LMFDB - Embedded newform 845.2.n.g.484.4

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [845,2,Mod(484,845)] 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("845.484"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(845, base_ring=CyclotomicField(6)) chi = DirichletCharacter(H, H._module([3, 2])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 845 = 5 \cdot 13^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	845.n (of order $6$, degree $2$, not minimal)

Newform invariants

comment:select newform

sage:traces = [12,0,0,10,0,4] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(6)] == traces)

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

Self dual:	no
Analytic conductor:	$6.74735897080$
Analytic rank:	$0$
Dimension:	$12$
Relative dimension:	$6$ over $\Q(\zeta_{6})$
Coefficient field:	12.0.89539436150784.1
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{12} - 2x^{11} + 2x^{10} - 8x^{9} + 4x^{8} + 16x^{7} - 8x^{6} + 20x^{5} + 20x^{4} - 24x^{3} + 8x^{2} - 8x + 4 $ x^12 - 2x^11 + 2x^10 - 8x^9 + 4x^8 + 16x^7 - 8x^6 + 20x^5 + 20x^4 - 24x^3 + 8x^2 - 8*x + 4
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 2^{2} $
Twist minimal:	no (minimal twist has level 65)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			484.4
Root			$1.98293 + 0.531325i$ of defining polynomial
Character	$\chi$	$=$	845.484
Dual form			845.2.n.g.529.4

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(1.05163 - 0.607160i) q^{2} +(-1.13545 + 0.655554i) q^{3} +(-0.262714 + 0.455034i) q^{4} +(2.21432 - 0.311108i) q^{5} +(-0.796052 + 1.37880i) q^{6} +(2.51426 + 1.45161i) q^{7} +3.06668i q^{8} +(-0.640498 + 1.10938i) q^{9} +(2.13976 - 1.67162i) q^{10} +(0.107160 + 0.185606i) q^{11} -0.688892i q^{12} +3.52543 q^{14} +(-2.31031 + 1.80485i) q^{15} +(1.33654 + 2.31495i) q^{16} +(-5.56737 - 3.21432i) q^{17} +1.55554i q^{18} +(-1.10716 + 1.91766i) q^{19} +(-0.440168 + 1.08932i) q^{20} -3.80642 q^{21} +(0.225385 + 0.130126i) q^{22} +(-4.06070 + 2.34445i) q^{23} +(-2.01037 - 3.48207i) q^{24} +(4.80642 - 1.37778i) q^{25} -5.61285i q^{27} +(-1.32106 + 0.762714i) q^{28} +(4.35482 + 7.54277i) q^{29} +(-1.33376 + 3.30077i) q^{30} +5.59210 q^{31} +(-2.50055 - 1.44370i) q^{32} +(-0.243350 - 0.140498i) q^{33} -7.80642 q^{34} +(6.01897 + 2.43212i) q^{35} +(-0.336535 - 0.582896i) q^{36} +(-1.97540 + 1.14050i) q^{37} +2.68889i q^{38} +(0.954067 + 6.79060i) q^{40} +(1.52543 + 2.64212i) q^{41} +(-4.00296 + 2.31111i) q^{42} +(5.50962 + 3.18098i) q^{43} -0.112610 q^{44} +(-1.07313 + 2.65578i) q^{45} +(-2.84691 + 4.93099i) q^{46} -1.09679i q^{47} +(-3.03515 - 1.75234i) q^{48} +(0.714320 + 1.23724i) q^{49} +(4.21805 - 4.36719i) q^{50} +8.42864 q^{51} +6.23506i q^{53} +(-3.40790 - 5.90265i) q^{54} +(0.295030 + 0.377654i) q^{55} +(-4.45161 + 7.71041i) q^{56} -2.90321i q^{57} +(9.15933 + 5.28814i) q^{58} +(4.63259 - 8.02388i) q^{59} +(-0.214320 - 1.52543i) q^{60} +(0.140498 - 0.243350i) q^{61} +(5.88083 - 3.39530i) q^{62} +(-3.22075 + 1.85950i) q^{63} -8.85236 q^{64} -0.341219 q^{66} +(6.72078 - 3.88025i) q^{67} +(2.92525 - 1.68889i) q^{68} +(3.07382 - 5.32402i) q^{69} +(7.80642 - 1.09679i) q^{70} +(-3.04048 + 5.26627i) q^{71} +(-3.40210 - 1.96420i) q^{72} -10.2810i q^{73} +(-1.38493 + 2.39877i) q^{74} +(-4.55425 + 4.71528i) q^{75} +(-0.581732 - 1.00759i) q^{76} +0.622216i q^{77} +14.2351 q^{79} +(3.67971 + 4.71023i) q^{80} +(1.75803 + 3.04500i) q^{81} +(3.20838 + 1.85236i) q^{82} +9.52543i q^{83} +(1.00000 - 1.73205i) q^{84} +(-13.3279 - 5.38548i) q^{85} +7.72546 q^{86} +(-9.88938 - 5.70964i) q^{87} +(-0.569195 + 0.328625i) q^{88} +(2.80642 + 4.86087i) q^{89} +(0.483940 + 3.44446i) q^{90} -2.46367i q^{92} +(-6.34957 + 3.66593i) q^{93} +(-0.665926 - 1.15342i) q^{94} +(-1.85501 + 4.59075i) q^{95} +3.78568 q^{96} +(-15.6244 - 9.02074i) q^{97} +(1.50240 + 0.867413i) q^{98} -0.274543 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q + 10 q^{4} + 4 q^{6} + 6 q^{9} - 2 q^{10} - 12 q^{11} + 16 q^{14} + 16 q^{15} - 10 q^{16} - 20 q^{20} + 8 q^{21} + 16 q^{24} + 4 q^{25} + 12 q^{29} - 8 q^{30} + 40 q^{31} - 40 q^{34} - 8 q^{35} + 22 q^{36}+ \cdots - 32 q^{99}+O(q^{100}) $ 12 * q + 10 * q^4 + 4 * q^6 + 6 * q^9 - 2 * q^10 - 12 * q^11 + 16 * q^14 + 16 * q^15 - 10 * q^16 - 20 * q^20 + 8 * q^21 + 16 * q^24 + 4 * q^25 + 12 * q^29 - 8 * q^30 + 40 * q^31 - 40 * q^34 - 8 * q^35 + 22 * q^36 - 68 * q^40 - 8 * q^41 - 80 * q^44 - 4 * q^45 + 32 * q^46 - 18 * q^49 + 16 * q^50 + 48 * q^51 - 68 * q^54 + 16 * q^55 - 40 * q^56 + 16 * q^59 + 24 * q^60 - 12 * q^61 - 132 * q^64 - 32 * q^66 + 24 * q^69 + 40 * q^70 - 24 * q^71 - 4 * q^74 - 16 * q^75 - 20 * q^76 + 64 * q^79 + 48 * q^80 - 46 * q^81 + 12 * q^84 - 12 * q^85 + 64 * q^86 - 20 * q^89 + 140 * q^90 + 32 * q^94 - 16 * q^95 + 72 * q^96 - 32 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/845\mathbb{Z}\right)^\times$.

