LMFDB - Embedded newform 252.2.w.a.101.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [252,2,Mod(5,252)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(252, 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("252.5");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 252 = 2^{2} \cdot 3^{2} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	252.w (of order $6$, degree $2$, 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:	$2.01223013094$
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:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 3^{4} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			101.3
Root			$1.68042 - 0.419752i$ of defining polynomial
Character	$\chi$	$=$	252.101
Dual form			252.2.w.a.5.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.36511 - 1.06606i) q^{3} +(-1.48494 + 2.57199i) q^{5} +(-0.200279 - 2.63816i) q^{7} +(0.727031 + 2.91057i) q^{9} +O(q^{10})$	\(q+(-1.36511 - 1.06606i) q^{3} +(-1.48494 + 2.57199i) q^{5} +(-0.200279 - 2.63816i) q^{7} +(0.727031 + 2.91057i) q^{9} +(-4.09466 + 2.36406i) q^{11} +(-3.54045 + 2.04408i) q^{13} +(4.76900 - 1.92801i) q^{15} +(-0.835278 + 1.44674i) q^{17} +(-4.25377 + 2.45592i) q^{19} +(-2.53904 + 3.81488i) q^{21} +(4.25297 + 2.45545i) q^{23} +(-1.91009 - 3.30837i) q^{25} +(2.11037 - 4.74830i) q^{27} +(0.238557 + 0.137731i) q^{29} -1.60327i q^{31} +(8.10988 + 1.13797i) q^{33} +(7.08273 + 3.40239i) q^{35} +(-1.69681 - 2.93896i) q^{37} +(7.01221 + 0.983947i) q^{39} +(-3.55632 - 6.15972i) q^{41} +(5.22930 - 9.05742i) q^{43} +(-8.56556 - 2.45211i) q^{45} -10.9977 q^{47} +(-6.91978 + 1.05674i) q^{49} +(2.68256 - 1.08450i) q^{51} +(0.707381 + 0.408407i) q^{53} -14.0419i q^{55} +(8.42500 + 1.18219i) q^{57} +2.74856 q^{59} +7.20310i q^{61} +(7.53294 - 2.50095i) q^{63} -12.1413i q^{65} +11.6103 q^{67} +(-3.18809 - 7.88587i) q^{69} +10.4406i q^{71} +(13.6493 + 7.88042i) q^{73} +(-0.919449 + 6.55255i) q^{75} +(7.05683 + 10.3289i) q^{77} -12.3033 q^{79} +(-7.94285 + 4.23215i) q^{81} +(-4.03981 + 6.99715i) q^{83} +(-2.48067 - 4.29665i) q^{85} +(-0.178826 - 0.442333i) q^{87} +(4.60872 + 7.98254i) q^{89} +(6.10169 + 8.93089i) q^{91} +(-1.70919 + 2.18864i) q^{93} -14.5875i q^{95} +(7.00772 + 4.04591i) q^{97} +(-9.85770 - 10.1991i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q - q^{7} + 6 q^{9}+O(q^{10}) $ 16 * q - q^7 + 6 * q^9	$ 16 q - q^{7} + 6 q^{9} - 6 q^{11} - 3 q^{13} - 3 q^{15} + 9 q^{17} + 6 q^{21} + 21 q^{23} - 8 q^{25} + 9 q^{27} + 6 q^{29} - 15 q^{35} + q^{37} - 3 q^{39} - 6 q^{41} - 2 q^{43} - 30 q^{45} - 36 q^{47} - 5 q^{49} - 33 q^{51} + 15 q^{57} - 30 q^{59} - 15 q^{63} + 14 q^{67} + 21 q^{69} - 57 q^{75} + 3 q^{77} + 2 q^{79} + 18 q^{81} + 6 q^{85} + 48 q^{87} + 21 q^{89} + 9 q^{91} + 21 q^{93} - 3 q^{97} - 9 q^{99}+O(q^{100}) $ 16 * q - q^7 + 6 * q^9 - 6 * q^11 - 3 * q^13 - 3 * q^15 + 9 * q^17 + 6 * q^21 + 21 * q^23 - 8 * q^25 + 9 * q^27 + 6 * q^29 - 15 * q^35 + q^37 - 3 * q^39 - 6 * q^41 - 2 * q^43 - 30 * q^45 - 36 * q^47 - 5 * q^49 - 33 * q^51 + 15 * q^57 - 30 * q^59 - 15 * q^63 + 14 * q^67 + 21 * q^69 - 57 * q^75 + 3 * q^77 + 2 * q^79 + 18 * q^81 + 6 * q^85 + 48 * q^87 + 21 * q^89 + 9 * q^91 + 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 $\left(\mathbb{Z}/252\mathbb{Z}\right)^\times$.

