LMFDB - Embedded newform 288.3.o.c.223.10

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [288,3,Mod(31,288)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(288, 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("288.31");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 288 = 2^{5} \cdot 3^{2} $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	288.o (of order $6$, degree $2$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

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

Self dual:	no
Analytic conductor:	$7.84743161358$
Analytic rank:	$0$
Dimension:	$24$
Relative dimension:	$12$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			223.10
Character	$\chi$	$=$	288.223
Dual form			288.3.o.c.31.10

$q$-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 $\left(\mathbb{Z}/288\mathbb{Z}\right)^\times$.

$n$	$37$	$65$	$127$
$\chi(n)$	$1$	$e\left(\frac{2}{3}\right)$	$-1$

Coefficient data

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

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

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

$2$		0			0
$2$		0			0
$3$	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	0.713176	−	0.700985i	$-0.247256\pi$
$5$	−1.25241	−	2.16924i	−0.250483	−	0.433849i	−0.963659	+	0.267136i	$0.913923\pi$
$6$		0			0
$7$	−0.842935	−	0.486669i	−0.120419	−	0.0695241i	0.438580	−	0.898692i	$-0.355481\pi$
$7$	−0.842935	−	0.486669i	−0.120419	−	0.0695241i	−0.559000	+	0.829168i	$0.688815\pi$
$8$		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	$-0.970514\pi$
$13$	−7.51352	−	13.0138i	−0.577963	−	1.00106i	0.417750	−	0.908562i	$-0.362819\pi$
$14$		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	−0.999036	−	0.0438947i	$-0.986023\pi$
$23$	−33.5924	+	19.3946i	−1.46054	+	0.843243i	−0.461504	+	0.887138i	$0.652690\pi$
$24$		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	−0.720828	−	0.693114i	$-0.756238\pi$
$29$	6.95537	−	12.0470i	0.239840	−	0.415415i	0.960668	+	0.277698i	$0.0895716\pi$
$30$		0			0
$31$	−12.1511	+	7.01542i	−0.391970	+	0.226304i	−0.683013	−	0.730406i	$-0.739331\pi$
$31$	−12.1511	+	7.01542i	−0.391970	+	0.226304i	0.291043	+	0.956710i	$0.405998\pi$
$32$		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	$-0.375863\pi$
$37$	28.1331			0.760354			0.380177	+	0.924914i	$0.375863\pi$
$38$		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	0.380811	−	0.924653i	$-0.375645\pi$
$47$	−10.7892	−	6.22913i	−0.229557	−	0.132535i	−0.610368	+	0.792118i	$0.708978\pi$
$48$		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	$-0.449799\pi$
$53$	16.6482			0.314116			0.157058	+	0.987589i	$0.449799\pi$
$54$		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	$-0.594956\pi$
$61$	41.5302	−	71.9324i	0.680823	−	1.17922i	0.974730	−	0.223386i	$-0.0717110\pi$
$62$		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	$0.237766\pi$
$71$			96.4767i			1.35883i	−0.733756	+	0.679413i	$0.762234\pi$
$72$		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	0.999780	−	0.0209890i	$-0.00668151\pi$
$79$	117.038	+	67.5719i	1.48149	+	0.855340i	0.481713	+	0.876329i	$0.340015\pi$
$80$		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	$0.337603\pi$
$101$	−51.6687	+	89.4929i	−0.511572	+	0.886068i	−0.999910	+	0.0134136i	$0.995730\pi$
$102$		0			0
$103$	−16.5726	+	9.56821i	−0.160899	+	0.0928952i	−0.578288	−	0.815833i	$-0.696279\pi$
$103$	−16.5726	+	9.56821i	−0.160899	+	0.0928952i	0.417388	+	0.908728i	$0.362946\pi$
