LMFDB - Embedded newform 684.3.t.a.265.7

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [684,3,Mod(265,684)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(684, base_ring=CyclotomicField(6))

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

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

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

chi := DirichletCharacter("684.265");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 684 = 2^{2} \cdot 3^{2} \cdot 19 $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	684.t (of order $6$, degree $2$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$18.6376500822$
Analytic rank:	$0$
Dimension:	$80$
Relative dimension:	$40$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			265.7
Character	$\chi$	$=$	684.265
Dual form			684.3.t.a.493.7

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-2.77003 - 1.15194i) q^{3} +(3.04651 - 5.27672i) q^{5} +(-4.19196 - 7.26070i) q^{7} +(6.34609 + 6.38179i) q^{9} +O(q^{10})$	\(q+(-2.77003 - 1.15194i) q^{3} +(3.04651 - 5.27672i) q^{5} +(-4.19196 - 7.26070i) q^{7} +(6.34609 + 6.38179i) q^{9} +(6.42960 + 11.1364i) q^{11} +(20.6063 + 11.8970i) q^{13} +(-14.5174 + 11.1073i) q^{15} +10.0091 q^{17} +(18.9431 + 1.46881i) q^{19} +(3.24799 + 24.9412i) q^{21} +(17.4467 - 30.2185i) q^{23} +(-6.06251 - 10.5006i) q^{25} +(-10.2274 - 24.9880i) q^{27} +(-24.5926 + 14.1985i) q^{29} +(1.25420 + 0.724110i) q^{31} +(-4.98174 - 38.2546i) q^{33} -51.0835 q^{35} +27.0526i q^{37} +(-43.3753 - 56.6922i) q^{39} +(45.1326 + 26.0573i) q^{41} +(-31.1671 - 53.9831i) q^{43} +(53.0083 - 14.0443i) q^{45} +(-18.8530 - 32.6543i) q^{47} +(-10.6451 + 18.4379i) q^{49} +(-27.7255 - 11.5298i) q^{51} -65.3005i q^{53} +78.3514 q^{55} +(-50.7810 - 25.8899i) q^{57} +(54.0935 + 31.2309i) q^{59} +(16.1009 + 27.8876i) q^{61} +(19.7336 - 72.8292i) q^{63} +(125.555 - 72.4890i) q^{65} +(-72.2013 - 41.6854i) q^{67} +(-83.1375 + 63.6086i) q^{69} +38.6773i q^{71} +1.94431 q^{73} +(4.69731 + 36.0705i) q^{75} +(53.9053 - 93.3667i) q^{77} +(28.6384 - 16.5344i) q^{79} +(-0.454400 + 80.9987i) q^{81} +(68.4179 + 118.503i) q^{83} +(30.4929 - 52.8152i) q^{85} +(84.4779 - 11.0012i) q^{87} -85.1744i q^{89} -199.488i q^{91} +(-2.64002 - 3.45056i) q^{93} +(65.4610 - 95.4829i) q^{95} +(-41.0225 + 23.6843i) q^{97} +(-30.2673 + 111.705i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 80 q + 2 q^{7} + 4 q^{9}+O(q^{10}) $ 80 * q + 2 * q^7 + 4 * q^9	$ 80 q + 2 q^{7} + 4 q^{9} + 12 q^{11} - 12 q^{17} - 2 q^{19} - 48 q^{23} - 200 q^{25} - 216 q^{35} + 102 q^{39} + 28 q^{43} + 2 q^{45} - 174 q^{47} - 306 q^{49} + 213 q^{57} + 14 q^{61} + 62 q^{63} + 220 q^{73} - 60 q^{77} + 340 q^{81} + 150 q^{83} - 252 q^{87} - 252 q^{93} + 360 q^{95} + 542 q^{99}+O(q^{100}) $ 80 * q + 2 * q^7 + 4 * q^9 + 12 * q^11 - 12 * q^17 - 2 * q^19 - 48 * q^23 - 200 * q^25 - 216 * q^35 + 102 * q^39 + 28 * q^43 + 2 * q^45 - 174 * q^47 - 306 * q^49 + 213 * q^57 + 14 * q^61 + 62 * q^63 + 220 * q^73 - 60 * q^77 + 340 * q^81 + 150 * q^83 - 252 * q^87 - 252 * q^93 + 360 * q^95 + 542 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/684\mathbb{Z}\right)^\times$.

$n$	$325$	$343$	$533$
$\chi(n)$	$-1$	$1$	$e\left(\frac{1}{3}\right)$

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
$3$	−2.77003	−	1.15194i	−0.923342	−	0.383979i
$3$	−2.77003	−	1.15194i	−0.923342	−	0.383979i
$4$		0			0
$5$	3.04651	−	5.27672i	0.609303	−	1.05534i	−0.382053	−	0.924141i	$-0.624783\pi$
$5$	3.04651	−	5.27672i	0.609303	−	1.05534i	0.991356	−	0.131203i	$-0.0418840\pi$
$6$		0			0
$7$	−4.19196	−	7.26070i	−0.598852	−	1.03724i	−0.992991	−	0.118191i	$-0.962290\pi$
$7$	−4.19196	−	7.26070i	−0.598852	−	1.03724i	0.394139	−	0.919051i	$-0.371043\pi$
$8$		0			0
$9$	6.34609	+	6.38179i	0.705121	+	0.709087i
$10$		0			0
$11$	6.42960	+	11.1364i	0.584509	+	1.01240i	0.994936	+	0.100506i	$0.0320461\pi$
$11$	6.42960	+	11.1364i	0.584509	+	1.01240i	−0.410428	+	0.911893i	$0.634621\pi$
$12$		0			0
$13$	20.6063	+	11.8970i	1.58510	+	0.915156i	0.994098	+	0.108484i	$0.0345995\pi$
$13$	20.6063	+	11.8970i	1.58510	+	0.915156i	0.590999	+	0.806672i	$0.298734\pi$
$14$		0			0
$15$	−14.5174	+	11.1073i	−0.967825	+	0.740484i
$16$		0			0
$17$	10.0091			0.588771			0.294385	−	0.955687i	$-0.404885\pi$
$17$	10.0091			0.588771			0.294385	+	0.955687i	$0.404885\pi$
$18$		0			0
$19$	18.9431	+	1.46881i	0.997007	+	0.0773056i
$19$	18.9431	+	1.46881i	0.997007	+	0.0773056i
$20$		0			0
$21$	3.24799	+	24.9412i	0.154666	+	1.18768i
$22$		0			0
$23$	17.4467	−	30.2185i	0.758550	−	1.31385i	−0.185039	−	0.982731i	$-0.559241\pi$
$23$	17.4467	−	30.2185i	0.758550	−	1.31385i	0.943590	−	0.331117i	$-0.107425\pi$
$24$		0			0
$25$	−6.06251	−	10.5006i	−0.242500	−	0.420023i
$26$		0			0
$27$	−10.2274	−	24.9880i	−0.378793	−	0.925481i
$28$		0			0
$29$	−24.5926	+	14.1985i	−0.848020	+	0.489605i	−0.859982	−	0.510324i	$-0.829526\pi$
$29$	−24.5926	+	14.1985i	−0.848020	+	0.489605i	0.0119623	+	0.999928i	$0.496192\pi$
$30$		0			0
$31$	1.25420	+	0.724110i	0.0404579	+	0.0233584i	0.520093	−	0.854110i	$-0.325897\pi$
$31$	1.25420	+	0.724110i	0.0404579	+	0.0233584i	−0.479635	+	0.877468i	$0.659231\pi$
$32$		0			0
$33$	−4.98174	−	38.2546i	−0.150962	−	1.15923i
$34$		0			0
$35$	−51.0835			−1.45953
$36$		0			0
$37$			27.0526i			0.731150i	0.930782	+	0.365575i	$0.119128\pi$
$37$			27.0526i			0.731150i	−0.930782	+	0.365575i	$0.880872\pi$
$38$		0			0
$39$	−43.3753	−	56.6922i	−1.11219	−	1.45365i
$40$		0			0
$41$	45.1326	+	26.0573i	1.10080	+	0.635545i	0.936430	−	0.350854i	$-0.114109\pi$
$41$	45.1326	+	26.0573i	1.10080	+	0.635545i	0.164366	+	0.986399i	$0.447442\pi$
$42$		0			0
$43$	−31.1671	−	53.9831i	−0.724817	−	1.25542i	−0.959049	−	0.283239i	$-0.908591\pi$
$43$	−31.1671	−	53.9831i	−0.724817	−	1.25542i	0.234232	−	0.972181i	$-0.424742\pi$
$44$		0			0
$45$	53.0083	−	14.0443i	1.17796	−	0.312096i
$46$		0			0
$47$	−18.8530	−	32.6543i	−0.401128	−	0.694773i	0.592735	−	0.805398i	$-0.298048\pi$
$47$	−18.8530	−	32.6543i	−0.401128	−	0.694773i	−0.993862	+	0.110624i	$0.964715\pi$
$48$		0			0
$49$	−10.6451	+	18.4379i	−0.217248	+	0.376284i
$50$		0			0
$51$	−27.7255	−	11.5298i	−0.543636	−	0.226075i
$52$		0			0
$53$		−	65.3005i		−	1.23209i	−0.787713	−	0.616043i	$-0.788735\pi$
$53$		−	65.3005i		−	1.23209i	0.787713	−	0.616043i	$-0.211265\pi$
$54$		0			0
$55$	78.3514			1.42457
$56$		0			0
$57$	−50.7810	−	25.8899i	−0.890895	−	0.454209i
$58$		0			0
$59$	54.0935	+	31.2309i	0.916838	+	0.529337i	0.882625	−	0.470078i	$-0.155774\pi$
$59$	54.0935	+	31.2309i	0.916838	+	0.529337i	0.0342134	+	0.999415i	$0.489107\pi$
$60$		0			0
$61$	16.1009	+	27.8876i	0.263949	+	0.457173i	0.967288	−	0.253682i	$-0.0816415\pi$
