LMFDB - Embedded newform 1170.2.q.c.359.6

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [1170,2,Mod(359,1170)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(1170, base_ring=CyclotomicField(4)) chi = DirichletCharacter(H, H._module([2, 2, 1])) N = Newforms(chi, 2, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("1170.359"); S:= CuspForms(chi, 2); N := Newforms(S);

Level:	$ N $	$=$	$ 1170 = 2 \cdot 3^{2} \cdot 5 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1170.q (of order $4$, degree $2$, minimal)

Newform invariants

comment:select newform

sage:traces = [24,0,0,0,0,0,0,0,0,0,0,0,-20] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(13)] == traces)

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

Self dual:	no
Analytic conductor:	$9.34249703649$
Analytic rank:	$0$
Dimension:	$24$
Relative dimension:	$12$ over $\Q(i)$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			359.6
Character	$\chi$	$=$	1170.359
Dual form			1170.2.q.c.629.6

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.707107 - 0.707107i) q^{2} +1.00000i q^{4} +(1.15322 + 1.91575i) q^{5} +(-1.83222 - 1.83222i) q^{7} +(0.707107 - 0.707107i) q^{8} +(0.539189 - 2.17009i) q^{10} +(-0.354163 - 0.354163i) q^{11} +(-2.54346 + 2.55555i) q^{13} +2.59114i q^{14} -1.00000 q^{16} -7.26066i q^{17} +(-0.706974 - 0.706974i) q^{19} +(-1.91575 + 1.15322i) q^{20} +0.500863i q^{22} -6.38553i q^{23} +(-2.34017 + 4.41855i) q^{25} +(3.60554 - 0.00854890i) q^{26} +(1.83222 - 1.83222i) q^{28} -5.05475i q^{29} +(5.80828 + 5.80828i) q^{31} +(0.707107 + 0.707107i) q^{32} +(-5.13406 + 5.13406i) q^{34} +(1.39712 - 5.62301i) q^{35} +(-6.17738 - 6.17738i) q^{37} +0.999812i q^{38} +(2.17009 + 0.539189i) q^{40} +(-0.648903 + 0.648903i) q^{41} +4.80832 q^{43} +(0.354163 - 0.354163i) q^{44} +(-4.51525 + 4.51525i) q^{46} +(5.03434 - 5.03434i) q^{47} -0.285975i q^{49} +(4.77914 - 1.46963i) q^{50} +(-2.55555 - 2.54346i) q^{52} +1.69186 q^{53} +(0.270060 - 1.08692i) q^{55} -2.59114 q^{56} +(-3.57425 + 3.57425i) q^{58} +(0.280424 + 0.280424i) q^{59} +0.831932 q^{61} -8.21415i q^{62} -1.00000i q^{64} +(-7.82895 - 1.92552i) q^{65} +(9.27168 - 9.27168i) q^{67} +7.26066 q^{68} +(-4.96398 + 2.98816i) q^{70} +(8.91541 - 8.91541i) q^{71} +(-8.01342 - 8.01342i) q^{73} +8.73614i q^{74} +(0.706974 - 0.706974i) q^{76} +1.29781i q^{77} -5.27178 q^{79} +(-1.15322 - 1.91575i) q^{80} +0.917688 q^{82} +(1.93946 + 1.93946i) q^{83} +(13.9096 - 8.37313i) q^{85} +(-3.39999 - 3.39999i) q^{86} -0.500863 q^{88} +(7.14378 + 7.14378i) q^{89} +(9.34247 - 0.0221514i) q^{91} +6.38553 q^{92} -7.11963 q^{94} +(0.539087 - 2.16968i) q^{95} +(-4.75163 + 4.75163i) q^{97} +(-0.202215 + 0.202215i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 24 q - 20 q^{13} - 24 q^{16} - 48 q^{19} + 32 q^{25} - 8 q^{31} + 16 q^{34} - 32 q^{37} + 8 q^{40} + 80 q^{43} + 8 q^{46} - 12 q^{52} + 16 q^{55} - 24 q^{58} - 16 q^{61} - 8 q^{67} - 24 q^{70} + 48 q^{73}+ \cdots + 64 q^{97}+O(q^{100}) $ 24 * q - 20 * q^13 - 24 * q^16 - 48 * q^19 + 32 * q^25 - 8 * q^31 + 16 * q^34 - 32 * q^37 + 8 * q^40 + 80 * q^43 + 8 * q^46 - 12 * q^52 + 16 * q^55 - 24 * q^58 - 16 * q^61 - 8 * q^67 - 24 * q^70 + 48 * q^73 + 48 * q^76 - 96 * q^79 - 72 * q^82 + 8 * q^85 + 8 * q^88 + 48 * q^91 - 16 * q^94 + 64 * q^97

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1170\mathbb{Z}\right)^\times$.

$n$	$911$	$937$	$1081$
$\chi(n)$	$-1$	$-1$	$e\left(\frac{1}{4}\right)$

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 $

$2$	−0.707107	−	0.707107i	−0.500000	−	0.500000i
$2$	−0.707107	−	0.707107i	−0.500000	−	0.500000i
$3$		0			0
$3$		0			0
$4$			1.00000i			0.500000i
$5$	1.15322	+	1.91575i	0.515735	+	0.856748i
$5$	1.15322	+	1.91575i	0.515735	+	0.856748i
$6$		0			0
$7$	−1.83222	−	1.83222i	−0.692512	−	0.692512i	0.270272	−	0.962784i	$-0.412886\pi$
$7$	−1.83222	−	1.83222i	−0.692512	−	0.692512i	−0.962784	+	0.270272i	$0.912886\pi$
$8$	0.707107	−	0.707107i	0.250000	−	0.250000i
$9$		0			0
$10$	0.539189	−	2.17009i	0.170506	−	0.686242i
$11$	−0.354163	−	0.354163i	−0.106784	−	0.106784i	0.651696	−	0.758480i	$-0.274058\pi$
$11$	−0.354163	−	0.354163i	−0.106784	−	0.106784i	−0.758480	+	0.651696i	$0.774058\pi$
$12$		0			0
$13$	−2.54346	+	2.55555i	−0.705428	+	0.708781i
$13$	−2.54346	+	2.55555i	−0.705428	+	0.708781i
$14$			2.59114i			0.692512i
$15$		0			0
$16$	−1.00000			−0.250000
$17$		−	7.26066i		−	1.76097i	−0.474075	−	0.880484i	$-0.657218\pi$
$17$		−	7.26066i		−	1.76097i	0.474075	−	0.880484i	$-0.342782\pi$
$18$		0			0
$19$	−0.706974	−	0.706974i	−0.162191	−	0.162191i	0.621346	−	0.783537i	$-0.286586\pi$
$19$	−0.706974	−	0.706974i	−0.162191	−	0.162191i	−0.783537	+	0.621346i	$0.786586\pi$
$20$	−1.91575	+	1.15322i	−0.428374	+	0.257868i
$21$		0			0
$22$			0.500863i			0.106784i
$23$		−	6.38553i		−	1.33148i	−0.746186	−	0.665738i	$-0.768117\pi$
$23$		−	6.38553i		−	1.33148i	0.746186	−	0.665738i	$-0.231883\pi$
$24$		0			0
$25$	−2.34017	+	4.41855i	−0.468035	+	0.883710i
$26$	3.60554	−	0.00854890i	0.707105	−	0.00167658i
$27$		0			0
$28$	1.83222	−	1.83222i	0.346256	−	0.346256i
$29$		−	5.05475i		−	0.938643i	−0.883027	−	0.469321i	$-0.844499\pi$
$29$		−	5.05475i		−	0.938643i	0.883027	−	0.469321i	$-0.155501\pi$
$30$		0			0
$31$	5.80828	+	5.80828i	1.04320	+	1.04320i	0.999024	+	0.0441741i	$0.0140656\pi$
$31$	5.80828	+	5.80828i	1.04320	+	1.04320i	0.0441741	+	0.999024i	$0.485934\pi$
$32$	0.707107	+	0.707107i	0.125000	+	0.125000i
$33$		0			0
$34$	−5.13406	+	5.13406i	−0.880484	+	0.880484i
$35$	1.39712	−	5.62301i	0.236156	−	0.950461i
$36$		0			0
$37$	−6.17738	−	6.17738i	−1.01556	−	1.01556i	−0.999877	−	0.0156784i	$-0.995009\pi$
$37$	−6.17738	−	6.17738i	−1.01556	−	1.01556i	−0.0156784	−	0.999877i	$-0.504991\pi$
$38$			0.999812i			0.162191i
$39$		0			0
$40$	2.17009	+	0.539189i	0.343121	+	0.0852532i
$41$	−0.648903	+	0.648903i	−0.101342	+	0.101342i	−0.755960	−	0.654618i	$-0.772829\pi$
$41$	−0.648903	+	0.648903i	−0.101342	+	0.101342i	0.654618	+	0.755960i	$0.272829\pi$
$42$		0			0
$43$	4.80832			0.733262			0.366631	−	0.930367i	$-0.380511\pi$
$43$	4.80832			0.733262			0.366631	+	0.930367i	$0.380511\pi$
$44$	0.354163	−	0.354163i	0.0533921	−	0.0533921i
$45$		0			0
$46$	−4.51525	+	4.51525i	−0.665738	+	0.665738i
$47$	5.03434	−	5.03434i	0.734334	−	0.734334i	−0.237141	−	0.971475i	$-0.576210\pi$
$47$	5.03434	−	5.03434i	0.734334	−	0.734334i	0.971475	+	0.237141i	$0.0762104\pi$
$48$		0			0
$49$		−	0.285975i		−	0.0408536i
$50$	4.77914	−	1.46963i	0.675872	−	0.207838i
$51$		0			0
$52$	−2.55555	−	2.54346i	−0.354391	−	0.352714i
$53$	1.69186			0.232394			0.116197	−	0.993226i	$-0.462930\pi$
$53$	1.69186			0.232394			0.116197	+	0.993226i	$0.462930\pi$
$54$		0			0
$55$	0.270060	−	1.08692i	0.0364148	−	0.146560i
$56$	−2.59114			−0.346256
$57$		0			0
$58$	−3.57425	+	3.57425i	−0.469321	+	0.469321i
$59$	0.280424	+	0.280424i	0.0365081	+	0.0365081i	0.725125	−	0.688617i	$-0.241782\pi$
$59$	0.280424	+	0.280424i	0.0365081	+	0.0365081i	−0.688617	+	0.725125i	$0.741782\pi$
$60$		0			0
$61$	0.831932			0.106518			0.0532590	−	0.998581i	$-0.483039\pi$
$61$	0.831932			0.106518			0.0532590	+	0.998581i	$0.483039\pi$
