LMFDB - Embedded newform 1764.2.bm.a.1697.8

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1764,2,Mod(1685,1764)]

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, 1, 5]))

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

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

chi := DirichletCharacter("1764.1685");

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.bm (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			1697.8
Root			$1.68042 - 0.419752i$ of defining polynomial
Character	$\chi$	$=$	1764.1697
Dual form			1764.2.bm.a.1685.8

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.60579 + 0.649187i) q^{3} +2.96988 q^{5} +(2.15711 + 2.08491i) q^{9} +O(q^{10})$	\(q+(1.60579 + 0.649187i) q^{3} +2.96988 q^{5} +(2.15711 + 2.08491i) q^{9} +4.72811i q^{11} +(-3.54045 - 2.04408i) q^{13} +(4.76900 + 1.92801i) q^{15} +(-0.835278 + 1.44674i) q^{17} +(4.25377 - 2.45592i) q^{19} +4.91090i q^{23} +3.82018 q^{25} +(2.11037 + 4.74830i) q^{27} +(0.238557 - 0.137731i) q^{29} +(1.38847 - 0.801636i) q^{31} +(-3.06943 + 7.59235i) q^{33} +(-1.69681 - 2.93896i) q^{37} +(-4.35823 - 5.58078i) q^{39} +(-3.55632 + 6.15972i) q^{41} +(5.22930 + 9.05742i) q^{43} +(6.40637 + 6.19194i) q^{45} +(5.49885 - 9.52430i) q^{47} +(-2.28049 + 1.78091i) q^{51} +(-0.707381 - 0.408407i) q^{53} +14.0419i q^{55} +(8.42500 - 1.18219i) q^{57} +(-1.37428 - 2.38032i) q^{59} +(6.23807 + 3.60155i) q^{61} +(-10.5147 - 6.07067i) q^{65} +(-5.80513 - 10.0548i) q^{67} +(-3.18809 + 7.88587i) q^{69} -10.4406i q^{71} +(-13.6493 - 7.88042i) q^{73} +(6.13440 + 2.48001i) q^{75} +(6.15163 - 10.6549i) q^{79} +(0.306275 + 8.99479i) q^{81} +(-4.03981 - 6.99715i) q^{83} +(-2.48067 + 4.29665i) q^{85} +(0.472485 - 0.0662987i) q^{87} +(4.60872 + 7.98254i) q^{89} +(2.75001 - 0.385879i) q^{93} +(12.6332 - 7.29377i) q^{95} +(7.00772 - 4.04591i) q^{97} +(-9.85770 + 10.1991i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q+O(q^{10}) $ 16 * q	$ 16 q - 3 q^{13} - 3 q^{15} + 9 q^{17} + 16 q^{25} + 9 q^{27} + 6 q^{29} - 6 q^{31} + 27 q^{33} + q^{37} - 3 q^{39} - 6 q^{41} - 2 q^{43} + 15 q^{45} + 18 q^{47} + 15 q^{51} + 15 q^{57} + 15 q^{59} - 3 q^{61} - 39 q^{65} - 7 q^{67} + 21 q^{69} + 15 q^{75} - q^{79} + 6 q^{85} + 3 q^{87} + 21 q^{89} - 69 q^{93} + 6 q^{95} - 3 q^{97} - 9 q^{99}+O(q^{100}) $ 16 * q - 3 * q^13 - 3 * q^15 + 9 * q^17 + 16 * q^25 + 9 * q^27 + 6 * q^29 - 6 * q^31 + 27 * q^33 + q^37 - 3 * q^39 - 6 * q^41 - 2 * q^43 + 15 * q^45 + 18 * q^47 + 15 * q^51 + 15 * q^57 + 15 * q^59 - 3 * q^61 - 39 * q^65 - 7 * q^67 + 21 * q^69 + 15 * q^75 - q^79 + 6 * q^85 + 3 * q^87 + 21 * q^89 - 69 * q^93 + 6 * q^95 - 3 * q^97 - 9 * q^99

Display 100 coefficients 10 coefficients

Character values

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

$n$	$785$	$883$	$1081$
$\chi(n)$	$e\left(\frac{5}{6}\right)$	$1$	$e\left(\frac{1}{6}\right)$