$104$		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	$-0.217697\pi$
$109$	168.973			1.55021			0.775104	+	0.631833i	$0.217697\pi$
$110$		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	$-0.785819\pi$
$127$		−	158.301i		−	1.24647i	0.782036	−	0.623233i	$-0.214181\pi$
$128$		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	0.667188	−	0.744889i	$-0.267498\pi$
$149$	−46.4133	−	80.3902i	−0.311499	−	0.539532i	−0.978687	+	0.205357i	$0.934164\pi$
$150$		0			0
$151$	85.2221	+	49.2030i	0.564385	+	0.325848i	0.754903	−	0.655836i	$-0.227684\pi$
$151$	85.2221	+	49.2030i	0.564385	+	0.325848i	−0.190519	+	0.981684i	$0.561017\pi$
$152$		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	0.514706	−	0.857367i	$-0.327901\pi$
$157$	−76.1683	−	131.927i	−0.485149	−	0.840302i	−0.999854	+	0.0170647i	$0.994568\pi$
$158$		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	$-0.289008\pi$
$167$	268.150	−	154.816i	1.60569	−	0.927043i	0.990320	−	0.138802i	$-0.0443251\pi$
$168$		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	$-0.539601\pi$
$173$	137.931	−	238.903i	0.797288	−	1.38094i	0.921376	−	0.388672i	$-0.127066\pi$
$174$		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	$-0.295070\pi$
$181$	217.288			1.20049			0.600244	+	0.799817i	$0.295070\pi$
$182$		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	−0.192370	−	0.981322i	$-0.561617\pi$
$191$	−217.435	−	125.536i	−1.13841	−	0.657258i	−0.946035	+	0.324064i	$0.894951\pi$
$192$		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	$-0.659403\pi$
$197$	−189.163			−0.960219			−0.480109	+	0.877209i	$0.659403\pi$
$198$		0			0
$199$		−	76.3625i		−	0.383731i	−0.981421	−	0.191866i	$-0.938546\pi$
$199$		−	76.3625i		−	0.383731i	0.981421	−	0.191866i	$-0.0614538\pi$
$200$		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	0.0940534	−	0.995567i	$-0.470018\pi$
$223$	−160.807	−	92.8418i	−0.721106	−	0.416331i	−0.815160	+	0.579236i	$0.803351\pi$
$224$		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	0.992829	−	0.119547i	$-0.0381441\pi$
$229$	89.9704	+	155.833i	0.392884	+	0.680495i	−0.599945	+	0.800041i	$0.704811\pi$
$230$		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	−0.295087	−	0.955470i	$-0.595349\pi$
$239$	91.9748	−	53.1017i	0.384832	−	0.222183i	0.679918	+	0.733288i	$0.262015\pi$
$240$		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	0.808882	−	0.587971i	$-0.200073\pi$
$263$	185.185	+	106.917i	0.704126	+	0.406527i	−0.104756	+	0.994498i	$0.533406\pi$
$264$		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	$-0.543574\pi$
$269$	−73.4182			−0.272930			−0.136465	+	0.990645i	$0.543574\pi$
$270$		0			0
$271$		−	95.2505i		−	0.351478i	−0.984437	−	0.175739i	$-0.943769\pi$
$271$		−	95.2505i		−	0.351478i	0.984437	−	0.175739i	$-0.0562315\pi$
$272$		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	$0.371221\pi$
$277$	−166.006	+	287.531i	−0.599299	+	1.03802i	−0.992925	+	0.118746i	$0.962113\pi$
$278$		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	0.677622	−	0.735410i	$-0.263010\pi$
$293$	−87.3353	−	151.269i	−0.298073	−	0.516277i	−0.975695	+	0.219133i	$0.929677\pi$
$294$		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	−0.101414	−	0.994844i	$-0.532337\pi$
$311$	220.636	−	127.384i	0.709440	−	0.409595i	0.810853	+	0.585249i	$0.199003\pi$
$312$		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	−0.943764	−	0.330619i	$-0.892742\pi$
