−	0.995112i	0.937606	−	0.347700i	$-0.113037\pi$
$6$		0			0
$7$	2.18351	+	3.78195i	0.825289	+	1.42944i	0.901699	+	0.432365i	$0.142321\pi$
$7$	2.18351	+	3.78195i	0.825289	+	1.42944i	−0.0764099	+	0.997076i	$0.524346\pi$
$8$		0			0
$9$	0.766044	−	0.642788i	0.255348	−	0.214263i
$10$		0			0
$11$	1.08468	−	1.87871i	0.327042	−	0.566454i	−0.654881	−	0.755732i	$-0.727281\pi$
$11$	1.08468	−	1.87871i	0.327042	−	0.566454i	0.981924	+	0.189278i	$0.0606147\pi$
$12$		0			0
$13$	−0.570168	−	0.207524i	−0.158136	−	0.0575568i	0.261739	−	0.965139i	$-0.415704\pi$
$13$	−0.570168	−	0.207524i	−0.158136	−	0.0575568i	−0.419875	+	0.907582i	$0.637926\pi$
$14$		0			0
$15$	0.392352	+	2.22514i	0.101305	+	0.574528i
$16$		0			0
$17$	4.25293	+	3.56863i	1.03149	+	0.865521i	0.991027	−	0.133660i	$-0.0426731\pi$
$17$	4.25293	+	3.56863i	1.03149	+	0.865521i	0.0404605	+	0.999181i	$0.487118\pi$
$18$		0			0
$19$	−4.26937	+	0.878888i	−0.979462	+	0.201631i
$19$	−4.26937	+	0.878888i	−0.979462	+	0.201631i
$20$		0			0
$21$	−3.34533	−	2.80706i	−0.730011	−	0.612552i
$22$		0			0
$23$	−0.944939	−	5.35902i	−0.197033	−	1.11743i	−0.909493	−	0.415719i	$-0.863530\pi$
$23$	−0.944939	−	5.35902i	−0.197033	−	1.11743i	0.712460	−	0.701713i	$-0.247581\pi$
$24$		0			0
$25$	−0.0988321	−	0.0359720i	−0.0197664	−	0.00719439i
$26$		0			0
$27$	−0.500000	+	0.866025i	−0.0962250	+	0.166667i
$28$		0			0
$29$	−1.22757	+	1.03005i	−0.227954	+	0.191276i	−0.749610	−	0.661880i	$-0.769759\pi$
$29$	−1.22757	+	1.03005i	−0.227954	+	0.191276i	0.521656	+	0.853156i	$0.325314\pi$
$30$		0			0
$31$	3.37280	+	5.84187i	0.605774	+	1.04923i	0.991929	+	0.126797i	$0.0404696\pi$
$31$	3.37280	+	5.84187i	0.605774	+	1.04923i	−0.386155	+	0.922434i	$0.626197\pi$
$32$		0			0
$33$	−0.376704	+	2.13640i	−0.0655758	+	0.371899i
$34$		0			0
$35$	9.27206	−	3.37475i	1.56726	−	0.570437i
$36$		0			0
$37$	6.55866			1.07824			0.539118	−	0.842230i	$-0.318758\pi$
$37$	6.55866			1.07824			0.539118	+	0.842230i	$0.318758\pi$
$38$		0			0
$39$	0.606760			0.0971593
$40$		0			0
$41$	6.77909	−	2.46739i	1.05872	−	0.385341i	0.246770	−	0.969074i	$-0.420631\pi$
$41$	6.77909	−	2.46739i	1.05872	−	0.385341i	0.811946	+	0.583733i	$0.198409\pi$
$42$		0			0
$43$	0.244654	−	1.38750i	0.0373094	−	0.211592i	−0.960454	−	0.278439i	$-0.910183\pi$
$43$	0.244654	−	1.38750i	0.0373094	−	0.211592i	0.997763	+	0.0668472i	$0.0212940\pi$
$44$		0			0
$45$	−1.12973	−	1.95675i	−0.168410	−	0.291695i
$46$		0			0
$47$	7.98289	−	6.69844i	1.16442	−	0.977068i	0.164468	−	0.986382i	$-0.447409\pi$
$47$	7.98289	−	6.69844i	1.16442	−	0.977068i	0.999957	+	0.00931405i	$0.00296480\pi$
$48$		0			0
$49$	−6.03542	+	10.4537i	−0.862203	+	1.49338i
$50$		0			0
$51$	−5.21699	−	1.89883i	−0.730525	−	0.265889i
$52$		0			0
$53$	1.95158	+	11.0680i	0.268070	+	1.52030i	0.760148	+	0.649750i	$0.225126\pi$
$53$	1.95158	+	11.0680i	0.268070	+	1.52030i	−0.492078	+	0.870551i	$0.663762\pi$
$54$		0			0
$55$	−3.75482	−	3.15067i	−0.506300	−	0.424836i
$56$		0			0
$57$	3.71130	−	2.28610i	0.491574	−	0.302801i
$58$		0			0
$59$	5.10210	+	4.28117i	0.664237	+	0.557361i	0.911354	−	0.411625i	$-0.135038\pi$
$59$	5.10210	+	4.28117i	0.664237	+	0.557361i	−0.247116	+	0.968986i	$0.579483\pi$
$60$		0			0
$61$	−1.28393	−	7.28155i	−0.164391	−	0.932307i	−0.949690	−	0.313191i	$-0.898602\pi$
$61$	−1.28393	−	7.28155i	−0.164391	−	0.932307i	0.785300	−	0.619116i	$-0.212509\pi$
$62$		0			0
$63$	4.10365	+	1.49361i	0.517012	+	0.188177i
$64$		0			0
$65$	−0.685476	+	1.18728i	−0.0850228	+	0.147264i
$66$		0			0
$67$	8.37325	−	7.02599i	1.02296	−	0.858361i	0.0329593	−	0.999457i	$-0.489507\pi$
$67$	8.37325	−	7.02599i	1.02296	−	0.858361i	0.989996	+	0.141095i	$0.0450624\pi$
$68$		0			0
$69$	2.72084	+	4.71264i	0.327551	+	0.567335i
$70$		0			0
$71$	−2.10032	+	11.9115i	−0.249263	+	1.41364i	0.561119	+	0.827735i	$0.310371\pi$
$71$	−2.10032	+	11.9115i	−0.249263	+	1.41364i	−0.810381	+	0.585903i	$0.800740\pi$
$72$		0			0
$73$	−0.491424	+	0.178864i	−0.0575168	+	0.0209344i	−0.370618	−	0.928785i	$-0.620854\pi$
$73$	−0.491424	+	0.178864i	−0.0575168	+	0.0209344i	0.313102	+	0.949720i	$0.398632\pi$
$74$		0			0
$75$	0.105175			0.0121446
$76$		0			0
$77$	9.47360			1.07962
$78$		0			0
$79$	9.14536	−	3.32864i	1.02893	−	0.374501i	0.228259	−	0.973600i	$-0.426697\pi$
$79$	9.14536	−	3.32864i	1.02893	−	0.374501i	0.800675	+	0.599099i	$0.204475\pi$
$80$		0			0
$81$	0.173648	−	0.984808i	0.0192942	−	0.109423i
$82$		0			0
$83$	−6.51587	−	11.2858i	−0.715210	−	1.23878i	−0.962879	−	0.269935i	$-0.912998\pi$
$83$	−6.51587	−	11.2858i	−0.715210	−	1.23878i	0.247669	−	0.968845i	$-0.420336\pi$
$84$		0			0
$85$	9.60935	−	8.06320i	1.04228	−	0.874577i
$86$		0			0
$87$	0.801239	−	1.38779i	0.0859019	−	0.148786i
$88$		0			0
$89$	−4.30653	−	1.56745i	−0.456491	−	0.166149i	0.103532	−	0.994626i	$-0.466986\pi$
$89$	−4.30653	−	1.56745i	−0.456491	−	0.166149i	−0.560023	+	0.828477i	$0.689208\pi$
$90$		0			0
$91$	−0.460121	−	2.60947i	−0.0482338	−	0.273547i
$92$		0			0
$93$	−5.16744	−	4.33599i	−0.535838	−	0.449622i
$94$		0			0
$95$	0.280550	+	9.84478i	0.0287839	+	1.01005i
$96$		0			0
$97$	−7.83934	−	6.57799i	−0.795964	−	0.667893i	0.151250	−	0.988496i	$-0.451670\pi$
$97$	−7.83934	−	6.57799i	−0.795964	−	0.667893i	−0.947214	+	0.320602i	$0.896115\pi$
$98$		0			0
$99$	−0.376704	−	2.13640i	−0.0378602	−	0.214716i
$100$		0			0
$101$	10.4007	+	3.78553i	1.03490	+	0.376674i	0.802946	−	0.596051i	$-0.203265\pi$
$101$	10.4007	+	3.78553i	1.03490	+	0.376674i	0.231958	+	0.972726i	$0.425487\pi$
$102$		0			0
$103$	−7.91284	+	13.7054i	−0.779675	+	1.35044i	0.152454	+	0.988311i	$0.451282\pi$
$103$	−7.91284	+	13.7054i	−0.779675	+	1.35044i	−0.932129	+	0.362126i	$0.882051\pi$
$104$		0			0
$105$	−7.55865	+	6.34246i	−0.737649	+	0.618961i
$106$		0			0
$107$	5.51903	+	9.55924i	0.533545	+	0.924126i	0.999232	+	0.0391771i	$0.0124737\pi$
$107$	5.51903	+	9.55924i	0.533545	+	0.924126i	−0.465688	+	0.884949i	$0.654193\pi$
$108$		0			0
$109$	−1.42162	+	8.06239i	−0.136166	+	0.772236i	0.837874	+	0.545863i	$0.183798\pi$
$109$	−1.42162	+	8.06239i	−0.136166	+	0.772236i	−0.974041	+	0.226373i	$0.927313\pi$
$110$		0			0
$111$	−6.16312	+	2.24319i	−0.584978	+	0.212914i
$112$		0			0
$113$	−5.70632			−0.536806			−0.268403	−	0.963307i	$-0.586496\pi$
$113$	−5.70632			−0.536806			−0.268403	+	0.963307i	$0.586496\pi$
$114$		0			0
$115$	−12.2953			−1.14654
$116$		0			0
$117$	−0.570168	+	0.207524i	−0.0527120	+	0.0191856i
$118$		0			0
$119$	−4.21007	+	23.8765i	−0.385937	+	2.18876i
$120$		0			0
$121$	3.14695	+	5.45068i	0.286087	+	0.495517i
$122$		0			0
$123$	−5.52636	+	4.63717i	−0.498295	+	0.418120i
$124$		0			0