$n$	$29$	$73$	$127$
$\chi(n)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{1}{6}\right)$	$1$

Coefficient data

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

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

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

$2$		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	$0.397845\pi$
$5$	−1.48494	+	2.57199i	−0.664085	+	1.15023i	−0.979532	+	0.201286i	$0.935488\pi$
$6$		0			0
$7$	−0.200279	−	2.63816i	−0.0756984	−	0.997131i
$7$	−0.200279	−	2.63816i	−0.0756984	−	0.997131i
$8$		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	−0.902857	−	0.429942i	$-0.858534\pi$
$13$	−3.54045	+	2.04408i	−0.981945	+	0.566926i	−0.0790880	+	0.996868i	$0.525201\pi$
$14$		0			0
$15$	4.76900	−	1.92801i	1.23135	−	0.497809i
$16$		0			0
$17$	−0.835278	+	1.44674i	−0.202585	+	0.350887i	−0.949360	−	0.314189i	$-0.898267\pi$
$17$	−0.835278	+	1.44674i	−0.202585	+	0.350887i	0.746776	+	0.665076i	$0.231601\pi$
$18$		0			0
$19$	−4.25377	+	2.45592i	−0.975882	+	0.563426i	−0.901024	−	0.433768i	$-0.857184\pi$
$19$	−4.25377	+	2.45592i	−0.975882	+	0.563426i	−0.0748577	+	0.997194i	$0.523850\pi$
$20$		0			0
$21$	−2.53904	+	3.81488i	−0.554063	+	0.832475i
$22$		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	$-0.954011\pi$
$31$		−	1.60327i		−	0.287956i	0.989581	−	0.143978i	$-0.0459895\pi$
$32$		0			0
$33$	8.10988	+	1.13797i	1.41175	+	0.198095i
$34$		0			0
$35$	7.08273	+	3.40239i	1.19720	+	0.575109i
$36$		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	$-0.979230\pi$
$41$	−3.55632	−	6.15972i	−0.555404	−	0.961987i	0.442468	−	0.896784i	$-0.354103\pi$
$42$		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	$-0.796279\pi$
$47$	−10.9977			−1.60418			−0.802090	+	0.597203i	$0.796279\pi$
$48$		0			0
$49$	−6.91978	+	1.05674i	−0.988540	+	0.150962i
$50$		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	$-0.442741\pi$
$59$	2.74856			0.357832			0.178916	+	0.983864i	$0.442741\pi$
$60$		0			0
$61$			7.20310i			0.922262i	0.887332	+	0.461131i	$0.152556\pi$
$61$			7.20310i			0.922262i	−0.887332	+	0.461131i	$0.847444\pi$
$62$		0			0
$63$	7.53294	−	2.50095i	0.949062	−	0.315090i
$64$		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	$0.0403870\pi$
$73$	13.6493	+	7.88042i	1.59753	+	0.922334i	0.605567	+	0.795794i	$0.292946\pi$
$74$		0			0
$75$	−0.919449	+	6.55255i	−0.106169	+	0.756624i
$76$		0			0
$77$	7.05683	+	10.3289i	0.804201	+	1.17709i
$78$		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	−0.997941	−	0.0641368i	$-0.979571\pi$
$83$	−4.03981	+	6.99715i	−0.443426	+	0.768037i	0.554515	+	0.832174i	$0.312904\pi$
$84$		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	0.999913	−	0.0132019i	$-0.00420240\pi$
$89$	4.60872	+	7.98254i	0.488523	+	0.846147i	−0.511390	+	0.859349i	$0.670869\pi$
$90$		0			0
$91$	6.10169	+	8.93089i	0.639631	+	0.936212i
$92$		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	0.811626	−	0.584177i	$-0.198583\pi$
$97$	7.00772	+	4.04591i	0.711527	+	0.410800i	−0.100099	+	0.994977i	$0.531916\pi$
$98$		0			0
$99$	−9.85770	−	10.1991i	−0.990736	−	1.02505i
$100$		0			0
$101$	−3.65365	−	6.32831i	−0.363552	−	0.629690i	0.624991	−	0.780632i	$-0.285103\pi$
$101$	−3.65365	−	6.32831i	−0.363552	−	0.629690i	−0.988543	+	0.150942i	$0.951769\pi$
$102$		0			0
$103$	−6.08409	−	3.51265i	−0.599483	−	0.346112i	0.169355	−	0.985555i	$-0.445832\pi$
$103$	−6.08409	−	3.51265i	−0.599483	−	0.346112i	−0.768838	+	0.639443i	$0.779165\pi$
$104$		0			0
$105$	−6.04152	−	12.1952i	−0.589592	−	1.19013i
$106$		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
$119$	3.98403	+	1.91384i	0.365215	+	0.175442i
$120$		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	$-0.633973\pi$
$131$	6.70890	−	11.6202i	0.586159	−	1.01526i	0.994730	−	0.102531i	$-0.0326941\pi$
