LMFDB - Embedded newform 264.2.q.e.25.1

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [264,2,Mod(25,264)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(264, base_ring=CyclotomicField(10)) chi = DirichletCharacter(H, H._module([0, 0, 0, 8])) N = Newforms(chi, 2, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("264.25"); S:= CuspForms(chi, 2); N := Newforms(S);

Level:	$ N $	$=$	$ 264 = 2^{3} \cdot 3 \cdot 11 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	264.q (of order $5$, degree $4$, minimal)

Newform invariants

comment:select newform

sage:traces = [8,0,2,0,-1] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(5)] == traces)

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

Self dual:	no
Analytic conductor:	$2.10805061336$
Analytic rank:	$0$
Dimension:	$8$
Relative dimension:	$2$ over $\Q(\zeta_{5})$
Coefficient field:	8.0.185640625.1
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} - 3x^{7} + x^{6} + x^{5} + 4x^{4} + 3x^{3} + 9x^{2} - 81x + 81 $ x^8 - 3x^7 + x^6 + x^5 + 4x^4 + 3x^3 + 9x^2 - 81*x + 81
Coefficient ring:	$\Z[a_1, \ldots, a_{11}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{5}]$

Embedding invariants

Embedding label			25.1
Root			$-0.245684 + 1.71454i$ of defining polynomial
Character	$\chi$	$=$	264.25
Dual form			264.2.q.e.169.1

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.309017 - 0.951057i) q^{3} +(-2.76124 - 2.00616i) q^{5} +(-0.348159 + 1.07152i) q^{7} +(-0.809017 + 0.587785i) q^{9} +(-0.151841 - 3.31315i) q^{11} +(-5.67433 + 4.12264i) q^{13} +(-1.05470 + 3.24604i) q^{15} +(-3.63359 - 2.63996i) q^{17} +(-1.71188 - 5.26862i) q^{19} +1.12667 q^{21} +6.03112 q^{23} +(2.05470 + 6.32372i) q^{25} +(0.809017 + 0.587785i) q^{27} +(-0.469489 + 1.44494i) q^{29} +(2.66581 - 1.93682i) q^{31} +(-3.10407 + 1.16823i) q^{33} +(3.11100 - 2.26027i) q^{35} +(2.24568 - 6.91151i) q^{37} +(5.67433 + 4.12264i) q^{39} +(-2.93133 - 9.02172i) q^{41} -1.96888 q^{43} +3.41309 q^{45} +(1.87928 + 5.78382i) q^{47} +(4.63617 + 3.36838i) q^{49} +(-1.38791 + 4.27155i) q^{51} +(-0.952227 + 0.691834i) q^{53} +(-6.22744 + 9.45303i) q^{55} +(-4.48175 + 3.25618i) q^{57} +(1.06965 - 3.29205i) q^{59} +(2.42270 + 1.76020i) q^{61} +(-0.348159 - 1.07152i) q^{63} +23.9389 q^{65} +11.1512 q^{67} +(-1.86372 - 5.73594i) q^{69} +(-13.1309 - 9.54016i) q^{71} +(-1.29444 + 3.98388i) q^{73} +(5.37928 - 3.90827i) q^{75} +(3.60298 + 0.990799i) q^{77} +(1.87235 - 1.36034i) q^{79} +(0.309017 - 0.951057i) q^{81} +(0.459264 + 0.333675i) q^{83} +(4.73705 + 14.5792i) q^{85} +1.51930 q^{87} -13.9581 q^{89} +(-2.44194 - 7.51550i) q^{91} +(-2.66581 - 1.93682i) q^{93} +(-5.84278 + 17.9822i) q^{95} +(8.17433 - 5.93900i) q^{97} +(2.07026 + 2.59114i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q + 2 q^{3} - q^{5} - 5 q^{7} - 2 q^{9} + q^{11} - q^{13} + q^{15} - 4 q^{17} - 2 q^{19} + 10 q^{21} + 16 q^{23} + 7 q^{25} + 2 q^{27} - 7 q^{29} + 29 q^{31} - 6 q^{33} - 20 q^{35} + 13 q^{37} + q^{39}+ \cdots - 9 q^{99}+O(q^{100}) $ 8 * q + 2 * q^3 - q^5 - 5 * q^7 - 2 * q^9 + q^11 - q^13 + q^15 - 4 * q^17 - 2 * q^19 + 10 * q^21 + 16 * q^23 + 7 * q^25 + 2 * q^27 - 7 * q^29 + 29 * q^31 - 6 * q^33 - 20 * q^35 + 13 * q^37 + q^39 - 23 * q^41 - 48 * q^43 + 4 * q^45 - 15 * q^47 - 11 * q^49 + 9 * q^51 + 9 * q^53 - 22 * q^55 - 13 * q^57 + 12 * q^59 + 9 * q^61 - 5 * q^63 + 42 * q^65 + 38 * q^67 - q^69 - 41 * q^71 - 25 * q^73 + 13 * q^75 - 55 * q^77 + 11 * q^79 - 2 * q^81 + 23 * q^83 + 23 * q^85 + 22 * q^87 + 12 * q^89 - 35 * q^91 - 29 * q^93 + 29 * q^95 + 21 * q^97 - 9 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/264\mathbb{Z}\right)^\times$.

