LMFDB - Embedded newform 504.2.q.d.25.10

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [504,2,Mod(25,504)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("504.25"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(504, base_ring=CyclotomicField(6)) chi = DirichletCharacter(H, H._module([0, 0, 4, 4])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 504 = 2^{3} \cdot 3^{2} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	504.q (of order $3$, degree $2$, minimal)

Newform invariants

comment:select newform

sage:traces = [22,0,2,0,3] 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:	$4.02446026187$
Analytic rank:	$0$
Dimension:	$22$
Relative dimension:	$11$ over $\Q(\zeta_{3})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			25.10
Character	$\chi$	$=$	504.25
Dual form			504.2.q.d.121.10

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(1.57901 + 0.711841i) q^{3} +(-1.92048 + 3.32636i) q^{5} +(-2.55336 + 0.693065i) q^{7} +(1.98656 + 2.24801i) q^{9} +(-0.903316 - 1.56459i) q^{11} +(-0.692713 - 1.19981i) q^{13} +(-5.40030 + 3.88530i) q^{15} +(-0.833405 + 1.44350i) q^{17} +(-0.0802084 - 0.138925i) q^{19} +(-4.52515 - 0.723229i) q^{21} +(-1.60019 + 2.77161i) q^{23} +(-4.87646 - 8.44627i) q^{25} +(1.53658 + 4.96376i) q^{27} +(-3.78000 + 6.54716i) q^{29} +3.22021 q^{31} +(-0.312609 - 3.11352i) q^{33} +(2.59829 - 9.82442i) q^{35} +(1.58395 + 2.74348i) q^{37} +(-0.239726 - 2.38762i) q^{39} +(6.00329 + 10.3980i) q^{41} +(3.45480 - 5.98389i) q^{43} +(-11.2929 + 2.29078i) q^{45} +11.4384 q^{47} +(6.03932 - 3.53929i) q^{49} +(-2.34350 + 1.68605i) q^{51} +(1.37450 - 2.38071i) q^{53} +6.93918 q^{55} +(-0.0277576 - 0.276460i) q^{57} +15.0705 q^{59} -9.20285 q^{61} +(-6.63044 - 4.36317i) q^{63} +5.32136 q^{65} -12.3366 q^{67} +(-4.49967 + 3.23733i) q^{69} -6.93289 q^{71} +(-6.22457 + 10.7813i) q^{73} +(-1.68759 - 16.8080i) q^{75} +(3.39085 + 3.36891i) q^{77} +16.0743 q^{79} +(-1.10712 + 8.93165i) q^{81} +(-1.45280 + 2.51633i) q^{83} +(-3.20107 - 5.54441i) q^{85} +(-10.6292 + 7.64729i) q^{87} +(5.04034 + 8.73012i) q^{89} +(2.60030 + 2.58347i) q^{91} +(5.08476 + 2.29228i) q^{93} +0.616153 q^{95} +(4.18830 - 7.25435i) q^{97} +(1.72272 - 5.13882i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 22 q + 2 q^{3} + 3 q^{5} - 5 q^{7} + 10 q^{9} - 3 q^{11} - 3 q^{13} - q^{15} + 7 q^{17} - q^{19} + 2 q^{23} - 10 q^{25} - 4 q^{27} + 9 q^{29} + 8 q^{31} + 29 q^{33} + 14 q^{35} + 2 q^{37} - 16 q^{39}+ \cdots - 56 q^{99}+O(q^{100}) $ 22 * q + 2 * q^3 + 3 * q^5 - 5 * q^7 + 10 * q^9 - 3 * q^11 - 3 * q^13 - q^15 + 7 * q^17 - q^19 + 2 * q^23 - 10 * q^25 - 4 * q^27 + 9 * q^29 + 8 * q^31 + 29 * q^33 + 14 * q^35 + 2 * q^37 - 16 * q^39 + 16 * q^41 + q^45 - 10 * q^47 + 15 * q^49 + 7 * q^51 + 11 * q^53 + 22 * q^55 + 7 * q^57 + 38 * q^59 + 26 * q^61 + 48 * q^63 - 26 * q^65 - 52 * q^67 - 4 * q^69 - 48 * q^71 - 35 * q^73 - 23 * q^75 + 17 * q^77 - 20 * q^79 - 38 * q^81 - 28 * q^83 - 20 * q^85 - 33 * q^87 + 6 * q^89 - 37 * q^91 + 19 * q^93 - 24 * q^95 - 29 * q^97 - 56 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/504\mathbb{Z}\right)^\times$.

$n$	$73$	$127$	$253$	$281$
$\chi(n)$	$e\left(\frac{2}{3}\right)$	$1$	$1$	$e\left(\frac{2}{3}\right)$