$317$	−58.8218	+	101.882i	−0.185558	+	0.321395i	0.758207	+	0.652014i	$0.226076\pi$
$318$		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	$0.489208\pi$
$349$	−296.154	+	512.954i	−0.848579	+	1.46978i	−0.882477	+	0.470356i	$0.844125\pi$
$350$		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	$0.145827\pi$
$359$			317.550i			0.884541i	−0.896882	+	0.442270i	$0.854173\pi$
$360$		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	0.695791	−	0.718245i	$-0.255054\pi$
$367$	154.752	+	89.3462i	0.421668	+	0.243450i	−0.274123	+	0.961695i	$0.588387\pi$
$368$		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	0.850440	−	0.526072i	$-0.176336\pi$
$373$	−11.3286	−	19.6218i	−0.0303717	−	0.0526053i	−0.880812	+	0.473467i	$0.843002\pi$
$374$		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	−0.461982	−	0.886889i	$-0.652862\pi$
$383$	28.7614	−	16.6054i	0.0750951	−	0.0433562i	0.537077	+	0.843533i	$0.319528\pi$
$384$		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	−0.954375	−	0.298610i	$-0.903477\pi$
$389$	−85.0289	+	147.274i	−0.218583	+	0.378598i	0.735792	+	0.677208i	$0.236810\pi$
$390$		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	$-0.358890\pi$
$397$	340.573			0.857866			0.428933	+	0.903336i	$0.358890\pi$
$398$		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	−0.783877	−	0.620916i	$-0.786761\pi$
$421$	61.3780	−	106.310i	0.145791	−	0.252517i	0.929668	+	0.368399i	$0.120094\pi$
$422$		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	$0.202489\pi$
$431$			512.109i			1.18819i	−0.804395	+	0.594094i	$0.797511\pi$
$432$		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	0.233660	−	0.972318i	$-0.424930\pi$
$439$	−215.796	−	124.590i	−0.491562	−	0.283803i	−0.725222	+	0.688515i	$0.758263\pi$
$440$		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	−0.811301	−	0.584629i	$-0.801240\pi$
$461$	46.4011	−	80.3691i	0.100653	−	0.174337i	0.911954	+	0.410293i	$0.134573\pi$
$462$		0			0
$463$	639.918	−	369.457i	1.38211	−	0.797962i	0.389702	−	0.920941i	$-0.372578\pi$
$463$	639.918	−	369.457i	1.38211	−	0.797962i	0.992409	+	0.122979i	$0.0392447\pi$
$464$		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	−0.371459	−	0.928449i	$-0.621143\pi$
$479$	−652.039	−	376.455i	−1.36125	−	0.785918i	−0.989790	+	0.142531i	$0.954476\pi$
$480$		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	$0.256805\pi$
$487$			703.286i			1.44412i	−0.691831	+	0.722060i	$0.743195\pi$
$488$		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	$0.000282130\pi$
$503$			0.891657i			0.00177268i	−1.00000		0.000886339i	$0.999718\pi$
$504$		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	$0.0246025\pi$
$509$	287.777	+	498.444i	0.565377	+	0.979261i	−0.431638	+	0.902047i	$0.642064\pi$
$510$		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	$-0.801710\pi$
$541$	−878.760			−1.62433			−0.812163	+	0.583431i	$0.801710\pi$
$542$		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	$-0.155780\pi$
$557$	983.235			1.76523			0.882616	+	0.470094i	$0.155780\pi$
$558$		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	0.215437	−	0.976518i	$-0.430882\pi$
$599$	700.138	−	404.225i	1.16884	−	0.674833i	0.953408	+	0.301685i	$0.0975491\pi$
$600$		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	0.330434	−	0.943829i	$-0.392805\pi$
$607$	797.010	−	460.154i	1.31303	−	0.758079i	0.982597	+	0.185750i	$0.0594714\pi$
$608$		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	$-0.774598\pi$
