LMFDB - Embedded newform 552.2.q.a.121.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [552,2,Mod(25,552)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(552, base_ring=CyclotomicField(22))

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

N = Newforms(chi, 2, names="a")

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

chi := DirichletCharacter("552.25");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 552 = 2^{3} \cdot 3 \cdot 23 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	552.q (of order $11$, degree $10$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$4.40774219157$
Analytic rank:	$0$
Dimension:	$30$
Relative dimension:	$3$ over $\Q(\zeta_{11})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{11}]$

Embedding invariants

Embedding label			121.3
Character	$\chi$	$=$	552.121
Dual form			552.2.q.a.73.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.959493 - 0.281733i) q^{3} +(3.62490 - 2.32958i) q^{5} +(-0.646888 + 4.49921i) q^{7} +(0.841254 + 0.540641i) q^{9} +O(q^{10})$	\(q+(-0.959493 - 0.281733i) q^{3} +(3.62490 - 2.32958i) q^{5} +(-0.646888 + 4.49921i) q^{7} +(0.841254 + 0.540641i) q^{9} +(0.125570 + 0.274960i) q^{11} +(0.987280 + 6.86668i) q^{13} +(-4.13439 + 1.21397i) q^{15} +(1.35274 - 1.56115i) q^{17} +(-0.419918 - 0.484611i) q^{19} +(1.88826 - 4.13471i) q^{21} +(3.13861 - 3.62618i) q^{23} +(5.63588 - 12.3409i) q^{25} +(-0.654861 - 0.755750i) q^{27} +(-5.09018 + 5.87438i) q^{29} +(-0.701655 + 0.206025i) q^{31} +(-0.0430184 - 0.299200i) q^{33} +(8.13637 + 17.8162i) q^{35} +(1.45251 + 0.933470i) q^{37} +(0.987280 - 6.86668i) q^{39} +(3.46640 - 2.22772i) q^{41} +(7.95341 + 2.33533i) q^{43} +4.30893 q^{45} +4.24149 q^{47} +(-13.1080 - 3.84884i) q^{49} +(-1.73777 + 1.11680i) q^{51} +(1.08283 - 7.53123i) q^{53} +(1.09572 + 0.704178i) q^{55} +(0.266377 + 0.583285i) q^{57} +(-0.279646 - 1.94498i) q^{59} +(-5.09249 + 1.49529i) q^{61} +(-2.97665 + 3.43524i) q^{63} +(19.5753 + 22.5911i) q^{65} +(3.79686 - 8.31396i) q^{67} +(-4.03308 + 2.59504i) q^{69} +(-3.53997 + 7.75146i) q^{71} +(-0.589083 - 0.679838i) q^{73} +(-8.88441 + 10.2532i) q^{75} +(-1.31833 + 0.387098i) q^{77} +(-1.30838 - 9.09996i) q^{79} +(0.415415 + 0.909632i) q^{81} +(-9.04610 - 5.81358i) q^{83} +(1.26673 - 8.81033i) q^{85} +(6.53900 - 4.20236i) q^{87} +(1.24040 + 0.364214i) q^{89} -31.5333 q^{91} +0.731277 q^{93} +(-2.65110 - 0.778434i) q^{95} +(-7.41833 + 4.76747i) q^{97} +(-0.0430184 + 0.299200i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 30 q - 3 q^{3} - 2 q^{7} - 3 q^{9}+O(q^{10}) $ 30 * q - 3 * q^3 - 2 * q^7 - 3 * q^9	$ 30 q - 3 q^{3} - 2 q^{7} - 3 q^{9} - 15 q^{11} + 5 q^{13} - 15 q^{17} + 5 q^{19} + 9 q^{21} + 14 q^{23} + 5 q^{25} - 3 q^{27} + 13 q^{29} - 29 q^{31} - 15 q^{33} + 8 q^{35} - 3 q^{37} + 5 q^{39} + 24 q^{41} + 2 q^{43} + 22 q^{45} + 38 q^{47} + 15 q^{49} + 7 q^{51} - 7 q^{53} + 46 q^{55} - 6 q^{57} - 43 q^{59} - 22 q^{61} - 2 q^{63} + 44 q^{65} + 31 q^{67} + 3 q^{69} + 19 q^{71} - 50 q^{73} + 5 q^{75} + 16 q^{77} - 84 q^{79} - 3 q^{81} - 73 q^{83} - 8 q^{85} + 2 q^{87} + 19 q^{89} + 18 q^{91} + 26 q^{93} - 67 q^{95} - 29 q^{97} - 15 q^{99}+O(q^{100}) $ 30 * q - 3 * q^3 - 2 * q^7 - 3 * q^9 - 15 * q^11 + 5 * q^13 - 15 * q^17 + 5 * q^19 + 9 * q^21 + 14 * q^23 + 5 * q^25 - 3 * q^27 + 13 * q^29 - 29 * q^31 - 15 * q^33 + 8 * q^35 - 3 * q^37 + 5 * q^39 + 24 * q^41 + 2 * q^43 + 22 * q^45 + 38 * q^47 + 15 * q^49 + 7 * q^51 - 7 * q^53 + 46 * q^55 - 6 * q^57 - 43 * q^59 - 22 * q^61 - 2 * q^63 + 44 * q^65 + 31 * q^67 + 3 * q^69 + 19 * q^71 - 50 * q^73 + 5 * q^75 + 16 * q^77 - 84 * q^79 - 3 * q^81 - 73 * q^83 - 8 * q^85 + 2 * q^87 + 19 * q^89 + 18 * q^91 + 26 * q^93 - 67 * q^95 - 29 * q^97 - 15 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/552\mathbb{Z}\right)^\times$.

$n$	$97$	$185$	$277$	$415$
$\chi(n)$	$e\left(\frac{9}{11}\right)$	$1$	$1$	$1$

Coefficient data

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

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

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

$2$		0			0
$2$		0			0
$3$	−0.959493	−	0.281733i	−0.553964	−	0.162658i
$3$	−0.959493	−	0.281733i	−0.553964	−	0.162658i
$4$		0			0
$5$	3.62490	−	2.32958i	1.62111	−	1.04182i	0.665830	−	0.746104i	$-0.268078\pi$
$5$	3.62490	−	2.32958i	1.62111	−	1.04182i	0.955275	−	0.295718i	$-0.0955587\pi$
$6$		0			0
$7$	−0.646888	+	4.49921i	−0.244501	+	1.70054i	0.384491	+	0.923129i	$0.374377\pi$
$7$	−0.646888	+	4.49921i	−0.244501	+	1.70054i	−0.628992	+	0.777412i	$0.716532\pi$
$8$		0			0
$9$	0.841254	+	0.540641i	0.280418	+	0.180214i
$10$		0			0
$11$	0.125570	+	0.274960i	0.0378608	+	0.0829036i	0.927617	−	0.373532i	$-0.121853\pi$
$11$	0.125570	+	0.274960i	0.0378608	+	0.0829036i	−0.889757	+	0.456435i	$0.849126\pi$
$12$		0			0
$13$	0.987280	+	6.86668i	0.273822	+	1.90447i	0.407078	+	0.913393i	$0.366548\pi$
$13$	0.987280	+	6.86668i	0.273822	+	1.90447i	−0.133256	+	0.991082i	$0.542543\pi$
$14$		0			0
$15$	−4.13439	+	1.21397i	−1.06749	+	0.313445i
$16$		0			0
$17$	1.35274	−	1.56115i	0.328088	−	0.378634i	−0.567609	−	0.823298i	$-0.692132\pi$
$17$	1.35274	−	1.56115i	0.328088	−	0.378634i	0.895697	+	0.444664i	$0.146677\pi$
$18$		0			0
$19$	−0.419918	−	0.484611i	−0.0963357	−	0.111177i	0.705535	−	0.708676i	$-0.250707\pi$
$19$	−0.419918	−	0.484611i	−0.0963357	−	0.111177i	−0.801870	+	0.597498i	$0.796162\pi$
$20$		0			0
$21$	1.88826	−	4.13471i	0.412052	−	0.902267i
$22$		0			0
$23$	3.13861	−	3.62618i	0.654445	−	0.756110i
$23$	3.13861	−	3.62618i	0.654445	−	0.756110i
$24$		0			0
$25$	5.63588	−	12.3409i	1.12718	−	2.46817i
$26$		0			0
$27$	−0.654861	−	0.755750i	−0.126028	−	0.145444i
$28$		0			0
$29$	−5.09018	+	5.87438i	−0.945223	+	1.09085i	0.0505243	+	0.998723i	$0.483911\pi$
$29$	−5.09018	+	5.87438i	−0.945223	+	1.09085i	−0.995748	+	0.0921230i	$0.970635\pi$
$30$		0			0
$31$	−0.701655	+	0.206025i	−0.126021	+	0.0370031i	−0.344135	−	0.938920i	$-0.611828\pi$
$31$	−0.701655	+	0.206025i	−0.126021	+	0.0370031i	0.218114	+	0.975923i	$0.430010\pi$
$32$		0			0
$33$	−0.0430184	−	0.299200i	−0.00748854	−	0.0520840i
$34$		0			0
$35$	8.13637	+	17.8162i	1.37530	+	3.01148i
$36$		0			0
$37$	1.45251	+	0.933470i	0.238791	+	0.153462i	0.654563	−	0.756007i	$-0.272852\pi$
$37$	1.45251	+	0.933470i	0.238791	+	0.153462i	−0.415773	+	0.909469i	$0.636489\pi$
$38$		0			0
$39$	0.987280	−	6.86668i	0.158091	−	1.09955i
$40$		0			0
$41$	3.46640	−	2.22772i	0.541361	−	0.347911i	−0.241210	−	0.970473i	$-0.577544\pi$
$41$	3.46640	−	2.22772i	0.541361	−	0.347911i	0.782571	+	0.622561i	$0.213908\pi$
$42$		0			0
$43$	7.95341	+	2.33533i	1.21288	+	0.356135i	0.824766	−	0.565475i	$-0.191307\pi$
$43$	7.95341	+	2.33533i	1.21288	+	0.356135i	0.388118	+	0.921610i	$0.373125\pi$
$44$		0			0
$45$	4.30893			0.642337
$46$		0			0
$47$	4.24149			0.618685			0.309343	−	0.950951i	$-0.399891\pi$
$47$	4.24149			0.618685			0.309343	+	0.950951i	$0.399891\pi$
$48$		0			0
$49$	−13.1080	−	3.84884i	−1.87256	−	0.549835i
$50$		0			0
$51$	−1.73777	+	1.11680i	−0.243337	+	0.156383i
$52$		0			0
$53$	1.08283	−	7.53123i	0.148738	−	1.03449i	−0.769552	−	0.638585i	$-0.779520\pi$