$n$	$171$	$677$
$\chi(n)$	$e\left(\frac{1}{3}\right)$	$-1$

Coefficient data

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

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

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

$2$	1.05163	−	0.607160i	0.743616	−	0.429327i	−0.0797666	−	0.996814i	$-0.525418\pi$
$2$	1.05163	−	0.607160i	0.743616	−	0.429327i	0.823383	+	0.567487i	$0.192084\pi$
$3$	−1.13545	+	0.655554i	−0.655554	+	0.378484i	−0.790581	−	0.612358i	$-0.790221\pi$
$3$	−1.13545	+	0.655554i	−0.655554	+	0.378484i	0.135027	+	0.990842i	$0.456888\pi$
$4$	−0.262714	+	0.455034i	−0.131357	+	0.227517i
$5$	2.21432	−	0.311108i	0.990274	−	0.139132i
$5$	2.21432	−	0.311108i	0.990274	−	0.139132i
$6$	−0.796052	+	1.37880i	−0.324987	+	0.562894i
$7$	2.51426	+	1.45161i	0.950299	+	0.548655i	0.893174	−	0.449712i	$-0.148473\pi$
$7$	2.51426	+	1.45161i	0.950299	+	0.548655i	0.0571253	+	0.998367i	$0.481807\pi$
$8$			3.06668i			1.08423i
$9$	−0.640498	+	1.10938i	−0.213499	+	0.369792i
$10$	2.13976	−	1.67162i	0.676650	−	0.528612i
$11$	0.107160	+	0.185606i	0.0323099	+	0.0559624i	0.881728	−	0.471758i	$-0.156380\pi$
$11$	0.107160	+	0.185606i	0.0323099	+	0.0559624i	−0.849418	+	0.527720i	$0.823047\pi$
$12$		−	0.688892i		−	0.198866i
$13$		0			0
$13$		0			0
$14$	3.52543			0.942210
$15$	−2.31031	+	1.80485i	−0.596519	+	0.466011i
$16$	1.33654	+	2.31495i	0.334134	+	0.578737i
$17$	−5.56737	−	3.21432i	−1.35028	−	0.779587i	−0.361995	−	0.932180i	$-0.617904\pi$
$17$	−5.56737	−	3.21432i	−1.35028	−	0.779587i	−0.988289	+	0.152593i	$0.951238\pi$
$18$			1.55554i			0.366644i
$19$	−1.10716	+	1.91766i	−0.254000	+	0.439941i	−0.964623	−	0.263632i	$-0.915080\pi$
$19$	−1.10716	+	1.91766i	−0.254000	+	0.439941i	0.710624	+	0.703572i	$0.248413\pi$
$20$	−0.440168	+	1.08932i	−0.0984245	+	0.243580i
$21$	−3.80642			−0.830630
$22$	0.225385	+	0.130126i	0.0480523	+	0.0277430i
$23$	−4.06070	+	2.34445i	−0.846714	+	0.488851i	−0.859541	−	0.511067i	$-0.829250\pi$
$23$	−4.06070	+	2.34445i	−0.846714	+	0.488851i	0.0128265	+	0.999918i	$0.495917\pi$
$24$	−2.01037	−	3.48207i	−0.410365	−	0.710774i
$25$	4.80642	−	1.37778i	0.961285	−	0.275557i
$26$		0			0
$27$		−	5.61285i		−	1.08019i
$28$	−1.32106	+	0.762714i	−0.249657	+	0.144139i
$29$	4.35482	+	7.54277i	0.808669	+	1.40066i	0.913786	+	0.406197i	$0.133145\pi$
$29$	4.35482	+	7.54277i	0.808669	+	1.40066i	−0.105116	+	0.994460i	$0.533522\pi$
$30$	−1.33376	+	3.30077i	−0.243510	+	0.602635i
$31$	5.59210			1.00437			0.502186	−	0.864760i	$-0.332529\pi$
$31$	5.59210			1.00437			0.502186	+	0.864760i	$0.332529\pi$
$32$	−2.50055	−	1.44370i	−0.442040	−	0.255212i
$33$	−0.243350	−	0.140498i	−0.0423618	−	0.0244576i
$34$	−7.80642			−1.33879
$35$	6.01897	+	2.43212i	1.01739	+	0.411103i
$36$	−0.336535	−	0.582896i	−0.0560892	−	0.0971494i
$37$	−1.97540	+	1.14050i	−0.324754	+	0.187497i	−0.653510	−	0.756918i	$-0.726704\pi$
$37$	−1.97540	+	1.14050i	−0.324754	+	0.187497i	0.328756	+	0.944415i	$0.393371\pi$
$38$			2.68889i			0.436196i
$39$		0			0
$40$	0.954067	+	6.79060i	0.150851	+	1.07369i
$41$	1.52543	+	2.64212i	0.238232	+	0.412630i	0.960207	−	0.279289i	$-0.0900989\pi$
$41$	1.52543	+	2.64212i	0.238232	+	0.412630i	−0.721975	+	0.691919i	$0.756766\pi$
$42$	−4.00296	+	2.31111i	−0.617670	+	0.356612i
$43$	5.50962	+	3.18098i	0.840209	+	0.485095i	0.857335	−	0.514758i	$-0.172118\pi$
$43$	5.50962	+	3.18098i	0.840209	+	0.485095i	−0.0171260	+	0.999853i	$0.505452\pi$
$44$	−0.112610			−0.0169765
$45$	−1.07313	+	2.65578i	−0.159973	+	0.395900i
$46$	−2.84691	+	4.93099i	−0.419754	+	0.727034i
$47$		−	1.09679i		−	0.159983i	−0.996796	−	0.0799915i	$-0.974511\pi$
$47$		−	1.09679i		−	0.159983i	0.996796	−	0.0799915i	$-0.0254893\pi$
$48$	−3.03515	−	1.75234i	−0.438085	−	0.252929i
$49$	0.714320	+	1.23724i	0.102046	+	0.176748i
$50$	4.21805	−	4.36719i	0.596523	−	0.617614i
$51$	8.42864			1.18025
$52$		0			0
$53$			6.23506i			0.856452i	0.903672	+	0.428226i	$0.140861\pi$
$53$			6.23506i			0.856452i	−0.903672	+	0.428226i	$0.859139\pi$
$54$	−3.40790	−	5.90265i	−0.463756	−	0.803249i
$55$	0.295030	+	0.377654i	0.0397818	+	0.0509228i
$56$	−4.45161	+	7.71041i	−0.594871	+	1.03035i
$57$		−	2.90321i		−	0.384540i
$58$	9.15933	+	5.28814i	1.20268	+	0.694367i
$59$	4.63259	−	8.02388i	0.603112	−	1.04462i	−0.389235	−	0.921138i	$-0.627261\pi$
$59$	4.63259	−	8.02388i	0.603112	−	1.04462i	0.992347	−	0.123481i	$-0.0394059\pi$
$60$	−0.214320	−	1.52543i	−0.0276686	−	0.196932i
$61$	0.140498	−	0.243350i	0.0179889	−	0.0311578i	−0.856891	−	0.515498i	$-0.827607\pi$
$61$	0.140498	−	0.243350i	0.0179889	−	0.0311578i	0.874880	+	0.484340i	$0.160940\pi$
$62$	5.88083	−	3.39530i	0.746867	−	0.431204i
$63$	−3.22075	+	1.85950i	−0.405777	+	0.234275i
$64$	−8.85236			−1.10654
$65$		0			0
$66$	−0.341219			−0.0420012
$67$	6.72078	−	3.88025i	0.821074	−	0.474047i	−0.0297125	−	0.999558i	$-0.509459\pi$
$67$	6.72078	−	3.88025i	0.821074	−	0.474047i	0.850787	+	0.525511i	$0.176126\pi$
$68$	2.92525	−	1.68889i	0.354738	−	0.204808i
$69$	3.07382	−	5.32402i	0.370045	−	0.640936i
$70$	7.80642	−	1.09679i	0.933046	−	0.131091i
$71$	−3.04048	+	5.26627i	−0.360839	+	0.624991i	−0.988099	−	0.153818i	$-0.950843\pi$
$71$	−3.04048	+	5.26627i	−0.360839	+	0.624991i	0.627260	+	0.778810i	$0.284176\pi$
$72$	−3.40210	−	1.96420i	−0.400941	−	0.231483i
$73$		−	10.2810i		−	1.20330i	−0.798760	−	0.601650i	$-0.794510\pi$
$73$		−	10.2810i		−	1.20330i	0.798760	−	0.601650i	$-0.205490\pi$
$74$	−1.38493	+	2.39877i	−0.160995	+	0.278851i
$75$	−4.55425	+	4.71528i	−0.525880	+	0.544474i
$76$	−0.581732	−	1.00759i	−0.0667293	−	0.115578i
$77$			0.622216i			0.0709081i
$78$		0			0
$79$	14.2351			1.60157			0.800785	−	0.598952i	$-0.204416\pi$
$79$	14.2351			1.60157			0.800785	+	0.598952i	$0.204416\pi$
$80$	3.67971	+	4.71023i	0.411405	+	0.526619i
$81$	1.75803	+	3.04500i	0.195337	+	0.338333i
$82$	3.20838	+	1.85236i	0.354306	+	0.204559i
$83$			9.52543i			1.04555i	0.852470	+	0.522776i	$0.175103\pi$
$83$			9.52543i			1.04555i	−0.852470	+	0.522776i	$0.824897\pi$
$84$	1.00000	−	1.73205i	0.109109	−	0.188982i
$85$	−13.3279	−	5.38548i	−1.44562	−	0.584137i
$86$	7.72546			0.833057
$87$	−9.88938	−	5.70964i	−1.06025	−	0.612137i
$88$	−0.569195	+	0.328625i	−0.0606764	+	0.0350315i
$89$	2.80642	+	4.86087i	0.297480	+	0.515251i	0.975559	−	0.219738i	$-0.0705204\pi$
$89$	2.80642	+	4.86087i	0.297480	+	0.515251i	−0.678078	+	0.734989i	$0.737187\pi$
$90$	0.483940	+	3.44446i	0.0510118	+	0.363078i
$91$		0			0
$92$		−	2.46367i		−	0.256856i
$93$	−6.34957	+	3.66593i	−0.658420	+	0.380139i
$94$	−0.665926	−	1.15342i	−0.0686850	−	0.118966i
$95$	−1.85501	+	4.59075i	−0.190320	+	0.471001i
$96$	3.78568			0.386374
$97$	−15.6244	−	9.02074i	−1.58642	−	0.915918i	−0.993891	−	0.110366i	$-0.964798\pi$
$97$	−15.6244	−	9.02074i	−1.58642	−	0.915918i	−0.592525	−	0.805552i	$-0.701869\pi$
$98$	1.50240	+	0.867413i	0.151766	+	0.0876219i
$99$	−0.274543			−0.0275926
$100$	−0.635776	+	2.54905i	−0.0635776	+	0.254905i
$101$	−1.96989	−	3.41195i	−0.196011	−	0.339501i	0.751220	−	0.660052i	$-0.229466\pi$
$101$	−1.96989	−	3.41195i	−0.196011	−	0.339501i	−0.947232	+	0.320550i	$0.896132\pi$
$102$	8.86382	−	5.11753i	0.877649	−	0.506711i
$103$		−	2.82225i		−	0.278084i	−0.990286	−	0.139042i	$-0.955598\pi$
$103$		−	2.82225i		−	0.278084i	0.990286	−	0.139042i	$-0.0444023\pi$
$104$		0			0
$105$	−8.42864	+	1.18421i	−0.822551	+	0.115567i
$106$	3.78568	+	6.55699i	0.367698	+	0.636871i
$107$	14.8242	−	8.55877i	1.43311	−	0.827407i	0.435754	−	0.900066i	$-0.356482\pi$
$107$	14.8242	−	8.55877i	1.43311	−	0.827407i	0.997357	+	0.0726585i	$0.0231483\pi$
$108$	2.55403	+	1.47457i	0.245762	+	0.141891i
$109$	−16.7239			−1.60186			−0.800931	−	0.598757i	$-0.795662\pi$
$109$	−16.7239			−1.60186			−0.800931	+	0.598757i	$0.795662\pi$
$110$	0.539559	+	0.218022i	0.0514449	+	0.0207876i
$111$	1.49532	−	2.58996i	0.141929	−	0.245828i
$112$			7.76049i			0.733297i
$113$	1.02555	+	0.592104i	0.0964760	+	0.0557005i	0.547462	−	0.836831i	$-0.315594\pi$
$113$	1.02555	+	0.592104i	0.0964760	+	0.0557005i	−0.450986	+	0.892531i	$0.648927\pi$
$114$	−1.76271	−	3.05311i	−0.165093	−	0.285950i
$115$	−8.26231	+	6.45467i	−0.770465	+	0.601901i
$116$	−4.57628			−0.424897
$117$		0			0
$118$		−	11.2509i		−	1.03573i
$119$	−9.33185	−	16.1632i	−0.855449	−	1.48168i
$120$	−5.53490	−	7.08497i	−0.505265	−	0.646766i
$121$	5.47703	−	9.48650i	0.497912	−	0.862409i
$122$		−	0.341219i		−	0.0308925i
$123$	−3.46410	−	2.00000i	−0.312348	−	0.180334i
$124$	−1.46912	+	2.54460i	−0.131931	+	0.228511i
$125$	10.2143	−	4.54617i	0.913597	−	0.406622i
$126$	−2.25803	+	3.91102i	−0.201161	+	0.348422i
$127$	1.99337	−	1.15087i	0.176883	−	0.102123i	−0.408945	−	0.912559i	$-0.634103\pi$
$127$	1.99337	−	1.15087i	0.176883	−	0.102123i	0.585827	+	0.810436i	$0.300770\pi$
$128$	−4.30831	+	2.48741i	−0.380805	+	0.219858i
$129$	−8.34122			−0.734403
$130$		0			0
$131$	−13.4193			−1.17245			−0.586224	−	0.810149i	$-0.699386\pi$
$131$	−13.4193			−1.17245			−0.586224	+	0.810149i	$0.699386\pi$
$132$	0.127863	−	0.0738216i	0.0111290	−	0.00642535i
$133$	−5.56737	+	3.21432i	−0.482752	+	0.278717i
$134$	4.71186	−	8.16118i	0.407043	−	0.705018i
$135$	−1.74620	−	12.4286i	−0.150289	−	1.06969i
$136$	9.85728	−	17.0733i	0.845255	−	1.46402i
$137$	16.5866	+	9.57628i	1.41709	+	0.818157i	0.996042	−	0.0888816i	$-0.0283293\pi$
$137$	16.5866	+	9.57628i	1.41709	+	0.818157i	0.421047	+	0.907039i	$0.361663\pi$
$138$		−	7.46520i		−	0.635480i
$139$	9.54617	−	16.5345i	0.809696	−	1.40243i	−0.103379	−	0.994642i	$-0.532966\pi$
$139$	9.54617	−	16.5345i	0.809696	−	1.40243i	0.913075	−	0.407792i	$-0.133701\pi$
$140$	−2.68796	+	2.09988i	−0.227174	+	0.177473i
$141$	0.719004	+	1.24535i	0.0605510	+	0.104877i
$142$			7.38424i			0.619671i
$143$		0			0
$144$	−3.42419			−0.285349
$145$	11.9896	+	15.3473i	0.995680	+	1.27452i
$146$	−6.24221	−	10.8118i	−0.516609	−	0.894793i
$147$	−1.62215	−	0.936550i	−0.133793	−	0.0772454i
$148$		−	1.19850i		−	0.0985160i
$149$	1.78568	−	3.09289i	0.146289	−	0.253379i	−0.783564	−	0.621311i	$-0.786601\pi$
$149$	1.78568	−	3.09289i	0.146289	−	0.253379i	0.929853	+	0.367931i	$0.119934\pi$
$150$	−1.92647	+	7.72390i	−0.157296	+	0.630654i
$151$	1.26517			0.102958			0.0514792	−	0.998674i	$-0.483606\pi$
$151$	1.26517			0.102958			0.0514792	+	0.998674i	$0.483606\pi$
$152$	−5.88083	−	3.39530i	−0.476999	−	0.275395i
$153$	7.13177	−	4.11753i	0.576570	−	0.332883i
$154$	0.377784	+	0.654342i	0.0304427	+	0.0527284i
$155$	12.3827	−	1.73975i	0.994603	−	0.139740i
$156$		0			0
$157$		−	5.61285i		−	0.447954i	−0.974594	−	0.223977i	$-0.928096\pi$
$157$		−	5.61285i		−	0.447954i	0.974594	−	0.223977i	$-0.0719041\pi$
$158$	14.9700	−	8.64296i	1.19095	−	0.687597i
$159$	−4.08742	−	7.07962i	−0.324154	−	0.561450i
$160$	−5.98617	−	2.41886i	−0.473248	−	0.191228i
$161$	−13.6128			−1.07284
$162$	3.69760	+	2.13481i	0.290511	+	0.167727i
$163$	−3.22075	−	1.85950i	−0.252269	−	0.145647i	0.368534	−	0.929614i	$-0.379860\pi$
$163$	−3.22075	−	1.85950i	−0.252269	−	0.145647i	−0.620803	+	0.783967i	$0.713193\pi$
$164$	−1.60300			−0.125174
$165$	−0.582565	−	0.235400i	−0.0453526	−	0.0183258i
$166$	5.78346	+	10.0172i	0.448883	+	0.777489i
$167$	6.09384	−	3.51828i	0.471556	−	0.272253i	−0.245335	−	0.969438i	$-0.578898\pi$
$167$	6.09384	−	3.51828i	0.471556	−	0.272253i	0.716891	+	0.697185i	$0.245565\pi$
$168$		−	11.6731i		−	0.900597i
$169$		0			0
$170$	−17.2859	+	2.42864i	−1.32577	+	0.186268i
$171$	−1.41827	−	2.45651i	−0.108458	−	0.187854i
$172$	−2.89491	+	1.67138i	−0.220735	+	0.127441i
$173$	0.626938	+	0.361963i	0.0476652	+	0.0275195i	0.523643	−	0.851938i	$-0.324572\pi$
$173$	0.626938	+	0.361963i	0.0476652	+	0.0275195i	−0.475978	+	0.879457i	$0.657906\pi$
$174$	−13.8666			−1.05123
$175$	14.0846	+	3.51293i	1.06469	+	0.265553i
$176$	−0.286446	+	0.496139i	−0.0215917	+	0.0373979i
$177$			12.1476i			0.913073i
$178$	5.90265	+	3.40790i	0.442422	+	0.255433i
$179$	−2.02074	−	3.50003i	−0.151037	−	0.261605i	0.780572	−	0.625066i	$-0.214928\pi$
$179$	−2.02074	−	3.50003i	−0.151037	−	0.261605i	−0.931609	+	0.363462i	$0.881595\pi$
$180$	−0.926541	−	1.18602i	−0.0690603	−	0.0884007i
$181$	2.34122			0.174021			0.0870107	−	0.996207i	$-0.472269\pi$
$181$	2.34122			0.174021			0.0870107	+	0.996207i	$0.472269\pi$
$182$		0			0
$183$			0.368416i			0.0272341i
$184$	−7.18966	−	12.4529i	−0.530029	−	0.918036i
