LMFDB - Embedded newform 576.3.o.g.319.3

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			319.3
Root			$-0.710719 + 1.86946i$ of defining polynomial
Character	$\chi$	$=$	576.319
Dual form			576.3.o.g.511.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-2.32245 + 1.89900i) q^{3} +(-1.35609 + 2.34881i) q^{5} +(-10.0431 + 5.79837i) q^{7} +(1.78756 - 8.82069i) q^{9} +O(q^{10})$	\(q+(-2.32245 + 1.89900i) q^{3} +(-1.35609 + 2.34881i) q^{5} +(-10.0431 + 5.79837i) q^{7} +(1.78756 - 8.82069i) q^{9} +(-8.54822 + 4.93532i) q^{11} +(-0.296185 + 0.513008i) q^{13} +(-1.31096 - 8.03023i) q^{15} -8.87968 q^{17} -14.0989i q^{19} +(12.3134 - 32.5383i) q^{21} +(18.2754 + 10.5513i) q^{23} +(8.82205 + 15.2802i) q^{25} +(12.5990 + 23.8802i) q^{27} +(-10.1764 - 17.6260i) q^{29} +(-14.3357 - 8.27670i) q^{31} +(10.4806 - 27.6952i) q^{33} -31.4524i q^{35} +40.6557 q^{37} +(-0.286328 - 1.75389i) q^{39} +(21.2177 - 36.7502i) q^{41} +(-32.2385 + 18.6129i) q^{43} +(18.2941 + 16.1603i) q^{45} +(-1.57134 + 0.907211i) q^{47} +(42.7423 - 74.0318i) q^{49} +(20.6226 - 16.8625i) q^{51} +21.1005 q^{53} -26.7709i q^{55} +(26.7738 + 32.7440i) q^{57} +(76.6879 + 44.2758i) q^{59} +(-36.4925 - 63.2069i) q^{61} +(33.1930 + 98.9519i) q^{63} +(-0.803307 - 1.39137i) q^{65} +(-38.3110 - 22.1189i) q^{67} +(-62.4808 + 10.2002i) q^{69} -111.798i q^{71} -76.2003 q^{73} +(-49.5060 - 18.7345i) q^{75} +(57.2337 - 99.1316i) q^{77} +(8.30434 - 4.79451i) q^{79} +(-74.6092 - 31.5351i) q^{81} +(73.6244 - 42.5070i) q^{83} +(12.0416 - 20.8567i) q^{85} +(57.1060 + 21.6106i) q^{87} +64.7845 q^{89} -6.86958i q^{91} +(49.0114 - 8.00125i) q^{93} +(33.1157 + 19.1193i) q^{95} +(-3.59139 - 6.22047i) q^{97} +(28.2524 + 84.2235i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $\left(\mathbb{Z}/576\mathbb{Z}\right)^\times$.

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

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
$3$	−2.32245	+	1.89900i	−0.774151	+	0.633001i
$3$	−2.32245	+	1.89900i	−0.774151	+	0.633001i
$4$		0			0
$5$	−1.35609	+	2.34881i	−0.271218	+	0.469763i	−0.969174	−	0.246378i	$-0.920760\pi$
$5$	−1.35609	+	2.34881i	−0.271218	+	0.469763i	0.697956	+	0.716140i	$0.254093\pi$
$6$		0			0
$7$	−10.0431	+	5.79837i	−1.43473	+	0.828339i	−0.997476	−	0.0710013i	$-0.977381\pi$
$7$	−10.0431	+	5.79837i	−1.43473	+	0.828339i	−0.437249	+	0.899340i	$0.644047\pi$
$8$		0			0
$9$	1.78756	−	8.82069i	0.198618	−	0.980077i
$10$		0			0
$11$	−8.54822	+	4.93532i	−0.777111	+	0.448665i	−0.835406	−	0.549634i	$-0.814767\pi$
$11$	−8.54822	+	4.93532i	−0.777111	+	0.448665i	0.0582943	+	0.998299i	$0.481434\pi$
$12$		0			0
$13$	−0.296185	+	0.513008i	−0.0227835	+	0.0394622i	−0.877192	−	0.480139i	$-0.840586\pi$
$13$	−0.296185	+	0.513008i	−0.0227835	+	0.0394622i	0.854409	+	0.519601i	$0.173920\pi$
$14$		0			0
$15$	−1.31096	−	8.03023i	−0.0873972	−	0.535348i
$16$		0			0
$17$	−8.87968			−0.522334			−0.261167	−	0.965294i	$-0.584107\pi$
$17$	−8.87968			−0.522334			−0.261167	+	0.965294i	$0.584107\pi$
$18$		0			0
$19$		−	14.0989i		−	0.742046i	−0.928624	−	0.371023i	$-0.879007\pi$
$19$		−	14.0989i		−	0.742046i	0.928624	−	0.371023i	$-0.120993\pi$
$20$		0			0
$21$	12.3134	−	32.5383i	0.586354	−	1.54944i
$22$		0			0
$23$	18.2754	+	10.5513i	0.794583	+	0.458753i	0.841574	−	0.540142i	$-0.181630\pi$
$23$	18.2754	+	10.5513i	0.794583	+	0.458753i	−0.0469902	+	0.998895i	$0.514963\pi$
$24$		0			0
$25$	8.82205	+	15.2802i	0.352882	+	0.611209i
$26$		0			0
$27$	12.5990	+	23.8802i	0.466630	+	0.884453i
$28$		0			0
$29$	−10.1764	−	17.6260i	−0.350910	−	0.607793i	0.635499	−	0.772101i	$-0.280794\pi$
$29$	−10.1764	−	17.6260i	−0.350910	−	0.607793i	−0.986409	+	0.164308i	$0.947461\pi$
$30$		0			0
$31$	−14.3357	−	8.27670i	−0.462441	−	0.266990i	0.250629	−	0.968083i	$-0.419362\pi$
$31$	−14.3357	−	8.27670i	−0.462441	−	0.266990i	−0.713070	+	0.701093i	$0.752696\pi$
$32$		0			0
$33$	10.4806	−	27.6952i	0.317595	−	0.839247i
$34$		0			0
$35$		−	31.4524i		−	0.898641i
$36$		0			0
$37$	40.6557			1.09880			0.549401	−	0.835559i	$-0.314856\pi$
$37$	40.6557			1.09880			0.549401	+	0.835559i	$0.314856\pi$
$38$		0			0
$39$	−0.286328	−	1.75389i	−0.00734176	−	0.0449716i
$40$		0			0
$41$	21.2177	−	36.7502i	0.517506	−	0.896346i	−0.482288	−	0.876013i	$-0.660194\pi$
$41$	21.2177	−	36.7502i	0.517506	−	0.896346i	0.999793	−	0.0203330i	$-0.00647263\pi$
$42$		0			0
$43$	−32.2385	+	18.6129i	−0.749732	+	0.432858i	−0.825597	−	0.564260i	$-0.809162\pi$
$43$	−32.2385	+	18.6129i	−0.749732	+	0.432858i	0.0758649	+	0.997118i	$0.475828\pi$
$44$		0			0
$45$	18.2941	+	16.1603i	0.406535	+	0.359118i
$46$		0			0
$47$	−1.57134	+	0.907211i	−0.0334327	+	0.0193024i	−0.516623	−	0.856213i	$-0.672811\pi$
$47$	−1.57134	+	0.907211i	−0.0334327	+	0.0193024i	0.483191	+	0.875515i	$0.339478\pi$
$48$		0			0
$49$	42.7423	−	74.0318i	0.872291	−	1.51085i
$50$		0			0
$51$	20.6226	−	16.8625i	0.404365	−	0.330638i
$52$		0			0
$53$	21.1005			0.398122			0.199061	−	0.979987i	$-0.436211\pi$
$53$	21.1005			0.398122			0.199061	+	0.979987i	$0.436211\pi$
$54$		0			0
$55$		−	26.7709i		−	0.486744i
$56$		0			0
$57$	26.7738	+	32.7440i	0.469716	+	0.574456i
$58$		0			0
$59$	76.6879	+	44.2758i	1.29980	+	0.750437i	0.980369	−	0.197174i	$-0.0631764\pi$
$59$	76.6879	+	44.2758i	1.29980	+	0.750437i	0.319427	+	0.947611i	$0.396510\pi$
$60$		0			0
$61$	−36.4925	−	63.2069i	−0.598238	−	1.03618i	−0.993081	−	0.117431i	$-0.962534\pi$
$61$	−36.4925	−	63.2069i	−0.598238	−	1.03618i	0.394843	−	0.918749i	$-0.370799\pi$
$62$		0			0
$63$	33.1930	+	98.9519i	0.526873	+	1.57066i
$64$		0			0
$65$	−0.803307	−	1.39137i	−0.0123586	−	0.0214057i
$66$		0			0
$67$	−38.3110	−	22.1189i	−0.571807	−	0.330133i	0.186064	−	0.982538i	$-0.440427\pi$
$67$	−38.3110	−	22.1189i	−0.571807	−	0.330133i	−0.757871	+	0.652405i	$0.773760\pi$
$68$		0			0
$69$	−62.4808	+	10.2002i	−0.905519	+	0.147829i
$70$		0			0
$71$		−	111.798i		−	1.57462i	−0.616557	−	0.787310i	$-0.711473\pi$
$71$		−	111.798i		−	1.57462i	0.616557	−	0.787310i	$-0.288527\pi$
$72$		0			0
$73$	−76.2003			−1.04384			−0.521920	−	0.852995i	$-0.674784\pi$
$73$	−76.2003			−1.04384			−0.521920	+	0.852995i	$0.674784\pi$
$74$		0			0
$75$	−49.5060	−	18.7345i	−0.660080	−	0.249793i
$76$		0			0
$77$	57.2337	−	99.1316i	0.743294	−	1.28742i
$78$		0			0
$79$	8.30434	−	4.79451i	0.105118	−	0.0606901i	−0.446519	−	0.894774i	$-0.647337\pi$
$79$	8.30434	−	4.79451i	0.105118	−	0.0606901i	0.551637	+	0.834084i	$0.314003\pi$
$80$		0			0
$81$	−74.6092	−	31.5351i	−0.921102	−	0.389322i
$82$		0			0
$83$	73.6244	−	42.5070i	0.887041	−	0.512133i	0.0140672	−	0.999901i	$-0.495522\pi$
