LMFDB - Embedded newform 576.3.q.i.65.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [576,3,Mod(65,576)]

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([0, 0, 1]))

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

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

chi := DirichletCharacter("576.65");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 576 = 2^{6} \cdot 3^{2} $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	576.q (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:	$8$
Relative dimension:	$4$ over $\Q(\zeta_{6})$
Coefficient field:	8.0.19269881856.9
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} - 2x^{7} + 15x^{6} - 2x^{5} + 133x^{4} - 84x^{3} + 276x^{2} + 144x + 144 $ x^8 - 2x^7 + 15x^6 - 2x^5 + 133x^4 - 84x^3 + 276x^2 + 144*x + 144
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 2^{2}\cdot 3 $
Twist minimal:	no (minimal twist has level 72)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			65.2
Root			$0.831167 - 1.43962i$ of defining polynomial
Character	$\chi$	$=$	576.65
Dual form			576.3.q.i.257.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.83117 - 2.37631i) q^{3} +(-3.44299 + 1.98781i) q^{5} +(-1.80469 + 3.12582i) q^{7} +(-2.29365 + 8.70282i) q^{9} +O(q^{10})$	\(q+(-1.83117 - 2.37631i) q^{3} +(-3.44299 + 1.98781i) q^{5} +(-1.80469 + 3.12582i) q^{7} +(-2.29365 + 8.70282i) q^{9} +(-11.8326 - 6.83153i) q^{11} +(8.96435 + 15.5267i) q^{13} +(11.0283 + 4.54158i) q^{15} -21.6750i q^{17} +23.4245 q^{19} +(10.7326 - 1.43540i) q^{21} +(13.0662 - 7.54376i) q^{23} +(-4.59721 + 7.96260i) q^{25} +(24.8806 - 10.4859i) q^{27} +(20.4862 + 11.8277i) q^{29} +(-23.5016 - 40.7060i) q^{31} +(5.43358 + 40.6274i) q^{33} -14.3495i q^{35} -54.6126 q^{37} +(20.4810 - 49.7340i) q^{39} +(24.6459 - 14.2293i) q^{41} +(23.8753 - 41.3532i) q^{43} +(-9.40254 - 34.5231i) q^{45} +(30.5323 + 17.6278i) q^{47} +(17.9862 + 31.1530i) q^{49} +(-51.5065 + 39.6906i) q^{51} -65.0193i q^{53} +54.3192 q^{55} +(-42.8942 - 55.6638i) q^{57} +(76.0156 - 43.8876i) q^{59} +(6.46852 - 11.2038i) q^{61} +(-23.0641 - 22.8755i) q^{63} +(-61.7284 - 35.6389i) q^{65} +(-1.55595 - 2.69499i) q^{67} +(-41.8526 - 17.2353i) q^{69} -49.5089i q^{71} +102.151 q^{73} +(27.3398 - 3.65648i) q^{75} +(42.7082 - 24.6576i) q^{77} +(-18.7220 + 32.4275i) q^{79} +(-70.4783 - 39.9225i) q^{81} +(-14.6999 - 8.48702i) q^{83} +(43.0859 + 74.6270i) q^{85} +(-9.40739 - 70.3399i) q^{87} -14.1990i q^{89} -64.7115 q^{91} +(-53.6945 + 130.387i) q^{93} +(-80.6505 + 46.5636i) q^{95} +(-24.1484 + 41.8262i) q^{97} +(86.5934 - 87.3074i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q - 10 q^{3} + 6 q^{5} + 6 q^{7} - 22 q^{9}+O(q^{10}) $ 8 * q - 10 * q^3 + 6 * q^5 + 6 * q^7 - 22 * q^9	$ 8 q - 10 q^{3} + 6 q^{5} + 6 q^{7} - 22 q^{9} - 36 q^{11} - 14 q^{13} + 10 q^{15} - 4 q^{19} + 54 q^{21} - 102 q^{23} + 10 q^{25} + 20 q^{27} + 114 q^{29} - 50 q^{31} - 104 q^{33} - 120 q^{37} + 82 q^{39} + 264 q^{41} + 28 q^{43} - 206 q^{45} + 150 q^{47} + 94 q^{49} - 170 q^{51} - 244 q^{55} - 178 q^{57} + 108 q^{59} - 14 q^{61} - 210 q^{63} - 198 q^{65} + 20 q^{67} + 14 q^{69} - 76 q^{73} - 326 q^{75} - 66 q^{77} + 26 q^{79} + 194 q^{81} - 246 q^{83} + 224 q^{85} - 18 q^{87} - 108 q^{91} + 130 q^{93} - 456 q^{95} - 236 q^{97} + 634 q^{99}+O(q^{100}) $ 8 * q - 10 * q^3 + 6 * q^5 + 6 * q^7 - 22 * q^9 - 36 * q^11 - 14 * q^13 + 10 * q^15 - 4 * q^19 + 54 * q^21 - 102 * q^23 + 10 * q^25 + 20 * q^27 + 114 * q^29 - 50 * q^31 - 104 * q^33 - 120 * q^37 + 82 * q^39 + 264 * q^41 + 28 * q^43 - 206 * q^45 + 150 * q^47 + 94 * q^49 - 170 * q^51 - 244 * q^55 - 178 * q^57 + 108 * q^59 - 14 * q^61 - 210 * q^63 - 198 * q^65 + 20 * q^67 + 14 * q^69 - 76 * q^73 - 326 * q^75 - 66 * q^77 + 26 * q^79 + 194 * q^81 - 246 * q^83 + 224 * q^85 - 18 * q^87 - 108 * q^91 + 130 * q^93 - 456 * q^95 - 236 * q^97 + 634 * q^99

Display 100 coefficients 10 coefficients

Character values

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

$n$	$65$	$127$	$325$
$\chi(n)$	$e\left(\frac{1}{6}\right)$	$1$	$1$

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
$3$	−1.83117	−	2.37631i	−0.610389	−	0.792102i
$3$	−1.83117	−	2.37631i	−0.610389	−	0.792102i
$4$		0			0
$5$	−3.44299	+	1.98781i	−0.688598	+	0.397562i	−0.803087	−	0.595862i	$-0.796810\pi$
$5$	−3.44299	+	1.98781i	−0.688598	+	0.397562i	0.114488	+	0.993425i	$0.463477\pi$
$6$		0			0
$7$	−1.80469	+	3.12582i	−0.257813	+	0.446545i	−0.965656	−	0.259825i	$-0.916335\pi$
$7$	−1.80469	+	3.12582i	−0.257813	+	0.446545i	0.707843	+	0.706370i	$0.249669\pi$
$8$		0			0
$9$	−2.29365	+	8.70282i	−0.254851	+	0.966980i
$10$		0			0
$11$	−11.8326	−	6.83153i	−1.07569	−	0.621048i	−0.145957	−	0.989291i	$-0.546626\pi$
$11$	−11.8326	−	6.83153i	−1.07569	−	0.621048i	−0.929730	+	0.368243i	$0.879959\pi$
$12$		0			0
$13$	8.96435	+	15.5267i	0.689565	+	1.19436i	0.971979	+	0.235070i	$0.0755318\pi$
$13$	8.96435	+	15.5267i	0.689565	+	1.19436i	−0.282413	+	0.959293i	$0.591135\pi$
$14$		0			0
$15$	11.0283	+	4.54158i	0.735223	+	0.302772i
$16$		0			0
$17$		−	21.6750i		−	1.27500i	−0.770449	−	0.637501i	$-0.779968\pi$
$17$		−	21.6750i		−	1.27500i	0.770449	−	0.637501i	$-0.220032\pi$
$18$		0			0
$19$	23.4245			1.23287			0.616435	−	0.787406i	$-0.288576\pi$
$19$	23.4245			1.23287			0.616435	+	0.787406i	$0.288576\pi$
$20$		0			0
$21$	10.7326	−	1.43540i	0.511076	−	0.0683522i
$22$		0			0
$23$	13.0662	−	7.54376i	0.568095	−	0.327990i	−0.188293	−	0.982113i	$-0.560296\pi$
$23$	13.0662	−	7.54376i	0.568095	−	0.327990i	0.756388	+	0.654123i	$0.226962\pi$
$24$		0			0
$25$	−4.59721	+	7.96260i	−0.183888	+	0.318504i
$26$		0			0
$27$	24.8806	−	10.4859i	0.921505	−	0.388367i
$28$		0			0
$29$	20.4862	+	11.8277i	0.706420	+	0.407852i	0.809734	−	0.586797i	$-0.199611\pi$
$29$	20.4862	+	11.8277i	0.706420	+	0.407852i	−0.103314	+	0.994649i	$0.532945\pi$
$30$		0			0
$31$	−23.5016	−	40.7060i	−0.758117	−	1.31310i	−0.943810	−	0.330489i	$-0.892786\pi$
$31$	−23.5016	−	40.7060i	−0.758117	−	1.31310i	0.185693	−	0.982608i	$-0.440547\pi$
$32$		0			0
$33$	5.43358	+	40.6274i	0.164654	+	1.23113i
$34$		0			0
$35$		−	14.3495i		−	0.409987i
$36$		0			0
$37$	−54.6126			−1.47602			−0.738009	−	0.674791i	$-0.764234\pi$
$37$	−54.6126			−1.47602			−0.738009	+	0.674791i	$0.764234\pi$
$38$		0			0
$39$	20.4810	−	49.7340i	0.525153	−	1.27523i
$40$		0			0
$41$	24.6459	−	14.2293i	0.601118	−	0.347056i	−0.168363	−	0.985725i	$-0.553848\pi$
$41$	24.6459	−	14.2293i	0.601118	−	0.347056i	0.769481	+	0.638669i	$0.220515\pi$
$42$		0			0
$43$	23.8753	−	41.3532i	0.555239	−	0.961702i	−0.442646	−	0.896696i	$-0.645960\pi$
$43$	23.8753	−	41.3532i	0.555239	−	0.961702i	0.997885	−	0.0650055i	$-0.0207065\pi$
$44$		0			0
$45$	−9.40254	−	34.5231i	−0.208945	−	0.767180i
$46$		0			0
$47$	30.5323	+	17.6278i	0.649623	+	0.375060i	0.788312	−	0.615276i	$-0.210955\pi$
$47$	30.5323	+	17.6278i	0.649623	+	0.375060i	−0.138689	+	0.990336i	$0.544289\pi$
$48$		0			0