$185$	−4.01935	+	3.13999i	−0.295509	+	0.230857i
$186$	−4.45161	+	7.71041i	−0.326408	+	0.565355i
$187$		−	1.37778i		−	0.100754i
$188$	0.499075	+	0.288141i	0.0363988	+	0.0210149i
$189$	8.14764	−	14.1121i	0.592654	−	1.02651i
$190$	0.836535	+	5.95407i	0.0606887	+	0.431953i
$191$	1.05086	−	1.82013i	0.0760372	−	0.131700i	−0.825500	−	0.564403i	$-0.809107\pi$
$191$	1.05086	−	1.82013i	0.0760372	−	0.131700i	0.901537	+	0.432702i	$0.142440\pi$
$192$	10.0514	−	5.80320i	0.725400	−	0.418810i
$193$	11.7095	−	6.76049i	0.842869	−	0.486631i	−0.0153692	−	0.999882i	$-0.504892\pi$
$193$	11.7095	−	6.76049i	0.842869	−	0.486631i	0.858238	+	0.513251i	$0.171559\pi$
$194$	−21.9081			−1.57291
$195$		0			0
$196$	−0.750647			−0.0536176
$197$	−1.73205	+	1.00000i	−0.123404	+	0.0712470i	−0.560431	−	0.828201i	$-0.689365\pi$
$197$	−1.73205	+	1.00000i	−0.123404	+	0.0712470i	0.437028	+	0.899448i	$0.356031\pi$
$198$	−0.288718	+	0.166691i	−0.0205183	+	0.0118462i
$199$	11.0716	−	19.1766i	0.784845	−	1.35939i	−0.144247	−	0.989542i	$-0.546076\pi$
$199$	11.0716	−	19.1766i	0.784845	−	1.35939i	0.929092	−	0.369849i	$-0.120591\pi$
$200$	4.22522	+	14.7397i	0.298768	+	1.04226i
$201$	−5.08742	+	8.81167i	−0.358839	+	0.621527i
$202$	−4.14319	−	2.39207i	−0.291514	−	0.168306i
$203$			25.2859i			1.77472i
$204$	−2.21432	+	3.83531i	−0.155033	+	0.268526i
$205$	4.19977	+	5.37592i	0.293325	+	0.375471i
$206$	−1.71355	−	2.96796i	−0.119389	−	0.206788i
$207$		−	6.00645i		−	0.417477i
$208$		0			0
$209$	−0.474572			−0.0328269
$210$	−8.14482	+	6.36288i	−0.562046	+	0.439081i
$211$	−9.82717	−	17.0212i	−0.676530	−	1.17178i	−0.976019	−	0.217685i	$-0.930150\pi$
$211$	−9.82717	−	17.0212i	−0.676530	−	1.17178i	0.299489	−	0.954100i	$-0.403184\pi$
$212$	−2.83716	−	1.63804i	−0.194857	−	0.112501i
$213$		−	7.97280i		−	0.546287i
$214$	10.3931	−	18.0013i	0.710456	−	1.23055i
$215$	13.1897	+	5.32962i	0.899530	+	0.363477i
$216$	17.2128			1.17118
$217$	14.0600	+	8.11753i	0.954453	+	0.551054i
$218$	−17.5874	+	10.1541i	−1.19117	+	0.687722i
$219$	6.73975	+	11.6736i	0.455430	+	0.788828i
$220$	−0.249353	+	0.0350337i	−0.0168114	+	0.00236197i
$221$		0			0
$222$		−	3.63158i		−	0.243736i
$223$	−17.0335	+	9.83431i	−1.14065	+	0.658554i	−0.946591	−	0.322436i	$-0.895498\pi$
$223$	−17.0335	+	9.83431i	−1.14065	+	0.658554i	−0.194058	+	0.980990i	$0.562165\pi$
$224$	−4.19135	−	7.25964i	−0.280047	−	0.485055i
$225$	−1.55003	+	6.21460i	−0.103335	+	0.414306i
$226$	1.43801			0.0956548
$227$	11.4936	+	6.63581i	0.762855	+	0.440434i	0.830320	−	0.557287i	$-0.188158\pi$
$227$	11.4936	+	6.63581i	0.762855	+	0.440434i	−0.0674650	+	0.997722i	$0.521491\pi$
$228$	1.32106	+	0.762714i	0.0874893	+	0.0505120i
$229$	−2.42864			−0.160489			−0.0802445	−	0.996775i	$-0.525570\pi$
$229$	−2.42864			−0.160489			−0.0802445	+	0.996775i	$0.525570\pi$
$230$	−4.76989	+	11.8045i	−0.314517	+	0.778364i
$231$	−0.407896	−	0.706496i	−0.0268376	−	0.0464841i
$232$	−23.1312	+	13.3548i	−1.51864	+	0.876787i
$233$			16.1748i			1.05965i	0.848107	+	0.529825i	$0.177742\pi$
$233$			16.1748i			1.05965i	−0.848107	+	0.529825i	$0.822258\pi$
$234$		0			0
$235$	−0.341219	−	2.42864i	−0.0222587	−	0.158427i
$236$	2.43409	+	4.21597i	0.158446	+	0.274436i
$237$	−16.1632	+	9.33185i	−1.04992	+	0.606169i
$238$	−19.6273	−	11.3319i	−1.27225	−	0.734535i
$239$	−12.7763			−0.826431			−0.413215	−	0.910633i	$-0.635594\pi$
$239$	−12.7763			−0.826431			−0.413215	+	0.910633i	$0.635594\pi$
$240$	−7.26595	−	2.93599i	−0.469015	−	0.189517i
$241$	−2.94914	+	5.10807i	−0.189971	+	0.329040i	−0.945240	−	0.326375i	$-0.894173\pi$
$241$	−2.94914	+	5.10807i	−0.189971	+	0.329040i	0.755269	+	0.655415i	$0.227506\pi$
$242$		−	13.3017i		−	0.855068i
$243$	10.5903	+	6.11430i	0.679367	+	0.392233i
$244$	0.0738216	+	0.127863i	0.00472594	+	0.00818557i
$245$	1.96665	+	2.51741i	0.125644	+	0.160831i
$246$	−4.85728			−0.309689
$247$		0			0
$248$			17.1492i			1.08897i
$249$	−6.24443	−	10.8157i	−0.395725	−	0.685415i
$250$	7.98145	−	10.9826i	0.504791	−	0.694602i
$251$	1.03657	−	1.79538i	0.0654274	−	0.113324i	−0.831456	−	0.555590i	$-0.812492\pi$
$251$	1.03657	−	1.79538i	0.0654274	−	0.113324i	0.896884	+	0.442267i	$0.145826\pi$
$252$		−	1.95407i		−	0.123095i
$253$	−0.870288	−	0.502461i	−0.0547145	−	0.0315895i
$254$	1.39752	−	2.42058i	0.0876885	−	0.151881i
$255$	18.6637	−	2.62222i	1.16877	−	0.164210i
$256$	5.83185	−	10.1011i	0.364491	−	0.631316i
$257$	−15.9323	+	9.19850i	−0.993827	+	0.573787i	−0.906416	−	0.422386i	$-0.861193\pi$
$257$	−15.9323	+	9.19850i	−0.993827	+	0.573787i	−0.0874113	+	0.996172i	$0.527859\pi$
$258$	−8.77189	+	5.06445i	−0.546114	+	0.315299i
$259$	−6.62222			−0.411484
$260$		0			0
$261$	−11.1570			−0.690602
$262$	−14.1121	+	8.14764i	−0.871850	+	0.503363i
$263$	9.54851	−	5.51283i	0.588786	−	0.339936i	−0.175831	−	0.984420i	$-0.556261\pi$
$263$	9.54851	−	5.51283i	0.588786	−	0.339936i	0.764617	+	0.644484i	$0.222928\pi$
$264$	0.430862	−	0.746276i	0.0265177	−	0.0459301i
$265$	1.93978	+	13.8064i	0.119160	+	0.848122i
$266$	−3.90321	+	6.76056i	−0.239321	+	0.414517i
$267$	−6.37312	−	3.67952i	−0.390029	−	0.225183i
$268$			4.07758i			0.249078i
$269$	−8.07160	+	13.9804i	−0.492134	+	0.852401i	−0.999959	−	0.00905911i	$-0.997116\pi$
$269$	−8.07160	+	13.9804i	−0.492134	+	0.852401i	0.507825	+	0.861460i	$0.330450\pi$
$270$	−9.38253	−	12.0101i	−0.571003	−	0.730913i
$271$	6.50569	+	11.2682i	0.395192	+	0.684493i	0.993126	−	0.117053i	$-0.0373446\pi$
$271$	6.50569	+	11.2682i	0.395192	+	0.684493i	−0.597933	+	0.801546i	$0.704011\pi$
$272$		−	17.1842i		−	1.04195i
$273$		0			0
$274$	23.2573			1.40503
$275$	0.770781	+	0.744460i	0.0464799	+	0.0448926i
$276$	1.61507	+	2.79738i	0.0972158	+	0.168383i
$277$	6.55699	+	3.78568i	0.393971	+	0.227459i	0.683879	−	0.729595i	$-0.260291\pi$
$277$	6.55699	+	3.78568i	0.393971	+	0.227459i	−0.289908	+	0.957054i	$0.593625\pi$
$278$		−	23.1842i		−	1.39050i
$279$	−3.58173	+	6.20374i	−0.214433	+	0.371408i
$280$	−7.45851	+	18.4582i	−0.445731	+	1.10309i
$281$	−6.75557			−0.403003			−0.201502	−	0.979488i	$-0.564582\pi$
$281$	−6.75557			−0.403003			−0.201502	+	0.979488i	$0.564582\pi$
$282$	1.51225	+	0.873100i	0.0900534	+	0.0519924i
$283$	16.5289	−	9.54294i	0.982539	−	0.567269i	0.0795033	−	0.996835i	$-0.474667\pi$
$283$	16.5289	−	9.54294i	0.982539	−	0.567269i	0.903036	+	0.429565i	$0.141333\pi$
$284$	−1.59755	−	2.76704i	−0.0947974	−	0.164194i
$285$	−0.903212	−	6.42864i	−0.0535017	−	0.380800i
$286$		0			0
$287$			8.85728i			0.522829i
$288$	3.20320	−	1.84937i	0.188750	−	0.108975i
$289$	12.1637	+	21.0682i	0.715512	+	1.23930i
$290$	21.9269	+	8.86010i	1.28759	+	0.520283i
$291$	23.6543			1.38664
$292$	4.67820	+	2.70096i	0.273771	+	0.158062i
$293$	−7.00391	−	4.04371i	−0.409173	−	0.236236i	0.281261	−	0.959631i	$-0.409247\pi$
$293$	−7.00391	−	4.04371i	−0.409173	−	0.236236i	−0.690434	+	0.723395i	$0.742581\pi$
$294$	−2.27454			−0.132654
$295$	7.76174	−	19.2087i	0.451906	−	1.11837i
$296$	−3.49754	−	6.05792i	−0.203290	−	0.352109i
$297$	1.04178	−	0.601472i	0.0604502	−	0.0349009i
$298$		−	4.33677i		−	0.251223i
$299$		0			0
$300$	−0.949145	−	3.31111i	−0.0547989	−	0.191167i
$301$	9.23506	+	15.9956i	0.532300	+	0.921971i
$302$	1.33050	−	0.768163i	0.0765616	−	0.0442028i
$303$	4.47343	+	2.58274i	0.256992	+	0.148374i
$304$	−5.91903			−0.339480
$305$	0.235400	−	0.582565i	0.0134790	−	0.0333576i
$306$	5.00000	−	8.66025i	0.285831	−	0.495074i
$307$		−	13.4336i		−	0.766694i	−0.923604	−	0.383347i	$-0.874771\pi$
$307$		−	13.4336i		−	0.766694i	0.923604	−	0.383347i	$-0.125229\pi$
$308$	−0.283129	−	0.163465i	−0.0161328	−	0.00931426i
$309$	1.85013	+	3.20453i	0.105250	+	0.182299i
$310$	11.9657	−	9.34786i	0.679609	−	0.530923i
$311$	20.2034			1.14563			0.572815	−	0.819684i	$-0.305851\pi$
$311$	20.2034			1.14563			0.572815	+	0.819684i	$0.305851\pi$
$312$		0			0
$313$			15.1111i			0.854129i	0.904221	+	0.427064i	$0.140452\pi$
$313$			15.1111i			0.854129i	−0.904221	+	0.427064i	$0.859548\pi$
$314$	−3.40790	−	5.90265i	−0.192319	−	0.333106i
$315$	−6.55327	+	5.11953i	−0.369235	+	0.288453i
$316$	−3.73975	+	6.47743i	−0.210377	+	0.364384i
$317$			22.2810i			1.25143i	0.780054	+	0.625713i	$0.215192\pi$
$317$			22.2810i			1.25143i	−0.780054	+	0.625713i	$0.784808\pi$
$318$	−8.59692	−	4.96343i	−0.482091	−	0.278336i
$319$	−0.933323	+	1.61656i	−0.0522561	+	0.0905102i
$320$	−19.6019	+	2.75404i	−1.09578	+	0.153955i
$321$	−11.2215	+	19.4361i	−0.626321	+	1.08482i
$322$	−14.3157	+	8.26517i	−0.797783	+	0.460600i
$323$	12.3279	−	7.11753i	0.685944	−	0.396030i
$324$	−1.84743			−0.102635
$325$		0			0
$326$	−4.51606			−0.250121
$327$	18.9892	−	10.9634i	1.05011	−	0.606279i
$328$	−8.10252	+	4.67799i	−0.447387	+	0.258299i
$329$	1.59210	−	2.75761i	0.0877755	−	0.152032i
$330$	−0.755569	+	0.106156i	−0.0415927	+	0.00584370i
$331$	4.12790	−	7.14974i	0.226890	−	0.392985i	−0.729995	−	0.683453i	$-0.760478\pi$
$331$	4.12790	−	7.14974i	0.226890	−	0.392985i	0.956885	+	0.290468i	$0.0938108\pi$
$332$	−4.33439	−	2.50246i	−0.237881	−	0.137340i
$333$		−	2.92195i		−	0.160122i
$334$	4.27232	−	7.39988i	0.233771	−	0.404903i
$335$	13.6748	−	10.6830i	0.747133	−	0.583674i
$336$	−5.08742	−	8.81167i	−0.277542	−	0.480716i
$337$			13.7462i			0.748803i	0.927267	+	0.374402i	$0.122152\pi$
$337$			13.7462i			0.748803i	−0.927267	+	0.374402i	$0.877848\pi$
$338$		0			0
$339$	−1.55262			−0.0843270
$340$	5.95200	−	4.64981i	0.322793	−	0.252172i
$341$	0.599249	+	1.03793i	0.0324512	+	0.0562071i
$342$	−2.98299	−	1.72223i	−0.161302	−	0.0931276i
$343$		−	16.1748i		−	0.873359i
$344$	−9.75504	+	16.8962i	−0.525957	+	0.910984i
$345$	5.15008	−	12.7454i	0.277271	−	0.686187i
$346$	0.879077			0.0472595
$347$	1.05589	+	0.609621i	0.0566834	+	0.0327262i	0.528074	−	0.849198i	$-0.322914\pi$
$347$	1.05589	+	0.609621i	0.0566834	+	0.0327262i	−0.471390	+	0.881925i	$0.656248\pi$
$348$	5.19615	−	3.00000i	0.278543	−	0.160817i
$349$	−11.2558	−	19.4956i	−0.602510	−	1.04358i	−0.992440	−	0.122733i	$-0.960834\pi$
$349$	−11.2558	−	19.4956i	−0.602510	−	1.04358i	0.389930	−	0.920844i	$-0.372499\pi$
$350$	16.9447	−	4.85728i	0.905732	−	0.259632i
$351$		0			0
$352$		−	0.618825i		−	0.0329835i
$353$	12.3677	−	7.14050i	0.658267	−	0.380050i	−0.133350	−	0.991069i	$-0.542573\pi$
$353$	12.3677	−	7.14050i	0.658267	−	0.380050i	0.791616	+	0.611019i	$0.209240\pi$
$354$	7.37556	+	12.7748i	0.392007	+	0.678975i
$355$	−5.09422	+	12.6071i	−0.270373	+	0.669117i
$356$	−2.94914			−0.156304
$357$	21.1918	+	12.2351i	1.12159	+	0.647548i
$358$	−4.25016	−	2.45383i	−0.224628	−	0.129689i
$359$	−12.1541			−0.641469			−0.320734	−	0.947169i	$-0.603930\pi$
$359$	−12.1541			−0.641469			−0.320734	+	0.947169i	$0.603930\pi$
$360$	−8.14440	−	3.29095i	−0.429248	−	0.173448i
$361$	7.04839	+	12.2082i	0.370968	+	0.642536i
$362$	2.46210	−	1.42149i	0.129405	−	0.0747121i
$363$			14.3620i			0.753808i
$364$		0			0
$365$	−3.19850	−	22.7654i	−0.167417	−	1.19160i
$366$	0.223688	+	0.387438i	0.0116923	+	0.0202517i
$367$	4.03330	−	2.32862i	0.210536	−	0.121553i	−0.391024	−	0.920380i	$-0.627879\pi$
$367$	4.03330	−	2.32862i	0.210536	−	0.121553i	0.601561	+	0.798827i	$0.294546\pi$
$368$	−10.8545	−	6.26687i	−0.565832	−	0.326683i
$369$	−3.90813			−0.203449
$370$	−2.32040	+	5.74250i	−0.120632	+	0.298538i
$371$	−9.05086	+	15.6765i	−0.469897	+	0.813885i
$372$		−	3.85236i		−	0.199735i
$373$	−30.2591	−	17.4701i	−1.56676	−	0.904569i	−0.996543	−	0.0830740i	$-0.973526\pi$
$373$	−30.2591	−	17.4701i	−1.56676	−	0.904569i	−0.570216	−	0.821495i	$-0.693140\pi$
$374$	−0.836535	−	1.44892i	−0.0432562	−	0.0749220i
$375$	−8.61762	+	11.8580i	−0.445012	+	0.612344i
$376$	3.36349			0.173459
$377$		0			0
$378$		−	19.7877i		−	1.01777i
$379$	8.73583	+	15.1309i	0.448729	+	0.777222i	0.998304	−	0.0582228i	$-0.0185434\pi$
$379$	8.73583	+	15.1309i	0.448729	+	0.777222i	−0.549574	+	0.835445i	$0.685210\pi$
$380$	−1.60161	−	2.05014i	−0.0821609	−	0.105170i
$381$	−1.50891	+	2.61352i	−0.0773040	+	0.133895i
$382$		−	2.55215i		−	0.130579i
$383$	−16.1756	−	9.33900i	−0.826535	−	0.477200i	0.0261296	−	0.999659i	$-0.491682\pi$
$383$	−16.1756	−	9.33900i	−0.826535	−	0.477200i	−0.852665	+	0.522458i	$0.825015\pi$
$384$	3.26126	−	5.64866i	0.166425	−	0.288257i
$385$	0.193576	+	1.37778i	0.00986555	+	0.0702184i
$386$	8.20940	−	14.2191i	0.417847	−	0.723733i
$387$	−7.05780	+	4.07483i	−0.358768	+	0.207135i