$61$	16.1009	+	27.8876i	0.263949	+	0.457173i	−0.703339	+	0.710855i	$0.748308\pi$
$62$		0			0
$63$	19.7336	−	72.8292i	0.313232	−	1.15602i
$64$		0			0
$65$	125.555	−	72.4890i	1.93161	−	1.11521i
$66$		0			0
$67$	−72.2013	−	41.6854i	−1.07763	−	0.622171i	−0.147375	−	0.989081i	$-0.547082\pi$
$67$	−72.2013	−	41.6854i	−1.07763	−	0.622171i	−0.930257	+	0.366910i	$0.880416\pi$
$68$		0			0
$69$	−83.1375	+	63.6086i	−1.20489	+	0.921864i
$70$		0			0
$71$			38.6773i			0.544751i	0.962191	+	0.272376i	$0.0878093\pi$
$71$			38.6773i			0.544751i	−0.962191	+	0.272376i	$0.912191\pi$
$72$		0			0
$73$	1.94431			0.0266344			0.0133172	−	0.999911i	$-0.495761\pi$
$73$	1.94431			0.0266344			0.0133172	+	0.999911i	$0.495761\pi$
$74$		0			0
$75$	4.69731	+	36.0705i	0.0626308	+	0.480940i
$76$		0			0
$77$	53.9053	−	93.3667i	0.700068	−	1.21255i
$78$		0			0
$79$	28.6384	−	16.5344i	0.362511	−	0.209296i	−0.307671	−	0.951493i	$-0.599550\pi$
$79$	28.6384	−	16.5344i	0.362511	−	0.209296i	0.670182	+	0.742197i	$0.266216\pi$
$80$		0			0
$81$	−0.454400	+	80.9987i	−0.00560988	+	0.999984i
$82$		0			0
$83$	68.4179	+	118.503i	0.824312	+	1.42775i	0.902444	+	0.430808i	$0.141771\pi$
$83$	68.4179	+	118.503i	0.824312	+	1.42775i	−0.0781316	+	0.996943i	$0.524895\pi$
$84$		0			0
$85$	30.4929	−	52.8152i	0.358740	−	0.621355i
$86$		0			0
$87$	84.4779	−	11.0012i	0.971010	−	0.126451i
$88$		0			0
$89$		−	85.1744i		−	0.957016i	−0.878083	−	0.478508i	$-0.841178\pi$
$89$		−	85.1744i		−	0.957016i	0.878083	−	0.478508i	$-0.158822\pi$
$90$		0			0
$91$		−	199.488i		−	2.19217i
$92$		0			0
$93$	−2.64002	−	3.45056i	−0.0283874	−	0.0371027i
$94$		0			0
$95$	65.4610	−	95.4829i	0.689064	−	1.00508i
$96$		0			0
$97$	−41.0225	+	23.6843i	−0.422912	+	0.244168i	−0.696322	−	0.717729i	$-0.745182\pi$
$97$	−41.0225	+	23.6843i	−0.422912	+	0.244168i	0.273410	+	0.961897i	$0.411848\pi$
$98$		0			0
$99$	−30.2673	+	111.705i	−0.305730	+	1.12833i
$100$		0			0
$101$	−28.7444	−	49.7868i	−0.284598	−	0.492938i	0.687914	−	0.725793i	$-0.258527\pi$
$101$	−28.7444	−	49.7868i	−0.284598	−	0.492938i	−0.972512	+	0.232854i	$0.925193\pi$
$102$		0			0
$103$	−139.431	−	80.5004i	−1.35370	−	0.781557i	−0.364931	−	0.931034i	$-0.618908\pi$
$103$	−139.431	−	80.5004i	−1.35370	−	0.781557i	−0.988765	+	0.149477i	$0.952241\pi$
$104$		0			0
$105$	141.503	+	58.8450i	1.34764	+	0.560428i
$106$		0			0
$107$			112.491i			1.05132i	0.850695	+	0.525659i	$0.176181\pi$
$107$			112.491i			1.05132i	−0.850695	+	0.525659i	$0.823819\pi$
$108$		0			0
$109$		−	168.605i		−	1.54684i	−0.633895	−	0.773419i	$-0.718545\pi$
$109$		−	168.605i		−	1.54684i	0.633895	−	0.773419i	$-0.281455\pi$
$110$		0			0
$111$	31.1628	−	74.9363i	0.280746	−	0.675102i
$112$		0			0
$113$	6.82119	+	3.93822i	0.0603645	+	0.0348515i	0.529879	−	0.848074i	$-0.322238\pi$
$113$	6.82119	+	3.93822i	0.0603645	+	0.0348515i	−0.469514	+	0.882925i	$0.655571\pi$
$114$		0			0
$115$	−106.303	−	184.122i	−0.924374	−	1.60106i
$116$		0			0
$117$	54.8448	+	207.004i	0.468759	+	1.76927i
$118$		0			0
$119$	−41.9578	−	72.6730i	−0.352586	−	0.610698i
$120$		0			0
$121$	−22.1794	+	38.4159i	−0.183301	+	0.317487i
$122$		0			0
$123$	−95.0022	−	124.169i	−0.772376	−	1.00951i
$124$		0			0
$125$	78.4477			0.627581
$126$		0			0
$127$		−	105.159i		−	0.828023i	−0.910272	−	0.414012i	$-0.864127\pi$
$127$		−	105.159i		−	0.828023i	0.910272	−	0.414012i	$-0.135873\pi$
$128$		0			0
$129$	24.1487	+	185.437i	0.187199	+	1.43750i
$130$		0			0
$131$	13.8130	−	23.9248i	0.105443	−	0.182632i	−0.808476	−	0.588529i	$-0.799707\pi$
$131$	13.8130	−	23.9248i	0.105443	−	0.182632i	0.913919	+	0.405897i	$0.133041\pi$
$132$		0			0
$133$	−68.7444	−	143.698i	−0.516875	−	1.08043i
$134$		0			0
$135$	−163.013	−	22.1592i	−1.20750	−	0.164142i
$136$		0			0
$137$	72.9125	+	126.288i	0.532208	+	0.921812i	0.999293	+	0.0375991i	$0.0119710\pi$
$137$	72.9125	+	126.288i	0.532208	+	0.921812i	−0.467085	+	0.884213i	$0.654696\pi$
$138$		0			0
$139$	−77.6019	+	134.410i	−0.558287	+	0.966982i	0.439353	+	0.898315i	$0.355208\pi$
$139$	−77.6019	+	134.410i	−0.558287	+	0.966982i	−0.997640	+	0.0686669i	$0.978125\pi$
$140$		0			0
$141$	14.6076	+	112.171i	0.103600	+	0.795538i
$142$		0			0
$143$			305.972i			2.13967i
$144$		0			0
$145$			173.024i			1.19327i
$146$		0			0
$147$	50.7266	−	38.8110i	0.345079	−	0.264020i
$148$		0			0
$149$	−96.4444	+	167.047i	−0.647278	+	1.12112i	0.336493	+	0.941686i	$0.390759\pi$
$149$	−96.4444	+	167.047i	−0.647278	+	1.12112i	−0.983770	+	0.179432i	$0.942574\pi$
$150$		0			0
$151$	131.356	−	75.8386i	0.869909	−	0.502242i	0.00259111	−	0.999997i	$-0.499175\pi$
$151$	131.356	−	75.8386i	0.869909	−	0.502242i	0.867318	+	0.497754i	$0.165842\pi$
$152$		0			0
$153$	63.5186	+	63.8759i	0.415154	+	0.417490i
$154$		0			0
$155$	7.64185	−	4.41202i	0.0493022	−	0.0284647i
$156$		0			0
$157$	−29.6487	+	51.3531i	−0.188846	+	0.327090i	−0.944866	−	0.327458i	$-0.893808\pi$
$157$	−29.6487	+	51.3531i	−0.188846	+	0.327090i	0.756020	+	0.654548i	$0.227141\pi$
$158$		0			0
$159$	−75.2220	+	180.884i	−0.473095	+	1.13764i
$160$		0			0
$161$	−292.543			−1.81704
$162$		0			0
$163$	156.958			0.962930			0.481465	−	0.876465i	$-0.340105\pi$
$163$	156.958			0.962930			0.481465	+	0.876465i	$0.340105\pi$
$164$		0			0
$165$	−217.036	−	90.2559i	−1.31537	−	0.547005i
$166$		0			0
$167$	−61.7585	−	35.6563i	−0.369811	−	0.213511i	0.303565	−	0.952811i	$-0.401823\pi$
$167$	−61.7585	−	35.6563i	−0.369811	−	0.213511i	−0.673376	+	0.739300i	$0.735156\pi$
$168$		0			0
$169$	198.579	+	343.948i	1.17502	+	2.03520i
$170$		0			0
$171$	110.841	+	130.212i	0.648194	+	0.761475i
$172$		0			0
$173$	135.973	−	78.5038i	0.785968	−	0.453779i	−0.0525729	−	0.998617i	$-0.516742\pi$
$173$	135.973	−	78.5038i	0.785968	−	0.453779i	0.838541	+	0.544838i	$0.183409\pi$
$174$		0			0
$175$	−50.8276	+	88.0360i	−0.290444	+	0.503063i
$176$		0			0
$177$	−113.864	−	148.823i	−0.643301	−	0.840805i
$178$		0			0
$179$			184.896i			1.03294i	0.856305	+	0.516470i	$0.172754\pi$
$179$			184.896i			1.03294i	−0.856305	+	0.516470i	$0.827246\pi$
$180$		0			0
$181$		−	303.089i		−	1.67452i	−0.546802	−	0.837262i	$-0.684155\pi$
$181$		−	303.089i		−	1.67452i	0.546802	−	0.837262i	$-0.315845\pi$
$182$		0			0
$183$	−12.4752	−	95.7965i	−0.0681705	−	0.523478i
$184$		0			0
$185$	142.749	+	82.4160i	0.771615	+	0.445492i
$186$		0			0
$187$	64.3545	+	111.465i	0.344142	+	0.596071i
$188$		0			0
$189$	−138.557	+	179.007i	−0.733107	+	0.947126i
$190$		0			0
$191$	12.9775	+	22.4776i	0.0679449	+	0.117684i	0.897997	−	0.440003i	$-0.145022\pi$
$191$	12.9775	+	22.4776i	0.0679449	+	0.117684i	−0.830052	+	0.557687i	$0.811689\pi$
$192$		0			0
$193$	−203.590	−	117.543i	−1.05487	−	0.609029i	−0.130860	−	0.991401i	$-0.541774\pi$
$193$	−203.590	−	117.543i	−1.05487	−	0.609029i	−0.924008	+	0.382372i	$0.875107\pi$