$83$	73.6244	−	42.5070i	0.887041	−	0.512133i	0.872973	+	0.487768i	$0.162189\pi$
$84$		0			0
$85$	12.0416	−	20.8567i	0.141666	−	0.245373i
$86$		0			0
$87$	57.1060	+	21.6106i	0.656391	+	0.248397i
$88$		0			0
$89$	64.7845			0.727916			0.363958	−	0.931415i	$-0.381425\pi$
$89$	64.7845			0.727916			0.363958	+	0.931415i	$0.381425\pi$
$90$		0			0
$91$		−	6.86958i		−	0.0754898i
$92$		0			0
$93$	49.0114	−	8.00125i	0.527004	−	0.0860350i
$94$		0			0
$95$	33.1157	+	19.1193i	0.348586	+	0.201256i
$96$		0			0
$97$	−3.59139	−	6.22047i	−0.0370246	−	0.0641285i	0.846919	−	0.531721i	$-0.178455\pi$
$97$	−3.59139	−	6.22047i	−0.0370246	−	0.0641285i	−0.883944	+	0.467593i	$0.845121\pi$
$98$		0			0
$99$	28.2524	+	84.2235i	0.285378	+	0.850742i
$100$		0			0
$101$	55.5037	+	96.1353i	0.549542	+	0.951834i	0.998306	+	0.0581840i	$0.0185310\pi$
$101$	55.5037	+	96.1353i	0.549542	+	0.951834i	−0.448764	+	0.893650i	$0.648136\pi$
$102$		0			0
$103$	−79.6133	−	45.9648i	−0.772945	−	0.446260i	0.0609793	−	0.998139i	$-0.480578\pi$
$103$	−79.6133	−	45.9648i	−0.772945	−	0.446260i	−0.833924	+	0.551879i	$0.813911\pi$
$104$		0			0
$105$	59.7283	+	73.0468i	0.568841	+	0.695683i
$106$		0			0
$107$		−	107.741i		−	1.00693i	−0.864016	−	0.503465i	$-0.832058\pi$
$107$		−	107.741i		−	1.00693i	0.864016	−	0.503465i	$-0.167942\pi$
$108$		0			0
$109$	−86.5562			−0.794093			−0.397047	−	0.917798i	$-0.629965\pi$
$109$	−86.5562			−0.794093			−0.397047	+	0.917798i	$0.629965\pi$
$110$		0			0
$111$	−94.4209	+	77.2054i	−0.850639	+	0.695544i
$112$		0			0
$113$	−2.35198	+	4.07376i	−0.0208140	+	0.0360509i	−0.876245	−	0.481866i	$-0.839959\pi$
$113$	−2.35198	+	4.07376i	−0.0208140	+	0.0360509i	0.855431	+	0.517917i	$0.173292\pi$
$114$		0			0
$115$	−49.5662	+	28.6170i	−0.431010	+	0.248844i
$116$		0			0
$117$	3.99564	+	3.52960i	0.0341507	+	0.0301675i
$118$		0			0
$119$	89.1793	−	51.4877i	0.749406	−	0.432670i
$120$		0			0
$121$	−11.7852	+	20.4126i	−0.0973987	+	0.168700i
$122$		0			0
$123$	20.5116	+	125.643i	0.166761	+	1.02149i
$124$		0			0
$125$	−115.658			−0.925267
$126$		0			0
$127$			8.37118i			0.0659148i	0.999457	+	0.0329574i	$0.0104926\pi$
$127$			8.37118i			0.0659148i	−0.999457	+	0.0329574i	$0.989507\pi$
$128$		0			0
$129$	39.5264	−	104.449i	0.306406	−	0.809679i
$130$		0			0
$131$	−115.067	−	66.4338i	−0.878372	−	0.507129i	−0.00825098	−	0.999966i	$-0.502626\pi$
$131$	−115.067	−	66.4338i	−0.878372	−	0.507129i	−0.870121	+	0.492837i	$0.835960\pi$
$132$		0			0
$133$	81.7506	+	141.596i	0.614666	+	1.06463i
$134$		0			0
$135$	−73.1756	−	2.79099i	−0.542041	−	0.0206740i
$136$		0			0
$137$	22.5579	+	39.0715i	0.164656	+	0.285193i	0.936533	−	0.350579i	$-0.114015\pi$
$137$	22.5579	+	39.0715i	0.164656	+	0.285193i	−0.771877	+	0.635772i	$0.780682\pi$
$138$		0			0
$139$	−130.744	−	75.4848i	−0.940601	−	0.543056i	−0.0504522	−	0.998726i	$-0.516066\pi$
$139$	−130.744	−	75.4848i	−0.940601	−	0.543056i	−0.890149	+	0.455670i	$0.849400\pi$
$140$		0			0
$141$	1.92655	−	5.09093i	0.0136635	−	0.0361059i
$142$		0			0
$143$		−	5.84708i		−	0.0408887i
$144$		0			0
$145$	55.2003			0.380692
$146$		0			0
$147$	41.3198	+	253.103i	0.281087	+	1.72179i
$148$		0			0
$149$	−71.3914	+	123.653i	−0.479137	+	0.829889i	−0.999714	−	0.0239255i	$-0.992384\pi$
$149$	−71.3914	+	123.653i	−0.479137	+	0.829889i	0.520577	+	0.853815i	$0.325717\pi$
$150$		0			0
$151$	−220.027	+	127.033i	−1.45713	+	0.841276i	−0.998869	−	0.0475407i	$-0.984862\pi$
$151$	−220.027	+	127.033i	−1.45713	+	0.841276i	−0.458263	+	0.888817i	$0.651528\pi$
$152$		0			0
$153$	−15.8730	+	78.3249i	−0.103745	+	0.511927i
$154$		0			0
$155$	38.8808	−	22.4479i	0.250844	−	0.144825i
$156$		0			0
$157$	−2.65361	+	4.59618i	−0.0169020	+	0.0292751i	−0.874353	−	0.485291i	$-0.838714\pi$
$157$	−2.65361	+	4.59618i	−0.0169020	+	0.0292751i	0.857451	+	0.514566i	$0.172047\pi$
$158$		0			0
$159$	−49.0048	+	40.0698i	−0.308206	+	0.252012i
$160$		0			0
$161$	−244.722			−1.52001
$162$		0			0
$163$		−	59.5534i		−	0.365359i	−0.983173	−	0.182679i	$-0.941523\pi$
$163$		−	59.5534i		−	0.365359i	0.983173	−	0.182679i	$-0.0584770\pi$
$164$		0			0
$165$	50.8381	+	62.1742i	0.308110	+	0.376813i
$166$		0			0
$167$	85.7434	+	49.5040i	0.513434	+	0.296431i	0.734244	−	0.678886i	$-0.237537\pi$
$167$	85.7434	+	49.5040i	0.513434	+	0.296431i	−0.220810	+	0.975317i	$0.570870\pi$
$168$		0			0
$169$	84.3245	+	146.054i	0.498962	+	0.864227i
$170$		0			0
$171$	−124.362	−	25.2027i	−0.727263	−	0.147384i
$172$		0			0
$173$	−19.2965	−	33.4225i	−0.111540	−	0.193193i	0.804851	−	0.593477i	$-0.202245\pi$
$173$	−19.2965	−	33.4225i	−0.111540	−	0.193193i	−0.916391	+	0.400283i	$0.868912\pi$
$174$		0			0
$175$	−177.201	−	102.307i	−1.01258	−	0.584612i
$176$		0			0
$177$	−262.184	+	42.8023i	−1.48126	+	0.241821i
$178$		0			0
$179$		−	36.4264i		−	0.203499i	−0.994810	−	0.101750i	$-0.967556\pi$
$179$		−	36.4264i		−	0.203499i	0.994810	−	0.101750i	$-0.0324441\pi$
$180$		0			0
$181$	18.5921			0.102719			0.0513594	−	0.998680i	$-0.483645\pi$
$181$	18.5921			0.102719			0.0513594	+	0.998680i	$0.483645\pi$
$182$		0			0
$183$	204.782	+	77.4956i	1.11903	+	0.423473i
$184$		0			0
$185$	−55.1327	+	95.4927i	−0.298015	+	0.516177i
$186$		0			0
$187$	75.9055	−	43.8240i	0.405912	−	0.234353i
$188$		0			0
$189$	−264.999	−	166.777i	−1.40211	−	0.882419i
$190$		0			0
$191$	244.973	−	141.435i	1.28258	−	0.740497i	0.305260	−	0.952269i	$-0.401257\pi$
$191$	244.973	−	141.435i	1.28258	−	0.740497i	0.977319	+	0.211772i	$0.0679233\pi$
$192$		0			0
$193$	−151.542	+	262.479i	−0.785193	+	1.35999i	0.143691	+	0.989623i	$0.454103\pi$
$193$	−151.542	+	262.479i	−0.785193	+	1.35999i	−0.928884	+	0.370372i	$0.879230\pi$
$194$		0			0
$195$	4.50786	+	1.70590i	0.0231172	+	0.00874822i
$196$		0			0
$197$	−139.184			−0.706520			−0.353260	−	0.935525i	$-0.614927\pi$
$197$	−139.184			−0.706520			−0.353260	+	0.935525i	$0.614927\pi$
$198$		0			0
$199$			11.2337i			0.0564505i	0.999602	+	0.0282253i	$0.00898558\pi$
$199$			11.2337i			0.0564505i	−0.999602	+	0.0282253i	$0.991014\pi$
$200$		0			0
$201$	130.979	−	21.3828i	0.651639	−	0.106382i
$202$		0			0
$203$	204.404	+	118.013i	1.00692	+	0.581344i
$204$		0			0
$205$	57.5462	+	99.6730i	0.280713	+	0.486210i
$206$		0			0
$207$	125.738	−	142.341i	0.607432	−	0.687636i
$208$		0			0
$209$	69.5825	+	120.520i	0.332931	+	0.576653i
$210$		0			0
$211$	−112.017	−	64.6728i	−0.530884	−	0.306506i	0.210492	−	0.977595i	$-0.432493\pi$
$211$	−112.017	−	64.6728i	−0.530884	−	0.306506i	−0.741376	+	0.671090i	$0.765827\pi$
$212$		0			0
$213$	212.305	+	259.646i	0.996737	+	1.21899i
$214$		0			0
$215$		−	100.963i		−	0.469595i