$388$	8.20948	−	4.73975i	0.416773	−	0.240624i
$389$	−1.61285			−0.0817746			−0.0408873	−	0.999164i	$-0.513018\pi$
$389$	−1.61285			−0.0817746			−0.0408873	+	0.999164i	$0.513018\pi$
$390$		0			0
$391$	30.1432			1.52441
$392$	−3.79421	+	2.19059i	−0.191636	+	0.110641i
$393$	15.2369	−	8.79706i	0.768602	−	0.443753i
$394$	−1.21432	+	2.10326i	−0.0611765	+	0.105961i
$395$	31.5210	−	4.42864i	1.58599	−	0.222829i
$396$	0.0721262	−	0.124926i	0.00362448	−	0.00627778i
$397$	−5.69523	−	3.28814i	−0.285835	−	0.165027i	0.350227	−	0.936665i	$-0.386104\pi$
$397$	−5.69523	−	3.28814i	−0.285835	−	0.165027i	−0.636062	+	0.771638i	$0.719438\pi$
$398$		−	26.8889i		−	1.34782i
$399$	4.21432	−	7.29942i	0.210980	−	0.365428i
$400$	9.61345	+	9.28516i	0.480673	+	0.464258i
$401$	−10.9541	−	18.9730i	−0.547020	−	0.947466i	−0.998477	−	0.0551735i	$-0.982429\pi$
$401$	−10.9541	−	18.9730i	−0.547020	−	0.947466i	0.451457	−	0.892293i	$-0.350905\pi$
$402$			12.3555i			0.616237i
$403$		0			0
$404$	2.07007			0.102990
$405$	4.84016	+	6.19566i	0.240510	+	0.307865i
$406$	15.3526	+	26.5915i	0.761936	+	1.31971i
$407$	−0.423367	−	0.244431i	−0.0209855	−	0.0121160i
$408$			25.8479i			1.27966i
$409$	5.09679	−	8.82790i	0.252020	−	0.436511i	−0.712062	−	0.702117i	$-0.752238\pi$
$409$	5.09679	−	8.82790i	0.252020	−	0.436511i	0.964082	+	0.265605i	$0.0855718\pi$
$410$	7.68065	+	3.10356i	0.379320	+	0.153274i
$411$	−25.1111			−1.23864
$412$	1.28422	+	0.741443i	0.0632688	+	0.0365283i
$413$	23.2950	−	13.4494i	1.14627	−	0.661801i
$414$	−3.64688	−	6.31658i	−0.179234	−	0.310443i
$415$	2.96343	+	21.0923i	0.145469	+	1.03538i
$416$		0			0
$417$			25.0321i			1.22583i
$418$	−0.499075	+	0.288141i	−0.0244106	+	0.0140935i
$419$	3.65878	+	6.33719i	0.178743	+	0.309592i	0.941450	−	0.337152i	$-0.109464\pi$
$419$	3.65878	+	6.33719i	0.178743	+	0.309592i	−0.762707	+	0.646744i	$0.776130\pi$
$420$	1.67547	−	4.14642i	0.0817543	−	0.202325i
$421$	7.86665			0.383397			0.191698	−	0.981454i	$-0.438600\pi$
$421$	7.86665			0.383397			0.191698	+	0.981454i	$0.438600\pi$
$422$	−20.6691	−	11.9333i	−1.00616	−	0.580905i
$423$	1.21675	+	0.702491i	0.0591604	+	0.0341563i
$424$	−19.1209			−0.928594
$425$	−31.1878	−	7.77875i	−1.51283	−	0.377325i
$426$	−4.84077	−	8.38445i	−0.234536	−	0.406228i
$427$	0.706496	−	0.407896i	0.0341898	−	0.0197395i
$428$			8.99402i			0.434743i
$429$		0			0
$430$	17.1066	−	2.40345i	0.824955	−	0.115905i
$431$	−19.4598	−	33.7053i	−0.937343	−	1.62353i	−0.770401	−	0.637560i	$-0.779944\pi$
$431$	−19.4598	−	33.7053i	−0.937343	−	1.62353i	−0.166943	−	0.985967i	$-0.553389\pi$
$432$	12.9934	−	7.50177i	0.625147	−	0.360929i
$433$	17.4967	+	10.1017i	0.840837	+	0.485457i	0.857548	−	0.514403i	$-0.171986\pi$
$433$	17.4967	+	10.1017i	0.840837	+	0.485457i	−0.0167119	+	0.999860i	$0.505320\pi$
$434$	19.7146			0.946329
$435$	−23.6746	−	9.56630i	−1.13511	−	0.458669i
$436$	4.39361	−	7.60995i	0.210416	−	0.364450i
$437$		−	10.3827i		−	0.496672i
$438$	14.1755	+	8.18421i	0.677330	+	0.391057i
$439$	5.44446	+	9.43008i	0.259850	+	0.450073i	0.966202	−	0.257788i	$-0.0829936\pi$
$439$	5.44446	+	9.43008i	0.259850	+	0.450073i	−0.706352	+	0.707861i	$0.749660\pi$
$440$	−1.15814	+	0.904761i	−0.0552122	+	0.0431328i
$441$	−1.83008			−0.0871468
$442$		0			0
$443$		−	28.6287i		−	1.36019i	−0.733124	−	0.680095i	$-0.761939\pi$
$443$		−	28.6287i		−	1.36019i	0.733124	−	0.680095i	$-0.238061\pi$
$444$	0.785680	+	1.36084i	0.0372867	+	0.0645825i
$445$	7.72657	+	9.89042i	0.366275	+	0.468851i
$446$	−11.9420	+	20.6842i	−0.565470	+	0.979423i
$447$			4.68244i			0.221472i
$448$	−22.2571	−	12.8501i	−1.05155	−	0.607112i
$449$	5.46520	−	9.46601i	0.257919	−	0.446729i	−0.707765	−	0.706448i	$-0.750297\pi$
$449$	5.46520	−	9.46601i	0.257919	−	0.446729i	0.965684	+	0.259719i	$0.0836299\pi$
$450$	2.14320	+	7.47658i	0.101031	+	0.352449i
$451$	−0.326929	+	0.566258i	−0.0153945	+	0.0266641i
$452$	−0.538855	+	0.311108i	−0.0253456	+	0.0146333i
$453$	−1.43655	+	0.829390i	−0.0674948	+	0.0389682i
$454$	16.1160			0.756361
$455$		0			0
$456$	8.90321			0.416931
$457$	−9.87820	+	5.70318i	−0.462083	+	0.266784i	−0.712920	−	0.701246i	$-0.752628\pi$
$457$	−9.87820	+	5.70318i	−0.462083	+	0.266784i	0.250837	+	0.968029i	$0.419294\pi$
$458$	−2.55403	+	1.47457i	−0.119342	+	0.0689022i
$459$	−18.0415	+	31.2488i	−0.842105	+	1.45857i
$460$	−0.766468	−	5.45536i	−0.0357368	−	0.254357i
$461$	−13.0667	+	22.6321i	−0.608576	+	1.05408i	0.382900	+	0.923790i	$0.374926\pi$
$461$	−13.0667	+	22.6321i	−0.608576	+	1.05408i	−0.991475	+	0.130294i	$0.958408\pi$
$462$	−0.857913	−	0.495316i	−0.0399137	−	0.0230442i
$463$			7.92242i			0.368186i	0.982909	+	0.184093i	$0.0589348\pi$
$463$			7.92242i			0.368186i	−0.982909	+	0.184093i	$0.941065\pi$
$464$	−11.6407	+	20.1623i	−0.540408	+	0.936013i
$465$	−12.9195	+	10.0929i	−0.599126	+	0.468049i
$466$	9.82071	+	17.0100i	0.454936	+	0.787972i
$467$		−	10.8923i		−	0.504036i	−0.967723	−	0.252018i	$-0.918906\pi$
$467$		−	10.8923i		−	0.504036i	0.967723	−	0.252018i	$-0.0810942\pi$
$468$		0			0
$469$	22.5303			1.04035
$470$	−1.83341	−	2.34686i	−0.0845689	−	0.108253i
$471$	3.67952	+	6.37312i	0.169544	+	0.293658i
$472$	24.6066	+	14.2066i	1.13261	+	0.653914i
$473$			1.36349i			0.0626935i
$474$	−11.3319	+	19.6273i	−0.520489	+	0.901514i
$475$	−2.67936	+	10.7425i	−0.122938	+	0.492900i
$476$	9.80642			0.449477
$477$	−6.91703	−	3.99355i	−0.316709	−	0.182852i
$478$	−13.4360	+	7.75726i	−0.614547	+	0.354809i
$479$	4.56591	+	7.90839i	0.208622	+	0.361344i	0.951281	−	0.308326i	$-0.0997689\pi$
$479$	4.56591	+	7.90839i	0.208622	+	0.361344i	−0.742659	+	0.669670i	$0.766436\pi$
$480$	8.38271	−	1.17775i	0.382616	−	0.0537569i
$481$		0			0
$482$			7.16241i			0.326239i
$483$	15.4567	−	8.92396i	0.703306	−	0.406054i
$484$	2.87778	+	4.98447i	0.130808	+	0.226567i
$485$	−37.4038	−	15.1139i	−1.69842	−	0.686289i
$486$	14.8494			0.673584
$487$	14.0202	+	8.09457i	0.635316	+	0.366800i	0.782808	−	0.622263i	$-0.213787\pi$
$487$	14.0202	+	8.09457i	0.635316	+	0.366800i	−0.147492	+	0.989063i	$0.547120\pi$
$488$	0.746276	+	0.430862i	0.0337823	+	0.0195042i
$489$	4.87601			0.220501
$490$	3.59666	+	1.45332i	0.162480	+	0.0656543i
$491$	−13.1318	−	22.7450i	−0.592631	−	1.02647i	−0.993877	−	0.110496i	$-0.964756\pi$
$491$	−13.1318	−	22.7450i	−0.592631	−	1.02647i	0.401246	−	0.915970i	$-0.368577\pi$
$492$	1.82013	−	1.05086i	0.0820580	−	0.0473762i
$493$		−	55.9911i		−	2.52171i
$494$		0			0
$495$	−0.607926	+	0.0854124i	−0.0273242	+	0.00383900i
$496$	7.47404	+	12.9454i	0.335595	+	0.581267i
$497$	−15.2891	+	8.82717i	−0.685810	+	0.395953i
$498$	−13.1337	−	7.58274i	−0.588534	−	0.339791i
$499$	30.0306			1.34435			0.672177	−	0.740391i	$-0.265359\pi$
$499$	30.0306			1.34435			0.672177	+	0.740391i	$0.265359\pi$
$500$	−0.614782	+	5.84220i	−0.0274939	+	0.261271i
$501$	−4.61285	+	7.98969i	−0.206087	+	0.356953i
$502$		−	2.51744i		−	0.112359i
$503$	14.4889	+	8.36519i	0.646030	+	0.372985i	0.786933	−	0.617038i	$-0.211667\pi$
$503$	14.4889	+	8.36519i	0.646030	+	0.372985i	−0.140904	+	0.990023i	$0.545001\pi$
$504$	−5.70249	−	9.87700i	−0.254009	−	0.439957i
$505$	−5.42345	−	6.94229i	−0.241340	−	0.308928i
$506$	−1.22030			−0.0542488
$507$		0			0
$508$			1.20940i			0.0536583i
$509$	5.98418	+	10.3649i	0.265244	+	0.459416i	0.967628	−	0.252383i	$-0.0812141\pi$
$509$	5.98418	+	10.3649i	0.265244	+	0.459416i	−0.702383	+	0.711799i	$0.747881\pi$
$510$	18.0352	−	14.0895i	0.798614	−	0.623892i
$511$	14.9240	−	25.8490i	0.660197	−	1.14349i
$512$		−	24.1131i		−	1.06566i
$513$	10.7635	+	6.21432i	0.475221	+	0.274369i
$514$	−11.1699	+	19.3469i	−0.492684	+	0.853354i
$515$	−0.878023	−	6.24935i	−0.0386903	−	0.275379i
$516$	2.19135	−	3.79554i	0.0964689	−	0.167089i
$517$	0.203571	−	0.117532i	0.00895303	−	0.00516904i
$518$	−6.96413	+	4.02074i	−0.305986	+	0.176661i
$519$	−0.949145			−0.0416628
$520$		0			0
$521$	5.75065			0.251940			0.125970	−	0.992034i	$-0.459796\pi$
$521$	5.75065			0.251940			0.125970	+	0.992034i	$0.459796\pi$
$522$	−11.7331	+	6.77409i	−0.513542	+	0.296494i
$523$	−18.0164	+	10.4018i	−0.787801	+	0.454837i	−0.839188	−	0.543842i	$-0.816969\pi$
$523$	−18.0164	+	10.4018i	−0.787801	+	0.454837i	0.0513870	+	0.998679i	$0.483636\pi$
$524$	3.52543	−	6.10622i	0.154009	−	0.266751i
$525$	−18.2953	+	5.24443i	−0.798472	+	0.228886i
$526$	6.69434	−	11.5949i	0.291887	−	0.505563i
$527$	−31.1333	−	17.9748i	−1.35619	−	0.782995i
$528$		−	0.751123i		−	0.0326884i
$529$	−0.507145	+	0.878401i	−0.0220498	+	0.0381913i
$530$	10.4226	+	13.3415i	0.452730	+	0.579519i
$531$	5.93433	+	10.2786i	0.257528	+	0.446051i
$532$		−	3.37778i		−	0.146446i
$533$		0			0
$534$	−8.93624			−0.386709
$535$	30.1629	−	23.5638i	1.30405	−	1.01875i
$536$	11.8995	+	20.6105i	0.513978	+	0.890237i
$537$	4.58892	+	2.64941i	0.198026	+	0.114331i
$538$			19.6030i			0.845145i
$539$	−0.153093	+	0.265165i	−0.00659417	+	0.0114214i
$540$	6.11420	+	2.47059i	0.263113	+	0.106317i
$541$	−16.6222			−0.714645			−0.357322	−	0.933981i	$-0.616310\pi$
$541$	−16.6222			−0.714645			−0.357322	+	0.933981i	$0.616310\pi$
$542$	13.6832	+	7.89999i	0.587743	+	0.339333i
$543$	−2.65834	+	1.53480i	−0.114080	+	0.0658644i
$544$	9.28100	+	16.0752i	0.397919	+	0.689217i
$545$	−37.0321	+	5.20294i	−1.58628	+	0.222870i
$546$		0			0
$547$			29.9748i			1.28163i	0.767695	+	0.640815i	$0.221404\pi$
$547$			29.9748i			1.28163i	−0.767695	+	0.640815i	$0.778596\pi$
$548$	−8.71506	+	5.03164i	−0.372289	+	0.214941i
$549$	0.179978	+	0.311730i	0.00768126	+	0.0133043i
$550$	1.26258	+	0.314910i	0.0538368	+	0.0134278i
$551$	−19.2859			−0.821608
$552$	16.3270	+	9.42642i	0.694925	+	0.401215i
$553$	35.7906	+	20.6637i	1.52197	+	0.878710i
$554$	9.19405			0.390618
$555$	2.50535	−	6.20021i	0.106346	−	0.263184i
$556$	5.01582	+	8.68766i	0.212718	+	0.368439i
$557$	−4.36179	+	2.51828i	−0.184815	+	0.106703i	−0.589553	−	0.807730i	$-0.700696\pi$
$557$	−4.36179	+	2.51828i	−0.184815	+	0.106703i	0.404738	+	0.914433i	$0.367363\pi$
$558$			8.69874i			0.368247i
$559$		0			0
$560$	2.41435	+	17.1842i	0.102025	+	0.726165i
$561$	0.903212	+	1.56441i	0.0381336	+	0.0660494i
$562$	−7.10437	+	4.10171i	−0.299680	+	0.173020i
$563$	−2.49629	−	1.44123i	−0.105206	−	0.0607408i	0.446474	−	0.894797i	$-0.352680\pi$
$563$	−2.49629	−	1.44123i	−0.105206	−	0.0607408i	−0.551680	+	0.834056i	$0.686013\pi$
$564$	−0.755569			−0.0318152
$565$	2.45511	+	0.992050i	0.103287	+	0.0417358i
$566$	11.5882	−	20.0713i	0.487088	−	0.843661i
$567$			10.2079i			0.428690i
$568$	−16.1500	−	9.32418i	−0.677637	−	0.391234i
$569$	−2.18643	−	3.78701i	−0.0916600	−	0.158760i	0.816550	−	0.577275i	$-0.195884\pi$
$569$	−2.18643	−	3.78701i	−0.0916600	−	0.158760i	−0.908210	+	0.418515i	$0.862551\pi$
$570$	−4.85306	−	6.21217i	−0.203272	−	0.260199i
$571$	−1.58120			−0.0661714			−0.0330857	−	0.999453i	$-0.510533\pi$
$571$	−1.58120			−0.0661714			−0.0330857	+	0.999453i	$0.510533\pi$
$572$		0			0
$573$			2.75557i			0.115116i
$574$	5.37778	+	9.31460i	0.224464	+	0.388784i
$575$	−16.2873	+	16.8632i	−0.679227	+	0.703243i
$576$	5.66992	−	9.82059i	0.236247	−	0.409191i
$577$		−	7.61729i		−	0.317112i	−0.987350	−	0.158556i	$-0.949316\pi$
$577$		−	7.61729i		−	0.317112i	0.987350	−	0.158556i	$-0.0506839\pi$
$578$	25.5835	+	14.7706i	1.06413	+	0.614377i
$579$	−8.86373	+	15.3524i	−0.368364	+	0.638025i
$580$	−10.1334	+	1.42372i	−0.420765	+	0.0591166i
$581$	−13.8272	+	23.9494i	−0.573648	+	0.993587i
$582$	24.8756	−	14.3620i	1.03113	−	0.595323i
$583$	−1.15727	+	0.668149i	−0.0479291	+	0.0276719i
$584$	31.5285			1.30466
$585$		0			0
$586$	−9.82071			−0.405690
$587$	−40.5510	+	23.4121i	−1.67372	+	0.966322i	−0.708191	+	0.706021i	$0.750488\pi$
$587$	−40.5510	+	23.4121i	−1.67372	+	0.966322i	−0.965528	+	0.260301i	$0.916178\pi$
$588$	0.852324	−	0.492089i	0.0351492	−	0.0202934i
$589$	−6.19135	+	10.7237i	−0.255110	+	0.441864i
$590$	−3.50024	−	24.9131i	−0.144103	−	1.02565i
$591$	1.31111	−	2.27091i	0.0539318	−	0.0934126i
$592$	−5.28039	−	3.04863i	−0.217023	−	0.125298i
$593$			15.9398i			0.654568i	0.944926	+	0.327284i	$0.106133\pi$
$593$			15.9398i			0.654568i	−0.944926	+	0.327284i	$0.893867\pi$
$594$	0.730379	−	1.26505i	0.0299678	−	0.0519058i
$595$	−25.6922	−	32.8874i	−1.05328	−	1.34825i
$596$	0.938246	+	1.62509i	0.0384320	+	0.0665662i
$597$			29.0321i			1.18821i
$598$		0			0