$53$	1.08283	−	7.53123i	0.148738	−	1.03449i	0.918289	−	0.395910i	$-0.129571\pi$
$54$		0			0
$55$	1.09572	+	0.704178i	0.147747	+	0.0949513i
$56$		0			0
$57$	0.266377	+	0.583285i	0.0352826	+	0.0772580i
$58$		0			0
$59$	−0.279646	−	1.94498i	−0.0364069	−	0.253215i	0.963487	−	0.267753i	$-0.0862813\pi$
$59$	−0.279646	−	1.94498i	−0.0364069	−	0.253215i	−0.999894	+	0.0145382i	$0.995372\pi$
$60$		0			0
$61$	−5.09249	+	1.49529i	−0.652026	+	0.191452i	−0.590984	−	0.806683i	$-0.701260\pi$
$61$	−5.09249	+	1.49529i	−0.652026	+	0.191452i	−0.0610417	+	0.998135i	$0.519442\pi$
$62$		0			0
$63$	−2.97665	+	3.43524i	−0.375023	+	0.432800i
$64$		0			0
$65$	19.5753	+	22.5911i	2.42802	+	2.80208i
$66$		0			0
$67$	3.79686	−	8.31396i	0.463860	−	1.01571i	−0.522731	−	0.852498i	$-0.675087\pi$
$67$	3.79686	−	8.31396i	0.463860	−	1.01571i	0.986591	−	0.163214i	$-0.0521861\pi$
$68$		0			0
$69$	−4.03308	+	2.59504i	−0.485526	+	0.312406i
$70$		0			0
$71$	−3.53997	+	7.75146i	−0.420118	+	0.919929i	0.574711	+	0.818357i	$0.305115\pi$
$71$	−3.53997	+	7.75146i	−0.420118	+	0.919929i	−0.994828	+	0.101572i	$0.967613\pi$
$72$		0			0
$73$	−0.589083	−	0.679838i	−0.0689470	−	0.0795690i	0.720228	−	0.693737i	$-0.244037\pi$
$73$	−0.589083	−	0.679838i	−0.0689470	−	0.0795690i	−0.789175	+	0.614168i	$0.789492\pi$
$74$		0			0
$75$	−8.88441	+	10.2532i	−1.02588	+	1.18393i
$76$		0			0
$77$	−1.31833	+	0.387098i	−0.150238	+	0.0441139i
$78$		0			0
$79$	−1.30838	−	9.09996i	−0.147204	−	1.02383i	−0.920769	−	0.390109i	$-0.872437\pi$
$79$	−1.30838	−	9.09996i	−0.147204	−	1.02383i	0.773565	−	0.633717i	$-0.218472\pi$
$80$		0			0
$81$	0.415415	+	0.909632i	0.0461572	+	0.101070i
$82$		0			0
$83$	−9.04610	−	5.81358i	−0.992939	−	0.638123i	−0.0600151	−	0.998197i	$-0.519115\pi$
$83$	−9.04610	−	5.81358i	−0.992939	−	0.638123i	−0.932924	+	0.360075i	$0.882751\pi$
$84$		0			0
$85$	1.26673	−	8.81033i	0.137397	−	0.955614i
$86$		0			0
$87$	6.53900	−	4.20236i	0.701054	−	0.450540i
$88$		0			0
$89$	1.24040	+	0.364214i	0.131482	+	0.0386066i	0.346811	−	0.937935i	$-0.387264\pi$
$89$	1.24040	+	0.364214i	0.131482	+	0.0386066i	−0.215330	+	0.976541i	$0.569083\pi$
$90$		0			0
$91$	−31.5333			−3.30559
$92$		0			0
$93$	0.731277			0.0758299
$94$		0			0
$95$	−2.65110	−	0.778434i	−0.271997	−	0.0798656i
$96$		0			0
$97$	−7.41833	+	4.76747i	−0.753217	+	0.484063i	−0.860047	−	0.510214i	$-0.829566\pi$
$97$	−7.41833	+	4.76747i	−0.753217	+	0.484063i	0.106830	+	0.994277i	$0.465930\pi$
$98$		0			0
$99$	−0.0430184	+	0.299200i	−0.00432351	+	0.0300707i
$100$		0			0
$101$	−1.60810	−	1.03346i	−0.160012	−	0.102833i	0.458185	−	0.888857i	$-0.348500\pi$
$101$	−1.60810	−	1.03346i	−0.160012	−	0.102833i	−0.618196	+	0.786024i	$0.712136\pi$
$102$		0			0
$103$	−4.20588	−	9.20958i	−0.414417	−	0.907447i	−0.995603	−	0.0936761i	$-0.970138\pi$
$103$	−4.20588	−	9.20958i	−0.414417	−	0.907447i	0.581185	−	0.813771i	$-0.302589\pi$
$104$		0			0
$105$	−2.78740	−	19.3868i	−0.272022	−	1.89195i
$106$		0			0
$107$	−13.4915	+	3.96146i	−1.30427	+	0.382969i	−0.858793	−	0.512323i	$-0.828785\pi$
$107$	−13.4915	+	3.96146i	−1.30427	+	0.382969i	−0.445480	+	0.895292i	$0.646967\pi$
$108$		0			0
$109$	−9.88758	+	11.4109i	−0.947059	+	1.09296i	0.0485004	+	0.998823i	$0.484556\pi$
$109$	−9.88758	+	11.4109i	−0.947059	+	1.09296i	−0.995559	+	0.0941407i	$0.969990\pi$
$110$		0			0
$111$	−1.13068	−	1.30488i	−0.107320	−	0.123853i
$112$		0			0
$113$	4.28015	−	9.37221i	0.402642	−	0.881663i	−0.594353	−	0.804204i	$-0.702592\pi$
$113$	4.28015	−	9.37221i	0.402642	−	0.881663i	0.996996	−	0.0774594i	$-0.0246808\pi$
$114$		0			0
$115$	2.92966	−	20.4562i	0.273192	−	1.90755i
$116$		0			0
$117$	−2.88186	+	6.31038i	−0.266428	+	0.583395i
$118$		0			0
$119$	6.14885	+	7.09615i	0.563664	+	0.650503i
$120$		0			0
$121$	7.14363	−	8.24419i	0.649421	−	0.749472i
$122$		0			0
$123$	−3.95361	+	1.16088i	−0.356485	+	0.104673i
$124$		0			0
$125$	−5.25341	−	36.5383i	−0.469880	−	3.26808i
$126$		0			0
$127$	5.33126	+	11.6738i	0.473073	+	1.03589i	0.984310	+	0.176446i	$0.0564601\pi$
$127$	5.33126	+	11.6738i	0.473073	+	1.03589i	−0.511237	+	0.859440i	$0.670813\pi$
$128$		0			0
$129$	−6.97330	−	4.48147i	−0.613965	−	0.394571i
$130$		0			0
$131$	0.305661	−	2.12592i	0.0267057	−	0.185742i	−0.972102	−	0.234558i	$-0.924636\pi$
$131$	0.305661	−	2.12592i	0.0267057	−	0.185742i	0.998808	+	0.0488159i	$0.0155448\pi$
$132$		0			0
$133$	2.45200	−	1.57581i	0.212616	−	0.136640i
$134$		0			0
$135$	−4.13439	−	1.21397i	−0.355831	−	0.104482i
$136$		0			0
$137$	−4.11092			−0.351220			−0.175610	−	0.984460i	$-0.556190\pi$
$137$	−4.11092			−0.351220			−0.175610	+	0.984460i	$0.556190\pi$
$138$		0			0
$139$	2.73665			0.232120			0.116060	−	0.993242i	$-0.462974\pi$
$139$	2.73665			0.232120			0.116060	+	0.993242i	$0.462974\pi$
$140$		0			0
$141$	−4.06968	−	1.19497i	−0.342729	−	0.100634i
$142$		0			0
$143$	−1.76409	+	1.13371i	−0.147521	+	0.0948058i
$144$		0			0
$145$	−4.76655	+	33.1521i	−0.395840	+	2.75313i
$146$		0			0
$147$	11.4926	+	7.38587i	0.947897	+	0.609177i
$148$		0			0
$149$	−0.232010	−	0.508030i	−0.0190070	−	0.0416195i	0.899890	−	0.436116i	$-0.143646\pi$
$149$	−0.232010	−	0.508030i	−0.0190070	−	0.0416195i	−0.918897	+	0.394497i	$0.870919\pi$
$150$		0			0
$151$	−0.633630	−	4.40699i	−0.0515641	−	0.358636i	−0.999225	−	0.0393581i	$-0.987469\pi$
$151$	−0.633630	−	4.40699i	−0.0515641	−	0.358636i	0.947661	−	0.319278i	$-0.103440\pi$
$152$		0			0
$153$	1.98202	−	0.581973i	0.160237	−	0.0470497i
$154$		0			0
$155$	−2.06348	+	2.38138i	−0.165743	+	0.191277i
$156$		0			0
$157$	8.45046	+	9.75236i	0.674421	+	0.778323i	0.985061	−	0.172205i	$-0.0550890\pi$
$157$	8.45046	+	9.75236i	0.674421	+	0.778323i	−0.310641	+	0.950527i	$0.600544\pi$
$158$		0			0
$159$	−3.16076	+	6.92110i	−0.250664	+	0.548879i
$160$		0			0
$161$	14.2846	+	16.4670i	1.12578	+	1.29778i
$162$		0			0
$163$	1.39007	−	3.04383i	0.108879	−	0.238411i	−0.847348	−	0.531038i	$-0.821802\pi$
$163$	1.39007	−	3.04383i	0.108879	−	0.238411i	0.956227	+	0.292627i	$0.0945294\pi$
$164$		0			0
$165$	−0.852948	−	0.984354i	−0.0664019	−	0.0766319i
$166$		0			0
$167$	6.43102	−	7.42179i	0.497647	−	0.574315i	−0.450246	−	0.892905i	$-0.648664\pi$
$167$	6.43102	−	7.42179i	0.497647	−	0.574315i	0.947893	+	0.318589i	$0.103209\pi$
$168$		0			0
$169$	−33.7032	+	9.89615i	−2.59255	+	0.761242i
$170$		0			0
$171$	−0.0912568	−	0.634705i	−0.00697859	−	0.0485371i
$172$		0			0
$173$	4.04798	+	8.86384i	0.307762	+	0.673905i	0.998803	−	0.0489104i	$-0.0155749\pi$
$173$	4.04798	+	8.86384i	0.307762	+	0.673905i	−0.691041	+	0.722816i	$0.742848\pi$
$174$		0			0
$175$	51.8783	+	33.3402i	3.92163	+	2.52028i
$176$		0			0
$177$	−0.279646	+	1.94498i	−0.0210195	+	0.146194i
$178$		0			0
$179$	−12.1822	+	7.82902i	−0.910540	+	0.585169i	−0.909898	−	0.414831i	$-0.863841\pi$
$179$	−12.1822	+	7.82902i	−0.910540	+	0.585169i	−0.000641841		1.00000i	$0.500204\pi$
$180$		0			0
$181$	−2.24164	−	0.658204i	−0.166620	−	0.0489239i	0.197359	−	0.980331i	$-0.436764\pi$
$181$	−2.24164	−	0.658204i	−0.166620	−	0.0489239i	−0.363978	+	0.931407i	$0.618582\pi$
$182$		0			0
$183$	5.30748			0.392340
$184$		0			0
$185$	7.43979			0.546984
