LMFDB - Embedded newform 845.2.n.f.529.4

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			529.4
Root			$1.98293 - 0.531325i$ of defining polynomial
Character	$\chi$	$=$	845.529
Dual form			845.2.n.f.484.4

$q$-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} +(-2.51754 - 1.01728i) q^{10} +(-0.107160 + 0.185606i) q^{11} -0.688892i q^{12} +3.52543 q^{14} +(-2.71820 - 1.09836i) q^{15} +(1.33654 - 2.31495i) q^{16} +(5.56737 - 3.21432i) q^{17} -1.55554i q^{18} +(1.10716 + 1.91766i) q^{19} +(0.723297 + 0.925858i) 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} +(-2.19167 - 2.80545i) q^{30} -5.59210 q^{31} +(-2.50055 + 1.44370i) q^{32} +(-0.243350 + 0.140498i) q^{33} +7.80642 q^{34} +(-5.11576 + 3.99652i) 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} +(1.76340 + 2.25725i) q^{45} +(2.84691 + 4.93099i) q^{46} +1.09679i q^{47} +(3.03515 - 1.75234i) q^{48} +(0.714320 - 1.23724i) q^{49} +(5.89112 + 1.46935i) q^{50} +8.42864 q^{51} +6.23506i q^{53} +(3.40790 - 5.90265i) q^{54} +(0.179543 - 0.444330i) 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} +(6.36068 + 1.58646i) q^{75} +(0.581732 - 1.00759i) q^{76} +0.622216i q^{77} +14.2351 q^{79} +(-2.23932 + 5.54184i) q^{80} +(1.75803 - 3.04500i) q^{81} +(-3.20838 + 1.85236i) q^{82} -9.52543i q^{83} +(-1.00000 - 1.73205i) q^{84} +(-11.3279 + 8.84958i) 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} +(-3.04820 - 3.90186i) 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 $\left(\mathbb{Z}/845\mathbb{Z}\right)^\times$.

$n$	$171$	$677$
$\chi(n)$	$e\left(\frac{2}{3}\right)$	$-1$

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	0.823383	−	0.567487i	$-0.192084\pi$
$2$	1.05163	+	0.607160i	0.743616	+	0.429327i	−0.0797666	+	0.996814i	$0.525418\pi$
$3$	1.13545	+	0.655554i	0.655554	+	0.378484i	0.790581	−	0.612358i	$-0.209779\pi$
$3$	1.13545	+	0.655554i	0.655554	+	0.378484i	−0.135027	+	0.990842i	$0.543112\pi$
$4$	−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	0.0571253	−	0.998367i	$-0.481807\pi$
$7$	2.51426	−	1.45161i	0.950299	−	0.548655i	0.893174	+	0.449712i	$0.148473\pi$
$8$		−	3.06668i		−	1.08423i
$9$	−0.640498	−	1.10938i	−0.213499	−	0.369792i
$10$	−2.51754	−	1.01728i	−0.796116	−	0.321691i
$11$	−0.107160	+	0.185606i	−0.0323099	+	0.0559624i	−0.881728	−	0.471758i	$-0.843620\pi$
$11$	−0.107160	+	0.185606i	−0.0323099	+	0.0559624i	0.849418	+	0.527720i	$0.176953\pi$
$12$		−	0.688892i		−	0.198866i
$13$		0			0
$13$		0			0
$14$	3.52543			0.942210
$15$	−2.71820	−	1.09836i	−0.701837	−	0.283595i
$16$	1.33654	−	2.31495i	0.334134	−	0.578737i
$17$	5.56737	−	3.21432i	1.35028	−	0.779587i	0.361995	−	0.932180i	$-0.382096\pi$
$17$	5.56737	−	3.21432i	1.35028	−	0.779587i	0.988289	+	0.152593i	$0.0487623\pi$
$18$		−	1.55554i		−	0.366644i
$19$	1.10716	+	1.91766i	0.254000	+	0.439941i	0.964623	−	0.263632i	$-0.0849204\pi$
$19$	1.10716	+	1.91766i	0.254000	+	0.439941i	−0.710624	+	0.703572i	$0.751587\pi$
$20$	0.723297	+	0.925858i	0.161734	+	0.207028i
$21$	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	$-0.170750\pi$
$23$	4.06070	+	2.34445i	0.846714	+	0.488851i	−0.0128265	+	0.999918i	$0.504083\pi$
$24$	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	−0.105116	−	0.994460i	$-0.533522\pi$
$29$	4.35482	−	7.54277i	0.808669	−	1.40066i	0.913786	−	0.406197i	$-0.133145\pi$
$30$	−2.19167	−	2.80545i	−0.400142	−	0.512203i
$31$	−5.59210			−1.00437			−0.502186	−	0.864760i	$-0.667471\pi$
$31$	−5.59210			−1.00437			−0.502186	+	0.864760i	$0.667471\pi$
$32$	−2.50055	+	1.44370i	−0.442040	+	0.255212i
$33$	−0.243350	+	0.140498i	−0.0423618	+	0.0244576i
$34$	7.80642			1.33879
$35$	−5.11576	+	3.99652i	−0.864721	+	0.675536i
$36$	−0.336535	+	0.582896i	−0.0560892	+	0.0971494i
$37$	−1.97540	−	1.14050i	−0.324754	−	0.187497i	0.328756	−	0.944415i	$-0.393371\pi$
$37$	−1.97540	−	1.14050i	−0.324754	−	0.187497i	−0.653510	+	0.756918i	$0.726704\pi$
$38$			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	$-0.909901\pi$
$41$	−1.52543	+	2.64212i	−0.238232	+	0.412630i	0.721975	+	0.691919i	$0.243234\pi$
$42$	4.00296	+	2.31111i	0.617670	+	0.356612i
$43$	−5.50962	+	3.18098i	−0.840209	+	0.485095i	−0.857335	−	0.514758i	$-0.827882\pi$
$43$	−5.50962	+	3.18098i	−0.840209	+	0.485095i	0.0171260	+	0.999853i	$0.494548\pi$
$44$	0.112610			0.0169765
$45$	1.76340	+	2.25725i	0.262873	+	0.336491i
$46$	2.84691	+	4.93099i	0.419754	+	0.727034i
$47$			1.09679i			0.159983i	0.996796	+	0.0799915i	$0.0254893\pi$
$47$			1.09679i			0.159983i	−0.996796	+	0.0799915i	$0.974511\pi$
$48$	3.03515	−	1.75234i	0.438085	−	0.252929i
$49$	0.714320	−	1.23724i	0.102046	−	0.176748i
$50$	5.89112	+	1.46935i	0.833131	+	0.207797i
$51$	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
$55$	0.179543	−	0.444330i	0.0242095	−	0.0599135i
$56$	−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	−0.992347	−	0.123481i	$-0.960594\pi$
$59$	−4.63259	−	8.02388i	−0.603112	−	1.04462i	0.389235	−	0.921138i	$-0.372739\pi$
$60$	0.214320	+	1.52543i	0.0276686	+	0.196932i
$61$	0.140498	+	0.243350i	0.0179889	+	0.0311578i	0.874880	−	0.484340i	$-0.160940\pi$
$61$	0.140498	+	0.243350i	0.0179889	+	0.0311578i	−0.856891	+	0.515498i	$0.827607\pi$
$62$	−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	0.850787	−	0.525511i	$-0.176126\pi$
$67$	6.72078	+	3.88025i	0.821074	+	0.474047i	−0.0297125	+	0.999558i	$0.509459\pi$
$68$	−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	$-0.0491571\pi$
$71$	3.04048	+	5.26627i	0.360839	+	0.624991i	−0.627260	+	0.778810i	$0.715824\pi$