$216$		0			0
$217$	191.966			0.884634
$218$		0			0
$219$	176.971	−	144.705i	0.808089	−	0.660752i
$220$		0			0
$221$	2.63003	−	4.55535i	0.0119006	−	0.0206124i
$222$		0			0
$223$	209.210	−	120.787i	0.938159	−	0.541647i	0.0487765	−	0.998810i	$-0.484468\pi$
$223$	209.210	−	120.787i	0.938159	−	0.541647i	0.889383	+	0.457163i	$0.151134\pi$
$224$		0			0
$225$	150.552	−	50.5022i	0.669121	−	0.224454i
$226$		0			0
$227$	330.710	−	190.936i	1.45687	−	0.841126i	0.458016	−	0.888944i	$-0.348560\pi$
$227$	330.710	−	190.936i	1.45687	−	0.841126i	0.998856	+	0.0478181i	$0.0152268\pi$
$228$		0			0
$229$	−74.6642	+	129.322i	−0.326044	+	0.564725i	−0.981723	−	0.190315i	$-0.939049\pi$
$229$	−74.6642	+	129.322i	−0.326044	+	0.564725i	0.655679	+	0.755040i	$0.272383\pi$
$230$		0			0
$231$	55.3289	+	338.915i	0.239519	+	1.46717i
$232$		0			0
$233$	−218.934			−0.939631			−0.469816	−	0.882765i	$-0.655680\pi$
$233$	−218.934			−0.939631			−0.469816	+	0.882765i	$0.655680\pi$
$234$		0			0
$235$		−	4.92103i		−	0.0209406i
$236$		0			0
$237$	−10.1816	+	26.9050i	−0.0429605	+	0.113523i
$238$		0			0
$239$	−218.254	−	126.009i	−0.913197	−	0.527235i	−0.0317388	−	0.999496i	$-0.510104\pi$
$239$	−218.254	−	126.009i	−0.913197	−	0.527235i	−0.881458	+	0.472262i	$0.843438\pi$
$240$		0			0
$241$	−226.014	−	391.467i	−0.937816	−	1.62435i	−0.769534	−	0.638606i	$-0.779511\pi$
$241$	−226.014	−	391.467i	−0.937816	−	1.62435i	−0.168282	−	0.985739i	$-0.553822\pi$
$242$		0			0
$243$	233.162	−	68.4445i	0.959513	−	0.281664i
$244$		0			0
$245$	115.925	+	200.787i	0.473162	+	0.819540i
$246$		0			0
$247$	7.23284	+	4.17588i	0.0292828	+	0.0169064i
$248$		0			0
$249$	−90.2680	+	238.534i	−0.362522	+	0.957966i
$250$		0			0
$251$			139.429i			0.555492i	0.960655	+	0.277746i	$0.0895874\pi$
$251$			139.429i			0.555492i	−0.960655	+	0.277746i	$0.910413\pi$
$252$		0			0
$253$	−208.297			−0.823306
$254$		0			0
$255$	11.6409	+	71.3058i	0.0456505	+	0.279631i
$256$		0			0
$257$	235.308	−	407.565i	0.915594	−	1.58586i	0.109564	−	0.993980i	$-0.465054\pi$
$257$	235.308	−	407.565i	0.915594	−	1.58586i	0.806029	−	0.591875i	$-0.201612\pi$
$258$		0			0
$259$	−408.308	+	235.737i	−1.57648	+	0.910181i
$260$		0			0
$261$	−173.665	+	58.2551i	−0.665381	+	0.223200i
$262$		0			0
$263$	−22.2028	+	12.8188i	−0.0844214	+	0.0487407i	−0.541616	−	0.840626i	$-0.682187\pi$
$263$	−22.2028	+	12.8188i	−0.0844214	+	0.0487407i	0.457195	+	0.889366i	$0.348854\pi$
$264$		0			0
$265$	−28.6141	+	49.5610i	−0.107978	+	0.187023i
$266$		0			0
$267$	−150.459	+	123.026i	−0.563517	+	0.460772i
$268$		0			0
$269$	−8.15075			−0.0303002			−0.0151501	−	0.999885i	$-0.504823\pi$
$269$	−8.15075			−0.0303002			−0.0151501	+	0.999885i	$0.504823\pi$
$270$		0			0
$271$		−	401.979i		−	1.48332i	−0.670777	−	0.741659i	$-0.734039\pi$
$271$		−	401.979i		−	1.48332i	0.670777	−	0.741659i	$-0.265961\pi$
$272$		0			0
$273$	13.0454	+	15.9543i	0.0477852	+	0.0584405i
$274$		0			0
$275$	−150.826	−	87.0792i	−0.548457	−	0.316652i
$276$		0			0
$277$	−56.2021	−	97.3449i	−0.202896	−	0.351426i	0.746565	−	0.665313i	$-0.231702\pi$
$277$	−56.2021	−	97.3449i	−0.202896	−	0.351426i	−0.949460	+	0.313887i	$0.898369\pi$
$278$		0			0
$279$	−98.6321	+	111.655i	−0.353520	+	0.400198i
$280$		0			0
$281$	268.867	+	465.692i	0.956823	+	1.65727i	0.730141	+	0.683296i	$0.239454\pi$
$281$	268.867	+	465.692i	0.956823	+	1.65727i	0.226681	+	0.973969i	$0.427212\pi$
$282$		0			0
$283$	−122.303	−	70.6114i	−0.432164	−	0.249510i	0.268104	−	0.963390i	$-0.413603\pi$
$283$	−122.303	−	70.6114i	−0.432164	−	0.249510i	−0.700268	+	0.713880i	$0.746936\pi$
$284$		0			0
$285$	−113.217	+	18.4830i	−0.397253	+	0.0648528i
$286$		0			0
$287$			492.113i			1.71468i
$288$		0			0
$289$	−210.151			−0.727167
$290$		0			0
$291$	20.1535	+	7.62667i	0.0692561	+	0.0262085i
$292$		0			0
$293$	230.291	−	398.875i	0.785975	−	1.36135i	−0.142440	−	0.989803i	$-0.545495\pi$
$293$	230.291	−	398.875i	0.785975	−	1.36135i	0.928415	−	0.371545i	$-0.121172\pi$
$294$		0			0
$295$	−207.991	+	120.084i	−0.705055	+	0.407064i
$296$		0			0
$297$	−225.556	−	141.953i	−0.759447	−	0.477958i
$298$		0			0
$299$	−10.8258	+	6.25029i	−0.0362068	+	0.0209040i
$300$		0			0
$301$	215.849	−	373.862i	0.717107	−	1.24206i
$302$		0			0
$303$	−311.466	−	117.868i	−1.02794	−	0.389002i
$304$		0			0
$305$	197.948			0.649011
$306$		0			0
$307$			210.322i			0.685089i	0.939502	+	0.342545i	$0.111289\pi$
$307$			210.322i			0.685089i	−0.939502	+	0.342545i	$0.888711\pi$
$308$		0			0
$309$	272.185	−	44.4351i	0.880859	−	0.143803i
$310$		0			0
$311$	−110.993	−	64.0821i	−0.356892	−	0.206052i	0.310824	−	0.950467i	$-0.399395\pi$
$311$	−110.993	−	64.0821i	−0.356892	−	0.206052i	−0.667717	+	0.744416i	$0.732728\pi$
$312$		0			0
$313$	−3.62140	−	6.27245i	−0.0115700	−	0.0200398i	0.860182	−	0.509986i	$-0.170350\pi$
$313$	−3.62140	−	6.27245i	−0.0115700	−	0.0200398i	−0.871752	+	0.489947i	$0.837016\pi$
$314$		0			0
$315$	−277.432	−	56.2233i	−0.880737	−	0.178487i
$316$		0			0
$317$	120.145	+	208.098i	0.379007	+	0.656460i	0.990918	−	0.134467i	$-0.0429322\pi$
$317$	120.145	+	208.098i	0.379007	+	0.656460i	−0.611911	+	0.790927i	$0.709599\pi$
$318$		0			0
$319$	173.980	+	100.447i	0.545392	+	0.314882i
$320$		0			0
$321$	204.602	+	250.224i	0.637388	+	0.779515i
$322$		0			0
$323$			125.194i			0.387596i
$324$		0			0
$325$	−10.4518			−0.0321595
$326$		0			0
$327$	201.023	−	164.371i	0.614748	−	0.502662i
$328$		0			0
$329$	10.5207	−	18.2224i	0.0319778	−	0.0553872i
$330$		0			0
$331$	370.385	−	213.842i	1.11899	−	0.646048i	0.177845	−	0.984058i	$-0.443087\pi$
$331$	370.385	−	213.842i	1.11899	−	0.646048i	0.941142	+	0.338011i	$0.109754\pi$
$332$		0			0
$333$	72.6747	−	358.612i	0.218242	−	1.07691i
$334$		0			0
$335$	103.906	−	59.9904i	0.310168	−	0.179076i
$336$		0			0
$337$	152.442	−	264.037i	0.452349	−	0.783492i	−0.546182	−	0.837666i	$-0.683919\pi$
$337$	152.442	−	264.037i	0.452349	−	0.783492i	0.998531	+	0.0541746i	$0.0172528\pi$
$338$		0			0
$339$	−2.27371	−	13.9275i	−0.00670711	−	0.0410842i
$340$		0			0
$341$	163.393			0.479157
$342$		0			0
$343$			423.102i			1.23353i
$344$		0			0
$345$	60.7712	−	160.588i	0.176148	−	0.465473i
$346$		0			0
$347$	−146.406	−	84.5276i	−0.421919	−	0.243595i	0.273979	−	0.961736i	$-0.411660\pi$
$347$	−146.406	−	84.5276i	−0.421919	−	0.243595i	−0.695898	+	0.718140i	$0.744994\pi$
$348$		0			0
$349$	−107.298	−	185.846i	−0.307444	−	0.532509i	0.670358	−	0.742037i	$-0.266140\pi$
$349$	−107.298	−	185.846i	−0.307444	−	0.532509i	−0.977802	+	0.209529i	$0.932807\pi$
$350$		0			0
$351$	−15.9824	−	0.609584i	−0.0455339	−	0.00173671i
