LMFDB - Embedded newform 728.2.bm.b.673.1

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [728,2,Mod(225,728)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(728, base_ring=CyclotomicField(6)) chi = DirichletCharacter(H, H._module([0, 0, 0, 1])) N = Newforms(chi, 2, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("728.225"); S:= CuspForms(chi, 2); N := Newforms(S);

Level:	$ N $	$=$	$ 728 = 2^{3} \cdot 7 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	728.bm (of order $6$, degree $2$, minimal)

Newform invariants

comment:select newform

sage:traces = [12] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(1)] == traces)

gp:f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$5.81310926715$
Analytic rank:	$0$
Dimension:	$12$
Relative dimension:	$6$ over $\Q(\zeta_{6})$
Coefficient field:	12.0.58891012706304.1
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{12} - 5x^{10} - 2x^{9} + 15x^{8} + 2x^{7} - 30x^{6} + 4x^{5} + 60x^{4} - 16x^{3} - 80x^{2} + 64 $ x^12 - 5x^10 - 2x^9 + 15x^8 + 2x^7 - 30x^6 + 4x^5 + 60x^4 - 16x^3 - 80*x^2 + 64
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			673.1
Root			$0.759479 - 1.19298i$ of defining polynomial
Character	$\chi$	$=$	728.673
Dual form			728.2.bm.b.225.1

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-1.19298 - 2.06630i) q^{3} -0.877521i q^{5} +(-0.866025 - 0.500000i) q^{7} +(-1.34638 + 2.33201i) q^{9} +(-2.75772 + 1.59217i) q^{11} +(-3.31140 + 1.42641i) q^{13} +(-1.81322 + 1.04686i) q^{15} +(-0.485622 + 0.841122i) q^{17} +(-1.37290 - 0.792646i) q^{19} +2.38595i q^{21} +(-1.63221 - 2.82708i) q^{23} +4.22996 q^{25} -0.733037 q^{27} +(4.86534 + 8.42702i) q^{29} -3.94150i q^{31} +(6.57978 + 3.79884i) q^{33} +(-0.438760 + 0.759955i) q^{35} +(-4.47595 + 2.58419i) q^{37} +(6.89781 + 5.14065i) q^{39} +(-3.91400 + 2.25975i) q^{41} +(-3.81322 + 6.60469i) q^{43} +(2.04638 + 1.18148i) q^{45} -4.12013i q^{47} +(0.500000 + 0.866025i) q^{49} +2.31734 q^{51} -2.01686 q^{53} +(1.39716 + 2.41995i) q^{55} +3.78243i q^{57} +(0.901366 + 0.520404i) q^{59} +(-2.50506 + 4.33888i) q^{61} +(2.33201 - 1.34638i) q^{63} +(1.25171 + 2.90582i) q^{65} +(-6.45768 + 3.72834i) q^{67} +(-3.89438 + 6.74527i) q^{69} +(3.53142 + 2.03887i) q^{71} -12.6820i q^{73} +(-5.04624 - 8.74034i) q^{75} +3.18434 q^{77} -9.79759 q^{79} +(4.91365 + 8.51069i) q^{81} +6.81690i q^{83} +(0.738102 + 0.426144i) q^{85} +(11.6085 - 20.1065i) q^{87} +(4.01085 - 2.31567i) q^{89} +(3.58096 + 0.420388i) q^{91} +(-8.14431 + 4.70212i) q^{93} +(-0.695563 + 1.20475i) q^{95} +(-3.55617 - 2.05315i) q^{97} -8.57469i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q - 2 q^{3} + 4 q^{9} + 2 q^{13} + 12 q^{15} + 2 q^{17} + 12 q^{19} - 6 q^{23} + 4 q^{25} + 4 q^{27} + 20 q^{29} + 6 q^{33} - 4 q^{35} - 6 q^{37} + 26 q^{39} - 12 q^{41} - 12 q^{43} + 18 q^{45} + 6 q^{49}+ \cdots - 6 q^{97}+O(q^{100}) $ 12 * q - 2 * q^3 + 4 * q^9 + 2 * q^13 + 12 * q^15 + 2 * q^17 + 12 * q^19 - 6 * q^23 + 4 * q^25 + 4 * q^27 + 20 * q^29 + 6 * q^33 - 4 * q^35 - 6 * q^37 + 26 * q^39 - 12 * q^41 - 12 * q^43 + 18 * q^45 + 6 * q^49 + 16 * q^51 + 20 * q^53 + 24 * q^55 - 12 * q^59 - 4 * q^61 + 8 * q^65 - 6 * q^67 + 36 * q^71 - 10 * q^75 + 20 * q^77 - 20 * q^79 + 18 * q^81 - 36 * q^85 + 32 * q^87 - 36 * q^89 + 2 * q^91 - 42 * q^93 - 26 * q^95 - 6 * q^97

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/728\mathbb{Z}\right)^\times$.

$n$	$183$	$365$	$521$	$561$
$\chi(n)$	$1$	$1$	$1$	$e\left(\frac{5}{6}\right)$

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
$3$	−1.19298	−	2.06630i	−0.688765	−	1.19298i	−0.972238	−	0.233996i	$-0.924820\pi$
$3$	−1.19298	−	2.06630i	−0.688765	−	1.19298i	0.283472	−	0.958980i	$-0.408514\pi$
$4$		0			0
$5$		−	0.877521i		−	0.392439i	−0.980560	−	0.196220i	$-0.937133\pi$
$5$		−	0.877521i		−	0.392439i	0.980560	−	0.196220i	$-0.0628666\pi$
$6$		0			0
$7$	−0.866025	−	0.500000i	−0.327327	−	0.188982i
$7$	−0.866025	−	0.500000i	−0.327327	−	0.188982i
$8$		0			0
$9$	−1.34638	+	2.33201i	−0.448795	+	0.777336i
$10$		0			0
$11$	−2.75772	+	1.59217i	−0.831483	+	0.480057i	−0.854360	−	0.519681i	$-0.826051\pi$
$11$	−2.75772	+	1.59217i	−0.831483	+	0.480057i	0.0228771	+	0.999738i	$0.492717\pi$
$12$		0			0
$13$	−3.31140	+	1.42641i	−0.918416	+	0.395616i
$13$	−3.31140	+	1.42641i	−0.918416	+	0.395616i
$14$		0			0
$15$	−1.81322	+	1.04686i	−0.468171	+	0.270299i
$16$		0			0
$17$	−0.485622	+	0.841122i	−0.117781	+	0.204002i	−0.918888	−	0.394519i	$-0.870911\pi$
$17$	−0.485622	+	0.841122i	−0.117781	+	0.204002i	0.801107	+	0.598521i	$0.204245\pi$
$18$		0			0
$19$	−1.37290	−	0.792646i	−0.314965	−	0.181845i	0.334181	−	0.942509i	$-0.391540\pi$
$19$	−1.37290	−	0.792646i	−0.314965	−	0.181845i	−0.649146	+	0.760664i	$0.724874\pi$
$20$		0			0
$21$			2.38595i			0.520658i
$22$		0			0
$23$	−1.63221	−	2.82708i	−0.340340	−	0.589486i	0.644156	−	0.764894i	$-0.277209\pi$
$23$	−1.63221	−	2.82708i	−0.340340	−	0.589486i	−0.984496	+	0.175408i	$0.943876\pi$
$24$		0			0
$25$	4.22996			0.845991
$26$		0			0
$27$	−0.733037			−0.141073
$28$		0			0
$29$	4.86534	+	8.42702i	0.903471	+	1.56486i	0.822956	+	0.568105i	$0.192323\pi$
$29$	4.86534	+	8.42702i	0.903471	+	1.56486i	0.0805151	+	0.996753i	$0.474343\pi$
$30$		0			0
$31$		−	3.94150i		−	0.707915i	−0.935262	−	0.353957i	$-0.884836\pi$
$31$		−	3.94150i		−	0.707915i	0.935262	−	0.353957i	$-0.115164\pi$
$32$		0			0
$33$	6.57978	+	3.79884i	1.14539	+	0.661293i
$34$		0			0
$35$	−0.438760	+	0.759955i	−0.0741641	+	0.128456i
$36$		0			0
$37$	−4.47595	+	2.58419i	−0.735842	+	0.424838i	−0.820555	−	0.571567i	$-0.806336\pi$
$37$	−4.47595	+	2.58419i	−0.735842	+	0.424838i	0.0847137	+	0.996405i	$0.473002\pi$
$38$		0			0
$39$	6.89781	+	5.14065i	1.10453	+	0.823162i
$40$		0			0
$41$	−3.91400	+	2.25975i	−0.611264	+	0.352913i	−0.773460	−	0.633845i	$-0.781476\pi$
$41$	−3.91400	+	2.25975i	−0.611264	+	0.352913i	0.162196	+	0.986759i	$0.448142\pi$
$42$		0			0
$43$	−3.81322	+	6.60469i	−0.581510	+	1.00721i	0.413790	+	0.910372i	$0.364205\pi$
$43$	−3.81322	+	6.60469i	−0.581510	+	1.00721i	−0.995301	+	0.0968331i	$0.969129\pi$
$44$		0			0
$45$	2.04638	+	1.18148i	0.305057	+	0.176125i
$46$		0			0
$47$		−	4.12013i		−	0.600982i	−0.953785	−	0.300491i	$-0.902849\pi$
$47$		−	4.12013i		−	0.600982i	0.953785	−	0.300491i	$-0.0971505\pi$
$48$		0			0
$49$	0.500000	+	0.866025i	0.0714286	+	0.123718i
$50$		0			0
$51$	2.31734			0.324493
$52$		0			0
$53$	−2.01686			−0.277037			−0.138519	−	0.990360i	$-0.544234\pi$
$53$	−2.01686			−0.277037			−0.138519	+	0.990360i	$0.544234\pi$
$54$		0			0
$55$	1.39716	+	2.41995i	0.188393	+	0.326307i
$56$		0			0