$72$	−3.40210	+	1.96420i	−0.400941	+	0.231483i
$73$			10.2810i			1.20330i	0.798760	+	0.601650i	$0.205490\pi$
$73$			10.2810i			1.20330i	−0.798760	+	0.601650i	$0.794510\pi$
$74$	−1.38493	−	2.39877i	−0.160995	−	0.278851i
$75$	6.36068	+	1.58646i	0.734468	+	0.183189i
$76$	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	$0.204416\pi$
$80$	−2.23932	+	5.54184i	−0.250363	+	0.619597i
$81$	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	$-0.824897\pi$
$83$		−	9.52543i		−	1.04555i	0.852470	−	0.522776i	$-0.175103\pi$
$84$	−1.00000	−	1.73205i	−0.109109	−	0.188982i
$85$	−11.3279	+	8.84958i	−1.22869	+	0.959872i
$86$	−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	$-0.929480\pi$
$89$	−2.80642	+	4.86087i	−0.297480	+	0.515251i	0.678078	+	0.734989i	$0.262813\pi$
$90$	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
$95$	−3.04820	−	3.90186i	−0.312739	−	0.400322i
$96$	−3.78568			−0.386374
$97$	−15.6244	+	9.02074i	−1.58642	+	0.915918i	−0.592525	+	0.805552i	$0.701869\pi$
$97$	−15.6244	+	9.02074i	−1.58642	+	0.915918i	−0.993891	+	0.110366i	$0.964798\pi$
$98$	1.50240	−	0.867413i	0.151766	−	0.0876219i
$99$	0.274543			0.0275926
$100$	−1.88965	−	1.82512i	−0.188965	−	0.182512i
$101$	−1.96989	+	3.41195i	−0.196011	+	0.339501i	−0.947232	−	0.320550i	$-0.896132\pi$
$101$	−1.96989	+	3.41195i	−0.196011	+	0.339501i	0.751220	+	0.660052i	$0.229466\pi$
$102$	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	$-0.643518\pi$
$107$	−14.8242	−	8.55877i	−1.43311	−	0.827407i	−0.997357	+	0.0726585i	$0.976852\pi$
$108$	−2.55403	+	1.47457i	−0.245762	+	0.141891i
$109$	16.7239			1.60186			0.800931	−	0.598757i	$-0.204338\pi$
$109$	16.7239			1.60186			0.800931	+	0.598757i	$0.204338\pi$
$110$	0.458592	−	0.358261i	0.0437250	−	0.0341588i
$111$	−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	$-0.684406\pi$
$113$	−1.02555	+	0.592104i	−0.0964760	+	0.0557005i	0.450986	+	0.892531i	$0.351073\pi$
$114$	−1.76271	+	3.05311i	−0.165093	+	0.285950i
$115$	−9.72106	−	3.92804i	−0.906494	−	0.366291i
$116$	−4.57628			−0.424897
$117$		0			0
$118$		−	11.2509i		−	1.03573i
$119$	9.33185	−	16.1632i	0.855449	−	1.48168i
$120$	−3.36831	+	8.33585i	−0.307483	+	0.760956i
$121$	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	$-0.365897\pi$
$127$	−1.99337	−	1.15087i	−0.176883	−	0.102123i	−0.585827	+	0.810436i	$0.699230\pi$
$128$	−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	0.421047	−	0.907039i	$-0.361663\pi$
$137$	16.5866	−	9.57628i	1.41709	−	0.818157i	0.996042	+	0.0888816i	$0.0283293\pi$
$138$			7.46520i			0.635480i
$139$	9.54617	+	16.5345i	0.809696	+	1.40243i	0.913075	+	0.407792i	$0.133701\pi$
$139$	9.54617	+	16.5345i	0.809696	+	1.40243i	−0.103379	+	0.994642i	$0.532966\pi$
$140$	3.16253	+	1.27790i	0.267283	+	0.108002i
$141$	−0.719004	+	1.24535i	−0.0605510	+	0.104877i
$142$			7.38424i			0.619671i
$143$		0			0
$144$	−3.42419			−0.285349
$145$	−7.29635	+	18.0569i	−0.605929	+	1.49955i
$146$	−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	$-0.213399\pi$
$149$	−1.78568	−	3.09289i	−0.146289	−	0.253379i	−0.929853	+	0.367931i	$0.880066\pi$
$150$	5.72586	+	5.53032i	0.467514	+	0.451549i
$151$	−1.26517			−0.102958			−0.0514792	−	0.998674i	$-0.516394\pi$
$151$	−1.26517			−0.102958			−0.0514792	+	0.998674i	$0.516394\pi$
$152$	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
$160$	5.08788	−	3.97474i	0.402232	−	0.314231i
$161$	13.6128			1.07284
$162$	3.69760	−	2.13481i	0.290511	−	0.167727i
$163$	−3.22075	+	1.85950i	−0.252269	+	0.145647i	−0.620803	−	0.783967i	$-0.713193\pi$
$163$	−3.22075	+	1.85950i	−0.252269	+	0.145647i	0.368534	+	0.929614i	$0.379860\pi$
$164$	1.60300			0.125174
$165$	0.495144	−	0.386816i	0.0385469	−	0.0301136i
$166$	5.78346	−	10.0172i	0.448883	−	0.777489i
$167$	6.09384	+	3.51828i	0.471556	+	0.272253i	0.716891	−	0.697185i	$-0.245565\pi$
$167$	6.09384	+	3.51828i	0.471556	+	0.272253i	−0.245335	+	0.969438i	$0.578898\pi$
$168$		−	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	$-0.675428\pi$
$173$	−0.626938	+	0.361963i	−0.0476652	+	0.0275195i	0.475978	+	0.879457i	$0.342094\pi$
$174$	13.8666			1.05123
$175$	10.0846	−	10.4411i	0.762322	−	0.789276i
$176$	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	−0.931609	−	0.363462i	$-0.881595\pi$
$179$	−2.02074	+	3.50003i	−0.151037	+	0.261605i	0.780572	+	0.625066i	$0.214928\pi$
$180$	0.563853	−	1.39542i	0.0420271	−	0.104008i
$181$	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
$185$	4.72899	+	1.91086i	0.347682	+	0.140490i
$186$	−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	0.901537	−	0.432702i	$-0.142440\pi$
$191$	1.05086	+	1.82013i	0.0760372	+	0.131700i	−0.825500	+	0.564403i	$0.809107\pi$
$192$	−10.0514	−	5.80320i	−0.725400	−	0.418810i
$193$	11.7095	+	6.76049i	0.842869	+	0.486631i	0.858238	−	0.513251i	$-0.171559\pi$
$193$	11.7095	+	6.76049i	0.842869	+	0.486631i	−0.0153692	+	0.999882i	$0.504892\pi$
$194$	−21.9081			−1.57291
$195$		0			0
$196$	−0.750647			−0.0536176
$197$	−1.73205	−	1.00000i	−0.123404	−	0.0712470i	0.437028	−	0.899448i	$-0.356031\pi$
$197$	−1.73205	−	1.00000i	−0.123404	−	0.0712470i	−0.560431	+	0.828201i	$0.689365\pi$
$198$	0.288718	+	0.166691i	0.0205183	+	0.0118462i
$199$	11.0716	+	19.1766i	0.784845	+	1.35939i	0.929092	+	0.369849i	$0.120591\pi$
$199$	11.0716	+	19.1766i	0.784845	+	1.35939i	−0.144247	+	0.989542i	$0.546076\pi$
$200$	−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
$205$	2.55580	−	6.32507i	0.178505	−	0.441762i