$125$	5.52984	−	9.57796i	0.494604	−	0.856679i
$126$		0			0
$127$	−7.97448	−	2.90247i	−0.707621	−	0.257553i	−0.0369596	−	0.999317i	$-0.511767\pi$
$127$	−7.97448	−	2.90247i	−0.707621	−	0.257553i	−0.670661	+	0.741764i	$0.733990\pi$
$128$		0			0
$129$	0.244654	+	1.38750i	0.0215406	+	0.122163i
$130$		0			0
$131$	1.46262	+	1.22728i	0.127789	+	0.107228i	0.704442	−	0.709761i	$-0.251197\pi$
$131$	1.46262	+	1.22728i	0.127789	+	0.107228i	−0.576653	+	0.816989i	$0.695642\pi$
$132$		0			0
$133$	−12.6461	−	14.2275i	−1.09656	−	1.23368i
$134$		0			0
$135$	1.73085	+	1.45236i	0.148968	+	0.124999i
$136$		0			0
$137$	−3.32243	−	18.8425i	−0.283855	−	1.60982i	−0.709348	−	0.704859i	$-0.751010\pi$
$137$	−3.32243	−	18.8425i	−0.283855	−	1.60982i	0.425493	−	0.904962i	$-0.360101\pi$
$138$		0			0
$139$	−13.3658	−	4.86476i	−1.13367	−	0.412624i	−0.294049	−	0.955790i	$-0.595003\pi$
$139$	−13.3658	−	4.86476i	−1.13367	−	0.412624i	−0.839625	+	0.543167i	$0.817225\pi$
$140$		0			0
$141$	−5.21046	+	9.02479i	−0.438800	+	0.760024i
$142$		0			0
$143$	−1.00833	+	0.846086i	−0.0843204	+	0.0707533i
$144$		0			0
$145$	1.81037	+	3.13566i	0.150343	+	0.260402i
$146$		0			0
$147$	2.09608	−	11.8875i	0.172882	−	0.980461i
$148$		0			0
$149$	−11.3128	+	4.11754i	−0.926785	+	0.337322i	−0.760934	−	0.648829i	$-0.775259\pi$
$149$	−11.3128	+	4.11754i	−0.926785	+	0.337322i	−0.165850	+	0.986151i	$0.553037\pi$
$150$		0			0
$151$	−10.7491			−0.874747			−0.437373	−	0.899280i	$-0.644091\pi$
$151$	−10.7491			−0.874747			−0.437373	+	0.899280i	$0.644091\pi$
$152$		0			0
$153$	5.55181			0.448837
$154$		0			0
$155$	14.3223	−	5.21288i	1.15039	−	0.418709i
$156$		0			0
$157$	−2.85893	+	16.2138i	−0.228167	+	1.29400i	0.628369	+	0.777915i	$0.283723\pi$
$157$	−2.85893	+	16.2138i	−0.228167	+	1.29400i	−0.856537	+	0.516086i	$0.827388\pi$
$158$		0			0
$159$	−5.61935	−	9.73300i	−0.445644	−	0.771877i
$160$		0			0
$161$	18.2042	−	15.2752i	1.43469	−	1.20385i
$162$		0			0
$163$	7.01313	−	12.1471i	0.549311	−	0.951434i	−0.449011	−	0.893526i	$-0.648224\pi$
$163$	7.01313	−	12.1471i	0.549311	−	0.951434i	0.998322	−	0.0579082i	$-0.0184431\pi$
$164$		0			0
$165$	4.60597	+	1.67644i	0.358574	+	0.130510i
$166$		0			0
$167$	−2.75423	−	15.6200i	−0.213129	−	1.20871i	−0.884124	−	0.467253i	$-0.845244\pi$
$167$	−2.75423	−	15.6200i	−0.213129	−	1.20871i	0.670995	−	0.741462i	$-0.265867\pi$
$168$		0			0
$169$	−9.67655	−	8.11959i	−0.744350	−	0.624584i
$170$		0			0
$171$	−2.70559	+	3.41757i	−0.206902	+	0.261348i
$172$		0			0
$173$	−12.9943	−	10.9035i	−0.987935	−	0.828976i	−0.00266719	−	0.999996i	$-0.500849\pi$
$173$	−12.9943	−	10.9035i	−0.987935	−	0.828976i	−0.985267	+	0.171021i	$0.945293\pi$
$174$		0			0
$175$	−0.0797567	−	0.452323i	−0.00602904	−	0.0341924i
$176$		0			0
$177$	−6.25866	−	2.27797i	−0.470430	−	0.171222i
$178$		0			0
$179$	8.87345	−	15.3693i	0.663233	−	1.14875i	−0.316528	−	0.948583i	$-0.602517\pi$
$179$	8.87345	−	15.3693i	0.663233	−	1.14875i	0.979761	−	0.200170i	$-0.0641495\pi$
$180$		0			0
$181$	−9.70433	+	8.14290i	−0.721317	+	0.605257i	−0.927749	−	0.373204i	$-0.878259\pi$
$181$	−9.70433	+	8.14290i	−0.721317	+	0.605257i	0.206432	+	0.978461i	$0.433815\pi$
$182$		0			0
$183$	3.69694	+	6.40329i	0.273286	+	0.473344i
$184$		0			0
$185$	2.57330	−	14.5939i	0.189193	−	1.07297i
$186$		0			0
$187$	11.3175	−	4.11923i	0.827618	−	0.301228i
$188$		0			0
$189$	−4.36702			−0.317654
$190$		0			0
$191$	−7.89322			−0.571133			−0.285567	−	0.958359i	$-0.592182\pi$
$191$	−7.89322			−0.571133			−0.285567	+	0.958359i	$0.592182\pi$
$192$		0			0
$193$	−0.110620	+	0.0402626i	−0.00796263	+	0.00289816i	−0.345998	−	0.938235i	$-0.612460\pi$
$193$	−0.110620	+	0.0402626i	−0.00796263	+	0.00289816i	0.338036	+	0.941133i	$0.390238\pi$
$194$		0			0
$195$	0.238063	−	1.35012i	0.0170481	−	0.0966844i
$196$		0			0
$197$	7.62847	+	13.2129i	0.543506	+	0.941380i	0.998699	+	0.0509872i	$0.0162368\pi$
$197$	7.62847	+	13.2129i	0.543506	+	0.941380i	−0.455193	+	0.890393i	$0.650430\pi$
$198$		0			0
$199$	−2.15407	+	1.80748i	−0.152698	+	0.128129i	−0.715936	−	0.698166i	$-0.754000\pi$
$199$	−2.15407	+	1.80748i	−0.152698	+	0.128129i	0.563238	+	0.826295i	$0.309555\pi$
$200$		0			0
$201$	−5.46525	+	9.46609i	−0.385489	+	0.667687i
$202$		0			0
$203$	−6.57602	−	2.39348i	−0.461546	−	0.167989i
$204$		0			0
$205$	−2.83049	−	16.0525i	−0.197690	−	1.12115i
$206$		0			0
$207$	−4.16857	−	3.49785i	−0.289736	−	0.243117i
$208$		0			0
$209$	−2.97971	+	8.97424i	−0.206111	+	0.620761i
$210$		0			0
$211$	−0.330119	−	0.277003i	−0.0227263	−	0.0190696i	0.631354	−	0.775495i	$-0.282500\pi$
$211$	−0.330119	−	0.277003i	−0.0227263	−	0.0190696i	−0.654080	+	0.756425i	$0.726944\pi$
$212$		0			0
$213$	−2.10032	−	11.9115i	−0.143912	−	0.816165i
$214$		0			0
$215$	−2.99139	−	1.08878i	−0.204011	−	0.0742540i
$216$		0			0
$217$	−14.7291	+	25.5115i	−0.999876	+	1.73184i
$218$		0			0
$219$	0.400612	−	0.336154i	0.0270709	−	0.0227152i
$220$		0			0
$221$	−1.68431	−	2.91731i	−0.113299	−	0.196239i
$222$		0			0
$223$	0.422205	−	2.39445i	0.0282730	−	0.160344i	−0.967402	−	0.253244i	$-0.918503\pi$
$223$	0.422205	−	2.39445i	0.0282730	−	0.160344i	0.995675	+	0.0928998i	$0.0296136\pi$
$224$		0			0
$225$	−0.0988321	+	0.0359720i	−0.00658881	+	0.00239813i
$226$		0			0
$227$	−11.4942			−0.762896			−0.381448	−	0.924390i	$-0.624575\pi$
$227$	−11.4942			−0.762896			−0.381448	+	0.924390i	$0.624575\pi$
$228$		0			0
$229$	5.13121			0.339080			0.169540	−	0.985523i	$-0.445772\pi$
$229$	5.13121			0.339080			0.169540	+	0.985523i	$0.445772\pi$
$230$		0			0
$231$	−8.90227	+	3.24016i	−0.585727	+	0.213187i
$232$		0			0
$233$	1.59200	−	9.02868i	0.104295	−	0.591489i	−0.887204	−	0.461377i	$-0.847355\pi$
$233$	1.59200	−	9.02868i	0.104295	−	0.591489i	0.991499	−	0.130111i	$-0.0415335\pi$
$234$		0			0
$235$	−11.7729	−	20.3912i	−0.767976	−	1.33017i
$236$		0			0
$237$	−7.45537	+	6.25580i	−0.484278	+	0.406358i
$238$		0			0
$239$	1.22469	−	2.12123i	0.0792188	−	0.137211i	−0.823694	−	0.567034i	$-0.808091\pi$
$239$	1.22469	−	2.12123i	0.0792188	−	0.137211i	0.902913	+	0.429823i	$0.141424\pi$
$240$		0			0
$241$	−2.21239	−	0.805242i	−0.142512	−	0.0518702i	0.269779	−	0.962922i	$-0.413049\pi$
$241$	−2.21239	−	0.805242i	−0.142512	−	0.0518702i	−0.412292	+	0.911052i	$0.635271\pi$
$242$		0			0
$243$	0.173648	+	0.984808i	0.0111395	+	0.0631754i
$244$		0			0
$245$	20.8928	+	17.5311i	1.33479	+	1.12002i
$246$		0			0
$247$	2.61665	+	0.384884i	0.166493	+	0.0244896i
$248$		0			0
$249$	9.98289	+	8.37664i	0.632640	+	0.530848i
$250$		0			0
$251$	−2.28777	−	12.9746i	−0.144402	−	0.818947i	−0.967845	−	0.251547i	$-0.919061\pi$