$n$	$89$	$133$	$145$	$199$
$\chi(n)$	$1$	$1$	$e\left(\frac{4}{5}\right)$	$1$

Coefficient data

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

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

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

$2$		0			0
$2$		0			0
$3$	−0.309017	−	0.951057i	−0.178411	−	0.549093i
$3$	−0.309017	−	0.951057i	−0.178411	−	0.549093i
$4$		0			0
$5$	−2.76124	−	2.00616i	−1.23487	−	0.897183i	−0.237621	−	0.971358i	$-0.576368\pi$
$5$	−2.76124	−	2.00616i	−1.23487	−	0.897183i	−0.997245	+	0.0741753i	$0.976368\pi$
$6$		0			0
$7$	−0.348159	+	1.07152i	−0.131592	+	0.404997i	−0.995044	−	0.0994325i	$-0.968297\pi$
$7$	−0.348159	+	1.07152i	−0.131592	+	0.404997i	0.863453	+	0.504430i	$0.168297\pi$
$8$		0			0
$9$	−0.809017	+	0.587785i	−0.269672	+	0.195928i
$10$		0			0
$11$	−0.151841	−	3.31315i	−0.0457819	−	0.998951i
$11$	−0.151841	−	3.31315i	−0.0457819	−	0.998951i
$12$		0			0
$13$	−5.67433	+	4.12264i	−1.57378	+	1.14342i	−0.650352	+	0.759633i	$0.725379\pi$
$13$	−5.67433	+	4.12264i	−1.57378	+	1.14342i	−0.923423	+	0.383783i	$0.874621\pi$
$14$		0			0
$15$	−1.05470	+	3.24604i	−0.272323	+	0.838123i
$16$		0			0
$17$	−3.63359	−	2.63996i	−0.881276	−	0.640284i	0.0523128	−	0.998631i	$-0.483341\pi$
$17$	−3.63359	−	2.63996i	−0.881276	−	0.640284i	−0.933589	+	0.358346i	$0.883341\pi$
$18$		0			0
$19$	−1.71188	−	5.26862i	−0.392732	−	1.20870i	−0.930714	−	0.365747i	$-0.880813\pi$
$19$	−1.71188	−	5.26862i	−0.392732	−	1.20870i	0.537983	−	0.842956i	$-0.319187\pi$
$20$		0			0
$21$	1.12667			0.245858
$22$		0			0
$23$	6.03112			1.25758			0.628788	−	0.777577i	$-0.283551\pi$
$23$	6.03112			1.25758			0.628788	+	0.777577i	$0.283551\pi$
$24$		0			0
$25$	2.05470	+	6.32372i	0.410940	+	1.26474i
$26$		0			0
$27$	0.809017	+	0.587785i	0.155695	+	0.113119i
$28$		0			0
$29$	−0.469489	+	1.44494i	−0.0871820	+	0.268319i	−0.985137	−	0.171768i	$-0.945052\pi$
$29$	−0.469489	+	1.44494i	−0.0871820	+	0.268319i	0.897955	+	0.440086i	$0.145052\pi$
$30$		0			0
$31$	2.66581	−	1.93682i	0.478793	−	0.347863i	−0.322065	−	0.946717i	$-0.604377\pi$
$31$	2.66581	−	1.93682i	0.478793	−	0.347863i	0.800858	+	0.598854i	$0.204377\pi$
$32$		0			0
$33$	−3.10407	+	1.16823i	−0.540349	+	0.203362i
$34$		0			0
$35$	3.11100	−	2.26027i	0.525855	−	0.382056i
$36$		0			0
$37$	2.24568	−	6.91151i	0.369188	−	1.13624i	−0.578128	−	0.815946i	$-0.696217\pi$
$37$	2.24568	−	6.91151i	0.369188	−	1.13624i	0.947317	−	0.320299i	$-0.103783\pi$
$38$		0			0
$39$	5.67433	+	4.12264i	0.908620	+	0.660151i
$40$		0			0
$41$	−2.93133	−	9.02172i	−0.457797	−	1.40896i	−0.867819	−	0.496880i	$-0.834479\pi$
$41$	−2.93133	−	9.02172i	−0.457797	−	1.40896i	0.410022	−	0.912076i	$-0.365521\pi$
$42$		0			0
$43$	−1.96888			−0.300251			−0.150126	−	0.988667i	$-0.547968\pi$
$43$	−1.96888			−0.300251			−0.150126	+	0.988667i	$0.547968\pi$
$44$		0			0
$45$	3.41309			0.508793
$46$		0			0
$47$	1.87928	+	5.78382i	0.274121	+	0.843657i	0.989451	+	0.144870i	$0.0462765\pi$
$47$	1.87928	+	5.78382i	0.274121	+	0.843657i	−0.715330	+	0.698787i	$0.753723\pi$
$48$		0			0
$49$	4.63617	+	3.36838i	0.662311	+	0.481197i
$50$		0			0
$51$	−1.38791	+	4.27155i	−0.194346	+	0.598136i
$52$		0			0
$53$	−0.952227	+	0.691834i	−0.130798	+	0.0950307i	−0.651261	−	0.758854i	$-0.725760\pi$
$53$	−0.952227	+	0.691834i	−0.130798	+	0.0950307i	0.520462	+	0.853885i	$0.325760\pi$
$54$		0			0
$55$	−6.22744	+	9.45303i	−0.839707	+	1.27465i
$56$		0			0
$57$	−4.48175	+	3.25618i	−0.593623	+	0.431292i
$58$		0			0
$59$	1.06965	−	3.29205i	0.139257	−	0.428589i	−0.856971	−	0.515365i	$-0.827656\pi$
$59$	1.06965	−	3.29205i	0.139257	−	0.428589i	0.996228	+	0.0867761i	$0.0276565\pi$
$60$		0			0
$61$	2.42270	+	1.76020i	0.310195	+	0.225370i	0.731980	−	0.681326i	$-0.238596\pi$
$61$	2.42270	+	1.76020i	0.310195	+	0.225370i	−0.421785	+	0.906696i	$0.638596\pi$
$62$		0			0
$63$	−0.348159	−	1.07152i	−0.0438639	−	0.134999i
$64$		0			0
$65$	23.9389			2.96925
$66$		0			0
$67$	11.1512			1.36233			0.681167	−	0.732128i	$-0.261473\pi$
$67$	11.1512			1.36233			0.681167	+	0.732128i	$0.261473\pi$
$68$		0			0
$69$	−1.86372	−	5.73594i	−0.224365	−	0.690526i
$70$		0			0
$71$	−13.1309	−	9.54016i	−1.55835	−	1.13221i	−0.937344	−	0.348404i	$-0.886724\pi$
$71$	−13.1309	−	9.54016i	−1.55835	−	1.13221i	−0.621007	−	0.783805i	$-0.713276\pi$
$72$		0			0
$73$	−1.29444	+	3.98388i	−0.151503	+	0.466278i	−0.997790	−	0.0664492i	$-0.978833\pi$
$73$	−1.29444	+	3.98388i	−0.151503	+	0.466278i	0.846287	+	0.532728i	$0.178833\pi$
$74$		0			0
$75$	5.37928	−	3.90827i	0.621146	−	0.451289i
$76$		0			0
$77$	3.60298	+	0.990799i	0.410597	+	0.112912i
$78$		0			0
$79$	1.87235	−	1.36034i	0.210656	−	0.153050i	−0.477455	−	0.878656i	$-0.658440\pi$
$79$	1.87235	−	1.36034i	0.210656	−	0.153050i	0.688110	+	0.725606i	$0.258440\pi$
$80$		0			0
$81$	0.309017	−	0.951057i	0.0343352	−	0.105673i
$82$		0			0
$83$	0.459264	+	0.333675i	0.0504108	+	0.0366256i	0.612705	−	0.790311i	$-0.290081\pi$
$83$	0.459264	+	0.333675i	0.0504108	+	0.0366256i	−0.562295	+	0.826937i	$0.690081\pi$
$84$		0			0
$85$	4.73705	+	14.5792i	0.513806	+	1.58133i
$86$		0			0
$87$	1.51930			0.162886
$88$		0			0
$89$	−13.9581			−1.47956			−0.739779	−	0.672850i	$-0.765070\pi$
$89$	−13.9581			−1.47956			−0.739779	+	0.672850i	$0.765070\pi$
$90$		0			0
$91$	−2.44194	−	7.51550i	−0.255984	−	0.787839i
$92$		0			0
$93$	−2.66581	−	1.93682i	−0.276431	−	0.200839i
$94$		0			0
$95$	−5.84278	+	17.9822i	−0.599457	+	1.84494i
$96$		0			0
$97$	8.17433	−	5.93900i	0.829977	−	0.603014i	−0.0895755	−	0.995980i	$-0.528551\pi$
$97$	8.17433	−	5.93900i	0.829977	−	0.603014i	0.919553	+	0.392966i	$0.128551\pi$
$98$		0			0
$99$	2.07026	+	2.59114i	0.208069	+	0.260420i
$100$		0			0
$101$	−3.31337	+	2.40730i	−0.329692	+	0.239535i	−0.740300	−	0.672277i	$-0.765317\pi$
$101$	−3.31337	+	2.40730i	−0.329692	+	0.239535i	0.410608	+	0.911812i	$0.365317\pi$
$102$		0			0
$103$	−0.321280	+	0.988798i	−0.0316567	+	0.0974292i	−0.965636	−	0.259897i	$-0.916311\pi$
$103$	−0.321280	+	0.988798i	−0.0316567	+	0.0974292i	0.933980	+	0.357326i	$0.116311\pi$
$104$		0			0
$105$	−3.11100	−	2.26027i	−0.303602	−	0.220580i
$106$		0			0
$107$	−0.542438	−	1.66945i	−0.0524395	−	0.161392i	0.921407	−	0.388599i	$-0.127041\pi$
$107$	−0.542438	−	1.66945i	−0.0524395	−	0.161392i	−0.973847	+	0.227207i	$0.927041\pi$
$108$		0			0
$109$	−1.11797			−0.107082			−0.0535409	−	0.998566i	$-0.517051\pi$
$109$	−1.11797			−0.107082			−0.0535409	+	0.998566i	$0.517051\pi$
$110$		0			0
$111$	−7.26719			−0.689771
$112$		0			0
$113$	0.203896	+	0.627528i	0.0191809	+	0.0590329i	0.960189	−	0.279352i	$-0.0901195\pi$
$113$	0.203896	+	0.627528i	0.0191809	+	0.0590329i	−0.941008	+	0.338385i	$0.890120\pi$
$114$		0			0
$115$	−16.6534	−	12.0994i	−1.55294	−	1.12827i
$116$		0			0
$117$	2.16740	−	6.67057i	0.200376	−	0.616695i
$118$		0			0
$119$	4.09384	−	2.97435i	0.375282	−	0.272658i
$120$		0			0
$121$	−10.9539	+	1.00615i	−0.995808	+	0.0914678i
$122$		0			0
$123$	−7.67433	+	5.57573i	−0.691971	+	0.502746i
$124$		0			0
$125$	1.73936	−	5.35321i	0.155574	−	0.478806i
$126$		0			0
$127$	−15.7897	−	11.4719i	−1.40111	−	1.01796i	−0.994541	−	0.104342i	$-0.966726\pi$
$127$	−15.7897	−	11.4719i	−1.40111	−	1.01796i	−0.406566	−	0.913622i	$-0.633274\pi$
$128$		0			0
$129$	0.608417	+	1.87252i	0.0535682	+	0.164866i
$130$		0			0
$131$	−4.41309			−0.385573			−0.192787	−	0.981241i	$-0.561752\pi$
$131$	−4.41309			−0.385573			−0.192787	+	0.981241i	$0.561752\pi$
$132$		0			0
$133$	6.24144			0.541202
$134$		0			0
$135$	−1.05470	−	3.24604i	−0.0907742	−	0.279374i
$136$		0			0
$137$	−2.46619	−	1.79179i	−0.210701	−	0.153083i	0.477430	−	0.878670i	$-0.341568\pi$
$137$	−2.46619	−	1.79179i	−0.210701	−	0.153083i	−0.688131	+	0.725587i	$0.741568\pi$
$138$		0			0
$139$	−1.13261	+	3.48581i	−0.0960666	+	0.295663i	−0.987530	−	0.157430i	$-0.949679\pi$
$139$	−1.13261	+	3.48581i	−0.0960666	+	0.295663i	0.891464	+	0.453092i	$0.149679\pi$
$140$		0			0
$141$	4.92001	−	3.57460i	0.414340	−	0.301036i
$142$		0			0
$143$	14.5205	+	18.1739i	1.21427	+	1.51978i
$144$		0			0
$145$	4.19516	−	3.04796i	0.348389	−	0.253119i
$146$		0			0
$147$	1.77086	−	5.45015i	0.146058	−	0.449521i
$148$		0			0
$149$	−1.86630	−	1.35595i	−0.152893	−	0.111083i	0.508709	−	0.860939i	$-0.330123\pi$