$206$	1.71355	−	2.96796i	0.119389	−	0.206788i
$207$		−	6.00645i		−	0.417477i
$208$		0			0
$209$	−0.474572			−0.0328269
$210$	−9.58283	−	3.87218i	−0.661278	−	0.267206i
$211$	−9.82717	+	17.0212i	−0.676530	+	1.17178i	0.299489	+	0.954100i	$0.403184\pi$
$211$	−9.82717	+	17.0212i	−0.676530	+	1.17178i	−0.976019	+	0.217685i	$0.930150\pi$
$212$	2.83716	−	1.63804i	0.194857	−	0.112501i
$213$			7.97280i			0.546287i
$214$	−10.3931	−	18.0013i	−0.710456	−	1.23055i
$215$	11.2104	−	8.75780i	0.764545	−	0.597277i
$216$	−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	−0.194058	−	0.980990i	$-0.562165\pi$
$223$	−17.0335	−	9.83431i	−1.14065	−	0.658554i	−0.946591	+	0.322436i	$0.895498\pi$
$224$	−4.19135	+	7.25964i	−0.280047	+	0.485055i
$225$	−4.60699	−	4.44966i	−0.307132	−	0.296644i
$226$	−1.43801			−0.0956548
$227$	11.4936	−	6.63581i	0.762855	−	0.440434i	−0.0674650	−	0.997722i	$-0.521491\pi$
$227$	11.4936	−	6.63581i	0.762855	−	0.440434i	0.830320	+	0.557287i	$0.188158\pi$
$228$	1.32106	−	0.762714i	0.0874893	−	0.0505120i
$229$	2.42864			0.160489			0.0802445	−	0.996775i	$-0.474430\pi$
$229$	2.42864			0.160489			0.0802445	+	0.996775i	$0.474430\pi$
$230$	−7.83803	−	10.0331i	−0.516825	−	0.661562i
$231$	−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	$-0.364406\pi$
$239$	12.7763			0.826431			0.413215	+	0.910633i	$0.364406\pi$
$240$	−6.17561	+	4.82450i	−0.398634	+	0.311420i
$241$	2.94914	+	5.10807i	0.189971	+	0.329040i	0.945240	−	0.326375i	$-0.105827\pi$
$241$	2.94914	+	5.10807i	0.189971	+	0.329040i	−0.755269	+	0.655415i	$0.772494\pi$
$242$			13.3017i			0.855068i
$243$	−10.5903	+	6.11430i	−0.679367	+	0.392233i
$244$	0.0738216	−	0.127863i	0.00472594	−	0.00818557i
$245$	−1.19682	+	2.96187i	−0.0764619	+	0.189227i
$246$	−4.85728			−0.309689
$247$		0			0
$248$			17.1492i			1.08897i
$249$	6.24443	−	10.8157i	0.395725	−	0.685415i
$250$	−13.5020	−	1.42083i	−0.853939	−	0.0898610i
$251$	1.03657	+	1.79538i	0.0654274	+	0.113324i	0.896884	−	0.442267i	$-0.145826\pi$
$251$	1.03657	+	1.79538i	0.0654274	+	0.113324i	−0.831456	+	0.555590i	$0.812492\pi$
$252$			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	$-0.138807\pi$
$257$	15.9323	+	9.19850i	0.993827	+	0.573787i	0.0874113	+	0.996172i	$0.472141\pi$
$258$	−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	$-0.443739\pi$
$263$	−9.54851	−	5.51283i	−0.588786	−	0.339936i	−0.764617	+	0.644484i	$0.777072\pi$
$264$	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	0.507825	−	0.861460i	$-0.330450\pi$
$269$	−8.07160	−	13.9804i	−0.492134	−	0.852401i	−0.999959	+	0.00905911i	$0.997116\pi$
$270$	−5.70981	+	14.1306i	−0.347488	+	0.859959i
$271$	−6.50569	+	11.2682i	−0.395192	+	0.684493i	−0.993126	−	0.117053i	$-0.962655\pi$
$271$	−6.50569	+	11.2682i	−0.395192	+	0.684493i	0.597933	+	0.801546i	$0.295989\pi$
$272$		−	17.1842i		−	1.04195i
$273$		0			0
$274$	23.2573			1.40503
$275$	−0.259330	+	1.03975i	−0.0156382	+	0.0626990i
$276$	1.61507	−	2.79738i	0.0972158	−	0.168383i
$277$	−6.55699	+	3.78568i	−0.393971	+	0.227459i	−0.683879	−	0.729595i	$-0.739709\pi$
$277$	−6.55699	+	3.78568i	−0.393971	+	0.227459i	0.289908	+	0.957054i	$0.406375\pi$
$278$			23.1842i			1.39050i
$279$	3.58173	+	6.20374i	0.214433	+	0.371408i
$280$	12.2560	+	15.6884i	0.732439	+	0.937560i
$281$	6.75557			0.403003			0.201502	−	0.979488i	$-0.435418\pi$
$281$	6.75557			0.403003			0.201502	+	0.979488i	$0.435418\pi$
$282$	−1.51225	+	0.873100i	−0.0900534	+	0.0519924i
$283$	−16.5289	−	9.54294i	−0.982539	−	0.567269i	−0.0795033	−	0.996835i	$-0.525333\pi$
$283$	−16.5289	−	9.54294i	−0.982539	−	0.567269i	−0.903036	+	0.429565i	$0.858667\pi$
$284$	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
$290$	−18.6365	+	14.5592i	−1.09437	+	0.854944i
$291$	−23.6543			−1.38664
$292$	4.67820	−	2.70096i	0.273771	−	0.158062i
$293$	−7.00391	+	4.04371i	−0.409173	+	0.236236i	−0.690434	−	0.723395i	$-0.742581\pi$
$293$	−7.00391	+	4.04371i	−0.409173	+	0.236236i	0.281261	+	0.959631i	$0.409247\pi$
$294$	2.27454			0.132654
$295$	12.7543	+	16.3262i	0.742585	+	0.950548i
$296$	−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
$305$	−0.386816	−	0.495144i	−0.0221490	−	0.0283519i
$306$	−5.00000	−	8.66025i	−0.285831	−	0.495074i
$307$			13.4336i			0.766694i	0.923604	+	0.383347i	$0.125229\pi$
$307$			13.4336i			0.766694i	−0.923604	+	0.383347i	$0.874771\pi$
$308$	0.283129	−	0.163465i	0.0161328	−	0.00931426i
$309$	1.85013	−	3.20453i	0.105250	−	0.182299i
$310$	14.0784	+	5.68871i	0.799597	+	0.323097i
$311$	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
$315$	7.71028	+	3.11553i	0.434425	+	0.175540i
$316$	−3.73975	−	6.47743i	−0.210377	−	0.364384i
$317$		−	22.2810i		−	1.25143i	−0.780054	−	0.625713i	$-0.784808\pi$
$317$		−	22.2810i		−	1.25143i	0.780054	−	0.625713i	$-0.215192\pi$
$318$	−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	$-0.239522\pi$
$331$	−4.12790	−	7.14974i	−0.226890	−	0.392985i	−0.956885	+	0.290468i	$0.906189\pi$
$332$	−4.33439	+	2.50246i	−0.237881	+	0.137340i
$333$			2.92195i			0.160122i
$334$	4.27232	+	7.39988i	0.233771	+	0.404903i
$335$	−16.0891	−	6.50122i	−0.879043	−	0.355199i
$336$	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
$340$	7.00286	+	2.82968i	0.379783	+	0.153461i
$341$	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
$345$	−8.46277	−	10.8328i	−0.455620	−	0.583217i
$346$	−0.879077			−0.0472595
$347$	−1.05589	+	0.609621i	−0.0566834	+	0.0327262i	−0.528074	−	0.849198i	$-0.677086\pi$
$347$	−1.05589	+	0.609621i	−0.0566834	+	0.0327262i	0.471390	+	0.881925i	$0.343752\pi$