$186$		0			0
$187$	0.599117	+	0.175917i	0.0438118	+	0.0128643i
$188$		0			0
$189$	3.82390	−	2.45747i	0.278147	−	0.178755i
$190$		0			0
$191$	−0.597313	+	4.15441i	−0.0432201	+	0.300602i	0.956733	+	0.290966i	$0.0939765\pi$
$191$	−0.597313	+	4.15441i	−0.0432201	+	0.300602i	−0.999954	+	0.00963655i	$0.996933\pi$
$192$		0			0
$193$	−17.7213	−	11.3888i	−1.27561	−	0.819784i	−0.285269	−	0.958447i	$-0.592083\pi$
$193$	−17.7213	−	11.3888i	−1.27561	−	0.819784i	−0.990340	+	0.138663i	$0.955719\pi$
$194$		0			0
$195$	−12.4177	−	27.1910i	−0.889251	−	1.94719i
$196$		0			0
$197$	0.846416	+	5.88696i	0.0603047	+	0.419428i	0.997503	+	0.0706301i	$0.0225010\pi$
$197$	0.846416	+	5.88696i	0.0603047	+	0.419428i	−0.937198	+	0.348798i	$0.886590\pi$
$198$		0			0
$199$	5.00049	−	1.46828i	0.354475	−	0.104083i	−0.0996466	−	0.995023i	$-0.531771\pi$
$199$	5.00049	−	1.46828i	0.354475	−	0.104083i	0.454122	+	0.890940i	$0.349953\pi$
$200$		0			0
$201$	−5.98537	+	6.90749i	−0.422176	+	0.487217i
$202$		0			0
$203$	−23.1373	−	26.7019i	−1.62392	−	1.87410i
$204$		0			0
$205$	7.37570	−	16.1505i	0.515141	−	1.12800i
$206$		0			0
$207$	4.60082	−	1.35368i	0.319779	−	0.0940869i
$208$		0			0
$209$	0.0805196	−	0.176313i	0.00556966	−	0.0121958i
$210$		0			0
$211$	3.17467	+	3.66377i	0.218553	+	0.252224i	0.854430	−	0.519567i	$-0.173907\pi$
$211$	3.17467	+	3.66377i	0.218553	+	0.252224i	−0.635876	+	0.771791i	$0.719361\pi$
$212$		0			0
$213$	5.58042	−	6.44015i	0.382364	−	0.441272i
$214$		0			0
$215$	34.2707	−	10.0628i	2.33724	−	0.686276i
$216$		0			0
$217$	−0.473055	−	3.29017i	−0.0321130	−	0.223351i
$218$		0			0
$219$	0.373689	+	0.818264i	0.0252515	+	0.0552932i
$220$		0			0
$221$	12.0554	+	7.74756i	0.810936	+	0.521157i
$222$		0			0
$223$	0.834333	−	5.80291i	0.0558711	−	0.388592i	−0.942629	−	0.333842i	$-0.891655\pi$
$223$	0.834333	−	5.80291i	0.0558711	−	0.388592i	0.998500	−	0.0547498i	$-0.0174361\pi$
$224$		0			0
$225$	11.4132	−	7.33480i	0.760878	−	0.488987i
$226$		0			0
$227$	−18.0114	−	5.28862i	−1.19546	−	0.351018i	−0.377344	−	0.926073i	$-0.623162\pi$
$227$	−18.0114	−	5.28862i	−1.19546	−	0.351018i	−0.818115	+	0.575055i	$0.804981\pi$
$228$		0			0
$229$	6.86545			0.453682			0.226841	−	0.973932i	$-0.427160\pi$
$229$	6.86545			0.453682			0.226841	+	0.973932i	$0.427160\pi$
$230$		0			0
$231$	1.37399			0.0904019
$232$		0			0
$233$	4.22217	+	1.23974i	0.276604	+	0.0812182i	0.417092	−	0.908864i	$-0.363049\pi$
$233$	4.22217	+	1.23974i	0.276604	+	0.0812182i	−0.140489	+	0.990082i	$0.544867\pi$
$234$		0			0
$235$	15.3750	−	9.88091i	1.00295	−	0.644559i
$236$		0			0
$237$	−1.30838	+	9.09996i	−0.0849882	+	0.591106i
$238$		0			0
$239$	−9.35122	−	6.00966i	−0.604880	−	0.388733i	0.202054	−	0.979374i	$-0.435238\pi$
$239$	−9.35122	−	6.00966i	−0.604880	−	0.388733i	−0.806934	+	0.590642i	$0.798875\pi$
$240$		0			0
$241$	3.66647	+	8.02844i	0.236178	+	0.517157i	0.990194	−	0.139698i	$-0.0446133\pi$
$241$	3.66647	+	8.02844i	0.236178	+	0.517157i	−0.754016	+	0.656856i	$0.771886\pi$
$242$		0			0
$243$	−0.142315	−	0.989821i	−0.00912950	−	0.0634971i
$244$		0			0
$245$	−56.4812	+	16.5844i	−3.60845	+	1.05954i
$246$		0			0
$247$	2.91309	−	3.36189i	0.185356	−	0.213912i
$248$		0			0
$249$	7.04180	+	8.12667i	0.446256	+	0.515007i
$250$		0			0
$251$	2.37224	−	5.19449i	0.149735	−	0.327873i	−0.819870	−	0.572549i	$-0.805954\pi$
$251$	2.37224	−	5.19449i	0.149735	−	0.327873i	0.969605	+	0.244676i	$0.0786817\pi$
$252$		0			0
$253$	1.39117	+	0.407652i	0.0874621	+	0.0256289i
$254$		0			0
$255$	−3.69758	+	8.09657i	−0.231551	+	0.507027i
$256$		0			0
$257$	−11.8383	−	13.6621i	−0.738453	−	0.852220i	0.254943	−	0.966956i	$-0.417943\pi$
$257$	−11.8383	−	13.6621i	−0.738453	−	0.852220i	−0.993396	+	0.114736i	$0.963398\pi$
$258$		0			0
$259$	−5.13948	+	5.93128i	−0.319352	+	0.368552i
$260$		0			0
$261$	−7.45807	+	2.18989i	−0.461643	+	0.135551i
$262$		0			0
$263$	0.628059	+	4.36824i	0.0387278	+	0.269357i	0.999980	−	0.00631258i	$-0.00200937\pi$
$263$	0.628059	+	4.36824i	0.0387278	+	0.269357i	−0.961252	+	0.275670i	$0.911100\pi$
$264$		0			0
$265$	−13.6195	−	29.8225i	−0.836638	−	1.83198i
$266$		0			0
$267$	−1.08754	−	0.698921i	−0.0665565	−	0.0427733i
$268$		0			0
$269$	−1.31708	+	9.16050i	−0.0803038	+	0.558525i	0.909458	+	0.415796i	$0.136497\pi$
$269$	−1.31708	+	9.16050i	−0.0803038	+	0.558525i	−0.989762	+	0.142729i	$0.954412\pi$
$270$		0			0
$271$	22.1074	−	14.2076i	1.34293	−	0.863049i	0.345767	−	0.938320i	$-0.387619\pi$
$271$	22.1074	−	14.2076i	1.34293	−	0.863049i	0.997163	+	0.0752717i	$0.0239824\pi$
$272$		0			0
$273$	30.2560	+	8.88395i	1.83117	+	0.537681i
$274$		0			0
$275$	4.10094			0.247296
$276$		0			0
$277$	1.07467			0.0645704			0.0322852	−	0.999479i	$-0.489722\pi$
$277$	1.07467			0.0645704			0.0322852	+	0.999479i	$0.489722\pi$
$278$		0			0
$279$	−0.701655	−	0.206025i	−0.0420070	−	0.0123344i
$280$		0			0
$281$	1.61104	−	1.03535i	0.0961067	−	0.0617640i	−0.491705	−	0.870762i	$-0.663626\pi$
$281$	1.61104	−	1.03535i	0.0961067	−	0.0617640i	0.587811	+	0.808998i	$0.299990\pi$
$282$		0			0
$283$	0.768941	−	5.34810i	0.0457088	−	0.317912i	−0.954120	−	0.299424i	$-0.903206\pi$
$283$	0.768941	−	5.34810i	0.0457088	−	0.317912i	0.999829	−	0.0184881i	$-0.00588529\pi$
$284$		0			0
$285$	2.32440	+	1.49380i	0.137686	+	0.0884853i
$286$		0			0
$287$	7.78060	+	17.0371i	0.459274	+	1.00567i
$288$		0			0
$289$	1.81208	+	12.6033i	0.106593	+	0.741371i
$290$		0			0
$291$	8.46099	−	2.48437i	0.495992	−	0.145636i
$292$		0			0
$293$	16.6366	−	19.1997i	0.971920	−	1.12166i	−0.0206260	−	0.999787i	$-0.506566\pi$
$293$	16.6366	−	19.1997i	0.971920	−	1.12166i	0.992546	−	0.121869i	$-0.0388886\pi$
$294$		0			0
$295$	−5.54469	−	6.39891i	−0.322824	−	0.372559i
$296$		0			0
$297$	0.125570	−	0.274960i	0.00728632	−	0.0159548i
$298$		0			0
$299$	27.9985	+	17.9718i	1.61919	+	1.03933i
$300$		0			0
$301$	−15.6521	+	34.2733i	−0.902173	+	1.97548i
$302$		0			0
$303$	1.25180	+	1.44465i	0.0719139	+	0.0829930i
$304$		0			0
$305$	−14.9764	+	17.2836i	−0.857544	+	0.989658i
$306$		0			0
$307$	−28.6075	+	8.39992i	−1.63272	+	0.479409i	−0.964395	−	0.264465i	$-0.914805\pi$
$307$	−28.6075	+	8.39992i	−1.63272	+	0.479409i	−0.668321	+	0.743873i	$0.732987\pi$
$308$		0			0
$309$	1.44087	+	10.0215i	0.0819682	+	0.570101i
$310$		0			0
$311$	9.48005	+	20.7584i	0.537565	+	1.17710i	0.962351	+	0.271809i	$0.0876218\pi$
$311$	9.48005	+	20.7584i	0.537565	+	1.17710i	−0.424787	+	0.905293i	$0.639651\pi$
$312$		0			0
$313$	−10.1017	−	6.49196i	−0.570981	−	0.366947i	0.223066	−	0.974803i	$-0.428393\pi$
$313$	−10.1017	−	6.49196i	−0.570981	−	0.366947i	−0.794047	+	0.607856i	$0.792030\pi$
$314$		0			0
$315$	−2.78740	+	19.3868i	−0.157052	+	1.09232i
$316$		0			0
$317$	5.36034	−	3.44488i	0.301067	−	0.193484i	−0.381382	−	0.924418i	$-0.624552\pi$
$317$	5.36034	−	3.44488i	0.301067	−	0.193484i	0.682448	+	0.730934i	$0.260915\pi$
$318$		0			0
$319$	−2.25440	−	0.661951i	−0.126222	−	0.0370621i
$320$		0			0
$321$	14.0611			0.784812
$322$		0			0
$323$	−1.32459			−0.0737021
$324$		0			0
$325$	90.3049	+	26.5159i	5.00922	+	1.47084i
$326$		0			0
$327$	12.7019	−	8.16300i	0.702416	−	0.451415i
$328$		0			0