$613$	−931.251			−1.51917			−0.759585	+	0.650408i	$0.774598\pi$
$614$		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	$0.108786\pi$
$631$			422.954i			0.670291i	−0.942166	+	0.335146i	$0.891214\pi$
$632$		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	$0.220663\pi$
$647$			826.902i			1.27806i	−0.769184	+	0.639028i	$0.779337\pi$
$648$		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	$0.189271\pi$
$653$	587.256	+	1017.16i	0.899320	+	1.55767i	0.0709551	+	0.997480i	$0.477395\pi$
$654$		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	0.713410	−	0.700747i	$-0.247150\pi$
$661$	−165.356	−	286.404i	−0.250160	−	0.433290i	−0.963570	+	0.267457i	$0.913817\pi$
$662$		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	−0.981951	−	0.189136i	$-0.939431\pi$
$677$	−221.500	+	383.649i	−0.327179	+	0.566690i	0.654772	+	0.755826i	$0.272765\pi$
$678$		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	$-0.896244\pi$
$701$	−1328.18			−1.89469			−0.947344	+	0.320217i	$0.896244\pi$
$702$		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	−0.871705	−	0.490031i	$-0.836986\pi$
$709$	−8.13480	+	14.0899i	−0.0114736	+	0.0198729i	0.860232	+	0.509904i	$0.170319\pi$
$710$		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	$-0.607493\pi$
$719$		−	1356.78i		−	1.88704i	0.331316	−	0.943520i	$-0.392507\pi$
$720$		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	0.929922	−	0.367756i	$-0.119874\pi$
$727$	782.541	+	451.800i	1.07640	+	0.621458i	0.146475	+	0.989214i	$0.453207\pi$
$728$		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	0.924566	−	0.381022i	$-0.124428\pi$
$733$	96.9820	+	167.978i	0.132308	+	0.229165i	−0.792258	+	0.610187i	$0.791094\pi$
$734$		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	−0.0279221	−	0.999610i	$-0.508889\pi$
$743$	612.087	−	353.389i	0.823805	−	0.475624i	0.851727	+	0.523986i	$0.175556\pi$
$744$		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	−0.515573	−	0.856846i	$-0.672421\pi$
$751$	−23.5131	+	13.5753i	−0.0313091	+	0.0180763i	0.484264	+	0.874922i	$0.339088\pi$
$752$		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	$-0.340527\pi$
$757$	727.176			0.960602			0.480301	+	0.877104i	$0.340527\pi$
$758$		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	$-0.315598\pi$
$773$	846.362			1.09491			0.547453	+	0.836837i	$0.315598\pi$
$774$		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	0.867443	−	0.497537i	$-0.165762\pi$
$797$	2.26487	+	3.92287i	0.00284175	+	0.00492205i	−0.864601	+	0.502459i	$0.832429\pi$
$798$		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	−0.849818	−	0.527076i	$-0.823288\pi$
$821$	25.9045	−	44.8679i	0.0315524	−	0.0546503i	0.881370	+	0.472426i	$0.156622\pi$
$822$		0			0
$823$	653.931	−	377.547i	0.794570	−	0.458745i	−0.0469992	−	0.998895i	$-0.514966\pi$
$823$	653.931	−	377.547i	0.794570	−	0.458745i	0.841569	+	0.540150i	$0.181632\pi$
$824$		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	$-0.667126\pi$
$829$	−831.072			−1.00250			−0.501250	+	0.865303i	$0.667126\pi$
$830$		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	0.914199	−	0.405266i	$-0.132821\pi$
$839$	856.055	+	494.243i	1.02033	+	0.589086i	0.106129	+	0.994352i	$0.466154\pi$
$840$		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	−0.747492	−	0.664270i	$-0.768742\pi$
$853$	171.904	−	297.747i	0.201529	−	0.349058i	0.949021	+	0.315212i	$0.102076\pi$