$352$		0			0
$353$	−275.895	−	477.865i	−0.781574	−	1.35373i	−0.931025	−	0.364956i	$-0.881084\pi$
$353$	−275.895	−	477.865i	−0.781574	−	1.35373i	0.149451	−	0.988769i	$-0.452249\pi$
$354$		0			0
$355$	262.593	+	151.608i	0.739698	+	0.427065i
$356$		0			0
$357$	−109.339	+	288.930i	−0.306272	+	0.809326i
$358$		0			0
$359$		−	554.828i		−	1.54548i	−0.634721	−	0.772741i	$-0.718885\pi$
$359$		−	554.828i		−	1.54548i	0.634721	−	0.772741i	$-0.281115\pi$
$360$		0			0
$361$	162.222			0.449367
$362$		0			0
$363$	−11.3930	−	69.7876i	−0.0313858	−	0.192252i
$364$		0			0
$365$	103.334	−	178.980i	0.283108	−	0.490357i
$366$		0			0
$367$	−145.642	+	84.0864i	−0.396845	+	0.229118i	−0.685122	−	0.728429i	$-0.740251\pi$
$367$	−145.642	+	84.0864i	−0.396845	+	0.229118i	0.288277	+	0.957547i	$0.406918\pi$
$368$		0			0
$369$	−286.234	−	252.848i	−0.775702	−	0.685226i
$370$		0			0
$371$	−211.913	+	122.348i	−0.571195	+	0.329780i
$372$		0			0
$373$	−171.699	+	297.391i	−0.460318	+	0.797295i	−0.998977	−	0.0452296i	$-0.985598\pi$
$373$	−171.699	+	297.391i	−0.460318	+	0.797295i	0.538658	+	0.842524i	$0.318931\pi$
$374$		0			0
$375$	268.611	−	219.636i	0.716296	−	0.585695i
$376$		0			0
$377$	12.0564			0.0319798
$378$		0			0
$379$		−	602.392i		−	1.58943i	−0.606986	−	0.794713i	$-0.707621\pi$
$379$		−	602.392i		−	1.58943i	0.606986	−	0.794713i	$-0.292379\pi$
$380$		0			0
$381$	−15.8969	−	19.4417i	−0.0417242	−	0.0510280i
$382$		0			0
$383$	315.762	+	182.305i	0.824443	+	0.475992i	0.851946	−	0.523630i	$-0.175422\pi$
$383$	315.762	+	182.305i	0.824443	+	0.475992i	−0.0275035	+	0.999622i	$0.508756\pi$
$384$		0			0
$385$	155.228	+	268.862i	0.403189	+	0.698344i
$386$		0			0
$387$	106.550	+	317.638i	0.275324	+	0.820769i
$388$		0			0
$389$	−107.326	−	185.893i	−0.275901	−	0.477875i	0.694461	−	0.719530i	$-0.255643\pi$
$389$	−107.326	−	185.893i	−0.275901	−	0.477875i	−0.970362	+	0.241656i	$0.922310\pi$
$390$		0			0
$391$	−162.280	−	93.6923i	−0.415038	−	0.239622i
$392$		0			0
$393$	393.395	−	64.2229i	1.00101	−	0.163417i
$394$		0			0
$395$			26.0071i			0.0658409i
$396$		0			0
$397$	684.628			1.72450			0.862251	−	0.506480i	$-0.169054\pi$
$397$	684.628			1.72450			0.862251	+	0.506480i	$0.169054\pi$
$398$		0			0
$399$	−458.754	−	173.606i	−1.14976	−	0.435102i
$400$		0			0
$401$	95.1918	−	164.877i	0.237386	−	0.411164i	−0.722577	−	0.691290i	$-0.757043\pi$
$401$	95.1918	−	164.877i	0.237386	−	0.411164i	0.959963	+	0.280125i	$0.0903761\pi$
$402$		0			0
$403$	8.49203	−	4.90287i	0.0210720	−	0.0121659i
$404$		0			0
$405$	175.247	−	132.479i	0.432708	−	0.327108i
$406$		0			0
$407$	−347.534	+	200.649i	−0.853892	+	0.492995i
$408$		0			0
$409$	188.978	−	327.320i	0.462049	−	0.800293i	−0.537014	−	0.843574i	$-0.680448\pi$
$409$	188.978	−	327.320i	0.462049	−	0.800293i	0.999063	+	0.0432806i	$0.0137809\pi$
$410$		0			0
$411$	−126.587	−	47.9040i	−0.307997	−	0.116555i
$412$		0			0
$413$	−1026.91			−2.48647
$414$		0			0
$415$			230.573i			0.555598i
$416$		0			0
$417$	446.991	−	72.9727i	1.07192	−	0.174994i
$418$		0			0
$419$	−267.326	−	154.341i	−0.638009	−	0.368355i	0.145838	−	0.989308i	$-0.453412\pi$
$419$	−267.326	−	154.341i	−0.638009	−	0.368355i	−0.783847	+	0.620954i	$0.786745\pi$
$420$		0			0
$421$	−176.834	−	306.286i	−0.420034	−	0.727521i	0.575908	−	0.817514i	$-0.304649\pi$
$421$	−176.834	−	306.286i	−0.420034	−	0.727521i	−0.995942	+	0.0899938i	$0.971315\pi$
$422$		0			0
$423$	5.19337	+	15.4820i	0.0122775	+	0.0366004i
$424$		0			0
$425$	−78.3369	−	135.684i	−0.184322	−	0.319255i
$426$		0			0
$427$	732.995	+	423.195i	1.71662	+	0.991088i
$428$		0			0
$429$	11.1036	+	13.5796i	0.0258826	+	0.0316540i
$430$		0			0
$431$			472.777i			1.09693i	0.836174	+	0.548465i	$0.184787\pi$
$431$			472.777i			1.09693i	−0.836174	+	0.548465i	$0.815213\pi$
$432$		0			0
$433$	61.4188			0.141845			0.0709224	−	0.997482i	$-0.477406\pi$
$433$	61.4188			0.141845			0.0709224	+	0.997482i	$0.477406\pi$
$434$		0			0
$435$	−128.200	+	104.826i	−0.294713	+	0.240978i
$436$		0			0
$437$	148.762	−	257.663i	0.340416	−	0.589618i
$438$		0			0
$439$	354.347	−	204.582i	0.807169	−	0.466019i	−0.0388030	−	0.999247i	$-0.512354\pi$
$439$	354.347	−	204.582i	0.807169	−	0.466019i	0.845972	+	0.533228i	$0.179021\pi$
$440$		0			0
$441$	−576.607	−	509.353i	−1.30750	−	1.15500i
$442$		0			0
$443$	−668.806	+	386.136i	−1.50972	+	0.871638i	−0.509785	+	0.860302i	$0.670275\pi$
$443$	−668.806	+	386.136i	−1.50972	+	0.871638i	−0.999936	+	0.0113360i	$0.996392\pi$
$444$		0			0
$445$	−87.8536	+	152.167i	−0.197424	+	0.341948i
$446$		0			0
$447$	−69.0155	−	422.752i	−0.154397	−	0.945753i
$448$		0			0
$449$	−789.037			−1.75732			−0.878660	−	0.477448i	$-0.841562\pi$
$449$	−789.037			−1.75732			−0.878660	+	0.477448i	$0.841562\pi$
$450$		0			0
$451$			418.865i			0.928747i
$452$		0			0
$453$	269.767	−	712.859i	0.595511	−	1.57364i
$454$		0			0
$455$	16.1354	+	9.31575i	0.0354623	+	0.0204742i
$456$		0			0
$457$	138.165	+	239.309i	0.302331	+	0.523653i	0.976664	−	0.214775i	$-0.0689018\pi$
$457$	138.165	+	239.309i	0.302331	+	0.523653i	−0.674332	+	0.738428i	$0.735568\pi$
$458$		0			0
$459$	−111.875	−	212.049i	−0.243737	−	0.461980i
$460$		0			0
$461$	294.041	+	509.295i	0.637834	+	1.10476i	0.985907	+	0.167293i	$0.0535027\pi$
$461$	294.041	+	509.295i	0.637834	+	1.10476i	−0.348073	+	0.937467i	$0.613164\pi$
$462$		0			0
$463$	677.285	+	391.031i	1.46282	+	0.844558i	0.999141	−	0.0414459i	$-0.0131964\pi$
$463$	677.285	+	391.031i	1.46282	+	0.844558i	0.463677	+	0.886004i	$0.346530\pi$
$464$		0			0
$465$	−47.6703	+	125.969i	−0.102517	+	0.270901i
$466$		0			0
$467$		−	663.203i		−	1.42014i	−0.704133	−	0.710068i	$-0.748664\pi$
$467$		−	663.203i		−	1.42014i	0.704133	−	0.710068i	$-0.251336\pi$
$468$		0			0
$469$	513.014			1.09385
$470$		0			0
$471$	−2.56530	−	15.7136i	−0.00544649	−	0.0333623i
$472$		0			0
$473$	183.721	−	318.214i	0.388417	−	0.672758i
$474$		0			0
$475$	215.434	−	124.381i	0.453546	−	0.261855i
$476$		0			0
$477$	37.7184	−	186.121i	0.0790743	−	0.390190i
$478$		0			0
$479$	−562.018	+	324.481i	−1.17331	+	0.677414i	−0.954459	−	0.298344i	$-0.903566\pi$
$479$	−562.018	+	324.481i	−1.17331	+	0.677414i	−0.218856	+	0.975757i	$0.570233\pi$
$480$		0			0
$481$	−12.0416	+	20.8567i	−0.0250346	+	0.0433611i
$482$		0			0
$483$	568.355	−	464.728i	1.17672	−	0.962170i
$484$		0			0
$485$	19.4810			0.0401669
$486$		0			0
$487$		−	282.104i		−	0.579269i	−0.957137	−	0.289635i	$-0.906466\pi$
$487$		−	282.104i		−	0.579269i	0.957137	−	0.289635i	$-0.0935338\pi$
$488$		0			0
$489$	113.092	+	138.310i	0.231272	+	0.282843i
$490$		0			0
