LMFDB - Embedded newform 576.3.o.g.511.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

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

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

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

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

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

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

chi := DirichletCharacter("576.319");

S:= CuspForms(chi, 3);

N := Newforms(S);

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

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$15.6948632272$
Analytic rank:	$0$
Dimension:	$16$
Relative dimension:	$8$ over $\Q(\zeta_{6})$
Coefficient field:	$\mathbb{Q}[x]/(x^{16} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} - 3 x^{15} + 7 x^{14} - 30 x^{13} + 76 x^{12} - 144 x^{11} + 424 x^{10} - 912 x^{9} + \cdots + 65536 $ x^16 - 3x^15 + 7x^14 - 30x^13 + 76x^12 - 144x^11 + 424x^10 - 912x^9 + 1552x^8 - 3648x^7 + 6784x^6 - 9216x^5 + 19456x^4 - 30720x^3 + 28672x^2 - 49152*x + 65536
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 2^{16}\cdot 3^{3} $
Twist minimal:	no (minimal twist has level 36)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			511.1
Root			$-0.523926 + 1.93016i$ of defining polynomial
Character	$\chi$	$=$	576.511
Dual form			576.3.o.g.319.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-2.76570 - 1.16229i) q^{3} +(4.03104 + 6.98197i) q^{5} +(3.90254 + 2.25313i) q^{7} +(6.29815 + 6.42910i) q^{9} +O(q^{10})$	\(q+(-2.76570 - 1.16229i) q^{3} +(4.03104 + 6.98197i) q^{5} +(3.90254 + 2.25313i) q^{7} +(6.29815 + 6.42910i) q^{9} +(3.25842 + 1.88125i) q^{11} +(3.52605 + 6.10730i) q^{13} +(-3.03354 - 23.9953i) q^{15} +0.517890 q^{17} -16.4164i q^{19} +(-8.17444 - 10.7674i) q^{21} +(-27.7049 + 15.9954i) q^{23} +(-19.9986 + 34.6387i) q^{25} +(-9.94627 - 25.1012i) q^{27} +(-9.48394 + 16.4267i) q^{29} +(13.1355 - 7.58377i) q^{31} +(-6.82524 - 8.99021i) q^{33} +36.3299i q^{35} -0.592061 q^{37} +(-2.65351 - 20.9892i) q^{39} +(12.3766 + 21.4369i) q^{41} +(27.8686 + 16.0900i) q^{43} +(-19.4997 + 69.8895i) q^{45} +(52.4682 + 30.2925i) q^{47} +(-14.3468 - 24.8493i) q^{49} +(-1.43233 - 0.601940i) q^{51} +0.664765 q^{53} +30.3336i q^{55} +(-19.0807 + 45.4029i) q^{57} +(-30.5921 + 17.6623i) q^{59} +(-33.7750 + 58.5000i) q^{61} +(10.0932 + 39.2804i) q^{63} +(-28.4273 + 49.2376i) q^{65} +(-74.4692 + 42.9948i) q^{67} +(95.2148 - 12.0373i) q^{69} +56.4434i q^{71} +131.921 q^{73} +(95.5705 - 72.5557i) q^{75} +(8.47743 + 14.6833i) q^{77} +(-126.869 - 73.2481i) q^{79} +(-1.66664 + 80.9829i) q^{81} +(87.1029 + 50.2889i) q^{83} +(2.08764 + 3.61589i) q^{85} +(45.3223 - 34.4081i) q^{87} -25.8362 q^{89} +31.7786i q^{91} +(-45.1433 + 5.70713i) q^{93} +(114.619 - 66.1754i) q^{95} +(-48.2534 + 83.5773i) q^{97} +(8.42728 + 32.7971i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q - 6 q^{5} + 18 q^{9}+O(q^{10}) $ 16 * q - 6 * q^5 + 18 * q^9	$ 16 q - 6 q^{5} + 18 q^{9} + 46 q^{13} + 12 q^{17} + 66 q^{21} - 30 q^{25} - 42 q^{29} - 168 q^{33} - 56 q^{37} + 84 q^{41} - 174 q^{45} + 58 q^{49} + 72 q^{53} + 366 q^{57} + 34 q^{61} - 30 q^{65} + 54 q^{69} + 116 q^{73} + 330 q^{77} - 102 q^{81} + 140 q^{85} - 384 q^{89} + 486 q^{93} - 148 q^{97}+O(q^{100}) $ 16 * q - 6 * q^5 + 18 * q^9 + 46 * q^13 + 12 * q^17 + 66 * q^21 - 30 * q^25 - 42 * q^29 - 168 * q^33 - 56 * q^37 + 84 * q^41 - 174 * q^45 + 58 * q^49 + 72 * q^53 + 366 * q^57 + 34 * q^61 - 30 * q^65 + 54 * q^69 + 116 * q^73 + 330 * q^77 - 102 * q^81 + 140 * q^85 - 384 * q^89 + 486 * q^93 - 148 * q^97