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
$3$	1.60579	+	0.649187i	0.927102	+	0.374808i
$3$	1.60579	+	0.649187i	0.927102	+	0.374808i
$4$		0			0
$5$	2.96988			1.32817			0.664085	−	0.747657i	$-0.268821\pi$
$5$	2.96988			1.32817			0.664085	+	0.747657i	$0.268821\pi$
$6$		0			0
$7$		0			0
$7$		0			0
$8$		0			0
$9$	2.15711	+	2.08491i	0.719038	+	0.694971i
$10$		0			0
$11$			4.72811i			1.42558i	0.701378	+	0.712790i	$0.252569\pi$
$11$			4.72811i			1.42558i	−0.701378	+	0.712790i	$0.747431\pi$
$12$		0			0
$13$	−3.54045	−	2.04408i	−0.981945	−	0.566926i	−0.0790880	−	0.996868i	$-0.525201\pi$
$13$	−3.54045	−	2.04408i	−0.981945	−	0.566926i	−0.902857	+	0.429942i	$0.858534\pi$
$14$		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	0.0748577	−	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
$23$			4.91090i			1.02399i	0.858987	+	0.511997i	$0.171094\pi$
$23$			4.91090i			1.02399i	−0.858987	+	0.511997i	$0.828906\pi$
$24$		0			0
$25$	3.82018			0.764036
$26$		0			0
$27$	2.11037	+	4.74830i	0.406141	+	0.913811i
$28$		0			0
$29$	0.238557	−	0.137731i	0.0442989	−	0.0255760i	−0.477687	−	0.878530i	$-0.658525\pi$
$29$	0.238557	−	0.137731i	0.0442989	−	0.0255760i	0.521986	+	0.852954i	$0.325191\pi$
$30$		0			0
$31$	1.38847	−	0.801636i	0.249377	−	0.143978i	−0.370102	−	0.928991i	$-0.620677\pi$
$31$	1.38847	−	0.801636i	0.249377	−	0.143978i	0.619479	+	0.785013i	$0.287344\pi$
$32$		0			0
$33$	−3.06943	+	7.59235i	−0.534319	+	1.32166i
$34$		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
$39$	−4.35823	−	5.58078i	−0.697875	−	0.893639i
$40$		0			0
$41$	−3.55632	+	6.15972i	−0.555404	+	0.961987i	0.442468	+	0.896784i	$0.354103\pi$
$41$	−3.55632	+	6.15972i	−0.555404	+	0.961987i	−0.997872	+	0.0652031i	$0.979230\pi$
$42$		0			0
$43$	5.22930	+	9.05742i	0.797461	+	1.38124i	0.921265	+	0.388936i	$0.127157\pi$
$43$	5.22930	+	9.05742i	0.797461	+	1.38124i	−0.123804	+	0.992307i	$0.539509\pi$
$44$		0			0
$45$	6.40637	+	6.19194i	0.955005	+	0.923040i
$46$		0			0
$47$	5.49885	−	9.52430i	0.802090	−	1.38926i	−0.116148	−	0.993232i	$-0.537055\pi$
$47$	5.49885	−	9.52430i	0.802090	−	1.38926i	0.918238	−	0.396029i	$-0.129612\pi$
$48$		0			0
$49$		0			0
$50$		0			0
$51$	−2.28049	+	1.78091i	−0.319332	+	0.249378i
$52$		0			0
$53$	−0.707381	−	0.408407i	−0.0971663	−	0.0560990i	0.450629	−	0.892711i	$-0.351200\pi$
$53$	−0.707381	−	0.408407i	−0.0971663	−	0.0560990i	−0.547796	+	0.836612i	$0.684533\pi$
$54$		0			0
$55$			14.0419i			1.89341i
$56$		0			0
$57$	8.42500	−	1.18219i	1.11592	−	0.156585i
$58$		0			0
$59$	−1.37428	−	2.38032i	−0.178916	−	0.309891i	0.762594	−	0.646878i	$-0.223926\pi$
$59$	−1.37428	−	2.38032i	−0.178916	−	0.309891i	−0.941509	+	0.336986i	$0.890592\pi$
$60$		0			0
$61$	6.23807	+	3.60155i	0.798703	+	0.461131i	0.843017	−	0.537886i	$-0.180777\pi$
$61$	6.23807	+	3.60155i	0.798703	+	0.461131i	−0.0443147	+	0.999018i	$0.514110\pi$
$62$		0			0
$63$		0			0
$64$		0			0
$65$	−10.5147	−	6.07067i	−1.30419	−	0.752974i
$66$		0			0
$67$	−5.80513	−	10.0548i	−0.709210	−	1.22839i	−0.965151	−	0.261695i	$-0.915719\pi$
$67$	−5.80513	−	10.0548i	−0.709210	−	1.22839i	0.255941	−	0.966692i	$-0.417615\pi$
$68$		0			0
$69$	−3.18809	+	7.88587i	−0.383801	+	0.949347i
$70$		0			0
$71$		−	10.4406i		−	1.23907i	−0.784968	−	0.619537i	$-0.787320\pi$
$71$		−	10.4406i		−	1.23907i	0.784968	−	0.619537i	$-0.212680\pi$
$72$		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
$75$	6.13440	+	2.48001i	0.708340	+	0.286367i
$76$		0			0
$77$		0			0
$78$		0			0
$79$	6.15163	−	10.6549i	0.692112	−	1.19877i	−0.279032	−	0.960282i	$-0.590014\pi$
$79$	6.15163	−	10.6549i	0.692112	−	1.19877i	0.971145	−	0.238492i	$-0.0766530\pi$
$80$		0			0
$81$	0.306275	+	8.99479i	0.0340305	+	0.999421i
$82$		0			0
$83$	−4.03981	−	6.99715i	−0.443426	−	0.768037i	0.554515	−	0.832174i	$-0.312904\pi$
$83$	−4.03981	−	6.99715i	−0.443426	−	0.768037i	−0.997941	+	0.0641368i	$0.979571\pi$
$84$		0			0
$85$	−2.48067	+	4.29665i	−0.269067	+	0.466037i
$86$		0			0
$87$	0.472485	−	0.0662987i	0.0506557	−	0.00710797i
$88$		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
$91$		0			0
$92$		0			0
$93$	2.75001	−	0.385879i	0.285163	−	0.0400138i
$94$		0			0
$95$	12.6332	−	7.29377i	1.29614	−	0.748325i
$96$		0			0
$97$	7.00772	−	4.04591i	0.711527	−	0.410800i	−0.100099	−	0.994977i	$-0.531916\pi$
$97$	7.00772	−	4.04591i	0.711527	−	0.410800i	0.811626	+	0.584177i	$0.198583\pi$
$98$		0			0
$99$	−9.85770	+	10.1991i	−0.990736	+	1.02505i
$100$		0			0
$101$	7.30730			0.727103			0.363552	−	0.931574i	$-0.381564\pi$
$101$	7.30730			0.727103			0.363552	+	0.931574i	$0.381564\pi$
$102$		0			0
$103$		−	7.02530i		−	0.692224i	−0.938193	−	0.346112i	$-0.887502\pi$
$103$		−	7.02530i		−	0.692224i	0.938193	−	0.346112i	$-0.112498\pi$
$104$		0			0
$105$		0			0
$106$		0			0
$107$	12.2618	−	7.07938i	1.18540	−	0.684389i	0.228140	−	0.973628i	$-0.426735\pi$
$107$	12.2618	−	7.07938i	1.18540	−	0.684389i	0.957257	+	0.289239i	$0.0934022\pi$
$108$		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	0.934930	−	0.354831i	$-0.115462\pi$
$113$	11.6411	+	6.72099i	1.09510	+	0.632258i	0.160172	+	0.987089i	$0.448795\pi$
$114$		0			0
$115$			14.5848i			1.36004i
$116$		0			0
$117$	−3.37542	−	11.7908i	−0.312058	−	1.09006i
$118$		0			0
$119$		0			0
$120$		0			0
$121$	−11.3550			−1.03228
$122$		0			0
$123$	−9.70951	+	7.58250i	−0.875477	+	0.683691i
$124$		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
$129$	2.51720	+	17.9391i	0.221627	+	1.57945i
$130$		0			0
$131$	−13.4178			−1.17232			−0.586159	−	0.810196i	$-0.699361\pi$
$131$	−13.4178			−1.17232			−0.586159	+	0.810196i	$0.699361\pi$
$132$		0			0
$133$		0			0
$134$		0			0
$135$	6.26754	+	14.1019i	0.539424	+	1.21370i
$136$		0			0
$137$			9.00030i			0.768948i	0.923136	+	0.384474i	$0.125617\pi$
$137$			9.00030i			0.768948i	−0.923136	+	0.384474i	$0.874383\pi$
$138$		0			0
$139$	1.54902	+	0.894326i	0.131386	+	0.0758557i	0.564252	−	0.825602i	$-0.309164\pi$
$139$	1.54902	+	0.894326i	0.131386	+	0.0758557i	−0.432866	+	0.901458i	$0.642498\pi$