Coefficient data

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

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

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

$2$		0			0
$2$		0			0
$3$	1.57901	+	0.711841i	0.911644	+	0.410982i
$3$	1.57901	+	0.711841i	0.911644	+	0.410982i
$4$		0			0
$5$	−1.92048	+	3.32636i	−0.858863	+	1.48759i	0.0141515	+	0.999900i	$0.495495\pi$
$5$	−1.92048	+	3.32636i	−0.858863	+	1.48759i	−0.873014	+	0.487694i	$0.837838\pi$
$6$		0			0
$7$	−2.55336	+	0.693065i	−0.965080	+	0.261954i
$7$	−2.55336	+	0.693065i	−0.965080	+	0.261954i
$8$		0			0
$9$	1.98656	+	2.24801i	0.662188	+	0.749337i
$10$		0			0
$11$	−0.903316	−	1.56459i	−0.272360	−	0.471741i	0.697106	−	0.716968i	$-0.254471\pi$
$11$	−0.903316	−	1.56459i	−0.272360	−	0.471741i	−0.969466	+	0.245227i	$0.921137\pi$
$12$		0			0
$13$	−0.692713	−	1.19981i	−0.192124	−	0.332769i	0.753830	−	0.657070i	$-0.228204\pi$
$13$	−0.692713	−	1.19981i	−0.192124	−	0.332769i	−0.945954	+	0.324301i	$0.894871\pi$
$14$		0			0
$15$	−5.40030	+	3.88530i	−1.39435	+	1.00318i
$16$		0			0
$17$	−0.833405	+	1.44350i	−0.202130	+	0.350100i	−0.949215	−	0.314629i	$-0.898120\pi$
$17$	−0.833405	+	1.44350i	−0.202130	+	0.350100i	0.747084	+	0.664729i	$0.231453\pi$
$18$		0			0
$19$	−0.0802084	−	0.138925i	−0.0184011	−	0.0318716i	0.856678	−	0.515851i	$-0.172524\pi$
$19$	−0.0802084	−	0.138925i	−0.0184011	−	0.0318716i	−0.875079	+	0.483980i	$0.839191\pi$
$20$		0			0
$21$	−4.52515	−	0.723229i	−0.987468	−	0.157822i
$22$		0			0
$23$	−1.60019	+	2.77161i	−0.333663	+	0.577921i	−0.983227	−	0.182386i	$-0.941618\pi$
$23$	−1.60019	+	2.77161i	−0.333663	+	0.577921i	0.649564	+	0.760307i	$0.274951\pi$
$24$		0			0
$25$	−4.87646	−	8.44627i	−0.975291	−	1.68925i
$26$		0			0
$27$	1.53658	+	4.96376i	0.295716	+	0.955276i
$28$		0			0
$29$	−3.78000	+	6.54716i	−0.701929	+	1.21578i	0.265859	+	0.964012i	$0.414344\pi$
$29$	−3.78000	+	6.54716i	−0.701929	+	1.21578i	−0.967788	+	0.251765i	$0.918989\pi$
$30$		0			0
$31$	3.22021			0.578367			0.289184	−	0.957274i	$-0.406616\pi$
$31$	3.22021			0.578367			0.289184	+	0.957274i	$0.406616\pi$
$32$		0			0
$33$	−0.312609	−	3.11352i	−0.0544182	−	0.541995i
$34$		0			0
$35$	2.59829	−	9.82442i	0.439190	−	1.66063i
$36$		0			0
$37$	1.58395	+	2.74348i	0.260399	+	0.451025i	0.966348	−	0.257238i	$-0.0828124\pi$
$37$	1.58395	+	2.74348i	0.260399	+	0.451025i	−0.705949	+	0.708263i	$0.749479\pi$
$38$		0			0
$39$	−0.239726	−	2.38762i	−0.0383869	−	0.382326i
$40$		0			0
$41$	6.00329	+	10.3980i	0.937556	+	1.62389i	0.770011	+	0.638030i	$0.220250\pi$
$41$	6.00329	+	10.3980i	0.937556	+	1.62389i	0.167545	+	0.985864i	$0.446416\pi$
$42$		0			0
$43$	3.45480	−	5.98389i	0.526852	−	0.912535i	−0.472658	−	0.881246i	$-0.656705\pi$
$43$	3.45480	−	5.98389i	0.526852	−	0.912535i	0.999510	−	0.0312891i	$-0.00996125\pi$
$44$		0			0
$45$	−11.2929	+	2.29078i	−1.68344	+	0.341489i
$46$		0			0
$47$	11.4384			1.66846			0.834232	−	0.551414i	$-0.185911\pi$
$47$	11.4384			1.66846			0.834232	+	0.551414i	$0.185911\pi$
$48$		0			0
$49$	6.03932	−	3.53929i	0.862760	−	0.505613i
$50$		0			0
$51$	−2.34350	+	1.68605i	−0.328156	+	0.236095i
$52$		0			0
$53$	1.37450	−	2.38071i	0.188802	−	0.327015i	−0.756049	−	0.654515i	$-0.772873\pi$
$53$	1.37450	−	2.38071i	0.188802	−	0.327015i	0.944851	+	0.327500i	$0.106206\pi$
$54$		0			0
$55$	6.93918			0.935679
$56$		0			0
$57$	−0.0277576	−	0.276460i	−0.00367658	−	0.0366180i
$58$		0			0
$59$	15.0705			1.96202			0.981009	−	0.193964i	$-0.0621344\pi$
$59$	15.0705			1.96202			0.981009	+	0.193964i	$0.0621344\pi$
$60$		0			0
$61$	−9.20285			−1.17830			−0.589152	−	0.808022i	$-0.700538\pi$
$61$	−9.20285			−1.17830			−0.589152	+	0.808022i	$0.700538\pi$
$62$		0			0
$63$	−6.63044	−	4.36317i	−0.835357	−	0.549708i
$64$		0			0
$65$	5.32136			0.660033
$66$		0			0
$67$	−12.3366			−1.50716			−0.753578	−	0.657359i	$-0.771674\pi$
$67$	−12.3366			−1.50716			−0.753578	+	0.657359i	$0.771674\pi$
$68$		0			0
$69$	−4.49967	+	3.23733i	−0.541697	+	0.389729i
$70$		0			0
$71$	−6.93289			−0.822783			−0.411391	−	0.911459i	$-0.634957\pi$
$71$	−6.93289			−0.822783			−0.411391	+	0.911459i	$0.634957\pi$
$72$		0			0
$73$	−6.22457	+	10.7813i	−0.728531	+	1.26185i	0.228973	+	0.973433i	$0.426463\pi$
$73$	−6.22457	+	10.7813i	−0.728531	+	1.26185i	−0.957504	+	0.288420i	$0.906870\pi$
$74$		0			0
$75$	−1.68759	−	16.8080i	−0.194866	−	1.94082i
$76$		0			0
$77$	3.39085	+	3.36891i	0.386424	+	0.383922i
$78$		0			0
$79$	16.0743			1.80850			0.904251	−	0.427001i	$-0.140430\pi$
$79$	16.0743			1.80850			0.904251	+	0.427001i	$0.140430\pi$
$80$		0			0
$81$	−1.10712	+	8.93165i	−0.123013	+	0.992405i
$82$		0			0
$83$	−1.45280	+	2.51633i	−0.159466	+	0.276203i	−0.934676	−	0.355500i	$-0.884311\pi$
$83$	−1.45280	+	2.51633i	−0.159466	+	0.276203i	0.775210	+	0.631703i	$0.217644\pi$
$84$		0			0
$85$	−3.20107	−	5.54441i	−0.347205	−	0.601376i
$86$		0			0
$87$	−10.6292	+	7.64729i	−1.13957	+	0.819875i
$88$		0			0
$89$	5.04034	+	8.73012i	0.534275	+	0.925391i	0.999198	+	0.0400399i	$0.0127485\pi$
$89$	5.04034	+	8.73012i	0.534275	+	0.925391i	−0.464923	+	0.885351i	$0.653918\pi$
$90$		0			0
$91$	2.60030	+	2.58347i	0.272585	+	0.270821i
$92$		0			0
$93$	5.08476	+	2.29228i	0.527265	+	0.237698i
$94$		0			0
$95$	0.616153			0.0632160
$96$		0			0
$97$	4.18830	−	7.25435i	0.425257	−	0.736567i	−0.571187	−	0.820820i	$-0.693517\pi$
$97$	4.18830	−	7.25435i	0.425257	−	0.736567i	0.996444	+	0.0842527i	$0.0268503\pi$
$98$		0			0
$99$	1.72272	−	5.13882i	0.173140	−	0.516471i
$100$		0			0
$101$	−4.05750	−	7.02780i	−0.403736	−	0.699292i	0.590437	−	0.807084i	$-0.298955\pi$
$101$	−4.05750	−	7.02780i	−0.403736	−	0.699292i	−0.994173	+	0.107792i	$0.965622\pi$
$102$		0			0
$103$	3.76891	−	6.52794i	0.371362	−	0.643217i	−0.618414	−	0.785853i	$-0.712224\pi$
$103$	3.76891	−	6.52794i	0.371362	−	0.643217i	0.989775	+	0.142635i	$0.0455577\pi$
$104$		0			0
$105$	11.0962	−	13.6633i	1.08287	−	1.33340i
$106$		0			0
$107$	−2.95731	−	5.12221i	−0.285894	−	0.495183i	0.686932	−	0.726722i	$-0.258957\pi$
$107$	−2.95731	−	5.12221i	−0.285894	−	0.495183i	−0.972826	+	0.231539i	$0.925624\pi$
$108$		0			0
$109$	−4.48409	+	7.76668i	−0.429498	+	0.743913i	−0.996829	−	0.0795776i	$-0.974643\pi$
$109$	−4.48409	+	7.76668i	−0.429498	+	0.743913i	0.567331	+	0.823490i	$0.307976\pi$
$110$		0			0
$111$	0.548154	+	5.45951i	0.0520285	+	0.518193i
$112$		0			0
$113$	−7.98131	−	13.8240i	−0.750819	−	1.30046i	−0.947426	−	0.319974i	$-0.896326\pi$
$113$	−7.98131	−	13.8240i	−0.750819	−	1.30046i	0.196608	−	0.980482i	$-0.437007\pi$
$114$		0			0
$115$	−6.14626	−	10.6456i	−0.573142	−	0.992710i
$116$		0			0
$117$	1.32108	−	3.94074i	0.122134	−	0.364321i
$118$		0			0
$119$	1.12755	−	4.26338i	0.103362	−	0.390824i
$120$		0			0
$121$	3.86804	−	6.69964i	0.351640	−	0.609059i
$122$		0			0
$123$	2.07755	+	20.6920i	0.187326	+	1.86573i
$124$		0			0
$125$	18.2557			1.63284
$126$		0			0
$127$	8.60913			0.763937			0.381968	−	0.924175i	$-0.375246\pi$
$127$	8.60913			0.763937			0.381968	+	0.924175i	$0.375246\pi$
$128$		0			0
$129$	9.71476	−	6.98937i	0.855337	−	0.615380i
$130$		0			0
$131$	0.964831	−	1.67114i	0.0842976	−	0.146008i	−0.820794	−	0.571224i	$-0.806469\pi$
$131$	0.964831	−	1.67114i	0.0842976	−	0.146008i	0.905092	+	0.425216i	$0.139802\pi$
$132$		0			0
$133$	0.301085	+	0.299136i	0.0261074	+	0.0259384i
$134$		0			0
$135$	−19.4622	−	4.42154i	−1.67504	−	0.380546i
$136$		0			0
$137$	1.85442	+	3.21195i	0.158434	+	0.274416i	0.934304	−	0.356477i	$-0.116022\pi$
$137$	1.85442	+	3.21195i	0.158434	+	0.274416i	−0.775870	+	0.630893i	$0.782689\pi$
$138$		0			0
$139$	0.134568	+	0.233079i	0.0114139	+	0.0197695i	0.871676	−	0.490083i	$-0.163033\pi$
$139$	0.134568	+	0.233079i	0.0114139	+	0.0197695i	−0.860262	+	0.509852i	$0.829700\pi$
$140$		0			0
$141$	18.0614	+	8.14233i	1.52104	+	0.685708i
$142$		0			0
$143$	−1.25148	+	2.16762i	−0.104654	+	0.181266i
$144$		0			0
$145$	−14.5188	−	25.1473i	−1.20572	−	2.08837i
$146$		0			0
$147$	12.0556	−	1.28955i	0.994328	−	0.106361i
$148$		0			0
$149$	−4.15880	+	7.20325i	−0.340702	+	0.590113i	−0.984563	−	0.175029i	$-0.943998\pi$