$49$	17.9862	+	31.1530i	0.367065	+	0.635775i
$50$		0			0
$51$	−51.5065	+	39.6906i	−1.00993	+	0.778248i
$52$		0			0
$53$		−	65.0193i		−	1.22678i	−0.789780	−	0.613390i	$-0.789805\pi$
$53$		−	65.0193i		−	1.22678i	0.789780	−	0.613390i	$-0.210195\pi$
$54$		0			0
$55$	54.3192			0.987621
$56$		0			0
$57$	−42.8942	−	55.6638i	−0.752530	−	0.976559i
$58$		0			0
$59$	76.0156	−	43.8876i	1.28840	−	0.743858i	0.310031	−	0.950726i	$-0.399661\pi$
$59$	76.0156	−	43.8876i	1.28840	−	0.743858i	0.978369	+	0.206869i	$0.0663272\pi$
$60$		0			0
$61$	6.46852	−	11.2038i	0.106041	−	0.183669i	−0.808122	−	0.589015i	$-0.799516\pi$
$61$	6.46852	−	11.2038i	0.106041	−	0.183669i	0.914163	+	0.405346i	$0.132849\pi$
$62$		0			0
$63$	−23.0641	−	22.8755i	−0.366097	−	0.363102i
$64$		0			0
$65$	−61.7284	−	35.6389i	−0.949667	−	0.548291i
$66$		0			0
$67$	−1.55595	−	2.69499i	−0.0232232	−	0.0402237i	0.854180	−	0.519977i	$-0.174059\pi$
$67$	−1.55595	−	2.69499i	−0.0232232	−	0.0402237i	−0.877403	+	0.479753i	$0.840726\pi$
$68$		0			0
$69$	−41.8526	−	17.2353i	−0.606560	−	0.249788i
$70$		0			0
$71$		−	49.5089i		−	0.697308i	−0.937251	−	0.348654i	$-0.886639\pi$
$71$		−	49.5089i		−	0.697308i	0.937251	−	0.348654i	$-0.113361\pi$
$72$		0			0
$73$	102.151			1.39932			0.699662	−	0.714474i	$-0.253334\pi$
$73$	102.151			1.39932			0.699662	+	0.714474i	$0.253334\pi$
$74$		0			0
$75$	27.3398	−	3.65648i	0.364531	−	0.0487530i
$76$		0			0
$77$	42.7082	−	24.6576i	0.554652	−	0.320228i
$78$		0			0
$79$	−18.7220	+	32.4275i	−0.236988	+	0.410475i	−0.959849	−	0.280519i	$-0.909494\pi$
$79$	−18.7220	+	32.4275i	−0.236988	+	0.410475i	0.722861	+	0.690994i	$0.242827\pi$
$80$		0			0
$81$	−70.4783	−	39.9225i	−0.870102	−	0.492871i
$82$		0			0
$83$	−14.6999	−	8.48702i	−0.177108	−	0.102253i	0.408825	−	0.912613i	$-0.365939\pi$
$83$	−14.6999	−	8.48702i	−0.177108	−	0.102253i	−0.585933	+	0.810359i	$0.699272\pi$
$84$		0			0
$85$	43.0859	+	74.6270i	0.506893	+	0.877964i
$86$		0			0
$87$	−9.40739	−	70.3399i	−0.108131	−	0.808505i
$88$		0			0
$89$		−	14.1990i		−	0.159540i	−0.996813	−	0.0797698i	$-0.974581\pi$
$89$		−	14.1990i		−	0.159540i	0.996813	−	0.0797698i	$-0.0254185\pi$
$90$		0			0
$91$	−64.7115			−0.711116
$92$		0			0
$93$	−53.6945	+	130.387i	−0.577360	+	1.40201i
$94$		0			0
$95$	−80.6505	+	46.5636i	−0.848952	+	0.490143i
$96$		0			0
$97$	−24.1484	+	41.8262i	−0.248952	+	0.431198i	−0.963235	−	0.268659i	$-0.913420\pi$
$97$	−24.1484	+	41.8262i	−0.248952	+	0.431198i	0.714283	+	0.699857i	$0.246753\pi$
$98$		0			0
$99$	86.5934	−	87.3074i	0.874680	−	0.881893i
$100$		0			0
$101$	34.5980	+	19.9752i	0.342554	+	0.197774i	0.661401	−	0.750032i	$-0.269962\pi$
$101$	34.5980	+	19.9752i	0.342554	+	0.197774i	−0.318847	+	0.947806i	$0.603296\pi$
$102$		0			0
$103$	10.9749	+	19.0091i	0.106552	+	0.184554i	0.914371	−	0.404876i	$-0.132685\pi$
$103$	10.9749	+	19.0091i	0.106552	+	0.184554i	−0.807819	+	0.589431i	$0.799352\pi$
$104$		0			0
$105$	−34.0989	+	26.2764i	−0.324751	+	0.250252i
$106$		0			0
$107$		−	0.521299i		−	0.00487195i	−0.999997	−	0.00243598i	$-0.999225\pi$
$107$		−	0.521299i		−	0.00487195i	0.999997	−	0.00243598i	$-0.000775396\pi$
$108$		0			0
$109$	198.784			1.82371			0.911855	−	0.410513i	$-0.134650\pi$
$109$	198.784			1.82371			0.911855	+	0.410513i	$0.134650\pi$
$110$		0			0
$111$	100.005	+	129.776i	0.900945	+	1.16916i
$112$		0			0
$113$	115.971	−	66.9557i	1.02629	−	0.592528i	0.110369	−	0.993891i	$-0.464797\pi$
$113$	115.971	−	66.9557i	1.02629	−	0.592528i	0.915919	+	0.401363i	$0.131463\pi$
$114$		0			0
$115$	−29.9912	+	51.9462i	−0.260793	+	0.451706i
$116$		0			0
$117$	−155.687	+	42.4023i	−1.33066	+	0.362412i
$118$		0			0
$119$	67.7522	+	39.1168i	0.569346	+	0.328712i
$120$		0			0
$121$	32.8395	+	56.8797i	0.271401	+	0.470080i
$122$		0			0
$123$	−78.9438	−	32.5099i	−0.641820	−	0.264308i
$124$		0			0
$125$		−	135.944i		−	1.08755i
$126$		0			0
$127$	45.8769			0.361235			0.180618	−	0.983553i	$-0.442190\pi$
$127$	45.8769			0.361235			0.180618	+	0.983553i	$0.442190\pi$
$128$		0			0
$129$	−141.987	+	18.9896i	−1.10068	+	0.147207i
$130$		0			0
$131$	−167.914	+	96.9453i	−1.28179	+	0.740040i	−0.977175	−	0.212436i	$-0.931860\pi$
$131$	−167.914	+	96.9453i	−1.28179	+	0.740040i	−0.304612	+	0.952476i	$0.598527\pi$
$132$		0			0
$133$	−42.2741	+	73.2208i	−0.317850	+	0.550532i
$134$		0			0
$135$	−64.8198	+	85.5609i	−0.480147	+	0.633784i
$136$		0			0
$137$	149.798	+	86.4859i	1.09342	+	0.631284i	0.934484	−	0.356005i	$-0.115862\pi$
$137$	149.798	+	86.4859i	1.09342	+	0.631284i	0.158932	+	0.987289i	$0.449195\pi$
$138$		0			0
$139$	−0.803631	−	1.39193i	−0.00578151	−	0.0100139i	0.863120	−	0.504999i	$-0.168507\pi$
$139$	−0.803631	−	1.39193i	−0.00578151	−	0.0100139i	−0.868902	+	0.494985i	$0.835174\pi$
$140$		0			0
$141$	−14.0206	−	104.834i	−0.0994370	−	0.743500i
$142$		0			0
$143$		−	244.961i		−	1.71301i
$144$		0			0
$145$	−94.0450			−0.648586
$146$		0			0
$147$	41.0933	−	99.7870i	0.279546	−	0.678823i
$148$		0			0
$149$	−76.1133	+	43.9441i	−0.510828	+	0.294927i	−0.733174	−	0.680041i	$-0.761962\pi$
$149$	−76.1133	+	43.9441i	−0.510828	+	0.294927i	0.222346	+	0.974968i	$0.428629\pi$
$150$		0			0
$151$	6.64118	−	11.5029i	0.0439813	−	0.0761778i	−0.843197	−	0.537605i	$-0.819329\pi$
$151$	6.64118	−	11.5029i	0.0439813	−	0.0761778i	0.887178	+	0.461427i	$0.152662\pi$
$152$		0			0
$153$	188.634	+	49.7151i	1.23290	+	0.324935i
$154$		0			0
$155$	161.832	+	93.4336i	1.04408	+	0.602798i
$156$		0			0
$157$	93.8926	+	162.627i	0.598042	+	1.03584i	0.993110	+	0.117188i	$0.0373879\pi$
$157$	93.8926	+	162.627i	0.598042	+	1.03584i	−0.395068	+	0.918652i	$0.629279\pi$
$158$		0			0
$159$	−154.506	+	119.061i	−0.971735	+	0.748813i
$160$		0			0
$161$			54.4566i			0.338240i
$162$		0			0
$163$	131.235			0.805123			0.402562	−	0.915393i	$-0.368120\pi$
$163$	131.235			0.805123			0.402562	+	0.915393i	$0.368120\pi$
$164$		0			0
$165$	−99.4674	−	129.079i	−0.602833	−	0.782296i
$166$		0			0
$167$	−158.636	+	91.5887i	−0.949918	+	0.548436i	−0.893056	−	0.449946i	$-0.851443\pi$
$167$	−158.636	+	91.5887i	−0.949918	+	0.548436i	−0.0568627	+	0.998382i	$0.518110\pi$
$168$		0			0
$169$	−76.2192	+	132.015i	−0.451001	+	0.781157i
$170$		0			0
$171$	−53.7278	+	203.860i	−0.314198	+	1.19216i
$172$		0			0
$173$	−22.6730	−	13.0903i	−0.131058	−	0.0756662i	0.433038	−	0.901376i	$-0.357442\pi$
$173$	−22.6730	−	13.0903i	−0.131058	−	0.0756662i	−0.564095	+	0.825710i	$0.690775\pi$
$174$		0			0
$175$	−16.5931	−	28.7401i	−0.0948176	−	0.164229i
$176$		0			0
$177$	−243.488	−	100.271i	−1.37564	−	0.566501i
$178$		0			0
$179$			175.092i			0.978165i	0.872238	+	0.489083i	$0.162668\pi$
$179$			175.092i			0.978165i	−0.872238	+	0.489083i	$0.837332\pi$
$180$		0			0
$181$	172.814			0.954772			0.477386	−	0.878694i	$-0.341584\pi$
$181$	172.814			0.954772			0.477386	+	0.878694i	$0.341584\pi$
$182$		0			0
$183$	−38.4686	+	5.14486i	−0.210211	+	0.0281140i
$184$		0			0
$185$	188.031	−	108.560i	1.01638	−	0.586809i
$186$		0			0
$187$	−148.074	+	256.471i	−0.791838	+	1.37150i