$140$		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
$149$		−	12.9072i		−	1.05740i	−0.848810	−	0.528698i	$-0.822680\pi$
$149$		−	12.9072i		−	1.05740i	0.848810	−	0.528698i	$-0.177320\pi$
$150$		0			0
$151$	−12.9673			−1.05526			−0.527631	−	0.849473i	$-0.676920\pi$
$151$	−12.9673			−1.05526			−0.527631	+	0.849473i	$0.676920\pi$
$152$		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
$157$	−14.8720	+	8.58638i	−1.18692	+	0.685268i	−0.957605	−	0.288085i	$-0.906981\pi$
$157$	−14.8720	+	8.58638i	−1.18692	+	0.685268i	−0.229314	+	0.973353i	$0.573648\pi$
$158$		0			0
$159$	−0.870773	−	1.11504i	−0.0690568	−	0.0884282i
$160$		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
$165$	−9.11583	+	22.5484i	−0.709666	+	1.75539i
$166$		0			0
$167$	−5.79673	+	10.0402i	−0.448564	+	0.776936i	−0.998293	−	0.0584072i	$-0.981398\pi$
$167$	−5.79673	+	10.0402i	−0.448564	+	0.776936i	0.549729	+	0.835343i	$0.314731\pi$
$168$		0			0
$169$	1.85653	+	3.21561i	0.142810	+	0.247354i
$170$		0			0
$171$	14.2962	+	3.57105i	1.09326	+	0.273085i
$172$		0			0
$173$	−3.13346	+	5.42730i	−0.238232	+	0.412630i	−0.960207	−	0.279289i	$-0.909901\pi$
$173$	−3.13346	+	5.42730i	−0.238232	+	0.412630i	0.721975	+	0.691919i	$0.243235\pi$
$174$		0			0
$175$		0			0
$176$		0			0
$177$	−0.661528	−	4.71446i	−0.0497235	−	0.354360i
$178$		0			0
$179$	12.7668	+	7.37089i	0.954233	+	0.550927i	0.894393	−	0.447281i	$-0.147608\pi$
$179$	12.7668	+	7.37089i	0.954233	+	0.550927i	0.0598395	+	0.998208i	$0.480941\pi$
$180$		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
$185$	−5.03932	−	8.72835i	−0.370498	−	0.641721i
$186$		0			0
$187$	−6.84036	−	3.94929i	−0.500217	−	0.288800i
$188$		0			0
$189$		0			0
$190$		0			0
$191$	13.3672	+	7.71754i	0.967214	+	0.558421i	0.898386	−	0.439207i	$-0.144741\pi$
$191$	13.3672	+	7.71754i	0.967214	+	0.558421i	0.0688282	+	0.997629i	$0.478074\pi$
$192$		0			0
$193$	−10.7779	−	18.6678i	−0.775808	−	1.34374i	−0.934339	−	0.356385i	$-0.884009\pi$
$193$	−10.7779	−	18.6678i	−0.775808	−	1.34374i	0.158532	−	0.987354i	$-0.449324\pi$
$194$		0			0
$195$	−12.9434	−	16.5742i	−0.926896	−	1.18691i
$196$		0			0
$197$		−	9.88306i		−	0.704139i	−0.935974	−	0.352069i	$-0.885478\pi$
$197$		−	9.88306i		−	0.704139i	0.935974	−	0.352069i	$-0.114522\pi$
$198$		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
$201$	−2.79438	−	19.9145i	−0.197100	−	1.40466i
$202$		0			0
$203$		0			0
$204$		0			0
$205$	−10.5618	+	18.2936i	−0.737670	+	1.27768i
$206$		0			0
$207$	−10.2388	+	10.5934i	−0.711646	+	0.736290i
$208$		0			0
$209$	11.6118	+	20.1123i	0.803208	+	1.39120i
$210$		0			0
$211$	6.08453	−	10.5387i	0.418876	−	0.725514i	−0.576951	−	0.816779i	$-0.695758\pi$
$211$	6.08453	−	10.5387i	0.418876	−	0.725514i	0.995827	+	0.0912645i	$0.0290909\pi$
$212$		0			0
$213$	6.77791	−	16.7654i	0.464415	−	1.14875i
$214$		0			0
$215$	15.5304	+	26.8994i	1.05916	+	1.83453i
$216$		0			0
$217$		0			0
$218$		0			0
$219$	−16.8020	−	21.5152i	−1.13537	−	1.45386i
$220$		0			0
$221$	5.91452	−	3.41475i	0.397854	−	0.229701i
$222$		0			0
$223$	0.714485	−	0.412508i	0.0478455	−	0.0276236i	−0.475886	−	0.879507i	$-0.657873\pi$
$223$	0.714485	−	0.412508i	0.0478455	−	0.0276236i	0.523732	+	0.851883i	$0.324539\pi$
$224$		0			0
$225$	8.24056	+	7.96475i	0.549371	+	0.530983i
$226$		0			0
$227$	−0.333557			−0.0221390			−0.0110695	−	0.999939i	$-0.503524\pi$
$227$	−0.333557			−0.0221390			−0.0110695	+	0.999939i	$0.503524\pi$
$228$		0			0
$229$			14.4214i			0.952996i	0.879176	+	0.476498i	$0.158094\pi$
$229$			14.4214i			0.952996i	−0.879176	+	0.476498i	$0.841906\pi$
$230$		0			0
$231$		0			0
$232$		0			0
$233$	12.7953	−	7.38739i	0.838250	−	0.483964i	−0.0184192	−	0.999830i	$-0.505863\pi$
$233$	12.7953	−	7.38739i	0.838250	−	0.483964i	0.856669	+	0.515867i	$0.172530\pi$
$234$		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	−0.458707	−	0.888588i	$-0.651687\pi$
$239$	−22.5339	−	13.0100i	−1.45760	−	0.841545i	−0.998893	+	0.0470423i	$0.985020\pi$
$240$		0			0
$241$		−	1.92021i		−	0.123692i	−0.998086	−	0.0618458i	$-0.980301\pi$
$241$		−	1.92021i		−	0.123692i	0.998086	−	0.0618458i	$-0.0196987\pi$
$242$		0			0
$243$	−5.34748	+	14.6426i	−0.343041	+	0.939320i
$244$		0			0
$245$		0			0
$246$		0			0
$247$	−20.0804			−1.27768
$248$		0			0
$249$	−1.94462	−	13.8585i	−0.123235	−	0.878249i
$250$		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
$255$	−6.77277	+	5.28909i	−0.424127	+	0.331216i
$256$		0			0
$257$	−15.0073			−0.936129			−0.468064	−	0.883694i	$-0.655048\pi$
$257$	−15.0073			−0.936129			−0.468064	+	0.883694i	$0.655048\pi$
$258$		0			0
$259$		0			0
$260$		0			0
$261$	0.801751	+	0.200269i	0.0496271	+	0.0123964i
$262$		0			0
$263$		−	7.05534i		−	0.435051i	−0.976055	−	0.217525i	$-0.930202\pi$
$263$		−	7.05534i		−	0.435051i	0.976055	−	0.217525i	$-0.0697985\pi$
$264$		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	−0.424865	−	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
$275$			18.0622i			1.08919i
$276$		0			0
$277$	13.5815			0.816032			0.408016	−	0.912975i	$-0.366221\pi$
$277$	13.5815			0.816032			0.408016	+	0.912975i	$0.366221\pi$
$278$		0			0
$279$	4.66644	+	1.16563i	0.279372	+	0.0697844i
$280$		0			0
$281$	−3.95777	+	2.28502i	−0.236101	+	0.136313i	−0.613383	−	0.789785i	$-0.710192\pi$
$281$	−3.95777	+	2.28502i	−0.236101	+	0.136313i	0.377283	+	0.926098i	$0.376859\pi$
$282$		0			0
$283$	−17.6685	+	10.2009i	−1.05029	+	0.606383i	−0.922729	−	0.385449i	$-0.874047\pi$
$283$	−17.6685	+	10.2009i	−1.05029	+	0.606383i	−0.127556	+	0.991831i	$0.540713\pi$
$284$		0			0
$285$	25.0212	−	3.51096i	1.48213	−	0.207971i
$286$		0			0
$287$		0			0
$288$		0			0
$289$	7.10462	+	12.3056i	0.417919	+	0.723857i
$290$		0			0
$291$	13.8795	−	1.94756i	0.813629	−	0.114168i
$292$		0			0
$293$	6.41037	−	11.1031i	0.374498	−	0.648649i	−0.615754	−	0.787939i	$-0.711148\pi$
$293$	6.41037	−	11.1031i	0.374498	−	0.648649i	0.990252	+	0.139289i	$0.0444818\pi$
$294$		0			0
$295$	−4.08144	−	7.06926i	−0.237631	−	0.411589i
$296$		0			0
$297$	−22.4505	+	9.97806i	−1.30271	+	0.578986i