$149$	−4.15880	+	7.20325i	−0.340702	+	0.590113i	0.643861	+	0.765142i	$0.277331\pi$
$150$		0			0
$151$	−4.87069	−	8.43628i	−0.396371	−	0.686535i	0.596904	−	0.802313i	$-0.296397\pi$
$151$	−4.87069	−	8.43628i	−0.396371	−	0.686535i	−0.993275	+	0.115778i	$0.963064\pi$
$152$		0			0
$153$	−4.90062	+	0.994101i	−0.396192	+	0.0803683i
$154$		0			0
$155$	−6.18434	+	10.7116i	−0.496738	+	0.860376i
$156$		0			0
$157$	24.2580			1.93600			0.968001	−	0.250947i	$-0.0807420\pi$
$157$	24.2580			1.93600			0.968001	+	0.250947i	$0.0807420\pi$
$158$		0			0
$159$	3.86504	−	2.78074i	0.306518	−	0.220527i
$160$		0			0
$161$	2.16496	−	8.18597i	0.170623	−	0.645145i
$162$		0			0
$163$	3.91401	+	6.77927i	0.306569	+	0.530993i	0.977609	−	0.210428i	$-0.0674857\pi$
$163$	3.91401	+	6.77927i	0.306569	+	0.530993i	−0.671040	+	0.741421i	$0.734152\pi$
$164$		0			0
$165$	10.9571	+	4.93960i	0.853006	+	0.384547i
$166$		0			0
$167$	−2.15395	−	3.73076i	−0.166678	−	0.288695i	0.770572	−	0.637353i	$-0.219971\pi$
$167$	−2.15395	−	3.73076i	−0.166678	−	0.288695i	−0.937250	+	0.348658i	$0.886637\pi$
$168$		0			0
$169$	5.54030	−	9.59608i	0.426177	−	0.738160i
$170$		0			0
$171$	0.152966	−	0.456293i	0.0116976	−	0.0348936i
$172$		0			0
$173$	−17.3359			−1.31803			−0.659014	−	0.752131i	$-0.729026\pi$
$173$	−17.3359			−1.31803			−0.659014	+	0.752131i	$0.729026\pi$
$174$		0			0
$175$	18.3052	+	18.1867i	1.38374	+	1.37478i
$176$		0			0
$177$	23.7966	+	10.7278i	1.78866	+	0.806353i
$178$		0			0
$179$	−9.68644	+	16.7774i	−0.723998	+	1.25400i	0.235387	+	0.971902i	$0.424364\pi$
$179$	−9.68644	+	16.7774i	−0.723998	+	1.25400i	−0.959385	+	0.282100i	$0.908969\pi$
$180$		0			0
$181$	2.89036			0.214839			0.107420	−	0.994214i	$-0.465741\pi$
$181$	2.89036			0.214839			0.107420	+	0.994214i	$0.465741\pi$
$182$		0			0
$183$	−14.5314	−	6.55097i	−1.07419	−	0.484261i
$184$		0			0
$185$	−12.1677			−0.894590
$186$		0			0
$187$	3.01131			0.220209
$188$		0			0
$189$	−7.36367	−	11.6093i	−0.535628	−	0.844454i
$190$		0			0
$191$	3.70044			0.267755			0.133877	−	0.990998i	$-0.457257\pi$
$191$	3.70044			0.267755			0.133877	+	0.990998i	$0.457257\pi$
$192$		0			0
$193$	−12.7670			−0.918991			−0.459495	−	0.888180i	$-0.651970\pi$
$193$	−12.7670			−0.918991			−0.459495	+	0.888180i	$0.651970\pi$
$194$		0			0
$195$	8.40249	+	3.78796i	0.601715	+	0.271261i
$196$		0			0
$197$	2.44715			0.174352			0.0871762	−	0.996193i	$-0.472216\pi$
$197$	2.44715			0.174352			0.0871762	+	0.996193i	$0.472216\pi$
$198$		0			0
$199$	2.24829	−	3.89415i	0.159377	−	0.276049i	−0.775267	−	0.631633i	$-0.782385\pi$
$199$	2.24829	−	3.89415i	0.159377	−	0.276049i	0.934644	+	0.355584i	$0.115718\pi$
$200$		0			0
$201$	−19.4797	−	8.78170i	−1.37399	−	0.619413i
$202$		0			0
$203$	5.11411	−	19.3371i	0.358940	−	1.35720i
$204$		0			0
$205$	−46.1167			−3.22093
$206$		0			0
$207$	−9.40950	+	1.90874i	−0.654006	+	0.132666i
$208$		0			0
$209$	−0.144907	+	0.250986i	−0.0100234	+	0.0173611i
$210$		0			0
$211$	1.09087	+	1.88945i	0.0750987	+	0.130075i	0.901129	−	0.433551i	$-0.142739\pi$
$211$	1.09087	+	1.88945i	0.0750987	+	0.130075i	−0.826030	+	0.563625i	$0.809406\pi$
$212$		0			0
$213$	−10.9471	−	4.93512i	−0.750085	−	0.338149i
$214$		0			0
$215$	13.2697	+	22.9838i	0.904988	+	1.56749i
$216$		0			0
$217$	−8.22237	+	2.23182i	−0.558171	+	0.151506i
$218$		0			0
$219$	−17.5032	+	12.5929i	−1.18276	+	0.850947i
$220$		0			0
$221$	2.30924			0.155336
$222$		0			0
$223$	−2.87967	+	4.98773i	−0.192837	+	0.334003i	−0.946189	−	0.323614i	$-0.895102\pi$
$223$	−2.87967	+	4.98773i	−0.192837	+	0.334003i	0.753352	+	0.657617i	$0.228436\pi$
$224$		0			0
$225$	9.29992	−	27.7414i	0.619995	−	1.84943i
$226$		0			0
$227$	−8.29135	−	14.3610i	−0.550316	−	0.953175i	−0.998252	−	0.0591094i	$-0.981174\pi$
$227$	−8.29135	−	14.3610i	−0.550316	−	0.953175i	0.447935	−	0.894066i	$-0.352159\pi$
$228$		0			0
$229$	7.29688	−	12.6386i	0.482191	−	0.835180i	−0.517600	−	0.855623i	$-0.673174\pi$
$229$	7.29688	−	12.6386i	0.482191	−	0.835180i	0.999791	+	0.0204432i	$0.00650771\pi$
$230$		0			0
$231$	2.95608	+	7.73329i	0.194496	+	0.508813i
$232$		0			0
$233$	0.949438	+	1.64448i	0.0621998	+	0.107733i	0.895448	−	0.445165i	$-0.146855\pi$
$233$	0.949438	+	1.64448i	0.0621998	+	0.107733i	−0.833249	+	0.552898i	$0.813522\pi$
$234$		0			0
$235$	−21.9672	+	38.0483i	−1.43298	+	2.48200i
$236$		0			0
$237$	25.3816	+	11.4424i	1.64871	+	0.743261i
$238$		0			0
$239$	−4.46351	−	7.73103i	−0.288721	−	0.500079i	0.684784	−	0.728746i	$-0.259897\pi$
$239$	−4.46351	−	7.73103i	−0.288721	−	0.500079i	−0.973505	+	0.228667i	$0.926563\pi$
$240$		0			0
$241$	12.1465	+	21.0383i	0.782423	+	1.35520i	0.930527	+	0.366224i	$0.119350\pi$
$241$	12.1465	+	21.0383i	0.782423	+	1.35520i	−0.148104	+	0.988972i	$0.547317\pi$
$242$		0			0
$243$	−8.10607	+	13.3151i	−0.520005	+	0.854164i
$244$		0			0
$245$	0.174600	+	26.8861i	0.0111548	+	1.71769i
$246$		0			0
$247$	−0.111123	+	0.192470i	−0.00707057	+	0.0122466i
$248$		0			0
$249$	−4.08522	+	2.93915i	−0.258890	+	0.186261i
$250$		0			0
$251$	−5.64873			−0.356545			−0.178272	−	0.983981i	$-0.557051\pi$
$251$	−5.64873			−0.356545			−0.178272	+	0.983981i	$0.557051\pi$
$252$		0			0
$253$	5.78191			0.363506
$254$		0			0
$255$	−1.10779	−	11.0334i	−0.0693724	−	0.690935i
$256$		0			0
$257$	11.7856	−	20.4132i	0.735163	−	1.27334i	−0.219489	−	0.975615i	$-0.570439\pi$
$257$	11.7856	−	20.4132i	0.735163	−	1.27334i	0.954652	−	0.297724i	$-0.0962275\pi$
$258$		0			0
$259$	−5.94580	−	5.90731i	−0.369454	−	0.367063i
$260$		0			0
$261$	−22.2273	+	4.50886i	−1.37584	+	0.279091i
$262$		0			0
$263$	−12.8203	−	22.2053i	−0.790531	−	1.36924i	−0.925639	−	0.378409i	$-0.876471\pi$
$263$	−12.8203	−	22.2053i	−0.790531	−	1.36924i	0.135108	−	0.990831i	$-0.456862\pi$
$264$		0			0
$265$	5.27940	+	9.14419i	0.324311	+	0.561723i
$266$		0			0
$267$	1.74430	+	17.3729i	0.106749	+	1.06320i
$268$		0			0
$269$	−8.27239	+	14.3282i	−0.504376	+	0.873606i	0.495611	+	0.868545i	$0.334944\pi$
$269$	−8.27239	+	14.3282i	−0.504376	+	0.873606i	−0.999987	+	0.00506090i	$0.998389\pi$
$270$		0			0
$271$	8.90748	+	15.4282i	0.541091	+	0.937197i	0.998842	+	0.0481166i	$0.0153219\pi$
$271$	8.90748	+	15.4282i	0.541091	+	0.937197i	−0.457751	+	0.889081i	$0.651345\pi$
$272$		0			0
$273$	2.26689	+	5.93032i	0.137198	+	0.358920i
$274$		0			0
$275$	−8.80996	+	15.2593i	−0.531260	+	0.920170i
$276$		0			0
$277$	2.92191	+	5.06089i	0.175560	+	0.304080i	0.940355	−	0.340194i	$-0.110493\pi$
$277$	2.92191	+	5.06089i	0.175560	+	0.304080i	−0.764795	+	0.644274i	$0.777160\pi$
$278$		0			0
$279$	6.39716	+	7.23908i	0.382988	+	0.433392i
$280$		0			0
$281$	−10.5591	+	18.2889i	−0.629905	+	1.09103i	0.357666	+	0.933850i	$0.383573\pi$
$281$	−10.5591	+	18.2889i	−0.629905	+	1.09103i	−0.987570	+	0.157177i	$0.949761\pi$
$282$		0			0
$283$	−12.7762			−0.759468			−0.379734	−	0.925096i	$-0.623984\pi$
$283$	−12.7762			−0.759468			−0.379734	+	0.925096i	$0.623984\pi$
$284$		0			0
$285$	0.972914	+	0.438603i	0.0576304	+	0.0259806i
$286$		0			0
$287$	−22.5351	−	22.3892i	−1.33020	−	1.32159i
$288$		0			0
$289$	7.11087	+	12.3164i	0.418287	+	0.724494i
$290$		0			0
$291$	11.7773	−	8.47330i	0.690399	−	0.496714i
$292$		0			0
$293$	5.93828	+	10.2854i	0.346918	+	0.600880i	0.985700	−	0.168508i	$-0.0538948\pi$
$293$	5.93828	+	10.2854i	0.346918	+	0.600880i	−0.638782	+	0.769388i	$0.720561\pi$
$294$		0			0
$295$	−28.9426	+	50.1301i	−1.68510	+	2.91869i
$296$		0			0
$297$	6.37822	−	6.88796i	0.370102	−	0.399680i
$298$		0			0
$299$	4.43389			0.256419
$300$		0			0
$301$	−4.67413	+	17.6734i	−0.269413	+	1.01868i
$302$		0			0
$303$	−1.40417	−	13.9853i	−0.0806676	−	0.803433i
$304$		0			0
$305$	17.6739	−	30.6120i	1.01200	−	1.75284i
$306$		0			0
$307$	−3.93298			−0.224467			−0.112234	−	0.993682i	$-0.535800\pi$
$307$	−3.93298			−0.224467			−0.112234	+	0.993682i	$0.535800\pi$
$308$		0			0
$309$	10.5980	−	7.62484i	0.602900	−	0.433762i
$310$		0			0
$311$	1.98221			0.112401			0.0562005	−	0.998420i	$-0.482101\pi$
$311$	1.98221			0.112401			0.0562005	+	0.998420i	$0.482101\pi$
