LMFDB - Embedded newform 576.3.o.i.511.10

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [576,3,Mod(319,576)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(576, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([3, 0, 2]))

N = Newforms(chi, 3, names="a")

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

chi := DirichletCharacter("576.319");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 576 = 2^{6} \cdot 3^{2} $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	576.o (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:	$15.6948632272$
Analytic rank:	$0$
Dimension:	$24$
Relative dimension:	$12$ over $\Q(\zeta_{6})$
Twist minimal:	no (minimal twist has level 288)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			511.10
Character	$\chi$	$=$	576.511
Dual form			576.3.o.i.319.10

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(2.10592 - 2.13661i) q^{3} +(1.25241 + 2.16924i) q^{5} +(0.842935 + 0.486669i) q^{7} +(-0.130192 - 8.99906i) q^{9} +O(q^{10})$	\(q+(2.10592 - 2.13661i) q^{3} +(1.25241 + 2.16924i) q^{5} +(0.842935 + 0.486669i) q^{7} +(-0.130192 - 8.99906i) q^{9} +(-3.01493 - 1.74067i) q^{11} +(7.51352 + 13.0138i) q^{13} +(7.27231 + 1.89234i) q^{15} +19.3227 q^{17} -13.9609i q^{19} +(2.81498 - 0.776136i) q^{21} +(33.5924 - 19.3946i) q^{23} +(9.36292 - 16.2170i) q^{25} +(-19.5016 - 18.6731i) q^{27} +(-6.95537 + 12.0470i) q^{29} +(12.1511 - 7.01542i) q^{31} +(-10.0683 + 2.77601i) q^{33} +2.43804i q^{35} -28.1331 q^{37} +(43.6283 + 11.3526i) q^{39} +(18.4281 + 31.9183i) q^{41} +(36.2892 + 20.9516i) q^{43} +(19.3581 - 11.5530i) q^{45} +(10.7892 + 6.22913i) q^{47} +(-24.0263 - 41.6148i) q^{49} +(40.6920 - 41.2850i) q^{51} -16.6482 q^{53} -8.72017i q^{55} +(-29.8289 - 29.4005i) q^{57} +(-11.3836 + 6.57234i) q^{59} +(-41.5302 + 71.9324i) q^{61} +(4.26982 - 7.64898i) q^{63} +(-18.8201 + 32.5973i) q^{65} +(95.1188 - 54.9169i) q^{67} +(29.3043 - 112.617i) q^{69} -96.4767i q^{71} -40.1094 q^{73} +(-14.9319 - 54.1567i) q^{75} +(-1.69426 - 2.93455i) q^{77} +(-117.038 - 67.5719i) q^{79} +(-80.9661 + 2.34320i) q^{81} +(52.4342 + 30.2729i) q^{83} +(24.2000 + 41.9156i) q^{85} +(11.0924 + 40.2310i) q^{87} +138.741 q^{89} +14.6264i q^{91} +(10.6000 - 40.7360i) q^{93} +(30.2846 - 17.4848i) q^{95} +(-79.4667 + 137.640i) q^{97} +(-15.2719 + 27.3582i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 24 q - 4 q^{9}+O(q^{10}) $ 24 * q - 4 * q^9	$ 24 q - 4 q^{9} + 24 q^{13} - 24 q^{17} - 56 q^{21} - 108 q^{25} + 24 q^{29} + 52 q^{33} - 96 q^{37} - 60 q^{41} + 224 q^{45} - 132 q^{49} - 96 q^{53} + 348 q^{57} + 336 q^{61} + 216 q^{65} - 416 q^{69} + 696 q^{73} + 24 q^{77} - 788 q^{81} + 528 q^{85} - 240 q^{89} - 1040 q^{93} - 444 q^{97}+O(q^{100}) $ 24 * q - 4 * q^9 + 24 * q^13 - 24 * q^17 - 56 * q^21 - 108 * q^25 + 24 * q^29 + 52 * q^33 - 96 * q^37 - 60 * q^41 + 224 * q^45 - 132 * q^49 - 96 * q^53 + 348 * q^57 + 336 * q^61 + 216 * q^65 - 416 * q^69 + 696 * q^73 + 24 * q^77 - 788 * q^81 + 528 * q^85 - 240 * q^89 - 1040 * q^93 - 444 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/576\mathbb{Z}\right)^\times$.