$348$	−5.19615	−	3.00000i	−0.278543	−	0.160817i
$349$	11.2558	−	19.4956i	0.602510	−	1.04358i	−0.389930	−	0.920844i	$-0.627501\pi$
$349$	11.2558	−	19.4956i	0.602510	−	1.04358i	0.992440	−	0.122733i	$-0.0391658\pi$
$350$	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	0.791616	−	0.611019i	$-0.209240\pi$
$353$	12.3677	+	7.14050i	0.658267	+	0.380050i	−0.133350	+	0.991069i	$0.542573\pi$
$354$	7.37556	−	12.7748i	0.392007	−	0.678975i
$355$	−8.37098	−	10.7153i	−0.444286	−	0.568709i
$356$	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	$-0.396070\pi$
$359$	12.1541			0.641469			0.320734	+	0.947169i	$0.396070\pi$
$360$	6.92225	−	5.40779i	0.364835	−	0.285015i
$361$	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	$-0.372121\pi$
$367$	−4.03330	−	2.32862i	−0.210536	−	0.121553i	−0.601561	+	0.798827i	$0.705454\pi$
$368$	10.8545	−	6.26687i	0.565832	−	0.326683i
$369$	3.90813			0.203449
$370$	3.81295	+	4.88078i	0.198226	+	0.253740i
$371$	9.05086	+	15.6765i	0.469897	+	0.813885i
$372$			3.85236i			0.199735i
$373$	30.2591	−	17.4701i	1.56676	−	0.904569i	0.570216	−	0.821495i	$-0.306860\pi$
$373$	30.2591	−	17.4701i	1.56676	−	0.904569i	0.996543	−	0.0830740i	$-0.0264738\pi$
$374$	−0.836535	+	1.44892i	−0.0432562	+	0.0749220i
$375$	−14.5781	−	1.53408i	−0.752812	−	0.0792193i
$376$	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	$-0.981457\pi$
$379$	−8.73583	+	15.1309i	−0.448729	+	0.777222i	0.549574	+	0.835445i	$0.314790\pi$
$380$	−0.974672	+	2.41211i	−0.0499996	+	0.123739i
$381$	−1.50891	−	2.61352i	−0.0773040	−	0.133895i
$382$			2.55215i			0.130579i
$383$	−16.1756	+	9.33900i	−0.826535	+	0.477200i	−0.852665	−	0.522458i	$-0.825015\pi$
$383$	−16.1756	+	9.33900i	−0.826535	+	0.477200i	0.0261296	+	0.999659i	$0.491682\pi$
$384$	−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	−0.636062	−	0.771638i	$-0.719438\pi$
$397$	−5.69523	+	3.28814i	−0.285835	+	0.165027i	0.350227	+	0.936665i	$0.386104\pi$
$398$			26.8889i			1.34782i
$399$	4.21432	+	7.29942i	0.210980	+	0.365428i
$400$	3.23446	−	12.9681i	0.161723	−	0.648404i
$401$	10.9541	−	18.9730i	0.547020	−	0.947466i	−0.451457	−	0.892293i	$-0.649095\pi$
$401$	10.9541	−	18.9730i	0.547020	−	0.947466i	0.998477	−	0.0551735i	$-0.0175712\pi$
$402$			12.3555i			0.616237i
$403$		0			0
$404$	2.07007			0.102990
$405$	−2.94552	+	7.28953i	−0.146364	+	0.362220i
$406$	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	$-0.247762\pi$
$409$	−5.09679	−	8.82790i	−0.252020	−	0.436511i	−0.964082	+	0.265605i	$0.914428\pi$
$410$	6.52809	−	5.09986i	0.322399	−	0.251864i
$411$	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	−0.762707	−	0.646744i	$-0.776130\pi$
$419$	3.65878	−	6.33719i	0.178743	−	0.309592i	0.941450	+	0.337152i	$0.109464\pi$
$420$	2.75317	+	3.52421i	0.134341	+	0.171964i
$421$	−7.86665			−0.383397			−0.191698	−	0.981454i	$-0.561400\pi$
$421$	−7.86665			−0.383397			−0.191698	+	0.981454i	$0.561400\pi$
$422$	−20.6691	+	11.9333i	−1.00616	+	0.580905i
$423$	1.21675	−	0.702491i	0.0591604	−	0.0341563i
$424$	19.1209			0.928594
$425$	22.3305	−	23.1200i	1.08319	−	1.12149i
$426$	−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	0.166943	−	0.985967i	$-0.446611\pi$
$431$	19.4598	−	33.7053i	0.937343	−	1.62353i	0.770401	−	0.637560i	$-0.220056\pi$
$432$	−12.9934	−	7.50177i	−0.625147	−	0.360929i
$433$	−17.4967	+	10.1017i	−0.840837	+	0.485457i	−0.857548	−	0.514403i	$-0.828014\pi$
$433$	−17.4967	+	10.1017i	−0.840837	+	0.485457i	0.0167119	+	0.999860i	$0.494680\pi$
$434$	−19.7146			−0.946329
$435$	−20.1219	+	15.7196i	−0.964773	+	0.753698i
$436$	−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	−0.706352	−	0.707861i	$-0.749660\pi$
$439$	5.44446	−	9.43008i	0.259850	−	0.450073i	0.966202	+	0.257788i	$0.0829936\pi$
$440$	−1.36262	−	0.550599i	−0.0649602	−	0.0262488i
$441$	−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
$445$	4.70207	−	11.6366i	0.222899	−	0.551629i
$446$	−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	$-0.249703\pi$
$449$	−5.46520	−	9.46601i	−0.257919	−	0.446729i	−0.965684	+	0.259719i	$0.916370\pi$
$450$	−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	0.250837	−	0.968029i	$-0.419294\pi$
$457$	−9.87820	−	5.70318i	−0.462083	−	0.266784i	−0.712920	+	0.701246i	$0.752628\pi$
$458$	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	0.991475	+	0.130294i	$0.0415922\pi$
$461$	13.0667	+	22.6321i	0.608576	+	1.05408i	−0.382900	+	0.923790i	$0.625074\pi$
$462$	−0.857913	+	0.495316i	−0.0399137	+	0.0230442i
$463$		−	7.92242i		−	0.368186i	−0.982909	−	0.184093i	$-0.941065\pi$
$463$		−	7.92242i		−	0.368186i	0.982909	−	0.184093i	$-0.0589348\pi$
$464$	−11.6407	−	20.1623i	−0.540408	−	0.936013i
$465$	15.2005	+	6.14213i	0.704905	+	0.284835i
$466$	−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
$470$	1.11574	−	2.76121i	0.0514650	−	0.127365i
$471$	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
$475$	7.96360	+	7.69165i	0.365395	+	0.352917i
$476$	−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	$-0.900231\pi$
$479$	−4.56591	+	7.90839i	−0.208622	+	0.361344i	0.742659	+	0.669670i	$0.233564\pi$
$480$	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
$485$	31.7910	−	24.8357i	1.44355	−	1.12773i
$486$	−14.8494			−0.673584
$487$	14.0202	−	8.09457i	0.635316	−	0.366800i	−0.147492	−	0.989063i	$-0.547120\pi$
$487$	14.0202	−	8.09457i	0.635316	−	0.366800i	0.782808	+	0.622263i	$0.213787\pi$
$488$	0.746276	−	0.430862i	0.0337823	−	0.0195042i
$489$	−4.87601			−0.220501
