LMFDB - Embedded newform 1452.2.i.f.565.1

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [1452,2,Mod(493,1452)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(1452, base_ring=CyclotomicField(10)) chi = DirichletCharacter(H, H._module([0, 0, 6])) N = Newforms(chi, 2, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("1452.493"); S:= CuspForms(chi, 2); N := Newforms(S);

Level:	$ N $	$=$	$ 1452 = 2^{2} \cdot 3 \cdot 11^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1452.i (of order $5$, degree $4$, not minimal)

Newform invariants

comment:select newform

sage:traces = [4,0,-1,0,-2,0,3] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(7)] == traces)

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

Self dual:	no
Analytic conductor:	$11.5942783735$
Analytic rank:	$0$
Dimension:	$4$
Coefficient field:	$\Q(\zeta_{10})$
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} - x^{3} + x^{2} - x + 1 $ x^4 - x^3 + x^2 - x + 1
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 132)
Sato-Tate group:	$\mathrm{SU}(2)[C_{5}]$

Embedding invariants

Embedding label			565.1
Root			$0.809017 - 0.587785i$ of defining polynomial
Character	$\chi$	$=$	1452.565
Dual form			1452.2.i.f.1213.1

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.309017 - 0.951057i) q^{3} +(-0.500000 + 0.363271i) q^{5} +(1.30902 + 4.02874i) q^{7} +(-0.809017 - 0.587785i) q^{9} +(0.190983 + 0.138757i) q^{13} +(0.190983 + 0.587785i) q^{15} +(-5.54508 + 4.02874i) q^{17} +(0.0450850 - 0.138757i) q^{19} +4.23607 q^{21} -5.00000 q^{23} +(-1.42705 + 4.39201i) q^{25} +(-0.809017 + 0.587785i) q^{27} +(-0.618034 - 1.90211i) q^{29} +(-4.54508 - 3.30220i) q^{31} +(-2.11803 - 1.53884i) q^{35} +(-0.690983 - 2.12663i) q^{37} +(0.190983 - 0.138757i) q^{39} +(-1.45492 + 4.47777i) q^{41} +11.4721 q^{43} +0.618034 q^{45} +(-3.26393 + 10.0453i) q^{47} +(-8.85410 + 6.43288i) q^{49} +(2.11803 + 6.51864i) q^{51} +(-3.54508 - 2.57565i) q^{53} +(-0.118034 - 0.0857567i) q^{57} +(-3.95492 - 12.1720i) q^{59} +(-3.35410 + 2.43690i) q^{61} +(1.30902 - 4.02874i) q^{63} -0.145898 q^{65} -6.61803 q^{67} +(-1.54508 + 4.75528i) q^{69} +(-4.50000 + 3.26944i) q^{71} +(0.708204 + 2.17963i) q^{73} +(3.73607 + 2.71441i) q^{75} +(3.80902 + 2.76741i) q^{79} +(0.309017 + 0.951057i) q^{81} +(-5.04508 + 3.66547i) q^{83} +(1.30902 - 4.02874i) q^{85} -2.00000 q^{87} +17.1803 q^{89} +(-0.309017 + 0.951057i) q^{91} +(-4.54508 + 3.30220i) q^{93} +(0.0278640 + 0.0857567i) q^{95} +(11.3541 + 8.24924i) q^{97} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q - q^{3} - 2 q^{5} + 3 q^{7} - q^{9} + 3 q^{13} + 3 q^{15} - 11 q^{17} - 11 q^{19} + 8 q^{21} - 20 q^{23} + q^{25} - q^{27} + 2 q^{29} - 7 q^{31} - 4 q^{35} - 5 q^{37} + 3 q^{39} - 17 q^{41} + 28 q^{43}+ \cdots + 32 q^{97}+O(q^{100}) $ 4 * q - q^3 - 2 * q^5 + 3 * q^7 - q^9 + 3 * q^13 + 3 * q^15 - 11 * q^17 - 11 * q^19 + 8 * q^21 - 20 * q^23 + q^25 - q^27 + 2 * q^29 - 7 * q^31 - 4 * q^35 - 5 * q^37 + 3 * q^39 - 17 * q^41 + 28 * q^43 - 2 * q^45 - 22 * q^47 - 22 * q^49 + 4 * q^51 - 3 * q^53 + 4 * q^57 - 27 * q^59 + 3 * q^63 - 14 * q^65 - 22 * q^67 + 5 * q^69 - 18 * q^71 - 24 * q^73 + 6 * q^75 + 13 * q^79 - q^81 - 9 * q^83 + 3 * q^85 - 8 * q^87 + 24 * q^89 + q^91 - 7 * q^93 + 18 * q^95 + 32 * q^97

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1452\mathbb{Z}\right)^\times$.