$132$		0			0
$133$	7.33104	+	10.7303i	0.635682	+	0.930432i
$134$		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	−0.432866	−	0.901458i	$-0.642498\pi$
$139$	1.54902	−	0.894326i	0.131386	−	0.0758557i	0.564252	+	0.825602i	$0.309164\pi$
$140$		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
$147$	10.5728	+	5.93434i	0.872028	+	0.489456i
$148$		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	$0.240315\pi$
$157$			17.1728i			1.37054i	−0.728291	+	0.685268i	$0.759685\pi$
$158$		0			0
$159$	−0.530265	−	1.31163i	−0.0420527	−	0.104019i
$160$		0			0
$161$	5.62609	−	11.7118i	0.443398	−	0.923017i
$162$		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	0.549729	−	0.835343i	$-0.314731\pi$
$167$	−5.79673	−	10.0402i	−0.448564	−	0.776936i	−0.998293	+	0.0584072i	$0.981398\pi$
$168$		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	$-0.423432\pi$
$173$	6.26691			0.476464			0.238232	+	0.971208i	$0.423432\pi$
$174$		0			0
$175$	−8.34547	+	5.70172i	−0.630858	+	0.431010i
$176$		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	$0.000986191\pi$
$181$			0.0833642i			0.00619641i	−0.999995	+	0.00309821i	$0.999014\pi$
$182$		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
$189$	−12.9494	−	4.61651i	−0.941933	−	0.335802i
$190$		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	0.139468	−	0.990227i	$-0.455461\pi$
$199$	−9.14623	−	5.28058i	−0.648359	−	0.374330i	−0.787827	+	0.615896i	$0.788794\pi$
$200$		0			0
$201$	−15.8492	−	12.3772i	−1.11792	−	0.873023i
$202$		0			0
$203$	0.315578	−	0.656936i	0.0221492	−	0.0461079i
$204$		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
$217$	−4.22969	+	0.321102i	−0.287130	+	0.0217978i
$218$		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	0.523732	−	0.851883i	$-0.324539\pi$
$223$	0.714485	+	0.412508i	0.0478455	+	0.0276236i	−0.475886	+	0.879507i	$0.657873\pi$
$224$		0			0
$225$	8.24056	−	7.96475i	0.549371	−	0.530983i
$226$		0			0
$227$	0.166778	+	0.288869i	0.0110695	+	0.0191729i	0.871507	−	0.490383i	$-0.163143\pi$
$227$	0.166778	+	0.288869i	0.0110695	+	0.0191729i	−0.860438	+	0.509556i	$0.829810\pi$
$228$		0			0
$229$	12.4893	+	7.21072i	0.825319	+	0.476498i	0.852247	−	0.523139i	$-0.175239\pi$
$229$	12.4893	+	7.21072i	0.825319	+	0.476498i	−0.0269285	+	0.999637i	$0.508573\pi$
$230$		0			0
$231$	1.37791	−	21.6231i	0.0906600	−	1.42269i
$232$		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	−0.445483	−	0.895290i	$-0.646968\pi$
$241$	1.66295	−	0.960105i	0.107120	−	0.0618458i	0.552603	+	0.833445i	$0.313635\pi$
$242$		0			0
$243$	15.3546	+	2.69022i	0.984996	+	0.172578i
$244$		0			0
$245$	7.55753	−	19.3668i	0.482833	−	1.23730i
$246$		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	$-0.398043\pi$
$251$	9.97663			0.629719			0.314860	+	0.949138i	$0.398043\pi$
$252$		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	−0.531270	−	0.847203i	$-0.678285\pi$
$257$	7.50364	−	12.9967i	0.468064	−	0.810711i	0.999334	+	0.0364915i	$0.0116182\pi$
$258$		0			0
$259$	−7.41361	+	5.06506i	−0.460659	+	0.314728i
$260$		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	$-0.471060\pi$
$269$	14.8898	−	25.7898i	0.907844	−	1.57243i	0.817053	−	0.576562i	$-0.195606\pi$
$270$		0			0
$271$	−2.41462	+	1.39408i	−0.146677	+	0.0846843i	−0.571543	−	0.820572i	$-0.693655\pi$
$271$	−2.41462	+	1.39408i	−0.146677	+	0.0846843i	0.424865	+	0.905257i	$0.360321\pi$
$272$		0			0
$273$	1.19141	−	18.6964i	0.0721075	−	1.13156i
$274$		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	$0.207380\pi$
$283$			20.4019i			1.21277i	−0.795173	+	0.606383i	$0.792620\pi$
$284$		0			0
$285$	−15.5512	+	19.9136i	−0.921174	+	1.17958i
$286$		0			0
$287$	−15.5381	+	10.6158i	−0.917184	+	0.626631i
$288$		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	0.990252	−	0.139289i	$-0.0444818\pi$