$149$	−1.86630	−	1.35595i	−0.152893	−	0.111083i	−0.661602	+	0.749855i	$0.730123\pi$
$150$		0			0
$151$	−0.391206	−	1.20401i	−0.0318359	−	0.0979808i	0.933876	−	0.357597i	$-0.116404\pi$
$151$	−0.391206	−	1.20401i	−0.0318359	−	0.0979808i	−0.965712	+	0.259616i	$0.916404\pi$
$152$		0			0
$153$	4.49137			0.363106
$154$		0			0
$155$	−11.2465			−0.903342
$156$		0			0
$157$	−3.21351	−	9.89018i	−0.256466	−	0.789322i	−0.993537	−	0.113507i	$-0.963792\pi$
$157$	−3.21351	−	9.89018i	−0.256466	−	0.789322i	0.737071	−	0.675815i	$-0.236208\pi$
$158$		0			0
$159$	0.952227	+	0.691834i	0.0755165	+	0.0548660i
$160$		0			0
$161$	−2.09979	+	6.46248i	−0.165486	+	0.509315i
$162$		0			0
$163$	−0.456576	+	0.331722i	−0.0357618	+	0.0259825i	−0.605523	−	0.795828i	$-0.707036\pi$
$163$	−0.456576	+	0.331722i	−0.0357618	+	0.0259825i	0.569761	+	0.821811i	$0.307036\pi$
$164$		0			0
$165$	10.9147	+	3.00150i	0.849712	+	0.233666i
$166$		0			0
$167$	−3.32716	+	2.41732i	−0.257463	+	0.187058i	−0.709028	−	0.705180i	$-0.750866\pi$
$167$	−3.32716	+	2.41732i	−0.257463	+	0.187058i	0.451565	+	0.892238i	$0.350866\pi$
$168$		0			0
$169$	11.1846	−	34.4227i	0.860356	−	2.64790i
$170$		0			0
$171$	4.48175	+	3.25618i	0.342728	+	0.249007i
$172$		0			0
$173$	2.52045	+	7.75715i	0.191626	+	0.589765i	0.999999	+	0.00109471i	$0.000348457\pi$
$173$	2.52045	+	7.75715i	0.191626	+	0.589765i	−0.808373	+	0.588671i	$0.799652\pi$
$174$		0			0
$175$	−7.49137			−0.566294
$176$		0			0
$177$	−3.46147			−0.260180
$178$		0			0
$179$	4.86637	+	14.9771i	0.363729	+	1.11944i	0.950773	+	0.309888i	$0.100292\pi$
$179$	4.86637	+	14.9771i	0.363729	+	1.11944i	−0.587044	+	0.809555i	$0.699708\pi$
$180$		0			0
$181$	−20.8771	−	15.1681i	−1.55178	−	1.12744i	−0.942365	−	0.334585i	$-0.891404\pi$
$181$	−20.8771	−	15.1681i	−1.55178	−	1.12744i	−0.609417	−	0.792850i	$-0.708596\pi$
$182$		0			0
$183$	0.925390	−	2.84806i	0.0684068	−	0.210534i
$184$		0			0
$185$	−20.0665	+	14.5792i	−1.47532	+	1.07188i
$186$		0			0
$187$	−8.19485	+	12.4395i	−0.599267	+	0.909665i
$188$		0			0
$189$	−0.911491	+	0.662237i	−0.0663012	+	0.0481707i
$190$		0			0
$191$	−1.94200	+	5.97687i	−0.140518	+	0.432471i	−0.996407	−	0.0846884i	$-0.973011\pi$
$191$	−1.94200	+	5.97687i	−0.140518	+	0.432471i	0.855889	+	0.517159i	$0.173011\pi$
$192$		0			0
$193$	17.1742	+	12.4778i	1.23623	+	0.898172i	0.997341	−	0.0728756i	$-0.0232176\pi$
$193$	17.1742	+	12.4778i	1.23623	+	0.898172i	0.238887	+	0.971047i	$0.423218\pi$
$194$		0			0
$195$	−7.39753	−	22.7672i	−0.529748	−	1.63040i
$196$		0			0
$197$	10.9336			0.778987			0.389493	−	0.921029i	$-0.372650\pi$
$197$	10.9336			0.778987			0.389493	+	0.921029i	$0.372650\pi$
$198$		0			0
$199$	13.7094			0.971835			0.485918	−	0.874005i	$-0.338486\pi$
$199$	13.7094			0.971835			0.485918	+	0.874005i	$0.338486\pi$
$200$		0			0
$201$	−3.44591	−	10.6054i	−0.243056	−	0.748048i
$202$		0			0
$203$	−1.38483	−	1.00614i	−0.0971959	−	0.0706169i
$204$		0			0
$205$	−10.0049	+	30.7919i	−0.698772	+	2.15060i
$206$		0			0
$207$	−4.87928	+	3.54500i	−0.339133	+	0.246395i
$208$		0			0
$209$	−17.1958	+	6.47169i	−1.18946	+	0.447656i
$210$		0			0
$211$	17.2966	−	12.5667i	1.19075	−	0.865129i	0.197404	−	0.980322i	$-0.436749\pi$
$211$	17.2966	−	12.5667i	1.19075	−	0.865129i	0.993343	+	0.115194i	$0.0367488\pi$
$212$		0			0
$213$	−5.01556	+	15.4363i	−0.343660	+	1.05768i
$214$		0			0
$215$	5.43656	+	3.94989i	0.370770	+	0.269380i
$216$		0			0
$217$	1.14722	+	3.53079i	0.0778786	+	0.239686i
$218$		0			0
$219$	4.18890			0.283060
$220$		0			0
$221$	31.5018			2.11904
$222$		0			0
$223$	7.51552	+	23.1304i	0.503276	+	1.54893i	0.803649	+	0.595103i	$0.202889\pi$
$223$	7.51552	+	23.1304i	0.503276	+	1.54893i	−0.300373	+	0.953822i	$0.597111\pi$
$224$		0			0
$225$	−5.37928	−	3.90827i	−0.358619	−	0.260552i
$226$		0			0
$227$	5.38356	−	16.5689i	0.357319	−	1.09972i	−0.597333	−	0.801993i	$-0.703773\pi$
$227$	5.38356	−	16.5689i	0.357319	−	1.09972i	0.954652	−	0.297723i	$-0.0962271\pi$
$228$		0			0
$229$	−11.1074	+	8.07002i	−0.734000	+	0.533282i	−0.890826	−	0.454344i	$-0.849874\pi$
$229$	−11.1074	+	8.07002i	−0.734000	+	0.533282i	0.156826	+	0.987626i	$0.449874\pi$
$230$		0			0
$231$	−0.171074	−	3.73281i	−0.0112559	−	0.245601i
$232$		0			0
$233$	−5.02150	+	3.64834i	−0.328970	+	0.239010i	−0.739993	−	0.672614i	$-0.765171\pi$
$233$	−5.02150	+	3.64834i	−0.328970	+	0.239010i	0.411024	+	0.911625i	$0.365171\pi$
$234$		0			0
$235$	6.41414	−	19.7407i	0.418412	−	1.28774i
$236$		0			0
$237$	−1.87235	−	1.36034i	−0.121622	−	0.0883637i
$238$		0			0
$239$	−2.97679	−	9.16163i	−0.192553	−	0.592617i	−0.999996	−	0.00267191i	$-0.999150\pi$
$239$	−2.97679	−	9.16163i	−0.192553	−	0.592617i	0.807444	−	0.589945i	$-0.200850\pi$
$240$		0			0
$241$	12.0675			0.777338			0.388669	−	0.921377i	$-0.372935\pi$
$241$	12.0675			0.777338			0.388669	+	0.921377i	$0.372935\pi$
$242$		0			0
$243$	−1.00000			−0.0641500
$244$		0			0
$245$	−6.04410	−	18.6018i	−0.386143	−	1.18843i
$246$		0			0
$247$	31.4344	+	22.8384i	2.00012	+	1.45317i
$248$		0			0
$249$	0.175423	−	0.539897i	0.0111170	−	0.0342146i
$250$		0			0
$251$	19.3381	−	14.0499i	1.22061	−	0.886823i	0.224457	−	0.974484i	$-0.427939\pi$
$251$	19.3381	−	14.0499i	1.22061	−	0.886823i	0.996150	+	0.0876608i	$0.0279392\pi$
$252$		0			0
$253$	−0.915773	−	19.9820i	−0.0575742	−	1.25626i
$254$		0			0
$255$	12.4018	−	9.01041i	0.776629	−	0.564254i
$256$		0			0
$257$	−3.20984	+	9.87887i	−0.200224	+	0.616227i	0.799651	+	0.600464i	$0.205018\pi$
$257$	−3.20984	+	9.87887i	−0.200224	+	0.616227i	−0.999876	+	0.0157626i	$0.994982\pi$
$258$		0			0
$259$	6.62398	+	4.81260i	0.411594	+	0.299040i
$260$		0			0
$261$	−0.469489	−	1.44494i	−0.0290607	−	0.0894395i
$262$		0			0
$263$	−1.30382			−0.0803967			−0.0401984	−	0.999192i	$-0.512799\pi$
$263$	−1.30382			−0.0803967			−0.0401984	+	0.999192i	$0.512799\pi$
$264$		0			0
$265$	4.01726			0.246778
$266$		0			0
$267$	4.31330	+	13.2750i	0.263970	+	0.812415i
$268$		0			0
$269$	7.26400	+	5.27760i	0.442894	+	0.321781i	0.786784	−	0.617229i	$-0.211745\pi$
$269$	7.26400	+	5.27760i	0.442894	+	0.321781i	−0.343890	+	0.939010i	$0.611745\pi$
$270$		0			0
$271$	8.34377	−	25.6795i	0.506848	−	1.55992i	−0.290794	−	0.956786i	$-0.593919\pi$
$271$	8.34377	−	25.6795i	0.506848	−	1.55992i	0.797642	−	0.603132i	$-0.206081\pi$
$272$		0			0
$273$	−6.39307	+	4.64484i	−0.386926	+	0.281118i
$274$		0			0
$275$	20.6394	−	7.76773i	1.24460	−	0.468412i
$276$		0			0
$277$	−20.0917	+	14.5974i	−1.20719	+	0.877075i	−0.994973	−	0.100147i	$-0.968069\pi$
$277$	−20.0917	+	14.5974i	−1.20719	+	0.877075i	−0.212218	+	0.977222i	$0.568069\pi$
$278$		0			0
$279$	−1.01825	+	3.13384i	−0.0609609	+	0.187618i
$280$		0			0
$281$	24.1855	+	17.5718i	1.44279	+	1.04825i	0.987451	+	0.157925i	$0.0504805\pi$
$281$	24.1855	+	17.5718i	1.44279	+	1.04825i	0.455335	+	0.890320i	$0.349520\pi$
$282$		0			0
$283$	2.94095	+	9.05131i	0.174821	+	0.538045i	0.999625	−	0.0273742i	$-0.00871455\pi$
$283$	2.94095	+	9.05131i	0.174821	+	0.538045i	−0.824804	+	0.565419i	$0.808715\pi$
$284$		0			0
$285$	18.9076			1.11999
$286$		0			0
$287$	10.6875			0.630865
$288$		0			0
$289$	0.980324	+	3.01713i	0.0576661	+	0.177478i
$290$		0			0
$291$	−8.17433	−	5.93900i	−0.479188	−	0.348150i
$292$		0			0
$293$	−3.34157	+	10.2843i	−0.195216	+	0.600814i	0.804758	+	0.593603i	$0.202295\pi$
$293$	−3.34157	+	10.2843i	−0.195216	+	0.600814i	−0.999974	+	0.00721059i	$0.997705\pi$
$294$		0			0
$295$	−9.55796	+	6.94426i	−0.556486	+	0.404311i
$296$		0			0
$297$	1.82458	−	2.76964i	0.105873	−	0.160711i
$298$		0			0
$299$	−34.2226	+	24.8641i	−1.97914	+	1.43793i
$300$		0			0
$301$	0.685483	−	2.10970i	0.0395106	−	0.121601i
$302$		0			0
$303$	3.31337	+	2.40730i	0.190348	+	0.138296i
$304$		0			0
$305$	−3.15843	−	9.72066i	−0.180851	−	0.556604i
$306$		0			0
$307$	−22.1996			−1.26700			−0.633498	−	0.773744i	$-0.718382\pi$
$307$	−22.1996			−1.26700			−0.633498	+	0.773744i	$0.718382\pi$
$308$		0			0
$309$	1.03968			0.0591456
$310$		0			0
$311$	−8.66074	−	26.6550i	−0.491106	−	1.51147i	−0.822939	−	0.568130i	$-0.807667\pi$
$311$	−8.66074	−	26.6550i	−0.491106	−	1.51147i	0.331834	−	0.943338i	$-0.392333\pi$
$312$		0			0