$312$		0			0
$313$	20.4995			1.15870			0.579349	−	0.815080i	$-0.303307\pi$
$313$	20.4995			1.15870			0.579349	+	0.815080i	$0.303307\pi$
$314$		0			0
$315$	27.2471	−	13.6759i	1.53520	−	0.770548i
$316$		0			0
$317$	9.51416			0.534369			0.267184	−	0.963645i	$-0.413907\pi$
$317$	9.51416			0.534369			0.267184	+	0.963645i	$0.413907\pi$
$318$		0			0
$319$	13.6581			0.764709
$320$		0			0
$321$	−1.02343	−	10.1932i	−0.0571224	−	0.568927i
$322$		0			0
$323$	0.267384			0.0148777
$324$		0			0
$325$	−6.75597	+	11.7017i	−0.374754	+	0.649093i
$326$		0			0
$327$	−12.6091	+	9.07172i	−0.697284	+	0.501667i
$328$		0			0
$329$	−29.2064	+	7.92756i	−1.61020	+	0.437061i
$330$		0			0
$331$	1.52986			0.0840886			0.0420443	−	0.999116i	$-0.486613\pi$
$331$	1.52986			0.0840886			0.0420443	+	0.999116i	$0.486613\pi$
$332$		0			0
$333$	−3.02076	+	9.01083i	−0.165536	+	0.493790i
$334$		0			0
$335$	23.6921	−	41.0360i	1.29444	−	2.24204i
$336$		0			0
$337$	10.6972	+	18.5281i	0.582714	+	1.00929i	0.995156	+	0.0983063i	$0.0313425\pi$
$337$	10.6972	+	18.5281i	0.582714	+	1.00929i	−0.412442	+	0.910984i	$0.635324\pi$
$338$		0			0
$339$	−2.76208	−	27.5098i	−0.150016	−	1.49413i
$340$		0			0
$341$	−2.90887	−	5.03831i	−0.157524	−	0.272840i
$342$		0			0
$343$	−12.9676	+	13.2227i	−0.700185	+	0.713961i
$344$		0			0
$345$	−2.12703	−	21.1848i	−0.114515	−	1.14055i
$346$		0			0
$347$	5.14381			0.276134			0.138067	−	0.990423i	$-0.455911\pi$
$347$	5.14381			0.276134			0.138067	+	0.990423i	$0.455911\pi$
$348$		0			0
$349$	0.207526	−	0.359446i	0.0111086	−	0.0192407i	−0.860418	−	0.509590i	$-0.829797\pi$
$349$	0.207526	−	0.359446i	0.0111086	−	0.0192407i	0.871526	+	0.490349i	$0.163131\pi$
$350$		0			0
$351$	4.89118	−	5.28208i	0.261072	−	0.281936i
$352$		0			0
$353$	6.04122	+	10.4637i	0.321542	+	0.556926i	0.980806	−	0.194985i	$-0.0624657\pi$
$353$	6.04122	+	10.4637i	0.321542	+	0.556926i	−0.659265	+	0.751911i	$0.729132\pi$
$354$		0			0
$355$	13.3145	−	23.0613i	0.706658	−	1.22397i
$356$		0			0
$357$	4.81526	−	5.92930i	0.254851	−	0.313812i
$358$		0			0
$359$	−8.14926	−	14.1149i	−0.430102	−	0.744958i	0.566780	−	0.823869i	$-0.308189\pi$
$359$	−8.14926	−	14.1149i	−0.430102	−	0.744958i	−0.996882	+	0.0789113i	$0.974856\pi$
$360$		0			0
$361$	9.48713	−	16.4322i	0.499323	−	0.864852i
$362$		0			0
$363$	10.8768	−	7.82540i	0.570882	−	0.410727i
$364$		0			0
$365$	−23.9083	−	41.4104i	−1.25142	−	2.16752i
$366$		0			0
$367$	−17.3500	−	30.0511i	−0.905664	−	1.56866i	−0.820024	−	0.572330i	$-0.806040\pi$
$367$	−17.3500	−	30.0511i	−0.905664	−	1.56866i	−0.0856404	−	0.996326i	$-0.527294\pi$
$368$		0			0
$369$	−11.4489	+	34.1518i	−0.596007	+	1.77787i
$370$		0			0
$371$	−1.85962	+	7.03143i	−0.0965465	+	0.365054i
$372$		0			0
$373$	7.75329	−	13.4291i	0.401450	−	0.695332i	−0.592451	−	0.805606i	$-0.701840\pi$
$373$	7.75329	−	13.4291i	0.401450	−	0.695332i	0.993901	+	0.110274i	$0.0351730\pi$
$374$		0			0
$375$	28.8260	+	12.9952i	1.48857	+	0.671067i
$376$		0			0
$377$	10.4738			0.539430
$378$		0			0
$379$	−16.1820			−0.831214			−0.415607	−	0.909544i	$-0.636431\pi$
$379$	−16.1820			−0.831214			−0.415607	+	0.909544i	$0.636431\pi$
$380$		0			0
$381$	13.5939	+	6.12833i	0.696438	+	0.313964i
$382$		0			0
$383$	−2.17027	+	3.75902i	−0.110896	+	0.192077i	−0.916132	−	0.400877i	$-0.868705\pi$
$383$	−2.17027	+	3.75902i	−0.110896	+	0.192077i	0.805236	+	0.592955i	$0.202039\pi$
$384$		0			0
$385$	−17.7183	+	4.80931i	−0.903006	+	0.245105i
$386$		0			0
$387$	20.3151	−	4.12095i	1.03267	−	0.209480i
$388$		0			0
$389$	−12.7731	−	22.1237i	−0.647624	−	1.12172i	−0.983689	−	0.179879i	$-0.942429\pi$
$389$	−12.7731	−	22.1237i	−0.647624	−	1.12172i	0.336065	−	0.941839i	$-0.390904\pi$
$390$		0			0
$391$	−2.66722	−	4.61975i	−0.134887	−	0.233631i
$392$		0			0
$393$	2.71306	−	1.95194i	0.136856	−	0.0984623i
$394$		0			0
$395$	−30.8703	+	53.4690i	−1.55326	+	2.69032i
$396$		0			0
$397$	2.28225	+	3.95297i	0.114543	+	0.198394i	0.917597	−	0.397512i	$-0.130126\pi$
$397$	2.28225	+	3.95297i	0.114543	+	0.198394i	−0.803054	+	0.595906i	$0.796793\pi$
$398$		0			0
$399$	0.262480	+	0.686665i	0.0131404	+	0.0343762i
$400$		0			0
$401$	−0.668128	+	1.15723i	−0.0333647	+	0.0577894i	−0.882226	−	0.470827i	$-0.843956\pi$
$401$	−0.668128	+	1.15723i	−0.0333647	+	0.0577894i	0.848861	+	0.528616i	$0.177289\pi$
$402$		0			0
$403$	−2.23068	−	3.86366i	−0.111118	−	0.192463i
$404$		0			0
$405$	−27.5837	−	20.8357i	−1.37064	−	1.03533i
$406$		0			0
$407$	2.86161	−	4.95645i	0.141845	−	0.245682i
$408$		0			0
$409$	20.6664			1.02189			0.510944	−	0.859614i	$-0.329296\pi$
$409$	20.6664			1.02189			0.510944	+	0.859614i	$0.329296\pi$
$410$		0			0
$411$	0.641757	+	6.39177i	0.0316555	+	0.315283i
$412$		0			0
$413$	−38.4806	+	10.4449i	−1.89350	+	0.513958i
$414$		0			0
$415$	−5.58015	−	9.66510i	−0.273919	−	0.474441i
$416$		0			0
$417$	0.0465699	+	0.463826i	0.00228054	+	0.0227137i
$418$		0			0
$419$	10.5227	+	18.2259i	0.514069	+	0.890394i	0.999867	+	0.0163228i	$0.00519594\pi$
$419$	10.5227	+	18.2259i	0.514069	+	0.890394i	−0.485797	+	0.874071i	$0.661471\pi$
$420$		0			0
$421$	−8.51630	+	14.7507i	−0.415059	+	0.718903i	−0.995435	−	0.0954456i	$-0.969572\pi$
$421$	−8.51630	+	14.7507i	−0.415059	+	0.718903i	0.580376	+	0.814349i	$0.302906\pi$
$422$		0			0
$423$	22.7231	+	25.7137i	1.10484	+	1.25024i
$424$		0			0
$425$	16.2563			0.788544
$426$		0			0
$427$	23.4982	−	6.37818i	1.13716	−	0.308662i
$428$		0			0
$429$	−3.51910	+	2.53185i	−0.169904	+	0.122239i
$430$		0			0
$431$	18.2925	−	31.6836i	0.881121	−	1.52615i	0.0310244	−	0.999519i	$-0.490123\pi$
$431$	18.2925	−	31.6836i	0.881121	−	1.52615i	0.850096	−	0.526627i	$-0.176544\pi$
$432$		0			0
$433$	−23.6571			−1.13689			−0.568444	−	0.822722i	$-0.692454\pi$
$433$	−23.6571			−1.13689			−0.568444	+	0.822722i	$0.692454\pi$
$434$		0			0
$435$	−5.02450	−	50.0430i	−0.240906	−	2.39938i
$436$		0			0
$437$	0.513395			0.0245590
$438$		0			0
$439$	20.7864			0.992082			0.496041	−	0.868299i	$-0.334787\pi$
$439$	20.7864			0.992082			0.496041	+	0.868299i	$0.334787\pi$
$440$		0			0
$441$	19.9539	+	6.54543i	0.950185	+	0.311687i
$442$		0			0
$443$	7.42807			0.352918			0.176459	−	0.984308i	$-0.443536\pi$
$443$	7.42807			0.352918			0.176459	+	0.984308i	$0.443536\pi$
$444$		0			0
$445$	−38.7194			−1.83547
$446$		0			0
$447$	−11.6944	+	8.41363i	−0.553125	+	0.397951i
$448$		0			0
$449$	−8.15800			−0.385000			−0.192500	−	0.981297i	$-0.561660\pi$
$449$	−8.15800			−0.385000			−0.192500	+	0.981297i	$0.561660\pi$
$450$		0			0
$451$	10.8457	−	18.7854i	0.510705	−	0.884568i
$452$		0			0
$453$	−1.68559	−	16.7882i	−0.0791960	−	0.788776i
$454$		0			0
$455$	−13.5873	+	3.68805i	−0.636985	+	0.172898i
$456$		0			0
$457$	14.3058			0.669199			0.334600	−	0.942360i	$-0.391399\pi$
$457$	14.3058			0.669199			0.334600	+	0.942360i	$0.391399\pi$
$458$		0			0
$459$	−8.44578	−	1.91876i	−0.394215	−	0.0895602i
$460$		0			0
$461$	7.71961	−	13.3708i	0.359538	−	0.622738i	−0.628346	−	0.777934i	$-0.716268\pi$
$461$	7.71961	−	13.3708i	0.359538	−	0.622738i	0.987884	+	0.155196i	$0.0496009\pi$
$462$		0			0
$463$	10.5531	+	18.2785i	0.490444	+	0.849474i	0.999940	−	0.0109995i	$-0.00350132\pi$
$463$	10.5531	+	18.2785i	0.490444	+	0.849474i	−0.509496	+	0.860473i	$0.670168\pi$
$464$		0			0
$465$	−17.3901	+	12.5115i	−0.806447	+	0.580206i
$466$		0			0
$467$	3.49896	+	6.06037i	0.161912	+	0.280440i	0.935555	−	0.353182i	$-0.114900\pi$
$467$	3.49896	+	6.06037i	0.161912	+	0.280440i	−0.773642	+	0.633623i	$0.781567\pi$
$468$		0			0
$469$	31.4998	−	8.55007i	1.45453	−	0.394805i
$470$		0			0
$471$	38.3037	+	17.2679i	1.76494	+	0.795661i
$472$		0			0
$473$	−12.4831			−0.573974
$474$		0			0
$475$	−0.782265	+	1.35492i	−0.0358928	+	0.0621681i
$476$		0			0
$477$	8.08240	−	1.63953i	0.370068	−	0.0750691i
$478$		0			0
$479$	−1.54406	−	2.67440i	−0.0705500	−	0.122196i	0.828592	−	0.559852i	$-0.189142\pi$
$479$	−1.54406	−	2.67440i	−0.0705500	−	0.122196i	−0.899142	+	0.437656i	$0.855809\pi$
$480$		0			0
$481$	2.19444	−	3.80089i	0.100058	−	0.173305i
$482$		0			0
$483$	9.24561	−	11.3846i	0.420690	−	0.518019i