$251$	−2.28777	−	12.9746i	−0.144402	−	0.818947i	0.823443	−	0.567400i	$-0.192051\pi$
$252$		0			0
$253$	−11.0930	−	4.03753i	−0.697412	−	0.253837i
$254$		0			0
$255$	−6.27206	+	10.8635i	−0.392771	+	0.680300i
$256$		0			0
$257$	−14.9008	+	12.5033i	−0.929488	+	0.779933i	−0.975725	−	0.218998i	$-0.929721\pi$
$257$	−14.9008	+	12.5033i	−0.929488	+	0.779933i	0.0462378	+	0.998930i	$0.485277\pi$
$258$		0			0
$259$	14.3209	+	24.8045i	0.889857	+	1.54128i
$260$		0			0
$261$	−0.278268	+	1.57813i	−0.0172243	+	0.0976840i
$262$		0			0
$263$	7.36433	−	2.68040i	0.454104	−	0.165280i	−0.104834	−	0.994490i	$-0.533431\pi$
$263$	7.36433	−	2.68040i	0.454104	−	0.165280i	0.558938	+	0.829209i	$0.311209\pi$
$264$		0			0
$265$	25.3934			1.55991
$266$		0			0
$267$	4.58292			0.280470
$268$		0			0
$269$	−15.7423	+	5.72974i	−0.959826	+	0.349348i	−0.773965	−	0.633228i	$-0.781730\pi$
$269$	−15.7423	+	5.72974i	−0.959826	+	0.349348i	−0.185861	+	0.982576i	$0.559507\pi$
$270$		0			0
$271$	−4.70011	+	26.6557i	−0.285512	+	1.61922i	0.417941	+	0.908474i	$0.362752\pi$
$271$	−4.70011	+	26.6557i	−0.285512	+	1.61922i	−0.703453	+	0.710742i	$0.748359\pi$
$272$		0			0
$273$	1.32487	+	2.29473i	0.0801845	+	0.138884i
$274$		0			0
$275$	−0.174782	+	0.146659i	−0.0105397	+	0.00884390i
$276$		0			0
$277$	−2.41553	+	4.18382i	−0.145135	+	0.251382i	−0.929423	−	0.369015i	$-0.879695\pi$
$277$	−2.41553	+	4.18382i	−0.145135	+	0.251382i	0.784288	+	0.620397i	$0.213028\pi$
$278$		0			0
$279$	6.33880	+	2.30713i	0.379494	+	0.138124i
$280$		0			0
$281$	−3.86633	−	21.9270i	−0.230646	−	1.30806i	−0.851592	−	0.524205i	$-0.824363\pi$
$281$	−3.86633	−	21.9270i	−0.230646	−	1.30806i	0.620946	−	0.783853i	$-0.286749\pi$
$282$		0			0
$283$	−4.31905	−	3.62411i	−0.256741	−	0.215431i	0.505328	−	0.862927i	$-0.331372\pi$
$283$	−4.31905	−	3.62411i	−0.256741	−	0.215431i	−0.762068	+	0.647497i	$0.775816\pi$
$284$		0			0
$285$	−3.63074	−	9.15511i	−0.215067	−	0.542302i
$286$		0			0
$287$	24.1337	+	20.2506i	1.42457	+	1.19536i
$288$		0			0
$289$	2.40027	+	13.6126i	0.141192	+	0.800741i
$290$		0			0
$291$	9.61637	+	3.50007i	0.563722	+	0.205178i
$292$		0			0
$293$	−11.6997	+	20.2646i	−0.683507	+	1.18387i	0.290397	+	0.956906i	$0.406213\pi$
$293$	−11.6997	+	20.2646i	−0.683507	+	1.18387i	−0.973904	+	0.226962i	$0.927121\pi$
$294$		0			0
$295$	11.5280	−	9.67316i	0.671187	−	0.563193i
$296$		0			0
$297$	1.08468	+	1.87871i	0.0629393	+	0.109014i
$298$		0			0
$299$	−0.573351	+	3.25164i	−0.0331577	+	0.188047i
$300$		0			0
$301$	5.78166	−	2.10435i	0.333249	−	0.121293i
$302$		0			0
$303$	−11.0682			−0.635849
$304$		0			0
$305$	−16.7062			−0.956594
$306$		0			0
$307$	−31.3120	+	11.3967i	−1.78707	+	0.650441i	−0.787663	+	0.616107i	$0.788709\pi$
$307$	−31.3120	+	11.3967i	−1.78707	+	0.650441i	−0.999410	+	0.0343346i	$0.989069\pi$
$308$		0			0
$309$	2.74810	−	15.5852i	0.156334	−	0.886614i
$310$		0			0
$311$	12.4338	+	21.5360i	0.705057	+	1.22119i	0.966671	+	0.256021i	$0.0824118\pi$
$311$	12.4338	+	21.5360i	0.705057	+	1.22119i	−0.261614	+	0.965172i	$0.584255\pi$
$312$		0			0
$313$	7.85375	−	6.59008i	0.443920	−	0.372493i	−0.393254	−	0.919430i	$-0.628651\pi$
$313$	7.85375	−	6.59008i	0.443920	−	0.372493i	0.837174	+	0.546937i	$0.184206\pi$
$314$		0			0
$315$	4.93356	−	8.54517i	0.277974	−	0.481466i
$316$		0			0
$317$	−9.14865	−	3.32983i	−0.513839	−	0.187022i	0.0720689	−	0.997400i	$-0.477040\pi$
$317$	−9.14865	−	3.32983i	−0.513839	−	0.187022i	−0.585908	+	0.810377i	$0.699262\pi$
$318$		0			0
$319$	0.603660	+	3.42353i	0.0337985	+	0.191681i
$320$		0			0
$321$	−8.45564	−	7.09513i	−0.471948	−	0.396011i
$322$		0			0
$323$	−21.2938	−	11.4980i	−1.18482	−	0.639765i
$324$		0			0
$325$	0.0488858	+	0.0410201i	0.00271170	+	0.00227539i
$326$		0			0
$327$	−1.42162	−	8.06239i	−0.0786155	−	0.445851i
$328$		0			0
$329$	42.7639	+	15.5648i	2.35765	+	0.858114i
$330$		0			0
$331$	−12.4709	+	21.6002i	−0.685460	+	1.18725i	0.287832	+	0.957681i	$0.407066\pi$
$331$	−12.4709	+	21.6002i	−0.685460	+	1.18725i	−0.973292	+	0.229571i	$0.926268\pi$
$332$		0			0
$333$	5.02422	−	4.21582i	0.275326	−	0.231026i
$334$		0			0
$335$	−12.3485	−	21.3883i	−0.674673	−	1.16857i
$336$		0			0
$337$	2.60846	−	14.7933i	0.142092	−	0.805843i	−0.827564	−	0.561371i	$-0.810274\pi$
$337$	2.60846	−	14.7933i	0.142092	−	0.805843i	0.969656	−	0.244472i	$-0.0786147\pi$
$338$		0			0
$339$	5.36219	−	1.95168i	0.291234	−	0.106001i
$340$		0			0
$341$	14.6336			0.792454
$342$		0			0
$343$	−22.1444			−1.19569
$344$		0			0
$345$	11.5538	−	4.20524i	0.622036	−	0.226402i
$346$		0			0
$347$	1.78358	−	10.1152i	0.0957476	−	0.543011i	−0.898768	−	0.438424i	$-0.855537\pi$
$347$	1.78358	−	10.1152i	0.0957476	−	0.543011i	0.994516	−	0.104587i	$-0.0333521\pi$
$348$		0			0
$349$	1.01578	+	1.75939i	0.0543736	+	0.0941779i	0.891931	−	0.452171i	$-0.149350\pi$
$349$	1.01578	+	1.75939i	0.0543736	+	0.0941779i	−0.837557	+	0.546349i	$0.816017\pi$
$350$		0			0
$351$	0.464805	−	0.390018i	0.0248095	−	0.0208176i
$352$		0			0
$353$	−10.5203	+	18.2216i	−0.559937	+	0.969839i	0.437564	+	0.899187i	$0.355841\pi$
$353$	−10.5203	+	18.2216i	−0.559937	+	0.969839i	−0.997501	+	0.0706522i	$0.977492\pi$
$354$		0			0
$355$	25.6807	+	9.34702i	1.36299	+	0.496088i
$356$		0			0
$357$	−4.21007	−	23.8765i	−0.222821	−	1.26368i
$358$		0			0
$359$	−5.93581	−	4.98074i	−0.313280	−	0.262873i	0.472566	−	0.881295i	$-0.343328\pi$
$359$	−5.93581	−	4.98074i	−0.313280	−	0.262873i	−0.785846	+	0.618422i	$0.787772\pi$
$360$		0			0
$361$	17.4551	−	7.50461i	0.918690	−	0.394979i
$362$		0			0
$363$	−4.82141	−	4.04565i	−0.253059	−	0.212341i
$364$		0			0
$365$	0.205185	+	1.16366i	0.0107399	+	0.0609089i
$366$		0			0
$367$	33.9531	+	12.3579i	1.77234	+	0.645077i	0.999951	+	0.00992253i	$0.00315849\pi$
$367$	33.9531	+	12.3579i	1.77234	+	0.645077i	0.772385	+	0.635155i	$0.219064\pi$
$368$		0			0
$369$	3.60708	−	6.24764i	0.187777	−	0.325239i
$370$		0			0
$371$	−37.5972	+	31.5478i	−1.95195	+	1.63788i
$372$		0			0
$373$	−9.97590	−	17.2788i	−0.516533	−	0.894661i	−0.999816	−	0.0191965i	$-0.993889\pi$
$373$	−9.97590	−	17.2788i	−0.516533	−	0.894661i	0.483283	−	0.875464i	$-0.339444\pi$
$374$		0			0
$375$	−1.92049	+	10.8917i	−0.0991738	+	0.562443i
$376$		0			0
$377$	0.913682	−	0.332553i	0.0470570	−	0.0171273i
$378$		0			0
$379$	34.1329			1.75329			0.876645	−	0.481138i	$-0.159776\pi$
$379$	34.1329			1.75329			0.876645	+	0.481138i	$0.159776\pi$
$380$		0			0
$381$	8.48627			0.434765
$382$		0			0
$383$	23.4883	−	8.54903i	1.20019	−	0.436835i	0.336902	−	0.941540i	$-0.390621\pi$
$383$	23.4883	−	8.54903i	1.20019	−	0.436835i	0.863292	+	0.504705i	$0.168399\pi$
