LMFDB - Embedded newform 1764.2.w.b.1109.6

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1764,2,Mod(509,1764)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1764, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 5, 5]))

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

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

chi := DirichletCharacter("1764.509");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1764 = 2^{2} \cdot 3^{2} \cdot 7^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1764.w (of order $6$, 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:	$14.0856109166$
Analytic rank:	$0$
Dimension:	$16$
Relative dimension:	$8$ over $\Q(\zeta_{6})$
Coefficient field:	$\mathbb{Q}[x]/(x^{16} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} - 2 x^{15} + 5 x^{14} - 17 x^{13} + 22 x^{12} - 31 x^{11} + 62 x^{10} - 52 x^{9} + 52 x^{8} + \cdots + 6561 $ x^16 - 2x^15 + 5x^14 - 17x^13 + 22x^12 - 31x^11 + 62x^10 - 52x^9 + 52x^8 - 156x^7 + 558x^6 - 837x^5 + 1782x^4 - 4131x^3 + 3645x^2 - 4374*x + 6561
Coefficient ring:	$\Z[a_1, \ldots, a_{13}]$
Coefficient ring index:	$ 3^{4} $
Twist minimal:	no (minimal twist has level 252)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			1109.6
Root			$1.68042 - 0.419752i$ of defining polynomial
Character	$\chi$	$=$	1764.1109
Dual form			1764.2.w.b.509.6

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.36511 + 1.06606i) q^{3} +(1.48494 - 2.57199i) q^{5} +(0.727031 + 2.91057i) q^{9} +O(q^{10})$	\(q+(1.36511 + 1.06606i) q^{3} +(1.48494 - 2.57199i) q^{5} +(0.727031 + 2.91057i) q^{9} +(-4.09466 + 2.36406i) q^{11} +(3.54045 - 2.04408i) q^{13} +(4.76900 - 1.92801i) q^{15} +(0.835278 - 1.44674i) q^{17} +(4.25377 - 2.45592i) q^{19} +(4.25297 + 2.45545i) q^{23} +(-1.91009 - 3.30837i) q^{25} +(-2.11037 + 4.74830i) q^{27} +(0.238557 + 0.137731i) q^{29} +1.60327i q^{31} +(-8.10988 - 1.13797i) q^{33} +(-1.69681 - 2.93896i) q^{37} +(7.01221 + 0.983947i) q^{39} +(3.55632 + 6.15972i) q^{41} +(5.22930 - 9.05742i) q^{43} +(8.56556 + 2.45211i) q^{45} +10.9977 q^{47} +(2.68256 - 1.08450i) q^{51} +(0.707381 + 0.408407i) q^{53} +14.0419i q^{55} +(8.42500 + 1.18219i) q^{57} -2.74856 q^{59} -7.20310i q^{61} -12.1413i q^{65} +11.6103 q^{67} +(3.18809 + 7.88587i) q^{69} +10.4406i q^{71} +(-13.6493 - 7.88042i) q^{73} +(0.919449 - 6.55255i) q^{75} -12.3033 q^{79} +(-7.94285 + 4.23215i) q^{81} +(4.03981 - 6.99715i) q^{83} +(-2.48067 - 4.29665i) q^{85} +(0.178826 + 0.442333i) q^{87} +(-4.60872 - 7.98254i) q^{89} +(-1.70919 + 2.18864i) q^{93} -14.5875i q^{95} +(-7.00772 - 4.04591i) q^{97} +(-9.85770 - 10.1991i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q + 6 q^{9}+O(q^{10}) $ 16 * q + 6 * q^9	$ 16 q + 6 q^{9} - 6 q^{11} + 3 q^{13} - 3 q^{15} - 9 q^{17} + 21 q^{23} - 8 q^{25} - 9 q^{27} + 6 q^{29} + q^{37} - 3 q^{39} + 6 q^{41} - 2 q^{43} + 30 q^{45} + 36 q^{47} - 33 q^{51} + 15 q^{57} + 30 q^{59} + 14 q^{67} - 21 q^{69} + 57 q^{75} + 2 q^{79} + 18 q^{81} + 6 q^{85} - 48 q^{87} - 21 q^{89} + 21 q^{93} + 3 q^{97} - 9 q^{99}+O(q^{100}) $ 16 * q + 6 * q^9 - 6 * q^11 + 3 * q^13 - 3 * q^15 - 9 * q^17 + 21 * q^23 - 8 * q^25 - 9 * q^27 + 6 * q^29 + q^37 - 3 * q^39 + 6 * q^41 - 2 * q^43 + 30 * q^45 + 36 * q^47 - 33 * q^51 + 15 * q^57 + 30 * q^59 + 14 * q^67 - 21 * q^69 + 57 * q^75 + 2 * q^79 + 18 * q^81 + 6 * q^85 - 48 * q^87 - 21 * q^89 + 21 * q^93 + 3 * q^97 - 9 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1764\mathbb{Z}\right)^\times$.

$n$	$785$	$883$	$1081$
$\chi(n)$	$e\left(\frac{1}{6}\right)$	$1$	$e\left(\frac{1}{6}\right)$

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
$3$	1.36511	+	1.06606i	0.788145	+	0.615490i
$3$	1.36511	+	1.06606i	0.788145	+	0.615490i
$4$		0			0
$5$	1.48494	−	2.57199i	0.664085	−	1.15023i	−0.315447	−	0.948943i	$-0.602155\pi$
$5$	1.48494	−	2.57199i	0.664085	−	1.15023i	0.979532	−	0.201286i	$-0.0645121\pi$
$6$		0			0
$7$		0			0
$7$		0			0
$8$		0			0
$9$	0.727031	+	2.91057i	0.242344	+	0.970190i
$10$		0			0
$11$	−4.09466	+	2.36406i	−1.23459	+	0.712790i	−0.967983	−	0.251016i	$-0.919235\pi$
$11$	−4.09466	+	2.36406i	−1.23459	+	0.712790i	−0.266605	+	0.963806i	$0.585902\pi$
$12$		0			0
$13$	3.54045	−	2.04408i	0.981945	−	0.566926i	0.0790880	−	0.996868i	$-0.474799\pi$
$13$	3.54045	−	2.04408i	0.981945	−	0.566926i	0.902857	+	0.429942i	$0.141466\pi$
$14$		0			0
$15$	4.76900	−	1.92801i	1.23135	−	0.497809i
$16$		0			0
$17$	0.835278	−	1.44674i	0.202585	−	0.350887i	−0.746776	−	0.665076i	$-0.768399\pi$
$17$	0.835278	−	1.44674i	0.202585	−	0.350887i	0.949360	+	0.314189i	$0.101733\pi$
$18$		0			0
$19$	4.25377	−	2.45592i	0.975882	−	0.563426i	0.0748577	−	0.997194i	$-0.476150\pi$
$19$	4.25377	−	2.45592i	0.975882	−	0.563426i	0.901024	+	0.433768i	$0.142816\pi$
$20$		0			0
$21$		0			0
$22$		0			0
$23$	4.25297	+	2.45545i	0.886805	+	0.511997i	0.872896	−	0.487906i	$-0.162239\pi$
$23$	4.25297	+	2.45545i	0.886805	+	0.511997i	0.0139086	+	0.999903i	$0.495573\pi$
$24$		0			0
$25$	−1.91009	−	3.30837i	−0.382018	−	0.661675i
$26$		0			0
$27$	−2.11037	+	4.74830i	−0.406141	+	0.913811i
$28$		0			0
$29$	0.238557	+	0.137731i	0.0442989	+	0.0255760i	0.521986	−	0.852954i	$-0.325191\pi$
$29$	0.238557	+	0.137731i	0.0442989	+	0.0255760i	−0.477687	+	0.878530i	$0.658525\pi$
$30$		0			0
$31$			1.60327i			0.287956i	0.989581	+	0.143978i	$0.0459895\pi$
$31$			1.60327i			0.287956i	−0.989581	+	0.143978i	$0.954011\pi$
$32$		0			0
$33$	−8.10988	−	1.13797i	−1.41175	−	0.198095i
$34$		0			0
$35$		0			0
$36$		0			0
$37$	−1.69681	−	2.93896i	−0.278954	−	0.483162i	0.692171	−	0.721733i	$-0.256654\pi$
$37$	−1.69681	−	2.93896i	−0.278954	−	0.483162i	−0.971125	+	0.238571i	$0.923321\pi$
$38$		0			0
$39$	7.01221	+	0.983947i	1.12285	+	0.157558i
$40$		0			0
$41$	3.55632	+	6.15972i	0.555404	+	0.961987i	0.997872	+	0.0652031i	$0.0207695\pi$
$41$	3.55632	+	6.15972i	0.555404	+	0.961987i	−0.442468	+	0.896784i	$0.645897\pi$
$42$		0			0
$43$	5.22930	−	9.05742i	0.797461	−	1.38124i	−0.123804	−	0.992307i	$-0.539509\pi$
$43$	5.22930	−	9.05742i	0.797461	−	1.38124i	0.921265	−	0.388936i	$-0.127157\pi$
$44$		0			0
$45$	8.56556	+	2.45211i	1.27688	+	0.365538i
$46$		0			0
$47$	10.9977			1.60418			0.802090	−	0.597203i	$-0.203721\pi$
$47$	10.9977			1.60418			0.802090	+	0.597203i	$0.203721\pi$
$48$		0			0
$49$		0			0
$50$		0			0
$51$	2.68256	−	1.08450i	0.375633	−	0.151861i
$52$		0			0
$53$	0.707381	+	0.408407i	0.0971663	+	0.0560990i	0.547796	−	0.836612i	$-0.315467\pi$
$53$	0.707381	+	0.408407i	0.0971663	+	0.0560990i	−0.450629	+	0.892711i	$0.648800\pi$
$54$		0			0
$55$			14.0419i			1.89341i
$56$		0			0
$57$	8.42500	+	1.18219i	1.11592	+	0.156585i
$58$		0			0
$59$	−2.74856			−0.357832			−0.178916	−	0.983864i	$-0.557259\pi$