$298$		0			0
$299$	10.0383	−	17.3868i	0.580529	−	1.00551i
$300$		0			0
$301$		0			0
$302$		0			0
$303$	11.7340	+	4.74380i	0.674099	+	0.272524i
$304$		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
$311$	−1.04458	−	1.80926i	−0.0592326	−	0.102594i	0.834889	−	0.550419i	$-0.185532\pi$
$311$	−1.04458	−	1.80926i	−0.0592326	−	0.102594i	−0.894121	+	0.447825i	$0.852199\pi$
$312$		0			0
$313$	−19.4066	−	11.2044i	−1.09692	−	0.633309i	−0.161512	−	0.986871i	$-0.551637\pi$
$313$	−19.4066	−	11.2044i	−1.09692	−	0.633309i	−0.935411	+	0.353562i	$0.884970\pi$
$314$		0			0
$315$		0			0
$316$		0			0
$317$	−3.01788	−	1.74237i	−0.169501	−	0.0978614i	0.412850	−	0.910799i	$-0.364534\pi$
$317$	−3.01788	−	1.74237i	−0.169501	−	0.0978614i	−0.582350	+	0.812938i	$0.697867\pi$
$318$		0			0
$319$	0.651207	+	1.12792i	0.0364606	+	0.0631516i
$320$		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
$327$	−7.70473	+	6.01690i	−0.426073	+	0.332735i
$328$		0			0
$329$		0			0
$330$		0			0
$331$	2.28857	−	3.96392i	0.125791	−	0.217877i	−0.796251	−	0.604967i	$-0.793186\pi$
$331$	2.28857	−	3.96392i	0.125791	−	0.217877i	0.922042	+	0.387090i	$0.126520\pi$
$332$		0			0
$333$	2.46727	−	9.87737i	0.135205	−	0.541276i
$334$		0			0
$335$	−17.2405	−	29.8615i	−0.941951	−	1.63151i
$336$		0			0
$337$	−14.7062	+	25.4720i	−0.801100	+	1.38755i	0.117793	+	0.993038i	$0.462418\pi$
$337$	−14.7062	+	25.4720i	−0.801100	+	1.38755i	−0.918893	+	0.394508i	$0.870915\pi$
$338$		0			0
$339$	14.3300	+	18.3497i	0.778297	+	0.996621i
$340$		0			0
$341$	3.79023	+	6.56486i	0.205252	+	0.355507i
$342$		0			0
$343$		0			0
$344$		0			0
$345$	−9.46825	+	23.4201i	−0.509753	+	1.26089i
$346$		0			0
$347$	17.0245	−	9.82911i	0.913924	−	0.527654i	0.0322323	−	0.999480i	$-0.489738\pi$
$347$	17.0245	−	9.82911i	0.913924	−	0.527654i	0.881692	+	0.471826i	$0.156405\pi$
$348$		0			0
$349$	−8.47286	+	4.89181i	−0.453542	+	0.261852i	−0.709325	−	0.704882i	$-0.751000\pi$
$349$	−8.47286	+	4.89181i	−0.453542	+	0.261852i	0.255783	+	0.966734i	$0.417667\pi$
$350$		0			0
$351$	2.23424	−	21.1249i	0.119255	−	1.12756i
$352$		0			0
$353$	−25.0645			−1.33405			−0.667023	−	0.745037i	$-0.732432\pi$
$353$	−25.0645			−1.33405			−0.667023	+	0.745037i	$0.732432\pi$
$354$		0			0
$355$		−	31.0074i		−	1.64570i
$356$		0			0
$357$		0			0
$358$		0			0
$359$	8.09861	−	4.67574i	0.427428	−	0.246776i	−0.270822	−	0.962629i	$-0.587296\pi$
$359$	8.09861	−	4.67574i	0.427428	−	0.246776i	0.698251	+	0.715853i	$0.253962\pi$
$360$		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
$367$		−	21.8850i		−	1.14239i	−0.820815	−	0.571194i	$-0.806480\pi$
$367$		−	21.8850i		−	1.14239i	0.820815	−	0.571194i	$-0.193520\pi$
$368$		0			0
$369$	−20.5139	+	5.87261i	−1.06791	+	0.305716i
$370$		0			0
$371$		0			0
$372$		0			0
$373$	4.61644			0.239030			0.119515	−	0.992832i	$-0.461866\pi$
$373$	4.61644			0.239030			0.119515	+	0.992832i	$0.461866\pi$
$374$		0			0
$375$	−5.62655	−	2.27470i	−0.290554	−	0.117465i
$376$		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
$381$	−20.5108	−	8.29209i	−1.05080	−	0.424817i
$382$		0			0
$383$	21.9977			1.12403			0.562015	−	0.827127i	$-0.310026\pi$
$383$	21.9977			1.12403			0.562015	+	0.827127i	$0.310026\pi$
$384$		0			0
$385$		0			0
$386$		0			0
$387$	−7.60373	+	30.4405i	−0.386519	+	1.54738i
$388$		0			0
$389$			9.82776i			0.498287i	0.968467	+	0.249144i	$0.0801491\pi$
$389$			9.82776i			0.498287i	−0.968467	+	0.249144i	$0.919851\pi$
$390$		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
$401$			17.0719i			0.852529i	0.904598	+	0.426265i	$0.140171\pi$
$401$			17.0719i			0.852529i	−0.904598	+	0.426265i	$0.859829\pi$
$402$		0			0
$403$	−6.55444			−0.326500
$404$		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
$409$	−16.9484	+	9.78516i	−0.838044	+	0.483845i	−0.856599	−	0.515983i	$-0.827427\pi$
$409$	−16.9484	+	9.78516i	−0.838044	+	0.483845i	0.0185546	+	0.999828i	$0.494094\pi$
$410$		0			0
$411$	−5.84288	+	14.4526i	−0.288208	+	0.712893i
$412$		0			0
$413$		0			0
$414$		0			0
$415$	−11.9977	−	20.7807i	−0.588946	−	1.02008i
$416$		0			0
$417$	1.90681	+	2.44170i	0.0933769	+	0.119571i
$418$		0			0
$419$	10.3073	−	17.8529i	0.503547	−	0.872169i	−0.496445	−	0.868068i	$-0.665361\pi$
$419$	10.3073	−	17.8529i	0.503547	−	0.872169i	0.999992	−	0.00410056i	$-0.00130525\pi$
$420$		0			0
$421$	0.704748	+	1.22066i	0.0343473	+	0.0594913i	0.882688	−	0.469959i	$-0.155731\pi$
$421$	0.704748	+	1.22066i	0.0343473	+	0.0594913i	−0.848341	+	0.529451i	$0.822398\pi$
$422$		0			0
$423$	31.7190	−	9.08035i	1.54223	−	0.441502i
$424$		0			0
$425$	−3.19091	+	5.52682i	−0.154782	+	0.268090i
$426$		0			0
$427$		0			0
$428$		0			0
$429$	26.3865	−	20.6062i	1.27395	−	0.994876i
$430$		0			0
$431$	−11.6666	−	6.73569i	−0.561959	−	0.324447i	0.191973	−	0.981400i	$-0.438512\pi$
$431$	−11.6666	−	6.73569i	−0.561959	−	0.324447i	−0.753931	+	0.656953i	$0.771845\pi$
$432$		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
$437$	12.0608	+	20.8899i	0.576944	+	0.999297i
$438$		0			0
$439$	−8.75023	−	5.05195i	−0.417626	−	0.241116i	0.276435	−	0.961033i	$-0.410847\pi$
$439$	−8.75023	−	5.05195i	−0.417626	−	0.241116i	−0.694061	+	0.719916i	$0.744180\pi$
$440$		0			0
$441$		0			0
$442$		0			0
$443$	−25.1220	−	14.5042i	−1.19358	−	0.689115i	−0.234466	−	0.972124i	$-0.575334\pi$
$443$	−25.1220	−	14.5042i	−1.19358	−	0.689115i	−0.959117	+	0.283009i	$0.908667\pi$
$444$		0			0
$445$	13.6873	+	23.7072i	0.648842	+	1.12383i
$446$		0			0
$447$	8.37916	−	20.7262i	0.396321	−	0.980314i
$448$		0			0
$449$		−	7.94881i		−	0.375127i	−0.982252	−	0.187564i	$-0.939941\pi$
$449$		−	7.94881i		−	0.375127i	0.982252	−	0.187564i	$-0.0600591\pi$
$450$		0			0
$451$	−29.1239	−	16.8147i	−1.37139	−	0.791772i
$452$		0			0
$453$	−20.8227	−	8.41819i	−0.978337	−	0.395521i
$454$		0			0
$455$		0			0
$456$		0			0
$457$	6.98084	−	12.0912i	0.326550	−	0.565601i	−0.655275	−	0.755391i	$-0.727447\pi$
$457$	6.98084	−	12.0912i	0.326550	−	0.565601i	0.981825	+	0.189789i	$0.0607805\pi$
$458$		0			0
$459$	−8.63231	−	0.912985i	−0.402922	−	0.0426145i