$293$	6.41037	+	11.1031i	0.374498	+	0.648649i	−0.615754	+	0.787939i	$0.711148\pi$
$294$		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
$301$	−24.9422	−	11.9817i	−1.43765	−	0.690615i
$302$		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	$0.0175773\pi$
$307$			1.93411i			0.110386i	−0.998476	+	0.0551928i	$0.982423\pi$
$308$		0			0
$309$	4.56073	+	11.2812i	0.259451	+	0.641762i
$310$		0			0
$311$	2.08916			0.118465			0.0592326	−	0.998244i	$-0.481135\pi$
$311$	2.08916			0.118465			0.0592326	+	0.998244i	$0.481135\pi$
$312$		0			0
$313$		−	22.4088i		−	1.26662i	−0.773899	−	0.633309i	$-0.781696\pi$
$313$		−	22.4088i		−	1.26662i	0.773899	−	0.633309i	$-0.218304\pi$
$314$		0			0
$315$	−4.75354	+	23.0884i	−0.267832	+	1.30089i
$316$		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
$329$	2.20261	+	29.0137i	0.121434	+	1.59958i
$330$		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
$343$	4.17373	+	18.0438i	0.225360	+	0.974276i
$344$		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	0.255783	−	0.966734i	$-0.417667\pi$
$349$	−8.47286	−	4.89181i	−0.453542	−	0.261852i	−0.709325	+	0.704882i	$0.751000\pi$
$350$		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	$0.0657652\pi$
$353$	12.5322	+	21.7065i	0.667023	+	1.15532i	−0.311709	+	0.950178i	$0.600901\pi$
$354$		0			0
$355$	−26.8532	−	15.5037i	−1.42522	−	0.822850i
$356$		0			0
$357$	−3.39835	−	6.85982i	−0.179860	−	0.363060i
$358$		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	0.0842608	−	0.996444i	$-0.473147\pi$
$367$	18.9530	−	10.9425i	0.989337	−	0.571194i	0.905076	+	0.425250i	$0.139814\pi$
$368$		0			0
$369$	15.3428	−	14.8292i	0.798712	−	0.771979i
$370$		0			0
$371$	0.935769	−	1.94798i	0.0485827	−	0.101134i
$372$		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	$0.356640\pi$
$383$	−10.9989	+	19.0506i	−0.562015	+	0.973439i	−0.997321	+	0.0731560i	$0.976693\pi$
$384$		0			0
$385$	−37.0448	+	2.81230i	−1.88798	+	0.143328i
$386$		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	−0.381369	−	0.924423i	$-0.624547\pi$
$397$	4.55324	−	2.62881i	0.228520	−	0.131936i	0.609889	+	0.792487i	$0.291214\pi$
$398$		0			0
$399$	1.43145	−	22.4633i	0.0716623	−	1.12457i
$400$		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	$0.160760\pi$
$409$			19.5703i			0.967690i	−0.875154	+	0.483845i	$0.839240\pi$
$410$		0			0
$411$	15.4377	+	2.16621i	0.761488	+	0.106851i
$412$		0			0
$413$	−0.550478	−	7.25114i	−0.0270873	−	0.356805i
$414$		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	$0.00130525\pi$
$419$	10.3073	+	17.8529i	0.503547	+	0.872169i	−0.496445	+	0.868068i	$0.665361\pi$
$420$		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
$427$	19.0029	−	1.44263i	0.919616	−	0.0698137i
$428$		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	$0.100605\pi$
$433$			12.9356i			0.621646i	−0.950468	+	0.310823i	$0.899395\pi$
$434$		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	$-0.922486\pi$
$439$		−	10.1039i		−	0.482233i	0.970496	−	0.241116i	$-0.0775135\pi$
$440$		0			0
$441$	−8.10660	−	19.3722i	−0.386029	−	0.922487i
$442$		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
$455$	−32.0308	+	2.43166i	−1.50163	+	0.113998i
$456$		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	$0.443416\pi$
$461$	−16.4030	+	28.4108i	−0.763964	+	1.32322i	−0.940793	+	0.338983i	$0.889917\pi$
$462$		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	$-0.989247\pi$
$467$	−11.4311	−	19.7992i	−0.528966	−	0.916196i	0.470463	−	0.882420i	$-0.344087\pi$
$468$		0			0
$469$	−2.32529	−	30.6297i	−0.107372	−	1.41435i
$470$		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	0.892388	−	0.451269i	$-0.149029\pi$
$479$	1.21212	+	2.09946i	0.0553834	+	0.0959269i	−0.837004	+	0.547196i	$0.815695\pi$
$480$		0			0
$481$	12.0149	+	6.93683i	0.547834	+	0.316292i