Display 100 coefficients 10 coefficients

Character values

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

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

Coefficient data

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

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

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

$2$		0			0
$2$		0			0
$3$	−2.76570	−	1.16229i	−0.921899	−	0.387431i
$3$	−2.76570	−	1.16229i	−0.921899	−	0.387431i
$4$		0			0
$5$	4.03104	+	6.98197i	0.806209	+	1.39639i	0.915472	+	0.402382i	$0.131818\pi$
$5$	4.03104	+	6.98197i	0.806209	+	1.39639i	−0.109263	+	0.994013i	$0.534849\pi$
$6$		0			0
$7$	3.90254	+	2.25313i	0.557506	+	0.321876i	0.752144	−	0.658999i	$-0.229020\pi$
$7$	3.90254	+	2.25313i	0.557506	+	0.321876i	−0.194638	+	0.980875i	$0.562353\pi$
$8$		0			0
$9$	6.29815	+	6.42910i	0.699794	+	0.714344i
$10$		0			0
$11$	3.25842	+	1.88125i	0.296220	+	0.171023i	0.640744	−	0.767755i	$-0.278626\pi$
$11$	3.25842	+	1.88125i	0.296220	+	0.171023i	−0.344523	+	0.938778i	$0.611959\pi$
$12$		0			0
$13$	3.52605	+	6.10730i	0.271235	+	0.469792i	0.969178	−	0.246361i	$-0.0792348\pi$
$13$	3.52605	+	6.10730i	0.271235	+	0.469792i	−0.697944	+	0.716153i	$0.745901\pi$
$14$		0			0
$15$	−3.03354	−	23.9953i	−0.202236	−	1.59968i
$16$		0			0
$17$	0.517890			0.0304641			0.0152321	−	0.999884i	$-0.495151\pi$
$17$	0.517890			0.0304641			0.0152321	+	0.999884i	$0.495151\pi$
$18$		0			0
$19$		−	16.4164i		−	0.864023i	−0.901868	−	0.432012i	$-0.857804\pi$
$19$		−	16.4164i		−	0.864023i	0.901868	−	0.432012i	$-0.142196\pi$
$20$		0			0
$21$	−8.17444	−	10.7674i	−0.389259	−	0.512733i
$22$		0			0
$23$	−27.7049	+	15.9954i	−1.20456	+	0.695454i	−0.961566	−	0.274573i	$-0.911463\pi$
$23$	−27.7049	+	15.9954i	−1.20456	+	0.695454i	−0.242996	+	0.970027i	$0.578130\pi$
$24$		0			0
$25$	−19.9986	+	34.6387i	−0.799946	+	1.38555i
$26$		0			0
$27$	−9.94627	−	25.1012i	−0.368380	−	0.929675i
$28$		0			0
$29$	−9.48394	+	16.4267i	−0.327032	+	0.566437i	−0.981922	−	0.189288i	$-0.939382\pi$
$29$	−9.48394	+	16.4267i	−0.327032	+	0.566437i	0.654889	+	0.755725i	$0.272715\pi$
$30$		0			0
$31$	13.1355	−	7.58377i	0.423725	−	0.244638i	−0.272945	−	0.962030i	$-0.587998\pi$
$31$	13.1355	−	7.58377i	0.423725	−	0.244638i	0.696670	+	0.717392i	$0.254664\pi$
$32$		0			0
$33$	−6.82524	−	8.99021i	−0.206826	−	0.272431i
$34$		0			0
$35$			36.3299i			1.03800i
$36$		0			0
$37$	−0.592061			−0.0160017			−0.00800083	−	0.999968i	$-0.502547\pi$
$37$	−0.592061			−0.0160017			−0.00800083	+	0.999968i	$0.502547\pi$
$38$		0			0
$39$	−2.65351	−	20.9892i	−0.0680387	−	0.538185i
$40$		0			0
$41$	12.3766	+	21.4369i	0.301868	+	0.522850i	0.976559	−	0.215250i	$-0.0690565\pi$
$41$	12.3766	+	21.4369i	0.301868	+	0.522850i	−0.674691	+	0.738100i	$0.735723\pi$
$42$		0			0
$43$	27.8686	+	16.0900i	0.648107	+	0.374185i	0.787731	−	0.616020i	$-0.211256\pi$
$43$	27.8686	+	16.0900i	0.648107	+	0.374185i	−0.139623	+	0.990205i	$0.544589\pi$
$44$		0			0
$45$	−19.4997	+	69.8895i	−0.433326	+	1.55310i
$46$		0			0
$47$	52.4682	+	30.2925i	1.11634	+	0.644521i	0.940465	−	0.339890i	$-0.110390\pi$
$47$	52.4682	+	30.2925i	1.11634	+	0.644521i	0.175879	+	0.984412i	$0.443723\pi$
$48$		0			0
$49$	−14.3468	−	24.8493i	−0.292791	−	0.507129i
$50$		0			0
$51$	−1.43233	−	0.601940i	−0.0280848	−	0.0118027i
$52$		0			0
$53$	0.664765			0.0125427			0.00627137	−	0.999980i	$-0.498004\pi$
$53$	0.664765			0.0125427			0.00627137	+	0.999980i	$0.498004\pi$
$54$		0			0
$55$			30.3336i			0.551521i
$56$		0			0
$57$	−19.0807	+	45.4029i	−0.334749	+	0.796542i
$58$		0			0
$59$	−30.5921	+	17.6623i	−0.518510	+	0.299362i	−0.736325	−	0.676628i	$-0.763440\pi$
$59$	−30.5921	+	17.6623i	−0.518510	+	0.299362i	0.217815	+	0.975990i	$0.430107\pi$
$60$		0			0
$61$	−33.7750	+	58.5000i	−0.553688	+	0.959016i	0.444316	+	0.895870i	$0.353447\pi$
$61$	−33.7750	+	58.5000i	−0.553688	+	0.959016i	−0.998004	+	0.0631460i	$0.979887\pi$
$62$		0			0
$63$	10.0932	+	39.2804i	0.160209	+	0.623499i
$64$		0			0
$65$	−28.4273	+	49.2376i	−0.437343	+	0.757501i
$66$		0			0
$67$	−74.4692	+	42.9948i	−1.11148	+	0.641714i	−0.939213	−	0.343336i	$-0.888443\pi$
$67$	−74.4692	+	42.9948i	−1.11148	+	0.641714i	−0.172269	+	0.985050i	$0.555110\pi$
$68$		0			0
$69$	95.2148	−	12.0373i	1.37992	−	0.174454i
$70$		0			0
$71$			56.4434i			0.794977i	0.917607	+	0.397489i	$0.130118\pi$
$71$			56.4434i			0.794977i	−0.917607	+	0.397489i	$0.869882\pi$
$72$		0			0
$73$	131.921			1.80713			0.903567	−	0.428447i	$-0.140939\pi$
$73$	131.921			1.80713			0.903567	+	0.428447i	$0.140939\pi$
$74$		0			0
$75$	95.5705	−	72.5557i	1.27427	−	0.967410i
$76$		0			0
$77$	8.47743	+	14.6833i	0.110096	+	0.190693i
$78$		0			0
$79$	−126.869	−	73.2481i	−1.60594	−	0.927191i	−0.990265	−	0.139192i	$-0.955549\pi$
$79$	−126.869	−	73.2481i	−1.60594	−	0.927191i	−0.615677	−	0.787999i	$-0.711117\pi$
$80$		0			0
$81$	−1.66664	+	80.9829i	−0.0205758	+	0.999788i
$82$		0			0
$83$	87.1029	+	50.2889i	1.04943	+	0.605890i	0.922491	−	0.386020i	$-0.126150\pi$
$83$	87.1029	+	50.2889i	1.04943	+	0.605890i	0.126942	+	0.991910i	$0.459484\pi$
$84$		0			0
$85$	2.08764	+	3.61589i	0.0245604	+	0.0425399i
$86$		0			0
$87$	45.3223	−	34.4081i	0.520946	−	0.395495i
$88$		0			0
$89$	−25.8362			−0.290295			−0.145147	−	0.989410i	$-0.546366\pi$
$89$	−25.8362			−0.290295			−0.145147	+	0.989410i	$0.546366\pi$
$90$		0			0
$91$			31.7786i			0.349216i
$92$		0			0
$93$	−45.1433	+	5.70713i	−0.485412	+	0.0613670i
$94$		0			0
$95$	114.619	−	66.1754i	1.20652	−	0.696583i
$96$		0			0
$97$	−48.2534	+	83.5773i	−0.497457	+	0.861621i	−0.999996	−	0.00293363i	$-0.999066\pi$
$97$	−48.2534	+	83.5773i	−0.497457	+	0.861621i	0.502538	+	0.864555i	$0.332400\pi$
$98$		0			0
$99$	8.42728	+	32.7971i	0.0851241	+	0.331284i
$100$		0			0
$101$	21.6600	−	37.5163i	0.214456	−	0.371448i	−0.738648	−	0.674091i	$-0.764536\pi$
$101$	21.6600	−	37.5163i	0.214456	−	0.371448i	0.953104	+	0.302643i	$0.0978689\pi$
$102$		0			0
$103$	−125.439	+	72.4223i	−1.21786	+	0.703129i	−0.964459	−	0.264233i	$-0.914881\pi$
$103$	−125.439	+	72.4223i	−1.21786	+	0.703129i	−0.253397	+	0.967362i	$0.581548\pi$
$104$		0			0
$105$	42.2260	−	100.478i	0.402153	−	0.956929i
$106$		0			0
$107$		−	54.9861i		−	0.513889i	−0.966426	−	0.256944i	$-0.917284\pi$
$107$		−	54.9861i		−	0.513889i	0.966426	−	0.256944i	$-0.0827158\pi$
$108$		0			0
$109$	63.9235			0.586454			0.293227	−	0.956043i	$-0.405271\pi$
$109$	63.9235			0.586454			0.293227	+	0.956043i	$0.405271\pi$
$110$		0			0
$111$	1.63746	+	0.688149i	0.0147519	+	0.00619954i
$112$		0			0
$113$	17.8239	+	30.8720i	0.157734	+	0.273203i	0.934051	−	0.357139i	$-0.116248\pi$
$113$	17.8239	+	30.8720i	0.157734	+	0.273203i	−0.776317	+	0.630342i	$0.782914\pi$
$114$		0			0
$115$	−223.360	−	128.957i	−1.94226	−	1.12136i
$116$		0			0
$117$	−17.0568	+	61.1340i	−0.145785	+	0.522513i
$118$		0			0
$119$	2.02109	+	1.16688i	0.0169839	+	0.00980568i
$120$		0			0
$121$	−53.4218	−	92.5292i	−0.441502	−	0.764704i
$122$		0			0
$123$	−9.31394	−	73.6731i	−0.0757231	−	0.598968i
$124$		0			0
$125$	−120.909			−0.967276
$126$		0			0
$127$		−	9.81219i		−	0.0772613i	−0.999254	−	0.0386307i	$-0.987700\pi$
$127$		−	9.81219i		−	0.0772613i	0.999254	−	0.0386307i	$-0.0122996\pi$
$128$		0			0
$129$	−58.3749	−	76.8914i	−0.452518	−	0.596057i
$130$		0			0
$131$	101.561	−	58.6365i	0.775278	−	0.447607i	−0.0594761	−	0.998230i	$-0.518943\pi$
$131$	101.561	−	58.6365i	0.775278	−	0.447607i	0.834754	+	0.550623i	$0.185610\pi$
$132$		0			0
$133$	36.9884	−	64.0659i	0.278109	−	0.481698i
$134$		0			0
$135$	135.162	−	170.629i	1.00120	−	1.26392i
$136$		0			0
$137$	125.606	−	217.556i	0.916831	−	1.58800i	0.112634	−	0.993637i	$-0.464071\pi$
$137$	125.606	−	217.556i	0.916831	−	1.58800i	0.804198	−	0.594362i	$-0.202595\pi$
$138$		0			0
$139$	−133.073	+	76.8298i	−0.957361	+	0.552732i	−0.895360	−	0.445344i	$-0.853081\pi$
$139$	−133.073	+	76.8298i	−0.957361	+	0.552732i	−0.0620009	+	0.998076i	$0.519748\pi$
$140$		0			0
$141$	−109.902	−	144.763i	−0.779448	−	1.02669i
$142$		0			0
$143$			26.5335i			0.185549i
$144$		0			0
$145$	−152.921			−1.05463
$146$		0			0
$147$	10.7966	+	85.4009i	0.0734462	+	0.580958i
$148$		0			0
$149$	45.8643	+	79.4393i	0.307814	+	0.533150i	0.977884	−	0.209148i	$-0.0670691\pi$