$460$		0			0
$461$	−16.4030	−	28.4108i	−0.763964	−	1.32322i	−0.940793	−	0.338983i	$-0.889917\pi$
$461$	−16.4030	−	28.4108i	−0.763964	−	1.32322i	0.176829	−	0.984242i	$-0.443416\pi$
$462$		0			0
$463$	−13.8812	+	24.0429i	−0.645112	+	1.11737i	0.339163	+	0.940727i	$0.389856\pi$
$463$	−13.8812	+	24.0429i	−0.645112	+	1.11737i	−0.984276	+	0.176640i	$0.943477\pi$
$464$		0			0
$465$	8.16719	−	1.14601i	0.378744	−	0.0531451i
$466$		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
$469$		0			0
$470$		0			0
$471$	−29.4555	+	4.13318i	−1.35724	+	0.190447i
$472$		0			0
$473$	−42.8245	+	24.7247i	−1.96907	+	1.13684i
$474$		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
$479$	−2.42425			−0.110767			−0.0553834	−	0.998465i	$-0.517638\pi$
$479$	−2.42425			−0.110767			−0.0553834	+	0.998465i	$0.517638\pi$
$480$		0			0
$481$			13.8737i			0.632584i
$482$		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	0.432423	−	0.901671i	$-0.357659\pi$
$491$	−2.93014	−	1.69172i	−0.132235	−	0.0763462i	−0.564658	+	0.825325i	$0.690992\pi$
$492$		0			0
$493$			0.460174i			0.0207252i
$494$		0			0
$495$	−29.2762	+	30.2900i	−1.31587	+	1.36143i
$496$		0			0
$497$		0			0
$498$		0			0
$499$	39.5603			1.77096			0.885481	−	0.464676i	$-0.153829\pi$
$499$	39.5603			1.77096			0.885481	+	0.464676i	$0.153829\pi$
$500$		0			0
$501$	−15.8263	+	12.3593i	−0.707067	+	0.552174i
$502$		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
$507$	0.893668	+	6.36882i	0.0396892	+	0.282849i
$508$		0			0
$509$	−20.3916			−0.903841			−0.451921	−	0.892058i	$-0.649261\pi$
$509$	−20.3916			−0.903841			−0.451921	+	0.892058i	$0.649261\pi$
$510$		0			0
$511$		0			0
$512$		0			0
$513$	20.6385	+	15.0153i	0.911210	+	0.662941i
$514$		0			0
$515$		−	20.8643i		−	0.919391i
$516$		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	−0.690480	−	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
$527$			2.67836i			0.116671i
$528$		0			0
$529$	−1.11695			−0.0485631
$530$		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
$535$	36.4162	−	21.0249i	1.57441	−	0.908986i
$536$		0			0
$537$	15.7156	+	20.1241i	0.678180	+	0.868419i
$538$		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
$543$	0.0541189	−	0.133865i	0.00232247	−	0.00574471i
$544$		0			0
$545$	−8.38108	+	14.5165i	−0.359006	+	0.621817i
$546$		0			0
$547$	−5.72451	−	9.91513i	−0.244762	−	0.423940i	0.717303	−	0.696762i	$-0.245377\pi$
$547$	−5.72451	−	9.91513i	−0.244762	−	0.423940i	−0.962065	+	0.272821i	$0.912043\pi$
$548$		0			0
$549$	5.94730	+	20.7748i	0.253824	+	0.886646i
$550$		0			0
$551$	0.676511	−	1.17175i	0.0288203	−	0.0499183i
$552$		0			0
$553$		0			0
$554$		0			0
$555$	−2.42575	−	17.2873i	−0.102967	−	0.733807i
$556$		0			0
$557$	32.9159	+	19.0040i	1.39469	+	0.805226i	0.993830	−	0.110912i	$-0.0353771\pi$
$557$	32.9159	+	19.0040i	1.39469	+	0.805226i	0.400863	+	0.916138i	$0.368710\pi$
$558$		0			0
$559$		−	42.7565i		−	1.80841i
$560$		0			0
$561$	−8.42035	−	10.7824i	−0.355508	−	0.455233i
$562$		0			0
$563$	8.88438	+	15.3882i	0.374432	+	0.648535i	0.990242	−	0.139360i	$-0.0445044\pi$
$563$	8.88438	+	15.3882i	0.374432	+	0.648535i	−0.615810	+	0.787895i	$0.711171\pi$
$564$		0			0
$565$	34.5727	+	19.9605i	1.45448	+	0.839746i
$566$		0			0
$567$		0			0
$568$		0			0
$569$	−33.7404	−	19.4801i	−1.41447	−	0.816646i	−0.418667	−	0.908140i	$-0.637503\pi$
$569$	−33.7404	−	19.4801i	−1.41447	−	0.816646i	−0.995806	+	0.0914936i	$0.970836\pi$
$570$		0			0
$571$	−8.45245	−	14.6401i	−0.353724	−	0.612668i	0.633175	−	0.774009i	$-0.281752\pi$
$571$	−8.45245	−	14.6401i	−0.353724	−	0.612668i	−0.986899	+	0.161341i	$0.948418\pi$
$572$		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
$579$	−5.18808	−	36.9734i	−0.215609	−	1.53656i
$580$		0			0
$581$		0			0
$582$		0			0
$583$	1.93099	−	3.34458i	0.0799736	−	0.138518i
$584$		0			0
$585$	−10.0246	−	35.0174i	−0.414466	−	1.44779i
$586$		0			0
$587$	11.6343	+	20.1513i	0.480200	+	0.831731i	0.999742	−	0.0227138i	$-0.00723065\pi$
$587$	11.6343	+	20.1513i	0.480200	+	0.831731i	−0.519542	+	0.854445i	$0.673897\pi$
$588$		0			0
$589$	3.93750	−	6.81995i	0.162242	−	0.281011i
$590$		0			0
$591$	6.41595	−	15.8701i	0.263917	−	0.652809i
$592$		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
$595$		0			0
$596$		0			0
$597$	11.2588	+	14.4171i	0.460793	+	0.590053i
$598$		0			0
$599$	27.9591	−	16.1422i	1.14238	−	0.659552i	0.195359	−	0.980732i	$-0.437413\pi$
$599$	27.9591	−	16.1422i	1.14238	−	0.659552i	0.947018	+	0.321180i	$0.104079\pi$
$600$		0			0
$601$	−14.7559	+	8.51933i	−0.601906	+	0.347511i	−0.769791	−	0.638296i	$-0.779640\pi$
$601$	−14.7559	+	8.51933i	−0.601906	+	0.347511i	0.167885	+	0.985807i	$0.446306\pi$
$602$		0			0
$603$	8.44102	−	33.7925i	0.343745	−	1.37614i
$604$		0			0
$605$	−33.7231			−1.37104
$606$		0			0
$607$			9.75021i			0.395749i	0.980227	+	0.197874i	$0.0634038\pi$
$607$			9.75021i			0.395749i	−0.980227	+	0.197874i	$0.936596\pi$
$608$		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	0.441680	−	0.897173i	$-0.354383\pi$
$617$	−2.84301	−	1.64141i	−0.114455	−	0.0660807i	−0.556135	+	0.831092i	$0.687716\pi$
$618$		0			0
$619$			17.3098i			0.695740i	0.937543	+	0.347870i	$0.113095\pi$
$619$			17.3098i			0.695740i	−0.937543	+	0.347870i	$0.886905\pi$
$620$		0			0
$621$	−23.3184	+	10.3638i	−0.935736	+	0.415886i
$622$		0			0
$623$		0			0
$624$		0			0
$625$	−29.5071			−1.18028
$626$		0			0
$627$	5.58952	+	39.8344i	0.223224	+	1.59083i
$628$		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
$633$	16.6120	−	12.9729i	0.660270	−	0.515628i
$634$		0			0
$635$	−37.9344			−1.50538
$636$		0			0
$637$		0			0
$638$		0			0
$639$	21.7678	−	22.5216i	0.861120	−	0.890941i
$640$		0			0
$641$			20.7601i			0.819976i	0.912091	+	0.409988i	$0.134467\pi$
$641$			20.7601i			0.819976i	−0.912091	+	0.409988i	$0.865533\pi$
$642$		0			0
$643$	−17.2553	−	9.96236i	−0.680483	−	0.392877i	0.119554	−	0.992828i	$-0.461854\pi$
$643$	−17.2553	−	9.96236i	−0.680483	−	0.392877i	−0.800037	+	0.599950i	$0.795187\pi$