$482$		0			0
$483$	−20.1657	+	9.99007i	−0.917570	+	0.454564i
$484$		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
$497$	27.5440	−	2.09104i	1.23552	−	0.0937958i
$498$		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	$-0.394864\pi$
$503$	14.5476			0.648645			0.324323	+	0.945947i	$0.394864\pi$
$504$		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	−0.546585	−	0.837404i	$-0.684072\pi$
$509$	10.1958	−	17.6596i	0.451921	−	0.782750i	0.998505	+	0.0546542i	$0.0174057\pi$
$510$		0			0
$511$	18.0561	−	37.5873i	0.798757	−	1.66276i
$512$		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	−0.984355	−	0.176196i	$-0.943621\pi$
$521$	−7.75122	+	13.4255i	−0.339587	+	0.588182i	0.644768	+	0.764379i	$0.276954\pi$
$522$		0			0
$523$	9.35989	−	5.40394i	0.409280	−	0.236298i	−0.281201	−	0.959649i	$-0.590733\pi$
$523$	9.35989	−	5.40394i	0.409280	−	0.236298i	0.690480	+	0.723351i	$0.257399\pi$
$524$		0			0
$525$	17.4708	+	1.11331i	0.762490	+	0.0485890i
$526$		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
$539$	25.8360	−	20.6857i	1.11283	−	0.890997i
$540$		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
$553$	2.46408	+	32.4580i	0.104784	+	1.38025i
$554$		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	$-0.622162\pi$
$563$	−17.7688			−0.748864			−0.374432	+	0.927254i	$0.622162\pi$
$564$		0			0
$565$			39.9211i			1.67949i
$566$		0			0
$567$	12.7559	+	20.1069i	0.535697	+	0.844411i
$568$		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	$-0.890636\pi$
$577$	−40.9329	−	23.6326i	−1.70406	−	0.983840i	−0.762506	−	0.646982i	$-0.776031\pi$
$578$		0			0
$579$	−29.4259	−	22.9797i	−1.22290	−	0.955004i
$580$		0			0
$581$	19.2687	+	9.25628i	0.799400	+	0.384015i
$582$		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	−0.519542	−	0.854445i	$-0.673897\pi$
$587$	11.6343	−	20.1513i	0.480200	−	0.831731i	0.999742	+	0.0227138i	$0.00723065\pi$
$588$		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	$-0.890070\pi$
$593$	−18.5962	−	32.2095i	−0.763654	−	1.32269i	0.177302	−	0.984157i	$-0.443263\pi$
$594$		0			0
$595$	−10.8384	+	7.40494i	−0.444332	+	0.303573i
$596$		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	0.167885	−	0.985807i	$-0.446306\pi$
$601$	−14.7559	−	8.51933i	−0.601906	−	0.347511i	−0.769791	+	0.638296i	$0.779640\pi$
$602$		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	0.661478	−	0.749965i	$-0.269930\pi$
$607$	8.44393	+	4.87510i	0.342728	+	0.197874i	−0.318749	+	0.947839i	$0.603263\pi$
$608$		0			0
$609$	−1.13113	+	0.560362i	−0.0458357	+	0.0227070i
$610$		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	−0.770036	−	0.638001i	$-0.779762\pi$
$619$	−14.9907	+	8.65490i	−0.602528	+	0.347870i	0.167507	+	0.985871i	$0.446428\pi$
$620$		0			0
$621$	20.6345	−	15.0124i	0.828036	−	0.602429i
$622$		0			0
$623$	20.1362	−	13.7573i	0.806739	−	0.551174i
$624$		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
$637$	22.3391	−	17.8859i	0.885107	−	0.708665i
$638$		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	−0.800037	−	0.599950i	$-0.795187\pi$
$643$	−17.2553	+	9.96236i	−0.680483	+	0.392877i	0.119554	+	0.992828i	$0.461854\pi$
$644$		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	$0.363830\pi$
$647$	−14.7670	+	25.5772i	−0.580551	+	1.00554i	−0.995414	+	0.0956605i	$0.969504\pi$
$648$		0			0
$649$	−11.2544	+	6.49774i	−0.441775	+	0.255059i
$650$		0			0
$651$	6.11629	+	4.07077i	0.239716	+	0.159546i
$652$		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	$0.0554048\pi$
$661$			8.90498i			0.346364i	−0.984890	+	0.173182i	$0.944595\pi$
$662$		0			0
$663$	−7.28066	+	9.32299i	−0.282757	+	0.362075i
$664$		0			0
$665$	−38.4843	+	2.92158i	−1.49236	+	0.113294i
$666$		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	$-0.445114\pi$