$n$	$65$	$127$	$325$
$\chi(n)$	$e\left(\frac{2}{3}\right)$	$-1$	$1$

Coefficient data

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

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

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

$2$		0			0
$2$		0			0
$3$	2.10592	−	2.13661i	0.701974	−	0.712203i
$3$	2.10592	−	2.13661i	0.701974	−	0.712203i
$4$		0			0
$5$	1.25241	+	2.16924i	0.250483	+	0.433849i	0.963659	−	0.267136i	$-0.0860773\pi$
$5$	1.25241	+	2.16924i	0.250483	+	0.433849i	−0.713176	+	0.700985i	$0.752744\pi$
$6$		0			0
$7$	0.842935	+	0.486669i	0.120419	+	0.0695241i	0.559000	−	0.829168i	$-0.311185\pi$
$7$	0.842935	+	0.486669i	0.120419	+	0.0695241i	−0.438580	+	0.898692i	$0.644519\pi$
$8$		0			0
$9$	−0.130192	−	8.99906i	−0.0144657	−	0.999895i
$10$		0			0
$11$	−3.01493	−	1.74067i	−0.274085	−	0.158243i	0.356658	−	0.934235i	$-0.383916\pi$
$11$	−3.01493	−	1.74067i	−0.274085	−	0.158243i	−0.630742	+	0.775992i	$0.717250\pi$
$12$		0			0
$13$	7.51352	+	13.0138i	0.577963	+	1.00106i	0.995713	+	0.0924992i	$0.0294856\pi$
$13$	7.51352	+	13.0138i	0.577963	+	1.00106i	−0.417750	+	0.908562i	$0.637181\pi$
$14$		0			0
$15$	7.27231	+	1.89234i	0.484821	+	0.126156i
$16$		0			0
$17$	19.3227			1.13663			0.568314	−	0.822812i	$-0.307596\pi$
$17$	19.3227			1.13663			0.568314	+	0.822812i	$0.307596\pi$
$18$		0			0
$19$		−	13.9609i		−	0.734783i	−0.930066	−	0.367392i	$-0.880251\pi$
$19$		−	13.9609i		−	0.734783i	0.930066	−	0.367392i	$-0.119749\pi$
$20$		0			0
$21$	2.81498	−	0.776136i	0.134046	−	0.0369589i
$22$		0			0
$23$	33.5924	−	19.3946i	1.46054	−	0.843243i	0.461504	−	0.887138i	$-0.347310\pi$
$23$	33.5924	−	19.3946i	1.46054	−	0.843243i	0.999036	+	0.0438947i	$0.0139766\pi$
$24$		0			0
$25$	9.36292	−	16.2170i	0.374517	−	0.648682i
$26$		0			0
$27$	−19.5016	−	18.6731i	−0.722283	−	0.691598i
$28$		0			0
$29$	−6.95537	+	12.0470i	−0.239840	+	0.415415i	−0.960668	−	0.277698i	$-0.910428\pi$
$29$	−6.95537	+	12.0470i	−0.239840	+	0.415415i	0.720828	+	0.693114i	$0.243762\pi$
$30$		0			0
$31$	12.1511	−	7.01542i	0.391970	−	0.226304i	−0.291043	−	0.956710i	$-0.594002\pi$
$31$	12.1511	−	7.01542i	0.391970	−	0.226304i	0.683013	+	0.730406i	$0.260669\pi$
$32$		0			0
$33$	−10.0683	+	2.77601i	−0.305101	+	0.0841216i
$34$		0			0
$35$			2.43804i			0.0696584i
$36$		0			0
$37$	−28.1331			−0.760354			−0.380177	−	0.924914i	$-0.624137\pi$
$37$	−28.1331			−0.760354			−0.380177	+	0.924914i	$0.624137\pi$
$38$		0			0
$39$	43.6283	+	11.3526i	1.11867	+	0.291092i
$40$		0			0
$41$	18.4281	+	31.9183i	0.449465	+	0.778496i	0.998351	−	0.0574009i	$-0.0182813\pi$
$41$	18.4281	+	31.9183i	0.449465	+	0.778496i	−0.548886	+	0.835897i	$0.684948\pi$
$42$		0			0
$43$	36.2892	+	20.9516i	0.843935	+	0.487246i	0.858600	−	0.512646i	$-0.171335\pi$
$43$	36.2892	+	20.9516i	0.843935	+	0.487246i	−0.0146648	+	0.999892i	$0.504668\pi$
$44$		0			0
$45$	19.3581	−	11.5530i	0.430180	−	0.256733i
$46$		0			0
$47$	10.7892	+	6.22913i	0.229557	+	0.132535i	0.610368	−	0.792118i	$-0.291022\pi$
$47$	10.7892	+	6.22913i	0.229557	+	0.132535i	−0.380811	+	0.924653i	$0.624355\pi$
$48$		0			0
$49$	−24.0263	−	41.6148i	−0.490333	−	0.849281i
$50$		0			0
$51$	40.6920	−	41.2850i	0.797883	−	0.809510i
$52$		0			0
$53$	−16.6482			−0.314116			−0.157058	−	0.987589i	$-0.550201\pi$
$53$	−16.6482			−0.314116			−0.157058	+	0.987589i	$0.550201\pi$
$54$		0			0
$55$		−	8.72017i		−	0.158548i
$56$		0			0
$57$	−29.8289	−	29.4005i	−0.523315	−	0.515799i
$58$		0			0
$59$	−11.3836	+	6.57234i	−0.192943	+	0.111396i	−0.593359	−	0.804938i	$-0.702199\pi$
$59$	−11.3836	+	6.57234i	−0.192943	+	0.111396i	0.400417	+	0.916333i	$0.368865\pi$
$60$		0			0
$61$	−41.5302	+	71.9324i	−0.680823	+	1.17922i	0.293907	+	0.955834i	$0.405044\pi$
$61$	−41.5302	+	71.9324i	−0.680823	+	1.17922i	−0.974730	+	0.223386i	$0.928289\pi$
$62$		0			0
$63$	4.26982	−	7.64898i	0.0677749	−	0.121412i
$64$		0			0
$65$	−18.8201	+	32.5973i	−0.289540	+	0.501497i
$66$		0			0
$67$	95.1188	−	54.9169i	1.41968	−	0.819655i	0.423413	−	0.905937i	$-0.360832\pi$
$67$	95.1188	−	54.9169i	1.41968	−	0.819655i	0.996271	+	0.0862815i	$0.0274984\pi$
$68$		0			0
$69$	29.3043	−	112.617i	0.424701	−	1.63214i
$70$		0			0
$71$		−	96.4767i		−	1.35883i	−0.733756	−	0.679413i	$-0.762234\pi$
$71$		−	96.4767i		−	1.35883i	0.733756	−	0.679413i	$-0.237766\pi$
$72$		0			0
$73$	−40.1094			−0.549444			−0.274722	−	0.961524i	$-0.588586\pi$
$73$	−40.1094			−0.549444			−0.274722	+	0.961524i	$0.588586\pi$
$74$		0			0
$75$	−14.9319	−	54.1567i	−0.199092	−	0.722090i
$76$		0			0
$77$	−1.69426	−	2.93455i	−0.0220034	−	0.0381110i
$78$		0			0
$79$	−117.038	−	67.5719i	−1.48149	−	0.855340i	−0.481713	−	0.876329i	$-0.659985\pi$
$79$	−117.038	−	67.5719i	−1.48149	−	0.855340i	−0.999780	+	0.0209890i	$0.993318\pi$
$80$		0			0
$81$	−80.9661	+	2.34320i	−0.999581	+	0.0289284i
$82$		0			0
$83$	52.4342	+	30.2729i	0.631738	+	0.364734i	0.781425	−	0.624000i	$-0.214493\pi$
$83$	52.4342	+	30.2729i	0.631738	+	0.364734i	−0.149687	+	0.988733i	$0.547827\pi$
$84$		0			0
$85$	24.2000	+	41.9156i	0.284706	+	0.493125i
$86$		0			0
$87$	11.0924	+	40.2310i	0.127499	+	0.462426i
$88$		0			0
$89$	138.741			1.55889			0.779444	−	0.626472i	$-0.215502\pi$
$89$	138.741			1.55889			0.779444	+	0.626472i	$0.215502\pi$
$90$		0			0
$91$			14.6264i			0.160729i
$92$		0			0
$93$	10.6000	−	40.7360i	0.113978	−	0.438021i
$94$		0			0
$95$	30.2846	−	17.4848i	0.318785	−	0.184051i
$96$		0			0
$97$	−79.4667	+	137.640i	−0.819244	+	1.41897i	0.0869954	+	0.996209i	$0.472273\pi$
$97$	−79.4667	+	137.640i	−0.819244	+	1.41897i	−0.906240	+	0.422764i	$0.861060\pi$
$98$		0			0
$99$	−15.2719	+	27.3582i	−0.154261	+	0.276345i
$100$		0			0
$101$	51.6687	−	89.4929i	0.511572	−	0.886068i	−0.488338	−	0.872654i	$-0.662397\pi$
$101$	51.6687	−	89.4929i	0.511572	−	0.886068i	0.999910	−	0.0134136i	$-0.00426982\pi$
$102$		0			0
$103$	16.5726	−	9.56821i	0.160899	−	0.0928952i	−0.417388	−	0.908728i	$-0.637054\pi$
$103$	16.5726	−	9.56821i	0.160899	−	0.0928952i	0.578288	+	0.815833i	$0.303721\pi$
$104$		0			0
$105$	5.20914	+	5.13433i	0.0496109	+	0.0488984i
$106$		0			0
$107$			14.1915i			0.132630i	0.997799	+	0.0663152i	$0.0211243\pi$
$107$			14.1915i			0.132630i	−0.997799	+	0.0663152i	$0.978876\pi$
$108$		0			0
$109$	−168.973			−1.55021			−0.775104	−	0.631833i	$-0.782303\pi$
$109$	−168.973			−1.55021			−0.775104	+	0.631833i	$0.782303\pi$
$110$		0			0
$111$	−59.2461	+	60.1094i	−0.533749	+	0.541526i
$112$		0			0
$113$	109.790	+	190.163i	0.971597	+	1.68286i	0.690737	+	0.723107i	$0.257286\pi$
$113$	109.790	+	190.163i	0.971597	+	1.68286i	0.280860	+	0.959749i	$0.409380\pi$
$114$		0			0
$115$	84.1433	+	48.5801i	0.731681	+	0.422436i
$116$		0			0
$117$	116.134	−	69.3089i	0.992596	−	0.592384i
$118$		0			0
$119$	16.2878	+	9.40374i	0.136872	+	0.0790231i
$120$		0			0
$121$	−54.4401	−	94.2931i	−0.449918	−	0.779282i
$122$		0			0
$123$	107.005	+	27.8440i	0.869960	+	0.226374i
$124$		0			0
$125$	109.526			0.876206
$126$		0			0
$127$			158.301i			1.24647i	0.782036	+	0.623233i	$0.214181\pi$
$127$			158.301i			1.24647i	−0.782036	+	0.623233i	$0.785819\pi$
$128$		0			0
$129$	121.188	−	33.4134i	0.939438	−	0.259019i
$130$		0			0
$131$	−154.026	+	88.9267i	−1.17577	+	0.678830i	−0.955032	−	0.296504i	$-0.904179\pi$
$131$	−154.026	+	88.9267i	−1.17577	+	0.678830i	−0.220736	+	0.975334i	$0.570846\pi$
$132$		0			0
$133$	6.79433	−	11.7681i	0.0510852	−	0.0884821i
$134$		0			0
$135$	16.0825	−	65.6903i	0.119130	−	0.486595i
$136$		0			0
$137$	31.8904	−	55.2358i	0.232776	−	0.403181i	−0.725848	−	0.687855i	$-0.758552\pi$
$137$	31.8904	−	55.2358i	0.232776	−	0.403181i	0.958624	+	0.284675i	$0.0918856\pi$
$138$		0			0
$139$	−140.171	+	80.9275i	−1.00842	+	0.582212i	−0.910729	−	0.413005i	$-0.864479\pi$
$139$	−140.171	+	80.9275i	−1.00842	+	0.582212i	−0.0976920	+	0.995217i	$0.531146\pi$
$140$		0			0
$141$	36.0304	−	9.93418i	0.255535	−	0.0704552i
$142$		0			0
$143$		−	52.3143i		−	0.365834i
$144$		0			0
$145$	−34.8440			−0.240303
$146$		0			0
$147$	−139.512	−	36.3026i	−0.949061	−	0.246957i
$148$		0			0
$149$	46.4133	+	80.3902i	0.311499	+	0.539532i	0.978687	−	0.205357i	$-0.0658357\pi$
$149$	46.4133	+	80.3902i	0.311499	+	0.539532i	−0.667188	+	0.744889i	$0.732502\pi$
$150$		0			0