$149$	45.8643	+	79.4393i	0.307814	+	0.533150i	−0.670070	+	0.742298i	$0.733736\pi$
$150$		0			0
$151$	−36.0215	−	20.7970i	−0.238553	−	0.137729i	0.375958	−	0.926637i	$-0.377314\pi$
$151$	−36.0215	−	20.7970i	−0.238553	−	0.137729i	−0.614512	+	0.788908i	$0.710647\pi$
$152$		0			0
$153$	3.26175	+	3.32957i	0.0213186	+	0.0217619i
$154$		0			0
$155$	105.899	+	61.1410i	0.683222	+	0.394458i
$156$		0			0
$157$	−112.909	−	195.565i	−0.719167	−	1.24563i	−0.961330	−	0.275399i	$-0.911190\pi$
$157$	−112.909	−	195.565i	−0.719167	−	1.24563i	0.242163	−	0.970236i	$-0.422143\pi$
$158$		0			0
$159$	−1.83854	−	0.772652i	−0.0115631	−	0.00485945i
$160$		0			0
$161$	−144.160			−0.895401
$162$		0			0
$163$		−	125.175i		−	0.767945i	−0.923344	−	0.383973i	$-0.874556\pi$
$163$		−	125.175i		−	0.767945i	0.923344	−	0.383973i	$-0.125444\pi$
$164$		0			0
$165$	35.2566	−	83.8936i	0.213676	−	0.508446i
$166$		0			0
$167$	−154.373	+	89.1274i	−0.924390	+	0.533697i	−0.885033	−	0.465528i	$-0.845864\pi$
$167$	−154.373	+	89.1274i	−0.924390	+	0.533697i	−0.0393573	+	0.999225i	$0.512531\pi$
$168$		0			0
$169$	59.6340	−	103.289i	0.352864	−	0.611178i
$170$		0			0
$171$	105.543	−	103.393i	0.617210	−	0.604638i
$172$		0			0
$173$	75.5904	−	130.926i	0.436939	−	0.756800i	−0.560513	−	0.828146i	$-0.689396\pi$
$173$	75.5904	−	130.926i	0.436939	−	0.756800i	0.997452	+	0.0713455i	$0.0227293\pi$
$174$		0			0
$175$	−156.091	+	90.1193i	−0.891949	+	0.514967i
$176$		0			0
$177$	105.137	−	13.2917i	0.593995	−	0.0750944i
$178$		0			0
$179$			276.827i			1.54652i	0.634088	+	0.773261i	$0.281376\pi$
$179$			276.827i			1.54652i	−0.634088	+	0.773261i	$0.718624\pi$
$180$		0			0
$181$	104.729			0.578612			0.289306	−	0.957237i	$-0.406575\pi$
$181$	104.729			0.578612			0.289306	+	0.957237i	$0.406575\pi$
$182$		0			0
$183$	161.405	−	122.537i	0.881997	−	0.669600i
$184$		0			0
$185$	−2.38663	−	4.13376i	−0.0129007	−	0.0223446i
$186$		0			0
$187$	1.68751	+	0.974282i	0.00902409	+	0.00521006i
$188$		0			0
$189$	17.7407	−	120.369i	0.0938662	−	0.636873i
$190$		0			0
$191$	192.972	+	111.413i	1.01033	+	0.583312i	0.911287	−	0.411772i	$-0.135090\pi$
$191$	192.972	+	111.413i	1.01033	+	0.583312i	0.0990389	+	0.995084i	$0.468423\pi$
$192$		0			0
$193$	56.6790	+	98.1709i	0.293674	+	0.508657i	0.974675	−	0.223624i	$-0.0717888\pi$
$193$	56.6790	+	98.1709i	0.293674	+	0.508657i	−0.681002	+	0.732282i	$0.738455\pi$
$194$		0			0
$195$	135.850	−	103.135i	0.696666	−	0.528899i
$196$		0			0
$197$	120.998			0.614201			0.307100	−	0.951677i	$-0.400641\pi$
$197$	120.998			0.614201			0.307100	+	0.951677i	$0.400641\pi$
$198$		0			0
$199$		−	82.2364i		−	0.413248i	−0.978420	−	0.206624i	$-0.933752\pi$
$199$		−	82.2364i		−	0.413248i	0.978420	−	0.206624i	$-0.0662477\pi$
$200$		0			0
$201$	255.932	−	32.3556i	1.27329	−	0.160973i
$202$		0			0
$203$	−74.0230	+	42.7372i	−0.364645	+	0.210528i
$204$		0			0
$205$	−99.7811	+	172.826i	−0.486737	+	0.843053i
$206$		0			0
$207$	−277.326	−	77.3760i	−1.33974	−	0.373797i
$208$		0			0
$209$	30.8835	−	53.4917i	0.147768	−	0.255941i
$210$		0			0
$211$	93.5819	−	54.0295i	0.443516	−	0.256064i	−0.261572	−	0.965184i	$-0.584241\pi$
$211$	93.5819	−	54.0295i	0.443516	−	0.256064i	0.705088	+	0.709120i	$0.250907\pi$
$212$		0			0
$213$	65.6038	−	156.105i	0.307999	−	0.732889i
$214$		0			0
$215$			259.437i			1.20668i
$216$		0			0
$217$	68.3490			0.314972
$218$		0			0
$219$	−364.853	−	153.331i	−1.66599	−	0.700140i
$220$		0			0
$221$	1.82611	+	3.16291i	0.00826292	+	0.0143118i
$222$		0			0
$223$	141.400	+	81.6371i	0.634079	+	0.366086i	0.782330	−	0.622864i	$-0.214031\pi$
$223$	141.400	+	81.6371i	0.634079	+	0.366086i	−0.148251	+	0.988950i	$0.547364\pi$
$224$		0			0
$225$	−348.650	+	89.5862i	−1.54955	+	0.398161i
$226$		0			0
$227$	9.56722	+	5.52364i	0.0421463	+	0.0243332i	0.520925	−	0.853602i	$-0.325587\pi$
$227$	9.56722	+	5.52364i	0.0421463	+	0.0243332i	−0.478779	+	0.877936i	$0.658920\pi$
$228$		0			0
$229$	16.1725	+	28.0116i	0.0706222	+	0.122321i	0.899174	−	0.437591i	$-0.144168\pi$
$229$	16.1725	+	28.0116i	0.0706222	+	0.122321i	−0.828552	+	0.559912i	$0.810835\pi$
$230$		0			0
$231$	−6.37965	−	50.4629i	−0.0276175	−	0.218454i
$232$		0			0
$233$	181.049			0.777036			0.388518	−	0.921441i	$-0.372987\pi$
$233$	181.049			0.777036			0.388518	+	0.921441i	$0.372987\pi$
$234$		0			0
$235$			488.442i			2.07848i
$236$		0			0
$237$	265.746	+	350.041i	1.12129	+	1.47697i
$238$		0			0
$239$	39.6432	−	22.8880i	0.165871	−	0.0957658i	−0.414766	−	0.909928i	$-0.636137\pi$
$239$	39.6432	−	22.8880i	0.165871	−	0.0957658i	0.580638	+	0.814162i	$0.302803\pi$
$240$		0			0
$241$	169.216	−	293.090i	0.702140	−	1.21614i	−0.265573	−	0.964091i	$-0.585561\pi$
$241$	169.216	−	293.090i	0.702140	−	1.21614i	0.967714	−	0.252052i	$-0.0811054\pi$
$242$		0			0
$243$	98.7353	−	222.037i	0.406318	−	0.913732i
$244$		0			0
$245$	115.665	−	200.338i	0.472102	−	0.817704i
$246$		0			0
$247$	100.260	−	57.8852i	0.405911	−	0.234353i
$248$		0			0
$249$	−182.450	−	240.323i	−0.732730	−	0.965152i
$250$		0			0
$251$			282.587i			1.12585i	0.826510	+	0.562923i	$0.190323\pi$
$251$			282.587i			1.12585i	−0.826510	+	0.562923i	$0.809677\pi$
$252$		0			0
$253$	−120.366			−0.475754
$254$		0			0
$255$	−1.57104	−	12.4269i	−0.00616095	−	0.0487330i
$256$		0			0
$257$	38.8897	+	67.3589i	0.151322	+	0.262097i	0.931714	−	0.363194i	$-0.118314\pi$
$257$	38.8897	+	67.3589i	0.151322	+	0.262097i	−0.780392	+	0.625291i	$0.784980\pi$
$258$		0			0
$259$	−2.31055	−	1.33399i	−0.00892102	−	0.00515056i
$260$		0			0
$261$	−165.340	+	42.4844i	−0.633486	+	0.162775i
$262$		0			0
$263$	195.201	+	112.700i	0.742211	+	0.428516i	0.822873	−	0.568226i	$-0.192370\pi$
$263$	195.201	+	112.700i	0.742211	+	0.428516i	−0.0806619	+	0.996742i	$0.525703\pi$
$264$		0			0
$265$	2.67970	+	4.64138i	0.0101121	+	0.0175146i
$266$		0			0
$267$	71.4552	+	30.0293i	0.267622	+	0.112469i
$268$		0			0
$269$	−425.808			−1.58293			−0.791465	−	0.611214i	$-0.790681\pi$
$269$	−425.808			−1.58293			−0.791465	+	0.611214i	$0.790681\pi$
$270$		0			0
$271$			56.3665i			0.207995i	0.994578	+	0.103997i	$0.0331633\pi$
$271$			56.3665i			0.207995i	−0.994578	+	0.103997i	$0.966837\pi$
$272$		0			0
$273$	36.9361	−	87.8901i	0.135297	−	0.321942i
$274$		0			0
$275$	−130.328	+	75.2450i	−0.473920	+	0.273618i
$276$		0			0
$277$	209.641	−	363.109i	0.756828	−	1.31086i	−0.187633	−	0.982239i	$-0.560082\pi$
$277$	209.641	−	363.109i	0.756828	−	1.31086i	0.944461	−	0.328625i	$-0.106585\pi$
$278$		0			0
$279$	131.486	+	36.6856i	0.471276	+	0.131489i
$280$		0			0
$281$	−73.9638	+	128.109i	−0.263216	+	0.455904i	−0.967095	−	0.254416i	$-0.918117\pi$
$281$	−73.9638	+	128.109i	−0.263216	+	0.455904i	0.703878	+	0.710320i	$0.251450\pi$
$282$		0			0
$283$	229.852	−	132.705i	0.812198	−	0.468923i	−0.0355207	−	0.999369i	$-0.511309\pi$
$283$	229.852	−	132.705i	0.812198	−	0.468923i	0.847719	+	0.530446i	$0.177976\pi$
$284$		0			0
$285$	−393.917	+	49.8000i	−1.38216	+	0.174737i
$286$		0			0
$287$			111.544i			0.388656i
$288$		0			0
$289$	−288.732			−0.999072
$290$		0			0
$291$	230.595	−	175.065i	0.792424	−	0.601597i
$292$		0			0
$293$	−124.844	−	216.236i	−0.426088	−	0.738006i	0.570433	−	0.821344i	$-0.306775\pi$
$293$	−124.844	−	216.236i	−0.426088	−	0.738006i	−0.996521	+	0.0833379i	$0.973442\pi$
$294$		0			0
$295$	−246.636	−	142.395i	−0.836054	−	0.482696i
$296$		0			0
$297$	14.8126	−	100.502i	0.0498740	−	0.338390i
$298$		0			0
$299$	−195.378	−	112.801i	−0.653438	−	0.377262i
$300$		0			0
$301$	72.5056	+	125.583i	0.240883	+	0.417221i
$302$		0			0
$303$	−103.510	+	78.5833i	−0.341617	+	0.259351i
$304$		0			0
$305$	−544.594			−1.78555
$306$		0			0
$307$		−	259.968i		−	0.846801i	−0.905943	−	0.423401i	$-0.860836\pi$
$307$		−	259.968i		−	0.846801i	0.905943	−	0.423401i	$-0.139164\pi$
$308$		0			0
$309$	431.102	−	54.5010i	1.39515	−	0.176379i
$310$		0			0
$311$	16.5959	−	9.58164i	0.0533630	−	0.0308091i	−0.473081	−	0.881019i	$-0.656858\pi$
$311$	16.5959	−	9.58164i	0.0533630	−	0.0308091i	0.526444	+	0.850210i	$0.323525\pi$
$312$		0			0
$313$	−21.9358	+	37.9939i	−0.0700823	+	0.121386i	−0.898937	−	0.438078i	$-0.855660\pi$
$313$	−21.9358	+	37.9939i	−0.0700823	+	0.121386i	0.828855	+	0.559464i	$0.188993\pi$