$677$	8.92848			0.343149			0.171575	+	0.985171i	$0.445114\pi$
$678$		0			0
$679$	9.27026	−	19.2978i	0.355760	−	0.740582i
$680$		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	$0.0346194\pi$
$691$			5.70665i			0.217091i	−0.994091	+	0.108546i	$0.965381\pi$
$692$		0			0
$693$	−24.9325	+	28.0489i	−0.947107	+	1.06549i
$694$		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
$707$	−15.9633	+	10.9063i	−0.600363	+	0.410175i
$708$		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	$0.237159\pi$
$719$	25.5996	+	44.3397i	0.954702	+	1.65359i	0.219654	+	0.975578i	$0.429507\pi$
$720$		0			0
$721$	−8.04842	+	16.7543i	−0.299739	+	0.623963i
$722$		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	0.733347	−	0.679854i	$-0.237957\pi$
$727$	13.7848	+	7.95865i	0.511249	+	0.295170i	−0.222098	+	0.975024i	$0.571290\pi$
$728$		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	0.566282	−	0.824212i	$-0.308381\pi$
$733$	3.67216	+	2.12012i	0.135634	+	0.0783086i	−0.430647	+	0.902520i	$0.641715\pi$
$734$		0			0
$735$	−30.9630	+	18.3809i	−1.14209	+	0.677991i
$736$		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
$749$	21.1323	+	30.9309i	0.772158	+	1.13019i
$750$		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	−0.931006	−	0.365003i	$-0.881068\pi$
$761$	−4.12142	+	7.13850i	−0.149401	+	0.258770i	0.781605	+	0.623774i	$0.214401\pi$
$762$		0			0
$763$	13.4602	+	6.46602i	0.487293	+	0.234086i
$764$		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	−0.818088	−	0.575094i	$-0.804966\pi$
$769$	−20.2182	+	11.6730i	−0.729086	+	0.420938i	0.0890020	+	0.996031i	$0.471632\pi$
$770$		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	$-0.620724\pi$
$773$	17.2201	−	29.8261i	0.619364	−	1.07277i	0.989602	−	0.143833i	$-0.0459428\pi$
$774$		0			0
$775$	−5.30422	+	3.06240i	−0.190533	+	0.110004i
$776$		0			0
$777$	15.5200	+	0.989001i	0.556778	+	0.0354802i
$778$		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	$-0.952661\pi$
$787$		−	8.31355i		−	0.296346i	0.988961	−	0.148173i	$-0.0473393\pi$
$788$		0			0
$789$	−12.1016	−	1.69809i	−0.430830	−	0.0604537i
$790$		0			0
$791$	−20.0625	−	29.3650i	−0.713341	−	1.04410i
$792$		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	0.858381	−	0.513012i	$-0.171470\pi$
$797$	−0.426036	−	0.737916i	−0.0150910	−	0.0261383i	−0.873472	+	0.486874i	$0.838137\pi$
$798$		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
$805$	21.7682	+	31.8615i	0.767227	+	1.12297i
$806$		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	$-0.993909\pi$
$811$		−	1.08986i		−	0.0382702i	0.999817	−	0.0191351i	$-0.00609126\pi$
$812$		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
$819$	−21.5579	+	24.2524i	−0.753293	+	0.847449i
$820$		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	0.491322	−	0.870978i	$-0.336514\pi$
$829$	−0.498269	−	0.287676i	−0.0173056	−	0.00999140i	−0.508628	+	0.860986i	$0.669847\pi$
$830$		0			0
$831$	−3.26882	+	23.2956i	−0.113394	+	0.808115i
$832$		0			0
$833$	4.25111	−	10.8938i	0.147292	−	0.377448i
$834$		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	$-0.523778\pi$
$839$	23.9341	−	41.4550i	0.826295	−	1.43119i	0.900925	−	0.433974i	$-0.142889\pi$
$840$		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
$847$	−27.0801	−	13.0087i	−0.930483	−	0.446985i
$848$		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	−0.394945	−	0.918705i	$-0.629236\pi$
$853$	−40.5393	−	23.4054i	−1.38804	−	0.801385i	−0.993094	+	0.117320i	$0.962570\pi$
$854$		0			0
$855$	42.4581	−	10.6056i	1.45204	−	0.362704i
$856$		0			0
$857$	4.78220	+	8.28302i	0.163357	+	0.282943i	0.936071	−	0.351812i	$-0.114434\pi$
$857$	4.78220	+	8.28302i	0.163357	+	0.282943i	−0.772714	+	0.634755i	$0.781101\pi$
$858$		0			0
$859$	−4.68311	−	2.70379i	−0.159786	−	0.0922523i	0.417975	−	0.908459i	$-0.362740\pi$