$484$		0			0
$485$	16.0871	+	27.8636i	0.730475	+	1.26522i
$486$		0			0
$487$	4.90011	−	8.48725i	0.222045	−	0.384594i	−0.733384	−	0.679815i	$-0.762060\pi$
$487$	4.90011	−	8.48725i	0.222045	−	0.384594i	0.955429	+	0.295221i	$0.0953934\pi$
$488$		0			0
$489$	1.35452	+	13.4907i	0.0612533	+	0.610071i
$490$		0			0
$491$	9.98641	+	17.2970i	0.450680	+	0.780601i	0.998428	−	0.0560419i	$-0.0178481\pi$
$491$	9.98641	+	17.2970i	0.450680	+	0.780601i	−0.547748	+	0.836643i	$0.684515\pi$
$492$		0			0
$493$	−6.30055	−	10.9129i	−0.283762	−	0.491491i
$494$		0			0
$495$	13.7851	+	15.5994i	0.619596	+	0.701140i
$496$		0			0
$497$	17.7022	−	4.80495i	0.794052	−	0.215531i
$498$		0			0
$499$	10.1650	−	17.6062i	0.455046	−	0.788163i	−0.543645	−	0.839315i	$-0.682956\pi$
$499$	10.1650	−	17.6062i	0.455046	−	0.788163i	0.998691	+	0.0511526i	$0.0162895\pi$
$500$		0			0
$501$	−0.745415	−	7.42419i	−0.0333027	−	0.331688i
$502$		0			0
$503$	−23.9595			−1.06830			−0.534151	−	0.845389i	$-0.679369\pi$
$503$	−23.9595			−1.06830			−0.534151	+	0.845389i	$0.679369\pi$
$504$		0			0
$505$	31.1693			1.38702
$506$		0			0
$507$	15.5791	−	11.2085i	0.691891	−	0.497788i
$508$		0			0
$509$	−5.03046	+	8.71302i	−0.222971	+	0.386198i	−0.955709	−	0.294314i	$-0.904909\pi$
$509$	−5.03046	+	8.71302i	−0.222971	+	0.386198i	0.732737	+	0.680511i	$0.238242\pi$
$510$		0			0
$511$	8.42146	−	31.8425i	0.372544	−	1.40863i
$512$		0			0
$513$	0.566343	−	0.611605i	0.0250047	−	0.0270030i
$514$		0			0
$515$	14.4762	+	25.0735i	0.637898	+	1.10487i
$516$		0			0
$517$	−10.3325	−	17.8964i	−0.454423	−	0.787083i
$518$		0			0
$519$	−27.3737	−	12.3404i	−1.20157	−	0.541685i
$520$		0			0
$521$	7.99821	−	13.8533i	0.350408	−	0.606924i	−0.635913	−	0.771761i	$-0.719376\pi$
$521$	7.99821	−	13.8533i	0.350408	−	0.606924i	0.986321	+	0.164836i	$0.0527096\pi$
$522$		0			0
$523$	−18.7103	−	32.4072i	−0.818146	−	1.41707i	−0.907047	−	0.421029i	$-0.861669\pi$
$523$	−18.7103	−	32.4072i	−0.818146	−	1.41707i	0.0889016	−	0.996040i	$-0.471664\pi$
$524$		0			0
$525$	15.9581	+	41.7474i	0.696468	+	1.82201i
$526$		0			0
$527$	−2.68374	+	4.64838i	−0.116906	+	0.202487i
$528$		0			0
$529$	6.37877	+	11.0484i	0.277338	+	0.480364i
$530$		0			0
$531$	29.9386	+	33.8788i	1.29922	+	1.47021i
$532$		0			0
$533$	8.31711	−	14.4057i	0.360254	−	0.623978i
$534$		0			0
$535$	22.7178			0.982175
$536$		0			0
$537$	−27.2379	+	19.5965i	−1.17540	+	0.845653i
$538$		0			0
$539$	−10.9930	−	6.25195i	−0.473500	−	0.269291i
$540$		0			0
$541$	0.229159	+	0.396916i	0.00985233	+	0.0170647i	0.870910	−	0.491443i	$-0.163531\pi$
$541$	0.229159	+	0.396916i	0.00985233	+	0.0170647i	−0.861057	+	0.508508i	$0.830197\pi$
$542$		0			0
$543$	4.56392	+	2.05748i	0.195857	+	0.0882949i
$544$		0			0
$545$	−17.2232	−	29.8314i	−0.737760	−	1.27784i
$546$		0			0
$547$	−11.2013	+	19.4011i	−0.478931	+	0.829533i	−0.999708	−	0.0241596i	$-0.992309\pi$
$547$	−11.2013	+	19.4011i	−0.478931	+	0.829533i	0.520777	+	0.853693i	$0.325642\pi$
$548$		0			0
$549$	−18.2821	−	20.6881i	−0.780259	−	0.882948i
$550$		0			0
$551$	1.21275			0.0516650
$552$		0			0
$553$	−41.0436	+	11.1405i	−1.74535	+	0.473744i
$554$		0			0
$555$	−19.2130	−	8.66149i	−0.815547	−	0.367660i
$556$		0			0
$557$	10.4155	−	18.0401i	0.441317	−	0.764383i	−0.556471	−	0.830867i	$-0.687845\pi$
$557$	10.4155	−	18.0401i	0.441317	−	0.764383i	0.997787	+	0.0664841i	$0.0211782\pi$
$558$		0			0
$559$	−9.57275			−0.404884
$560$		0			0
$561$	4.75490	+	2.14357i	0.200752	+	0.0905018i
$562$		0			0
$563$	8.80605			0.371131			0.185565	−	0.982632i	$-0.440588\pi$
$563$	8.80605			0.371131			0.185565	+	0.982632i	$0.440588\pi$
$564$		0			0
$565$	61.3117			2.57940
$566$		0			0
$567$	−3.36333	−	23.5730i	−0.141247	−	0.989974i
$568$		0			0
$569$	18.9857			0.795923			0.397962	−	0.917402i	$-0.369718\pi$
$569$	18.9857			0.795923			0.397962	+	0.917402i	$0.369718\pi$
$570$		0			0
$571$	−15.7597			−0.659523			−0.329762	−	0.944064i	$-0.606968\pi$
$571$	−15.7597			−0.659523			−0.329762	+	0.944064i	$0.606968\pi$
$572$		0			0
$573$	5.84305	+	2.63413i	0.244097	+	0.110042i
$574$		0			0
$575$	31.2131			1.30167
$576$		0			0
$577$	−15.9306	+	27.5927i	−0.663201	+	1.14870i	0.316569	+	0.948570i	$0.397469\pi$
$577$	−15.9306	+	27.5927i	−0.663201	+	1.14870i	−0.979770	+	0.200128i	$0.935864\pi$
$578$		0			0
$579$	−20.1593	−	9.08809i	−0.837792	−	0.377688i
$580$		0			0
$581$	1.96555	−	7.43199i	0.0815449	−	0.308331i
$582$		0			0
$583$	−4.96644			−0.205689
$584$		0			0
$585$	10.5712	+	11.9625i	0.437066	+	0.494587i
$586$		0			0
$587$	−20.3597	+	35.2640i	−0.840333	+	1.45550i	0.0492799	+	0.998785i	$0.484307\pi$
$587$	−20.3597	+	35.2640i	−0.840333	+	1.45550i	−0.889613	+	0.456715i	$0.849026\pi$
$588$		0			0
$589$	−0.258288	−	0.447368i	−0.0106426	−	0.0184335i
$590$		0			0
$591$	3.86409	+	1.74198i	0.158947	+	0.0716557i
$592$		0			0
$593$	−14.0693	−	24.3688i	−0.577759	−	1.00071i	−0.995736	−	0.0922500i	$-0.970594\pi$
$593$	−14.0693	−	24.3688i	−0.577759	−	1.00071i	0.417977	−	0.908458i	$-0.362739\pi$
$594$		0			0
$595$	12.0161	+	11.9383i	0.492613	+	0.489425i
$596$		0			0
$597$	6.32209	−	4.54849i	0.258746	−	0.186157i
$598$		0			0
$599$	32.9926			1.34804			0.674020	−	0.738713i	$-0.264566\pi$
$599$	32.9926			1.34804			0.674020	+	0.738713i	$0.264566\pi$
$600$		0			0
$601$	−1.98103	+	3.43124i	−0.0808079	+	0.139963i	−0.903597	−	0.428383i	$-0.859083\pi$
$601$	−1.98103	+	3.43124i	−0.0808079	+	0.139963i	0.822789	+	0.568347i	$0.192417\pi$
$602$		0			0
$603$	−24.5075	−	27.7328i	−0.998021	−	1.12937i
$604$		0			0
$605$	14.8570	+	25.7330i	0.604021	+	1.04620i
$606$		0			0
$607$	−17.0132	+	29.4676i	−0.690543	+	1.19605i	0.281118	+	0.959673i	$0.409295\pi$
$607$	−17.0132	+	29.4676i	−0.690543	+	1.19605i	−0.971660	+	0.236382i	$0.924038\pi$
$608$		0			0
$609$	21.8402	−	26.8930i	0.885008	−	1.08976i
$610$		0			0
$611$	−7.92354	−	13.7240i	−0.320552	−	0.555212i
$612$		0			0
$613$	−15.2967	+	26.4946i	−0.617827	+	1.07011i	0.372054	+	0.928211i	$0.378654\pi$
$613$	−15.2967	+	26.4946i	−0.617827	+	1.07011i	−0.989881	+	0.141897i	$0.954680\pi$
$614$		0			0
$615$	−72.8188	−	32.8277i	−2.93634	−	1.32374i
$616$		0			0
$617$	18.7646	+	32.5013i	0.755435	+	1.30845i	0.945158	+	0.326614i	$0.105908\pi$
$617$	18.7646	+	32.5013i	0.755435	+	1.30845i	−0.189723	+	0.981838i	$0.560759\pi$
$618$		0			0
$619$	2.92302	+	5.06282i	0.117486	+	0.203492i	0.918771	−	0.394791i	$-0.129183\pi$
$619$	2.92302	+	5.06282i	0.117486	+	0.203492i	−0.801285	+	0.598283i	$0.795850\pi$
$620$		0			0
$621$	−16.2164	−	3.68415i	−0.650744	−	0.147840i
$622$		0			0
$623$	−18.9203	−	18.7979i	−0.758028	−	0.753121i
$624$		0			0
$625$	−10.6774	+	18.4937i	−0.427095	+	0.739749i
$626$		0			0
$627$	−0.407472	+	0.293160i	−0.0162729	+	0.0117077i
$628$		0			0
$629$	−5.28028			−0.210539
$630$		0			0
$631$	25.6347			1.02050			0.510251	−	0.860025i	$-0.329552\pi$
$631$	25.6347			1.02050			0.510251	+	0.860025i	$0.329552\pi$
$632$		0			0
$633$	0.377516	+	3.75999i	0.0150049	+	0.149446i
$634$		0			0
$635$	−16.5336	+	28.6371i	−0.656117	+	1.13643i
$636$		0			0
$637$	−8.43001	−	4.79435i	−0.334009	−	0.189959i
$638$		0			0
$639$	−13.7726	−	15.5852i	−0.544837	−	0.616542i
$640$		0			0
$641$	−12.9824	−	22.4861i	−0.512772	−	0.888147i	−0.999890	−	0.0148113i	$-0.995285\pi$
$641$	−12.9824	−	22.4861i	−0.512772	−	0.888147i	0.487118	−	0.873336i	$-0.338048\pi$
$642$		0			0
$643$	−22.5634	−	39.0809i	−0.889812	−	1.54120i	−0.840097	−	0.542436i	$-0.817502\pi$
$643$	−22.5634	−	39.0809i	−0.889812	−	1.54120i	−0.0497151	−	0.998763i	$-0.515831\pi$
$644$		0			0
$645$	4.59223	+	45.7377i	0.180819	+	1.80092i
$646$		0			0
$647$	2.70324	−	4.68215i	0.106275	−	0.184074i	−0.807983	−	0.589206i	$-0.799441\pi$
$647$	2.70324	−	4.68215i	0.106275	−	0.184074i	0.914259	+	0.405131i	$0.132774\pi$
$648$		0			0
$649$	−13.6135	−	23.5792i	−0.534375	−	0.925564i
$650$		0			0
$651$	−14.5719	−	2.32895i	−0.571119	−	0.0912788i
$652$		0			0
$653$	15.9515	−	27.6288i	0.624231	−	1.08120i	−0.364458	−	0.931220i	$-0.618746\pi$
$653$	15.9515	−	27.6288i	0.624231	−	1.08120i	0.988689	−	0.149980i	$-0.0479211\pi$