$329$	−2.74377	+	19.0834i	−0.151269	+	1.05210i
$330$		0			0
$331$	−1.36406	−	0.876628i	−0.0749755	−	0.0481838i	0.502616	−	0.864510i	$-0.332371\pi$
$331$	−1.36406	−	0.876628i	−0.0749755	−	0.0481838i	−0.577591	+	0.816326i	$0.696007\pi$
$332$		0			0
$333$	0.717255	+	1.57057i	0.0393053	+	0.0860667i
$334$		0			0
$335$	−5.60482	−	38.9824i	−0.306224	−	2.12984i
$336$		0			0
$337$	19.0818	−	5.60291i	1.03945	−	0.305210i	0.282902	−	0.959149i	$-0.408703\pi$
$337$	19.0818	−	5.60291i	1.03945	−	0.305210i	0.756548	+	0.653939i	$0.226885\pi$
$338$		0			0
$339$	−6.74723	+	7.78671i	−0.366459	+	0.422916i
$340$		0			0
$341$	−0.144756	−	0.167057i	−0.00783895	−	0.00904663i
$342$		0			0
$343$	12.5783	−	27.5427i	0.679165	−	1.48716i
$344$		0			0
$345$	−8.57416	+	18.8022i	−0.461617	+	1.01228i
$346$		0			0
$347$	0.0126672	−	0.0277373i	0.000680010	−	0.00148901i	−0.909292	−	0.416159i	$-0.863376\pi$
$347$	0.0126672	−	0.0277373i	0.000680010	−	0.00148901i	0.909972	+	0.414670i	$0.136103\pi$
$348$		0			0
$349$	−13.7281	−	15.8431i	−0.734847	−	0.848059i	0.258161	−	0.966102i	$-0.416883\pi$
$349$	−13.7281	−	15.8431i	−0.734847	−	0.848059i	−0.993009	+	0.118043i	$0.962338\pi$
$350$		0			0
$351$	4.54296	−	5.24286i	0.242485	−	0.279843i
$352$		0			0
$353$	26.1491	−	7.67807i	1.39178	−	0.408663i	0.501925	−	0.864911i	$-0.332625\pi$
$353$	26.1491	−	7.67807i	1.39178	−	0.408663i	0.889852	+	0.456249i	$0.150807\pi$
$354$		0			0
$355$	5.22561	+	36.3449i	0.277347	+	1.92899i
$356$		0			0
$357$	−3.90056	−	8.54104i	−0.206440	−	0.452040i
$358$		0			0
$359$	−27.6091	−	17.7433i	−1.45715	−	0.936455i	−0.998864	−	0.0476511i	$-0.984826\pi$
$359$	−27.6091	−	17.7433i	−1.45715	−	0.936455i	−0.458288	−	0.888804i	$-0.651537\pi$
$360$		0			0
$361$	2.64547	−	18.3996i	0.139235	−	0.968401i
$362$		0			0
$363$	−9.17692	+	5.89765i	−0.481664	+	0.309546i
$364$		0			0
$365$	−3.71911	−	1.09203i	−0.194667	−	0.0571594i
$366$		0			0
$367$	−9.91125			−0.517363			−0.258681	−	0.965963i	$-0.583288\pi$
$367$	−9.91125			−0.517363			−0.258681	+	0.965963i	$0.583288\pi$
$368$		0			0
$369$	4.12052			0.214506
$370$		0			0
$371$	33.1841	+	9.74373i	1.72283	+	0.505869i
$372$		0			0
$373$	−24.4970	+	15.7432i	−1.26841	+	0.815155i	−0.989411	−	0.145138i	$-0.953637\pi$
$373$	−24.4970	+	15.7432i	−1.26841	+	0.815155i	−0.278994	+	0.960293i	$0.590001\pi$
$374$		0			0
$375$	−5.25341	+	36.5383i	−0.271285	+	1.88683i
$376$		0			0
$377$	−45.3630	−	29.1530i	−2.33631	−	1.50146i
$378$		0			0
$379$	14.9049	+	32.6371i	0.765612	+	1.67646i	0.736081	+	0.676893i	$0.236674\pi$
$379$	14.9049	+	32.6371i	0.765612	+	1.67646i	0.0295309	+	0.999564i	$0.490599\pi$
$380$		0			0
$381$	−1.82641	−	12.7030i	−0.0935698	−	0.650792i
$382$		0			0
$383$	23.7694	−	6.97932i	1.21456	−	0.356626i	0.389156	−	0.921172i	$-0.372767\pi$
$383$	23.7694	−	6.97932i	1.21456	−	0.356626i	0.825402	+	0.564546i	$0.190949\pi$
$384$		0			0
$385$	−3.87705	+	4.47436i	−0.197593	+	0.228034i
$386$		0			0
$387$	5.42826	+	6.26454i	0.275934	+	0.318445i
$388$		0			0
$389$	3.77500	−	8.26610i	0.191400	−	0.419108i	−0.789465	−	0.613795i	$-0.789642\pi$
$389$	3.77500	−	8.26610i	0.191400	−	0.419108i	0.980865	+	0.194688i	$0.0623693\pi$
$390$		0			0
$391$	−1.41527	−	9.80511i	−0.0715734	−	0.495865i
$392$		0			0
$393$	−0.892219	+	1.95369i	−0.0450065	+	0.0985505i
$394$		0			0
$395$	−25.9418	−	29.9385i	−1.30528	−	1.50637i
$396$		0			0
$397$	4.64164	−	5.35674i	0.232957	−	0.268847i	−0.627220	−	0.778842i	$-0.715807\pi$
$397$	4.64164	−	5.35674i	0.232957	−	0.268847i	0.860177	+	0.509995i	$0.170353\pi$
$398$		0			0
$399$	−2.79664	+	0.821167i	−0.140007	+	0.0411098i
$400$		0			0
$401$	−3.15036	−	21.9113i	−0.157322	−	1.09420i	−0.903543	−	0.428498i	$-0.859043\pi$
$401$	−3.15036	−	21.9113i	−0.157322	−	1.09420i	0.746221	−	0.665698i	$-0.231866\pi$
$402$		0			0
$403$	−2.10744	−	4.61464i	−0.104979	−	0.229872i
$404$		0			0
$405$	3.62490	+	2.32958i	0.180123	+	0.115758i
$406$		0			0
$407$	−0.0742756	+	0.516598i	−0.00368170	+	0.0256068i
$408$		0			0
$409$	−23.6663	+	15.2094i	−1.17022	+	0.752057i	−0.973564	−	0.228415i	$-0.926646\pi$
$409$	−23.6663	+	15.2094i	−1.17022	+	0.752057i	−0.196659	+	0.980472i	$0.563009\pi$
$410$		0			0
$411$	3.94440	+	1.15818i	0.194563	+	0.0571288i
$412$		0			0
$413$	8.93178			0.439504
$414$		0			0
$415$	−46.3344			−2.27447
$416$		0			0
$417$	−2.62580	−	0.771004i	−0.128586	−	0.0377562i
$418$		0			0
$419$	22.7661	−	14.6309i	1.11220	−	0.714764i	0.150425	−	0.988621i	$-0.451936\pi$
$419$	22.7661	−	14.6309i	1.11220	−	0.714764i	0.961770	+	0.273857i	$0.0882995\pi$
$420$		0			0
$421$	3.87414	−	26.9452i	0.188814	−	1.31323i	−0.646270	−	0.763109i	$-0.723672\pi$
$421$	3.87414	−	26.9452i	0.188814	−	1.31323i	0.835084	−	0.550122i	$-0.185419\pi$
$422$		0			0
$423$	3.56817	+	2.29312i	0.173490	+	0.111495i
$424$		0			0
$425$	−11.6420	−	25.4924i	−0.564720	−	1.23656i
$426$		0			0
$427$	−3.43334	−	23.8794i	−0.166151	−	1.15561i
$428$		0			0
$429$	2.01204	−	0.590788i	0.0971421	−	0.0285235i
$430$		0			0
$431$	20.6777	−	23.8633i	0.996008	−	1.14945i	0.00724305	−	0.999974i	$-0.497694\pi$
$431$	20.6777	−	23.8633i	0.996008	−	1.14945i	0.988765	−	0.149480i	$-0.0477601\pi$
$432$		0			0
$433$	13.8928	+	16.0332i	0.667646	+	0.770505i	0.984006	−	0.178135i	$-0.0570062\pi$
$433$	13.8928	+	16.0332i	0.667646	+	0.770505i	−0.316360	+	0.948639i	$0.602461\pi$
$434$		0			0
$435$	13.9135	−	30.4663i	0.667101	−	1.46075i
$436$		0			0
$437$	−3.07524	+	0.00169316i	−0.147109	+	8.09950e-5i
$438$		0			0
$439$	9.98488	−	21.8638i	0.476552	−	1.04350i	−0.506845	−	0.862037i	$-0.669188\pi$
$439$	9.98488	−	21.8638i	0.476552	−	1.04350i	0.983397	−	0.181466i	$-0.0580844\pi$
$440$		0			0
$441$	−8.94627	−	10.3245i	−0.426013	−	0.491645i
$442$		0			0
$443$	19.6601	−	22.6889i	0.934077	−	1.07798i	−0.0627215	−	0.998031i	$-0.519978\pi$
$443$	19.6601	−	22.6889i	0.934077	−	1.07798i	0.996799	−	0.0799515i	$-0.0254765\pi$
$444$		0			0
$445$	5.34479	−	1.56937i	0.253367	−	0.0743953i
$446$		0			0
$447$	0.0794829	+	0.552816i	0.00375941	+	0.0261473i
$448$		0			0
$449$	−2.16047	−	4.73077i	−0.101959	−	0.223259i	0.851777	−	0.523904i	$-0.175525\pi$
$449$	−2.16047	−	4.73077i	−0.101959	−	0.223259i	−0.953736	+	0.300646i	$0.902798\pi$
$450$		0			0
$451$	1.04781	+	0.673387i	0.0493395	+	0.0317086i
$452$		0			0
$453$	−0.633630	+	4.40699i	−0.0297705	+	0.207059i
$454$		0			0
$455$	−114.305	+	73.4594i	−5.35870	+	3.44383i
$456$		0			0
$457$	23.5283	+	6.90852i	1.10061	+	0.323167i	0.781093	−	0.624415i	$-0.214663\pi$
$457$	23.5283	+	6.90852i	1.10061	+	0.323167i	0.319513	+	0.947582i	$0.396481\pi$
$458$		0			0
$459$	−2.06569			−0.0964183
$460$		0			0
$461$	−38.5046			−1.79334			−0.896669	−	0.442702i	$-0.854020\pi$
$461$	−38.5046			−1.79334			−0.896669	+	0.442702i	$0.854020\pi$
$462$		0			0
$463$	10.9618	+	3.21868i	0.509440	+	0.149585i	0.526343	−	0.850272i	$-0.323563\pi$
$463$	10.9618	+	3.21868i	0.509440	+	0.149585i	−0.0169037	+	0.999857i	$0.505381\pi$
$464$		0			0
$465$	2.65081	−	1.70357i	0.122928	−	0.0790012i
$466$		0			0
$467$	−4.57277	+	31.8043i	−0.211603	+	1.47173i	0.556203	+	0.831046i	$0.312258\pi$
$467$	−4.57277	+	31.8043i	−0.211603	+	1.47173i	−0.767806	+	0.640682i	$0.778652\pi$