$59$	−2.74856			−0.357832			−0.178916	+	0.983864i	$0.557259\pi$
$60$		0			0
$61$		−	7.20310i		−	0.922262i	−0.887332	−	0.461131i	$-0.847444\pi$
$61$		−	7.20310i		−	0.922262i	0.887332	−	0.461131i	$-0.152556\pi$
$62$		0			0
$63$		0			0
$64$		0			0
$65$		−	12.1413i		−	1.50595i
$66$		0			0
$67$	11.6103			1.41842			0.709210	−	0.704998i	$-0.249052\pi$
$67$	11.6103			1.41842			0.709210	+	0.704998i	$0.249052\pi$
$68$		0			0
$69$	3.18809	+	7.88587i	0.383801	+	0.949347i
$70$		0			0
$71$			10.4406i			1.23907i	0.784968	+	0.619537i	$0.212680\pi$
$71$			10.4406i			1.23907i	−0.784968	+	0.619537i	$0.787320\pi$
$72$		0			0
$73$	−13.6493	−	7.88042i	−1.59753	−	0.922334i	−0.991962	−	0.126539i	$-0.959613\pi$
$73$	−13.6493	−	7.88042i	−1.59753	−	0.922334i	−0.605567	−	0.795794i	$-0.707054\pi$
$74$		0			0
$75$	0.919449	−	6.55255i	0.106169	−	0.756624i
$76$		0			0
$77$		0			0
$78$		0			0
$79$	−12.3033			−1.38422			−0.692112	−	0.721790i	$-0.743320\pi$
$79$	−12.3033			−1.38422			−0.692112	+	0.721790i	$0.743320\pi$
$80$		0			0
$81$	−7.94285	+	4.23215i	−0.882539	+	0.470239i
$82$		0			0
$83$	4.03981	−	6.99715i	0.443426	−	0.768037i	−0.554515	−	0.832174i	$-0.687096\pi$
$83$	4.03981	−	6.99715i	0.443426	−	0.768037i	0.997941	+	0.0641368i	$0.0204294\pi$
$84$		0			0
$85$	−2.48067	−	4.29665i	−0.269067	−	0.466037i
$86$		0			0
$87$	0.178826	+	0.442333i	0.0191722	+	0.0474231i
$88$		0			0
$89$	−4.60872	−	7.98254i	−0.488523	−	0.846147i	0.511390	−	0.859349i	$-0.329131\pi$
$89$	−4.60872	−	7.98254i	−0.488523	−	0.846147i	−0.999913	+	0.0132019i	$0.995798\pi$
$90$		0			0
$91$		0			0
$92$		0			0
$93$	−1.70919	+	2.18864i	−0.177234	+	0.226951i
$94$		0			0
$95$		−	14.5875i		−	1.49665i
$96$		0			0
$97$	−7.00772	−	4.04591i	−0.711527	−	0.410800i	0.100099	−	0.994977i	$-0.468084\pi$
$97$	−7.00772	−	4.04591i	−0.711527	−	0.410800i	−0.811626	+	0.584177i	$0.801417\pi$
$98$		0			0
$99$	−9.85770	−	10.1991i	−0.990736	−	1.02505i
$100$		0			0
$101$	3.65365	+	6.32831i	0.363552	+	0.629690i	0.988543	−	0.150942i	$-0.0482307\pi$
$101$	3.65365	+	6.32831i	0.363552	+	0.629690i	−0.624991	+	0.780632i	$0.714897\pi$
$102$		0			0
$103$	6.08409	+	3.51265i	0.599483	+	0.346112i	0.768838	−	0.639443i	$-0.220835\pi$
$103$	6.08409	+	3.51265i	0.599483	+	0.346112i	−0.169355	+	0.985555i	$0.554168\pi$
$104$		0			0
$105$		0			0
$106$		0			0
$107$	−12.2618	+	7.07938i	−1.18540	+	0.684389i	−0.957257	−	0.289239i	$-0.906598\pi$
$107$	−12.2618	+	7.07938i	−1.18540	+	0.684389i	−0.228140	+	0.973628i	$0.573265\pi$
$108$		0			0
$109$	−2.82203	+	4.88789i	−0.270301	+	0.468175i	−0.968939	−	0.247300i	$-0.920457\pi$
$109$	−2.82203	+	4.88789i	−0.270301	+	0.468175i	0.698638	+	0.715476i	$0.253790\pi$
$110$		0			0
$111$	0.816783	−	5.82089i	0.0775256	−	0.552495i
$112$		0			0
$113$	11.6411	−	6.72099i	1.09510	−	0.632258i	0.160172	−	0.987089i	$-0.448795\pi$
$113$	11.6411	−	6.72099i	1.09510	−	0.632258i	0.934930	+	0.354831i	$0.115462\pi$
$114$		0			0
$115$	12.6308	−	7.29239i	1.17783	−	0.680019i
$116$		0			0
$117$	8.52346	+	8.81863i	0.787994	+	0.815282i
$118$		0			0
$119$		0			0
$120$		0			0
$121$	5.67752	−	9.83375i	0.516138	−	0.893977i
$122$		0			0
$123$	−1.71188	+	12.1999i	−0.154355	+	1.10003i
$124$		0			0
$125$	3.50392			0.313400
$126$		0			0
$127$	−12.7730			−1.13342			−0.566712	−	0.823916i	$-0.691785\pi$
$127$	−12.7730			−1.13342			−0.566712	+	0.823916i	$0.691785\pi$
$128$		0			0
$129$	16.7943	−	6.78959i	1.47866	−	0.597790i
$130$		0			0
$131$	−6.70890	+	11.6202i	−0.586159	+	1.01526i	0.408570	+	0.912727i	$0.366027\pi$
$131$	−6.70890	+	11.6202i	−0.586159	+	1.01526i	−0.994730	+	0.102531i	$0.967306\pi$
$132$		0			0
$133$		0			0
$134$		0			0
$135$	9.07881	+	12.4788i	0.781379	+	1.07400i
$136$		0			0
$137$	−7.79449	+	4.50015i	−0.665928	+	0.384474i	−0.794532	−	0.607222i	$-0.792284\pi$
$137$	−7.79449	+	4.50015i	−0.665928	+	0.384474i	0.128604	+	0.991696i	$0.458950\pi$
$138$		0			0
$139$	−1.54902	+	0.894326i	−0.131386	+	0.0758557i	−0.564252	−	0.825602i	$-0.690836\pi$
$139$	−1.54902	+	0.894326i	−0.131386	+	0.0758557i	0.432866	+	0.901458i	$0.357502\pi$
$140$		0			0
$141$	15.0130	+	11.7242i	1.26433	+	0.987357i
$142$		0			0
$143$	−9.66464	+	16.7397i	−0.808198	+	1.39984i
$144$		0			0
$145$	0.708485	−	0.409044i	0.0588365	−	0.0339693i
$146$		0			0
$147$		0			0
$148$		0			0
$149$	−11.1779	−	6.45358i	−0.915732	−	0.528698i	−0.0334609	−	0.999440i	$-0.510653\pi$
$149$	−11.1779	−	6.45358i	−0.915732	−	0.528698i	−0.882271	+	0.470742i	$0.843986\pi$
$150$		0			0
$151$	6.48364	+	11.2300i	0.527631	+	0.913884i	0.999481	+	0.0322054i	$0.0102531\pi$
$151$	6.48364	+	11.2300i	0.527631	+	0.913884i	−0.471850	+	0.881679i	$0.656414\pi$
$152$		0			0
$153$	4.81812	+	1.37931i	0.389522	+	0.111510i
$154$		0			0
$155$	4.12360	+	2.38076i	0.331216	+	0.191227i
$156$		0			0
$157$		−	17.1728i		−	1.37054i	−0.728291	−	0.685268i	$-0.759685\pi$
$157$		−	17.1728i		−	1.37054i	0.728291	−	0.685268i	$-0.240315\pi$
$158$		0			0
$159$	0.530265	+	1.31163i	0.0420527	+	0.104019i
$160$		0			0
$161$		0			0
$162$		0			0
$163$	2.53107	+	4.38394i	0.198249	+	0.343377i	0.947961	−	0.318387i	$-0.103141\pi$
$163$	2.53107	+	4.38394i	0.198249	+	0.343377i	−0.749712	+	0.661764i	$0.769808\pi$
$164$		0			0
$165$	−14.9695	+	19.1687i	−1.16538	+	1.49228i
$166$		0			0
$167$	5.79673	+	10.0402i	0.448564	+	0.776936i	0.998293	−	0.0584072i	$-0.0186022\pi$
$167$	5.79673	+	10.0402i	0.448564	+	0.776936i	−0.549729	+	0.835343i	$0.685269\pi$
$168$		0			0
$169$	1.85653	−	3.21561i	0.142810	−	0.247354i
$170$		0			0
$171$	10.2407	+	10.5954i	0.783129	+	0.810249i
$172$		0			0
$173$	−6.26691			−0.476464			−0.238232	−	0.971208i	$-0.576568\pi$
$173$	−6.26691			−0.476464			−0.238232	+	0.971208i	$0.576568\pi$
$174$		0			0
$175$		0			0
$176$		0			0
$177$	−3.75207	−	2.93013i	−0.282023	−	0.220242i
$178$		0			0
$179$	−12.7668	−	7.37089i	−0.954233	−	0.550927i	−0.0598395	−	0.998208i	$-0.519059\pi$
$179$	−12.7668	−	7.37089i	−0.954233	−	0.550927i	−0.894393	+	0.447281i	$0.852392\pi$
$180$		0			0
$181$		−	0.0833642i		−	0.00619641i	−0.999995	−	0.00309821i	$-0.999014\pi$
$181$		−	0.0833642i		−	0.00619641i	0.999995	−	0.00309821i	$-0.000986191\pi$
$182$		0			0
$183$	7.67894	−	9.83300i	0.567643	−	0.726876i
$184$		0			0
$185$	−10.0786			−0.740996
$186$		0			0
$187$			7.89857i			0.577601i
$188$		0			0
$189$		0			0
$190$		0			0
$191$			15.4351i			1.11684i	0.829558	+	0.558421i	$0.188593\pi$
$191$			15.4351i			1.11684i	−0.829558	+	0.558421i	$0.811407\pi$
$192$		0			0
$193$	21.5557			1.55162			0.775808	−	0.630969i	$-0.217343\pi$
$193$	21.5557			1.55162			0.775808	+	0.630969i	$0.217343\pi$
$194$		0			0
$195$	12.9434	−	16.5742i	0.926896	−	1.18691i
$196$		0			0
$197$			9.88306i			0.704139i	0.935974	+	0.352069i	$0.114522\pi$