$62$		−	8.21415i		−	1.04320i
$63$		0			0
$64$		−	1.00000i		−	0.125000i
$65$	−7.82895	−	1.92552i	−0.971061	−	0.238831i
$66$		0			0
$67$	9.27168	−	9.27168i	1.13272	−	1.13272i	0.142992	−	0.989724i	$-0.454328\pi$
$67$	9.27168	−	9.27168i	1.13272	−	1.13272i	0.989724	−	0.142992i	$-0.0456722\pi$
$68$	7.26066			0.880484
$69$		0			0
$70$	−4.96398	+	2.98816i	−0.593309	+	0.357153i
$71$	8.91541	−	8.91541i	1.05806	−	1.05806i	0.0598578	−	0.998207i	$-0.480935\pi$
$71$	8.91541	−	8.91541i	1.05806	−	1.05806i	0.998207	−	0.0598578i	$-0.0190647\pi$
$72$		0			0
$73$	−8.01342	−	8.01342i	−0.937900	−	0.937900i	0.0602811	−	0.998181i	$-0.480800\pi$
$73$	−8.01342	−	8.01342i	−0.937900	−	0.937900i	−0.998181	+	0.0602811i	$0.980800\pi$
$74$			8.73614i			1.01556i
$75$		0			0
$76$	0.706974	−	0.706974i	0.0810954	−	0.0810954i
$77$			1.29781i			0.147899i
$78$		0			0
$79$	−5.27178			−0.593122			−0.296561	−	0.955014i	$-0.595840\pi$
$79$	−5.27178			−0.593122			−0.296561	+	0.955014i	$0.595840\pi$
$80$	−1.15322	−	1.91575i	−0.128934	−	0.214187i
$81$		0			0
$82$	0.917688			0.101342
$83$	1.93946	+	1.93946i	0.212883	+	0.212883i	0.805491	−	0.592608i	$-0.201902\pi$
$83$	1.93946	+	1.93946i	0.212883	+	0.212883i	−0.592608	+	0.805491i	$0.701902\pi$
$84$		0			0
$85$	13.9096	−	8.37313i	1.50871	−	0.908193i
$86$	−3.39999	−	3.39999i	−0.366631	−	0.366631i
$87$		0			0
$88$	−0.500863			−0.0533921
$89$	7.14378	+	7.14378i	0.757239	+	0.757239i	0.975819	−	0.218580i	$-0.0701424\pi$
$89$	7.14378	+	7.14378i	0.757239	+	0.757239i	−0.218580	+	0.975819i	$0.570142\pi$
$90$		0			0
$91$	9.34247	−	0.0221514i	0.979357	−	0.00232210i
$92$	6.38553			0.665738
$93$		0			0
$94$	−7.11963			−0.734334
$95$	0.539087	−	2.16968i	0.0553092	−	0.222604i
$96$		0			0
$97$	−4.75163	+	4.75163i	−0.482455	+	0.482455i	−0.905915	−	0.423460i	$-0.860815\pi$
$97$	−4.75163	+	4.75163i	−0.482455	+	0.482455i	0.423460	+	0.905915i	$0.360815\pi$
$98$	−0.202215	+	0.202215i	−0.0204268	+	0.0204268i
$99$		0			0
$100$	−4.41855	−	2.34017i	−0.441855	−	0.234017i
$101$	−13.7859			−1.37174			−0.685872	−	0.727722i	$-0.740579\pi$
$101$	−13.7859			−1.37174			−0.685872	+	0.727722i	$0.740579\pi$
$102$		0			0
$103$	−9.99607			−0.984942			−0.492471	−	0.870329i	$-0.663906\pi$
$103$	−9.99607			−0.984942			−0.492471	+	0.870329i	$0.663906\pi$
$104$	0.00854890	+	3.60554i	0.000838289	+	0.353552i
$105$		0			0
$106$	−1.19632	−	1.19632i	−0.116197	−	0.116197i
$107$	6.51985			0.630298			0.315149	−	0.949042i	$-0.397946\pi$
$107$	6.51985			0.630298			0.315149	+	0.949042i	$0.397946\pi$
$108$		0			0
$109$	−3.20780	−	3.20780i	−0.307251	−	0.307251i	0.536591	−	0.843842i	$-0.319712\pi$
$109$	−3.20780	−	3.20780i	−0.307251	−	0.307251i	−0.843842	+	0.536591i	$0.819712\pi$
$110$	−0.959526	+	0.577604i	−0.0914872	+	0.0550724i
$111$		0			0
$112$	1.83222	+	1.83222i	0.173128	+	0.173128i
$113$	−19.2771			−1.81344			−0.906720	−	0.421733i	$-0.861422\pi$
$113$	−19.2771			−1.81344			−0.906720	+	0.421733i	$0.861422\pi$
$114$		0			0
$115$	12.2331	−	7.36392i	1.14074	−	0.686689i
$116$	5.05475			0.469321
$117$		0			0
$118$		−	0.396580i		−	0.0365081i
$119$	−13.3031	+	13.3031i	−1.21949	+	1.21949i
$120$		0			0
$121$		−	10.7491i		−	0.977194i
$122$	−0.588265	−	0.588265i	−0.0532590	−	0.0532590i
$123$		0			0
$124$	−5.80828	+	5.80828i	−0.521599	+	0.521599i
$125$	−11.1636	+	0.612376i	−0.998499	+	0.0547726i
$126$		0			0
$127$	−15.3792			−1.36469			−0.682343	−	0.731033i	$-0.739039\pi$
$127$	−15.3792			−1.36469			−0.682343	+	0.731033i	$0.739039\pi$
$128$	−0.707107	+	0.707107i	−0.0625000	+	0.0625000i
$129$		0			0
$130$	4.17436	+	6.89745i	0.366115	+	0.604946i
$131$		−	12.6532i		−	1.10551i	−0.833343	−	0.552756i	$-0.813576\pi$
$131$		−	12.6532i		−	1.10551i	0.833343	−	0.552756i	$-0.186424\pi$
$132$		0			0
$133$			2.59066i			0.224638i
$134$	−13.1121			−1.13272
$135$		0			0
$136$	−5.13406	−	5.13406i	−0.440242	−	0.440242i
$137$	0.760088	−	0.760088i	0.0649387	−	0.0649387i	−0.673892	−	0.738830i	$-0.735379\pi$
$137$	0.760088	−	0.760088i	0.0649387	−	0.0649387i	0.738830	+	0.673892i	$0.235379\pi$
$138$		0			0
$139$	−14.2793			−1.21115			−0.605576	−	0.795788i	$-0.707057\pi$
$139$	−14.2793			−1.21115			−0.605576	+	0.795788i	$0.707057\pi$
$140$	5.62301	+	1.39712i	0.475231	+	0.118078i
$141$		0			0
$142$	−12.6083			−1.05806
$143$	1.80588	−	0.00428182i	0.151015	−	0.000358064i
$144$		0			0
$145$	9.68362	−	5.82923i	0.804180	−	0.484091i
$146$			11.3327i			0.937900i
$147$		0			0
$148$	6.17738	−	6.17738i	0.507778	−	0.507778i
$149$	1.92914	−	1.92914i	0.158041	−	0.158041i	−0.623657	−	0.781698i	$-0.714354\pi$
$149$	1.92914	−	1.92914i	0.158041	−	0.158041i	0.781698	+	0.623657i	$0.214354\pi$
$150$		0			0
$151$	−3.21224	+	3.21224i	−0.261408	+	0.261408i	−0.825626	−	0.564218i	$-0.809178\pi$
$151$	−3.21224	+	3.21224i	−0.261408	+	0.261408i	0.564218	+	0.825626i	$0.309178\pi$
$152$	−0.999812			−0.0810954
$153$		0			0
$154$	0.917688	−	0.917688i	0.0739494	−	0.0739494i
$155$	−4.42898	+	17.8254i	−0.355744	+	1.43177i
$156$		0			0
$157$			19.0790i			1.52267i	0.648357	+	0.761337i	$0.275457\pi$
$157$			19.0790i			1.52267i	−0.648357	+	0.761337i	$0.724543\pi$
$158$	3.72771	+	3.72771i	0.296561	+	0.296561i
$159$		0			0
$160$	−0.539189	+	2.17009i	−0.0426266	+	0.171560i
$161$	−11.6997	+	11.6997i	−0.922063	+	0.922063i
$162$		0			0
$163$	11.1149	+	11.1149i	0.870588	+	0.870588i	0.992536	−	0.121949i	$-0.0389143\pi$
$163$	11.1149	+	11.1149i	0.870588	+	0.870588i	−0.121949	+	0.992536i	$0.538914\pi$
$164$	−0.648903	−	0.648903i	−0.0506708	−	0.0506708i
$165$		0			0
$166$		−	2.74281i		−	0.212883i
$167$	4.82453	−	4.82453i	0.373333	−	0.373333i	−0.495357	−	0.868690i	$-0.664963\pi$
$167$	4.82453	−	4.82453i	0.373333	−	0.373333i	0.868690	+	0.495357i	$0.164963\pi$
$168$		0			0
$169$	−0.0616468	−	12.9999i	−0.00474206	−	0.999989i
$170$	−15.7563	−	3.91487i	−1.20845	−	0.300257i
$171$		0			0
$172$			4.80832i			0.366631i
$173$			3.67792i			0.279627i	0.990178	+	0.139814i	$0.0446503\pi$
$173$			3.67792i			0.279627i	−0.990178	+	0.139814i	$0.955350\pi$
$174$		0			0
$175$	12.3834	−	3.80804i	0.936100	−	0.287860i
$176$	0.354163	+	0.354163i	0.0266961	+	0.0266961i
$177$		0			0
$178$		−	10.1028i		−	0.757239i
$179$	25.9594			1.94030			0.970150	−	0.242506i	$-0.0779693\pi$
$179$	25.9594			1.94030			0.970150	+	0.242506i	$0.0779693\pi$
$180$		0			0
$181$		−	5.14332i		−	0.382300i	−0.981561	−	0.191150i	$-0.938778\pi$
$181$		−	5.14332i		−	0.382300i	0.981561	−	0.191150i	$-0.0612217\pi$
$182$	−6.62179	−	6.59046i	−0.490840	−	0.488518i
$183$		0			0
$184$	−4.51525	−	4.51525i	−0.332869	−	0.332869i
$185$	4.71043	−	18.9582i	0.346318	−	1.39383i
$186$		0			0
$187$	−2.57146	+	2.57146i	−0.188044	+	0.188044i
$188$	5.03434	+	5.03434i	0.367167	+	0.367167i
$189$		0			0
$190$	−1.91539	+	1.15300i	−0.138957	+	0.0836475i
$191$		−	23.4969i		−	1.70018i	−0.526639	−	0.850089i	$-0.676548\pi$
$191$		−	23.4969i		−	1.70018i	0.526639	−	0.850089i	$-0.323452\pi$
$192$		0			0
$193$	13.7670	+	13.7670i	0.990969	+	0.990969i	0.999960	−	0.00899081i	$-0.00286190\pi$
$193$	13.7670	+	13.7670i	0.990969	+	0.990969i	−0.00899081	+	0.999960i	$0.502862\pi$
$194$	6.71982			0.482455