$194$		0			0
$195$	−431.292	+	56.1654i	−2.21175	+	0.288028i
$196$		0			0
$197$	9.67137			0.0490932			0.0245466	−	0.999699i	$-0.492186\pi$
$197$	9.67137			0.0490932			0.0245466	+	0.999699i	$0.492186\pi$
$198$		0			0
$199$	−287.927			−1.44687			−0.723435	−	0.690393i	$-0.757438\pi$
$199$	−287.927			−1.44687			−0.723435	+	0.690393i	$0.757438\pi$
$200$		0			0
$201$	151.981	+	198.641i	0.756122	+	0.988264i
$202$		0			0
$203$	206.182	+	119.039i	1.01568	+	0.586401i
$204$		0			0
$205$	274.995	−	158.768i	1.34144	−	0.774479i
$206$		0			0
$207$	303.566	−	80.4283i	1.46650	−	0.388543i
$208$		0			0
$209$	105.440	+	220.402i	0.504495	+	1.05455i
$210$		0			0
$211$	58.5250	+	33.7894i	0.277370	+	0.160139i	0.632232	−	0.774779i	$-0.282139\pi$
$211$	58.5250	+	33.7894i	0.277370	+	0.160139i	−0.354862	+	0.934919i	$0.615472\pi$
$212$		0			0
$213$	44.5538	−	107.137i	0.209173	−	0.502991i
$214$		0			0
$215$	−379.804			−1.76653
$216$		0			0
$217$		−	12.1418i		−	0.0559529i
$218$		0			0
$219$	−5.38578	−	2.23972i	−0.0245926	−	0.0102270i
$220$		0			0
$221$	206.250	+	119.079i	0.933258	+	0.538817i
$222$		0			0
$223$	−315.468	+	182.136i	−1.41466	+	0.816752i	−0.995822	−	0.0913119i	$-0.970894\pi$
$223$	−315.468	+	182.136i	−1.41466	+	0.816752i	−0.418833	+	0.908063i	$0.637561\pi$
$224$		0			0
$225$	28.5392	−	105.327i	0.126841	−	0.468121i
$226$		0			0
$227$	209.201	−	120.782i	0.921589	−	0.532079i	0.0374471	−	0.999299i	$-0.488077\pi$
$227$	209.201	−	120.782i	0.921589	−	0.532079i	0.884142	+	0.467219i	$0.154744\pi$
$228$		0			0
$229$	47.2751	−	81.8829i	0.206442	−	0.357567i	−0.744149	−	0.668013i	$-0.767145\pi$
$229$	47.2751	−	81.8829i	0.206442	−	0.357567i	0.950591	+	0.310446i	$0.100478\pi$
$230$		0			0
$231$	−256.871	+	196.533i	−1.11200	+	0.850791i
$232$		0			0
$233$	341.383			1.46516			0.732582	−	0.680679i	$-0.238315\pi$
$233$	341.383			1.46516			0.732582	+	0.680679i	$0.238315\pi$
$234$		0			0
$235$	−229.744			−0.977633
$236$		0			0
$237$	−98.3756	+	12.8111i	−0.415087	+	0.0540551i
$238$		0			0
$239$	22.4819	−	38.9398i	0.0940666	−	0.162928i	−0.815152	−	0.579247i	$-0.803347\pi$
$239$	22.4819	−	38.9398i	0.0940666	−	0.162928i	0.909219	+	0.416319i	$0.136680\pi$
$240$		0			0
$241$	−112.634	+	65.0292i	−0.467360	+	0.269831i	−0.715134	−	0.698987i	$-0.753634\pi$
$241$	−112.634	+	65.0292i	−0.467360	+	0.269831i	0.247774	+	0.968818i	$0.420301\pi$
$242$		0			0
$243$	94.5641	−	223.845i	0.389153	−	0.921173i
$244$		0			0
$245$	64.8611	+	112.343i	0.264739	+	0.458542i
$246$		0			0
$247$	372.873	+	255.634i	1.50961	+	1.03495i
$248$		0			0
$249$	−53.0111	−	407.070i	−0.212896	−	1.63482i
$250$		0			0
$251$	−166.592			−0.663715			−0.331858	−	0.943330i	$-0.607675\pi$
$251$	−166.592			−0.663715			−0.331858	+	0.943330i	$0.607675\pi$
$252$		0			0
$253$	448.700			1.77352
$254$		0			0
$255$	−145.306	+	111.174i	−0.569827	+	0.435975i
$256$		0			0
$257$	−215.719	−	124.546i	−0.839375	−	0.484613i	0.0176769	−	0.999844i	$-0.494373\pi$
$257$	−215.719	−	124.546i	−0.839375	−	0.484613i	−0.857052	+	0.515231i	$0.827706\pi$
$258$		0			0
$259$	196.420	−	113.403i	0.758380	−	0.437851i
$260$		0			0
$261$	−246.679	−	66.8395i	−0.945129	−	0.256090i
$262$		0			0
$263$	−15.6768	−	27.1530i	−0.0596075	−	0.103243i	0.834682	−	0.550733i	$-0.185652\pi$
$263$	−15.6768	−	27.1530i	−0.0596075	−	0.103243i	−0.894289	+	0.447489i	$0.852318\pi$
$264$		0			0
$265$	−344.572	−	198.939i	−1.30027	−	0.750713i
$266$		0			0
$267$	−98.1155	+	235.935i	−0.367474	+	0.883653i
$268$		0			0
$269$		−	273.925i		−	1.01831i	−0.860675	−	0.509154i	$-0.829958\pi$
$269$		−	273.925i		−	1.01831i	0.860675	−	0.509154i	$-0.170042\pi$
$270$		0			0
$271$	−396.574			−1.46337			−0.731686	−	0.681642i	$-0.761266\pi$
$271$	−396.574			−1.46337			−0.731686	+	0.681642i	$0.761266\pi$
$272$		0			0
$273$	−229.797	+	552.586i	−0.841748	+	2.02412i
$274$		0			0
$275$	77.9589	−	135.029i	0.283487	−	0.491014i
$276$		0			0
$277$	−16.2685	−	28.1779i	−0.0587311	−	0.101725i	0.835165	−	0.550000i	$-0.185372\pi$
$277$	−16.2685	−	28.1779i	−0.0587311	−	0.101725i	−0.893896	+	0.448274i	$0.852039\pi$
$278$		0			0
$279$	3.33811	+	12.5993i	0.0119646	+	0.0451587i
$280$		0			0
$281$	−276.086	+	159.398i	−0.982512	+	0.567253i	−0.903028	−	0.429583i	$-0.858661\pi$
$281$	−276.086	+	159.398i	−0.982512	+	0.567253i	−0.0794842	+	0.996836i	$0.525327\pi$
$282$		0			0
$283$	260.782	−	451.688i	0.921491	−	1.59607i	0.124382	−	0.992234i	$-0.460305\pi$
$283$	260.782	−	451.688i	0.921491	−	1.59607i	0.797109	−	0.603835i	$-0.206361\pi$
$284$		0			0
$285$	−291.319	+	189.083i	−1.02217	+	0.663449i
$286$		0			0
$287$		−	436.926i		−	1.52239i
$288$		0			0
$289$	−188.818			−0.653349
$290$		0			0
$291$	140.916	−	18.3509i	0.484248	−	0.0630616i
$292$		0			0
$293$	391.936	+	226.284i	1.33766	+	0.772301i	0.986461	−	0.163999i	$-0.0524393\pi$
$293$	391.936	+	226.284i	1.33766	+	0.772301i	0.351203	+	0.936299i	$0.385773\pi$
$294$		0			0
$295$	329.593	−	190.291i	1.11726	−	0.645053i
$296$		0			0
$297$	212.518	−	274.559i	0.715549	−	0.924441i
$298$		0			0
$299$	719.021	−	415.127i	2.40475	−	1.38838i
$300$		0			0
$301$	−261.303	+	452.590i	−0.868116	+	1.50362i
$302$		0			0
$303$	22.2716	+	171.022i	0.0735035	+	0.564430i
$304$		0			0
$305$	196.207			0.643300
$306$		0			0
$307$			303.979i			0.990159i	0.868848	+	0.495080i	$0.164861\pi$
$307$			303.979i			0.990159i	−0.868848	+	0.495080i	$0.835139\pi$
$308$		0			0
$309$	293.495	+	383.603i	0.949823	+	1.24144i
$310$		0			0
$311$	52.7296	−	91.3304i	0.169549	−	0.293667i	−0.768713	−	0.639594i	$-0.779102\pi$
$311$	52.7296	−	91.3304i	0.169549	−	0.293667i	0.938261	+	0.345927i	$0.112436\pi$
$312$		0			0
$313$	49.3956	+	85.5556i	0.157813	+	0.273341i	0.934080	−	0.357064i	$-0.116222\pi$
$313$	49.3956	+	85.5556i	0.157813	+	0.273341i	−0.776267	+	0.630405i	$0.782889\pi$
$314$		0			0
$315$	−324.180	−	326.004i	−1.02914	−	1.03493i
$316$		0			0
$317$	404.563	−	233.574i	1.27622	−	0.736828i	0.300072	−	0.953917i	$-0.402989\pi$
$317$	404.563	−	233.574i	1.27622	−	0.736828i	0.976152	+	0.217089i	$0.0696561\pi$
$318$		0			0
$319$	−316.241	−	182.582i	−0.991350	−	0.572356i
$320$		0			0
$321$	129.582	−	311.603i	0.403684	−	0.970726i
$322$		0			0
$323$	189.604	+	14.7014i	0.587009	+	0.0455153i
$324$		0			0
$325$		−	288.503i		−	0.887702i
$326$		0			0
$327$	−194.223	+	467.041i	−0.593953	+	1.42826i
$328$		0			0
$329$	−158.062	+	273.772i	−0.480432	+	0.832133i
$330$		0			0
$331$	−414.398	+	239.253i	−1.25196	+	0.722819i	−0.971498	−	0.237047i	$-0.923821\pi$
$331$	−414.398	+	239.253i	−1.25196	+	0.722819i	−0.280461	+	0.959866i	$0.590487\pi$
$332$		0			0
$333$	−172.644	+	171.678i	−0.518449	+	0.515549i
$334$		0			0
$335$	−439.925	+	253.991i	−1.31321	+	0.758181i
$336$		0			0