$188$		0			0
$189$	−12.1249	+	96.6961i	−0.0641527	+	0.511620i
$190$		0			0
$191$	76.1098	+	43.9420i	0.398481	+	0.230063i	0.685828	−	0.727764i	$-0.259440\pi$
$191$	76.1098	+	43.9420i	0.398481	+	0.230063i	−0.287348	+	0.957826i	$0.592773\pi$
$192$		0			0
$193$	68.6377	+	118.884i	0.355636	+	0.615979i	0.987227	−	0.159323i	$-0.0509310\pi$
$193$	68.6377	+	118.884i	0.355636	+	0.615979i	−0.631591	+	0.775302i	$0.717598\pi$
$194$		0			0
$195$	28.3461	+	211.946i	0.145364	+	1.08690i
$196$		0			0
$197$		−	239.073i		−	1.21357i	−0.794867	−	0.606784i	$-0.792459\pi$
$197$		−	239.073i		−	1.21357i	0.794867	−	0.606784i	$-0.207541\pi$
$198$		0			0
$199$	−250.574			−1.25916			−0.629582	−	0.776934i	$-0.716774\pi$
$199$	−250.574			−1.25916			−0.629582	+	0.776934i	$0.716774\pi$
$200$		0			0
$201$	−3.55490	+	8.63239i	−0.0176861	+	0.0429472i
$202$		0			0
$203$	−73.9425	+	42.6907i	−0.364249	+	0.210299i
$204$		0			0
$205$	−56.5703	+	97.9826i	−0.275953	+	0.477964i
$206$		0			0
$207$	35.6827	+	131.015i	0.172380	+	0.632925i
$208$		0			0
$209$	−277.172	−	160.025i	−1.32618	−	0.765671i
$210$		0			0
$211$	−118.043	−	204.456i	−0.559445	−	0.968988i	−0.997543	−	0.0700601i	$-0.977681\pi$
$211$	−118.043	−	204.456i	−0.559445	−	0.968988i	0.438098	−	0.898927i	$-0.355652\pi$
$212$		0			0
$213$	−117.648	+	90.6590i	−0.552339	+	0.425629i
$214$		0			0
$215$			189.838i			0.882968i
$216$		0			0
$217$	169.653			0.781810
$218$		0			0
$219$	−187.055	−	242.741i	−0.854132	−	1.10841i
$220$		0			0
$221$	336.542	−	194.303i	1.52282	−	0.879198i
$222$		0			0
$223$	42.8742	−	74.2603i	0.192261	−	0.333006i	−0.753738	−	0.657175i	$-0.771751\pi$
$223$	42.8742	−	74.2603i	0.192261	−	0.333006i	0.945999	+	0.324169i	$0.105085\pi$
$224$		0			0
$225$	−58.7527	−	58.2722i	−0.261123	−	0.258987i
$226$		0			0
$227$	−160.187	−	92.4841i	−0.705671	−	0.407419i	0.103785	−	0.994600i	$-0.466905\pi$
$227$	−160.187	−	92.4841i	−0.705671	−	0.407419i	−0.809456	+	0.587181i	$0.800238\pi$
$228$		0			0
$229$	−128.199	−	222.048i	−0.559822	−	0.969640i	−0.997511	−	0.0705135i	$-0.977536\pi$
$229$	−128.199	−	222.048i	−0.559822	−	0.969640i	0.437689	−	0.899126i	$-0.355797\pi$
$230$		0			0
$231$	−136.800	−	56.3356i	−0.592207	−	0.243877i
$232$		0			0
$233$		−	403.712i		−	1.73267i	−0.499464	−	0.866335i	$-0.666470\pi$
$233$		−	403.712i		−	1.73267i	0.499464	−	0.866335i	$-0.333530\pi$
$234$		0			0
$235$	−140.163			−0.596439
$236$		0			0
$237$	111.341	−	14.8909i	0.469793	−	0.0628309i
$238$		0			0
$239$	−215.728	+	124.551i	−0.902630	+	0.521133i	−0.878052	−	0.478565i	$-0.841157\pi$
$239$	−215.728	+	124.551i	−0.902630	+	0.521133i	−0.0245772	+	0.999698i	$0.507824\pi$
$240$		0			0
$241$	85.7023	−	148.441i	0.355611	−	0.615937i	−0.631611	−	0.775285i	$-0.717606\pi$
$241$	85.7023	−	148.441i	0.355611	−	0.615937i	0.987222	+	0.159349i	$0.0509394\pi$
$242$		0			0
$243$	34.1894	+	240.583i	0.140697	+	0.990053i
$244$		0			0
$245$	−123.852	−	71.5063i	−0.505520	−	0.291862i
$246$		0			0
$247$	209.986	+	363.706i	0.850145	+	1.47249i
$248$		0			0
$249$	6.75031	+	50.4727i	0.0271097	+	0.202702i
$250$		0			0
$251$		−	287.980i		−	1.14733i	−0.819089	−	0.573666i	$-0.805521\pi$
$251$		−	287.980i		−	1.14733i	0.819089	−	0.573666i	$-0.194479\pi$
$252$		0			0
$253$	−206.142			−0.814789
$254$		0			0
$255$	98.4390	−	239.040i	0.386035	−	0.937411i
$256$		0			0
$257$	−60.1268	+	34.7142i	−0.233957	+	0.135075i	−0.612396	−	0.790551i	$-0.709794\pi$
$257$	−60.1268	+	34.7142i	−0.233957	+	0.135075i	0.378439	+	0.925626i	$0.376461\pi$
$258$		0			0
$259$	98.5590	−	170.709i	0.380537	−	0.659109i
$260$		0			0
$261$	−149.923	+	151.159i	−0.574416	+	0.579153i
$262$		0			0
$263$	68.7357	+	39.6845i	0.261352	+	0.150892i	0.624951	−	0.780664i	$-0.285119\pi$
$263$	68.7357	+	39.6845i	0.261352	+	0.150892i	−0.363599	+	0.931556i	$0.618452\pi$
$264$		0			0
$265$	129.246	+	223.861i	0.487722	+	0.844758i
$266$		0			0
$267$	−33.7412	+	26.0008i	−0.126372	+	0.0973812i
$268$		0			0
$269$			41.6217i			0.154728i	0.997003	+	0.0773638i	$0.0246503\pi$
$269$			41.6217i			0.154728i	−0.997003	+	0.0773638i	$0.975350\pi$
$270$		0			0
$271$	98.0065			0.361648			0.180824	−	0.983516i	$-0.442124\pi$
$271$	98.0065			0.361648			0.180824	+	0.983516i	$0.442124\pi$
$272$		0			0
$273$	118.498	+	153.774i	0.434057	+	0.563276i
$274$		0			0
$275$	108.793	−	62.8119i	0.395612	−	0.228407i
$276$		0			0
$277$	−153.400	+	265.696i	−0.553790	+	0.959193i	0.444206	+	0.895924i	$0.353486\pi$
$277$	−153.400	+	265.696i	−0.553790	+	0.959193i	−0.997997	+	0.0632681i	$0.979848\pi$
$278$		0			0
$279$	408.162	−	111.165i	1.46295	−	0.398441i
$280$		0			0
$281$	−54.8876	−	31.6894i	−0.195330	−	0.112774i	0.399146	−	0.916888i	$-0.369307\pi$
$281$	−54.8876	−	31.6894i	−0.195330	−	0.112774i	−0.594475	+	0.804114i	$0.702640\pi$
$282$		0			0
$283$	163.299	+	282.842i	0.577027	+	0.999440i	0.995818	+	0.0913578i	$0.0291207\pi$
$283$	163.299	+	282.842i	0.577027	+	0.999440i	−0.418791	+	0.908083i	$0.637546\pi$
$284$		0			0
$285$	258.334	+	106.384i	0.906434	+	0.373279i
$286$		0			0
$287$			102.718i			0.357902i
$288$		0			0
$289$	−180.808			−0.625632
$290$		0			0
$291$	143.612	−	19.2069i	0.493511	−	0.0660030i
$292$		0			0
$293$	62.3120	−	35.9759i	0.212669	−	0.122784i	−0.389882	−	0.920865i	$-0.627484\pi$
$293$	62.3120	−	35.9759i	0.212669	−	0.122784i	0.602551	+	0.798080i	$0.294151\pi$
$294$		0			0
$295$	−174.481	+	302.209i	−0.591460	+	1.02444i
$296$		0			0
$297$	−366.036	−	45.8977i	−1.23244	−	0.154538i
$298$		0			0
$299$	234.260	+	135.250i	0.783477	+	0.452341i
$300$		0			0
$301$	86.1750	+	149.259i	0.286296	+	0.495879i
$302$		0			0
$303$	−15.8876	−	118.793i	−0.0524344	−	0.392057i
$304$		0			0
$305$			51.4328i			0.168632i
$306$		0			0
$307$	161.023			0.524504			0.262252	−	0.964999i	$-0.415535\pi$
$307$	161.023			0.524504			0.262252	+	0.964999i	$0.415535\pi$
$308$		0			0
$309$	25.0745	−	60.8885i	0.0811473	−	0.197050i
$310$		0			0
$311$	352.553	−	203.547i	1.13361	−	0.654491i	0.188771	−	0.982021i	$-0.439549\pi$
$311$	352.553	−	203.547i	1.13361	−	0.654491i	0.944841	+	0.327530i	$0.106216\pi$
$312$		0			0
$313$	79.7548	−	138.139i	0.254808	−	0.441340i	−0.710035	−	0.704166i	$-0.751321\pi$
$313$	79.7548	−	138.139i	0.254808	−	0.441340i	0.964843	+	0.262826i	$0.0846545\pi$
$314$		0			0
$315$	124.882	+	32.9129i	0.396449	+	0.104485i
$316$		0			0
$317$	364.877	+	210.662i	1.15103	+	0.664549i	0.949139	−	0.314859i	$-0.101957\pi$
$317$	364.877	+	210.662i	1.15103	+	0.664549i	0.201894	+	0.979407i	$0.435290\pi$
$318$		0			0
$319$	−161.602	−	279.904i	−0.506591	−	0.877441i
$320$		0			0
$321$	−1.23877	+	0.954585i	−0.00385908	+	0.00297379i
$322$		0			0
$323$		−	507.728i		−	1.57191i
$324$		0			0
$325$	−164.844			−0.507212
$326$		0			0
$327$	−364.007	−	472.372i	−1.11317	−	1.44456i
$328$		0			0
$329$	−110.203	+	63.6256i	−0.334963	+	0.193391i
$330$		0			0
$331$	64.9715	−	112.534i	0.196289	−	0.339982i	−0.751034	−	0.660264i	$-0.770444\pi$
$331$	64.9715	−	112.534i	0.196289	−	0.339982i	0.947322	+	0.320282i	$0.103778\pi$