$313$	−1.52347	−	1.10687i	−0.0861118	−	0.0625639i	0.543896	−	0.839152i	$-0.316948\pi$
$313$	−1.52347	−	1.10687i	−0.0861118	−	0.0625639i	−0.630008	+	0.776589i	$0.716948\pi$
$314$		0			0
$315$	−1.18830	+	3.65720i	−0.0669529	+	0.206060i
$316$		0			0
$317$	4.37384	−	3.17778i	0.245659	−	0.178482i	−0.458142	−	0.888879i	$-0.651485\pi$
$317$	4.37384	−	3.17778i	0.245659	−	0.178482i	0.703801	+	0.710397i	$0.251485\pi$
$318$		0			0
$319$	4.85859	+	1.33609i	0.272029	+	0.0748064i
$320$		0			0
$321$	−1.42012	+	1.03178i	−0.0792635	+	0.0575883i
$322$		0			0
$323$	−7.68867	+	23.6633i	−0.427809	+	1.31666i
$324$		0			0
$325$	−37.7295	−	27.4121i	−2.09286	−	1.52055i
$326$		0			0
$327$	0.345471	+	1.06325i	0.0191046	+	0.0587979i
$328$		0			0
$329$	−6.85178			−0.377751
$330$		0			0
$331$	17.9023			0.983998			0.491999	−	0.870596i	$-0.336266\pi$
$331$	17.9023			0.983998			0.491999	+	0.870596i	$0.336266\pi$
$332$		0			0
$333$	2.24568	+	6.91151i	0.123063	+	0.378748i
$334$		0			0
$335$	−30.7912	−	22.3711i	−1.68230	−	1.22226i
$336$		0			0
$337$	9.32086	−	28.6867i	0.507740	−	1.56266i	−0.288376	−	0.957517i	$-0.593115\pi$
$337$	9.32086	−	28.6867i	0.507740	−	1.56266i	0.796115	−	0.605145i	$-0.206885\pi$
$338$		0			0
$339$	0.533807	−	0.387834i	0.0289924	−	0.0210642i
$340$		0			0
$341$	−6.82176	−	8.53812i	−0.369419	−	0.462365i
$342$		0			0
$343$	−11.6039	+	8.43069i	−0.626549	+	0.455215i
$344$		0			0
$345$	−6.36103	+	19.5772i	−0.342466	+	1.05400i
$346$		0			0
$347$	7.60308	+	5.52396i	0.408155	+	0.296542i	0.772854	−	0.634583i	$-0.218828\pi$
$347$	7.60308	+	5.52396i	0.408155	+	0.296542i	−0.364700	+	0.931125i	$0.618828\pi$
$348$		0			0
$349$	3.01499	+	9.27919i	0.161389	+	0.496704i	0.998752	−	0.0499432i	$-0.0159040\pi$
$349$	3.01499	+	9.27919i	0.161389	+	0.496704i	−0.837363	+	0.546647i	$0.815904\pi$
$350$		0			0
$351$	−7.01386			−0.374372
$352$		0			0
$353$	−16.6632			−0.886894			−0.443447	−	0.896301i	$-0.646245\pi$
$353$	−16.6632			−0.886894			−0.443447	+	0.896301i	$0.646245\pi$
$354$		0			0
$355$	17.1185	+	52.6854i	0.908558	+	2.79625i
$356$		0			0
$357$	−4.09384	−	2.97435i	−0.216669	−	0.157419i
$358$		0			0
$359$	8.75734	−	26.9523i	0.462195	−	1.42249i	−0.400282	−	0.916392i	$-0.631088\pi$
$359$	8.75734	−	26.9523i	0.462195	−	1.42249i	0.862477	−	0.506097i	$-0.168912\pi$
$360$		0			0
$361$	−9.45647	+	6.87053i	−0.497709	+	0.361607i
$362$		0			0
$363$	4.34184	+	10.1069i	0.227887	+	0.530472i
$364$		0			0
$365$	11.5666	−	8.40362i	0.605423	−	0.439865i
$366$		0			0
$367$	7.10505	−	21.8671i	0.370881	−	1.14145i	−0.575335	−	0.817918i	$-0.695128\pi$
$367$	7.10505	−	21.8671i	0.370881	−	1.14145i	0.946216	−	0.323536i	$-0.104872\pi$
$368$		0			0
$369$	7.67433	+	5.57573i	0.399510	+	0.290261i
$370$		0			0
$371$	−0.409789	−	1.26120i	−0.0212752	−	0.0654783i
$372$		0			0
$373$	−31.2842			−1.61983			−0.809916	−	0.586546i	$-0.800487\pi$
$373$	−31.2842			−1.61983			−0.809916	+	0.586546i	$0.800487\pi$
$374$		0			0
$375$	−5.62870			−0.290665
$376$		0			0
$377$	−3.29293	−	10.1346i	−0.169595	−	0.521959i
$378$		0			0
$379$	2.19703	+	1.59624i	0.112854	+	0.0819933i	0.642781	−	0.766050i	$-0.277781\pi$
$379$	2.19703	+	1.59624i	0.112854	+	0.0819933i	−0.529927	+	0.848043i	$0.677781\pi$
$380$		0			0
$381$	−6.03112	+	18.5619i	−0.308984	+	0.950954i
$382$		0			0
$383$	26.6777	−	19.3824i	1.36316	−	0.990397i	0.364928	−	0.931036i	$-0.381094\pi$
$383$	26.6777	−	19.3824i	1.36316	−	0.990397i	0.998237	−	0.0593610i	$-0.0189063\pi$
$384$		0			0
$385$	−7.96099	−	9.96399i	−0.405730	−	0.507812i
$386$		0			0
$387$	1.59286	−	1.15728i	0.0809695	−	0.0588278i
$388$		0			0
$389$	0.777222	−	2.39204i	0.0394067	−	0.121281i	−0.929418	−	0.369029i	$-0.879690\pi$
$389$	0.777222	−	2.39204i	0.0394067	−	0.121281i	0.968825	+	0.247748i	$0.0796903\pi$
$390$		0			0
$391$	−21.9146	−	15.9219i	−1.10827	−	0.805206i
$392$		0			0
$393$	1.36372	+	4.19709i	0.0687905	+	0.211715i
$394$		0			0
$395$	−7.89908			−0.397446
$396$		0			0
$397$	6.18374			0.310353			0.155177	−	0.987887i	$-0.450405\pi$
$397$	6.18374			0.310353			0.155177	+	0.987887i	$0.450405\pi$
$398$		0			0
$399$	−1.92871	−	5.93597i	−0.0965564	−	0.297170i
$400$		0			0
$401$	15.2879	+	11.1073i	0.763442	+	0.554673i	0.899964	−	0.435964i	$-0.143593\pi$
$401$	15.2879	+	11.1073i	0.763442	+	0.554673i	−0.136522	+	0.990637i	$0.543593\pi$
$402$		0			0
$403$	−7.14184	+	21.9803i	−0.355761	+	1.09492i
$404$		0			0
$405$	−2.76124	+	2.00616i	−0.137207	+	0.0996870i
$406$		0			0
$407$	−23.2398	−	6.39083i	−1.15196	−	0.316782i
$408$		0			0
$409$	13.2151	−	9.60131i	0.653443	−	0.474754i	−0.210999	−	0.977486i	$-0.567672\pi$
$409$	13.2151	−	9.60131i	0.653443	−	0.474754i	0.864442	+	0.502732i	$0.167672\pi$
$410$		0			0
$411$	−0.942002	+	2.89918i	−0.0464655	+	0.143006i
$412$		0			0
$413$	3.15510	+	2.29231i	0.155252	+	0.112797i
$414$		0			0
$415$	−0.598734	−	1.84271i	−0.0293907	−	0.0904553i
$416$		0			0
$417$	3.66520			0.179486
$418$		0			0
$419$	−14.2738			−0.697320			−0.348660	−	0.937249i	$-0.613363\pi$
$419$	−14.2738			−0.697320			−0.348660	+	0.937249i	$0.613363\pi$
$420$		0			0
$421$	1.24306	+	3.82576i	0.0605832	+	0.186456i	0.976768	−	0.214301i	$-0.0687473\pi$
$421$	1.24306	+	3.82576i	0.0605832	+	0.186456i	−0.916185	+	0.400757i	$0.868747\pi$
$422$		0			0
$423$	−4.92001	−	3.57460i	−0.239219	−	0.173803i
$424$		0			0
$425$	9.22842	−	28.4022i	0.447644	−	1.37771i
$426$		0			0
$427$	−2.72957	+	1.98315i	−0.132093	+	0.0959714i
$428$		0			0
$429$	12.7973	−	19.4259i	0.617861	−	0.937890i
$430$		0			0
$431$	11.7600	−	8.54417i	0.566461	−	0.411558i	−0.267357	−	0.963598i	$-0.586150\pi$
$431$	11.7600	−	8.54417i	0.566461	−	0.411558i	0.833818	+	0.552039i	$0.186150\pi$
$432$		0			0
$433$	1.24421	−	3.82930i	0.0597931	−	0.184024i	−0.916699	−	0.399580i	$-0.869156\pi$
$433$	1.24421	−	3.82930i	0.0597931	−	0.184024i	0.976492	+	0.215555i	$0.0691561\pi$
$434$		0			0
$435$	−4.19516	−	3.04796i	−0.201142	−	0.146139i
$436$		0			0
$437$	−10.3245	−	31.7757i	−0.493890	−	1.52004i
$438$		0			0
$439$	11.9183			0.568830			0.284415	−	0.958701i	$-0.408201\pi$
$439$	11.9183			0.568830			0.284415	+	0.958701i	$0.408201\pi$
$440$		0			0
$441$	−5.73063			−0.272887
$442$		0			0
$443$	−9.98232	−	30.7224i	−0.474274	−	1.45967i	−0.846934	−	0.531698i	$-0.821554\pi$
$443$	−9.98232	−	30.7224i	−0.474274	−	1.45967i	0.372660	−	0.927968i	$-0.378446\pi$
$444$		0			0
$445$	38.5418	+	28.0023i	1.82706	+	1.32743i
$446$		0			0
$447$	−0.712863	+	2.19397i	−0.0337172	+	0.103771i
$448$		0			0
$449$	−13.5173	+	9.82091i	−0.637922	+	0.463478i	−0.859136	−	0.511748i	$-0.828998\pi$
$449$	−13.5173	+	9.82091i	−0.637922	+	0.463478i	0.221214	+	0.975225i	$0.428998\pi$
$450$		0			0
$451$	−29.4452	+	11.0818i	−1.38652	+	0.521822i
$452$		0			0
$453$	−1.02419	+	0.744118i	−0.0481207	+	0.0349617i
$454$		0			0
$455$	−8.33453	+	25.6511i	−0.390729	+	1.20254i
$456$		0			0
$457$	−23.1717	−	16.8352i	−1.08393	−	0.787519i	−0.105563	−	0.994413i	$-0.533665\pi$
$457$	−23.1717	−	16.8352i	−1.08393	−	0.787519i	−0.978363	+	0.206894i	$0.933665\pi$
$458$		0			0
$459$	−1.38791	−	4.27155i	−0.0647821	−	0.199379i
$460$		0			0
$461$	−3.66860			−0.170864			−0.0854319	−	0.996344i	$-0.527227\pi$
$461$	−3.66860			−0.170864			−0.0854319	+	0.996344i	$0.527227\pi$
$462$		0			0
$463$	−34.3251			−1.59522			−0.797612	−	0.603171i	$-0.793904\pi$
$463$	−34.3251			−1.59522			−0.797612	+	0.603171i	$0.793904\pi$
$464$		0			0
$465$	3.47537	+	10.6961i	0.161166	+	0.496019i
$466$		0			0
$467$	22.4565	+	16.3156i	1.03916	+	0.754997i	0.970122	−	0.242617i	$-0.0780057\pi$
$467$	22.4565	+	16.3156i	1.03916	+	0.754997i	0.0690422	+	0.997614i	$0.478006\pi$
$468$		0			0
$469$	−3.88238	+	11.9487i	−0.179272	+	0.551742i
$470$		0			0
$471$	−8.41309	+	6.11246i	−0.387655	+	0.281647i
$472$		0			0
$473$	0.298957	+	6.52319i	0.0137461	+	0.299937i
$474$		0			0
$475$	29.7999	−	21.6509i	1.36731	−	0.993410i
$476$		0			0
$477$	0.363718	−	1.11941i	0.0166535	−	0.0512543i
$478$		0			0
$479$	−2.32991	−	1.69278i	−0.106456	−	0.0773451i	0.533283	−	0.845937i	$-0.320958\pi$
$479$	−2.32991	−	1.69278i	−0.106456	−	0.0773451i	−0.639740	+	0.768592i	$0.720958\pi$
$480$		0			0
$481$	15.7509	+	48.4763i	0.718180	+	2.21033i
$482$		0			0
$483$	6.79505			0.309186
$484$		0			0
$485$	−34.4859			−1.56592