$57$			3.78243i			0.500995i
$58$		0			0
$59$	0.901366	+	0.520404i	0.117348	+	0.0677508i	0.557525	−	0.830160i	$-0.311751\pi$
$59$	0.901366	+	0.520404i	0.117348	+	0.0677508i	−0.440177	+	0.897911i	$0.645084\pi$
$60$		0			0
$61$	−2.50506	+	4.33888i	−0.320740	+	0.555537i	−0.980641	−	0.195815i	$-0.937265\pi$
$61$	−2.50506	+	4.33888i	−0.320740	+	0.555537i	0.659901	+	0.751352i	$0.270598\pi$
$62$		0			0
$63$	2.33201	−	1.34638i	0.293805	−	0.169629i
$64$		0			0
$65$	1.25171	+	2.90582i	0.155255	+	0.360423i
$66$		0			0
$67$	−6.45768	+	3.72834i	−0.788931	+	0.455490i	−0.839586	−	0.543227i	$-0.817202\pi$
$67$	−6.45768	+	3.72834i	−0.788931	+	0.455490i	0.0506551	+	0.998716i	$0.483869\pi$
$68$		0			0
$69$	−3.89438	+	6.74527i	−0.468829	+	0.812035i
$70$		0			0
$71$	3.53142	+	2.03887i	0.419103	+	0.241969i	0.694693	−	0.719306i	$-0.255540\pi$
$71$	3.53142	+	2.03887i	0.419103	+	0.241969i	−0.275591	+	0.961275i	$0.588873\pi$
$72$		0			0
$73$		−	12.6820i		−	1.48432i	−0.670224	−	0.742159i	$-0.733802\pi$
$73$		−	12.6820i		−	1.48432i	0.670224	−	0.742159i	$-0.266198\pi$
$74$		0			0
$75$	−5.04624	−	8.74034i	−0.582689	−	1.00925i
$76$		0			0
$77$	3.18434			0.362889
$78$		0			0
$79$	−9.79759			−1.10232			−0.551158	−	0.834401i	$-0.685814\pi$
$79$	−9.79759			−1.10232			−0.551158	+	0.834401i	$0.685814\pi$
$80$		0			0
$81$	4.91365	+	8.51069i	0.545961	+	0.945632i
$82$		0			0
$83$			6.81690i			0.748252i	0.927378	+	0.374126i	$0.122057\pi$
$83$			6.81690i			0.748252i	−0.927378	+	0.374126i	$0.877943\pi$
$84$		0			0
$85$	0.738102	+	0.426144i	0.0800584	+	0.0462218i
$86$		0			0
$87$	11.6085	−	20.1065i	1.24456	−	2.15564i
$88$		0			0
$89$	4.01085	−	2.31567i	0.425149	−	0.245460i	−0.272129	−	0.962261i	$-0.587728\pi$
$89$	4.01085	−	2.31567i	0.425149	−	0.245460i	0.697278	+	0.716801i	$0.254394\pi$
$90$		0			0
$91$	3.58096	+	0.420388i	0.375387	+	0.0440686i
$92$		0			0
$93$	−8.14431	+	4.70212i	−0.844525	+	0.487587i
$94$		0			0
$95$	−0.695563	+	1.20475i	−0.0713633	+	0.123605i
$96$		0			0
$97$	−3.55617	−	2.05315i	−0.361074	−	0.208466i	0.308478	−	0.951232i	$-0.400180\pi$
$97$	−3.55617	−	2.05315i	−0.361074	−	0.208466i	−0.669552	+	0.742765i	$0.733514\pi$
$98$		0			0
$99$		−	8.57469i		−	0.861789i
$100$		0			0
$101$	−6.86743	−	11.8947i	−0.683335	−	1.18357i	−0.973957	−	0.226733i	$-0.927195\pi$
$101$	−6.86743	−	11.8947i	−0.683335	−	1.18357i	0.290622	−	0.956838i	$-0.406138\pi$
$102$		0			0
$103$	2.35474			0.232019			0.116010	−	0.993248i	$-0.462990\pi$
$103$	2.35474			0.232019			0.116010	+	0.993248i	$0.462990\pi$
$104$		0			0
$105$	2.09372			0.204326
$106$		0			0
$107$	−2.12281	−	3.67682i	−0.205220	−	0.355452i	0.744983	−	0.667084i	$-0.232458\pi$
$107$	−2.12281	−	3.67682i	−0.205220	−	0.355452i	−0.950203	+	0.311632i	$0.899124\pi$
$108$		0			0
$109$		−	18.8556i		−	1.80604i	−0.429600	−	0.903019i	$-0.641345\pi$
$109$		−	18.8556i		−	1.80604i	0.429600	−	0.903019i	$-0.358655\pi$
$110$		0			0
$111$	10.6794	+	6.16576i	1.01364	+	0.585228i
$112$		0			0
$113$	−9.37263	+	16.2339i	−0.881703	+	1.52715i	−0.0322566	+	0.999480i	$0.510269\pi$
$113$	−9.37263	+	16.2339i	−0.881703	+	1.52715i	−0.849446	+	0.527675i	$0.823064\pi$
$114$		0			0
$115$	−2.48082	+	1.43230i	−0.231338	+	0.133563i
$116$		0			0
$117$	1.13201	−	9.64270i	0.104654	−	0.891468i
$118$		0			0
$119$	0.841122	−	0.485622i	0.0771055	−	0.0445169i
$120$		0			0
$121$	−0.429996	+	0.744775i	−0.0390906	+	0.0677068i
$122$		0			0
$123$	9.33862	+	5.39165i	0.842035	+	0.486149i
$124$		0			0
$125$		−	8.09948i		−	0.724440i
$126$		0			0
$127$	−10.3900	−	17.9961i	−0.921967	−	1.59689i	−0.796368	−	0.604813i	$-0.793248\pi$
$127$	−10.3900	−	17.9961i	−0.921967	−	1.59689i	−0.125599	−	0.992081i	$-0.540085\pi$
$128$		0			0
$129$	18.1963			1.60210
$130$		0			0
$131$	1.78298			0.155780			0.0778898	−	0.996962i	$-0.475182\pi$
$131$	1.78298			0.155780			0.0778898	+	0.996962i	$0.475182\pi$
$132$		0			0
$133$	0.792646	+	1.37290i	0.0687311	+	0.119046i
$134$		0			0
$135$			0.643256i			0.0553626i
$136$		0			0
$137$	−14.4084	−	8.31871i	−1.23099	−	0.710715i	−0.263758	−	0.964589i	$-0.584962\pi$
$137$	−14.4084	−	8.31871i	−1.23099	−	0.710715i	−0.967237	+	0.253874i	$0.918295\pi$
$138$		0			0
$139$	0.776363	−	1.34470i	0.0658502	−	0.114056i	−0.831221	−	0.555943i	$-0.812357\pi$
$139$	0.776363	−	1.34470i	0.0658502	−	0.114056i	0.897071	+	0.441887i	$0.145691\pi$
$140$		0			0
$141$	−8.51340	+	4.91521i	−0.716957	+	0.413936i
$142$		0			0
$143$	6.86080	−	9.20595i	0.573729	−	0.769840i
$144$		0			0
$145$	7.39489	−	4.26944i	0.614112	−	0.354558i
$146$		0			0
$147$	1.19298	−	2.06630i	0.0983950	−	0.170425i
$148$		0			0
$149$	0.139302	+	0.0804260i	0.0114121	+	0.00658875i	0.505695	−	0.862712i	$-0.331236\pi$
$149$	0.139302	+	0.0804260i	0.0114121	+	0.00658875i	−0.494283	+	0.869301i	$0.664569\pi$
$150$		0			0
$151$		−	11.8322i		−	0.962892i	−0.876476	−	0.481446i	$-0.840112\pi$
$151$		−	11.8322i		−	0.962892i	0.876476	−	0.481446i	$-0.159888\pi$
$152$		0			0
$153$	−1.30767	−	2.26495i	−0.105719	−	0.183110i
$154$		0			0
$155$	−3.45875			−0.277813
$156$		0			0
$157$	−14.9635			−1.19421			−0.597107	−	0.802162i	$-0.703683\pi$
$157$	−14.9635			−1.19421			−0.597107	+	0.802162i	$0.703683\pi$
$158$		0			0
$159$	2.40607	+	4.16744i	0.190814	+	0.330499i
$160$		0			0
$161$			3.26443i			0.257273i
$162$		0			0
$163$	−10.6083	−	6.12469i	−0.830904	−	0.479723i	0.0232580	−	0.999729i	$-0.492596\pi$
$163$	−10.6083	−	6.12469i	−0.830904	−	0.479723i	−0.854162	+	0.520007i	$0.825929\pi$
$164$		0			0
$165$	3.33356	−	5.77390i	0.259517	−	0.449497i
$166$		0			0
$167$	7.28458	−	4.20576i	0.563698	−	0.325451i	−0.190930	−	0.981604i	$-0.561150\pi$
$167$	7.28458	−	4.20576i	0.563698	−	0.325451i	0.754628	+	0.656152i	$0.227817\pi$
$168$		0			0
$169$	8.93069	−	9.44684i	0.686976	−	0.726680i
$170$		0			0
$171$	3.69691	−	2.13441i	0.282710	−	0.163223i
$172$		0			0
$173$	6.87089	−	11.9007i	0.522384	−	0.904796i	−0.477276	−	0.878753i	$-0.658376\pi$
$173$	6.87089	−	11.9007i	0.522384	−	0.904796i	0.999661	−	0.0260431i	$-0.00829071\pi$
$174$		0			0
$175$	−3.66325	−	2.11498i	−0.276916	−	0.159877i
$176$		0			0
$177$		−	2.48332i		−	0.186658i
$178$		0			0
$179$	10.9025	+	18.8836i	0.814887	+	1.41143i	0.909409	+	0.415904i	$0.136535\pi$
$179$	10.9025	+	18.8836i	0.814887	+	1.41143i	−0.0945212	+	0.995523i	$0.530132\pi$
$180$		0			0
$181$	−16.3948			−1.21862			−0.609309	−	0.792933i	$-0.708553\pi$
$181$	−16.3948			−1.21862			−0.609309	+	0.792933i	$0.708553\pi$
$182$		0			0
$183$	11.9539			0.883657
$184$		0			0
$185$	2.26768	+	3.92774i	0.166723	+	0.288773i
$186$		0			0
$187$		−	3.09277i		−	0.226166i
$188$		0			0
$189$	0.634829	+	0.366519i	0.0461770	+	0.0266603i
$190$		0			0