$n$	$485$	$727$	$1333$
$\chi(n)$	$1$	$1$	$e\left(\frac{1}{5}\right)$

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
$3$	0.309017	−	0.951057i	0.178411	−	0.549093i
$3$	0.309017	−	0.951057i	0.178411	−	0.549093i
$4$		0			0
$5$	−0.500000	+	0.363271i	−0.223607	+	0.162460i	−0.693949	−	0.720024i	$-0.744131\pi$
$5$	−0.500000	+	0.363271i	−0.223607	+	0.162460i	0.470342	+	0.882484i	$0.344131\pi$
$6$		0			0
$7$	1.30902	+	4.02874i	0.494762	+	1.52272i	0.817327	+	0.576173i	$0.195455\pi$
$7$	1.30902	+	4.02874i	0.494762	+	1.52272i	−0.322566	+	0.946547i	$0.604545\pi$
$8$		0			0
$9$	−0.809017	−	0.587785i	−0.269672	−	0.195928i
$10$		0			0
$11$		0			0
$11$		0			0
$12$		0			0
$13$	0.190983	+	0.138757i	0.0529692	+	0.0384843i	0.613955	−	0.789341i	$-0.289578\pi$
$13$	0.190983	+	0.138757i	0.0529692	+	0.0384843i	−0.560986	+	0.827826i	$0.689578\pi$
$14$		0			0
$15$	0.190983	+	0.587785i	0.0493116	+	0.151765i
$16$		0			0
$17$	−5.54508	+	4.02874i	−1.34488	+	0.977113i	−0.345631	+	0.938370i	$0.612335\pi$
$17$	−5.54508	+	4.02874i	−1.34488	+	0.977113i	−0.999249	+	0.0387426i	$0.987665\pi$
$18$		0			0
$19$	0.0450850	−	0.138757i	0.0103432	−	0.0318331i	−0.945752	−	0.324890i	$-0.894673\pi$
$19$	0.0450850	−	0.138757i	0.0103432	−	0.0318331i	0.956095	+	0.293057i	$0.0946726\pi$
$20$		0			0
$21$	4.23607			0.924386
$22$		0			0
$23$	−5.00000			−1.04257			−0.521286	−	0.853382i	$-0.674548\pi$
$23$	−5.00000			−1.04257			−0.521286	+	0.853382i	$0.674548\pi$
$24$		0			0
$25$	−1.42705	+	4.39201i	−0.285410	+	0.878402i
$26$		0			0
$27$	−0.809017	+	0.587785i	−0.155695	+	0.113119i
$28$		0			0
$29$	−0.618034	−	1.90211i	−0.114766	−	0.353214i	0.877132	−	0.480249i	$-0.159454\pi$
$29$	−0.618034	−	1.90211i	−0.114766	−	0.353214i	−0.991898	+	0.127036i	$0.959454\pi$
$30$		0			0
$31$	−4.54508	−	3.30220i	−0.816321	−	0.593092i	0.0993351	−	0.995054i	$-0.468328\pi$
$31$	−4.54508	−	3.30220i	−0.816321	−	0.593092i	−0.915656	+	0.401962i	$0.868328\pi$
$32$		0			0
$33$		0			0
$34$		0			0
$35$	−2.11803	−	1.53884i	−0.358013	−	0.260112i
$36$		0			0
$37$	−0.690983	−	2.12663i	−0.113597	−	0.349615i	0.878055	−	0.478560i	$-0.158841\pi$
$37$	−0.690983	−	2.12663i	−0.113597	−	0.349615i	−0.991652	+	0.128945i	$0.958841\pi$
$38$		0			0
$39$	0.190983	−	0.138757i	0.0305818	−	0.0222189i
$40$		0			0
$41$	−1.45492	+	4.47777i	−0.227220	+	0.699310i	0.770839	+	0.637030i	$0.219837\pi$
$41$	−1.45492	+	4.47777i	−0.227220	+	0.699310i	−0.998059	+	0.0622801i	$0.980163\pi$
$42$		0			0
$43$	11.4721			1.74948			0.874742	−	0.484589i	$-0.161031\pi$
$43$	11.4721			1.74948			0.874742	+	0.484589i	$0.161031\pi$
$44$		0			0
$45$	0.618034			0.0921311
$46$		0			0
$47$	−3.26393	+	10.0453i	−0.476093	+	1.46526i	0.368384	+	0.929674i	$0.379911\pi$
$47$	−3.26393	+	10.0453i	−0.476093	+	1.46526i	−0.844477	+	0.535591i	$0.820089\pi$
$48$		0			0
$49$	−8.85410	+	6.43288i	−1.26487	+	0.918983i
$50$		0			0
$51$	2.11803	+	6.51864i	0.296584	+	0.912792i
$52$		0			0
$53$	−3.54508	−	2.57565i	−0.486955	−	0.353793i	0.317057	−	0.948406i	$-0.397305\pi$
$53$	−3.54508	−	2.57565i	−0.486955	−	0.353793i	−0.804012	+	0.594613i	$0.797305\pi$
$54$		0			0
$55$		0			0
$56$		0			0
$57$	−0.118034	−	0.0857567i	−0.0156340	−	0.0113588i
$58$		0			0
$59$	−3.95492	−	12.1720i	−0.514886	−	1.58466i	−0.783489	−	0.621405i	$-0.786562\pi$
$59$	−3.95492	−	12.1720i	−0.514886	−	1.58466i	0.268603	−	0.963251i	$-0.413438\pi$
$60$		0			0
$61$	−3.35410	+	2.43690i	−0.429449	+	0.312013i	−0.781428	−	0.623995i	$-0.785509\pi$
$61$	−3.35410	+	2.43690i	−0.429449	+	0.312013i	0.351980	+	0.936008i	$0.385509\pi$
$62$		0			0
$63$	1.30902	−	4.02874i	0.164921	−	0.507574i
$64$		0			0
$65$	−0.145898			−0.0180964
$66$		0			0
$67$	−6.61803			−0.808522			−0.404261	−	0.914644i	$-0.632471\pi$
$67$	−6.61803			−0.808522			−0.404261	+	0.914644i	$0.632471\pi$
$68$		0			0
$69$	−1.54508	+	4.75528i	−0.186006	+	0.572469i
$70$		0			0
$71$	−4.50000	+	3.26944i	−0.534052	+	0.388011i	−0.821871	−	0.569673i	$-0.807070\pi$
$71$	−4.50000	+	3.26944i	−0.534052	+	0.388011i	0.287819	+	0.957685i	$0.407070\pi$
$72$		0			0
$73$	0.708204	+	2.17963i	0.0828890	+	0.255106i	0.983909	−	0.178672i	$-0.0571801\pi$
$73$	0.708204	+	2.17963i	0.0828890	+	0.255106i	−0.901020	+	0.433778i	$0.857180\pi$
$74$		0			0
$75$	3.73607	+	2.71441i	0.431404	+	0.313433i
$76$		0			0
$77$		0			0
$78$		0			0
$79$	3.80902	+	2.76741i	0.428548	+	0.311358i	0.781068	−	0.624446i	$-0.214675\pi$
$79$	3.80902	+	2.76741i	0.428548	+	0.311358i	−0.352520	+	0.935804i	$0.614675\pi$
$80$		0			0
$81$	0.309017	+	0.951057i	0.0343352	+	0.105673i
$82$		0			0
$83$	−5.04508	+	3.66547i	−0.553770	+	0.402337i	−0.829174	−	0.558991i	$-0.811189\pi$
$83$	−5.04508	+	3.66547i	−0.553770	+	0.402337i	0.275404	+	0.961329i	$0.411189\pi$
$84$		0			0
$85$	1.30902	−	4.02874i	0.141983	−	0.436978i
$86$		0			0
$87$	−2.00000			−0.214423
$88$		0			0
$89$	17.1803			1.82111			0.910556	−	0.413385i	$-0.135654\pi$
$89$	17.1803			1.82111			0.910556	+	0.413385i	$0.135654\pi$
$90$		0			0
$91$	−0.309017	+	0.951057i	−0.0323938	+	0.0996978i
$92$		0			0
$93$	−4.54508	+	3.30220i	−0.471303	+	0.342422i
$94$		0			0
$95$	0.0278640	+	0.0857567i	0.00285879	+	0.00879845i
$96$		0			0
$97$	11.3541	+	8.24924i	1.15283	+	0.837583i	0.988855	−	0.148881i	$-0.0475670\pi$
$97$	11.3541	+	8.24924i	1.15283	+	0.837583i	0.163979	+	0.986464i	$0.447567\pi$
$98$		0			0
$99$		0			0
$100$		0			0
$101$	9.51722	+	6.91467i	0.946999	+	0.688035i	0.950095	−	0.311960i	$-0.100986\pi$
$101$	9.51722	+	6.91467i	0.946999	+	0.688035i	−0.00309628	+	0.999995i	$0.500986\pi$
$102$		0			0
$103$	5.38197	+	16.5640i	0.530301	+	1.63210i	0.753589	+	0.657346i	$0.228321\pi$
$103$	5.38197	+	16.5640i	0.530301	+	1.63210i	−0.223288	+	0.974752i	$0.571679\pi$
$104$		0			0
$105$	−2.11803	+	1.53884i	−0.206699	+	0.150176i
$106$		0			0
$107$	−4.83688	+	14.8864i	−0.467599	+	1.43912i	0.388085	+	0.921623i	$0.373137\pi$
$107$	−4.83688	+	14.8864i	−0.467599	+	1.43912i	−0.855684	+	0.517498i	$0.826863\pi$
$108$		0			0
$109$	8.94427			0.856706			0.428353	−	0.903612i	$-0.359094\pi$
$109$	8.94427			0.856706			0.428353	+	0.903612i	$0.359094\pi$
$110$		0			0
$111$	−2.23607			−0.212238
$112$		0			0
$113$	3.07295	−	9.45756i	0.289079	−	0.889693i	−0.696068	−	0.717976i	$-0.745069\pi$
$113$	3.07295	−	9.45756i	0.289079	−	0.889693i	0.985146	−	0.171717i	$-0.0549314\pi$
$114$		0			0
$115$	2.50000	−	1.81636i	0.233126	−	0.169376i
$116$		0			0
$117$	−0.0729490	−	0.224514i	−0.00674414	−	0.0207563i
$118$		0			0
$119$	−23.4894	−	17.0660i	−2.15327	−	1.56444i
$120$		0			0
$121$		0			0
$122$		0			0
$123$	3.80902	+	2.76741i	0.343447	+	0.249529i
$124$		0			0
$125$	−1.83688	−	5.65334i	−0.164296	−	0.505650i
$126$		0			0
$127$	−9.47214	+	6.88191i	−0.840516	+	0.610671i	−0.922515	−	0.385962i	$-0.873870\pi$
$127$	−9.47214	+	6.88191i	−0.840516	+	0.610671i	0.0819987	+	0.996632i	$0.473870\pi$
$128$		0			0
$129$	3.54508	−	10.9106i	0.312127	−	0.960629i
$130$		0			0
$131$	8.85410			0.773586			0.386793	−	0.922166i	$-0.373583\pi$
$131$	8.85410			0.773586			0.386793	+	0.922166i	$0.373583\pi$
$132$		0			0
$133$	0.618034			0.0535903
$134$		0			0
$135$	0.190983	−	0.587785i	0.0164372	−	0.0505885i
$136$		0			0
$137$	7.89919	−	5.73910i	0.674873	−	0.490324i	−0.196780	−	0.980448i	$-0.563048\pi$
$137$	7.89919	−	5.73910i	0.674873	−	0.490324i	0.871653	+	0.490124i	$0.163048\pi$
$138$		0			0
$139$	2.64590	+	8.14324i	0.224422	+	0.690700i	0.998350	+	0.0574263i	$0.0182894\pi$
$139$	2.64590	+	8.14324i	0.224422	+	0.690700i	−0.773928	+	0.633274i	$0.781711\pi$
$140$		0			0
$141$	8.54508	+	6.20837i	0.719626	+	0.522839i
$142$		0			0
$143$		0			0
$144$		0			0
$145$	1.00000	+	0.726543i	0.0830455	+	0.0603361i
$146$		0			0
$147$	3.38197	+	10.4086i	0.278940	+	0.858489i
$148$		0			0
$149$	14.3713	−	10.4414i	1.17734	−	0.855391i	0.185475	−	0.982649i	$-0.440618\pi$
$149$	14.3713	−	10.4414i	1.17734	−	0.855391i	0.991870	+	0.127258i	$0.0406176\pi$
$150$		0			0
$151$	1.38197	−	4.25325i	0.112463	−	0.346125i	−0.878947	−	0.476920i	$-0.841753\pi$