$486$		0			0
$487$	−2.22271	−	6.84080i	−0.100721	−	0.309986i	0.887982	−	0.459879i	$-0.152107\pi$
$487$	−2.22271	−	6.84080i	−0.100721	−	0.309986i	−0.988702	+	0.149893i	$0.952107\pi$
$488$		0			0
$489$	0.456576	+	0.331722i	0.0206471	+	0.0150010i
$490$		0			0
$491$	−2.71620	+	8.35961i	−0.122580	+	0.377264i	−0.993452	−	0.114246i	$-0.963555\pi$
$491$	−2.71620	+	8.35961i	−0.122580	+	0.377264i	0.870872	+	0.491510i	$0.163555\pi$
$492$		0			0
$493$	5.52052	−	4.01089i	0.248632	−	0.180641i
$494$		0			0
$495$	−0.518248	−	11.3081i	−0.0232935	−	0.508259i
$496$		0			0
$497$	14.7941	−	10.7486i	0.663608	−	0.482139i
$498$		0			0
$499$	−9.44250	+	29.0610i	−0.422704	+	1.30095i	0.482471	+	0.875912i	$0.339739\pi$
$499$	−9.44250	+	29.0610i	−0.422704	+	1.30095i	−0.905175	+	0.425039i	$0.860261\pi$
$500$		0			0
$501$	3.32716	+	2.41732i	0.148646	+	0.107998i
$502$		0			0
$503$	−0.260676	−	0.802280i	−0.0116230	−	0.0357719i	0.945077	−	0.326848i	$-0.105987\pi$
$503$	−0.260676	−	0.802280i	−0.0116230	−	0.0357719i	−0.956700	+	0.291076i	$0.905987\pi$
$504$		0			0
$505$	13.9784			0.622033
$506$		0			0
$507$	−36.1942			−1.60744
$508$		0			0
$509$	−9.62894	−	29.6348i	−0.426795	−	1.31354i	−0.901265	−	0.433268i	$-0.857360\pi$
$509$	−9.62894	−	29.6348i	−0.426795	−	1.31354i	0.474470	−	0.880272i	$-0.342640\pi$
$510$		0			0
$511$	−3.81815	−	2.77405i	−0.168905	−	0.122717i
$512$		0			0
$513$	1.71188	−	5.26862i	0.0755812	−	0.232615i
$514$		0			0
$515$	2.87082	−	2.08577i	0.126504	−	0.0919102i
$516$		0			0
$517$	18.8773	−	7.10455i	0.830223	−	0.312458i
$518$		0			0
$519$	6.59863	−	4.79418i	0.289648	−	0.210441i
$520$		0			0
$521$	9.07950	−	27.9438i	0.397780	−	1.22424i	−0.528995	−	0.848625i	$-0.677431\pi$
$521$	9.07950	−	27.9438i	0.397780	−	1.22424i	0.926775	−	0.375617i	$-0.122569\pi$
$522$		0			0
$523$	30.4510	+	22.1239i	1.33153	+	0.967412i	0.999710	+	0.0240688i	$0.00766209\pi$
$523$	30.4510	+	22.1239i	1.33153	+	0.967412i	0.331818	+	0.943343i	$0.392338\pi$
$524$		0			0
$525$	2.31496	+	7.12472i	0.101033	+	0.310948i
$526$		0			0
$527$	−14.7996			−0.644680
$528$		0			0
$529$	13.3744			0.581496
$530$		0			0
$531$	1.06965	+	3.29205i	0.0464190	+	0.142863i
$532$		0			0
$533$	53.8267	+	39.1074i	2.33149	+	1.69393i
$534$		0			0
$535$	−1.85139	+	5.69799i	−0.0800425	+	0.246346i
$536$		0			0
$537$	12.7403	−	9.25638i	0.549785	−	0.399442i
$538$		0			0
$539$	10.4560	−	15.8718i	0.450370	−	0.683646i
$540$		0			0
$541$	24.1255	−	17.5282i	1.03724	−	0.753597i	0.0674932	−	0.997720i	$-0.478500\pi$
$541$	24.1255	−	17.5282i	1.03724	−	0.753597i	0.969744	+	0.244123i	$0.0784999\pi$
$542$		0			0
$543$	−7.97434	+	24.5425i	−0.342212	+	1.05322i
$544$		0			0
$545$	3.08698	+	2.24282i	0.132232	+	0.0960720i
$546$		0			0
$547$	3.47476	+	10.6942i	0.148570	+	0.457251i	0.997453	−	0.0713299i	$-0.0227243\pi$
$547$	3.47476	+	10.6942i	0.148570	+	0.457251i	−0.848883	+	0.528581i	$0.822724\pi$
$548$		0			0
$549$	−2.99462			−0.127807
$550$		0			0
$551$	8.41654			0.358557
$552$		0			0
$553$	0.805761	+	2.47988i	0.0342645	+	0.105455i
$554$		0			0
$555$	20.0665	+	14.5792i	0.851775	+	0.618851i
$556$		0			0
$557$	−5.02908	+	15.4779i	−0.213089	+	0.655821i	0.786195	+	0.617979i	$0.212048\pi$
$557$	−5.02908	+	15.4779i	−0.213089	+	0.655821i	−0.999284	+	0.0378418i	$0.987952\pi$
$558$		0			0
$559$	11.1721	−	8.11699i	0.472529	−	0.343312i
$560$		0			0
$561$	14.3630	+	3.94975i	0.606406	+	0.166759i
$562$		0			0
$563$	7.38791	−	5.36763i	0.311363	−	0.226219i	−0.421118	−	0.907006i	$-0.638362\pi$
$563$	7.38791	−	5.36763i	0.311363	−	0.226219i	0.732481	+	0.680787i	$0.238362\pi$
$564$		0			0
$565$	0.695915	−	2.14181i	0.0292774	−	0.0901065i
$566$		0			0
$567$	0.911491	+	0.662237i	0.0382790	+	0.0278113i
$568$		0			0
$569$	4.62992	+	14.2494i	0.194096	+	0.597367i	0.999986	+	0.00530134i	$0.00168748\pi$
$569$	4.62992	+	14.2494i	0.194096	+	0.597367i	−0.805890	+	0.592066i	$0.798313\pi$
$570$		0			0
$571$	−34.5185			−1.44456			−0.722278	−	0.691603i	$-0.756905\pi$
$571$	−34.5185			−1.44456			−0.722278	+	0.691603i	$0.756905\pi$
$572$		0			0
$573$	6.28445			0.262537
$574$		0			0
$575$	12.3922	+	38.1391i	0.516788	+	1.59051i
$576$		0			0
$577$	−4.37020	−	3.17514i	−0.181934	−	0.132183i	0.493091	−	0.869978i	$-0.335867\pi$
$577$	−4.37020	−	3.17514i	−0.181934	−	0.132183i	−0.675025	+	0.737795i	$0.735867\pi$
$578$		0			0
$579$	6.55997	−	20.1895i	0.272623	−	0.839047i
$580$		0			0
$581$	−0.517437	+	0.375940i	−0.0214669	+	0.0155966i
$582$		0			0
$583$	2.43673	+	3.04982i	0.100919	+	0.126311i
$584$		0			0
$585$	−19.3670	+	14.0709i	−0.800726	+	0.581761i
$586$		0			0
$587$	−2.24711	+	6.91590i	−0.0927483	+	0.285450i	−0.986660	−	0.162793i	$-0.947950\pi$
$587$	−2.24711	+	6.91590i	−0.0927483	+	0.285450i	0.893912	+	0.448242i	$0.147950\pi$
$588$		0			0
$589$	−14.7679	−	10.7295i	−0.608501	−	0.442102i
$590$		0			0
$591$	−3.37867	−	10.3985i	−0.138980	−	0.427736i
$592$		0			0
$593$	35.3724			1.45257			0.726286	−	0.687393i	$-0.241245\pi$
$593$	35.3724			1.45257			0.726286	+	0.687393i	$0.241245\pi$
$594$		0			0
$595$	−17.2711			−0.708047
$596$		0			0
$597$	−4.23644	−	13.0384i	−0.173386	−	0.533628i
$598$		0			0
$599$	9.57087	+	6.95364i	0.391055	+	0.284118i	0.765888	−	0.642974i	$-0.222300\pi$
$599$	9.57087	+	6.95364i	0.391055	+	0.284118i	−0.374833	+	0.927093i	$0.622300\pi$
$600$		0			0
$601$	3.80106	−	11.6985i	0.155049	−	0.477190i	−0.843117	−	0.537730i	$-0.819282\pi$
$601$	3.80106	−	11.6985i	0.155049	−	0.477190i	0.998166	+	0.0605394i	$0.0192821\pi$
$602$		0			0
$603$	−9.02150	+	6.55451i	−0.367384	+	0.266920i
$604$		0			0
$605$	32.2649	+	19.1971i	1.31175	+	0.780471i
$606$		0			0
$607$	27.4199	−	19.9217i	1.11294	−	0.808597i	0.129814	−	0.991538i	$-0.458562\pi$
$607$	27.4199	−	19.9217i	1.11294	−	0.808597i	0.983124	+	0.182942i	$0.0585619\pi$
$608$		0			0
$609$	−0.528957	+	1.62796i	−0.0214344	+	0.0659684i
$610$		0			0
$611$	−34.5083	−	25.0717i	−1.39606	−	1.01429i
$612$		0			0
$613$	−3.20420	−	9.86150i	−0.129416	−	0.398302i	0.865264	−	0.501317i	$-0.167151\pi$
$613$	−3.20420	−	9.86150i	−0.129416	−	0.398302i	−0.994680	+	0.103015i	$0.967151\pi$
$614$		0			0
$615$	32.3765			1.30555
$616$		0			0
$617$	−45.0416			−1.81331			−0.906653	−	0.421878i	$-0.861371\pi$
$617$	−45.0416			−1.81331			−0.906653	+	0.421878i	$0.861371\pi$
$618$		0			0
$619$	−12.3390	−	37.9757i	−0.495948	−	1.52637i	−0.815474	−	0.578794i	$-0.803524\pi$
$619$	−12.3390	−	37.9757i	−0.495948	−	1.52637i	0.319526	−	0.947577i	$-0.396476\pi$
$620$		0			0
$621$	4.87928	+	3.54500i	0.195799	+	0.142256i
$622$		0			0
$623$	4.85964	−	14.9564i	0.194698	−	0.599217i
$624$		0			0
$625$	11.3542	−	8.24929i	0.454167	−	0.329971i
$626$		0			0
$627$	11.4687	+	14.3543i	0.458017	+	0.573255i
$628$		0			0
$629$	−26.4060	+	19.1851i	−1.05288	+	0.764960i
$630$		0			0
$631$	8.37989	−	25.7906i	0.333598	−	1.02671i	−0.633810	−	0.773488i	$-0.718510\pi$
$631$	8.37989	−	25.7906i	0.333598	−	1.02671i	0.967409	−	0.253221i	$-0.0814899\pi$
$632$		0			0
$633$	−17.2966	−	12.5667i	−0.687478	−	0.499482i
$634$		0			0
$635$	20.5847	+	63.3533i	0.816880	+	2.51410i
$636$		0			0
$637$	−40.1938			−1.59254
$638$		0			0
$639$	16.2307			0.642076
$640$		0			0
$641$	7.65480	+	23.5590i	0.302346	+	0.930526i	0.980654	+	0.195748i	$0.0627136\pi$
$641$	7.65480	+	23.5590i	0.302346	+	0.930526i	−0.678308	+	0.734778i	$0.737286\pi$
$642$		0			0
$643$	1.13904	+	0.827558i	0.0449192	+	0.0326357i	0.610018	−	0.792387i	$-0.291162\pi$
$643$	1.13904	+	0.827558i	0.0449192	+	0.0326357i	−0.565099	+	0.825023i	$0.691162\pi$
$644$		0			0
$645$	2.07658	−	6.39106i	0.0817653	−	0.251648i
$646$		0			0
$647$	2.66471	−	1.93603i	0.104761	−	0.0761131i	−0.534172	−	0.845376i	$-0.679376\pi$
$647$	2.66471	−	1.93603i	0.104761	−	0.0761131i	0.638932	+	0.769263i	$0.279376\pi$
$648$		0			0
$649$	−11.0695	−	3.04405i	−0.434515	−	0.119489i
$650$		0			0
$651$	3.00347	−	2.18215i	0.117715	−	0.0855252i
$652$		0			0
$653$	−7.08687	+	21.8112i	−0.277331	+	0.853536i	0.711262	+	0.702926i	$0.248124\pi$
$653$	−7.08687	+	21.8112i	−0.277331	+	0.853536i	−0.988593	+	0.150610i	$0.951876\pi$
$654$		0			0
$655$	12.1856	+	8.85336i	0.476131	+	0.345929i
$656$		0			0
$657$	−1.29444	−	3.98388i	−0.0505010	−	0.155426i
$658$		0			0