$151$	−85.2221	−	49.2030i	−0.564385	−	0.325848i	0.190519	−	0.981684i	$-0.438983\pi$
$151$	−85.2221	−	49.2030i	−0.564385	−	0.325848i	−0.754903	+	0.655836i	$0.772316\pi$
$152$		0			0
$153$	−2.51565	−	173.886i	−0.0164422	−	1.13651i
$154$		0			0
$155$	30.4363	+	17.5724i	0.196363	+	0.113370i
$156$		0			0
$157$	76.1683	+	131.927i	0.485149	+	0.840302i	0.999854	−	0.0170647i	$-0.00543213\pi$
$157$	76.1683	+	131.927i	0.485149	+	0.840302i	−0.514706	+	0.857367i	$0.672099\pi$
$158$		0			0
$159$	−35.0597	+	35.5706i	−0.220502	+	0.223715i
$160$		0			0
$161$	37.7550			0.234503
$162$		0			0
$163$		−	107.979i		−	0.662450i	−0.943552	−	0.331225i	$-0.892538\pi$
$163$		−	107.979i		−	0.662450i	0.943552	−	0.331225i	$-0.107462\pi$
$164$		0			0
$165$	−18.6316	−	18.3640i	−0.112919	−	0.111297i
$166$		0			0
$167$	−268.150	+	154.816i	−1.60569	+	0.927043i	−0.615366	+	0.788241i	$0.710992\pi$
$167$	−268.150	+	154.816i	−1.60569	+	0.927043i	−0.990320	+	0.138802i	$0.955675\pi$
$168$		0			0
$169$	−28.4060	+	49.2006i	−0.168083	+	0.291128i
$170$		0			0
$171$	−125.635	+	1.81759i	−0.734706	+	0.0106292i
$172$		0			0
$173$	−137.931	+	238.903i	−0.797288	+	1.38094i	0.124089	+	0.992271i	$0.460399\pi$
$173$	−137.931	+	238.903i	−0.797288	+	1.38094i	−0.921376	+	0.388672i	$0.872934\pi$
$174$		0			0
$175$	15.7847	−	9.11328i	0.0901981	−	0.0520759i
$176$		0			0
$177$	−9.93050	+	38.1632i	−0.0561045	+	0.215611i
$178$		0			0
$179$		−	66.7842i		−	0.373096i	−0.982446	−	0.186548i	$-0.940270\pi$
$179$		−	66.7842i		−	0.373096i	0.982446	−	0.186548i	$-0.0597300\pi$
$180$		0			0
$181$	−217.288			−1.20049			−0.600244	−	0.799817i	$-0.704930\pi$
$181$	−217.288			−1.20049			−0.600244	+	0.799817i	$0.704930\pi$
$182$		0			0
$183$	66.2321	+	240.218i	0.361924	+	1.31267i
$184$		0			0
$185$	−35.2343	−	61.0276i	−0.190456	−	0.329879i
$186$		0			0
$187$	−58.2565	−	33.6344i	−0.311532	−	0.179863i
$188$		0			0
$189$	−7.35098	−	25.2311i	−0.0388941	−	0.133498i
$190$		0			0
$191$	217.435	+	125.536i	1.13841	+	0.657258i	0.946035	−	0.324064i	$-0.105049\pi$
$191$	217.435	+	125.536i	1.13841	+	0.657258i	0.192370	+	0.981322i	$0.438383\pi$
$192$		0			0
$193$	−20.4473	−	35.4158i	−0.105945	−	0.183501i	0.808179	−	0.588937i	$-0.200453\pi$
$193$	−20.4473	−	35.4158i	−0.105945	−	0.183501i	−0.914124	+	0.405435i	$0.867120\pi$
$194$		0			0
$195$	30.0141	+	108.859i	0.153919	+	0.558249i
$196$		0			0
$197$	189.163			0.960219			0.480109	−	0.877209i	$-0.340597\pi$
$197$	189.163			0.960219			0.480109	+	0.877209i	$0.340597\pi$
$198$		0			0
$199$			76.3625i			0.383731i	0.981421	+	0.191866i	$0.0614538\pi$
$199$			76.3625i			0.383731i	−0.981421	+	0.191866i	$0.938546\pi$
$200$		0			0
$201$	82.9769	−	318.882i	0.412820	−	1.58648i
$202$		0			0
$203$	−11.7258	+	6.76992i	−0.0577628	+	0.0333494i
$204$		0			0
$205$	−46.1591	+	79.9500i	−0.225167	+	0.390000i
$206$		0			0
$207$	−178.907	−	299.775i	−0.864283	−	1.44819i
$208$		0			0
$209$	−24.3013	+	42.0911i	−0.116274	+	0.201393i
$210$		0			0
$211$	−301.301	+	173.956i	−1.42797	+	0.824436i	−0.996960	−	0.0779128i	$-0.975174\pi$
$211$	−301.301	+	173.956i	−1.42797	+	0.824436i	−0.431006	+	0.902349i	$0.641841\pi$
$212$		0			0
$213$	−206.133	−	203.172i	−0.967760	−	0.953860i
$214$		0			0
$215$			104.960i			0.488187i
$216$		0			0
$217$	13.6567			0.0629343
$218$		0			0
$219$	−84.4673	+	85.6982i	−0.385695	+	0.391316i
$220$		0			0
$221$	145.181	+	251.461i	0.656929	+	1.13783i
$222$		0			0
$223$	160.807	+	92.8418i	0.721106	+	0.416331i	0.815160	−	0.579236i	$-0.196649\pi$
$223$	160.807	+	92.8418i	0.721106	+	0.416331i	−0.0940534	+	0.995567i	$0.529982\pi$
$224$		0			0
$225$	−147.157	−	82.1461i	−0.654032	−	0.365094i
$226$		0			0
$227$	−123.810	−	71.4817i	−0.545418	−	0.314897i	0.201854	−	0.979416i	$-0.435303\pi$
$227$	−123.810	−	71.4817i	−0.545418	−	0.314897i	−0.747272	+	0.664518i	$0.768637\pi$
$228$		0			0
$229$	−89.9704	−	155.833i	−0.392884	−	0.680495i	0.599945	−	0.800041i	$-0.295189\pi$
$229$	−89.9704	−	155.833i	−0.392884	−	0.680495i	−0.992829	+	0.119547i	$0.961856\pi$
$230$		0			0
$231$	−9.83796	−	2.55995i	−0.0425886	−	0.0110820i
$232$		0			0
$233$	3.00836			0.0129114			0.00645570	−	0.999979i	$-0.497945\pi$
$233$	3.00836			0.0129114			0.00645570	+	0.999979i	$0.497945\pi$
$234$		0			0
$235$			31.2058i			0.132791i
$236$		0			0
$237$	−390.847	+	107.763i	−1.64914	+	0.454697i
$238$		0			0
$239$	−91.9748	+	53.1017i	−0.384832	+	0.222183i	−0.679918	−	0.733288i	$-0.737985\pi$
$239$	−91.9748	+	53.1017i	−0.384832	+	0.222183i	0.295087	+	0.955470i	$0.404651\pi$
$240$		0			0
$241$	−218.501	+	378.454i	−0.906642	+	1.57035i	−0.0879447	+	0.996125i	$0.528030\pi$
$241$	−218.501	+	378.454i	−0.906642	+	1.57035i	−0.818698	+	0.574225i	$0.805303\pi$
$242$		0			0
$243$	−165.502	+	177.927i	−0.681077	+	0.732212i
$244$		0			0
$245$	60.1818	−	104.238i	0.245640	−	0.425461i
$246$		0			0
$247$	181.684	−	104.895i	0.735563	−	0.424678i
$248$		0			0
$249$	175.104	−	48.2790i	0.703228	−	0.193892i
$250$		0			0
$251$		−	224.126i		−	0.892931i	−0.894801	−	0.446466i	$-0.852682\pi$
$251$		−	224.126i		−	0.892931i	0.894801	−	0.446466i	$-0.147318\pi$
$252$		0			0
$253$	−135.038			−0.533749
$254$		0			0
$255$	140.521	+	36.5651i	0.551061	+	0.143392i
$256$		0			0
$257$	−9.46397	−	16.3921i	−0.0368248	−	0.0637824i	0.847026	−	0.531552i	$-0.178391\pi$
$257$	−9.46397	−	16.3921i	−0.0368248	−	0.0637824i	−0.883850	+	0.467770i	$0.845058\pi$
$258$		0			0
$259$	−23.7144	−	13.6915i	−0.0915613	−	0.0528630i
$260$		0			0
$261$	109.318	+	61.0233i	0.418841	+	0.233806i
$262$		0			0
$263$	−185.185	−	106.917i	−0.704126	−	0.406527i	0.104756	−	0.994498i	$-0.466594\pi$
$263$	−185.185	−	106.917i	−0.704126	−	0.406527i	−0.808882	+	0.587971i	$0.799927\pi$
$264$		0			0
$265$	−20.8504	−	36.1140i	−0.0786808	−	0.136279i
$266$		0			0
$267$	292.178	−	296.435i	1.09430	−	1.11024i
$268$		0			0
$269$	73.4182			0.272930			0.136465	−	0.990645i	$-0.456426\pi$
$269$	73.4182			0.272930			0.136465	+	0.990645i	$0.456426\pi$
$270$		0			0
$271$			95.2505i			0.351478i	0.984437	+	0.175739i	$0.0562315\pi$
$271$			95.2505i			0.351478i	−0.984437	+	0.175739i	$0.943769\pi$
$272$		0			0
$273$	31.2509	+	30.8020i	0.114472	+	0.112828i
$274$		0			0
$275$	−56.4571	+	32.5955i	−0.205299	+	0.118529i
$276$		0			0
$277$	166.006	−	287.531i	0.599299	−	1.03802i	−0.393625	−	0.919271i	$-0.628779\pi$
$277$	166.006	−	287.531i	0.599299	−	1.03802i	0.992925	−	0.118746i	$-0.0378874\pi$
$278$		0			0
$279$	−64.7142	−	108.435i	−0.231950	−	0.388655i
$280$		0			0
$281$	37.0286	−	64.1353i	0.131774	−	0.228240i	−0.792586	−	0.609760i	$-0.791266\pi$
$281$	37.0286	−	64.1353i	0.131774	−	0.228240i	0.924361	+	0.381520i	$0.124599\pi$
$282$		0			0
$283$	−179.846	+	103.834i	−0.635499	+	0.366905i	−0.782879	−	0.622175i	$-0.786249\pi$
$283$	−179.846	+	103.834i	−0.635499	+	0.366905i	0.147380	+	0.989080i	$0.452916\pi$
$284$		0			0
$285$	26.4187	−	101.528i	0.0926973	−	0.356238i
$286$		0			0
$287$			35.8735i			0.124995i
$288$		0			0
$289$	84.3657			0.291923
$290$		0			0
$291$	126.733	+	459.649i	0.435508	+	1.57955i
$292$		0			0
$293$	87.3353	+	151.269i	0.298073	+	0.516277i	0.975695	−	0.219133i	$-0.0703228\pi$
$293$	87.3353	+	151.269i	0.298073	+	0.516277i	−0.677622	+	0.735410i	$0.736990\pi$
$294$		0			0
$295$	−28.5140	−	16.4626i	−0.0966577	−	0.0558054i
$296$		0			0
$297$	26.2923	+	90.2442i	0.0885263	+	0.303852i
$298$		0			0
$299$	504.795	+	291.443i	1.68828	+	0.974727i
$300$		0			0
$301$	20.3930	+	35.3217i	0.0677507	+	0.117348i
$302$		0			0
$303$	−82.4009	−	298.861i	−0.271950	−	0.986339i
$304$		0			0
$305$	−208.052			−0.682138
$306$		0			0
$307$		−	485.954i		−	1.58291i	−0.611227	−	0.791456i	$-0.709324\pi$
$307$		−	485.954i		−	1.58291i	0.611227	−	0.791456i	$-0.290676\pi$
$308$		0			0
$309$	14.4571	−	55.5591i	0.0467868	−	0.179803i
$310$		0			0
$311$	−220.636	+	127.384i	−0.709440	+	0.409595i	−0.810853	−	0.585249i	$-0.800997\pi$
$311$	−220.636	+	127.384i	−0.709440	+	0.409595i	0.101414	+	0.994844i	$0.467663\pi$
$312$		0			0
$313$	−71.0799	+	123.114i	−0.227092	+	0.393336i	−0.956945	−	0.290269i	$-0.906255\pi$
$313$	−71.0799	+	123.114i	−0.227092	+	0.393336i	0.729853	+	0.683604i	$0.239589\pi$
$314$		0			0
$315$	21.9401	−	0.317413i	0.0696511	−	0.00100766i