$314$		0			0
$315$	−233.569	+	228.811i	−0.741488	+	0.726385i
$316$		0			0
$317$	−68.9690	+	119.458i	−0.217568	+	0.376838i	−0.954064	−	0.299603i	$-0.903146\pi$
$317$	−68.9690	+	119.458i	−0.217568	+	0.376838i	0.736496	+	0.676442i	$0.236479\pi$
$318$		0			0
$319$	−61.8054	+	35.6834i	−0.193747	+	0.111860i
$320$		0			0
$321$	−63.9100	+	152.075i	−0.199097	+	0.473754i
$322$		0			0
$323$		−	8.50191i		−	0.0263217i
$324$		0			0
$325$	−282.065			−0.867892
$326$		0			0
$327$	−176.793	−	74.2978i	−0.540651	−	0.227211i
$328$		0			0
$329$	136.506	+	236.436i	0.414912	+	0.718649i
$330$		0			0
$331$	−51.7490	−	29.8773i	−0.156341	−	0.0902638i	0.419788	−	0.907622i	$-0.362104\pi$
$331$	−51.7490	−	29.8773i	−0.156341	−	0.0902638i	−0.576130	+	0.817358i	$0.695438\pi$
$332$		0			0
$333$	−3.72889	−	3.80642i	−0.0111979	−	0.0114307i
$334$		0			0
$335$	−600.378	−	346.628i	−1.79217	−	1.03471i
$336$		0			0
$337$	224.356	+	388.595i	0.665743	+	1.15310i	0.979083	+	0.203460i	$0.0652188\pi$
$337$	224.356	+	388.595i	0.665743	+	1.15310i	−0.313340	+	0.949641i	$0.601448\pi$
$338$		0			0
$339$	−13.4133	−	106.099i	−0.0395673	−	0.312977i
$340$		0			0
$341$	57.0679			0.167355
$342$		0			0
$343$		−	350.108i		−	1.02072i
$344$		0			0
$345$	467.859	+	616.264i	1.35611	+	1.78627i
$346$		0			0
$347$	500.441	−	288.930i	1.44219	−	0.832651i	0.444198	−	0.895929i	$-0.353489\pi$
$347$	500.441	−	288.930i	1.44219	−	0.832651i	0.997996	+	0.0632779i	$0.0201555\pi$
$348$		0			0
$349$	−66.1311	+	114.542i	−0.189487	+	0.328202i	−0.945079	−	0.326841i	$-0.894016\pi$
$349$	−66.1311	+	114.542i	−0.189487	+	0.328202i	0.755592	+	0.655042i	$0.227349\pi$
$350$		0			0
$351$	118.230	−	149.253i	0.336837	−	0.425222i
$352$		0			0
$353$	270.562	−	468.628i	0.766465	−	1.32756i	−0.173003	−	0.984921i	$-0.555347\pi$
$353$	270.562	−	468.628i	0.766465	−	1.32756i	0.939468	−	0.342636i	$-0.111320\pi$
$354$		0			0
$355$	−394.086	+	227.526i	−1.11010	+	0.640918i
$356$		0			0
$357$	−4.23346	−	5.57632i	−0.0118584	−	0.0156199i
$358$		0			0
$359$		−	292.754i		−	0.815470i	−0.913100	−	0.407735i	$-0.866319\pi$
$359$		−	292.754i		−	0.815470i	0.913100	−	0.407735i	$-0.133681\pi$
$360$		0			0
$361$	91.5006			0.253464
$362$		0			0
$363$	40.2023	+	318.000i	0.110750	+	0.876032i
$364$		0			0
$365$	531.779	+	921.067i	1.45693	+	2.52347i
$366$		0			0
$367$	378.870	+	218.741i	1.03234	+	0.596024i	0.917655	−	0.397377i	$-0.130080\pi$
$367$	378.870	+	218.741i	1.03234	+	0.596024i	0.114689	+	0.993401i	$0.463413\pi$
$368$		0			0
$369$	−59.8702	+	214.583i	−0.162250	+	0.581525i
$370$		0			0
$371$	2.59428	+	1.49781i	0.00699266	+	0.00403721i
$372$		0			0
$373$	352.979	+	611.377i	0.946323	+	1.63908i	0.753080	+	0.657929i	$0.228567\pi$
$373$	352.979	+	611.377i	0.946323	+	1.63908i	0.193243	+	0.981151i	$0.438099\pi$
$374$		0			0
$375$	334.399	+	140.532i	0.891730	+	0.374753i
$376$		0			0
$377$	−133.763			−0.354810
$378$		0			0
$379$		−	541.432i		−	1.42858i	−0.699850	−	0.714290i	$-0.746750\pi$
$379$		−	541.432i		−	1.42858i	0.699850	−	0.714290i	$-0.253250\pi$
$380$		0			0
$381$	−11.4046	+	27.1375i	−0.0299334	+	0.0712271i
$382$		0			0
$383$	311.941	−	180.099i	0.814467	−	0.470233i	−0.0340377	−	0.999421i	$-0.510837\pi$
$383$	311.941	−	180.099i	0.814467	−	0.470233i	0.848505	+	0.529188i	$0.177503\pi$
$384$		0			0
$385$	−68.3458	+	118.378i	−0.177521	+	0.307476i
$386$		0			0
$387$	72.0768	+	280.507i	0.186245	+	0.724824i
$388$		0			0
$389$	43.9057	−	76.0468i	0.112868	−	0.195493i	−0.804057	−	0.594552i	$-0.797330\pi$
$389$	43.9057	−	76.0468i	0.112868	−	0.195493i	0.916926	+	0.399058i	$0.130663\pi$
$390$		0			0
$391$	−14.3481	+	8.28388i	−0.0366959	+	0.0211864i
$392$		0			0
$393$	−349.041	+	44.1266i	−0.888145	+	0.112281i
$394$		0			0
$395$		−	1181.07i		−	2.99004i
$396$		0			0
$397$	48.4128			0.121947			0.0609733	−	0.998139i	$-0.480580\pi$
$397$	48.4128			0.121947			0.0609733	+	0.998139i	$0.480580\pi$
$398$		0			0
$399$	−176.762	+	134.195i	−0.443013	+	0.336329i
$400$		0			0
$401$	217.859	+	377.343i	0.543290	+	0.941005i	0.998712	+	0.0507299i	$0.0161548\pi$
$401$	217.859	+	377.343i	0.543290	+	0.941005i	−0.455423	+	0.890275i	$0.650512\pi$
$402$		0			0
$403$	92.6326	+	53.4815i	0.229858	+	0.132708i
$404$		0			0
$405$	−572.138	+	314.809i	−1.41269	+	0.777306i
$406$		0			0
$407$	−1.92919	−	1.11382i	−0.00474002	−	0.00273665i
$408$		0			0
$409$	−27.1145	−	46.9636i	−0.0662945	−	0.114825i	0.830973	−	0.556313i	$-0.187784\pi$
$409$	−27.1145	−	46.9636i	−0.0662945	−	0.114825i	−0.897267	+	0.441487i	$0.854451\pi$
$410$		0			0
$411$	−600.251	+	455.702i	−1.46047	+	1.10876i
$412$		0			0
$413$	−159.182			−0.385430
$414$		0			0
$415$			810.867i			1.95390i
$416$		0			0
$417$	457.339	−	57.8179i	1.09674	−	0.138652i
$418$		0			0
$419$	−552.029	+	318.714i	−1.31749	+	0.760655i	−0.983325	−	0.181859i	$-0.941789\pi$
$419$	−552.029	+	318.714i	−1.31749	+	0.760655i	−0.334168	+	0.942514i	$0.608455\pi$
$420$		0			0
$421$	95.7757	−	165.888i	0.227496	−	0.394034i	−0.729570	−	0.683907i	$-0.760280\pi$
$421$	95.7757	−	165.888i	0.227496	−	0.394034i	0.957065	+	0.289873i	$0.0936129\pi$
$422$		0			0
$423$	135.699	+	528.110i	0.320801	+	1.24849i
$424$		0			0
$425$	−10.3571	+	17.9390i	−0.0243696	+	0.0422095i
$426$		0			0
$427$	−263.617	+	152.199i	−0.617369	+	0.356438i
$428$		0			0
$429$	30.8398	−	73.3837i	0.0718876	−	0.171058i
$430$		0			0
$431$		−	481.190i		−	1.11645i	−0.829689	−	0.558225i	$-0.811482\pi$
$431$		−	481.190i		−	1.11645i	0.829689	−	0.558225i	$-0.188518\pi$
$432$		0			0
$433$	−360.347			−0.832209			−0.416105	−	0.909317i	$-0.636605\pi$
$433$	−360.347			−0.832209			−0.416105	+	0.909317i	$0.636605\pi$
$434$		0			0
$435$	422.932	+	177.739i	0.972258	+	0.408595i
$436$		0			0
$437$	262.588	+	454.816i	0.600888	+	1.04077i
$438$		0			0
$439$	−488.267	−	281.901i	−1.11223	−	0.642144i	−0.172821	−	0.984953i	$-0.555288\pi$
$439$	−488.267	−	281.901i	−1.11223	−	0.642144i	−0.939405	+	0.342809i	$0.888622\pi$
$440$		0			0
$441$	69.4008	−	248.742i	0.157371	−	0.564040i
$442$		0			0
$443$	569.917	+	329.042i	1.28649	+	0.742757i	0.978027	−	0.208478i	$-0.0668509\pi$
$443$	569.917	+	329.042i	1.28649	+	0.742757i	0.308467	+	0.951235i	$0.400184\pi$
$444$		0			0
$445$	−104.147	−	180.388i	−0.234038	−	0.405366i
$446$		0			0
$447$	−34.5150	−	273.013i	−0.0772147	−	0.610767i
$448$		0			0
$449$	227.569			0.506836			0.253418	−	0.967357i	$-0.418445\pi$
$449$	227.569			0.506836			0.253418	+	0.967357i	$0.418445\pi$
$450$		0			0
$451$			93.1339i			0.206505i
$452$		0			0
$453$	75.4523	+	99.3858i	0.166561	+	0.219395i
$454$		0			0
$455$	−221.878	+	128.101i	−0.487643	+	0.281541i
$456$		0			0
$457$	−358.879	+	621.596i	−0.785292	+	1.36017i	0.143532	+	0.989646i	$0.454154\pi$
$457$	−358.879	+	621.596i	−0.785292	+	1.36017i	−0.928824	+	0.370520i	$0.879179\pi$
$458$		0			0
$459$	−5.15107	−	12.9997i	−0.0112224	−	0.0283217i
$460$		0			0
$461$	200.873	−	347.922i	0.435733	−	0.754712i	−0.561622	−	0.827394i	$-0.689822\pi$
$461$	200.873	−	347.922i	0.435733	−	0.754712i	0.997355	+	0.0726819i	$0.0231558\pi$
$462$		0			0
$463$	396.754	−	229.066i	0.856920	−	0.494743i	−0.00605956	−	0.999982i	$-0.501929\pi$
$463$	396.754	−	229.066i	0.856920	−	0.494743i	0.862980	+	0.505239i	$0.168595\pi$
$464$		0			0
$465$	−221.822	−	292.184i	−0.477036	−	0.628352i
$466$		0			0
$467$			204.395i			0.437677i	0.975761	+	0.218838i	$0.0702267\pi$
$467$			204.395i			0.437677i	−0.975761	+	0.218838i	$0.929773\pi$
$468$		0			0
$469$	−387.493			−0.826210
$470$		0			0
$471$	84.9693	+	672.106i	0.180402	+	1.42698i
$472$		0			0
$473$	60.5385	+	104.856i	0.127988	+	0.221682i
$474$		0			0
$475$	568.643	+	328.306i	1.19714	+	0.691172i
$476$		0			0
$477$	4.18679	+	4.27384i	0.00877734	+	0.00895984i
$478$		0			0
$479$	−78.4548	−	45.2959i	−0.163789	−	0.0945634i	0.415865	−	0.909426i	$-0.363479\pi$
$479$	−78.4548	−	45.2959i	−0.163789	−	0.0945634i	−0.579654	+	0.814863i	$0.696812\pi$
$480$		0			0
$481$	−2.08764	−	3.61589i	−0.00434020	−	0.00751745i
$482$		0			0
$483$	398.701	+	167.556i	0.825469	+	0.346906i
$484$		0			0
$485$	−778.046			−1.60422
$486$		0			0
$487$		−	301.289i		−	0.618663i	−0.950954	−	0.309332i	$-0.899895\pi$
$487$		−	301.289i		−	0.618663i	0.950954	−	0.309332i	$-0.100105\pi$