$490$	−3.05694	+	2.38814i	−0.138099	+	0.107885i
$491$	−13.1318	+	22.7450i	−0.592631	+	1.02647i	0.401246	+	0.915970i	$0.368577\pi$
$491$	−13.1318	+	22.7450i	−0.592631	+	1.02647i	−0.993877	+	0.110496i	$0.964756\pi$
$492$	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	$-0.734641\pi$
$499$	−30.0306			−1.34435			−0.672177	+	0.740391i	$0.734641\pi$
$500$	4.75210	+	3.45352i	0.212521	+	0.154446i
$501$	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	$-0.788333\pi$
$503$	−14.4889	+	8.36519i	−0.646030	+	0.372985i	0.140904	+	0.990023i	$0.454999\pi$
$504$	−5.70249	+	9.87700i	−0.254009	+	0.439957i
$505$	3.30048	−	8.16799i	0.146869	−	0.363471i
$506$	−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	$-0.918786\pi$
$509$	−5.98418	+	10.3649i	−0.265244	+	0.459416i	0.702383	+	0.711799i	$0.252119\pi$
$510$	−21.2194	−	8.57425i	−0.939613	−	0.379674i
$511$	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	$-0.183031\pi$
$523$	18.0164	+	10.4018i	0.787801	+	0.454837i	−0.0513870	+	0.998679i	$0.516364\pi$
$524$	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
$530$	6.34278	−	15.6970i	0.275513	−	0.681835i
$531$	−5.93433	+	10.2786i	−0.257528	+	0.446051i
$532$		−	3.37778i		−	0.146446i
$533$		0			0
$534$	−8.93624			−0.386709
$535$	35.4883	+	14.3399i	1.53429	+	0.619969i
$536$	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
$540$	5.19670	−	4.05975i	0.223630	−	0.174704i
$541$	16.6222			0.714645			0.357322	−	0.933981i	$-0.383690\pi$
$541$	16.6222			0.714645			0.357322	+	0.933981i	$0.383690\pi$
$542$	−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
$550$	−0.904012	+	0.935975i	−0.0385472	+	0.0399101i
$551$	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
$555$	4.11687	+	5.26980i	0.174751	+	0.223691i
$556$	5.01582	−	8.68766i	0.212718	−	0.368439i
$557$	−4.36179	−	2.51828i	−0.184815	−	0.106703i	0.404738	−	0.914433i	$-0.367363\pi$
$557$	−4.36179	−	2.51828i	−0.184815	−	0.106703i	−0.589553	+	0.807730i	$0.700696\pi$
$558$			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	$-0.647320\pi$
$563$	2.49629	−	1.44123i	0.105206	−	0.0607408i	0.551680	+	0.834056i	$0.313987\pi$
$564$	0.755569			0.0318152
$565$	2.08670	−	1.63017i	0.0877880	−	0.0685816i
$566$	−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	−0.908210	−	0.418515i	$-0.862551\pi$
$569$	−2.18643	+	3.78701i	−0.0916600	+	0.158760i	0.816550	+	0.577275i	$0.195884\pi$
$570$	2.95337	−	7.30896i	0.123703	−	0.306138i
$571$	−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
$575$	22.7476	+	5.67363i	0.948640	+	0.236607i
$576$	5.66992	+	9.82059i	0.236247	+	0.409191i
$577$			7.61729i			0.317112i	0.987350	+	0.158556i	$0.0506839\pi$
$577$			7.61729i			0.317112i	−0.987350	+	0.158556i	$0.949316\pi$
$578$	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	−0.965528	−	0.260301i	$-0.916178\pi$
$587$	−40.5510	−	23.4121i	−1.67372	−	0.966322i	−0.708191	−	0.706021i	$-0.750488\pi$
$588$	−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	$-0.893867\pi$
$593$		−	15.9398i		−	0.654568i	0.944926	−	0.327284i	$-0.106133\pi$
$594$	0.730379	+	1.26505i	0.0299678	+	0.0519058i
$595$	−15.6352	+	38.6938i	−0.640980	+	1.58629i
$596$	−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	$0.623291\pi$
$600$	4.86516	−	19.5061i	0.198619	−	0.796335i
$601$	−10.3778	+	17.9748i	−0.423319	+	0.733209i	−0.996262	−	0.0863857i	$-0.972468\pi$
$601$	−10.3778	+	17.9748i	−0.423319	+	0.733209i	0.572943	+	0.819595i	$0.305802\pi$
$602$	−19.4238	+	11.2143i	−0.791654	+	0.457062i
$603$		−	9.94116i		−	0.404835i
$604$	0.332379	+	0.575697i	0.0135243	+	0.0234248i
$605$	−15.0792	−	19.3022i	−0.613058	−	0.784746i
$606$	−6.27254			−0.254804
$607$	−31.2432	+	18.0383i	−1.26812	+	0.732150i	−0.974632	−	0.223812i	$-0.928150\pi$
$607$	−31.2432	+	18.0383i	−1.26812	+	0.732150i	−0.293489	+	0.955962i	$0.594817\pi$
$608$	−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	0.315792	−	0.948829i	$-0.397730\pi$
$613$	−8.61662	−	4.97481i	−0.348022	−	0.200931i	−0.663814	+	0.747898i	$0.731063\pi$
$614$	−8.15632	+	14.1272i	−0.329162	+	0.570126i
$615$	7.04841	−	5.50635i	0.284219	−	0.222037i
$616$	1.90813			0.0768809
$617$	−1.81161	+	1.04593i	−0.0729326	+	0.0421077i	−0.536023	−	0.844203i	$-0.680074\pi$
$617$	−1.81161	+	1.04593i	−0.0729326	+	0.0421077i	0.463090	+	0.886311i	$0.346741\pi$
$618$	3.89132	−	2.24665i	0.156532	−	0.0903737i
$619$	−18.4681			−0.742296			−0.371148	−	0.928574i	$-0.621036\pi$
$619$	−18.4681			−0.742296			−0.371148	+	0.928574i	$0.621036\pi$
$620$	−4.04475	−	5.17749i	−0.162441	−	0.207933i
$621$	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
$630$	6.21675	+	7.95776i	0.247681	+	0.317045i
$631$	19.3329	+	33.4855i	0.769629	+	1.33304i	0.937764	+	0.347272i	$0.112892\pi$
$631$	19.3329	+	33.4855i	0.769629	+	1.33304i	−0.168136	+	0.985764i	$0.553775\pi$
$632$		−	43.6543i		−	1.73648i
$633$	−22.3166	+	12.8845i	−0.887004	+	0.512112i
$634$	13.5281	−	23.4314i	0.537271	−	0.930580i
$635$	4.77199	+	1.92824i	0.189371	+	0.0765200i
$636$	4.29529			0.170319
$637$		0			0
$638$			2.26671i			0.0897398i
$639$	3.89485	−	6.74607i	0.154078	−	0.266871i
$640$	10.3138	+	4.16756i	0.407690	+	0.164737i
$641$	−12.2859	−	21.2798i	−0.485265	−	0.840503i	0.514592	−	0.857435i	$-0.327943\pi$
$641$	−12.2859	−	21.2798i	−0.485265	−	0.840503i	−0.999857	+	0.0169322i	$0.994610\pi$
$642$		−	27.2529i		−	1.07559i
$643$	23.8103	−	13.7469i	0.938987	−	0.542125i	0.0493445	−	0.998782i	$-0.484287\pi$
$643$	23.8103	−	13.7469i	0.938987	−	0.542125i	0.889643	+	0.456657i	$0.150953\pi$