$316$		0			0
$317$	58.8218	−	101.882i	0.185558	−	0.321395i	−0.758207	−	0.652014i	$-0.773924\pi$
$317$	58.8218	−	101.882i	0.185558	−	0.321395i	0.943764	+	0.330619i	$0.107258\pi$
$318$		0			0
$319$	41.9399	−	24.2140i	0.131473	−	0.0759060i
$320$		0			0
$321$	30.3216	+	29.8861i	0.0944597	+	0.0931030i
$322$		0			0
$323$		−	269.762i		−	0.835175i
$324$		0			0
$325$	281.394			0.865827
$326$		0			0
$327$	−355.843	+	361.029i	−1.08821	+	1.10406i
$328$		0			0
$329$	6.06305	+	10.5015i	0.0184287	+	0.0319195i
$330$		0			0
$331$	190.553	+	110.016i	0.575690	+	0.332375i	0.759419	−	0.650602i	$-0.225484\pi$
$331$	190.553	+	110.016i	0.575690	+	0.332375i	−0.183729	+	0.982977i	$0.558817\pi$
$332$		0			0
$333$	3.66269	+	253.171i	0.0109991	+	0.760275i
$334$		0			0
$335$	238.256	+	137.557i	0.711213	+	0.410619i
$336$		0			0
$337$	110.267	+	190.989i	0.327203	+	0.566733i	0.981956	−	0.189111i	$-0.0605605\pi$
$337$	110.267	+	190.989i	0.327203	+	0.566733i	−0.654753	+	0.755843i	$0.727227\pi$
$338$		0			0
$339$	637.513	+	165.888i	1.88057	+	0.489346i
$340$		0			0
$341$	−48.8462			−0.143244
$342$		0			0
$343$		−	94.4650i		−	0.275408i
$344$		0			0
$345$	280.996	−	77.4753i	0.814481	−	0.224566i
$346$		0			0
$347$	360.081	−	207.893i	1.03770	−	0.599115i	0.118518	−	0.992952i	$-0.462186\pi$
$347$	360.081	−	207.893i	1.03770	−	0.599115i	0.919180	+	0.393837i	$0.128852\pi$
$348$		0			0
$349$	296.154	−	512.954i	0.848579	−	1.46978i	−0.0338977	−	0.999425i	$-0.510792\pi$
$349$	296.154	−	512.954i	0.848579	−	1.46978i	0.882477	−	0.470356i	$-0.155875\pi$
$350$		0			0
$351$	96.4825	−	394.091i	0.274879	−	1.12277i
$352$		0			0
$353$	−144.258	+	249.862i	−0.408663	+	0.707826i	−0.994740	−	0.102430i	$-0.967338\pi$
$353$	−144.258	+	249.862i	−0.408663	+	0.707826i	0.586077	+	0.810255i	$0.300672\pi$
$354$		0			0
$355$	209.281	−	120.829i	0.589525	−	0.340363i
$356$		0			0
$357$	54.3929	−	14.9970i	0.152361	−	0.0420085i
$358$		0			0
$359$		−	317.550i		−	0.884541i	−0.896882	−	0.442270i	$-0.854173\pi$
$359$		−	317.550i		−	0.884541i	0.896882	−	0.442270i	$-0.145827\pi$
$360$		0			0
$361$	166.094			0.460094
$362$		0			0
$363$	−316.114	−	82.2565i	−0.870837	−	0.226602i
$364$		0			0
$365$	−50.2336	−	87.0072i	−0.137626	−	0.238376i
$366$		0			0
$367$	−154.752	−	89.3462i	−0.421668	−	0.243450i	0.274123	−	0.961695i	$-0.411613\pi$
$367$	−154.752	−	89.3462i	−0.421668	−	0.243450i	−0.695791	+	0.718245i	$0.744946\pi$
$368$		0			0
$369$	284.836	−	169.991i	0.771913	−	0.460679i
$370$		0			0
$371$	−14.0333	−	8.10215i	−0.0378257	−	0.0218387i
$372$		0			0
$373$	11.3286	+	19.6218i	0.0303717	+	0.0526053i	0.880812	−	0.473467i	$-0.156998\pi$
$373$	11.3286	+	19.6218i	0.0303717	+	0.0526053i	−0.850440	+	0.526072i	$0.823664\pi$
$374$		0			0
$375$	230.653	−	234.014i	0.615073	−	0.624036i
$376$		0			0
$377$	−209.037			−0.554475
$378$		0			0
$379$			156.270i			0.412321i	0.978518	+	0.206160i	$0.0660969\pi$
$379$			156.270i			0.412321i	−0.978518	+	0.206160i	$0.933903\pi$
$380$		0			0
$381$	338.228	+	333.370i	0.887736	+	0.874986i
$382$		0			0
$383$	−28.7614	+	16.6054i	−0.0750951	+	0.0433562i	−0.537077	−	0.843533i	$-0.680472\pi$
$383$	−28.7614	+	16.6054i	−0.0750951	+	0.0433562i	0.461982	+	0.886889i	$0.347138\pi$
$384$		0			0
$385$	4.24383	−	7.35054i	0.0110229	−	0.0190923i
$386$		0			0
$387$	183.820	−	329.296i	0.474987	−	0.850895i
$388$		0			0
$389$	85.0289	−	147.274i	0.218583	−	0.378598i	−0.735792	−	0.677208i	$-0.763190\pi$
$389$	85.0289	−	147.274i	0.218583	−	0.378598i	0.954375	+	0.298610i	$0.0965231\pi$
$390$		0			0
$391$	649.095	−	374.755i	1.66009	−	0.958454i
$392$		0			0
$393$	−134.364	+	516.365i	−0.341893	+	1.31391i
$394$		0			0
$395$		−	338.512i		−	0.856992i
$396$		0			0
$397$	−340.573			−0.857866			−0.428933	−	0.903336i	$-0.641110\pi$
$397$	−340.573			−0.857866			−0.428933	+	0.903336i	$0.641110\pi$
$398$		0			0
$399$	−10.8355	−	39.2995i	−0.0271568	−	0.0984951i
$400$		0			0
$401$	−236.842	−	410.223i	−0.590630	−	1.02300i	−0.994148	−	0.108029i	$-0.965546\pi$
$401$	−236.842	−	410.223i	−0.590630	−	1.02300i	0.403518	−	0.914972i	$-0.367787\pi$
$402$		0			0
$403$	182.595	+	105.421i	0.453088	+	0.261591i
$404$		0			0
$405$	−106.486	−	172.701i	−0.262929	−	0.426421i
$406$		0			0
$407$	84.8194	+	48.9705i	0.208401	+	0.120321i
$408$		0			0
$409$	20.6558	+	35.7768i	0.0505031	+	0.0874740i	0.890172	−	0.455625i	$-0.150584\pi$
$409$	20.6558	+	35.7768i	0.0505031	+	0.0874740i	−0.839669	+	0.543099i	$0.817251\pi$
$410$		0			0
$411$	−50.8586	−	184.459i	−0.123743	−	0.448806i
$412$		0			0
$413$	−12.7942			−0.0309787
$414$		0			0
$415$			151.657i			0.365438i
$416$		0			0
$417$	−122.278	+	469.916i	−0.293232	+	1.12690i
$418$		0			0
$419$	−431.309	+	249.016i	−1.02938	+	0.594310i	−0.916806	−	0.399333i	$-0.869242\pi$
$419$	−431.309	+	249.016i	−1.02938	+	0.594310i	−0.112570	+	0.993644i	$0.535908\pi$
$420$		0			0
$421$	−61.3780	+	106.310i	−0.145791	+	0.252517i	−0.929668	−	0.368399i	$-0.879906\pi$
$421$	−61.3780	+	106.310i	−0.145791	+	0.252517i	0.783877	+	0.620916i	$0.213239\pi$
$422$		0			0
$423$	54.6517	−	97.9034i	0.129200	−	0.231450i
$424$		0			0
$425$	180.917	−	313.357i	0.425686	−	0.737310i
$426$		0			0
$427$	−70.0145	+	40.4229i	−0.163968	+	0.0946672i
$428$		0			0
$429$	−111.775	−	110.170i	−0.260548	−	0.256806i
$430$		0			0
$431$		−	512.109i		−	1.18819i	−0.804395	−	0.594094i	$-0.797511\pi$
$431$		−	512.109i		−	1.18819i	0.804395	−	0.594094i	$-0.202489\pi$
$432$		0			0
$433$	35.8368			0.0827640			0.0413820	−	0.999143i	$-0.486824\pi$
$433$	35.8368			0.0827640			0.0413820	+	0.999143i	$0.486824\pi$
$434$		0			0
$435$	−73.3787	+	74.4480i	−0.168687	+	0.171145i
$436$		0			0
$437$	−270.766	−	468.980i	−0.619601	−	1.07318i
$438$		0			0
$439$	215.796	+	124.590i	0.491562	+	0.283803i	0.725222	−	0.688515i	$-0.241737\pi$
$439$	215.796	+	124.590i	0.491562	+	0.283803i	−0.233660	+	0.972318i	$0.575070\pi$
$440$		0			0
$441$	−371.366	+	221.632i	−0.842099	+	0.502567i
$442$		0			0
$443$	477.985	+	275.965i	1.07897	+	0.622946i	0.930619	−	0.365989i	$-0.119269\pi$
$443$	477.985	+	275.965i	1.07897	+	0.622946i	0.148354	+	0.988934i	$0.452602\pi$
$444$		0			0
$445$	173.761	+	300.963i	0.390475	+	0.676322i
$446$		0			0
$447$	269.505	+	70.1284i	0.602920	+	0.156887i
$448$		0			0
$449$	344.049			0.766256			0.383128	−	0.923695i	$-0.374847\pi$
$449$	344.049			0.766256			0.383128	+	0.923695i	$0.374847\pi$
$450$		0			0
$451$		−	128.309i		−	0.284499i
$452$		0			0
$453$	−284.599	+	78.4686i	−0.628253	+	0.173220i
$454$		0			0
$455$	−31.7282	+	18.3183i	−0.0697323	+	0.0402600i
$456$		0			0
$457$	193.531	−	335.206i	0.423481	−	0.733491i	−0.572796	−	0.819698i	$-0.694141\pi$
$457$	193.531	−	335.206i	0.423481	−	0.733491i	0.996277	+	0.0862068i	$0.0274746\pi$
$458$		0			0
$459$	−376.824	−	360.815i	−0.820967	−	0.786089i
$460$		0			0
$461$	−46.4011	+	80.3691i	−0.100653	+	0.174337i	−0.911954	−	0.410293i	$-0.865427\pi$
$461$	−46.4011	+	80.3691i	−0.100653	+	0.174337i	0.811301	+	0.584629i	$0.198760\pi$
$462$		0			0
$463$	−639.918	+	369.457i	−1.38211	+	0.797962i	−0.992409	−	0.122979i	$-0.960755\pi$
$463$	−639.918	+	369.457i	−1.38211	+	0.797962i	−0.389702	+	0.920941i	$0.627422\pi$
$464$		0			0
$465$	101.642	−	28.0244i	0.218585	−	0.0602675i
$466$		0			0
$467$		−	423.746i		−	0.907379i	−0.891160	−	0.453689i	$-0.850108\pi$
$467$		−	423.746i		−	0.907379i	0.891160	−	0.453689i	$-0.149892\pi$
$468$		0			0
$469$	106.905			0.227943
$470$		0			0
$471$	442.282	+	115.087i	0.939027	+	0.244346i
$472$		0			0
$473$	−72.9397	−	126.335i	−0.154206	−	0.267093i
$474$		0			0
$475$	−226.404	−	130.715i	−0.476641	−	0.275189i
$476$		0			0
$477$	2.16745	+	149.818i	0.00454393	+	0.314084i
$478$		0			0
$479$	652.039	+	376.455i	1.36125	+	0.785918i	0.989790	−	0.142531i	$-0.0455241\pi$
$479$	652.039	+	376.455i	1.36125	+	0.785918i	0.371459	+	0.928449i	$0.378857\pi$
$480$		0			0
$481$	−211.379	−	366.118i	−0.439457	−	0.761161i
$482$		0			0
$483$	79.5090	−	80.6676i	0.164615	−	0.167014i
$484$		0			0
$485$	−398.101			−0.820827
$486$		0			0
$487$		−	703.286i		−	1.44412i	−0.691831	−	0.722060i	$-0.743195\pi$
$487$		−	703.286i		−	1.44412i	0.691831	−	0.722060i	$-0.256805\pi$
$488$		0			0
$489$	−230.710	−	227.396i	−0.471799	−	0.465023i
$490$		0			0