$659$	−21.6953			−0.845128			−0.422564	−	0.906333i	$-0.638870\pi$
$659$	−21.6953			−0.845128			−0.422564	+	0.906333i	$0.638870\pi$
$660$		0			0
$661$	24.5020			0.953016			0.476508	−	0.879170i	$-0.341902\pi$
$661$	24.5020			0.953016			0.476508	+	0.879170i	$0.341902\pi$
$662$		0			0
$663$	−9.73460	−	29.9600i	−0.378060	−	1.16355i
$664$		0			0
$665$	−17.2342	−	12.5213i	−0.668312	−	0.485557i
$666$		0			0
$667$	−2.83155	+	8.71460i	−0.109638	+	0.337431i
$668$		0			0
$669$	19.6759	−	14.2954i	0.760714	−	0.552691i
$670$		0			0
$671$	5.46392	−	8.29404i	0.210932	−	0.320188i
$672$		0			0
$673$	−13.8894	+	10.0912i	−0.535397	+	0.388989i	−0.822373	−	0.568949i	$-0.807350\pi$
$673$	−13.8894	+	10.0912i	−0.535397	+	0.388989i	0.286976	+	0.957938i	$0.407350\pi$
$674$		0			0
$675$	−2.05470	+	6.32372i	−0.0790855	+	0.243400i
$676$		0			0
$677$	22.4121	+	16.2834i	0.861368	+	0.625820i	0.928257	−	0.371940i	$-0.121307\pi$
$677$	22.4121	+	16.2834i	0.861368	+	0.625820i	−0.0668888	+	0.997760i	$0.521307\pi$
$678$		0			0
$679$	3.51780	+	10.8267i	0.135001	+	0.415490i
$680$		0			0
$681$	−17.4216			−0.667596
$682$		0			0
$683$	19.1156			0.731440			0.365720	−	0.930725i	$-0.380823\pi$
$683$	19.1156			0.731440			0.365720	+	0.930725i	$0.380823\pi$
$684$		0			0
$685$	3.21513	+	9.89516i	0.122844	+	0.378075i
$686$		0			0
$687$	11.1074	+	8.07002i	0.423775	+	0.307891i
$688$		0			0
$689$	2.55107	−	7.85138i	0.0971880	−	0.299114i
$690$		0			0
$691$	7.49456	−	5.44512i	0.285106	−	0.207142i	−0.436035	−	0.899930i	$-0.643618\pi$
$691$	7.49456	−	5.44512i	0.285106	−	0.207142i	0.721142	+	0.692788i	$0.243618\pi$
$692$		0			0
$693$	−3.49725	+	1.31620i	−0.132849	+	0.0499984i
$694$		0			0
$695$	10.1205	−	7.35298i	0.383893	−	0.278914i
$696$		0			0
$697$	−13.1657	+	40.5199i	−0.498686	+	1.53480i
$698$		0			0
$699$	5.02150	+	3.64834i	0.189931	+	0.137993i
$700$		0			0
$701$	−8.14752	−	25.0755i	−0.307728	−	0.947088i	−0.978645	−	0.205556i	$-0.934100\pi$
$701$	−8.14752	−	25.0755i	−0.307728	−	0.947088i	0.670918	−	0.741532i	$-0.265900\pi$
$702$		0			0
$703$	−40.2584			−1.51837
$704$		0			0
$705$	−20.7566			−0.781738
$706$		0			0
$707$	−1.42590	−	4.38847i	−0.0536265	−	0.165045i
$708$		0			0
$709$	9.73784	+	7.07495i	0.365712	+	0.265705i	0.755431	−	0.655229i	$-0.227428\pi$
$709$	9.73784	+	7.07495i	0.365712	+	0.265705i	−0.389719	+	0.920934i	$0.627428\pi$
$710$		0			0
$711$	−0.715174	+	2.20108i	−0.0268211	+	0.0825469i
$712$		0			0
$713$	16.0778	−	11.6812i	0.602118	−	0.437465i
$714$		0			0
$715$	−3.63491	−	79.3131i	−0.135938	−	2.96614i
$716$		0			0
$717$	−7.79335	+	5.66220i	−0.291048	+	0.211459i
$718$		0			0
$719$	−14.9955	+	46.1515i	−0.559239	+	1.72116i	0.125237	+	0.992127i	$0.460031\pi$
$719$	−14.9955	+	46.1515i	−0.559239	+	1.72116i	−0.684476	+	0.729035i	$0.739969\pi$
$720$		0			0
$721$	−0.947663	−	0.688517i	−0.0352928	−	0.0256417i
$722$		0			0
$723$	−3.72907	−	11.4769i	−0.138686	−	0.426831i
$724$		0			0
$725$	−10.1021			−0.375181
$726$		0			0
$727$	15.2577			0.565878			0.282939	−	0.959138i	$-0.408691\pi$
$727$	15.2577			0.565878			0.282939	+	0.959138i	$0.408691\pi$
$728$		0			0
$729$	0.309017	+	0.951057i	0.0114451	+	0.0352243i
$730$		0			0
$731$	7.15411	+	5.19777i	0.264604	+	0.192246i
$732$		0			0
$733$	10.6093	−	32.6522i	0.391865	−	1.20604i	−0.539512	−	0.841978i	$-0.681391\pi$
$733$	10.6093	−	32.6522i	0.391865	−	1.20604i	0.931376	−	0.364058i	$-0.118609\pi$
$734$		0			0
$735$	−15.8237	+	11.4966i	−0.583664	+	0.424057i
$736$		0			0
$737$	−1.69321	−	36.9455i	−0.0623703	−	1.36091i
$738$		0			0
$739$	20.3011	−	14.7496i	0.746787	−	0.542572i	−0.148043	−	0.988981i	$-0.547297\pi$
$739$	20.3011	−	14.7496i	0.746787	−	0.542572i	0.894829	+	0.446409i	$0.147297\pi$
$740$		0			0
$741$	12.0069	−	36.9533i	0.441083	−	1.35751i
$742$		0			0
$743$	−19.3062	−	14.0268i	−0.708277	−	0.514593i	0.174341	−	0.984685i	$-0.444221\pi$
$743$	−19.3062	−	14.0268i	−0.708277	−	0.514593i	−0.882617	+	0.470092i	$0.844221\pi$
$744$		0			0
$745$	2.43306	+	7.48819i	0.0891405	+	0.274346i
$746$		0			0
$747$	−0.567681			−0.0207704
$748$		0			0
$749$	1.97771			0.0722640
$750$		0			0
$751$	2.15949	+	6.64622i	0.0788008	+	0.242524i	0.982695	−	0.185233i	$-0.0593040\pi$
$751$	2.15949	+	6.64622i	0.0788008	+	0.242524i	−0.903894	+	0.427757i	$0.859304\pi$
$752$		0			0
$753$	−19.3381	−	14.0499i	−0.704718	−	0.512008i
$754$		0			0
$755$	−1.33522	+	4.10938i	−0.0485936	+	0.149556i
$756$		0			0
$757$	−13.9467	+	10.1329i	−0.506901	+	0.368285i	−0.811647	−	0.584149i	$-0.801428\pi$
$757$	−13.9467	+	10.1329i	−0.506901	+	0.368285i	0.304746	+	0.952434i	$0.401428\pi$
$758$		0			0
$759$	−18.7210	+	7.04573i	−0.679530	+	0.255744i
$760$		0			0
$761$	−0.601206	+	0.436802i	−0.0217937	+	0.0158341i	−0.598629	−	0.801027i	$-0.704288\pi$
$761$	−0.601206	+	0.436802i	−0.0217937	+	0.0158341i	0.576835	+	0.816861i	$0.304288\pi$
$762$		0			0
$763$	0.389230	−	1.19793i	0.0140911	−	0.0433679i
$764$		0			0
$765$	−12.4018	−	9.01041i	−0.448387	−	0.325772i
$766$		0			0
$767$	7.50239	+	23.0900i	0.270896	+	0.833731i
$768$		0			0
$769$	−24.8227			−0.895129			−0.447564	−	0.894252i	$-0.647708\pi$
$769$	−24.8227			−0.895129			−0.447564	+	0.894252i	$0.647708\pi$
$770$		0			0
$771$	10.3873			0.374088
$772$		0			0
$773$	−0.191385	−	0.589022i	−0.00688364	−	0.0211857i	0.947556	−	0.319591i	$-0.103545\pi$
$773$	−0.191385	−	0.589022i	−0.00688364	−	0.0211857i	−0.954439	+	0.298405i	$0.903545\pi$
$774$		0			0
$775$	17.7254	+	12.8782i	0.636714	+	0.462600i
$776$		0			0
$777$	2.53013	−	7.78695i	0.0907681	−	0.279355i
$778$		0			0
$779$	−42.5139	+	30.8881i	−1.52322	+	1.10668i
$780$		0			0
$781$	−29.6141	+	44.9532i	−1.05968	+	1.60855i
$782$		0			0
$783$	−1.22914	+	0.893022i	−0.0439259	+	0.0319140i
$784$		0			0
$785$	−10.9680	+	33.7560i	−0.391465	+	1.20480i
$786$		0			0
$787$	14.1072	+	10.2495i	0.502868	+	0.365355i	0.810111	−	0.586276i	$-0.199407\pi$
$787$	14.1072	+	10.2495i	0.502868	+	0.365355i	−0.307243	+	0.951631i	$0.599407\pi$
$788$		0			0
$789$	0.402901	+	1.24000i	0.0143437	+	0.0441453i
$790$		0			0
$791$	−0.743399			−0.0264322
$792$		0			0
$793$	−21.0039			−0.745869
$794$		0			0
$795$	−1.24140	−	3.82064i	−0.0440280	−	0.135504i
$796$		0			0
$797$	−15.5856	−	11.3236i	−0.552070	−	0.401103i	0.276478	−	0.961020i	$-0.410833\pi$
$797$	−15.5856	−	11.3236i	−0.552070	−	0.401103i	−0.828548	+	0.559918i	$0.810833\pi$
$798$		0			0
$799$	8.44053	−	25.9773i	0.298605	−	0.919010i
$800$		0			0
$801$	11.2924	−	8.20438i	0.398996	−	0.289888i
$802$		0			0
$803$	13.3957	+	3.68376i	0.472726	+	0.129997i
$804$		0			0
$805$	18.7628	−	13.6320i	0.661302	−	0.480464i
$806$		0			0
$807$	2.77460	−	8.53934i	0.0976706	−	0.300599i
$808$		0			0
$809$	−12.1919	−	8.85795i	−0.428645	−	0.311429i	0.352462	−	0.935826i	$-0.385345\pi$
$809$	−12.1919	−	8.85795i	−0.428645	−	0.311429i	−0.781107	+	0.624397i	$0.785345\pi$
$810$		0			0
$811$	−5.93492	−	18.2658i	−0.208403	−	0.641400i	−0.999556	−	0.0297814i	$-0.990519\pi$
$811$	−5.93492	−	18.2658i	−0.208403	−	0.641400i	0.791153	−	0.611618i	$-0.209481\pi$
$812$		0			0
$813$	−27.0010			−0.946966
$814$		0			0
$815$	1.92621			0.0674721
$816$		0			0
$817$	3.37048	+	10.3733i	0.117918	+	0.362915i
$818$		0			0
$819$	6.39307	+	4.64484i	0.223392	+	0.162304i
$820$		0			0
$821$	−3.40380	+	10.4758i	−0.118794	+	0.365609i	−0.992719	−	0.120450i	$-0.961566\pi$
$821$	−3.40380	+	10.4758i	−0.118794	+	0.365609i	0.873926	+	0.486059i	$0.161566\pi$
$822$		0			0
$823$	−42.5890	+	30.9427i	−1.48456	+	1.07860i	−0.508509	+	0.861057i	$0.669803\pi$
$823$	−42.5890	+	30.9427i	−1.48456	+	1.07860i	−0.976051	+	0.217540i	$0.930197\pi$
$824$		0			0
$825$	−13.7655	−	17.2289i	−0.479253	−	0.599833i
$826$		0			0
$827$	−9.15350	+	6.65041i	−0.318298	+	0.231257i	−0.735449	−	0.677580i	$-0.763029\pi$
$827$	−9.15350	+	6.65041i	−0.318298	+	0.231257i	0.417151	+	0.908837i	$0.363029\pi$
$828$		0			0
$829$	3.09279	−	9.51863i	0.107417	−	0.330596i	−0.882873	−	0.469612i	$-0.844394\pi$
$829$	3.09279	−	9.51863i	0.107417	−	0.330596i	0.990290	+	0.139016i	$0.0443939\pi$
$830$		0			0
$831$	20.0917	+	14.5974i	0.696972	+	0.506380i
$832$		0			0
$833$	−7.95359	−	24.4786i	−0.275576	−	0.848134i
$834$		0			0
$835$	14.0366			0.485758
$836$		0			0
$837$	3.29512			0.113896
$838$		0			0