$332$		0			0
$333$	125.263	−	475.284i	0.376164	−	1.42728i
$334$		0			0
$335$	10.7143	+	6.18588i	0.0319828	+	0.0184653i
$336$		0			0
$337$	53.6006	+	92.8389i	0.159052	+	0.275486i	0.934527	−	0.355892i	$-0.115823\pi$
$337$	53.6006	+	92.8389i	0.159052	+	0.275486i	−0.775475	+	0.631378i	$0.782490\pi$
$338$		0			0
$339$	−371.469	−	152.975i	−1.09578	−	0.451253i
$340$		0			0
$341$			642.208i			1.88331i
$342$		0			0
$343$	−306.698			−0.894163
$344$		0			0
$345$	178.359	−	23.8540i	0.516982	−	0.0691421i
$346$		0			0
$347$	−347.832	+	200.821i	−1.00240	+	0.578735i	−0.908957	−	0.416890i	$-0.863120\pi$
$347$	−347.832	+	200.821i	−1.00240	+	0.578735i	−0.0934416	+	0.995625i	$0.529787\pi$
$348$		0			0
$349$	218.729	−	378.849i	0.626730	−	1.08553i	−0.361474	−	0.932382i	$-0.617726\pi$
$349$	218.729	−	378.849i	0.626730	−	1.08553i	0.988204	−	0.153146i	$-0.0489404\pi$
$350$		0			0
$351$	385.850	+	292.315i	1.09929	+	0.832807i
$352$		0			0
$353$	303.639	+	175.306i	0.860167	+	0.496618i	0.864068	−	0.503375i	$-0.167908\pi$
$353$	303.639	+	175.306i	0.860167	+	0.496618i	−0.00390098	+	0.999992i	$0.501242\pi$
$354$		0			0
$355$	98.4143	+	170.459i	0.277223	+	0.480165i
$356$		0			0
$357$	−31.1123	−	232.629i	−0.0871492	−	0.651623i
$358$		0			0
$359$		−	529.816i		−	1.47581i	−0.674904	−	0.737906i	$-0.735815\pi$
$359$		−	529.816i		−	1.47581i	0.674904	−	0.737906i	$-0.264185\pi$
$360$		0			0
$361$	187.709			0.519969
$362$		0			0
$363$	75.0289	−	182.193i	0.206691	−	0.501909i
$364$		0			0
$365$	−351.704	+	203.056i	−0.963572	+	0.556319i
$366$		0			0
$367$	361.971	−	626.953i	0.986298	−	1.70832i	0.350278	−	0.936646i	$-0.386087\pi$
$367$	361.971	−	626.953i	0.986298	−	1.70832i	0.636020	−	0.771673i	$-0.280580\pi$
$368$		0			0
$369$	67.3059	+	247.126i	0.182401	+	0.669717i
$370$		0			0
$371$	203.239	+	117.340i	0.547813	+	0.316280i
$372$		0			0
$373$	29.6005	+	51.2696i	0.0793580	+	0.137452i	0.902973	−	0.429697i	$-0.141380\pi$
$373$	29.6005	+	51.2696i	0.0793580	+	0.137452i	−0.823615	+	0.567149i	$0.808046\pi$
$374$		0			0
$375$	−323.045	+	248.936i	−0.861453	+	0.663830i
$376$		0			0
$377$			424.111i			1.12496i
$378$		0			0
$379$	−32.5366			−0.0858485			−0.0429243	−	0.999078i	$-0.513667\pi$
$379$	−32.5366			−0.0858485			−0.0429243	+	0.999078i	$0.513667\pi$
$380$		0			0
$381$	−84.0082	−	109.017i	−0.220494	−	0.286135i
$382$		0			0
$383$	−188.264	+	108.694i	−0.491551	+	0.283797i	−0.725218	−	0.688519i	$-0.758261\pi$
$383$	−188.264	+	108.694i	−0.491551	+	0.283797i	0.233666	+	0.972317i	$0.424928\pi$
$384$		0			0
$385$	−98.0293	+	169.792i	−0.254622	+	0.441017i
$386$		0			0
$387$	305.128	+	302.632i	0.788444	+	0.781995i
$388$		0			0
$389$	−579.712	−	334.697i	−1.49026	−	0.860403i	−0.490324	−	0.871540i	$-0.663122\pi$
$389$	−579.712	−	334.697i	−1.49026	−	0.860403i	−0.999938	+	0.0111369i	$0.996455\pi$
$390$		0			0
$391$	−163.511	−	283.210i	−0.418188	−	0.724322i
$392$		0			0
$393$	537.850	+	221.492i	1.36858	+	0.563594i
$394$		0			0
$395$		−	148.864i		−	0.376870i
$396$		0			0
$397$	−22.3088			−0.0561935			−0.0280967	−	0.999605i	$-0.508945\pi$
$397$	−22.3088			−0.0561935			−0.0280967	+	0.999605i	$0.508945\pi$
$398$		0			0
$399$	251.406	−	33.6235i	0.630090	−	0.0842693i
$400$		0			0
$401$	−77.7666	+	44.8986i	−0.193932	+	0.111967i	−0.593822	−	0.804597i	$-0.702382\pi$
$401$	−77.7666	+	44.8986i	−0.193932	+	0.111967i	0.399890	+	0.916563i	$0.369048\pi$
$402$		0			0
$403$	421.354	−	729.806i	1.04554	−	1.81093i
$404$		0			0
$405$	322.015	−	2.64463i	0.795098	−	0.00652995i
$406$		0			0
$407$	646.207	+	373.088i	1.58773	+	0.916677i
$408$		0			0
$409$	−308.464	−	534.276i	−0.754191	−	1.30630i	−0.945775	−	0.324821i	$-0.894696\pi$
$409$	−308.464	−	534.276i	−0.754191	−	1.30630i	0.191584	−	0.981476i	$-0.438637\pi$
$410$		0			0
$411$	−68.7882	−	514.336i	−0.167368	−	1.25143i
$412$		0			0
$413$			316.814i			0.767105i
$414$		0			0
$415$	67.4824			0.162608
$416$		0			0
$417$	−1.83607	+	4.45853i	−0.00440304	+	0.0106919i
$418$		0			0
$419$	−566.501	+	327.069i	−1.35203	+	0.780595i	−0.988534	−	0.151001i	$-0.951750\pi$
$419$	−566.501	+	327.069i	−1.35203	+	0.780595i	−0.363496	+	0.931596i	$0.618417\pi$
$420$		0			0
$421$	209.287	−	362.495i	0.497118	−	0.861033i	−0.502877	−	0.864358i	$-0.667725\pi$
$421$	209.287	−	362.495i	0.497118	−	0.861033i	0.999994	+	0.00332489i	$0.00105835\pi$
$422$		0			0
$423$	−223.442	+	225.285i	−0.528233	+	0.532589i
$424$		0			0
$425$	172.590	+	99.6447i	0.406093	+	0.234458i
$426$		0			0
$427$	23.3474	+	40.4388i	0.0546777	+	0.0947045i
$428$		0			0
$429$	−582.102	+	448.564i	−1.35688	+	1.04560i
$430$		0			0
$431$		−	111.970i		−	0.259792i	−0.991528	−	0.129896i	$-0.958536\pi$
$431$		−	111.970i		−	0.259792i	0.991528	−	0.129896i	$-0.0414644\pi$
$432$		0			0
$433$	−158.770			−0.366673			−0.183337	−	0.983050i	$-0.558690\pi$
$433$	−158.770			−0.366673			−0.183337	+	0.983050i	$0.558690\pi$
$434$		0			0
$435$	172.212	+	223.480i	0.395890	+	0.513746i
$436$		0			0
$437$	306.069	−	176.709i	0.700387	−	0.404369i
$438$		0			0
$439$	61.8211	−	107.077i	0.140823	−	0.243912i	−0.786984	−	0.616973i	$-0.788359\pi$
$439$	61.8211	−	107.077i	0.140823	−	0.243912i	0.927807	+	0.373061i	$0.121692\pi$
$440$		0			0
$441$	−312.373	+	85.0764i	−0.708329	+	0.192917i
$442$		0			0
$443$	680.397	+	392.827i	1.53588	+	0.886743i	0.999073	+	0.0430402i	$0.0137044\pi$
$443$	680.397	+	392.827i	1.53588	+	0.886743i	0.536811	+	0.843703i	$0.319629\pi$
$444$		0			0
$445$	28.2250	+	48.8871i	0.0634269	+	0.109859i
$446$		0			0
$447$	243.801	+	100.400i	0.545416	+	0.224608i
$448$		0			0
$449$		−	387.277i		−	0.862533i	−0.902225	−	0.431266i	$-0.858067\pi$
$449$		−	387.277i		−	0.862533i	0.902225	−	0.431266i	$-0.141933\pi$
$450$		0			0
$451$	−388.831			−0.862153
$452$		0			0
$453$	−39.4954	+	5.28219i	−0.0871863	+	0.0116605i
$454$		0			0
$455$	222.801	−	128.634i	0.489673	−	0.282713i
$456$		0			0
$457$	160.668	−	278.284i	0.351570	−	0.608938i	−0.634954	−	0.772550i	$-0.718981\pi$
$457$	160.668	−	278.284i	0.351570	−	0.608938i	0.986525	+	0.163612i	$0.0523145\pi$
$458$		0			0
$459$	−227.282	−	539.289i	−0.495169	−	1.17492i
$460$		0			0
$461$	−61.0565	−	35.2510i	−0.132444	−	0.0764663i	0.432314	−	0.901723i	$-0.357697\pi$
$461$	−61.0565	−	35.2510i	−0.132444	−	0.0764663i	−0.564758	+	0.825257i	$0.691030\pi$
$462$		0			0
$463$	181.170	+	313.796i	0.391297	+	0.677746i	0.992621	−	0.121259i	$-0.0386933\pi$
$463$	181.170	+	313.796i	0.391297	+	0.677746i	−0.601324	+	0.799005i	$0.705360\pi$
$464$		0			0
$465$	−74.3142	−	555.654i	−0.159816	−	1.19496i
$466$		0			0
$467$		−	478.151i		−	1.02388i	−0.859022	−	0.511939i	$-0.828927\pi$
$467$		−	478.151i		−	1.02388i	0.859022	−	0.511939i	$-0.171073\pi$
$468$		0			0
$469$	11.2320			0.0239489
$470$		0			0
$471$	214.518	−	520.914i	0.455452	−	1.10598i
$472$		0			0
$473$	−565.011	+	326.209i	−1.19453	+	0.689660i
$474$		0			0
$475$	−107.687	+	186.520i	−0.226710	+	0.392674i
$476$		0			0
$477$	565.852	+	149.132i	1.18627	+	0.312645i
$478$		0			0