$384$		0			0
$385$	3.71698	−	21.0801i	0.189435	−	1.07434i
$386$		0			0
$387$	−0.704453	−	1.22015i	−0.0358094	−	0.0620236i
$388$		0			0
$389$	22.0835	−	18.5303i	1.11968	−	0.939521i	0.121090	−	0.992642i	$-0.461361\pi$
$389$	22.0835	−	18.5303i	1.11968	−	0.939521i	0.998588	+	0.0531205i	$0.0169167\pi$
$390$		0			0
$391$	15.1056	−	26.1637i	0.763923	−	1.32315i
$392$		0			0
$393$	−1.79416	−	0.653022i	−0.0905036	−	0.0329406i
$394$		0			0
$395$	−3.81848	−	21.6557i	−0.192129	−	1.08962i
$396$		0			0
$397$	−1.65047	−	1.38491i	−0.0828348	−	0.0695066i	0.600430	−	0.799677i	$-0.294996\pi$
$397$	−1.65047	−	1.38491i	−0.0828348	−	0.0695066i	−0.683265	+	0.730171i	$0.739441\pi$
$398$		0			0
$399$	16.7496	+	9.04424i	0.838527	+	0.452778i
$400$		0			0
$401$	−22.9070	−	19.2213i	−1.14392	−	0.959865i	−0.144362	−	0.989525i	$-0.546113\pi$
$401$	−22.9070	−	19.2213i	−1.14392	−	0.959865i	−0.999560	+	0.0296600i	$0.990558\pi$
$402$		0			0
$403$	−0.710736	−	4.03078i	−0.0354043	−	0.200788i
$404$		0			0
$405$	−2.12320	−	0.772782i	−0.105503	−	0.0383998i
$406$		0			0
$407$	7.11402	−	12.3218i	0.352629	−	0.610771i
$408$		0			0
$409$	6.27041	−	5.26150i	0.310052	−	0.260165i	−0.474462	−	0.880276i	$-0.657357\pi$
$409$	6.27041	−	5.26150i	0.310052	−	0.260165i	0.784513	+	0.620112i	$0.212913\pi$
$410$		0			0
$411$	9.56657	+	16.5698i	0.471884	+	0.817327i
$412$		0			0
$413$	−5.05069	+	28.6439i	−0.248528	+	1.40947i
$414$		0			0
$415$	−27.6690	+	10.0707i	−1.35822	+	0.494351i
$416$		0			0
$417$	14.2236			0.696533
$418$		0			0
$419$	−6.29279			−0.307423			−0.153712	−	0.988116i	$-0.549123\pi$
$419$	−6.29279			−0.307423			−0.153712	+	0.988116i	$0.549123\pi$
$420$		0			0
$421$	16.2411	−	5.91129i	0.791544	−	0.288099i	0.0855664	−	0.996332i	$-0.472730\pi$
$421$	16.2411	−	5.91129i	0.791544	−	0.288099i	0.705978	+	0.708234i	$0.250508\pi$
$422$		0			0
$423$	1.80958	−	10.2626i	0.0879846	−	0.498985i
$424$		0			0
$425$	−0.291956	−	0.505682i	−0.0141619	−	0.0245292i
$426$		0			0
$427$	24.7350	−	20.7551i	1.19701	−	1.00441i
$428$		0			0
$429$	0.658138	−	1.13993i	0.0317752	−	0.0550363i
$430$		0			0
$431$	9.08293	+	3.30592i	0.437509	+	0.159240i	0.551378	−	0.834255i	$-0.314102\pi$
$431$	9.08293	+	3.30592i	0.437509	+	0.159240i	−0.113869	+	0.993496i	$0.536324\pi$
$432$		0			0
$433$	3.67942	+	20.8670i	0.176822	+	1.00281i	0.936020	+	0.351946i	$0.114480\pi$
$433$	3.67942	+	20.8670i	0.176822	+	1.00281i	−0.759199	+	0.650859i	$0.774409\pi$
$434$		0			0
$435$	−2.77365	−	2.32737i	−0.132986	−	0.111589i
$436$		0			0
$437$	8.74428	+	22.0492i	0.418295	+	1.05475i
$438$		0			0
$439$	3.92619	+	3.29446i	0.187387	+	0.157236i	0.731655	−	0.681675i	$-0.238748\pi$
$439$	3.92619	+	3.29446i	0.187387	+	0.157236i	−0.544268	+	0.838911i	$0.683193\pi$
$440$		0			0
$441$	2.09608	+	11.8875i	0.0998133	+	0.566069i
$442$		0			0
$443$	1.70577	+	0.620849i	0.0810436	+	0.0294974i	0.382224	−	0.924070i	$-0.375158\pi$
$443$	1.70577	+	0.620849i	0.0810436	+	0.0294974i	−0.301180	+	0.953567i	$0.597381\pi$
$444$		0			0
$445$	−5.17746	+	8.96763i	−0.245435	+	0.425107i
$446$		0			0
$447$	9.22232	−	7.73844i	0.436201	−	0.366016i
$448$		0			0
$449$	−8.63865	−	14.9626i	−0.407683	−	0.706128i	0.586947	−	0.809626i	$-0.300330\pi$
$449$	−8.63865	−	14.9626i	−0.407683	−	0.706128i	−0.994630	+	0.103498i	$0.966996\pi$
$450$		0			0
$451$	2.71760	−	15.4123i	0.127967	−	0.725736i
$452$		0			0
$453$	10.1008	−	3.67640i	0.474578	−	0.172732i
$454$		0			0
$455$	−5.98697			−0.280673
$456$		0			0
$457$	−28.8598			−1.35001			−0.675003	−	0.737815i	$-0.735858\pi$
$457$	−28.8598			−1.35001			−0.675003	+	0.737815i	$0.735858\pi$
$458$		0			0
$459$	−5.21699	+	1.89883i	−0.243508	+	0.0886298i
$460$		0			0
$461$	−3.75107	+	21.2734i	−0.174705	+	0.990800i	0.763779	+	0.645478i	$0.223342\pi$
$461$	−3.75107	+	21.2734i	−0.174705	+	0.990800i	−0.938484	+	0.345323i	$0.887769\pi$
$462$		0			0
$463$	3.81671	+	6.61074i	0.177378	+	0.307227i	0.940982	−	0.338458i	$-0.109905\pi$
$463$	3.81671	+	6.61074i	0.177378	+	0.307227i	−0.763604	+	0.645685i	$0.776572\pi$
$464$		0			0
$465$	−11.6756	+	9.79702i	−0.541444	+	0.454326i
$466$		0			0
$467$	−12.8773	+	22.3042i	−0.595891	+	1.03211i	0.397529	+	0.917590i	$0.369868\pi$
$467$	−12.8773	+	22.3042i	−0.595891	+	1.03211i	−0.993420	+	0.114524i	$0.963466\pi$
$468$		0			0
$469$	44.8550	+	16.3259i	2.07121	+	0.753859i
$470$		0			0
$471$	−2.85893	−	16.2138i	−0.131732	−	0.747092i
$472$		0			0
$473$	−2.34135	−	1.96463i	−0.107655	−	0.0903336i
$474$		0			0
$475$	0.453567	+	0.0667153i	0.0208111	+	0.00306111i
$476$		0			0
$477$	8.60935	+	7.22410i	0.394195	+	0.330769i
$478$		0			0
$479$	−4.81928	−	27.3315i	−0.220198	−	1.24881i	−0.871655	−	0.490121i	$-0.836953\pi$
$479$	−4.81928	−	27.3315i	−0.220198	−	1.24881i	0.651456	−	0.758686i	$-0.274158\pi$
$480$		0			0
$481$	−3.73954	−	1.36108i	−0.170508	−	0.0620599i
$482$		0			0
$483$	−11.8820	+	20.5802i	−0.540648	+	0.936431i
$484$		0			0
$485$	−17.7127	+	14.8627i	−0.804292	+	0.674881i
$486$		0			0
$487$	−17.7231	−	30.6973i	−0.803110	−	1.39103i	−0.917559	−	0.397599i	$-0.869844\pi$
$487$	−17.7231	−	30.6973i	−0.803110	−	1.39103i	0.114449	−	0.993429i	$-0.463490\pi$
$488$		0			0
$489$	−2.43564	+	13.8132i	−0.110143	+	0.624653i
$490$		0			0
$491$	16.4863	−	6.00052i	0.744016	−	0.270800i	0.0579303	−	0.998321i	$-0.481550\pi$
$491$	16.4863	−	6.00052i	0.744016	−	0.270800i	0.686085	+	0.727521i	$0.259328\pi$
$492$		0			0
$493$	−8.89666			−0.400685
$494$		0			0
$495$	−4.90157			−0.220309
$496$		0			0
$497$	−49.6349	+	18.0656i	−2.22643	+	0.810353i
$498$		0			0
$499$	3.62329	−	20.5487i	0.162201	−	0.919886i	−0.789703	−	0.613489i	$-0.789765\pi$
$499$	3.62329	−	20.5487i	0.162201	−	0.919886i	0.951904	−	0.306397i	$-0.0991235\pi$
$500$		0			0
$501$	7.93050	+	13.7360i	0.354309	+	0.613681i
$502$		0			0
$503$	−4.17161	+	3.50040i	−0.186003	+	0.156075i	−0.731035	−	0.682340i	$-0.760962\pi$
$503$	−4.17161	+	3.50040i	−0.186003	+	0.156075i	0.545031	+	0.838416i	$0.316518\pi$
$504$		0			0
$505$	12.5040	−	21.6576i	0.556423	−	0.963752i
$506$		0			0
$507$	11.8700	+	4.32034i	0.527167	+	0.191873i
$508$		0			0
$509$	2.40893	+	13.6617i	0.106774	+	0.605545i	0.990497	+	0.137534i	$0.0439178\pi$
$509$	2.40893	+	13.6617i	0.106774	+	0.605545i	−0.883723	+	0.468010i	$0.844971\pi$
$510$		0			0
$511$	−1.74948	−	1.46799i	−0.0773925	−	0.0649400i
$512$		0			0
$513$	1.37355	−	4.13683i	0.0606436	−	0.182646i
$514$		0			0
$515$	27.3919	+	22.9845i	1.20703	+	1.01282i
$516$		0			0
$517$	−3.92561	−	22.2632i	−0.172648	−	0.979135i
$518$		0			0
$519$	15.9398	+	5.80162i	0.699680	+	0.254663i
$520$		0			0
$521$	17.0703	−	29.5666i	0.747863	−	1.29534i	−0.200982	−	0.979595i	$-0.564413\pi$