$859$	−4.68311	−	2.70379i	−0.159786	−	0.0922523i	−0.577761	+	0.816206i	$0.696073\pi$
$860$		0			0
$861$	32.5282	+	2.07283i	1.10856	+	0.0706420i
$862$		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
$875$	0.701762	+	9.24390i	0.0237239	+	0.312501i
$876$		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	$-0.227553\pi$
$881$	44.8295			1.51034			0.755172	+	0.655527i	$0.227553\pi$
$882$		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	−0.998255	−	0.0590523i	$-0.981192\pi$
$887$	−13.3422	+	23.1093i	−0.447987	+	0.775936i	0.550268	+	0.834988i	$0.314525\pi$
$888$		0			0
$889$	2.55817	+	33.6973i	0.0857984	+	1.13017i
$890$		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
$903$	21.2756	+	42.9463i	0.708006	+	1.42916i
$904$		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
$917$	−31.9995	−	15.3719i	−1.05672	−	0.507624i
$918$		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	$-0.316439\pi$
$929$	33.2372			1.09048			0.545238	+	0.838281i	$0.316439\pi$
$930$		0			0
$931$	26.8399	−	21.4895i	0.879642	−	0.704290i
$932$		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	$-0.872797\pi$
$937$		−	23.8190i		−	0.778134i	0.921209	−	0.389067i	$-0.127203\pi$
$938$		0			0
$939$	−23.8891	+	30.5903i	−0.779591	+	0.998278i
$940$		0			0
$941$	−54.2403			−1.76818			−0.884091	−	0.467315i	$-0.845221\pi$
$941$	−54.2403			−1.76818			−0.884091	+	0.467315i	$0.845221\pi$
$942$		0			0
$943$		−	34.9295i		−	1.13746i
$944$		0			0
$945$	31.1027	−	26.4506i	1.01177	−	0.860438i
$946$		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
$959$	13.4332	+	19.6618i	0.433780	+	0.634913i
$960$		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	$0.105629\pi$
$971$	23.5222	+	40.7416i	0.754862	+	1.30746i	−0.190581	+	0.981671i	$0.561037\pi$
$972$		0			0
$973$	−2.66961	−	3.90744i	−0.0855838	−	0.125267i
$974$		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	$-0.970684\pi$
$983$	−18.1071	−	31.3624i	−0.577527	−	1.00031i	0.418235	−	0.908339i	$-0.362649\pi$
$984$		0			0
$985$	−25.4191	−	14.6757i	−0.809921	−	0.467608i
$986$		0			0
$987$	27.9236	−	41.9549i	0.888817	−	1.33544i
$988$		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	−0.720220	−	0.693746i	$-0.755959\pi$
$997$	−15.1413	+	8.74181i	−0.479528	+	0.276856i	0.240691	+	0.970602i	$0.422626\pi$
$998$		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	252.2.w.a.101.3	yes	16
3.2	odd	2		756.2.w.a.521.7		16
4.3	odd	2		1008.2.ca.d.353.6		16
7.2	even	3		1764.2.bm.a.1685.8		16
7.3	odd	6		1764.2.x.b.1469.5		16
7.4	even	3		1764.2.x.a.1469.4		16
7.5	odd	6		252.2.bm.a.173.1	yes	16
7.6	odd	2		1764.2.w.b.1109.6		16
9.2	odd	6		2268.2.t.a.1781.7		16
9.4	even	3		756.2.bm.a.17.7		16
9.5	odd	6		252.2.bm.a.185.1	yes	16
9.7	even	3		2268.2.t.b.1781.2		16
12.11	even	2		3024.2.ca.d.2033.7		16
21.2	odd	6		5292.2.bm.a.4625.2		16
21.5	even	6		756.2.bm.a.89.7		16
21.11	odd	6		5292.2.x.a.4409.7		16
21.17	even	6		5292.2.x.b.4409.2		16
21.20	even	2		5292.2.w.b.521.2		16
28.19	even	6		1008.2.df.d.929.8		16
36.23	even	6		1008.2.df.d.689.8		16
36.31	odd	6		3024.2.df.d.17.7		16
63.4	even	3		5292.2.x.b.881.2		16
63.5	even	6	inner	252.2.w.a.5.3	✓	16
63.13	odd	6		5292.2.bm.a.2285.2		16
63.23	odd	6		1764.2.w.b.509.6		16
63.31	odd	6		5292.2.x.a.881.7		16
63.32	odd	6		1764.2.x.b.293.5		16
63.40	odd	6		756.2.w.a.341.7		16
63.41	even	6		1764.2.bm.a.1697.8		16
63.47	even	6		2268.2.t.b.2105.2		16
63.58	even	3		5292.2.w.b.1097.2		16
63.59	even	6		1764.2.x.a.293.4		16
63.61	odd	6		2268.2.t.a.2105.7		16
84.47	odd	6		3024.2.df.d.1601.7		16
252.103	even	6		3024.2.ca.d.2609.7		16
252.131	odd	6		1008.2.ca.d.257.6		16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
252.2.w.a.5.3	✓	16	63.5	even	6	inner
252.2.w.a.101.3	yes	16	1.1	even	1	trivial
252.2.bm.a.173.1	yes	16	7.5	odd	6
252.2.bm.a.185.1	yes	16	9.5	odd	6