$195$		0			0
$196$	0.285975			0.0204268
$197$	−3.99829	−	3.99829i	−0.284867	−	0.284867i	0.550180	−	0.835046i	$-0.314559\pi$
$197$	−3.99829	−	3.99829i	−0.284867	−	0.284867i	−0.835046	+	0.550180i	$0.814559\pi$
$198$		0			0
$199$			19.3636i			1.37265i	0.727296	+	0.686324i	$0.240777\pi$
$199$			19.3636i			1.37265i	−0.727296	+	0.686324i	$0.759223\pi$
$200$	1.46963	+	4.77914i	0.103919	+	0.337936i
$201$		0			0
$202$	9.74808	+	9.74808i	0.685872	+	0.685872i
$203$	−9.26138	+	9.26138i	−0.650022	+	0.650022i
$204$		0			0
$205$	−1.99146	−	0.494807i	−0.139090	−	0.0345588i
$206$	7.06829	+	7.06829i	0.492471	+	0.492471i
$207$		0			0
$208$	2.54346	−	2.55555i	0.176357	−	0.177195i
$209$			0.500768i			0.0346389i
$210$		0			0
$211$	21.2220			1.46098			0.730491	−	0.682923i	$-0.239291\pi$
$211$	21.2220			1.46098			0.730491	+	0.682923i	$0.239291\pi$
$212$			1.69186i			0.116197i
$213$		0			0
$214$	−4.61023	−	4.61023i	−0.315149	−	0.315149i
$215$	5.54504	+	9.21152i	0.378169	+	0.628221i
$216$		0			0
$217$		−	21.2840i		−	1.44485i
$218$			4.53651i			0.307251i
$219$		0			0
$220$	1.08692	+	0.270060i	0.0732798	+	0.0182074i
$221$	18.5550	+	18.4672i	1.24814	+	1.24224i
$222$		0			0
$223$	7.43025	−	7.43025i	0.497566	−	0.497566i	−0.413113	−	0.910680i	$-0.635559\pi$
$223$	7.43025	−	7.43025i	0.497566	−	0.497566i	0.910680	+	0.413113i	$0.135559\pi$
$224$		−	2.59114i		−	0.173128i
$225$		0			0
$226$	13.6310	+	13.6310i	0.906720	+	0.906720i
$227$	−0.320995	−	0.320995i	−0.0213052	−	0.0213052i	0.696374	−	0.717679i	$-0.254796\pi$
$227$	−0.320995	−	0.320995i	−0.0213052	−	0.0213052i	−0.717679	+	0.696374i	$0.754796\pi$
$228$		0			0
$229$	−8.52207	+	8.52207i	−0.563154	+	0.563154i	−0.930202	−	0.367048i	$-0.880368\pi$
$229$	−8.52207	+	8.52207i	−0.563154	+	0.563154i	0.367048	+	0.930202i	$0.380368\pi$
$230$	−13.8572	−	3.44301i	−0.913714	−	0.227025i
$231$		0			0
$232$	−3.57425	−	3.57425i	−0.234661	−	0.234661i
$233$			7.38750i			0.483971i	0.970280	+	0.241986i	$0.0777987\pi$
$233$			7.38750i			0.483971i	−0.970280	+	0.241986i	$0.922201\pi$
$234$		0			0
$235$	15.4502	+	3.83883i	1.00786	+	0.250417i
$236$	−0.280424	+	0.280424i	−0.0182541	+	0.0182541i
$237$		0			0
$238$	18.8134			1.21949
$239$	−6.45533	+	6.45533i	−0.417561	+	0.417561i	−0.884362	−	0.466801i	$-0.845406\pi$
$239$	−6.45533	+	6.45533i	−0.417561	+	0.417561i	0.466801	+	0.884362i	$0.345406\pi$
$240$		0			0
$241$	14.0266	−	14.0266i	0.903531	−	0.903531i	−0.0922086	−	0.995740i	$-0.529393\pi$
$241$	14.0266	−	14.0266i	0.903531	−	0.903531i	0.995740	+	0.0922086i	$0.0293927\pi$
$242$	−7.60079	+	7.60079i	−0.488597	+	0.488597i
$243$		0			0
$244$			0.831932i			0.0532590i
$245$	0.547856	−	0.329792i	0.0350012	−	0.0210696i
$246$		0			0
$247$	3.60486	−	0.00854729i	0.229372	−	0.000543851i
$248$	8.21415			0.521599
$249$		0			0
$250$	8.32684	+	7.46081i	0.526636	+	0.471863i
$251$	−0.913999			−0.0576911			−0.0288455	−	0.999584i	$-0.509183\pi$
$251$	−0.913999			−0.0576911			−0.0288455	+	0.999584i	$0.509183\pi$
$252$		0			0
$253$	−2.26152	+	2.26152i	−0.142181	+	0.142181i
$254$	10.8747	+	10.8747i	0.682343	+	0.682343i
$255$		0			0
$256$	1.00000			0.0625000
$257$			19.2222i			1.19905i	0.800357	+	0.599524i	$0.204643\pi$
$257$			19.2222i			1.19905i	−0.800357	+	0.599524i	$0.795357\pi$
$258$		0			0
$259$			22.6366i			1.40657i
$260$	1.92552	−	7.82895i	0.119415	−	0.485531i
$261$		0			0
$262$	−8.94714	+	8.94714i	−0.552756	+	0.552756i
$263$	−28.0638			−1.73049			−0.865245	−	0.501350i	$-0.832837\pi$
$263$	−28.0638			−1.73049			−0.865245	+	0.501350i	$0.832837\pi$
$264$		0			0
$265$	1.95108	+	3.24117i	0.119854	+	0.199103i
$266$	1.83187	−	1.83187i	0.112319	−	0.112319i
$267$		0			0
$268$	9.27168	+	9.27168i	0.566358	+	0.566358i
$269$			16.7710i			1.02255i	0.859418	+	0.511273i	$0.170826\pi$
$269$			16.7710i			1.02255i	−0.859418	+	0.511273i	$0.829174\pi$
$270$		0			0
$271$	−10.1913	+	10.1913i	−0.619080	+	0.619080i	−0.945295	−	0.326216i	$-0.894226\pi$
$271$	−10.1913	+	10.1913i	−0.619080	+	0.619080i	0.326216	+	0.945295i	$0.394226\pi$
$272$			7.26066i			0.440242i
$273$		0			0
$274$	−1.07493			−0.0649387
$275$	2.39369	−	0.736085i	0.144345	−	0.0443876i
$276$		0			0
$277$	8.94647			0.537541			0.268771	−	0.963204i	$-0.413383\pi$
$277$	8.94647			0.537541			0.268771	+	0.963204i	$0.413383\pi$
$278$	10.0970	+	10.0970i	0.605576	+	0.605576i
$279$		0			0
$280$	−2.98816	−	4.96398i	−0.178576	−	0.296654i
$281$	−14.6154	−	14.6154i	−0.871879	−	0.871879i	0.120798	−	0.992677i	$-0.461455\pi$
$281$	−14.6154	−	14.6154i	−0.871879	−	0.871879i	−0.992677	+	0.120798i	$0.961455\pi$
$282$		0			0
$283$	3.17095			0.188494			0.0942468	−	0.995549i	$-0.469956\pi$
$283$	3.17095			0.188494			0.0942468	+	0.995549i	$0.469956\pi$
$284$	8.91541	+	8.91541i	0.529032	+	0.529032i
$285$		0			0
$286$	−1.27998	−	1.27392i	−0.0756867	−	0.0753286i
$287$	2.37786			0.140361
$288$		0			0
$289$	−35.7172			−2.10101
$290$	−10.9692	−	2.72546i	−0.644136	−	0.160045i
$291$		0			0
$292$	8.01342	−	8.01342i	0.468950	−	0.468950i
$293$	15.5465	−	15.5465i	0.908237	−	0.908237i	−0.0878932	−	0.996130i	$-0.528013\pi$
$293$	15.5465	−	15.5465i	0.908237	−	0.908237i	0.996130	+	0.0878932i	$0.0280134\pi$
$294$		0			0
$295$	−0.213831	+	0.860612i	−0.0124497	+	0.0501068i
$296$	−8.73614			−0.507778
$297$		0			0
$298$	−2.72822			−0.158041
$299$	16.3185	+	16.2413i	0.943725	+	0.939261i
$300$		0			0
$301$	−8.80987	−	8.80987i	−0.507793	−	0.507793i
$302$	4.54279			0.261408
$303$		0			0
$304$	0.706974	+	0.706974i	0.0405477	+	0.0405477i
$305$	0.959400	+	1.59377i	0.0549351	+	0.0912591i
$306$		0			0
$307$	2.32127	+	2.32127i	0.132482	+	0.132482i	0.770238	−	0.637756i	$-0.220137\pi$
$307$	2.32127	+	2.32127i	0.132482	+	0.132482i	−0.637756	+	0.770238i	$0.720137\pi$
$308$	−1.29781			−0.0739494
$309$		0			0
$310$	15.7362	−	9.47271i	0.893758	−	0.538014i
$311$	12.0683			0.684331			0.342165	−	0.939640i	$-0.388840\pi$
$311$	12.0683			0.684331			0.342165	+	0.939640i	$0.388840\pi$
$312$		0			0
$313$			5.12431i			0.289643i	0.989458	+	0.144822i	$0.0462608\pi$
$313$			5.12431i			0.289643i	−0.989458	+	0.144822i	$0.953739\pi$
$314$	13.4909	−	13.4909i	0.761337	−	0.761337i
$315$		0			0
$316$		−	5.27178i		−	0.296561i
$317$	21.2033	+	21.2033i	1.19090	+	1.19090i	0.976816	+	0.214080i	$0.0686753\pi$
$317$	21.2033	+	21.2033i	1.19090	+	1.19090i	0.214080	+	0.976816i	$0.431325\pi$
$318$		0			0
$319$	−1.79021	+	1.79021i	−0.100232	+	0.100232i
$320$	1.91575	−	1.15322i	0.107094	−	0.0644669i
$321$		0			0
$322$	16.5458			0.922063
$323$	−5.13310	+	5.13310i	−0.285613	+	0.285613i
$324$		0			0
$325$	−5.33969	−	17.2188i	−0.296192	−	0.955128i
$326$		−	15.7189i		−	0.870588i
$327$		0			0
$328$			0.917688i			0.0506708i
$329$	−18.4480			−1.01707
$330$		0			0
$331$	7.96572	+	7.96572i	0.437836	+	0.437836i	0.891283	−	0.453447i	$-0.149806\pi$
$331$	7.96572	+	7.96572i	0.437836	+	0.437836i	−0.453447	+	0.891283i	$0.649806\pi$
$332$	−1.93946	+	1.93946i	−0.106442	+	0.106442i
$333$		0			0
$334$	−6.82291			−0.373333
$335$	28.4545	+	7.06991i	1.55463	+	0.386271i
$336$		0			0
$337$	31.4402			1.71266			0.856329	−	0.516430i	$-0.172739\pi$
$337$	31.4402			1.71266			0.856329	+	0.516430i	$0.172739\pi$