$191$	−5.47982	+	9.49132i	−0.396506	+	0.686768i	−0.993292	−	0.115632i	$-0.963111\pi$
$191$	−5.47982	+	9.49132i	−0.396506	+	0.686768i	0.596787	+	0.802400i	$0.296444\pi$
$192$		0			0
$193$	1.82754	−	1.05513i	0.131549	−	0.0759498i	−0.432781	−	0.901499i	$-0.642468\pi$
$193$	1.82754	−	1.05513i	0.131549	−	0.0759498i	0.564330	+	0.825549i	$0.309134\pi$
$194$		0			0
$195$	4.51102	−	6.05297i	0.323041	−	0.433462i
$196$		0			0
$197$	4.17834	−	2.41236i	0.297694	−	0.171874i	−0.343712	−	0.939075i	$-0.611685\pi$
$197$	4.17834	−	2.41236i	0.297694	−	0.171874i	0.641407	+	0.767201i	$0.278351\pi$
$198$		0			0
$199$	−3.69982	+	6.40827i	−0.262273	+	0.454270i	−0.966846	−	0.255362i	$-0.917805\pi$
$199$	−3.69982	+	6.40827i	−0.262273	+	0.454270i	0.704573	+	0.709632i	$0.251139\pi$
$200$		0			0
$201$	15.4077	+	8.89565i	1.08678	+	0.627451i
$202$		0			0
$203$		−	9.73068i		−	0.682960i
$204$		0			0
$205$	1.98298	+	3.43462i	0.138497	+	0.239884i
$206$		0			0
$207$	8.79035			0.610972
$208$		0			0
$209$	5.04810			0.349185
$210$		0			0
$211$	−1.07002	−	1.85333i	−0.0736634	−	0.127589i	0.826841	−	0.562436i	$-0.190136\pi$
$211$	−1.07002	−	1.85333i	−0.0736634	−	0.127589i	−0.900504	+	0.434847i	$0.856802\pi$
$212$		0			0
$213$		−	9.72928i		−	0.666640i
$214$		0			0
$215$	5.79575	+	3.34618i	0.395267	+	0.228207i
$216$		0			0
$217$	−1.97075	+	3.41344i	−0.133783	+	0.231719i
$218$		0			0
$219$	−26.2048	+	15.1293i	−1.77076	+	1.02235i
$220$		0			0
$221$	0.408299	−	3.47799i	0.0274652	−	0.233955i
$222$		0			0
$223$	−21.9260	+	12.6590i	−1.46828	+	0.847710i	−0.999368	−	0.0355373i	$-0.988686\pi$
$223$	−21.9260	+	12.6590i	−1.46828	+	0.847710i	−0.468908	+	0.883247i	$0.655352\pi$
$224$		0			0
$225$	−5.69515	+	9.86429i	−0.379677	+	0.657619i
$226$		0			0
$227$	7.53993	+	4.35318i	0.500443	+	0.288931i	0.728896	−	0.684624i	$-0.240034\pi$
$227$	7.53993	+	4.35318i	0.500443	+	0.288931i	−0.228454	+	0.973555i	$0.573367\pi$
$228$		0			0
$229$		−	13.7265i		−	0.907076i	−0.891237	−	0.453538i	$-0.850162\pi$
$229$		−	13.7265i		−	0.907076i	0.891237	−	0.453538i	$-0.149838\pi$
$230$		0			0
$231$	−3.79884	−	6.57978i	−0.249945	−	0.432918i
$232$		0			0
$233$	16.8245			1.10221			0.551106	−	0.834435i	$-0.314206\pi$
$233$	16.8245			1.10221			0.551106	+	0.834435i	$0.314206\pi$
$234$		0			0
$235$	−3.61550			−0.235849
$236$		0			0
$237$	11.6883	+	20.2447i	0.759236	+	1.31504i
$238$		0			0
$239$			4.27266i			0.276376i	0.990406	+	0.138188i	$0.0441278\pi$
$239$			4.27266i			0.276376i	−0.990406	+	0.138188i	$0.955872\pi$
$240$		0			0
$241$	22.0530	+	12.7323i	1.42056	+	0.820159i	0.996346	−	0.0854042i	$-0.0272182\pi$
$241$	22.0530	+	12.7323i	1.42056	+	0.820159i	0.424211	+	0.905563i	$0.360551\pi$
$242$		0			0
$243$	10.6242	−	18.4016i	0.681542	−	1.18046i
$244$		0			0
$245$	0.759955	−	0.438760i	0.0485518	−	0.0280314i
$246$		0			0
$247$	5.67687	+	0.666437i	0.361210	+	0.0424044i
$248$		0			0
$249$	14.0857	−	8.13240i	0.892647	−	0.515370i
$250$		0			0
$251$	−11.8568	+	20.5366i	−0.748395	+	1.29626i	0.200196	+	0.979756i	$0.435842\pi$
$251$	−11.8568	+	20.5366i	−0.748395	+	1.29626i	−0.948592	+	0.316503i	$0.897491\pi$
$252$		0			0
$253$	9.00237	+	5.19752i	0.565974	+	0.326765i
$254$		0			0
$255$		−	2.03352i		−	0.127344i
$256$		0			0
$257$	−1.81772	−	3.14838i	−0.113386	−	0.196390i	0.803747	−	0.594971i	$-0.202836\pi$
$257$	−1.81772	−	3.14838i	−0.113386	−	0.196390i	−0.917133	+	0.398580i	$0.869503\pi$
$258$		0			0
$259$	5.16838			0.321148
$260$		0			0
$261$	−26.2025			−1.62189
$262$		0			0
$263$	7.97941	+	13.8207i	0.492031	+	0.852223i	0.999958	−	0.00917702i	$-0.00292118\pi$
$263$	7.97941	+	13.8207i	0.492031	+	0.852223i	−0.507926	+	0.861400i	$0.669588\pi$
$264$		0			0
$265$			1.76984i			0.108720i
$266$		0			0
$267$	−9.56970	−	5.52507i	−0.585656	−	0.338129i
$268$		0			0
$269$	−7.89435	+	13.6734i	−0.481327	+	0.833683i	−0.999770	−	0.0214290i	$-0.993178\pi$
$269$	−7.89435	+	13.6734i	−0.481327	+	0.833683i	0.518443	+	0.855112i	$0.326512\pi$
$270$		0			0
$271$	−6.70460	+	3.87090i	−0.407275	+	0.235140i	−0.689618	−	0.724173i	$-0.742222\pi$
$271$	−6.70460	+	3.87090i	−0.407275	+	0.235140i	0.282343	+	0.959313i	$0.408888\pi$
$272$		0			0
$273$	−3.40336	−	7.90083i	−0.205980	−	0.478180i
$274$		0			0
$275$	−11.6650	+	6.73481i	−0.703428	+	0.406124i
$276$		0			0
$277$	15.8147	−	27.3919i	0.950215	−	1.64582i	0.205259	−	0.978708i	$-0.434196\pi$
$277$	15.8147	−	27.3919i	0.950215	−	1.64582i	0.744956	−	0.667114i	$-0.232470\pi$
$278$		0			0
$279$	9.19161	+	5.30678i	0.550287	+	0.317708i
$280$		0			0
$281$		−	7.36786i		−	0.439530i	−0.975553	−	0.219765i	$-0.929471\pi$
$281$		−	7.36786i		−	0.439530i	0.975553	−	0.219765i	$-0.0705290\pi$
$282$		0			0
$283$	5.47174	+	9.47734i	0.325261	+	0.563369i	0.981565	−	0.191128i	$-0.0612144\pi$
$283$	5.47174	+	9.47734i	0.325261	+	0.563369i	−0.656304	+	0.754497i	$0.727881\pi$
$284$		0			0
$285$	3.31916			0.196610
$286$		0			0
$287$	4.51950			0.266777
$288$		0			0
$289$	8.02834	+	13.9055i	0.472255	+	0.817970i
$290$		0			0
$291$			9.79746i			0.574337i
$292$		0			0
$293$	−27.5849	−	15.9261i	−1.61153	−	0.930415i	−0.989017	−	0.147802i	$-0.952780\pi$
$293$	−27.5849	−	15.9261i	−1.61153	−	0.930415i	−0.622509	−	0.782613i	$-0.713887\pi$
$294$		0			0
$295$	0.456665	−	0.790968i	0.0265881	−	0.0460519i
$296$		0			0
$297$	2.02151	−	1.16712i	0.117300	−	0.0677231i
$298$		0			0
$299$	9.43749	+	7.03336i	0.545784	+	0.406750i
$300$		0			0
$301$	6.60469	−	3.81322i	0.380688	−	0.219790i
$302$		0			0
$303$	−16.3854	+	28.3803i	−0.941315	+	1.63041i
$304$		0			0
$305$	3.80746	+	2.19824i	0.218015	+	0.125871i
$306$		0			0
$307$		−	32.6251i		−	1.86201i	−0.365002	−	0.931007i	$-0.618932\pi$
$307$		−	32.6251i		−	1.86201i	0.365002	−	0.931007i	$-0.381068\pi$
$308$		0			0
$309$	−2.80915	−	4.86559i	−0.159807	−	0.276794i
$310$		0			0
$311$	−6.86932			−0.389524			−0.194762	−	0.980851i	$-0.562393\pi$
$311$	−6.86932			−0.389524			−0.194762	+	0.980851i	$0.562393\pi$
$312$		0			0
$313$	−2.13137			−0.120472			−0.0602360	−	0.998184i	$-0.519185\pi$
$313$	−2.13137			−0.120472			−0.0602360	+	0.998184i	$0.519185\pi$
$314$		0			0
$315$	−1.18148	−	2.04638i	−0.0665689	−	0.115301i
$316$		0			0
$317$			5.52242i			0.310170i	0.987901	+	0.155085i	$0.0495651\pi$
$317$			5.52242i			0.310170i	−0.987901	+	0.155085i	$0.950435\pi$
$318$		0			0
$319$	−26.8345	−	15.4929i	−1.50244	−	0.867435i
$320$		0			0
$321$	−5.06494	+	8.77273i	−0.282697	+	0.489646i
$322$		0			0
$323$	1.33342	−	0.769853i	0.0741937	−	0.0428357i
$324$		0			0
$325$	−14.0071	+	6.03367i	−0.776972	+	0.334688i
$326$		0			0
$327$	−38.9612	+	22.4943i	−2.15456	+	1.24394i
$328$		0			0
$329$	−2.06006	+	3.56813i	−0.113575	+	0.196718i