$521$	17.0703	−	29.5666i	0.747863	−	1.29534i	0.948845	−	0.315741i	$-0.102253\pi$
$522$		0			0
$523$	−17.0575	+	14.3129i	−0.745872	+	0.625861i	−0.934408	−	0.356205i	$-0.884070\pi$
$523$	−17.0575	+	14.3129i	−0.745872	+	0.625861i	0.188535	+	0.982066i	$0.439626\pi$
$524$		0			0
$525$	0.229650	+	0.397766i	0.0100228	+	0.0173599i
$526$		0			0
$527$	−6.50318	+	36.8814i	−0.283283	+	1.60658i
$528$		0			0
$529$	−6.21322	+	2.26143i	−0.270140	+	0.0983229i
$530$		0			0
$531$	6.66032			0.289033
$532$		0			0
$533$	−4.37726			−0.189600
$534$		0			0
$535$	23.4360	−	8.53001i	1.01323	−	0.368785i
$536$		0			0
$537$	−3.08172	+	17.4773i	−0.132986	+	0.754201i
$538$		0			0
$539$	13.0930	+	22.6777i	0.563953	+	0.976796i
$540$		0			0
$541$	−24.3976	+	20.4720i	−1.04893	+	0.880160i	−0.992981	−	0.118273i	$-0.962264\pi$
$541$	−24.3976	+	20.4720i	−1.04893	+	0.880160i	−0.0559529	+	0.998433i	$0.517820\pi$
$542$		0			0
$543$	6.33405	−	10.9709i	0.271820	−	0.470806i
$544$		0			0
$545$	17.3821	+	6.32658i	0.744569	+	0.271001i
$546$		0			0
$547$	1.03033	+	5.84330i	0.0440538	+	0.249842i	0.998880	−	0.0473247i	$-0.0150696\pi$
$547$	1.03033	+	5.84330i	0.0440538	+	0.249842i	−0.954826	+	0.297166i	$0.903958\pi$
$548$		0			0
$549$	−5.66404	−	4.75269i	−0.241735	−	0.202840i
$550$		0			0
$551$	4.33565	−	5.47658i	0.184705	−	0.233310i
$552$		0			0
$553$	32.5577	+	27.3192i	1.38450	+	1.16173i
$554$		0			0
$555$	2.57330	+	14.5939i	0.109231	+	0.619477i
$556$		0			0
$557$	23.6477	+	8.60705i	1.00198	+	0.364693i	0.790350	−	0.612656i	$-0.209899\pi$
$557$	23.6477	+	8.60705i	1.00198	+	0.364693i	0.211635	+	0.977349i	$0.432121\pi$
$558$		0			0
$559$	−0.427434	+	0.740337i	−0.0180785	+	0.0313129i
$560$		0			0
$561$	−9.22611	+	7.74163i	−0.389527	+	0.326852i
$562$		0			0
$563$	−14.8587	−	25.7361i	−0.626221	−	1.08465i	−0.988303	−	0.152501i	$-0.951267\pi$
$563$	−14.8587	−	25.7361i	−0.626221	−	1.08465i	0.362082	−	0.932146i	$-0.382066\pi$
$564$		0			0
$565$	−2.23889	+	12.6974i	−0.0941906	+	0.534182i
$566$		0			0
$567$	4.10365	−	1.49361i	0.172337	−	0.0627256i
$568$		0			0
$569$	−26.6200			−1.11597			−0.557985	−	0.829851i	$-0.688425\pi$
$569$	−26.6200			−1.11597			−0.557985	+	0.829851i	$0.688425\pi$
$570$		0			0
$571$	−35.6248			−1.49085			−0.745425	−	0.666589i	$-0.767754\pi$
$571$	−35.6248			−1.49085			−0.745425	+	0.666589i	$0.767754\pi$
$572$		0			0
$573$	7.41720	−	2.69964i	0.309858	−	0.112779i
$574$		0			0
$575$	−0.0993839	+	0.563634i	−0.00414460	+	0.0235052i
$576$		0			0
$577$	21.6806	+	37.5520i	0.902577	+	1.56331i	0.824138	+	0.566390i	$0.191660\pi$
$577$	21.6806	+	37.5520i	0.902577	+	1.56331i	0.0784390	+	0.996919i	$0.475006\pi$
$578$		0			0
$579$	0.0901786	−	0.0756689i	0.00374770	−	0.00314469i
$580$		0			0
$581$	28.4549	−	49.2854i	1.18051	−	2.04470i
$582$		0			0
$583$	22.9104	+	8.33869i	0.948851	+	0.345353i
$584$		0			0
$585$	0.238063	+	1.35012i	0.00984270	+	0.0558207i
$586$		0			0
$587$	−7.27986	−	6.10852i	−0.300472	−	0.252126i	0.480069	−	0.877231i	$-0.340612\pi$
$587$	−7.27986	−	6.10852i	−0.300472	−	0.252126i	−0.780541	+	0.625105i	$0.785056\pi$
$588$		0			0
$589$	−19.5341	−	21.9768i	−0.804889	−	0.905538i
$590$		0			0
$591$	−11.6875	−	9.80697i	−0.480759	−	0.403405i
$592$		0			0
$593$	−3.49910	−	19.8444i	−0.143691	−	0.814910i	−0.968409	−	0.249367i	$-0.919778\pi$
$593$	−3.49910	−	19.8444i	−0.143691	−	0.814910i	0.824719	−	0.565543i	$-0.191334\pi$
$594$		0			0
$595$	51.4767	+	18.7360i	2.11034	+	0.768100i
$596$		0			0
$597$	1.40597	−	2.43521i	0.0575424	−	0.0996663i
$598$		0			0
$599$	−10.6487	+	8.93534i	−0.435095	+	0.365088i	−0.833870	−	0.551961i	$-0.813880\pi$
$599$	−10.6487	+	8.93534i	−0.435095	+	0.365088i	0.398775	+	0.917049i	$0.369435\pi$
$600$		0			0
$601$	18.6544	+	32.3104i	0.760931	+	1.31797i	0.942371	+	0.334569i	$0.108591\pi$
$601$	18.6544	+	32.3104i	0.760931	+	1.31797i	−0.181441	+	0.983402i	$0.558076\pi$
$602$		0			0
$603$	1.89806	−	10.7644i	0.0772950	−	0.438362i
$604$		0			0
$605$	13.3632	−	4.86382i	0.543293	−	0.197742i
$606$		0			0
$607$	−18.1639			−0.737249			−0.368624	−	0.929578i	$-0.620171\pi$
$607$	−18.1639			−0.737249			−0.368624	+	0.929578i	$0.620171\pi$
$608$		0			0
$609$	6.99805			0.283575
$610$		0			0
$611$	−5.94168	+	2.16259i	−0.240374	+	0.0874892i
$612$		0			0
$613$	4.64117	−	26.3214i	0.187455	−	1.06311i	−0.735305	−	0.677736i	$-0.762961\pi$
$613$	4.64117	−	26.3214i	0.187455	−	1.06311i	0.922760	−	0.385375i	$-0.125928\pi$
$614$		0			0
$615$	8.15006	+	14.1163i	0.328642	+	0.569225i
$616$		0			0
$617$	0.330289	−	0.277145i	0.0132969	−	0.0111574i	−0.636115	−	0.771594i	$-0.719460\pi$
$617$	0.330289	−	0.277145i	0.0132969	−	0.0111574i	0.649412	+	0.760437i	$0.275015\pi$
$618$		0			0
$619$	−8.40534	+	14.5585i	−0.337839	+	0.585154i	−0.984026	−	0.178025i	$-0.943029\pi$
$619$	−8.40534	+	14.5585i	−0.337839	+	0.585154i	0.646187	+	0.763179i	$0.276363\pi$
$620$		0			0
$621$	5.11351	+	1.86117i	0.205198	+	0.0746861i
$622$		0			0
$623$	−3.47534	−	19.7096i	−0.139236	−	0.789649i
$624$		0			0
$625$	−19.5455	−	16.4006i	−0.781819	−	0.656024i
$626$		0			0
$627$	−0.269362	−	9.45215i	−0.0107573	−	0.377483i
$628$		0			0
$629$	27.8935	+	23.4055i	1.11219	+	0.933237i
$630$		0			0
$631$	1.87914	+	10.6571i	0.0748073	+	0.424253i	0.999094	+	0.0425545i	$0.0135496\pi$
$631$	1.87914	+	10.6571i	0.0748073	+	0.424253i	−0.924287	+	0.381698i	$0.875339\pi$
$632$		0			0
$633$	0.404951	+	0.147390i	0.0160953	+	0.00585823i
$634$		0			0
$635$	−9.58720	+	16.6055i	−0.380457	+	0.658970i
$636$		0			0
$637$	5.61058	−	4.70784i	0.222299	−	0.186531i
$638$		0			0
$639$	6.04764	+	10.4748i	0.239241	+	0.414378i
$640$		0			0
$641$	7.44930	−	42.2471i	0.294230	−	1.66866i	−0.376087	−	0.926585i	$-0.622730\pi$
$641$	7.44930	−	42.2471i	0.294230	−	1.66866i	0.670316	−	0.742075i	$-0.266158\pi$
$642$		0			0
$643$	8.50831	−	3.09677i	0.335535	−	0.122125i	−0.168758	−	0.985658i	$-0.553976\pi$
$643$	8.50831	−	3.09677i	0.335535	−	0.122125i	0.504293	+	0.863533i	$0.331753\pi$
$644$		0			0
$645$	3.18337			0.125345
$646$		0			0
$647$	−23.3186			−0.916748			−0.458374	−	0.888759i	$-0.651568\pi$
$647$	−23.3186			−0.916748			−0.458374	+	0.888759i	$0.651568\pi$
$648$		0			0
$649$	13.5772	−	4.94171i	0.532953	−	0.193979i
$650$		0			0
$651$	5.11536	−	29.0107i	0.200487	−	1.13702i
$652$		0			0
$653$	−22.8315	−	39.5453i	−0.893466	−	1.54753i	−0.835692	−	0.549198i	$-0.814933\pi$
$653$	−22.8315	−	39.5453i	−0.893466	−	1.54753i	−0.0577733	−	0.998330i	$-0.518400\pi$
$654$		0			0
$655$	3.30473	−	2.77299i	0.129126	−	0.108350i
$656$		0			0
$657$	−0.261481	+	0.452899i	−0.0102013	+	0.0176693i