$479$	−790.996	−	456.682i	−1.65135	−	0.953407i	−0.976518	−	0.215434i	$-0.930883\pi$
$479$	−790.996	−	456.682i	−1.65135	−	0.953407i	−0.674830	−	0.737973i	$-0.735783\pi$
$480$		0			0
$481$	−489.567	−	847.955i	−1.01781	−	1.76290i
$482$		0			0
$483$	129.406	−	99.7192i	0.267921	−	0.206458i
$484$		0			0
$485$		−	192.010i		−	0.395896i
$486$		0			0
$487$	700.870			1.43916			0.719579	−	0.694411i	$-0.244335\pi$
$487$	700.870			1.43916			0.719579	+	0.694411i	$0.244335\pi$
$488$		0			0
$489$	−240.313	−	311.855i	−0.491438	−	0.637740i
$490$		0			0
$491$	479.646	−	276.924i	0.976876	−	0.564000i	0.0755505	−	0.997142i	$-0.475929\pi$
$491$	479.646	−	276.924i	0.976876	−	0.564000i	0.901326	+	0.433142i	$0.142595\pi$
$492$		0			0
$493$	256.366	−	444.039i	0.520012	−	0.900687i
$494$		0			0
$495$	−124.589	+	472.730i	−0.251696	+	0.955010i
$496$		0			0
$497$	154.756	+	89.3482i	0.311380	+	0.179775i
$498$		0			0
$499$	−162.874	−	282.107i	−0.326401	−	0.565344i	0.655394	−	0.755287i	$-0.272503\pi$
$499$	−162.874	−	282.107i	−0.326401	−	0.565344i	−0.981795	+	0.189944i	$0.939169\pi$
$500$		0			0
$501$	508.132	+	209.254i	1.01424	+	0.417673i
$502$		0			0
$503$		−	610.492i		−	1.21370i	−0.794816	−	0.606851i	$-0.792433\pi$
$503$		−	610.492i		−	1.21370i	0.794816	−	0.606851i	$-0.207567\pi$
$504$		0			0
$505$	−158.827			−0.314510
$506$		0			0
$507$	453.279	−	60.6224i	0.894042	−	0.119571i
$508$		0			0
$509$	−774.630	+	447.233i	−1.52187	+	0.878650i	−0.522200	+	0.852823i	$0.674889\pi$
$509$	−774.630	+	447.233i	−1.52187	+	0.878650i	−0.999666	+	0.0258270i	$0.991778\pi$
$510$		0			0
$511$	−184.350	+	319.304i	−0.360764	+	0.624862i
$512$		0			0
$513$	582.817	−	245.627i	1.13610	−	0.478806i
$514$		0			0
$515$	−75.5729	−	43.6320i	−0.146744	−	0.0847224i
$516$		0			0
$517$	−240.850	−	417.164i	−0.465860	−	0.806894i
$518$		0			0
$519$	10.4116	+	77.8484i	0.0200608	+	0.149997i
$520$		0			0
$521$			244.209i			0.468732i	0.972148	+	0.234366i	$0.0753014\pi$
$521$			244.209i			0.468732i	−0.972148	+	0.234366i	$0.924699\pi$
$522$		0			0
$523$	4.79146			0.00916150			0.00458075	−	0.999990i	$-0.498542\pi$
$523$	4.79146			0.00916150			0.00458075	+	0.999990i	$0.498542\pi$
$524$		0			0
$525$	−37.9105	+	92.0581i	−0.0722104	+	0.175349i
$526$		0			0
$527$	−882.305	+	509.399i	−1.67420	+	0.966601i
$528$		0			0
$529$	−150.683	+	260.991i	−0.284846	+	0.493367i
$530$		0			0
$531$	207.593	+	762.213i	0.390947	+	1.43543i
$532$		0			0
$533$	441.868	+	255.113i	0.829021	+	0.478636i
$534$		0			0
$535$	1.03624	+	1.79483i	0.00193690	+	0.00335482i
$536$		0			0
$537$	416.071	−	320.622i	0.774806	−	0.597061i
$538$		0			0
$539$		−	491.492i		−	0.911859i
$540$		0			0
$541$	−406.633			−0.751633			−0.375816	−	0.926694i	$-0.622638\pi$
$541$	−406.633			−0.751633			−0.375816	+	0.926694i	$0.622638\pi$
$542$		0			0
$543$	−316.451	−	410.658i	−0.582782	−	0.756276i
$544$		0			0
$545$	−684.413	+	395.146i	−1.25580	+	0.725038i
$546$		0			0
$547$	−250.283	+	433.503i	−0.457556	+	0.792509i	−0.998831	−	0.0483358i	$-0.984608\pi$
$547$	−250.283	+	433.503i	−0.457556	+	0.792509i	0.541276	+	0.840845i	$0.317942\pi$
$548$		0			0
$549$	82.6682	+	81.9920i	0.150580	+	0.149348i
$550$		0			0
$551$	479.879	+	277.058i	0.870924	+	0.502828i
$552$		0			0
$553$	−67.5750	−	117.043i	−0.122197	−	0.211652i
$554$		0			0
$555$	−602.287	−	248.028i	−1.08520	−	0.446897i
$556$		0			0
$557$		−	549.645i		−	0.986796i	−0.869804	−	0.493398i	$-0.835755\pi$
$557$		−	549.645i		−	0.986796i	0.869804	−	0.493398i	$-0.164245\pi$
$558$		0			0
$559$	856.105			1.53149
$560$		0			0
$561$	880.601	−	117.773i	1.56970	−	0.209934i
$562$		0			0
$563$	−799.025	+	461.317i	−1.41923	+	0.819391i	−0.996231	−	0.0867404i	$-0.972355\pi$
$563$	−799.025	+	461.317i	−1.41923	+	0.819391i	−0.422996	+	0.906132i	$0.639022\pi$
$564$		0			0
$565$	−266.191	+	461.056i	−0.471134	+	0.816027i
$566$		0			0
$567$	251.982	−	148.254i	0.444413	−	0.261472i
$568$		0			0
$569$	281.820	+	162.709i	0.495289	+	0.285955i	0.726766	−	0.686885i	$-0.241022\pi$
$569$	281.820	+	162.709i	0.495289	+	0.285955i	−0.231477	+	0.972840i	$0.574356\pi$
$570$		0			0
$571$	−64.8487	−	112.321i	−0.113570	−	0.196710i	0.803637	−	0.595120i	$-0.202895\pi$
$571$	−64.8487	−	112.321i	−0.113570	−	0.196710i	−0.917207	+	0.398410i	$0.869562\pi$
$572$		0			0
$573$	−34.9501	−	261.325i	−0.0609949	−	0.456065i
$574$		0			0
$575$			138.721i			0.241254i
$576$		0			0
$577$	401.374			0.695621			0.347811	−	0.937565i	$-0.386925\pi$
$577$	401.374			0.695621			0.347811	+	0.937565i	$0.386925\pi$
$578$		0			0
$579$	156.818	−	380.801i	0.270842	−	0.657687i
$580$		0			0
$581$	53.0577	−	30.6329i	0.0913214	−	0.0527244i
$582$		0			0
$583$	−444.181	+	769.345i	−0.761889	+	1.31963i
$584$		0			0
$585$	451.742	−	455.468i	0.772209	−	0.778577i
$586$		0			0
$587$	650.079	+	375.323i	1.10746	+	0.639392i	0.938170	−	0.346174i	$-0.112519\pi$
$587$	650.079	+	375.323i	1.10746	+	0.639392i	0.169290	+	0.985566i	$0.445853\pi$
$588$		0			0
$589$	−550.515	−	953.519i	−0.934660	−	1.61888i
$590$		0			0
$591$	−568.110	+	437.782i	−0.961270	+	0.740749i
$592$		0			0
$593$			969.193i			1.63439i	0.576362	+	0.817195i	$0.304472\pi$
$593$			969.193i			1.63439i	−0.576362	+	0.817195i	$0.695528\pi$
$594$		0			0
$595$	−311.027			−0.522735
$596$		0			0
$597$	458.842	+	595.440i	0.768580	+	0.997386i
$598$		0			0
$599$	−9.76897	+	5.64012i	−0.0163088	+	0.00941589i	−0.508132	−	0.861279i	$-0.669664\pi$
$599$	−9.76897	+	5.64012i	−0.0163088	+	0.00941589i	0.491823	+	0.870695i	$0.336331\pi$
$600$		0			0
$601$	−425.209	+	736.483i	−0.707502	+	1.22543i	0.258279	+	0.966070i	$0.416845\pi$
$601$	−425.209	+	736.483i	−0.707502	+	1.22543i	−0.965781	+	0.259359i	$0.916489\pi$
$602$		0			0
$603$	27.0228	−	7.35980i	0.0448139	−	0.0122053i
$604$		0			0
$605$	−226.132	−	130.557i	−0.373772	−	0.215797i
$606$		0			0
$607$	−91.2085	−	157.978i	−0.150261	−	0.260260i	0.781062	−	0.624453i	$-0.214678\pi$
$607$	−91.2085	−	157.978i	−0.150261	−	0.260260i	−0.931323	+	0.364193i	$0.881345\pi$
$608$		0			0
$609$	236.847	+	97.5361i	0.388912	+	0.160158i
$610$		0			0
$611$			632.088i			1.03451i
$612$		0			0
$613$	334.345			0.545425			0.272712	−	0.962096i	$-0.412079\pi$
$613$	334.345			0.545425			0.272712	+	0.962096i	$0.412079\pi$
$614$		0			0
$615$	336.426	−	44.9943i	0.547035	−	0.0731614i
$616$		0			0
$617$	−154.140	+	88.9929i	−0.249822	+	0.144235i	−0.619683	−	0.784852i	$-0.712739\pi$
$617$	−154.140	+	88.9929i	−0.249822	+	0.144235i	0.369861	+	0.929087i	$0.379405\pi$
$618$		0			0
$619$	−529.724	+	917.510i	−0.855775	+	1.48225i	0.0201500	+	0.999797i	$0.493586\pi$
$619$	−529.724	+	917.510i	−0.855775	+	1.48225i	−0.875925	+	0.482448i	$0.839748\pi$
$620$		0			0
$621$	245.992	−	324.704i	0.396122	−	0.522873i
$622$		0			0
$623$	44.3836	+	25.6249i	0.0712417	+	0.0411314i
$624$		0			0
$625$	155.301	+	268.989i	0.248482	+	0.430383i
$626$		0			0
$627$	127.279	+	951.678i	0.202997	+	1.51783i
$628$		0			0
$629$			1183.73i			1.88193i
$630$		0			0
$631$	−950.275			−1.50598			−0.752991	−	0.658031i	$-0.771390\pi$