$468$		0			0
$469$	34.9501	+	22.4611i	1.61385	+	1.03716i
$470$		0			0
$471$	−5.36061	−	11.7381i	−0.247004	−	0.540863i
$472$		0			0
$473$	0.356587	+	2.48012i	0.0163959	+	0.114036i
$474$		0			0
$475$	−8.34712	+	2.45094i	−0.382992	+	0.112457i
$476$		0			0
$477$	4.98262	−	5.75025i	0.228139	−	0.263286i
$478$		0			0
$479$	9.78136	+	11.2883i	0.446922	+	0.515775i	0.933849	−	0.357667i	$-0.116428\pi$
$479$	9.78136	+	11.2883i	0.446922	+	0.515775i	−0.486927	+	0.873442i	$0.661882\pi$
$480$		0			0
$481$	−4.97581	+	10.8955i	−0.226877	+	0.496792i
$482$		0			0
$483$	−9.06668	−	19.8244i	−0.412548	−	0.902040i
$484$		0			0
$485$	−15.7845	+	34.5632i	−0.716737	+	1.56944i
$486$		0			0
$487$	−9.29506	−	10.7271i	−0.421199	−	0.486090i	0.505003	−	0.863118i	$-0.331492\pi$
$487$	−9.29506	−	10.7271i	−0.421199	−	0.486090i	−0.926202	+	0.377028i	$0.876946\pi$
$488$		0			0
$489$	−2.19131	+	2.52890i	−0.0990943	+	0.114361i
$490$		0			0
$491$	−31.6856	+	9.30372i	−1.42995	+	0.419871i	−0.902859	−	0.429938i	$-0.858536\pi$
$491$	−31.6856	+	9.30372i	−1.42995	+	0.419871i	−0.527091	+	0.849809i	$0.676717\pi$
$492$		0			0
$493$	2.28508	+	15.8931i	0.102915	+	0.715787i
$494$		0			0
$495$	0.541073	+	1.18478i	0.0243194	+	0.0532521i
$496$		0			0
$497$	−32.5855	−	20.9414i	−1.46166	−	0.939350i
$498$		0			0
$499$	−5.00390	+	34.8029i	−0.224005	+	1.55799i	0.498663	+	0.866796i	$0.333824\pi$
$499$	−5.00390	+	34.8029i	−0.224005	+	1.55799i	−0.722669	+	0.691195i	$0.757085\pi$
$500$		0			0
$501$	−8.26148	+	5.30933i	−0.369096	+	0.237203i
$502$		0			0
$503$	31.3570	+	9.20723i	1.39814	+	0.410530i	0.892044	−	0.451948i	$-0.149271\pi$
$503$	31.3570	+	9.20723i	1.39814	+	0.410530i	0.506094	+	0.862479i	$0.331089\pi$
$504$		0			0
$505$	−8.23672			−0.366529
$506$		0			0
$507$	35.1260			1.56000
$508$		0			0
$509$	−5.37491	−	1.57822i	−0.238239	−	0.0699532i	0.160434	−	0.987047i	$-0.448711\pi$
$509$	−5.37491	−	1.57822i	−0.238239	−	0.0699532i	−0.398672	+	0.917093i	$0.630529\pi$
$510$		0			0
$511$	3.43980	−	2.21063i	0.152168	−	0.0977924i
$512$		0			0
$513$	−0.0912568	+	0.634705i	−0.00402909	+	0.0280229i
$514$		0			0
$515$	−36.7004	−	23.5859i	−1.61721	−	1.03932i
$516$		0			0
$517$	0.532605	+	1.16624i	0.0234239	+	0.0512913i
$518$		0			0
$519$	−1.38678	−	9.64524i	−0.0608727	−	0.423379i
$520$		0			0
$521$	6.83603	−	2.00724i	0.299492	−	0.0879387i	−0.128534	−	0.991705i	$-0.541027\pi$
$521$	6.83603	−	2.00724i	0.299492	−	0.0879387i	0.428026	+	0.903766i	$0.359209\pi$
$522$		0			0
$523$	13.8325	−	15.9636i	0.604855	−	0.698040i	−0.367903	−	0.929864i	$-0.619924\pi$
$523$	13.8325	−	15.9636i	0.604855	−	0.698040i	0.972758	+	0.231824i	$0.0744695\pi$
$524$		0			0
$525$	−40.3839	−	46.6054i	−1.76250	−	2.03403i
$526$		0			0
$527$	−0.627524	+	1.37409i	−0.0273354	+	0.0598561i
$528$		0			0
$529$	−3.29831	−	22.7623i	−0.143405	−	0.989664i
$530$		0			0
$531$	0.816284	−	1.78741i	0.0354237	−	0.0775671i
$532$		0			0
$533$	18.7194	+	21.6033i	0.810825	+	0.935742i
$534$		0			0
$535$	−39.6768	+	45.7895i	−1.71538	+	1.97965i
$536$		0			0
$537$	13.8944	−	4.07977i	0.599589	−	0.176055i
$538$		0			0
$539$	−0.587689	−	4.08747i	−0.0253135	−	0.176060i
$540$		0			0
$541$	−13.0130	−	28.4946i	−0.559474	−	1.22508i	−0.952215	−	0.305429i	$-0.901200\pi$
$541$	−13.0130	−	28.4946i	−0.559474	−	1.22508i	0.392741	−	0.919649i	$-0.371527\pi$
$542$		0			0
$543$	1.96540	+	1.26308i	0.0843433	+	0.0542041i
$544$		0			0
$545$	−9.25893	+	64.3973i	−0.396609	+	2.75848i
$546$		0			0
$547$	−19.9452	+	12.8180i	−0.852793	+	0.548057i	−0.892445	−	0.451157i	$-0.851012\pi$
$547$	−19.9452	+	12.8180i	−0.852793	+	0.548057i	0.0396516	+	0.999214i	$0.487375\pi$
$548$		0			0
$549$	−5.09249	−	1.49529i	−0.217342	−	0.0638174i
$550$		0			0
$551$	4.98425			0.212336
$552$		0			0
$553$	41.7890			1.77705
$554$		0			0
$555$	−7.13843	−	2.09603i	−0.303009	−	0.0889716i
$556$		0			0
$557$	14.5583	−	9.35602i	0.616853	−	0.396427i	−0.194568	−	0.980889i	$-0.562331\pi$
$557$	14.5583	−	9.35602i	0.616853	−	0.396427i	0.811421	+	0.584462i	$0.198694\pi$
$558$		0			0
$559$	−8.18374	+	56.9192i	−0.346135	+	2.40742i
$560$		0			0
$561$	−0.525287	−	0.337582i	−0.0221777	−	0.0142527i
$562$		0			0
$563$	9.84706	+	21.5621i	0.415004	+	0.908733i	0.995526	+	0.0944878i	$0.0301213\pi$
$563$	9.84706	+	21.5621i	0.415004	+	0.908733i	−0.580522	+	0.814245i	$0.697151\pi$
$564$		0			0
$565$	−6.31824	−	43.9443i	−0.265810	−	1.84875i
$566$		0			0
$567$	−4.36135	+	1.28061i	−0.183159	+	0.0537805i
$568$		0			0
$569$	9.88016	−	11.4023i	0.414198	−	0.478010i	−0.509863	−	0.860256i	$-0.670304\pi$
$569$	9.88016	−	11.4023i	0.414198	−	0.478010i	0.924061	+	0.382246i	$0.124849\pi$
$570$		0			0
$571$	−10.2628	−	11.8439i	−0.429484	−	0.495651i	0.499219	−	0.866476i	$-0.333620\pi$
$571$	−10.2628	−	11.8439i	−0.429484	−	0.495651i	−0.928703	+	0.370825i	$0.879075\pi$
$572$		0			0
$573$	1.74355	−	3.81784i	0.0728378	−	0.159493i
$574$		0			0
$575$	−27.0613	−	59.1698i	−1.12853	−	2.46755i
$576$		0			0
$577$	−6.30194	+	13.7993i	−0.262353	+	0.574474i	−0.994267	−	0.106923i	$-0.965900\pi$
$577$	−6.30194	+	13.7993i	−0.262353	+	0.574474i	0.731914	+	0.681397i	$0.238627\pi$
$578$		0			0
$579$	13.7949	+	15.9202i	0.573296	+	0.661619i
$580$		0			0
$581$	32.0083	−	36.9396i	1.32793	−	1.53251i
$582$		0			0
$583$	2.20676	−	0.647963i	0.0913947	−	0.0268359i
$584$		0			0
$585$	4.25412	+	29.5880i	0.175886	+	1.22332i
$586$		0			0
$587$	−12.7678	−	27.9575i	−0.526982	−	1.15393i	−0.966728	−	0.255807i	$-0.917659\pi$
$587$	−12.7678	−	27.9575i	−0.526982	−	1.15393i	0.439746	−	0.898122i	$-0.355069\pi$
$588$		0			0
$589$	0.394479	+	0.253516i	0.0162542	+	0.0104460i
$590$		0			0
$591$	0.846416	−	5.88696i	0.0348169	−	0.242157i
$592$		0			0
$593$	21.4804	−	13.8046i	0.882096	−	0.566889i	−0.0193344	−	0.999813i	$-0.506155\pi$
$593$	21.4804	−	13.8046i	0.882096	−	0.566889i	0.901430	+	0.432925i	$0.142518\pi$
$594$		0			0
$595$	38.8201	+	11.3986i	1.59147	+	0.467297i
$596$		0			0
$597$	−5.21160			−0.213296
$598$		0			0
$599$	−24.7147			−1.00982			−0.504908	−	0.863173i	$-0.668474\pi$
$599$	−24.7147			−1.00982			−0.504908	+	0.863173i	$0.668474\pi$
$600$		0			0
$601$	15.4958	+	4.54998i	0.632088	+	0.185598i	0.582054	−	0.813150i	$-0.302249\pi$
$601$	15.4958	+	4.54998i	0.632088	+	0.185598i	0.0500334	+	0.998748i	$0.484067\pi$
$602$		0			0
$603$	7.68899	−	4.94141i	0.313120	−	0.201230i
$604$		0			0
$605$	6.68944	−	46.5261i	0.271964	−	1.89155i
$606$		0			0
$607$	−23.7514	−	15.2641i	−0.964039	−	0.619550i	−0.0389258	−	0.999242i	$-0.512394\pi$
$607$	−23.7514	−	15.2641i	−0.964039	−	0.619550i	−0.925113	+	0.379692i	$0.876030\pi$
$608$		0			0
$609$	14.6773	+	32.1388i	0.594754	+	1.30233i
$610$		0			0
$611$	4.18754	+	29.1250i	0.169410	+	1.17827i
$612$		0			0
$613$	−11.6862	+	3.43138i	−0.472001	+	0.138592i	−0.509078	−	0.860720i	$-0.670014\pi$
$613$	−11.6862	+	3.43138i	−0.472001	+	0.138592i	0.0370769	+	0.999312i	$0.488195\pi$
$614$		0			0
$615$	−11.6271	+	13.4183i	−0.468849	+	0.541080i
$616$		0			0
$617$	2.26678	+	2.61600i	0.0912572	+	0.105316i	0.799541	−	0.600611i	$-0.205076\pi$
$617$	2.26678	+	2.61600i	0.0912572	+	0.105316i	−0.708284	+	0.705927i	$0.750530\pi$