$491$	−364.667	+	210.540i	−0.742702	+	0.428799i	−0.823051	−	0.567968i	$-0.807730\pi$
$491$	−364.667	+	210.540i	−0.742702	+	0.428799i	0.0803490	+	0.996767i	$0.474397\pi$
$492$		0			0
$493$	−134.396	+	232.781i	−0.272609	+	0.472173i
$494$		0			0
$495$	−78.4733	+	1.13529i	−0.158532	+	0.00229352i
$496$		0			0
$497$	46.9522	−	81.3236i	0.0944712	−	0.163629i
$498$		0			0
$499$	587.432	−	339.154i	1.17722	−	0.679668i	0.221850	−	0.975081i	$-0.428791\pi$
$499$	587.432	−	339.154i	1.17722	−	0.679668i	0.955370	+	0.295413i	$0.0954572\pi$
$500$		0			0
$501$	−233.920	+	898.962i	−0.466907	+	1.79433i
$502$		0			0
$503$		−	0.891657i		−	0.00177268i	−1.00000		0.000886339i	$-0.999718\pi$
$503$		−	0.891657i		−	0.00177268i	1.00000		0.000886339i	$-0.000282130\pi$
$504$		0			0
$505$	258.843			0.512560
$506$		0			0
$507$	45.3016	+	164.305i	0.0893523	+	0.324073i
$508$		0			0
$509$	−287.777	−	498.444i	−0.565377	−	0.979261i	−0.997015	−	0.0772141i	$-0.975398\pi$
$509$	−287.777	−	498.444i	−0.565377	−	0.979261i	0.431638	−	0.902047i	$-0.357936\pi$
$510$		0			0
$511$	−33.8097	−	19.5200i	−0.0661637	−	0.0381996i
$512$		0			0
$513$	−260.693	+	272.260i	−0.508174	+	0.530721i
$514$		0			0
$515$	41.5116	+	23.9667i	0.0806050	+	0.0465373i
$516$		0			0
$517$	−21.6858	−	37.5608i	−0.0419454	−	0.0726515i
$518$		0			0
$519$	219.971	+	797.815i	0.423836	+	1.53722i
$520$		0			0
$521$	−735.526			−1.41176			−0.705879	−	0.708332i	$-0.749448\pi$
$521$	−735.526			−1.41176			−0.705879	+	0.708332i	$0.749448\pi$
$522$		0			0
$523$			112.072i			0.214286i	0.994244	+	0.107143i	$0.0341703\pi$
$523$			112.072i			0.214286i	−0.994244	+	0.107143i	$0.965830\pi$
$524$		0			0
$525$	13.7697	−	52.9175i	0.0262281	−	0.100795i
$526$		0			0
$527$	234.791	−	135.557i	0.445524	−	0.257223i
$528$		0			0
$529$	487.801	−	844.896i	0.922119	−	1.59716i
$530$		0			0
$531$	60.6269	+	101.586i	0.114175	+	0.191311i
$532$		0			0
$533$	−276.919	+	479.638i	−0.519548	+	0.899884i
$534$		0			0
$535$	−30.7847	+	17.7736i	−0.0575416	+	0.0332216i
$536$		0			0
$537$	−142.692	−	140.642i	−0.265720	−	0.261904i
$538$		0			0
$539$			167.288i			0.310367i
$540$		0			0
$541$	878.760			1.62433			0.812163	−	0.583431i	$-0.198290\pi$
$541$	878.760			1.62433			0.812163	+	0.583431i	$0.198290\pi$
$542$		0			0
$543$	−457.592	+	464.260i	−0.842711	+	0.854991i
$544$		0			0
$545$	−211.624	−	366.543i	−0.388301	−	0.672557i
$546$		0			0
$547$	101.275	+	58.4709i	0.185146	+	0.106894i	0.589708	−	0.807617i	$-0.299243\pi$
$547$	101.275	+	58.4709i	0.185146	+	0.106894i	−0.404562	+	0.914510i	$0.632576\pi$
$548$		0			0
$549$	652.731	+	364.368i	1.18894	+	0.663693i
$550$		0			0
$551$	168.187	+	97.1030i	0.305240	+	0.176231i
$552$		0			0
$553$	−65.7702	−	113.917i	−0.118934	−	0.205999i
$554$		0			0
$555$	−204.593	−	53.2374i	−0.368636	−	0.0959232i
$556$		0			0
$557$	−983.235			−1.76523			−0.882616	−	0.470094i	$-0.844220\pi$
$557$	−983.235			−1.76523			−0.882616	+	0.470094i	$0.844220\pi$
$558$		0			0
$559$			629.681i			1.12644i
$560$		0			0
$561$	−194.547	+	53.6400i	−0.346787	+	0.0956149i
$562$		0			0
$563$	−721.045	+	416.296i	−1.28072	+	0.739424i	−0.976980	−	0.213331i	$-0.931569\pi$
$563$	−721.045	+	416.296i	−1.28072	+	0.739424i	−0.303740	+	0.952755i	$0.598235\pi$
$564$		0			0
$565$	−275.006	+	476.325i	−0.486737	+	0.843053i
$566$		0			0
$567$	−69.3895	−	37.4285i	−0.122380	−	0.0660115i
$568$		0			0
$569$	−151.574	+	262.534i	−0.266386	+	0.461395i	−0.967926	−	0.251236i	$-0.919163\pi$
$569$	−151.574	+	262.534i	−0.266386	+	0.461395i	0.701540	+	0.712631i	$0.252496\pi$
$570$		0			0
$571$	−630.357	+	363.937i	−1.10395	+	0.637368i	−0.937257	−	0.348640i	$-0.886643\pi$
$571$	−630.357	+	363.937i	−1.10395	+	0.637368i	−0.166697	+	0.986008i	$0.553310\pi$
$572$		0			0
$573$	726.124	−	200.205i	1.26723	−	0.349397i
$574$		0			0
$575$		−	726.360i		−	1.26323i
$576$		0			0
$577$	694.935			1.20439			0.602197	−	0.798348i	$-0.294292\pi$
$577$	694.935			1.20439			0.602197	+	0.798348i	$0.294292\pi$
$578$		0			0
$579$	−118.730	−	30.8949i	−0.205061	−	0.0533591i
$580$		0			0
$581$	29.4658	+	51.0362i	0.0507156	+	0.0878420i
$582$		0			0
$583$	50.1931	+	28.9790i	0.0860945	+	0.0497067i
$584$		0			0
$585$	295.795	+	165.119i	0.505633	+	0.282255i
$586$		0			0
$587$	−22.3821	−	12.9223i	−0.0381297	−	0.0220142i	0.480814	−	0.876823i	$-0.340341\pi$
$587$	−22.3821	−	12.9223i	−0.0381297	−	0.0220142i	−0.518944	+	0.854808i	$0.673675\pi$
$588$		0			0
$589$	−97.9415	−	169.640i	−0.166284	−	0.288013i
$590$		0			0
$591$	398.363	−	404.167i	0.674048	−	0.683870i
$592$		0			0
$593$	441.443			0.744424			0.372212	−	0.928148i	$-0.378600\pi$
$593$	441.443			0.744424			0.372212	+	0.928148i	$0.378600\pi$
$594$		0			0
$595$			47.1095i			0.0791757i
$596$		0			0
$597$	163.157	+	160.813i	0.273294	+	0.269369i
$598$		0			0
$599$	−700.138	+	404.225i	−1.16884	+	0.674833i	−0.953408	−	0.301685i	$-0.902451\pi$
$599$	−700.138	+	404.225i	−1.16884	+	0.674833i	−0.215437	+	0.976518i	$0.569118\pi$
$600$		0			0
$601$	239.504	−	414.833i	0.398509	−	0.690238i	−0.595033	−	0.803701i	$-0.702861\pi$
$601$	239.504	−	414.833i	0.398509	−	0.690238i	0.993542	+	0.113463i	$0.0361944\pi$
$602$		0			0
$603$	−506.584	−	848.830i	−0.840106	−	1.40768i
$604$		0			0
$605$	136.363	−	236.188i	0.225394	−	0.390393i
$606$		0			0
$607$	−797.010	+	460.154i	−1.31303	+	0.758079i	−0.982597	−	0.185750i	$-0.940529\pi$
$607$	−797.010	+	460.154i	−1.31303	+	0.758079i	−0.330434	+	0.943829i	$0.607195\pi$
$608$		0			0
$609$	−10.2290	+	39.3105i	−0.0167965	+	0.0645492i
$610$		0			0
$611$			187.211i			0.306401i
$612$		0			0
$613$	931.251			1.51917			0.759585	−	0.650408i	$-0.225402\pi$
$613$	931.251			1.51917			0.759585	+	0.650408i	$0.225402\pi$
$614$		0			0
$615$	73.6143	+	266.992i	0.119698	+	0.434134i
$616$		0			0
$617$	480.293	+	831.891i	0.778432	+	1.34828i	0.932845	+	0.360278i	$0.117318\pi$
$617$	480.293	+	831.891i	0.778432	+	1.34828i	−0.154413	+	0.988006i	$0.549349\pi$
$618$		0			0
$619$	248.873	+	143.687i	0.402057	+	0.232128i	0.687371	−	0.726306i	$-0.258765\pi$
$619$	248.873	+	143.687i	0.402057	+	0.232128i	−0.285314	+	0.958434i	$0.592098\pi$
$620$		0			0
$621$	−1017.27	−	249.050i	−1.63811	−	0.401046i
$622$		0			0
$623$	116.950	+	67.5210i	0.187720	+	0.108380i
$624$		0			0
$625$	−96.9014	−	167.838i	−0.155042	−	0.268541i
$626$		0			0
$627$	38.7556	+	140.563i	0.0618111	+	0.224183i
$628$		0			0
$629$	−543.607			−0.864240
$630$		0			0
$631$		−	422.954i		−	0.670291i	−0.942166	−	0.335146i	$-0.891214\pi$
$631$		−	422.954i		−	0.670291i	0.942166	−	0.335146i	$-0.108786\pi$
$632$		0			0
$633$	−262.840	+	1010.10i	−0.415229	+	1.59573i
$634$		0			0
$635$	−343.394	+	198.259i	−0.540778	+	0.312218i
$636$		0			0
$637$	361.044	−	625.347i	0.566788	−	0.981706i
$638$		0			0
$639$	−868.199	+	12.5605i	−1.35868	+	0.0196564i
$640$		0			0
$641$	−25.3956	+	43.9865i	−0.0396188	+	0.0686217i	−0.885155	−	0.465297i	$-0.845948\pi$
$641$	−25.3956	+	43.9865i	−0.0396188	+	0.0686217i	0.845536	+	0.533918i	$0.179281\pi$
$642$		0			0
$643$	722.106	−	416.908i	1.12303	−	0.648380i	0.180855	−	0.983510i	$-0.442113\pi$
$643$	722.106	−	416.908i	1.12303	−	0.648380i	0.942172	+	0.335130i	$0.108780\pi$
$644$		0			0
$645$	224.259	+	221.038i	0.347688	+	0.342695i
$646$		0			0
$647$		−	826.902i		−	1.27806i	−0.769184	−	0.639028i	$-0.779337\pi$
$647$		−	826.902i		−	1.27806i	0.769184	−	0.639028i	$-0.220663\pi$
$648$		0			0
$649$	45.7611			0.0705102
$650$		0			0
$651$	28.7600	−	29.1791i	0.0441782	−	0.0448220i
$652$		0			0
$653$	−587.256	−	1017.16i	−0.899320	−	1.55767i	−0.828365	−	0.560189i	$-0.810729\pi$
$653$	−587.256	−	1017.16i	−0.899320	−	1.55767i	−0.0709551	−	0.997480i	$-0.522605\pi$
$654$		0			0
$655$	−385.807	−	222.746i	−0.589019	−	0.340070i
$656$		0			0
$657$	5.22191	+	360.947i	0.00794812	+	0.549387i
$658$		0			0
$659$	−575.835	−	332.458i	−0.873801	−	0.504489i	−0.00519133	−	0.999987i	$-0.501652\pi$
$659$	−575.835	−	332.458i	−0.873801	−	0.504489i	−0.868609	+	0.495497i	$0.834986\pi$
$660$		0			0
$661$	165.356	+	286.404i	0.250160	+	0.433290i	0.963570	−	0.267457i	$-0.0861835\pi$
$661$	165.356	+	286.404i	0.250160	+	0.433290i	−0.713410	+	0.700747i	$0.752850\pi$
$662$		0			0
$663$	843.015	+	219.362i	1.27152	+	0.330863i
$664$		0			0