$337$	−87.1391	−	50.3098i	−0.258573	−	0.149287i	0.365110	−	0.930964i	$-0.381031\pi$
$337$	−87.1391	−	50.3098i	−0.258573	−	0.149287i	−0.623683	+	0.781677i	$0.714365\pi$
$338$		0			0
$339$	−14.3583	−	18.7665i	−0.0423549	−	0.0553585i
$340$		0			0
$341$			18.6229i			0.0546127i
$342$		0			0
$343$	−232.317			−0.677308
$344$		0			0
$345$	82.3650	+	632.478i	0.238739	+	1.83327i
$346$		0			0
$347$	−2.53286	+	4.38705i	−0.00729932	+	0.0126428i	−0.869652	−	0.493665i	$-0.835657\pi$
$347$	−2.53286	+	4.38705i	−0.00729932	+	0.0126428i	0.862353	+	0.506308i	$0.168990\pi$
$348$		0			0
$349$	75.3208	+	130.459i	0.215819	+	0.373809i	0.953526	−	0.301312i	$-0.0974246\pi$
$349$	75.3208	+	130.459i	0.215819	+	0.373809i	−0.737707	+	0.675121i	$0.764091\pi$
$350$		0			0
$351$	86.5343	−	636.585i	0.246537	−	1.81363i
$352$		0			0
$353$	−7.95384	−	13.7764i	−0.0225321	−	0.0390268i	0.854539	−	0.519386i	$-0.173839\pi$
$353$	−7.95384	−	13.7764i	−0.0225321	−	0.0390268i	−0.877072	+	0.480360i	$0.840506\pi$
$354$		0			0
$355$	204.089	+	117.831i	0.574900	+	0.331918i
$356$		0			0
$357$	32.5095	+	249.639i	0.0910629	+	0.699268i
$358$		0			0
$359$	−217.516			−0.605895			−0.302948	−	0.953007i	$-0.597971\pi$
$359$	−217.516			−0.605895			−0.302948	+	0.953007i	$0.597971\pi$
$360$		0			0
$361$	356.685	+	55.6476i	0.988048	+	0.154149i
$362$		0			0
$363$	105.690	−	80.8637i	0.291157	−	0.222765i
$364$		0			0
$365$	5.92336	−	10.2596i	0.0162284	−	0.0281084i
$366$		0			0
$367$	194.382	+	336.679i	0.529650	+	0.917381i	0.999402	+	0.0345827i	$0.0110102\pi$
$367$	194.382	+	336.679i	0.529650	+	0.917381i	−0.469751	+	0.882799i	$0.655656\pi$
$368$		0			0
$369$	120.123	+	453.389i	0.325537	+	1.22870i
$370$		0			0
$371$	−474.127	+	273.737i	−1.27797	+	0.737837i
$372$		0			0
$373$	−124.180	−	71.6956i	−0.332923	−	0.192213i	0.324215	−	0.945983i	$-0.394900\pi$
$373$	−124.180	−	71.6956i	−0.332923	−	0.192213i	−0.657138	+	0.753770i	$0.728233\pi$
$374$		0			0
$375$	−217.302	−	90.3667i	−0.579472	−	0.240978i
$376$		0			0
$377$	−675.681			−1.79226
$378$		0			0
$379$		−	284.585i		−	0.750884i	−0.926846	−	0.375442i	$-0.877491\pi$
$379$		−	284.585i		−	0.750884i	0.926846	−	0.375442i	$-0.122509\pi$
$380$		0			0
$381$	−121.136	+	291.293i	−0.317943	+	0.764548i
$382$		0			0
$383$	436.653	+	252.102i	1.14009	+	0.658229i	0.946452	−	0.322844i	$-0.104639\pi$
$383$	436.653	+	252.102i	1.14009	+	0.658229i	0.193635	+	0.981074i	$0.437972\pi$
$384$		0			0
$385$	−328.446	−	568.886i	−0.853108	−	1.47763i
$386$		0			0
$387$	146.719	−	541.483i	0.379119	−	1.39918i
$388$		0			0
$389$	−69.0922	−	119.671i	−0.177615	−	0.307638i	0.763448	−	0.645869i	$-0.223505\pi$
$389$	−69.0922	−	119.671i	−0.177615	−	0.307638i	−0.941063	+	0.338231i	$0.890172\pi$
$390$		0			0
$391$	174.625	−	302.460i	0.446612	−	0.773555i
$392$		0			0
$393$	−65.8222	+	50.3607i	−0.167487	+	0.128144i
$394$		0			0
$395$		−	201.489i		−	0.510098i
$396$		0			0
$397$	−409.212			−1.03076			−0.515380	−	0.856962i	$-0.672349\pi$
$397$	−409.212			−1.03076			−0.515380	+	0.856962i	$0.672349\pi$
$398$		0			0
$399$	24.8934	+	477.235i	0.0623894	+	1.19608i
$400$		0			0
$401$	−113.047	−	65.2676i	−0.281912	−	0.162762i	0.352377	−	0.935858i	$-0.385374\pi$
$401$	−113.047	−	65.2676i	−0.281912	−	0.162762i	−0.634289	+	0.773096i	$0.718707\pi$
$402$		0			0
$403$	17.2295	+	29.8424i	0.0427531	+	0.0740506i
$404$		0			0
$405$	426.023	+	249.162i	1.05191	+	0.615214i
$406$		0			0
$407$	−301.268	+	173.937i	−0.740216	+	0.427364i
$408$		0			0
$409$	628.942	+	363.120i	1.53775	+	0.887823i	0.998970	+	0.0453796i	$0.0144497\pi$
$409$	628.942	+	363.120i	1.53775	+	0.887823i	0.538785	+	0.842443i	$0.318884\pi$
$410$		0			0
$411$	−56.4936	−	433.812i	−0.137454	−	1.05550i
$412$		0			0
$413$		−	523.675i		−	1.26798i
$414$		0			0
$415$	833.745			2.00902
$416$		0			0
$417$	369.792	−	282.928i	0.886790	−	0.678484i
$418$		0			0
$419$	209.510	−	362.882i	0.500023	−	0.866066i	−0.499977	−	0.866039i	$-0.666658\pi$
$419$	209.510	−	362.882i	0.500023	−	0.866066i	1.00000		2.69008e-5i	$-8.56279e-6\pi$
$420$		0			0
$421$	−422.074	+	243.685i	−1.00255	+	0.578824i	−0.909002	−	0.416791i	$-0.863155\pi$
$421$	−422.074	+	243.685i	−1.00255	+	0.578824i	−0.0935495	+	0.995615i	$0.529821\pi$
$422$		0			0
$423$	88.7503	−	327.543i	0.209812	−	0.774333i
$424$		0			0
$425$	−60.6802	−	105.101i	−0.142777	−	0.247297i
$426$		0			0
$427$	134.989	−	233.807i	0.316133	−	0.547558i
$428$		0			0
$429$	352.461	−	847.551i	0.821587	−	1.97564i
$430$		0			0
$431$			550.100i			1.27633i	0.769898	+	0.638167i	$0.220307\pi$
$431$			550.100i			1.27633i	−0.769898	+	0.638167i	$0.779693\pi$
$432$		0			0
$433$		−	788.599i		−	1.82125i	−0.413239	−	0.910623i	$-0.635602\pi$
$433$		−	788.599i		−	1.82125i	0.413239	−	0.910623i	$-0.364398\pi$
$434$		0			0
$435$	199.313	−	479.281i	0.458190	−	1.10180i
$436$		0			0
$437$	374.880	−	546.808i	0.857848	−	1.25128i
$438$		0			0
$439$	361.886	−	208.935i	0.824342	−	0.475934i	−0.0275695	−	0.999620i	$-0.508777\pi$
$439$	361.886	−	208.935i	0.824342	−	0.475934i	0.851911	+	0.523686i	$0.175443\pi$
$440$		0			0
$441$	−185.222	+	49.0736i	−0.420004	+	0.111278i
$442$		0			0
$443$	278.803	+	482.902i	0.629353	+	1.09007i	0.987682	+	0.156476i	$0.0500134\pi$
$443$	278.803	+	482.902i	0.629353	+	1.09007i	−0.358329	+	0.933595i	$0.616653\pi$
$444$		0			0
$445$	−449.441	−	259.485i	−1.00998	−	0.583112i
$446$		0			0
$447$	459.580	−	351.626i	1.02814	−	0.786634i
$448$		0			0
$449$			784.111i			1.74635i	0.487407	+	0.873175i	$0.337943\pi$
$449$			784.111i			1.74635i	−0.487407	+	0.873175i	$0.662057\pi$
$450$		0			0
$451$			670.153i			1.48593i
$452$		0			0
$453$	−451.222	+	58.7608i	−0.996074	+	0.129715i
$454$		0			0
$455$	−1052.64	−	607.742i	−2.31350	−	1.33570i
$456$		0			0
$457$	187.527	+	324.806i	0.410344	+	0.710736i	0.994927	−	0.100597i	$-0.0320754\pi$
$457$	187.527	+	324.806i	0.410344	+	0.710736i	−0.584583	+	0.811334i	$0.698742\pi$
$458$		0			0
$459$	−102.367	−	250.107i	−0.223022	−	0.544896i
$460$		0			0
$461$	18.7960	+	32.5556i	0.0407722	+	0.0706195i	0.885691	−	0.464274i	$-0.153685\pi$
$461$	18.7960	+	32.5556i	0.0407722	+	0.0706195i	−0.844919	+	0.534894i	$0.820352\pi$
$462$		0			0
$463$	186.365	−	322.793i	0.402516	−	0.697177i	−0.591513	−	0.806295i	$-0.701469\pi$
$463$	186.365	−	322.793i	0.402516	−	0.697177i	0.994029	+	0.109118i	$0.0348026\pi$
$464$		0			0
$465$	−26.2505	+	3.41849i	−0.0564527	+	0.00735160i
$466$		0			0
$467$	−328.337			−0.703077			−0.351538	−	0.936174i	$-0.614341\pi$
$467$	−328.337			−0.703077			−0.351538	+	0.936174i	$0.614341\pi$
$468$		0			0
$469$			698.976i			1.49035i
$470$		0			0
$471$	141.283	−	108.096i	0.299965	−	0.229503i
$472$		0			0
$473$	400.784	−	694.178i	0.847324	−	1.46761i
$474$		0			0
$475$	−99.4196	−	207.818i	−0.209304	−	0.437512i