$631$	−950.275			−1.50598			−0.752991	+	0.658031i	$0.771390\pi$
$632$		0			0
$633$	−269.694	+	654.900i	−0.426058	+	1.03460i
$634$		0			0
$635$	−157.954	+	91.1946i	−0.248746	+	0.143614i
$636$		0			0
$637$	−322.469	+	558.532i	−0.506230	+	0.876817i
$638$		0			0
$639$	430.867	+	113.556i	0.674283	+	0.177709i
$640$		0			0
$641$	−74.1661	−	42.8198i	−0.115704	−	0.0668016i	0.441031	−	0.897492i	$-0.354613\pi$
$641$	−74.1661	−	42.8198i	−0.115704	−	0.0668016i	−0.556735	+	0.830690i	$0.687946\pi$
$642$		0			0
$643$	−139.447	−	241.529i	−0.216869	−	0.375629i	0.736980	−	0.675915i	$-0.236251\pi$
$643$	−139.447	−	241.529i	−0.216869	−	0.375629i	−0.953849	+	0.300286i	$0.902918\pi$
$644$		0			0
$645$	451.113	−	347.625i	0.699401	−	0.538954i
$646$		0			0
$647$			654.758i			1.01199i	0.862536	+	0.505995i	$0.168875\pi$
$647$			654.758i			1.01199i	−0.862536	+	0.505995i	$0.831125\pi$
$648$		0			0
$649$	−1199.28			−1.84789
$650$		0			0
$651$	−310.663	−	403.147i	−0.477208	−	0.619273i
$652$		0			0
$653$	159.696	−	92.2004i	0.244557	−	0.141195i	−0.372712	−	0.927947i	$-0.621572\pi$
$653$	159.696	−	92.2004i	0.244557	−	0.141195i	0.617269	+	0.786752i	$0.288239\pi$
$654$		0			0
$655$	385.418	−	667.563i	0.588424	−	1.01918i
$656$		0			0
$657$	−234.298	+	888.999i	−0.356619	+	1.35312i
$658$		0			0
$659$	165.641	+	95.6328i	0.251352	+	0.145118i	0.620383	−	0.784299i	$-0.286977\pi$
$659$	165.641	+	95.6328i	0.251352	+	0.145118i	−0.369031	+	0.929417i	$0.620310\pi$
$660$		0			0
$661$	−66.6012	−	115.357i	−0.100758	−	0.174518i	0.811239	−	0.584715i	$-0.198794\pi$
$661$	−66.6012	−	115.357i	−0.100758	−	0.174518i	−0.911997	+	0.410196i	$0.865460\pi$
$662$		0			0
$663$	−1077.99	−	443.926i	−1.62592	−	0.669572i
$664$		0			0
$665$		−	336.131i		−	0.505461i
$666$		0			0
$667$	356.901			0.535085
$668$		0			0
$669$	−254.975	+	34.1008i	−0.381129	+	0.0509728i
$670$		0			0
$671$	−153.078	+	88.3797i	−0.228134	+	0.131713i
$672$		0			0
$673$	661.521	−	1145.79i	0.982943	−	1.70251i	0.332201	−	0.943208i	$-0.392209\pi$
$673$	661.521	−	1145.79i	0.982943	−	1.70251i	0.650742	−	0.759299i	$-0.274458\pi$
$674$		0			0
$675$	−30.8864	+	246.320i	−0.0457577	+	0.364919i
$676$		0			0
$677$	−288.213	−	166.400i	−0.425720	−	0.245790i	0.271801	−	0.962353i	$-0.412381\pi$
$677$	−288.213	−	166.400i	−0.425720	−	0.245790i	−0.697522	+	0.716564i	$0.745714\pi$
$678$		0			0
$679$	−87.1607	−	150.967i	−0.128366	−	0.222337i
$680$		0			0
$681$	73.5590	+	550.008i	0.108016	+	0.807647i
$682$		0			0
$683$			190.785i			0.279333i	0.990199	+	0.139667i	$0.0446031\pi$
$683$			190.785i			0.279333i	−0.990199	+	0.139667i	$0.955397\pi$
$684$		0			0
$685$	−687.671			−1.00390
$686$		0			0
$687$	−292.899	+	711.247i	−0.426344	+	1.03529i
$688$		0			0
$689$	1009.54	−	582.856i	1.46522	−	0.845945i
$690$		0			0
$691$	360.135	−	623.771i	0.521179	−	0.902708i	−0.478518	−	0.878078i	$-0.658826\pi$
$691$	360.135	−	623.771i	0.521179	−	0.902708i	0.999697	−	0.0246304i	$-0.00784089\pi$
$692$		0			0
$693$	116.633	+	428.238i	0.168301	+	0.617948i
$694$		0			0
$695$	5.53379	+	3.19493i	0.00796228	+	0.00459703i
$696$		0			0
$697$	−308.421	−	534.200i	−0.442497	−	0.766428i
$698$		0			0
$699$	−959.343	+	739.264i	−1.37245	+	1.05760i
$700$		0			0
$701$			145.736i			0.207897i	0.994583	+	0.103949i	$0.0331477\pi$
$701$			145.736i			0.207897i	−0.994583	+	0.103949i	$0.966852\pi$
$702$		0			0
$703$	−1279.28			−1.81974
$704$		0			0
$705$	256.662	+	333.071i	0.364060	+	0.472440i
$706$		0			0
$707$	−124.877	+	72.0980i	−0.176630	+	0.101977i
$708$		0			0
$709$	394.430	−	683.173i	0.556319	−	0.963572i	−0.441481	−	0.897271i	$-0.645547\pi$
$709$	394.430	−	683.173i	0.556319	−	0.963572i	0.997800	−	0.0663017i	$-0.0211200\pi$
$710$		0			0
$711$	−239.269	−	237.312i	−0.336525	−	0.333772i
$712$		0			0
$713$	−614.153	−	354.581i	−0.861365	−	0.497309i
$714$		0			0
$715$	486.936	+	843.398i	0.681029	+	1.17958i
$716$		0			0
$717$	691.006	+	284.563i	0.963746	+	0.396880i
$718$		0			0
$719$		−	721.671i		−	1.00372i	−0.864950	−	0.501858i	$-0.832650\pi$
$719$		−	721.671i		−	1.00372i	0.864950	−	0.501858i	$-0.167350\pi$
$720$		0			0
$721$	−79.2252			−0.109882
$722$		0			0
$723$	−509.676	+	68.1650i	−0.704946	+	0.0942807i
$724$		0			0
$725$	−188.358	+	108.749i	−0.259805	+	0.149998i
$726$		0			0
$727$	−543.433	+	941.253i	−0.747500	+	1.29471i	0.201518	+	0.979485i	$0.435413\pi$
$727$	−543.433	+	941.253i	−0.747500	+	1.29471i	−0.949018	+	0.315223i	$0.897921\pi$
$728$		0			0
$729$	509.092	−	521.792i	0.698343	−	0.715764i
$730$		0			0
$731$	−896.332	−	517.498i	−1.22617	−	0.707931i
$732$		0			0
$733$	352.753	+	610.985i	0.481245	+	0.833541i	0.999768	−	0.0215227i	$-0.00685140\pi$
$733$	352.753	+	610.985i	0.481245	+	0.833541i	−0.518523	+	0.855063i	$0.673518\pi$
$734$		0			0
$735$	56.8739	+	425.251i	0.0773794	+	0.578573i
$736$		0			0
$737$			42.5181i			0.0576908i
$738$		0			0
$739$	1183.74			1.60182			0.800909	−	0.598786i	$-0.204350\pi$
$739$	1183.74			1.60182			0.800909	+	0.598786i	$0.204350\pi$
$740$		0			0
$741$	479.757	−	1165.00i	0.647446	−	1.57220i
$742$		0			0
$743$	187.727	−	108.384i	0.252661	−	0.145874i	−0.368321	−	0.929699i	$-0.620067\pi$
$743$	187.727	−	108.384i	0.252661	−	0.145874i	0.620982	+	0.783825i	$0.286734\pi$
$744$		0			0
$745$	174.705	−	302.598i	0.234503	−	0.406172i
$746$		0			0
$747$	107.578	−	108.465i	0.144013	−	0.145200i
$748$		0			0
$749$	1.62949	+	0.940784i	0.00217555	+	0.00125605i
$750$		0			0
$751$	76.7045	+	132.856i	0.102137	+	0.176906i	0.912565	−	0.408932i	$-0.134099\pi$
$751$	76.7045	+	132.856i	0.102137	+	0.176906i	−0.810428	+	0.585838i	$0.800765\pi$
$752$		0			0
$753$	−684.329	+	527.340i	−0.908804	+	0.700319i
$754$		0			0
$755$			52.8056i			0.0699412i
$756$		0			0
$757$	585.893			0.773967			0.386983	−	0.922087i	$-0.373517\pi$
$757$	585.893			0.773967			0.386983	+	0.922087i	$0.373517\pi$
$758$		0			0
$759$	377.480	+	489.855i	0.497338	+	0.645396i
$760$		0			0
$761$	−290.563	+	167.757i	−0.381817	+	0.220442i	−0.678609	−	0.734500i	$-0.737417\pi$
$761$	−290.563	+	167.757i	−0.381817	+	0.220442i	0.296791	+	0.954942i	$0.404083\pi$
$762$		0			0
$763$	−358.744	+	621.364i	−0.470176	+	0.814369i
$764$		0			0
$765$	−748.290	+	203.801i	−0.978156	+	0.266406i
$766$		0			0
$767$	1362.86	+	786.848i	1.77687	+	1.02588i
$768$		0			0
$769$	613.797	+	1063.13i	0.798175	+	1.38248i	0.920803	+	0.390028i	$0.127535\pi$
$769$	613.797	+	1063.13i	0.798175	+	1.38248i	−0.122628	+	0.992453i	$0.539132\pi$
$770$		0			0
$771$	192.594	+	79.3121i	0.249798	+	0.102869i
$772$		0			0
$773$			512.944i			0.663576i	0.943354	+	0.331788i	$0.107652\pi$
$773$			512.944i			0.663576i	−0.943354	+	0.331788i	$0.892348\pi$
$774$		0			0
$775$	432.168			0.557636
$776$		0			0
$777$	−586.135	+	78.3907i	−0.754356	+	0.100889i
$778$		0			0
$779$	577.318	−	333.315i	0.741101	−	0.427875i
$780$		0			0
$781$	−338.221	+	585.816i	−0.433062	+	0.750085i
$782$		0			0
$783$	633.733	+	79.4646i	0.809365	+	0.101487i
$784$		0			0
$785$	−646.543	−	373.282i	−0.823622	−	0.475518i