$197$			9.88306i			0.704139i	−0.935974	+	0.352069i	$0.885478\pi$
$198$		0			0
$199$	9.14623	+	5.28058i	0.648359	+	0.374330i	0.787827	−	0.615896i	$-0.211206\pi$
$199$	9.14623	+	5.28058i	0.648359	+	0.374330i	−0.139468	+	0.990227i	$0.544539\pi$
$200$		0			0
$201$	15.8492	+	12.3772i	1.11792	+	0.873023i
$202$		0			0
$203$		0			0
$204$		0			0
$205$	21.1237			1.47534
$206$		0			0
$207$	−4.05473	+	14.1637i	−0.281823	+	0.984449i
$208$		0			0
$209$	−11.6118	+	20.1123i	−0.803208	+	1.39120i
$210$		0			0
$211$	6.08453	+	10.5387i	0.418876	+	0.725514i	0.995827	−	0.0912645i	$-0.0290909\pi$
$211$	6.08453	+	10.5387i	0.418876	+	0.725514i	−0.576951	+	0.816779i	$0.695758\pi$
$212$		0			0
$213$	−11.1303	+	14.2526i	−0.762638	+	0.976569i
$214$		0			0
$215$	−15.5304	−	26.8994i	−1.05916	−	1.83453i
$216$		0			0
$217$		0			0
$218$		0			0
$219$	−10.2317	−	25.3086i	−0.691396	−	1.71020i
$220$		0			0
$221$		−	6.82950i		−	0.459402i
$222$		0			0
$223$	−0.714485	−	0.412508i	−0.0478455	−	0.0276236i	0.475886	−	0.879507i	$-0.342127\pi$
$223$	−0.714485	−	0.412508i	−0.0478455	−	0.0276236i	−0.523732	+	0.851883i	$0.675461\pi$
$224$		0			0
$225$	8.24056	−	7.96475i	0.549371	−	0.530983i
$226$		0			0
$227$	−0.166778	−	0.288869i	−0.0110695	−	0.0191729i	0.860438	−	0.509556i	$-0.170190\pi$
$227$	−0.166778	−	0.288869i	−0.0110695	−	0.0191729i	−0.871507	+	0.490383i	$0.836857\pi$
$228$		0			0
$229$	−12.4893	−	7.21072i	−0.825319	−	0.476498i	0.0269285	−	0.999637i	$-0.491427\pi$
$229$	−12.4893	−	7.21072i	−0.825319	−	0.476498i	−0.852247	+	0.523139i	$0.824761\pi$
$230$		0			0
$231$		0			0
$232$		0			0
$233$	−12.7953	+	7.38739i	−0.838250	+	0.483964i	−0.856669	−	0.515867i	$-0.827470\pi$
$233$	−12.7953	+	7.38739i	−0.838250	+	0.483964i	0.0184192	+	0.999830i	$0.494137\pi$
$234$		0			0
$235$	16.3309	−	28.2860i	1.06531	−	1.84518i
$236$		0			0
$237$	−16.7953	−	13.1160i	−1.09097	−	0.851976i
$238$		0			0
$239$	−22.5339	+	13.0100i	−1.45760	+	0.841545i	−0.998893	−	0.0470423i	$-0.985020\pi$
$239$	−22.5339	+	13.0100i	−1.45760	+	0.841545i	−0.458707	+	0.888588i	$0.651687\pi$
$240$		0			0
$241$	−1.66295	+	0.960105i	−0.107120	+	0.0618458i	−0.552603	−	0.833445i	$-0.686365\pi$
$241$	−1.66295	+	0.960105i	−0.107120	+	0.0618458i	0.445483	+	0.895290i	$0.353032\pi$
$242$		0			0
$243$	−15.3546	−	2.69022i	−0.984996	−	0.172578i
$244$		0			0
$245$		0			0
$246$		0			0
$247$	10.0402	−	17.3901i	0.638841	−	1.10651i
$248$		0			0
$249$	12.9742	−	5.24518i	0.822203	−	0.332400i
$250$		0			0
$251$	−9.97663			−0.629719			−0.314860	−	0.949138i	$-0.601957\pi$
$251$	−9.97663			−0.629719			−0.314860	+	0.949138i	$0.601957\pi$
$252$		0			0
$253$	−23.2193			−1.45978
$254$		0			0
$255$	1.19411	−	8.50994i	0.0747779	−	0.532913i
$256$		0			0
$257$	−7.50364	+	12.9967i	−0.468064	+	0.810711i	−0.999334	−	0.0364915i	$-0.988382\pi$
$257$	−7.50364	+	12.9967i	−0.468064	+	0.810711i	0.531270	+	0.847203i	$0.321715\pi$
$258$		0			0
$259$		0			0
$260$		0			0
$261$	−0.227437	+	0.794471i	−0.0140780	+	0.0491765i
$262$		0			0
$263$	6.11010	−	3.52767i	0.376765	−	0.217525i	−0.299645	−	0.954051i	$-0.596868\pi$
$263$	6.11010	−	3.52767i	0.376765	−	0.217525i	0.676410	+	0.736525i	$0.263535\pi$
$264$		0			0
$265$	2.10084	−	1.21292i	0.129053	−	0.0745090i
$266$		0			0
$267$	2.21847	−	15.8102i	0.135768	−	0.967568i
$268$		0			0
$269$	−14.8898	+	25.7898i	−0.907844	+	1.57243i	−0.0907911	+	0.995870i	$0.528940\pi$
$269$	−14.8898	+	25.7898i	−0.907844	+	1.57243i	−0.817053	+	0.576562i	$0.804394\pi$
$270$		0			0
$271$	2.41462	−	1.39408i	0.146677	−	0.0846843i	−0.424865	−	0.905257i	$-0.639679\pi$
$271$	2.41462	−	1.39408i	0.146677	−	0.0846843i	0.571543	+	0.820572i	$0.306345\pi$
$272$		0			0
$273$		0			0
$274$		0			0
$275$	15.6424	+	9.03112i	0.943270	+	0.544597i
$276$		0			0
$277$	−6.79074	−	11.7619i	−0.408016	−	0.706705i	0.586651	−	0.809840i	$-0.300446\pi$
$277$	−6.79074	−	11.7619i	−0.408016	−	0.706705i	−0.994667	+	0.103135i	$0.967113\pi$
$278$		0			0
$279$	−4.66644	+	1.16563i	−0.279372	+	0.0697844i
$280$		0			0
$281$	−3.95777	−	2.28502i	−0.236101	−	0.136313i	0.377283	−	0.926098i	$-0.376859\pi$
$281$	−3.95777	−	2.28502i	−0.236101	−	0.136313i	−0.613383	+	0.789785i	$0.710192\pi$
$282$		0			0
$283$		−	20.4019i		−	1.21277i	−0.795173	−	0.606383i	$-0.792620\pi$
$283$		−	20.4019i		−	1.21277i	0.795173	−	0.606383i	$-0.207380\pi$
$284$		0			0
$285$	15.5512	−	19.9136i	0.921174	−	1.17958i
$286$		0			0
$287$		0			0
$288$		0			0
$289$	7.10462	+	12.3056i	0.417919	+	0.723857i
$290$		0			0
$291$	−5.25310	−	12.9938i	−0.307942	−	0.761707i
$292$		0			0
$293$	−6.41037	−	11.1031i	−0.374498	−	0.648649i	0.615754	−	0.787939i	$-0.288852\pi$
$293$	−6.41037	−	11.1031i	−0.374498	−	0.648649i	−0.990252	+	0.139289i	$0.955518\pi$
$294$		0			0
$295$	−4.08144	+	7.06926i	−0.237631	+	0.411589i
$296$		0			0
$297$	−2.58399	−	24.4317i	−0.149938	−	1.41767i
$298$		0			0
$299$	20.0766			1.16106
$300$		0			0
$301$		0			0
$302$		0			0
$303$	−1.75874	+	12.5338i	−0.101037	+	0.720049i
$304$		0			0
$305$	−18.5263	−	10.6962i	−1.06081	−	0.612461i
$306$		0			0
$307$		−	1.93411i		−	0.110386i	−0.998476	−	0.0551928i	$-0.982423\pi$
$307$		−	1.93411i		−	0.110386i	0.998476	−	0.0551928i	$-0.0175773\pi$
$308$		0			0
$309$	4.56073	+	11.2812i	0.259451	+	0.641762i
$310$		0			0
$311$	−2.08916			−0.118465			−0.0592326	−	0.998244i	$-0.518865\pi$
$311$	−2.08916			−0.118465			−0.0592326	+	0.998244i	$0.518865\pi$
$312$		0			0
$313$			22.4088i			1.26662i	0.773899	+	0.633309i	$0.218304\pi$
$313$			22.4088i			1.26662i	−0.773899	+	0.633309i	$0.781696\pi$
$314$		0			0
$315$		0			0
$316$		0			0
$317$		−	3.48474i		−	0.195723i	−0.995200	−	0.0978614i	$-0.968800\pi$
$317$		−	3.48474i		−	0.195723i	0.995200	−	0.0978614i	$-0.0312002\pi$
$318$		0			0
$319$	−1.30241			−0.0729212
$320$		0			0
$321$	−24.2858	−	3.40776i	−1.35550	−	0.190203i
$322$		0			0
$323$		−	8.20549i		−	0.456565i
$324$		0			0
$325$	−13.5252	−	7.80876i	−0.750241	−	0.433152i
$326$		0			0
$327$	−9.06316	+	3.66405i	−0.501194	+	0.202622i
$328$		0			0
$329$		0			0
$330$		0			0
$331$	−4.57715			−0.251583			−0.125791	−	0.992057i	$-0.540147\pi$
$331$	−4.57715			−0.251583			−0.125791	+	0.992057i	$0.540147\pi$
$332$		0			0
$333$	7.32042	−	7.07540i	0.401156	−	0.387729i
$334$		0			0
$335$	17.2405	−	29.8615i	0.941951	−	1.63151i
$336$		0			0
$337$	−14.7062	−	25.4720i	−0.801100	−	1.38755i	−0.918893	−	0.394508i	$-0.870915\pi$
$337$	−14.7062	−	25.4720i	−0.801100	−	1.38755i	0.117793	−	0.993038i	$-0.462418\pi$
$338$		0			0
$339$	23.0563	+	3.23524i	1.25225	+	0.175714i
$340$		0			0
$341$	−3.79023	−	6.56486i	−0.205252	−	0.355507i
$342$		0			0
$343$		0			0
$344$		0			0
$345$	25.0165	+	3.51030i	1.34684	+	0.188988i
$346$		0			0