$665$	34.0372			0.0511838
$666$		0			0
$667$			539.586i			0.808975i
$668$		0			0
$669$	537.013	−	148.063i	0.802710	−	0.221321i
$670$		0			0
$671$	250.421	−	144.581i	0.373206	−	0.215471i
$672$		0			0
$673$	256.452	−	444.187i	0.381057	−	0.660011i	−0.610156	−	0.792281i	$-0.708893\pi$
$673$	256.452	−	444.187i	0.381057	−	0.660011i	0.991214	+	0.132270i	$0.0422267\pi$
$674$		0			0
$675$	−485.415	+	141.424i	−0.719134	+	0.209517i
$676$		0			0
$677$	221.500	−	383.649i	0.327179	−	0.566690i	−0.654772	−	0.755826i	$-0.727235\pi$
$677$	221.500	−	383.649i	0.327179	−	0.566690i	0.981951	+	0.189136i	$0.0605688\pi$
$678$		0			0
$679$	−133.971	+	77.3479i	−0.197306	+	0.113914i
$680$		0			0
$681$	−413.462	+	113.998i	−0.607140	+	0.167399i
$682$		0			0
$683$			1159.07i			1.69703i	0.529169	+	0.848516i	$0.322504\pi$
$683$			1159.07i			1.69703i	−0.529169	+	0.848516i	$0.677496\pi$
$684$		0			0
$685$	159.760			0.233226
$686$		0			0
$687$	−522.425	−	135.941i	−0.760444	−	0.197876i
$688$		0			0
$689$	−125.086	−	216.656i	−0.181548	−	0.314450i
$690$		0			0
$691$	−338.634	−	195.510i	−0.490064	−	0.282938i	0.234537	−	0.972107i	$-0.424643\pi$
$691$	−338.634	−	195.510i	−0.490064	−	0.282938i	−0.724601	+	0.689169i	$0.757976\pi$
$692$		0			0
$693$	−26.1876	+	15.6288i	−0.0377887	+	0.0225524i
$694$		0			0
$695$	−351.103	−	202.709i	−0.505184	−	0.291668i
$696$		0			0
$697$	356.079	+	616.748i	0.510874	+	0.884860i
$698$		0			0
$699$	6.33537	−	6.42768i	0.00906347	−	0.00919554i
$700$		0			0
$701$	1328.18			1.89469			0.947344	−	0.320217i	$-0.103756\pi$
$701$	1328.18			1.89469			0.947344	+	0.320217i	$0.103756\pi$
$702$		0			0
$703$			392.763i			0.558695i
$704$		0			0
$705$	66.6746	+	65.7170i	0.0945739	+	0.0932156i
$706$		0			0
$707$	87.1068	−	50.2911i	0.123206	−	0.0711331i
$708$		0			0
$709$	8.13480	−	14.0899i	0.0114736	−	0.0198729i	−0.860232	−	0.509904i	$-0.829681\pi$
$709$	8.13480	−	14.0899i	0.0114736	−	0.0198729i	0.871705	+	0.490031i	$0.163014\pi$
$710$		0			0
$711$	−592.846	+	1062.03i	−0.833820	+	1.49371i
$712$		0			0
$713$	272.123	−	471.330i	0.381659	−	0.661052i
$714$		0			0
$715$	113.482	−	65.5191i	0.158717	−	0.0916352i
$716$		0			0
$717$	−80.2342	+	308.342i	−0.111903	+	0.430045i
$718$		0			0
$719$			1356.78i			1.88704i	0.331316	+	0.943520i	$0.392507\pi$
$719$			1356.78i			1.88704i	−0.331316	+	0.943520i	$0.607493\pi$
$720$		0			0
$721$	18.6262			0.0258338
$722$		0			0
$723$	348.464	+	1263.85i	0.481969	+	1.74806i
$724$		0			0
$725$	130.245	+	225.591i	0.179648	+	0.311160i
$726$		0			0
$727$	−782.541	−	451.800i	−1.07640	−	0.621458i	−0.146475	−	0.989214i	$-0.546793\pi$
$727$	−782.541	−	451.800i	−1.07640	−	0.621458i	−0.929922	+	0.367756i	$0.880126\pi$
$728$		0			0
$729$	31.6277	+	728.314i	0.0433851	+	0.999058i
$730$		0			0
$731$	701.204	+	404.841i	0.959240	+	0.553818i
$732$		0			0
$733$	−96.9820	−	167.978i	−0.132308	−	0.229165i	0.792258	−	0.610187i	$-0.208906\pi$
$733$	−96.9820	−	167.978i	−0.132308	−	0.229165i	−0.924566	+	0.381022i	$0.875572\pi$
$734$		0			0
$735$	−95.9775	−	348.102i	−0.130582	−	0.473608i
$736$		0			0
$737$	−382.369			−0.518818
$738$		0			0
$739$			947.887i			1.28266i	0.767265	+	0.641331i	$0.221617\pi$
$739$			947.887i			1.28266i	−0.767265	+	0.641331i	$0.778383\pi$
$740$		0			0
$741$	158.492	−	609.089i	0.213889	−	0.821983i
$742$		0			0
$743$	−612.087	+	353.389i	−0.823805	+	0.475624i	−0.851727	−	0.523986i	$-0.824444\pi$
$743$	−612.087	+	353.389i	−0.823805	+	0.475624i	0.0279221	+	0.999610i	$0.491111\pi$
$744$		0			0
$745$	−116.257	+	201.364i	−0.156050	+	0.270287i
$746$		0			0
$747$	265.601	−	475.800i	0.355557	−	0.636948i
$748$		0			0
$749$	−6.90654	+	11.9625i	−0.00922101	+	0.0159713i
$750$		0			0
$751$	23.5131	−	13.5753i	0.0313091	−	0.0180763i	−0.484264	−	0.874922i	$-0.660912\pi$
$751$	23.5131	−	13.5753i	0.0313091	−	0.0180763i	0.515573	+	0.856846i	$0.327579\pi$
$752$		0			0
$753$	−478.869	−	471.991i	−0.635948	−	0.626814i
$754$		0			0
$755$		−	246.490i		−	0.326477i
$756$		0			0
$757$	−727.176			−0.960602			−0.480301	−	0.877104i	$-0.659473\pi$
$757$	−727.176			−0.960602			−0.480301	+	0.877104i	$0.659473\pi$
$758$		0			0
$759$	−284.380	+	288.524i	−0.374678	+	0.380138i
$760$		0			0
$761$	145.954	+	252.799i	0.191792	+	0.332194i	0.945844	−	0.324621i	$-0.105237\pi$
$761$	145.954	+	252.799i	0.191792	+	0.332194i	−0.754052	+	0.656815i	$0.771903\pi$
$762$		0			0
$763$	−142.433	−	82.2338i	−0.186675	−	0.107777i
$764$		0			0
$765$	374.050	−	223.234i	0.488955	−	0.291809i
$766$		0			0
$767$	−171.062	−	98.7628i	−0.223028	−	0.128765i
$768$		0			0
$769$	232.025	+	401.879i	0.301723	+	0.522600i	0.976526	−	0.215398i	$-0.0691048\pi$
$769$	232.025	+	401.879i	0.301723	+	0.522600i	−0.674803	+	0.737998i	$0.735771\pi$
$770$		0			0
$771$	−54.9538	−	14.2996i	−0.0712761	−	0.0185469i
$772$		0			0
$773$	−846.362			−1.09491			−0.547453	−	0.836837i	$-0.684402\pi$
$773$	−846.362			−1.09491			−0.547453	+	0.836837i	$0.684402\pi$
$774$		0			0
$775$		−	262.739i		−	0.339018i
$776$		0			0
$777$	−79.1940	+	21.8351i	−0.101923	+	0.0281018i
$778$		0			0
$779$	445.608	−	257.272i	0.572026	−	0.330259i
$780$		0			0
$781$	−167.934	+	290.871i	−0.215025	+	0.372433i
$782$		0			0
$783$	360.597	−	105.059i	0.460533	−	0.134175i
$784$		0			0
$785$	−190.789	+	330.456i	−0.243043	+	0.420963i
$786$		0			0
$787$	558.431	−	322.410i	0.709569	−	0.409670i	−0.101332	−	0.994853i	$-0.532311\pi$
$787$	558.431	−	322.410i	0.709569	−	0.409670i	0.810901	+	0.585183i	$0.198977\pi$
$788$		0			0
$789$	−618.424	+	170.510i	−0.783808	+	0.216109i
$790$		0			0
$791$			213.726i			0.270198i
$792$		0			0
$793$	−1248.15			−1.57396
$794$		0			0
$795$	−121.071	−	31.5040i	−0.152290	−	0.0396277i
$796$		0			0
$797$	−2.26487	−	3.92287i	−0.00284175	−	0.00492205i	0.864601	−	0.502459i	$-0.167571\pi$
$797$	−2.26487	−	3.92287i	−0.00284175	−	0.00492205i	−0.867443	+	0.497537i	$0.834238\pi$
$798$		0			0
$799$	208.476	+	120.364i	0.260921	+	0.150643i
$800$		0			0
$801$	−18.0629	−	1248.54i	−0.0225505	−	1.55873i
$802$		0			0
$803$	120.927	+	69.8174i	0.150594	+	0.0869456i
$804$		0			0
$805$	47.2849	+	81.8998i	0.0587390	+	0.101739i
$806$		0			0
$807$	154.613	−	156.866i	0.191590	−	0.194382i
$808$		0			0
$809$	−748.596			−0.925335			−0.462668	−	0.886532i	$-0.653108\pi$
$809$	−748.596			−0.925335			−0.462668	+	0.886532i	$0.653108\pi$
$810$		0			0
$811$			817.917i			1.00853i	0.863549	+	0.504265i	$0.168236\pi$
$811$			817.917i			1.00853i	−0.863549	+	0.504265i	$0.831764\pi$
$812$		0			0
$813$	203.513	+	200.590i	0.250324	+	0.246728i
$814$		0			0
$815$	234.234	−	135.235i	0.287403	−	0.165932i
$816$		0			0
$817$	292.503	−	506.629i	0.358020	−	0.620109i
$818$		0			0
$819$	131.624	−	1.90423i	0.160713	−	0.00232507i
$820$		0			0
$821$	−25.9045	+	44.8679i	−0.0315524	+	0.0546503i	−0.881370	−	0.472426i	$-0.843378\pi$
$821$	−25.9045	+	44.8679i	−0.0315524	+	0.0546503i	0.849818	+	0.527076i	$0.176712\pi$
$822$		0			0
$823$	−653.931	+	377.547i	−0.794570	+	0.458745i	−0.841569	−	0.540150i	$-0.818368\pi$
$823$	−653.931	+	377.547i	−0.794570	+	0.458745i	0.0469992	+	0.998895i	$0.485034\pi$
$824$		0			0
$825$	−49.2503	+	189.270i	−0.0596974	+	0.229419i
$826$		0			0
$827$		−	1215.15i		−	1.46935i	−0.678421	−	0.734673i	$-0.737336\pi$
$827$		−	1215.15i		−	1.46935i	0.678421	−	0.734673i	$-0.262664\pi$
$828$		0			0
$829$	831.072			1.00250			0.501250	−	0.865303i	$-0.332874\pi$
$829$	831.072			1.00250			0.501250	+	0.865303i	$0.332874\pi$
$830$		0			0
$831$	−264.745	−	960.207i	−0.318586	−	1.15548i
$832$		0			0
$833$	−464.252	−	804.109i	−0.557326	−	0.965317i
$834$		0			0
$835$	−671.669	−	387.788i	−0.804394	−	0.464417i
$836$		0			0
$837$	−367.966	−	90.0863i	−0.439624	−	0.107630i
$838$		0			0
$839$	−856.055	−	494.243i	−1.02033	−	0.589086i	−0.106129	−	0.994352i	$-0.533846\pi$
$839$	−856.055	−	494.243i	−1.02033	−	0.589086i	−0.914199	+	0.405266i	$0.867179\pi$
$840$		0			0
$841$	323.746	+	560.744i	0.384953	+	0.666759i
$842$		0			0
$843$	−59.0529	−	214.180i	−0.0700509	−	0.254068i
$844$		0			0
$845$	−142.304			−0.168407
$846$		0			0
$847$		−	105.977i		−	0.125121i
$848$		0			0
$849$	−156.889	+	602.927i	−0.184792	+	0.710162i
$850$		0			0
$851$	−945.059	+	545.630i	−1.11053	+	0.641164i
$852$		0			0