$658$		0			0
$659$	7.24846	+	2.63822i	0.282360	+	0.102771i	0.479318	−	0.877641i	$-0.340884\pi$
$659$	7.24846	+	2.63822i	0.282360	+	0.102771i	−0.196958	+	0.980412i	$0.563106\pi$
$660$		0			0
$661$	−1.80015	−	10.2091i	−0.0700176	−	0.397089i	−0.999595	−	0.0284622i	$-0.990939\pi$
$661$	−1.80015	−	10.2091i	−0.0700176	−	0.397089i	0.929577	−	0.368627i	$-0.120172\pi$
$662$		0			0
$663$	2.58051	+	2.16530i	0.100219	+	0.0840934i
$664$		0			0
$665$	−36.6198	+	22.5572i	−1.42006	+	0.874730i
$666$		0			0
$667$	6.68005	+	5.60523i	0.258653	+	0.217035i
$668$		0			0
$669$	0.422205	+	2.39445i	0.0163234	+	0.0925746i
$670$		0			0
$671$	−15.0726	−	5.48598i	−0.581871	−	0.211784i
$672$		0			0
$673$	8.63202	−	14.9511i	0.332740	−	0.576322i	−0.650308	−	0.759670i	$-0.725360\pi$
$673$	8.63202	−	14.9511i	0.332740	−	0.576322i	0.983048	+	0.183348i	$0.0586936\pi$
$674$		0			0
$675$	0.0805687	−	0.0676052i	0.00310109	−	0.00260212i
$676$		0			0
$677$	−16.5624	−	28.6869i	−0.636544	−	1.10253i	−0.986186	−	0.165643i	$-0.947030\pi$
$677$	−16.5624	−	28.6869i	−0.636544	−	1.10253i	0.349642	−	0.936883i	$-0.386303\pi$
$678$		0			0
$679$	7.76034	−	44.0111i	0.297814	−	1.68899i
$680$		0			0
$681$	10.8010	−	3.93124i	0.413895	−	0.150646i
$682$		0			0
$683$	32.6531			1.24944			0.624718	−	0.780851i	$-0.285214\pi$
$683$	32.6531			1.24944			0.624718	+	0.780851i	$0.285214\pi$
$684$		0			0
$685$	−43.2306			−1.65176
$686$		0			0
$687$	−4.82176	+	1.75498i	−0.183962	+	0.0669565i
$688$		0			0
$689$	1.18414	−	6.71559i	0.0451122	−	0.255844i
$690$		0			0
$691$	1.40650	+	2.43613i	0.0535058	+	0.0926748i	0.891538	−	0.452946i	$-0.149627\pi$
$691$	1.40650	+	2.43613i	0.0535058	+	0.0926748i	−0.838032	+	0.545621i	$0.816294\pi$
$692$		0			0
$693$	7.25720	−	6.08951i	0.275678	−	0.231321i
$694$		0			0
$695$	−16.0689	+	27.8321i	−0.609527	+	1.05573i
$696$		0			0
$697$	37.6362	+	13.6985i	1.42557	+	0.518866i
$698$		0			0
$699$	1.59200	+	9.02868i	0.0602150	+	0.341496i
$700$		0			0
$701$	−5.28484	−	4.43451i	−0.199606	−	0.167489i	0.537506	−	0.843260i	$-0.319366\pi$
$701$	−5.28484	−	4.43451i	−0.199606	−	0.167489i	−0.737112	+	0.675771i	$0.763811\pi$
$702$		0			0
$703$	−28.0014	+	5.76433i	−1.05609	+	0.217406i
$704$		0			0
$705$	18.0371	+	15.1349i	0.679315	+	0.570013i
$706$		0			0
$707$	8.39325	+	47.6005i	0.315661	+	1.79020i
$708$		0			0
$709$	32.9972	+	12.0100i	1.23923	+	0.451044i	0.876750	−	0.480946i	$-0.159707\pi$
$709$	32.9972	+	12.0100i	1.23923	+	0.451044i	0.362484	+	0.931990i	$0.381929\pi$
$710$		0			0
$711$	4.86615	−	8.42841i	0.182495	−	0.316090i
$712$		0			0
$713$	28.1196	−	23.5951i	1.05309	−	0.883644i
$714$		0			0
$715$	1.48704	+	2.57563i	0.0556121	+	0.0963230i
$716$		0			0
$717$	−0.425332	+	2.41218i	−0.0158843	+	0.0900843i
$718$		0			0
$719$	−12.8274	+	4.66880i	−0.478382	+	0.174117i	−0.569945	−	0.821683i	$-0.693036\pi$
$719$	−12.8274	+	4.66880i	−0.478382	+	0.174117i	0.0915638	+	0.995799i	$0.470813\pi$
$720$		0			0
$721$	−69.1110			−2.57383
$722$		0			0
$723$	2.35437			0.0875600
$724$		0			0
$725$	0.158376	−	0.0576443i	0.00588195	−	0.00214086i
$726$		0			0
$727$	6.59150	−	37.3823i	0.244465	−	1.38643i	−0.577266	−	0.816556i	$-0.695880\pi$
$727$	6.59150	−	37.3823i	0.244465	−	1.38643i	0.821731	−	0.569875i	$-0.193008\pi$
$728$		0			0
$729$	−0.500000	−	0.866025i	−0.0185185	−	0.0320750i
$730$		0			0
$731$	5.99198	−	5.02787i	0.221621	−	0.185963i
$732$		0			0
$733$	3.64378	−	6.31122i	0.134586	−	0.233110i	−0.790853	−	0.612006i	$-0.790363\pi$
$733$	3.64378	−	6.31122i	0.134586	−	0.233110i	0.925439	+	0.378896i	$0.123696\pi$
$734$		0			0
$735$	−25.6288	−	9.32813i	−0.945333	−	0.344073i
$736$		0			0
$737$	−4.11757	−	23.3519i	−0.151672	−	0.860177i
$738$		0			0
$739$	10.7726	+	9.03929i	0.396277	+	0.332516i	0.819052	−	0.573719i	$-0.194500\pi$
$739$	10.7726	+	9.03929i	0.396277	+	0.332516i	−0.422776	+	0.906234i	$0.638944\pi$
$740$		0			0
$741$	−2.59048	+	0.533274i	−0.0951638	+	0.0195903i
$742$		0			0
$743$	−19.6806	−	16.5140i	−0.722011	−	0.605839i	0.205930	−	0.978567i	$-0.433978\pi$
$743$	−19.6806	−	16.5140i	−0.722011	−	0.605839i	−0.927941	+	0.372728i	$0.878422\pi$
$744$		0			0
$745$	4.72348	+	26.7882i	0.173055	+	0.981442i
$746$		0			0
$747$	−12.2458	−	4.45712i	−0.448052	−	0.163077i
$748$		0			0
$749$	−24.1017	+	41.7453i	−0.880656	+	1.52534i
$750$		0			0
$751$	8.84443	−	7.42136i	0.322738	−	0.270809i	−0.466995	−	0.884260i	$-0.654663\pi$
$751$	8.84443	−	7.42136i	0.322738	−	0.270809i	0.789733	+	0.613451i	$0.210219\pi$
$752$		0			0
$753$	6.58736	+	11.4096i	0.240057	+	0.415790i
$754$		0			0
$755$	−4.21742	+	23.9182i	−0.153487	+	0.870471i
$756$		0			0
$757$	4.71337	−	1.71553i	0.171310	−	0.0623519i	−0.254941	−	0.966957i	$-0.582056\pi$
$757$	4.71337	−	1.71553i	0.171310	−	0.0623519i	0.426252	+	0.904605i	$0.359834\pi$
$758$		0			0
$759$	11.8049			0.428492
$760$		0			0
$761$	−41.7464			−1.51331			−0.756653	−	0.653816i	$-0.773167\pi$
$761$	−41.7464			−1.51331			−0.756653	+	0.653816i	$0.773167\pi$
$762$		0			0
$763$	−33.5956	+	12.2278i	−1.21624	+	0.442676i
$764$		0			0
$765$	2.17826	−	12.3535i	0.0787552	−	0.446643i
$766$		0			0
$767$	−2.02061	−	3.49980i	−0.0729599	−	0.126370i
$768$		0			0
$769$	34.4563	−	28.9123i	1.24253	−	1.04260i	0.245204	−	0.969471i	$-0.421145\pi$
$769$	34.4563	−	28.9123i	1.24253	−	1.04260i	0.997322	−	0.0731323i	$-0.0232995\pi$
$770$		0			0
$771$	9.72582	−	16.8456i	0.350267	−	0.606680i
$772$		0			0
$773$	−45.2766	−	16.4793i	−1.62849	−	0.592720i	−0.643513	−	0.765435i	$-0.722524\pi$
$773$	−45.2766	−	16.4793i	−1.62849	−	0.592720i	−0.984972	+	0.172715i	$0.944746\pi$
$774$		0			0
$775$	−0.123198	−	0.698691i	−0.00442540	−	0.0250977i
$776$		0			0
$777$	−21.9409	−	18.4106i	−0.787124	−	0.660476i
$778$		0			0
$779$	−26.7739	+	16.4923i	−0.959275	+	0.590896i
$780$		0			0
$781$	20.1002	+	16.8661i	0.719241	+	0.603515i
$782$		0			0
$783$	−0.278268	−	1.57813i	−0.00994447	−	0.0563979i
$784$		0			0
$785$	34.9562	+	12.7230i	1.24764	+	0.454104i
$786$		0			0
$787$	−19.3475	+	33.5108i	−0.689663	+	1.19453i	0.282284	+	0.959331i	$0.408908\pi$
$787$	−19.3475	+	33.5108i	−0.689663	+	1.19453i	−0.971947	+	0.235200i	$0.924426\pi$
$788$		0			0
$789$	−6.00346	+	5.03750i	−0.213729	+	0.179340i
$790$		0			0
$791$	−12.4598	−	21.5810i	−0.443020	−	0.767333i
$792$		0			0
$793$	−0.779039	+	4.41815i	−0.0276645	+	0.156893i
$794$		0			0
$795$	−23.8620	+	8.68507i	−0.846299	+	0.308028i
$796$		0			0
$797$	−5.37913			−0.190538			−0.0952692	−	0.995452i	$-0.530371\pi$
$797$	−5.37913			−0.190538			−0.0952692	+	0.995452i	$0.530371\pi$
$798$		0			0
$799$	57.8550			2.04676
$800$		0			0
$801$	−4.30653	+	1.56745i	−0.152164	+	0.0553831i