$618$		0			0
$619$	−7.78111	+	17.0382i	−0.312749	+	0.684825i	−0.999099	−	0.0424467i	$-0.986485\pi$
$619$	−7.78111	+	17.0382i	−0.312749	+	0.684825i	0.686350	+	0.727272i	$0.259212\pi$
$620$		0			0
$621$	−4.79583	+	0.00264049i	−0.192450	+	0.000105959i
$622$		0			0
$623$	−2.44107	+	5.34520i	−0.0977995	+	0.214151i
$624$		0			0
$625$	−59.7401	−	68.9437i	−2.38960	−	2.75775i
$626$		0			0
$627$	−0.126931	+	0.146486i	−0.00506914	+	0.00585010i
$628$		0			0
$629$	3.42215	−	1.00483i	0.136450	−	0.0400654i
$630$		0			0
$631$	0.225957	+	1.57157i	0.00899521	+	0.0625630i	0.993825	−	0.110962i	$-0.0353933\pi$
$631$	0.225957	+	1.57157i	0.00899521	+	0.0625630i	−0.984829	+	0.173525i	$0.944484\pi$
$632$		0			0
$633$	−2.01387	−	4.40977i	−0.0800443	−	0.175273i
$634$		0			0
$635$	46.5205	+	29.8969i	1.84611	+	1.18642i
$636$		0			0
$637$	13.4876	−	93.8080i	0.534396	−	3.71681i
$638$		0			0
$639$	−7.16877	+	4.60709i	−0.283592	+	0.182254i
$640$		0			0
$641$	13.1380	+	3.85766i	0.518919	+	0.152368i	0.530696	−	0.847562i	$-0.321931\pi$
$641$	13.1380	+	3.85766i	0.518919	+	0.152368i	−0.0117769	+	0.999931i	$0.503749\pi$
$642$		0			0
$643$	7.60826			0.300041			0.150020	−	0.988683i	$-0.452066\pi$
$643$	7.60826			0.300041			0.150020	+	0.988683i	$0.452066\pi$
$644$		0			0
$645$	−35.7175			−1.40637
$646$		0			0
$647$	17.6551	+	5.18401i	0.694094	+	0.203804i	0.609705	−	0.792629i	$-0.291288\pi$
$647$	17.6551	+	5.18401i	0.694094	+	0.203804i	0.0843890	+	0.996433i	$0.473106\pi$
$648$		0			0
$649$	0.499678	−	0.321123i	0.0196141	−	0.0126052i
$650$		0			0
$651$	−0.473055	+	3.29017i	−0.0185405	+	0.128952i
$652$		0			0
$653$	−16.7156	−	10.7425i	−0.654132	−	0.420385i	0.171042	−	0.985264i	$-0.445287\pi$
$653$	−16.7156	−	10.7425i	−0.654132	−	0.420385i	−0.825174	+	0.564879i	$0.808923\pi$
$654$		0			0
$655$	−3.84451	−	8.41830i	−0.150217	−	0.328930i
$656$		0			0
$657$	−0.128020	−	0.890399i	−0.00499454	−	0.0347378i
$658$		0			0
$659$	−40.0275	+	11.7531i	−1.55925	+	0.457837i	−0.943849	−	0.330378i	$-0.892824\pi$
$659$	−40.0275	+	11.7531i	−1.55925	+	0.457837i	−0.615400	+	0.788215i	$0.711005\pi$
$660$		0			0
$661$	−22.9578	+	26.4948i	−0.892956	+	1.03053i	0.106388	+	0.994325i	$0.466071\pi$
$661$	−22.9578	+	26.4948i	−0.892956	+	1.03053i	−0.999344	+	0.0362019i	$0.988474\pi$
$662$		0			0
$663$	−9.38437	−	10.8301i	−0.364459	−	0.420608i
$664$		0			0
$665$	5.21730	−	11.4243i	0.202318	−	0.443015i
$666$		0			0
$667$	5.32548	+	36.8953i	0.206203	+	1.42859i
$668$		0			0
$669$	−2.43541	+	5.33280i	−0.0941583	+	0.206178i
$670$		0			0
$671$	−1.05061	−	1.21247i	−0.0405583	−	0.0468068i
$672$		0			0
$673$	−9.66135	+	11.1498i	−0.372418	+	0.429793i	−0.910762	−	0.412932i	$-0.864505\pi$
$673$	−9.66135	+	11.1498i	−0.372418	+	0.429793i	0.538344	+	0.842725i	$0.319050\pi$
$674$		0			0
$675$	−13.0173	+	3.82223i	−0.501037	+	0.147118i
$676$		0			0
$677$	5.26032	+	36.5863i	0.202170	+	1.40613i	0.797827	+	0.602887i	$0.205983\pi$
$677$	5.26032	+	36.5863i	0.202170	+	1.40613i	−0.595656	+	0.803239i	$0.703108\pi$
$678$		0			0
$679$	−16.6510	−	36.4606i	−0.639007	−	1.39923i
$680$		0			0
$681$	15.7918	+	10.1488i	0.605144	+	0.388903i
$682$		0			0
$683$	−0.565062	+	3.93009i	−0.0216215	+	0.150381i	−0.997772	−	0.0667133i	$-0.978749\pi$
$683$	−0.565062	+	3.93009i	−0.0216215	+	0.150381i	0.976151	+	0.217094i	$0.0696578\pi$
$684$		0			0
$685$	−14.9017	+	9.57673i	−0.569364	+	0.365908i
$686$		0			0
$687$	−6.58735	−	1.93422i	−0.251323	−	0.0737951i
$688$		0			0
$689$	52.7836			2.01090
$690$		0			0
$691$	−8.46447			−0.322004			−0.161002	−	0.986954i	$-0.551473\pi$
$691$	−8.46447			−0.322004			−0.161002	+	0.986954i	$0.551473\pi$
$692$		0			0
$693$	−1.31833	−	0.387098i	−0.0500793	−	0.0147046i
$694$		0			0
$695$	9.92009	−	6.37526i	0.376291	−	0.241827i
$696$		0			0
$697$	1.21135	−	8.42509i	0.0458830	−	0.319123i
$698$		0			0
$699$	−3.70187	−	2.37905i	−0.140018	−	0.0899838i
$700$		0			0
$701$	3.60477	+	7.89335i	0.136150	+	0.298128i	0.965410	−	0.260735i	$-0.0839650\pi$
$701$	3.60477	+	7.89335i	0.136150	+	0.298128i	−0.829260	+	0.558863i	$0.811238\pi$
$702$		0			0
$703$	−0.157564	−	1.09588i	−0.00594264	−	0.0413320i
$704$		0			0
$705$	−17.5360	+	5.14903i	−0.660443	+	0.193924i
$706$		0			0
$707$	5.69001	−	6.56662i	0.213995	−	0.246963i
$708$		0			0
$709$	13.8622	+	15.9978i	0.520606	+	0.600811i	0.953782	−	0.300498i	$-0.0971528\pi$
$709$	13.8622	+	15.9978i	0.520606	+	0.600811i	−0.433177	+	0.901309i	$0.642607\pi$
$710$		0			0
$711$	3.81913	−	8.36274i	0.143229	−	0.313627i
$712$		0			0
$713$	−1.45514	+	3.19096i	−0.0544953	+	0.119502i
$714$		0			0
$715$	−3.75358	+	8.21920i	−0.140376	+	0.307381i
$716$		0			0
$717$	7.27931	+	8.40077i	0.271851	+	0.313733i
$718$		0			0
$719$	3.80047	−	4.38598i	0.141734	−	0.163569i	−0.680444	−	0.732800i	$-0.738213\pi$
$719$	3.80047	−	4.38598i	0.141734	−	0.163569i	0.822178	+	0.569230i	$0.192759\pi$
$720$		0			0
$721$	44.1566	−	12.9655i	1.64448	−	0.482862i
$722$		0			0
$723$	−1.25608	−	8.73620i	−0.0467139	−	0.324903i
$724$		0			0
$725$	43.8073	+	95.9246i	1.62696	+	3.56255i
$726$		0			0
$727$	8.69608	+	5.58863i	0.322520	+	0.207271i	0.691875	−	0.722017i	$-0.256785\pi$
$727$	8.69608	+	5.58863i	0.322520	+	0.207271i	−0.369355	+	0.929288i	$0.620421\pi$
$728$		0			0
$729$	−0.142315	+	0.989821i	−0.00527092	+	0.0366601i
$730$		0			0
$731$	14.4047	−	9.25734i	0.532777	−	0.342395i
$732$		0			0
$733$	36.8010	+	10.8057i	1.35928	+	0.399119i	0.878508	−	0.477728i	$-0.158540\pi$
$733$	36.8010	+	10.8057i	1.35928	+	0.399119i	0.480768	+	0.876848i	$0.340358\pi$
$734$		0			0
$735$	58.8657			2.17129
$736$		0			0
$737$	2.76278			0.101768
$738$		0			0
$739$	−3.13708	−	0.921131i	−0.115399	−	0.0338843i	0.223523	−	0.974699i	$-0.428244\pi$
$739$	−3.13708	−	0.921131i	−0.115399	−	0.0338843i	−0.338922	+	0.940814i	$0.610062\pi$
$740$		0			0
$741$	−3.74225	+	2.40500i	−0.137475	+	0.0883497i
$742$		0			0
$743$	−1.39492	+	9.70189i	−0.0511747	+	0.355928i	0.948104	+	0.317960i	$0.102998\pi$
$743$	−1.39492	+	9.70189i	−0.0511747	+	0.355928i	−0.999279	+	0.0379681i	$0.987911\pi$
$744$		0			0
$745$	−2.02451	−	1.30107i	−0.0741723	−	0.0476677i
$746$		0			0
$747$	−4.46701	−	9.78138i	−0.163439	−	0.357882i
$748$		0			0
$749$	−9.09594	−	63.2637i	−0.332359	−	2.31160i
$750$		0			0
$751$	−39.7789	+	11.6801i	−1.45155	+	0.426214i	−0.910054	−	0.414489i	$-0.863960\pi$
$751$	−39.7789	+	11.6801i	−1.45155	+	0.426214i	−0.541497	+	0.840703i	$0.682142\pi$
$752$		0			0
$753$	−3.73961	+	4.31574i	−0.136279	+	0.157274i
$754$		0			0
$755$	−12.5633	−	14.4988i	−0.457226	−	0.527666i
$756$		0			0
$757$	−7.51355	+	16.4524i	−0.273085	+	0.597972i	−0.995634	−	0.0933478i	$-0.970243\pi$
$757$	−7.51355	+	16.4524i	−0.273085	+	0.597972i	0.722549	+	0.691320i	$0.242970\pi$
$758$		0			0
$759$	−1.21997	−	0.783077i	−0.0442820	−	0.0284239i
$760$		0			0
$761$	0.849836	−	1.86088i	0.0308065	−	0.0674569i	−0.893603	−	0.448858i	$-0.851831\pi$
$761$	0.849836	−	1.86088i	0.0308065	−	0.0674569i	0.924410	+	0.381401i	$0.124558\pi$
$762$		0			0
$763$	−44.9437	−	51.8678i	−1.62707	−	1.87774i
$764$		0			0
$765$	5.82887	−	6.72687i	0.210743	−	0.243211i
$766$		0			0
$767$	13.0795	−	3.84049i	0.472273	−	0.138672i