756.2.w.a.341.7		16	63.40	odd	6
756.2.w.a.521.7		16	3.2	odd	2
756.2.bm.a.17.7		16	9.4	even	3
756.2.bm.a.89.7		16	21.5	even	6
1008.2.ca.d.257.6		16	252.131	odd	6
1008.2.ca.d.353.6		16	4.3	odd	2
1008.2.df.d.689.8		16	36.23	even	6
1008.2.df.d.929.8		16	28.19	even	6
1764.2.w.b.509.6		16	63.23	odd	6
1764.2.w.b.1109.6		16	7.6	odd	2
1764.2.x.a.293.4		16	63.59	even	6
1764.2.x.a.1469.4		16	7.4	even	3
1764.2.x.b.293.5		16	63.32	odd	6
1764.2.x.b.1469.5		16	7.3	odd	6
1764.2.bm.a.1685.8		16	7.2	even	3
1764.2.bm.a.1697.8		16	63.41	even	6
2268.2.t.a.1781.7		16	9.2	odd	6
2268.2.t.a.2105.7		16	63.61	odd	6
2268.2.t.b.1781.2		16	9.7	even	3
2268.2.t.b.2105.2		16	63.47	even	6
3024.2.ca.d.2033.7		16	12.11	even	2
3024.2.ca.d.2609.7		16	252.103	even	6
3024.2.df.d.17.7		16	36.31	odd	6
3024.2.df.d.1601.7		16	84.47	odd	6
5292.2.w.b.521.2		16	21.20	even	2
5292.2.w.b.1097.2		16	63.58	even	3
5292.2.x.a.881.7		16	63.31	odd	6
5292.2.x.a.4409.7		16	21.11	odd	6
5292.2.x.b.881.2		16	63.4	even	3
5292.2.x.b.4409.2		16	21.17	even	6
5292.2.bm.a.2285.2		16	63.13	odd	6
5292.2.bm.a.4625.2		16	21.2	odd	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:	\( N \)	\(=\)	\( 252 = 2^{2} \cdot 3^{2} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	252.w (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.36511 - 1.06606i) q^{3} +(-1.48494 + 2.57199i) q^{5} +(-0.200279 - 2.63816i) q^{7} +(0.727031 + 2.91057i) q^{9} +O(q^{10})\)	\(q+(-1.36511 - 1.06606i) q^{3} +(-1.48494 + 2.57199i) q^{5} +(-0.200279 - 2.63816i) q^{7} +(0.727031 + 2.91057i) q^{9} +(-4.09466 + 2.36406i) q^{11} +(-3.54045 + 2.04408i) q^{13} +(4.76900 - 1.92801i) q^{15} +(-0.835278 + 1.44674i) q^{17} +(-4.25377 + 2.45592i) q^{19} +(-2.53904 + 3.81488i) q^{21} +(4.25297 + 2.45545i) q^{23} +(-1.91009 - 3.30837i) q^{25} +(2.11037 - 4.74830i) q^{27} +(0.238557 + 0.137731i) q^{29} -1.60327i q^{31} +(8.10988 + 1.13797i) q^{33} +(7.08273 + 3.40239i) q^{35} +(-1.69681 - 2.93896i) q^{37} +(7.01221 + 0.983947i) q^{39} +(-3.55632 - 6.15972i) q^{41} +(5.22930 - 9.05742i) q^{43} +(-8.56556 - 2.45211i) q^{45} -10.9977 q^{47} +(-6.91978 + 1.05674i) q^{49} +(2.68256 - 1.08450i) q^{51} +(0.707381 + 0.408407i) q^{53} -14.0419i q^{55} +(8.42500 + 1.18219i) q^{57} +2.74856 q^{59} +7.20310i q^{61} +(7.53294 - 2.50095i) q^{63} -12.1413i q^{65} +11.6103 q^{67} +(-3.18809 - 7.88587i) q^{69} +10.4406i q^{71} +(13.6493 + 7.88042i) q^{73} +(-0.919449 + 6.55255i) q^{75} +(7.05683 + 10.3289i) q^{77} -12.3033 q^{79} +(-7.94285 + 4.23215i) q^{81} +(-4.03981 + 6.99715i) q^{83} +(-2.48067 - 4.29665i) q^{85} +(-0.178826 - 0.442333i) q^{87} +(4.60872 + 7.98254i) q^{89} +(6.10169 + 8.93089i) q^{91} +(-1.70919 + 2.18864i) q^{93} -14.5875i q^{95} +(7.00772 + 4.04591i) q^{97} +(-9.85770 - 10.1991i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q - q^{7} + 6 q^{9}+O(q^{10}) \) 16 * q - q^7 + 6 * q^9	\( 16 q - q^{7} + 6 q^{9} - 6 q^{11} - 3 q^{13} - 3 q^{15} + 9 q^{17} + 6 q^{21} + 21 q^{23} - 8 q^{25} + 9 q^{27} + 6 q^{29} - 15 q^{35} + q^{37} - 3 q^{39} - 6 q^{41} - 2 q^{43} - 30 q^{45} - 36 q^{47} - 5 q^{49} - 33 q^{51} + 15 q^{57} - 30 q^{59} - 15 q^{63} + 14 q^{67} + 21 q^{69} - 57 q^{75} + 3 q^{77} + 2 q^{79} + 18 q^{81} + 6 q^{85} + 48 q^{87} + 21 q^{89} + 9 q^{91} + 21 q^{93} - 3 q^{97} - 9 q^{99}+O(q^{100}) \) 16 * q - q^7 + 6 * q^9 - 6 * q^11 - 3 * q^13 - 3 * q^15 + 9 * q^17 + 6 * q^21 + 21 * q^23 - 8 * q^25 + 9 * q^27 + 6 * q^29 - 15 * q^35 + q^37 - 3 * q^39 - 6 * q^41 - 2 * q^43 - 30 * q^45 - 36 * q^47 - 5 * q^49 - 33 * q^51 + 15 * q^57 - 30 * q^59 - 15 * q^63 + 14 * q^67 + 21 * q^69 - 57 * q^75 + 3 * q^77 + 2 * q^79 + 18 * q^81 + 6 * q^85 + 48 * q^87 + 21 * q^89 + 9 * q^91 + 21 * q^93 - 3 * q^97 - 9 * q^99

Introduction

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