$802$		0			0
$803$	−0.197002	+	1.11725i	−0.00695205	+	0.0394270i
$804$		0			0
$805$	−26.8469	−	46.5002i	−0.946228	−	1.63892i
$806$		0			0
$807$	12.8333	−	10.7684i	0.451752	−	0.379065i
$808$		0			0
$809$	−2.18762	+	3.78907i	−0.0769126	+	0.133217i	−0.901916	−	0.431911i	$-0.857840\pi$
$809$	−2.18762	+	3.78907i	−0.0769126	+	0.133217i	0.825004	+	0.565127i	$0.191173\pi$
$810$		0			0
$811$	6.53177	+	2.37737i	0.229361	+	0.0834807i	0.454144	−	0.890928i	$-0.349945\pi$
$811$	6.53177	+	2.37737i	0.229361	+	0.0834807i	−0.224783	+	0.974409i	$0.572167\pi$
$812$		0			0
$813$	−4.70011	−	26.6557i	−0.164840	−	0.934855i
$814$		0			0
$815$	−24.2774	−	20.3711i	−0.850399	−	0.713569i
$816$		0			0
$817$	0.174939	+	6.13879i	0.00612036	+	0.214769i
$818$		0			0
$819$	−2.02981	−	1.70321i	−0.0709273	−	0.0595151i
$820$		0			0
$821$	4.60348	+	26.1076i	0.160662	+	0.911162i	0.953425	+	0.301631i	$0.0975311\pi$
$821$	4.60348	+	26.1076i	0.160662	+	0.911162i	−0.792762	+	0.609531i	$0.791358\pi$
$822$		0			0
$823$	−11.6911	−	4.25523i	−0.407528	−	0.148328i	0.130119	−	0.991498i	$-0.458464\pi$
$823$	−11.6911	−	4.25523i	−0.407528	−	0.148328i	−0.537646	+	0.843171i	$0.680686\pi$
$824$		0			0
$825$	0.114081	−	0.197594i	0.00397178	−	0.00687933i
$826$		0			0
$827$	−18.4462	+	15.4782i	−0.641439	+	0.538231i	−0.904460	−	0.426559i	$-0.859726\pi$
$827$	−18.4462	+	15.4782i	−0.641439	+	0.538231i	0.263021	+	0.964790i	$0.415281\pi$
$828$		0			0
$829$	10.2182	+	17.6984i	0.354893	+	0.614692i	0.987100	−	0.160108i	$-0.0511841\pi$
$829$	10.2182	+	17.6984i	0.354893	+	0.614692i	−0.632207	+	0.774800i	$0.717851\pi$
$830$		0			0
$831$	0.838905	−	4.75767i	0.0291013	−	0.165042i
$832$		0			0
$833$	−62.9735	+	22.9205i	−2.18190	+	0.794147i
$834$		0			0
$835$	−35.8374			−1.24020
$836$		0			0
$837$	−6.74561			−0.233162
$838$		0			0
$839$	−31.4323	+	11.4404i	−1.08516	+	0.394968i	−0.821828	−	0.569736i	$-0.807045\pi$
$839$	−31.4323	+	11.4404i	−1.08516	+	0.394968i	−0.263337	+	0.964704i	$0.584823\pi$
$840$		0			0
$841$	−4.58988	+	26.0305i	−0.158272	+	0.897603i
$842$		0			0
$843$	11.1327	+	19.2823i	0.383429	+	0.664118i
$844$		0			0
$845$	−21.8638	+	18.3459i	−0.752138	+	0.631119i
$846$		0			0
$847$	−13.7428	+	23.8032i	−0.472208	+	0.817889i
$848$		0			0
$849$	5.29809	+	1.92835i	0.181830	+	0.0661808i
$850$		0			0
$851$	−6.19753	−	35.1480i	−0.212449	−	1.20486i
$852$		0			0
$853$	0.500291	+	0.419794i	0.0171297	+	0.0143735i	0.651312	−	0.758810i	$-0.274219\pi$
$853$	0.500291	+	0.419794i	0.0171297	+	0.0143735i	−0.634183	+	0.773183i	$0.718663\pi$
$854$		0			0
$855$	6.54301	+	7.36120i	0.223766	+	0.251748i
$856$		0			0
$857$	41.0839	+	34.4735i	1.40340	+	1.17759i	0.959566	+	0.281485i	$0.0908269\pi$
$857$	41.0839	+	34.4735i	1.40340	+	1.17759i	0.443835	+	0.896108i	$0.353618\pi$
$858$		0			0
$859$	−3.79974	−	21.5494i	−0.129646	−	0.735256i	−0.978440	−	0.206533i	$-0.933782\pi$
$859$	−3.79974	−	21.5494i	−0.129646	−	0.735256i	0.848794	−	0.528723i	$-0.177329\pi$
$860$		0			0
$861$	−29.6044	−	10.7751i	−1.00892	−	0.367215i
$862$		0			0
$863$	13.3479	−	23.1192i	0.454366	−	0.786985i	−0.544285	−	0.838900i	$-0.683199\pi$
$863$	13.3479	−	23.1192i	0.454366	−	0.786985i	0.998652	+	0.0519148i	$0.0165324\pi$
$864$		0			0
$865$	−29.3600	+	24.6360i	−0.998271	+	0.837649i
$866$		0			0
$867$	−6.91129	−	11.9707i	−0.234720	−	0.406547i
$868$		0			0
$869$	3.66619	−	20.7920i	0.124367	−	0.705321i
$870$		0			0
$871$	−6.23222	+	2.26834i	−0.211171	+	0.0768598i
$872$		0			0
$873$	−10.2335			−0.346353
$874$		0			0
$875$	48.2978			1.63276
$876$		0			0
$877$	25.7568	−	9.37471i	0.869746	−	0.316562i	0.131681	−	0.991292i	$-0.457962\pi$
$877$	25.7568	−	9.37471i	0.869746	−	0.316562i	0.738064	+	0.674731i	$0.235740\pi$
$878$		0			0
$879$	4.06328	−	23.0440i	0.137051	−	0.777255i
$880$		0			0
$881$	8.53145	+	14.7769i	0.287432	+	0.497847i	0.973196	−	0.229977i	$-0.0738652\pi$
$881$	8.53145	+	14.7769i	0.287432	+	0.497847i	−0.685764	+	0.727824i	$0.740532\pi$
$882$		0			0
$883$	2.61617	−	2.19523i	0.0880413	−	0.0738754i	−0.597705	−	0.801716i	$-0.703921\pi$
$883$	2.61617	−	2.19523i	0.0880413	−	0.0738754i	0.685746	+	0.727841i	$0.259476\pi$
$884$		0			0
$885$	−7.52438	+	13.0326i	−0.252929	+	0.438086i
$886$		0			0
$887$	−12.9915	−	4.72854i	−0.436213	−	0.158769i	0.114573	−	0.993415i	$-0.463450\pi$
$887$	−12.9915	−	4.72854i	−0.436213	−	0.158769i	−0.550787	+	0.834646i	$0.685672\pi$
$888$		0			0
$889$	−6.43534	−	36.4966i	−0.215834	−	1.22406i
$890$		0			0
$891$	−1.66182	−	1.39443i	−0.0556731	−	0.0467153i
$892$		0			0
$893$	−28.1948	+	35.6142i	−0.943502	+	1.19178i
$894$		0			0
$895$	−30.7172	−	25.7748i	−1.02676	−	0.861557i
$896$		0			0
$897$	−0.573351	−	3.25164i	−0.0191436	−	0.108569i
$898$		0			0
$899$	−10.1578	−	3.69713i	−0.338781	−	0.123306i
$900$		0			0
$901$	−31.1976	+	54.0358i	−1.03934	+	1.80019i
$902$		0			0
$903$	−4.71325	+	3.95489i	−0.156847	+	0.131610i
$904$		0			0
$905$	14.3116	+	24.7883i	0.475732	+	0.823992i
$906$		0			0
$907$	0.460472	−	2.61146i	0.0152897	−	0.0867123i	−0.976208	−	0.216836i	$-0.930426\pi$
$907$	0.460472	−	2.61146i	0.0152897	−	0.0867123i	0.991498	+	0.130124i	$0.0415374\pi$
$908$		0			0
$909$	10.4007	−	3.78553i	0.344968	−	0.125558i
$910$		0			0
$911$	−0.443526			−0.0146947			−0.00734733	−	0.999973i	$-0.502339\pi$
$911$	−0.443526			−0.0146947			−0.00734733	+	0.999973i	$0.502339\pi$
$912$		0			0
$913$	−28.2704			−0.935615
$914$		0			0
$915$	15.6987	−	5.71385i	0.518983	−	0.188894i
$916$		0			0
$917$	−1.44788	+	8.21131i	−0.0478131	+	0.271161i
$918$		0			0
$919$	28.0481	+	48.5807i	0.925220	+	1.60253i	0.791207	+	0.611548i	$0.209453\pi$
$919$	28.0481	+	48.5807i	0.925220	+	1.60253i	0.134013	+	0.990980i	$0.457214\pi$
$920$		0			0
$921$	25.5258	−	21.4187i	0.841104	−	0.705770i
$922$		0			0
$923$	3.66947	−	6.35570i	0.120782	−	0.209200i
$924$		0			0
$925$	−0.648206	−	0.235928i	−0.0213129	−	0.00775726i
$926$		0			0
$927$	2.74810	+	15.5852i	0.0902594	+	0.511887i
$928$		0			0
$929$	−14.5755	−	12.2303i	−0.478206	−	0.401263i	0.371571	−	0.928405i	$-0.378819\pi$
$929$	−14.5755	−	12.2303i	−0.478206	−	0.401263i	−0.849777	+	0.527142i	$0.823264\pi$
$930$		0			0
$931$	16.5799	−	49.9350i	0.543383	−	1.63655i
$932$		0			0
$933$	−19.0497	−	15.9846i	−0.623659	−	0.523312i
$934$		0			0
$935$	−4.72542	−	26.7992i	−0.154538	−	0.876427i
$936$		0			0
$937$	−46.5000	−	16.9246i	−1.51909	−	0.552903i	−0.558168	−	0.829728i	$-0.688495\pi$
$937$	−46.5000	−	16.9246i	−1.51909	−	0.552903i	−0.960920	+	0.276825i	$0.910718\pi$
$938$		0			0
$939$	−5.12617	+	8.87879i	−0.167286	+	0.289748i
$940$		0			0