$786$		0			0
$787$	−284.387	−	492.573i	−0.361356	−	0.625886i	0.626828	−	0.779157i	$-0.284353\pi$
$787$	−284.387	−	492.573i	−0.361356	−	0.625886i	−0.988184	+	0.153271i	$0.951019\pi$
$788$		0			0
$789$	−31.5639	−	236.006i	−0.0400049	−	0.299120i
$790$		0			0
$791$			483.337i			0.611046i
$792$		0			0
$793$	231.944			0.292490
$794$		0			0
$795$	295.291	−	717.055i	0.371435	−	0.901956i
$796$		0			0
$797$	−1026.79	+	592.819i	−1.28832	+	0.743813i	−0.978355	−	0.206934i	$-0.933651\pi$
$797$	−1026.79	+	592.819i	−1.28832	+	0.743813i	−0.309967	+	0.950747i	$0.600318\pi$
$798$		0			0
$799$	382.084	−	661.789i	0.478203	−	0.828271i
$800$		0			0
$801$	123.572	+	32.5677i	0.154272	+	0.0406587i
$802$		0			0
$803$	−1208.70	−	697.845i	−1.50523	−	0.869047i
$804$		0			0
$805$	−108.250	−	187.494i	−0.134471	−	0.232911i
$806$		0			0
$807$	98.9060	−	76.2164i	0.122560	−	0.0944441i
$808$		0			0
$809$		−	185.707i		−	0.229552i	−0.993391	−	0.114776i	$-0.963385\pi$
$809$		−	185.707i		−	0.229552i	0.993391	−	0.114776i	$-0.0366150\pi$
$810$		0			0
$811$	−451.817			−0.557111			−0.278555	−	0.960420i	$-0.589856\pi$
$811$	−451.817			−0.557111			−0.278555	+	0.960420i	$0.589856\pi$
$812$		0			0
$813$	−179.466	−	232.893i	−0.220746	−	0.286462i
$814$		0			0
$815$	−451.841	+	260.871i	−0.554406	+	0.320087i
$816$		0			0
$817$	559.267	−	968.679i	0.684537	−	1.18565i
$818$		0			0
$819$	148.426	−	563.173i	0.181228	−	0.687635i
$820$		0			0
$821$	1029.67	+	594.478i	1.25416	+	0.724090i	0.971933	−	0.235257i	$-0.0755932\pi$
$821$	1029.67	+	594.478i	1.25416	+	0.724090i	0.282228	+	0.959347i	$0.408927\pi$
$822$		0			0
$823$	329.832	+	571.286i	0.400768	+	0.694151i	0.993819	−	0.111014i	$-0.0354099\pi$
$823$	329.832	+	571.286i	0.400768	+	0.694151i	−0.593051	+	0.805165i	$0.702077\pi$
$824$		0			0
$825$	−348.479	−	143.507i	−0.422399	−	0.173948i
$826$		0			0
$827$			291.986i			0.353067i	0.984295	+	0.176533i	$0.0564883\pi$
$827$			291.986i			0.353067i	−0.984295	+	0.176533i	$0.943512\pi$
$828$		0			0
$829$	452.809			0.546212			0.273106	−	0.961984i	$-0.411949\pi$
$829$	452.809			0.546212			0.273106	+	0.961984i	$0.411949\pi$
$830$		0			0
$831$	912.276	−	122.009i	1.09781	−	0.146822i
$832$		0			0
$833$	675.242	−	389.851i	0.810615	−	0.468009i
$834$		0			0
$835$	364.122	−	630.678i	0.436075	−	0.755303i
$836$		0			0
$837$	−1011.57	−	766.356i	−1.20857	−	0.915598i
$838$		0			0
$839$	62.7098	+	36.2055i	0.0747435	+	0.0431532i	0.536906	−	0.843642i	$-0.319593\pi$
$839$	62.7098	+	36.2055i	0.0747435	+	0.0431532i	−0.462162	+	0.886795i	$0.652926\pi$
$840$		0			0
$841$	−140.711	−	243.719i	−0.167314	−	0.289796i
$842$		0			0
$843$	25.2047	+	188.458i	0.0298989	+	0.223557i
$844$		0			0
$845$		−	606.037i		−	0.717204i
$846$		0			0
$847$	−237.061			−0.279883
$848$		0			0
$849$	373.091	−	905.978i	0.439448	−	1.06711i
$850$		0			0
$851$	−713.578	+	411.985i	−0.838518	+	0.484118i
$852$		0			0
$853$	165.809	−	287.189i	0.194383	−	0.336681i	−0.752315	−	0.658803i	$-0.771063\pi$
$853$	165.809	−	287.189i	0.194383	−	0.336681i	0.946698	+	0.322122i	$0.104396\pi$
$854$		0			0
$855$	−220.250	−	808.687i	−0.257603	−	0.945833i
$856$		0			0
$857$	−426.279	−	246.112i	−0.497408	−	0.287179i	0.230234	−	0.973135i	$-0.426051\pi$
$857$	−426.279	−	246.112i	−0.497408	−	0.287179i	−0.727643	+	0.685956i	$0.759384\pi$
$858$		0			0
$859$	−379.885	−	657.980i	−0.442241	−	0.765984i	0.555614	−	0.831440i	$-0.312483\pi$
$859$	−379.885	−	657.980i	−0.442241	−	0.765984i	−0.997855	+	0.0654561i	$0.979150\pi$
$860$		0			0
$861$	244.089	−	188.094i	0.283495	−	0.218460i
$862$		0			0
$863$			263.506i			0.305337i	0.988277	+	0.152668i	$0.0487867\pi$
$863$			263.506i			0.305337i	−0.988277	+	0.152668i	$0.951213\pi$
$864$		0			0
$865$	104.084			0.120328
$866$		0			0
$867$	331.089	+	429.654i	0.381879	+	0.495564i
$868$		0			0
$869$	443.059	−	255.800i	0.509849	−	0.294362i
$870$		0			0
$871$	27.8962	−	48.3176i	0.0320278	−	0.0554737i
$872$		0			0
$873$	−308.618	−	306.094i	−0.353514	−	0.350623i
$874$		0			0
$875$	424.936	+	245.337i	0.485642	+	0.280385i
$876$		0			0
$877$	−707.946	−	1226.20i	−0.807236	−	1.39817i	−0.914771	−	0.403973i	$-0.867629\pi$
$877$	−707.946	−	1226.20i	−0.807236	−	1.39817i	0.107534	−	0.994201i	$-0.465704\pi$
$878$		0			0
$879$	−199.593	−	82.1946i	−0.227069	−	0.0935092i
$880$		0			0
$881$			992.699i			1.12679i	0.826189	+	0.563393i	$0.190504\pi$
$881$			992.699i			1.12679i	−0.826189	+	0.563393i	$0.809496\pi$
$882$		0			0
$883$	800.265			0.906303			0.453151	−	0.891434i	$-0.350300\pi$
$883$	800.265			0.906303			0.453151	+	0.891434i	$0.350300\pi$
$884$		0			0
$885$	1037.64	−	138.776i	1.17248	−	0.156810i
$886$		0			0
$887$	−522.975	+	301.940i	−0.589600	+	0.340405i	−0.764939	−	0.644103i	$-0.777231\pi$
$887$	−522.975	+	301.940i	−0.589600	+	0.340405i	0.175340	+	0.984508i	$0.443898\pi$
$888$		0			0
$889$	−82.7936	+	143.403i	−0.0931312	+	0.161308i
$890$		0			0
$891$	561.206	+	953.860i	0.629861	+	1.07055i
$892$		0			0
$893$	715.205	+	412.924i	0.800901	+	0.462400i
$894$		0			0
$895$	−348.049	−	602.839i	−0.388882	−	0.673563i
$896$		0			0
$897$	−107.574	−	804.337i	−0.119926	−	0.896697i
$898$		0			0
$899$		−	1111.88i		−	1.23680i
$900$		0			0
$901$	−1409.30			−1.56415
$902$		0			0
$903$	196.885	−	478.097i	0.218035	−	0.529454i
$904$		0			0
$905$	−594.996	+	343.521i	−0.657454	+	0.379581i
$906$		0			0
$907$	−327.494	+	567.237i	−0.361074	+	0.625399i	−0.988138	−	0.153569i	$-0.950923\pi$
$907$	−327.494	+	567.237i	−0.361074	+	0.625399i	0.627064	+	0.778968i	$0.284257\pi$
$908$		0			0
$909$	−253.196	+	255.284i	−0.278544	+	0.280841i
$910$		0			0
$911$	−1475.55	−	851.907i	−1.61970	−	0.935134i	−0.986997	−	0.160740i	$-0.948612\pi$
$911$	−1475.55	−	851.907i	−1.61970	−	0.935134i	−0.632703	−	0.774394i	$-0.718055\pi$
$912$		0			0
$913$	115.959	+	200.846i	0.127008	+	0.219985i
$914$		0			0
$915$	122.220	−	94.1820i	0.133574	−	0.102931i
$916$		0			0
$917$		−	699.825i		−	0.763168i
$918$		0			0
$919$	−412.015			−0.448330			−0.224165	−	0.974551i	$-0.571965\pi$
$919$	−412.015			−0.448330			−0.224165	+	0.974551i	$0.571965\pi$
$920$		0			0
$921$	−294.859	−	382.639i	−0.320151	−	0.415460i
$922$		0			0
$923$	768.710	−	443.815i	0.832839	−	0.480840i
$924$		0			0
$925$	251.066	−	434.859i	0.271422	−	0.470117i
$926$		0			0
$927$	−190.605	+	51.9123i	−0.205615	+	0.0560004i
$928$		0			0
$929$	645.658	+	372.771i	0.695003	+	0.401260i	0.805484	−	0.592618i	$-0.201906\pi$
$929$	645.658	+	372.771i	0.695003	+	0.401260i	−0.110480	+	0.993878i	$0.535239\pi$
$930$		0			0
$931$	421.318	+	729.744i	0.452543	+	0.783828i
$932$		0			0
$933$	−1129.27	−	465.046i	−1.21037	−	0.498442i
$934$		0			0
$935$		−	1177.37i		−	1.25922i
$936$		0			0
$937$	227.643			0.242948			0.121474	−	0.992595i	$-0.461238\pi$
$937$	227.643			0.242948			0.121474	+	0.992595i	$0.461238\pi$
$938$		0			0
$939$	−474.306	+	63.4345i	−0.505118	+	0.0675554i
$940$		0			0
$941$	108.079	−	62.3995i	0.114856	−	0.0663119i	−0.441472	−	0.897275i	$-0.645543\pi$