$347$		−	19.6582i		−	1.05531i	−0.849459	−	0.527654i	$-0.823072\pi$
$347$		−	19.6582i		−	1.05531i	0.849459	−	0.527654i	$-0.176928\pi$
$348$		0			0
$349$	8.47286	+	4.89181i	0.453542	+	0.261852i	0.709325	−	0.704882i	$-0.249000\pi$
$349$	8.47286	+	4.89181i	0.453542	+	0.261852i	−0.255783	+	0.966734i	$0.582333\pi$
$350$		0			0
$351$	2.23424	+	21.1249i	0.119255	+	1.12756i
$352$		0			0
$353$	−12.5322	−	21.7065i	−0.667023	−	1.15532i	−0.978733	−	0.205141i	$-0.934235\pi$
$353$	−12.5322	−	21.7065i	−0.667023	−	1.15532i	0.311709	−	0.950178i	$-0.399099\pi$
$354$		0			0
$355$	26.8532	+	15.5037i	1.42522	+	0.822850i
$356$		0			0
$357$		0			0
$358$		0			0
$359$	−8.09861	+	4.67574i	−0.427428	+	0.246776i	−0.698251	−	0.715853i	$-0.746038\pi$
$359$	−8.09861	+	4.67574i	−0.427428	+	0.246776i	0.270822	+	0.962629i	$0.412704\pi$
$360$		0			0
$361$	2.56305	−	4.43933i	0.134897	−	0.233649i
$362$		0			0
$363$	18.2338	−	7.37154i	0.957026	−	0.386906i
$364$		0			0
$365$	−40.5367	+	23.4039i	−2.12179	+	1.22502i
$366$		0			0
$367$	−18.9530	+	10.9425i	−0.989337	+	0.571194i	−0.905076	−	0.425250i	$-0.860186\pi$
$367$	−18.9530	+	10.9425i	−0.989337	+	0.571194i	−0.0842608	+	0.996444i	$0.526853\pi$
$368$		0			0
$369$	−15.3428	+	14.8292i	−0.798712	+	0.771979i
$370$		0			0
$371$		0			0
$372$		0			0
$373$	−2.30822	+	3.99795i	−0.119515	+	0.207006i	−0.919576	−	0.392913i	$-0.871467\pi$
$373$	−2.30822	+	3.99795i	−0.119515	+	0.207006i	0.800061	+	0.599919i	$0.204801\pi$
$374$		0			0
$375$	4.78322	+	3.73539i	0.247005	+	0.192895i
$376$		0			0
$377$	1.12613			0.0579988
$378$		0			0
$379$	−6.22396			−0.319703			−0.159852	−	0.987141i	$-0.551102\pi$
$379$	−6.22396			−0.319703			−0.159852	+	0.987141i	$0.551102\pi$
$380$		0			0
$381$	−17.4366	−	13.6168i	−0.893303	−	0.697612i
$382$		0			0
$383$	10.9989	−	19.0506i	0.562015	−	0.973439i	−0.435305	−	0.900283i	$-0.643360\pi$
$383$	10.9989	−	19.0506i	0.562015	−	0.973439i	0.997321	−	0.0731560i	$-0.0233071\pi$
$384$		0			0
$385$		0			0
$386$		0			0
$387$	30.1641	+	8.63523i	1.53333	+	0.438954i
$388$		0			0
$389$	−8.51109	+	4.91388i	−0.431529	+	0.249144i	−0.699998	−	0.714145i	$-0.746816\pi$
$389$	−8.51109	+	4.91388i	−0.431529	+	0.249144i	0.268469	+	0.963288i	$0.413482\pi$
$390$		0			0
$391$	7.10481	−	4.10197i	0.359306	−	0.207445i
$392$		0			0
$393$	−21.5462	+	8.71066i	−1.08686	+	0.439395i
$394$		0			0
$395$	−18.2696	+	31.6439i	−0.919243	+	1.59218i
$396$		0			0
$397$	−4.55324	+	2.62881i	−0.228520	+	0.131936i	−0.609889	−	0.792487i	$-0.708786\pi$
$397$	−4.55324	+	2.62881i	−0.228520	+	0.131936i	0.381369	+	0.924423i	$0.375453\pi$
$398$		0			0
$399$		0			0
$400$		0			0
$401$	14.7847	+	8.53594i	0.738312	+	0.426265i	0.821455	−	0.570273i	$-0.193163\pi$
$401$	14.7847	+	8.53594i	0.738312	+	0.426265i	−0.0831432	+	0.996538i	$0.526496\pi$
$402$		0			0
$403$	3.27722	+	5.67631i	0.163250	+	0.282757i
$404$		0			0
$405$	−0.909599	+	26.7134i	−0.0451983	+	1.32740i
$406$		0			0
$407$	13.8957	+	8.02270i	0.688786	+	0.397671i
$408$		0			0
$409$		−	19.5703i		−	0.967690i	−0.875154	−	0.483845i	$-0.839240\pi$
$409$		−	19.5703i		−	0.967690i	0.875154	−	0.483845i	$-0.160760\pi$
$410$		0			0
$411$	−15.4377	−	2.16621i	−0.761488	−	0.106851i
$412$		0			0
$413$		0			0
$414$		0			0
$415$	−11.9977	−	20.7807i	−0.588946	−	1.02008i
$416$		0			0
$417$	−3.06798	−	0.430496i	−0.150240	−	0.0210815i
$418$		0			0
$419$	−10.3073	−	17.8529i	−0.503547	−	0.872169i	−0.999992	−	0.00410056i	$-0.998695\pi$
$419$	−10.3073	−	17.8529i	−0.503547	−	0.872169i	0.496445	−	0.868068i	$-0.334639\pi$
$420$		0			0
$421$	0.704748	−	1.22066i	0.0343473	−	0.0594913i	−0.848341	−	0.529451i	$-0.822398\pi$
$421$	0.704748	−	1.22066i	0.0343473	−	0.0594913i	0.882688	+	0.469959i	$0.155731\pi$
$422$		0			0
$423$	7.99568	+	32.0096i	0.388763	+	1.55636i
$424$		0			0
$425$	−6.38182			−0.309564
$426$		0			0
$427$		0			0
$428$		0			0
$429$	−31.0387	+	12.5483i	−1.49856	+	0.605838i
$430$		0			0
$431$	11.6666	+	6.73569i	0.561959	+	0.324447i	0.753931	−	0.656953i	$-0.228155\pi$
$431$	11.6666	+	6.73569i	0.561959	+	0.324447i	−0.191973	+	0.981400i	$0.561488\pi$
$432$		0			0
$433$		−	12.9356i		−	0.621646i	−0.950468	−	0.310823i	$-0.899395\pi$
$433$		−	12.9356i		−	0.621646i	0.950468	−	0.310823i	$-0.100605\pi$
$434$		0			0
$435$	1.40322	+	0.196899i	0.0672794	+	0.00944059i
$436$		0			0
$437$	24.1215			1.15389
$438$		0			0
$439$			10.1039i			0.482233i	0.970496	+	0.241116i	$0.0775135\pi$
$439$			10.1039i			0.482233i	−0.970496	+	0.241116i	$0.922486\pi$
$440$		0			0
$441$		0			0
$442$		0			0
$443$		−	29.0084i		−	1.37823i	−0.724652	−	0.689115i	$-0.757999\pi$
$443$		−	29.0084i		−	1.37823i	0.724652	−	0.689115i	$-0.242001\pi$
$444$		0			0
$445$	−27.3747			−1.29768
$446$		0			0
$447$	−8.37916	−	20.7262i	−0.396321	−	0.980314i
$448$		0			0
$449$			7.94881i			0.375127i	0.982252	+	0.187564i	$0.0600591\pi$
$449$			7.94881i			0.375127i	−0.982252	+	0.187564i	$0.939941\pi$
$450$		0			0
$451$	−29.1239	−	16.8147i	−1.37139	−	0.791772i
$452$		0			0
$453$	−3.12099	+	22.2421i	−0.146637	+	1.04502i
$454$		0			0
$455$		0			0
$456$		0			0
$457$	−13.9617			−0.653100			−0.326550	−	0.945180i	$-0.605886\pi$
$457$	−13.9617			−0.653100			−0.326550	+	0.945180i	$0.605886\pi$
$458$		0			0
$459$	5.10682	+	7.01931i	0.238366	+	0.327633i
$460$		0			0
$461$	16.4030	−	28.4108i	0.763964	−	1.32322i	−0.176829	−	0.984242i	$-0.556584\pi$
$461$	16.4030	−	28.4108i	0.763964	−	1.32322i	0.940793	−	0.338983i	$-0.110083\pi$
$462$		0			0
$463$	−13.8812	−	24.0429i	−0.645112	−	1.11737i	−0.984276	−	0.176640i	$-0.943477\pi$
$463$	−13.8812	−	24.0429i	−0.645112	−	1.11737i	0.339163	−	0.940727i	$-0.389856\pi$
$464$		0			0
$465$	3.09112	+	7.64600i	0.143347	+	0.354575i
$466$		0			0
$467$	11.4311	+	19.7992i	0.528966	+	0.916196i	0.999429	+	0.0337767i	$0.0107535\pi$
$467$	11.4311	+	19.7992i	0.528966	+	0.916196i	−0.470463	+	0.882420i	$0.655913\pi$
$468$		0			0
$469$		0			0
$470$		0			0
$471$	18.3072	−	23.4426i	0.843551	−	1.08018i
$472$		0			0
$473$			49.4494i			2.27369i
$474$		0			0
$475$	−16.2502	−	9.38204i	−0.745609	−	0.430478i
$476$		0			0
$477$	−0.674409	+	2.35581i	−0.0308791	+	0.107865i
$478$		0			0
$479$	−1.21212	−	2.09946i	−0.0553834	−	0.0959269i	0.837004	−	0.547196i	$-0.184305\pi$
$479$	−1.21212	−	2.09946i	−0.0553834	−	0.0959269i	−0.892388	+	0.451269i	$0.850971\pi$
$480$		0			0
$481$	−12.0149	−	6.93683i	−0.547834	−	0.316292i
$482$		0			0
$483$		0			0
$484$		0			0
$485$	−20.8121	+	12.0159i	−0.945028	+	0.545612i
$486$		0			0
$487$	5.19651	−	9.00061i	0.235476	−	0.407857i	−0.723935	−	0.689868i	$-0.757668\pi$
$487$	5.19651	−	9.00061i	0.235476	−	0.407857i	0.959411	+	0.282012i	$0.0910017\pi$
$488$		0			0
$489$	−1.21837	+	8.68282i	−0.0550964	+	0.392651i
$490$		0			0