$491$	652.933	+	376.971i	1.32980	+	0.767762i	0.985269	−	0.171012i	$-0.0547036\pi$
$491$	652.933	+	376.971i	1.32980	+	0.767762i	0.344534	+	0.938774i	$0.388037\pi$
$492$		0			0
$493$	90.3630	+	156.513i	0.183292	+	0.317471i
$494$		0			0
$495$	−236.138	−	47.8548i	−0.477047	−	0.0966763i
$496$		0			0
$497$	648.247	+	1122.80i	1.30432	+	2.25915i
$498$		0			0
$499$	−446.169	−	257.596i	−0.894126	−	0.516224i	−0.0188362	−	0.999823i	$-0.505996\pi$
$499$	−446.169	−	257.596i	−0.894126	−	0.516224i	−0.875290	+	0.483599i	$0.839329\pi$
$500$		0			0
$501$	−293.143	+	47.8565i	−0.585116	+	0.0955220i
$502$		0			0
$503$		−	523.660i		−	1.04107i	−0.853839	−	0.520537i	$-0.825732\pi$
$503$		−	523.660i		−	1.04107i	0.853839	−	0.520537i	$-0.174268\pi$
$504$		0			0
$505$	−301.072			−0.596182
$506$		0			0
$507$	−473.198	−	179.072i	−0.933329	−	0.353198i
$508$		0			0
$509$	267.685	−	463.645i	0.525905	−	0.910893i	−0.473640	−	0.880719i	$-0.657060\pi$
$509$	267.685	−	463.645i	0.525905	−	0.910893i	0.999545	−	0.0301749i	$-0.00960643\pi$
$510$		0			0
$511$	765.285	−	441.838i	1.49762	−	0.864653i
$512$		0			0
$513$	336.684	−	177.632i	0.656305	−	0.346261i
$514$		0			0
$515$	215.925	−	124.665i	0.419273	−	0.242067i
$516$		0			0
$517$	8.95475	−	15.5101i	0.0173206	−	0.0300002i
$518$		0			0
$519$	108.285	+	40.9780i	0.208641	+	0.0789557i
$520$		0			0
$521$	177.268			0.340246			0.170123	−	0.985423i	$-0.445584\pi$
$521$	177.268			0.340246			0.170123	+	0.985423i	$0.445584\pi$
$522$		0			0
$523$			444.206i			0.849343i	0.905347	+	0.424672i	$0.139610\pi$
$523$			444.206i			0.849343i	−0.905347	+	0.424672i	$0.860390\pi$
$524$		0			0
$525$	605.822	−	98.9023i	1.15395	−	0.188385i
$526$		0			0
$527$	127.296	+	73.4944i	0.241548	+	0.139458i
$528$		0			0
$529$	−41.8394	−	72.4679i	−0.0790914	−	0.136990i
$530$		0			0
$531$	527.628	−	597.295i	0.993649	−	1.12485i
$532$		0			0
$533$	12.5688	+	21.7697i	0.0235812	+	0.0408438i
$534$		0			0
$535$	253.065	+	146.107i	0.473018	+	0.273097i
$536$		0			0
$537$	69.1739	+	84.5986i	0.128815	+	0.157539i
$538$		0			0
$539$			843.787i			1.56547i
$540$		0			0
$541$	−571.163			−1.05575			−0.527877	−	0.849321i	$-0.677012\pi$
$541$	−571.163			−1.05575			−0.527877	+	0.849321i	$0.677012\pi$
$542$		0			0
$543$	−43.1793	+	35.3065i	−0.0795198	+	0.0650211i
$544$		0			0
$545$	117.378	−	203.304i	0.215372	−	0.373036i
$546$		0			0
$547$	139.875	−	80.7569i	0.255713	−	0.147636i	−0.366664	−	0.930353i	$-0.619500\pi$
$547$	139.875	−	80.7569i	0.255713	−	0.147636i	0.622377	+	0.782717i	$0.286167\pi$
$548$		0			0
$549$	−622.762	+	208.903i	−1.13436	+	0.380515i
$550$		0			0
$551$	−248.507	+	143.476i	−0.451011	+	0.260391i
$552$		0			0
$553$	−55.6008	+	96.3034i	−0.100544	+	0.174147i
$554$		0			0
$555$	−53.2979	−	326.475i	−0.0960323	−	0.588242i
$556$		0			0
$557$	568.917			1.02139			0.510697	−	0.859761i	$-0.329387\pi$
$557$	568.917			1.02139			0.510697	+	0.859761i	$0.329387\pi$
$558$		0			0
$559$		−	22.0515i		−	0.0394481i
$560$		0			0
$561$	−93.0647	+	245.924i	−0.165891	+	0.438367i
$562$		0			0
$563$	250.527	+	144.642i	0.444985	+	0.256912i	0.705710	−	0.708501i	$-0.250628\pi$
$563$	250.527	+	144.642i	0.444985	+	0.256912i	−0.260725	+	0.965413i	$0.583962\pi$
$564$		0			0
$565$	−6.37900	−	11.0487i	−0.0112903	−	0.0195553i
$566$		0			0
$567$	932.159	−	115.903i	1.64402	−	0.204414i
$568$		0			0
$569$	−223.117	−	386.450i	−0.392121	−	0.679174i	0.600608	−	0.799544i	$-0.294925\pi$
$569$	−223.117	−	386.450i	−0.392121	−	0.679174i	−0.992729	+	0.120370i	$0.961592\pi$
$570$		0			0
$571$	372.386	+	214.997i	0.652164	+	0.376527i	0.789285	−	0.614027i	$-0.210451\pi$
$571$	372.386	+	214.997i	0.652164	+	0.376527i	−0.137121	+	0.990554i	$0.543785\pi$
$572$		0			0
$573$	−300.351	+	793.680i	−0.524173	+	1.38513i
$574$		0			0
$575$			372.337i			0.647542i
$576$		0			0
$577$	50.9694			0.0883353			0.0441676	−	0.999024i	$-0.485936\pi$
$577$	50.9694			0.0883353			0.0441676	+	0.999024i	$0.485936\pi$
$578$		0			0
$579$	−146.499	−	897.374i	−0.253021	−	1.54987i
$580$		0			0
$581$	−492.943	+	853.803i	−0.848440	+	1.46954i
$582$		0			0
$583$	−180.371	+	104.137i	−0.309385	+	0.178623i
$584$		0			0
$585$	−13.7088	+	4.59856i	−0.0234339	+	0.00786079i
$586$		0			0
$587$	−643.771	+	371.681i	−1.09671	+	0.633188i	−0.935356	−	0.353708i	$-0.884921\pi$
$587$	−643.771	+	371.681i	−1.09671	+	0.633188i	−0.161358	+	0.986896i	$0.551587\pi$
$588$		0			0
$589$	−116.692	+	202.117i	−0.198119	+	0.343152i
$590$		0			0
$591$	323.249	−	264.312i	0.546953	−	0.447228i
$592$		0			0
$593$	−382.547			−0.645104			−0.322552	−	0.946552i	$-0.604541\pi$
$593$	−382.547			−0.645104			−0.322552	+	0.946552i	$0.604541\pi$
$594$		0			0
$595$			279.287i			0.469391i
$596$		0			0
$597$	−21.3328	−	26.0896i	−0.0357333	−	0.0437012i
$598$		0			0
$599$	−856.248	−	494.355i	−1.42946	−	0.825301i	−0.432384	−	0.901689i	$-0.642328\pi$
$599$	−856.248	−	494.355i	−1.42946	−	0.825301i	−0.997078	+	0.0763888i	$0.975661\pi$
$600$		0			0
$601$	−263.280	−	456.015i	−0.438070	−	0.758760i	0.559470	−	0.828850i	$-0.311005\pi$
$601$	−263.280	−	456.015i	−0.438070	−	0.758760i	−0.997541	+	0.0700905i	$0.977671\pi$
$602$		0			0
$603$	−263.587	+	298.391i	−0.437127	+	0.494844i
$604$		0			0
$605$	−31.9637	−	55.3627i	−0.0528325	−	0.0915086i
$606$		0			0
$607$	−447.631	−	258.440i	−0.737448	−	0.425766i	0.0836928	−	0.996492i	$-0.473329\pi$
$607$	−447.631	−	258.440i	−0.737448	−	0.425766i	−0.821141	+	0.570726i	$0.806662\pi$
$608$		0			0
$609$	−698.826	+	114.085i	−1.14750	+	0.187332i
$610$		0			0
$611$		−	1.07481i		−	0.00175910i
$612$		0			0
$613$	−762.957			−1.24463			−0.622314	−	0.782768i	$-0.713807\pi$
$613$	−762.957			−1.24463			−0.622314	+	0.782768i	$0.713807\pi$
$614$		0			0
$615$	−322.928	−	122.205i	−0.525086	−	0.198708i
$616$		0			0
$617$	60.9168	−	105.511i	0.0987307	−	0.171007i	−0.812429	−	0.583060i	$-0.801855\pi$
$617$	60.9168	−	105.511i	0.0987307	−	0.171007i	0.911160	+	0.412054i	$0.135188\pi$
$618$		0			0
$619$	265.675	−	153.388i	0.429200	−	0.247799i	−0.269806	−	0.962915i	$-0.586959\pi$
$619$	265.675	−	153.388i	0.429200	−	0.247799i	0.699006	+	0.715116i	$0.253626\pi$
$620$		0			0
$621$	−21.7158	+	569.357i	−0.0349692	+	0.916839i
$622$		0			0
$623$	−650.636	+	375.645i	−1.04436	+	0.602961i
$624$		0			0
$625$	−63.7082	+	110.346i	−0.101933	+	0.176553i
$626$		0			0
$627$	−390.471	−	147.765i	−0.622760	−	0.235670i
$628$		0			0
$629$	−361.010			−0.573942
$630$		0			0
$631$			1071.11i			1.69749i	0.528805	+	0.848744i	$0.322640\pi$
$631$			1071.11i			1.69749i	−0.528805	+	0.848744i	$0.677360\pi$
$632$		0			0
$633$	382.967	−	62.5205i	0.605003	−	0.0987685i
$634$		0			0