$768$		0			0
$769$	1.96907	+	13.6952i	0.0710064	+	0.493860i	0.994029	+	0.109115i	$0.0348016\pi$
$769$	1.96907	+	13.6952i	0.0710064	+	0.493860i	−0.923023	+	0.384745i	$0.874289\pi$
$770$		0			0
$771$	7.50970	+	16.4439i	0.270455	+	0.592214i
$772$		0			0
$773$	26.8434	+	17.2512i	0.965492	+	0.620484i	0.925513	−	0.378717i	$-0.123635\pi$
$773$	26.8434	+	17.2512i	0.965492	+	0.620484i	0.0399790	+	0.999201i	$0.487271\pi$
$774$		0			0
$775$	−1.41193	+	9.82016i	−0.0507179	+	0.352750i
$776$		0			0
$777$	6.60233	−	4.24306i	0.236857	−	0.152219i
$778$		0			0
$779$	−2.53518	−	0.744396i	−0.0908323	−	0.0266708i
$780$		0			0
$781$	−2.57586			−0.0921715
$782$		0			0
$783$	7.77293			0.277782
$784$		0			0
$785$	53.3510	+	15.6653i	1.90418	+	0.559118i
$786$		0			0
$787$	13.0097	−	8.36084i	0.463746	−	0.298032i	−0.287826	−	0.957683i	$-0.592932\pi$
$787$	13.0097	−	8.36084i	0.463746	−	0.298032i	0.751572	+	0.659651i	$0.229296\pi$
$788$		0			0
$789$	0.628059	−	4.36824i	0.0223595	−	0.155514i
$790$		0			0
$791$	39.3987	+	25.3200i	1.40086	+	0.900277i
$792$		0			0
$793$	−15.2954	−	33.4922i	−0.543155	−	1.18934i
$794$		0			0
$795$	4.66583	+	32.4515i	0.165480	+	1.15094i
$796$		0			0
$797$	2.78443	−	0.817583i	0.0986296	−	0.0289603i	−0.232045	−	0.972705i	$-0.574542\pi$
$797$	2.78443	−	0.817583i	0.0986296	−	0.0289603i	0.330675	+	0.943745i	$0.392724\pi$
$798$		0			0
$799$	5.73764	−	6.62159i	0.202983	−	0.234255i
$800$		0			0
$801$	0.846580	+	0.977006i	0.0299124	+	0.0345208i
$802$		0			0
$803$	0.112957	−	0.247342i	0.00398617	−	0.00872850i
$804$		0			0
$805$	90.1414	+	26.4140i	3.17707	+	0.930971i
$806$		0			0
$807$	3.84454	−	8.41837i	0.135334	−	0.296341i
$808$		0			0
$809$	6.18707	+	7.14026i	0.217526	+	0.251038i	0.854016	−	0.520247i	$-0.174160\pi$
$809$	6.18707	+	7.14026i	0.217526	+	0.251038i	−0.636490	+	0.771285i	$0.719614\pi$
$810$		0			0
$811$	30.6615	−	35.3852i	1.07667	−	1.24254i	0.108010	−	0.994150i	$-0.465552\pi$
$811$	30.6615	−	35.3852i	1.07667	−	1.24254i	0.968659	−	0.248393i	$-0.0799024\pi$
$812$		0			0
$813$	−25.2146	+	7.40369i	−0.884316	+	0.259659i
$814$		0			0
$815$	−2.05198	−	14.2719i	−0.0718778	−	0.499921i
$816$		0			0
$817$	−2.20805	−	4.83496i	−0.0772499	−	0.169154i
$818$		0			0
$819$	−26.5275	−	17.0482i	−0.926945	−	0.595712i
$820$		0			0
$821$	3.88817	−	27.0428i	0.135698	−	0.943801i	−0.802241	−	0.597000i	$-0.796359\pi$
$821$	3.88817	−	27.0428i	0.135698	−	0.943801i	0.937939	−	0.346800i	$-0.112732\pi$
$822$		0			0
$823$	33.8854	−	21.7768i	1.18117	−	0.759093i	0.205570	−	0.978642i	$-0.434095\pi$
$823$	33.8854	−	21.7768i	1.18117	−	0.759093i	0.975601	+	0.219550i	$0.0704588\pi$
$824$		0			0
$825$	−3.93483	−	1.15537i	−0.136993	−	0.0402248i
$826$		0			0
$827$	45.0593			1.56686			0.783432	−	0.621478i	$-0.213467\pi$
$827$	45.0593			1.56686			0.783432	+	0.621478i	$0.213467\pi$
$828$		0			0
$829$	−33.6006			−1.16700			−0.583498	−	0.812114i	$-0.698317\pi$
$829$	−33.6006			−1.16700			−0.583498	+	0.812114i	$0.698317\pi$
$830$		0			0
$831$	−1.03113	−	0.302769i	−0.0357697	−	0.0105029i
$832$		0			0
$833$	−23.7403	+	15.2570i	−0.822552	+	0.528622i
$834$		0			0
$835$	6.02213	−	41.8849i	0.208404	−	1.44949i
$836$		0			0
$837$	0.615189	+	0.395358i	0.0212641	+	0.0136656i
$838$		0			0
$839$	18.1432	+	39.7281i	0.626373	+	1.37156i	0.910792	+	0.412865i	$0.135472\pi$
$839$	18.1432	+	39.7281i	0.626373	+	1.37156i	−0.284420	+	0.958700i	$0.591801\pi$
$840$		0			0
$841$	−4.47130	−	31.0986i	−0.154183	−	1.07236i
$842$		0			0
$843$	−1.83748	+	0.539532i	−0.0632860	+	0.0185825i
$844$		0			0
$845$	−99.1169	+	114.387i	−3.40972	+	3.93503i
$846$		0			0
$847$	32.4712	+	37.4738i	1.11572	+	1.28761i
$848$		0			0
$849$	−2.24453	+	4.91483i	−0.0770320	+	0.168677i
$850$		0			0
$851$	7.94378	−	2.33725i	0.272309	−	0.0801200i
$852$		0			0
$853$	−10.6678	+	23.3592i	−0.365258	+	0.799803i	0.634384	+	0.773018i	$0.281254\pi$
$853$	−10.6678	+	23.3592i	−0.365258	+	0.799803i	−0.999641	+	0.0267844i	$0.991473\pi$
$854$		0			0
$855$	−1.80940	−	2.08815i	−0.0618800	−	0.0714134i
$856$		0			0
$857$	−31.3940	+	36.2306i	−1.07240	+	1.23761i	−0.102338	+	0.994750i	$0.532632\pi$
$857$	−31.3940	+	36.2306i	−1.07240	+	1.23761i	−0.970060	+	0.242864i	$0.921913\pi$
$858$		0			0
$859$	−46.1838	+	13.5608i	−1.57577	+	0.462688i	−0.948675	−	0.316254i	$-0.897575\pi$
$859$	−46.1838	+	13.5608i	−1.57577	+	0.462688i	−0.627096	+	0.778942i	$0.715757\pi$
$860$		0			0
$861$	−2.66552	−	18.5391i	−0.0908405	−	0.631810i
$862$		0			0
$863$	−11.3839	−	24.9273i	−0.387514	−	0.848536i	−0.998385	−	0.0568067i	$-0.981908\pi$
$863$	−11.3839	−	24.9273i	−0.387514	−	0.848536i	0.610872	−	0.791730i	$-0.290819\pi$
$864$		0			0
$865$	35.3226	+	22.7004i	1.20100	+	0.771838i
$866$		0			0
$867$	1.81208	−	12.6033i	0.0615415	−	0.428031i
$868$		0			0
$869$	2.33783	−	1.50243i	0.0793056	−	0.0509666i
$870$		0			0
$871$	60.8379	+	17.8636i	2.06141	+	0.605286i
$872$		0			0
$873$	−8.81818			−0.298450
$874$		0			0
$875$	167.792			5.67240
$876$		0			0
$877$	1.00427	+	0.294880i	0.0339118	+	0.00995741i	0.298644	−	0.954364i	$-0.403466\pi$
$877$	1.00427	+	0.294880i	0.0339118	+	0.00995741i	−0.264733	+	0.964322i	$0.585284\pi$
$878$		0			0
$879$	−21.3719	+	13.7349i	−0.720855	+	0.463265i
$880$		0			0
$881$	3.24038	−	22.5373i	0.109171	−	0.759302i	−0.859532	−	0.511081i	$-0.829245\pi$
$881$	3.24038	−	22.5373i	0.109171	−	0.759302i	0.968704	−	0.248221i	$-0.0798458\pi$
$882$		0			0
$883$	−9.86459	−	6.33959i	−0.331970	−	0.213344i	0.364028	−	0.931388i	$-0.381401\pi$
$883$	−9.86459	−	6.33959i	−0.331970	−	0.213344i	−0.695998	+	0.718044i	$0.745038\pi$
$884$		0			0
$885$	3.51731	+	7.70183i	0.118233	+	0.258894i
$886$		0			0
$887$	6.09981	+	42.4251i	0.204812	+	1.42450i	0.789755	+	0.613422i	$0.210208\pi$
$887$	6.09981	+	42.4251i	0.204812	+	1.42450i	−0.584944	+	0.811074i	$0.698883\pi$
$888$		0			0
$889$	−55.9718	+	16.4348i	−1.87723	+	0.551205i
$890$		0			0
$891$	−0.197949	+	0.228445i	−0.00663154	+	0.00765320i
$892$		0			0
$893$	−1.78108	−	2.05547i	−0.0596015	−	0.0687838i
$894$		0			0
$895$	−25.9209	+	56.7589i	−0.866441	+	1.89724i
$896$		0			0
$897$	−21.8011	−	25.1319i	−0.727918	−	0.839128i
$898$		0			0
$899$	2.36129	−	5.17050i	0.0787533	−	0.172446i
$900$		0			0
$901$	−10.2926	−	11.8783i	−0.342895	−	0.395722i
$902$		0			0
$903$	24.6740	−	28.4753i	0.821099	−	0.947599i
$904$		0			0
$905$	−9.65906	+	2.83615i	−0.321078	+	0.0942770i
$906$		0			0
$907$	−2.76790	−	19.2511i	−0.0919065	−	0.639224i	−0.982754	−	0.184920i	$-0.940797\pi$
$907$	−2.76790	−	19.2511i	−0.0919065	−	0.639224i	0.890847	−	0.454303i	$-0.150112\pi$
$908$		0			0
$909$	−0.794085	−	1.73880i	−0.0263382	−	0.0576725i
$910$		0			0
$911$	4.89855	+	3.14811i	0.162296	+	0.104302i	0.619268	−	0.785180i	$-0.287430\pi$
$911$	4.89855	+	3.14811i	0.162296	+	0.104302i	−0.456972	+	0.889481i	$0.651066\pi$
$912$		0			0
$913$	0.462582	−	3.21733i	0.0153092	−	0.106478i
$914$		0			0
$915$	19.2391	−	12.3642i	0.636024	−	0.408748i
$916$		0			0
$917$	9.36721	+	2.75046i	0.309333	+	0.0908283i
$918$		0			0
$919$	−23.5552			−0.777016			−0.388508	−	0.921445i	$-0.627009\pi$
$919$	−23.5552			−0.777016			−0.388508	+	0.921445i	$0.627009\pi$