$330$		0			0
$331$	−8.20848	−	4.73917i	−0.451179	−	0.260488i	0.257149	−	0.966372i	$-0.417217\pi$
$331$	−8.20848	−	4.73917i	−0.451179	−	0.260488i	−0.708328	+	0.705884i	$0.750550\pi$
$332$		0			0
$333$		−	13.9173i		−	0.762661i
$334$		0			0
$335$	3.27170	+	5.66675i	0.178752	+	0.309608i
$336$		0			0
$337$	−12.8597			−0.700511			−0.350255	−	0.936654i	$-0.613905\pi$
$337$	−12.8597			−0.700511			−0.350255	+	0.936654i	$0.613905\pi$
$338$		0			0
$339$	44.7253			2.42915
$340$		0			0
$341$	6.27554	+	10.8695i	0.339839	+	0.588619i
$342$		0			0
$343$		−	1.00000i		−	0.0539949i
$344$		0			0
$345$	5.91912	+	3.41740i	0.318675	+	0.183987i
$346$		0			0
$347$	−0.0442657	+	0.0766704i	−0.00237631	+	0.00411588i	−0.867211	−	0.497941i	$-0.834090\pi$
$347$	−0.0442657	+	0.0766704i	−0.00237631	+	0.00411588i	0.864835	+	0.502057i	$0.167423\pi$
$348$		0			0
$349$	5.08379	−	2.93513i	0.272129	−	0.157114i	−0.357726	−	0.933827i	$-0.616448\pi$
$349$	5.08379	−	2.93513i	0.272129	−	0.157114i	0.629855	+	0.776713i	$0.283114\pi$
$350$		0			0
$351$	2.42738	−	1.04561i	0.129564	−	0.0558108i
$352$		0			0
$353$	12.0949	−	6.98298i	0.643746	−	0.371667i	−0.142310	−	0.989822i	$-0.545453\pi$
$353$	12.0949	−	6.98298i	0.643746	−	0.371667i	0.786056	+	0.618155i	$0.212120\pi$
$354$		0			0
$355$	1.78915	−	3.09890i	0.0949582	−	0.164472i
$356$		0			0
$357$	−2.00688	−	1.15867i	−0.106215	−	0.0613234i
$358$		0			0
$359$			21.4343i			1.13126i	0.824659	+	0.565629i	$0.191367\pi$
$359$			21.4343i			1.13126i	−0.824659	+	0.565629i	$0.808633\pi$
$360$		0			0
$361$	−8.24343	−	14.2780i	−0.433864	−	0.751475i
$362$		0			0
$363$	2.05190			0.107697
$364$		0			0
$365$	−11.1287			−0.582504
$366$		0			0
$367$	1.85247	+	3.20858i	0.0966983	+	0.167486i	0.910316	−	0.413914i	$-0.135838\pi$
$367$	1.85247	+	3.20858i	0.0966983	+	0.167486i	−0.813618	+	0.581400i	$0.802505\pi$
$368$		0			0
$369$		−	12.1700i		−	0.633543i
$370$		0			0
$371$	1.74665	+	1.00843i	0.0906818	+	0.0523552i
$372$		0			0
$373$	0.889596	−	1.54083i	0.0460615	−	0.0797809i	−0.842075	−	0.539360i	$-0.818666\pi$
$373$	0.889596	−	1.54083i	0.0460615	−	0.0797809i	0.888137	+	0.459579i	$0.152000\pi$
$374$		0			0
$375$	−16.7359	+	9.66249i	−0.864239	+	0.498969i
$376$		0			0
$377$	−28.1315	−	20.9652i	−1.44885	−	1.07976i
$378$		0			0
$379$	0.274585	−	0.158532i	0.0141045	−	0.00814323i	−0.492931	−	0.870068i	$-0.664075\pi$
$379$	0.274585	−	0.158532i	0.0141045	−	0.00814323i	0.507036	+	0.861925i	$0.330741\pi$
$380$		0			0
$381$	−24.7901	+	42.9378i	−1.27004	+	2.19977i
$382$		0			0
$383$	22.7483	+	13.1337i	1.16238	+	0.671102i	0.951874	−	0.306490i	$-0.0991545\pi$
$383$	22.7483	+	13.1337i	1.16238	+	0.671102i	0.210509	+	0.977592i	$0.432488\pi$
$384$		0			0
$385$		−	2.79432i		−	0.142412i
$386$		0			0
$387$	−10.2681	−	17.7849i	−0.521958	−	0.904057i
$388$		0			0
$389$	26.0221			1.31937			0.659686	−	0.751542i	$-0.270689\pi$
$389$	26.0221			1.31937			0.659686	+	0.751542i	$0.270689\pi$
$390$		0			0
$391$	3.17056			0.160342
$392$		0			0
$393$	−2.12705	−	3.68416i	−0.107296	−	0.185841i
$394$		0			0
$395$			8.59759i			0.432592i
$396$		0			0
$397$	−28.0114	−	16.1724i	−1.40585	−	0.811668i	−0.410865	−	0.911696i	$-0.634773\pi$
$397$	−28.0114	−	16.1724i	−1.40585	−	0.811668i	−0.994985	+	0.100028i	$0.968107\pi$
$398$		0			0
$399$	1.89122	−	3.27568i	0.0946792	−	0.163989i
$400$		0			0
$401$	−25.2907	+	14.6016i	−1.26296	+	0.729168i	−0.973646	−	0.228067i	$-0.926760\pi$
$401$	−25.2907	+	14.6016i	−1.26296	+	0.729168i	−0.289311	+	0.957235i	$0.593426\pi$
$402$		0			0
$403$	5.62221	+	13.0519i	0.280062	+	0.650160i
$404$		0			0
$405$	7.46831	−	4.31183i	0.371103	−	0.214257i
$406$		0			0
$407$	8.22894	−	14.2529i	0.407893	−	0.706492i
$408$		0			0
$409$	11.6490	+	6.72553i	0.576004	+	0.332556i	0.759544	−	0.650456i	$-0.225422\pi$
$409$	11.6490	+	6.72553i	0.576004	+	0.332556i	−0.183540	+	0.983012i	$0.558756\pi$
$410$		0			0
$411$			39.6961i			1.95806i
$412$		0			0
$413$	−0.520404	−	0.901366i	−0.0256074	−	0.0443533i
$414$		0			0
$415$	5.98197			0.293643
$416$		0			0
$417$	−3.70473			−0.181421
$418$		0			0
$419$	−4.13345	−	7.15934i	−0.201932	−	0.349757i	0.747219	−	0.664578i	$-0.231389\pi$
$419$	−4.13345	−	7.15934i	−0.201932	−	0.349757i	−0.949151	+	0.314822i	$0.898055\pi$
$420$		0			0
$421$		−	11.3220i		−	0.551802i	−0.961186	−	0.275901i	$-0.911024\pi$
$421$		−	11.3220i		−	0.551802i	0.961186	−	0.275901i	$-0.0889763\pi$
$422$		0			0
$423$	9.60816	+	5.54727i	0.467165	+	0.269718i
$424$		0			0
$425$	−2.05416	+	3.55791i	−0.0996414	+	0.172584i
$426$		0			0
$427$	4.33888	−	2.50506i	0.209973	−	0.121228i
$428$		0			0
$429$	−27.2070	−	3.19397i	−1.31357	−	0.154206i
$430$		0			0
$431$	−14.4011	+	8.31449i	−0.693677	+	0.400495i	−0.804988	−	0.593291i	$-0.797828\pi$
$431$	−14.4011	+	8.31449i	−0.693677	+	0.400495i	0.111311	+	0.993786i	$0.464495\pi$
$432$		0			0
$433$	−11.6439	+	20.1678i	−0.559569	+	0.969201i	0.437964	+	0.898993i	$0.355700\pi$
$433$	−11.6439	+	20.1678i	−0.559569	+	0.969201i	−0.997532	+	0.0702085i	$0.977634\pi$
$434$		0			0
$435$	−17.6438	−	10.1867i	−0.845958	−	0.488414i
$436$		0			0
$437$			5.17507i			0.247557i
$438$		0			0
$439$	−10.8185	−	18.7382i	−0.516338	−	0.894324i	−0.999820	−	0.0189699i	$-0.993961\pi$
$439$	−10.8185	−	18.7382i	−0.516338	−	0.894324i	0.483482	−	0.875355i	$-0.339372\pi$
$440$		0			0
$441$	−2.69277			−0.128227
$442$		0			0
$443$	32.7018			1.55371			0.776855	−	0.629680i	$-0.216814\pi$
$443$	32.7018			1.55371			0.776855	+	0.629680i	$0.216814\pi$
$444$		0			0
$445$	−2.03204	−	3.51960i	−0.0963281	−	0.166845i
$446$		0			0
$447$		−	0.383785i		−	0.0181524i
$448$		0			0
$449$	4.24023	+	2.44810i	0.200109	+	0.115533i	0.596706	−	0.802460i	$-0.296476\pi$
$449$	4.24023	+	2.44810i	0.200109	+	0.115533i	−0.396597	+	0.917993i	$0.629809\pi$
$450$		0			0
$451$	7.19580	−	12.4635i	0.338837	−	0.586883i
$452$		0			0
$453$	−24.4488	+	14.1155i	−1.14871	+	0.663206i
$454$		0			0
$455$	0.368899	−	3.14237i	0.0172942	−	0.147316i
$456$		0			0
$457$	14.4664	−	8.35217i	0.676709	−	0.390698i	−0.121905	−	0.992542i	$-0.538900\pi$
$457$	14.4664	−	8.35217i	0.676709	−	0.390698i	0.798614	+	0.601844i	$0.205567\pi$
$458$		0			0
$459$	0.355979	−	0.616574i	0.0166157	−	0.0287792i
$460$		0			0
$461$	17.9658	+	10.3725i	0.836750	+	0.483098i	0.856158	−	0.516714i	$-0.172845\pi$
$461$	17.9658	+	10.3725i	0.836750	+	0.483098i	−0.0194084	+	0.999812i	$0.506178\pi$
$462$		0			0
$463$			27.0197i			1.25571i	0.778330	+	0.627855i	$0.216067\pi$
$463$			27.0197i			1.25571i	−0.778330	+	0.627855i	$0.783933\pi$
$464$		0			0
$465$	4.12621	+	7.14680i	0.191348	+	0.331425i
$466$		0			0
$467$	33.8384			1.56586			0.782928	−	0.622112i	$-0.213725\pi$