$491$	−2.93014	+	1.69172i	−0.132235	+	0.0763462i	−0.564658	−	0.825325i	$-0.690992\pi$
$491$	−2.93014	+	1.69172i	−0.132235	+	0.0763462i	0.432423	+	0.901671i	$0.357659\pi$
$492$		0			0
$493$	0.398522	−	0.230087i	0.0179485	−	0.0103626i
$494$		0			0
$495$	−40.8700	+	10.2089i	−1.83697	+	0.458856i
$496$		0			0
$497$		0			0
$498$		0			0
$499$	−19.7801	+	34.2602i	−0.885481	+	1.53370i	−0.0403188	+	0.999187i	$0.512837\pi$
$499$	−19.7801	+	34.2602i	−0.885481	+	1.53370i	−0.845162	+	0.534511i	$0.820496\pi$
$500$		0			0
$501$	−2.79034	+	19.8856i	−0.124663	+	0.888425i
$502$		0			0
$503$	−14.5476			−0.648645			−0.324323	−	0.945947i	$-0.605136\pi$
$503$	−14.5476			−0.648645			−0.324323	+	0.945947i	$0.605136\pi$
$504$		0			0
$505$	21.7018			0.965717
$506$		0			0
$507$	5.96240	−	2.41047i	0.264799	−	0.107053i
$508$		0			0
$509$	−10.1958	+	17.6596i	−0.451921	+	0.782750i	−0.998505	−	0.0546542i	$-0.982594\pi$
$509$	−10.1958	+	17.6596i	−0.451921	+	0.782750i	0.546585	+	0.837404i	$0.315928\pi$
$510$		0			0
$511$		0			0
$512$		0			0
$513$	2.68439	+	25.3811i	0.118519	+	1.12060i
$514$		0			0
$515$	18.0690	−	10.4322i	0.796216	−	0.459696i
$516$		0			0
$517$	−45.0319	+	25.9992i	−1.98050	+	1.14344i
$518$		0			0
$519$	−8.55500	−	6.68091i	−0.375523	−	0.293259i
$520$		0			0
$521$	7.75122	−	13.4255i	0.339587	−	0.588182i	−0.644768	−	0.764379i	$-0.723046\pi$
$521$	7.75122	−	13.4255i	0.339587	−	0.588182i	0.984355	+	0.176196i	$0.0563793\pi$
$522$		0			0
$523$	−9.35989	+	5.40394i	−0.409280	+	0.236298i	−0.690480	−	0.723351i	$-0.742601\pi$
$523$	−9.35989	+	5.40394i	−0.409280	+	0.236298i	0.281201	+	0.959649i	$0.409267\pi$
$524$		0			0
$525$		0			0
$526$		0			0
$527$	2.31952	+	1.33918i	0.101040	+	0.0583355i
$528$		0			0
$529$	0.558476	+	0.967309i	0.0242816	+	0.0420569i
$530$		0			0
$531$	−1.99829	−	7.99987i	−0.0867183	−	0.347165i
$532$		0			0
$533$	25.1819	+	14.5388i	1.09075	+	0.629745i
$534$		0			0
$535$			42.0498i			1.81797i
$536$		0			0
$537$	−9.57017	−	23.6722i	−0.412983	−	1.02153i
$538$		0			0
$539$		0			0
$540$		0			0
$541$	−8.79357	−	15.2309i	−0.378065	−	0.654828i	0.612716	−	0.790303i	$-0.290077\pi$
$541$	−8.79357	−	15.2309i	−0.378065	−	0.654828i	−0.990781	+	0.135476i	$0.956744\pi$
$542$		0			0
$543$	0.0888713	−	0.113801i	0.00381383	−	0.00488367i
$544$		0			0
$545$	8.38108	+	14.5165i	0.359006	+	0.621817i
$546$		0			0
$547$	−5.72451	+	9.91513i	−0.244762	+	0.423940i	−0.962065	−	0.272821i	$-0.912043\pi$
$547$	−5.72451	+	9.91513i	−0.244762	+	0.423940i	0.717303	+	0.696762i	$0.245377\pi$
$548$		0			0
$549$	20.9651	−	5.23688i	0.894770	−	0.223504i
$550$		0			0
$551$	1.35302			0.0576407
$552$		0			0
$553$		0			0
$554$		0			0
$555$	−13.7584	−	10.7444i	−0.584012	−	0.456076i
$556$		0			0
$557$	−32.9159	−	19.0040i	−1.39469	−	0.805226i	−0.400863	−	0.916138i	$-0.631290\pi$
$557$	−32.9159	−	19.0040i	−1.39469	−	0.805226i	−0.993830	+	0.110912i	$0.964623\pi$
$558$		0			0
$559$		−	42.7565i		−	1.80841i
$560$		0			0
$561$	−8.42035	+	10.7824i	−0.355508	+	0.455233i
$562$		0			0
$563$	17.7688			0.748864			0.374432	−	0.927254i	$-0.377838\pi$
$563$	17.7688			0.748864			0.374432	+	0.927254i	$0.377838\pi$
$564$		0			0
$565$		−	39.9211i		−	1.67949i
$566$		0			0
$567$		0			0
$568$		0			0
$569$		−	38.9601i		−	1.63329i	−0.577139	−	0.816646i	$-0.695831\pi$
$569$		−	38.9601i		−	1.63329i	0.577139	−	0.816646i	$-0.304169\pi$
$570$		0			0
$571$	16.9049			0.707448			0.353724	−	0.935350i	$-0.384915\pi$
$571$	16.9049			0.707448			0.353724	+	0.935350i	$0.384915\pi$
$572$		0			0
$573$	−16.4547	+	21.0705i	−0.687406	+	0.880233i
$574$		0			0
$575$		−	18.7605i		−	0.782368i
$576$		0			0
$577$	40.9329	+	23.6326i	1.70406	+	0.983840i	0.941555	+	0.336858i	$0.109364\pi$
$577$	40.9329	+	23.6326i	1.70406	+	0.983840i	0.762506	+	0.646982i	$0.223969\pi$
$578$		0			0
$579$	29.4259	+	22.9797i	1.22290	+	0.955004i
$580$		0			0
$581$		0			0
$582$		0			0
$583$	−3.86199			−0.159947
$584$		0			0
$585$	35.3383	−	8.82714i	1.46106	−	0.364957i
$586$		0			0
$587$	−11.6343	+	20.1513i	−0.480200	+	0.831731i	−0.999742	−	0.0227138i	$-0.992769\pi$
$587$	−11.6343	+	20.1513i	−0.480200	+	0.831731i	0.519542	+	0.854445i	$0.326103\pi$
$588$		0			0
$589$	3.93750	+	6.81995i	0.162242	+	0.281011i
$590$		0			0
$591$	−10.5359	+	13.4914i	−0.433391	+	0.554963i
$592$		0			0
$593$	18.5962	+	32.2095i	0.763654	+	1.32269i	0.940955	+	0.338530i	$0.109930\pi$
$593$	18.5962	+	32.2095i	0.763654	+	1.32269i	−0.177302	+	0.984157i	$0.556737\pi$
$594$		0			0
$595$		0			0
$596$		0			0
$597$	6.85616	+	16.9590i	0.280604	+	0.694085i
$598$		0			0
$599$		−	32.2844i		−	1.31910i	−0.751659	−	0.659552i	$-0.770746\pi$
$599$		−	32.2844i		−	1.31910i	0.751659	−	0.659552i	$-0.229254\pi$
$600$		0			0
$601$	14.7559	+	8.51933i	0.601906	+	0.347511i	0.769791	−	0.638296i	$-0.220360\pi$
$601$	14.7559	+	8.51933i	0.601906	+	0.347511i	−0.167885	+	0.985807i	$0.553694\pi$
$602$		0			0
$603$	8.44102	+	33.7925i	0.343745	+	1.37614i
$604$		0			0
$605$	−16.8615	−	29.2051i	−0.685519	−	1.18735i
$606$		0			0
$607$	−8.44393	−	4.87510i	−0.342728	−	0.197874i	0.318749	−	0.947839i	$-0.396737\pi$
$607$	−8.44393	−	4.87510i	−0.342728	−	0.197874i	−0.661478	+	0.749965i	$0.730070\pi$
$608$		0			0
$609$		0			0
$610$		0			0
$611$	38.9369	−	22.4802i	1.57522	−	0.909452i
$612$		0			0
$613$	−6.86332	+	11.8876i	−0.277207	+	0.480136i	−0.970690	−	0.240337i	$-0.922742\pi$
$613$	−6.86332	+	11.8876i	−0.277207	+	0.480136i	0.693483	+	0.720473i	$0.256075\pi$
$614$		0			0
$615$	28.8361	+	22.5191i	1.16278	+	0.908058i
$616$		0			0
$617$	−2.84301	+	1.64141i	−0.114455	+	0.0660807i	−0.556135	−	0.831092i	$-0.687716\pi$
$617$	−2.84301	+	1.64141i	−0.114455	+	0.0660807i	0.441680	+	0.897173i	$0.354383\pi$
$618$		0			0
$619$	14.9907	−	8.65490i	0.602528	−	0.347870i	−0.167507	−	0.985871i	$-0.553572\pi$
$619$	14.9907	−	8.65490i	0.602528	−	0.347870i	0.770036	+	0.638001i	$0.220238\pi$
$620$		0			0
$621$	−20.6345	+	15.0124i	−0.828036	+	0.602429i
$622$		0			0
$623$		0			0
$624$		0			0
$625$	14.7536	−	25.5539i	0.590142	−	1.02216i
$626$		0			0
$627$	−37.2923	+	15.0765i	−1.48931	+	0.602098i
$628$		0			0
$629$	−5.66923			−0.226047
$630$		0			0
$631$	−6.27821			−0.249932			−0.124966	−	0.992161i	$-0.539882\pi$
$631$	−6.27821			−0.249932			−0.124966	+	0.992161i	$0.539882\pi$
$632$		0			0
$633$	−2.92887	+	20.8729i	−0.116412	+	0.829624i
$634$		0			0
$635$	−18.9672	+	32.8522i	−0.752691	+	1.30370i
$636$		0			0
$637$		0			0
$638$		0			0
$639$	−30.3882	+	7.59066i	−1.20214	+	0.300282i
$640$		0			0
$641$	−17.9788	+	10.3801i	−0.710120	+	0.409988i	−0.811105	−	0.584900i	$-0.801134\pi$
$641$	−17.9788	+	10.3801i	−0.710120	+	0.409988i	0.100986	+	0.994888i	$0.467800\pi$
$642$		0			0
$643$	17.2553	−	9.96236i	0.680483	−	0.392877i	−0.119554	−	0.992828i	$-0.538146\pi$