$853$	−171.904	+	297.747i	−0.201529	+	0.349058i	−0.949021	−	0.315212i	$-0.897924\pi$
$853$	−171.904	+	297.747i	−0.201529	+	0.349058i	0.747492	+	0.664270i	$0.231258\pi$
$854$		0			0
$855$	−161.290	−	270.256i	−0.188643	−	0.316089i
$856$		0			0
$857$	−278.107	+	481.696i	−0.324513	+	0.562072i	−0.981414	−	0.191904i	$-0.938534\pi$
$857$	−278.107	+	481.696i	−0.324513	+	0.562072i	0.656901	+	0.753977i	$0.271867\pi$
$858$		0			0
$859$	227.344	−	131.257i	0.264661	−	0.152802i	−0.361798	−	0.932257i	$-0.617837\pi$
$859$	227.344	−	131.257i	0.264661	−	0.152802i	0.626459	+	0.779455i	$0.284504\pi$
$860$		0			0
$861$	76.6475	+	75.5467i	0.0890215	+	0.0877429i
$862$		0			0
$863$		−	601.806i		−	0.697342i	−0.937245	−	0.348671i	$-0.886633\pi$
$863$		−	601.806i		−	0.697342i	0.937245	−	0.348671i	$-0.113367\pi$
$864$		0			0
$865$	−690.986			−0.798827
$866$		0			0
$867$	177.668	−	180.257i	0.204922	−	0.207908i
$868$		0			0
$869$	235.241	+	407.449i	0.270703	+	0.468871i
$870$		0			0
$871$	1429.35	+	825.238i	1.64105	+	0.947461i
$872$		0			0
$873$	1248.98	+	697.206i	1.43068	+	0.798632i
$874$		0			0
$875$	92.3231	+	53.3027i	0.105512	+	0.0609174i
$876$		0			0
$877$	−803.626	−	1391.92i	−0.916335	−	1.58714i	−0.804935	−	0.593363i	$-0.797800\pi$
$877$	−803.626	−	1391.92i	−0.916335	−	1.58714i	−0.111399	−	0.993776i	$-0.535533\pi$
$878$		0			0
$879$	507.124	+	131.960i	0.576933	+	0.150125i
$880$		0			0
$881$	553.611			0.628389			0.314194	−	0.949359i	$-0.398266\pi$
$881$	553.611			0.628389			0.314194	+	0.949359i	$0.398266\pi$
$882$		0			0
$883$		−	890.278i		−	1.00824i	−0.863633	−	0.504121i	$-0.831816\pi$
$883$		−	890.278i		−	1.00824i	0.863633	−	0.504121i	$-0.168184\pi$
$884$		0			0
$885$	−95.2224	+	26.2544i	−0.107596	+	0.0296660i
$886$		0			0
$887$	63.4815	−	36.6511i	0.0715688	−	0.0413203i	−0.463789	−	0.885946i	$-0.653510\pi$
$887$	63.4815	−	36.6511i	0.0715688	−	0.0413203i	0.535357	+	0.844626i	$0.320177\pi$
$888$		0			0
$889$	−77.0402	+	133.438i	−0.0866594	+	0.150099i
$890$		0			0
$891$	248.186	+	133.871i	0.278548	+	0.150248i
$892$		0			0
$893$	86.9642	−	150.626i	0.0973843	−	0.168675i
$894$		0			0
$895$	144.871	−	83.6415i	0.161867	−	0.0934542i
$896$		0			0
$897$	1685.76	−	464.792i	1.87933	−	0.518163i
$898$		0			0
$899$			195.179i			0.217107i
$900$		0			0
$901$	−321.687			−0.357034
$902$		0			0
$903$	118.415	+	30.8128i	0.131135	+	0.0341227i
$904$		0			0
$905$	−272.135	−	471.351i	−0.300702	−	0.520830i
$906$		0			0
$907$	−831.864	−	480.277i	−0.917159	−	0.529522i	−0.0344316	−	0.999407i	$-0.510962\pi$
$907$	−831.864	−	480.277i	−0.917159	−	0.529522i	−0.882728	+	0.469885i	$0.844295\pi$
$908$		0			0
$909$	−812.078	−	453.319i	−0.893376	−	0.498700i
$910$		0			0
$911$	1574.75	+	909.184i	1.72860	+	0.998007i	0.895852	+	0.444352i	$0.146566\pi$
$911$	1574.75	+	909.184i	1.72860	+	0.998007i	0.832746	+	0.553655i	$0.186767\pi$
$912$		0			0
$913$	−105.390	−	182.542i	−0.115433	−	0.199936i
$914$		0			0
$915$	−438.141	+	444.526i	−0.478843	+	0.485820i
$916$		0			0
$917$	−173.111			−0.188780
$918$		0			0
$919$		−	345.325i		−	0.375762i	−0.982192	−	0.187881i	$-0.939838\pi$
$919$		−	345.325i		−	0.375762i	0.982192	−	0.187881i	$-0.0601619\pi$
$920$		0			0
$921$	−1038.29	−	1023.38i	−1.12735	−	1.11116i
$922$		0			0
$923$	1255.53	−	724.879i	1.36027	−	0.785351i
$924$		0			0
$925$	−263.408	+	456.236i	−0.284765	+	0.493228i
$926$		0			0
$927$	−88.2625	−	147.892i	−0.0952130	−	0.159539i
$928$		0			0
$929$	360.436	−	624.293i	0.387982	−	0.672005i	−0.604196	−	0.796836i	$-0.706505\pi$
$929$	360.436	−	624.293i	0.387982	−	0.672005i	0.992178	+	0.124831i	$0.0398388\pi$
$930$		0			0
$931$	−580.979	+	335.428i	−0.624038	+	0.360288i
$932$		0			0
$933$	−192.472	+	739.673i	−0.206293	+	0.792790i
$934$		0			0
$935$		−	168.497i		−	0.180211i
$936$		0			0
$937$	−277.841			−0.296522			−0.148261	−	0.988948i	$-0.547368\pi$
$937$	−277.841			−0.296522			−0.148261	+	0.988948i	$0.547368\pi$
$938$		0			0
$939$	113.358	+	411.138i	0.120722	+	0.437847i
$940$		0			0
$941$	313.560	+	543.101i	0.333220	+	0.577153i	0.983141	−	0.182848i	$-0.0585316\pi$
$941$	313.560	+	543.101i	0.333220	+	0.577153i	−0.649922	+	0.760001i	$0.725198\pi$
$942$		0			0
$943$	1238.09	+	714.810i	1.31292	+	0.758017i
$944$		0			0
$945$	45.5259	−	47.5458i	0.0481756	−	0.0503131i
$946$		0			0
$947$	72.1510	+	41.6564i	0.0761890	+	0.0439877i	0.537611	−	0.843193i	$-0.319327\pi$
$947$	72.1510	+	41.6564i	0.0761890	+	0.0439877i	−0.461422	+	0.887181i	$0.652660\pi$
$948$		0			0
$949$	−301.363	−	521.976i	−0.317559	−	0.550027i
$950$		0			0
$951$	−93.8086	−	340.235i	−0.0986420	−	0.357766i
$952$		0			0
$953$	341.249			0.358079			0.179039	−	0.983842i	$-0.442701\pi$
$953$	341.249			0.358079			0.179039	+	0.983842i	$0.442701\pi$
$954$		0			0
$955$			628.894i			0.658528i
$956$		0			0
$957$	36.5863	−	140.602i	0.0382302	−	0.146920i
$958$		0			0
$959$	53.7630	−	31.0401i	0.0560616	−	0.0323672i
$960$		0			0
$961$	−382.068	+	661.761i	−0.397573	+	0.688617i
$962$		0			0
$963$	127.710	−	1.84761i	0.132617	−	0.00191860i
$964$		0			0
$965$	51.2170	−	88.7104i	0.0530746	−	0.0919279i
$966$		0			0
$967$	1556.33	−	898.550i	1.60945	−	0.929214i	0.619951	−	0.784640i	$-0.287152\pi$
$967$	1556.33	−	898.550i	1.60945	−	0.929214i	0.989494	−	0.144573i	$-0.0461809\pi$
$968$		0			0
$969$	−576.375	−	568.097i	−0.594814	−	0.586271i
$970$		0			0
$971$		−	1706.81i		−	1.75779i	−0.477019	−	0.878893i	$-0.658283\pi$
$971$		−	1706.81i		−	1.75779i	0.477019	−	0.878893i	$-0.341717\pi$
$972$		0			0
$973$	−157.540			−0.161911
$974$		0			0
$975$	592.593	−	601.229i	0.607788	−	0.616645i
$976$		0			0
$977$	181.062	+	313.609i	0.185325	+	0.320992i	0.943686	−	0.330843i	$-0.107333\pi$
$977$	181.062	+	313.609i	0.185325	+	0.320992i	−0.758361	+	0.651835i	$0.774000\pi$
$978$		0			0
$979$	−418.295	−	241.503i	−0.427267	−	0.246683i
$980$		0			0
$981$	21.9988	+	1520.60i	0.0224249	+	1.55005i
$982$		0			0
$983$	900.133	+	519.692i	0.915700	+	0.528680i	0.882261	−	0.470761i	$-0.156021\pi$
$983$	900.133	+	519.692i	0.915700	+	0.528680i	0.0334391	+	0.999441i	$0.489354\pi$
$984$		0			0
$985$	236.910	+	410.341i	0.240518	+	0.416590i
$986$		0			0
$987$	35.2059	+	9.16099i	0.0356696	+	0.00928165i
$988$		0			0
$989$	1625.39			1.64347
$990$		0			0
$991$		−	1717.76i		−	1.73336i	−0.498863	−	0.866681i	$-0.666249\pi$
$991$		−	1717.76i		−	1.73336i	0.498863	−	0.866681i	$-0.333751\pi$
$992$		0			0
$993$	636.351	−	175.453i	0.640837	−	0.176690i
$994$		0			0
$995$	−165.649	+	95.6375i	−0.166481	+	0.0961181i
$996$		0			0
$997$	−77.3349	+	133.948i	−0.0775676	+	0.134351i	−0.902200	−	0.431318i	$-0.858049\pi$
$997$	−77.3349	+	133.948i	−0.0775676	+	0.134351i	0.824632	+	0.565669i	$0.191382\pi$
$998$		0			0
$999$	548.642	+	525.333i	0.549191	+	0.525859i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	576.3.o.i.511.10		24
3.2	odd	2		1728.3.o.i.127.5		24
4.3	odd	2	inner	576.3.o.i.511.3		24
8.3	odd	2		288.3.o.c.223.10	yes	24
8.5	even	2		288.3.o.c.223.3	yes	24
9.4	even	3	inner	576.3.o.i.319.3		24
9.5	odd	6		1728.3.o.i.1279.6		24
12.11	even	2		1728.3.o.i.127.6		24
24.5	odd	2		864.3.o.c.127.8		24
24.11	even	2		864.3.o.c.127.7		24
36.23	even	6		1728.3.o.i.1279.5		24
36.31	odd	6	inner	576.3.o.i.319.10		24
72.5	odd	6		864.3.o.c.415.7		24
72.11	even	6		2592.3.g.l.2431.6		12
72.13	even	6		288.3.o.c.31.10	yes	24
72.29	odd	6		2592.3.g.l.2431.5		12
72.43	odd	6		2592.3.g.k.2431.8		12
72.59	even	6		864.3.o.c.415.8		24
72.61	even	6		2592.3.g.k.2431.7		12
72.67	odd	6		288.3.o.c.31.3	✓	24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
288.3.o.c.31.3	✓	24	72.67	odd	6
288.3.o.c.31.10	yes	24	72.13	even	6
288.3.o.c.223.3	yes	24	8.5	even	2
288.3.o.c.223.10	yes	24	8.3	odd	2
576.3.o.i.319.3		24	9.4	even	3	inner
576.3.o.i.319.10		24	36.31	odd	6	inner
576.3.o.i.511.3		24	4.3	odd	2	inner
576.3.o.i.511.10		24	1.1	even	1	trivial
864.3.o.c.127.7		24	24.11	even	2
864.3.o.c.127.8		24	24.5	odd	2
864.3.o.c.415.7		24	72.5	odd	6
864.3.o.c.415.8		24	72.59	even	6
1728.3.o.i.127.5		24	3.2	odd	2
1728.3.o.i.127.6		24	12.11	even	2
1728.3.o.i.1279.5		24	36.23	even	6
1728.3.o.i.1279.6		24	9.5	odd	6
2592.3.g.k.2431.7		12	72.61	even	6
2592.3.g.k.2431.8		12	72.43	odd	6
2592.3.g.l.2431.5		12	72.29	odd	6
2592.3.g.l.2431.6		12	72.11	even	6