$467$	33.8384			1.56586			0.782928	+	0.622112i	$0.213725\pi$
$468$		0			0
$469$	7.45668			0.344318
$470$		0			0
$471$	17.8511	+	30.9189i	0.822533	+	1.42467i
$472$		0			0
$473$		−	24.2851i		−	1.11663i
$474$		0			0
$475$	−5.80732	−	3.35286i	−0.266458	−	0.153840i
$476$		0			0
$477$	2.71547	−	4.70334i	0.124333	−	0.215351i
$478$		0			0
$479$	−10.4316	+	6.02268i	−0.476632	+	0.275183i	−0.719012	−	0.694998i	$-0.755405\pi$
$479$	−10.4316	+	6.02268i	−0.476632	+	0.275183i	0.242380	+	0.970181i	$0.422072\pi$
$480$		0			0
$481$	11.1355	−	14.9418i	0.507736	−	0.681289i
$482$		0			0
$483$	6.74527	−	3.89438i	0.306920	−	0.177201i
$484$		0			0
$485$	−1.80169	+	3.12061i	−0.0818104	+	0.141700i
$486$		0			0
$487$	−12.3401	−	7.12454i	−0.559182	−	0.322844i	0.193635	−	0.981074i	$-0.437972\pi$
$487$	−12.3401	−	7.12454i	−0.559182	−	0.322844i	−0.752817	+	0.658230i	$0.771306\pi$
$488$		0			0
$489$			29.2264i			1.32167i
$490$		0			0
$491$	12.8017	+	22.1731i	0.577731	+	1.00066i	0.995739	+	0.0922167i	$0.0293952\pi$
$491$	12.8017	+	22.1731i	0.577731	+	1.00066i	−0.418008	+	0.908444i	$0.637271\pi$
$492$		0			0
$493$	−9.45087			−0.425646
$494$		0			0
$495$	−7.52447			−0.338200
$496$		0			0
$497$	−2.03887	−	3.53142i	−0.0914557	−	0.158406i
$498$		0			0
$499$			12.8345i			0.574550i	0.957848	+	0.287275i	$0.0927494\pi$
$499$			12.8345i			0.574550i	−0.957848	+	0.287275i	$0.907251\pi$
$500$		0			0
$501$	−17.3807	−	10.0347i	−0.776511	−	0.448319i
$502$		0			0
$503$	13.0620	−	22.6241i	0.582406	−	1.00876i	−0.412787	−	0.910828i	$-0.635445\pi$
$503$	13.0620	−	22.6241i	0.582406	−	1.00876i	0.995193	−	0.0979300i	$-0.0312221\pi$
$504$		0			0
$505$	−10.4379	+	6.02632i	−0.464480	+	0.268168i
$506$		0			0
$507$	−30.1741	−	7.18358i	−1.34008	−	0.319034i
$508$		0			0
$509$	−0.0256478	+	0.0148077i	−0.00113682	+	0.000656342i	−0.500568	−	0.865697i	$-0.666876\pi$
$509$	−0.0256478	+	0.0148077i	−0.00113682	+	0.000656342i	0.499431	+	0.866353i	$0.333542\pi$
$510$		0			0
$511$	−6.34101	+	10.9829i	−0.280510	+	0.485857i
$512$		0			0
$513$	1.00639	+	0.581039i	0.0444332	+	0.0256535i
$514$		0			0
$515$		−	2.06633i		−	0.0910535i
$516$		0			0
$517$	6.55994	+	11.3621i	0.288506	+	0.499706i
$518$		0			0
$519$	−32.7873			−1.43920
$520$		0			0
$521$	25.4799			1.11630			0.558148	−	0.829742i	$-0.311512\pi$
$521$	25.4799			1.11630			0.558148	+	0.829742i	$0.311512\pi$
$522$		0			0
$523$	19.5050	+	33.7836i	0.852892	+	1.47725i	0.878587	+	0.477583i	$0.158487\pi$
$523$	19.5050	+	33.7836i	0.852892	+	1.47725i	−0.0256945	+	0.999670i	$0.508180\pi$
$524$		0			0
$525$			10.0925i			0.440472i
$526$		0			0
$527$	3.31528	+	1.91408i	0.144416	+	0.0833786i
$528$		0			0
$529$	6.17176	−	10.6898i	0.268337	−	0.464774i
$530$		0			0
$531$	−2.42717	+	1.40133i	−0.105330	+	0.0608125i
$532$		0			0
$533$	9.73747	−	13.0659i	0.421776	−	0.565947i
$534$		0			0
$535$	−3.22649	+	1.86281i	−0.139493	+	0.0805365i
$536$		0			0
$537$	26.0127	−	45.0554i	1.12253	−	1.94428i
$538$		0			0
$539$	−2.75772	−	1.59217i	−0.118783	−	0.0685796i
$540$		0			0
$541$			3.87645i			0.166662i	0.996522	+	0.0833308i	$0.0265558\pi$
$541$			3.87645i			0.166662i	−0.996522	+	0.0833308i	$0.973444\pi$
$542$		0			0
$543$	19.5586	+	33.8766i	0.839341	+	1.45378i
$544$		0			0
$545$	−16.5462			−0.708761
$546$		0			0
$547$	38.8022			1.65906			0.829532	−	0.558460i	$-0.188607\pi$
$547$	38.8022			1.65906			0.829532	+	0.558460i	$0.188607\pi$
$548$		0			0
$549$	−6.74554	−	11.6836i	−0.287893	−	0.498645i
$550$		0			0
$551$		−	15.4260i		−	0.657168i
$552$		0			0
$553$	8.48496	+	4.89880i	0.360817	+	0.208318i
$554$		0			0
$555$	5.41058	−	9.37140i	0.229666	−	0.397794i
$556$		0			0
$557$	−3.33235	+	1.92393i	−0.141196	+	0.0815197i	−0.568934	−	0.822383i	$-0.692644\pi$
$557$	−3.33235	+	1.92393i	−0.141196	+	0.0815197i	0.427738	+	0.903903i	$0.359311\pi$
$558$		0			0
$559$	3.20606	−	27.3100i	0.135602	−	1.15509i
$560$		0			0
$561$	−6.39058	+	3.68960i	−0.269810	+	0.155775i
$562$		0			0
$563$	−6.73279	+	11.6615i	−0.283753	+	0.491475i	−0.972306	−	0.233711i	$-0.924913\pi$
$563$	−6.73279	+	11.6615i	−0.283753	+	0.491475i	0.688553	+	0.725186i	$0.258246\pi$
$564$		0			0
$565$	14.2456	+	8.22468i	0.599315	+	0.346015i
$566$		0			0
$567$		−	9.82730i		−	0.412708i
$568$		0			0
$569$	3.75922	+	6.51117i	0.157595	+	0.272962i	0.934001	−	0.357271i	$-0.116293\pi$
$569$	3.75922	+	6.51117i	0.157595	+	0.272962i	−0.776406	+	0.630233i	$0.782959\pi$
$570$		0			0
$571$	−4.48050			−0.187503			−0.0937515	−	0.995596i	$-0.529886\pi$
$571$	−4.48050			−0.187503			−0.0937515	+	0.995596i	$0.529886\pi$
$572$		0			0
$573$	26.1492			1.09240
$574$		0			0
$575$	−6.90419	−	11.9584i	−0.287925	−	0.498700i
$576$		0			0
$577$			8.68801i			0.361686i	0.983512	+	0.180843i	$0.0578827\pi$
$577$			8.68801i			0.361686i	−0.983512	+	0.180843i	$0.942117\pi$
$578$		0			0
$579$	−4.36041	−	2.51749i	−0.181213	−	0.104623i
$580$		0			0
$581$	3.40845	−	5.90361i	0.141406	−	0.244923i
$582$		0			0
$583$	5.56194	−	3.21119i	0.230352	−	0.132994i
$584$		0			0
$585$	−8.46167	−	0.993360i	−0.349847	−	0.0410704i
$586$		0			0
$587$	26.9326	−	15.5496i	1.11163	−	0.641799i	0.172378	−	0.985031i	$-0.444855\pi$
$587$	26.9326	−	15.5496i	1.11163	−	0.641799i	0.939251	+	0.343232i	$0.111522\pi$
$588$		0			0
$589$	−3.12421	+	5.41130i	−0.128731	+	0.222969i
$590$		0			0
$591$	−9.96931	−	5.75578i	−0.410083	−	0.236761i
$592$		0			0
$593$			45.7116i			1.87715i	0.345076	+	0.938575i	$0.387853\pi$
$593$			45.7116i			1.87715i	−0.345076	+	0.938575i	$0.612147\pi$
$594$		0			0
$595$	−0.426144	−	0.738102i	−0.0174702	−	0.0302592i
$596$		0			0
$597$	17.6552			0.722578
$598$		0			0
$599$	−10.2396			−0.418380			−0.209190	−	0.977875i	$-0.567083\pi$
$599$	−10.2396			−0.418380			−0.209190	+	0.977875i	$0.567083\pi$
$600$		0			0
$601$	7.93494	+	13.7437i	0.323673	+	0.560618i	0.981243	−	0.192776i	$-0.0617490\pi$
$601$	7.93494	+	13.7437i	0.323673	+	0.560618i	−0.657570	+	0.753393i	$0.728416\pi$
$602$		0			0
$603$		−	20.0791i		−	0.817686i
$604$		0			0
$605$	0.653556	+	0.377331i	0.0265708	+	0.0153407i
$606$		0			0
$607$	17.6740	−	30.6124i	0.717368	−	1.24252i	−0.244672	−	0.969606i	$-0.578680\pi$
$607$	17.6740	−	30.6124i	0.717368	−	1.24252i	0.962039	−	0.272911i	$-0.0879865\pi$
$608$		0			0
$609$	−20.1065	+	11.6085i	−0.814755	+	0.470399i
$610$		0			0
$611$	5.87700	+	13.6434i	0.237758	+	0.551952i
$612$		0			0
$613$	−1.35615	+	0.782973i	−0.0547743	+	0.0316240i	−0.527137	−	0.849780i	$-0.676735\pi$
$613$	−1.35615	+	0.782973i	−0.0547743	+	0.0316240i	0.472363	+	0.881404i	$0.343401\pi$
$614$		0			0
$615$	4.73129	−	8.19483i	0.190784	−	0.330448i
$616$		0			0