$644$		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
$651$		0			0
$652$		0			0
$653$			15.9250i			0.623193i	0.950215	+	0.311596i	$0.100864\pi$
$653$			15.9250i			0.623193i	−0.950215	+	0.311596i	$0.899136\pi$
$654$		0			0
$655$	−39.8493			−1.55704
$656$		0			0
$657$	−13.0131	−	45.4565i	−0.507688	−	1.77343i
$658$		0			0
$659$	2.80283	−	1.61822i	0.109183	−	0.0630368i	−0.444414	−	0.895821i	$-0.646588\pi$
$659$	2.80283	−	1.61822i	0.109183	−	0.0630368i	0.553597	+	0.832785i	$0.313255\pi$
$660$		0			0
$661$	−7.71194	+	4.45249i	−0.299960	+	0.173182i	−0.642425	−	0.766349i	$-0.722072\pi$
$661$	−7.71194	+	4.45249i	−0.299960	+	0.173182i	0.342465	+	0.939531i	$0.388738\pi$
$662$		0			0
$663$	11.7143	−	1.64374i	0.454945	−	0.0638375i
$664$		0			0
$665$		0			0
$666$		0			0
$667$	0.676383	+	1.17153i	0.0261896	+	0.0453618i
$668$		0			0
$669$	1.41511	−	0.198567i	0.0547112	−	0.00767703i
$670$		0			0
$671$	−17.0285	+	29.4943i	−0.657379	+	1.13861i
$672$		0			0
$673$	−13.2311	−	22.9169i	−0.510021	−	0.883382i	−0.999933	−	0.0116101i	$-0.996304\pi$
$673$	−13.2311	−	22.9169i	−0.510021	−	0.883382i	0.489912	−	0.871772i	$-0.337029\pi$
$674$		0			0
$675$	8.06199	+	18.1394i	0.310306	+	0.698184i
$676$		0			0
$677$	−4.46424	+	7.73229i	−0.171575	+	0.297176i	−0.938971	−	0.343997i	$-0.888219\pi$
$677$	−4.46424	+	7.73229i	−0.171575	+	0.297176i	0.767396	+	0.641174i	$0.221552\pi$
$678$		0			0
$679$		0			0
$680$		0			0
$681$	−0.535622	−	0.216541i	−0.0205251	−	0.00829786i
$682$		0			0
$683$	−32.7902	−	18.9314i	−1.25468	−	0.724390i	−0.282645	−	0.959225i	$-0.591212\pi$
$683$	−32.7902	−	18.9314i	−1.25468	−	0.724390i	−0.972035	+	0.234834i	$0.924545\pi$
$684$		0			0
$685$			26.7298i			1.02129i
$686$		0			0
$687$	−9.36221	+	23.1578i	−0.357191	+	0.883525i
$688$		0			0
$689$	1.66963	+	2.89189i	0.0636080	+	0.110172i
$690$		0			0
$691$	4.94211	+	2.85333i	0.188007	+	0.108546i	0.591049	−	0.806636i	$-0.298714\pi$
$691$	4.94211	+	2.85333i	0.188007	+	0.108546i	−0.403042	+	0.915181i	$0.632047\pi$
$692$		0			0
$693$		0			0
$694$		0			0
$695$	4.60039	+	2.65604i	0.174503	+	0.100749i
$696$		0			0
$697$	−5.94103	−	10.2902i	−0.225032	−	0.389768i
$698$		0			0
$699$	25.3424	−	3.55602i	0.958537	−	0.134501i
$700$		0			0
$701$			8.19949i			0.309690i	0.987939	+	0.154845i	$0.0494879\pi$
$701$			8.19949i			0.309690i	−0.987939	+	0.154845i	$0.950512\pi$
$702$		0			0
$703$	−14.4357	−	8.33444i	−0.544452	−	0.314339i
$704$		0			0
$705$	44.5869	−	34.8195i	1.67924	−	1.31138i
$706$		0			0
$707$		0			0
$708$		0			0
$709$	−10.0757	+	17.4517i	−0.378402	+	0.655412i	−0.990830	−	0.135115i	$-0.956860\pi$
$709$	−10.0757	+	17.4517i	−0.378402	+	0.655412i	0.612428	+	0.790527i	$0.290193\pi$
$710$		0			0
$711$	35.4844	−	10.1583i	1.33077	−	0.380965i
$712$		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
$717$	−27.7388	−	35.5200i	−1.03593	−	1.32652i
$718$		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
$721$		0			0
$722$		0			0
$723$	1.24657	−	3.08345i	0.0463606	−	0.114675i
$724$		0			0
$725$	0.911330	−	0.526157i	0.0338460	−	0.0195410i
$726$		0			0
$727$	13.7848	−	7.95865i	0.511249	−	0.295170i	−0.222098	−	0.975024i	$-0.571290\pi$
$727$	13.7848	−	7.95865i	0.511249	−	0.295170i	0.733347	+	0.679854i	$0.237957\pi$
$728$		0			0
$729$	−18.0927	+	20.0413i	−0.670099	+	0.742271i
$730$		0			0
$731$	−17.4717			−0.646213
$732$		0			0
$733$			4.24025i			0.156617i	0.996929	+	0.0783086i	$0.0249519\pi$
$733$			4.24025i			0.156617i	−0.996929	+	0.0783086i	$0.975048\pi$
$734$		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	0.844479	−	0.535589i	$-0.179910\pi$
$743$	21.8850	+	12.6353i	0.802884	+	0.463545i	−0.0415945	+	0.999135i	$0.513244\pi$
$744$		0			0
$745$		−	38.3327i		−	1.40440i
$746$		0			0
$747$	5.87413	−	23.5163i	0.214923	−	0.860416i
$748$		0			0
$749$		0			0
$750$		0			0
$751$	47.5460			1.73498			0.867490	−	0.497455i	$-0.165732\pi$
$751$	47.5460			1.73498			0.867490	+	0.497455i	$0.165732\pi$
$752$		0			0
$753$	16.0204	+	6.47670i	0.583814	+	0.236024i
$754$		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
$759$	−37.2853	−	15.0737i	−1.35337	−	0.547139i
$760$		0			0
$761$	8.24283			0.298802			0.149401	−	0.988777i	$-0.452265\pi$
$761$	8.24283			0.298802			0.149401	+	0.988777i	$0.452265\pi$
$762$		0			0
$763$		0			0
$764$		0			0
$765$	−14.3092	+	4.09638i	−0.517352	+	0.148105i
$766$		0			0
$767$			11.2365i			0.405728i
$768$		0			0
$769$	−20.2182	−	11.6730i	−0.729086	−	0.420938i	0.0890020	−	0.996031i	$-0.471632\pi$
$769$	−20.2182	−	11.6730i	−0.729086	−	0.420938i	−0.818088	+	0.575094i	$0.804966\pi$
$770$		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
$777$		0			0
$778$		0			0
$779$			34.9361i			1.25171i
$780$		0			0
$781$	49.3644			1.76640
$782$		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
$787$	7.19975	−	4.15678i	0.256643	−	0.148173i	−0.366159	−	0.930552i	$-0.619327\pi$
$787$	7.19975	−	4.15678i	0.256643	−	0.148173i	0.622802	+	0.782379i	$0.285994\pi$
$788$		0			0
$789$	4.58023	−	11.3294i	0.163061	−	0.403337i
$790$		0			0
$791$		0			0
$792$		0			0
$793$	−14.7237	−	25.5022i	−0.522854	−	0.905610i
$794$		0			0
$795$	−2.58609	−	3.31153i	−0.0917191	−	0.117448i
$796$		0			0
$797$	−0.426036	+	0.737916i	−0.0150910	+	0.0261383i	−0.873472	−	0.486874i	$-0.838137\pi$
$797$	−0.426036	+	0.737916i	−0.0150910	+	0.0261383i	0.858381	+	0.513012i	$0.171470\pi$
$798$		0			0
$799$	9.18614	+	15.9109i	0.324982	+	0.562886i
$800$		0			0
$801$	−6.70136	+	26.8280i	−0.236781	+	0.947921i
$802$		0			0
$803$	37.2595	−	64.5354i	1.31486	−	2.27740i
$804$		0			0
$805$		0			0
$806$		0			0
$807$	40.6522	−	31.7467i	1.43102	−	1.11754i
$808$		0			0
$809$	−31.5580	−	18.2200i	−1.10952	−	0.640581i	−0.170814	−	0.985303i	$-0.554640\pi$
$809$	−31.5580	−	18.2200i	−1.10952	−	0.640581i	−0.938705	+	0.344722i	$0.887973\pi$
$810$		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
$815$	7.51697	+	13.0198i	0.263308	+	0.456063i
$816$		0			0
$817$	44.4885	+	25.6855i	1.55646	+	0.898620i
$818$		0			0
$819$		0			0
$820$		0			0