$643$	17.2553	−	9.96236i	0.680483	−	0.392877i	0.800037	+	0.599950i	$0.204813\pi$
$644$		0			0
$645$	7.47577	−	53.2769i	0.294358	−	2.09778i
$646$		0			0
$647$	14.7670	−	25.5772i	0.580551	−	1.00554i	−0.414863	−	0.909884i	$-0.636170\pi$
$647$	14.7670	−	25.5772i	0.580551	−	1.00554i	0.995414	−	0.0956605i	$-0.0304963\pi$
$648$		0			0
$649$	11.2544	−	6.49774i	0.441775	−	0.255059i
$650$		0			0
$651$		0			0
$652$		0			0
$653$	13.7914	+	7.96249i	0.539701	+	0.311596i	0.744958	−	0.667112i	$-0.232470\pi$
$653$	13.7914	+	7.96249i	0.539701	+	0.311596i	−0.205257	+	0.978708i	$0.565803\pi$
$654$		0			0
$655$	19.9246	+	34.5105i	0.778520	+	1.34844i
$656$		0			0
$657$	13.0131	−	45.4565i	0.507688	−	1.77343i
$658$		0			0
$659$	2.80283	+	1.61822i	0.109183	+	0.0630368i	0.553597	−	0.832785i	$-0.313255\pi$
$659$	2.80283	+	1.61822i	0.109183	+	0.0630368i	−0.444414	+	0.895821i	$0.646588\pi$
$660$		0			0
$661$		−	8.90498i		−	0.346364i	−0.984890	−	0.173182i	$-0.944595\pi$
$661$		−	8.90498i		−	0.346364i	0.984890	−	0.173182i	$-0.0554048\pi$
$662$		0			0
$663$	7.28066	−	9.32299i	0.282757	−	0.362075i
$664$		0			0
$665$		0			0
$666$		0			0
$667$	0.676383	+	1.17153i	0.0261896	+	0.0453618i
$668$		0			0
$669$	−0.535590	−	1.32480i	−0.0207071	−	0.0512198i
$670$		0			0
$671$	17.0285	+	29.4943i	0.657379	+	1.13861i
$672$		0			0
$673$	−13.2311	+	22.9169i	−0.510021	+	0.883382i	0.489912	+	0.871772i	$0.337029\pi$
$673$	−13.2311	+	22.9169i	−0.510021	+	0.883382i	−0.999933	+	0.0116101i	$0.996304\pi$
$674$		0			0
$675$	19.7401	−	2.08779i	0.759799	−	0.0803590i
$676$		0			0
$677$	−8.92848			−0.343149			−0.171575	−	0.985171i	$-0.554886\pi$
$677$	−8.92848			−0.343149			−0.171575	+	0.985171i	$0.554886\pi$
$678$		0			0
$679$		0			0
$680$		0			0
$681$	0.0802812	−	0.572132i	0.00307638	−	0.0219242i
$682$		0			0
$683$	32.7902	+	18.9314i	1.25468	+	0.724390i	0.972035	−	0.234834i	$-0.0754547\pi$
$683$	32.7902	+	18.9314i	1.25468	+	0.724390i	0.282645	+	0.959225i	$0.408788\pi$
$684$		0			0
$685$			26.7298i			1.02129i
$686$		0			0
$687$	−9.36221	−	23.1578i	−0.357191	−	0.883525i
$688$		0			0
$689$	3.33927			0.127216
$690$		0			0
$691$		−	5.70665i		−	0.217091i	−0.994091	−	0.108546i	$-0.965381\pi$
$691$		−	5.70665i		−	0.217091i	0.994091	−	0.108546i	$-0.0346194\pi$
$692$		0			0
$693$		0			0
$694$		0			0
$695$			5.31208i			0.201499i
$696$		0			0
$697$	11.8821			0.450065
$698$		0			0
$699$	−25.3424	−	3.55602i	−0.958537	−	0.134501i
$700$		0			0
$701$		−	8.19949i		−	0.309690i	−0.987939	−	0.154845i	$-0.950512\pi$
$701$		−	8.19949i		−	0.309690i	0.987939	−	0.154845i	$-0.0494879\pi$
$702$		0			0
$703$	−14.4357	−	8.33444i	−0.544452	−	0.314339i
$704$		0			0
$705$	52.4480	−	21.2036i	1.97531	−	0.798576i
$706$		0			0
$707$		0			0
$708$		0			0
$709$	20.1515			0.756805			0.378402	−	0.925641i	$-0.376474\pi$
$709$	20.1515			0.756805			0.378402	+	0.925641i	$0.376474\pi$
$710$		0			0
$711$	−8.94485	−	35.8095i	−0.335458	−	1.34296i
$712$		0			0
$713$	−3.93676	+	6.81866i	−0.147433	+	0.255361i
$714$		0			0
$715$	28.7028	+	49.7147i	1.07342	+	1.85923i
$716$		0			0
$717$	−44.6306	−	6.26254i	−1.66676	−	0.233879i
$718$		0			0
$719$	−25.5996	−	44.3397i	−0.954702	−	1.65359i	−0.735048	−	0.678015i	$-0.762841\pi$
$719$	−25.5996	−	44.3397i	−0.954702	−	1.65359i	−0.219654	−	0.975578i	$-0.570493\pi$
$720$		0			0
$721$		0			0
$722$		0			0
$723$	−3.29363	−	0.462160i	−0.122492	−	0.0171879i
$724$		0			0
$725$		−	1.05231i		−	0.0390820i
$726$		0			0
$727$	−13.7848	−	7.95865i	−0.511249	−	0.295170i	0.222098	−	0.975024i	$-0.428710\pi$
$727$	−13.7848	−	7.95865i	−0.511249	−	0.295170i	−0.733347	+	0.679854i	$0.762043\pi$
$728$		0			0
$729$	−18.0927	−	20.0413i	−0.670099	−	0.742271i
$730$		0			0
$731$	−8.73584	−	15.1309i	−0.323107	−	0.559637i
$732$		0			0
$733$	−3.67216	−	2.12012i	−0.135634	−	0.0783086i	0.430647	−	0.902520i	$-0.358285\pi$
$733$	−3.67216	−	2.12012i	−0.135634	−	0.0783086i	−0.566282	+	0.824212i	$0.691619\pi$
$734$		0			0
$735$		0			0
$736$		0			0
$737$	−47.5401	+	27.4473i	−1.75116	+	1.01103i
$738$		0			0
$739$	−14.1835	+	24.5665i	−0.521747	+	0.903693i	0.477933	+	0.878397i	$0.341386\pi$
$739$	−14.1835	+	24.5665i	−0.521747	+	0.903693i	−0.999680	+	0.0252966i	$0.991947\pi$
$740$		0			0
$741$	32.2448	−	13.0359i	1.18454	−	0.478886i
$742$		0			0
$743$	21.8850	−	12.6353i	0.802884	−	0.463545i	−0.0415945	−	0.999135i	$-0.513244\pi$
$743$	21.8850	−	12.6353i	0.802884	−	0.463545i	0.844479	+	0.535589i	$0.179910\pi$
$744$		0			0
$745$	−33.1971	+	19.1664i	−1.21625	+	0.702201i
$746$		0			0
$747$	23.3028	+	6.67100i	0.852604	+	0.244079i
$748$		0			0
$749$		0			0
$750$		0			0
$751$	−23.7730	+	41.1761i	−0.867490	+	1.50254i	−0.00293597	+	0.999996i	$0.500935\pi$
$751$	−23.7730	+	41.1761i	−0.867490	+	1.50254i	−0.864554	+	0.502540i	$0.832399\pi$
$752$		0			0
$753$	−13.6192	−	10.6357i	−0.496310	−	0.387586i
$754$		0			0
$755$	38.5113			1.40157
$756$		0			0
$757$	37.3922			1.35904			0.679521	−	0.733656i	$-0.262188\pi$
$757$	37.3922			1.35904			0.679521	+	0.733656i	$0.262188\pi$
$758$		0			0
$759$	−31.6968	−	24.7532i	−1.15052	−	0.898483i
$760$		0			0
$761$	4.12142	−	7.13850i	0.149401	−	0.258770i	−0.781605	−	0.623774i	$-0.785599\pi$
$761$	4.12142	−	7.13850i	0.149401	−	0.258770i	0.931006	+	0.365003i	$0.118932\pi$
$762$		0			0
$763$		0			0
$764$		0			0
$765$	10.7022	−	10.3440i	0.386938	−	0.373987i
$766$		0			0
$767$	−9.73114	+	5.61827i	−0.351371	+	0.202864i
$768$		0			0
$769$	20.2182	−	11.6730i	0.729086	−	0.420938i	−0.0890020	−	0.996031i	$-0.528368\pi$
$769$	20.2182	−	11.6730i	0.729086	−	0.420938i	0.818088	+	0.575094i	$0.195034\pi$
$770$		0			0
$771$	−24.0985	+	9.74253i	−0.867887	+	0.350869i
$772$		0			0
$773$	−17.2201	+	29.8261i	−0.619364	+	1.07277i	0.370238	+	0.928937i	$0.379276\pi$
$773$	−17.2201	+	29.8261i	−0.619364	+	1.07277i	−0.989602	+	0.143833i	$0.954057\pi$
$774$		0			0
$775$	5.30422	−	3.06240i	0.190533	−	0.110004i
$776$		0			0
$777$		0			0
$778$		0			0
$779$	30.2555	+	17.4680i	1.08402	+	0.625857i
$780$		0			0
$781$	−24.6822	−	42.7508i	−0.883199	−	1.52975i
$782$		0			0
$783$	−1.15743	+	0.842076i	−0.0413632	+	0.0300933i
$784$		0			0
$785$	−44.1682	−	25.5005i	−1.57643	−	0.910152i
$786$		0			0
$787$			8.31355i			0.296346i	0.988961	+	0.148173i	$0.0473393\pi$
$787$			8.31355i			0.296346i	−0.988961	+	0.148173i	$0.952661\pi$
$788$		0			0
$789$	12.1016	+	1.69809i	0.430830	+	0.0604537i
$790$		0			0
$791$		0			0
$792$		0			0
$793$	−14.7237	−	25.5022i	−0.522854	−	0.905610i
$794$		0			0
$795$	4.16091	+	0.583856i	0.147572	+	0.0207072i
$796$		0			0
$797$	0.426036	+	0.737916i	0.0150910	+	0.0261383i	0.873472	−	0.486874i	$-0.161863\pi$
$797$	0.426036	+	0.737916i	0.0150910	+	0.0261383i	−0.858381	+	0.513012i	$0.828530\pi$
$798$		0			0