$617$	8.26395	+	4.77119i	0.332694	+	0.192081i	0.657037	−	0.753859i	$-0.271810\pi$
$617$	8.26395	+	4.77119i	0.332694	+	0.192081i	−0.324342	+	0.945940i	$0.605143\pi$
$618$		0			0
$619$		−	25.6394i		−	1.03053i	−0.857030	−	0.515267i	$-0.827693\pi$
$619$		−	25.6394i		−	1.03053i	0.857030	−	0.515267i	$-0.172307\pi$
$620$		0			0
$621$	1.19647	+	2.07235i	0.0480128	+	0.0831607i
$622$		0			0
$623$	−4.63133			−0.185550
$624$		0			0
$625$	14.0423			0.561693
$626$		0			0
$627$	−6.02227	−	10.4309i	−0.240506	−	0.416569i
$628$		0			0
$629$		−	5.01976i		−	0.200151i
$630$		0			0
$631$	26.4492	+	15.2704i	1.05293	+	0.607907i	0.923467	−	0.383678i	$-0.125343\pi$
$631$	26.4492	+	15.2704i	1.05293	+	0.607907i	0.129458	+	0.991585i	$0.458676\pi$
$632$		0			0
$633$	−2.55302	+	4.42197i	−0.101474	+	0.175757i
$634$		0			0
$635$	−15.7919	+	9.11748i	−0.626684	+	0.361816i
$636$		0			0
$637$	−2.89101	−	2.15455i	−0.114546	−	0.0853662i
$638$		0			0
$639$	−9.50931	+	5.49020i	−0.376182	+	0.217189i
$640$		0			0
$641$	−5.03286	+	8.71717i	−0.198786	+	0.344307i	−0.948135	−	0.317868i	$-0.897033\pi$
$641$	−5.03286	+	8.71717i	−0.198786	+	0.344307i	0.749349	+	0.662175i	$0.230367\pi$
$642$		0			0
$643$	−29.6059	−	17.0930i	−1.16754	−	0.674080i	−0.214442	−	0.976737i	$-0.568793\pi$
$643$	−29.6059	−	17.0930i	−1.16754	−	0.674080i	−0.953100	+	0.302656i	$0.902127\pi$
$644$		0			0
$645$		−	15.9676i		−	0.628725i
$646$		0			0
$647$	−21.7629	−	37.6944i	−0.855587	−	1.48192i	−0.876099	−	0.482131i	$-0.839863\pi$
$647$	−21.7629	−	37.6944i	−0.855587	−	1.48192i	0.0205115	−	0.999790i	$-0.493471\pi$
$648$		0			0
$649$	−3.31428			−0.130097
$650$		0			0
$651$	9.40424			0.368581
$652$		0			0
$653$	−24.5301	−	42.4874i	−0.959937	−	1.66266i	−0.722643	−	0.691221i	$-0.757073\pi$
$653$	−24.5301	−	42.4874i	−0.959937	−	1.66266i	−0.237293	−	0.971438i	$-0.576260\pi$
$654$		0			0
$655$		−	1.56460i		−	0.0611340i
$656$		0			0
$657$	29.5745	+	17.0749i	1.15381	+	0.666154i
$658$		0			0
$659$	18.8093	−	32.5787i	0.732707	−	1.26909i	−0.223015	−	0.974815i	$-0.571590\pi$
$659$	18.8093	−	32.5787i	0.732707	−	1.26909i	0.955722	−	0.294271i	$-0.0950769\pi$
$660$		0			0
$661$	8.11902	−	4.68752i	0.315793	−	0.182323i	−0.333723	−	0.942671i	$-0.608305\pi$
$661$	8.11902	−	4.68752i	0.315793	−	0.182323i	0.649516	+	0.760348i	$0.274972\pi$
$662$		0			0
$663$	−7.67364	+	3.30549i	−0.298019	+	0.128375i
$664$		0			0
$665$	1.20475	−	0.695563i	0.0467182	−	0.0269728i
$666$		0			0
$667$	15.8826	−	27.5094i	0.614975	−	1.06517i
$668$		0			0
$669$	52.3145	+	30.2038i	2.02260	+	1.16775i
$670$		0			0
$671$		−	15.9539i		−	0.615893i
$672$		0			0
$673$	−11.7415	−	20.3369i	−0.452603	−	0.783932i	0.545944	−	0.837822i	$-0.316171\pi$
$673$	−11.7415	−	20.3369i	−0.452603	−	0.783932i	−0.998547	+	0.0538903i	$0.982838\pi$
$674$		0			0
$675$	−3.10072			−0.119347
$676$		0			0
$677$	2.71645			0.104401			0.0522007	−	0.998637i	$-0.483376\pi$
$677$	2.71645			0.104401			0.0522007	+	0.998637i	$0.483376\pi$
$678$		0			0
$679$	2.05315	+	3.55617i	0.0787929	+	0.136473i
$680$		0			0
$681$		−	20.7730i		−	0.796022i
$682$		0			0
$683$	−38.9846	−	22.5078i	−1.49170	−	0.861235i	−0.491749	−	0.870737i	$-0.663642\pi$
$683$	−38.9846	−	22.5078i	−1.49170	−	0.861235i	−0.999955	+	0.00950165i	$0.996975\pi$
$684$		0			0
$685$	−7.29984	+	12.6437i	−0.278913	+	0.483091i
$686$		0			0
$687$	−28.3631	+	16.3754i	−1.08212	+	0.624762i
$688$		0			0
$689$	6.67863	−	2.87688i	0.254436	−	0.109600i
$690$		0			0
$691$	−15.3578	+	8.86682i	−0.584237	+	0.337310i	−0.762816	−	0.646616i	$-0.776184\pi$
$691$	−15.3578	+	8.86682i	−0.584237	+	0.337310i	0.178578	+	0.983926i	$0.442850\pi$
$692$		0			0
$693$	−4.28734	+	7.42590i	−0.162863	+	0.282087i
$694$		0			0
$695$	−1.18000	−	0.681275i	−0.0447600	−	0.0258422i
$696$		0			0
$697$		−	4.38954i		−	0.166266i
$698$		0			0
$699$	−20.0713	−	34.7645i	−0.759166	−	1.31491i
$700$		0			0
$701$	−7.97397			−0.301173			−0.150586	−	0.988597i	$-0.548116\pi$
$701$	−7.97397			−0.301173			−0.150586	+	0.988597i	$0.548116\pi$
$702$		0			0
$703$	8.19339			0.309020
$704$		0			0
$705$	4.31320	+	7.47068i	0.162445	+	0.281362i
$706$		0			0
$707$			13.7349i			0.516553i
$708$		0			0
$709$	−28.0054	−	16.1689i	−1.05177	−	0.607237i	−0.128622	−	0.991694i	$-0.541055\pi$
$709$	−28.0054	−	16.1689i	−1.05177	−	0.607237i	−0.923143	+	0.384457i	$0.874389\pi$
$710$		0			0
$711$	13.1913	−	22.8480i	0.494713	−	0.856869i
$712$		0			0
$713$	−11.1429	+	6.43337i	−0.417306	+	0.240932i
$714$		0			0
$715$	−8.07841	−	6.02050i	−0.302115	−	0.225154i
$716$		0			0
$717$	8.82859	−	5.09719i	0.329710	−	0.190358i
$718$		0			0
$719$	14.3814	−	24.9093i	0.536335	−	0.928960i	−0.462762	−	0.886483i	$-0.653142\pi$
$719$	14.3814	−	24.9093i	0.536335	−	0.928960i	0.999097	−	0.0424776i	$-0.0135251\pi$
$720$		0			0
$721$	−2.03926	−	1.17737i	−0.0759462	−	0.0438475i
$722$		0			0
$723$		−	60.7573i		−	2.25959i
$724$		0			0
$725$	20.5802	+	35.6459i	0.764329	+	1.32386i
$726$		0			0
$727$	−27.5051			−1.02011			−0.510054	−	0.860143i	$-0.670374\pi$
$727$	−27.5051			−1.02011			−0.510054	+	0.860143i	$0.670374\pi$
$728$		0			0
$729$	−21.2157			−0.785766
$730$		0			0
$731$	−3.70357	−	6.41476i	−0.136981	−	0.237259i
$732$		0			0
$733$		−	6.53199i		−	0.241265i	−0.992697	−	0.120632i	$-0.961508\pi$
$733$		−	6.53199i		−	0.241265i	0.992697	−	0.120632i	$-0.0384922\pi$
$734$		0			0
$735$	−1.81322	−	1.04686i	−0.0668815	−	0.0386141i
$736$		0			0
$737$	11.8723	−	20.5634i	0.437322	−	0.757464i
$738$		0			0
$739$	−23.0282	+	13.2953i	−0.847106	+	0.489077i	−0.859673	−	0.510844i	$-0.829333\pi$
$739$	−23.0282	+	13.2953i	−0.847106	+	0.489077i	0.0125673	+	0.999921i	$0.496000\pi$
$740$		0			0
$741$	−5.39531	−	12.5251i	−0.198202	−	0.460122i
$742$		0			0
$743$	32.3053	−	18.6515i	1.18517	−	0.684257i	0.227963	−	0.973670i	$-0.426793\pi$
$743$	32.3053	−	18.6515i	1.18517	−	0.684257i	0.957204	+	0.289413i	$0.0934601\pi$
$744$		0			0
$745$	0.0705755	−	0.122240i	0.00258569	−	0.00447854i
$746$		0			0
$747$	−15.8971	−	9.17817i	−0.581643	−	0.335812i
$748$		0			0
$749$			4.24563i			0.155132i
$750$		0			0
$751$	1.83497	+	3.17826i	0.0669591	+	0.115977i	0.897561	−	0.440890i	$-0.145337\pi$
$751$	1.83497	+	3.17826i	0.0669591	+	0.115977i	−0.830602	+	0.556866i	$0.812004\pi$
$752$		0			0
$753$	56.5796			2.06187
$754$		0			0
$755$	−10.3830			−0.377876
$756$		0			0
$757$	22.3521	+	38.7150i	0.812401	+	1.40712i	0.911179	+	0.412010i	$0.135173\pi$
$757$	22.3521	+	38.7150i	0.812401	+	1.40712i	−0.0987785	+	0.995109i	$0.531494\pi$
$758$		0			0
$759$		−	24.8021i		−	0.900258i
$760$		0			0
$761$	−34.1854	−	19.7369i	−1.23922	−	0.715463i	−0.270284	−	0.962781i	$-0.587118\pi$