$854$		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	$0.113367\pi$
$863$			601.806i			0.697342i	−0.937245	+	0.348671i	$0.886633\pi$
$864$		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	$0.202200\pi$
$877$	803.626	+	1391.92i	0.916335	+	1.58714i	0.111399	+	0.993776i	$0.464467\pi$
$878$		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	−0.535357	−	0.844626i	$-0.679823\pi$
$887$	−63.4815	+	36.6511i	−0.0715688	+	0.0413203i	0.463789	+	0.885946i	$0.346490\pi$
$888$		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	$-0.853434\pi$
$911$	−1574.75	−	909.184i	−1.72860	−	0.998007i	−0.832746	−	0.553655i	$-0.813233\pi$
$912$		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	$0.0601619\pi$
$919$			345.325i			0.375762i	−0.982192	+	0.187881i	$0.939838\pi$
$920$		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	0.649922	−	0.760001i	$-0.274802\pi$
$941$	−313.560	−	543.101i	−0.333220	−	0.577153i	−0.983141	+	0.182848i	$0.941468\pi$
$942$		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	$0.712848\pi$
$967$	−1556.33	+	898.550i	−1.60945	+	0.929214i	−0.989494	+	0.144573i	$0.953819\pi$
$968$		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	−0.0334391	−	0.999441i	$-0.510646\pi$
$983$	−900.133	−	519.692i	−0.915700	−	0.528680i	−0.882261	+	0.470761i	$0.843979\pi$
$984$		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	$0.333751\pi$
$991$			1717.76i			1.73336i	−0.498863	+	0.866681i	$0.666249\pi$
$992$		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	−0.824632	−	0.565669i	$-0.808618\pi$
$997$	77.3349	−	133.948i	0.0775676	−	0.134351i	0.902200	+	0.431318i	$0.141951\pi$
$998$		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	288.3.o.c.223.10	yes	24
3.2	odd	2		864.3.o.c.127.7		24
4.3	odd	2	inner	288.3.o.c.223.3	yes	24
8.3	odd	2		576.3.o.i.511.10		24
8.5	even	2		576.3.o.i.511.3		24
9.2	odd	6		2592.3.g.l.2431.6		12
9.4	even	3	inner	288.3.o.c.31.3	✓	24
9.5	odd	6		864.3.o.c.415.8		24
9.7	even	3		2592.3.g.k.2431.8		12
12.11	even	2		864.3.o.c.127.8		24
24.5	odd	2		1728.3.o.i.127.6		24
24.11	even	2		1728.3.o.i.127.5		24
36.7	odd	6		2592.3.g.k.2431.7		12
36.11	even	6		2592.3.g.l.2431.5		12
36.23	even	6		864.3.o.c.415.7		24
36.31	odd	6	inner	288.3.o.c.31.10	yes	24
72.5	odd	6		1728.3.o.i.1279.5		24
72.13	even	6		576.3.o.i.319.10		24
72.59	even	6		1728.3.o.i.1279.6		24
72.67	odd	6		576.3.o.i.319.3		24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
288.3.o.c.31.3	✓	24	9.4	even	3	inner
288.3.o.c.31.10	yes	24	36.31	odd	6	inner
288.3.o.c.223.3	yes	24	4.3	odd	2	inner
288.3.o.c.223.10	yes	24	1.1	even	1	trivial
576.3.o.i.319.3		24	72.67	odd	6
576.3.o.i.319.10		24	72.13	even	6
576.3.o.i.511.3		24	8.5	even	2
576.3.o.i.511.10		24	8.3	odd	2
864.3.o.c.127.7		24	3.2	odd	2
864.3.o.c.127.8		24	12.11	even	2
864.3.o.c.415.7		24	36.23	even	6
864.3.o.c.415.8		24	9.5	odd	6
1728.3.o.i.127.5		24	24.11	even	2
1728.3.o.i.127.6		24	24.5	odd	2
1728.3.o.i.1279.5		24	72.5	odd	6
1728.3.o.i.1279.6		24	72.59	even	6
2592.3.g.k.2431.7		12	36.7	odd	6
2592.3.g.k.2431.8		12	9.7	even	3
2592.3.g.l.2431.5		12	36.11	even	6
2592.3.g.l.2431.6		12	9.2	odd	6

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 288 = 2^{5} \cdot 3^{2} \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	288.o (of order \(6\), degree \(2\), 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

Fields

Representations

Groups

Database

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