$635$	−19.6623	−	11.3521i	−0.0309643	−	0.0178773i
$636$		0			0
$637$	25.3193	+	43.8543i	0.0397477	+	0.0688450i
$638$		0			0
$639$	−986.136	−	199.846i	−1.54325	−	0.312748i
$640$		0			0
$641$	527.259	+	913.240i	0.822557	+	1.42471i	0.903772	+	0.428015i	$0.140787\pi$
$641$	527.259	+	913.240i	0.822557	+	1.42471i	−0.0812143	+	0.996697i	$0.525880\pi$
$642$		0			0
$643$	−42.0680	−	24.2880i	−0.0654246	−	0.0377729i	0.466931	−	0.884294i	$-0.345360\pi$
$643$	−42.0680	−	24.2880i	−0.0654246	−	0.0377729i	−0.532355	+	0.846521i	$0.678693\pi$
$644$		0			0
$645$	191.729	+	234.482i	0.297254	+	0.363537i
$646$		0			0
$647$			539.373i			0.833653i	0.908986	+	0.416826i	$0.136858\pi$
$647$			539.373i			0.833653i	−0.908986	+	0.416826i	$0.863142\pi$
$648$		0			0
$649$	−874.061			−1.34678
$650$		0			0
$651$	−445.831	+	364.543i	−0.684840	+	0.559974i
$652$		0			0
$653$	276.457	−	478.838i	0.423365	−	0.733290i	−0.572901	−	0.819624i	$-0.694182\pi$
$653$	276.457	−	478.838i	0.423365	−	0.733290i	0.996266	+	0.0863348i	$0.0275155\pi$
$654$		0			0
$655$	312.081	−	180.180i	0.476460	−	0.275084i
$656$		0			0
$657$	−136.213	+	672.139i	−0.207326	+	1.02304i
$658$		0			0
$659$	−734.162	+	423.869i	−1.11406	+	0.643200i	−0.939877	−	0.341514i	$-0.889060\pi$
$659$	−734.162	+	423.869i	−1.11406	+	0.643200i	−0.174178	+	0.984714i	$0.555727\pi$
$660$		0			0
$661$	359.447	−	622.580i	0.543792	−	0.941876i	−0.454890	−	0.890548i	$-0.650321\pi$
$661$	359.447	−	622.580i	0.543792	−	0.941876i	0.998682	−	0.0513280i	$-0.0163454\pi$
$662$		0			0
$663$	2.54250	+	15.5740i	0.00383485	+	0.0234902i
$664$		0			0
$665$	−443.444			−0.666833
$666$		0			0
$667$		−	429.497i		−	0.643923i
$668$		0			0
$669$	−256.504	+	677.812i	−0.383414	+	1.01317i
$670$		0			0
$671$	623.893	+	360.205i	0.929796	+	0.536818i
$672$		0			0
$673$	288.488	+	499.675i	0.428659	+	0.742460i	0.996754	−	0.0805033i	$-0.0256528\pi$
$673$	288.488	+	499.675i	0.428659	+	0.742460i	−0.568095	+	0.822963i	$0.692319\pi$
$674$		0			0
$675$	−253.746	+	403.188i	−0.375921	+	0.597316i
$676$		0			0
$677$	101.021	+	174.974i	0.149219	+	0.258454i	0.930939	−	0.365175i	$-0.118991\pi$
$677$	101.021	+	174.974i	0.149219	+	0.258454i	−0.781720	+	0.623629i	$0.785657\pi$
$678$		0			0
$679$	72.1372	+	41.6484i	0.106240	+	0.0613379i
$680$		0			0
$681$	−405.471	+	1071.46i	−0.595405	+	1.57336i
$682$		0			0
$683$			568.249i			0.831990i	0.909367	+	0.415995i	$0.136567\pi$
$683$			568.249i			0.831990i	−0.909367	+	0.415995i	$0.863433\pi$
$684$		0			0
$685$	−122.362			−0.178631
$686$		0			0
$687$	−72.1793	−	442.132i	−0.105065	−	0.643569i
$688$		0			0
$689$	−6.24965	+	10.8247i	−0.00907060	+	0.0157107i
$690$		0			0
$691$	−351.376	+	202.867i	−0.508504	+	0.293585i	−0.732218	−	0.681070i	$-0.761515\pi$
$691$	−351.376	+	202.867i	−0.508504	+	0.293585i	0.223714	+	0.974655i	$0.428182\pi$
$692$		0			0
$693$	−772.100	−	682.045i	−1.11414	−	0.984191i
$694$		0			0
$695$	354.600	−	204.728i	0.510215	−	0.294573i
$696$		0			0
$697$	−188.407	+	326.330i	−0.270311	+	0.468192i
$698$		0			0
$699$	508.464	−	415.757i	0.727416	−	0.594788i
$700$		0			0
$701$	−83.5164			−0.119139			−0.0595695	−	0.998224i	$-0.518973\pi$
$701$	−83.5164			−0.119139			−0.0595695	+	0.998224i	$0.518973\pi$
$702$		0			0
$703$		−	573.200i		−	0.815363i
$704$		0			0
$705$	9.34506	+	11.4289i	0.0132554	+	0.0162112i
$706$		0			0
$707$	−1114.86	−	643.663i	−1.57688	−	0.910414i
$708$		0			0
$709$	173.908	+	301.217i	0.245286	+	0.424848i	0.962212	−	0.272302i	$-0.0877849\pi$
$709$	173.908	+	301.217i	0.245286	+	0.424848i	−0.716926	+	0.697149i	$0.754452\pi$
$710$		0			0
$711$	−27.4464	−	81.8205i	−0.0386025	−	0.115078i
$712$		0			0
$713$	−174.660	−	302.520i	−0.244965	−	0.424292i
$714$		0			0
$715$	13.7337	+	7.92916i	0.0192080	+	0.0110897i
$716$		0			0
$717$	746.177	−	121.816i	1.04069	−	0.169896i
$718$		0			0
$719$			536.277i			0.745865i	0.927858	+	0.372933i	$0.121648\pi$
$719$			536.277i			0.745865i	−0.927858	+	0.372933i	$0.878352\pi$
$720$		0			0
$721$	1066.08			1.47862
$722$		0			0
$723$	1268.30	+	479.963i	1.75422	+	0.663849i
$724$		0			0
$725$	179.553	−	310.995i	0.247659	−	0.428959i
$726$		0			0
$727$	−815.055	+	470.573i	−1.12112	+	0.647280i	−0.941687	−	0.336490i	$-0.890760\pi$
$727$	−815.055	+	470.573i	−1.12112	+	0.647280i	−0.179435	+	0.983770i	$0.557427\pi$
$728$		0			0
$729$	−411.530	+	601.734i	−0.564514	+	0.825424i
$730$		0			0
$731$	286.267	−	165.277i	0.391611	−	0.226096i
$732$		0			0
$733$	−311.063	+	538.777i	−0.424370	+	0.735030i	−0.996361	−	0.0852294i	$-0.972838\pi$
$733$	−311.063	+	538.777i	−0.424370	+	0.735030i	0.571991	+	0.820260i	$0.306171\pi$
$734$		0			0
$735$	−650.525	−	246.178i	−0.885068	−	0.334935i
$736$		0			0
$737$	436.655			0.592477
$738$		0			0
$739$			444.439i			0.601406i	0.953718	+	0.300703i	$0.0972213\pi$
$739$			444.439i			0.601406i	−0.953718	+	0.300703i	$0.902779\pi$
$740$		0			0
$741$	−24.7279	+	4.03691i	−0.0333710	+	0.00544792i
$742$		0			0
$743$	66.2270	+	38.2362i	0.0891346	+	0.0514619i	0.543905	−	0.839147i	$-0.316945\pi$
$743$	66.2270	+	38.2362i	0.0891346	+	0.0514619i	−0.454770	+	0.890609i	$0.650279\pi$
$744$		0			0
$745$	−193.626	−	335.370i	−0.259901	−	0.450161i
$746$		0			0
$747$	−243.333	−	725.402i	−0.325747	−	0.971087i
$748$		0			0
$749$	624.725	+	1082.06i	0.834079	+	1.44467i
$750$		0			0
$751$	949.025	+	547.920i	1.26368	+	0.729587i	0.973785	−	0.227471i	$-0.0730457\pi$
$751$	949.025	+	547.920i	1.26368	+	0.729587i	0.289897	+	0.957058i	$0.406379\pi$
$752$		0			0
$753$	−264.775	−	323.816i	−0.351627	−	0.430034i
$754$		0			0
$755$		−	689.070i		−	0.912676i
$756$		0			0
$757$	346.346			0.457525			0.228762	−	0.973482i	$-0.426532\pi$
$757$	346.346			0.457525			0.228762	+	0.973482i	$0.426532\pi$
$758$		0			0
$759$	483.759	−	395.556i	0.637363	−	0.521154i
$760$		0			0
$761$	−106.565	+	184.576i	−0.140033	+	0.242544i	−0.927509	−	0.373802i	$-0.878054\pi$
$761$	−106.565	+	184.576i	−0.140033	+	0.242544i	0.787476	+	0.616345i	$0.211387\pi$
$762$		0			0
$763$	869.291	−	501.885i	1.13931	−	0.657779i
$764$		0			0
$765$	−162.445	−	143.498i	−0.212347	−	0.187579i
$766$		0			0
$767$	−45.4277	+	26.2277i	−0.0592277	+	0.0341952i
$768$		0			0
$769$	−270.786	+	469.015i	−0.352127	+	0.609902i	−0.986622	−	0.163025i	$-0.947875\pi$
$769$	−270.786	+	469.015i	−0.352127	+	0.609902i	0.634495	+	0.772927i	$0.281208\pi$
$770$		0			0
$771$	227.477	+	1393.40i	0.295041	+	1.80726i
$772$		0			0
$773$	−1255.73			−1.62449			−0.812245	−	0.583317i	$-0.801755\pi$
$773$	−1255.73			−1.62449			−0.812245	+	0.583317i	$0.801755\pi$
$774$		0			0
$775$		−	292.070i		−	0.376864i
$776$		0			0