$476$		0			0
$477$	416.734	−	414.403i	0.873656	−	0.868769i
$478$		0			0
$479$	103.750	+	179.701i	0.216598	+	0.375159i	0.953766	−	0.300551i	$-0.0971706\pi$
$479$	103.750	+	179.701i	0.216598	+	0.375159i	−0.737168	+	0.675710i	$0.763837\pi$
$480$		0			0
$481$	−321.845	+	557.452i	−0.669117	+	1.15894i
$482$		0			0
$483$	810.352	+	336.991i	1.67775	+	0.697704i
$484$		0			0
$485$			288.619i			0.595090i
$486$		0			0
$487$			741.944i			1.52350i	0.647871	+	0.761750i	$0.275659\pi$
$487$			741.944i			1.52350i	−0.647871	+	0.761750i	$0.724341\pi$
$488$		0			0
$489$	−434.777	−	180.805i	−0.889114	−	0.369745i
$490$		0			0
$491$	222.677	−	385.688i	0.453518	−	0.785516i	−0.545084	−	0.838382i	$-0.683502\pi$
$491$	222.677	−	385.688i	0.453518	−	0.785516i	0.998602	+	0.0528657i	$0.0168355\pi$
$492$		0			0
$493$	−246.150	+	142.115i	−0.499289	+	0.288265i
$494$		0			0
$495$	497.225	+	500.022i	1.00449	+	1.01015i
$496$		0			0
$497$	280.824	−	162.134i	0.565039	−	0.326225i
$498$		0			0
$499$	375.203	−	649.871i	0.751910	−	1.30235i	−0.194986	−	0.980806i	$-0.562466\pi$
$499$	375.203	−	649.871i	0.751910	−	1.30235i	0.946896	−	0.321541i	$-0.104201\pi$
$500$		0			0
$501$	129.999	+	169.911i	0.259479	+	0.339143i
$502$		0			0
$503$	430.516			0.855896			0.427948	−	0.903803i	$-0.359237\pi$
$503$	430.516			0.855896			0.427948	+	0.903803i	$0.359237\pi$
$504$		0			0
$505$	−350.281			−0.693626
$506$		0			0
$507$	−153.861	−	1181.50i	−0.303474	−	2.33037i
$508$		0			0
$509$	−8.58430	−	4.95615i	−0.0168650	−	0.00973703i	0.491544	−	0.870853i	$-0.336433\pi$
$509$	−8.58430	−	4.95615i	−0.0168650	−	0.00973703i	−0.508409	+	0.861116i	$0.669766\pi$
$510$		0			0
$511$	−8.15047	−	14.1170i	−0.0159500	−	0.0276263i
$512$		0			0
$513$	−157.037	−	488.373i	−0.306114	−	0.951995i
$514$		0			0
$515$	−849.556	+	490.491i	−1.64962	+	0.952410i
$516$		0			0
$517$	242.434	−	419.908i	0.468925	−	0.812202i
$518$		0			0
$519$	−467.079	+	60.8258i	−0.899959	+	0.117198i
$520$		0			0
$521$			326.056i			0.625828i	0.949782	+	0.312914i	$0.101305\pi$
$521$			326.056i			0.625828i	−0.949782	+	0.312914i	$0.898695\pi$
$522$		0			0
$523$			405.401i			0.775145i	0.921839	+	0.387573i	$0.126686\pi$
$523$			405.401i			0.775145i	−0.921839	+	0.387573i	$0.873314\pi$
$524$		0			0
$525$	242.206	−	185.312i	0.461344	−	0.352975i
$526$		0			0
$527$	12.5534	+	7.24769i	0.0238204	+	0.0137527i
$528$		0			0
$529$	−344.272	−	596.296i	−0.650798	−	1.12721i
$530$		0			0
$531$	143.973	+	543.407i	0.271136	+	1.02336i
$532$		0			0
$533$	620.010	+	1073.89i	1.16325	+	2.01480i
$534$		0			0
$535$	593.583	+	342.705i	1.10950	+	0.640571i
$536$		0			0
$537$	212.989	−	512.168i	0.396627	−	0.953757i
$538$		0			0
$539$	−273.776			−0.507932
$540$		0			0
$541$	794.987			1.46948			0.734739	−	0.678350i	$-0.237305\pi$
$541$	794.987			1.46948			0.734739	+	0.678350i	$0.237305\pi$
$542$		0			0
$543$	−349.139	+	839.564i	−0.642982	+	1.54616i
$544$		0			0
$545$	−889.683	−	513.659i	−1.63245	−	0.942494i
$546$		0			0
$547$	435.407	−	251.382i	0.795990	−	0.459565i	−0.0460770	−	0.998938i	$-0.514672\pi$
$547$	435.407	−	251.382i	0.795990	−	0.459565i	0.842067	+	0.539373i	$0.181339\pi$
$548$		0			0
$549$	−75.7949	+	279.729i	−0.138060	+	0.509525i
$550$		0			0
$551$	−486.716	+	232.843i	−0.883331	+	0.422583i
$552$		0			0
$553$	−240.102	−	138.623i	−0.434181	−	0.250674i
$554$		0			0
$555$	−300.480	−	392.732i	−0.541405	−	0.707625i
$556$		0			0
$557$	−1.18236			−0.00212272			−0.00106136	−	0.999999i	$-0.500338\pi$
$557$	−1.18236			−0.00212272			−0.00106136	+	0.999999i	$0.500338\pi$
$558$		0			0
$559$		−	1483.19i		−	2.65328i
$560$		0			0
$561$	−49.8627	−	382.894i	−0.0888818	−	0.682520i
$562$		0			0
$563$	−303.674	−	175.327i	−0.539386	−	0.311415i	0.205444	−	0.978669i	$-0.434136\pi$
$563$	−303.674	−	175.327i	−0.539386	−	0.311415i	−0.744830	+	0.667254i	$0.767470\pi$
$564$		0			0
$565$	41.5617	−	23.9957i	0.0735606	−	0.0424702i
$566$		0			0
$567$	590.012	−	336.244i	1.04059	−	0.593024i
$568$		0			0
$569$	702.831	−	405.780i	1.23520	−	0.713146i	0.267094	−	0.963670i	$-0.413936\pi$
$569$	702.831	−	405.780i	1.23520	−	0.713146i	0.968110	+	0.250525i	$0.0806031\pi$
$570$		0			0
$571$	−322.924	+	559.320i	−0.565540	+	0.979545i	0.431459	+	0.902133i	$0.357999\pi$
$571$	−322.924	+	559.320i	−0.565540	+	0.979545i	−0.996999	+	0.0774119i	$0.975334\pi$
$572$		0			0
$573$	−10.0551	−	77.2128i	−0.0175482	−	0.134752i
$574$		0			0
$575$	−423.082			−0.735795
$576$		0			0
$577$	−856.580			−1.48454			−0.742271	−	0.670100i	$-0.766251\pi$
$577$	−856.580			−1.48454			−0.742271	+	0.670100i	$0.766251\pi$
$578$		0			0
$579$	428.547	+	560.118i	0.740150	+	0.967389i
$580$		0			0
$581$	573.611	−	993.523i	0.987282	−	1.71002i
$582$		0			0
$583$	727.212	−	419.856i	1.24736	−	0.720165i
$584$		0			0
$585$	1259.39	+	341.241i	2.15280	+	0.583318i
$586$		0			0
$587$	13.9326	+	24.1320i	0.0237353	+	0.0411108i	0.877649	−	0.479304i	$-0.159111\pi$
$587$	13.9326	+	24.1320i	0.0237353	+	0.0411108i	−0.853914	+	0.520415i	$0.825777\pi$
$588$		0			0
$589$	22.6948	+	15.5591i	0.0385311	+	0.0264161i
$590$		0			0
$591$	−26.7899	−	11.1408i	−0.0453298	−	0.0188508i
$592$		0			0
$593$	−530.272			−0.894220			−0.447110	−	0.894479i	$-0.647547\pi$
$593$	−530.272			−0.894220			−0.447110	+	0.894479i	$0.647547\pi$
$594$		0			0
$595$	−511.300			−0.859328
$596$		0			0
$597$	797.565	+	331.674i	1.33596	+	0.555567i
$598$		0			0
$599$	−781.680	−	451.303i	−1.30498	−	0.753428i	−0.323723	−	0.946152i	$-0.604934\pi$
$599$	−781.680	−	451.303i	−1.30498	−	0.753428i	−0.981253	+	0.192724i	$0.938268\pi$
$600$		0			0
$601$	−559.200	+	322.854i	−0.930450	+	0.537195i	−0.886954	−	0.461858i	$-0.847183\pi$
$601$	−559.200	+	322.854i	−0.930450	+	0.537195i	−0.0434961	+	0.999054i	$0.513850\pi$
$602$		0			0
$603$	−192.168	−	725.313i	−0.318687	−	1.20284i
$604$		0			0
$605$	135.140	+	234.069i	0.223372	+	0.386891i
$606$		0			0
$607$	726.323	+	419.343i	1.19658	+	0.690845i	0.959791	−	0.280716i	$-0.0905720\pi$
$607$	726.323	+	419.343i	1.19658	+	0.690845i	0.236788	+	0.971561i	$0.423905\pi$
$608$		0			0
$609$	−434.005	−	567.251i	−0.712651	−	0.931447i
$610$		0			0
$611$		−	897.179i		−	1.46838i
$612$		0			0
$613$	691.048			1.12732			0.563661	−	0.826006i	$-0.309393\pi$
$613$	691.048			1.12732			0.563661	+	0.826006i	$0.309393\pi$
$614$		0			0
$615$	−944.633	+	123.016i	−1.53599	+	0.200026i
$616$		0			0
$617$	−49.1637	+	85.1540i	−0.0796819	+	0.138013i	−0.903113	−	0.429404i	$-0.858724\pi$
$617$	−49.1637	+	85.1540i	−0.0796819	+	0.138013i	0.823431	+	0.567417i	$0.192057\pi$
$618$		0			0
$619$	179.166	+	310.325i	0.289445	+	0.501333i	0.973677	−	0.227931i	$-0.0731960\pi$
$619$	179.166	+	310.325i	0.289445	+	0.501333i	−0.684232	+	0.729264i	$0.739863\pi$
$620$		0			0
$621$	−933.534	−	126.900i	−1.50328	−	0.204348i