$654$		0			0
$655$	3.70587	+	6.41875i	0.144800	+	0.250801i
$656$		0			0
$657$	−36.6020	+	7.42479i	−1.42798	+	0.289669i
$658$		0			0
$659$	2.50215	−	4.33385i	0.0974699	−	0.168823i	−0.813167	−	0.582031i	$-0.802258\pi$
$659$	2.50215	−	4.33385i	0.0974699	−	0.168823i	0.910637	+	0.413208i	$0.135592\pi$
$660$		0			0
$661$	9.63406			0.374721			0.187361	−	0.982291i	$-0.440007\pi$
$661$	9.63406			0.374721			0.187361	+	0.982291i	$0.440007\pi$
$662$		0			0
$663$	3.64632	+	1.64381i	0.141611	+	0.0638404i
$664$		0			0
$665$	−1.57326	+	0.427034i	−0.0610085	+	0.0165597i
$666$		0			0
$667$	−12.0975	−	20.9534i	−0.468415	−	0.811319i
$668$		0			0
$669$	−8.09751	+	5.82583i	−0.313068	+	0.225240i
$670$		0			0
$671$	8.31308	+	14.3987i	0.320923	+	0.555855i
$672$		0			0
$673$	13.5885	−	23.5359i	0.523797	−	0.907243i	−0.475819	−	0.879543i	$-0.657848\pi$
$673$	13.5885	−	23.5359i	0.523797	−	0.907243i	0.999616	−	0.0276998i	$-0.00881825\pi$
$674$		0			0
$675$	34.4322	−	37.1840i	1.32529	−	1.43121i
$676$		0			0
$677$	−38.0502			−1.46239			−0.731194	−	0.682169i	$-0.761037\pi$
$677$	−38.0502			−1.46239			−0.731194	+	0.682169i	$0.761037\pi$
$678$		0			0
$679$	−5.66651	+	21.4257i	−0.217461	+	0.822244i
$680$		0			0
$681$	−2.86937	−	28.5784i	−0.109955	−	1.09513i
$682$		0			0
$683$	15.0571	−	26.0797i	0.576146	−	0.997913i	−0.419771	−	0.907630i	$-0.637889\pi$
$683$	15.0571	−	26.0797i	0.576146	−	0.997913i	0.995916	−	0.0902831i	$-0.0287772\pi$
$684$		0			0
$685$	−14.2455			−0.544293
$686$		0			0
$687$	20.5185	−	14.7622i	0.782830	−	0.563215i
$688$		0			0
$689$	−3.80854			−0.145094
$690$		0			0
$691$	14.3902			0.547429			0.273714	−	0.961811i	$-0.411748\pi$
$691$	14.3902			0.547429			0.273714	+	0.961811i	$0.411748\pi$
$692$		0			0
$693$	−0.837189	+	14.3152i	−0.0318022	+	0.543791i
$694$		0			0
$695$	−1.03374			−0.0392120
$696$		0			0
$697$	−20.0127			−0.758034
$698$		0			0
$699$	0.328571	+	3.27250i	0.0124277	+	0.123777i
$700$		0			0
$701$	14.4170			0.544521			0.272261	−	0.962224i	$-0.412229\pi$
$701$	14.4170			0.544521			0.272261	+	0.962224i	$0.412229\pi$
$702$		0			0
$703$	0.254092	−	0.440100i	0.00958325	−	0.0165987i
$704$		0			0
$705$	−61.7708	+	44.4416i	−2.32642	+	1.67377i
$706$		0			0
$707$	15.2310	+	15.1324i	0.572820	+	0.569113i
$708$		0			0
$709$	11.4882			0.431448			0.215724	−	0.976454i	$-0.430789\pi$
$709$	11.4882			0.431448			0.215724	+	0.976454i	$0.430789\pi$
$710$		0			0
$711$	31.9327	+	36.1353i	1.19757	+	1.35518i
$712$		0			0
$713$	−5.15296	+	8.92519i	−0.192980	+	0.334251i
$714$		0			0
$715$	−4.80686	−	8.32573i	−0.179766	−	0.311365i
$716$		0			0
$717$	−1.54468	−	15.3847i	−0.0576871	−	0.574552i
$718$		0			0
$719$	17.9451	+	31.0818i	0.669240	+	1.15916i	0.978117	+	0.208055i	$0.0667134\pi$
$719$	17.9451	+	31.0818i	0.669240	+	1.15916i	−0.308877	+	0.951102i	$0.599953\pi$
$720$		0			0
$721$	−5.09910	+	19.2803i	−0.189901	+	0.718036i
$722$		0			0
$723$	4.20351	+	41.8661i	0.156330	+	1.55702i
$724$		0			0
$725$	73.7321			2.73834
$726$		0			0
$727$	−5.03060	+	8.71326i	−0.186575	+	0.323157i	−0.944106	−	0.329642i	$-0.893072\pi$
$727$	−5.03060	+	8.71326i	−0.186575	+	0.323157i	0.757531	+	0.652799i	$0.226405\pi$
$728$		0			0
$729$	−22.2778	+	15.2545i	−0.825104	+	0.564980i
$730$		0			0
$731$	5.75850	+	9.97401i	0.212986	+	0.368902i
$732$		0			0
$733$	−16.5690	+	28.6984i	−0.611992	+	1.06000i	0.378913	+	0.925432i	$0.376298\pi$
$733$	−16.5690	+	28.6984i	−0.611992	+	1.06000i	−0.990904	+	0.134568i	$0.957035\pi$
$734$		0			0
$735$	−18.8629	+	42.5778i	−0.695770	+	1.57051i
$736$		0			0
$737$	11.1438	+	19.3017i	0.410489	+	0.710987i
$738$		0			0
$739$	21.9237	−	37.9729i	0.806475	−	1.39686i	−0.108816	−	0.994062i	$-0.534706\pi$
$739$	21.9237	−	37.9729i	0.806475	−	1.39686i	0.915291	−	0.402793i	$-0.131961\pi$
$740$		0			0
$741$	−0.312473	+	0.224811i	−0.0114790	+	0.00825865i
$742$		0			0
$743$	4.50115	+	7.79622i	0.165131	+	0.286016i	0.936702	−	0.350128i	$-0.113862\pi$
$743$	4.50115	+	7.79622i	0.165131	+	0.286016i	−0.771571	+	0.636144i	$0.780529\pi$
$744$		0			0
$745$	−15.9738	−	27.6673i	−0.585233	−	1.01365i
$746$		0			0
$747$	−8.54283	+	1.73293i	−0.312566	+	0.0634046i
$748$		0			0
$749$	11.1011	+	11.0293i	0.405626	+	0.403000i
$750$		0			0
$751$	−5.59141	+	9.68460i	−0.204033	+	0.353396i	−0.949824	−	0.312784i	$-0.898738\pi$
$751$	−5.59141	+	9.68460i	−0.204033	+	0.353396i	0.745791	+	0.666180i	$0.232072\pi$
$752$		0			0
$753$	−8.91942	−	4.02100i	−0.325042	−	0.146533i
$754$		0			0
$755$	37.4162			1.36171
$756$		0			0
$757$	42.1431			1.53172			0.765859	−	0.643009i	$-0.222314\pi$
$757$	42.1431			1.53172			0.765859	+	0.643009i	$0.222314\pi$
$758$		0			0
$759$	9.12971	+	4.11580i	0.331388	+	0.149394i
$760$		0			0
$761$	−1.14155	+	1.97721i	−0.0413810	+	0.0716740i	−0.885974	−	0.463735i	$-0.846509\pi$
$761$	−1.14155	+	1.97721i	−0.0413810	+	0.0716740i	0.844593	+	0.535409i	$0.179842\pi$
$762$		0			0
$763$	6.06670	−	22.9389i	0.219629	−	0.830444i
$764$		0			0
$765$	6.10478	−	18.2104i	0.220719	−	0.658398i
$766$		0			0
$767$	−10.4396	−	18.0819i	−0.376951	−	0.652898i
$768$		0			0
$769$	8.96676	+	15.5309i	0.323350	+	0.560058i	0.981177	−	0.193111i	$-0.0618577\pi$
$769$	8.96676	+	15.5309i	0.323350	+	0.560058i	−0.657827	+	0.753169i	$0.728524\pi$
$770$		0			0
$771$	33.1405	−	23.8432i	1.19353	−	0.858693i
$772$		0			0
$773$	17.4807	−	30.2775i	0.628737	−	1.08901i	−0.359068	−	0.933311i	$-0.616905\pi$
$773$	17.4807	−	30.2775i	0.628737	−	1.08901i	0.987805	−	0.155694i	$-0.0497613\pi$
$774$		0			0
$775$	−15.7032	−	27.1988i	−0.564077	−	0.977009i
$776$		0			0
$777$	−5.18343	−	13.5602i	−0.185955	−	0.486469i
$778$		0			0
$779$	0.963028	−	1.66801i	0.0345041	−	0.0597628i
$780$		0			0
$781$	6.26259	+	10.8471i	0.224093	+	0.388141i
$782$		0			0
$783$	−38.3068	−	8.70277i	−1.36897	−	0.311011i
$784$		0			0
$785$	−46.5870	+	80.6910i	−1.66276	+	2.87998i
$786$		0			0
$787$	−28.3564			−1.01079			−0.505397	−	0.862887i	$-0.668654\pi$
$787$	−28.3564			−1.01079			−0.505397	+	0.862887i	$0.668654\pi$
$788$		0			0
$789$	−4.43668	−	44.1885i	−0.157950	−	1.57315i
$790$		0			0
$791$	29.9601	+	29.7662i	1.06526	+	1.05836i
$792$		0			0
$793$	6.37494	+	11.0417i	0.226381	+	0.392103i
$794$		0			0
$795$	1.82703	+	18.1969i	0.0647982	+	0.645377i
$796$		0			0
$797$	−9.51922	−	16.4878i	−0.337188	−	0.584027i	0.646715	−	0.762732i	$-0.276143\pi$
$797$	−9.51922	−	16.4878i	−0.337188	−	0.584027i	−0.983903	+	0.178705i	$0.942809\pi$
$798$		0			0
$799$	−9.53283	+	16.5113i	−0.337247	+	0.584129i
$800$		0			0
$801$	−9.61246	+	28.6737i	−0.339640	+	1.01313i
$802$		0			0
$803$	22.4910			0.793691
$804$		0			0
$805$	23.0717	+	22.9224i	0.813172	+	0.807908i
$806$		0			0
$807$	−23.2616	+	16.7358i	−0.818847	+	0.589128i
$808$		0			0
$809$	−10.4529	+	18.1050i	−0.367505	+	0.636538i	−0.989175	−	0.146742i	$-0.953121\pi$
$809$	−10.4529	+	18.1050i	−0.367505	+	0.636538i	0.621670	+	0.783280i	$0.286455\pi$
$810$		0			0
$811$	17.5392			0.615884			0.307942	−	0.951405i	$-0.400360\pi$
$811$	17.5392			0.615884			0.307942	+	0.951405i	$0.400360\pi$
$812$		0			0
$813$	3.08260	+	30.7021i	0.108111	+	1.07677i
$814$		0			0
$815$	−30.0671			−1.05320
$816$		0			0
$817$	−1.10842			−0.0387786
$818$		0			0
$819$	−0.642004	+	10.9777i	−0.0224334	+	0.383593i
$820$		0			0
$821$	−34.9762			−1.22068			−0.610339	−	0.792140i	$-0.708967\pi$
$821$	−34.9762			−1.22068			−0.610339	+	0.792140i	$0.708967\pi$
$822$		0			0
$823$	−30.4235			−1.06050			−0.530249	−	0.847842i	$-0.677901\pi$
$823$	−30.4235			−1.06050			−0.530249	+	0.847842i	$0.677901\pi$
$824$		0			0
$825$	−24.7732	+	17.8233i	−0.862493	+	0.620529i
$826$		0			0
$827$	−25.6276			−0.891158			−0.445579	−	0.895243i	$-0.647002\pi$
$827$	−25.6276			−0.891158			−0.445579	+	0.895243i	$0.647002\pi$
$828$		0			0
$829$	23.9403	−	41.4658i	0.831481	−	1.44017i	−0.0653833	−	0.997860i	$-0.520827\pi$
$829$	23.9403	−	41.4658i	0.831481	−	1.44017i	0.896864	−	0.442307i	$-0.145840\pi$
$830$		0			0
$831$	1.01118	+	10.0712i	0.0350775	+	0.349364i
$832$		0			0
$833$	0.0757689	+	11.6674i	0.00262524	+	0.404252i