$839$	0.766202	+	2.35813i	0.0264522	+	0.0814116i	0.963411	−	0.268028i	$-0.0863720\pi$
$839$	0.766202	+	2.35813i	0.0264522	+	0.0814116i	−0.936959	+	0.349440i	$0.886372\pi$
$840$		0			0
$841$	21.5941	+	15.6890i	0.744623	+	0.541000i
$842$		0			0
$843$	9.23804	−	28.4318i	0.318175	−	0.979242i
$844$		0			0
$845$	−99.9410	+	72.6114i	−3.43808	+	2.49791i
$846$		0			0
$847$	2.73558	−	12.0876i	0.0939958	−	0.415336i
$848$		0			0
$849$	7.69951	−	5.59402i	0.264246	−	0.191986i
$850$		0			0
$851$	13.5440	−	41.6841i	0.464282	−	1.42891i
$852$		0			0
$853$	17.5627	+	12.7601i	0.601337	+	0.436897i	0.846353	−	0.532622i	$-0.178793\pi$
$853$	17.5627	+	12.7601i	0.601337	+	0.436897i	−0.245016	+	0.969519i	$0.578793\pi$
$854$		0			0
$855$	−5.84278	−	17.9822i	−0.199819	−	0.614980i
$856$		0			0
$857$	−27.8959			−0.952905			−0.476453	−	0.879200i	$-0.658078\pi$
$857$	−27.8959			−0.952905			−0.476453	+	0.879200i	$0.658078\pi$
$858$		0			0
$859$	−38.9369			−1.32851			−0.664255	−	0.747506i	$-0.731251\pi$
$859$	−38.9369			−1.32851			−0.664255	+	0.747506i	$0.731251\pi$
$860$		0			0
$861$	−3.30263	−	10.1645i	−0.112553	−	0.346404i
$862$		0			0
$863$	−16.9583	−	12.3210i	−0.577269	−	0.419410i	0.260470	−	0.965482i	$-0.416123\pi$
$863$	−16.9583	−	12.3210i	−0.577269	−	0.419410i	−0.837738	+	0.546072i	$0.816123\pi$
$864$		0			0
$865$	8.60252	−	26.4758i	0.292494	−	0.900205i
$866$		0			0
$867$	2.56652	−	1.86469i	0.0871636	−	0.0633281i
$868$		0			0
$869$	−4.79131	−	5.99681i	−0.162534	−	0.203428i
$870$		0			0
$871$	−63.2755	+	45.9724i	−2.14401	+	1.55771i
$872$		0			0
$873$	−3.12232	+	9.60950i	−0.105674	+	0.325232i
$874$		0			0
$875$	5.13051	+	3.72754i	0.173443	+	0.126014i
$876$		0			0
$877$	−1.87758	−	5.77858i	−0.0634012	−	0.195129i	0.914338	−	0.404951i	$-0.132711\pi$
$877$	−1.87758	−	5.77858i	−0.0634012	−	0.195129i	−0.977740	+	0.209822i	$0.932711\pi$
$878$		0			0
$879$	10.8135			0.364731
$880$		0			0
$881$	−9.25951			−0.311961			−0.155980	−	0.987760i	$-0.549854\pi$
$881$	−9.25951			−0.311961			−0.155980	+	0.987760i	$0.549854\pi$
$882$		0			0
$883$	−4.72865	−	14.5533i	−0.159132	−	0.489758i	0.839424	−	0.543477i	$-0.182892\pi$
$883$	−4.72865	−	14.5533i	−0.159132	−	0.489758i	−0.998556	+	0.0537192i	$0.982892\pi$
$884$		0			0
$885$	9.55796	+	6.94426i	0.321287	+	0.233429i
$886$		0			0
$887$	1.23712	−	3.80746i	0.0415384	−	0.127842i	−0.928137	−	0.372239i	$-0.878590\pi$
$887$	1.23712	−	3.80746i	0.0415384	−	0.127842i	0.969675	+	0.244397i	$0.0785901\pi$
$888$		0			0
$889$	17.7897	−	12.9250i	0.596647	−	0.433489i
$890$		0			0
$891$	−3.19791	−	0.879409i	−0.107134	−	0.0294613i
$892$		0			0
$893$	27.2557	−	19.8024i	0.912076	−	0.662662i
$894$		0			0
$895$	16.6093	−	51.1182i	0.555188	−	1.70869i
$896$		0			0
$897$	34.2226	+	24.8641i	1.14266	+	0.830190i
$898$		0			0
$899$	1.54702	+	4.76125i	0.0515961	+	0.158796i
$900$		0			0
$901$	5.28642			0.176116
$902$		0			0
$903$	−2.21827			−0.0738194
$904$		0			0
$905$	27.2171	+	83.7656i	0.904727	+	2.78446i
$906$		0			0
$907$	0.115830	+	0.0841558i	0.00384609	+	0.00279435i	0.589707	−	0.807618i	$-0.299243\pi$
$907$	0.115830	+	0.0841558i	0.00384609	+	0.00279435i	−0.585861	+	0.810412i	$0.699243\pi$
$908$		0			0
$909$	1.26559	−	3.89510i	0.0419771	−	0.129192i
$910$		0			0
$911$	15.8741	−	11.5332i	0.525933	−	0.382113i	−0.292901	−	0.956143i	$-0.594621\pi$
$911$	15.8741	−	11.5332i	0.525933	−	0.382113i	0.818834	+	0.574030i	$0.194621\pi$
$912$		0			0
$913$	1.03578	−	1.57227i	0.0342793	−	0.0520347i
$914$		0			0
$915$	−8.26889	+	6.00770i	−0.273361	+	0.198608i
$916$		0			0
$917$	1.53645	−	4.72872i	0.0507382	−	0.156156i
$918$		0			0
$919$	7.50743	+	5.45447i	0.247647	+	0.179926i	0.704683	−	0.709522i	$-0.251089\pi$
$919$	7.50743	+	5.45447i	0.247647	+	0.179926i	−0.457036	+	0.889448i	$0.651089\pi$
$920$		0			0
$921$	6.86005	+	21.1130i	0.226046	+	0.695699i
$922$		0			0
$923$	113.840			3.74708
$924$		0			0
$925$	48.3206			1.58877
$926$		0			0
$927$	−0.321280	−	0.988798i	−0.0105522	−	0.0324764i
$928$		0			0
$929$	−1.48345	−	1.07779i	−0.0486706	−	0.0353612i	0.563184	−	0.826332i	$-0.309576\pi$
$929$	−1.48345	−	1.07779i	−0.0486706	−	0.0353612i	−0.611855	+	0.790970i	$0.709576\pi$
$930$		0			0
$931$	9.81013	−	30.1925i	0.321514	−	0.989518i
$932$		0			0
$933$	−22.6741	+	16.4737i	−0.742317	+	0.539325i
$934$		0			0
$935$	47.5836	−	17.9083i	1.55615	−	0.585663i
$936$		0			0
$937$	−27.5380	+	20.0075i	−0.899627	+	0.653618i	−0.938370	−	0.345632i	$-0.887665\pi$
$937$	−27.5380	+	20.0075i	−0.899627	+	0.653618i	0.0387428	+	0.999249i	$0.487665\pi$
$938$		0			0
$939$	−0.581915	+	1.79095i	−0.0189901	+	0.0584455i
$940$		0			0
$941$	30.5584	+	22.2020i	0.996176	+	0.723764i	0.961265	−	0.275626i	$-0.0888852\pi$
$941$	30.5584	+	22.2020i	0.996176	+	0.723764i	0.0349110	+	0.999390i	$0.488885\pi$
$942$		0			0
$943$	−17.6792	−	54.4110i	−0.575715	−	1.77187i
$944$		0			0
$945$	3.84540			0.125091
$946$		0			0
$947$	22.7292			0.738600			0.369300	−	0.929310i	$-0.379598\pi$
$947$	22.7292			0.738600			0.369300	+	0.929310i	$0.379598\pi$
$948$		0			0
$949$	−9.07904	−	27.9424i	−0.294718	−	0.907049i
$950$		0			0
$951$	−4.37384	−	3.17778i	−0.141831	−	0.103047i
$952$		0			0
$953$	11.9557	−	36.7958i	0.387283	−	1.19193i	−0.547528	−	0.836788i	$-0.684431\pi$
$953$	11.9557	−	36.7958i	0.387283	−	1.19193i	0.934811	−	0.355147i	$-0.115569\pi$
$954$		0			0
$955$	17.3529	−	12.6076i	0.561527	−	0.407973i
$956$		0			0
$957$	−0.230693	−	5.03366i	−0.00745723	−	0.162715i
$958$		0			0
$959$	2.77857	−	2.01875i	0.0897248	−	0.0651889i
$960$		0			0
$961$	−6.22428	+	19.1564i	−0.200783	+	0.617947i
$962$		0			0
$963$	1.42012	+	1.03178i	0.0457628	+	0.0332486i
$964$		0			0
$965$	−22.3897	−	68.9085i	−0.720751	−	2.21824i
$966$		0			0
$967$	17.0338			0.547769			0.273885	−	0.961763i	$-0.411691\pi$
$967$	17.0338			0.547769			0.273885	+	0.961763i	$0.411691\pi$
$968$		0			0
$969$	24.8811			0.799295
$970$		0			0
$971$	9.97002	+	30.6846i	0.319953	+	0.984714i	0.973667	+	0.227973i	$0.0732098\pi$
$971$	9.97002	+	30.6846i	0.319953	+	0.984714i	−0.653714	+	0.756741i	$0.726790\pi$
$972$		0			0
$973$	−3.34080	−	2.42723i	−0.107101	−	0.0778134i
$974$		0			0
$975$	−14.4114	+	44.3537i	−0.461534	+	1.42045i
$976$		0			0
$977$	37.6581	−	27.3602i	1.20479	−	0.875330i	0.210041	−	0.977693i	$-0.432640\pi$
$977$	37.6581	−	27.3602i	1.20479	−	0.875330i	0.994747	+	0.102363i	$0.0326402\pi$
$978$		0			0
$979$	2.11942	+	46.2453i	0.0677370	+	1.47801i
$980$		0			0
$981$	0.904455	−	0.657125i	0.0288770	−	0.0209804i
$982$		0			0
$983$	−8.69019	+	26.7457i	−0.277174	+	0.853054i	0.711462	+	0.702725i	$0.248033\pi$
$983$	−8.69019	+	26.7457i	−0.277174	+	0.853054i	−0.988636	+	0.150329i	$0.951967\pi$
$984$		0			0
$985$	−30.1903	−	21.9346i	−0.961945	−	0.698894i
$986$		0			0
$987$	2.11732	+	6.51643i	0.0673949	+	0.207420i
$988$		0			0
$989$	−11.8746			−0.377589
$990$		0			0
$991$	20.6254			0.655187			0.327593	−	0.944819i	$-0.393762\pi$
$991$	20.6254			0.655187			0.327593	+	0.944819i	$0.393762\pi$
$992$		0			0
$993$	−5.53211	−	17.0261i	−0.175556	−	0.540306i
$994$		0			0
$995$	−37.8551	−	27.5033i	−1.20009	−	0.871914i
$996$		0			0
$997$	−1.37829	+	4.24195i	−0.0436510	+	0.134344i	−0.970507	−	0.241073i	$-0.922501\pi$
$997$	−1.37829	+	4.24195i	−0.0436510	+	0.134344i	0.926856	+	0.375417i	$0.122501\pi$
$998$		0			0
$999$	5.87928	−	4.27155i	0.186012	−	0.135146i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	264.2.q.e.25.1	✓	8
3.2	odd	2		792.2.r.f.289.2		8
4.3	odd	2		528.2.y.k.289.1		8
11.2	odd	10		2904.2.a.be.1.4		4
11.4	even	5	inner	264.2.q.e.169.1	yes	8
11.9	even	5		2904.2.a.bb.1.4		4
33.2	even	10		8712.2.a.cc.1.1		4
33.20	odd	10		8712.2.a.bz.1.1		4
33.26	odd	10		792.2.r.f.433.2		8
44.15	odd	10		528.2.y.k.433.1		8
44.31	odd	10		5808.2.a.co.1.4		4
44.35	even	10		5808.2.a.cl.1.4		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
264.2.q.e.25.1	✓	8	1.1	even	1	trivial
264.2.q.e.169.1	yes	8	11.4	even	5	inner
528.2.y.k.289.1		8	4.3	odd	2
528.2.y.k.433.1		8	44.15	odd	10
792.2.r.f.289.2		8	3.2	odd	2
792.2.r.f.433.2		8	33.26	odd	10
2904.2.a.bb.1.4		4	11.9	even	5
2904.2.a.be.1.4		4	11.2	odd	10
5808.2.a.cl.1.4		4	44.35	even	10
5808.2.a.co.1.4		4	44.31	odd	10
8712.2.a.bz.1.1		4	33.20	odd	10
8712.2.a.cc.1.1		4	33.2	even	10