$151$	1.38197	−	4.25325i	0.112463	−	0.346125i	0.991409	+	0.130795i	$0.0417531\pi$
$152$		0			0
$153$	6.85410			0.554121
$154$		0			0
$155$	3.47214			0.278889
$156$		0			0
$157$	−4.85410	+	14.9394i	−0.387400	+	1.19229i	0.547325	+	0.836920i	$0.315646\pi$
$157$	−4.85410	+	14.9394i	−0.387400	+	1.19229i	−0.934725	+	0.355373i	$0.884354\pi$
$158$		0			0
$159$	−3.54508	+	2.57565i	−0.281144	+	0.204263i
$160$		0			0
$161$	−6.54508	−	20.1437i	−0.515825	−	1.58755i
$162$		0			0
$163$	8.39919	+	6.10237i	0.657875	+	0.477974i	0.865945	−	0.500140i	$-0.166718\pi$
$163$	8.39919	+	6.10237i	0.657875	+	0.477974i	−0.208070	+	0.978114i	$0.566718\pi$
$164$		0			0
$165$		0			0
$166$		0			0
$167$	−12.5902	−	9.14729i	−0.974257	−	0.707839i	−0.0178389	−	0.999841i	$-0.505679\pi$
$167$	−12.5902	−	9.14729i	−0.974257	−	0.707839i	−0.956418	+	0.292002i	$0.905679\pi$
$168$		0			0
$169$	−4.00000	−	12.3107i	−0.307692	−	0.946980i
$170$		0			0
$171$	−0.118034	+	0.0857567i	−0.00902628	+	0.00655798i
$172$		0			0
$173$	−2.98936	+	9.20029i	−0.227277	+	0.699485i	0.770776	+	0.637106i	$0.219869\pi$
$173$	−2.98936	+	9.20029i	−0.227277	+	0.699485i	−0.998053	+	0.0623791i	$0.980131\pi$
$174$		0			0
$175$	−19.5623			−1.47877
$176$		0			0
$177$	−12.7984			−0.961985
$178$		0			0
$179$	0.399187	−	1.22857i	0.0298366	−	0.0918277i	−0.935029	−	0.354571i	$-0.884627\pi$
$179$	0.399187	−	1.22857i	0.0298366	−	0.0918277i	0.964866	+	0.262743i	$0.0846271\pi$
$180$		0			0
$181$	−4.04508	+	2.93893i	−0.300669	+	0.218449i	−0.727882	−	0.685702i	$-0.759495\pi$
$181$	−4.04508	+	2.93893i	−0.300669	+	0.218449i	0.427213	+	0.904151i	$0.359495\pi$
$182$		0			0
$183$	1.28115	+	3.94298i	0.0947056	+	0.291474i
$184$		0			0
$185$	1.11803	+	0.812299i	0.0821995	+	0.0597214i
$186$		0			0
$187$		0			0
$188$		0			0
$189$	−3.42705	−	2.48990i	−0.249281	−	0.181113i
$190$		0			0
$191$	−4.16312	−	12.8128i	−0.301233	−	0.927099i	−0.981056	−	0.193723i	$-0.937944\pi$
$191$	−4.16312	−	12.8128i	−0.301233	−	0.927099i	0.679824	−	0.733376i	$-0.262056\pi$
$192$		0			0
$193$	14.3992	−	10.4616i	1.03648	−	0.753044i	0.0668816	−	0.997761i	$-0.478695\pi$
$193$	14.3992	−	10.4616i	1.03648	−	0.753044i	0.969595	+	0.244717i	$0.0786950\pi$
$194$		0			0
$195$	−0.0450850	+	0.138757i	−0.00322860	+	0.00993661i
$196$		0			0
$197$	−19.3262			−1.37694			−0.688469	−	0.725266i	$-0.741717\pi$
$197$	−19.3262			−1.37694			−0.688469	+	0.725266i	$0.741717\pi$
$198$		0			0
$199$	0.0557281			0.00395046			0.00197523	−	0.999998i	$-0.499371\pi$
$199$	0.0557281			0.00395046			0.00197523	+	0.999998i	$0.499371\pi$
$200$		0			0
$201$	−2.04508	+	6.29412i	−0.144249	+	0.443953i
$202$		0			0
$203$	6.85410	−	4.97980i	0.481064	−	0.349513i
$204$		0			0
$205$	−0.899187	−	2.76741i	−0.0628019	−	0.193284i
$206$		0			0
$207$	4.04508	+	2.93893i	0.281153	+	0.204269i
$208$		0			0
$209$		0			0
$210$		0			0
$211$	−16.2533	−	11.8087i	−1.11892	−	0.812945i	−0.134877	−	0.990862i	$-0.543064\pi$
$211$	−16.2533	−	11.8087i	−1.11892	−	0.812945i	−0.984045	+	0.177918i	$0.943064\pi$
$212$		0			0
$213$	1.71885	+	5.29007i	0.117773	+	0.362469i
$214$		0			0
$215$	−5.73607	+	4.16750i	−0.391197	+	0.284221i
$216$		0			0
$217$	7.35410	−	22.6336i	0.499229	−	1.53647i
$218$		0			0
$219$	2.29180			0.154865
$220$		0			0
$221$	−1.61803			−0.108841
$222$		0			0
$223$	6.16312	−	18.9681i	0.412713	−	1.27020i	−0.501568	−	0.865118i	$-0.667243\pi$
$223$	6.16312	−	18.9681i	0.412713	−	1.27020i	0.914281	−	0.405081i	$-0.132757\pi$
$224$		0			0
$225$	3.73607	−	2.71441i	0.249071	−	0.180961i
$226$		0			0
$227$	−1.69098	−	5.20431i	−0.112234	−	0.345422i	0.879126	−	0.476590i	$-0.158127\pi$
$227$	−1.69098	−	5.20431i	−0.112234	−	0.345422i	−0.991360	+	0.131168i	$0.958127\pi$
$228$		0			0
$229$	−7.61803	−	5.53483i	−0.503414	−	0.365752i	0.306906	−	0.951740i	$-0.400706\pi$
$229$	−7.61803	−	5.53483i	−0.503414	−	0.365752i	−0.810319	+	0.585988i	$0.800706\pi$
$230$		0			0
$231$		0			0
$232$		0			0
$233$	−0.645898	−	0.469272i	−0.0423142	−	0.0307431i	0.566427	−	0.824112i	$-0.308325\pi$
$233$	−0.645898	−	0.469272i	−0.0423142	−	0.0307431i	−0.608741	+	0.793369i	$0.708325\pi$
$234$		0			0
$235$	−2.01722	−	6.20837i	−0.131589	−	0.404989i
$236$		0			0
$237$	3.80902	−	2.76741i	0.247422	−	0.179763i
$238$		0			0
$239$	−7.02786	+	21.6295i	−0.454595	+	1.39910i	0.417016	+	0.908899i	$0.363076\pi$
$239$	−7.02786	+	21.6295i	−0.454595	+	1.39910i	−0.871610	+	0.490199i	$0.836924\pi$
$240$		0			0
$241$	5.23607			0.337285			0.168642	−	0.985677i	$-0.446062\pi$
$241$	5.23607			0.337285			0.168642	+	0.985677i	$0.446062\pi$
$242$		0			0
$243$	1.00000			0.0641500
$244$		0			0
$245$	2.09017	−	6.43288i	0.133536	−	0.410982i
$246$		0			0
$247$	0.0278640	−	0.0202444i	0.00177295	−	0.00128812i
$248$		0			0
$249$	1.92705	+	5.93085i	0.122122	+	0.375853i
$250$		0			0
$251$	−7.54508	−	5.48183i	−0.476242	−	0.346010i	0.323627	−	0.946185i	$-0.395098\pi$
$251$	−7.54508	−	5.48183i	−0.476242	−	0.346010i	−0.799869	+	0.600175i	$0.795098\pi$
$252$		0			0
$253$		0			0
$254$		0			0
$255$	−3.42705	−	2.48990i	−0.214610	−	0.155923i
$256$		0			0
$257$	1.28115	+	3.94298i	0.0799161	+	0.245957i	0.983030	−	0.183444i	$-0.0587247\pi$
$257$	1.28115	+	3.94298i	0.0799161	+	0.245957i	−0.903114	+	0.429401i	$0.858725\pi$
$258$		0			0
$259$	7.66312	−	5.56758i	0.476163	−	0.345953i
$260$		0			0
$261$	−0.618034	+	1.90211i	−0.0382553	+	0.117738i
$262$		0			0
$263$	−19.7426			−1.21738			−0.608692	−	0.793407i	$-0.708305\pi$
$263$	−19.7426			−1.21738			−0.608692	+	0.793407i	$0.708305\pi$
$264$		0			0
$265$	2.70820			0.166364
$266$		0			0
$267$	5.30902	−	16.3395i	0.324907	−	0.999960i
$268$		0			0
$269$	20.5623	−	14.9394i	1.25371	−	0.910871i	0.255275	−	0.966868i	$-0.417834\pi$
$269$	20.5623	−	14.9394i	1.25371	−	0.910871i	0.998431	+	0.0559978i	$0.0178340\pi$
$270$		0			0
$271$	3.51722	+	10.8249i	0.213656	+	0.657565i	0.999246	+	0.0388184i	$0.0123594\pi$
$271$	3.51722	+	10.8249i	0.213656	+	0.657565i	−0.785590	+	0.618747i	$0.787641\pi$
$272$		0			0
$273$	0.809017	+	0.587785i	0.0489639	+	0.0355744i
$274$		0			0
$275$		0			0
$276$		0			0
$277$	21.4894	+	15.6129i	1.29117	+	0.938090i	0.999828	−	0.0185288i	$-0.00589824\pi$
$277$	21.4894	+	15.6129i	1.29117	+	0.938090i	0.291342	+	0.956619i	$0.405898\pi$
$278$		0			0
$279$	1.73607	+	5.34307i	0.103936	+	0.319881i
$280$		0			0
$281$	−3.38197	+	2.45714i	−0.201751	+	0.146581i	−0.684074	−	0.729413i	$-0.739793\pi$
$281$	−3.38197	+	2.45714i	−0.201751	+	0.146581i	0.482323	+	0.875994i	$0.339793\pi$
$282$		0			0
$283$	2.05573	−	6.32688i	0.122200	−	0.376094i	−0.871180	−	0.490963i	$-0.836645\pi$
$283$	2.05573	−	6.32688i	0.122200	−	0.376094i	0.993381	+	0.114869i	$0.0366449\pi$
$284$		0			0
$285$	0.0901699			0.00534121
$286$		0			0
$287$	−19.9443			−1.17727
$288$		0			0
$289$	9.26393	−	28.5115i	0.544937	−	1.67714i
$290$		0			0
$291$	11.3541	−	8.24924i	0.665589	−	0.483579i
$292$		0			0
$293$	−6.87132	−	21.1478i	−0.401427	−	1.23547i	−0.923842	−	0.382774i	$-0.874969\pi$
$293$	−6.87132	−	21.1478i	−0.401427	−	1.23547i	0.522415	−	0.852691i	$-0.325031\pi$
$294$		0			0
$295$	6.39919	+	4.64928i	0.372575	+	0.270692i
$296$		0			0
$297$		0			0
$298$		0			0
$299$	−0.954915	−	0.693786i	−0.0552242	−	0.0401227i
$300$		0			0
$301$	15.0172	+	46.2183i	0.865578	+	2.66398i
$302$		0			0
$303$	9.51722	−	6.91467i	0.546750	−	0.397237i
$304$		0			0
$305$	0.791796	−	2.43690i	0.0453381	−	0.139536i
$306$		0			0
$307$	−10.7426			−0.613115			−0.306558	−	0.951852i	$-0.599177\pi$
$307$	−10.7426			−0.613115			−0.306558	+	0.951852i	$0.599177\pi$
$308$		0			0
$309$	17.4164			0.990785
$310$		0			0
$311$	4.16312	−	12.8128i	0.236069	−	0.726545i	−0.760909	−	0.648859i	$-0.775247\pi$
$311$	4.16312	−	12.8128i	0.236069	−	0.726545i	0.996978	−	0.0776865i	$-0.0247533\pi$
$312$		0			0
$313$	13.2812	−	9.64932i	0.750695	−	0.545412i	−0.145347	−	0.989381i	$-0.546430\pi$
$313$	13.2812	−	9.64932i	0.750695	−	0.545412i	0.896042	+	0.443969i	$0.146430\pi$
$314$		0			0
$315$	0.809017	+	2.48990i	0.0455829	+	0.140290i
$316$		0			0