$761$	−34.1854	−	19.7369i	−1.23922	−	0.715463i	−0.968935	+	0.247317i	$0.920451\pi$
$762$		0			0
$763$	−9.42780	+	16.3294i	−0.341309	+	0.591165i
$764$		0			0
$765$	−1.98754	+	1.14751i	−0.0718596	+	0.0414882i
$766$		0			0
$767$	−3.72709	−	0.437543i	−0.134577	−	0.0157988i
$768$		0			0
$769$	6.02163	−	3.47659i	0.217146	−	0.125369i	−0.387482	−	0.921877i	$-0.626655\pi$
$769$	6.02163	−	3.47659i	0.217146	−	0.125369i	0.604628	+	0.796508i	$0.293322\pi$
$770$		0			0
$771$	−4.33699	+	7.51188i	−0.156193	+	0.270534i
$772$		0			0
$773$	−42.8106	−	24.7167i	−1.53979	−	0.888998i	−0.998850	−	0.0479361i	$-0.984736\pi$
$773$	−42.8106	−	24.7167i	−1.53979	−	0.888998i	−0.540939	−	0.841062i	$-0.681931\pi$
$774$		0			0
$775$		−	16.6724i		−	0.598890i
$776$		0			0
$777$	−6.16576	−	10.6794i	−0.221195	−	0.383122i
$778$		0			0
$779$	7.16472			0.256703
$780$		0			0
$781$	−12.9849			−0.464636
$782$		0			0
$783$	−3.56648	−	6.17732i	−0.127455	−	0.220759i
$784$		0			0
$785$			13.1307i			0.468657i
$786$		0			0
$787$	−24.5560	−	14.1774i	−0.875327	−	0.505370i	−0.00621204	−	0.999981i	$-0.501977\pi$
$787$	−24.5560	−	14.1774i	−0.875327	−	0.505370i	−0.869115	+	0.494611i	$0.835311\pi$
$788$		0			0
$789$	19.0385	−	32.9756i	0.677788	−	1.17396i
$790$		0			0
$791$	16.2339	−	9.37263i	0.577210	−	0.333252i
$792$		0			0
$793$	2.10619	−	17.9410i	0.0747930	−	0.637104i
$794$		0			0
$795$	3.65701	−	2.11138i	0.129701	−	0.0748828i
$796$		0			0
$797$	−8.85202	+	15.3322i	−0.313555	+	0.543093i	−0.979129	−	0.203239i	$-0.934853\pi$
$797$	−8.85202	+	15.3322i	−0.313555	+	0.543093i	0.665574	+	0.746331i	$0.268187\pi$
$798$		0			0
$799$	3.46553	+	2.00082i	0.122602	+	0.0707841i
$800$		0			0
$801$			12.4711i			0.440645i
$802$		0			0
$803$	20.1919	+	34.9734i	0.712557	+	1.23418i
$804$		0			0
$805$	2.86460			0.100964
$806$		0			0
$807$	37.6711			1.32609
$808$		0			0
$809$	−4.67520	−	8.09768i	−0.164371	−	0.284699i	0.772061	−	0.635549i	$-0.219226\pi$
$809$	−4.67520	−	8.09768i	−0.164371	−	0.284699i	−0.936432	+	0.350850i	$0.885893\pi$
$810$		0			0
$811$			35.5948i			1.24990i	0.780664	+	0.624951i	$0.214881\pi$
$811$			35.5948i			1.24990i	−0.780664	+	0.624951i	$0.785119\pi$
$812$		0			0
$813$	15.9968	+	9.23578i	0.561034	+	0.323913i
$814$		0			0
$815$	−5.37454	+	9.30898i	−0.188262	+	0.326079i
$816$		0			0
$817$	10.4704	−	6.04506i	0.366311	−	0.211490i
$818$		0			0
$819$	−5.80170	+	7.78482i	−0.202728	+	0.272024i
$820$		0			0
$821$	33.4223	−	19.2964i	1.16645	−	0.673449i	0.213607	−	0.976920i	$-0.431479\pi$
$821$	33.4223	−	19.2964i	1.16645	−	0.673449i	0.952841	+	0.303471i	$0.0981455\pi$
$822$		0			0
$823$	25.3601	−	43.9250i	0.883999	−	1.53113i	0.0371413	−	0.999310i	$-0.488175\pi$
$823$	25.3601	−	43.9250i	0.883999	−	1.53113i	0.846857	−	0.531820i	$-0.178492\pi$
$824$		0			0
$825$	27.8322	+	16.0689i	0.968993	+	0.559448i
$826$		0			0
$827$			21.9754i			0.764158i	0.924130	+	0.382079i	$0.124792\pi$
$827$			21.9754i			0.764158i	−0.924130	+	0.382079i	$0.875208\pi$
$828$		0			0
$829$	4.42741	+	7.66849i	0.153770	+	0.266338i	0.932611	−	0.360884i	$-0.117525\pi$
$829$	4.42741	+	7.66849i	0.153770	+	0.266338i	−0.778840	+	0.627222i	$0.784192\pi$
$830$		0			0
$831$	−75.4664			−2.61790
$832$		0			0
$833$	−0.971244			−0.0336516
$834$		0			0
$835$	−3.69064	−	6.39237i	−0.127720	−	0.221217i
$836$		0			0
$837$			2.88927i			0.0998677i
$838$		0			0
$839$	25.9070	+	14.9574i	0.894409	+	0.516387i	0.875382	−	0.483432i	$-0.160610\pi$
$839$	25.9070	+	14.9574i	0.894409	+	0.516387i	0.0190269	+	0.999819i	$0.493943\pi$
$840$		0			0
$841$	−32.8431	+	56.8859i	−1.13252	+	1.96158i
$842$		0			0
$843$	−15.2242	+	8.78969i	−0.524349	+	0.302733i
$844$		0			0
$845$	−8.28980	−	7.83687i	−0.285178	−	0.269596i
$846$		0			0
$847$	0.744775	−	0.429996i	0.0255908	−	0.0147748i
$848$		0			0
$849$	13.0553	−	22.6125i	0.448057	−	0.776058i
$850$		0			0
$851$	14.6114	+	8.43591i	0.500873	+	0.289179i
$852$		0			0
$853$			39.7867i			1.36227i	0.732158	+	0.681135i	$0.238513\pi$
$853$			39.7867i			1.36227i	−0.732158	+	0.681135i	$0.761487\pi$
$854$		0			0
$855$	−1.87299	−	3.24412i	−0.0640550	−	0.110946i
$856$		0			0
$857$	17.0715			0.583150			0.291575	−	0.956548i	$-0.405821\pi$
$857$	17.0715			0.583150			0.291575	+	0.956548i	$0.405821\pi$
$858$		0			0
$859$	−45.4327			−1.55014			−0.775071	−	0.631874i	$-0.782286\pi$
$859$	−45.4327			−1.55014			−0.775071	+	0.631874i	$0.782286\pi$
$860$		0			0
$861$	−5.39165	−	9.33862i	−0.183747	−	0.318259i
$862$		0			0
$863$			22.8572i			0.778068i	0.921223	+	0.389034i	$0.127191\pi$
$863$			22.8572i			0.778068i	−0.921223	+	0.389034i	$0.872809\pi$
$864$		0			0
$865$	−10.4431	−	6.02935i	−0.355078	−	0.205004i
$866$		0			0
$867$	19.1552	−	33.1779i	0.650546	−	1.12678i
$868$		0			0
$869$	27.0190	−	15.5994i	0.916556	−	0.529174i
$870$		0			0
$871$	16.0658	−	21.5573i	0.544368	−	0.730443i
$872$		0			0
$873$	9.57594	−	5.52867i	0.324097	−	0.187117i
$874$		0			0
$875$	−4.04974	+	7.01436i	−0.136906	+	0.237129i
$876$		0			0
$877$	25.8613	+	14.9310i	0.873273	+	0.504185i	0.868435	−	0.495804i	$-0.165126\pi$
$877$	25.8613	+	14.9310i	0.873273	+	0.504185i	0.00483876	+	0.999988i	$0.498460\pi$
$878$		0			0
$879$			75.9980i			2.56335i
$880$		0			0
$881$	−12.4867	−	21.6277i	−0.420689	−	0.728655i	0.575318	−	0.817930i	$-0.304878\pi$
$881$	−12.4867	−	21.6277i	−0.420689	−	0.728655i	−0.996007	+	0.0892748i	$0.971545\pi$
$882$		0			0
$883$	12.3025			0.414011			0.207005	−	0.978340i	$-0.433628\pi$
$883$	12.3025			0.414011			0.207005	+	0.978340i	$0.433628\pi$
$884$		0			0
$885$	−2.17916			−0.0732518
$886$		0			0
$887$	19.1931	+	33.2434i	0.644441	+	1.11620i	0.984430	+	0.175775i	$0.0562433\pi$
$887$	19.1931	+	33.2434i	0.644441	+	1.11620i	−0.339989	+	0.940429i	$0.610423\pi$
$888$		0			0
$889$			20.7801i			0.696942i
$890$		0			0
$891$	−27.1009	−	15.6467i	−0.907915	−	0.524185i
$892$		0			0
$893$	−3.26580	+	5.65653i	−0.109286	+	0.189289i
$894$		0			0
$895$	16.5708	−	9.56713i	0.553899	−	0.319794i
$896$		0			0
$897$	3.27430	−	27.8913i	0.109326	−	0.931262i
$898$		0			0
$899$	33.2151	−	19.1768i	1.10779	−	0.639581i
$900$		0			0
$901$	0.979433	−	1.69643i	0.0326297	−	0.0565162i
$902$		0			0
$903$	−15.7585	−	9.09816i	−0.524409	−	0.302768i
$904$		0			0
$905$			14.3868i			0.478233i
$906$		0			0
$907$	7.59821	+	13.1605i	0.252294	+	0.436987i	0.964157	−	0.265332i	$-0.0854815\pi$
$907$	7.59821	+	13.1605i	0.252294	+	0.436987i	−0.711863	+	0.702319i	$0.752148\pi$
$908$		0			0
$909$	36.9848			1.22671
$910$		0			0
$911$	46.1592			1.52932			0.764661	−	0.644433i	$-0.222907\pi$
$911$	46.1592			1.52932			0.764661	+	0.644433i	$0.222907\pi$
$912$		0			0
$913$	−10.8537	−	18.7991i	−0.359204	−	0.622159i
$914$		0			0