$338$	−9.14869	+	9.23588i	−0.497623	+	0.502365i
$339$		0			0
$340$	8.37313	+	13.9096i	0.454097	+	0.754353i
$341$		−	4.11416i		−	0.222794i
$342$		0			0
$343$	−13.3495	+	13.3495i	−0.720804	+	0.720804i
$344$	3.39999	−	3.39999i	0.183315	−	0.183315i
$345$		0			0
$346$	2.60068	−	2.60068i	0.139814	−	0.139814i
$347$	−31.4466			−1.68814			−0.844070	−	0.536233i	$-0.819847\pi$
$347$	−31.4466			−1.68814			−0.844070	+	0.536233i	$0.819847\pi$
$348$		0			0
$349$	4.21075	−	4.21075i	0.225396	−	0.225396i	−0.585370	−	0.810766i	$-0.699051\pi$
$349$	4.21075	−	4.21075i	0.225396	−	0.225396i	0.810766	+	0.585370i	$0.199051\pi$
$350$	−11.4491	−	6.06372i	−0.611980	−	0.324120i
$351$		0			0
$352$		−	0.500863i		−	0.0266961i
$353$	−13.2011	−	13.2011i	−0.702622	−	0.702622i	0.262351	−	0.964973i	$-0.415502\pi$
$353$	−13.2011	−	13.2011i	−0.702622	−	0.702622i	−0.964973	+	0.262351i	$0.915502\pi$
$354$		0			0
$355$	27.3611	+	6.79825i	1.45218	+	0.360814i
$356$	−7.14378	+	7.14378i	−0.378620	+	0.378620i
$357$		0			0
$358$	−18.3561	−	18.3561i	−0.970150	−	0.970150i
$359$	1.18359	+	1.18359i	0.0624677	+	0.0624677i	0.737650	−	0.675183i	$-0.235935\pi$
$359$	1.18359	+	1.18359i	0.0624677	+	0.0624677i	−0.675183	+	0.737650i	$0.735935\pi$
$360$		0			0
$361$		−	18.0004i		−	0.947388i
$362$	−3.63688	+	3.63688i	−0.191150	+	0.191150i
$363$		0			0
$364$	0.0221514	+	9.34247i	0.00116105	+	0.489679i
$365$	6.11046	−	24.5929i	0.319836	−	1.28725i
$366$		0			0
$367$		−	7.64534i		−	0.399083i	−0.979889	−	0.199542i	$-0.936055\pi$
$367$		−	7.64534i		−	0.399083i	0.979889	−	0.199542i	$-0.0639453\pi$
$368$			6.38553i			0.332869i
$369$		0			0
$370$	−16.7362	+	10.0747i	−0.870075	+	0.523758i
$371$	−3.09984	−	3.09984i	−0.160936	−	0.160936i
$372$		0			0
$373$			5.47536i			0.283503i	0.989902	+	0.141752i	$0.0452735\pi$
$373$			5.47536i			0.283503i	−0.989902	+	0.141752i	$0.954727\pi$
$374$	3.63659			0.188044
$375$		0			0
$376$		−	7.11963i		−	0.367167i
$377$	12.9176	+	12.8565i	0.665293	+	0.662145i
$378$		0			0
$379$	8.42587	+	8.42587i	0.432808	+	0.432808i	0.889583	−	0.456774i	$-0.150995\pi$
$379$	8.42587	+	8.42587i	0.432808	+	0.432808i	−0.456774	+	0.889583i	$0.650995\pi$
$380$	2.16968	+	0.539087i	0.111302	+	0.0276546i
$381$		0			0
$382$	−16.6148	+	16.6148i	−0.850089	+	0.850089i
$383$	−6.57975	−	6.57975i	−0.336210	−	0.336210i	0.518729	−	0.854939i	$-0.326405\pi$
$383$	−6.57975	−	6.57975i	−0.336210	−	0.336210i	−0.854939	+	0.518729i	$0.826405\pi$
$384$		0			0
$385$	−2.48627	+	1.49666i	−0.126712	+	0.0762766i
$386$		−	19.4694i		−	0.990969i
$387$		0			0
$388$	−4.75163	−	4.75163i	−0.241227	−	0.241227i
$389$	−19.7122			−0.999446			−0.499723	−	0.866185i	$-0.666565\pi$
$389$	−19.7122			−0.999446			−0.499723	+	0.866185i	$0.666565\pi$
$390$		0			0
$391$	−46.3632			−2.34469
$392$	−0.202215	−	0.202215i	−0.0102134	−	0.0102134i
$393$		0			0
$394$			5.65444i			0.284867i
$395$	−6.07952	−	10.0994i	−0.305894	−	0.508156i
$396$		0			0
$397$	5.60945	+	5.60945i	0.281530	+	0.281530i	0.833719	−	0.552189i	$-0.186207\pi$
$397$	5.60945	+	5.60945i	0.281530	+	0.281530i	−0.552189	+	0.833719i	$0.686207\pi$
$398$	13.6921	−	13.6921i	0.686324	−	0.686324i
$399$		0			0
$400$	2.34017	−	4.41855i	0.117009	−	0.220928i
$401$	13.7311	+	13.7311i	0.685697	+	0.685697i	0.961278	−	0.275581i	$-0.0888703\pi$
$401$	13.7311	+	13.7311i	0.685697	+	0.685697i	−0.275581	+	0.961278i	$0.588870\pi$
$402$		0			0
$403$	−29.6165	+	0.0702219i	−1.47530	+	0.00349800i
$404$		−	13.7859i		−	0.685872i
$405$		0			0
$406$	13.0976			0.650022
$407$			4.37561i			0.216891i
$408$		0			0
$409$	−13.1325	−	13.1325i	−0.649360	−	0.649360i	0.303478	−	0.952838i	$-0.401852\pi$
$409$	−13.1325	−	13.1325i	−0.649360	−	0.649360i	−0.952838	+	0.303478i	$0.901852\pi$
$410$	1.05830	+	1.75806i	0.0522655	+	0.0868243i
$411$		0			0
$412$		−	9.99607i		−	0.492471i
$413$		−	1.02759i		−	0.0505646i
$414$		0			0
$415$	−1.47889	+	5.95213i	−0.0725959	+	0.292179i
$416$	−3.60554	+	0.00854890i	−0.176776	+	0.000419144i
$417$		0			0
$418$	0.354097	−	0.354097i	0.0173194	−	0.0173194i
$419$			4.43719i			0.216771i	0.994109	+	0.108386i	$0.0345681\pi$
$419$			4.43719i			0.216771i	−0.994109	+	0.108386i	$0.965432\pi$
$420$		0			0
$421$	10.8256	+	10.8256i	0.527607	+	0.527607i	0.919858	−	0.392251i	$-0.128304\pi$
$421$	10.8256	+	10.8256i	0.527607	+	0.527607i	−0.392251	+	0.919858i	$0.628304\pi$
$422$	−15.0062	−	15.0062i	−0.730491	−	0.730491i
$423$		0			0
$424$	1.19632	−	1.19632i	0.0580986	−	0.0580986i
$425$	32.0816	+	16.9912i	1.55619	+	0.824194i
$426$		0			0
$427$	−1.52428	−	1.52428i	−0.0737650	−	0.0737650i
$428$			6.51985i			0.315149i
$429$		0			0
$430$	2.59259	−	10.4345i	0.125026	−	0.503195i
$431$	−24.6265	+	24.6265i	−1.18622	+	1.18622i	−0.208112	+	0.978105i	$0.566732\pi$
$431$	−24.6265	+	24.6265i	−1.18622	+	1.18622i	−0.978105	+	0.208112i	$0.933268\pi$
$432$		0			0
$433$	−6.93926			−0.333480			−0.166740	−	0.986001i	$-0.553324\pi$
$433$	−6.93926			−0.333480			−0.166740	+	0.986001i	$0.553324\pi$
$434$	−15.0501	+	15.0501i	−0.722427	+	0.722427i
$435$		0			0
$436$	3.20780	−	3.20780i	0.153626	−	0.153626i
$437$	−4.51440	+	4.51440i	−0.215953	+	0.215953i
$438$		0			0
$439$		−	10.1110i		−	0.482570i	−0.970454	−	0.241285i	$-0.922431\pi$
$439$		−	10.1110i		−	0.482570i	0.970454	−	0.241285i	$-0.0775689\pi$
$440$	−0.577604	−	0.959526i	−0.0275362	−	0.0457436i
$441$		0			0
$442$	−0.0620707	−	26.1786i	−0.00295240	−	1.24519i
$443$	−22.6212			−1.07476			−0.537382	−	0.843339i	$-0.680587\pi$
$443$	−22.6212			−1.07476			−0.537382	+	0.843339i	$0.680587\pi$
$444$		0			0
$445$	−5.44733	+	21.9240i	−0.258228	+	1.03930i
$446$	−10.5080			−0.497566
$447$		0			0
$448$	−1.83222	+	1.83222i	−0.0865640	+	0.0865640i
$449$	11.7909	+	11.7909i	0.556445	+	0.556445i	0.928293	−	0.371849i	$-0.121276\pi$
$449$	11.7909	+	11.7909i	0.556445	+	0.556445i	−0.371849	+	0.928293i	$0.621276\pi$
$450$		0			0
$451$	0.459636			0.0216434
$452$		−	19.2771i		−	0.906720i
$453$		0			0
$454$			0.453955i			0.0213052i
$455$	10.8164	+	17.8723i	0.507078	+	0.837865i
$456$		0			0
$457$	4.16806	−	4.16806i	0.194974	−	0.194974i	−0.602868	−	0.797841i	$-0.705975\pi$
$457$	4.16806	−	4.16806i	0.194974	−	0.194974i	0.797841	+	0.602868i	$0.205975\pi$
$458$	12.0520			0.563154
$459$		0			0
$460$	7.36392	+	12.2331i	0.343344	+	0.570370i
$461$	2.68524	−	2.68524i	0.125064	−	0.125064i	−0.641804	−	0.766868i	$-0.721814\pi$
$461$	2.68524	−	2.68524i	0.125064	−	0.125064i	0.766868	+	0.641804i	$0.221814\pi$
$462$		0			0
$463$	25.0700	+	25.0700i	1.16510	+	1.16510i	0.983343	+	0.181759i	$0.0581792\pi$
$463$	25.0700	+	25.0700i	1.16510	+	1.16510i	0.181759	+	0.983343i	$0.441821\pi$
$464$			5.05475i			0.234661i
$465$		0			0
$466$	5.22375	−	5.22375i	0.241986	−	0.241986i
$467$		−	27.9680i		−	1.29420i	−0.762403	−	0.647102i	$-0.775981\pi$
$467$		−	27.9680i		−	1.29420i	0.762403	−	0.647102i	$-0.224019\pi$
$468$		0			0
$469$	−33.9754			−1.56884
$470$	−8.21049	−	13.6394i	−0.378722	−	0.629139i
$471$		0			0
$472$	0.396580			0.0182541
$473$	−1.70293	−	1.70293i	−0.0783008	−	0.0783008i
$474$		0			0
$475$	4.77824	−	1.46936i	0.219241	−	0.0674188i
$476$	−13.3031	−	13.3031i	−0.609746	−	0.609746i
$477$		0			0