$317$	17.6074	+	12.7925i	0.988930	+	0.718499i	0.959686	−	0.281073i	$-0.0906903\pi$
$317$	17.6074	+	12.7925i	0.988930	+	0.718499i	0.0292432	+	0.999572i	$0.490690\pi$
$318$		0			0
$319$		0			0
$320$		0			0
$321$	12.6631	+	9.20029i	0.706786	+	0.513510i
$322$		0			0
$323$	0.309017	+	0.951057i	0.0171942	+	0.0529182i
$324$		0			0
$325$	−0.881966	+	0.640786i	−0.0489227	+	0.0355444i
$326$		0			0
$327$	2.76393	−	8.50651i	0.152846	−	0.470411i
$328$		0			0
$329$	−44.7426			−2.46674
$330$		0			0
$331$	−5.94427			−0.326727			−0.163363	−	0.986566i	$-0.552234\pi$
$331$	−5.94427			−0.326727			−0.163363	+	0.986566i	$0.552234\pi$
$332$		0			0
$333$	−0.690983	+	2.12663i	−0.0378656	+	0.116538i
$334$		0			0
$335$	3.30902	−	2.40414i	0.180791	−	0.131352i
$336$		0			0
$337$	−3.14590	−	9.68208i	−0.171368	−	0.527416i	0.828081	−	0.560608i	$-0.189433\pi$
$337$	−3.14590	−	9.68208i	−0.171368	−	0.527416i	−0.999449	+	0.0331920i	$0.989433\pi$
$338$		0			0
$339$	−8.04508	−	5.84510i	−0.436949	−	0.317462i
$340$		0			0
$341$		0			0
$342$		0			0
$343$	−13.5172	−	9.82084i	−0.729861	−	0.530275i
$344$		0			0
$345$	−0.954915	−	2.93893i	−0.0514109	−	0.158226i
$346$		0			0
$347$	−11.7082	+	8.50651i	−0.628529	+	0.456653i	−0.855890	−	0.517157i	$-0.826990\pi$
$347$	−11.7082	+	8.50651i	−0.628529	+	0.456653i	0.227361	+	0.973811i	$0.426990\pi$
$348$		0			0
$349$	−10.1074	+	31.1074i	−0.541036	+	1.66514i	0.189196	+	0.981939i	$0.439412\pi$
$349$	−10.1074	+	31.1074i	−0.541036	+	1.66514i	−0.730232	+	0.683199i	$0.760588\pi$
$350$		0			0
$351$	−0.236068			−0.0126004
$352$		0			0
$353$	15.0557			0.801336			0.400668	−	0.916223i	$-0.368778\pi$
$353$	15.0557			0.801336			0.400668	+	0.916223i	$0.368778\pi$
$354$		0			0
$355$	1.06231	−	3.26944i	0.0563813	−	0.173524i
$356$		0			0
$357$	−23.4894	+	17.0660i	−1.24319	+	0.903229i
$358$		0			0
$359$	1.29180	+	3.97574i	0.0681784	+	0.209832i	0.979341	−	0.202215i	$-0.0648140\pi$
$359$	1.29180	+	3.97574i	0.0681784	+	0.209832i	−0.911163	+	0.412047i	$0.864814\pi$
$360$		0			0
$361$	15.3541	+	11.1554i	0.808111	+	0.587127i
$362$		0			0
$363$		0			0
$364$		0			0
$365$	−1.14590	−	0.832544i	−0.0599790	−	0.0435773i
$366$		0			0
$367$	−3.37132	−	10.3759i	−0.175982	−	0.541616i	0.823695	−	0.567033i	$-0.191909\pi$
$367$	−3.37132	−	10.3759i	−0.175982	−	0.541616i	−0.999677	+	0.0254169i	$0.991909\pi$
$368$		0			0
$369$	3.80902	−	2.76741i	0.198290	−	0.144066i
$370$		0			0
$371$	5.73607	−	17.6538i	0.297802	−	0.916540i
$372$		0			0
$373$	4.41641			0.228673			0.114336	−	0.993442i	$-0.463526\pi$
$373$	4.41641			0.228673			0.114336	+	0.993442i	$0.463526\pi$
$374$		0			0
$375$	−5.94427			−0.306961
$376$		0			0
$377$	0.145898	−	0.449028i	0.00751413	−	0.0231261i
$378$		0			0
$379$	21.2254	−	15.4212i	1.09028	−	0.792132i	0.110831	−	0.993839i	$-0.464649\pi$
$379$	21.2254	−	15.4212i	1.09028	−	0.792132i	0.979446	+	0.201707i	$0.0646488\pi$
$380$		0			0
$381$	3.61803	+	11.1352i	0.185357	+	0.570472i
$382$		0			0
$383$	4.04508	+	2.93893i	0.206694	+	0.150172i	0.686317	−	0.727303i	$-0.259226\pi$
$383$	4.04508	+	2.93893i	0.206694	+	0.150172i	−0.479623	+	0.877475i	$0.659226\pi$
$384$		0			0
$385$		0			0
$386$		0			0
$387$	−9.28115	−	6.74315i	−0.471788	−	0.342774i
$388$		0			0
$389$	−2.35410	−	7.24518i	−0.119358	−	0.367345i	0.873473	−	0.486872i	$-0.161862\pi$
$389$	−2.35410	−	7.24518i	−0.119358	−	0.367345i	−0.992831	+	0.119527i	$0.961862\pi$
$390$		0			0
$391$	27.7254	−	20.1437i	1.40214	−	1.01871i
$392$		0			0
$393$	2.73607	−	8.42075i	0.138016	−	0.424771i
$394$		0			0
$395$	−2.90983			−0.146409
$396$		0			0
$397$	10.2361			0.513734			0.256867	−	0.966447i	$-0.417310\pi$
$397$	10.2361			0.513734			0.256867	+	0.966447i	$0.417310\pi$
$398$		0			0
$399$	0.190983	−	0.587785i	0.00956111	−	0.0294261i
$400$		0			0
$401$	−10.3992	+	7.55545i	−0.519311	+	0.377301i	−0.816344	−	0.577566i	$-0.804003\pi$
$401$	−10.3992	+	7.55545i	−0.519311	+	0.377301i	0.297034	+	0.954867i	$0.404003\pi$
$402$		0			0
$403$	−0.409830	−	1.26133i	−0.0204151	−	0.0628312i
$404$		0			0
$405$	−0.500000	−	0.363271i	−0.0248452	−	0.0180511i
$406$		0			0
$407$		0			0
$408$		0			0
$409$	−2.76393	−	2.00811i	−0.136668	−	0.0992949i	0.517351	−	0.855773i	$-0.326918\pi$
$409$	−2.76393	−	2.00811i	−0.136668	−	0.0992949i	−0.654019	+	0.756478i	$0.726918\pi$
$410$		0			0
$411$	−3.01722	−	9.28605i	−0.148829	−	0.458047i
$412$		0			0
$413$	43.8607	−	31.8666i	2.15824	−	1.56806i
$414$		0			0
$415$	1.19098	−	3.66547i	0.0584631	−	0.179931i
$416$		0			0
$417$	8.56231			0.419298
$418$		0			0
$419$	12.7984			0.625241			0.312621	−	0.949878i	$-0.398793\pi$
$419$	12.7984			0.625241			0.312621	+	0.949878i	$0.398793\pi$
$420$		0			0
$421$	−7.51722	+	23.1356i	−0.366367	+	1.12756i	0.582754	+	0.812649i	$0.301975\pi$
$421$	−7.51722	+	23.1356i	−0.366367	+	1.12756i	−0.949121	+	0.314913i	$0.898025\pi$
$422$		0			0
$423$	8.54508	−	6.20837i	0.415476	−	0.301861i
$424$		0			0
$425$	−9.78115	−	30.1033i	−0.474456	−	1.46022i
$426$		0			0
$427$	−14.2082	−	10.3229i	−0.687583	−	0.499558i
$428$		0			0
$429$		0			0
$430$		0			0
$431$	6.07295	+	4.41226i	0.292524	+	0.212531i	0.724361	−	0.689420i	$-0.242135\pi$
$431$	6.07295	+	4.41226i	0.292524	+	0.212531i	−0.431838	+	0.901951i	$0.642135\pi$
$432$		0			0
$433$	−3.85410	−	11.8617i	−0.185216	−	0.570037i	0.814736	−	0.579833i	$-0.196882\pi$
$433$	−3.85410	−	11.8617i	−0.185216	−	0.570037i	−0.999952	+	0.00979528i	$0.996882\pi$
$434$		0			0
$435$	1.00000	−	0.726543i	0.0479463	−	0.0348350i
$436$		0			0
$437$	−0.225425	+	0.693786i	−0.0107835	+	0.0331883i
$438$		0			0
$439$	5.47214			0.261171			0.130585	−	0.991437i	$-0.458314\pi$
$439$	5.47214			0.261171			0.130585	+	0.991437i	$0.458314\pi$
$440$		0			0
$441$	10.9443			0.521156
$442$		0			0
$443$	−1.94427	+	5.98385i	−0.0923751	+	0.284301i	−0.986561	−	0.163395i	$-0.947755\pi$
$443$	−1.94427	+	5.98385i	−0.0923751	+	0.284301i	0.894186	+	0.447696i	$0.147755\pi$
$444$		0			0
$445$	−8.59017	+	6.24112i	−0.407213	+	0.295858i
$446$		0			0
$447$	−5.48936	−	16.8945i	−0.259638	−	0.799083i
$448$		0			0
$449$	5.61803	+	4.08174i	0.265131	+	0.192629i	0.712406	−	0.701767i	$-0.247605\pi$
$449$	5.61803	+	4.08174i	0.265131	+	0.192629i	−0.447275	+	0.894397i	$0.647605\pi$
$450$		0			0
$451$		0			0
$452$		0			0
$453$	−3.61803	−	2.62866i	−0.169990	−	0.123505i
$454$		0			0
$455$	−0.190983	−	0.587785i	−0.00895342	−	0.0275558i
$456$		0			0
$457$	−6.30902	+	4.58377i	−0.295123	+	0.214420i	−0.725487	−	0.688236i	$-0.758385\pi$
$457$	−6.30902	+	4.58377i	−0.295123	+	0.214420i	0.430364	+	0.902656i	$0.358385\pi$
$458$		0			0
$459$	2.11803	−	6.51864i	0.0988614	−	0.304264i
$460$		0			0
$461$	17.2705			0.804368			0.402184	−	0.915559i	$-0.368251\pi$
$461$	17.2705			0.804368			0.402184	+	0.915559i	$0.368251\pi$
$462$		0			0
$463$	−13.0344			−0.605762			−0.302881	−	0.953028i	$-0.597948\pi$
$463$	−13.0344			−0.605762			−0.302881	+	0.953028i	$0.597948\pi$
$464$		0			0
$465$	1.07295	−	3.30220i	0.0497568	−	0.153136i
$466$		0			0
$467$	6.28115	−	4.56352i	0.290657	−	0.211175i	−0.432895	−	0.901444i	$-0.642508\pi$
$467$	6.28115	−	4.56352i	0.290657	−	0.211175i	0.723552	+	0.690269i	$0.242508\pi$
$468$		0			0
$469$	−8.66312	−	26.6623i	−0.400026	−	1.23115i
$470$		0			0
$471$	12.7082	+	9.23305i	0.585563	+	0.425437i
$472$		0			0
$473$		0			0
$474$		0			0
$475$	0.545085	+	0.396027i	0.0250102	+	0.0181710i
$476$		0			0
$477$	1.35410	+	4.16750i	0.0620001	+	0.190817i
$478$		0			0
$479$	−20.3992	+	14.8209i	−0.932063	+	0.677183i	−0.946497	−	0.322713i	$-0.895405\pi$
$479$	−20.3992	+	14.8209i	−0.932063	+	0.677183i	0.0144343	+	0.999896i	$0.495405\pi$
$480$		0			0
$481$	0.163119	−	0.502029i	0.00743758	−	0.0228905i
$482$		0			0
$483$	−21.1803			−0.963739
$484$		0			0
$485$	−8.67376			−0.393855
$486$		0			0
$487$	2.89261	−	8.90254i	0.131077	−	0.403412i	−0.863883	−	0.503693i	$-0.831974\pi$
$487$	2.89261	−	8.90254i	0.131077	−	0.403412i	0.994959	+	0.100281i	$0.0319742\pi$
$488$		0			0
$489$	8.39919	−	6.10237i	0.379824	−	0.275959i
$490$		0			0
$491$	3.68034	+	11.3269i	0.166091	+	0.511177i	0.999115	−	0.0420606i	$-0.0133922\pi$