$622$		0			0
$623$	−618.425	+	357.048i	−0.992657	+	0.573111i
$624$		0			0
$625$	390.555	−	676.461i	0.624888	−	1.08234i
$626$		0			0
$627$	−38.1812	−	731.979i	−0.0608950	−	1.16743i
$628$		0			0
$629$			270.772i			0.430480i
$630$		0			0
$631$	−1052.56			−1.66808			−0.834042	−	0.551700i	$-0.813979\pi$
$631$	−1052.56			−1.66808			−0.834042	+	0.551700i	$0.813979\pi$
$632$		0			0
$633$	−123.193	−	161.015i	−0.194617	−	0.254368i
$634$		0			0
$635$	−554.894	−	320.368i	−0.873849	−	0.504517i
$636$		0			0
$637$	−438.713	+	253.291i	−0.688717	+	0.397631i
$638$		0			0
$639$	−246.830	+	245.450i	−0.386276	+	0.384115i
$640$		0			0
$641$	680.385	−	392.820i	1.06144	−	0.612824i	0.135612	−	0.990762i	$-0.456700\pi$
$641$	680.385	−	392.820i	1.06144	−	0.612824i	0.925831	+	0.377938i	$0.123367\pi$
$642$		0			0
$643$	−202.842	+	351.333i	−0.315463	+	0.546397i	−0.979536	−	0.201270i	$-0.935493\pi$
$643$	−202.842	+	351.333i	−0.315463	+	0.546397i	0.664073	+	0.747668i	$0.268826\pi$
$644$		0			0
$645$	1052.07	+	437.511i	1.63111	+	0.678311i
$646$		0			0
$647$	−885.395			−1.36846			−0.684231	−	0.729265i	$-0.739862\pi$
$647$	−885.395			−1.36846			−0.684231	+	0.729265i	$0.739862\pi$
$648$		0			0
$649$			803.208i			1.23761i
$650$		0			0
$651$	−13.9865	+	33.6330i	−0.0214847	+	0.0516636i
$652$		0			0
$653$	−257.356	+	445.753i	−0.394113	+	0.682624i	−0.992988	−	0.118219i	$-0.962282\pi$
$653$	−257.356	+	445.753i	−0.394113	+	0.682624i	0.598874	+	0.800843i	$0.295615\pi$
$654$		0			0
$655$	−84.1630	−	145.775i	−0.128493	−	0.222557i
$656$		0			0
$657$	12.3387	+	12.4082i	0.0187804	+	0.0188861i
$658$		0			0
$659$	301.373	−	173.998i	0.457318	−	0.264033i	−0.253598	−	0.967310i	$-0.581614\pi$
$659$	301.373	−	173.998i	0.457318	−	0.264033i	0.710916	+	0.703277i	$0.248281\pi$
$660$		0			0
$661$	−781.658	−	451.290i	−1.18254	−	0.682739i	−0.225938	−	0.974142i	$-0.572545\pi$
$661$	−781.658	−	451.290i	−1.18254	−	0.682739i	−0.956600	+	0.291403i	$0.905878\pi$
$662$		0			0
$663$	−434.147	−	567.438i	−0.654822	−	0.855864i
$664$		0			0
$665$	−967.682	−	75.0318i	−1.45516	−	0.112830i
$666$		0			0
$667$			990.868i			1.48556i
$668$		0			0
$669$	1083.66	−	141.121i	1.61983	−	0.210943i
$670$		0			0
$671$	−207.045	+	358.612i	−0.308561	+	0.534444i
$672$		0			0
$673$	−20.6579	+	11.9268i	−0.0306952	+	0.0177219i	−0.515269	−	0.857028i	$-0.672308\pi$
$673$	−20.6579	+	11.9268i	−0.0306952	+	0.0177219i	0.484574	+	0.874750i	$0.338975\pi$
$674$		0			0
$675$	−200.384	+	258.883i	−0.296866	+	0.383531i
$676$		0			0
$677$	−773.099	+	446.349i	−1.14195	+	0.659304i	−0.946912	−	0.321492i	$-0.895816\pi$
$677$	−773.099	+	446.349i	−1.14195	+	0.659304i	−0.195036	+	0.980796i	$0.562482\pi$
$678$		0			0
$679$	343.929	+	198.568i	0.506523	+	0.292441i
$680$		0			0
$681$	−718.624	+	93.5836i	−1.05525	+	0.137421i
$682$		0			0
$683$			216.685i			0.317254i	0.987339	+	0.158627i	$0.0507068\pi$
$683$			216.685i			0.317254i	−0.987339	+	0.158627i	$0.949293\pi$
$684$		0			0
$685$	888.516			1.29710
$686$		0			0
$687$	−225.277	+	172.360i	−0.327915	+	0.250888i
$688$		0			0
$689$	776.882	−	1345.60i	1.12755	−	1.95297i
$690$		0			0
$691$	468.139	+	810.841i	0.677481	+	1.17343i	0.975737	+	0.218946i	$0.0702617\pi$
$691$	468.139	+	810.841i	0.677481	+	1.17343i	−0.298256	+	0.954486i	$0.596405\pi$
$692$		0			0
$693$	937.934	−	248.501i	1.35344	−	0.358587i
$694$		0			0
$695$	472.831	+	818.967i	0.680332	+	1.17837i
$696$		0			0
$697$	451.737	+	260.811i	0.648116	+	0.374190i
$698$		0			0
$699$	−945.640	−	393.252i	−1.35285	−	0.562592i
$700$		0			0
$701$	−1083.51			−1.54566			−0.772832	−	0.634610i	$-0.781161\pi$
$701$	−1083.51			−1.54566			−0.772832	+	0.634610i	$0.781161\pi$
$702$		0			0
$703$	−39.7350	+	512.461i	−0.0565220	+	0.728962i
$704$		0			0
$705$	636.396	+	264.650i	0.902689	+	0.375390i
$706$		0			0
$707$	−240.991	+	417.409i	−0.340864	+	0.590394i
$708$		0			0
$709$	−135.783	−	235.182i	−0.191513	−	0.331710i	0.754239	−	0.656600i	$-0.228006\pi$
$709$	−135.783	−	235.182i	−0.191513	−	0.331710i	−0.945752	+	0.324890i	$0.894673\pi$
$710$		0			0
$711$	287.260	+	77.8354i	0.404023	+	0.109473i
$712$		0			0
$713$	43.7630	−	25.2666i	0.0613787	−	0.0354370i
$714$		0			0
$715$	1614.53	+	932.149i	2.25808	+	1.30371i
$716$		0			0
$717$	−107.132	+	81.9666i	−0.149417	+	0.114319i
$718$		0			0
$719$	1128.40			1.56941			0.784703	−	0.619872i	$-0.212815\pi$
$719$	1128.40			1.56941			0.784703	+	0.619872i	$0.212815\pi$
$720$		0			0
$721$			1349.82i			1.87215i
$722$		0			0
$723$	386.908	−	50.3855i	0.535143	−	0.0696895i
$724$		0			0
$725$	298.185	+	172.157i	0.411290	+	0.237458i
$726$		0			0
$727$	687.571	+	1190.91i	0.945765	+	1.63811i	0.754212	+	0.656631i	$0.228019\pi$
$727$	687.571	+	1190.91i	0.945765	+	1.63811i	0.191553	+	0.981482i	$0.438647\pi$
$728$		0			0
$729$	−519.800	+	511.125i	−0.713032	+	0.701132i
$730$		0			0
$731$	−311.955	−	540.322i	−0.426751	−	0.739154i
$732$		0			0
$733$	−74.6985	+	129.382i	−0.101908	+	0.176510i	−0.912471	−	0.409142i	$-0.865828\pi$
$733$	−74.6985	+	129.382i	−0.101908	+	0.176510i	0.810563	+	0.585652i	$0.199161\pi$
$734$		0			0
$735$	−50.2552	−	385.908i	−0.0683745	−	0.525045i
$736$		0			0
$737$		−	1072.08i		−	1.45466i
$738$		0			0
$739$	−25.5378			−0.0345573			−0.0172786	−	0.999851i	$-0.505500\pi$
$739$	−25.5378			−0.0345573			−0.0172786	+	0.999851i	$0.505500\pi$
$740$		0			0
$741$	−738.394	−	1137.64i	−0.996483	−	1.53527i
$742$		0			0
$743$	−293.904	−	169.685i	−0.395563	−	0.228379i	0.289004	−	0.957328i	$-0.406676\pi$
$743$	−293.904	−	169.685i	−0.395563	−	0.228379i	−0.684568	+	0.728949i	$0.740009\pi$
$744$		0			0
$745$	587.639	+	1017.82i	0.788777	+	1.36620i
$746$		0			0
$747$	−322.077	+	1188.66i	−0.431160	+	1.59125i
$748$		0			0
$749$	816.763	−	471.558i	1.09047	−	0.629584i
$750$		0			0
$751$	−134.854	−	77.8583i	−0.179567	−	0.103673i	0.407522	−	0.913195i	$-0.366393\pi$
$751$	−134.854	−	77.8583i	−0.179567	−	0.103673i	−0.587089	+	0.809522i	$0.699726\pi$
$752$		0			0
$753$	461.465	+	191.904i	0.612836	+	0.254852i
$754$		0			0
$755$		−	924.174i		−	1.22407i
$756$		0			0
$757$	−61.9788			−0.0818742			−0.0409371	−	0.999162i	$-0.513034\pi$
$757$	−61.9788			−0.0818742			−0.0409371	+	0.999162i	$0.513034\pi$
$758$		0			0
$759$	−1242.91	−	516.874i	−1.63756	−	0.680993i
$760$		0			0
$761$	−659.196	+	1141.76i	−0.866223	+	1.50034i	−0.000395849		1.00000i	$0.500126\pi$
$761$	−659.196	+	1141.76i	−0.866223	+	1.50034i	−0.865827	+	0.500343i	$0.833207\pi$
$762$		0			0
$763$	−1224.19	+	706.788i	−1.60445	+	0.926328i
$764$		0			0
$765$	530.566	−	140.571i	0.693550	−	0.183753i
$766$		0			0
$767$	743.109	+	1287.10i	0.968852	+	1.67810i
$768$		0			0
$769$	388.828	−	673.470i	0.505628	−	0.875774i	−0.494350	−	0.869263i	$-0.664594\pi$