$478$	9.12922			0.417561
$479$	10.1126	+	10.1126i	0.462055	+	0.462055i	0.899328	−	0.437274i	$-0.144056\pi$
$479$	10.1126	+	10.1126i	0.462055	+	0.462055i	−0.437274	+	0.899328i	$0.644056\pi$
$480$		0			0
$481$	31.4985	−	0.0746844i	1.43621	−	0.00340531i
$482$	−19.8366			−0.903531
$483$		0			0
$484$	10.7491			0.488597
$485$	−14.5826	−	3.62325i	−0.662161	−	0.164523i
$486$		0			0
$487$	−5.25815	+	5.25815i	−0.238270	+	0.238270i	−0.816133	−	0.577864i	$-0.803887\pi$
$487$	−5.25815	+	5.25815i	−0.238270	+	0.238270i	0.577864	+	0.816133i	$0.303887\pi$
$488$	0.588265	−	0.588265i	0.0266295	−	0.0266295i
$489$		0			0
$490$	−0.620591	−	0.154195i	−0.0280354	−	0.00696580i
$491$	27.6899			1.24963			0.624813	−	0.780774i	$-0.285175\pi$
$491$	27.6899			1.24963			0.624813	+	0.780774i	$0.285175\pi$
$492$		0			0
$493$	−36.7008			−1.65292
$494$	−2.55507	−	2.54298i	−0.114958	−	0.114414i
$495$		0			0
$496$	−5.80828	−	5.80828i	−0.260799	−	0.260799i
$497$	−32.6699			−1.46545
$498$		0			0
$499$	17.3395	+	17.3395i	0.776220	+	0.776220i	0.979186	−	0.202965i	$-0.0650579\pi$
$499$	17.3395	+	17.3395i	0.776220	+	0.776220i	−0.202965	+	0.979186i	$0.565058\pi$
$500$	−0.612376	−	11.1636i	−0.0273863	−	0.499249i
$501$		0			0
$502$	0.646295	+	0.646295i	0.0288455	+	0.0288455i
$503$	30.5297			1.36125			0.680626	−	0.732631i	$-0.261708\pi$
$503$	30.5297			1.36125			0.680626	+	0.732631i	$0.261708\pi$
$504$		0			0
$505$	−15.8981	−	26.4102i	−0.707457	−	1.17524i
$506$	3.19828			0.142181
$507$		0			0
$508$		−	15.3792i		−	0.682343i
$509$	−2.01041	+	2.01041i	−0.0891099	+	0.0891099i	−0.750257	−	0.661147i	$-0.770070\pi$
$509$	−2.01041	+	2.01041i	−0.0891099	+	0.0891099i	0.661147	+	0.750257i	$0.270070\pi$
$510$		0			0
$511$			29.3646i			1.29901i
$512$	−0.707107	−	0.707107i	−0.0312500	−	0.0312500i
$513$		0			0
$514$	13.5921	−	13.5921i	0.599524	−	0.599524i
$515$	−11.5277	−	19.1499i	−0.507969	−	0.843847i
$516$		0			0
$517$	−3.56596			−0.156831
$518$	16.0065	−	16.0065i	0.703285	−	0.703285i
$519$		0			0
$520$	−6.89745	+	4.17436i	−0.302473	+	0.183058i
$521$		−	1.70791i		−	0.0748248i	−0.999300	−	0.0374124i	$-0.988088\pi$
$521$		−	1.70791i		−	0.0748248i	0.999300	−	0.0374124i	$-0.0119115\pi$
$522$		0			0
$523$		−	13.1798i		−	0.576311i	−0.957584	−	0.288155i	$-0.906958\pi$
$523$		−	13.1798i		−	0.576311i	0.957584	−	0.288155i	$-0.0930419\pi$
$524$	12.6532			0.552756
$525$		0			0
$526$	19.8441	+	19.8441i	0.865245	+	0.865245i
$527$	42.1719	−	42.1719i	1.83704	−	1.83704i
$528$		0			0
$529$	−17.7750			−0.772828
$530$	0.912230	−	3.67147i	0.0396247	−	0.159479i
$531$		0			0
$532$	−2.59066			−0.112319
$533$	−0.00784522	−	3.30876i	−0.000339814	−	0.143318i
$534$		0			0
$535$	7.51882	+	12.4904i	0.325067	+	0.540007i
$536$		−	13.1121i		−	0.566358i
$537$		0			0
$538$	11.8589	−	11.8589i	0.511273	−	0.511273i
$539$	−0.101282	+	0.101282i	−0.00436252	+	0.00436252i
$540$		0			0
$541$	4.98676	−	4.98676i	0.214398	−	0.214398i	−0.591735	−	0.806133i	$-0.701557\pi$
$541$	4.98676	−	4.98676i	0.214398	−	0.214398i	0.806133	+	0.591735i	$0.201557\pi$
$542$	14.4127			0.619080
$543$		0			0
$544$	5.13406	−	5.13406i	0.220121	−	0.220121i
$545$	2.44604	−	9.84462i	0.104777	−	0.421697i
$546$		0			0
$547$		−	27.5714i		−	1.17887i	−0.807817	−	0.589433i	$-0.799351\pi$
$547$		−	27.5714i		−	1.17887i	0.807817	−	0.589433i	$-0.200649\pi$
$548$	0.760088	+	0.760088i	0.0324694	+	0.0324694i
$549$		0			0
$550$	−2.21309	−	1.17211i	−0.0943663	−	0.0499787i
$551$	−3.57357	+	3.57357i	−0.152239	+	0.152239i
$552$		0			0
$553$	9.65904	+	9.65904i	0.410744	+	0.410744i
$554$	−6.32611	−	6.32611i	−0.268771	−	0.268771i
$555$		0			0
$556$		−	14.2793i		−	0.605576i
$557$	−13.3493	+	13.3493i	−0.565627	+	0.565627i	−0.930900	−	0.365273i	$-0.880976\pi$
$557$	−13.3493	+	13.3493i	−0.565627	+	0.565627i	0.365273	+	0.930900i	$0.380976\pi$
$558$		0			0
$559$	−12.2298	+	12.2879i	−0.517263	+	0.519722i
$560$	−1.39712	+	5.62301i	−0.0590389	+	0.237615i
$561$		0			0
$562$			20.6692i			0.871879i
$563$		−	19.1342i		−	0.806410i	−0.915110	−	0.403205i	$-0.867896\pi$
$563$		−	19.1342i		−	0.806410i	0.915110	−	0.403205i	$-0.132104\pi$
$564$		0			0
$565$	−22.2307	−	36.9301i	−0.935255	−	1.55366i
$566$	−2.24220	−	2.24220i	−0.0942468	−	0.0942468i
$567$		0			0
$568$		−	12.6083i		−	0.529032i
$569$	17.1664			0.719654			0.359827	−	0.933019i	$-0.382836\pi$
$569$	17.1664			0.719654			0.359827	+	0.933019i	$0.382836\pi$
$570$		0			0
$571$		−	36.0432i		−	1.50836i	−0.656668	−	0.754180i	$-0.728035\pi$
$571$		−	36.0432i		−	1.50836i	0.656668	−	0.754180i	$-0.271965\pi$
$572$	0.00428182	+	1.80588i	0.000179032	+	0.0755077i
$573$		0			0
$574$	−1.68140	−	1.68140i	−0.0701804	−	0.0701804i
$575$	28.2148	+	14.9433i	1.17664	+	0.623177i
$576$		0			0
$577$	−17.6716	+	17.6716i	−0.735679	+	0.735679i	−0.971739	−	0.236059i	$-0.924144\pi$
$577$	−17.6716	+	17.6716i	−0.735679	+	0.735679i	0.236059	+	0.971739i	$0.424144\pi$
$578$	25.2559	+	25.2559i	1.05051	+	1.05051i
$579$		0			0
$580$	5.82923	+	9.68362i	0.242046	+	0.402090i
$581$		−	7.10701i		−	0.294848i
$582$		0			0
$583$	−0.599193	−	0.599193i	−0.0248161	−	0.0248161i
$584$	−11.3327			−0.468950
$585$		0			0
$586$	−21.9861			−0.908237
$587$	2.44651	+	2.44651i	0.100978	+	0.100978i	0.755791	−	0.654813i	$-0.227253\pi$
$587$	2.44651	+	2.44651i	0.100978	+	0.100978i	−0.654813	+	0.755791i	$0.727253\pi$
$588$		0			0
$589$		−	8.21260i		−	0.338394i
$590$	0.759746	−	0.457343i	0.0312783	−	0.0188285i
$591$		0			0
$592$	6.17738	+	6.17738i	0.253889	+	0.253889i
$593$	2.25681	−	2.25681i	0.0926759	−	0.0926759i	−0.659249	−	0.751925i	$-0.729126\pi$
$593$	2.25681	−	2.25681i	0.0926759	−	0.0926759i	0.751925	+	0.659249i	$0.229126\pi$
$594$		0			0
$595$	−40.8267	−	10.1440i	−1.67373	−	0.415863i
$596$	1.92914	+	1.92914i	0.0790206	+	0.0790206i
$597$		0			0
$598$	−0.0545893	−	23.0233i	−0.00223232	−	0.941493i
$599$		−	22.7673i		−	0.930246i	−0.885246	−	0.465123i	$-0.846010\pi$
$599$		−	22.7673i		−	0.930246i	0.885246	−	0.465123i	$-0.153990\pi$
$600$		0			0
$601$	−46.4603			−1.89515			−0.947577	−	0.319528i	$-0.896476\pi$
$601$	−46.4603			−1.89515			−0.947577	+	0.319528i	$0.896476\pi$
$602$			12.4590i			0.507793i
$603$		0			0
$604$	−3.21224	−	3.21224i	−0.130704	−	0.130704i
$605$	20.5926	−	12.3961i	0.837209	−	0.503973i
$606$		0			0
$607$			0.451739i			0.0183355i	0.999958	+	0.00916777i	$0.00291823\pi$
$607$			0.451739i			0.0183355i	−0.999958	+	0.00916777i	$0.997082\pi$
$608$		−	0.999812i		−	0.0405477i
$609$		0			0
$610$	0.448569	−	1.80536i	0.0181620	−	0.0730971i
$611$	0.0608650	+	25.6701i	0.00246234	+	1.03850i
$612$		0			0
$613$	3.68562	−	3.68562i	0.148861	−	0.148861i	−0.628748	−	0.777609i	$-0.716432\pi$
$613$	3.68562	−	3.68562i	0.148861	−	0.148861i	0.777609	+	0.628748i	$0.216432\pi$
$614$		−	3.28277i		−	0.132482i
$615$		0			0
$616$	0.917688	+	0.917688i	0.0369747	+	0.0369747i
$617$	11.4145	+	11.4145i	0.459531	+	0.459531i	0.898501	−	0.438971i	$-0.144657\pi$
$617$	11.4145	+	11.4145i	0.459531	+	0.459531i	−0.438971	+	0.898501i	$0.644657\pi$
$618$		0			0
$619$	−29.3159	+	29.3159i	−1.17831	+	1.17831i	−0.198132	+	0.980175i	$0.563487\pi$
$619$	−29.3159	+	29.3159i	−1.17831	+	1.17831i	−0.980175	+	0.198132i	$0.936513\pi$