$821$	−20.9748	−	12.1098i	−0.732025	−	0.422635i	0.0871374	−	0.996196i	$-0.472228\pi$
$821$	−20.9748	−	12.1098i	−0.732025	−	0.422635i	−0.819163	+	0.573561i	$0.805561\pi$
$822$		0			0
$823$	−2.85592	−	4.94660i	−0.0995512	−	0.172428i	0.811948	−	0.583730i	$-0.198407\pi$
$823$	−2.85592	−	4.94660i	−0.0995512	−	0.172428i	−0.911499	+	0.411302i	$0.865074\pi$
$824$		0			0
$825$	−11.7258	+	29.0041i	−0.408239	+	1.00979i
$826$		0			0
$827$			36.4579i			1.26777i	0.773429	+	0.633883i	$0.218540\pi$
$827$			36.4579i			1.26777i	−0.773429	+	0.633883i	$0.781460\pi$
$828$		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
$831$	21.8090	+	8.81692i	0.756545	+	0.305856i
$832$		0			0
$833$		0			0
$834$		0			0
$835$	−17.2156	+	29.8183i	−0.595770	+	1.03190i
$836$		0			0
$837$	6.73660	+	4.90114i	0.232851	+	0.169408i
$838$		0			0
$839$	23.9341	+	41.4550i	0.826295	+	1.43119i	0.900925	+	0.433974i	$0.142889\pi$
$839$	23.9341	+	41.4550i	0.826295	+	1.43119i	−0.0746300	+	0.997211i	$0.523778\pi$
$840$		0			0
$841$	−14.4621	+	25.0490i	−0.498692	+	0.863759i
$842$		0			0
$843$	−7.83874	+	1.09993i	−0.269981	+	0.0378835i
$844$		0			0
$845$	5.51368	+	9.54997i	0.189676	+	0.328529i
$846$		0			0
$847$		0			0
$848$		0			0
$849$	−34.9943	+	4.91036i	−1.20100	+	0.168523i
$850$		0			0
$851$	14.4329	−	8.33286i	0.494755	−	0.285647i
$852$		0			0
$853$	−40.5393	+	23.4054i	−1.38804	+	0.801385i	−0.993094	−	0.117320i	$-0.962570\pi$
$853$	−40.5393	+	23.4054i	−1.38804	+	0.801385i	−0.394945	+	0.918705i	$0.629236\pi$
$854$		0			0
$855$	42.4581	+	10.6056i	1.45204	+	0.362704i
$856$		0			0
$857$	−9.56441			−0.326714			−0.163357	−	0.986567i	$-0.552232\pi$
$857$	−9.56441			−0.326714			−0.163357	+	0.986567i	$0.552232\pi$
$858$		0			0
$859$		−	5.40759i		−	0.184505i	−0.995736	−	0.0922523i	$-0.970593\pi$
$859$		−	5.40759i		−	0.184505i	0.995736	−	0.0922523i	$-0.0294066\pi$
$860$		0			0
$861$		0			0
$862$		0			0
$863$	35.5402	−	20.5191i	1.20980	−	0.698480i	0.247086	−	0.968994i	$-0.420527\pi$
$863$	35.5402	−	20.5191i	1.20980	−	0.698480i	0.962716	+	0.270514i	$0.0871936\pi$
$864$		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
$871$			47.4646i			1.60828i
$872$		0			0
$873$	23.5518	+	5.88301i	0.797109	+	0.199110i
$874$		0			0
$875$		0			0
$876$		0			0
$877$	−14.6502			−0.494701			−0.247351	−	0.968926i	$-0.579560\pi$
$877$	−14.6502			−0.494701			−0.247351	+	0.968926i	$0.579560\pi$
$878$		0			0
$879$	17.5017	−	13.6677i	0.590317	−	0.460999i
$880$		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
$885$	−1.96466	−	14.0014i	−0.0660413	−	0.470651i
$886$		0			0
$887$	26.6844			0.895973			0.447987	−	0.894040i	$-0.352141\pi$
$887$	26.6844			0.895973			0.447987	+	0.894040i	$0.352141\pi$
$888$		0			0
$889$		0			0
$890$		0			0
$891$	−42.5284	+	1.44810i	−1.42475	+	0.0485132i
$892$		0			0
$893$		−	54.0189i		−	1.80767i
$894$		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
$905$		−	0.247582i		−	0.00822989i
$906$		0			0
$907$	−15.9442			−0.529419			−0.264710	−	0.964328i	$-0.585276\pi$
$907$	−15.9442			−0.529419			−0.264710	+	0.964328i	$0.585276\pi$
$908$		0			0
$909$	15.7627	+	15.2351i	0.522815	+	0.505316i
$910$		0			0
$911$	40.9207	−	23.6256i	1.35576	−	0.782750i	0.366713	−	0.930334i	$-0.380483\pi$
$911$	40.9207	−	23.6256i	1.35576	−	0.782750i	0.989050	+	0.147584i	$0.0471496\pi$
$912$		0			0
$913$	33.0833	−	19.1007i	1.09490	−	0.632140i
$914$		0			0
$915$	22.8055	+	29.2028i	0.753927	+	0.965415i
$916$		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
$921$	1.25560	−	3.10578i	0.0413734	−	0.102339i
$922$		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
$927$	14.6471	−	15.1544i	0.481075	−	0.497735i
$928$		0			0
$929$	−16.6186	+	28.7842i	−0.545238	+	0.944380i	0.453354	+	0.891331i	$0.350227\pi$
$929$	−16.6186	+	28.7842i	−0.545238	+	0.944380i	−0.998592	+	0.0530496i	$0.983106\pi$
$930$		0			0
$931$		0			0
$932$		0			0
$933$	−0.502822	−	3.58342i	−0.0164617	−	0.117316i
$934$		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
$941$	27.1201	+	46.9734i	0.884091	+	1.53129i	0.846752	+	0.531988i	$0.178555\pi$
$941$	27.1201	+	46.9734i	0.884091	+	1.53129i	0.0373389	+	0.999303i	$0.488112\pi$
$942$		0			0
$943$	−30.2498	−	17.4647i	−0.985069	−	0.568730i
$944$		0			0
$945$		0			0
$946$		0			0
$947$	18.2427	+	10.5324i	0.592807	+	0.342257i	0.766207	−	0.642594i	$-0.222142\pi$
$947$	18.2427	+	10.5324i	0.592807	+	0.342257i	−0.173399	+	0.984852i	$0.555475\pi$
$948$		0			0
$949$	32.2164	+	55.8005i	1.04579	+	1.81136i
$950$		0			0
$951$	−3.71495	−	4.75705i	−0.120465	−	0.154258i
$952$		0			0
$953$			4.50028i			0.145778i	0.997340	+	0.0728892i	$0.0232219\pi$
$953$			4.50028i			0.145778i	−0.997340	+	0.0728892i	$0.976778\pi$
$954$		0			0
$955$	39.6989	+	22.9201i	1.28462	+	0.741679i
$956$		0			0
$957$	0.313468	+	2.23396i	0.0101330	+	0.0722137i
$958$		0			0
$959$		0			0
$960$		0			0
$961$	−14.2148	+	24.6207i	−0.458541	+	0.794216i
$962$		0			0
$963$	41.2101	+	10.2939i	1.32798	+	0.331715i
$964$		0			0
$965$	−32.0090	−	55.4411i	−1.03040	−	1.78471i
$966$		0			0
$967$	−10.8811	+	18.8466i	−0.349912	+	0.606065i	−0.986233	−	0.165359i	$-0.947122\pi$
$967$	−10.8811	+	18.8466i	−0.349912	+	0.606065i	0.636322	+	0.771424i	$0.280455\pi$
$968$		0			0
$969$	−5.32689	+	13.1763i	−0.171124	+	0.423283i
$970$		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
$973$		0			0
$974$		0			0
$975$	−16.6492	−	21.3196i	−0.533202	−	0.682773i
$976$		0			0
$977$	−21.7766	+	12.5727i	−0.696695	+	0.402237i	−0.806115	−	0.591758i	$-0.798434\pi$
$977$	−21.7766	+	12.5727i	−0.696695	+	0.402237i	0.109420	+	0.993996i	$0.465101\pi$
$978$		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
$983$	36.2142			1.15505			0.577527	−	0.816372i	$-0.304018\pi$
$983$	36.2142			1.15505			0.577527	+	0.816372i	$0.304018\pi$
$984$		0			0
$985$		−	29.3515i		−	0.935216i
$986$		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
$997$			17.4836i			0.553712i	0.960911	+	0.276856i	$0.0892925\pi$
$997$			17.4836i			0.553712i	−0.960911	+	0.276856i	$0.910708\pi$
$998$		0			0
$999$	10.3742	−	14.2592i	0.328224	−	0.451143i