$915$		−	10.4898i		−	0.346782i
$916$		0			0
$917$	−1.54410	−	0.891489i	−0.0509908	−	0.0294396i
$918$		0			0
$919$	8.72945	−	15.1198i	0.287958	−	0.498758i	−0.685364	−	0.728200i	$-0.740357\pi$
$919$	8.72945	−	15.1198i	0.287958	−	0.498758i	0.973322	+	0.229443i	$0.0736904\pi$
$920$		0			0
$921$	−67.4131	+	38.9210i	−2.22134	+	1.28249i
$922$		0			0
$923$	−14.6022	−	1.71423i	−0.480638	−	0.0564245i
$924$		0			0
$925$	−18.9331	+	10.9310i	−0.622516	+	0.359410i
$926$		0			0
$927$	−3.17039	+	5.49127i	−0.104129	+	0.180357i
$928$		0			0
$929$	−47.9927	−	27.7086i	−1.57459	−	0.909091i	−0.995595	−	0.0937602i	$-0.970111\pi$
$929$	−47.9927	−	27.7086i	−1.57459	−	0.909091i	−0.578996	−	0.815330i	$-0.696555\pi$
$930$		0			0
$931$		−	1.58529i		−	0.0519558i
$932$		0			0
$933$	8.19494	+	14.1941i	0.268290	+	0.464692i
$934$		0			0
$935$	−2.71397			−0.0887563
$936$		0			0
$937$	28.3045			0.924668			0.462334	−	0.886706i	$-0.347012\pi$
$937$	28.3045			0.924668			0.462334	+	0.886706i	$0.347012\pi$
$938$		0			0
$939$	2.54267	+	4.40403i	0.0829769	+	0.143720i
$940$		0			0
$941$			20.5105i			0.668622i	0.942463	+	0.334311i	$0.108504\pi$
$941$			20.5105i			0.668622i	−0.942463	+	0.334311i	$0.891496\pi$
$942$		0			0
$943$	12.7770	+	7.37679i	0.416075	+	0.240221i
$944$		0			0
$945$	0.321628	−	0.557076i	0.0104626	−	0.0181217i
$946$		0			0
$947$	−5.34051	+	3.08334i	−0.173543	+	0.100195i	−0.584256	−	0.811570i	$-0.698613\pi$
$947$	−5.34051	+	3.08334i	−0.173543	+	0.100195i	0.410712	+	0.911765i	$0.365280\pi$
$948$		0			0
$949$	18.0898	+	41.9952i	0.587220	+	1.36322i
$950$		0			0
$951$	11.4110	−	6.58812i	0.370025	−	0.213634i
$952$		0			0
$953$	−20.5522	+	35.5975i	−0.665751	+	1.15312i	0.313330	+	0.949644i	$0.398556\pi$
$953$	−20.5522	+	35.5975i	−0.665751	+	1.15312i	−0.979081	+	0.203471i	$0.934778\pi$
$954$		0			0
$955$	8.32883	+	4.80865i	0.269515	+	0.155604i
$956$		0			0
$957$			73.9306i			2.38984i
$958$		0			0
$959$	8.31871	+	14.4084i	0.268625	+	0.465272i
$960$		0			0
$961$	15.4646			0.498857
$962$		0			0
$963$	11.4325			0.368407
$964$		0			0
$965$	−0.925897	−	1.60370i	−0.0298057	−	0.0516250i
$966$		0			0
$967$			45.3751i			1.45917i	0.683892	+	0.729583i	$0.260286\pi$
$967$			45.3751i			1.45917i	−0.683892	+	0.729583i	$0.739714\pi$
$968$		0			0
$969$	−3.18149	−	1.83683i	−0.102204	−	0.0590075i
$970$		0			0
$971$	−20.6103	+	35.6980i	−0.661415	+	1.14560i	0.318829	+	0.947812i	$0.396710\pi$
$971$	−20.6103	+	35.6980i	−0.661415	+	1.14560i	−0.980244	+	0.197792i	$0.936623\pi$
$972$		0			0
$973$	−1.34470	+	0.776363i	−0.0431091	+	0.0248890i
$974$		0			0
$975$	29.1774	+	21.7447i	0.934426	+	0.696388i
$976$		0			0
$977$	−49.5561	+	28.6112i	−1.58544	+	0.915355i	−0.591397	+	0.806381i	$0.701423\pi$
$977$	−49.5561	+	28.6112i	−1.58544	+	0.915355i	−0.994045	+	0.108974i	$0.965243\pi$
$978$		0			0
$979$	−7.37386	+	12.7719i	−0.235670	+	0.408192i
$980$		0			0
$981$	43.9714	+	25.3869i	1.40390	+	0.810541i
$982$		0			0
$983$		−	45.1712i		−	1.44074i	−0.693592	−	0.720368i	$-0.743973\pi$
$983$		−	45.1712i		−	1.44074i	0.693592	−	0.720368i	$-0.256027\pi$
$984$		0			0
$985$	−2.11690	−	3.66658i	−0.0674500	−	0.116827i
$986$		0			0
$987$	9.83042			0.312906
$988$		0			0
$989$	24.8959			0.791645
$990$		0			0
$991$	−5.79069	−	10.0298i	−0.183947	−	0.318606i	0.759274	−	0.650771i	$-0.225554\pi$
$991$	−5.79069	−	10.0298i	−0.183947	−	0.318606i	−0.943221	+	0.332165i	$0.892221\pi$
$992$		0			0
$993$			22.6148i			0.717661i
$994$		0			0
$995$	5.62339	+	3.24667i	0.178273	+	0.102926i
$996$		0			0
$997$	−20.0031	+	34.6464i	−0.633505	+	1.09726i	0.353324	+	0.935501i	$0.385051\pi$
$997$	−20.0031	+	34.6464i	−0.633505	+	1.09726i	−0.986830	+	0.161763i	$0.948282\pi$
$998$		0			0
$999$	3.28104	−	1.89431i	0.103807	−	0.0599333i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	728.2.bm.b.673.1	yes	12
4.3	odd	2		1456.2.cc.e.673.6		12
13.2	odd	12		9464.2.a.bf.1.6		6
13.4	even	6	inner	728.2.bm.b.225.1	✓	12
13.11	odd	12		9464.2.a.bg.1.6		6
52.43	odd	6		1456.2.cc.e.225.6		12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
728.2.bm.b.225.1	✓	12	13.4	even	6	inner
728.2.bm.b.673.1	yes	12	1.1	even	1	trivial
1456.2.cc.e.225.6		12	52.43	odd	6
1456.2.cc.e.673.6		12	4.3	odd	2
9464.2.a.bf.1.6		6	13.2	odd	12
9464.2.a.bg.1.6		6	13.11	odd	12

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 $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 728 = 2^{3} \cdot 7 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	728.bm (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.19298 - 2.06630i) q^{3} -0.877521i q^{5} +(-0.866025 - 0.500000i) q^{7} +(-1.34638 + 2.33201i) q^{9} +(-2.75772 + 1.59217i) q^{11} +(-3.31140 + 1.42641i) q^{13} +(-1.81322 + 1.04686i) q^{15} +(-0.485622 + 0.841122i) q^{17} +(-1.37290 - 0.792646i) q^{19} +2.38595i q^{21} +(-1.63221 - 2.82708i) q^{23} +4.22996 q^{25} -0.733037 q^{27} +(4.86534 + 8.42702i) q^{29} -3.94150i q^{31} +(6.57978 + 3.79884i) q^{33} +(-0.438760 + 0.759955i) q^{35} +(-4.47595 + 2.58419i) q^{37} +(6.89781 + 5.14065i) q^{39} +(-3.91400 + 2.25975i) q^{41} +(-3.81322 + 6.60469i) q^{43} +(2.04638 + 1.18148i) q^{45} -4.12013i q^{47} +(0.500000 + 0.866025i) q^{49} +2.31734 q^{51} -2.01686 q^{53} +(1.39716 + 2.41995i) q^{55} +3.78243i q^{57} +(0.901366 + 0.520404i) q^{59} +(-2.50506 + 4.33888i) q^{61} +(2.33201 - 1.34638i) q^{63} +(1.25171 + 2.90582i) q^{65} +(-6.45768 + 3.72834i) q^{67} +(-3.89438 + 6.74527i) q^{69} +(3.53142 + 2.03887i) q^{71} -12.6820i q^{73} +(-5.04624 - 8.74034i) q^{75} +3.18434 q^{77} -9.79759 q^{79} +(4.91365 + 8.51069i) q^{81} +6.81690i q^{83} +(0.738102 + 0.426144i) q^{85} +(11.6085 - 20.1065i) q^{87} +(4.01085 - 2.31567i) q^{89} +(3.58096 + 0.420388i) q^{91} +(-8.14431 + 4.70212i) q^{93} +(-0.695563 + 1.20475i) q^{95} +(-3.55617 - 2.05315i) q^{97} -8.57469i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q - 2 q^{3} + 4 q^{9} + 2 q^{13} + 12 q^{15} + 2 q^{17} + 12 q^{19} - 6 q^{23} + 4 q^{25} + 4 q^{27} + 20 q^{29} + 6 q^{33} - 4 q^{35} - 6 q^{37} + 26 q^{39} - 12 q^{41} - 12 q^{43} + 18 q^{45} + 6 q^{49}+ \cdots - 6 q^{97}+O(q^{100}) \) 12 * q - 2 * q^3 + 4 * q^9 + 2 * q^13 + 12 * q^15 + 2 * q^17 + 12 * q^19 - 6 * q^23 + 4 * q^25 + 4 * q^27 + 20 * q^29 + 6 * q^33 - 4 * q^35 - 6 * q^37 + 26 * q^39 - 12 * q^41 - 12 * q^43 + 18 * q^45 + 6 * q^49 + 16 * q^51 + 20 * q^53 + 24 * q^55 - 12 * q^59 - 4 * q^61 + 8 * q^65 - 6 * q^67 + 36 * q^71 - 10 * q^75 + 20 * q^77 - 20 * q^79 + 18 * q^81 - 36 * q^85 + 32 * q^87 - 36 * q^89 + 2 * q^91 - 42 * q^93 - 26 * q^95 - 6 * q^97

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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