$769$	388.828	−	673.470i	0.505628	−	0.875774i	0.999979	−	0.00651144i	$-0.00207267\pi$
$770$		0			0
$771$	454.079	+	593.489i	0.588949	+	0.769766i
$772$		0			0
$773$		−	1335.38i		−	1.72752i	−0.503900	−	0.863762i	$-0.668102\pi$
$773$		−	1335.38i		−	1.72752i	0.503900	−	0.863762i	$-0.331898\pi$
$774$		0			0
$775$		−	17.5597i		−	0.0226577i
$776$		0			0
$777$	−674.723	+	87.8665i	−0.868369	+	0.113084i
$778$		0			0
$779$	816.681	+	559.899i	1.04837	+	0.718741i
$780$		0			0
$781$	−430.726	+	248.680i	−0.551505	+	0.318412i
$782$		0			0
$783$	606.311	+	469.305i	0.774344	+	0.599368i
$784$		0			0
$785$	180.651	+	312.896i	0.230128	+	0.398594i
$786$		0			0
$787$	−1001.12	−	577.996i	−1.27207	−	0.734430i	−0.296693	−	0.954973i	$-0.595884\pi$
$787$	−1001.12	−	577.996i	−1.27207	−	0.734430i	−0.975377	+	0.220543i	$0.929217\pi$
$788$		0			0
$789$	12.1466	+	93.2730i	0.0153949	+	0.118217i
$790$		0			0
$791$		−	66.0355i		−	0.0834835i
$792$		0			0
$793$			766.212i			0.966219i
$794$		0			0
$795$	725.309	+	947.992i	0.912339	+	1.19244i
$796$		0			0
$797$	73.0294	+	42.1635i	0.0916303	+	0.0529028i	0.545115	−	0.838361i	$-0.316486\pi$
$797$	73.0294	+	42.1635i	0.0916303	+	0.0529028i	−0.453485	+	0.891264i	$0.649819\pi$
$798$		0			0
$799$	−188.701	−	326.841i	−0.236172	−	0.409062i
$800$		0			0
$801$	543.565	−	540.524i	0.678608	−	0.674811i
$802$		0			0
$803$	12.5011	+	21.6526i	0.0155680	+	0.0269646i
$804$		0			0
$805$	−891.237	+	1543.67i	−1.10713	+	1.91760i
$806$		0			0
$807$	−315.544	+	758.780i	−0.391009	+	0.940247i
$808$		0			0
$809$	−1091.41			−1.34908			−0.674540	−	0.738238i	$-0.735658\pi$
$809$	−1091.41			−1.34908			−0.674540	+	0.738238i	$0.735658\pi$
$810$		0			0
$811$			879.672i			1.08468i	0.840160	+	0.542338i	$0.182461\pi$
$811$			879.672i			1.08468i	−0.840160	+	0.542338i	$0.817539\pi$
$812$		0			0
$813$	1098.52	+	456.828i	1.35119	+	0.561904i
$814$		0			0
$815$	478.174	−	828.221i	0.586716	−	1.01622i
$816$		0			0
$817$	−511.113	−	1068.39i	−0.625597	−	1.30770i
$818$		0			0
$819$	1273.09	−	1265.97i	1.55444	−	1.54575i
$820$		0			0
$821$	314.534	+	544.790i	0.383111	+	0.663568i	0.991505	−	0.130067i	$-0.0415192\pi$
$821$	314.534	+	544.790i	0.383111	+	0.663568i	−0.608394	+	0.793635i	$0.708186\pi$
$822$		0			0
$823$	−151.110	+	261.730i	−0.183608	+	0.318019i	−0.943107	−	0.332490i	$-0.892111\pi$
$823$	−151.110	+	261.730i	−0.183608	+	0.318019i	0.759498	+	0.650509i	$0.225445\pi$
$824$		0			0
$825$	−371.493	+	284.230i	−0.450294	+	0.344521i
$826$		0			0
$827$			1572.93i			1.90197i	0.309235	+	0.950986i	$0.399927\pi$
$827$			1572.93i			1.90197i	−0.309235	+	0.950986i	$0.600073\pi$
$828$		0			0
$829$		−	448.299i		−	0.540771i	−0.962752	−	0.270385i	$-0.912849\pi$
$829$		−	448.299i		−	0.540771i	0.962752	−	0.270385i	$-0.0871511\pi$
$830$		0			0
$831$	12.6051	+	96.7938i	0.0151685	+	0.116479i
$832$		0			0
$833$	−106.548	+	184.547i	−0.127909	+	0.221545i
$834$		0			0
$835$	−376.296	+	217.255i	−0.450654	+	0.260185i
$836$		0			0
$837$	5.26689	−	38.7456i	0.00629258	−	0.0462910i
$838$		0			0
$839$	−278.227	+	160.635i	−0.331618	+	0.191460i	−0.656559	−	0.754275i	$-0.727989\pi$
$839$	−278.227	+	160.635i	−0.331618	+	0.191460i	0.324941	+	0.945734i	$0.394655\pi$
$840$		0			0
$841$	−17.3034	+	29.9704i	−0.0205748	+	0.0356366i
$842$		0			0
$843$	948.381	−	123.504i	1.12501	−	0.146505i
$844$		0			0
$845$	2419.89			2.86378
$846$		0			0
$847$	371.901			0.439081
$848$		0			0
$849$	−1242.69	+	950.782i	−1.46371	+	1.11988i
$850$		0			0
$851$	817.488	+	471.977i	0.960620	+	0.554614i
$852$		0			0
$853$	−491.614	−	851.500i	−0.576335	−	0.998242i	−0.995895	−	0.0905140i	$-0.971149\pi$
$853$	−491.614	−	851.500i	−0.576335	−	0.998242i	0.419560	−	0.907728i	$-0.362184\pi$
$854$		0			0
$855$	1024.77	−	188.184i	1.19856	−	0.220098i
$856$		0			0
$857$	−1207.97	+	697.420i	−1.40953	+	0.813792i	−0.995343	−	0.0964005i	$-0.969267\pi$
$857$	−1207.97	+	697.420i	−1.40953	+	0.813792i	−0.414186	+	0.910192i	$0.635934\pi$
$858$		0			0
$859$	−605.715	+	1049.13i	−0.705139	+	1.22134i	0.261502	+	0.965203i	$0.415782\pi$
$859$	−605.715	+	1049.13i	−0.705139	+	1.22134i	−0.966641	+	0.256134i	$0.917551\pi$
$860$		0			0
$861$	−503.311	+	1210.30i	−0.584565	+	1.40569i
$862$		0			0
$863$			850.382i			0.985379i	0.870205	+	0.492689i	$0.163986\pi$
$863$			850.382i			0.985379i	−0.870205	+	0.492689i	$0.836014\pi$
$864$		0			0
$865$		−	956.652i		−	1.10596i
$866$		0			0
$867$	523.031	+	217.506i	0.603265	+	0.250872i
$868$		0			0
$869$	368.266	+	212.619i	0.423782	+	0.244670i
$870$		0			0
$871$	−991.866	−	1717.96i	−1.13877	−	1.97240i
$872$		0			0
$873$	−411.480	−	111.494i	−0.471341	−	0.127713i
$874$		0			0
$875$	−328.850	−	569.585i	−0.375828	−	0.650954i
$876$		0			0
$877$	170.794	+	98.6077i	0.194748	+	0.112438i	0.594203	−	0.804315i	$-0.297468\pi$
$877$	170.794	+	98.6077i	0.194748	+	0.112438i	−0.399456	+	0.916753i	$0.630801\pi$
$878$		0			0
$879$	−825.007	−	1078.30i	−0.938574	−	1.22673i
$880$		0			0
$881$	−1326.04			−1.50515			−0.752576	−	0.658505i	$-0.771189\pi$
$881$	−1326.04			−1.50515			−0.752576	+	0.658505i	$0.771189\pi$
$882$		0			0
$883$	691.535			0.783165			0.391583	−	0.920143i	$-0.371928\pi$
$883$	691.535			0.783165			0.391583	+	0.920143i	$0.371928\pi$
$884$		0			0
$885$	−1132.18	+	147.440i	−1.27930	+	0.166599i
$886$		0			0
$887$	644.397	+	372.043i	0.726490	+	0.419439i	0.817137	−	0.576444i	$-0.195560\pi$
$887$	644.397	+	372.043i	0.726490	+	0.419439i	−0.0906467	+	0.995883i	$0.528893\pi$
$888$		0			0
$889$	−763.527	+	440.822i	−0.858860	+	0.495863i
$890$		0			0
$891$	−904.955	+	515.729i	−1.01566	+	0.578820i
$892$		0			0
$893$	−309.172	−	646.267i	−0.346217	−	0.723704i
$894$		0			0
$895$	975.646	+	563.289i	1.09011	+	0.629374i
$896$		0			0
$897$	−2469.91	+	321.646i	−2.75352	+	0.358580i
$898$		0			0
$899$	−41.1252			−0.0457455
$900$		0			0
$901$		−	653.599i		−	0.725415i
$902$		0			0
$903$	1245.17	−	952.682i	1.37893	−	1.05502i
$904$		0			0
$905$	−1599.31	−	923.365i	−1.76720	−	1.02029i
$906$		0			0
$907$	−7.44423	+	4.29793i	−0.00820753	+	0.00473862i	−0.504098	−	0.863646i	$-0.668175\pi$
$907$	−7.44423	+	4.29793i	−0.00820753	+	0.00473862i	0.495891	+	0.868385i	$0.334842\pi$
$908$		0			0
$909$	135.314	−	499.392i	0.148860	−	0.549386i
$910$		0			0
$911$	−234.138	+	135.180i	−0.257012	+	0.148386i	−0.622971	−	0.782245i	$-0.714074\pi$
$911$	−234.138	+	135.180i	−0.257012	+	0.148386i	0.365959	+	0.930631i	$0.380741\pi$
$912$		0			0
$913$	−879.799	+	1523.86i	−0.963635	+	1.66907i
$914$		0			0
$915$	−543.497	−	226.017i	−0.593986	−	0.247014i
$916$		0			0
$917$	−231.614			−0.252578
$918$		0			0
$919$	1201.48			1.30737			0.653687	−	0.756765i	$-0.273221\pi$
$919$	1201.48			1.30737			0.653687	+	0.756765i	$0.273221\pi$
$920$		0			0
$921$	350.164	−	842.029i	0.380200	−	0.914256i