$491$	3.68034	+	11.3269i	0.166091	+	0.511177i	−0.833024	+	0.553237i	$0.813392\pi$
$492$		0			0
$493$	11.0902	+	8.05748i	0.499476	+	0.362891i
$494$		0			0
$495$		0			0
$496$		0			0
$497$	−19.0623	−	13.8496i	−0.855061	−	0.621238i
$498$		0			0
$499$	3.37132	+	10.3759i	0.150921	+	0.464488i	0.997725	−	0.0674181i	$-0.0214761\pi$
$499$	3.37132	+	10.3759i	0.150921	+	0.464488i	−0.846804	+	0.531906i	$0.821476\pi$
$500$		0			0
$501$	−12.5902	+	9.14729i	−0.562487	+	0.408671i
$502$		0			0
$503$	2.56231	−	7.88597i	0.114248	−	0.351618i	−0.877542	−	0.479500i	$-0.840818\pi$
$503$	2.56231	−	7.88597i	0.114248	−	0.351618i	0.991789	+	0.127882i	$0.0408180\pi$
$504$		0			0
$505$	−7.27051			−0.323533
$506$		0			0
$507$	−12.9443			−0.574875
$508$		0			0
$509$	−5.02786	+	15.4742i	−0.222856	+	0.685881i	0.775646	+	0.631168i	$0.217424\pi$
$509$	−5.02786	+	15.4742i	−0.222856	+	0.685881i	−0.998502	+	0.0547125i	$0.982576\pi$
$510$		0			0
$511$	−7.85410	+	5.70634i	−0.347445	+	0.252434i
$512$		0			0
$513$	0.0450850	+	0.138757i	0.00199055	+	0.00612628i
$514$		0			0
$515$	−8.70820	−	6.32688i	−0.383729	−	0.278796i
$516$		0			0
$517$		0			0
$518$		0			0
$519$	7.82624	+	5.68609i	0.343534	+	0.249592i
$520$		0			0
$521$	−1.23607	−	3.80423i	−0.0541531	−	0.166666i	0.920322	−	0.391162i	$-0.127927\pi$
$521$	−1.23607	−	3.80423i	−0.0541531	−	0.166666i	−0.974475	+	0.224495i	$0.927927\pi$
$522$		0			0
$523$	−15.6353	+	11.3597i	−0.683682	+	0.496724i	−0.874577	−	0.484886i	$-0.838861\pi$
$523$	−15.6353	+	11.3597i	−0.683682	+	0.496724i	0.190895	+	0.981610i	$0.438861\pi$
$524$		0			0
$525$	−6.04508	+	18.6049i	−0.263829	+	0.811983i
$526$		0			0
$527$	38.5066			1.67737
$528$		0			0
$529$	2.00000			0.0869565
$530$		0			0
$531$	−3.95492	+	12.1720i	−0.171629	+	0.528219i
$532$		0			0
$533$	−0.899187	+	0.653298i	−0.0389481	+	0.0282975i
$534$		0			0
$535$	−2.98936	−	9.20029i	−0.129241	−	0.397763i
$536$		0			0
$537$	−1.04508	−	0.759299i	−0.0450987	−	0.0327662i
$538$		0			0
$539$		0			0
$540$		0			0
$541$	6.88197	+	5.00004i	0.295879	+	0.214969i	0.725814	−	0.687891i	$-0.241463\pi$
$541$	6.88197	+	5.00004i	0.295879	+	0.214969i	−0.429935	+	0.902860i	$0.641463\pi$
$542$		0			0
$543$	1.54508	+	4.75528i	0.0663059	+	0.204069i
$544$		0			0
$545$	−4.47214	+	3.24920i	−0.191565	+	0.139180i
$546$		0			0
$547$	6.53444	−	20.1109i	0.279393	−	0.859882i	−0.708631	−	0.705579i	$-0.750687\pi$
$547$	6.53444	−	20.1109i	0.279393	−	0.859882i	0.988024	−	0.154303i	$-0.0493131\pi$
$548$		0			0
$549$	4.14590			0.176943
$550$		0			0
$551$	−0.291796			−0.0124309
$552$		0			0
$553$	−6.16312	+	18.9681i	−0.262082	+	0.806607i
$554$		0			0
$555$	1.11803	−	0.812299i	0.0474579	−	0.0344802i
$556$		0			0
$557$	6.28115	+	19.3314i	0.266141	+	0.819098i	0.991428	+	0.130651i	$0.0417069\pi$
$557$	6.28115	+	19.3314i	0.266141	+	0.819098i	−0.725287	+	0.688446i	$0.758293\pi$
$558$		0			0
$559$	2.19098	+	1.59184i	0.0926687	+	0.0673278i
$560$		0			0
$561$		0			0
$562$		0			0
$563$	20.8992	+	15.1841i	0.880796	+	0.639936i	0.933462	−	0.358677i	$-0.116772\pi$
$563$	20.8992	+	15.1841i	0.880796	+	0.639936i	−0.0526662	+	0.998612i	$0.516772\pi$
$564$		0			0
$565$	1.89919	+	5.84510i	0.0798994	+	0.245905i
$566$		0			0
$567$	−3.42705	+	2.48990i	−0.143923	+	0.104566i
$568$		0			0
$569$	−8.09017	+	24.8990i	−0.339158	+	1.04382i	0.625480	+	0.780240i	$0.284903\pi$
$569$	−8.09017	+	24.8990i	−0.339158	+	1.04382i	−0.964638	+	0.263580i	$0.915097\pi$
$570$		0			0
$571$	−11.3820			−0.476320			−0.238160	−	0.971226i	$-0.576544\pi$
$571$	−11.3820			−0.476320			−0.238160	+	0.971226i	$0.576544\pi$
$572$		0			0
$573$	−13.4721			−0.562807
$574$		0			0
$575$	7.13525	−	21.9601i	0.297561	−	0.915798i
$576$		0			0
$577$	−22.7082	+	16.4985i	−0.945355	+	0.686841i	−0.949704	−	0.313150i	$-0.898616\pi$
$577$	−22.7082	+	16.4985i	−0.945355	+	0.686841i	0.00434878	+	0.999991i	$0.498616\pi$
$578$		0			0
$579$	−5.50000	−	16.9273i	−0.228572	−	0.703473i
$580$		0			0
$581$	−21.3713	−	15.5272i	−0.886632	−	0.644176i
$582$		0			0
$583$		0			0
$584$		0			0
$585$	0.118034	+	0.0857567i	0.00488010	+	0.00354560i
$586$		0			0
$587$	7.25329	+	22.3233i	0.299375	+	0.921382i	0.981717	+	0.190349i	$0.0609618\pi$
$587$	7.25329	+	22.3233i	0.299375	+	0.921382i	−0.682341	+	0.731034i	$0.739038\pi$
$588$		0			0
$589$	−0.663119	+	0.481784i	−0.0273233	+	0.0198516i
$590$		0			0
$591$	−5.97214	+	18.3803i	−0.245661	+	0.756066i
$592$		0			0
$593$	17.3820			0.713792			0.356896	−	0.934144i	$-0.383835\pi$
$593$	17.3820			0.713792			0.356896	+	0.934144i	$0.383835\pi$
$594$		0			0
$595$	17.9443			0.735643
$596$		0			0
$597$	0.0172209	−	0.0530006i	0.000704806	−	0.00216917i
$598$		0			0
$599$	−11.0000	+	7.99197i	−0.449448	+	0.326543i	−0.789378	−	0.613908i	$-0.789597\pi$
$599$	−11.0000	+	7.99197i	−0.449448	+	0.326543i	0.339930	+	0.940451i	$0.389597\pi$
$600$		0			0
$601$	13.2533	+	40.7894i	0.540613	+	1.66384i	0.731198	+	0.682165i	$0.238961\pi$
$601$	13.2533	+	40.7894i	0.540613	+	1.66384i	−0.190585	+	0.981671i	$0.561039\pi$
$602$		0			0
$603$	5.35410	+	3.88998i	0.218036	+	0.158412i
$604$		0			0
$605$		0			0
$606$		0			0
$607$	28.7254	+	20.8702i	1.16593	+	0.847097i	0.990516	−	0.137398i	$-0.0438739\pi$
$607$	28.7254	+	20.8702i	1.16593	+	0.847097i	0.175413	+	0.984495i	$0.443874\pi$
$608$		0			0
$609$	−2.61803	−	8.05748i	−0.106088	−	0.326506i
$610$		0			0
$611$	−2.01722	+	1.46560i	−0.0816080	+	0.0592917i
$612$		0			0
$613$	6.41641	−	19.7477i	0.259156	−	0.797601i	−0.733826	−	0.679337i	$-0.762267\pi$
$613$	6.41641	−	19.7477i	0.259156	−	0.797601i	0.992982	−	0.118263i	$-0.0377327\pi$
$614$		0			0
$615$	−2.90983			−0.117336
$616$		0			0
$617$	26.7082			1.07523			0.537616	−	0.843190i	$-0.319325\pi$
$617$	26.7082			1.07523			0.537616	+	0.843190i	$0.319325\pi$
$618$		0			0
$619$	−0.128677	+	0.396027i	−0.00517197	+	0.0159177i	−0.953609	−	0.301047i	$-0.902664\pi$
$619$	−0.128677	+	0.396027i	−0.00517197	+	0.0159177i	0.948437	+	0.316965i	$0.102664\pi$
$620$		0			0
$621$	4.04508	−	2.93893i	0.162324	−	0.117935i
$622$		0			0
$623$	22.4894	+	69.2151i	0.901017	+	2.77305i
$624$		0			0
$625$	−15.7082	−	11.4127i	−0.628328	−	0.456507i
$626$		0			0
$627$		0			0
$628$		0			0
$629$	12.3992	+	9.00854i	0.494388	+	0.359194i
$630$		0			0
$631$	−13.0279	−	40.0956i	−0.518631	−	1.59618i	−0.776577	−	0.630023i	$-0.783046\pi$
$631$	−13.0279	−	40.0956i	−0.518631	−	1.59618i	0.257946	−	0.966159i	$-0.416954\pi$
$632$		0			0
$633$	−16.2533	+	11.8087i	−0.646010	+	0.469354i
$634$		0			0
$635$	2.23607	−	6.88191i	0.0887357	−	0.273100i
$636$		0			0
$637$	−2.58359			−0.102366
$638$		0			0
$639$	5.56231			0.220041
$640$		0			0
$641$	9.10081	−	28.0094i	0.359461	−	1.10631i	−0.593917	−	0.804526i	$-0.702419\pi$
$641$	9.10081	−	28.0094i	0.359461	−	1.10631i	0.953378	−	0.301780i	$-0.0975807\pi$
$642$		0			0
$643$	−10.6353	+	7.72696i	−0.419414	+	0.304722i	−0.777402	−	0.629004i	$-0.783463\pi$
$643$	−10.6353	+	7.72696i	−0.419414	+	0.304722i	0.357988	+	0.933726i	$0.383463\pi$
$644$		0			0
$645$	2.19098	+	6.74315i	0.0862699	+	0.265511i
$646$		0			0
$647$	1.07295	+	0.779543i	0.0421820	+	0.0306470i	0.608676	−	0.793419i	$-0.291701\pi$
$647$	1.07295	+	0.779543i	0.0421820	+	0.0306470i	−0.566494	+	0.824066i	$0.691701\pi$
$648$		0			0
$649$		0			0
$650$		0			0
$651$	−19.2533	−	13.9883i	−0.754596	−	0.548246i
$652$		0			0
$653$	7.84752	+	24.1522i	0.307097	+	0.945148i	0.978886	+	0.204406i	$0.0655262\pi$
$653$	7.84752	+	24.1522i	0.307097	+	0.945148i	−0.671789	+	0.740743i	$0.734474\pi$
$654$		0			0
$655$	−4.42705	+	3.21644i	−0.172979	+	0.125677i
$656$		0			0
$657$	0.708204	−	2.17963i	0.0276297	−	0.0850354i
$658$		0			0
$659$	30.6525			1.19405			0.597025	−	0.802222i	$-0.296349\pi$
$659$	30.6525			1.19405			0.597025	+	0.802222i	$0.296349\pi$
$660$		0			0
$661$	−12.9656			−0.504302			−0.252151	−	0.967688i	$-0.581138\pi$
$661$	−12.9656			−0.504302			−0.252151	+	0.967688i	$0.581138\pi$
$662$		0			0
$663$	−0.500000	+	1.53884i	−0.0194184	+	0.0597637i
$664$		0			0