Twists

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

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
252.2.w.a.5.3	✓	16	7.2	even	3
252.2.w.a.101.3	yes	16	63.20	even	6
252.2.bm.a.173.1	yes	16	63.2	odd	6
252.2.bm.a.185.1	yes	16	7.6	odd	2
756.2.w.a.341.7		16	21.2	odd	6
756.2.w.a.521.7		16	63.34	odd	6
756.2.bm.a.17.7		16	21.20	even	2
756.2.bm.a.89.7		16	63.16	even	3
1008.2.ca.d.257.6		16	28.23	odd	6
1008.2.ca.d.353.6		16	252.83	odd	6
1008.2.df.d.689.8		16	28.27	even	2
1008.2.df.d.929.8		16	252.191	even	6
1764.2.w.b.509.6		16	7.5	odd	6
1764.2.w.b.1109.6		16	9.2	odd	6
1764.2.x.a.293.4		16	7.4	even	3
1764.2.x.a.1469.4		16	63.38	even	6
1764.2.x.b.293.5		16	7.3	odd	6
1764.2.x.b.1469.5		16	63.11	odd	6
1764.2.bm.a.1685.8		16	63.47	even	6	inner
1764.2.bm.a.1697.8		16	1.1	even	1	trivial
2268.2.t.a.1781.7		16	63.13	odd	6
2268.2.t.a.2105.7		16	63.23	odd	6
2268.2.t.b.1781.2		16	63.41	even	6
2268.2.t.b.2105.2		16	63.58	even	3
3024.2.ca.d.2033.7		16	252.223	even	6
3024.2.ca.d.2609.7		16	84.23	even	6
3024.2.df.d.17.7		16	84.83	odd	2
3024.2.df.d.1601.7		16	252.79	odd	6
5292.2.w.b.521.2		16	9.7	even	3
5292.2.w.b.1097.2		16	21.5	even	6
5292.2.x.a.881.7		16	21.11	odd	6
5292.2.x.a.4409.7		16	63.52	odd	6
5292.2.x.b.881.2		16	21.17	even	6
5292.2.x.b.4409.2		16	63.25	even	3
5292.2.bm.a.2285.2		16	3.2	odd	2
5292.2.bm.a.4625.2		16	63.61	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:	\( N \)	\(=\)	\( 1764 = 2^{2} \cdot 3^{2} \cdot 7^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1764.bm (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(1.60579 + 0.649187i) q^{3} +2.96988 q^{5} +(2.15711 + 2.08491i) q^{9} +O(q^{10})\)	\(q+(1.60579 + 0.649187i) q^{3} +2.96988 q^{5} +(2.15711 + 2.08491i) q^{9} +4.72811i q^{11} +(-3.54045 - 2.04408i) q^{13} +(4.76900 + 1.92801i) q^{15} +(-0.835278 + 1.44674i) q^{17} +(4.25377 - 2.45592i) q^{19} +4.91090i q^{23} +3.82018 q^{25} +(2.11037 + 4.74830i) q^{27} +(0.238557 - 0.137731i) q^{29} +(1.38847 - 0.801636i) q^{31} +(-3.06943 + 7.59235i) q^{33} +(-1.69681 - 2.93896i) q^{37} +(-4.35823 - 5.58078i) q^{39} +(-3.55632 + 6.15972i) q^{41} +(5.22930 + 9.05742i) q^{43} +(6.40637 + 6.19194i) q^{45} +(5.49885 - 9.52430i) q^{47} +(-2.28049 + 1.78091i) q^{51} +(-0.707381 - 0.408407i) q^{53} +14.0419i q^{55} +(8.42500 - 1.18219i) q^{57} +(-1.37428 - 2.38032i) q^{59} +(6.23807 + 3.60155i) q^{61} +(-10.5147 - 6.07067i) q^{65} +(-5.80513 - 10.0548i) q^{67} +(-3.18809 + 7.88587i) q^{69} -10.4406i q^{71} +(-13.6493 - 7.88042i) q^{73} +(6.13440 + 2.48001i) q^{75} +(6.15163 - 10.6549i) q^{79} +(0.306275 + 8.99479i) q^{81} +(-4.03981 - 6.99715i) q^{83} +(-2.48067 + 4.29665i) q^{85} +(0.472485 - 0.0662987i) q^{87} +(4.60872 + 7.98254i) q^{89} +(2.75001 - 0.385879i) q^{93} +(12.6332 - 7.29377i) q^{95} +(7.00772 - 4.04591i) q^{97} +(-9.85770 + 10.1991i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q+O(q^{10}) \) 16 * q	\( 16 q - 3 q^{13} - 3 q^{15} + 9 q^{17} + 16 q^{25} + 9 q^{27} + 6 q^{29} - 6 q^{31} + 27 q^{33} + q^{37} - 3 q^{39} - 6 q^{41} - 2 q^{43} + 15 q^{45} + 18 q^{47} + 15 q^{51} + 15 q^{57} + 15 q^{59} - 3 q^{61} - 39 q^{65} - 7 q^{67} + 21 q^{69} + 15 q^{75} - q^{79} + 6 q^{85} + 3 q^{87} + 21 q^{89} - 69 q^{93} + 6 q^{95} - 3 q^{97} - 9 q^{99}+O(q^{100}) \) 16 * q - 3 * q^13 - 3 * q^15 + 9 * q^17 + 16 * q^25 + 9 * q^27 + 6 * q^29 - 6 * q^31 + 27 * q^33 + q^37 - 3 * q^39 - 6 * q^41 - 2 * q^43 + 15 * q^45 + 18 * q^47 + 15 * q^51 + 15 * q^57 + 15 * q^59 - 3 * q^61 - 39 * q^65 - 7 * q^67 + 21 * q^69 + 15 * q^75 - q^79 + 6 * q^85 + 3 * q^87 + 21 * q^89 - 69 * q^93 + 6 * q^95 - 3 * q^97 - 9 * q^99

Introduction

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