$488$		0			0
$489$	−145.490	+	346.196i	−0.297526	+	0.707968i
$490$		0			0
$491$	389.556	−	224.911i	0.793394	−	0.458066i	−0.0477620	−	0.998859i	$-0.515209\pi$
$491$	389.556	−	224.911i	0.793394	−	0.458066i	0.841156	+	0.540792i	$0.181876\pi$
$492$		0			0
$493$	−4.91164	+	8.50721i	−0.00996276	+	0.0172560i
$494$		0			0
$495$	−195.018	+	191.046i	−0.393976	+	0.385951i
$496$		0			0
$497$	−127.175	+	220.273i	−0.255884	+	0.443205i
$498$		0			0
$499$	552.630	−	319.061i	1.10748	−	0.639401i	0.169301	−	0.985564i	$-0.445849\pi$
$499$	552.630	−	319.061i	1.10748	−	0.639401i	0.938174	+	0.346163i	$0.112516\pi$
$500$		0			0
$501$	530.541	−	67.0724i	1.05897	−	0.133877i
$502$		0			0
$503$			182.179i			0.362185i	0.983466	+	0.181093i	$0.0579634\pi$
$503$			182.179i			0.362185i	−0.983466	+	0.181093i	$0.942037\pi$
$504$		0			0
$505$	349.250			0.691585
$506$		0			0
$507$	−284.982	+	216.354i	−0.562094	+	0.426734i
$508$		0			0
$509$	−471.123	−	816.009i	−0.925585	−	1.60316i	−0.790617	−	0.612311i	$-0.790240\pi$
$509$	−471.123	−	816.009i	−0.925585	−	1.60316i	−0.134968	−	0.990850i	$-0.543093\pi$
$510$		0			0
$511$	514.827	+	297.235i	1.00749	+	0.581674i
$512$		0			0
$513$	−412.073	+	163.282i	−0.803261	+	0.318289i
$514$		0			0
$515$	−1011.30	−	583.875i	−1.96369	−	1.13374i
$516$		0			0
$517$	113.976	+	197.412i	0.220456	+	0.381841i
$518$		0			0
$519$	−361.235	+	274.245i	−0.696021	+	0.528409i
$520$		0			0
$521$	−634.330			−1.21752			−0.608762	−	0.793353i	$-0.708334\pi$
$521$	−634.330			−1.21752			−0.608762	+	0.793353i	$0.708334\pi$
$522$		0			0
$523$			534.777i			1.02252i	0.859426	+	0.511259i	$0.170821\pi$
$523$			534.777i			1.02252i	−0.859426	+	0.511259i	$0.829179\pi$
$524$		0			0
$525$	536.446	−	67.8188i	1.02180	−	0.129179i
$526$		0			0
$527$	6.80273	−	3.92756i	0.0129084	−	0.00745267i
$528$		0			0
$529$	247.208	−	428.178i	0.467313	−	0.809409i
$530$		0			0
$531$	−306.226	−	85.4394i	−0.576697	−	0.160903i
$532$		0			0
$533$	−87.2809	+	151.175i	−0.163754	+	0.283630i
$534$		0			0
$535$	383.912	−	221.652i	0.717592	−	0.414302i
$536$		0			0
$537$	321.755	−	765.620i	0.599170	−	1.42574i
$538$		0			0
$539$		−	107.960i		−	0.200296i
$540$		0			0
$541$	61.0097			0.112772			0.0563860	−	0.998409i	$-0.482042\pi$
$541$	61.0097			0.112772			0.0563860	+	0.998409i	$0.482042\pi$
$542$		0			0
$543$	−289.648	−	121.726i	−0.533422	−	0.224172i
$544$		0			0
$545$	257.678	+	446.312i	0.472805	+	0.818921i
$546$		0			0
$547$	104.430	+	60.2925i	0.190914	+	0.110224i	0.592410	−	0.805637i	$-0.298177\pi$
$547$	104.430	+	60.2925i	0.190914	+	0.110224i	−0.401497	+	0.915861i	$0.631510\pi$
$548$		0			0
$549$	−588.822	+	151.299i	−1.07254	+	0.275590i
$550$		0			0
$551$	269.667	+	155.693i	0.489415	+	0.282564i
$552$		0			0
$553$	−330.076	−	571.708i	−0.596882	−	1.03383i
$554$		0			0
$555$	1.79604	+	14.2067i	0.00323611	+	0.0255976i
$556$		0			0
$557$	527.461			0.946968			0.473484	−	0.880802i	$-0.342996\pi$
$557$	527.461			0.946968			0.473484	+	0.880802i	$0.342996\pi$
$558$		0			0
$559$			226.936i			0.405967i
$560$		0			0
$561$	−3.53473	−	4.65594i	−0.00630076	−	0.00829936i
$562$		0			0
$563$	−595.478	+	343.800i	−1.05769	+	0.610656i	−0.924792	−	0.380474i	$-0.875761\pi$
$563$	−595.478	+	343.800i	−1.05769	+	0.610656i	−0.132896	+	0.991130i	$0.542428\pi$
$564$		0			0
$565$	−143.698	+	248.893i	−0.254333	+	0.440518i
$566$		0			0
$567$	−188.969	+	312.284i	−0.333279	+	0.550765i
$568$		0			0
$569$	293.677	−	508.664i	0.516128	−	0.893961i	−0.483696	−	0.875236i	$-0.660706\pi$
$569$	293.677	−	508.664i	0.516128	−	0.893961i	0.999825	−	0.0187248i	$-0.00596063\pi$
$570$		0			0
$571$	742.245	−	428.535i	1.29990	−	0.750500i	0.319517	−	0.947581i	$-0.396479\pi$
$571$	742.245	−	428.535i	1.29990	−	0.750500i	0.980387	+	0.197081i	$0.0631461\pi$
$572$		0			0
$573$	−404.209	−	532.424i	−0.705425	−	0.929186i
$574$		0			0
$575$		−	1279.55i		−	2.22530i
$576$		0			0
$577$	871.732			1.51080			0.755401	−	0.655263i	$-0.227442\pi$
$577$	871.732			1.51080			0.755401	+	0.655263i	$0.227442\pi$
$578$		0			0
$579$	−42.6535	−	337.388i	−0.0736675	−	0.582709i
$580$		0			0
$581$	226.615	+	392.509i	0.390044	+	0.675575i
$582$		0			0
$583$	2.16609	+	1.25059i	0.00371542	+	0.00214510i
$584$		0			0
$585$	−495.593	+	127.343i	−0.847167	+	0.217681i
$586$		0			0
$587$	−700.071	−	404.186i	−1.19263	−	0.688563i	−0.233725	−	0.972303i	$-0.575091\pi$
$587$	−700.071	−	404.186i	−1.19263	−	0.688563i	−0.958901	+	0.283740i	$0.908425\pi$
$588$		0			0
$589$	−124.498	−	215.638i	−0.211373	−	0.366108i
$590$		0			0
$591$	−334.642	−	140.635i	−0.566231	−	0.237960i
$592$		0			0
$593$	−445.123			−0.750628			−0.375314	−	0.926898i	$-0.622465\pi$
$593$	−445.123			−0.750628			−0.375314	+	0.926898i	$0.622465\pi$
$594$		0			0
$595$			18.8149i			0.0316217i
$596$		0			0
$597$	−95.5828	+	227.441i	−0.160105	+	0.380973i
$598$		0			0
$599$	−684.932	+	395.445i	−1.14346	+	0.660176i	−0.947285	−	0.320393i	$-0.896185\pi$
$599$	−684.932	+	395.445i	−1.14346	+	0.660176i	−0.196174	+	0.980569i	$0.562852\pi$
$600$		0			0
$601$	193.532	−	335.208i	0.322017	−	0.557750i	−0.658887	−	0.752242i	$-0.728972\pi$
$601$	193.532	−	335.208i	0.322017	−	0.557750i	0.980904	+	0.194492i	$0.0623057\pi$
$602$		0			0
$603$	−745.436	−	207.982i	−1.23621	−	0.344913i
$604$		0			0
$605$	430.691	−	745.979i	0.711886	−	1.23302i
$606$		0			0
$607$	902.512	−	521.066i	1.48684	−	0.858428i	0.486953	−	0.873428i	$-0.338108\pi$
$607$	902.512	−	521.066i	1.48684	−	0.858428i	0.999887	+	0.0150003i	$0.00477491\pi$
$608$		0			0
$609$	254.398	−	32.1617i	0.417731	−	0.0528106i
$610$		0			0
$611$			427.251i			0.699266i
$612$		0			0
$613$	−256.336			−0.418166			−0.209083	−	0.977898i	$-0.567048\pi$
$613$	−256.336			−0.418166			−0.209083	+	0.977898i	$0.567048\pi$
$614$		0			0
$615$	476.839	−	362.009i	0.775347	−	0.588633i
$616$		0			0
$617$	−253.519	−	439.108i	−0.410890	−	0.711683i	0.584097	−	0.811684i	$-0.301449\pi$
$617$	−253.519	−	439.108i	−0.410890	−	0.711683i	−0.994987	+	0.100001i	$0.968115\pi$
$618$		0			0
$619$	662.787	+	382.660i	1.07074	+	0.618191i	0.928383	−	0.371624i	$-0.121199\pi$
$619$	662.787	+	382.660i	1.07074	+	0.618191i	0.142355	+	0.989816i	$0.454532\pi$
$620$		0			0
$621$	677.066	+	536.333i	1.09028	+	0.863660i
$622$		0			0
$623$	−100.827	−	58.2125i	−0.161841	−	0.0934390i
$624$		0			0
$625$	12.5746	+	21.7799i	0.0201194	+	0.0348479i
$626$		0			0
$627$	−147.587	+	112.046i	−0.235386	+	0.178702i
$628$		0			0
$629$	−0.306623			−0.000487477
$630$		0			0
$631$		−	719.756i		−	1.14066i	−0.821416	−	0.570330i	$-0.806815\pi$
$631$		−	719.756i		−	1.14066i	0.821416	−	0.570330i	$-0.193185\pi$
$632$		0			0
$633$	−321.617	+	40.6597i	−0.508084	+	0.0642333i
$634$		0			0
$635$	68.5084	−	39.5534i	0.107887	−	0.0622888i
$636$		0			0
$637$	101.175	−	175.240i	0.158830	−	0.275102i
$638$		0			0
$639$	−362.880	+	355.489i	−0.567888	+	0.556321i
$640$		0			0
$641$	351.516	−	608.844i	0.548388	−	0.949835i	−0.449998	−	0.893030i	$-0.648575\pi$
$641$	351.516	−	608.844i	0.548388	−	0.949835i	0.998385	−	0.0568054i	$-0.0180915\pi$
$642$		0			0
$643$	507.224	−	292.846i	0.788841	−	0.455437i	−0.0507136	−	0.998713i	$-0.516150\pi$
$643$	507.224	−	292.846i	0.788841	−	0.455437i	0.839554	+	0.543276i	$0.182816\pi$
$644$		0			0
$645$	301.542	−	717.525i	0.467507	−	1.11244i
$646$		0			0
$647$			791.553i			1.22342i	0.791082	+	0.611710i	$0.209518\pi$
$647$			791.553i			1.22342i	−0.791082	+	0.611710i	$0.790482\pi$
$648$		0			0
$649$	−132.909			−0.204791
$650$		0			0
$651$	−189.033	−	79.4416i	−0.290373	−	0.122030i
$652$		0			0
$653$	196.385	+	340.148i	0.300742	+	0.520901i	0.976304	−	0.216402i	$-0.0694323\pi$
$653$	196.385	+	340.148i	0.300742	+	0.520901i	−0.675562	+	0.737303i	$0.736099\pi$
$654$		0			0
$655$	818.797	+	472.733i	1.25007	+	0.721730i
$656$		0			0
$657$	830.857	+	848.132i	1.26462	+	1.29092i
$658$		0			0
$659$	372.557	+	215.096i	0.565337	+	0.326398i	0.755285	−	0.655397i	$-0.227499\pi$
$659$	372.557	+	215.096i	0.565337	+	0.326398i	−0.189948	+	0.981794i	$0.560832\pi$
$660$		0			0
$661$	−453.865	−	786.117i	−0.686633	−	1.18928i	−0.972920	−	0.231140i	$-0.925754\pi$
$661$	−453.865	−	786.117i	−0.686633	−	1.18928i	0.286287	−	0.958144i	$-0.407579\pi$
$662$		0			0
$663$	−1.37423	−	10.8701i	−0.00207274	−	0.0163953i