$777$	500.611	−	1322.87i	0.644287	−	1.70253i
$778$		0			0
$779$	−518.136	−	299.146i	−0.665130	−	0.384013i
$780$		0			0
$781$	551.759	+	955.675i	0.706478	+	1.22366i
$782$		0			0
$783$	292.701	−	465.084i	0.373820	−	0.593977i
$784$		0			0
$785$	−7.19706	−	12.4657i	−0.00916822	−	0.0158798i
$786$		0			0
$787$	859.448	+	496.202i	1.09206	+	0.630499i	0.934123	−	0.356951i	$-0.116184\pi$
$787$	859.448	+	496.202i	1.09206	+	0.630499i	0.157933	+	0.987450i	$0.449517\pi$
$788$		0			0
$789$	27.2220	−	71.9343i	0.0345019	−	0.0911715i
$790$		0			0
$791$		−	54.5507i		−	0.0689643i
$792$		0			0
$793$	43.2342			0.0545198
$794$		0			0
$795$	−27.6618	−	169.441i	−0.0347947	−	0.213134i
$796$		0			0
$797$	−319.262	+	552.978i	−0.400580	+	0.693824i	−0.993796	−	0.111219i	$-0.964525\pi$
$797$	−319.262	+	552.978i	−0.400580	+	0.693824i	0.593216	+	0.805043i	$0.297858\pi$
$798$		0			0
$799$	13.9530	−	8.05574i	0.0174630	−	0.0100823i
$800$		0			0
$801$	115.807	−	571.445i	0.144577	−	0.713414i
$802$		0			0
$803$	651.377	−	376.073i	0.811179	−	0.468335i
$804$		0			0
$805$	331.865	−	574.806i	0.412254	−	0.714045i
$806$		0			0
$807$	18.9297	−	15.4783i	0.0234569	−	0.0191801i
$808$		0			0
$809$	−174.260			−0.215401			−0.107701	−	0.994183i	$-0.534349\pi$
$809$	−174.260			−0.215401			−0.107701	+	0.994183i	$0.534349\pi$
$810$		0			0
$811$		−	1182.19i		−	1.45770i	−0.684675	−	0.728849i	$-0.740056\pi$
$811$		−	1182.19i		−	1.45770i	0.684675	−	0.728849i	$-0.259944\pi$
$812$		0			0
$813$	763.360	+	933.577i	0.938942	+	1.14831i
$814$		0			0
$815$	139.880	+	80.7597i	0.171632	+	0.0990917i
$816$		0			0
$817$	262.421	+	454.527i	0.321201	+	0.556336i
$818$		0			0
$819$	−60.5944	−	12.2798i	−0.0739858	−	0.0149937i
$820$		0			0
$821$	−293.955	−	509.144i	−0.358045	−	0.620151i	0.629590	−	0.776928i	$-0.283223\pi$
$821$	−293.955	−	509.144i	−0.358045	−	0.620151i	−0.987634	+	0.156777i	$0.949890\pi$
$822$		0			0
$823$	−98.0750	−	56.6236i	−0.119168	−	0.0688015i	0.439231	−	0.898374i	$-0.355251\pi$
$823$	−98.0750	−	56.6236i	−0.119168	−	0.0688015i	−0.558399	+	0.829573i	$0.688584\pi$
$824$		0			0
$825$	515.649	−	84.1813i	0.625029	−	0.102038i
$826$		0			0
$827$			800.560i			0.968030i	0.875060	+	0.484015i	$0.160822\pi$
$827$			800.560i			0.968030i	−0.875060	+	0.484015i	$0.839178\pi$
$828$		0			0
$829$	−1162.87			−1.40274			−0.701369	−	0.712798i	$-0.747427\pi$
$829$	−1162.87			−1.40274			−0.701369	+	0.712798i	$0.747427\pi$
$830$		0			0
$831$	315.385	+	119.351i	0.379525	+	0.143623i
$832$		0			0
$833$	−379.538	+	657.378i	−0.455627	+	0.789170i
$834$		0			0
$835$	−232.551	+	134.264i	−0.278505	+	0.160795i
$836$		0			0
$837$	17.0344	−	446.617i	0.0203517	−	0.533592i
$838$		0			0
$839$	1355.92	−	782.842i	1.61612	−	0.933065i	0.628205	−	0.778048i	$-0.283790\pi$
$839$	1355.92	−	782.842i	1.61612	−	0.933065i	0.987912	−	0.155017i	$-0.0495432\pi$
$840$		0			0
$841$	213.383	−	369.590i	0.253725	−	0.439464i
$842$		0			0
$843$	−1508.78	−	570.966i	−1.78978	−	0.677303i
$844$		0			0
$845$	−457.406			−0.541309
$846$		0			0
$847$		−	273.341i		−	0.322717i
$848$		0			0
$849$	418.133	−	68.2615i	0.492501	−	0.0804022i
$850$		0			0
$851$	743.000	+	428.971i	0.873091	+	0.504079i
$852$		0			0
$853$	68.8088	+	119.180i	0.0806668	+	0.139719i	0.903537	−	0.428511i	$-0.140962\pi$
$853$	68.8088	+	119.180i	0.0806668	+	0.139719i	−0.822870	+	0.568230i	$0.807628\pi$
$854$		0			0
$855$	227.842	−	257.926i	0.266482	−	0.301668i
$856$		0			0
$857$	−384.489	−	665.955i	−0.448646	−	0.777077i	0.549653	−	0.835393i	$-0.314760\pi$
$857$	−384.489	−	665.955i	−0.448646	−	0.777077i	−0.998298	+	0.0583164i	$0.981427\pi$
$858$		0			0
$859$	178.353	+	102.972i	0.207629	+	0.119875i	0.600209	−	0.799843i	$-0.295084\pi$
$859$	178.353	+	102.972i	0.207629	+	0.119875i	−0.392580	+	0.919718i	$0.628417\pi$
$860$		0			0
$861$	−934.525	−	1142.91i	−1.08540	−	1.32742i
$862$		0			0
$863$		−	772.757i		−	0.895431i	−0.894176	−	0.447716i	$-0.852238\pi$
$863$		−	772.757i		−	0.895431i	0.894176	−	0.447716i	$-0.147762\pi$
$864$		0			0
$865$	104.671			0.121007
$866$		0			0
$867$	488.066	−	399.078i	0.562937	−	0.460298i
$868$		0			0
$869$	−47.3249	+	81.9692i	−0.0544591	+	0.0943258i
$870$		0			0
$871$	22.6943	−	13.1026i	0.0260555	−	0.0150432i
$872$		0			0
$873$	−61.2887	+	20.5590i	−0.0702047	+	0.0235499i
$874$		0			0
$875$	1161.57	−	670.630i	1.32750	−	0.766435i
$876$		0			0
$877$	200.096	−	346.577i	0.228160	−	0.395185i	−0.729103	−	0.684404i	$-0.760062\pi$
$877$	200.096	−	346.577i	0.228160	−	0.395185i	0.957263	+	0.289219i	$0.0933957\pi$
$878$		0			0
$879$	222.627	+	1363.69i	0.253273	+	1.55141i
$880$		0			0
$881$	−728.323			−0.826700			−0.413350	−	0.910572i	$-0.635641\pi$
$881$	−728.323			−0.826700			−0.413350	+	0.910572i	$0.635641\pi$
$882$		0			0
$883$			383.413i			0.434216i	0.976148	+	0.217108i	$0.0696625\pi$
$883$			383.413i			0.434216i	−0.976148	+	0.217108i	$0.930338\pi$
$884$		0			0
$885$	255.010	−	673.865i	0.288147	−	0.761429i
$886$		0			0
$887$	−1255.91	−	725.098i	−1.41590	−	0.817473i	−0.419968	−	0.907539i	$-0.637959\pi$
$887$	−1255.91	−	725.098i	−1.41590	−	0.817473i	−0.995936	+	0.0900662i	$0.971292\pi$
$888$		0			0
$889$	−48.5392	−	84.0724i	−0.0545998	−	0.0945696i
$890$		0			0
$891$	793.412	−	98.6511i	0.890474	−	0.110720i
$892$		0			0
$893$	12.7907	+	22.1541i	0.0143232	+	0.0248086i
$894$		0			0
$895$	85.5589	+	49.3974i	0.0955965	+	0.0551927i
$896$		0			0
$897$	13.2731	−	35.0743i	0.0147972	−	0.0391018i
$898$		0			0
$899$			336.907i			0.374758i
$900$		0			0
$901$	−187.365			−0.207952
$902$		0			0
$903$	208.666	+	1278.17i	0.231080	+	1.41547i
$904$		0			0
$905$	−25.2125	+	43.6694i	−0.0278592	+	0.0482535i
$906$		0			0
$907$	−533.290	+	307.895i	−0.587971	+	0.339465i	−0.764295	−	0.644867i	$-0.776913\pi$
$907$	−533.290	+	307.895i	−0.587971	+	0.339465i	0.176324	+	0.984332i	$0.443580\pi$
$908$		0			0
$909$	947.196	−	317.733i	1.04202	−	0.349541i
$910$		0			0
$911$	−227.031	+	131.076i	−0.249211	+	0.143882i	−0.619403	−	0.785073i	$-0.712625\pi$
$911$	−227.031	+	131.076i	−0.249211	+	0.143882i	0.370192	+	0.928955i	$0.379292\pi$
$912$		0			0
$913$	−419.572	+	726.720i	−0.459553	+	0.795969i
$914$		0			0
$915$	−459.726	+	375.905i	−0.502433	+	0.410825i
$916$		0			0
$917$	1540.83			1.68030
$918$		0			0
$919$			566.458i			0.616385i	0.951324	+	0.308193i	$0.0997241\pi$
$919$			566.458i			0.616385i	−0.951324	+	0.308193i	$0.900276\pi$
$920$		0			0
$921$	−399.403	−	488.464i	−0.433663	−	0.530362i
$922$		0			0
$923$	57.3533	+	33.1130i	0.0621379	+	0.0358754i
$924$		0			0
$925$	358.667	+	621.229i	0.387748	+	0.671599i
$926$		0			0
$927$	−547.755	+	620.080i	−0.590890	+	0.668910i