$799$	9.18614	−	15.9109i	0.324982	−	0.562886i
$800$		0			0
$801$	19.8831	−	19.2176i	0.702533	−	0.679019i
$802$		0			0
$803$	74.5190			2.62972
$804$		0			0
$805$		0			0
$806$		0			0
$807$	−47.8196	+	19.3325i	−1.68333	+	0.680535i
$808$		0			0
$809$	31.5580	+	18.2200i	1.10952	+	0.640581i	0.938705	−	0.344722i	$-0.112027\pi$
$809$	31.5580	+	18.2200i	1.10952	+	0.640581i	0.170814	+	0.985303i	$0.445360\pi$
$810$		0			0
$811$			1.08986i			0.0382702i	0.999817	+	0.0191351i	$0.00609126\pi$
$811$			1.08986i			0.0382702i	−0.999817	+	0.0191351i	$0.993909\pi$
$812$		0			0
$813$	4.78238	+	0.671060i	0.167725	+	0.0235351i
$814$		0			0
$815$	15.0339			0.526616
$816$		0			0
$817$		−	51.3709i		−	1.79724i
$818$		0			0
$819$		0			0
$820$		0			0
$821$		−	24.2196i		−	0.845270i	−0.906300	−	0.422635i	$-0.861105\pi$
$821$		−	24.2196i		−	0.845270i	0.906300	−	0.422635i	$-0.138895\pi$
$822$		0			0
$823$	5.71185			0.199102			0.0995512	−	0.995032i	$-0.468259\pi$
$823$	5.71185			0.199102			0.0995512	+	0.995032i	$0.468259\pi$
$824$		0			0
$825$	11.7258	+	29.0041i	0.408239	+	1.00979i
$826$		0			0
$827$		−	36.4579i		−	1.26777i	−0.773429	−	0.633883i	$-0.781460\pi$
$827$		−	36.4579i		−	1.26777i	0.773429	−	0.633883i	$-0.218540\pi$
$828$		0			0
$829$	0.498269	+	0.287676i	0.0173056	+	0.00999140i	0.508628	−	0.860986i	$-0.330153\pi$
$829$	0.498269	+	0.287676i	0.0173056	+	0.00999140i	−0.491322	+	0.870978i	$0.663486\pi$
$830$		0			0
$831$	3.26882	−	23.2956i	0.113394	−	0.808115i
$832$		0			0
$833$		0			0
$834$		0			0
$835$	34.4312			1.19154
$836$		0			0
$837$	−7.61282	−	3.38350i	−0.263137	−	0.116951i
$838$		0			0
$839$	−23.9341	+	41.4550i	−0.826295	+	1.43119i	0.0746300	+	0.997211i	$0.476222\pi$
$839$	−23.9341	+	41.4550i	−0.826295	+	1.43119i	−0.900925	+	0.433974i	$0.857111\pi$
$840$		0			0
$841$	−14.4621	−	25.0490i	−0.498692	−	0.863759i
$842$		0			0
$843$	−2.96681	−	7.33851i	−0.102182	−	0.252752i
$844$		0			0
$845$	−5.51368	−	9.54997i	−0.189676	−	0.328529i
$846$		0			0
$847$		0			0
$848$		0			0
$849$	21.7496	−	27.8507i	0.746445	−	0.955835i
$850$		0			0
$851$		−	16.6657i		−	0.571294i
$852$		0			0
$853$	40.5393	+	23.4054i	1.38804	+	0.801385i	0.993094	−	0.117320i	$-0.0374303\pi$
$853$	40.5393	+	23.4054i	1.38804	+	0.801385i	0.394945	+	0.918705i	$0.370764\pi$
$854$		0			0
$855$	42.4581	−	10.6056i	1.45204	−	0.362704i
$856$		0			0
$857$	−4.78220	−	8.28302i	−0.163357	−	0.282943i	0.772714	−	0.634755i	$-0.218899\pi$
$857$	−4.78220	−	8.28302i	−0.163357	−	0.282943i	−0.936071	+	0.351812i	$0.885566\pi$
$858$		0			0
$859$	4.68311	+	2.70379i	0.159786	+	0.0922523i	0.577761	−	0.816206i	$-0.303927\pi$
$859$	4.68311	+	2.70379i	0.159786	+	0.0922523i	−0.417975	+	0.908459i	$0.637260\pi$
$860$		0			0
$861$		0			0
$862$		0			0
$863$	−35.5402	+	20.5191i	−1.20980	+	0.698480i	−0.962716	−	0.270514i	$-0.912806\pi$
$863$	−35.5402	+	20.5191i	−1.20980	+	0.698480i	−0.247086	+	0.968994i	$0.579473\pi$
$864$		0			0
$865$	−9.30598	+	16.1184i	−0.316413	+	0.548043i
$866$		0			0
$867$	−3.41991	+	24.3724i	−0.116146	+	0.827729i
$868$		0			0
$869$	50.3777	−	29.0856i	1.70895	−	0.986661i
$870$		0			0
$871$	41.1056	−	23.7323i	1.39281	−	0.804139i
$872$		0			0
$873$	6.68108	−	23.3380i	0.226120	−	0.789871i
$874$		0			0
$875$		0			0
$876$		0			0
$877$	7.32509	−	12.6874i	0.247351	−	0.428424i	−0.715439	−	0.698675i	$-0.753773\pi$
$877$	7.32509	−	12.6874i	0.247351	−	0.428424i	0.962790	+	0.270251i	$0.0871067\pi$
$878$		0			0
$879$	3.08572	−	21.9907i	0.104079	−	0.741729i
$880$		0			0
$881$	−44.8295			−1.51034			−0.755172	−	0.655527i	$-0.772447\pi$
$881$	−44.8295			−1.51034			−0.755172	+	0.655527i	$0.772447\pi$
$882$		0			0
$883$	33.8527			1.13923			0.569617	−	0.821910i	$-0.307091\pi$
$883$	33.8527			1.13923			0.569617	+	0.821910i	$0.307091\pi$
$884$		0			0
$885$	−13.1079	+	5.29924i	−0.440616	+	0.178132i
$886$		0			0
$887$	13.3422	−	23.1093i	0.447987	−	0.775936i	−0.550268	−	0.834988i	$-0.685475\pi$
$887$	13.3422	−	23.1093i	0.447987	−	0.775936i	0.998255	+	0.0590523i	$0.0188079\pi$
$888$		0			0
$889$		0			0
$890$		0			0
$891$	22.5183	−	36.1066i	0.754390	−	1.20962i
$892$		0			0
$893$	46.7817	−	27.0094i	1.56549	−	0.903837i
$894$		0			0
$895$	−37.9157	+	21.8907i	−1.26738	+	0.731724i
$896$		0			0
$897$	27.4066	+	21.4028i	0.915081	+	0.714619i
$898$		0			0
$899$	−0.220820	+	0.382472i	−0.00736476	+	0.0127561i
$900$		0			0
$901$	1.18172	−	0.682266i	0.0393688	−	0.0227296i
$902$		0			0
$903$		0			0
$904$		0			0
$905$	−0.214412	−	0.123791i	−0.00712729	−	0.00411494i
$906$		0			0
$907$	7.97211	+	13.8081i	0.264710	+	0.458490i	0.967487	−	0.252919i	$-0.0813906\pi$
$907$	7.97211	+	13.8081i	0.264710	+	0.458490i	−0.702778	+	0.711409i	$0.748057\pi$
$908$		0			0
$909$	−15.7627	+	15.2351i	−0.522815	+	0.505316i
$910$		0			0
$911$	40.9207	+	23.6256i	1.35576	+	0.782750i	0.989050	−	0.147584i	$-0.0471496\pi$
$911$	40.9207	+	23.6256i	1.35576	+	0.782750i	0.366713	+	0.930334i	$0.380483\pi$
$912$		0			0
$913$			38.2013i			1.26428i
$914$		0			0
$915$	−13.8876	−	34.3516i	−0.459110	−	1.13563i
$916$		0			0
$917$		0			0
$918$		0			0
$919$	14.8163	+	25.6625i	0.488743	+	0.846528i	0.999916	−	0.0129500i	$-0.00412223\pi$
$919$	14.8163	+	25.6625i	0.488743	+	0.846528i	−0.511173	+	0.859478i	$0.670789\pi$
$920$		0			0
$921$	2.06188	−	2.64027i	0.0679413	−	0.0869998i
$922$		0			0
$923$	21.3415	+	36.9645i	0.702463	+	1.21670i
$924$		0			0
$925$	−6.48212	+	11.2274i	−0.213131	+	0.369153i
$926$		0			0
$927$	−5.80050	+	20.2620i	−0.190513	+	0.665491i
$928$		0			0
$929$	−33.2372			−1.09048			−0.545238	−	0.838281i	$-0.683561\pi$
$929$	−33.2372			−1.09048			−0.545238	+	0.838281i	$0.683561\pi$
$930$		0			0
$931$		0			0
$932$		0			0
$933$	−2.85192	−	2.22717i	−0.0933677	−	0.0729142i
$934$		0			0
$935$	20.3151	+	11.7289i	0.664373	+	0.383576i
$936$		0			0
$937$			23.8190i			0.778134i	0.921209	+	0.389067i	$0.127203\pi$
$937$			23.8190i			0.778134i	−0.921209	+	0.389067i	$0.872797\pi$
$938$		0			0
$939$	−23.8891	+	30.5903i	−0.779591	+	0.998278i
$940$		0			0
$941$	54.2403			1.76818			0.884091	−	0.467315i	$-0.154779\pi$
$941$	54.2403			1.76818			0.884091	+	0.467315i	$0.154779\pi$
$942$		0			0
$943$			34.9295i			1.13746i
$944$		0			0
$945$		0			0
$946$		0			0
$947$			21.0648i			0.684515i	0.939606	+	0.342257i	$0.111191\pi$
$947$			21.0648i			0.684515i	−0.939606	+	0.342257i	$0.888809\pi$
$948$		0			0
$949$	−64.4329			−2.09158
$950$		0			0
$951$	3.71495	−	4.75705i	0.120465	−	0.154258i
$952$		0			0
$953$		−	4.50028i		−	0.145778i	−0.997340	−	0.0728892i	$-0.976778\pi$
$953$		−	4.50028i		−	0.145778i	0.997340	−	0.0728892i	$-0.0232219\pi$
$954$		0			0
$955$	39.6989	+	22.9201i	1.28462	+	0.741679i
$956$		0			0
$957$	−1.77793	−	1.38845i	−0.0574724	−	0.0448823i
$958$		0			0
$959$		0			0