$644$	−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	$-0.246013\pi$
$647$	11.9349	+	6.89062i	0.469209	+	0.270898i	−0.246699	+	0.969092i	$0.579346\pi$
$648$	−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	$-0.320123\pi$
$653$	1.83636	+	1.06022i	0.0718623	+	0.0414897i	−0.463638	+	0.886025i	$0.653456\pi$
$654$	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	0.980596	+	0.196038i	$0.0628075\pi$
$659$	16.9447	+	29.3491i	0.660072	+	1.14328i	−0.320525	+	0.947240i	$0.603859\pi$
$660$	−0.306096	−	0.123686i	−0.0119148	−	0.00481445i
$661$	18.6844	−	32.3624i	0.726741	−	1.25875i	−0.231513	−	0.972832i	$-0.574368\pi$
$661$	18.6844	−	32.3624i	0.726741	−	1.25875i	0.958253	−	0.285920i	$-0.0922992\pi$
$662$		−	10.0252i		−	0.389640i
$663$		0			0
$664$	−29.2114			−1.13362
$665$	−13.3279	−	5.38548i	−0.516835	−	0.208840i
$666$	−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
$670$	−12.9726	−	16.6056i	−0.501174	−	0.641529i
$671$	−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	$-0.0938095\pi$
$673$	30.7099	+	17.7304i	1.18378	+	0.683456i	0.226894	+	0.973919i	$0.427143\pi$
$674$	−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
$680$	27.1388	+	34.7391i	1.04073	+	1.33218i
$681$	17.4005			0.666790
$682$	1.26038	−	0.727680i	0.0482624	−	0.0278643i
$683$	−11.3422	+	6.54839i	−0.433995	+	0.250567i	−0.701047	−	0.713115i	$-0.747284\pi$
$683$	−11.3422	+	6.54839i	−0.433995	+	0.250567i	0.267052	+	0.963682i	$0.413950\pi$
$684$	−1.49039			−0.0569866
$685$	−33.7488	+	26.3652i	−1.28948	+	1.00736i
$686$	−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	$-0.719469\pi$
$691$	9.20395	−	15.9417i	0.350135	−	0.606451i	0.986273	+	0.165124i	$0.0528025\pi$
$692$	0.329411	+	0.190185i	0.0125223	+	0.00722976i
$693$	0.690271	−	0.398528i	0.0262212	−	0.0151388i
$694$	−1.48055			−0.0562009
$695$	−26.2823	−	33.6427i	−0.996943	−	1.27614i
$696$	−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
$700$	−7.40042	−	1.84579i	−0.279710	−	0.0697644i
$701$	−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
$705$	1.20467	−	2.98129i	0.0453703	−	0.112282i
$706$	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	$-0.109702\pi$
$709$	4.73975	+	8.20948i	0.178005	+	0.308314i	−0.763192	+	0.646172i	$0.776369\pi$
$710$	−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	−0.998103	−	0.0615669i	$-0.980390\pi$
$719$	−14.8113	−	25.6540i	−0.552370	−	0.956733i	0.445733	−	0.895166i	$-0.352943\pi$
$720$	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
$725$	10.5388	−	42.2537i	0.391401	−	1.56926i
$726$	−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
$730$	10.4586	−	25.8828i	0.387090	−	0.957967i
$731$	−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	$0.159980\pi$
$733$			26.0830i			0.963397i	−0.876337	+	0.481698i	$0.840020\pi$
$734$	−2.82769	−	4.89771i	−0.104372	−	0.180778i
$735$	−3.30060	+	2.57849i	−0.121744	+	0.0951089i
$736$	−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	0.479791	+	0.877383i	$0.340713\pi$
$739$	−14.1344	+	24.4814i	−0.519941	+	0.900564i	−0.999731	+	0.0231807i	$0.992621\pi$
$740$	−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	0.134346	−	0.990935i	$-0.457107\pi$
$743$	−17.8991	−	10.3341i	−0.656656	−	0.379120i	−0.791002	+	0.611814i	$0.790440\pi$
$744$	−11.2422	+	19.4721i	−0.412159	+	0.713881i
$745$	4.91629	+	6.29311i	0.180119	+	0.230562i
$746$	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
$750$	−14.3994	−	10.4645i	−0.525792	−	0.382111i
$751$	−1.23014	+	2.13067i	−0.0448885	+	0.0777491i	−0.887597	−	0.460621i	$-0.847627\pi$
$751$	−1.23014	+	2.13067i	−0.0448885	+	0.0777491i	0.842708	+	0.538371i	$0.180960\pi$
$752$	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	−0.999367	−	0.0355687i	$-0.988676\pi$
$757$	−42.0918	−	24.3017i	−1.52985	−	0.883262i	−0.530487	−	0.847693i	$-0.677991\pi$
$758$	−18.3738	+	10.6081i	−0.667365	+	0.385303i
$759$	−1.31756			−0.0478244
$760$	−11.9657	+	9.34786i	−0.434043	+	0.339082i
$761$	6.91258	+	11.9729i	0.250581	+	0.434019i	0.963686	−	0.267038i	$-0.0860451\pi$
$761$	6.91258	+	11.9729i	0.250581	+	0.434019i	−0.713105	+	0.701057i	$0.752712\pi$
$762$		−	3.66461i		−	0.132755i
$763$	42.0482	−	24.2766i	1.52225	−	0.878870i
$764$	0.552148	−	0.956349i	0.0199760	−	0.0345995i
$765$	17.0730	+	6.89878i	0.617276	+	0.249426i
$766$	−22.6811			−0.819500
$767$		0			0
$768$			15.2924i			0.551816i
$769$	−19.4844	+	33.7480i	−0.702626	+	1.21698i	0.264915	+	0.964272i	$0.414656\pi$
$769$	−19.4844	+	33.7480i	−0.702626	+	1.21698i	−0.967541	+	0.252712i	$0.918677\pi$
$770$	0.632965	−	1.56645i	0.0228105	−	0.0564511i
$771$	12.0602	+	20.8889i	0.434338	+	0.752296i
$772$		−	7.10430i		−	0.255689i
$773$	−0.386241	+	0.222996i	−0.0138921	+	0.00802061i	−0.506930	−	0.861987i	$-0.669220\pi$
$773$	−0.386241	+	0.222996i	−0.0138921	+	0.00802061i	0.493038	+	0.870008i	$0.335886\pi$
$774$	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	0.124921	−	0.992167i	$-0.460132\pi$
$787$	29.3615	−	16.9518i	1.04662	−	0.604268i	0.921702	+	0.387899i	$0.126799\pi$
$788$			1.05086i			0.0374352i
$789$	−7.22792	−	12.5191i	−0.257321	−	0.445693i
$790$	−35.8374	−	14.4810i	−1.27504	−	0.515210i
$791$	−1.71900	+	2.97740i	−0.0611207	+	0.105864i
$792$		−	0.841934i		−	0.0299168i
$793$		0			0
$794$	−7.98571			−0.283402
$795$	6.84833	−	16.9482i	0.242885	−	0.601090i
$796$	5.81732	−	10.0759i	0.206190	−	0.357131i
$797$	−8.91598	+	5.14764i	−0.315820	+	0.182339i	−0.649528	−	0.760338i	$-0.725033\pi$