$664$		0			0
$665$	596.408			0.896854
$666$		0			0
$667$		−	606.799i		−	0.909744i
$668$		0			0
$669$	−296.182	−	390.131i	−0.442724	−	0.583156i
$670$		0			0
$671$	−220.106	+	127.078i	−0.328027	+	0.189387i
$672$		0			0
$673$	−34.8528	+	60.3668i	−0.0517872	+	0.0896980i	−0.890757	−	0.454480i	$-0.849825\pi$
$673$	−34.8528	+	60.3668i	−0.0517872	+	0.0896980i	0.838970	+	0.544178i	$0.183158\pi$
$674$		0			0
$675$	1068.38	+	157.465i	1.58279	+	0.233282i
$676$		0			0
$677$	144.502	−	250.285i	0.213444	−	0.369697i	−0.739346	−	0.673326i	$-0.764865\pi$
$677$	144.502	−	250.285i	0.213444	−	0.369697i	0.952790	+	0.303629i	$0.0981984\pi$
$678$		0			0
$679$	−376.622	+	217.443i	−0.554671	+	0.320239i
$680$		0			0
$681$	−20.0399	−	26.3966i	−0.0294272	−	0.0387616i
$682$		0			0
$683$		−	522.729i		−	0.765343i	−0.923884	−	0.382672i	$-0.875004\pi$
$683$		−	522.729i		−	0.765343i	0.923884	−	0.382672i	$-0.124996\pi$
$684$		0			0
$685$	2025.29			2.95663
$686$		0			0
$687$	−12.1705	−	96.2687i	−0.0177155	−	0.140129i
$688$		0			0
$689$	2.34400	+	4.05992i	0.00340203	+	0.00589248i
$690$		0			0
$691$	−485.917	−	280.544i	−0.703208	−	0.405997i	0.105333	−	0.994437i	$-0.466409\pi$
$691$	−485.917	−	280.544i	−0.703208	−	0.405997i	−0.808541	+	0.588440i	$0.799742\pi$
$692$		0			0
$693$	−41.0085	+	146.980i	−0.0591753	+	0.212092i
$694$		0			0
$695$	−1072.85	−	619.409i	−1.54367	−	0.891236i
$696$		0			0
$697$	6.40971	+	11.1019i	0.00919614	+	0.0159282i
$698$		0			0
$699$	−500.728	−	210.433i	−0.716349	−	0.301048i
$700$		0			0
$701$	−1203.11			−1.71627			−0.858137	−	0.513421i	$-0.828378\pi$
$701$	−1203.11			−1.71627			−0.858137	+	0.513421i	$0.828378\pi$
$702$		0			0
$703$			9.71954i			0.0138258i
$704$		0			0
$705$	567.713	−	1350.88i	0.805266	−	1.91614i
$706$		0			0
$707$	169.058	−	97.6059i	0.239121	−	0.138056i
$708$		0			0
$709$	−89.2724	+	154.624i	−0.125913	+	0.218088i	−0.922090	−	0.386977i	$-0.873519\pi$
$709$	−89.2724	+	154.624i	−0.125913	+	0.218088i	0.796176	+	0.605065i	$0.206853\pi$
$710$		0			0
$711$	−328.123	−	1276.98i	−0.461495	−	1.79604i
$712$		0			0
$713$	−242.611	+	420.215i	−0.340269	+	0.589362i
$714$		0			0
$715$	−185.257	+	106.958i	−0.259100	+	0.149591i
$716$		0			0
$717$	−136.244	+	17.2243i	−0.190019	+	0.0240227i
$718$		0			0
$719$		−	53.0278i		−	0.0737521i	−0.999320	−	0.0368760i	$-0.988259\pi$
$719$		−	53.0278i		−	0.0737521i	0.999320	−	0.0368760i	$-0.0117407\pi$
$720$		0			0
$721$	−652.709			−0.905282
$722$		0			0
$723$	−808.656	+	613.920i	−1.11847	+	0.849129i
$724$		0			0
$725$	−379.332	−	657.022i	−0.523216	−	0.906238i
$726$		0			0
$727$	436.956	+	252.277i	0.601041	+	0.347011i	0.769451	−	0.638706i	$-0.220530\pi$
$727$	436.956	+	252.277i	0.601041	+	0.347011i	−0.168410	+	0.985717i	$0.553863\pi$
$728$		0			0
$729$	−531.144	+	499.327i	−0.728592	+	0.684948i
$730$		0			0
$731$	14.4329	+	8.33283i	0.0197440	+	0.0113992i
$732$		0			0
$733$	−410.964	−	711.811i	−0.560660	−	0.971092i	−0.997439	−	0.0715233i	$-0.977214\pi$
$733$	−410.964	−	711.811i	−0.560660	−	0.971092i	0.436779	−	0.899569i	$-0.356119\pi$
$734$		0			0
$735$	−552.745	+	419.636i	−0.752034	+	0.570934i
$736$		0			0
$737$	−323.536			−0.438991
$738$		0			0
$739$		−	190.298i		−	0.257507i	−0.991677	−	0.128754i	$-0.958902\pi$
$739$		−	190.298i		−	0.257507i	0.991677	−	0.128754i	$-0.0410977\pi$
$740$		0			0
$741$	−344.568	+	43.5612i	−0.465005	+	0.0587870i
$742$		0			0
$743$	664.128	−	383.435i	0.893847	−	0.516063i	0.0186481	−	0.999826i	$-0.494064\pi$
$743$	664.128	−	383.435i	0.893847	−	0.516063i	0.875199	+	0.483763i	$0.160730\pi$
$744$		0			0
$745$	−369.762	+	640.447i	−0.496325	+	0.859660i
$746$		0			0
$747$	225.275	+	876.720i	0.301573	+	1.17366i
$748$		0			0
$749$	123.891	−	214.586i	0.165409	−	0.286496i
$750$		0			0
$751$	−519.601	+	299.992i	−0.691879	+	0.399456i	−0.804315	−	0.594202i	$-0.797468\pi$
$751$	−519.601	+	299.992i	−0.691879	+	0.399456i	0.112437	+	0.993659i	$0.464134\pi$
$752$		0			0
$753$	328.449	−	781.550i	0.436188	−	1.03792i
$754$		0			0
$755$		−	335.335i		−	0.444152i
$756$		0			0
$757$	343.082			0.453213			0.226606	−	0.973986i	$-0.427237\pi$
$757$	343.082			0.453213			0.226606	+	0.973986i	$0.427237\pi$
$758$		0			0
$759$	332.895	+	139.900i	0.438597	+	0.184322i
$760$		0			0
$761$	−149.365	−	258.708i	−0.196275	−	0.339958i	0.751043	−	0.660253i	$-0.229551\pi$
$761$	−149.365	−	258.708i	−0.196275	−	0.339958i	−0.947318	+	0.320295i	$0.896218\pi$
$762$		0			0
$763$	249.464	+	144.028i	0.326952	+	0.188766i
$764$		0			0
$765$	−10.0987	+	36.1951i	−0.0132009	+	0.0473138i
$766$		0			0
$767$	−215.738	−	124.557i	−0.281275	−	0.162394i
$768$		0			0
$769$	−466.241	−	807.553i	−0.606295	−	1.05013i	−0.991845	−	0.127447i	$-0.959322\pi$
$769$	−466.241	−	807.553i	−0.606295	−	1.05013i	0.385550	−	0.922687i	$-0.374012\pi$
$770$		0			0
$771$	−29.2662	−	231.495i	−0.0379588	−	0.300253i
$772$		0			0
$773$	173.239			0.224113			0.112056	−	0.993702i	$-0.464256\pi$
$773$	173.239			0.224113			0.112056	+	0.993702i	$0.464256\pi$
$774$		0			0
$775$			606.660i			0.782787i
$776$		0			0
$777$	4.83977	+	6.37495i	0.00622880	+	0.00820457i
$778$		0			0
$779$	351.917	−	203.179i	0.451755	−	0.260821i
$780$		0			0
$781$	−106.184	+	183.916i	−0.135959	+	0.235488i
$782$		0			0
$783$	506.659	+	74.6746i	0.647075	+	0.0953699i
$784$		0			0
$785$	910.285	−	1576.66i	1.15960	−	2.00848i
$786$		0			0
$787$	−43.1896	+	24.9355i	−0.0548788	+	0.0316843i	−0.527188	−	0.849748i	$-0.676754\pi$
$787$	−43.1896	+	24.9355i	−0.0548788	+	0.0316843i	0.472310	+	0.881433i	$0.343420\pi$
$788$		0			0
$789$	−408.878	−	538.574i	−0.518223	−	0.682603i
$790$		0			0
$791$			160.639i			0.203083i
$792$		0			0
$793$	−476.369			−0.600717
$794$		0			0
$795$	−2.01659	−	15.9512i	−0.00253660	−	0.0200644i
$796$		0			0
$797$	513.753	+	889.846i	0.644608	+	1.11649i	0.984392	+	0.175991i	$0.0563129\pi$
$797$	513.753	+	889.846i	0.644608	+	1.11649i	−0.339784	+	0.940504i	$0.610354\pi$
$798$		0			0
$799$	27.1727	+	15.6882i	0.0340084	+	0.0196348i
$800$		0			0
$801$	−162.720	−	166.104i	−0.203147	−	0.207370i
$802$		0			0
$803$	429.854	+	248.176i	0.535310	+	0.309061i
$804$		0			0
$805$	−581.114	−	1006.52i	−0.721880	−	1.25033i
$806$		0			0
$807$	1177.66	+	494.914i	1.45930	+	0.613277i
$808$		0			0
$809$	−637.363			−0.787841			−0.393920	−	0.919145i	$-0.628881\pi$
$809$	−637.363			−0.787841			−0.393920	+	0.919145i	$0.628881\pi$
$810$		0			0
$811$			1486.54i			1.83298i	0.400061	+	0.916489i	$0.368989\pi$
$811$			1486.54i			1.83298i	−0.400061	+	0.916489i	$0.631011\pi$
$812$		0			0
$813$	65.5144	−	155.893i	0.0805836	−	0.191750i
$814$		0			0
$815$	873.969	−	504.586i	1.07235	−	0.619124i
$816$		0			0
$817$	264.140	−	457.503i	0.323304	−	0.559980i
$818$		0			0
$819$	−204.308	+	200.147i	−0.249460	+	0.244379i
$820$		0			0
$821$	−517.865	+	896.969i	−0.630773	+	1.09253i	0.356620	+	0.934249i	$0.383929\pi$
$821$	−517.865	+	896.969i	−0.630773	+	1.09253i	−0.987394	+	0.158282i	$0.949404\pi$
$822$		0			0
$823$	278.230	−	160.636i	0.338068	−	0.195184i	−0.321349	−	0.946961i	$-0.604136\pi$
$823$	278.230	−	160.636i	0.338068	−	0.195184i	0.659417	+	0.751777i	$0.270803\pi$
$824$		0			0
$825$	447.905	−	56.6252i	0.542915	−	0.0686366i
$826$		0			0
$827$		−	119.865i		−	0.144939i	−0.997371	−	0.0724695i	$-0.976912\pi$
$827$		−	119.865i		−	0.144939i	0.997371	−	0.0724695i	$-0.0230880\pi$
$828$		0			0
$829$	−810.947			−0.978223			−0.489112	−	0.872221i	$-0.662679\pi$
$829$	−810.947			−0.978223			−0.489112	+	0.872221i	$0.662679\pi$
$830$		0			0
$831$	−1001.84	+	760.585i	−1.20559	+	0.915265i
$832$		0			0
$833$	−7.43005	−	12.8692i	−0.00891963	−	0.0154492i
$834$		0			0
$835$	−1244.57	−	718.553i	−1.49050	−	0.860543i
$836$		0			0
$837$	−321.011	−	254.286i	−0.383525	−	0.303807i
$838$		0			0
$839$	51.3491	+	29.6464i	0.0612027	+	0.0353354i	0.530289	−	0.847817i	$-0.322083\pi$
$839$	51.3491	+	29.6464i	0.0612027	+	0.0353354i	−0.469086	+	0.883152i	$0.655417\pi$
$840$		0			0
$841$	240.610	+	416.748i	0.286100	+	0.495539i
$842$		0			0
$843$	353.462	−	268.343i	0.419290	−	0.318319i
$844$		0			0
$845$	961.549			1.13793
$846$		0			0
$847$		−	481.466i		−	0.568437i
$848$		0			0
$849$	−789.943	+	99.8666i	−0.930439	+	0.117628i
$850$		0			0