$620$	−17.8254	−	4.42898i	−0.715886	−	0.177872i
$621$		0			0
$622$	−8.53358	−	8.53358i	−0.342165	−	0.342165i
$623$		−	26.1779i		−	1.04879i
$624$		0			0
$625$	−14.0472	−	20.6803i	−0.561887	−	0.827214i
$626$	3.62344	−	3.62344i	0.144822	−	0.144822i
$627$		0			0
$628$	−19.0790			−0.761337
$629$	−44.8519	+	44.8519i	−1.78836	+	1.78836i
$630$		0			0
$631$	−12.2618	+	12.2618i	−0.488133	+	0.488133i	−0.907717	−	0.419584i	$-0.862176\pi$
$631$	−12.2618	+	12.2618i	−0.488133	+	0.488133i	0.419584	+	0.907717i	$0.362176\pi$
$632$	−3.72771	+	3.72771i	−0.148281	+	0.148281i
$633$		0			0
$634$		−	29.9860i		−	1.19090i
$635$	−17.7356	−	29.4627i	−0.703816	−	1.16919i
$636$		0			0
$637$	0.730823	+	0.727366i	0.0289563	+	0.0288193i
$638$	2.53173			0.100232
$639$		0			0
$640$	−2.17009	−	0.539189i	−0.0857802	−	0.0213133i
$641$	−33.8547			−1.33718			−0.668590	−	0.743631i	$-0.733102\pi$
$641$	−33.8547			−1.33718			−0.668590	+	0.743631i	$0.733102\pi$
$642$		0			0
$643$	3.10245	−	3.10245i	0.122349	−	0.122349i	−0.643281	−	0.765630i	$-0.722427\pi$
$643$	3.10245	−	3.10245i	0.122349	−	0.122349i	0.765630	+	0.643281i	$0.222427\pi$
$644$	−11.6997	−	11.6997i	−0.461032	−	0.461032i
$645$		0			0
$646$	7.25929			0.285613
$647$			17.2546i			0.678349i	0.940723	+	0.339175i	$0.110148\pi$
$647$			17.2546i			0.678349i	−0.940723	+	0.339175i	$0.889852\pi$
$648$		0			0
$649$		−	0.198632i		−	0.00779699i
$650$	−8.39982	+	15.9513i	−0.329468	+	0.625660i
$651$		0			0
$652$	−11.1149	+	11.1149i	−0.435294	+	0.435294i
$653$	−12.8033			−0.501030			−0.250515	−	0.968113i	$-0.580600\pi$
$653$	−12.8033			−0.501030			−0.250515	+	0.968113i	$0.580600\pi$
$654$		0			0
$655$	24.2403	−	14.5919i	0.947145	−	0.570151i
$656$	0.648903	−	0.648903i	0.0253354	−	0.0253354i
$657$		0			0
$658$	13.0447	+	13.0447i	0.508535	+	0.508535i
$659$		−	34.7256i		−	1.35272i	−0.736573	−	0.676358i	$-0.763557\pi$
$659$		−	34.7256i		−	1.35272i	0.736573	−	0.676358i	$-0.236443\pi$
$660$		0			0
$661$	−4.42529	+	4.42529i	−0.172124	+	0.172124i	−0.787912	−	0.615788i	$-0.788838\pi$
$661$	−4.42529	+	4.42529i	−0.172124	+	0.172124i	0.615788	+	0.787912i	$0.288838\pi$
$662$		−	11.2652i		−	0.437836i
$663$		0			0
$664$	2.74281			0.106442
$665$	−4.96304	+	2.98759i	−0.192458	+	0.115854i
$666$		0			0
$667$	−32.2773			−1.24978
$668$	4.82453	+	4.82453i	0.186667	+	0.186667i
$669$		0			0
$670$	−15.1212	−	25.1195i	−0.584181	−	0.970452i
$671$	−0.294640	−	0.294640i	−0.0113744	−	0.0113744i
$672$		0			0
$673$	−51.3180			−1.97816			−0.989082	−	0.147366i	$-0.952920\pi$
$673$	−51.3180			−1.97816			−0.989082	+	0.147366i	$0.952920\pi$
$674$	−22.2316	−	22.2316i	−0.856329	−	0.856329i
$675$		0			0
$676$	12.9999	−	0.0616468i	0.499994	−	0.00237103i
$677$	9.74584			0.374563			0.187282	−	0.982306i	$-0.440032\pi$
$677$	9.74584			0.374563			0.187282	+	0.982306i	$0.440032\pi$
$678$		0			0
$679$	17.4120			0.668212
$680$	3.91487	−	15.7563i	0.150128	−	0.604225i
$681$		0			0
$682$	−2.90915	+	2.90915i	−0.111397	+	0.111397i
$683$	10.1828	−	10.1828i	0.389635	−	0.389635i	−0.484922	−	0.874557i	$-0.661152\pi$
$683$	10.1828	−	10.1828i	0.389635	−	0.389635i	0.874557	+	0.484922i	$0.161152\pi$
$684$		0			0
$685$	2.33269	+	0.579589i	0.0891273	+	0.0221450i
$686$	18.8790			0.720804
$687$		0			0
$688$	−4.80832			−0.183315
$689$	−4.30316	+	4.32362i	−0.163937	+	0.164717i
$690$		0			0
$691$	−2.35261	−	2.35261i	−0.0894975	−	0.0894975i	0.660941	−	0.750438i	$-0.270157\pi$
$691$	−2.35261	−	2.35261i	−0.0894975	−	0.0894975i	−0.750438	+	0.660941i	$0.770157\pi$
$692$	−3.67792			−0.139814
$693$		0			0
$694$	22.2361	+	22.2361i	0.844070	+	0.844070i
$695$	−16.4671	−	27.3555i	−0.624633	−	1.03765i
$696$		0			0
$697$	4.71147	+	4.71147i	0.178460	+	0.178460i
$698$	−5.95490			−0.225396
$699$		0			0
$700$	3.80804	+	12.3834i	0.143930	+	0.468050i
$701$	−3.37586			−0.127504			−0.0637522	−	0.997966i	$-0.520307\pi$
$701$	−3.37586			−0.127504			−0.0637522	+	0.997966i	$0.520307\pi$
$702$		0			0
$703$			8.73449i			0.329428i
$704$	−0.354163	+	0.354163i	−0.0133480	+	0.0133480i
$705$		0			0
$706$			18.6691i			0.702622i
$707$	25.2587	+	25.2587i	0.949950	+	0.949950i
$708$		0			0
$709$	20.9010	−	20.9010i	0.784954	−	0.784954i	−0.195708	−	0.980662i	$-0.562701\pi$
$709$	20.9010	−	20.9010i	0.784954	−	0.784954i	0.980662	+	0.195708i	$0.0627005\pi$
$710$	−14.5401	−	24.1543i	−0.545681	−	0.906495i
$711$		0			0
$712$	10.1028			0.378620
$713$	37.0890	−	37.0890i	1.38899	−	1.38899i
$714$		0			0
$715$	2.09078	+	3.45467i	0.0781907	+	0.129197i
$716$			25.9594i			0.970150i
$717$		0			0
$718$		−	1.67385i		−	0.0624677i
$719$	17.5314			0.653812			0.326906	−	0.945057i	$-0.393994\pi$
$719$	17.5314			0.653812			0.326906	+	0.945057i	$0.393994\pi$
$720$		0			0
$721$	18.3149	+	18.3149i	0.682084	+	0.682084i
$722$	−12.7282	+	12.7282i	−0.473694	+	0.473694i
$723$		0			0
$724$	5.14332			0.191150
$725$	22.3347	+	11.8290i	0.829488	+	0.439317i
$726$		0			0
$727$	46.6544			1.73031			0.865157	−	0.501501i	$-0.167219\pi$
$727$	46.6544			1.73031			0.865157	+	0.501501i	$0.167219\pi$
$728$	6.59046	−	6.62179i	0.244259	−	0.245420i
$729$		0			0
$730$	−21.7106	+	13.0691i	−0.803544	+	0.483708i
$731$		−	34.9116i		−	1.29125i
$732$		0			0
$733$	22.0546	−	22.0546i	0.814604	−	0.814604i	−0.170716	−	0.985320i	$-0.554608\pi$
$733$	22.0546	−	22.0546i	0.814604	−	0.814604i	0.985320	+	0.170716i	$0.0546080\pi$
$734$	−5.40607	+	5.40607i	−0.199542	+	0.199542i
$735$		0			0
$736$	4.51525	−	4.51525i	0.166434	−	0.166434i
$737$	−6.56738			−0.241912
$738$		0			0
$739$	19.4720	−	19.4720i	0.716287	−	0.716287i	−0.251556	−	0.967843i	$-0.580942\pi$
$739$	19.4720	−	19.4720i	0.716287	−	0.716287i	0.967843	+	0.251556i	$0.0809421\pi$
$740$	18.9582	+	4.71043i	0.696916	+	0.173159i
$741$		0			0
$742$			4.38384i			0.160936i
$743$	−8.02456	−	8.02456i	−0.294392	−	0.294392i	0.544420	−	0.838813i	$-0.316750\pi$
$743$	−8.02456	−	8.02456i	−0.294392	−	0.294392i	−0.838813	+	0.544420i	$0.816750\pi$
$744$		0			0
$745$	5.92046	+	1.47102i	0.216909	+	0.0538941i
$746$	3.87166	−	3.87166i	0.141752	−	0.141752i
$747$		0			0
$748$	−2.57146	−	2.57146i	−0.0940219	−	0.0940219i
$749$	−11.9458	−	11.9458i	−0.436489	−	0.436489i
$750$		0			0
$751$		−	15.5966i		−	0.569127i	−0.958657	−	0.284564i	$-0.908151\pi$
$751$		−	15.5966i		−	0.569127i	0.958657	−	0.284564i	$-0.0918487\pi$
$752$	−5.03434	+	5.03434i	−0.183584	+	0.183584i
$753$		0			0
$754$	−0.0432125	−	18.2251i	−0.00157371	−	0.663719i
$755$	−9.85825	−	2.44942i	−0.358778	−	0.0891436i
$756$		0			0
$757$		−	26.9241i		−	0.978573i	−0.872123	−	0.489287i	$-0.837257\pi$
$757$		−	26.9241i		−	0.978573i	0.872123	−	0.489287i	$-0.162743\pi$
$758$		−	11.9160i		−	0.432808i
$759$		0			0
$760$	−1.15300	−	1.91539i	−0.0418238	−	0.0694784i
$761$	−11.8366	−	11.8366i	−0.429075	−	0.429075i	0.459238	−	0.888313i	$-0.348123\pi$
$761$	−11.8366	−	11.8366i	−0.429075	−	0.429075i	−0.888313	+	0.459238i	$0.848123\pi$
$762$		0			0
$763$			11.7548i			0.425551i
$764$	23.4969			0.850089
$765$		0			0
$766$			9.30517i			0.336210i
$767$	−1.42988	+	0.00339032i	−0.0516301	+	0.000122417i
$768$		0			0
$769$	−2.00901	−	2.00901i	−0.0724467	−	0.0724467i	0.669955	−	0.742402i	$-0.266313\pi$