$599$	−18.4889			−0.755434			−0.377717	−	0.925921i	$-0.623291\pi$
$599$	−18.4889			−0.755434			−0.377717	+	0.925921i	$0.623291\pi$
$600$	−14.4602	−	13.9664i	−0.590337	−	0.570177i
$601$	−10.3778	−	17.9748i	−0.423319	−	0.733209i	0.572943	−	0.819595i	$-0.305802\pi$
$601$	−10.3778	−	17.9748i	−0.423319	−	0.733209i	−0.996262	+	0.0863857i	$0.972468\pi$
$602$	19.4238	+	11.2143i	0.791654	+	0.457062i
$603$			9.94116i			0.404835i
$604$	−0.332379	+	0.575697i	−0.0135243	+	0.0234248i
$605$	9.17658	−	22.7101i	0.373081	−	0.923297i
$606$	6.27254			0.254804
$607$	31.2432	+	18.0383i	1.26812	+	0.732150i	0.974632	−	0.223812i	$-0.0718501\pi$
$607$	31.2432	+	18.0383i	1.26812	+	0.732150i	0.293489	+	0.955962i	$0.405183\pi$
$608$	5.53703	−	3.19680i	0.224556	−	0.129647i
$609$	−16.5763	−	28.7110i	−0.671705	−	1.16343i
$610$	−0.106156	−	0.755569i	−0.00429813	−	0.0305921i
$611$		0			0
$612$			4.32693i			0.174906i
$613$	−8.61662	+	4.97481i	−0.348022	+	0.200931i	−0.663814	−	0.747898i	$-0.731063\pi$
$613$	−8.61662	+	4.97481i	−0.348022	+	0.200931i	0.315792	+	0.948829i	$0.397730\pi$
$614$	−8.15632	−	14.1272i	−0.329162	−	0.570126i
$615$	−8.29284	−	3.35093i	−0.334400	−	0.135123i
$616$	−1.90813			−0.0768809
$617$	−1.81161	−	1.04593i	−0.0729326	−	0.0421077i	0.463090	−	0.886311i	$-0.346741\pi$
$617$	−1.81161	−	1.04593i	−0.0729326	−	0.0421077i	−0.536023	+	0.844203i	$0.680074\pi$
$618$	3.89132	+	2.24665i	0.156532	+	0.0903737i
$619$	18.4681			0.742296			0.371148	−	0.928574i	$-0.378964\pi$
$619$	18.4681			0.742296			0.371148	+	0.928574i	$0.378964\pi$
$620$	−2.46146	+	6.09160i	−0.0988548	+	0.244645i
$621$	13.1590	+	22.7921i	0.528053	+	0.914615i
$622$	21.2466	−	12.2667i	0.851909	−	0.491850i
$623$			16.2953i			0.652857i
$624$		0			0
$625$	21.2034	−	13.2444i	0.848137	−	0.529777i
$626$	9.17484	+	15.8913i	0.366700	+	0.635144i
$627$	0.538855	−	0.311108i	0.0215198	−	0.0124244i
$628$	2.55403	+	1.47457i	0.101917	+	0.0588418i
$629$	14.6637			0.584680
$630$	−3.78325	+	9.36274i	−0.150728	+	0.373021i
$631$	−19.3329	+	33.4855i	−0.769629	+	1.33304i	0.168136	+	0.985764i	$0.446225\pi$
$631$	−19.3329	+	33.4855i	−0.769629	+	1.33304i	−0.937764	+	0.347272i	$0.887108\pi$
$632$			43.6543i			1.73648i
$633$	22.3166	+	12.8845i	0.887004	+	0.512112i
$634$	13.5281	+	23.4314i	0.537271	+	0.930580i
$635$	4.05590	−	3.16855i	0.160954	−	0.125740i
$636$	4.29529			0.170319
$637$		0			0
$638$			2.26671i			0.0897398i
$639$	−3.89485	−	6.74607i	−0.154078	−	0.266871i
$640$	−8.76613	+	6.84826i	−0.346512	+	0.270701i
$641$	−12.2859	+	21.2798i	−0.485265	+	0.840503i	−0.999857	−	0.0169322i	$-0.994610\pi$
$641$	−12.2859	+	21.2798i	−0.485265	+	0.840503i	0.514592	+	0.857435i	$0.327943\pi$
$642$			27.2529i			1.07559i
$643$	23.8103	+	13.7469i	0.938987	+	0.542125i	0.889643	−	0.456657i	$-0.150953\pi$
$643$	23.8103	+	13.7469i	0.938987	+	0.542125i	0.0493445	+	0.998782i	$0.484287\pi$
$644$	3.57628	−	6.19430i	0.140925	−	0.244090i
$645$	−18.4701	+	2.59502i	−0.727261	+	0.102179i
$646$	8.64296	−	14.9700i	0.340053	−	0.588989i
$647$	−11.9349	+	6.89062i	−0.469209	+	0.270898i	−0.715909	−	0.698194i	$-0.753987\pi$
$647$	−11.9349	+	6.89062i	−0.469209	+	0.270898i	0.246699	+	0.969092i	$0.420654\pi$
$648$	−9.33802	+	5.39131i	−0.366832	+	0.211791i
$649$	1.98571			0.0779459
$650$		0			0
$651$	−21.2859			−0.834261
$652$	1.69227	−	0.977034i	0.0662745	−	0.0382636i
$653$	−1.83636	+	1.06022i	−0.0718623	+	0.0414897i	−0.535501	−	0.844535i	$-0.679877\pi$
$653$	−1.83636	+	1.06022i	−0.0718623	+	0.0414897i	0.463638	+	0.886025i	$0.346544\pi$
$654$	13.3131	−	23.0590i	0.520584	−	0.901678i
$655$	−29.7146	+	4.17484i	−1.16104	+	0.163125i
$656$	−4.07758	+	7.06257i	−0.159203	+	0.275747i
$657$	11.4055	+	6.58496i	0.444970	+	0.256904i
$658$		−	3.86665i		−	0.150738i
$659$	16.9447	−	29.3491i	0.660072	−	1.14328i	−0.320525	−	0.947240i	$-0.603859\pi$
$659$	16.9447	−	29.3491i	0.660072	−	1.14328i	0.980596	−	0.196038i	$-0.0628075\pi$
$660$	0.260163	−	0.203244i	0.0101268	−	0.00791125i
$661$	−18.6844	−	32.3624i	−0.726741	−	1.25875i	−0.958253	−	0.285920i	$-0.907701\pi$
$661$	−18.6844	−	32.3624i	−0.726741	−	1.25875i	0.231513	−	0.972832i	$-0.425632\pi$
$662$		−	10.0252i		−	0.389640i
$663$		0			0
$664$	−29.2114			−1.13362
$665$	−11.3279	+	8.84958i	−0.439278	+	0.343172i
$666$	−1.77409	−	3.07281i	−0.0687446	−	0.119069i
$667$	−35.3672	−	20.4193i	−1.36942	−	0.790637i
$668$			3.69721i			0.143049i
$669$	12.8938	−	22.3328i	0.498505	−	0.863436i
$670$	7.89456	−	19.5374i	0.304993	−	0.754794i
$671$	0.0602231			0.00232489
$672$	9.51817	+	5.49532i	0.367171	+	0.211986i
$673$	−30.7099	+	17.7304i	−1.18378	+	0.683456i	−0.956886	−	0.290463i	$-0.906191\pi$
$673$	−30.7099	+	17.7304i	−1.18378	+	0.683456i	−0.226894	+	0.973919i	$0.572857\pi$
$674$	8.34614	+	14.4559i	0.321481	+	0.556822i
$675$	−7.73329	−	26.9777i	−0.297655	−	1.03837i
$676$		0			0
$677$		−	15.3047i		−	0.588206i	−0.955774	−	0.294103i	$-0.904979\pi$
$677$		−	15.3047i		−	0.588206i	0.955774	−	0.294103i	$-0.0950208\pi$
$678$	−1.63279	+	0.942691i	−0.0627069	+	0.0362038i
$679$	−26.1891	−	45.3609i	−1.00505	−	1.74079i
$680$	16.5155	−	40.8724i	0.633342	−	1.56739i
$681$	−17.4005			−0.666790
$682$	1.26038	+	0.727680i	0.0482624	+	0.0278643i
$683$	−11.3422	−	6.54839i	−0.433995	−	0.250567i	0.267052	−	0.963682i	$-0.413950\pi$
$683$	−11.3422	−	6.54839i	−0.433995	−	0.250567i	−0.701047	+	0.713115i	$0.747284\pi$
$684$	1.49039			0.0569866
$685$	39.7073	+	16.0447i	1.51714	+	0.613038i
$686$	−9.82071	−	17.0100i	−0.374957	−	0.649444i
$687$	2.75761	−	1.59210i	0.105209	−	0.0607426i
$688$			17.0060i			0.648347i
$689$		0			0
$690$	−2.32248	−	16.5303i	−0.0884154	−	0.629300i
$691$	−9.20395	−	15.9417i	−0.350135	−	0.606451i	0.636138	−	0.771575i	$-0.280531\pi$
$691$	−9.20395	−	15.9417i	−0.350135	−	0.606451i	−0.986273	+	0.165124i	$0.947198\pi$
$692$	−0.329411	+	0.190185i	−0.0125223	+	0.00722976i
$693$	−0.690271	−	0.398528i	−0.0262212	−	0.0151388i
$694$	1.48055			0.0562009
$695$	15.9943	−	39.5825i	0.606698	−	1.50145i
$696$	17.5096	−	30.3275i	0.663700	−	1.14956i
$697$		−	19.6128i		−	0.742890i
$698$	−23.6739	−	13.6681i	−0.896071	−	0.517347i
$699$	−10.6035	−	18.3658i	−0.401060	−	0.694657i
$700$	−5.29871	+	5.48606i	−0.200273	+	0.207354i
$701$	−31.3689			−1.18479			−0.592393	−	0.805649i	$-0.701817\pi$
$701$	−31.3689			−1.18479			−0.592393	+	0.805649i	$0.701817\pi$
$702$		0			0
$703$		−	5.05086i		−	0.190497i
$704$	−0.948617	−	1.64305i	−0.0357524	−	0.0619249i
$705$	1.97954	+	2.53392i	0.0745539	+	0.0954329i
$706$	8.67085	−	15.0183i	0.326332	−	0.565223i
$707$		−	11.4380i		−	0.430171i
$708$	−5.52759	−	3.19135i	−0.207739	−	0.119938i
$709$	−4.73975	+	8.20948i	−0.178005	+	0.308314i	−0.941197	−	0.337858i	$-0.890298\pi$
$709$	−4.73975	+	8.20948i	−0.178005	+	0.308314i	0.763192	+	0.646172i	$0.223631\pi$
$710$	2.29729	+	16.3511i	0.0862159	+	0.613644i
$711$	−9.11753	+	15.7920i	−0.341934	+	0.592247i
$712$	−14.9067	+	8.60639i	−0.558653	+	0.322538i
$713$	−22.7079	+	13.1104i	−0.850416	+	0.490988i
$714$	29.7146			1.11204
$715$		0			0
$716$	2.12351			0.0793592
$717$	14.5069	−	8.37556i	0.541770	−	0.312791i
$718$	−12.7816	+	7.37948i	−0.477006	+	0.275400i
$719$	−14.8113	+	25.6540i	−0.552370	+	0.956733i	0.445733	+	0.895166i	$0.352943\pi$
$719$	−14.8113	+	25.6540i	−0.552370	+	0.956733i	−0.998103	+	0.0615669i	$0.980390\pi$
$720$	−7.58226	+	1.06529i	−0.282574	+	0.0397011i
$721$	4.09679	−	7.09585i	0.152572	−	0.264263i
$722$	14.8246	+	8.55900i	0.551716	+	0.318533i
$723$		−	7.73329i		−	0.287604i
$724$	−0.615071	+	1.06533i	−0.0228589	+	0.0395928i
$725$	31.3234	+	30.2537i	1.16332	+	1.12360i
$726$	8.72001	+	15.1035i	0.323630	+	0.560543i
$727$		−	42.6702i		−	1.58255i	−0.611461	−	0.791274i	$-0.709418\pi$
$727$		−	42.6702i		−	1.58255i	0.611461	−	0.791274i	$-0.290582\pi$
$728$		0			0
$729$	−26.5812			−0.984489
$730$	−17.1859	−	21.9988i	−0.636078	−	0.814213i
$731$	−20.4494	−	35.4194i	−0.756348	−	1.31003i
$732$	−0.167642	−	0.0967881i	−0.00619622	−	0.00357739i
$733$		−	26.0830i		−	0.963397i	−0.876337	−	0.481698i	$-0.840020\pi$
$733$		−	26.0830i		−	0.963397i	0.876337	−	0.481698i	$-0.159980\pi$
$734$	2.82769	−	4.89771i	0.104372	−	0.180778i
$735$	−3.88333	−	1.56916i	−0.143239	−	0.0578792i
$736$	13.5387			0.499042
$737$	1.44040	+	0.831613i	0.0530577	+	0.0306329i
$738$	−4.10992	+	2.37286i	−0.151288	+	0.0873463i
$739$	14.1344	+	24.4814i	0.519941	+	0.900564i	0.999731	+	0.0231807i	$0.00737931\pi$
$739$	14.1344	+	24.4814i	0.519941	+	0.900564i	−0.479791	+	0.877383i	$0.659287\pi$
$740$	−0.372862	−	2.65386i	−0.0137067	−	0.0975578i
$741$		0			0
$742$			21.9813i			0.806958i
$743$	−17.8991	+	10.3341i	−0.656656	+	0.379120i	−0.791002	−	0.611814i	$-0.790440\pi$
$743$	−17.8991	+	10.3341i	−0.656656	+	0.379120i	0.134346	+	0.990935i	$0.457107\pi$
$744$	−11.2422	−	19.4721i	−0.412159	−	0.713881i
$745$	2.99185	−	7.40418i	0.109613	−	0.271268i
$746$	−42.4286			−1.55342
$747$	−10.5673	−	6.10102i	−0.386636	−	0.223225i
$748$	0.626938	+	0.361963i	0.0229231	+	0.0132347i
$749$	49.6958			1.81585
$750$	−1.86286	+	17.7025i	−0.0680219	+	0.646405i
$751$	−1.23014	−	2.13067i	−0.0448885	−	0.0777491i	0.842708	−	0.538371i	$-0.180960\pi$
$751$	−1.23014	−	2.13067i	−0.0448885	−	0.0777491i	−0.887597	+	0.460621i	$0.847627\pi$
$752$	2.53901	−	1.46590i	0.0925880	−	0.0534557i
$753$			2.71810i			0.0990530i
$754$		0			0
$755$	2.80150	−	0.393606i	0.101957	−	0.0143248i
$756$	4.28100	+	7.41490i	0.155698	+	0.269677i
$757$	42.0918	−	24.3017i	1.52985	−	0.883262i	0.530487	−	0.847693i	$-0.322009\pi$
$757$	42.0918	−	24.3017i	1.52985	−	0.883262i	0.999367	−	0.0355687i	$-0.0113243\pi$
$758$	18.3738	+	10.6081i	0.667365	+	0.385303i
$759$	1.31756			0.0478244
$760$	−14.0784	−	5.68871i	−0.510676	−	0.206351i
$761$	−6.91258	+	11.9729i	−0.250581	+	0.434019i	−0.963686	−	0.267038i	$-0.913955\pi$
$761$	−6.91258	+	11.9729i	−0.250581	+	0.434019i	0.713105	+	0.701057i	$0.247288\pi$
$762$			3.66461i			0.132755i
$763$	−42.0482	−	24.2766i	−1.52225	−	0.878870i
$764$	0.552148	+	0.956349i	0.0199760	+	0.0345995i
$765$	14.5110	−	11.3363i	0.524647	−	0.409864i
$766$	−22.6811			−0.819500
$767$		0			0
$768$			15.2924i			0.551816i
$769$	19.4844	+	33.7480i	0.702626	+	1.21698i	0.967541	+	0.252712i	$0.0813226\pi$
$769$	19.4844	+	33.7480i	0.702626	+	1.21698i	−0.264915	+	0.964272i	$0.585344\pi$
$770$	1.04011	+	1.33139i	0.0374828	+	0.0479800i
$771$	12.0602	−	20.8889i	0.434338	−	0.752296i
$772$			7.10430i			0.255689i
$773$	−0.386241	−	0.222996i	−0.0138921	−	0.00802061i	0.493038	−	0.870008i	$-0.335886\pi$
$773$	−0.386241	−	0.222996i	−0.0138921	−	0.00802061i	−0.506930	+	0.861987i	$0.669220\pi$
$774$	−4.94814	+	8.57043i	−0.177857	+	0.308058i
$775$	26.8780	−	7.70471i	0.965487	−	0.276761i
$776$	27.6637	−	47.9149i	0.993069	−	1.72005i
$777$	7.51921	−	4.34122i	0.269750	−	0.155740i
$778$	−1.69612	+	0.979256i	−0.0608089	+	0.0351080i
$779$	−6.75557			−0.242043
$780$		0			0
$781$	−1.30327			−0.0466347
$782$	31.6995	−	18.3017i	1.13357	−	0.654469i
$783$	42.3364	−	24.4429i	1.51298	−	0.873519i
$784$	−1.90943	+	3.30722i	−0.0681938	+	0.118115i
$785$	−1.74620	−	12.4286i	−0.0623246	−	0.443597i
$786$	10.6824	−	18.5025i	0.381030	−	0.659963i
$787$	29.3615	+	16.9518i	1.04662	+	0.604268i	0.921702	−	0.387899i	$-0.126799\pi$
$787$	29.3615	+	16.9518i	1.04662	+	0.604268i	0.124921	+	0.992167i	$0.460132\pi$
$788$		−	1.05086i		−	0.0374352i
$789$	−7.22792	+	12.5191i	−0.257321	+	0.445693i
$790$	30.4596	−	23.7956i	1.08370	−	0.846608i
$791$	1.71900	+	2.97740i	0.0611207	+	0.105864i
$792$		−	0.841934i		−	0.0299168i
$793$		0			0
$794$	−7.98571			−0.283402
$795$	−11.2534	−	14.4049i	−0.399116	−	0.510890i
$796$	5.81732	+	10.0759i	0.206190	+	0.357131i
$797$	8.91598	+	5.14764i	0.315820	+	0.182339i	0.649528	−	0.760338i	$-0.274967\pi$
$797$	8.91598	+	5.14764i	0.315820	+	0.182339i	−0.333708	+	0.942677i	$0.608300\pi$
$798$		−	10.2351i		−	0.362317i
$799$	−3.52543	+	6.10622i	−0.124721	+	0.216023i
$800$	−14.0078	−	3.49379i	−0.495251	−	0.123524i
$801$	−7.19004			−0.254047
$802$	−23.0393	−	13.3017i	−0.813546	−	0.469701i
$803$	1.90822	−	1.10171i	0.0673396	−	0.0388785i
$804$	−2.67307	−	4.62989i	−0.0942719	−	0.163284i
$805$	−30.1432	+	4.23506i	−1.06241	+	0.149266i
$806$		0			0
$807$		−	21.1655i		−	0.745060i
$808$	10.4633	−	6.04101i	0.368099	−	0.212522i
$809$	3.97211	+	6.87990i	0.139652	+	0.241884i	0.927365	−	0.374158i	$-0.122068\pi$