$920$		0			0
$921$	29.8152			0.982445
$922$		0			0
$923$	−56.7218	−	16.6550i	−1.86702	−	0.548206i
$924$		0			0
$925$	19.7060	−	12.6643i	0.647929	−	0.416398i
$926$		0			0
$927$	1.44087	−	10.0215i	0.0473243	−	0.329148i
$928$		0			0
$929$	−29.4830	−	18.9476i	−0.967307	−	0.621651i	−0.0412962	−	0.999147i	$-0.513149\pi$
$929$	−29.4830	−	18.9476i	−0.967307	−	0.621651i	−0.926011	+	0.377496i	$0.876785\pi$
$930$		0			0
$931$	3.63907	+	7.96845i	0.119266	+	0.261155i
$932$		0			0
$933$	−3.24772	−	22.5884i	−0.106326	−	0.739511i
$934$		0			0
$935$	2.58155	−	0.758013i	0.0844259	−	0.0247897i
$936$		0			0
$937$	6.66016	−	7.68624i	0.217578	−	0.251099i	−0.636459	−	0.771310i	$-0.719602\pi$
$937$	6.66016	−	7.68624i	0.217578	−	0.251099i	0.854037	+	0.520212i	$0.174147\pi$
$938$		0			0
$939$	7.86350	+	9.07496i	0.256615	+	0.296150i
$940$		0			0
$941$	8.27076	−	18.1104i	0.269619	−	0.590384i	−0.725593	−	0.688124i	$-0.758434\pi$
$941$	8.27076	−	18.1104i	0.269619	−	0.590384i	0.995212	+	0.0977407i	$0.0311616\pi$
$942$		0			0
$943$	2.80156	−	19.5617i	0.0912313	−	0.637017i
$944$		0			0
$945$	8.13637	−	17.8162i	0.264676	−	0.579560i
$946$		0			0
$947$	18.4094	+	21.2456i	0.598226	+	0.690390i	0.971421	−	0.237363i	$-0.0762831\pi$
$947$	18.4094	+	21.2456i	0.598226	+	0.690390i	−0.373195	+	0.927753i	$0.621738\pi$
$948$		0			0
$949$	4.08664	−	4.71624i	0.132658	−	0.153096i
$950$		0			0
$951$	−6.11374	+	1.79516i	−0.198252	+	0.0582119i
$952$		0			0
$953$	−0.0103832	−	0.0722169i	−0.000336346	−	0.00233933i	0.989653	−	0.143484i	$-0.0458307\pi$
$953$	−0.0103832	−	0.0722169i	−0.000336346	−	0.00233933i	−0.989989	+	0.141145i	$0.954922\pi$
$954$		0			0
$955$	7.51283	+	16.4508i	0.243109	+	0.532335i
$956$		0			0
$957$	1.97659	+	1.27027i	0.0638939	+	0.0410621i
$958$		0			0
$959$	2.65931	−	18.4959i	0.0858735	−	0.597264i
$960$		0			0
$961$	−25.6290	+	16.4707i	−0.826741	+	0.531314i
$962$		0			0
$963$	−13.4915	−	3.96146i	−0.434757	−	0.127656i
$964$		0			0
$965$	−90.7692			−2.92196
$966$		0			0
$967$	18.8188			0.605172			0.302586	−	0.953122i	$-0.402150\pi$
$967$	18.8188			0.605172			0.302586	+	0.953122i	$0.402150\pi$
$968$		0			0
$969$	1.27093	+	0.373180i	0.0408283	+	0.0119883i
$970$		0			0
$971$	−7.62997	+	4.90348i	−0.244857	+	0.157360i	−0.657314	−	0.753617i	$-0.728307\pi$
$971$	−7.62997	+	4.90348i	−0.244857	+	0.157360i	0.412456	+	0.910977i	$0.364671\pi$
$972$		0			0
$973$	−1.77031	+	12.3128i	−0.0567535	+	0.394729i
$974$		0			0
$975$	−79.1766	−	50.8837i	−2.53568	−	1.62958i
$976$		0			0
$977$	6.86686	+	15.0363i	0.219690	+	0.481055i	0.987101	−	0.160102i	$-0.0511823\pi$
$977$	6.86686	+	15.0363i	0.219690	+	0.481055i	−0.767410	+	0.641156i	$0.778455\pi$
$978$		0			0
$979$	0.0556126	+	0.386794i	0.00177739	+	0.0123620i
$980$		0			0
$981$	−14.4871	+	4.25381i	−0.462539	+	0.135814i
$982$		0			0
$983$	9.42107	−	10.8725i	0.300486	−	0.346779i	−0.585348	−	0.810782i	$-0.699042\pi$
$983$	9.42107	−	10.8725i	0.300486	−	0.346779i	0.885833	+	0.464004i	$0.153587\pi$
$984$		0			0
$985$	16.7823	+	19.3678i	0.534729	+	0.617111i
$986$		0			0
$987$	8.00903	−	17.5373i	0.254930	−	0.558219i
$988$		0			0
$989$	33.4309	−	21.5108i	1.06304	−	0.684003i
$990$		0			0
$991$	−22.1032	+	48.3993i	−0.702132	+	1.53745i	0.135235	+	0.990814i	$0.456821\pi$
$991$	−22.1032	+	48.3993i	−0.702132	+	1.53745i	−0.837367	+	0.546641i	$0.815906\pi$
$992$		0			0
$993$	1.06183	+	1.22542i	0.0336962	+	0.0388875i
$994$		0			0
$995$	14.7058	−	16.9714i	0.466206	−	0.538030i
$996$		0			0
$997$	19.2290	−	5.64613i	0.608987	−	0.178815i	0.0373240	−	0.999303i	$-0.488117\pi$
$997$	19.2290	−	5.64613i	0.608987	−	0.178815i	0.571663	+	0.820488i	$0.306298\pi$
$998$		0			0
$999$	−0.245721	−	1.70902i	−0.00777426	−	0.0540712i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	552.2.q.a.121.3	yes	30
23.4	even	11	inner	552.2.q.a.73.3	✓	30

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
552.2.q.a.73.3	✓	30	23.4	even	11	inner
552.2.q.a.121.3	yes	30	1.1	even	1	trivial

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 552 = 2^{3} \cdot 3 \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	552.q (of order \(11\), degree \(10\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.959493 - 0.281733i) q^{3} +(3.62490 - 2.32958i) q^{5} +(-0.646888 + 4.49921i) q^{7} +(0.841254 + 0.540641i) q^{9} +O(q^{10})\)	\(q+(-0.959493 - 0.281733i) q^{3} +(3.62490 - 2.32958i) q^{5} +(-0.646888 + 4.49921i) q^{7} +(0.841254 + 0.540641i) q^{9} +(0.125570 + 0.274960i) q^{11} +(0.987280 + 6.86668i) q^{13} +(-4.13439 + 1.21397i) q^{15} +(1.35274 - 1.56115i) q^{17} +(-0.419918 - 0.484611i) q^{19} +(1.88826 - 4.13471i) q^{21} +(3.13861 - 3.62618i) q^{23} +(5.63588 - 12.3409i) q^{25} +(-0.654861 - 0.755750i) q^{27} +(-5.09018 + 5.87438i) q^{29} +(-0.701655 + 0.206025i) q^{31} +(-0.0430184 - 0.299200i) q^{33} +(8.13637 + 17.8162i) q^{35} +(1.45251 + 0.933470i) q^{37} +(0.987280 - 6.86668i) q^{39} +(3.46640 - 2.22772i) q^{41} +(7.95341 + 2.33533i) q^{43} +4.30893 q^{45} +4.24149 q^{47} +(-13.1080 - 3.84884i) q^{49} +(-1.73777 + 1.11680i) q^{51} +(1.08283 - 7.53123i) q^{53} +(1.09572 + 0.704178i) q^{55} +(0.266377 + 0.583285i) q^{57} +(-0.279646 - 1.94498i) q^{59} +(-5.09249 + 1.49529i) q^{61} +(-2.97665 + 3.43524i) q^{63} +(19.5753 + 22.5911i) q^{65} +(3.79686 - 8.31396i) q^{67} +(-4.03308 + 2.59504i) q^{69} +(-3.53997 + 7.75146i) q^{71} +(-0.589083 - 0.679838i) q^{73} +(-8.88441 + 10.2532i) q^{75} +(-1.31833 + 0.387098i) q^{77} +(-1.30838 - 9.09996i) q^{79} +(0.415415 + 0.909632i) q^{81} +(-9.04610 - 5.81358i) q^{83} +(1.26673 - 8.81033i) q^{85} +(6.53900 - 4.20236i) q^{87} +(1.24040 + 0.364214i) q^{89} -31.5333 q^{91} +0.731277 q^{93} +(-2.65110 - 0.778434i) q^{95} +(-7.41833 + 4.76747i) q^{97} +(-0.0430184 + 0.299200i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 30 q - 3 q^{3} - 2 q^{7} - 3 q^{9}+O(q^{10}) \) 30 * q - 3 * q^3 - 2 * q^7 - 3 * q^9	\( 30 q - 3 q^{3} - 2 q^{7} - 3 q^{9} - 15 q^{11} + 5 q^{13} - 15 q^{17} + 5 q^{19} + 9 q^{21} + 14 q^{23} + 5 q^{25} - 3 q^{27} + 13 q^{29} - 29 q^{31} - 15 q^{33} + 8 q^{35} - 3 q^{37} + 5 q^{39} + 24 q^{41} + 2 q^{43} + 22 q^{45} + 38 q^{47} + 15 q^{49} + 7 q^{51} - 7 q^{53} + 46 q^{55} - 6 q^{57} - 43 q^{59} - 22 q^{61} - 2 q^{63} + 44 q^{65} + 31 q^{67} + 3 q^{69} + 19 q^{71} - 50 q^{73} + 5 q^{75} + 16 q^{77} - 84 q^{79} - 3 q^{81} - 73 q^{83} - 8 q^{85} + 2 q^{87} + 19 q^{89} + 18 q^{91} + 26 q^{93} - 67 q^{95} - 29 q^{97} - 15 q^{99}+O(q^{100}) \) 30 * q - 3 * q^3 - 2 * q^7 - 3 * q^9 - 15 * q^11 + 5 * q^13 - 15 * q^17 + 5 * q^19 + 9 * q^21 + 14 * q^23 + 5 * q^25 - 3 * q^27 + 13 * q^29 - 29 * q^31 - 15 * q^33 + 8 * q^35 - 3 * q^37 + 5 * q^39 + 24 * q^41 + 2 * q^43 + 22 * q^45 + 38 * q^47 + 15 * q^49 + 7 * q^51 - 7 * q^53 + 46 * q^55 - 6 * q^57 - 43 * q^59 - 22 * q^61 - 2 * q^63 + 44 * q^65 + 31 * q^67 + 3 * q^69 + 19 * q^71 - 50 * q^73 + 5 * q^75 + 16 * q^77 - 84 * q^79 - 3 * q^81 - 73 * q^83 - 8 * q^85 + 2 * q^87 + 19 * q^89 + 18 * q^91 + 26 * q^93 - 67 * q^95 - 29 * q^97 - 15 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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