$928$		0			0
$929$	298.745	+	517.442i	0.321577	+	0.556988i	0.980814	−	0.194948i	$-0.0624537\pi$
$929$	298.745	+	517.442i	0.321577	+	0.556988i	−0.659236	+	0.751936i	$0.729120\pi$
$930$		0			0
$931$	−1043.77	−	602.618i	−1.12112	−	0.647281i
$932$		0			0
$933$	379.469	−	61.9495i	0.406719	−	0.0663982i
$934$		0			0
$935$			237.717i			0.254243i
$936$		0			0
$937$	457.785			0.488564			0.244282	−	0.969704i	$-0.421448\pi$
$937$	457.785			0.488564			0.244282	+	0.969704i	$0.421448\pi$
$938$		0			0
$939$	20.3220	+	7.69041i	0.0216421	+	0.00819000i
$940$		0			0
$941$	677.858	−	1174.09i	0.720360	−	1.24770i	−0.240496	−	0.970650i	$-0.577310\pi$
$941$	677.858	−	1174.09i	0.720360	−	1.24770i	0.960856	−	0.277049i	$-0.0893566\pi$
$942$		0			0
$943$	775.526	−	447.750i	0.822403	−	0.474814i
$944$		0			0
$945$	751.091	−	396.269i	0.794805	−	0.419332i
$946$		0			0
$947$	−567.925	+	327.891i	−0.599709	+	0.346242i	−0.768927	−	0.639336i	$-0.779209\pi$
$947$	−567.925	+	327.891i	−0.599709	+	0.346242i	0.169218	+	0.985579i	$0.445876\pi$
$948$		0			0
$949$	22.5694	−	39.0914i	0.0237823	−	0.0411922i
$950$		0			0
$951$	−674.210	−	255.141i	−0.708949	−	0.268287i
$952$		0			0
$953$	554.778			0.582139			0.291069	−	0.956702i	$-0.405989\pi$
$953$	554.778			0.582139			0.291069	+	0.956702i	$0.405989\pi$
$954$		0			0
$955$			767.193i			0.803344i
$956$		0			0
$957$	−594.810	+	97.1045i	−0.621536	+	0.101468i
$958$		0			0
$959$	−453.102	−	261.599i	−0.472474	−	0.272783i
$960$		0			0
$961$	−343.493	−	594.947i	−0.357432	−	0.619091i
$962$		0			0
$963$	−950.354	−	192.595i	−0.986869	−	0.199995i
$964$		0			0
$965$	−411.009	−	711.889i	−0.425917	−	0.737709i
$966$		0			0
$967$	−502.000	−	289.830i	−0.519131	−	0.299720i	0.217448	−	0.976072i	$-0.430227\pi$
$967$	−502.000	−	289.830i	−0.519131	−	0.299720i	−0.736579	+	0.676351i	$0.763560\pi$
$968$		0			0
$969$	−237.743	−	290.756i	−0.245349	−	0.300058i
$970$		0			0
$971$		−	260.660i		−	0.268445i	−0.990951	−	0.134223i	$-0.957146\pi$
$971$		−	260.660i		−	0.268445i	0.990951	−	0.134223i	$-0.0428537\pi$
$972$		0			0
$973$	1750.76			1.79934
$974$		0			0
$975$	24.2739	−	19.8481i	0.0248963	−	0.0203570i
$976$		0			0
$977$	638.953	−	1106.70i	0.653995	−	1.13275i	−0.328149	−	0.944626i	$-0.606425\pi$
$977$	638.953	−	1106.70i	0.653995	−	1.13275i	0.982145	−	0.188127i	$-0.0602417\pi$
$978$		0			0
$979$	−553.793	+	319.732i	−0.565672	+	0.326591i
$980$		0			0
$981$	−154.725	+	763.486i	−0.157721	+	0.778273i
$982$		0			0
$983$	−378.325	+	218.426i	−0.384868	+	0.222204i	−0.679934	−	0.733273i	$-0.737992\pi$
$983$	−378.325	+	218.426i	−0.384868	+	0.222204i	0.295066	+	0.955477i	$0.404658\pi$
$984$		0			0
$985$	188.746	−	326.918i	0.191621	−	0.331897i
$986$		0			0
$987$	10.1706	+	62.2994i	0.0103045	+	0.0631200i
$988$		0			0
$989$	−785.562			−0.794300
$990$		0			0
$991$		−	1344.50i		−	1.35671i	−0.734734	−	0.678356i	$-0.762693\pi$
$991$		−	1344.50i		−	1.35671i	0.734734	−	0.678356i	$-0.237307\pi$
$992$		0			0
$993$	−454.114	+	1200.00i	−0.457316	+	1.20846i
$994$		0			0
$995$	−26.3858	−	15.2338i	−0.0265184	−	0.0153104i
$996$		0			0
$997$	−942.397	−	1632.28i	−0.945233	−	1.63719i	−0.755284	−	0.655398i	$-0.772501\pi$
$997$	−942.397	−	1632.28i	−0.945233	−	1.63719i	−0.189949	−	0.981794i	$-0.560832\pi$
$998$		0			0
$999$	512.221	+	970.868i	0.512734	+	0.971839i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	576.3.o.g.319.3		16
3.2	odd	2		1728.3.o.g.1279.5		16
4.3	odd	2	inner	576.3.o.g.319.6		16
8.3	odd	2		36.3.f.c.31.7	yes	16
8.5	even	2		36.3.f.c.31.6	yes	16
9.2	odd	6		1728.3.o.g.127.6		16
9.7	even	3	inner	576.3.o.g.511.6		16
12.11	even	2		1728.3.o.g.1279.6		16
24.5	odd	2		108.3.f.c.91.3		16
24.11	even	2		108.3.f.c.91.2		16
36.7	odd	6	inner	576.3.o.g.511.3		16
36.11	even	6		1728.3.o.g.127.5		16
72.5	odd	6		324.3.d.g.163.8		8
72.11	even	6		108.3.f.c.19.3		16
72.13	even	6		324.3.d.i.163.1		8
72.29	odd	6		108.3.f.c.19.2		16
72.43	odd	6		36.3.f.c.7.6	✓	16
72.59	even	6		324.3.d.g.163.7		8
72.61	even	6		36.3.f.c.7.7	yes	16
72.67	odd	6		324.3.d.i.163.2		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
36.3.f.c.7.6	✓	16	72.43	odd	6
36.3.f.c.7.7	yes	16	72.61	even	6
36.3.f.c.31.6	yes	16	8.5	even	2
36.3.f.c.31.7	yes	16	8.3	odd	2
108.3.f.c.19.2		16	72.29	odd	6
108.3.f.c.19.3		16	72.11	even	6
108.3.f.c.91.2		16	24.11	even	2
108.3.f.c.91.3		16	24.5	odd	2
324.3.d.g.163.7		8	72.59	even	6
324.3.d.g.163.8		8	72.5	odd	6
324.3.d.i.163.1		8	72.13	even	6
324.3.d.i.163.2		8	72.67	odd	6
576.3.o.g.319.3		16	1.1	even	1	trivial
576.3.o.g.319.6		16	4.3	odd	2	inner
576.3.o.g.511.3		16	36.7	odd	6	inner
576.3.o.g.511.6		16	9.7	even	3	inner
1728.3.o.g.127.5		16	36.11	even	6
1728.3.o.g.127.6		16	9.2	odd	6
1728.3.o.g.1279.5		16	3.2	odd	2
1728.3.o.g.1279.6		16	12.11	even	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.o (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(-2.32245 + 1.89900i) q^{3} +(-1.35609 + 2.34881i) q^{5} +(-10.0431 + 5.79837i) q^{7} +(1.78756 - 8.82069i) q^{9} +O(q^{10})\)	\(q+(-2.32245 + 1.89900i) q^{3} +(-1.35609 + 2.34881i) q^{5} +(-10.0431 + 5.79837i) q^{7} +(1.78756 - 8.82069i) q^{9} +(-8.54822 + 4.93532i) q^{11} +(-0.296185 + 0.513008i) q^{13} +(-1.31096 - 8.03023i) q^{15} -8.87968 q^{17} -14.0989i q^{19} +(12.3134 - 32.5383i) q^{21} +(18.2754 + 10.5513i) q^{23} +(8.82205 + 15.2802i) q^{25} +(12.5990 + 23.8802i) q^{27} +(-10.1764 - 17.6260i) q^{29} +(-14.3357 - 8.27670i) q^{31} +(10.4806 - 27.6952i) q^{33} -31.4524i q^{35} +40.6557 q^{37} +(-0.286328 - 1.75389i) q^{39} +(21.2177 - 36.7502i) q^{41} +(-32.2385 + 18.6129i) q^{43} +(18.2941 + 16.1603i) q^{45} +(-1.57134 + 0.907211i) q^{47} +(42.7423 - 74.0318i) q^{49} +(20.6226 - 16.8625i) q^{51} +21.1005 q^{53} -26.7709i q^{55} +(26.7738 + 32.7440i) q^{57} +(76.6879 + 44.2758i) q^{59} +(-36.4925 - 63.2069i) q^{61} +(33.1930 + 98.9519i) q^{63} +(-0.803307 - 1.39137i) q^{65} +(-38.3110 - 22.1189i) q^{67} +(-62.4808 + 10.2002i) q^{69} -111.798i q^{71} -76.2003 q^{73} +(-49.5060 - 18.7345i) q^{75} +(57.2337 - 99.1316i) q^{77} +(8.30434 - 4.79451i) q^{79} +(-74.6092 - 31.5351i) q^{81} +(73.6244 - 42.5070i) q^{83} +(12.0416 - 20.8567i) q^{85} +(57.1060 + 21.6106i) q^{87} +64.7845 q^{89} -6.86958i q^{91} +(49.0114 - 8.00125i) q^{93} +(33.1157 + 19.1193i) q^{95} +(-3.59139 - 6.22047i) q^{97} +(28.2524 + 84.2235i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q - 6 q^{5} + 18 q^{9}+O(q^{10}) \) 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

Fields

Representations

Groups

Database

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