$665$	−0.309017	+	0.224514i	−0.0119832	+	0.00870628i
$666$		0			0
$667$	3.09017	+	9.51057i	0.119652	+	0.368251i
$668$		0			0
$669$	−16.1353	−	11.7229i	−0.623825	−	0.453235i
$670$		0			0
$671$		0			0
$672$		0			0
$673$	−14.6074	−	10.6129i	−0.563074	−	0.409097i	0.269509	−	0.962998i	$-0.413139\pi$
$673$	−14.6074	−	10.6129i	−0.563074	−	0.409097i	−0.832583	+	0.553901i	$0.813139\pi$
$674$		0			0
$675$	−1.42705	−	4.39201i	−0.0549272	−	0.169049i
$676$		0			0
$677$	30.9443	−	22.4823i	1.18928	−	0.864066i	0.196096	−	0.980585i	$-0.437173\pi$
$677$	30.9443	−	22.4823i	1.18928	−	0.864066i	0.993189	+	0.116518i	$0.0371734\pi$
$678$		0			0
$679$	−18.3713	+	56.5411i	−0.705027	+	2.16985i
$680$		0			0
$681$	−5.47214			−0.209693
$682$		0			0
$683$	0.0557281			0.00213238			0.00106619	−	0.999999i	$-0.499661\pi$
$683$	0.0557281			0.00213238			0.00106619	+	0.999999i	$0.499661\pi$
$684$		0			0
$685$	−1.86475	+	5.73910i	−0.0712482	+	0.219280i
$686$		0			0
$687$	−7.61803	+	5.53483i	−0.290646	+	0.211167i
$688$		0			0
$689$	−0.319660	−	0.983813i	−0.0121781	−	0.0374803i
$690$		0			0
$691$	−13.8541	−	10.0656i	−0.527035	−	0.382913i	0.292213	−	0.956353i	$-0.405609\pi$
$691$	−13.8541	−	10.0656i	−0.527035	−	0.382913i	−0.819247	+	0.573440i	$0.805609\pi$
$692$		0			0
$693$		0			0
$694$		0			0
$695$	−4.28115	−	3.11044i	−0.162393	−	0.117986i
$696$		0			0
$697$	−9.97214	−	30.6911i	−0.377722	−	1.16251i
$698$		0			0
$699$	−0.645898	+	0.469272i	−0.0244301	+	0.0177495i
$700$		0			0
$701$	12.0795	−	37.1770i	0.456237	−	1.40415i	−0.413439	−	0.910532i	$-0.635672\pi$
$701$	12.0795	−	37.1770i	0.456237	−	1.40415i	0.869676	−	0.493623i	$-0.164328\pi$
$702$		0			0
$703$	−0.326238			−0.0123043
$704$		0			0
$705$	−6.52786			−0.245854
$706$		0			0
$707$	−15.3992	+	47.3938i	−0.579146	+	1.78243i
$708$		0			0
$709$	1.39919	−	1.01657i	0.0525476	−	0.0381780i	−0.561201	−	0.827679i	$-0.689661\pi$
$709$	1.39919	−	1.01657i	0.0525476	−	0.0381780i	0.613749	+	0.789501i	$0.289661\pi$
$710$		0			0
$711$	−1.45492	−	4.47777i	−0.0545636	−	0.167929i
$712$		0			0
$713$	22.7254	+	16.5110i	0.851074	+	0.618341i
$714$		0			0
$715$		0			0
$716$		0			0
$717$	18.3992	+	13.3678i	0.687130	+	0.499229i
$718$		0			0
$719$	−2.92705	−	9.00854i	−0.109161	−	0.335962i	0.881524	−	0.472140i	$-0.156518\pi$
$719$	−2.92705	−	9.00854i	−0.109161	−	0.335962i	−0.990684	+	0.136178i	$0.956518\pi$
$720$		0			0
$721$	−59.6869	+	43.3651i	−2.22286	+	1.61500i
$722$		0			0
$723$	1.61803	−	4.97980i	0.0601753	−	0.185201i
$724$		0			0
$725$	9.23607			0.343019
$726$		0			0
$727$	−2.02129			−0.0749654			−0.0374827	−	0.999297i	$-0.511934\pi$
$727$	−2.02129			−0.0749654			−0.0374827	+	0.999297i	$0.511934\pi$
$728$		0			0
$729$	0.309017	−	0.951057i	0.0114451	−	0.0352243i
$730$		0			0
$731$	−63.6140	+	46.2183i	−2.35285	+	1.70944i
$732$		0			0
$733$	10.3475	+	31.8464i	0.382195	+	1.17627i	0.938495	+	0.345293i	$0.112220\pi$
$733$	10.3475	+	31.8464i	0.382195	+	1.17627i	−0.556301	+	0.830981i	$0.687780\pi$
$734$		0			0
$735$	−5.47214	−	3.97574i	−0.201843	−	0.146647i
$736$		0			0
$737$		0			0
$738$		0			0
$739$	−37.6074	−	27.3234i	−1.38341	−	1.00511i	−0.996552	−	0.0829670i	$-0.973560\pi$
$739$	−37.6074	−	27.3234i	−1.38341	−	1.00511i	−0.386858	−	0.922139i	$-0.626440\pi$
$740$		0			0
$741$	−0.0106431	−	0.0327561i	−0.000390985	−	0.00120333i
$742$		0			0
$743$	−34.1697	+	24.8257i	−1.25356	+	0.910768i	−0.998423	−	0.0561357i	$-0.982122\pi$
$743$	−34.1697	+	24.8257i	−1.25356	+	0.910768i	−0.255141	+	0.966904i	$0.582122\pi$
$744$		0			0
$745$	−3.39261	+	10.4414i	−0.124296	+	0.382542i
$746$		0			0
$747$	6.23607			0.228166
$748$		0			0
$749$	−66.3050			−2.42273
$750$		0			0
$751$	−13.8090	+	42.4998i	−0.503898	+	1.55084i	0.298717	+	0.954342i	$0.403441\pi$
$751$	−13.8090	+	42.4998i	−0.503898	+	1.55084i	−0.802615	+	0.596497i	$0.796559\pi$
$752$		0			0
$753$	−7.54508	+	5.48183i	−0.274958	+	0.199769i
$754$		0			0
$755$	0.854102	+	2.62866i	0.0310840	+	0.0956666i
$756$		0			0
$757$	−27.9336	−	20.2950i	−1.01527	−	0.737633i	−0.0499581	−	0.998751i	$-0.515909\pi$
$757$	−27.9336	−	20.2950i	−1.01527	−	0.737633i	−0.965307	+	0.261118i	$0.915909\pi$
$758$		0			0
$759$		0			0
$760$		0			0
$761$	−3.51722	−	2.55541i	−0.127499	−	0.0926336i	0.522208	−	0.852818i	$-0.325108\pi$
$761$	−3.51722	−	2.55541i	−0.127499	−	0.0926336i	−0.649707	+	0.760185i	$0.725108\pi$
$762$		0			0
$763$	11.7082	+	36.0341i	0.423865	+	1.30452i
$764$		0			0
$765$	−3.42705	+	2.48990i	−0.123905	+	0.0900225i
$766$		0			0
$767$	0.933629	−	2.87341i	0.0337114	−	0.103753i
$768$		0			0
$769$	36.9787			1.33349			0.666743	−	0.745287i	$-0.267688\pi$
$769$	36.9787			1.33349			0.666743	+	0.745287i	$0.267688\pi$
$770$		0			0
$771$	4.14590			0.149311
$772$		0			0
$773$	−6.10739	+	18.7966i	−0.219668	+	0.676067i	0.779122	+	0.626873i	$0.215665\pi$
$773$	−6.10739	+	18.7966i	−0.219668	+	0.676067i	−0.998789	+	0.0491945i	$0.984335\pi$
$774$		0			0
$775$	20.9894	−	15.2497i	0.753960	−	0.547784i
$776$		0			0
$777$	−2.92705	−	9.00854i	−0.105007	−	0.323179i
$778$		0			0
$779$	0.555728	+	0.403760i	0.0199110	+	0.0144662i
$780$		0			0
$781$		0			0
$782$		0			0
$783$	1.61803	+	1.17557i	0.0578238	+	0.0420115i
$784$		0			0
$785$	−3.00000	−	9.23305i	−0.107075	−	0.329542i
$786$		0			0
$787$	1.85410	−	1.34708i	0.0660916	−	0.0480184i	−0.554249	−	0.832351i	$-0.686994\pi$
$787$	1.85410	−	1.34708i	0.0660916	−	0.0480184i	0.620340	+	0.784333i	$0.286994\pi$
$788$		0			0
$789$	−6.10081	+	18.7764i	−0.217195	+	0.668457i
$790$		0			0
$791$	42.1246			1.49778
$792$		0			0
$793$	−0.978714			−0.0347551
$794$		0			0
$795$	0.836881	−	2.57565i	0.0296811	−	0.0913491i
$796$		0			0
$797$	25.9443	−	18.8496i	0.918993	−	0.667688i	−0.0242800	−	0.999705i	$-0.507729\pi$
$797$	25.9443	−	18.8496i	0.918993	−	0.667688i	0.943273	+	0.332018i	$0.107729\pi$
$798$		0			0
$799$	−22.3713	−	68.8519i	−0.791441	−	2.43580i
$800$		0			0
$801$	−13.8992	−	10.0984i	−0.491104	−	0.356808i
$802$		0			0
$803$		0			0
$804$		0			0
$805$	10.5902	+	7.69421i	0.373254	+	0.271185i
$806$		0			0
$807$	−7.85410	−	24.1724i	−0.276477	−	0.850910i
$808$		0			0
$809$	−43.1525	+	31.3521i	−1.51716	+	1.10228i	−0.554288	+	0.832325i	$0.687009\pi$
$809$	−43.1525	+	31.3521i	−1.51716	+	1.10228i	−0.962873	+	0.269956i	$0.912991\pi$
$810$		0			0
$811$	−1.02786	+	3.16344i	−0.0360932	+	0.111083i	−0.967480	−	0.252948i	$-0.918600\pi$
$811$	−1.02786	+	3.16344i	−0.0360932	+	0.111083i	0.931387	+	0.364031i	$0.118600\pi$
$812$		0			0
$813$	11.3820			0.399183
$814$		0			0
$815$	−6.41641			−0.224757
$816$		0			0
$817$	0.517221	−	1.59184i	0.0180953	−	0.0556915i
$818$		0			0
$819$	0.809017	−	0.587785i	0.0282693	−	0.0205389i
$820$		0			0
$821$	4.36475	+	13.4333i	0.152331	+	0.468826i	0.997881	−	0.0650707i	$-0.0207273\pi$
$821$	4.36475	+	13.4333i	0.152331	+	0.468826i	−0.845550	+	0.533896i	$0.820727\pi$
$822$		0			0
$823$	17.8992	+	13.0045i	0.623926	+	0.453309i	0.854291	−	0.519795i	$-0.173992\pi$
$823$	17.8992	+	13.0045i	0.623926	+	0.453309i	−0.230364	+	0.973104i	$0.573992\pi$
$824$		0			0
$825$		0			0
$826$		0			0
$827$	−14.0344	−	10.1966i	−0.488025	−	0.354571i	0.316399	−	0.948626i	$-0.397526\pi$
$827$	−14.0344	−	10.1966i	−0.488025	−	0.354571i	−0.804424	+	0.594055i	$0.797526\pi$
$828$		0			0
$829$	−13.1180	−	40.3732i	−0.455608	−	1.40222i	−0.870420	−	0.492310i	$-0.836153\pi$
$829$	−13.1180	−	40.3732i	−0.455608	−	1.40222i	0.414812	−	0.909907i	$-0.363847\pi$
$830$		0			0
$831$	21.4894	−	15.6129i	0.745458	−	0.541607i
$832$		0			0
$833$	23.1803	−	71.3418i	0.803151	−	2.47185i
$834$		0			0
$835$	9.61803			0.332846
$836$		0			0
$837$	5.61803			0.194188
$838$		0			0
$839$	−13.7812	+	42.4140i	−0.475778	+	1.46429i	0.369127	+	0.929379i	$0.379657\pi$
$839$	−13.7812	+	42.4140i	−0.475778	+	1.46429i	−0.844905	+	0.534916i	$0.820343\pi$
$840$		0			0
$841$	20.2254	−	14.6946i	0.697428	−	0.506711i
$842$		0			0
$843$	1.29180	+	3.97574i	0.0444918	+	0.136932i
$844$		0			0
$845$	6.47214	+	4.70228i	0.222648	+	0.161763i
$846$		0			0
$847$		0			0
$848$		0			0