$809$	3.97211	+	6.87990i	0.139652	+	0.241884i	−0.787713	+	0.616043i	$0.788735\pi$
$810$	8.85182	+	3.57680i	0.311021	+	0.125676i
$811$	8.12245			0.285218			0.142609	−	0.989779i	$-0.454451\pi$
$811$	8.12245			0.285218			0.142609	+	0.989779i	$0.454451\pi$
$812$	−11.5059	−	6.64296i	−0.403779	−	0.233122i
$813$	−14.7738	−	8.52966i	−0.518140	−	0.299148i
$814$	−0.593635			−0.0208069
$815$	−7.71028	−	3.11553i	−0.270079	−	0.109132i
$816$	11.2652	+	19.5119i	0.394360	+	0.683052i
$817$	−12.2001	+	7.04371i	−0.426826	+	0.246428i
$818$		−	12.3783i		−	0.432796i
$819$		0			0
$820$	−3.54956	+	0.498707i	−0.123956	+	0.0174156i
$821$	−11.1032	−	19.2314i	−0.387506	−	0.671180i	0.604608	−	0.796524i	$-0.293330\pi$
$821$	−11.1032	−	19.2314i	−0.387506	−	0.671180i	−0.992113	+	0.125344i	$0.959997\pi$
$822$	−26.4076	+	15.2464i	−0.921071	+	0.531781i
$823$	9.62806	+	5.55877i	0.335613	+	0.193766i	0.658330	−	0.752729i	$-0.271263\pi$
$823$	9.62806	+	5.55877i	0.335613	+	0.193766i	−0.322717	+	0.946495i	$0.604596\pi$
$824$	8.65491			0.301508
$825$	−1.36322	−	0.340010i	−0.0474612	−	0.0118376i
$826$	16.3319	−	28.2876i	0.568258	−	0.984251i
$827$		−	23.1570i		−	0.805248i	−0.915365	−	0.402624i	$-0.868098\pi$
$827$		−	23.1570i		−	0.805248i	0.915365	−	0.402624i	$-0.131902\pi$
$828$	2.73314	+	1.57798i	0.0949831	+	0.0548385i
$829$	−13.5598	−	23.4862i	−0.470950	−	0.815710i	0.528498	−	0.848935i	$-0.322756\pi$
$829$	−13.5598	−	23.4862i	−0.470950	−	0.815710i	−0.999448	+	0.0332250i	$0.989422\pi$
$830$	15.9229	+	20.3821i	0.552691	+	0.707473i
$831$	−9.92687			−0.344359
$832$		0			0
$833$		−	9.18421i		−	0.318214i
$834$	15.1985	+	26.3246i	0.526281	+	0.911545i
$835$	12.3992	−	9.68644i	0.429090	−	0.335213i
$836$	0.124677	−	0.215946i	0.00431203	−	0.00746866i
$837$		−	31.3876i		−	1.08492i
$838$	7.69538	+	4.44293i	0.265832	+	0.153478i
$839$	−12.6977	+	21.9931i	−0.438374	+	0.759287i	−0.997564	−	0.0697528i	$-0.977779\pi$
$839$	−12.6977	+	21.9931i	−0.438374	+	0.759287i	0.559190	+	0.829040i	$0.311112\pi$
$840$	−3.63158	−	25.8479i	−0.125302	−	0.891838i
$841$	−23.4289	+	40.5800i	−0.807892	+	1.39931i
$842$	8.27282	−	4.77631i	0.285100	−	0.164603i
$843$	7.67063	−	4.42864i	0.264190	−	0.152530i
$844$	10.3269			0.355468
$845$		0			0
$846$	1.70610			0.0586568
$847$	27.5413	−	15.9010i	0.946331	−	0.546364i
$848$	−14.4338	+	8.33338i	−0.495660	+	0.286170i
$849$	−12.5118	+	21.6711i	−0.429405	+	0.743751i
$850$	−37.5210	+	10.7556i	−1.28696	+	0.368913i
$851$	5.34767	−	9.26244i	0.183316	−	0.317512i
$852$	3.62789	+	2.09457i	0.124290	+	0.0717586i
$853$			25.0651i			0.858214i	0.903254	+	0.429107i	$0.141172\pi$
$853$			25.0651i			0.858214i	−0.903254	+	0.429107i	$0.858828\pi$
$854$	0.495316	−	0.857913i	0.0169494	−	0.0293572i
$855$	−3.90474	−	4.99827i	−0.133539	−	0.170937i
$856$	26.2470	+	45.4611i	0.897103	+	1.55383i
$857$			7.61285i			0.260050i	0.991511	+	0.130025i	$0.0415057\pi$
$857$			7.61285i			0.260050i	−0.991511	+	0.130025i	$0.958494\pi$
$858$		0			0
$859$	−42.1432			−1.43791			−0.718954	−	0.695058i	$-0.755379\pi$
$859$	−42.1432			−1.43791			−0.718954	+	0.695058i	$0.755379\pi$
$860$	−5.89027	+	4.60159i	−0.200857	+	0.156913i
$861$	−5.80642	−	10.0570i	−0.197882	−	0.342742i
$862$	−40.9290	−	23.6304i	−1.39405	−	0.804853i
$863$			51.5768i			1.75569i	0.478942	+	0.877847i	$0.341020\pi$
$863$			51.5768i			1.75569i	−0.478942	+	0.877847i	$0.658980\pi$
$864$	−8.10324	+	14.0352i	−0.275678	+	0.477488i
$865$	1.50085	+	0.606456i	0.0510305	+	0.0206201i
$866$	24.5334			0.833679
$867$	−27.6226	−	15.9479i	−0.938113	−	0.541620i
$868$	−7.38750	+	4.26517i	−0.250748	+	0.144769i
$869$	1.52543	+	2.64212i	0.0517466	+	0.0896277i
$870$	−30.7052	+	4.31402i	−1.04100	+	0.146259i
$871$		0			0
$872$		−	51.2869i		−	1.73679i
$873$	20.0148	−	11.5555i	0.677398	−	0.391096i
$874$	−6.30396	−	10.9188i	−0.213235	−	0.369333i
$875$	32.2807	+	3.39693i	1.09129	+	0.114837i
$876$	−7.08250			−0.239295
$877$	−29.5055	−	17.0350i	−0.996331	−	0.575232i	−0.0891706	−	0.996016i	$-0.528422\pi$
$877$	−29.5055	−	17.0350i	−0.996331	−	0.575232i	−0.907161	+	0.420784i	$0.861755\pi$
$878$	11.4511	+	6.61132i	0.386457	+	0.223121i
$879$	10.6035			0.357646
$880$	−0.479930	+	1.18773i	−0.0161784	+	0.0400382i
$881$	−1.85950	−	3.22075i	−0.0626482	−	0.108510i	0.833000	−	0.553273i	$-0.186621\pi$
$881$	−1.85950	−	3.22075i	−0.0626482	−	0.108510i	−0.895648	+	0.444763i	$0.853288\pi$
$882$	−1.92457	+	1.11115i	−0.0648037	+	0.0374144i
$883$			42.0163i			1.41396i	0.707233	+	0.706981i	$0.249943\pi$
$883$			42.0163i			1.41396i	−0.707233	+	0.706981i	$0.750057\pi$
$884$		0			0
$885$	3.77923	+	26.8988i	0.127037	+	0.904192i
$886$	−17.3822	−	30.1068i	−0.583966	−	1.01146i
$887$	−34.9109	+	20.1558i	−1.17219	+	0.676765i	−0.954195	−	0.299184i	$-0.903285\pi$
$887$	−34.9109	+	20.1558i	−1.17219	+	0.676765i	−0.217996	+	0.975950i	$0.569952\pi$
$888$	7.94258	+	4.58565i	0.266536	+	0.153884i
$889$	6.68244			0.224122
$890$	14.1306	+	5.70981i	0.473658	+	0.191393i
$891$	−0.376780	+	0.652603i	−0.0126226	+	0.0218630i
$892$		−	10.3344i		−	0.346023i
$893$	2.10326	+	1.21432i	0.0703830	+	0.0406357i
$894$	2.84299	+	4.92420i	0.0950838	+	0.164690i
$895$	−5.56346	−	7.12152i	−0.185966	−	0.238046i
$896$	−14.4429			−0.482504
$897$		0			0
$898$		−	13.2730i		−	0.442926i
$899$	24.3526	+	42.1799i	0.812205	+	1.40678i
$900$	−2.42064	−	2.33797i	−0.0806879	−	0.0779325i
$901$	20.0415	−	34.7129i	0.667679	−	1.15645i
$902$			0.793993i			0.0264371i
$903$	−20.9720	−	12.1082i	−0.697903	−	0.402934i
$904$	−1.81579	+	3.14504i	−0.0603923	+	0.104603i
$905$	5.18421	−	0.728372i	0.172329	−	0.0242119i
$906$	−1.00715	+	1.74443i	−0.0334602	+	0.0579547i
$907$	30.1740	−	17.4210i	1.00191	−	0.578454i	0.0930980	−	0.995657i	$-0.470323\pi$
$907$	30.1740	−	17.4210i	1.00191	−	0.578454i	0.908813	+	0.417203i	$0.136990\pi$
$908$	−6.03904	+	3.48664i	−0.200412	+	0.115708i
$909$	5.04684			0.167393
$910$		0			0
$911$	23.2672			0.770876			0.385438	−	0.922734i	$-0.374050\pi$
$911$	23.2672			0.770876			0.385438	+	0.922734i	$0.374050\pi$
$912$	6.72078	−	3.88025i	0.222547	−	0.128488i
$913$	−1.76798	+	1.02074i	−0.0585116	+	0.0337817i
$914$	−6.92549	+	11.9953i	−0.229075	+	0.396769i
$915$	0.114617	+	0.815792i	0.00378913	+	0.0269692i
$916$	0.638037	−	1.10511i	0.0210813	−	0.0365139i
$917$	−33.7395	−	19.4795i	−1.11418	−	0.643270i
$918$			43.8163i			1.44615i
$919$	−1.61285	+	2.79353i	−0.0532029	+	0.0921502i	−0.891400	−	0.453217i	$-0.850276\pi$
$919$	−1.61285	+	2.79353i	−0.0532029	+	0.0921502i	0.838197	+	0.545367i	$0.183610\pi$
$920$	−19.7944	−	25.3378i	−0.652601	−	0.835364i
$921$	8.80642	+	15.2532i	0.290182	+	0.502609i
$922$			31.7342i			1.04511i
$923$		0			0
$924$	0.428639			0.0141012
$925$	−7.92325	+	8.20339i	−0.260515	+	0.269726i
$926$	4.81018	+	8.33147i	0.158072	+	0.273789i
$927$	3.13093	+	1.80764i	0.102833	+	0.0593708i
$928$		−	25.1481i		−	0.825527i
$929$	19.6731	−	34.0748i	0.645453	−	1.11796i	−0.338744	−	0.940878i	$-0.610002\pi$
$929$	19.6731	−	34.0748i	0.645453	−	1.11796i	0.984197	−	0.177078i	$-0.0566645\pi$
$930$	−7.45851	+	18.4582i	−0.244574	+	0.605269i
$931$	−3.16346			−0.103678
$932$	−7.36010	−	4.24935i	−0.241088	−	0.139192i
$933$	−22.9400	+	13.2444i	−0.751023	+	0.433603i
$934$	−6.61338	−	11.4547i	−0.216396	−	0.374809i
$935$	−0.428639	−	3.05086i	−0.0140180	−	0.0997736i
$936$		0			0
$937$		−	51.6040i		−	1.68583i	−0.538048	−	0.842914i	$-0.680838\pi$
$937$		−	51.6040i		−	1.68583i	0.538048	−	0.842914i	$-0.319162\pi$
$938$	23.6936	−	13.6795i	0.773624	−	0.446652i
$939$	−9.90613	−	17.1579i	−0.323274	−	0.559927i
$940$	1.19476	+	0.482771i	0.0389686	+	0.0157462i
$941$	−37.5081			−1.22273			−0.611364	−	0.791349i	$-0.709379\pi$
$941$	−37.5081			−1.22273			−0.611364	+	0.791349i	$0.709379\pi$
$942$	7.73901	+	4.46812i	0.252151	+	0.145579i
$943$	−12.3886	−	7.15257i	−0.403429	−	0.232920i
$944$	24.7665			0.806080
$945$	13.6511	−	33.7836i	0.444070	−	1.09898i
$946$	0.827859	+	1.43389i	0.0269160	+	0.0466199i
$947$	−33.0094	+	19.0580i	−1.07266	+	0.619302i	−0.928908	−	0.370312i	$-0.879251\pi$
$947$	−33.0094	+	19.0580i	−1.07266	+	0.619302i	−0.143755	+	0.989613i	$0.545918\pi$
$948$		−	9.80642i		−	0.318498i
$949$		0			0
$950$	3.70471	+	12.9240i	0.120197	+	0.419308i
$951$	−14.6064	−	25.2990i	−0.473645	−	0.820377i
$952$	49.5674	−	28.6178i	1.60649	−	0.927507i
$953$	24.8868	+	14.3684i	0.806163	+	0.465439i	0.845622	−	0.533783i	$-0.179230\pi$
$953$	24.8868	+	14.3684i	0.806163	+	0.465439i	−0.0394584	+	0.999221i	$0.512563\pi$
$954$	−9.69888			−0.314013
$955$	1.76067	−	4.35729i	0.0569740	−	0.140999i
$956$	3.35651	−	5.81365i	0.108557	−	0.188027i
$957$		−	2.44738i		−	0.0791124i
$958$	9.60331	+	5.54448i	0.310269	+	0.179134i
$959$	27.8020	+	48.1544i	0.897773	+	1.55499i
$960$	20.4517	−	15.9772i	0.660075	−	0.515662i
$961$	0.271628			0.00876221
$962$		0			0
$963$			21.9275i			0.706604i
$964$	−1.54956	−	2.68392i	−0.0499080	−	0.0864432i
$965$	23.8254	−	18.6128i	0.766966	−	0.599168i
$966$	10.8365	−	18.7694i	0.348660	−	0.603897i
$967$			29.0593i			0.934485i	0.884129	+	0.467242i	$0.154752\pi$
$967$			29.0593i			0.934485i	−0.884129	+	0.467242i	$0.845248\pi$
$968$	29.0920	+	16.7963i	0.935053	+	0.539853i
$969$	−9.33185	+	16.1632i	−0.299782	+	0.519238i
$970$	−48.5116	+	6.81579i	−1.55761	+	0.218842i
$971$	19.9289	−	34.5178i	0.639548	−	1.10773i	−0.345984	−	0.938240i	$-0.612455\pi$
$971$	19.9289	−	34.5178i	0.639548	−	1.10773i	0.985532	−	0.169489i	$-0.0542118\pi$
$972$	−5.56443	+	3.21262i	−0.178479	+	0.103045i
$973$	48.0030	−	27.7146i	1.53891	−	0.888488i
$974$	19.6588			0.629908
$975$		0			0
$976$	0.751123			0.0240429
$977$	−11.1386	+	6.43086i	−0.356355	+	0.205742i	−0.667481	−	0.744627i	$-0.732627\pi$
$977$	−11.1386	+	6.43086i	−0.356355	+	0.205742i	0.311126	+	0.950369i	$0.399294\pi$
$978$	5.12777	−	2.96052i	0.163968	−	0.0946670i
$979$	−0.601472	+	1.04178i	−0.0192231	+	0.0332954i
$980$	−1.66217	+	0.233532i	−0.0530961	+	0.00745991i
$981$	10.7116	−	18.5531i	0.341996	−	0.592355i
$982$	−27.6197	−	15.9462i	−0.881379	−	0.508865i
$983$		−	45.4880i		−	1.45084i	−0.688306	−	0.725420i	$-0.741645\pi$
$983$		−	45.4880i		−	1.45084i	0.688306	−	0.725420i	$-0.258355\pi$
$984$	6.13335	−	10.6233i	0.195524	−	0.338658i
$985$	−3.52421	+	2.75317i	−0.112291	+	0.0877234i
$986$	−33.9956	−	58.8820i	−1.08264	−	1.87519i
$987$			4.17484i			0.132887i
$988$		0			0
$989$	−29.8306			−0.948557
$990$	−0.587455	+	0.458930i	−0.0186705	+	0.0145858i
$991$	−4.03503	−	6.98888i	−0.128177	−	0.222009i	0.794793	−	0.606880i	$-0.207579\pi$
$991$	−4.03503	−	6.98888i	−0.128177	−	0.222009i	−0.922970	+	0.384871i	$0.874246\pi$
$992$	−13.9834	−	8.07329i	−0.443972	−	0.256327i
$993$			10.8243i			0.343497i
$994$	−10.7190	+	18.5659i	−0.339986	+	0.588873i
$995$	18.5501	−	45.9075i	0.588077	−	1.45537i
$996$	6.56199			0.207925
$997$	−28.4193	−	16.4079i	−0.900049	−	0.519643i	−0.0228326	−	0.999739i	$-0.507268\pi$
$997$	−28.4193	−	16.4079i	−0.900049	−	0.519643i	−0.877216	+	0.480096i	$0.840602\pi$
$998$	31.5811	−	18.2334i	0.999683	−	0.577167i
$999$	6.40144	+	11.0876i	0.202533	+	0.350797i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	845.2.n.g.484.4		12
5.4	even	2	inner	845.2.n.g.484.3		12
13.2	odd	12		845.2.d.a.844.5		6
13.3	even	3		845.2.b.c.339.4		6
13.4	even	6		845.2.n.f.529.4		12
13.5	odd	4		845.2.l.e.699.1		12
13.6	odd	12		845.2.l.e.654.2		12
13.7	odd	12		845.2.l.d.654.6		12
13.8	odd	4		845.2.l.d.699.5		12
13.9	even	3	inner	845.2.n.g.529.3		12
13.10	even	6		65.2.b.a.14.3	✓	6
13.11	odd	12		845.2.d.b.844.1		6
13.12	even	2		845.2.n.f.484.3		12
39.23	odd	6		585.2.c.b.469.4		6
52.23	odd	6		1040.2.d.c.209.5		6
65.3	odd	12		4225.2.a.ba.1.3		3
65.4	even	6		845.2.n.f.529.3		12
65.9	even	6	inner	845.2.n.g.529.4		12
65.19	odd	12		845.2.l.d.654.5		12
65.23	odd	12		325.2.a.k.1.1		3
65.24	odd	12		845.2.d.a.844.6		6
65.29	even	6		845.2.b.c.339.3		6
65.34	odd	4		845.2.l.e.699.2		12
65.42	odd	12		4225.2.a.bh.1.1		3
65.44	odd	4		845.2.l.d.699.6		12
65.49	even	6		65.2.b.a.14.4	yes	6
65.54	odd	12		845.2.d.b.844.2		6
65.59	odd	12		845.2.l.e.654.1		12
65.62	odd	12		325.2.a.j.1.3		3
65.64	even	2		845.2.n.f.484.4		12
195.23	even	12		2925.2.a.bf.1.3		3
195.62	even	12		2925.2.a.bj.1.1		3
195.179	odd	6		585.2.c.b.469.3		6
260.23	even	12		5200.2.a.cb.1.2		3
260.127	even	12		5200.2.a.cj.1.2		3
260.179	odd	6		1040.2.d.c.209.2		6