$769$	−2.00901	−	2.00901i	−0.0724467	−	0.0724467i	−0.742402	+	0.669955i	$0.766313\pi$
$770$	2.81635	+	0.699763i	0.101494	+	0.0252177i
$771$		0			0
$772$	−13.7670	+	13.7670i	−0.495484	+	0.495484i
$773$	−32.7629	−	32.7629i	−1.17840	−	1.17840i	−0.980152	−	0.198248i	$-0.936475\pi$
$773$	−32.7629	−	32.7629i	−1.17840	−	1.17840i	−0.198248	−	0.980152i	$-0.563525\pi$
$774$		0			0
$775$	−39.2566	+	12.0718i	−1.41014	+	0.433632i
$776$			6.71982i			0.241227i
$777$		0			0
$778$	13.9386	+	13.9386i	0.499723	+	0.499723i
$779$	0.917515			0.0328734
$780$		0			0
$781$	−6.31502			−0.225969
$782$	32.7837	+	32.7837i	1.17234	+	1.17234i
$783$		0			0
$784$			0.285975i			0.0102134i
$785$	−36.5506	+	22.0023i	−1.30455	+	0.785296i
$786$		0			0
$787$	32.0175	+	32.0175i	1.14130	+	1.14130i	0.988212	+	0.153089i	$0.0489223\pi$
$787$	32.0175	+	32.0175i	1.14130	+	1.14130i	0.153089	+	0.988212i	$0.451078\pi$
$788$	3.99829	−	3.99829i	0.142433	−	0.142433i
$789$		0			0
$790$	−2.84249	+	11.4402i	−0.101131	+	0.407025i
$791$	35.3199	+	35.3199i	1.25583	+	1.25583i
$792$		0			0
$793$	−2.11598	+	2.12604i	−0.0751408	+	0.0754980i
$794$		−	7.93297i		−	0.281530i
$795$		0			0
$796$	−19.3636			−0.686324
$797$			16.4460i			0.582547i	0.956640	+	0.291273i	$0.0940789\pi$
$797$			16.4460i			0.582547i	−0.956640	+	0.291273i	$0.905921\pi$
$798$		0			0
$799$	−36.5526	−	36.5526i	−1.29314	−	1.29314i
$800$	−4.77914	+	1.46963i	−0.168968	+	0.0519594i
$801$		0			0
$802$		−	19.4187i		−	0.685697i
$803$			5.67612i			0.200306i
$804$		0			0
$805$	−35.9059	−	8.92133i	−1.26552	−	0.314436i
$806$	20.9916	+	20.8923i	0.739399	+	0.735901i
$807$		0			0
$808$	−9.74808	+	9.74808i	−0.342936	+	0.342936i
$809$		−	15.8402i		−	0.556911i	−0.960449	−	0.278455i	$-0.910178\pi$
$809$		−	15.8402i		−	0.556911i	0.960449	−	0.278455i	$-0.0898224\pi$
$810$		0			0
$811$	28.5680	+	28.5680i	1.00316	+	1.00316i	0.999995	+	0.00316183i	$0.00100644\pi$
$811$	28.5680	+	28.5680i	1.00316	+	1.00316i	0.00316183	+	0.999995i	$0.498994\pi$
$812$	−9.26138	−	9.26138i	−0.325011	−	0.325011i
$813$		0			0
$814$	3.09402	−	3.09402i	0.108445	−	0.108445i
$815$	−8.47544	+	34.1113i	−0.296882	+	1.19487i
$816$		0			0
$817$	−3.39935	−	3.39935i	−0.118928	−	0.118928i
$818$			18.5722i			0.649360i
$819$		0			0
$820$	0.494807	−	1.99146i	0.0172794	−	0.0695449i
$821$	31.5019	−	31.5019i	1.09942	−	1.09942i	0.104945	−	0.994478i	$-0.466533\pi$
$821$	31.5019	−	31.5019i	1.09942	−	1.09942i	0.994478	−	0.104945i	$-0.0334665\pi$
$822$		0			0
$823$	−16.5588			−0.577204			−0.288602	−	0.957449i	$-0.593190\pi$
$823$	−16.5588			−0.577204			−0.288602	+	0.957449i	$0.593190\pi$
$824$	−7.06829	+	7.06829i	−0.246235	+	0.246235i
$825$		0			0
$826$	−0.726619	+	0.726619i	−0.0252823	+	0.0252823i
$827$	0.0668289	−	0.0668289i	0.00232387	−	0.00232387i	−0.705944	−	0.708268i	$-0.749477\pi$
$827$	0.0668289	−	0.0668289i	0.00232387	−	0.00232387i	0.708268	+	0.705944i	$0.249477\pi$
$828$		0			0
$829$			25.0065i			0.868512i	0.900789	+	0.434256i	$0.142989\pi$
$829$			25.0065i			0.868512i	−0.900789	+	0.434256i	$0.857011\pi$
$830$	5.25453	−	3.16306i	0.182387	−	0.109791i
$831$		0			0
$832$	2.55555	+	2.54346i	0.0885977	+	0.0881785i
$833$	−2.07637			−0.0719419
$834$		0			0
$835$	14.8063	+	3.67884i	0.512393	+	0.127311i
$836$	−0.500768			−0.0173194
$837$		0			0
$838$	3.13757	−	3.13757i	0.108386	−	0.108386i
$839$	23.2100	+	23.2100i	0.801299	+	0.801299i	0.983299	−	0.181999i	$-0.0582568\pi$
$839$	23.2100	+	23.2100i	0.801299	+	0.801299i	−0.181999	+	0.983299i	$0.558257\pi$
$840$		0			0
$841$	3.44954			0.118950
$842$		−	15.3097i		−	0.527607i
$843$		0			0
$844$			21.2220i			0.730491i
$845$	24.8333	−	15.1098i	0.854293	−	0.519792i
$846$		0			0
$847$	−19.6947	+	19.6947i	−0.676719	+	0.676719i
$848$	−1.69186			−0.0580986
$849$		0			0
$850$	−10.6705	−	34.6997i	−0.365996	−	1.19019i
$851$	−39.4459	+	39.4459i	−1.35219	+	1.35219i
$852$		0			0
$853$	−25.1767	−	25.1767i	−0.862034	−	0.862034i	0.129541	−	0.991574i	$-0.458650\pi$
$853$	−25.1767	−	25.1767i	−0.862034	−	0.862034i	−0.991574	+	0.129541i	$0.958650\pi$
$854$			2.15566i			0.0737650i
$855$		0			0
$856$	4.61023	−	4.61023i	0.157575	−	0.157575i
$857$			8.40369i			0.287065i	0.989646	+	0.143532i	$0.0458461\pi$
$857$			8.40369i			0.287065i	−0.989646	+	0.143532i	$0.954154\pi$
$858$		0			0
$859$	24.6372			0.840611			0.420306	−	0.907383i	$-0.361923\pi$
$859$	24.6372			0.840611			0.420306	+	0.907383i	$0.361923\pi$
$860$	−9.21152	+	5.54504i	−0.314110	+	0.189084i
$861$		0			0
$862$	34.8271			1.18622
$863$	−22.7765	−	22.7765i	−0.775321	−	0.775321i	0.203710	−	0.979031i	$-0.434700\pi$
$863$	−22.7765	−	22.7765i	−0.775321	−	0.775321i	−0.979031	+	0.203710i	$0.934700\pi$
$864$		0			0
$865$	−7.04597	+	4.24145i	−0.239570	+	0.144214i
$866$	4.90680	+	4.90680i	0.166740	+	0.166740i
$867$		0			0
$868$	21.2840			0.722427
$869$	1.86707	+	1.86707i	0.0633361	+	0.0633361i
$870$		0			0
$871$	0.112094	+	47.2763i	0.00379817	+	1.60190i
$872$	−4.53651			−0.153626
$873$		0			0
$874$	6.38433			0.215953
$875$	21.5760	+	19.3320i	0.729403	+	0.653542i
$876$		0			0
$877$	14.0020	−	14.0020i	0.472815	−	0.472815i	−0.430010	−	0.902824i	$-0.641490\pi$
$877$	14.0020	−	14.0020i	0.472815	−	0.472815i	0.902824	+	0.430010i	$0.141490\pi$
$878$	−7.14953	+	7.14953i	−0.241285	+	0.241285i
$879$		0			0
$880$	−0.270060	+	1.08692i	−0.00910371	+	0.0366399i
$881$	37.2299			1.25431			0.627153	−	0.778896i	$-0.284220\pi$
$881$	37.2299			1.25431			0.627153	+	0.778896i	$0.284220\pi$
$882$		0			0
$883$	34.4647			1.15983			0.579915	−	0.814677i	$-0.303086\pi$
$883$	34.4647			1.15983			0.579915	+	0.814677i	$0.303086\pi$
$884$	−18.4672	+	18.5550i	−0.621119	+	0.624071i
$885$		0			0
$886$	15.9956	+	15.9956i	0.537382	+	0.537382i
$887$	9.90737			0.332657			0.166328	−	0.986070i	$-0.446809\pi$
$887$	9.90737			0.332657			0.166328	+	0.986070i	$0.446809\pi$
$888$		0			0
$889$	28.1780	+	28.1780i	0.945061	+	0.945061i
$890$	19.3545	−	11.6508i	0.648763	−	0.390535i
$891$		0			0
$892$	7.43025	+	7.43025i	0.248783	+	0.248783i
$893$	−7.11829			−0.238205
$894$		0			0
$895$	29.9369	+	49.7317i	1.00068	+	1.66235i
$896$	2.59114			0.0865640
$897$		0			0
$898$		−	16.6748i		−	0.556445i
$899$	29.3594	−	29.3594i	0.979190	−	0.979190i
$900$		0			0
$901$		−	12.2840i		−	0.409239i
$902$	−0.325011	−	0.325011i	−0.0108217	−	0.0108217i
$903$		0			0
$904$	−13.6310	+	13.6310i	−0.453360	+	0.453360i
$905$	9.85330	−	5.93138i	0.327535	−	0.197166i
$906$		0			0
$907$	−47.9102			−1.59083			−0.795416	−	0.606064i	$-0.792748\pi$
$907$	−47.9102			−1.59083			−0.795416	+	0.606064i	$0.792748\pi$
$908$	0.320995	−	0.320995i	0.0106526	−	0.0106526i
$909$		0			0
$910$	4.98929	−	20.2859i	0.165393	−	0.672472i
$911$		−	56.7132i		−	1.87899i	−0.342561	−	0.939496i	$-0.611294\pi$
$911$		−	56.7132i		−	1.87899i	0.342561	−	0.939496i	$-0.388706\pi$
$912$		0			0
$913$		−	1.37377i		−	0.0454652i
$914$	−5.89452			−0.194974
$915$		0			0
$916$	−8.52207	−	8.52207i	−0.281577	−	0.281577i
$917$	−23.1833	+	23.1833i	−0.765580	+	0.765580i
$918$		0			0
$919$	30.6139			1.00986			0.504929	−	0.863161i	$-0.331519\pi$
$919$	30.6139			1.00986			0.504929	+	0.863161i	$0.331519\pi$