$849$	−5.38197	−	3.91023i	−0.184709	−	0.134199i
$850$		0			0
$851$	3.45492	+	10.6331i	0.118433	+	0.364499i
$852$		0			0
$853$	25.3713	−	18.4333i	0.868698	−	0.631146i	−0.0615396	−	0.998105i	$-0.519601\pi$
$853$	25.3713	−	18.4333i	0.868698	−	0.631146i	0.930237	+	0.366959i	$0.119601\pi$
$854$		0			0
$855$	0.0278640	−	0.0857567i	0.000952930	−	0.00293282i
$856$		0			0
$857$	6.81966			0.232955			0.116478	−	0.993193i	$-0.462840\pi$
$857$	6.81966			0.232955			0.116478	+	0.993193i	$0.462840\pi$
$858$		0			0
$859$	−17.8754			−0.609900			−0.304950	−	0.952368i	$-0.598640\pi$
$859$	−17.8754			−0.609900			−0.304950	+	0.952368i	$0.598640\pi$
$860$		0			0
$861$	−6.16312	+	18.9681i	−0.210039	+	0.646432i
$862$		0			0
$863$	−36.7426	+	26.6951i	−1.25073	+	0.908712i	−0.998264	−	0.0588932i	$-0.981243\pi$
$863$	−36.7426	+	26.6951i	−1.25073	+	0.908712i	−0.252470	+	0.967605i	$0.581243\pi$
$864$		0			0
$865$	−1.84752	−	5.68609i	−0.0628177	−	0.193333i
$866$		0			0
$867$	−24.2533	−	17.6210i	−0.823685	−	0.598442i
$868$		0			0
$869$		0			0
$870$		0			0
$871$	−1.26393	−	0.918300i	−0.0428267	−	0.0311154i
$872$		0			0
$873$	−4.33688	−	13.3475i	−0.146781	−	0.451746i
$874$		0			0
$875$	20.3713	−	14.8006i	0.688676	−	0.500353i
$876$		0			0
$877$	−15.5795	+	47.9489i	−0.526083	+	1.61912i	0.236081	+	0.971733i	$0.424137\pi$
$877$	−15.5795	+	47.9489i	−0.526083	+	1.61912i	−0.762164	+	0.647384i	$0.775863\pi$
$878$		0			0
$879$	−22.2361			−0.750004
$880$		0			0
$881$	−15.5066			−0.522430			−0.261215	−	0.965281i	$-0.584123\pi$
$881$	−15.5066			−0.522430			−0.261215	+	0.965281i	$0.584123\pi$
$882$		0			0
$883$	13.6738	−	42.0835i	0.460159	−	1.41622i	−0.404812	−	0.914400i	$-0.632663\pi$
$883$	13.6738	−	42.0835i	0.460159	−	1.41622i	0.864970	−	0.501823i	$-0.167337\pi$
$884$		0			0
$885$	6.39919	−	4.64928i	0.215106	−	0.156284i
$886$		0			0
$887$	11.5795	+	35.6381i	0.388802	+	1.19661i	0.933684	+	0.358098i	$0.116575\pi$
$887$	11.5795	+	35.6381i	0.388802	+	1.19661i	−0.544882	+	0.838513i	$0.683425\pi$
$888$		0			0
$889$	−40.1246	−	29.1522i	−1.34574	−	0.977735i
$890$		0			0
$891$		0			0
$892$		0			0
$893$	1.24671	+	0.905789i	0.0417196	+	0.0303111i
$894$		0			0
$895$	0.246711	+	0.759299i	0.00824664	+	0.0253806i
$896$		0			0
$897$	−0.954915	+	0.693786i	−0.0318837	+	0.0231649i
$898$		0			0
$899$	−3.47214	+	10.6861i	−0.115802	+	0.356403i
$900$		0			0
$901$	30.0344			1.00059
$902$		0			0
$903$	48.5967			1.61720
$904$		0			0
$905$	0.954915	−	2.93893i	0.0317424	−	0.0976932i
$906$		0			0
$907$	−23.6803	+	17.2048i	−0.786293	+	0.571275i	−0.906861	−	0.421430i	$-0.861528\pi$
$907$	−23.6803	+	17.2048i	−0.786293	+	0.571275i	0.120568	+	0.992705i	$0.461528\pi$
$908$		0			0
$909$	−3.63525	−	11.1882i	−0.120574	−	0.371088i
$910$		0			0
$911$	27.3713	+	19.8864i	0.906852	+	0.658867i	0.940217	−	0.340576i	$-0.110622\pi$
$911$	27.3713	+	19.8864i	0.906852	+	0.658867i	−0.0333645	+	0.999443i	$0.510622\pi$
$912$		0			0
$913$		0			0
$914$		0			0
$915$	−2.07295	−	1.50609i	−0.0685296	−	0.0497897i
$916$		0			0
$917$	11.5902	+	35.6709i	0.382741	+	1.17796i
$918$		0			0
$919$	−22.9894	+	16.7027i	−0.758349	+	0.550973i	−0.898403	−	0.439171i	$-0.855272\pi$
$919$	−22.9894	+	16.7027i	−0.758349	+	0.550973i	0.140055	+	0.990144i	$0.455272\pi$
$920$		0			0
$921$	−3.31966	+	10.2169i	−0.109387	+	0.336657i
$922$		0			0
$923$	−1.31308			−0.0432206
$924$		0			0
$925$	10.3262			0.339525
$926$		0			0
$927$	5.38197	−	16.5640i	0.176767	−	0.544033i
$928$		0			0
$929$	−3.04508	+	2.21238i	−0.0999060	+	0.0725860i	−0.636617	−	0.771180i	$-0.719667\pi$
$929$	−3.04508	+	2.21238i	−0.0999060	+	0.0725860i	0.536711	+	0.843766i	$0.319667\pi$
$930$		0			0
$931$	0.493422	+	1.51860i	0.0161713	+	0.0497700i
$932$		0			0
$933$	−10.8992	−	7.91872i	−0.356823	−	0.259247i
$934$		0			0
$935$		0			0
$936$		0			0
$937$	−19.1353	−	13.9026i	−0.625122	−	0.454177i	0.229585	−	0.973289i	$-0.426263\pi$
$937$	−19.1353	−	13.9026i	−0.625122	−	0.454177i	−0.854707	+	0.519111i	$0.826263\pi$
$938$		0			0
$939$	−5.07295	−	15.6129i	−0.165549	−	0.509509i
$940$		0			0
$941$	−4.78115	+	3.47371i	−0.155861	+	0.113240i	−0.662982	−	0.748635i	$-0.730710\pi$
$941$	−4.78115	+	3.47371i	−0.155861	+	0.113240i	0.507121	+	0.861875i	$0.330710\pi$
$942$		0			0
$943$	7.27458	−	22.3888i	0.236893	−	0.729081i
$944$		0			0
$945$	2.61803			0.0851647
$946$		0			0
$947$	31.9230			1.03736			0.518679	−	0.854969i	$-0.326424\pi$
$947$	31.9230			1.03736			0.518679	+	0.854969i	$0.326424\pi$
$948$		0			0
$949$	−0.167184	+	0.514540i	−0.00542703	+	0.0167027i
$950$		0			0
$951$	17.6074	−	12.7925i	0.570959	−	0.414826i
$952$		0			0
$953$	11.6869	+	35.9686i	0.378576	+	1.16514i	0.941034	+	0.338312i	$0.109856\pi$
$953$	11.6869	+	35.9686i	0.378576	+	1.16514i	−0.562458	+	0.826826i	$0.690144\pi$
$954$		0			0
$955$	6.73607	+	4.89404i	0.217974	+	0.158367i
$956$		0			0
$957$		0			0
$958$		0			0
$959$	33.4615	+	24.3112i	1.08053	+	0.785050i
$960$		0			0
$961$	0.173762	+	0.534785i	0.00560523	+	0.0172511i
$962$		0			0
$963$	12.6631	−	9.20029i	0.408063	−	0.296475i
$964$		0			0
$965$	−3.39919	+	10.4616i	−0.109424	+	0.336772i
$966$		0			0
$967$	23.1591			0.744745			0.372372	−	0.928083i	$-0.378544\pi$
$967$	23.1591			0.744745			0.372372	+	0.928083i	$0.378544\pi$
$968$		0			0
$969$	1.00000			0.0321246
$970$		0			0
$971$	−10.9787	+	33.7890i	−0.352324	+	1.08434i	0.605221	+	0.796057i	$0.293085\pi$
$971$	−10.9787	+	33.7890i	−0.352324	+	1.08434i	−0.957545	+	0.288284i	$0.906915\pi$
$972$		0			0
$973$	−29.3435	+	21.3193i	−0.940708	+	0.683464i
$974$		0			0
$975$	0.336881	+	1.03681i	0.0107888	+	0.0332046i
$976$		0			0
$977$	34.9336	+	25.3808i	1.11763	+	0.812003i	0.983848	−	0.179009i	$-0.0572890\pi$
$977$	34.9336	+	25.3808i	1.11763	+	0.812003i	0.133778	+	0.991011i	$0.457289\pi$
$978$		0			0
$979$		0			0
$980$		0			0
$981$	−7.23607	−	5.25731i	−0.231030	−	0.167853i
$982$		0			0
$983$	9.38197	+	28.8747i	0.299238	+	0.920961i	0.981765	+	0.190100i	$0.0608812\pi$
$983$	9.38197	+	28.8747i	0.299238	+	0.920961i	−0.682527	+	0.730861i	$0.739119\pi$
$984$		0			0
$985$	9.66312	−	7.02067i	0.307893	−	0.223697i
$986$		0			0
$987$	−13.8262	+	42.5528i	−0.440094	+	1.35447i
$988$		0			0
$989$	−57.3607			−1.82396
$990$		0			0
$991$	39.8541			1.26601			0.633004	−	0.774149i	$-0.281822\pi$
$991$	39.8541			1.26601			0.633004	+	0.774149i	$0.281822\pi$
$992$		0			0
$993$	−1.83688	+	5.65334i	−0.0582917	+	0.179403i
$994$		0			0
$995$	−0.0278640	+	0.0202444i	−0.000883350	+	0.000641791i
$996$		0			0
$997$	7.24671	+	22.3031i	0.229506	+	0.706346i	0.997803	+	0.0662525i	$0.0211043\pi$
$997$	7.24671	+	22.3031i	0.229506	+	0.706346i	−0.768297	+	0.640093i	$0.778896\pi$
$998$		0			0
$999$	1.80902	+	1.31433i	0.0572348	+	0.0415835i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1452.2.i.f.565.1		4
11.2	odd	10		132.2.i.a.49.1	✓	4
11.3	even	5	inner	1452.2.i.f.1213.1		4
11.4	even	5		1452.2.i.g.493.1		4
11.5	even	5		1452.2.a.m.1.2		2
11.6	odd	10		1452.2.a.l.1.2		2
11.7	odd	10		132.2.i.a.97.1	yes	4
11.8	odd	10		1452.2.i.c.1213.1		4
11.9	even	5		1452.2.i.g.1237.1		4
11.10	odd	2		1452.2.i.c.565.1		4
33.2	even	10		396.2.j.b.181.1		4
33.5	odd	10		4356.2.a.w.1.1		2
33.17	even	10		4356.2.a.r.1.1		2
33.29	even	10		396.2.j.b.361.1		4
44.7	even	10		528.2.y.i.97.1		4
44.27	odd	10		5808.2.a.bn.1.2		2
44.35	even	10		528.2.y.i.49.1		4
44.39	even	10		5808.2.a.bq.1.2		2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
132.2.i.a.49.1	✓	4	11.2	odd	10
132.2.i.a.97.1	yes	4	11.7	odd	10
396.2.j.b.181.1		4	33.2	even	10
396.2.j.b.361.1		4	33.29	even	10
528.2.y.i.49.1		4	44.35	even	10
528.2.y.i.97.1		4	44.7	even	10
1452.2.a.l.1.2		2	11.6	odd	10
1452.2.a.m.1.2		2	11.5	even	5
1452.2.i.c.565.1		4	11.10	odd	2
1452.2.i.c.1213.1		4	11.8	odd	10
1452.2.i.f.565.1		4	1.1	even	1	trivial
1452.2.i.f.1213.1		4	11.3	even	5	inner
1452.2.i.g.493.1		4	11.4	even	5
1452.2.i.g.1237.1		4	11.9	even	5
4356.2.a.r.1.1		2	33.17	even	10
4356.2.a.w.1.1		2	33.5	odd	10
5808.2.a.bn.1.2		2	44.27	odd	10
5808.2.a.bq.1.2		2	44.39	even	10