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
65.2.b.a.14.3	✓	6	13.10	even	6
65.2.b.a.14.4	yes	6	65.49	even	6
325.2.a.j.1.3		3	65.62	odd	12
325.2.a.k.1.1		3	65.23	odd	12
585.2.c.b.469.3		6	195.179	odd	6
585.2.c.b.469.4		6	39.23	odd	6
845.2.b.c.339.3		6	65.29	even	6
845.2.b.c.339.4		6	13.3	even	3
845.2.d.a.844.5		6	13.2	odd	12
845.2.d.a.844.6		6	65.24	odd	12
845.2.d.b.844.1		6	13.11	odd	12
845.2.d.b.844.2		6	65.54	odd	12
845.2.l.d.654.5		12	65.19	odd	12
845.2.l.d.654.6		12	13.7	odd	12
845.2.l.d.699.5		12	13.8	odd	4
845.2.l.d.699.6		12	65.44	odd	4
845.2.l.e.654.1		12	65.59	odd	12
845.2.l.e.654.2		12	13.6	odd	12
845.2.l.e.699.1		12	13.5	odd	4
845.2.l.e.699.2		12	65.34	odd	4
845.2.n.f.484.3		12	13.12	even	2
845.2.n.f.484.4		12	65.64	even	2
845.2.n.f.529.3		12	65.4	even	6
845.2.n.f.529.4		12	13.4	even	6
845.2.n.g.484.3		12	5.4	even	2	inner
845.2.n.g.484.4		12	1.1	even	1	trivial
845.2.n.g.529.3		12	13.9	even	3	inner
845.2.n.g.529.4		12	65.9	even	6	inner
1040.2.d.c.209.2		6	260.179	odd	6
1040.2.d.c.209.5		6	52.23	odd	6
2925.2.a.bf.1.3		3	195.23	even	12
2925.2.a.bj.1.1		3	195.62	even	12
4225.2.a.ba.1.3		3	65.3	odd	12
4225.2.a.bh.1.1		3	65.42	odd	12
5200.2.a.cb.1.2		3	260.23	even	12
5200.2.a.cj.1.2		3	260.127	even	12