$851$	16.4030	−	9.47029i	0.0192750	−	0.0111284i
$852$		0			0
$853$	−547.729	+	948.694i	−0.642121	+	1.11219i	0.342838	+	0.939395i	$0.388612\pi$
$853$	−547.729	+	948.694i	−0.642121	+	1.11219i	−0.984959	+	0.172791i	$0.944722\pi$
$854$		0			0
$855$	1147.34	+	320.115i	1.34191	+	0.374404i
$856$		0			0
$857$	−692.162	+	1198.86i	−0.807658	+	1.39890i	0.106825	+	0.994278i	$0.465932\pi$
$857$	−692.162	+	1198.86i	−0.807658	+	1.39890i	−0.914482	+	0.404626i	$0.867402\pi$
$858$		0			0
$859$	−414.983	+	239.591i	−0.483101	+	0.278918i	−0.721708	−	0.692198i	$-0.756643\pi$
$859$	−414.983	+	239.591i	−0.483101	+	0.278918i	0.238607	+	0.971116i	$0.423309\pi$
$860$		0			0
$861$	129.647	−	308.498i	0.150578	−	0.358302i
$862$		0			0
$863$			4.93230i			0.00571530i	0.999996	+	0.00285765i	$0.000909619\pi$
$863$			4.93230i			0.00571530i	−0.999996	+	0.00285765i	$0.999090\pi$
$864$		0			0
$865$	1218.83			1.40906
$866$		0			0
$867$	798.544	+	335.591i	0.921043	+	0.387072i
$868$		0			0
$869$	−275.596	−	477.347i	−0.317142	−	0.549306i
$870$		0			0
$871$	−525.164	−	303.204i	−0.602944	−	0.348110i
$872$		0			0
$873$	−841.233	+	216.156i	−0.963612	+	0.247602i
$874$		0			0
$875$	−471.854	−	272.425i	−0.539262	−	0.311343i
$876$		0			0
$877$	839.494	+	1454.05i	0.957234	+	1.65798i	0.729172	+	0.684331i	$0.239905\pi$
$877$	839.494	+	1454.05i	0.957234	+	1.65798i	0.228062	+	0.973647i	$0.426761\pi$
$878$		0			0
$879$	93.9506	+	743.147i	0.106883	+	0.845446i
$880$		0			0
$881$	830.879			0.943109			0.471555	−	0.881837i	$-0.343693\pi$
$881$	830.879			0.943109			0.471555	+	0.881837i	$0.343693\pi$
$882$		0			0
$883$		−	1228.46i		−	1.39123i	−0.718414	−	0.695615i	$-0.755132\pi$
$883$		−	1228.46i		−	1.39123i	0.718414	−	0.695615i	$-0.244868\pi$
$884$		0			0
$885$	516.615	+	680.486i	0.583746	+	0.768910i
$886$		0			0
$887$	−660.079	+	381.097i	−0.744170	+	0.429647i	−0.823584	−	0.567195i	$-0.808029\pi$
$887$	−660.079	+	381.097i	−0.744170	+	0.429647i	0.0794134	+	0.996842i	$0.474695\pi$
$888$		0			0
$889$	22.1082	−	38.2925i	0.0248686	−	0.0430737i
$890$		0			0
$891$	−157.780	+	260.741i	−0.177082	+	0.292639i
$892$		0			0
$893$	497.295	−	861.340i	0.556881	−	0.964547i
$894$		0			0
$895$	−1932.80	+	1115.90i	−2.15955	+	1.24682i
$896$		0			0
$897$	409.247	+	539.061i	0.456240	+	0.600960i
$898$		0			0
$899$			287.696i			0.320018i
$900$		0			0
$901$	0.344275			0.000382104
$902$		0			0
$903$	−54.5638	−	431.598i	−0.0604250	−	0.477961i
$904$		0			0
$905$	422.166	+	731.214i	0.466482	+	0.807971i
$906$		0			0
$907$	324.076	+	187.106i	0.357306	+	0.206291i	0.667898	−	0.744253i	$-0.267194\pi$
$907$	324.076	+	187.106i	0.357306	+	0.206291i	−0.310592	+	0.950543i	$0.600527\pi$
$908$		0			0
$909$	377.614	−	97.0286i	0.415417	−	0.106742i
$910$		0			0
$911$	1265.50	+	730.639i	1.38914	+	0.802018i	0.993218	−	0.116268i	$-0.0370930\pi$
$911$	1265.50	+	730.639i	1.38914	+	0.802018i	0.395918	+	0.918286i	$0.370426\pi$
$912$		0			0
$913$	189.212	+	327.725i	0.207242	+	0.358954i
$914$		0			0
$915$	1506.18	+	632.978i	1.64610	+	0.691779i
$916$		0			0
$917$	528.464			0.576296
$918$		0			0
$919$		−	1112.72i		−	1.21080i	−0.795923	−	0.605398i	$-0.793014\pi$
$919$		−	1112.72i		−	1.21080i	0.795923	−	0.605398i	$-0.206986\pi$
$920$		0			0
$921$	−302.159	+	718.993i	−0.328077	+	0.780665i
$922$		0			0
$923$	−344.717	+	199.022i	−0.373474	+	0.215625i
$924$		0			0
$925$	11.8404	−	20.5082i	0.0128005	−	0.0221710i
$926$		0			0
$927$	−1255.64	−	350.334i	−1.35452	−	0.377922i
$928$		0			0
$929$	−508.204	+	880.234i	−0.547044	+	0.947507i	0.451432	+	0.892306i	$0.350914\pi$
$929$	−508.204	+	880.234i	−0.547044	+	0.947507i	−0.998475	+	0.0552017i	$0.982420\pi$
$930$		0			0
$931$	−407.938	+	235.523i	−0.438171	+	0.252978i
$932$		0			0
$933$	−57.0358	+	7.21061i	−0.0611317	+	0.00772842i
$934$		0			0
$935$			15.7095i			0.0168016i
$936$		0			0
$937$	170.282			0.181731			0.0908654	−	0.995863i	$-0.471037\pi$
$937$	170.282			0.181731			0.0908654	+	0.995863i	$0.471037\pi$
$938$		0			0
$939$	104.828	−	79.5837i	0.111638	−	0.0847537i
$940$		0			0
$941$	150.929	+	261.417i	0.160392	+	0.277808i	0.935009	−	0.354623i	$-0.115391\pi$
$941$	150.929	+	261.417i	0.160392	+	0.277808i	−0.774617	+	0.632430i	$0.782057\pi$
$942$		0			0
$943$	−685.784	−	395.938i	−0.727237	−	0.419870i
$944$		0			0
$945$	911.926	−	361.347i	0.965001	−	0.382378i
$946$		0			0
$947$	730.155	+	421.555i	0.771019	+	0.445148i	0.833238	−	0.552914i	$-0.186484\pi$
$947$	730.155	+	421.555i	0.771019	+	0.445148i	−0.0622189	+	0.998063i	$0.519818\pi$
$948$		0			0
$949$	465.159	+	805.679i	0.490157	+	0.848977i
$950$		0			0
$951$	329.592	−	250.222i	0.346574	−	0.263114i
$952$		0			0
$953$	306.171			0.321270			0.160635	−	0.987014i	$-0.448646\pi$
$953$	306.171			0.321270			0.160635	+	0.987014i	$0.448646\pi$
$954$		0			0
$955$			1796.44i			1.88109i
$956$		0			0
$957$	212.409	−	26.8533i	0.221953	−	0.0280599i
$958$		0			0
$959$	980.365	−	566.014i	1.02228	−	0.590213i
$960$		0			0
$961$	−365.473	+	633.018i	−0.380305	+	0.658707i
$962$		0			0
$963$	353.511	−	346.311i	0.367094	−	0.359617i
$964$		0			0
$965$	−456.951	+	791.462i	−0.473524	+	0.820168i
$966$		0			0
$967$	103.822	−	59.9417i	0.107365	−	0.0619873i	−0.445356	−	0.895354i	$-0.646923\pi$
$967$	103.822	−	59.9417i	0.107365	−	0.0619873i	0.552721	+	0.833366i	$0.313590\pi$
$968$		0			0
$969$	−9.88171	+	23.5137i	−0.0101978	+	0.0242659i
$970$		0			0
$971$			62.7602i			0.0646346i	0.999478	+	0.0323173i	$0.0102887\pi$
$971$			62.7602i			0.0646346i	−0.999478	+	0.0323173i	$0.989711\pi$
$972$		0			0
$973$	−692.431			−0.711646
$974$		0			0
$975$	780.105	+	327.842i	0.800108	+	0.336248i
$976$		0			0
$977$	618.115	+	1070.61i	0.632666	+	1.09581i	0.987004	+	0.160693i	$0.0513728\pi$
$977$	618.115	+	1070.61i	0.632666	+	1.09581i	−0.354338	+	0.935117i	$0.615294\pi$
$978$		0			0
$979$	−84.1854	−	48.6045i	−0.0859912	−	0.0496471i
$980$		0			0
$981$	402.600	+	410.970i	0.410397	+	0.418930i
$982$		0			0
$983$	−490.618	−	283.258i	−0.499103	−	0.288157i	0.229240	−	0.973370i	$-0.426376\pi$
$983$	−490.618	−	283.258i	−0.499103	−	0.288157i	−0.728343	+	0.685213i	$0.759709\pi$
$984$		0			0
$985$	487.746	+	844.801i	0.495174	+	0.857666i
$986$		0			0
$987$	−102.727	−	812.569i	−0.104080	−	0.823272i
$988$		0			0
$989$	−1029.46			−1.04091
$990$		0			0
$991$			457.774i			0.461931i	0.972962	+	0.230966i	$0.0741885\pi$
$991$			457.774i			0.461931i	−0.972962	+	0.230966i	$0.925812\pi$
$992$		0			0
$993$	108.396	+	142.779i	0.109160	+	0.143786i
$994$		0			0
$995$	574.172	−	331.498i	0.577057	−	0.333164i
$996$		0			0
$997$	−19.3798	+	33.5667i	−0.0194381	+	0.0336677i	−0.875581	−	0.483072i	$-0.839521\pi$
$997$	−19.3798	+	33.5667i	−0.0194381	+	0.0336677i	0.856143	+	0.516739i	$0.172854\pi$
$998$		0			0
$999$	5.88880	+	14.8615i	0.00589470	+	0.0148763i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	576.3.o.g.511.1		16
3.2	odd	2		1728.3.o.g.127.2		16
4.3	odd	2	inner	576.3.o.g.511.8		16
8.3	odd	2		36.3.f.c.7.1	✓	16
8.5	even	2		36.3.f.c.7.5	yes	16
9.4	even	3	inner	576.3.o.g.319.8		16
9.5	odd	6		1728.3.o.g.1279.1		16
12.11	even	2		1728.3.o.g.127.1		16
24.5	odd	2		108.3.f.c.19.4		16
24.11	even	2		108.3.f.c.19.8		16
36.23	even	6		1728.3.o.g.1279.2		16
36.31	odd	6	inner	576.3.o.g.319.1		16
72.5	odd	6		108.3.f.c.91.8		16
72.11	even	6		324.3.d.g.163.3		8
72.13	even	6		36.3.f.c.31.1	yes	16
72.29	odd	6		324.3.d.g.163.4		8
72.43	odd	6		324.3.d.i.163.6		8
72.59	even	6		108.3.f.c.91.4		16
72.61	even	6		324.3.d.i.163.5		8
72.67	odd	6		36.3.f.c.31.5	yes	16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
36.3.f.c.7.1	✓	16	8.3	odd	2
36.3.f.c.7.5	yes	16	8.5	even	2
36.3.f.c.31.1	yes	16	72.13	even	6
36.3.f.c.31.5	yes	16	72.67	odd	6
108.3.f.c.19.4		16	24.5	odd	2
108.3.f.c.19.8		16	24.11	even	2
108.3.f.c.91.4		16	72.59	even	6
108.3.f.c.91.8		16	72.5	odd	6
324.3.d.g.163.3		8	72.11	even	6
324.3.d.g.163.4		8	72.29	odd	6
324.3.d.i.163.5		8	72.61	even	6
324.3.d.i.163.6		8	72.43	odd	6
576.3.o.g.319.1		16	36.31	odd	6	inner
576.3.o.g.319.8		16	9.4	even	3	inner
576.3.o.g.511.1		16	1.1	even	1	trivial
576.3.o.g.511.8		16	4.3	odd	2	inner
1728.3.o.g.127.1		16	12.11	even	2
1728.3.o.g.127.2		16	3.2	odd	2
1728.3.o.g.1279.1		16	9.5	odd	6
1728.3.o.g.1279.2		16	36.23	even	6