$834$		0			0
$835$	16.5465			0.572614
$836$		0			0
$837$	4.94813	+	15.9844i	0.171032	+	0.552501i
$838$		0			0
$839$	−21.8466	+	37.8394i	−0.754227	+	1.30636i	0.191530	+	0.981487i	$0.438655\pi$
$839$	−21.8466	+	37.8394i	−0.754227	+	1.30636i	−0.945758	+	0.324873i	$0.894678\pi$
$840$		0			0
$841$	−14.0769	−	24.3818i	−0.485409	−	0.840753i
$842$		0			0
$843$	−29.6918	+	21.3621i	−1.02264	+	0.735749i
$844$		0			0
$845$	21.2800	+	36.8581i	0.732055	+	1.26796i
$846$		0			0
$847$	−5.23322	+	19.7874i	−0.179816	+	0.679904i
$848$		0			0
$849$	−20.1738	−	9.09464i	−0.692364	−	0.312127i
$850$		0			0
$851$	−10.1385			−0.347543
$852$		0			0
$853$	8.33994	−	14.4452i	0.285554	−	0.494594i	−0.687189	−	0.726478i	$-0.741156\pi$
$853$	8.33994	−	14.4452i	0.285554	−	0.494594i	0.972743	+	0.231884i	$0.0744890\pi$
$854$		0			0
$855$	1.22403	+	1.38512i	0.0418609	+	0.0473701i
$856$		0			0
$857$	−7.21452	−	12.4959i	−0.246443	−	0.426852i	0.716093	−	0.698005i	$-0.245929\pi$
$857$	−7.21452	−	12.4959i	−0.246443	−	0.426852i	−0.962536	+	0.271152i	$0.912595\pi$
$858$		0			0
$859$	−11.3867	+	19.7223i	−0.388508	+	0.672915i	−0.992249	−	0.124265i	$-0.960343\pi$
$859$	−11.3867	+	19.7223i	−0.388508	+	0.672915i	0.603741	+	0.797180i	$0.293676\pi$
$860$		0			0
$861$	−19.6456	−	51.3942i	−0.669521	−	1.75151i
$862$		0			0
$863$	−5.97266	−	10.3450i	−0.203312	−	0.352146i	0.746282	−	0.665630i	$-0.231837\pi$
$863$	−5.97266	−	10.3450i	−0.203312	−	0.352146i	−0.949594	+	0.313484i	$0.898504\pi$
$864$		0			0
$865$	33.2933	−	57.6656i	1.13200	−	1.96069i
$866$		0			0
$867$	2.46085	+	24.5096i	0.0835748	+	0.832388i
$868$		0			0
$869$	−14.5202	−	25.1497i	−0.492563	−	0.853145i
$870$		0			0
$871$	8.54572	+	14.8016i	0.289561	+	0.501534i
$872$		0			0
$873$	24.6282	−	4.99588i	0.833538	−	0.169085i
$874$		0			0
$875$	−46.6134	+	12.6524i	−1.57582	+	0.427729i
$876$		0			0
$877$	28.3099	−	49.0342i	0.955957	−	1.65577i	0.223794	−	0.974636i	$-0.428156\pi$
$877$	28.3099	−	49.0342i	0.955957	−	1.65577i	0.732163	−	0.681130i	$-0.238511\pi$
$878$		0			0
$879$	2.05505	+	20.4679i	0.0693152	+	0.690365i
$880$		0			0
$881$	−6.41130			−0.216002			−0.108001	−	0.994151i	$-0.534445\pi$
$881$	−6.41130			−0.216002			−0.108001	+	0.994151i	$0.534445\pi$
$882$		0			0
$883$	−25.7180			−0.865481			−0.432741	−	0.901518i	$-0.642453\pi$
$883$	−25.7180			−0.865481			−0.432741	+	0.901518i	$0.642453\pi$
$884$		0			0
$885$	−81.3854	+	58.5535i	−2.73574	+	1.96825i
$886$		0			0
$887$	−9.99472	+	17.3114i	−0.335590	+	0.581259i	−0.983598	−	0.180375i	$-0.942269\pi$
$887$	−9.99472	+	17.3114i	−0.335590	+	0.581259i	0.648008	+	0.761633i	$0.275602\pi$
$888$		0			0
$889$	−21.9822	+	5.96669i	−0.737261	+	0.200116i
$890$		0			0
$891$	14.9744	−	6.33591i	0.501662	−	0.212261i
$892$		0			0
$893$	−0.917456	−	1.58908i	−0.0307015	−	0.0531766i
$894$		0			0
$895$	−37.2051	−	64.4412i	−1.24363	−	2.15403i
$896$		0			0
$897$	7.00118	+	3.15623i	0.233762	+	0.105383i
$898$		0			0
$899$	−12.1724	+	21.0832i	−0.405973	+	0.703166i
$900$		0			0
$901$	2.29104	+	3.96819i	0.0763254	+	0.132200i
$902$		0			0
$903$	−19.9612	+	24.5794i	−0.664267	+	0.817950i
$904$		0			0
$905$	−5.55087	+	9.61439i	−0.184517	+	0.319593i
$906$		0			0
$907$	−12.1517	−	21.0474i	−0.403491	−	0.698866i	0.590654	−	0.806925i	$-0.298870\pi$
$907$	−12.1517	−	21.0474i	−0.403491	−	0.698866i	−0.994145	+	0.108059i	$0.965537\pi$
$908$		0			0
$909$	7.73809	−	23.0825i	0.256656	−	0.765598i
$910$		0			0
$911$	19.7871	−	34.2723i	0.655577	−	1.13549i	−0.326171	−	0.945311i	$-0.605759\pi$
$911$	19.7871	−	34.2723i	0.655577	−	1.13549i	0.981749	−	0.190183i	$-0.0609080\pi$
$912$		0			0
$913$	5.24936			0.173728
$914$		0			0
$915$	49.6981	−	35.7558i	1.64297	−	1.18205i
$916$		0			0
$917$	−1.30536	+	4.93571i	−0.0431067	+	0.162991i
$918$		0			0
$919$	−12.9220	−	22.3815i	−0.426257	−	0.738298i	0.570280	−	0.821450i	$-0.306835\pi$
$919$	−12.9220	−	22.3815i	−0.426257	−	0.738298i	−0.996537	+	0.0831519i	$0.973501\pi$
$920$		0			0
$921$	−6.21023	−	2.79966i	−0.204634	−	0.0922518i
$922$		0			0
$923$	4.80251	+	8.31818i	0.158076	+	0.273796i
$924$		0			0
$925$	15.4481	−	26.7569i	0.507930	−	0.879761i
$926$		0			0
$927$	22.1621	−	4.49563i	0.727898	−	0.147656i
$928$		0			0
$929$	50.8506			1.66836			0.834178	−	0.551496i	$-0.185943\pi$
$929$	50.8506			1.66836			0.834178	+	0.551496i	$0.185943\pi$
$930$		0			0
$931$	−0.976100	−	0.555132i	−0.0319904	−	0.0181937i
$932$		0			0
$933$	3.12994	+	1.41102i	0.102470	+	0.0461948i
$934$		0			0
$935$	−5.78315	+	10.0167i	−0.189129	+	0.327581i
$936$		0			0
$937$	32.7623			1.07030			0.535149	−	0.844758i	$-0.320256\pi$
$937$	32.7623			1.07030			0.535149	+	0.844758i	$0.320256\pi$
$938$		0			0
$939$	32.3689	+	14.5923i	1.05632	+	0.476203i
$940$		0			0
$941$	50.6793			1.65210			0.826048	−	0.563599i	$-0.190584\pi$
$941$	50.6793			1.65210			0.826048	+	0.563599i	$0.190584\pi$
$942$		0			0
$943$	−38.4256			−1.25131
$944$		0			0
$945$	52.7586	−	2.19879i	1.71624	−	0.0715267i
$946$		0			0
$947$	−11.5255			−0.374530			−0.187265	−	0.982309i	$-0.559962\pi$
$947$	−11.5255			−0.374530			−0.187265	+	0.982309i	$0.559962\pi$
$948$		0			0
$949$	17.2474			0.559873
$950$		0			0
$951$	15.0230	+	6.77257i	0.487154	+	0.219616i
$952$		0			0
$953$	−45.7747			−1.48279			−0.741395	−	0.671069i	$-0.765835\pi$
$953$	−45.7747			−1.48279			−0.741395	+	0.671069i	$0.765835\pi$
$954$		0			0
$955$	−7.10661	+	12.3090i	−0.229965	+	0.398310i
$956$		0			0
$957$	21.5664	+	9.72243i	0.697142	+	0.314281i
$958$		0			0
$959$	−6.96111	−	6.91605i	−0.224786	−	0.223331i
$960$		0			0
$961$	−20.6302			−0.665491
$962$		0			0
$963$	5.63990	−	16.8237i	0.181743	−	0.542135i
$964$		0			0
$965$	24.5188	−	42.4678i	0.789287	−	1.36709i
$966$		0			0
$967$	−4.07666	−	7.06098i	−0.131097	−	0.227066i	0.793003	−	0.609218i	$-0.208516\pi$
$967$	−4.07666	−	7.06098i	−0.131097	−	0.227066i	−0.924100	+	0.382152i	$0.875183\pi$
$968$		0			0
$969$	0.422203	+	0.190335i	0.0135631	+	0.00611444i
$970$		0			0
$971$	14.1137	+	24.4457i	0.452932	+	0.784501i	0.998567	−	0.0535223i	$-0.0170448\pi$
$971$	14.1137	+	24.4457i	0.452932	+	0.784501i	−0.545635	+	0.838023i	$0.683712\pi$
$972$		0			0
$973$	−0.505141	−	0.501871i	−0.0161941	−	0.0160893i
$974$		0			0
$975$	−18.9975	+	13.6679i	−0.608407	+	0.437724i
$976$		0			0
$977$	−15.6502			−0.500694			−0.250347	−	0.968156i	$-0.580545\pi$
$977$	−15.6502			−0.500694			−0.250347	+	0.968156i	$0.580545\pi$
$978$		0			0
$979$	9.10603	−	15.7721i	0.291030	−	0.504079i
$980$		0			0
$981$	−26.3675	+	5.34871i	−0.841850	+	0.170771i
$982$		0			0
$983$	−1.47581	−	2.55617i	−0.0470710	−	0.0815293i	0.841530	−	0.540210i	$-0.181655\pi$
$983$	−1.47581	−	2.55617i	−0.0470710	−	0.0815293i	−0.888601	+	0.458681i	$0.848322\pi$
$984$		0			0
$985$	−4.69970	+	8.14012i	−0.149745	+	0.259366i
$986$		0			0
$987$	−51.7605	−	8.27259i	−1.64755	−	0.263319i
$988$		0			0
$989$	11.0567	+	19.1507i	0.351582	+	0.608958i
$990$		0			0
$991$	15.8182	−	27.3979i	0.502482	−	0.870324i	−0.497514	−	0.867456i	$-0.665754\pi$
$991$	15.8182	−	27.3979i	0.502482	−	0.870324i	0.999996	−	0.00286819i	$-0.000912976\pi$
$992$		0			0
$993$	2.41567	+	1.08902i	0.0766588	+	0.0345589i
$994$		0			0
$995$	8.63557	+	14.9572i	0.273766	+	0.474176i
$996$		0			0
$997$	0.792608	+	1.37284i	0.0251021	+	0.0434782i	0.878304	−	0.478103i	$-0.158676\pi$
$997$	0.792608	+	1.37284i	0.0251021	+	0.0434782i	−0.853201	+	0.521582i	$0.825342\pi$
$998$		0			0
$999$	−11.1841	+	12.0779i	−0.353849	+	0.382129i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	504.2.q.d.25.10	✓	22
3.2	odd	2		1512.2.q.c.1369.11		22
4.3	odd	2		1008.2.q.k.529.2		22
7.2	even	3		504.2.t.d.457.2	yes	22
9.4	even	3		504.2.t.d.193.2	yes	22
9.5	odd	6		1512.2.t.d.361.1		22
12.11	even	2		3024.2.q.k.2881.11		22
21.2	odd	6		1512.2.t.d.289.1		22
28.23	odd	6		1008.2.t.k.961.10		22
36.23	even	6		3024.2.t.l.1873.1		22
36.31	odd	6		1008.2.t.k.193.10		22
63.23	odd	6		1512.2.q.c.793.11		22
63.58	even	3	inner	504.2.q.d.121.10	yes	22
84.23	even	6		3024.2.t.l.289.1		22
252.23	even	6		3024.2.q.k.2305.11		22
252.247	odd	6		1008.2.q.k.625.2		22