$797$	−8.91598	+	5.14764i	−0.315820	+	0.182339i	0.333708	+	0.942677i	$0.391700\pi$
$798$			10.2351i			0.362317i
$799$	3.52543	+	6.10622i	0.124721	+	0.216023i
$800$	−10.0296	+	10.3842i	−0.354601	+	0.367138i
$801$	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	−0.787713	−	0.616043i	$-0.788735\pi$
$809$	3.97211	−	6.87990i	0.139652	−	0.241884i	0.927365	+	0.374158i	$0.122068\pi$
$810$	−7.52351	+	5.87750i	−0.264349	+	0.206514i
$811$	−8.12245			−0.285218			−0.142609	−	0.989779i	$-0.545549\pi$
$811$	−8.12245			−0.285218			−0.142609	+	0.989779i	$0.545549\pi$
$812$	−11.5059	+	6.64296i	−0.403779	+	0.233122i
$813$	−14.7738	+	8.52966i	−0.518140	+	0.299148i
$814$	0.593635			0.0208069
$815$	6.55327	−	5.11953i	0.229551	−	0.179329i
$816$	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	$-0.706670\pi$
$821$	11.1032	−	19.2314i	0.387506	−	0.671180i	0.992113	+	0.125344i	$0.0400034\pi$
$822$	26.4076	+	15.2464i	0.921071	+	0.531781i
$823$	−9.62806	+	5.55877i	−0.335613	+	0.193766i	−0.658330	−	0.752729i	$-0.728737\pi$
$823$	−9.62806	+	5.55877i	−0.335613	+	0.193766i	0.322717	+	0.946495i	$0.395404\pi$
$824$	−8.65491			−0.301508
$825$	−0.976067	+	1.01058i	−0.0339823	+	0.0351838i
$826$	−16.3319	−	28.2876i	−0.568258	−	0.984251i
$827$			23.1570i			0.805248i	0.915365	+	0.402624i	$0.131902\pi$
$827$			23.1570i			0.805248i	−0.915365	+	0.402624i	$0.868098\pi$
$828$	−2.73314	+	1.57798i	−0.0949831	+	0.0548385i
$829$	−13.5598	+	23.4862i	−0.470950	+	0.815710i	−0.999448	−	0.0332250i	$-0.989422\pi$
$829$	−13.5598	+	23.4862i	−0.470950	+	0.815710i	0.528498	+	0.848935i	$0.322756\pi$
$830$	−9.68998	+	23.9807i	−0.336344	+	0.832381i
$831$	−9.92687			−0.344359
$832$		0			0
$833$		−	9.18421i		−	0.318214i
$834$	−15.1985	+	26.3246i	−0.526281	+	0.911545i
$835$	−14.5883	−	5.89476i	−0.504848	−	0.203997i
$836$	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	$-0.0222211\pi$
$839$	12.6977	+	21.9931i	0.438374	+	0.759287i	−0.559190	+	0.829040i	$0.688888\pi$
$840$	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	$-0.858828\pi$
$853$		−	25.0651i		−	0.858214i	0.903254	−	0.429107i	$-0.141172\pi$
$854$	0.495316	+	0.857913i	0.0169494	+	0.0293572i
$855$	−2.37626	+	5.88074i	−0.0812663	+	0.201117i
$856$	−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	$0.755379\pi$
$860$	−6.93023	−	2.80033i	−0.236319	−	0.0954905i
$861$	−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	$-0.658980\pi$
$863$		−	51.5768i		−	1.75569i	0.478942	−	0.877847i	$-0.341020\pi$
$864$	8.10324	+	14.0352i	0.275678	+	0.477488i
$865$	1.27563	−	0.996547i	0.0433728	−	0.0338836i
$866$	−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
$875$	−19.0822	+	26.2574i	−0.645095	+	0.887662i
$876$	7.08250			0.239295
$877$	−29.5055	+	17.0350i	−0.996331	+	0.575232i	−0.907161	−	0.420784i	$-0.861755\pi$
$877$	−29.5055	+	17.0350i	−0.996331	+	0.575232i	−0.0891706	+	0.996016i	$0.528422\pi$
$878$	11.4511	−	6.61132i	0.386457	−	0.223121i
$879$	−10.6035			−0.357646
$880$	−0.788636	−	1.00949i	−0.0265849	−	0.0340301i
$881$	−1.85950	+	3.22075i	−0.0626482	+	0.108510i	−0.895648	−	0.444763i	$-0.853288\pi$
$881$	−1.85950	+	3.22075i	−0.0626482	+	0.108510i	0.833000	+	0.553273i	$0.186621\pi$
$882$	−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	$-0.0967145\pi$
$887$	34.9109	+	20.1558i	1.17219	+	0.676765i	0.217996	+	0.975950i	$0.430048\pi$
$888$	−7.94258	+	4.58565i	−0.266536	+	0.153884i
$889$	−6.68244			−0.224122
$890$	12.0101	−	9.38253i	0.402580	−	0.314503i
$891$	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
$895$	3.38569	−	8.37886i	0.113171	−	0.280074i
$896$	−14.4429			−0.482504
$897$		0			0
$898$		−	13.2730i		−	0.442926i
$899$	−24.3526	+	42.1799i	−0.812205	+	1.40678i
$900$	−0.814426	+	3.26532i	−0.0271475	+	0.108844i
$901$	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	$-0.529677\pi$
$907$	−30.1740	−	17.4210i	−1.00191	−	0.578454i	−0.908813	+	0.417203i	$0.863010\pi$
$908$	−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	0.838197	−	0.545367i	$-0.183610\pi$
$919$	−1.61285	−	2.79353i	−0.0532029	−	0.0921502i	−0.891400	+	0.453217i	$0.850276\pi$
$920$	−12.0460	+	29.8114i	−0.397146	+	0.982851i
$921$	−8.80642	+	15.2532i	−0.290182	+	0.502609i
$922$			31.7342i			1.04511i
$923$		0			0
$924$	0.428639			0.0141012
$925$	−11.0660	−	2.76004i	−0.363847	−	0.0907496i
$926$	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	−0.984197	−	0.177078i	$-0.943335\pi$
$929$	−19.6731	−	34.0748i	−0.645453	−	1.11796i	0.338744	−	0.940878i	$-0.389998\pi$
$930$	12.2560	+	15.6884i	0.401892	+	0.514442i
$931$	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
$940$	−1.01547	+	0.793303i	−0.0331210	+	0.0258747i
$941$	37.5081			1.22273			0.611364	−	0.791349i	$-0.290621\pi$
$941$	37.5081			1.22273			0.611364	+	0.791349i	$0.290621\pi$
$942$	7.73901	−	4.46812i	0.252151	−	0.145579i
$943$	−12.3886	+	7.15257i	−0.403429	+	0.232920i
$944$	−24.7665			−0.806080
$945$	22.4319	+	28.7140i	0.729709	+	0.934066i
$946$	0.827859	−	1.43389i	0.0269160	−	0.0466199i
$947$	−33.0094	−	19.0580i	−1.07266	−	0.619302i	−0.143755	−	0.989613i	$-0.545918\pi$
$947$	−33.0094	−	19.0580i	−1.07266	−	0.619302i	−0.928908	+	0.370312i	$0.879251\pi$
$948$		−	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	$-0.820770\pi$
$953$	−24.8868	+	14.3684i	−0.806163	+	0.465439i	0.0394584	+	0.999221i	$0.487437\pi$
$954$	9.69888			0.314013
$955$	−2.89319	−	3.70343i	−0.0936213	−	0.119840i
$956$	−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
$960$	24.0625	+	9.72305i	0.776614	+	0.313810i