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

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

\(f(q)\)	\(=\)	\(q+(-2.76570 - 1.16229i) q^{3} +(4.03104 + 6.98197i) q^{5} +(3.90254 + 2.25313i) q^{7} +(6.29815 + 6.42910i) q^{9} +O(q^{10})\)	\(q+(-2.76570 - 1.16229i) q^{3} +(4.03104 + 6.98197i) q^{5} +(3.90254 + 2.25313i) q^{7} +(6.29815 + 6.42910i) q^{9} +(3.25842 + 1.88125i) q^{11} +(3.52605 + 6.10730i) q^{13} +(-3.03354 - 23.9953i) q^{15} +0.517890 q^{17} -16.4164i q^{19} +(-8.17444 - 10.7674i) q^{21} +(-27.7049 + 15.9954i) q^{23} +(-19.9986 + 34.6387i) q^{25} +(-9.94627 - 25.1012i) q^{27} +(-9.48394 + 16.4267i) q^{29} +(13.1355 - 7.58377i) q^{31} +(-6.82524 - 8.99021i) q^{33} +36.3299i q^{35} -0.592061 q^{37} +(-2.65351 - 20.9892i) q^{39} +(12.3766 + 21.4369i) q^{41} +(27.8686 + 16.0900i) q^{43} +(-19.4997 + 69.8895i) q^{45} +(52.4682 + 30.2925i) q^{47} +(-14.3468 - 24.8493i) q^{49} +(-1.43233 - 0.601940i) q^{51} +0.664765 q^{53} +30.3336i q^{55} +(-19.0807 + 45.4029i) q^{57} +(-30.5921 + 17.6623i) q^{59} +(-33.7750 + 58.5000i) q^{61} +(10.0932 + 39.2804i) q^{63} +(-28.4273 + 49.2376i) q^{65} +(-74.4692 + 42.9948i) q^{67} +(95.2148 - 12.0373i) q^{69} +56.4434i q^{71} +131.921 q^{73} +(95.5705 - 72.5557i) q^{75} +(8.47743 + 14.6833i) q^{77} +(-126.869 - 73.2481i) q^{79} +(-1.66664 + 80.9829i) q^{81} +(87.1029 + 50.2889i) q^{83} +(2.08764 + 3.61589i) q^{85} +(45.3223 - 34.4081i) q^{87} -25.8362 q^{89} +31.7786i q^{91} +(-45.1433 + 5.70713i) q^{93} +(114.619 - 66.1754i) q^{95} +(-48.2534 + 83.5773i) q^{97} +(8.42728 + 32.7971i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q - 6 q^{5} + 18 q^{9}+O(q^{10}) \) 16 * q - 6 * q^5 + 18 * q^9	\( 16 q - 6 q^{5} + 18 q^{9} + 46 q^{13} + 12 q^{17} + 66 q^{21} - 30 q^{25} - 42 q^{29} - 168 q^{33} - 56 q^{37} + 84 q^{41} - 174 q^{45} + 58 q^{49} + 72 q^{53} + 366 q^{57} + 34 q^{61} - 30 q^{65} + 54 q^{69} + 116 q^{73} + 330 q^{77} - 102 q^{81} + 140 q^{85} - 384 q^{89} + 486 q^{93} - 148 q^{97}+O(q^{100}) \) 16 * q - 6 * q^5 + 18 * q^9 + 46 * q^13 + 12 * q^17 + 66 * q^21 - 30 * q^25 - 42 * q^29 - 168 * q^33 - 56 * q^37 + 84 * q^41 - 174 * q^45 + 58 * q^49 + 72 * q^53 + 366 * q^57 + 34 * q^61 - 30 * q^65 + 54 * q^69 + 116 * q^73 + 330 * q^77 - 102 * q^81 + 140 * q^85 - 384 * q^89 + 486 * q^93 - 148 * q^97

Introduction

L-functions

Modular forms

Varieties

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Representations

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Database

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