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:	\( N \)	\(=\)	\( 264 = 2^{3} \cdot 3 \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	264.q (of order \(5\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.309017 - 0.951057i) q^{3} +(-2.76124 - 2.00616i) q^{5} +(-0.348159 + 1.07152i) q^{7} +(-0.809017 + 0.587785i) q^{9} +(-0.151841 - 3.31315i) q^{11} +(-5.67433 + 4.12264i) q^{13} +(-1.05470 + 3.24604i) q^{15} +(-3.63359 - 2.63996i) q^{17} +(-1.71188 - 5.26862i) q^{19} +1.12667 q^{21} +6.03112 q^{23} +(2.05470 + 6.32372i) q^{25} +(0.809017 + 0.587785i) q^{27} +(-0.469489 + 1.44494i) q^{29} +(2.66581 - 1.93682i) q^{31} +(-3.10407 + 1.16823i) q^{33} +(3.11100 - 2.26027i) q^{35} +(2.24568 - 6.91151i) q^{37} +(5.67433 + 4.12264i) q^{39} +(-2.93133 - 9.02172i) q^{41} -1.96888 q^{43} +3.41309 q^{45} +(1.87928 + 5.78382i) q^{47} +(4.63617 + 3.36838i) q^{49} +(-1.38791 + 4.27155i) q^{51} +(-0.952227 + 0.691834i) q^{53} +(-6.22744 + 9.45303i) q^{55} +(-4.48175 + 3.25618i) q^{57} +(1.06965 - 3.29205i) q^{59} +(2.42270 + 1.76020i) q^{61} +(-0.348159 - 1.07152i) q^{63} +23.9389 q^{65} +11.1512 q^{67} +(-1.86372 - 5.73594i) q^{69} +(-13.1309 - 9.54016i) q^{71} +(-1.29444 + 3.98388i) q^{73} +(5.37928 - 3.90827i) q^{75} +(3.60298 + 0.990799i) q^{77} +(1.87235 - 1.36034i) q^{79} +(0.309017 - 0.951057i) q^{81} +(0.459264 + 0.333675i) q^{83} +(4.73705 + 14.5792i) q^{85} +1.51930 q^{87} -13.9581 q^{89} +(-2.44194 - 7.51550i) q^{91} +(-2.66581 - 1.93682i) q^{93} +(-5.84278 + 17.9822i) q^{95} +(8.17433 - 5.93900i) q^{97} +(2.07026 + 2.59114i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q + 2 q^{3} - q^{5} - 5 q^{7} - 2 q^{9} + q^{11} - q^{13} + q^{15} - 4 q^{17} - 2 q^{19} + 10 q^{21} + 16 q^{23} + 7 q^{25} + 2 q^{27} - 7 q^{29} + 29 q^{31} - 6 q^{33} - 20 q^{35} + 13 q^{37} + q^{39}+ \cdots - 9 q^{99}+O(q^{100}) \) 8 * q + 2 * q^3 - q^5 - 5 * q^7 - 2 * q^9 + q^11 - q^13 + q^15 - 4 * q^17 - 2 * q^19 + 10 * q^21 + 16 * q^23 + 7 * q^25 + 2 * q^27 - 7 * q^29 + 29 * q^31 - 6 * q^33 - 20 * q^35 + 13 * q^37 + q^39 - 23 * q^41 - 48 * q^43 + 4 * q^45 - 15 * q^47 - 11 * q^49 + 9 * q^51 + 9 * q^53 - 22 * q^55 - 13 * q^57 + 12 * q^59 + 9 * q^61 - 5 * q^63 + 42 * q^65 + 38 * q^67 - q^69 - 41 * q^71 - 25 * q^73 + 13 * q^75 - 55 * q^77 + 11 * q^79 - 2 * q^81 + 23 * q^83 + 23 * q^85 + 22 * q^87 + 12 * q^89 - 35 * q^91 - 29 * q^93 + 29 * q^95 + 21 * q^97 - 9 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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