$941$	−1.17706	+	0.987675i	−0.0383712	+	0.0321973i	−0.661772	−	0.749706i	$-0.730195\pi$
$941$	−1.17706	+	0.987675i	−0.0383712	+	0.0321973i	0.623400	+	0.781903i	$0.285751\pi$
$942$		0			0
$943$	−19.6286	−	33.9977i	−0.639195	−	1.10712i
$944$		0			0
$945$	−1.71341	+	9.71721i	−0.0557371	+	0.316101i
$946$		0			0
$947$	−14.8158	+	5.39253i	−0.481450	+	0.175234i	−0.571332	−	0.820719i	$-0.693573\pi$
$947$	−14.8158	+	5.39253i	−0.481450	+	0.175234i	0.0898820	+	0.995952i	$0.471351\pi$
$948$		0			0
$949$	0.317312			0.0103004
$950$		0			0
$951$	9.73579			0.315704
$952$		0			0
$953$	6.89211	−	2.50852i	0.223257	−	0.0812590i	−0.227970	−	0.973668i	$-0.573209\pi$
$953$	6.89211	−	2.50852i	0.223257	−	0.0812590i	0.451227	+	0.892409i	$0.350986\pi$
$954$		0			0
$955$	−3.09692	+	17.5635i	−0.100214	+	0.568341i
$956$		0			0
$957$	−1.73817	−	3.01060i	−0.0561871	−	0.0973189i
$958$		0			0
$959$	64.0066	−	53.7079i	2.06688	−	1.73432i
$960$		0			0
$961$	−7.25162	+	12.5602i	−0.233923	+	0.405167i
$962$		0			0
$963$	10.3724	+	3.77524i	0.334245	+	0.121655i
$964$		0			0
$965$	0.0461876	+	0.261943i	0.00148683	+	0.00843224i
$966$		0			0
$967$	0.143324	+	0.120263i	0.00460899	+	0.00386740i	0.645089	−	0.764107i	$-0.276820\pi$
$967$	0.143324	+	0.120263i	0.00460899	+	0.00386740i	−0.640480	+	0.767975i	$0.721265\pi$
$968$		0			0
$969$	23.9422	+	3.52166i	0.769133	+	0.113132i
$970$		0			0
$971$	17.6661	+	14.8236i	0.566931	+	0.475712i	0.880626	−	0.473812i	$-0.157122\pi$
$971$	17.6661	+	14.8236i	0.566931	+	0.475712i	−0.313695	+	0.949524i	$0.601567\pi$
$972$		0			0
$973$	−10.7861	−	61.1711i	−0.345787	−	1.96105i
$974$		0			0
$975$	−0.0599674	−	0.0218263i	−0.00192049	−	0.000699002i
$976$		0			0
$977$	15.4121	−	26.6946i	0.493077	−	0.854035i	−0.506891	−	0.862010i	$-0.669205\pi$
$977$	15.4121	−	26.6946i	0.493077	−	0.854035i	0.999968	+	0.00797538i	$0.00253867\pi$
$978$		0			0
$979$	−7.61598	+	6.39057i	−0.243408	+	0.204243i
$980$		0			0
$981$	4.09338	+	7.08994i	0.130692	+	0.226364i
$982$		0			0
$983$	1.11074	−	6.29933i	0.0354272	−	0.200917i	−0.961957	−	0.273201i	$-0.911918\pi$
$983$	1.11074	−	6.29933i	0.0354272	−	0.200917i	0.997384	+	0.0722836i	$0.0230287\pi$
$984$		0			0
$985$	32.3935	−	11.7903i	1.03214	−	0.375670i
$986$		0			0
$987$	−45.5084			−1.44855
$988$		0			0
$989$	−7.66683			−0.243791
$990$		0			0
$991$	9.19218	−	3.34568i	0.291999	−	0.106279i	−0.191867	−	0.981421i	$-0.561454\pi$
$991$	9.19218	−	3.34568i	0.291999	−	0.106279i	0.483866	+	0.875142i	$0.339232\pi$
$992$		0			0
$993$	4.33108	−	24.5628i	0.137443	−	0.779476i
$994$		0			0
$995$	3.17673	+	5.50226i	0.100709	+	0.174433i
$996$		0			0
$997$	−7.13937	+	5.99065i	−0.226106	+	0.189726i	−0.748802	−	0.662793i	$-0.769371\pi$
$997$	−7.13937	+	5.99065i	−0.226106	+	0.189726i	0.522696	+	0.852519i	$0.324926\pi$
$998$		0			0
$999$	−3.27933	+	5.67996i	−0.103753	+	0.179706i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	912.2.bo.g.529.2		12
4.3	odd	2		228.2.q.b.73.2	yes	12
12.11	even	2		684.2.bo.e.73.1		12
19.6	even	9	inner	912.2.bo.g.481.2		12
76.43	odd	18		4332.2.a.t.1.4		6
76.63	odd	18		228.2.q.b.25.2	✓	12
76.71	even	18		4332.2.a.u.1.4		6
228.215	even	18		684.2.bo.e.253.1		12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
228.2.q.b.25.2	✓	12	76.63	odd	18
228.2.q.b.73.2	yes	12	4.3	odd	2
684.2.bo.e.73.1		12	12.11	even	2
684.2.bo.e.253.1		12	228.215	even	18
912.2.bo.g.481.2		12	19.6	even	9	inner
912.2.bo.g.529.2		12	1.1	even	1	trivial
4332.2.a.t.1.4		6	76.43	odd	18
4332.2.a.u.1.4		6	76.71	even	18

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:	\( N \)	\(=\)	\( 912 = 2^{4} \cdot 3 \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	912.bo (of order \(9\), degree \(6\), not minimal)

\(f(q)\)	\(=\)	\(q+(-0.939693 + 0.342020i) q^{3} +(0.392352 - 2.22514i) q^{5} +(2.18351 + 3.78195i) q^{7} +(0.766044 - 0.642788i) q^{9} +O(q^{10})\)	\(q+(-0.939693 + 0.342020i) q^{3} +(0.392352 - 2.22514i) q^{5} +(2.18351 + 3.78195i) q^{7} +(0.766044 - 0.642788i) q^{9} +(1.08468 - 1.87871i) q^{11} +(-0.570168 - 0.207524i) q^{13} +(0.392352 + 2.22514i) q^{15} +(4.25293 + 3.56863i) q^{17} +(-4.26937 + 0.878888i) q^{19} +(-3.34533 - 2.80706i) q^{21} +(-0.944939 - 5.35902i) q^{23} +(-0.0988321 - 0.0359720i) q^{25} +(-0.500000 + 0.866025i) q^{27} +(-1.22757 + 1.03005i) q^{29} +(3.37280 + 5.84187i) q^{31} +(-0.376704 + 2.13640i) q^{33} +(9.27206 - 3.37475i) q^{35} +6.55866 q^{37} +0.606760 q^{39} +(6.77909 - 2.46739i) q^{41} +(0.244654 - 1.38750i) q^{43} +(-1.12973 - 1.95675i) q^{45} +(7.98289 - 6.69844i) q^{47} +(-6.03542 + 10.4537i) q^{49} +(-5.21699 - 1.89883i) q^{51} +(1.95158 + 11.0680i) q^{53} +(-3.75482 - 3.15067i) q^{55} +(3.71130 - 2.28610i) q^{57} +(5.10210 + 4.28117i) q^{59} +(-1.28393 - 7.28155i) q^{61} +(4.10365 + 1.49361i) q^{63} +(-0.685476 + 1.18728i) q^{65} +(8.37325 - 7.02599i) q^{67} +(2.72084 + 4.71264i) q^{69} +(-2.10032 + 11.9115i) q^{71} +(-0.491424 + 0.178864i) q^{73} +0.105175 q^{75} +9.47360 q^{77} +(9.14536 - 3.32864i) q^{79} +(0.173648 - 0.984808i) q^{81} +(-6.51587 - 11.2858i) q^{83} +(9.60935 - 8.06320i) q^{85} +(0.801239 - 1.38779i) q^{87} +(-4.30653 - 1.56745i) q^{89} +(-0.460121 - 2.60947i) q^{91} +(-5.16744 - 4.33599i) q^{93} +(0.280550 + 9.84478i) q^{95} +(-7.83934 - 6.57799i) q^{97} +(-0.376704 - 2.13640i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q - 6 q^{5} + 9 q^{7}+O(q^{10}) \) 12 * q - 6 * q^5 + 9 * q^7	\( 12 q - 6 q^{5} + 9 q^{7} + 9 q^{11} - 3 q^{13} - 6 q^{15} + 12 q^{17} - 9 q^{19} + 6 q^{21} - 15 q^{23} + 12 q^{25} - 6 q^{27} - 24 q^{29} + 6 q^{31} - 9 q^{33} + 42 q^{35} + 12 q^{37} - 18 q^{39} + 6 q^{41} + 39 q^{43} - 3 q^{45} + 3 q^{47} - 21 q^{49} + 3 q^{51} + 18 q^{53} - 45 q^{55} + 3 q^{57} + 33 q^{61} - 3 q^{63} - 33 q^{65} + 27 q^{67} + 12 q^{69} - 6 q^{71} - 24 q^{73} + 30 q^{75} - 18 q^{79} - 3 q^{83} + 39 q^{85} + 9 q^{87} - 15 q^{89} - 18 q^{91} - 6 q^{93} + 30 q^{95} - 15 q^{97} - 9 q^{99}+O(q^{100}) \) 12 * q - 6 * q^5 + 9 * q^7 + 9 * q^11 - 3 * q^13 - 6 * q^15 + 12 * q^17 - 9 * q^19 + 6 * q^21 - 15 * q^23 + 12 * q^25 - 6 * q^27 - 24 * q^29 + 6 * q^31 - 9 * q^33 + 42 * q^35 + 12 * q^37 - 18 * q^39 + 6 * q^41 + 39 * q^43 - 3 * q^45 + 3 * q^47 - 21 * q^49 + 3 * q^51 + 18 * q^53 - 45 * q^55 + 3 * q^57 + 33 * q^61 - 3 * q^63 - 33 * q^65 + 27 * q^67 + 12 * q^69 - 6 * q^71 - 24 * q^73 + 30 * q^75 - 18 * q^79 - 3 * q^83 + 39 * q^85 + 9 * q^87 - 15 * q^89 - 18 * q^91 - 6 * q^93 + 30 * q^95 - 15 * q^97 - 9 * q^99

Introduction

L-functions

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Database

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