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 1452 = 2^{2} \cdot 3 \cdot 11^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1452.i (of order \(5\), degree \(4\), not minimal)

\(f(q)\)	\(=\)	\(q+(0.309017 - 0.951057i) q^{3} +(-0.500000 + 0.363271i) q^{5} +(1.30902 + 4.02874i) q^{7} +(-0.809017 - 0.587785i) q^{9} +(0.190983 + 0.138757i) q^{13} +(0.190983 + 0.587785i) q^{15} +(-5.54508 + 4.02874i) q^{17} +(0.0450850 - 0.138757i) q^{19} +4.23607 q^{21} -5.00000 q^{23} +(-1.42705 + 4.39201i) q^{25} +(-0.809017 + 0.587785i) q^{27} +(-0.618034 - 1.90211i) q^{29} +(-4.54508 - 3.30220i) q^{31} +(-2.11803 - 1.53884i) q^{35} +(-0.690983 - 2.12663i) q^{37} +(0.190983 - 0.138757i) q^{39} +(-1.45492 + 4.47777i) q^{41} +11.4721 q^{43} +0.618034 q^{45} +(-3.26393 + 10.0453i) q^{47} +(-8.85410 + 6.43288i) q^{49} +(2.11803 + 6.51864i) q^{51} +(-3.54508 - 2.57565i) q^{53} +(-0.118034 - 0.0857567i) q^{57} +(-3.95492 - 12.1720i) q^{59} +(-3.35410 + 2.43690i) q^{61} +(1.30902 - 4.02874i) q^{63} -0.145898 q^{65} -6.61803 q^{67} +(-1.54508 + 4.75528i) q^{69} +(-4.50000 + 3.26944i) q^{71} +(0.708204 + 2.17963i) q^{73} +(3.73607 + 2.71441i) q^{75} +(3.80902 + 2.76741i) q^{79} +(0.309017 + 0.951057i) q^{81} +(-5.04508 + 3.66547i) q^{83} +(1.30902 - 4.02874i) q^{85} -2.00000 q^{87} +17.1803 q^{89} +(-0.309017 + 0.951057i) q^{91} +(-4.54508 + 3.30220i) q^{93} +(0.0278640 + 0.0857567i) q^{95} +(11.3541 + 8.24924i) q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q - q^{3} - 2 q^{5} + 3 q^{7} - q^{9} + 3 q^{13} + 3 q^{15} - 11 q^{17} - 11 q^{19} + 8 q^{21} - 20 q^{23} + q^{25} - q^{27} + 2 q^{29} - 7 q^{31} - 4 q^{35} - 5 q^{37} + 3 q^{39} - 17 q^{41} + 28 q^{43}+ \cdots + 32 q^{97}+O(q^{100}) \) 4 * q - q^3 - 2 * q^5 + 3 * q^7 - q^9 + 3 * q^13 + 3 * q^15 - 11 * q^17 - 11 * q^19 + 8 * q^21 - 20 * q^23 + q^25 - q^27 + 2 * q^29 - 7 * q^31 - 4 * q^35 - 5 * q^37 + 3 * q^39 - 17 * q^41 + 28 * q^43 - 2 * q^45 - 22 * q^47 - 22 * q^49 + 4 * q^51 - 3 * q^53 + 4 * q^57 - 27 * q^59 + 3 * q^63 - 14 * q^65 - 22 * q^67 + 5 * q^69 - 18 * q^71 - 24 * q^73 + 6 * q^75 + 13 * q^79 - q^81 - 9 * q^83 + 3 * q^85 - 8 * q^87 + 24 * q^89 + q^91 - 7 * q^93 + 18 * q^95 + 32 * q^97

Introduction

L-functions

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