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:	\( N \)	\(=\)	\( 845 = 5 \cdot 13^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	845.n (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(1.05163 - 0.607160i) q^{2} +(-1.13545 + 0.655554i) q^{3} +(-0.262714 + 0.455034i) q^{4} +(2.21432 - 0.311108i) q^{5} +(-0.796052 + 1.37880i) q^{6} +(2.51426 + 1.45161i) q^{7} +3.06668i q^{8} +(-0.640498 + 1.10938i) q^{9} +(2.13976 - 1.67162i) q^{10} +(0.107160 + 0.185606i) q^{11} -0.688892i q^{12} +3.52543 q^{14} +(-2.31031 + 1.80485i) q^{15} +(1.33654 + 2.31495i) q^{16} +(-5.56737 - 3.21432i) q^{17} +1.55554i q^{18} +(-1.10716 + 1.91766i) q^{19} +(-0.440168 + 1.08932i) q^{20} -3.80642 q^{21} +(0.225385 + 0.130126i) q^{22} +(-4.06070 + 2.34445i) q^{23} +(-2.01037 - 3.48207i) q^{24} +(4.80642 - 1.37778i) q^{25} -5.61285i q^{27} +(-1.32106 + 0.762714i) q^{28} +(4.35482 + 7.54277i) q^{29} +(-1.33376 + 3.30077i) q^{30} +5.59210 q^{31} +(-2.50055 - 1.44370i) q^{32} +(-0.243350 - 0.140498i) q^{33} -7.80642 q^{34} +(6.01897 + 2.43212i) q^{35} +(-0.336535 - 0.582896i) q^{36} +(-1.97540 + 1.14050i) q^{37} +2.68889i q^{38} +(0.954067 + 6.79060i) q^{40} +(1.52543 + 2.64212i) q^{41} +(-4.00296 + 2.31111i) q^{42} +(5.50962 + 3.18098i) q^{43} -0.112610 q^{44} +(-1.07313 + 2.65578i) q^{45} +(-2.84691 + 4.93099i) q^{46} -1.09679i q^{47} +(-3.03515 - 1.75234i) q^{48} +(0.714320 + 1.23724i) q^{49} +(4.21805 - 4.36719i) q^{50} +8.42864 q^{51} +6.23506i q^{53} +(-3.40790 - 5.90265i) q^{54} +(0.295030 + 0.377654i) q^{55} +(-4.45161 + 7.71041i) q^{56} -2.90321i q^{57} +(9.15933 + 5.28814i) q^{58} +(4.63259 - 8.02388i) q^{59} +(-0.214320 - 1.52543i) q^{60} +(0.140498 - 0.243350i) q^{61} +(5.88083 - 3.39530i) q^{62} +(-3.22075 + 1.85950i) q^{63} -8.85236 q^{64} -0.341219 q^{66} +(6.72078 - 3.88025i) q^{67} +(2.92525 - 1.68889i) q^{68} +(3.07382 - 5.32402i) q^{69} +(7.80642 - 1.09679i) q^{70} +(-3.04048 + 5.26627i) q^{71} +(-3.40210 - 1.96420i) q^{72} -10.2810i q^{73} +(-1.38493 + 2.39877i) q^{74} +(-4.55425 + 4.71528i) q^{75} +(-0.581732 - 1.00759i) q^{76} +0.622216i q^{77} +14.2351 q^{79} +(3.67971 + 4.71023i) q^{80} +(1.75803 + 3.04500i) q^{81} +(3.20838 + 1.85236i) q^{82} +9.52543i q^{83} +(1.00000 - 1.73205i) q^{84} +(-13.3279 - 5.38548i) q^{85} +7.72546 q^{86} +(-9.88938 - 5.70964i) q^{87} +(-0.569195 + 0.328625i) q^{88} +(2.80642 + 4.86087i) q^{89} +(0.483940 + 3.44446i) q^{90} -2.46367i q^{92} +(-6.34957 + 3.66593i) q^{93} +(-0.665926 - 1.15342i) q^{94} +(-1.85501 + 4.59075i) q^{95} +3.78568 q^{96} +(-15.6244 - 9.02074i) q^{97} +(1.50240 + 0.867413i) q^{98} -0.274543 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q + 10 q^{4} + 4 q^{6} + 6 q^{9} - 2 q^{10} - 12 q^{11} + 16 q^{14} + 16 q^{15} - 10 q^{16} - 20 q^{20} + 8 q^{21} + 16 q^{24} + 4 q^{25} + 12 q^{29} - 8 q^{30} + 40 q^{31} - 40 q^{34} - 8 q^{35} + 22 q^{36}+ \cdots - 32 q^{99}+O(q^{100}) \) 12 * q + 10 * q^4 + 4 * q^6 + 6 * q^9 - 2 * q^10 - 12 * q^11 + 16 * q^14 + 16 * q^15 - 10 * q^16 - 20 * q^20 + 8 * q^21 + 16 * q^24 + 4 * q^25 + 12 * q^29 - 8 * q^30 + 40 * q^31 - 40 * q^34 - 8 * q^35 + 22 * q^36 - 68 * q^40 - 8 * q^41 - 80 * q^44 - 4 * q^45 + 32 * q^46 - 18 * q^49 + 16 * q^50 + 48 * q^51 - 68 * q^54 + 16 * q^55 - 40 * q^56 + 16 * q^59 + 24 * q^60 - 12 * q^61 - 132 * q^64 - 32 * q^66 + 24 * q^69 + 40 * q^70 - 24 * q^71 - 4 * q^74 - 16 * q^75 - 20 * q^76 + 64 * q^79 + 48 * q^80 - 46 * q^81 + 12 * q^84 - 12 * q^85 + 64 * q^86 - 20 * q^89 + 140 * q^90 + 32 * q^94 - 16 * q^95 + 72 * q^96 - 32 * q^99

Introduction

L-functions

Modular forms

Varieties

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Database

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