$960$		0			0
$961$	28.4295			0.917081
$962$		0			0
$963$	−29.5198	−	30.5420i	−0.951262	−	0.984204i
$964$		0			0
$965$	32.0090	−	55.4411i	1.03040	−	1.78471i
$966$		0			0
$967$	−10.8811	−	18.8466i	−0.349912	−	0.606065i	0.636322	−	0.771424i	$-0.280455\pi$
$967$	−10.8811	−	18.8466i	−0.349912	−	0.606065i	−0.986233	+	0.165359i	$0.947122\pi$
$968$		0			0
$969$	8.74754	−	11.2014i	0.281012	−	0.359840i
$970$		0			0
$971$	−23.5222	−	40.7416i	−0.754862	−	1.30746i	−0.945443	−	0.325788i	$-0.894371\pi$
$971$	−23.5222	−	40.7416i	−0.754862	−	1.30746i	0.190581	−	0.981671i	$-0.438963\pi$
$972$		0			0
$973$		0			0
$974$		0			0
$975$	−10.1387	−	25.0784i	−0.324698	−	0.803153i
$976$		0			0
$977$			25.1455i			0.804475i	0.915535	+	0.402237i	$0.131767\pi$
$977$			25.1455i			0.804475i	−0.915535	+	0.402237i	$0.868233\pi$
$978$		0			0
$979$	37.7423	+	21.7905i	1.20625	+	0.696429i
$980$		0			0
$981$	−16.2783	−	4.66006i	−0.519725	−	0.148784i
$982$		0			0
$983$	18.1071	+	31.3624i	0.577527	+	1.00031i	0.995762	+	0.0919674i	$0.0293156\pi$
$983$	18.1071	+	31.3624i	0.577527	+	1.00031i	−0.418235	+	0.908339i	$0.637351\pi$
$984$		0			0
$985$	25.4191	+	14.6757i	0.809921	+	0.467608i
$986$		0			0
$987$		0			0
$988$		0			0
$989$	44.4801	−	25.6806i	1.41438	−	0.816595i
$990$		0			0
$991$	−9.32769	+	16.1560i	−0.296304	+	0.513213i	−0.975287	−	0.220940i	$-0.929087\pi$
$991$	−9.32769	+	16.1560i	−0.296304	+	0.513213i	0.678984	+	0.734153i	$0.262421\pi$
$992$		0			0
$993$	−6.24829	−	4.87951i	−0.198284	−	0.154847i
$994$		0			0
$995$	27.1632	−	15.6827i	0.861131	−	0.497174i
$996$		0			0
$997$	15.1413	−	8.74181i	0.479528	−	0.276856i	−0.240691	−	0.970602i	$-0.577374\pi$
$997$	15.1413	−	8.74181i	0.479528	−	0.276856i	0.720220	+	0.693746i	$0.244041\pi$
$998$		0			0
$999$	17.5359	−	1.85466i	0.554813	−	0.0586790i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1764.2.w.b.1109.6		16
3.2	odd	2		5292.2.w.b.521.2		16
7.2	even	3		252.2.bm.a.173.1	yes	16
7.3	odd	6		1764.2.x.a.1469.4		16
7.4	even	3		1764.2.x.b.1469.5		16
7.5	odd	6		1764.2.bm.a.1685.8		16
7.6	odd	2		252.2.w.a.101.3	yes	16
9.4	even	3		5292.2.bm.a.2285.2		16
9.5	odd	6		1764.2.bm.a.1697.8		16
21.2	odd	6		756.2.bm.a.89.7		16
21.5	even	6		5292.2.bm.a.4625.2		16
21.11	odd	6		5292.2.x.b.4409.2		16
21.17	even	6		5292.2.x.a.4409.7		16
21.20	even	2		756.2.w.a.521.7		16
28.23	odd	6		1008.2.df.d.929.8		16
28.27	even	2		1008.2.ca.d.353.6		16
63.2	odd	6		2268.2.t.b.2105.2		16
63.4	even	3		5292.2.x.a.881.7		16
63.5	even	6	inner	1764.2.w.b.509.6		16
63.13	odd	6		756.2.bm.a.17.7		16
63.16	even	3		2268.2.t.a.2105.7		16
63.20	even	6		2268.2.t.a.1781.7		16
63.23	odd	6		252.2.w.a.5.3	✓	16
63.31	odd	6		5292.2.x.b.881.2		16
63.32	odd	6		1764.2.x.a.293.4		16
63.34	odd	6		2268.2.t.b.1781.2		16
63.40	odd	6		5292.2.w.b.1097.2		16
63.41	even	6		252.2.bm.a.185.1	yes	16
63.58	even	3		756.2.w.a.341.7		16
63.59	even	6		1764.2.x.b.293.5		16
84.23	even	6		3024.2.df.d.1601.7		16
84.83	odd	2		3024.2.ca.d.2033.7		16
252.23	even	6		1008.2.ca.d.257.6		16
252.139	even	6		3024.2.df.d.17.7		16
252.167	odd	6		1008.2.df.d.689.8		16
252.247	odd	6		3024.2.ca.d.2609.7		16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
252.2.w.a.5.3	✓	16	63.23	odd	6
252.2.w.a.101.3	yes	16	7.6	odd	2
252.2.bm.a.173.1	yes	16	7.2	even	3
252.2.bm.a.185.1	yes	16	63.41	even	6
756.2.w.a.341.7		16	63.58	even	3
756.2.w.a.521.7		16	21.20	even	2
756.2.bm.a.17.7		16	63.13	odd	6
756.2.bm.a.89.7		16	21.2	odd	6
1008.2.ca.d.257.6		16	252.23	even	6
1008.2.ca.d.353.6		16	28.27	even	2
1008.2.df.d.689.8		16	252.167	odd	6
1008.2.df.d.929.8		16	28.23	odd	6
1764.2.w.b.509.6		16	63.5	even	6	inner
1764.2.w.b.1109.6		16	1.1	even	1	trivial
1764.2.x.a.293.4		16	63.32	odd	6
1764.2.x.a.1469.4		16	7.3	odd	6
1764.2.x.b.293.5		16	63.59	even	6
1764.2.x.b.1469.5		16	7.4	even	3
1764.2.bm.a.1685.8		16	7.5	odd	6
1764.2.bm.a.1697.8		16	9.5	odd	6
2268.2.t.a.1781.7		16	63.20	even	6
2268.2.t.a.2105.7		16	63.16	even	3
2268.2.t.b.1781.2		16	63.34	odd	6
2268.2.t.b.2105.2		16	63.2	odd	6
3024.2.ca.d.2033.7		16	84.83	odd	2
3024.2.ca.d.2609.7		16	252.247	odd	6
3024.2.df.d.17.7		16	252.139	even	6
3024.2.df.d.1601.7		16	84.23	even	6
5292.2.w.b.521.2		16	3.2	odd	2
5292.2.w.b.1097.2		16	63.40	odd	6
5292.2.x.a.881.7		16	63.4	even	3
5292.2.x.a.4409.7		16	21.17	even	6
5292.2.x.b.881.2		16	63.31	odd	6
5292.2.x.b.4409.2		16	21.11	odd	6
5292.2.bm.a.2285.2		16	9.4	even	3
5292.2.bm.a.4625.2		16	21.5	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:	\( N \)	\(=\)	\( 1764 = 2^{2} \cdot 3^{2} \cdot 7^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1764.w (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(1.36511 + 1.06606i) q^{3} +(1.48494 - 2.57199i) q^{5} +(0.727031 + 2.91057i) q^{9} +O(q^{10})\)	\(q+(1.36511 + 1.06606i) q^{3} +(1.48494 - 2.57199i) q^{5} +(0.727031 + 2.91057i) q^{9} +(-4.09466 + 2.36406i) q^{11} +(3.54045 - 2.04408i) q^{13} +(4.76900 - 1.92801i) q^{15} +(0.835278 - 1.44674i) q^{17} +(4.25377 - 2.45592i) q^{19} +(4.25297 + 2.45545i) q^{23} +(-1.91009 - 3.30837i) q^{25} +(-2.11037 + 4.74830i) q^{27} +(0.238557 + 0.137731i) q^{29} +1.60327i q^{31} +(-8.10988 - 1.13797i) q^{33} +(-1.69681 - 2.93896i) q^{37} +(7.01221 + 0.983947i) q^{39} +(3.55632 + 6.15972i) q^{41} +(5.22930 - 9.05742i) q^{43} +(8.56556 + 2.45211i) q^{45} +10.9977 q^{47} +(2.68256 - 1.08450i) q^{51} +(0.707381 + 0.408407i) q^{53} +14.0419i q^{55} +(8.42500 + 1.18219i) q^{57} -2.74856 q^{59} -7.20310i q^{61} -12.1413i q^{65} +11.6103 q^{67} +(3.18809 + 7.88587i) q^{69} +10.4406i q^{71} +(-13.6493 - 7.88042i) q^{73} +(0.919449 - 6.55255i) q^{75} -12.3033 q^{79} +(-7.94285 + 4.23215i) q^{81} +(4.03981 - 6.99715i) q^{83} +(-2.48067 - 4.29665i) q^{85} +(0.178826 + 0.442333i) q^{87} +(-4.60872 - 7.98254i) q^{89} +(-1.70919 + 2.18864i) q^{93} -14.5875i q^{95} +(-7.00772 - 4.04591i) q^{97} +(-9.85770 - 10.1991i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q + 6 q^{9}+O(q^{10}) \) 16 * q + 6 * q^9	\( 16 q + 6 q^{9} - 6 q^{11} + 3 q^{13} - 3 q^{15} - 9 q^{17} + 21 q^{23} - 8 q^{25} - 9 q^{27} + 6 q^{29} + q^{37} - 3 q^{39} + 6 q^{41} - 2 q^{43} + 30 q^{45} + 36 q^{47} - 33 q^{51} + 15 q^{57} + 30 q^{59} + 14 q^{67} - 21 q^{69} + 57 q^{75} + 2 q^{79} + 18 q^{81} + 6 q^{85} - 48 q^{87} - 21 q^{89} + 21 q^{93} + 3 q^{97} - 9 q^{99}+O(q^{100}) \) 16 * q + 6 * q^9 - 6 * q^11 + 3 * q^13 - 3 * q^15 - 9 * q^17 + 21 * q^23 - 8 * q^25 - 9 * q^27 + 6 * q^29 + q^37 - 3 * q^39 + 6 * q^41 - 2 * q^43 + 30 * q^45 + 36 * q^47 - 33 * q^51 + 15 * q^57 + 30 * q^59 + 14 * q^67 - 21 * q^69 + 57 * q^75 + 2 * q^79 + 18 * q^81 + 6 * q^85 - 48 * q^87 - 21 * q^89 + 21 * q^93 + 3 * q^97 - 9 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more