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 576 = 2^{6} \cdot 3^{2} \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	576.o (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(2.10592 - 2.13661i) q^{3} +(1.25241 + 2.16924i) q^{5} +(0.842935 + 0.486669i) q^{7} +(-0.130192 - 8.99906i) q^{9} +O(q^{10})\)	\(q+(2.10592 - 2.13661i) q^{3} +(1.25241 + 2.16924i) q^{5} +(0.842935 + 0.486669i) q^{7} +(-0.130192 - 8.99906i) q^{9} +(-3.01493 - 1.74067i) q^{11} +(7.51352 + 13.0138i) q^{13} +(7.27231 + 1.89234i) q^{15} +19.3227 q^{17} -13.9609i q^{19} +(2.81498 - 0.776136i) q^{21} +(33.5924 - 19.3946i) q^{23} +(9.36292 - 16.2170i) q^{25} +(-19.5016 - 18.6731i) q^{27} +(-6.95537 + 12.0470i) q^{29} +(12.1511 - 7.01542i) q^{31} +(-10.0683 + 2.77601i) q^{33} +2.43804i q^{35} -28.1331 q^{37} +(43.6283 + 11.3526i) q^{39} +(18.4281 + 31.9183i) q^{41} +(36.2892 + 20.9516i) q^{43} +(19.3581 - 11.5530i) q^{45} +(10.7892 + 6.22913i) q^{47} +(-24.0263 - 41.6148i) q^{49} +(40.6920 - 41.2850i) q^{51} -16.6482 q^{53} -8.72017i q^{55} +(-29.8289 - 29.4005i) q^{57} +(-11.3836 + 6.57234i) q^{59} +(-41.5302 + 71.9324i) q^{61} +(4.26982 - 7.64898i) q^{63} +(-18.8201 + 32.5973i) q^{65} +(95.1188 - 54.9169i) q^{67} +(29.3043 - 112.617i) q^{69} -96.4767i q^{71} -40.1094 q^{73} +(-14.9319 - 54.1567i) q^{75} +(-1.69426 - 2.93455i) q^{77} +(-117.038 - 67.5719i) q^{79} +(-80.9661 + 2.34320i) q^{81} +(52.4342 + 30.2729i) q^{83} +(24.2000 + 41.9156i) q^{85} +(11.0924 + 40.2310i) q^{87} +138.741 q^{89} +14.6264i q^{91} +(10.6000 - 40.7360i) q^{93} +(30.2846 - 17.4848i) q^{95} +(-79.4667 + 137.640i) q^{97} +(-15.2719 + 27.3582i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q - 4 q^{9}+O(q^{10}) \) 24 * q - 4 * q^9	\( 24 q - 4 q^{9} + 24 q^{13} - 24 q^{17} - 56 q^{21} - 108 q^{25} + 24 q^{29} + 52 q^{33} - 96 q^{37} - 60 q^{41} + 224 q^{45} - 132 q^{49} - 96 q^{53} + 348 q^{57} + 336 q^{61} + 216 q^{65} - 416 q^{69} + 696 q^{73} + 24 q^{77} - 788 q^{81} + 528 q^{85} - 240 q^{89} - 1040 q^{93} - 444 q^{97}+O(q^{100}) \) 24 * q - 4 * q^9 + 24 * q^13 - 24 * q^17 - 56 * q^21 - 108 * q^25 + 24 * q^29 + 52 * q^33 - 96 * q^37 - 60 * q^41 + 224 * q^45 - 132 * q^49 - 96 * q^53 + 348 * q^57 + 336 * q^61 + 216 * q^65 - 416 * q^69 + 696 * q^73 + 24 * q^77 - 788 * q^81 + 528 * q^85 - 240 * q^89 - 1040 * q^93 - 444 * q^97

Introduction

L-functions

Modular forms

Varieties

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Representations

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Database

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