$920$	3.44301	−	13.8572i	0.113513	−	0.456857i
$921$		0			0
$922$	−3.79750			−0.125064
$923$	0.107787	+	45.4597i	0.00354785	+	1.49633i
$924$		0			0
$925$	41.7512	−	12.8389i	1.37277	−	0.422142i
$926$		−	35.4544i		−	1.16510i
$927$		0			0
$928$	3.57425	−	3.57425i	0.117330	−	0.117330i
$929$	40.9956	−	40.9956i	1.34502	−	1.34502i	0.454045	−	0.890979i	$-0.349981\pi$
$929$	40.9956	−	40.9956i	1.34502	−	1.34502i	0.890979	−	0.454045i	$-0.150019\pi$
$930$		0			0
$931$	−0.202177	+	0.202177i	−0.00662608	+	0.00662608i
$932$	−7.38750			−0.241986
$933$		0			0
$934$	−19.7764	+	19.7764i	−0.647102	+	0.647102i
$935$	−7.89172	−	1.96081i	−0.258087	−	0.0641254i
$936$		0			0
$937$			54.0419i			1.76547i	0.469868	+	0.882736i	$0.344301\pi$
$937$			54.0419i			1.76547i	−0.469868	+	0.882736i	$0.655699\pi$
$938$	24.0242	+	24.0242i	0.784419	+	0.784419i
$939$		0			0
$940$	−3.83883	+	15.4502i	−0.125209	+	0.503931i
$941$	−22.3817	+	22.3817i	−0.729621	+	0.729621i	−0.970544	−	0.240923i	$-0.922550\pi$
$941$	−22.3817	+	22.3817i	−0.729621	+	0.729621i	0.240923	+	0.970544i	$0.422550\pi$
$942$		0			0
$943$	4.14360	+	4.14360i	0.134934	+	0.134934i
$944$	−0.280424	−	0.280424i	−0.00912703	−	0.00912703i
$945$		0			0
$946$			2.40831i			0.0783008i
$947$	2.33220	−	2.33220i	0.0757863	−	0.0757863i	−0.668198	−	0.743984i	$-0.732934\pi$
$947$	2.33220	−	2.33220i	0.0757863	−	0.0757863i	0.743984	+	0.668198i	$0.232934\pi$
$948$		0			0
$949$	40.8605	−	0.0968820i	1.32639	−	0.00314492i
$950$	−4.41772	−	2.33973i	−0.143330	−	0.0759109i
$951$		0			0
$952$			18.8134i			0.609746i
$953$			35.2587i			1.14214i	0.820901	+	0.571070i	$0.193471\pi$
$953$			35.2587i			1.14214i	−0.820901	+	0.571070i	$0.806529\pi$
$954$		0			0
$955$	45.0142	−	27.0971i	1.45662	−	0.876841i
$956$	−6.45533	−	6.45533i	−0.208780	−	0.208780i
$957$		0			0
$958$		−	14.3013i		−	0.462055i
$959$	−2.78529			−0.0899417
$960$		0			0
$961$			36.4722i			1.17652i
$962$	−22.3256	−	22.2200i	−0.719807	−	0.716402i
$963$		0			0
$964$	14.0266	+	14.0266i	0.451766	+	0.451766i
$965$	−10.4977	+	42.2504i	−0.337933	+	1.36009i
$966$		0			0
$967$	22.4885	−	22.4885i	0.723181	−	0.723181i	−0.246071	−	0.969252i	$-0.579140\pi$
$967$	22.4885	−	22.4885i	0.723181	−	0.723181i	0.969252	+	0.246071i	$0.0791396\pi$
$968$	−7.60079	−	7.60079i	−0.244299	−	0.244299i
$969$		0			0
$970$	7.74942	+	12.8735i	0.248819	+	0.413342i
$971$		−	27.3073i		−	0.876333i	−0.898894	−	0.438167i	$-0.855628\pi$
$971$		−	27.3073i		−	0.876333i	0.898894	−	0.438167i	$-0.144372\pi$
$972$		0			0
$973$	26.1627	+	26.1627i	0.838737	+	0.838737i
$974$	7.43615			0.238270
$975$		0			0
$976$	−0.831932			−0.0266295
$977$	−27.2827	−	27.2827i	−0.872850	−	0.872850i	0.119932	−	0.992782i	$-0.461732\pi$
$977$	−27.2827	−	27.2827i	−0.872850	−	0.872850i	−0.992782	+	0.119932i	$0.961732\pi$
$978$		0			0
$979$		−	5.06013i		−	0.161722i
$980$	0.329792	+	0.547856i	0.0105348	+	0.0175006i
$981$		0			0
$982$	−19.5797	−	19.5797i	−0.624813	−	0.624813i
$983$	−23.5964	+	23.5964i	−0.752607	+	0.752607i	−0.974965	−	0.222358i	$-0.928625\pi$
$983$	−23.5964	+	23.5964i	−0.752607	+	0.752607i	0.222358	+	0.974965i	$0.428625\pi$
$984$		0			0
$985$	3.04881	−	12.2706i	0.0971432	−	0.390975i
$986$	25.9514	+	25.9514i	0.826460	+	0.826460i
$987$		0			0
$988$	0.00854729	+	3.60486i	0.000271926	+	0.114686i
$989$		−	30.7037i		−	0.976320i
$990$		0			0
$991$	−48.3091			−1.53459			−0.767294	−	0.641295i	$-0.778397\pi$
$991$	−48.3091			−1.53459			−0.767294	+	0.641295i	$0.778397\pi$
$992$			8.21415i			0.260799i
$993$		0			0
$994$	23.1011	+	23.1011i	0.732723	+	0.732723i
$995$	−37.0957	+	22.3304i	−1.17601	+	0.707923i
$996$		0			0
$997$			48.8044i			1.54565i	0.634619	+	0.772825i	$0.281157\pi$
$997$			48.8044i			1.54565i	−0.634619	+	0.772825i	$0.718843\pi$
$998$		−	24.5217i		−	0.776220i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1170.2.q.c.359.6	✓	24
3.2	odd	2	inner	1170.2.q.c.359.11	yes	24
5.4	even	2		1170.2.q.d.359.7	yes	24
13.5	odd	4		1170.2.q.d.629.2	yes	24
15.14	odd	2		1170.2.q.d.359.2	yes	24
39.5	even	4		1170.2.q.d.629.7	yes	24
65.44	odd	4	inner	1170.2.q.c.629.11	yes	24
195.44	even	4	inner	1170.2.q.c.629.6	yes	24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1170.2.q.c.359.6	✓	24	1.1	even	1	trivial
1170.2.q.c.359.11	yes	24	3.2	odd	2	inner
1170.2.q.c.629.6	yes	24	195.44	even	4	inner
1170.2.q.c.629.11	yes	24	65.44	odd	4	inner
1170.2.q.d.359.2	yes	24	15.14	odd	2
1170.2.q.d.359.7	yes	24	5.4	even	2
1170.2.q.d.629.2	yes	24	13.5	odd	4
1170.2.q.d.629.7	yes	24	39.5	even	4

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 $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 1170 = 2 \cdot 3^{2} \cdot 5 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1170.q (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.707107 - 0.707107i) q^{2} +1.00000i q^{4} +(1.15322 + 1.91575i) q^{5} +(-1.83222 - 1.83222i) q^{7} +(0.707107 - 0.707107i) q^{8} +(0.539189 - 2.17009i) q^{10} +(-0.354163 - 0.354163i) q^{11} +(-2.54346 + 2.55555i) q^{13} +2.59114i q^{14} -1.00000 q^{16} -7.26066i q^{17} +(-0.706974 - 0.706974i) q^{19} +(-1.91575 + 1.15322i) q^{20} +0.500863i q^{22} -6.38553i q^{23} +(-2.34017 + 4.41855i) q^{25} +(3.60554 - 0.00854890i) q^{26} +(1.83222 - 1.83222i) q^{28} -5.05475i q^{29} +(5.80828 + 5.80828i) q^{31} +(0.707107 + 0.707107i) q^{32} +(-5.13406 + 5.13406i) q^{34} +(1.39712 - 5.62301i) q^{35} +(-6.17738 - 6.17738i) q^{37} +0.999812i q^{38} +(2.17009 + 0.539189i) q^{40} +(-0.648903 + 0.648903i) q^{41} +4.80832 q^{43} +(0.354163 - 0.354163i) q^{44} +(-4.51525 + 4.51525i) q^{46} +(5.03434 - 5.03434i) q^{47} -0.285975i q^{49} +(4.77914 - 1.46963i) q^{50} +(-2.55555 - 2.54346i) q^{52} +1.69186 q^{53} +(0.270060 - 1.08692i) q^{55} -2.59114 q^{56} +(-3.57425 + 3.57425i) q^{58} +(0.280424 + 0.280424i) q^{59} +0.831932 q^{61} -8.21415i q^{62} -1.00000i q^{64} +(-7.82895 - 1.92552i) q^{65} +(9.27168 - 9.27168i) q^{67} +7.26066 q^{68} +(-4.96398 + 2.98816i) q^{70} +(8.91541 - 8.91541i) q^{71} +(-8.01342 - 8.01342i) q^{73} +8.73614i q^{74} +(0.706974 - 0.706974i) q^{76} +1.29781i q^{77} -5.27178 q^{79} +(-1.15322 - 1.91575i) q^{80} +0.917688 q^{82} +(1.93946 + 1.93946i) q^{83} +(13.9096 - 8.37313i) q^{85} +(-3.39999 - 3.39999i) q^{86} -0.500863 q^{88} +(7.14378 + 7.14378i) q^{89} +(9.34247 - 0.0221514i) q^{91} +6.38553 q^{92} -7.11963 q^{94} +(0.539087 - 2.16968i) q^{95} +(-4.75163 + 4.75163i) q^{97} +(-0.202215 + 0.202215i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q - 20 q^{13} - 24 q^{16} - 48 q^{19} + 32 q^{25} - 8 q^{31} + 16 q^{34} - 32 q^{37} + 8 q^{40} + 80 q^{43} + 8 q^{46} - 12 q^{52} + 16 q^{55} - 24 q^{58} - 16 q^{61} - 8 q^{67} - 24 q^{70} + 48 q^{73}+ \cdots + 64 q^{97}+O(q^{100}) \) 24 * q - 20 * q^13 - 24 * q^16 - 48 * q^19 + 32 * q^25 - 8 * q^31 + 16 * q^34 - 32 * q^37 + 8 * q^40 + 80 * q^43 + 8 * q^46 - 12 * q^52 + 16 * q^55 - 24 * q^58 - 16 * q^61 - 8 * q^67 - 24 * q^70 + 48 * q^73 + 48 * q^76 - 96 * q^79 - 72 * q^82 + 8 * q^85 + 8 * q^88 + 48 * q^91 - 16 * q^94 + 64 * q^97

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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