$941$	108.079	−	62.3995i	0.114856	−	0.0663119i	0.556327	+	0.830963i	$0.312210\pi$
$942$		0			0
$943$	214.685	−	371.845i	0.227661	−	0.394321i
$944$		0			0
$945$	−150.468	−	357.026i	−0.159225	−	0.377805i
$946$		0			0
$947$	508.817	+	293.766i	0.537294	+	0.310207i	0.743981	−	0.668200i	$-0.232935\pi$
$947$	508.817	+	293.766i	0.537294	+	0.310207i	−0.206688	+	0.978407i	$0.566268\pi$
$948$		0			0
$949$	915.715	+	1586.06i	0.964926	+	1.67130i
$950$		0			0
$951$	−167.554	−	1252.82i	−0.176187	−	1.31737i
$952$		0			0
$953$		−	413.855i		−	0.434266i	−0.976142	−	0.217133i	$-0.930330\pi$
$953$		−	413.855i		−	0.434266i	0.976142	−	0.217133i	$-0.0696705\pi$
$954$		0			0
$955$	−349.394			−0.365857
$956$		0			0
$957$	−369.216	+	896.567i	−0.385805	+	0.936852i
$958$		0			0
$959$	−540.678	+	312.161i	−0.563794	+	0.325507i
$960$		0			0
$961$	−624.153	+	1081.07i	−0.649483	+	1.12494i
$962$		0			0
$963$	4.53677	+	1.19568i	0.00471108	+	0.00124162i
$964$		0			0
$965$	−472.638	−	272.878i	−0.489780	−	0.282775i
$966$		0			0
$967$	512.963	+	888.477i	0.530468	+	0.918798i	0.999368	+	0.0355464i	$0.0113172\pi$
$967$	512.963	+	888.477i	0.530468	+	0.918798i	−0.468900	+	0.883251i	$0.655350\pi$
$968$		0			0
$969$	−1206.52	+	929.734i	−1.24511	+	0.959478i
$970$		0			0
$971$			610.884i			0.629129i	0.949236	+	0.314564i	$0.101858\pi$
$971$			610.884i			0.629129i	−0.949236	+	0.314564i	$0.898142\pi$
$972$		0			0
$973$	5.80122			0.00596220
$974$		0			0
$975$	301.857	+	391.720i	0.309597	+	0.401764i
$976$		0			0
$977$	408.200	−	235.674i	0.417809	−	0.241222i	−0.276330	−	0.961063i	$-0.589118\pi$
$977$	408.200	−	235.674i	0.417809	−	0.241222i	0.694140	+	0.719840i	$0.255785\pi$
$978$		0			0
$979$	−97.0010	+	168.011i	−0.0990817	+	0.171615i
$980$		0			0
$981$	−455.943	+	1729.99i	−0.464773	+	1.76349i
$982$		0			0
$983$	828.578	+	478.380i	0.842908	+	0.486653i	0.858252	−	0.513229i	$-0.171551\pi$
$983$	828.578	+	478.380i	0.842908	+	0.486653i	−0.0153438	+	0.999882i	$0.504884\pi$
$984$		0			0
$985$	475.232	+	823.126i	0.482469	+	0.835661i
$986$		0			0
$987$	352.993	+	145.366i	0.357643	+	0.147281i
$988$		0			0
$989$		−	720.437i		−	0.728450i
$990$		0			0
$991$	1743.95			1.75978			0.879892	−	0.475174i	$-0.157615\pi$
$991$	1743.95			1.75978			0.879892	+	0.475174i	$0.157615\pi$
$992$		0			0
$993$	−386.389	+	51.6763i	−0.389113	+	0.0520406i
$994$		0			0
$995$	862.723	−	498.093i	0.867058	−	0.500596i
$996$		0			0
$997$	−81.8646	+	141.794i	−0.0821109	+	0.142220i	−0.904156	−	0.427201i	$-0.859500\pi$
$997$	−81.8646	+	141.794i	−0.0821109	+	0.142220i	0.822046	+	0.569422i	$0.192833\pi$
$998$		0			0
$999$	−1358.80	+	572.663i	−1.36016	+	0.573236i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	576.3.q.i.65.2		8
3.2	odd	2		1728.3.q.j.1601.4		8
4.3	odd	2		576.3.q.j.65.3		8
8.3	odd	2		144.3.q.e.65.2		8
8.5	even	2		72.3.m.b.65.3	yes	8
9.4	even	3		1728.3.q.j.449.4		8
9.5	odd	6	inner	576.3.q.i.257.2		8
12.11	even	2		1728.3.q.i.1601.4		8
24.5	odd	2		216.3.m.b.89.1		8
24.11	even	2		432.3.q.e.305.1		8
36.23	even	6		576.3.q.j.257.3		8
36.31	odd	6		1728.3.q.i.449.4		8
72.5	odd	6		72.3.m.b.41.3	✓	8
72.11	even	6		1296.3.e.i.161.2		8
72.13	even	6		216.3.m.b.17.1		8
72.29	odd	6		648.3.e.c.161.2		8
72.43	odd	6		1296.3.e.i.161.7		8
72.59	even	6		144.3.q.e.113.2		8
72.61	even	6		648.3.e.c.161.7		8
72.67	odd	6		432.3.q.e.17.1		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
72.3.m.b.41.3	✓	8	72.5	odd	6
72.3.m.b.65.3	yes	8	8.5	even	2
144.3.q.e.65.2		8	8.3	odd	2
144.3.q.e.113.2		8	72.59	even	6
216.3.m.b.17.1		8	72.13	even	6
216.3.m.b.89.1		8	24.5	odd	2
432.3.q.e.17.1		8	72.67	odd	6
432.3.q.e.305.1		8	24.11	even	2
576.3.q.i.65.2		8	1.1	even	1	trivial
576.3.q.i.257.2		8	9.5	odd	6	inner
576.3.q.j.65.3		8	4.3	odd	2
576.3.q.j.257.3		8	36.23	even	6
648.3.e.c.161.2		8	72.29	odd	6
648.3.e.c.161.7		8	72.61	even	6
1296.3.e.i.161.2		8	72.11	even	6
1296.3.e.i.161.7		8	72.43	odd	6
1728.3.q.i.449.4		8	36.31	odd	6
1728.3.q.i.1601.4		8	12.11	even	2
1728.3.q.j.449.4		8	9.4	even	3
1728.3.q.j.1601.4		8	3.2	odd	2

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.q (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(-1.83117 - 2.37631i) q^{3} +(-3.44299 + 1.98781i) q^{5} +(-1.80469 + 3.12582i) q^{7} +(-2.29365 + 8.70282i) q^{9} +O(q^{10})\)	\(q+(-1.83117 - 2.37631i) q^{3} +(-3.44299 + 1.98781i) q^{5} +(-1.80469 + 3.12582i) q^{7} +(-2.29365 + 8.70282i) q^{9} +(-11.8326 - 6.83153i) q^{11} +(8.96435 + 15.5267i) q^{13} +(11.0283 + 4.54158i) q^{15} -21.6750i q^{17} +23.4245 q^{19} +(10.7326 - 1.43540i) q^{21} +(13.0662 - 7.54376i) q^{23} +(-4.59721 + 7.96260i) q^{25} +(24.8806 - 10.4859i) q^{27} +(20.4862 + 11.8277i) q^{29} +(-23.5016 - 40.7060i) q^{31} +(5.43358 + 40.6274i) q^{33} -14.3495i q^{35} -54.6126 q^{37} +(20.4810 - 49.7340i) q^{39} +(24.6459 - 14.2293i) q^{41} +(23.8753 - 41.3532i) q^{43} +(-9.40254 - 34.5231i) q^{45} +(30.5323 + 17.6278i) q^{47} +(17.9862 + 31.1530i) q^{49} +(-51.5065 + 39.6906i) q^{51} -65.0193i q^{53} +54.3192 q^{55} +(-42.8942 - 55.6638i) q^{57} +(76.0156 - 43.8876i) q^{59} +(6.46852 - 11.2038i) q^{61} +(-23.0641 - 22.8755i) q^{63} +(-61.7284 - 35.6389i) q^{65} +(-1.55595 - 2.69499i) q^{67} +(-41.8526 - 17.2353i) q^{69} -49.5089i q^{71} +102.151 q^{73} +(27.3398 - 3.65648i) q^{75} +(42.7082 - 24.6576i) q^{77} +(-18.7220 + 32.4275i) q^{79} +(-70.4783 - 39.9225i) q^{81} +(-14.6999 - 8.48702i) q^{83} +(43.0859 + 74.6270i) q^{85} +(-9.40739 - 70.3399i) q^{87} -14.1990i q^{89} -64.7115 q^{91} +(-53.6945 + 130.387i) q^{93} +(-80.6505 + 46.5636i) q^{95} +(-24.1484 + 41.8262i) q^{97} +(86.5934 - 87.3074i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q - 10 q^{3} + 6 q^{5} + 6 q^{7} - 22 q^{9}+O(q^{10}) \) 8 * q - 10 * q^3 + 6 * q^5 + 6 * q^7 - 22 * q^9	\( 8 q - 10 q^{3} + 6 q^{5} + 6 q^{7} - 22 q^{9} - 36 q^{11} - 14 q^{13} + 10 q^{15} - 4 q^{19} + 54 q^{21} - 102 q^{23} + 10 q^{25} + 20 q^{27} + 114 q^{29} - 50 q^{31} - 104 q^{33} - 120 q^{37} + 82 q^{39} + 264 q^{41} + 28 q^{43} - 206 q^{45} + 150 q^{47} + 94 q^{49} - 170 q^{51} - 244 q^{55} - 178 q^{57} + 108 q^{59} - 14 q^{61} - 210 q^{63} - 198 q^{65} + 20 q^{67} + 14 q^{69} - 76 q^{73} - 326 q^{75} - 66 q^{77} + 26 q^{79} + 194 q^{81} - 246 q^{83} + 224 q^{85} - 18 q^{87} - 108 q^{91} + 130 q^{93} - 456 q^{95} - 236 q^{97} + 634 q^{99}+O(q^{100}) \) 8 * q - 10 * q^3 + 6 * q^5 + 6 * q^7 - 22 * q^9 - 36 * q^11 - 14 * q^13 + 10 * q^15 - 4 * q^19 + 54 * q^21 - 102 * q^23 + 10 * q^25 + 20 * q^27 + 114 * q^29 - 50 * q^31 - 104 * q^33 - 120 * q^37 + 82 * q^39 + 264 * q^41 + 28 * q^43 - 206 * q^45 + 150 * q^47 + 94 * q^49 - 170 * q^51 - 244 * q^55 - 178 * q^57 + 108 * q^59 - 14 * q^61 - 210 * q^63 - 198 * q^65 + 20 * q^67 + 14 * q^69 - 76 * q^73 - 326 * q^75 - 66 * q^77 + 26 * q^79 + 194 * q^81 - 246 * q^83 + 224 * q^85 - 18 * q^87 - 108 * q^91 + 130 * q^93 - 456 * q^95 - 236 * q^97 + 634 * q^99

Introduction

L-functions

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