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
504.2.q.d.25.10	✓	22	1.1	even	1	trivial
504.2.q.d.121.10	yes	22	63.58	even	3	inner
504.2.t.d.193.2	yes	22	9.4	even	3
504.2.t.d.457.2	yes	22	7.2	even	3
1008.2.q.k.529.2		22	4.3	odd	2
1008.2.q.k.625.2		22	252.247	odd	6
1008.2.t.k.193.10		22	36.31	odd	6
1008.2.t.k.961.10		22	28.23	odd	6
1512.2.q.c.793.11		22	63.23	odd	6
1512.2.q.c.1369.11		22	3.2	odd	2
1512.2.t.d.289.1		22	21.2	odd	6
1512.2.t.d.361.1		22	9.5	odd	6
3024.2.q.k.2305.11		22	252.23	even	6
3024.2.q.k.2881.11		22	12.11	even	2
3024.2.t.l.289.1		22	84.23	even	6
3024.2.t.l.1873.1		22	36.23	even	6

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 504 = 2^{3} \cdot 3^{2} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	504.q (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(1.57901 + 0.711841i) q^{3} +(-1.92048 + 3.32636i) q^{5} +(-2.55336 + 0.693065i) q^{7} +(1.98656 + 2.24801i) q^{9} +(-0.903316 - 1.56459i) q^{11} +(-0.692713 - 1.19981i) q^{13} +(-5.40030 + 3.88530i) q^{15} +(-0.833405 + 1.44350i) q^{17} +(-0.0802084 - 0.138925i) q^{19} +(-4.52515 - 0.723229i) q^{21} +(-1.60019 + 2.77161i) q^{23} +(-4.87646 - 8.44627i) q^{25} +(1.53658 + 4.96376i) q^{27} +(-3.78000 + 6.54716i) q^{29} +3.22021 q^{31} +(-0.312609 - 3.11352i) q^{33} +(2.59829 - 9.82442i) q^{35} +(1.58395 + 2.74348i) q^{37} +(-0.239726 - 2.38762i) q^{39} +(6.00329 + 10.3980i) q^{41} +(3.45480 - 5.98389i) q^{43} +(-11.2929 + 2.29078i) q^{45} +11.4384 q^{47} +(6.03932 - 3.53929i) q^{49} +(-2.34350 + 1.68605i) q^{51} +(1.37450 - 2.38071i) q^{53} +6.93918 q^{55} +(-0.0277576 - 0.276460i) q^{57} +15.0705 q^{59} -9.20285 q^{61} +(-6.63044 - 4.36317i) q^{63} +5.32136 q^{65} -12.3366 q^{67} +(-4.49967 + 3.23733i) q^{69} -6.93289 q^{71} +(-6.22457 + 10.7813i) q^{73} +(-1.68759 - 16.8080i) q^{75} +(3.39085 + 3.36891i) q^{77} +16.0743 q^{79} +(-1.10712 + 8.93165i) q^{81} +(-1.45280 + 2.51633i) q^{83} +(-3.20107 - 5.54441i) q^{85} +(-10.6292 + 7.64729i) q^{87} +(5.04034 + 8.73012i) q^{89} +(2.60030 + 2.58347i) q^{91} +(5.08476 + 2.29228i) q^{93} +0.616153 q^{95} +(4.18830 - 7.25435i) q^{97} +(1.72272 - 5.13882i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 22 q + 2 q^{3} + 3 q^{5} - 5 q^{7} + 10 q^{9} - 3 q^{11} - 3 q^{13} - q^{15} + 7 q^{17} - q^{19} + 2 q^{23} - 10 q^{25} - 4 q^{27} + 9 q^{29} + 8 q^{31} + 29 q^{33} + 14 q^{35} + 2 q^{37} - 16 q^{39}+ \cdots - 56 q^{99}+O(q^{100}) \) 22 * q + 2 * q^3 + 3 * q^5 - 5 * q^7 + 10 * q^9 - 3 * q^11 - 3 * q^13 - q^15 + 7 * q^17 - q^19 + 2 * q^23 - 10 * q^25 - 4 * q^27 + 9 * q^29 + 8 * q^31 + 29 * q^33 + 14 * q^35 + 2 * q^37 - 16 * q^39 + 16 * q^41 + q^45 - 10 * q^47 + 15 * q^49 + 7 * q^51 + 11 * q^53 + 22 * q^55 + 7 * q^57 + 38 * q^59 + 26 * q^61 + 48 * q^63 - 26 * q^65 - 52 * q^67 - 4 * q^69 - 48 * q^71 - 35 * q^73 - 23 * q^75 + 17 * q^77 - 20 * q^79 - 38 * q^81 - 28 * q^83 - 20 * q^85 - 33 * q^87 + 6 * q^89 - 37 * q^91 + 19 * q^93 - 24 * q^95 - 29 * q^97 - 56 * q^99

Introduction

L-functions

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