$922$		0			0
$923$	−460.145	+	796.995i	−0.498532	+	0.863483i
$924$		0			0
$925$	284.067	−	164.006i	0.307100	−	0.177304i
$926$		0			0
$927$	−371.103	−	1400.68i	−0.400327	−	1.51098i
$928$		0			0
$929$	168.333	+	291.561i	0.181198	+	0.313844i	0.942289	−	0.334801i	$-0.108669\pi$
$929$	168.333	+	291.561i	0.181198	+	0.313844i	−0.761091	+	0.648646i	$0.775336\pi$
$930$		0			0
$931$	−228.734	+	333.636i	−0.245686	+	0.358363i
$932$		0			0
$933$	−251.269	+	192.246i	−0.269313	+	0.206052i
$934$		0			0
$935$	784.227			0.838746
$936$		0			0
$937$	−1755.22			−1.87324			−0.936618	−	0.350351i	$-0.886062\pi$
$937$	−1755.22			−1.87324			−0.936618	+	0.350351i	$0.886062\pi$
$938$		0			0
$939$	−38.2724	−	293.892i	−0.0407586	−	0.312984i
$940$		0			0
$941$	−502.403	−	290.062i	−0.533903	−	0.308249i	0.208701	−	0.977979i	$-0.433076\pi$
$941$	−502.403	−	290.062i	−0.533903	−	0.308249i	−0.742604	+	0.669730i	$0.766410\pi$
$942$		0			0
$943$	1574.83	−	909.227i	1.67002	−	0.964186i
$944$		0			0
$945$	522.452	+	1276.48i	0.552859	+	1.35077i
$946$		0			0
$947$	−309.292	−	535.710i	−0.326602	−	0.565691i	0.655233	−	0.755427i	$-0.272570\pi$
$947$	−309.292	−	535.710i	−0.326602	−	0.565691i	−0.981835	+	0.189735i	$0.939237\pi$
$948$		0			0
$949$	40.0649	+	23.1315i	0.0422180	+	0.0243746i
$950$		0			0
$951$	−1389.71	+	180.977i	−1.46132	+	0.190301i
$952$		0			0
$953$		−	263.216i		−	0.276197i	−0.990419	−	0.138098i	$-0.955901\pi$
$953$		−	263.216i		−	0.276197i	0.990419	−	0.138098i	$-0.0440990\pi$
$954$		0			0
$955$	158.144			0.165596
$956$		0			0
$957$	665.672	+	870.045i	0.695582	+	0.909138i
$958$		0			0
$959$	611.293	−	1058.79i	0.637428	−	1.10406i
$960$		0			0
$961$	−479.451	−	830.434i	−0.498909	−	0.864135i
$962$		0			0
$963$	−717.893	+	713.877i	−0.745476	+	0.741306i
$964$		0			0
$965$	−1240.48	+	716.190i	−1.28547	+	0.742166i
$966$		0			0
$967$	177.096	−	306.740i	0.183140	−	0.317208i	−0.759808	−	0.650147i	$-0.774707\pi$
$967$	177.096	−	306.740i	0.183140	−	0.317208i	0.942948	+	0.332939i	$0.108040\pi$
$968$		0			0
$969$	−508.272	−	259.135i	−0.524533	−	0.267425i
$970$		0			0
$971$		−	621.484i		−	0.640045i	−0.947410	−	0.320023i	$-0.896309\pi$
$971$		−	621.484i		−	0.640045i	0.947410	−	0.320023i	$-0.103691\pi$
$972$		0			0
$973$	1301.22			1.33733
$974$		0			0
$975$	−332.337	+	799.161i	−0.340859	+	0.819653i
$976$		0			0
$977$	−823.689	−	475.557i	−0.843079	−	0.486752i	0.0152304	−	0.999884i	$-0.495152\pi$
$977$	−823.689	−	475.557i	−0.843079	−	0.486752i	−0.858310	+	0.513132i	$0.828485\pi$
$978$		0			0
$979$	948.535	−	547.637i	0.968882	−	0.559384i
$980$		0			0
$981$	1076.00	−	1069.98i	1.09684	−	1.09071i
$982$		0			0
$983$	−898.969	+	519.020i	−0.914516	+	0.527996i	−0.881881	−	0.471471i	$-0.843723\pi$
$983$	−898.969	+	519.020i	−0.914516	+	0.527996i	−0.0326344	+	0.999467i	$0.510390\pi$
$984$		0			0
$985$	29.4640	−	51.0331i	0.0299126	−	0.0518102i
$986$		0			0
$987$	753.204	−	576.277i	0.763124	−	0.583867i
$988$		0			0
$989$	−2175.05			−2.19924
$990$		0			0
$991$		−	459.127i		−	0.463297i	−0.972800	−	0.231648i	$-0.925588\pi$
$991$		−	459.127i		−	0.463297i	0.972800	−	0.231648i	$-0.0744119\pi$
$992$		0			0
$993$	1423.50	−	185.376i	1.43353	−	0.186683i
$994$		0			0
$995$	−877.174	+	1519.31i	−0.881582	+	1.52694i
$996$		0			0
$997$	−540.716	−	936.547i	−0.542343	−	0.939365i	−0.998769	−	0.0496038i	$-0.984204\pi$
$997$	−540.716	−	936.547i	−0.542343	−	0.939365i	0.456426	−	0.889761i	$-0.349129\pi$
$998$		0			0
$999$	675.989	−	276.678i	0.676666	−	0.276955i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	684.3.t.a.265.7	✓	80
3.2	odd	2		2052.3.t.a.37.9		80
9.2	odd	6		2052.3.t.a.721.10		80
9.7	even	3	inner	684.3.t.a.493.34	yes	80
19.18	odd	2	inner	684.3.t.a.265.34	yes	80
57.56	even	2		2052.3.t.a.37.10		80
171.56	even	6		2052.3.t.a.721.9		80
171.151	odd	6	inner	684.3.t.a.493.7	yes	80

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
684.3.t.a.265.7	✓	80	1.1	even	1	trivial
684.3.t.a.265.34	yes	80	19.18	odd	2	inner
684.3.t.a.493.7	yes	80	171.151	odd	6	inner
684.3.t.a.493.34	yes	80	9.7	even	3	inner
2052.3.t.a.37.9		80	3.2	odd	2
2052.3.t.a.37.10		80	57.56	even	2
2052.3.t.a.721.9		80	171.56	even	6
2052.3.t.a.721.10		80	9.2	odd	6

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 684 = 2^{2} \cdot 3^{2} \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	684.t (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-2.77003 - 1.15194i) q^{3} +(3.04651 - 5.27672i) q^{5} +(-4.19196 - 7.26070i) q^{7} +(6.34609 + 6.38179i) q^{9} +O(q^{10})\)	\(q+(-2.77003 - 1.15194i) q^{3} +(3.04651 - 5.27672i) q^{5} +(-4.19196 - 7.26070i) q^{7} +(6.34609 + 6.38179i) q^{9} +(6.42960 + 11.1364i) q^{11} +(20.6063 + 11.8970i) q^{13} +(-14.5174 + 11.1073i) q^{15} +10.0091 q^{17} +(18.9431 + 1.46881i) q^{19} +(3.24799 + 24.9412i) q^{21} +(17.4467 - 30.2185i) q^{23} +(-6.06251 - 10.5006i) q^{25} +(-10.2274 - 24.9880i) q^{27} +(-24.5926 + 14.1985i) q^{29} +(1.25420 + 0.724110i) q^{31} +(-4.98174 - 38.2546i) q^{33} -51.0835 q^{35} +27.0526i q^{37} +(-43.3753 - 56.6922i) q^{39} +(45.1326 + 26.0573i) q^{41} +(-31.1671 - 53.9831i) q^{43} +(53.0083 - 14.0443i) q^{45} +(-18.8530 - 32.6543i) q^{47} +(-10.6451 + 18.4379i) q^{49} +(-27.7255 - 11.5298i) q^{51} -65.3005i q^{53} +78.3514 q^{55} +(-50.7810 - 25.8899i) q^{57} +(54.0935 + 31.2309i) q^{59} +(16.1009 + 27.8876i) q^{61} +(19.7336 - 72.8292i) q^{63} +(125.555 - 72.4890i) q^{65} +(-72.2013 - 41.6854i) q^{67} +(-83.1375 + 63.6086i) q^{69} +38.6773i q^{71} +1.94431 q^{73} +(4.69731 + 36.0705i) q^{75} +(53.9053 - 93.3667i) q^{77} +(28.6384 - 16.5344i) q^{79} +(-0.454400 + 80.9987i) q^{81} +(68.4179 + 118.503i) q^{83} +(30.4929 - 52.8152i) q^{85} +(84.4779 - 11.0012i) q^{87} -85.1744i q^{89} -199.488i q^{91} +(-2.64002 - 3.45056i) q^{93} +(65.4610 - 95.4829i) q^{95} +(-41.0225 + 23.6843i) q^{97} +(-30.2673 + 111.705i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 80 q + 2 q^{7} + 4 q^{9}+O(q^{10}) \) 80 * q + 2 * q^7 + 4 * q^9	\( 80 q + 2 q^{7} + 4 q^{9} + 12 q^{11} - 12 q^{17} - 2 q^{19} - 48 q^{23} - 200 q^{25} - 216 q^{35} + 102 q^{39} + 28 q^{43} + 2 q^{45} - 174 q^{47} - 306 q^{49} + 213 q^{57} + 14 q^{61} + 62 q^{63} + 220 q^{73} - 60 q^{77} + 340 q^{81} + 150 q^{83} - 252 q^{87} - 252 q^{93} + 360 q^{95} + 542 q^{99}+O(q^{100}) \) 80 * q + 2 * q^7 + 4 * q^9 + 12 * q^11 - 12 * q^17 - 2 * q^19 - 48 * q^23 - 200 * q^25 - 216 * q^35 + 102 * q^39 + 28 * q^43 + 2 * q^45 - 174 * q^47 - 306 * q^49 + 213 * q^57 + 14 * q^61 + 62 * q^63 + 220 * q^73 - 60 * q^77 + 340 * q^81 + 150 * q^83 - 252 * q^87 - 252 * q^93 + 360 * q^95 + 542 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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