$961$	0.271628			0.00876221
$962$		0			0
$963$			21.9275i			0.706604i
$964$	1.54956	−	2.68392i	0.0499080	−	0.0864432i
$965$	−28.0318	−	11.3270i	−0.902377	−	0.364628i
$966$	10.8365	+	18.7694i	0.348660	+	0.603897i
$967$		−	29.0593i		−	0.934485i	−0.884129	−	0.467242i	$-0.845248\pi$
$967$		−	29.0593i		−	0.934485i	0.884129	−	0.467242i	$-0.154752\pi$
$968$	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	0.985532	+	0.169489i	$0.0542118\pi$
$971$	19.9289	+	34.5178i	0.639548	+	1.10773i	−0.345984	+	0.938240i	$0.612455\pi$
$972$	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	0.311126	−	0.950369i	$-0.399294\pi$
$977$	−11.1386	−	6.43086i	−0.356355	−	0.205742i	−0.667481	+	0.744627i	$0.732627\pi$
$978$	−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	$0.258355\pi$
$983$			45.4880i			1.45084i	−0.688306	+	0.725420i	$0.741645\pi$
$984$	6.13335	+	10.6233i	0.195524	+	0.338658i
$985$	4.14642	+	1.67547i	0.132116	+	0.0533848i
$986$	33.9956	−	58.8820i	1.08264	−	1.87519i
$987$			4.17484i			0.132887i
$988$		0			0
$989$	−29.8306			−0.948557
$990$	−0.691173	−	0.279286i	−0.0219669	−	0.00887628i
$991$	−4.03503	+	6.98888i	−0.128177	+	0.222009i	−0.922970	−	0.384871i	$-0.874246\pi$
$991$	−4.03503	+	6.98888i	−0.128177	+	0.222009i	0.794793	+	0.606880i	$0.207579\pi$
$992$	13.9834	−	8.07329i	0.443972	−	0.256327i
$993$		−	10.8243i		−	0.343497i
$994$	10.7190	+	18.5659i	0.339986	+	0.588873i
$995$	−30.4820	−	39.0186i	−0.966346	−	1.23697i
$996$	−6.56199			−0.207925
$997$	28.4193	−	16.4079i	0.900049	−	0.519643i	0.0228326	−	0.999739i	$-0.492732\pi$
$997$	28.4193	−	16.4079i	0.900049	−	0.519643i	0.877216	+	0.480096i	$0.159398\pi$
$998$	−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.f.529.4		12
5.4	even	2	inner	845.2.n.f.529.3		12
13.2	odd	12		845.2.l.d.699.5		12
13.3	even	3	inner	845.2.n.f.484.3		12
13.4	even	6		845.2.b.c.339.4		6
13.5	odd	4		845.2.l.d.654.6		12
13.6	odd	12		845.2.d.b.844.1		6
13.7	odd	12		845.2.d.a.844.5		6
13.8	odd	4		845.2.l.e.654.2		12
13.9	even	3		65.2.b.a.14.3	✓	6
13.10	even	6		845.2.n.g.484.4		12
13.11	odd	12		845.2.l.e.699.1		12
13.12	even	2		845.2.n.g.529.3		12
39.35	odd	6		585.2.c.b.469.4		6
52.35	odd	6		1040.2.d.c.209.5		6
65.4	even	6		845.2.b.c.339.3		6
65.9	even	6		65.2.b.a.14.4	yes	6
65.17	odd	12		4225.2.a.bh.1.1		3
65.19	odd	12		845.2.d.a.844.6		6
65.22	odd	12		325.2.a.j.1.3		3
65.24	odd	12		845.2.l.d.699.6		12
65.29	even	6	inner	845.2.n.f.484.4		12
65.34	odd	4		845.2.l.d.654.5		12
65.43	odd	12		4225.2.a.ba.1.3		3
65.44	odd	4		845.2.l.e.654.1		12
65.48	odd	12		325.2.a.k.1.1		3
65.49	even	6		845.2.n.g.484.3		12
65.54	odd	12		845.2.l.e.699.2		12
65.59	odd	12		845.2.d.b.844.2		6
65.64	even	2		845.2.n.g.529.4		12
195.74	odd	6		585.2.c.b.469.3		6
195.113	even	12		2925.2.a.bf.1.3		3
195.152	even	12		2925.2.a.bj.1.1		3
260.87	even	12		5200.2.a.cj.1.2		3
260.139	odd	6		1040.2.d.c.209.2		6
260.243	even	12		5200.2.a.cb.1.2		3

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
65.2.b.a.14.3	✓	6	13.9	even	3
65.2.b.a.14.4	yes	6	65.9	even	6
325.2.a.j.1.3		3	65.22	odd	12
325.2.a.k.1.1		3	65.48	odd	12
585.2.c.b.469.3		6	195.74	odd	6
585.2.c.b.469.4		6	39.35	odd	6
845.2.b.c.339.3		6	65.4	even	6
845.2.b.c.339.4		6	13.4	even	6
845.2.d.a.844.5		6	13.7	odd	12
845.2.d.a.844.6		6	65.19	odd	12
845.2.d.b.844.1		6	13.6	odd	12
845.2.d.b.844.2		6	65.59	odd	12
845.2.l.d.654.5		12	65.34	odd	4
845.2.l.d.654.6		12	13.5	odd	4
845.2.l.d.699.5		12	13.2	odd	12
845.2.l.d.699.6		12	65.24	odd	12
845.2.l.e.654.1		12	65.44	odd	4
845.2.l.e.654.2		12	13.8	odd	4
845.2.l.e.699.1		12	13.11	odd	12
845.2.l.e.699.2		12	65.54	odd	12
845.2.n.f.484.3		12	13.3	even	3	inner
845.2.n.f.484.4		12	65.29	even	6	inner
845.2.n.f.529.3		12	5.4	even	2	inner
845.2.n.f.529.4		12	1.1	even	1	trivial
845.2.n.g.484.3		12	65.49	even	6
845.2.n.g.484.4		12	13.10	even	6
845.2.n.g.529.3		12	13.12	even	2
845.2.n.g.529.4		12	65.64	even	2
1040.2.d.c.209.2		6	260.139	odd	6
1040.2.d.c.209.5		6	52.35	odd	6
2925.2.a.bf.1.3		3	195.113	even	12
2925.2.a.bj.1.1		3	195.152	even	12
4225.2.a.ba.1.3		3	65.43	odd	12
4225.2.a.bh.1.1		3	65.17	odd	12
5200.2.a.cb.1.2		3	260.243	even	12
5200.2.a.cj.1.2		3	260.87	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} +(-2.51754 - 1.01728i) q^{10} +(-0.107160 + 0.185606i) q^{11} -0.688892i q^{12} +3.52543 q^{14} +(-2.71820 - 1.09836i) q^{15} +(1.33654 - 2.31495i) q^{16} +(5.56737 - 3.21432i) q^{17} -1.55554i q^{18} +(1.10716 + 1.91766i) q^{19} +(0.723297 + 0.925858i) 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} +(-2.19167 - 2.80545i) q^{30} -5.59210 q^{31} +(-2.50055 + 1.44370i) q^{32} +(-0.243350 + 0.140498i) q^{33} +7.80642 q^{34} +(-5.11576 + 3.99652i) 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} +(1.76340 + 2.25725i) q^{45} +(2.84691 + 4.93099i) q^{46} +1.09679i q^{47} +(3.03515 - 1.75234i) q^{48} +(0.714320 - 1.23724i) q^{49} +(5.89112 + 1.46935i) q^{50} +8.42864 q^{51} +6.23506i q^{53} +(3.40790 - 5.90265i) q^{54} +(0.179543 - 0.444330i) 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} +(6.36068 + 1.58646i) q^{75} +(0.581732 - 1.00759i) q^{76} +0.622216i q^{77} +14.2351 q^{79} +(-2.23932 + 5.54184i) q^{80} +(1.75803 - 3.04500i) q^{81} +(-3.20838 + 1.85236i) q^{82} -9.52543i q^{83} +(-1.00000 - 1.73205i) q^{84} +(-11.3279 + 8.84958i) 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} +(-3.04820 - 3.90186i) 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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